Subgroups — D₅₃×#3537 #28291321

Order 13568.

8890 conjugacy classes of subgroups.

The subgroup lattice has 1632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288954	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288953	C₂	1	2	yes	maximal, complemented
3	#20288952	C₂	1	4	yes	maximal, complemented
4	#20288951	C₂	1	4	yes	maximal, complemented
5	#20288950	C₂	1	2	yes	maximal, complemented
6	#20288949	C₂	1	4	yes	maximal, complemented
7	#20288948	C₂	1	2	yes	maximal, complemented
8	#20288947	C₂	1	4	yes	maximal, complemented
9	#20288946	C₂	1	4	yes	maximal, complemented
10	#20288945	C₂	1	4	yes	maximal, complemented
11	#560×D₅₃	C₂	1	4	yes	maximal, complemented
12	#553×D₅₃	C₂	1	4	yes	maximal, complemented
13	D₄²×D₅₃	C₂	1	4	yes	maximal, complemented
14	D₄²×D₅₃	C₂	1	4	yes	maximal, complemented
15	#540×D₅₃	C₂	1	2	yes	maximal, complemented
16	#538×D₅₃	C₂	1	4	yes	maximal, complemented
17	#535×D₅₃	C₂	1	2	yes	maximal, complemented
18	#534×D₅₃	C₂	1	4	yes	maximal, complemented
19	#525×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#121×D₅₃	C₂	1	2	yes	maximal, complemented
21	C₅₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
26	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
27	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
28	#16811364	C₂²	1	8	yes	complemented
29	#16811363	C₂²	1	4	yes	complemented
30	#16811363	C₂²	1	8	yes	complemented
31	#16811362	C₂²	1	4	yes	complemented
32	#16811362	C₂²	1	8	yes	complemented
33	#16811361	C₂²	1	8	yes	complemented
34	#16811361	C₂²	1	8	yes	complemented
35	#16811361	C₂²	1	8	yes	complemented
36	#16811360	C₂²	1	4	yes	complemented
37	#16811326	C₂²	1	4	yes	complemented
38	#16811325	C₂²	1	4	yes	complemented
39	#16811324	C₂²	1	8	yes	complemented
40	#16811323	C₂²	1	4	yes	complemented
41	#16811322	C₂²	1	8	yes	complemented
42	#16811321	C₂²	1	4	yes	complemented
43	#16811320	C₂²	1	4	yes	complemented
44	#16811319	C₂²	1	4	yes	complemented
45	#16811318	C₂²	1	8	yes	complemented
46	#16811317	C₂²	1	4	yes	complemented
47	#16811316	C₂²	1	8	yes	complemented
48	D₄×D₂₁₂	C₂²	1	8	yes	complemented
49	D₄×D₂₁₂	C₂²	1	4	yes	complemented
50	D₄×D₂₁₂	C₂²	1	4	yes	complemented
51	#16811258	C₂²	1	4	yes	complemented
52	#16811258	C₂²	1	4	yes	complemented
53	#16811257	C₂²	1	8	yes	complemented
54	#16811257	C₂²	1	4	yes	complemented
55	#16811257	C₂²	1	8	yes	complemented
56	#16811257	C₂²	1	4	yes	complemented
57	#16811257	C₂²	1	8	yes	complemented
58	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
59	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
60	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
61	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
62	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
63	#16811255	C₂²	1	8	yes	complemented
64	#16811255	C₂²	1	4	yes	complemented
65	#16811255	C₂²	1	8	yes	complemented
66	#16811255	C₂²	1	4	yes	complemented
67	#16811255	C₂²	1	8	yes	complemented
68	#16811229	C₂²	1	2	yes	complemented
69	#16811228	C₂²	1	2	yes	complemented
70	#16811227	C₂²	1	2	yes	complemented
71	#16811226	C₂²	1	4	yes	complemented
72	#16811225	C₂²	1	8	yes	complemented
73	#16811224	C₂²	1	4	yes	complemented
74	#16811223	C₂²	1	8	yes	complemented
75	#16811213	C₂²	1	4	yes	complemented
76	#16811212	C₂²	1	8	yes	complemented
77	#16811211	C₂²	1	4	yes	complemented
78	#16811210	C₂²	1	4	yes	complemented
79	#16811209	C₂²	1	8	yes	complemented
80	#16811208	C₂²	1	8	yes	complemented
81	#16811207	C₂²	1	8	yes	complemented
82	#16811206	C₂²	1	8	yes	complemented
83	#16811205	C₂²	1	8	yes	complemented
84	#16811192	C₂²	1	2	yes	complemented
85	#16811191	C₂²	1	4	yes	complemented
86	#16811190	C₂²	1	2	yes	complemented
87	#16811189	C₂²	1	4	yes	complemented
88	#16811189	C₂²	1	4	yes	complemented
89	#16811188	C₂²	1	4	yes	complemented
90	#16811188	C₂²	1	4	yes	complemented
91	#16811187	C₂²	1	2	yes	complemented
92	#16811186	C₂²	1	4	yes	complemented
93	#16811185	C₂²	1	4	yes	complemented
94	#16811184	C₂²	1	8	yes	complemented
95	#16811184	C₂²	1	8	yes	complemented
96	#16811183	C₂²	1	8	yes	complemented
97	#16811183	C₂²	1	8	yes	complemented
98	#16811182	C₂²	1	8	yes	complemented
99	#16811181	C₂²	1	8	yes	complemented
100	#16811181	C₂²	1	4	yes	complemented
101	#16811181	C₂²	1	4	yes	complemented
102	#127×D₅₃	C₂²	1	4	yes	complemented
103	#127×D₅₃	C₂²	1	2	yes	complemented
104	#126×D₅₃	C₂²	1	8	yes	complemented
105	#125×D₅₃	C₂²	1	2	yes	complemented
106	#124×D₅₃	C₂²	1	4	yes	complemented
107	#16811136	C₂²	1	2	yes	complemented
108	#16811135	C₂²	1	1	yes	characteristic, complemented
109	#16811134	C₂²	1	1	yes	characteristic, complemented
110	#16811133	C₂²	1	2	yes	complemented
111	#16811132	C₂²	1	4	yes	complemented
112	#16811131	C₂²	1	2	yes	complemented
113	#16811130	C₂²	1	1	yes	characteristic, complemented
114	#16811129	C₂²	1	2	yes	complemented
115	#123×D₅₃	C₂²	1	8	yes	complemented
116	#123×D₅₃	C₂²	1	8	yes	complemented
117	#123×D₅₃	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
119	C₂×#13133192	C₂²	1	2	yes	complemented
120	C₂×#13133191	C₂²	1	2	yes	complemented
121	C₂×#13133190	C₂²	1	4	yes	complemented
122	C₂×#13133189	C₂²	1	4	yes	complemented
123	C₂×#13133188	C₂²	1	2	yes	complemented
124	#121×D₅₃	C₂²	1	2	yes	complemented
125	#121×D₅₃	C₂²	1	4	yes	complemented
126	#121×D₅₃	C₂²	1	8	yes	complemented
127	#121×D₅₃	C₂²	1	4	yes	complemented
128	#121×D₅₃	C₂²	1	4	yes	complemented
129	#121×D₅₃	C₂²	1	8	yes	complemented
130	#121×D₅₃	C₂²	1	4	yes	complemented
131	#121×D₅₃	C₂²	1	8	yes	complemented
132	#121×D₅₃	C₂²	1	4	yes	complemented
133	#121×D₅₃	C₂²	1	4	yes	complemented
134	#121×D₅₃	C₂²	1	4	yes	complemented
135	#121×D₅₃	C₂²	1	4	yes	complemented
136	#121×D₅₃	C₂²	1	4	yes	complemented
137	#120×D₅₃	C₂²	1	4	yes	complemented
138	#120×D₅₃	C₂²	1	8	yes	complemented
139	#120×D₅₃	C₂²	1	4	yes	complemented
140	#120×D₅₃	C₂²	1	8	yes	complemented
141	#120×D₅₃	C₂²	1	2	yes	complemented
142	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
143	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
144	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
145	#117×D₅₃	C₂²	1	2	yes	complemented
146	#117×D₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
148	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
149	C₅₃×#560	C₂²	1	4	yes	complemented
150	C₅₃×#553	C₂²	1	4	yes	complemented
151	D₄²×C₅₃	C₂²	1	4	yes	complemented
152	D₄²×C₅₃	C₂²	1	4	yes	complemented
153	C₅₃×#540	C₂²	1	2	yes	complemented
154	C₅₃×#538	C₂²	1	4	yes	complemented
155	C₅₃×#535	C₂²	1	2	yes	complemented
156	C₅₃×#534	C₂²	1	4	yes	complemented
157	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
158	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
159	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
160	C₂⁴×D₅₃	C₂³	1	4	yes	—
161	C₂⁴×D₅₃	C₂³	1	4	yes	—
162	C₂×#11719949	C₂³	1	1	yes	characteristic, complemented
163	C₂×#11719945	C₂³	1	2	yes	complemented
164	C₂×#11719945	C₂³	1	1	yes	characteristic, complemented
165	C₂×#11719947	C₂³	1	2	yes	complemented
166	C₂×#11719947	C₂³	1	1	yes	characteristic, complemented
167	#41×D₅₃	—	4	4	no	—
168	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
169	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
170	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
171	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
172	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
173	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
174	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
175	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
176	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
177	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
178	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
179	C₂×D₄×D₅₃	—	4	8	no	—
180	C₂×D₄×D₅₃	—	4	8	no	—
181	C₂×D₄×D₅₃	—	4	16	no	—
182	C₂×D₄×D₅₃	—	4	32	no	—
183	C₂×D₄×D₅₃	C₂³	1	8	yes	—
184	C₂×D₄×D₅₃	C₂³	1	4	yes	—
185	C₂×D₄×D₅₃	C₂³	1	4	yes	—
186	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
187	C₂×D₄×D₅₃	C₂³	1	2	yes	—
188	C₂×D₄×D₅₃	C₂³	1	4	yes	—
189	C₂×D₄×D₅₃	C₂³	1	8	yes	—
190	C₂×D₄×D₅₃	C₂³	1	8	yes	—
191	C₂×D₄×D₅₃	C₂³	1	4	yes	—
192	C₂×D₄×D₅₃	C₂³	1	8	yes	—
193	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
194	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
195	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
196	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
197	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
198	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
199	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
200	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
201	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
202	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
203	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
204	C₂²×C₄×D₅₃	—	4	4	no	—
205	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
206	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
209	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
210	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
214	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
215	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
216	#13133214	C₂³	1	4	yes	complemented
217	#13133214	C₂³	1	2	yes	complemented
218	#13133213	C₂³	1	8	yes	complemented
219	#13133213	C₂³	1	4	yes	complemented
220	#13133213	C₂³	1	4	yes	complemented
221	#13133213	C₂³	1	8	yes	complemented
222	#13133213	C₂³	1	8	yes	complemented
223	#13133213	C₂³	1	4	yes	complemented
224	#13133212	C₂³	1	8	yes	complemented
225	#13133212	C₂³	1	8	yes	complemented
226	#13133212	C₂³	1	8	yes	complemented
227	#13133211	C₂³	1	8	yes	complemented
228	#13133210	C₂³	1	8	yes	complemented
229	#13133210	C₂³	1	8	yes	complemented
230	#13133210	C₂³	1	8	yes	complemented
231	#13133209	C₂³	1	2	yes	complemented
232	#13133208	C₂³	1	4	yes	complemented
233	#13133207	C₂³	1	8	yes	complemented
234	#13133206	C₂³	1	4	yes	complemented
235	#13133205	C₂³	1	4	yes	complemented
236	#13133204	C₂³	1	4	yes	complemented
237	#13133203	C₂³	1	8	yes	complemented
238	#13133203	C₂³	1	8	yes	complemented
239	#13133202	C₂³	1	8	yes	complemented
240	#13133202	C₂³	1	8	yes	complemented
241	#13133202	C₂³	1	4	yes	complemented
242	#13133202	C₂³	1	8	yes	complemented
243	#13133202	C₂³	1	8	yes	complemented
244	#13133201	C₂³	1	8	yes	complemented
245	#13133201	C₂³	1	2	yes	complemented
246	#13133201	C₂³	1	8	yes	complemented
247	#13133200	C₂³	1	8	yes	complemented
248	#13133200	C₂³	1	2	yes	complemented
249	#13133200	C₂³	1	8	yes	complemented
250	#13133199	C₂³	1	8	yes	complemented
251	#13133199	C₂³	1	8	yes	complemented
252	#13133199	C₂³	1	4	yes	complemented
253	#13133199	C₂³	1	8	yes	complemented
254	#13133199	C₂³	1	8	yes	complemented
255	#13133198	C₂³	1	8	yes	complemented
256	#13133198	C₂³	1	2	yes	complemented
257	#13133198	C₂³	1	8	yes	complemented
258	#13133197	C₂³	1	2	yes	complemented
259	#13133196	C₂³	1	2	yes	complemented
260	#13133195	C₂³	1	4	yes	complemented
261	#13133194	C₂³	1	4	yes	complemented
262	#13133193	C₂³	1	2	yes	complemented
263	#13133192	C₂³	1	4	yes	complemented
264	#13133192	C₂³	1	4	yes	complemented
265	#13133192	C₂³	1	8	yes	complemented
266	#13133192	C₂³	1	4	yes	complemented
267	#13133192	C₂³	1	8	yes	complemented
268	#13133192	C₂³	1	8	yes	complemented
269	#13133192	C₂³	1	4	yes	complemented
270	#13133192	C₂³	1	4	yes	complemented
271	#13133192	C₂³	1	2	yes	complemented
272	#13133191	C₂³	1	4	yes	complemented
273	#13133191	C₂³	1	4	yes	complemented
274	#13133191	C₂³	1	8	yes	complemented
275	#13133191	C₂³	1	4	yes	complemented
276	#13133191	C₂³	1	8	yes	complemented
277	#13133191	C₂³	1	8	yes	complemented
278	#13133191	C₂³	1	4	yes	complemented
279	#13133191	C₂³	1	4	yes	complemented
280	#13133191	C₂³	1	2	yes	complemented
281	#13133190	C₂³	1	8	yes	complemented
282	#13133190	C₂³	1	8	yes	complemented
283	#13133190	C₂³	1	8	yes	complemented
284	#13133190	C₂³	1	8	yes	complemented
285	#13133190	C₂³	1	8	yes	complemented
286	#13133190	C₂³	1	8	yes	complemented
287	#13133190	C₂³	1	8	yes	complemented
288	#13133190	C₂³	1	8	yes	complemented
289	#13133190	C₂³	1	8	yes	complemented
290	#13133190	C₂³	1	8	yes	complemented
291	#13133190	C₂³	1	8	yes	complemented
292	#13133190	C₂³	1	4	yes	complemented
293	#13133189	C₂³	1	8	yes	complemented
294	#13133189	C₂³	1	8	yes	complemented
295	#13133189	C₂³	1	8	yes	complemented
296	#13133189	C₂³	1	8	yes	complemented
297	#13133189	C₂³	1	8	yes	complemented
298	#13133189	C₂³	1	8	yes	complemented
299	#13133189	C₂³	1	8	yes	complemented
300	#13133189	C₂³	1	8	yes	complemented
301	#13133189	C₂³	1	8	yes	complemented
302	#13133189	C₂³	1	8	yes	complemented
303	#13133189	C₂³	1	8	yes	complemented
304	#13133189	C₂³	1	4	yes	complemented
305	#13133188	C₂³	1	8	yes	complemented
306	#13133188	C₂³	1	4	yes	complemented
307	#13133188	C₂³	1	4	yes	complemented
308	#13133188	C₂³	1	4	yes	complemented
309	#13133188	C₂³	1	8	yes	complemented
310	#13133188	C₂³	1	8	yes	complemented
311	#13133188	C₂³	1	4	yes	complemented
312	#13133188	C₂³	1	4	yes	complemented
313	#13133188	C₂³	1	2	yes	complemented
314	#13133187	C₂³	1	8	yes	complemented
315	#13133187	C₂³	1	8	yes	complemented
316	#13133187	C₂³	1	8	yes	complemented
317	#13133187	C₂³	1	8	yes	complemented
318	#13133187	C₂³	1	4	yes	complemented
319	#13133187	C₂³	1	2	yes	complemented
320	#13133187	C₂³	1	4	yes	complemented
321	#13133187	C₂³	1	4	yes	complemented
322	#13133187	C₂³	1	8	yes	complemented
323	#13133187	C₂³	1	8	yes	complemented
324	#13133187	C₂³	1	8	yes	complemented
325	#13133187	C₂³	1	8	yes	complemented
326	#13133186	C₂³	1	8	yes	complemented
327	#13133186	C₂³	1	4	yes	complemented
328	#13133186	C₂³	1	2	yes	complemented
329	#13133186	C₂³	1	4	yes	complemented
330	#13133186	C₂³	1	8	yes	complemented
331	#13133185	C₂³	1	8	yes	complemented
332	#13133185	C₂³	1	4	yes	complemented
333	#13133185	C₂³	1	8	yes	complemented
334	#13133185	C₂³	1	8	yes	complemented
335	#13133185	C₂³	1	8	yes	complemented
336	#13133185	C₂³	1	2	yes	complemented
337	#13133185	C₂³	1	4	yes	complemented
338	#13133185	C₂³	1	4	yes	complemented
339	#13133185	C₂³	1	8	yes	complemented
340	#13133185	C₂³	1	8	yes	complemented
341	#13133185	C₂³	1	8	yes	complemented
342	#13133185	C₂³	1	8	yes	complemented
343	C₄×D₂₁₂	C₂³	1	8	yes	complemented
344	C₄×D₂₁₂	C₂³	1	4	yes	complemented
345	C₄×D₂₁₂	C₂³	1	4	yes	complemented
346	D₄×Dic₅₃	C₂³	1	4	yes	complemented
347	D₄×Dic₅₃	C₂³	1	8	yes	complemented
348	D₄×Dic₅₃	C₂³	1	4	yes	complemented
349	#13133179	C₂³	1	4	yes	complemented
350	#13133179	C₂³	1	8	yes	complemented
351	#13133179	C₂³	1	4	yes	complemented
352	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
353	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
354	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
355	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
356	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
357	#13133177	C₂³	1	8	yes	complemented
358	#13133177	C₂³	1	4	yes	complemented
359	#13133177	C₂³	1	8	yes	complemented
360	#13133177	C₂³	1	8	yes	complemented
361	#13133177	C₂³	1	4	yes	complemented
362	#13133176	C₂³	1	2	yes	complemented
363	#13133176	C₂³	1	1	yes	characteristic, complemented
364	#13133175	C₂³	1	4	yes	complemented
365	#13133175	C₂³	1	2	yes	complemented
366	#13133174	C₂³	1	4	yes	complemented
367	#13133174	C₂³	1	2	yes	complemented
368	#13133173	C₂³	1	4	yes	complemented
369	#13133173	C₂³	1	2	yes	complemented
370	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
371	C₂×#11719919	C₂³	1	4	yes	complemented
372	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
373	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
374	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
375	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
376	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
377	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
378	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
379	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
380	C₂×#11719921	C₂³	1	4	yes	complemented
381	C₂×#11719921	C₂³	1	4	yes	complemented
382	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
383	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
384	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
385	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
386	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
387	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
388	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
389	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
390	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
391	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
392	C₄²×D₅₃	C₂³	1	2	yes	—
393	C₄²×D₅₃	C₂³	1	4	yes	—
394	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic, complemented
395	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
396	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
397	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
398	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
399	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
400	#127×C₅₃	C₂³	1	4	yes	complemented
401	#127×C₅₃	C₂³	1	2	yes	complemented
402	#126×C₅₃	C₂³	1	8	yes	complemented
403	#125×C₅₃	C₂³	1	2	yes	complemented
404	#124×C₅₃	C₂³	1	4	yes	complemented
405	#123×C₅₃	C₂³	1	2	yes	complemented
406	#123×C₅₃	C₂³	1	8	yes	complemented
407	#123×C₅₃	C₂³	1	8	yes	complemented
408	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
409	#121×C₅₃	C₂³	1	4	yes	complemented
410	#121×C₅₃	C₂³	1	4	yes	complemented
411	#121×C₅₃	C₂³	1	4	yes	complemented
412	#121×C₅₃	C₂³	1	4	yes	complemented
413	#121×C₅₃	C₂³	1	2	yes	complemented
414	#121×C₅₃	C₂³	1	8	yes	complemented
415	#121×C₅₃	C₂³	1	4	yes	complemented
416	#121×C₅₃	C₂³	1	8	yes	complemented
417	#121×C₅₃	C₂³	1	8	yes	complemented
418	#120×C₅₃	C₂³	1	2	yes	complemented
419	#120×C₅₃	C₂³	1	4	yes	complemented
420	#120×C₅₃	C₂³	1	8	yes	complemented
421	#120×C₅₃	C₂³	1	4	yes	complemented
422	#120×C₅₃	C₂³	1	8	yes	complemented
423	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
424	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
425	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
426	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
427	#117×C₅₃	C₂³	1	2	yes	complemented
428	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
429	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
430	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
432	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
433	C₂³×D₅₃	—	2	8	no	—
434	C₂³×D₅₃	—	2	16	no	—
435	C₂³×D₅₃	—	4	2	no	—
436	C₂³×D₅₃	—	4	8	no	—
437	C₂³×D₅₃	—	4	8	no	—
438	C₂³×D₅₃	—	4	8	no	—
439	C₂³×D₅₃	—	4	16	no	—
440	C₂³×D₅₃	C₂⁴	1	2	yes	—
441	C₂³×D₅₃	C₂⁴	1	8	yes	—
442	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
443	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
444	C₂³×D₅₃	C₂⁴	1	2	yes	—
445	C₂³×D₅₃	C₂⁴	1	2	yes	—
446	C₂³×D₅₃	C₂⁴	1	8	yes	—
447	C₂³×D₅₃	C₂⁴	1	4	yes	—
448	C₂³×D₅₃	C₂⁴	1	4	yes	—
449	C₂³×D₅₃	C₂⁴	1	8	yes	—
450	#41×C₅₃	—	4	2	no	—
451	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₂×D₄×C₅₃	—	4	4	no	—
453	C₂×D₄×C₅₃	—	4	4	no	—
454	C₂×D₄×C₅₃	—	4	8	no	—
455	C₂×D₄×C₅₃	—	4	16	no	—
456	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
457	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
458	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
459	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
461	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
462	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
463	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
464	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
465	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
466	C₂²×C₄×C₅₃	—	4	2	no	—
467	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
468	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
469	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
471	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
472	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
473	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂×C₂²⋊D₅₃	—	4	8	no	—
475	C₂×C₂²⋊D₅₃	—	4	8	no	—
476	C₂×C₂²⋊D₅₃	—	4	8	no	—
477	C₂×C₂²⋊D₅₃	—	4	16	no	—
478	C₂×C₂²⋊D₅₃	—	4	8	no	—
479	C₂×C₂²⋊D₅₃	—	4	16	no	—
480	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
481	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
482	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
483	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
484	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
485	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
486	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
487	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
488	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
489	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
490	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
491	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
492	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
493	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
494	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
495	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
496	C₂²×Dic₅₃	—	4	2	no	—
497	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
498	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
499	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
500	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
501	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
502	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
503	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
504	#11719949	—	4	2	no	—
505	Q₈×D₅₃	—	4	2	no	—
506	#11719947	—	4	2	no	—
507	#11719947	—	4	4	no	—
508	D₄×D₅₃	—	2	32	no	—
509	D₄×D₅₃	—	2	16	no	—
510	D₄×D₅₃	—	2	16	no	—
511	D₄×D₅₃	—	4	8	no	—
512	D₄×D₅₃	—	4	8	no	—
513	D₄×D₅₃	—	4	8	no	—
514	D₄×D₅₃	—	4	8	no	—
515	D₄×D₅₃	—	4	8	no	—
516	D₄×D₅₃	—	4	8	no	—
517	D₄×D₅₃	—	4	16	no	—
518	D₄×D₅₃	—	4	16	no	—
519	D₄×D₅₃	—	4	16	no	—
520	D₄×D₅₃	—	4	2	no	—
521	D₄×D₅₃	—	4	4	no	—
522	D₄×D₅₃	—	4	16	no	—
523	D₄×D₅₃	—	4	16	no	—
524	D₄×D₅₃	—	4	16	no	—
525	D₄×D₅₃	—	4	16	no	—
526	D₄×D₅₃	—	4	16	no	—
527	D₄×D₅₃	—	4	16	no	—
528	#11719945	—	4	4	no	—
529	#11719945	—	4	2	no	—
530	C₂×D₂₁₂	—	4	4	no	—
531	C₂×D₂₁₂	—	4	4	no	—
532	C₂×D₂₁₂	—	4	8	no	—
533	C₂×D₂₁₂	—	4	16	no	—
534	C₂×D₂₁₂	C₂⁴	1	8	yes	—
535	C₂×D₂₁₂	C₂⁴	1	4	yes	—
536	C₂×D₂₁₂	C₂⁴	1	4	yes	—
537	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
538	C₂×D₂₁₂	C₂⁴	1	2	yes	—
539	C₂×D₂₁₂	C₂⁴	1	4	yes	—
540	C₂×D₂₁₂	C₂⁴	1	4	yes	—
541	C₂×D₂₁₂	C₂⁴	1	8	yes	—
542	C₂×D₂₁₂	C₂⁴	1	8	yes	—
543	C₂×D₂₁₂	C₂⁴	1	8	yes	—
544	C₂×C₄×D₅₃	—	2	8	no	—
545	C₂×C₄×D₅₃	—	2	4	no	—
546	C₂×C₄×D₅₃	—	2	8	no	—
547	C₂×C₄×D₅₃	—	4	2	no	—
548	C₂×C₄×D₅₃	—	4	4	no	—
549	C₂×C₄×D₅₃	—	4	4	no	—
550	C₂×C₄×D₅₃	—	4	2	no	—
551	C₂×C₄×D₅₃	—	4	2	no	—
552	C₂×C₄×D₅₃	—	4	4	no	—
553	C₂×C₄×D₅₃	—	4	8	no	—
554	C₂×C₄×D₅₃	—	4	16	no	—
555	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
556	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
557	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
558	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
559	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
560	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
561	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
562	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
563	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
564	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
565	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
566	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
567	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
568	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
569	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
570	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
571	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
572	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
573	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
574	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
575	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
576	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
577	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
578	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
579	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
580	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
581	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
582	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
583	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
584	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
585	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
586	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
587	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
588	C₄²×C₅₃	C₂⁴	1	2	yes	—
589	C₄²×C₅₃	C₂⁴	1	4	yes	—
590	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
591	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
592	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
593	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
594	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
595	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
596	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
597	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
598	#11719921	C₂⁴	1	8	yes	—
599	#11719921	C₂⁴	1	8	yes	—
600	#11719921	C₂⁴	1	8	yes	—
601	#11719921	C₂⁴	1	8	yes	—
602	#11719921	C₂⁴	1	8	yes	—
603	#11719921	C₂⁴	1	4	yes	—
604	#11719921	C₂⁴	1	4	yes	—
605	#11719921	C₂⁴	1	4	yes	—
606	#11719921	C₂⁴	1	8	yes	—
607	#11719921	C₂⁴	1	8	yes	—
608	#11719921	C₂⁴	1	4	yes	—
609	#11719921	C₂⁴	1	8	yes	—
610	#11719921	C₂⁴	1	8	yes	—
611	#11719921	C₂⁴	1	4	yes	—
612	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
613	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
614	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
615	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
616	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
617	#11719919	C₂⁴	1	8	yes	—
618	#11719919	C₂⁴	1	8	yes	—
619	#11719919	C₂⁴	1	4	yes	—
620	#11719919	C₂⁴	1	4	yes	—
621	#11719919	C₂⁴	1	4	yes	—
622	#11719919	C₂⁴	1	8	yes	—
623	#11719919	C₂⁴	1	8	yes	—
624	C₄×Dic₅₃	C₂⁴	1	4	yes	—
625	C₄×Dic₅₃	C₂⁴	1	8	yes	—
626	C₄×Dic₅₃	C₂⁴	1	4	yes	—
627	C₄×Dic₅₃	C₂⁴	1	2	yes	—
628	C₂³×C₅₃	—	2	4	no	—
629	C₂³×C₅₃	—	2	8	no	—
630	C₂³×C₅₃	—	4	1	no	—
631	C₂³×C₅₃	—	4	4	no	—
632	C₂³×C₅₃	—	4	4	no	—
633	C₂³×C₅₃	—	4	4	no	—
634	C₂³×C₅₃	—	4	8	no	—
635	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
636	C₂³×C₅₃	C₂⁵	1	2	yes	—
637	C₂³×C₅₃	C₂⁵	1	8	yes	—
638	C₂³×C₅₃	C₂⁵	1	2	yes	—
639	C₂²×D₅₃	—	2	4	no	—
640	C₂²×D₅₃	—	2	4	no	—
641	C₂²×D₅₃	—	2	4	no	—
642	C₂²×D₅₃	—	2	8	no	—
643	C₂²×D₅₃	—	2	2	no	—
644	C₂²×D₅₃	—	2	4	no	—
645	C₂²×D₅₃	—	2	16	no	—
646	C₂²×D₅₃	—	2	4	no	—
647	C₂²×D₅₃	—	2	8	no	—
648	C₂²×D₅₃	—	2	16	no	—
649	C₂²×D₅₃	—	2	16	no	—
650	C₂²×D₅₃	—	2	4	no	—
651	C₂²×D₅₃	—	2	4	no	—
652	C₂²×D₅₃	—	2	16	no	—
653	C₂²×D₅₃	—	4	1	no	—
654	C₂²×D₅₃	—	4	2	no	—
655	C₂²×D₅₃	—	4	16	no	—
656	C₂²×D₅₃	—	4	4	no	—
657	C₂²×D₅₃	—	4	4	no	—
658	C₂²×D₅₃	—	4	4	no	—
659	C₂²×D₅₃	—	4	8	no	—
660	C₂²×D₅₃	—	4	8	no	—
661	C₂²×D₅₃	—	4	8	no	—
662	C₂²×D₅₃	—	4	8	no	—
663	C₂²×D₅₃	—	4	8	no	—
664	C₂²×D₅₃	—	4	8	no	—
665	C₂²×D₅₃	—	8	32	no	—
666	C₂²×D₅₃	—	8	32	no	—
667	C₂²×D₅₃	H(5,𝔽₂)	1	8	yes	—
668	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
669	C₂²×D₅₃	C₂⁵	1	2	yes	—
670	C₂²×D₅₃	C₂⁵	1	8	yes	—
671	C₂²×D₅₃	C₂⁵	1	2	yes	—
672	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
673	Q₈×C₅₃	—	4	1	no	—
674	D₄×C₅₃	—	2	16	no	—
675	D₄×C₅₃	—	2	8	no	—
676	D₄×C₅₃	—	2	8	no	—
677	D₄×C₅₃	—	4	4	no	—
678	D₄×C₅₃	—	4	4	no	—
679	D₄×C₅₃	—	4	8	no	—
680	D₄×C₅₃	—	4	8	no	—
681	D₄×C₅₃	—	4	8	no	—
682	D₄×C₅₃	—	4	1	no	—
683	D₄×C₅₃	—	4	2	no	—
684	C₂×C₄×C₅₃	—	2	4	no	—
685	C₂×C₄×C₅₃	—	2	2	no	—
686	C₂×C₄×C₅₃	—	2	4	no	—
687	C₂×C₄×C₅₃	—	4	2	no	—
688	C₂×C₄×C₅₃	—	4	1	no	—
689	C₂×C₄×C₅₃	—	4	4	no	—
690	C₂×C₄×C₅₃	—	4	8	no	—
691	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
692	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
693	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
694	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
695	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
696	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
697	C₂²⋊D₅₃	—	2	16	no	—
698	C₂²⋊D₅₃	—	2	8	no	—
699	C₂²⋊D₅₃	—	2	16	no	—
700	C₂²⋊D₅₃	—	2	8	no	—
701	C₂²⋊D₅₃	—	2	16	no	—
702	C₂²⋊D₅₃	—	4	2	no	—
703	C₂²⋊D₅₃	—	4	2	no	—
704	C₂²⋊D₅₃	—	4	2	no	—
705	C₂²⋊D₅₃	—	4	8	no	—
706	C₂²⋊D₅₃	—	4	8	no	—
707	C₂²⋊D₅₃	—	4	8	no	—
708	C₂²⋊D₅₃	—	4	8	no	—
709	C₂²⋊D₅₃	—	4	8	no	—
710	C₂²⋊D₅₃	—	4	8	no	—
711	C₂²⋊D₅₃	—	4	8	no	—
712	C₂²⋊D₅₃	—	4	8	no	—
713	C₂×Dic₅₃	—	2	2	no	—
714	C₂×Dic₅₃	—	2	4	no	—
715	C₂×Dic₅₃	—	2	4	no	—
716	C₂×Dic₅₃	—	4	2	no	—
717	C₂×Dic₅₃	—	4	1	no	—
718	C₂×Dic₅₃	—	4	4	no	—
719	C₂×Dic₅₃	—	4	8	no	—
720	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
721	C₂×Dic₅₃	C₂⁵	1	2	yes	—
722	C₂×Dic₅₃	C₂⁵	1	2	yes	—
723	C₂×Dic₅₃	C₂⁵	1	8	yes	—
724	C₂×Dic₅₃	C₂⁵	1	4	yes	—
725	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
726	D₂₁₂	—	2	16	no	—
727	D₂₁₂	—	2	8	no	—
728	D₂₁₂	—	2	8	no	—
729	D₂₁₂	—	4	4	no	—
730	D₂₁₂	—	4	4	no	—
731	D₂₁₂	—	4	8	no	—
732	D₂₁₂	—	4	8	no	—
733	D₂₁₂	—	4	8	no	—
734	D₂₁₂	—	4	1	no	—
735	D₂₁₂	—	4	2	no	—
736	C₄×D₅₃	—	2	4	no	—
737	C₄×D₅₃	—	2	2	no	—
738	C₄×D₅₃	—	2	4	no	—
739	C₄×D₅₃	—	2	16	no	—
740	C₄×D₅₃	—	2	8	no	—
741	C₄×D₅₃	—	2	2	no	—
742	C₄×D₅₃	—	2	4	no	—
743	C₄×D₅₃	—	2	4	no	—
744	C₄×D₅₃	—	2	4	no	—
745	C₄×D₅₃	—	2	2	no	—
746	C₄×D₅₃	—	2	4	no	—
747	C₄×D₅₃	—	4	2	no	—
748	C₄×D₅₃	—	4	2	no	—
749	C₄×D₅₃	—	4	2	no	—
750	C₄×D₅₃	—	4	8	no	—
751	C₄×D₅₃	—	4	8	no	—
752	C₄×D₅₃	—	4	8	no	—
753	C₄×D₅₃	H(5,𝔽₂)	1	4	yes	—
754	Dic₁₀₆	—	4	2	no	—
755	Dic₁₀₆	—	4	1	no	—
756	C₂×#3537	—	53	1	no	maximal, Sylow
757	C₂²×C₅₃	—	2	2	no	—
758	C₂²×C₅₃	—	2	2	no	—
759	C₂²×C₅₃	—	2	1	no	—
760	C₂²×C₅₃	—	2	2	no	—
761	C₂²×C₅₃	—	2	8	no	—
762	C₂²×C₅₃	—	2	8	no	—
763	C₂²×C₅₃	—	2	4	no	—
764	C₂²×C₅₃	—	2	8	no	—
765	C₂²×C₅₃	—	2	2	no	—
766	C₂²×C₅₃	—	4	4	no	—
767	C₂²×C₅₃	—	8	8	no	—
768	C₂²×C₅₃	—	8	8	no	—
769	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
770	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
771	C₂×D₅₃	—	2	2	no	—
772	C₂×D₅₃	—	2	2	no	—
773	C₂×D₅₃	—	2	16	no	—
774	C₂×D₅₃	—	2	1	no	—
775	C₂×D₅₃	—	2	2	no	—
776	C₂×D₅₃	—	2	8	no	—
777	C₂×D₅₃	—	2	4	no	—
778	C₂×D₅₃	—	2	8	no	—
779	C₂×D₅₃	—	2	8	no	—
780	C₂×D₅₃	—	2	2	no	—
781	C₂×D₅₃	—	4	4	no	—
782	C₂×D₅₃	—	4	8	no	—
783	C₂×D₅₃	—	4	4	no	—
784	C₂×D₅₃	—	4	8	no	—
785	C₂×D₅₃	—	4	32	no	—
786	C₂×D₅₃	—	8	16	no	—
787	C₂×D₅₃	—	8	8	no	—
788	C₂×D₅₃	—	8	16	no	—
789	C₂×D₅₃	—	8	8	no	—
790	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
791	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
792	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
793	C₄×C₅₃	—	2	1	no	—
794	C₄×C₅₃	—	2	2	no	—
795	C₄×C₅₃	—	2	2	no	—
796	C₄×C₅₃	—	2	8	no	—
797	C₄×C₅₃	—	2	4	no	—
798	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
799	Dic₅₃	—	2	1	no	—
800	Dic₅₃	—	2	2	no	—
801	Dic₅₃	—	2	2	no	—
802	Dic₅₃	—	2	8	no	—
803	Dic₅₃	—	2	4	no	—
804	Dic₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
805	#3537	—	53	4	no	—
806	#3537	—	53	4	no	—
807	#3537	—	53	4	no	—
808	#3537	—	53	4	no	—
809	#3537	—	53	2	no	—
810	#3537	—	53	4	no	—
811	#3537	—	53	2	no	—
812	#3537	—	53	4	no	—
813	#3537	—	53	1	no	—
814	#3537	—	53	2	no	—
815	#3537	D₅₃	1	1	yes	characteristic, direct product factor
816	C₂×#560	—	53	4	no	—
817	C₂×#553	—	53	4	no	—
818	C₂×D₄²	—	53	4	no	—
819	C₂×D₄²	—	53	4	no	—
820	C₂×#540	—	53	2	no	—
821	C₂×#538	—	53	4	no	—
822	C₂×#535	—	53	2	no	—
823	C₂×#534	—	53	4	no	—
824	C₂×#525	—	53	1	no	—
825	C₂²×#121	—	53	2	no	—
826	C₂×C₅₃	—	2	4	no	—
827	C₂×C₅₃	—	4	1	no	—
828	C₂×C₅₃	—	4	8	no	—
829	C₂×C₅₃	—	4	2	no	—
830	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
831	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
832	D₅₃	—	2	4	no	—
833	D₅₃	—	4	1	no	—
834	D₅₃	—	4	2	no	—
835	D₅₃	—	4	8	no	—
836	D₅₃	#3537	1	4	yes	direct product factor
837	C₂²×#41	—	53	1	no	—
838	C₂³×D₄	—	53	2	no	—
839	C₂³×D₄	—	53	4	no	—
840	C₂³×D₄	—	53	8	no	—
841	C₂³×D₄	—	53	2	no	—
842	C₂⁴×C₄	—	53	1	no	—
843	#560	—	53	4	no	—
844	#560	—	53	8	no	—
845	#560	—	53	8	no	—
846	#560	—	53	4	no	—
847	#560	—	53	8	no	—
848	#560	—	53	8	no	—
849	#560	—	53	8	no	—
850	#560	—	53	4	no	—
851	#560	—	53	8	no	—
852	#560	C₂×D₅₃	1	4	yes	complemented
853	#553	—	53	8	no	—
854	#553	—	53	4	no	—
855	#553	—	53	8	no	—
856	#553	—	53	8	no	—
857	#553	—	53	4	no	—
858	#553	—	53	4	no	—
859	#553	—	53	4	no	—
860	#553	—	53	8	no	—
861	#553	—	53	4	no	—
862	#553	—	53	4	no	—
863	#553	—	53	4	no	—
864	#553	C₂×D₅₃	1	4	yes	complemented
865	D₄²	—	53	8	no	—
866	D₄²	—	53	8	no	—
867	D₄²	—	53	8	no	—
868	D₄²	—	53	4	no	—
869	D₄²	—	53	4	no	—
870	D₄²	—	53	4	no	—
871	D₄²	—	53	4	no	—
872	D₄²	—	53	4	no	—
873	D₄²	—	53	4	no	—
874	D₄²	—	53	8	no	—
875	D₄²	—	53	8	no	—
876	D₄²	—	53	8	no	—
877	D₄²	—	53	8	no	—
878	D₄²	—	53	8	no	—
879	D₄²	—	53	4	no	—
880	D₄²	—	53	4	no	—
881	D₄²	—	53	8	no	—
882	D₄²	—	53	4	no	—
883	D₄²	—	53	8	no	—
884	D₄²	—	53	4	no	—
885	D₄²	C₂×D₅₃	1	4	yes	complemented
886	D₄²	C₂×D₅₃	1	4	yes	complemented
887	#540	—	53	2	no	—
888	#540	—	53	2	no	—
889	#540	—	53	8	no	—
890	#540	—	53	8	no	—
891	#540	—	53	4	no	—
892	#540	—	53	4	no	—
893	#540	—	53	2	no	—
894	#540	C₂×D₅₃	1	2	yes	complemented
895	#538	—	53	8	no	—
896	#538	—	53	8	no	—
897	#538	—	53	8	no	—
898	#538	—	53	4	no	—
899	#538	—	53	8	no	—
900	#538	—	53	4	no	—
901	#538	—	53	8	no	—
902	#538	—	53	8	no	—
903	#538	—	53	4	no	—
904	#538	C₂×D₅₃	1	4	yes	complemented
905	#535	—	53	2	no	—
906	#535	—	53	2	no	—
907	#535	—	53	4	no	—
908	#535	—	53	4	no	—
909	#535	—	53	4	no	—
910	#535	—	53	4	no	—
911	#535	—	53	4	no	—
912	#535	—	53	4	no	—
913	#535	—	53	2	no	—
914	#535	C₂×D₅₃	1	2	yes	complemented
915	#534	—	53	8	no	—
916	#534	—	53	8	no	—
917	#534	—	53	8	no	—
918	#534	—	53	4	no	—
919	#534	—	53	8	no	—
920	#534	—	53	4	no	—
921	#534	—	53	8	no	—
922	#534	—	53	8	no	—
923	#534	—	53	4	no	—
924	#534	C₂×D₅₃	1	4	yes	complemented
925	C₂×#127	—	53	4	no	—
926	C₂×#127	—	53	2	no	—
927	C₂×#126	—	53	8	no	—
928	C₂×#125	—	53	2	no	—
929	C₂×#124	—	53	4	no	—
930	#525	—	53	1	no	—
931	#525	—	53	1	no	—
932	#525	—	53	2	no	—
933	#525	—	53	2	no	—
934	#525	—	53	2	no	—
935	#525	—	53	2	no	—
936	#525	—	53	4	no	—
937	#525	—	53	1	no	—
938	#525	C₂×D₅₃	1	1	yes	characteristic, complemented
939	C₂×#123	—	53	2	no	—
940	C₂×#123	—	53	8	no	—
941	C₂×#123	—	53	8	no	—
942	C₂×C₂²⋊Q₈	—	53	2	no	—
943	C₂×#121	—	53	2	no	—
944	C₂×#121	—	53	4	no	—
945	C₂×#121	—	53	2	no	—
946	C₂×#121	—	53	4	no	—
947	C₂×#121	—	53	4	no	—
948	C₂×#121	—	53	4	no	—
949	C₂×#121	—	53	4	no	—
950	C₂×#121	—	53	4	no	—
951	C₂×#121	—	53	4	no	—
952	C₂×#121	—	53	4	no	—
953	C₂×#121	—	53	4	no	—
954	C₂×#121	—	53	2	no	—
955	C₂×#121	—	53	8	no	—
956	C₂×#121	—	53	4	no	—
957	C₂×#121	—	53	8	no	—
958	C₂×#121	—	53	8	no	—
959	C₂×#121	—	53	2	no	—
960	C₂×#121	—	53	4	no	—
961	C₂×#121	C₂×D₅₃	1	2	yes	complemented
962	C₂×#120	—	53	2	no	—
963	C₂×#120	—	53	4	no	—
964	C₂×#120	—	53	8	no	—
965	C₂×#120	—	53	4	no	—
966	C₂×#120	—	53	8	no	—
967	C₂×C₄×D₄	—	53	4	no	—
968	C₂×C₄×D₄	—	53	8	no	—
969	C₂×C₄×D₄	—	53	4	no	—
970	C₂×#117	—	53	1	no	—
971	C₂×#117	—	53	2	no	—
972	C₂²×C₄⋊C₄	—	53	2	no	—
973	C₂²×C₂²⋊C₄	—	53	4	no	—
974	C₅₃	C₂×#3537	1	1	yes	characteristic, complemented, Sylow
975	C₂⁵	—	53	1	no	—
976	C₂⁵	—	53	4	no	—
977	C₂⁵	—	53	4	no	—
978	C₂×#41	—	53	1	no	—
979	C₂×#41	—	53	1	no	—
980	C₂×#41	—	53	2	no	—
981	C₂×#41	—	53	1	no	—
982	C₂×#41	—	53	2	no	—
983	C₂×#41	—	212	4	no	—
984	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic, complemented
985	C₂²×Q₈	—	53	1	no	—
986	C₂²×D₄	—	53	4	no	—
987	C₂²×D₄	—	53	4	no	—
988	C₂²×D₄	—	53	4	no	—
989	C₂²×D₄	—	53	8	no	—
990	C₂²×D₄	—	53	8	no	—
991	C₂²×D₄	—	53	4	no	—
992	C₂²×D₄	—	53	4	no	—
993	C₂²×D₄	—	53	8	no	—
994	C₂²×D₄	—	53	4	no	—
995	C₂²×D₄	—	53	1	no	—
996	C₂²×D₄	—	53	2	no	—
997	C₂²×D₄	—	53	4	no	—
998	C₂²×D₄	—	53	8	no	—
999	C₂²×D₄	—	53	8	no	—
1000	C₂²×D₄	—	53	4	no	—
1001	C₂²×D₄	—	53	8	no	—
1002	C₂²×D₄	—	53	4	no	—
1003	C₂²×D₄	—	53	4	no	—
1004	C₂²×D₄	—	53	8	no	—
1005	C₂²×D₄	—	53	8	no	—
1006	C₂²×D₄	—	53	8	no	—
1007	C₂²×D₄	—	53	8	no	—
1008	C₂²×D₄	—	53	8	no	—
1009	C₂²×D₄	—	53	8	no	—
1010	C₂²×D₄	—	53	4	no	—
1011	C₂²×D₄	—	53	4	no	—
1012	C₂²×D₄	—	53	2	no	—
1013	C₂²×D₄	—	53	4	no	—
1014	C₂²×D₄	—	53	8	no	—
1015	C₂²×D₄	—	53	2	no	—
1016	C₂²×D₄	—	212	8	no	—
1017	C₂²×D₄	—	212	8	no	—
1018	C₂²×D₄	—	212	32	no	—
1019	C₂²×D₄	—	212	16	no	—
1020	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
1021	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
1022	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
1023	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
1024	C₂³×C₄	—	53	1	no	—
1025	C₂³×C₄	—	53	2	no	—
1026	C₂³×C₄	—	53	2	no	—
1027	C₂³×C₄	—	53	1	no	—
1028	C₂³×C₄	—	53	2	no	—
1029	C₂³×C₄	—	53	4	no	—
1030	C₂³×C₄	—	53	8	no	—
1031	C₂³×C₄	—	53	1	no	—
1032	C₂³×C₄	—	53	2	no	—
1033	C₂³×C₄	—	53	1	no	—
1034	C₂³×C₄	—	53	2	no	—
1035	C₂³×C₄	—	53	1	no	—
1036	C₂³×C₄	—	212	4	no	—
1037	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1038	#127	—	53	8	no	—
1039	#127	—	53	8	no	—
1040	#127	—	53	4	no	—
1041	#127	—	53	4	no	—
1042	#127	—	53	8	no	—
1043	#127	—	53	4	no	—
1044	#127	—	53	4	no	—
1045	#127	—	53	2	no	—
1046	#127	C₂²×D₅₃	1	4	yes	complemented
1047	#127	C₂²×D₅₃	1	2	yes	complemented
1048	#126	—	53	8	no	—
1049	#126	—	53	8	no	—
1050	#126	—	53	8	no	—
1051	#126	—	53	8	no	—
1052	#126	—	53	8	no	—
1053	#126	—	53	8	no	—
1054	#126	—	53	8	no	—
1055	#126	C₂²×D₅₃	1	8	yes	complemented
1056	#125	—	53	8	no	—
1057	#125	—	53	4	no	—
1058	#125	—	53	2	no	—
1059	#125	C₂²×D₅₃	1	2	yes	complemented
1060	#124	—	53	4	no	—
1061	#124	—	53	4	no	—
1062	#124	—	53	8	no	—
1063	#124	—	53	8	no	—
1064	#124	—	53	4	no	—
1065	#124	C₂²×D₅₃	1	4	yes	complemented
1066	#123	—	53	2	no	—
1067	#123	—	53	8	no	—
1068	#123	—	53	8	no	—
1069	#123	—	53	2	no	—
1070	#123	—	53	8	no	—
1071	#123	—	53	8	no	—
1072	#123	—	53	4	no	—
1073	#123	—	53	8	no	—
1074	#123	—	53	8	no	—
1075	#123	—	53	8	no	—
1076	#123	—	53	8	no	—
1077	#123	—	53	4	no	—
1078	#123	—	53	2	no	—
1079	#123	—	53	8	no	—
1080	#123	—	53	8	no	—
1081	#123	—	53	8	no	—
1082	#123	—	53	8	no	—
1083	#123	—	53	8	no	—
1084	#123	—	53	8	no	—
1085	#123	C₂²×D₅₃	1	2	yes	complemented
1086	#123	C₂²×D₅₃	1	8	yes	complemented
1087	#123	C₂²×D₅₃	1	8	yes	complemented
1088	C₂²⋊Q₈	—	53	2	no	—
1089	C₂²⋊Q₈	—	53	2	no	—
1090	C₂²⋊Q₈	—	53	4	no	—
1091	C₂²⋊Q₈	—	53	2	no	—
1092	C₂²⋊Q₈	—	53	4	no	—
1093	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1094	#121	—	53	4	no	—
1095	#121	—	53	8	no	—
1096	#121	—	53	4	no	—
1097	#121	—	53	8	no	—
1098	#121	—	53	4	no	—
1099	#121	—	53	8	no	—
1100	#121	—	53	4	no	—
1101	#121	—	53	8	no	—
1102	#121	—	53	2	no	—
1103	#121	—	53	4	no	—
1104	#121	—	53	8	no	—
1105	#121	—	53	8	no	—
1106	#121	—	53	8	no	—
1107	#121	—	53	4	no	—
1108	#121	—	53	8	no	—
1109	#121	—	53	8	no	—
1110	#121	—	53	8	no	—
1111	#121	—	53	8	no	—
1112	#121	—	53	8	no	—
1113	#121	—	53	8	no	—
1114	#121	—	53	8	no	—
1115	#121	—	53	4	no	—
1116	#121	—	53	4	no	—
1117	#121	—	53	4	no	—
1118	#121	—	53	4	no	—
1119	#121	—	53	2	no	—
1120	#121	—	53	8	no	—
1121	#121	—	53	4	no	—
1122	#121	—	53	8	no	—
1123	#121	—	53	8	no	—
1124	#121	—	53	4	no	—
1125	#121	—	53	4	no	—
1126	#121	—	53	4	no	—
1127	#121	—	53	4	no	—
1128	#121	—	53	2	no	—
1129	#121	—	53	8	no	—
1130	#121	—	53	4	no	—
1131	#121	—	53	8	no	—
1132	#121	—	53	8	no	—
1133	#121	—	53	8	no	—
1134	#121	—	53	8	no	—
1135	#121	—	53	8	no	—
1136	#121	—	53	8	no	—
1137	#121	—	53	4	no	—
1138	#121	—	53	8	no	—
1139	#121	—	53	8	no	—
1140	#121	—	53	8	no	—
1141	#121	—	53	8	no	—
1142	#121	—	53	8	no	—
1143	#121	—	53	8	no	—
1144	#121	—	53	8	no	—
1145	#121	C₂²×D₅₃	1	4	yes	complemented
1146	#121	C₂²×D₅₃	1	4	yes	complemented
1147	#121	C₂²×D₅₃	1	4	yes	complemented
1148	#121	C₂²×D₅₃	1	4	yes	complemented
1149	#121	C₂²×D₅₃	1	2	yes	complemented
1150	#121	C₂²×D₅₃	1	8	yes	complemented
1151	#121	C₂²×D₅₃	1	4	yes	complemented
1152	#121	C₂²×D₅₃	1	8	yes	complemented
1153	#121	C₂²×D₅₃	1	8	yes	complemented
1154	#120	—	53	2	no	—
1155	#120	—	53	4	no	—
1156	#120	—	53	8	no	—
1157	#120	—	53	4	no	—
1158	#120	—	53	8	no	—
1159	#120	—	53	2	no	—
1160	#120	—	53	4	no	—
1161	#120	—	53	8	no	—
1162	#120	—	53	4	no	—
1163	#120	—	53	8	no	—
1164	#120	—	53	8	no	—
1165	#120	—	53	8	no	—
1166	#120	—	53	4	no	—
1167	#120	—	53	8	no	—
1168	#120	—	53	8	no	—
1169	#120	—	53	8	no	—
1170	#120	—	53	8	no	—
1171	#120	—	53	4	no	—
1172	#120	—	53	2	no	—
1173	#120	—	53	4	no	—
1174	#120	—	53	8	no	—
1175	#120	—	53	8	no	—
1176	#120	—	53	8	no	—
1177	#120	—	53	8	no	—
1178	#120	—	53	8	no	—
1179	#120	—	53	4	no	—
1180	#120	—	53	8	no	—
1181	#120	—	53	8	no	—
1182	#120	—	53	8	no	—
1183	#120	C₂²×D₅₃	1	2	yes	complemented
1184	#120	C₂²×D₅₃	1	4	yes	complemented
1185	#120	C₂²×D₅₃	1	8	yes	complemented
1186	#120	C₂²×D₅₃	1	4	yes	complemented
1187	#120	C₂²×D₅₃	1	8	yes	complemented
1188	C₄×D₄	—	53	4	no	—
1189	C₄×D₄	—	53	8	no	—
1190	C₄×D₄	—	53	4	no	—
1191	C₄×D₄	—	53	4	no	—
1192	C₄×D₄	—	53	4	no	—
1193	C₄×D₄	—	53	8	no	—
1194	C₄×D₄	—	53	8	no	—
1195	C₄×D₄	—	53	8	no	—
1196	C₄×D₄	—	53	4	no	—
1197	C₄×D₄	—	53	8	no	—
1198	C₄×D₄	—	53	4	no	—
1199	C₄×D₄	—	53	4	no	—
1200	C₄×D₄	—	53	4	no	—
1201	C₄×D₄	—	53	8	no	—
1202	C₄×D₄	—	53	8	no	—
1203	C₄×D₄	—	53	8	no	—
1204	C₄×D₄	—	53	4	no	—
1205	C₄×D₄	—	53	8	no	—
1206	C₄×D₄	—	53	4	no	—
1207	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1208	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1209	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1210	#117	—	53	1	no	—
1211	#117	—	53	2	no	—
1212	#117	—	53	2	no	—
1213	#117	—	53	4	no	—
1214	#117	—	53	2	no	—
1215	#117	—	53	4	no	—
1216	#117	—	53	2	no	—
1217	#117	—	53	4	no	—
1218	#117	C₂²×D₅₃	1	1	yes	characteristic, complemented
1219	#117	C₂²×D₅₃	1	2	yes	complemented
1220	C₂×C₄⋊C₄	—	53	4	no	—
1221	C₂×C₄⋊C₄	—	53	2	no	—
1222	C₂×C₄⋊C₄	—	53	4	no	—
1223	C₂×C₄⋊C₄	—	53	4	no	—
1224	C₂×C₄⋊C₄	—	53	4	no	—
1225	C₂×C₄⋊C₄	—	53	4	no	—
1226	C₂×C₄⋊C₄	—	53	2	no	—
1227	C₂×C₄⋊C₄	—	53	4	no	—
1228	C₂×C₄⋊C₄	—	53	8	no	—
1229	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1230	C₂×C₂²⋊C₄	—	53	4	no	—
1231	C₂×C₂²⋊C₄	—	53	4	no	—
1232	C₂×C₂²⋊C₄	—	53	4	no	—
1233	C₂×C₂²⋊C₄	—	53	8	no	—
1234	C₂×C₂²⋊C₄	—	53	8	no	—
1235	C₂×C₂²⋊C₄	—	53	8	no	—
1236	C₂×C₂²⋊C₄	—	53	8	no	—
1237	C₂×C₂²⋊C₄	—	53	4	no	—
1238	C₂×C₂²⋊C₄	—	53	2	no	—
1239	C₂×C₂²⋊C₄	—	53	4	no	—
1240	C₂×C₂²⋊C₄	—	53	8	no	—
1241	C₂×C₂²⋊C₄	—	53	8	no	—
1242	C₂×C₂²⋊C₄	—	53	4	no	—
1243	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1244	C₂×C₄²	—	53	2	no	—
1245	C₂×C₄²	—	53	4	no	—
1246	C₂⁴	—	53	2	no	—
1247	C₂⁴	—	53	2	no	—
1248	C₂⁴	—	53	8	no	—
1249	C₂⁴	—	53	1	no	—
1250	C₂⁴	—	53	1	no	—
1251	C₂⁴	—	53	2	no	—
1252	C₂⁴	—	53	8	no	—
1253	C₂⁴	—	53	4	no	—
1254	C₂⁴	—	53	8	no	—
1255	C₂⁴	—	53	4	no	—
1256	C₂⁴	—	106	16	no	—
1257	C₂⁴	—	106	8	no	—
1258	C₂⁴	—	212	8	no	—
1259	C₂⁴	—	212	8	no	—
1260	C₂⁴	—	212	8	no	—
1261	C₂⁴	—	212	16	no	—
1262	C₂⁴	—	212	2	no	—
1263	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1264	C₂⁴	C₂³×D₅₃	1	4	yes	—
1265	C₂⁴	C₂³×D₅₃	1	4	yes	—
1266	#41	—	4	2	no	—
1267	#41	—	212	2	no	—
1268	#41	—	212	4	no	—
1269	#41	—	212	2	no	—
1270	#41	—	212	4	no	—
1271	#41	—	212	2	no	—
1272	C₂×Q₈	—	53	1	no	—
1273	C₂×Q₈	—	53	2	no	—
1274	C₂×Q₈	—	212	2	no	—
1275	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1276	C₂×D₄	—	4	4	no	—
1277	C₂×D₄	—	4	4	no	—
1278	C₂×D₄	—	4	8	no	—
1279	C₂×D₄	—	4	16	no	—
1280	C₂×D₄	—	53	4	no	—
1281	C₂×D₄	—	53	8	no	—
1282	C₂×D₄	—	53	4	no	—
1283	C₂×D₄	—	53	8	no	—
1284	C₂×D₄	—	53	8	no	—
1285	C₂×D₄	—	53	2	no	—
1286	C₂×D₄	—	53	2	no	—
1287	C₂×D₄	—	53	2	no	—
1288	C₂×D₄	—	53	8	no	—
1289	C₂×D₄	—	53	8	no	—
1290	C₂×D₄	—	53	8	no	—
1291	C₂×D₄	—	53	8	no	—
1292	C₂×D₄	—	53	8	no	—
1293	C₂×D₄	—	53	8	no	—
1294	C₂×D₄	—	53	8	no	—
1295	C₂×D₄	—	53	8	no	—
1296	C₂×D₄	—	53	4	no	—
1297	C₂×D₄	—	53	8	no	—
1298	C₂×D₄	—	53	4	no	—
1299	C₂×D₄	—	53	1	no	—
1300	C₂×D₄	—	53	2	no	—
1301	C₂×D₄	—	53	4	no	—
1302	C₂×D₄	—	53	8	no	—
1303	C₂×D₄	—	53	8	no	—
1304	C₂×D₄	—	53	4	no	—
1305	C₂×D₄	—	53	8	no	—
1306	C₂×D₄	—	106	16	no	—
1307	C₂×D₄	—	106	16	no	—
1308	C₂×D₄	—	106	32	no	—
1309	C₂×D₄	—	212	4	no	—
1310	C₂×D₄	—	212	4	no	—
1311	C₂×D₄	—	212	16	no	—
1312	C₂×D₄	—	212	8	no	—
1313	C₂×D₄	—	212	8	no	—
1314	C₂×D₄	—	212	8	no	—
1315	C₂×D₄	—	212	8	no	—
1316	C₂×D₄	—	212	8	no	—
1317	C₂×D₄	—	212	8	no	—
1318	C₂×D₄	—	212	8	no	—
1319	C₂×D₄	—	212	16	no	—
1320	C₂×D₄	—	212	16	no	—
1321	C₂×D₄	—	212	16	no	—
1322	C₂×D₄	—	212	2	no	—
1323	C₂×D₄	—	212	4	no	—
1324	C₂×D₄	—	212	8	no	—
1325	C₂×D₄	—	212	8	no	—
1326	C₂×D₄	—	212	16	no	—
1327	C₂×D₄	—	212	16	no	—
1328	C₂×D₄	—	212	16	no	—
1329	C₂×D₄	—	212	16	no	—
1330	C₂×D₄	—	212	16	no	—
1331	C₂×D₄	—	212	16	no	—
1332	C₂×D₄	—	212	8	no	—
1333	C₂×D₄	—	212	16	no	—
1334	C₂×D₄	—	212	16	no	—
1335	C₂×D₄	—	212	8	no	—
1336	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1337	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1338	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1339	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1340	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1341	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1342	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1343	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1344	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1345	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1346	C₂²×C₄	—	4	2	no	—
1347	C₂²×C₄	—	53	1	no	—
1348	C₂²×C₄	—	53	2	no	—
1349	C₂²×C₄	—	53	2	no	—
1350	C₂²×C₄	—	53	1	no	—
1351	C₂²×C₄	—	53	2	no	—
1352	C₂²×C₄	—	53	4	no	—
1353	C₂²×C₄	—	53	8	no	—
1354	C₂²×C₄	—	53	1	no	—
1355	C₂²×C₄	—	53	2	no	—
1356	C₂²×C₄	—	53	4	no	—
1357	C₂²×C₄	—	53	8	no	—
1358	C₂²×C₄	—	53	1	no	—
1359	C₂²×C₄	—	53	2	no	—
1360	C₂²×C₄	—	53	2	no	—
1361	C₂²×C₄	—	53	2	no	—
1362	C₂²×C₄	—	53	2	no	—
1363	C₂²×C₄	—	53	2	no	—
1364	C₂²×C₄	—	53	1	no	—
1365	C₂²×C₄	—	53	1	no	—
1366	C₂²×C₄	—	53	2	no	—
1367	C₂²×C₄	—	53	2	no	—
1368	C₂²×C₄	—	53	8	no	—
1369	C₂²×C₄	—	53	8	no	—
1370	C₂²×C₄	—	53	8	no	—
1371	C₂²×C₄	—	53	2	no	—
1372	C₂²×C₄	—	106	8	no	—
1373	C₂²×C₄	—	106	4	no	—
1374	C₂²×C₄	—	106	8	no	—
1375	C₂²×C₄	—	212	4	no	—
1376	C₂²×C₄	—	212	2	no	—
1377	C₂²×C₄	—	212	2	no	—
1378	C₂²×C₄	—	212	4	no	—
1379	C₂²×C₄	—	212	2	no	—
1380	C₂²×C₄	—	212	4	no	—
1381	C₂²×C₄	—	212	8	no	—
1382	C₂²×C₄	—	212	16	no	—
1383	C₂²×C₄	—	212	2	no	—
1384	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1385	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1386	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1387	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1388	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1389	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1390	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1391	C₄⋊C₄	—	53	8	no	—
1392	C₄⋊C₄	—	53	4	no	—
1393	C₄⋊C₄	—	53	8	no	—
1394	C₄⋊C₄	—	53	4	no	—
1395	C₄⋊C₄	—	53	4	no	—
1396	C₄⋊C₄	—	53	2	no	—
1397	C₄⋊C₄	—	53	4	no	—
1398	C₄⋊C₄	—	53	4	no	—
1399	C₄⋊C₄	—	53	4	no	—
1400	C₄⋊C₄	—	53	8	no	—
1401	C₄⋊C₄	—	53	8	no	—
1402	C₄⋊C₄	—	53	8	no	—
1403	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1404	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1405	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1406	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1407	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1408	C₂²⋊C₄	—	53	8	no	—
1409	C₂²⋊C₄	—	53	8	no	—
1410	C₂²⋊C₄	—	53	4	no	—
1411	C₂²⋊C₄	—	53	2	no	—
1412	C₂²⋊C₄	—	53	4	no	—
1413	C₂²⋊C₄	—	53	8	no	—
1414	C₂²⋊C₄	—	53	8	no	—
1415	C₂²⋊C₄	—	53	4	no	—
1416	C₂²⋊C₄	—	53	8	no	—
1417	C₂²⋊C₄	—	53	8	no	—
1418	C₂²⋊C₄	—	53	8	no	—
1419	C₂²⋊C₄	—	53	8	no	—
1420	C₂²⋊C₄	—	53	8	no	—
1421	C₂²⋊C₄	—	53	4	no	—
1422	C₂²⋊C₄	—	53	4	no	—
1423	C₂²⋊C₄	—	53	4	no	—
1424	C₂²⋊C₄	—	53	8	no	—
1425	C₂²⋊C₄	—	53	8	no	—
1426	C₂²⋊C₄	—	53	8	no	—
1427	C₂²⋊C₄	—	53	8	no	—
1428	C₂²⋊C₄	—	53	4	no	—
1429	C₂²⋊C₄	—	53	4	no	—
1430	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1431	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1432	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1433	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1434	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1435	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1436	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1437	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1438	C₄²	—	53	4	no	—
1439	C₄²	—	53	2	no	—
1440	C₄²	—	53	8	no	—
1441	C₄²	—	53	4	no	—
1442	C₄²	C₂³×D₅₃	1	2	yes	—
1443	C₄²	C₂³×D₅₃	1	4	yes	—
1444	C₂³	—	2	4	no	—
1445	C₂³	—	2	8	no	—
1446	C₂³	—	4	1	no	—
1447	C₂³	—	4	4	no	—
1448	C₂³	—	4	4	no	—
1449	C₂³	—	4	4	no	—
1450	C₂³	—	4	8	no	—
1451	C₂³	—	53	1	no	—
1452	C₂³	—	53	8	no	—
1453	C₂³	—	53	2	no	—
1454	C₂³	—	53	2	no	—
1455	C₂³	—	53	8	no	—
1456	C₂³	—	53	1	no	—
1457	C₂³	—	106	4	no	—
1458	C₂³	—	106	4	no	—
1459	C₂³	—	106	16	no	—
1460	C₂³	—	106	2	no	—
1461	C₂³	—	106	4	no	—
1462	C₂³	—	106	16	no	—
1463	C₂³	—	106	16	no	—
1464	C₂³	—	106	8	no	—
1465	C₂³	—	106	16	no	—
1466	C₂³	—	106	4	no	—
1467	C₂³	—	106	4	no	—
1468	C₂³	—	106	4	no	—
1469	C₂³	—	106	8	no	—
1470	C₂³	—	106	4	no	—
1471	C₂³	—	424	32	no	—
1472	C₂³	—	424	32	no	—
1473	C₂³	—	212	4	no	—
1474	C₂³	—	212	4	no	—
1475	C₂³	—	212	4	no	—
1476	C₂³	—	212	8	no	—
1477	C₂³	—	212	8	no	—
1478	C₂³	—	212	8	no	—
1479	C₂³	—	212	8	no	—
1480	C₂³	—	212	8	no	—
1481	C₂³	—	212	8	no	—
1482	C₂³	—	212	2	no	—
1483	C₂³	—	212	1	no	—
1484	C₂³	—	212	16	no	—
1485	C₂³	C₂⁴×D₅₃	1	2	yes	—
1486	C₂³	C₂⁴×D₅₃	1	8	yes	—
1487	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1488	C₂³	C₂⁴×D₅₃	1	2	yes	—
1489	Q₈	—	4	1	no	—
1490	Q₈	—	212	1	no	—
1491	Q₈	—	212	2	no	—
1492	D₄	—	2	16	no	—
1493	D₄	—	2	8	no	—
1494	D₄	—	2	8	no	—
1495	D₄	—	4	4	no	—
1496	D₄	—	4	4	no	—
1497	D₄	—	4	8	no	—
1498	D₄	—	4	8	no	—
1499	D₄	—	4	8	no	—
1500	D₄	—	4	1	no	—
1501	D₄	—	4	2	no	—
1502	D₄	—	106	8	no	—
1503	D₄	—	106	16	no	—
1504	D₄	—	106	16	no	—
1505	D₄	—	106	8	no	—
1506	D₄	—	106	16	no	—
1507	D₄	—	106	8	no	—
1508	D₄	—	106	16	no	—
1509	D₄	—	106	8	no	—
1510	D₄	—	212	4	no	—
1511	D₄	—	212	4	no	—
1512	D₄	—	212	8	no	—
1513	D₄	—	212	8	no	—
1514	D₄	—	212	8	no	—
1515	D₄	—	212	1	no	—
1516	D₄	—	212	2	no	—
1517	D₄	—	212	8	no	—
1518	D₄	—	212	8	no	—
1519	D₄	—	212	8	no	—
1520	D₄	—	212	8	no	—
1521	D₄	—	212	8	no	—
1522	D₄	—	212	8	no	—
1523	D₄	—	212	8	no	—
1524	D₄	—	212	8	no	—
1525	D₄	—	212	2	no	—
1526	D₄	—	212	2	no	—
1527	D₄	—	212	2	no	—
1528	C₂×C₄	—	2	4	no	—
1529	C₂×C₄	—	2	2	no	—
1530	C₂×C₄	—	2	4	no	—
1531	C₂×C₄	—	4	1	no	—
1532	C₂×C₄	—	4	2	no	—
1533	C₂×C₄	—	4	4	no	—
1534	C₂×C₄	—	4	8	no	—
1535	C₂×C₄	—	53	1	no	—
1536	C₂×C₄	—	53	4	no	—
1537	C₂×C₄	—	53	2	no	—
1538	C₂×C₄	—	53	4	no	—
1539	C₂×C₄	—	53	8	no	—
1540	C₂×C₄	—	53	1	no	—
1541	C₂×C₄	—	53	2	no	—
1542	C₂×C₄	—	106	4	no	—
1543	C₂×C₄	—	106	2	no	—
1544	C₂×C₄	—	106	4	no	—
1545	C₂×C₄	—	106	4	no	—
1546	C₂×C₄	—	106	2	no	—
1547	C₂×C₄	—	106	4	no	—
1548	C₂×C₄	—	106	8	no	—
1549	C₂×C₄	—	106	16	no	—
1550	C₂×C₄	—	106	4	no	—
1551	C₂×C₄	—	106	2	no	—
1552	C₂×C₄	—	106	4	no	—
1553	C₂×C₄	—	106	4	no	—
1554	C₂×C₄	—	106	2	no	—
1555	C₂×C₄	—	106	4	no	—
1556	C₂×C₄	—	212	2	no	—
1557	C₂×C₄	—	212	2	no	—
1558	C₂×C₄	—	212	2	no	—
1559	C₂×C₄	—	212	8	no	—
1560	C₂×C₄	—	212	8	no	—
1561	C₂×C₄	—	212	8	no	—
1562	C₂×C₄	—	212	1	no	—
1563	C₂×C₄	—	212	2	no	—
1564	C₂×C₄	—	212	4	no	—
1565	C₂×C₄	—	212	8	no	—
1566	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1567	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1568	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1569	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1570	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1571	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1572	C₂²	—	2	2	no	—
1573	C₂²	—	2	2	no	—
1574	C₂²	—	2	1	no	—
1575	C₂²	—	2	2	no	—
1576	C₂²	—	2	8	no	—
1577	C₂²	—	2	4	no	—
1578	C₂²	—	2	8	no	—
1579	C₂²	—	2	8	no	—
1580	C₂²	—	2	2	no	—
1581	C₂²	—	4	4	no	—
1582	C₂²	—	8	8	no	—
1583	C₂²	—	8	8	no	—
1584	C₂²	—	53	2	no	—
1585	C₂²	—	53	4	no	—
1586	C₂²	—	53	4	no	—
1587	C₂²	—	106	16	no	—
1588	C₂²	—	106	2	no	—
1589	C₂²	—	106	2	no	—
1590	C₂²	—	106	1	no	—
1591	C₂²	—	106	2	no	—
1592	C₂²	—	106	8	no	—
1593	C₂²	—	106	4	no	—
1594	C₂²	—	106	8	no	—
1595	C₂²	—	106	8	no	—
1596	C₂²	—	106	2	no	—
1597	C₂²	—	424	8	no	—
1598	C₂²	—	424	16	no	—
1599	C₂²	—	424	8	no	—
1600	C₂²	—	424	16	no	—
1601	C₂²	—	212	8	no	—
1602	C₂²	—	212	8	no	—
1603	C₂²	—	212	32	no	—
1604	C₂²	—	212	4	no	—
1605	C₂²	—	212	4	no	—
1606	C₂²	H(5,𝔽₂)×D₅₃	1	4	yes	—
1607	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1608	C₄	—	2	2	no	—
1609	C₄	—	2	1	no	—
1610	C₄	—	2	2	no	—
1611	C₄	—	2	8	no	—
1612	C₄	—	2	4	no	—
1613	C₄	—	53	2	no	—
1614	C₄	—	106	2	no	—
1615	C₄	—	106	1	no	—
1616	C₄	—	106	2	no	—
1617	C₄	—	106	4	no	—
1618	C₄	—	106	8	no	—
1619	C₄	H(5,𝔽₂)×D₅₃	1	2	yes	—
1620	C₂	—	2	4	no	—
1621	C₂	—	4	1	no	—
1622	C₂	—	4	2	no	—
1623	C₂	—	4	8	no	—
1624	C₂	—	53	4	no	—
1625	C₂	—	106	4	no	—
1626	C₂	—	212	2	no	—
1627	C₂	—	212	8	no	—
1628	C₂	—	212	1	no	—
1629	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—
1630	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3537	C₂
hypercenter	#3537	D₅₃
hypocenter	C₅₃	C₂×#3537
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3537

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20288954	C₂	semidirect
2. #20288953	C₂	semidirect
3. #20288952	C₂	semidirect
4. #20288951	C₂	semidirect
5. #20288950	C₂	semidirect
6. #20288949	C₂	semidirect
7. #20288948	C₂	semidirect
8. #20288947	C₂	semidirect
9. #20288946	C₂	semidirect
10. #20288945	C₂	semidirect
11. #560×D₅₃	C₂	semidirect
12. #553×D₅₃	C₂	semidirect
13. D₄²×D₅₃	C₂	semidirect
14. D₄²×D₅₃	C₂	semidirect
15. #540×D₅₃	C₂	semidirect
16. #538×D₅₃	C₂	semidirect
17. #535×D₅₃	C₂	semidirect
18. #534×D₅₃	C₂	semidirect
19. #525×D₅₃	C₂	semidirect
20. C₂×#121×D₅₃	C₂	semidirect
21. C₅₃×#3537	C₂	semidirect
22. C₂×#41×D₅₃	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. C₂²×D₄×D₅₃	C₂²	semidirect
26. C₂²×D₄×D₅₃	C₂²	semidirect
27. C₂³×C₄×D₅₃	C₂²	semidirect
28. #16811364	C₂²	semidirect
29. #16811363	C₂²	semidirect
30. #16811363	C₂²	semidirect
31. #16811362	C₂²	semidirect
32. #16811362	C₂²	semidirect
33. #16811361	C₂²	semidirect
34. #16811361	C₂²	semidirect
35. #16811361	C₂²	semidirect
36. #16811360	C₂²	semidirect
37. #16811326	C₂²	semidirect
38. #16811325	C₂²	semidirect
39. #16811324	C₂²	semidirect
40. #16811323	C₂²	semidirect
41. #16811322	C₂²	semidirect
42. #16811321	C₂²	semidirect
43. #16811320	C₂²	semidirect
44. #16811319	C₂²	semidirect
45. #16811318	C₂²	semidirect
46. #16811317	C₂²	semidirect
47. #16811316	C₂²	semidirect
48. D₄×D₂₁₂	C₂²	semidirect
49. D₄×D₂₁₂	C₂²	semidirect
50. D₄×D₂₁₂	C₂²	semidirect
51. #16811258	C₂²	semidirect
52. #16811258	C₂²	semidirect
53. #16811257	C₂²	semidirect
54. #16811257	C₂²	semidirect
55. #16811257	C₂²	semidirect
56. #16811257	C₂²	semidirect
57. #16811257	C₂²	semidirect
58. D₄×C₂²⋊D₅₃	C₂²	semidirect
59. D₄×C₂²⋊D₅₃	C₂²	semidirect
60. D₄×C₂²⋊D₅₃	C₂²	semidirect
61. D₄×C₂²⋊D₅₃	C₂²	semidirect
62. D₄×C₂²⋊D₅₃	C₂²	semidirect
63. #16811255	C₂²	semidirect
64. #16811255	C₂²	semidirect
65. #16811255	C₂²	semidirect
66. #16811255	C₂²	semidirect
67. #16811255	C₂²	semidirect
68. #16811229	C₂²	semidirect
69. #16811228	C₂²	semidirect
70. #16811227	C₂²	semidirect
71. #16811226	C₂²	semidirect
72. #16811225	C₂²	semidirect
73. #16811224	C₂²	semidirect
74. #16811223	C₂²	semidirect
75. #16811213	C₂²	semidirect
76. #16811212	C₂²	semidirect
77. #16811211	C₂²	semidirect
78. #16811210	C₂²	semidirect
79. #16811209	C₂²	semidirect
80. #16811208	C₂²	semidirect
81. #16811207	C₂²	semidirect
82. #16811206	C₂²	semidirect
83. #16811205	C₂²	semidirect
84. #16811192	C₂²	semidirect
85. #16811191	C₂²	semidirect
86. #16811190	C₂²	semidirect
87. #16811189	C₂²	semidirect
88. #16811189	C₂²	semidirect
89. #16811188	C₂²	semidirect
90. #16811188	C₂²	semidirect
91. #16811187	C₂²	semidirect
92. #16811186	C₂²	semidirect
93. #16811185	C₂²	semidirect
94. #16811184	C₂²	semidirect
95. #16811184	C₂²	semidirect
96. #16811183	C₂²	semidirect
97. #16811183	C₂²	semidirect
98. #16811182	C₂²	semidirect
99. #16811181	C₂²	semidirect
100. #16811181	C₂²	semidirect
101. #16811181	C₂²	semidirect
102. #127×D₅₃	C₂²	semidirect
103. #127×D₅₃	C₂²	semidirect
104. #126×D₅₃	C₂²	semidirect
105. #125×D₅₃	C₂²	semidirect
106. #124×D₅₃	C₂²	semidirect
107. #16811136	C₂²	semidirect
108. #16811135	C₂²	semidirect
109. #16811134	C₂²	semidirect
110. #16811133	C₂²	semidirect
111. #16811132	C₂²	semidirect
112. #16811131	C₂²	semidirect
113. #16811130	C₂²	semidirect
114. #16811129	C₂²	semidirect
115. #123×D₅₃	C₂²	semidirect
116. #123×D₅₃	C₂²	semidirect
117. #123×D₅₃	C₂²	semidirect
118. C₂²⋊Q₈×D₅₃	C₂²	semidirect
119. C₂×#13133192	C₂²	semidirect
120. C₂×#13133191	C₂²	semidirect
121. C₂×#13133190	C₂²	semidirect
122. C₂×#13133189	C₂²	semidirect
123. C₂×#13133188	C₂²	semidirect
124. #121×D₅₃	C₂²	semidirect
125. #121×D₅₃	C₂²	semidirect
126. #121×D₅₃	C₂²	semidirect
127. #121×D₅₃	C₂²	semidirect
128. #121×D₅₃	C₂²	semidirect
129. #121×D₅₃	C₂²	semidirect
130. #121×D₅₃	C₂²	semidirect
131. #121×D₅₃	C₂²	semidirect
132. #121×D₅₃	C₂²	semidirect
133. #121×D₅₃	C₂²	semidirect
134. #121×D₅₃	C₂²	semidirect
135. #121×D₅₃	C₂²	semidirect
136. #121×D₅₃	C₂²	semidirect
137. #120×D₅₃	C₂²	semidirect
138. #120×D₅₃	C₂²	semidirect
139. #120×D₅₃	C₂²	semidirect
140. #120×D₅₃	C₂²	semidirect
141. #120×D₅₃	C₂²	semidirect
142. C₄×D₄×D₅₃	C₂²	semidirect
143. C₄×D₄×D₅₃	C₂²	semidirect
144. C₄×D₄×D₅₃	C₂²	semidirect
145. #117×D₅₃	C₂²	semidirect
146. #117×D₅₃	C₂²	semidirect
147. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
148. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
149. C₅₃×#560	C₂²	semidirect
150. C₅₃×#553	C₂²	semidirect
151. D₄²×C₅₃	C₂²	semidirect
152. D₄²×C₅₃	C₂²	semidirect
153. C₅₃×#540	C₂²	semidirect
154. C₅₃×#538	C₂²	semidirect
155. C₅₃×#535	C₂²	semidirect
156. C₅₃×#534	C₂²	semidirect
157. C₅₃×#525	C₂²	semidirect
158. C₂×#121×C₅₃	C₂²	semidirect
162. C₂×#11719949	C₂³	semidirect
163. C₂×#11719945	C₂³	semidirect
164. C₂×#11719945	C₂³	semidirect
165. C₂×#11719947	C₂³	semidirect
166. C₂×#11719947	C₂³	semidirect
169. C₂²×D₂₁₂	C₂³	semidirect
170. C₂²×D₂₁₂	C₂³	semidirect
171. C₂²×D₂₁₂	C₂³	semidirect
172. C₂²×D₂₁₂	C₂³	semidirect
173. C₂²×C₂²⋊D₅₃	C₂³	semidirect
174. C₂²×C₂²⋊D₅₃	C₂³	semidirect
175. C₂²×C₂²⋊D₅₃	C₂³	semidirect
176. C₂²×C₂²⋊D₅₃	C₂³	semidirect
177. C₂²×C₂²⋊D₅₃	C₂³	semidirect
178. C₂²×C₂²⋊D₅₃	C₂³	semidirect
193. C₂×D₄×D₅₃	C₂³	semidirect
194. C₂×D₄×D₅₃	C₂³	semidirect
195. C₂×D₄×D₅₃	C₂³	semidirect
196. C₂×D₄×D₅₃	C₂³	semidirect
197. C₂×D₄×D₅₃	C₂³	semidirect
198. C₂×D₄×D₅₃	C₂³	semidirect
199. C₂×D₄×D₅₃	C₂³	semidirect
200. C₂×D₄×D₅₃	C₂³	semidirect
201. C₂×D₄×D₅₃	C₂³	semidirect
202. C₂×D₄×D₅₃	C₂³	semidirect
203. C₂³×Dic₅₃	C₂³	semidirect
212. C₂²×C₄×D₅₃	C₂³	semidirect
213. C₂²×C₄×D₅₃	C₂³	semidirect
214. C₂²×C₄×D₅₃	C₂³	semidirect
215. C₂²×C₄×D₅₃	C₂³	semidirect
216. #13133214	C₂³	semidirect
217. #13133214	C₂³	semidirect
218. #13133213	C₂³	semidirect
219. #13133213	C₂³	semidirect
220. #13133213	C₂³	semidirect
221. #13133213	C₂³	semidirect
222. #13133213	C₂³	semidirect
223. #13133213	C₂³	semidirect
224. #13133212	C₂³	semidirect
225. #13133212	C₂³	semidirect
226. #13133212	C₂³	semidirect
227. #13133211	C₂³	semidirect
228. #13133210	C₂³	semidirect
229. #13133210	C₂³	semidirect
230. #13133210	C₂³	semidirect
231. #13133209	C₂³	semidirect
232. #13133208	C₂³	semidirect
233. #13133207	C₂³	semidirect
234. #13133206	C₂³	semidirect
235. #13133205	C₂³	semidirect
236. #13133204	C₂³	semidirect
237. #13133203	C₂³	semidirect
238. #13133203	C₂³	semidirect
239. #13133202	C₂³	semidirect
240. #13133202	C₂³	semidirect
241. #13133202	C₂³	semidirect
242. #13133202	C₂³	semidirect
243. #13133202	C₂³	semidirect
244. #13133201	C₂³	semidirect
245. #13133201	C₂³	semidirect
246. #13133201	C₂³	semidirect
247. #13133200	C₂³	semidirect
248. #13133200	C₂³	semidirect
249. #13133200	C₂³	semidirect
250. #13133199	C₂³	semidirect
251. #13133199	C₂³	semidirect
252. #13133199	C₂³	semidirect
253. #13133199	C₂³	semidirect
254. #13133199	C₂³	semidirect
255. #13133198	C₂³	semidirect
256. #13133198	C₂³	semidirect
257. #13133198	C₂³	semidirect
258. #13133197	C₂³	semidirect
259. #13133196	C₂³	semidirect
260. #13133195	C₂³	semidirect
261. #13133194	C₂³	semidirect
262. #13133193	C₂³	semidirect
263. #13133192	C₂³	semidirect
264. #13133192	C₂³	semidirect
265. #13133192	C₂³	semidirect
266. #13133192	C₂³	semidirect
267. #13133192	C₂³	semidirect
268. #13133192	C₂³	semidirect
269. #13133192	C₂³	semidirect
270. #13133192	C₂³	semidirect
271. #13133192	C₂³	semidirect
272. #13133191	C₂³	semidirect
273. #13133191	C₂³	semidirect
274. #13133191	C₂³	semidirect
275. #13133191	C₂³	semidirect
276. #13133191	C₂³	semidirect
277. #13133191	C₂³	semidirect
278. #13133191	C₂³	semidirect
279. #13133191	C₂³	semidirect
280. #13133191	C₂³	semidirect
281. #13133190	C₂³	semidirect
282. #13133190	C₂³	semidirect
283. #13133190	C₂³	semidirect
284. #13133190	C₂³	semidirect
285. #13133190	C₂³	semidirect
286. #13133190	C₂³	semidirect
287. #13133190	C₂³	semidirect
288. #13133190	C₂³	semidirect
289. #13133190	C₂³	semidirect
290. #13133190	C₂³	semidirect
291. #13133190	C₂³	semidirect
292. #13133190	C₂³	semidirect
293. #13133189	C₂³	semidirect
294. #13133189	C₂³	semidirect
295. #13133189	C₂³	semidirect
296. #13133189	C₂³	semidirect
297. #13133189	C₂³	semidirect
298. #13133189	C₂³	semidirect
299. #13133189	C₂³	semidirect
300. #13133189	C₂³	semidirect
301. #13133189	C₂³	semidirect
302. #13133189	C₂³	semidirect
303. #13133189	C₂³	semidirect
304. #13133189	C₂³	semidirect
305. #13133188	C₂³	semidirect
306. #13133188	C₂³	semidirect
307. #13133188	C₂³	semidirect
308. #13133188	C₂³	semidirect
309. #13133188	C₂³	semidirect
310. #13133188	C₂³	semidirect
311. #13133188	C₂³	semidirect
312. #13133188	C₂³	semidirect
313. #13133188	C₂³	semidirect
314. #13133187	C₂³	semidirect
315. #13133187	C₂³	semidirect
316. #13133187	C₂³	semidirect
317. #13133187	C₂³	semidirect
318. #13133187	C₂³	semidirect
319. #13133187	C₂³	semidirect
320. #13133187	C₂³	semidirect
321. #13133187	C₂³	semidirect
322. #13133187	C₂³	semidirect
323. #13133187	C₂³	semidirect
324. #13133187	C₂³	semidirect
325. #13133187	C₂³	semidirect
326. #13133186	C₂³	semidirect
327. #13133186	C₂³	semidirect
328. #13133186	C₂³	semidirect
329. #13133186	C₂³	semidirect
330. #13133186	C₂³	semidirect
331. #13133185	C₂³	semidirect
332. #13133185	C₂³	semidirect
333. #13133185	C₂³	semidirect
334. #13133185	C₂³	semidirect
335. #13133185	C₂³	semidirect
336. #13133185	C₂³	semidirect
337. #13133185	C₂³	semidirect
338. #13133185	C₂³	semidirect
339. #13133185	C₂³	semidirect
340. #13133185	C₂³	semidirect
341. #13133185	C₂³	semidirect
342. #13133185	C₂³	semidirect
343. C₄×D₂₁₂	C₂³	semidirect
344. C₄×D₂₁₂	C₂³	semidirect
345. C₄×D₂₁₂	C₂³	semidirect
346. D₄×Dic₅₃	C₂³	semidirect
347. D₄×Dic₅₃	C₂³	semidirect
348. D₄×Dic₅₃	C₂³	semidirect
349. #13133179	C₂³	semidirect
350. #13133179	C₂³	semidirect
351. #13133179	C₂³	semidirect
352. C₄×C₂²⋊D₅₃	C₂³	semidirect
353. C₄×C₂²⋊D₅₃	C₂³	semidirect
354. C₄×C₂²⋊D₅₃	C₂³	semidirect
355. C₄×C₂²⋊D₅₃	C₂³	semidirect
356. C₄×C₂²⋊D₅₃	C₂³	semidirect
357. #13133177	C₂³	semidirect
358. #13133177	C₂³	semidirect
359. #13133177	C₂³	semidirect
360. #13133177	C₂³	semidirect
361. #13133177	C₂³	semidirect
362. #13133176	C₂³	semidirect
363. #13133176	C₂³	semidirect
364. #13133175	C₂³	semidirect
365. #13133175	C₂³	semidirect
366. #13133174	C₂³	semidirect
367. #13133174	C₂³	semidirect
368. #13133173	C₂³	semidirect
369. #13133173	C₂³	semidirect
370. C₂×C₄⋊Dic₅₃	C₂³	semidirect
371. C₂×#11719919	C₂³	semidirect
377. C₄⋊C₄×D₅₃	C₂³	semidirect
378. C₄⋊C₄×D₅₃	C₂³	semidirect
379. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
380. C₂×#11719921	C₂³	semidirect
381. C₂×#11719921	C₂³	semidirect
390. C₂²⋊C₄×D₅₃	C₂³	semidirect
391. C₂²⋊C₄×D₅₃	C₂³	semidirect
394. C₂×#41×C₅₃	C₂³	semidirect
395. C₂²×D₄×C₅₃	C₂³	semidirect
396. C₂²×D₄×C₅₃	C₂³	semidirect
397. C₂²×D₄×C₅₃	C₂³	semidirect
398. C₂²×D₄×C₅₃	C₂³	semidirect
399. C₂³×C₄×C₅₃	C₂³	semidirect
400. #127×C₅₃	C₂³	semidirect
401. #127×C₅₃	C₂³	semidirect
402. #126×C₅₃	C₂³	semidirect
403. #125×C₅₃	C₂³	semidirect
404. #124×C₅₃	C₂³	semidirect
405. #123×C₅₃	C₂³	semidirect
406. #123×C₅₃	C₂³	semidirect
407. #123×C₅₃	C₂³	semidirect
408. C₂²⋊Q₈×C₅₃	C₂³	semidirect
409. #121×C₅₃	C₂³	semidirect
410. #121×C₅₃	C₂³	semidirect
411. #121×C₅₃	C₂³	semidirect
412. #121×C₅₃	C₂³	semidirect
413. #121×C₅₃	C₂³	semidirect
414. #121×C₅₃	C₂³	semidirect
415. #121×C₅₃	C₂³	semidirect
416. #121×C₅₃	C₂³	semidirect
417. #121×C₅₃	C₂³	semidirect
418. #120×C₅₃	C₂³	semidirect
419. #120×C₅₃	C₂³	semidirect
420. #120×C₅₃	C₂³	semidirect
421. #120×C₅₃	C₂³	semidirect
422. #120×C₅₃	C₂³	semidirect
423. C₄×D₄×C₅₃	C₂³	semidirect
424. C₄×D₄×C₅₃	C₂³	semidirect
425. C₄×D₄×C₅₃	C₂³	semidirect
426. #117×C₅₃	C₂³	semidirect
427. #117×C₅₃	C₂³	semidirect
428. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
429. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
815. #3537	D₅₃	direct (N × H)
836. D₅₃	#3537	direct (N × H)
852. #560	C₂×D₅₃	semidirect
864. #553	C₂×D₅₃	semidirect
885. D₄²	C₂×D₅₃	semidirect
886. D₄²	C₂×D₅₃	semidirect
894. #540	C₂×D₅₃	semidirect
904. #538	C₂×D₅₃	semidirect
914. #535	C₂×D₅₃	semidirect
924. #534	C₂×D₅₃	semidirect
938. #525	C₂×D₅₃	semidirect
961. C₂×#121	C₂×D₅₃	semidirect
974. C₅₃	C₂×#3537	semidirect
984. C₂×#41	C₂²×D₅₃	semidirect
1020. C₂²×D₄	C₂²×D₅₃	semidirect
1021. C₂²×D₄	C₂²×D₅₃	semidirect
1022. C₂²×D₄	C₂²×D₅₃	semidirect
1023. C₂²×D₄	C₂²×D₅₃	semidirect
1037. C₂³×C₄	C₂²×D₅₃	semidirect
1046. #127	C₂²×D₅₃	semidirect
1047. #127	C₂²×D₅₃	semidirect
1055. #126	C₂²×D₅₃	semidirect
1059. #125	C₂²×D₅₃	semidirect
1065. #124	C₂²×D₅₃	semidirect
1085. #123	C₂²×D₅₃	semidirect
1086. #123	C₂²×D₅₃	semidirect
1087. #123	C₂²×D₅₃	semidirect
1093. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1145. #121	C₂²×D₅₃	semidirect
1146. #121	C₂²×D₅₃	semidirect
1147. #121	C₂²×D₅₃	semidirect
1148. #121	C₂²×D₅₃	semidirect
1149. #121	C₂²×D₅₃	semidirect
1150. #121	C₂²×D₅₃	semidirect
1151. #121	C₂²×D₅₃	semidirect
1152. #121	C₂²×D₅₃	semidirect
1153. #121	C₂²×D₅₃	semidirect
1183. #120	C₂²×D₅₃	semidirect
1184. #120	C₂²×D₅₃	semidirect
1185. #120	C₂²×D₅₃	semidirect
1186. #120	C₂²×D₅₃	semidirect
1187. #120	C₂²×D₅₃	semidirect
1207. C₄×D₄	C₂²×D₅₃	semidirect
1208. C₄×D₄	C₂²×D₅₃	semidirect
1209. C₄×D₄	C₂²×D₅₃	semidirect
1218. #117	C₂²×D₅₃	semidirect
1219. #117	C₂²×D₅₃	semidirect
1229. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1243. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20288954	2
#20288953	2
#20288952	2
#20288951	2
#20288950	2
#20288949	2
#20288948	2
#20288947	2
#20288946	2
#20288945	2
#560×D₅₃	2
#553×D₅₃	2
D₄²×D₅₃	2
#540×D₅₃	2
#538×D₅₃	2
#535×D₅₃	2
#534×D₅₃	2
#525×D₅₃	2
C₂×#121×D₅₃	2
C₅₃×#3537	2
C₂×#3537	53

Subgroups — D53×#3537 #28291321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3537 #28291321