Subgroups — D₅₃×#3490 #28291997

Order 13568.

9502 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288405	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288404	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288403	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288402	C₂	1	2	yes	maximal, complemented
5	#20288401	C₂	1	4	yes	maximal, complemented
6	#20288400	C₂	1	2	yes	maximal, complemented
7	#20288399	C₂	1	8	yes	maximal, complemented
8	#20288398	C₂	1	4	yes	maximal, complemented
9	#20288397	C₂	1	8	yes	maximal, complemented
10	#551×D₅₃	C₂	1	8	yes	maximal, complemented
11	#546×D₅₃	C₂	1	8	yes	maximal, complemented
12	#543×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#538×D₅₃	C₂	1	4	yes	maximal, complemented
14	#534×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#525×D₅₃	C₂	1	4	yes	maximal, complemented
16	C₂×#120×D₅₃	C₂	1	2	yes	maximal, complemented
17	#518×D₅₃	C₂	1	2	yes	maximal, complemented
18	C₂²×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3490	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic
21	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₅₃	C₂²	1	2	yes	—
23	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
24	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
25	#16811304	C₂²	1	8	yes	complemented
26	#16811303	C₂²	1	8	yes	complemented
27	#16811302	C₂²	1	8	yes	complemented
28	#16811302	C₂²	1	8	yes	complemented
29	#16811301	C₂²	1	8	yes	complemented
30	#16811300	C₂²	1	8	yes	complemented
31	#16811300	C₂²	1	8	yes	complemented
32	#16811299	C₂²	1	8	yes	complemented
33	#16811299	C₂²	1	8	yes	complemented
34	#16811298	C₂²	1	8	yes	complemented
35	#16811298	C₂²	1	8	yes	complemented
36	#16811297	C₂²	1	8	yes	complemented
37	#16811297	C₂²	1	8	yes	complemented
38	#16811296	C₂²	1	8	yes	complemented
39	#16811296	C₂²	1	8	yes	complemented
40	#16811270	C₂²	1	8	yes	complemented
41	#16811269	C₂²	1	8	yes	complemented
42	#16811268	C₂²	1	8	yes	complemented
43	#16811267	C₂²	1	8	yes	complemented
44	#16811266	C₂²	1	8	yes	complemented
45	#16811265	C₂²	1	8	yes	complemented
46	#16811265	C₂²	1	8	yes	complemented
47	#16811264	C₂²	1	8	yes	complemented
48	#16811263	C₂²	1	8	yes	complemented
49	#16811263	C₂²	1	8	yes	complemented
50	#16811262	C₂²	1	8	yes	complemented
51	#16811262	C₂²	1	8	yes	complemented
52	#16811261	C₂²	1	8	yes	complemented
53	#16811260	C₂²	1	8	yes	complemented
54	#16811260	C₂²	1	8	yes	complemented
55	#16811249	C₂²	1	2	yes	complemented
56	#16811249	C₂²	1	1	yes	characteristic, complemented
57	#16811248	C₂²	1	8	yes	complemented
58	#16811248	C₂²	1	4	yes	complemented
59	#16811213	C₂²	1	4	yes	complemented
60	#16811212	C₂²	1	8	yes	complemented
61	#16811211	C₂²	1	4	yes	complemented
62	#16811210	C₂²	1	4	yes	complemented
63	#16811209	C₂²	1	8	yes	complemented
64	#16811208	C₂²	1	8	yes	complemented
65	#16811207	C₂²	1	8	yes	complemented
66	#16811206	C₂²	1	8	yes	complemented
67	#16811205	C₂²	1	8	yes	complemented
68	#16811185	C₂²	1	1	yes	characteristic, complemented
69	#16811184	C₂²	1	4	yes	complemented
70	#16811183	C₂²	1	4	yes	complemented
71	#16811182	C₂²	1	2	yes	complemented
72	#16811181	C₂²	1	4	yes	complemented
73	#126×D₅₃	C₂²	1	8	yes	complemented
74	#124×D₅₃	C₂²	1	8	yes	complemented
75	#16811136	C₂²	1	4	yes	complemented
76	#16811136	C₂²	1	4	yes	complemented
77	#16811135	C₂²	1	4	yes	complemented
78	#16811134	C₂²	1	4	yes	complemented
79	#16811133	C₂²	1	4	yes	complemented
80	#16811133	C₂²	1	4	yes	complemented
81	#16811132	C₂²	1	8	yes	complemented
82	#16811132	C₂²	1	8	yes	complemented
83	#16811131	C₂²	1	8	yes	complemented
84	#16811130	C₂²	1	4	yes	complemented
85	#16811129	C₂²	1	8	yes	complemented
86	#123×D₅₃	C₂²	1	8	yes	complemented
87	#123×D₅₃	C₂²	1	4	yes	complemented
88	#123×D₅₃	C₂²	1	8	yes	complemented
89	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
90	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
91	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
92	#121×D₅₃	C₂²	1	8	yes	complemented
93	#121×D₅₃	C₂²	1	4	yes	complemented
94	#121×D₅₃	C₂²	1	4	yes	complemented
95	C₂×#13133187	C₂²	1	2	yes	complemented
96	C₂×#13133187	C₂²	1	4	yes	complemented
97	C₂×#13133186	C₂²	1	2	yes	complemented
98	C₂×#13133185	C₂²	1	2	yes	complemented
99	C₂×#13133185	C₂²	1	4	yes	complemented
100	#120×D₅₃	C₂²	1	8	yes	—
101	#120×D₅₃	C₂²	1	8	yes	complemented
102	#120×D₅₃	C₂²	1	4	yes	complemented
103	#120×D₅₃	C₂²	1	4	yes	complemented
104	#120×D₅₃	C₂²	1	4	yes	complemented
105	#120×D₅₃	C₂²	1	4	yes	complemented
106	#120×D₅₃	C₂²	1	4	yes	complemented
107	#16811098	C₂²	1	2	yes	complemented
108	#16811097	C₂²	1	4	yes	complemented
109	#16811096	C₂²	1	2	yes	complemented
110	#16811096	C₂²	1	2	yes	complemented
111	#16811096	C₂²	1	4	yes	complemented
112	#16811095	C₂²	1	8	yes	complemented
113	#16811095	C₂²	1	8	yes	complemented
114	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
115	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
116	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
117	#117×D₅₃	C₂²	1	4	yes	complemented
118	#117×D₅₃	C₂²	1	4	yes	complemented
119	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂²×#11719921	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
123	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
128	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
129	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
130	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
131	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
132	C₅₃×#551	C₂²	1	8	yes	complemented
133	C₅₃×#546	C₂²	1	8	yes	complemented
134	C₅₃×#543	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#538	C₂²	1	4	yes	complemented
136	C₅₃×#534	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#525	C₂²	1	4	yes	complemented
138	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
139	C₅₃×#518	C₂²	1	2	yes	complemented
140	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂⁴×D₅₃	—	2	8	no	—
142	C₂⁴×D₅₃	—	4	8	no	—
143	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
144	C₂⁴×D₅₃	C₂³	1	4	yes	—
145	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
146	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
147	C₂⁴×D₅₃	C₂³	1	4	yes	—
148	C₂⁴×D₅₃	C₂³	1	2	yes	—
149	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
150	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
151	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
152	C₂×#11719949	C₂³	1	4	yes	complemented
153	C₂×#11719945	C₂³	1	8	yes	complemented
154	C₂×#11719945	C₂³	1	4	yes	complemented
155	C₂×#11719947	C₂³	1	4	yes	complemented
156	C₂×#11719947	C₂³	1	8	yes	complemented
157	#41×D₅₃	—	4	16	no	—
158	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
159	C₂²×D₂₁₂	C₂³	1	2	yes	—
160	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
161	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
163	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
164	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
165	C₂×D₄×D₅₃	—	2	16	no	—
166	C₂×D₄×D₅₃	—	4	16	no	—
167	C₂×D₄×D₅₃	C₂³	1	4	yes	—
168	C₂×D₄×D₅₃	C₂³	1	4	yes	—
169	C₂×D₄×D₅₃	C₂³	1	8	yes	—
170	C₂×D₄×D₅₃	C₂³	1	4	yes	—
171	C₂×D₄×D₅₃	C₂³	1	4	yes	—
172	C₂×D₄×D₅₃	C₂³	1	8	yes	—
173	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
174	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
175	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
176	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
177	C₂²×C₄×D₅₃	—	4	8	no	—
178	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
179	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
180	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
181	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
182	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
183	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
184	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
185	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
186	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
187	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
188	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
189	#13133212	C₂³	1	8	yes	complemented
190	#13133212	C₂³	1	8	yes	complemented
191	#13133212	C₂³	1	8	yes	complemented
192	#13133211	C₂³	1	8	yes	complemented
193	#13133210	C₂³	1	8	yes	complemented
194	#13133210	C₂³	1	8	yes	complemented
195	#13133210	C₂³	1	8	yes	complemented
196	#13133206	C₂³	1	8	yes	complemented
197	#13133205	C₂³	1	8	yes	complemented
198	#13133204	C₂³	1	8	yes	complemented
199	#13133203	C₂³	1	8	yes	complemented
200	#13133203	C₂³	1	8	yes	complemented
201	#13133203	C₂³	1	8	yes	complemented
202	#13133203	C₂³	1	8	yes	complemented
203	#13133202	C₂³	1	8	yes	complemented
204	#13133202	C₂³	1	8	yes	complemented
205	#13133202	C₂³	1	8	yes	complemented
206	#13133202	C₂³	1	8	yes	complemented
207	#13133202	C₂³	1	8	yes	complemented
208	#13133201	C₂³	1	8	yes	complemented
209	#13133201	C₂³	1	4	yes	complemented
210	#13133201	C₂³	1	8	yes	complemented
211	#13133200	C₂³	1	4	yes	complemented
212	#13133200	C₂³	1	8	yes	complemented
213	#13133200	C₂³	1	8	yes	complemented
214	#13133199	C₂³	1	8	yes	complemented
215	#13133199	C₂³	1	8	yes	complemented
216	#13133199	C₂³	1	8	yes	complemented
217	#13133199	C₂³	1	8	yes	complemented
218	#13133199	C₂³	1	8	yes	complemented
219	#13133198	C₂³	1	8	yes	complemented
220	#13133198	C₂³	1	4	yes	complemented
221	#13133198	C₂³	1	8	yes	complemented
222	#13133197	C₂³	1	8	yes	complemented
223	#13133197	C₂³	1	4	yes	complemented
224	#13133197	C₂³	1	4	yes	complemented
225	#13133196	C₂³	1	8	yes	complemented
226	#13133196	C₂³	1	4	yes	complemented
227	#13133196	C₂³	1	4	yes	complemented
228	#13133195	C₂³	1	8	yes	complemented
229	#13133195	C₂³	1	8	yes	complemented
230	#13133195	C₂³	1	8	yes	complemented
231	#13133195	C₂³	1	8	yes	complemented
232	#13133194	C₂³	1	8	yes	complemented
233	#13133194	C₂³	1	8	yes	complemented
234	#13133194	C₂³	1	8	yes	complemented
235	#13133194	C₂³	1	8	yes	complemented
236	#13133193	C₂³	1	8	yes	complemented
237	#13133193	C₂³	1	4	yes	complemented
238	#13133193	C₂³	1	4	yes	complemented
239	#13133192	C₂³	1	4	yes	complemented
240	#13133192	C₂³	1	4	yes	complemented
241	#13133192	C₂³	1	8	yes	complemented
242	#13133191	C₂³	1	8	yes	complemented
243	#13133191	C₂³	1	4	yes	complemented
244	#13133191	C₂³	1	4	yes	complemented
245	#13133190	C₂³	1	8	yes	complemented
246	#13133190	C₂³	1	8	yes	complemented
247	#13133190	C₂³	1	8	yes	complemented
248	#13133190	C₂³	1	8	yes	complemented
249	#13133189	C₂³	1	8	yes	complemented
250	#13133189	C₂³	1	8	yes	complemented
251	#13133189	C₂³	1	8	yes	complemented
252	#13133189	C₂³	1	8	yes	complemented
253	#13133188	C₂³	1	4	yes	complemented
254	#13133188	C₂³	1	4	yes	complemented
255	#13133188	C₂³	1	8	yes	complemented
256	#13133187	C₂³	1	8	yes	—
257	#13133187	C₂³	1	8	yes	—
258	#13133187	C₂³	1	8	yes	—
259	#13133187	C₂³	1	8	yes	complemented
260	#13133187	C₂³	1	4	yes	complemented
261	#13133187	C₂³	1	4	yes	complemented
262	#13133187	C₂³	1	8	yes	complemented
263	#13133187	C₂³	1	8	yes	complemented
264	#13133187	C₂³	1	4	yes	complemented
265	#13133186	C₂³	1	8	yes	—
266	#13133186	C₂³	1	4	yes	complemented
267	#13133186	C₂³	1	4	yes	complemented
268	#13133186	C₂³	1	4	yes	complemented
269	#13133185	C₂³	1	8	yes	—
270	#13133185	C₂³	1	8	yes	—
271	#13133185	C₂³	1	8	yes	—
272	#13133185	C₂³	1	8	yes	complemented
273	#13133185	C₂³	1	4	yes	complemented
274	#13133185	C₂³	1	8	yes	complemented
275	#13133185	C₂³	1	4	yes	complemented
276	#13133185	C₂³	1	8	yes	complemented
277	#13133185	C₂³	1	4	yes	complemented
278	C₄×D₂₁₂	C₂³	1	8	yes	complemented
279	C₄×D₂₁₂	C₂³	1	8	yes	complemented
280	C₄×D₂₁₂	C₂³	1	8	yes	complemented
281	D₄×Dic₅₃	C₂³	1	8	yes	complemented
282	D₄×Dic₅₃	C₂³	1	8	yes	complemented
283	D₄×Dic₅₃	C₂³	1	8	yes	complemented
284	#13133179	C₂³	1	8	yes	complemented
285	#13133179	C₂³	1	8	yes	complemented
286	#13133179	C₂³	1	8	yes	complemented
287	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
288	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
289	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
290	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
291	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
292	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
293	#13133177	C₂³	1	8	yes	complemented
294	#13133177	C₂³	1	8	yes	complemented
295	#13133177	C₂³	1	8	yes	complemented
296	#13133177	C₂³	1	8	yes	complemented
297	#13133177	C₂³	1	8	yes	complemented
298	#13133177	C₂³	1	8	yes	complemented
299	#13133176	C₂³	1	4	yes	complemented
300	#13133176	C₂³	1	4	yes	complemented
301	#13133175	C₂³	1	4	yes	complemented
302	#13133175	C₂³	1	8	yes	complemented
303	#13133175	C₂³	1	4	yes	complemented
304	#13133174	C₂³	1	8	yes	complemented
305	#13133174	C₂³	1	8	yes	complemented
306	#13133173	C₂³	1	4	yes	complemented
307	#13133173	C₂³	1	8	yes	complemented
308	#13133173	C₂³	1	4	yes	complemented
309	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
310	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
311	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
312	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
313	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
316	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
317	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
318	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
319	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
320	C₂×#11719921	C₂³	1	2	yes	—
321	C₂×#11719921	C₂³	1	2	yes	—
322	C₂×#11719921	C₂³	1	4	yes	—
323	C₂×#11719921	C₂³	1	8	yes	complemented
324	C₂×#11719921	C₂³	1	8	yes	complemented
325	C₂×#11719921	C₂³	1	4	yes	complemented
326	C₂×#11719921	C₂³	1	4	yes	complemented
327	C₂×#11719921	C₂³	1	2	yes	complemented
328	C₂×#11719921	C₂³	1	2	yes	complemented
329	C₂×#11719921	C₂³	1	8	yes	complemented
330	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
331	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
332	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
333	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
334	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
335	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
336	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
337	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
338	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
339	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
340	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
341	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
342	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
343	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
344	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
345	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
346	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
347	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
348	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
349	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
350	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
351	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
352	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
353	C₄²×D₅₃	C₂³	1	8	yes	complemented
354	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
356	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
357	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
358	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
359	#126×C₅₃	C₂³	1	8	yes	complemented
360	#124×C₅₃	C₂³	1	8	yes	complemented
361	#123×C₅₃	C₂³	1	8	yes	complemented
362	#123×C₅₃	C₂³	1	4	yes	complemented
363	#123×C₅₃	C₂³	1	8	yes	complemented
364	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
365	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
366	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
367	#121×C₅₃	C₂³	1	4	yes	complemented
368	#121×C₅₃	C₂³	1	4	yes	complemented
369	#121×C₅₃	C₂³	1	8	yes	complemented
370	#120×C₅₃	C₂³	1	8	yes	—
371	#120×C₅₃	C₂³	1	4	yes	complemented
372	#120×C₅₃	C₂³	1	4	yes	complemented
373	#120×C₅₃	C₂³	1	4	yes	complemented
374	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
375	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
376	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
377	#117×C₅₃	C₂³	1	4	yes	complemented
378	#117×C₅₃	C₂³	1	4	yes	complemented
379	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
380	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
381	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
382	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
383	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
384	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
385	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
386	C₂⁴×C₅₃	—	2	4	no	—
387	C₂⁴×C₅₃	—	4	4	no	—
388	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
390	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
392	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂³×D₅₃	—	2	4	no	—
394	C₂³×D₅₃	—	2	8	no	—
395	C₂³×D₅₃	—	2	4	no	—
396	C₂³×D₅₃	—	2	16	no	—
397	C₂³×D₅₃	—	2	4	no	—
398	C₂³×D₅₃	—	2	4	no	—
399	C₂³×D₅₃	—	2	16	no	—
400	C₂³×D₅₃	—	2	4	no	—
401	C₂³×D₅₃	—	2	16	no	—
402	C₂³×D₅₃	—	2	8	no	—
403	C₂³×D₅₃	—	4	4	no	—
404	C₂³×D₅₃	—	4	8	no	—
405	C₂³×D₅₃	—	4	4	no	—
406	C₂³×D₅₃	—	4	8	no	—
407	C₂³×D₅₃	—	4	4	no	—
408	C₂³×D₅₃	—	4	4	no	—
409	C₂³×D₅₃	—	4	8	no	—
410	C₂³×D₅₃	—	4	8	no	—
411	C₂³×D₅₃	—	4	4	no	—
412	C₂³×D₅₃	—	4	64	no	—
413	C₂³×D₅₃	#41	1	8	yes	complemented
414	C₂³×D₅₃	C₂⁴	1	2	yes	—
415	C₂³×D₅₃	C₂⁴	1	4	yes	—
416	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
417	C₂³×D₅₃	C₂⁴	1	2	yes	—
418	C₂³×D₅₃	C₂⁴	1	4	yes	—
419	C₂³×D₅₃	C₂⁴	1	4	yes	—
420	C₂³×D₅₃	C₂⁴	1	4	yes	—
421	C₂³×D₅₃	C₂⁴	1	2	yes	—
422	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
423	C₂³×D₅₃	C₂⁴	1	2	yes	—
424	C₂³×D₅₃	C₂⁴	1	2	yes	—
425	C₂³×D₅₃	C₂⁴	1	2	yes	—
426	C₂³×D₅₃	C₂⁴	1	4	yes	—
427	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
428	C₂³×D₅₃	C₂⁴	1	2	yes	—
429	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
430	#41×C₅₃	—	4	8	no	—
431	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	complemented
432	C₂×D₄×C₅₃	—	2	8	no	—
433	C₂×D₄×C₅₃	—	4	8	no	—
434	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
435	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
436	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
437	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
438	C₂×D₄×C₅₃	C₂⁴	1	4	yes	complemented
439	C₂²×C₄×C₅₃	—	4	4	no	—
440	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
441	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
442	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
443	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
444	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
445	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
446	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
447	C₂×C₂²⋊D₅₃	—	2	8	no	—
448	C₂×C₂²⋊D₅₃	—	2	8	no	—
449	C₂×C₂²⋊D₅₃	—	4	8	no	—
450	C₂×C₂²⋊D₅₃	—	4	8	no	—
451	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
452	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
453	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
454	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
455	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
456	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
457	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
458	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
459	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
460	C₂²×Dic₅₃	—	4	4	no	—
461	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
462	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
463	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
464	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
465	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
466	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
467	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
468	#11719949	—	4	8	no	—
469	Q₈×D₅₃	—	4	8	no	—
470	#11719947	—	4	8	no	—
471	#11719947	—	4	16	no	—
472	D₄×D₅₃	—	2	16	no	—
473	D₄×D₅₃	—	2	16	no	—
474	D₄×D₅₃	—	2	16	no	—
475	D₄×D₅₃	—	2	16	no	—
476	D₄×D₅₃	—	2	32	no	—
477	D₄×D₅₃	—	4	16	no	—
478	D₄×D₅₃	—	4	8	no	—
479	D₄×D₅₃	—	4	16	no	—
480	D₄×D₅₃	—	4	16	no	—
481	#11719945	—	4	16	no	—
482	#11719945	—	4	8	no	—
483	C₂×D₂₁₂	—	2	8	no	—
484	C₂×D₂₁₂	—	4	8	no	—
485	C₂×D₂₁₂	C₂⁴	1	4	yes	—
486	C₂×D₂₁₂	C₂⁴	1	4	yes	—
487	C₂×D₂₁₂	C₂⁴	1	8	yes	—
488	C₂×D₂₁₂	C₂⁴	1	8	yes	—
489	C₂×D₂₁₂	C₂⁴	1	4	yes	complemented
490	C₂×C₄×D₅₃	—	2	8	no	—
491	C₂×C₄×D₅₃	—	2	16	no	—
492	C₂×C₄×D₅₃	—	4	4	no	—
493	C₂×C₄×D₅₃	—	4	8	no	—
494	C₂×C₄×D₅₃	—	4	4	no	—
495	C₂×C₄×D₅₃	—	4	4	no	—
496	C₂×C₄×D₅₃	—	4	8	no	—
497	C₂×C₄×D₅₃	—	4	4	no	—
498	C₂×C₄×D₅₃	—	4	8	no	—
499	C₂×C₄×D₅₃	—	4	16	no	—
500	C₂×C₄×D₅₃	—	4	8	no	—
501	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
502	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
503	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
504	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
505	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
506	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
507	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
508	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
509	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
510	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
511	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
512	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
513	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
514	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
515	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
516	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
517	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
518	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
519	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
520	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
521	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
522	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
523	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
524	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
525	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
526	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
527	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
528	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
529	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
530	C₄²×C₅₃	C₂⁴	1	8	yes	complemented
531	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
532	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
533	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
534	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
535	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
536	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
537	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
538	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
539	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
540	#11719921	C₂⁴	1	8	yes	—
541	#11719921	C₂⁴	1	8	yes	—
542	#11719921	C₂⁴	1	8	yes	—
543	#11719921	C₂⁴	1	8	yes	—
544	#11719921	C₂⁴	1	8	yes	—
545	#11719921	C₂⁴	1	8	yes	—
546	#11719921	C₂⁴	1	8	yes	—
547	#11719921	C₂⁴	1	8	yes	—
548	#11719921	C₂⁴	1	8	yes	—
549	#11719921	C₂⁴	1	8	yes	—
550	#11719921	C₂⁴	1	8	yes	complemented
551	#11719921	C₂⁴	1	8	yes	complemented
552	#11719921	C₂⁴	1	8	yes	complemented
553	#11719921	C₂⁴	1	8	yes	complemented
554	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
555	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
556	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
557	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
558	#11719919	C₂⁴	1	8	yes	complemented
559	#11719919	C₂⁴	1	8	yes	complemented
560	#11719919	C₂⁴	1	8	yes	complemented
561	#11719919	C₂⁴	1	8	yes	complemented
562	#11719919	C₂⁴	1	8	yes	complemented
563	#11719919	C₂⁴	1	8	yes	complemented
564	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
565	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
566	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
567	C₂³×C₅₃	—	2	2	no	—
568	C₂³×C₅₃	—	2	4	no	—
569	C₂³×C₅₃	—	2	8	no	—
570	C₂³×C₅₃	—	2	2	no	—
571	C₂³×C₅₃	—	2	8	no	—
572	C₂³×C₅₃	—	2	4	no	—
573	C₂³×C₅₃	—	4	2	no	—
574	C₂³×C₅₃	—	4	4	no	—
575	C₂³×C₅₃	—	4	2	no	—
576	C₂³×C₅₃	—	4	4	no	—
577	C₂³×C₅₃	—	4	16	no	—
578	C₂³×C₅₃	C₂×#41	1	4	yes	complemented
579	C₂³×C₅₃	C₂⁵	1	4	yes	—
580	C₂³×C₅₃	C₂⁵	1	2	yes	—
581	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
582	C₂³×C₅₃	C₂⁵	1	2	yes	—
583	C₂³×C₅₃	C₂⁵	1	2	yes	—
584	C₂²×D₅₃	—	2	32	no	—
585	C₂²×D₅₃	—	2	2	no	—
586	C₂²×D₅₃	—	2	4	no	—
587	C₂²×D₅₃	—	2	4	no	—
588	C₂²×D₅₃	—	2	4	no	—
589	C₂²×D₅₃	—	2	4	no	—
590	C₂²×D₅₃	—	2	4	no	—
591	C₂²×D₅₃	—	2	4	no	—
592	C₂²×D₅₃	—	2	4	no	—
593	C₂²×D₅₃	—	2	8	no	—
594	C₂²×D₅₃	—	2	8	no	—
595	C₂²×D₅₃	—	2	2	no	—
596	C₂²×D₅₃	—	2	8	no	—
597	C₂²×D₅₃	—	2	4	no	—
598	C₂²×D₅₃	—	2	8	no	—
599	C₂²×D₅₃	—	2	8	no	—
600	C₂²×D₅₃	—	2	8	no	—
601	C₂²×D₅₃	—	2	4	no	—
602	C₂²×D₅₃	—	2	4	no	—
603	C₂²×D₅₃	—	2	16	no	—
604	C₂²×D₅₃	—	2	8	no	—
605	C₂²×D₅₃	—	2	8	no	—
606	C₂²×D₅₃	—	2	8	no	—
607	C₂²×D₅₃	—	2	8	no	—
608	C₂²×D₅₃	—	4	16	no	—
609	C₂²×D₅₃	—	4	4	no	—
610	C₂²×D₅₃	—	4	4	no	—
611	C₂²×D₅₃	—	4	4	no	—
612	C₂²×D₅₃	—	4	4	no	—
613	C₂²×D₅₃	—	4	2	no	—
614	C₂²×D₅₃	—	4	4	no	—
615	C₂²×D₅₃	—	4	2	no	—
616	C₂²×D₅₃	—	4	64	no	—
617	C₂²×D₅₃	—	4	4	no	—
618	C₂²×D₅₃	—	4	8	no	—
619	C₂²×D₅₃	—	4	16	no	—
620	C₂²×D₅₃	—	4	64	no	—
621	C₂²×D₅₃	—	4	16	no	—
622	C₂²×D₅₃	—	4	16	no	—
623	C₂²×D₅₃	—	4	16	no	—
624	C₂²×D₅₃	—	8	16	no	—
625	C₂²×D₅₃	C₂×#41	1	8	yes	—
626	C₂²×D₅₃	C₂×#41	1	4	yes	—
627	C₂²×D₅₃	C₂×#41	1	8	yes	complemented
628	C₂²×D₅₃	C₂×#41	1	4	yes	complemented
629	C₂²×D₅₃	H(5,𝔽₂)	1	8	yes	—
630	C₂²×D₅₃	C₂⁵	1	4	yes	—
631	C₂²×D₅₃	C₂⁵	1	2	yes	—
632	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
633	C₂²×D₅₃	C₂⁵	1	2	yes	—
634	C₂²×D₅₃	C₂⁵	1	2	yes	—
635	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
636	Q₈×C₅₃	—	4	4	no	—
637	D₄×C₅₃	—	2	8	no	—
638	D₄×C₅₃	—	2	8	no	—
639	D₄×C₅₃	—	2	16	no	—
640	D₄×C₅₃	—	4	8	no	—
641	D₄×C₅₃	—	4	4	no	—
642	C₂×C₄×C₅₃	—	2	4	no	—
643	C₂×C₄×C₅₃	—	2	8	no	—
644	C₂×C₄×C₅₃	—	4	2	no	—
645	C₂×C₄×C₅₃	—	4	4	no	—
646	C₂×C₄×C₅₃	—	4	2	no	—
647	C₂×C₄×C₅₃	—	4	4	no	—
648	C₂×C₄×C₅₃	—	4	8	no	—
649	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
650	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
651	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
652	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
653	C₂²⋊D₅₃	—	2	8	no	—
654	C₂²⋊D₅₃	—	2	8	no	—
655	C₂²⋊D₅₃	—	2	16	no	—
656	C₂²⋊D₅₃	—	2	8	no	—
657	C₂²⋊D₅₃	—	2	8	no	—
658	C₂²⋊D₅₃	—	2	16	no	—
659	C₂²⋊D₅₃	—	4	8	no	—
660	C₂²⋊D₅₃	—	4	8	no	—
661	C₂²⋊D₅₃	—	4	8	no	—
662	C₂×Dic₅₃	—	2	4	no	—
663	C₂×Dic₅₃	—	2	8	no	—
664	C₂×Dic₅₃	—	4	2	no	—
665	C₂×Dic₅₃	—	4	4	no	—
666	C₂×Dic₅₃	—	4	2	no	—
667	C₂×Dic₅₃	—	4	8	no	—
668	C₂×Dic₅₃	—	4	4	no	—
669	C₂×Dic₅₃	C₂⁵	1	4	yes	—
670	C₂×Dic₅₃	C₂⁵	1	8	yes	—
671	C₂×Dic₅₃	C₂⁵	1	4	yes	—
672	C₂×Dic₅₃	C₂⁵	1	4	yes	—
673	D₂₁₂	—	2	8	no	—
674	D₂₁₂	—	2	8	no	—
675	D₂₁₂	—	2	16	no	—
676	D₂₁₂	—	4	8	no	—
677	D₂₁₂	—	4	4	no	—
678	C₄×D₅₃	—	2	8	no	—
679	C₄×D₅₃	—	2	8	no	—
680	C₄×D₅₃	—	2	8	no	—
681	C₄×D₅₃	—	2	8	no	—
682	C₄×D₅₃	—	2	8	no	—
683	C₄×D₅₃	—	2	8	no	—
684	C₄×D₅₃	—	2	16	no	—
685	C₄×D₅₃	—	4	4	no	—
686	C₄×D₅₃	—	4	4	no	—
687	C₄×D₅₃	—	4	4	no	—
688	C₄×D₅₃	—	4	4	no	—
689	C₄×D₅₃	—	4	8	no	—
690	C₄×D₅₃	—	4	8	no	—
691	C₄×D₅₃	—	4	8	no	—
692	Dic₁₀₆	—	4	8	no	—
693	Dic₁₀₆	—	4	4	no	—
694	C₂×#3490	—	53	1	no	maximal, Sylow
695	C₂²×C₅₃	—	2	8	no	—
696	C₂²×C₅₃	—	2	2	no	—
697	C₂²×C₅₃	—	2	2	no	—
698	C₂²×C₅₃	—	2	2	no	—
699	C₂²×C₅₃	—	2	4	no	—
700	C₂²×C₅₃	—	2	4	no	—
701	C₂²×C₅₃	—	2	2	no	—
702	C₂²×C₅₃	—	2	8	no	—
703	C₂²×C₅₃	—	2	4	no	—
704	C₂²×C₅₃	—	4	4	no	—
705	C₂²×C₅₃	—	4	16	no	—
706	C₂²×C₅₃	—	4	4	no	—
707	C₂²×C₅₃	—	8	4	no	—
708	C₂²×C₅₃	C₂²×#41	1	4	yes	—
709	C₂²×C₅₃	C₂²×#41	1	2	yes	—
710	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
711	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
712	C₂×D₅₃	—	2	16	no	—
713	C₂×D₅₃	—	2	8	no	—
714	C₂×D₅₃	—	2	2	no	—
715	C₂×D₅₃	—	2	2	no	—
716	C₂×D₅₃	—	2	2	no	—
717	C₂×D₅₃	—	2	4	no	—
718	C₂×D₅₃	—	2	8	no	—
719	C₂×D₅₃	—	2	16	no	—
720	C₂×D₅₃	—	2	16	no	—
721	C₂×D₅₃	—	2	4	no	—
722	C₂×D₅₃	—	2	2	no	—
723	C₂×D₅₃	—	2	8	no	—
724	C₂×D₅₃	—	2	4	no	—
725	C₂×D₅₃	—	4	8	no	—
726	C₂×D₅₃	—	4	4	no	—
727	C₂×D₅₃	—	4	16	no	—
728	C₂×D₅₃	—	4	16	no	—
729	C₂×D₅₃	—	4	16	no	—
730	C₂×D₅₃	—	4	8	no	—
731	C₂×D₅₃	—	4	4	no	—
732	C₂×D₅₃	—	4	8	no	—
733	C₂×D₅₃	—	4	16	no	—
734	C₂×D₅₃	—	8	8	no	—
735	C₂×D₅₃	—	8	4	no	—
736	C₂×D₅₃	C₂²×#41	1	4	yes	—
737	C₂×D₅₃	C₂²×#41	1	2	yes	—
738	C₂×D₅₃	C₂²×#41	1	2	yes	—
739	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
740	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
741	C₄×C₅₃	—	2	4	no	—
742	C₄×C₅₃	—	2	4	no	—
743	C₄×C₅₃	—	2	8	no	—
744	C₄×C₅₃	—	2	4	no	—
745	Dic₅₃	—	2	4	no	—
746	Dic₅₃	—	2	4	no	—
747	Dic₅₃	—	2	8	no	—
748	Dic₅₃	—	2	4	no	—
749	#3490	—	53	8	no	—
750	#3490	—	53	8	no	—
751	#3490	—	53	1	no	—
752	#3490	—	53	4	no	—
753	#3490	—	53	1	no	—
754	#3490	—	53	4	no	—
755	#3490	—	53	2	no	—
756	#3490	—	53	2	no	—
757	#3490	—	53	1	no	—
758	#3490	D₅₃	1	1	yes	characteristic, direct product factor
759	C₂×#551	—	53	8	no	—
760	C₂×#546	—	53	8	no	—
761	C₂×#543	—	53	1	no	—
762	C₂×#538	—	53	4	no	—
763	C₂×#534	—	53	1	no	—
764	C₂×#525	—	53	4	no	—
765	C₂²×#120	—	53	2	no	—
766	C₂×#518	—	53	2	no	—
767	C₂³×C₂²⋊C₄	—	53	1	no	—
768	C₂×C₅₃	—	2	2	no	—
769	C₂×C₅₃	—	2	4	no	—
770	C₂×C₅₃	—	2	4	no	—
771	C₂×C₅₃	—	4	2	no	—
772	C₂×C₅₃	—	4	4	no	—
773	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
774	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
775	D₅₃	—	2	2	no	—
776	D₅₃	—	2	4	no	—
777	D₅₃	—	2	4	no	—
778	D₅₃	—	4	2	no	—
779	D₅₃	—	4	4	no	—
780	D₅₃	#3490	1	4	yes	direct product factor
781	C₂⁶	—	53	1	no	—
782	C₂²×#41	—	53	4	no	—
783	C₂³×D₄	—	53	2	no	—
784	C₂³×D₄	—	53	4	no	—
785	C₂⁴×C₄	—	53	2	no	—
786	#551	—	53	8	no	—
787	#551	—	53	8	no	—
788	#551	—	53	8	no	—
789	#551	—	53	8	no	—
790	#551	—	53	8	no	—
791	#551	—	53	8	no	—
792	#551	—	53	8	no	—
793	#551	—	53	8	no	—
794	#551	—	53	8	no	—
795	#551	—	53	8	no	—
796	#551	—	53	8	no	—
797	#551	—	53	8	no	—
798	#551	—	53	8	no	—
799	#551	—	53	8	no	—
800	#551	—	53	8	no	—
801	#551	C₂×D₅₃	1	8	yes	complemented
802	#546	—	53	8	no	—
803	#546	—	53	8	no	—
804	#546	—	53	8	no	—
805	#546	—	53	8	no	—
806	#546	—	53	8	no	—
807	#546	—	53	8	no	—
808	#546	—	53	8	no	—
809	#546	—	53	8	no	—
810	#546	—	53	8	no	—
811	#546	—	53	8	no	—
812	#546	—	53	8	no	—
813	#546	—	53	8	no	—
814	#546	—	53	8	no	—
815	#546	—	53	8	no	—
816	#546	—	53	8	no	—
817	#546	C₂×D₅₃	1	8	yes	complemented
818	#543	—	53	4	no	—
819	#543	—	53	8	no	—
820	#543	—	53	2	no	—
821	#543	—	53	1	no	—
822	#543	C₂×D₅₃	1	1	yes	characteristic, complemented
823	#538	—	53	8	no	—
824	#538	—	53	8	no	—
825	#538	—	53	8	no	—
826	#538	—	53	4	no	—
827	#538	—	53	8	no	—
828	#538	—	53	4	no	—
829	#538	—	53	8	no	—
830	#538	—	53	8	no	—
831	#538	—	53	4	no	—
832	#538	C₂×D₅₃	1	4	yes	complemented
833	#534	—	53	2	no	—
834	#534	—	53	4	no	—
835	#534	—	53	4	no	—
836	#534	—	53	4	no	—
837	#534	—	53	1	no	—
838	#534	C₂×D₅₃	1	1	yes	characteristic, complemented
839	C₂×#126	—	53	8	no	—
840	C₂×#124	—	53	8	no	—
841	#525	—	53	4	no	—
842	#525	—	53	4	no	—
843	#525	—	53	8	no	—
844	#525	—	53	4	no	—
845	#525	—	53	4	no	—
846	#525	—	53	4	no	—
847	#525	—	53	4	no	—
848	#525	—	53	8	no	—
849	#525	—	53	8	no	—
850	#525	—	53	8	no	—
851	#525	—	53	4	no	—
852	#525	C₂×D₅₃	1	4	yes	complemented
853	C₂×#123	—	53	8	no	—
854	C₂×#123	—	53	4	no	—
855	C₂×#123	—	53	8	no	—
856	C₂×C₂²⋊Q₈	—	53	4	no	—
857	C₂×C₂²⋊Q₈	—	53	4	no	—
858	C₂×C₂²⋊Q₈	—	53	8	no	—
859	C₂×#121	—	53	4	no	—
860	C₂×#121	—	53	4	no	—
861	C₂×#121	—	53	8	no	—
862	C₂×#120	—	53	2	no	—
863	C₂×#120	—	53	2	no	—
864	C₂×#120	—	53	4	no	—
865	C₂×#120	—	53	8	no	—
866	C₂×#120	—	53	8	no	—
867	C₂×#120	—	53	4	no	—
868	C₂×#120	—	53	4	no	—
869	C₂×#120	—	53	4	no	—
870	C₂×#120	—	53	4	no	—
871	C₂×#120	—	53	4	no	—
872	C₂×#120	—	53	2	no	—
873	C₂×#120	—	53	4	no	—
874	C₂×#120	C₂×D₅₃	1	2	yes	complemented
875	#518	—	53	2	no	—
876	#518	—	53	8	no	—
877	#518	—	53	8	no	—
878	#518	—	53	4	no	—
879	#518	—	53	2	no	—
880	#518	—	53	2	no	—
881	#518	—	53	4	no	—
882	#518	C₂×D₅₃	1	2	yes	complemented
883	C₂×C₄×D₄	—	53	8	no	—
884	C₂×C₄×D₄	—	53	8	no	—
885	C₂×C₄×D₄	—	53	8	no	—
886	C₂×#117	—	53	4	no	—
887	C₂×#117	—	53	4	no	—
888	C₂²×C₂²⋊C₄	—	53	1	no	—
889	C₂²×C₂²⋊C₄	—	53	2	no	—
890	C₂²×C₂²⋊C₄	—	53	1	no	—
891	C₂²×C₂²⋊C₄	—	53	1	no	—
892	C₂²×C₂²⋊C₄	—	53	2	no	—
893	C₂²×C₂²⋊C₄	—	53	1	no	—
894	C₂²×C₂²⋊C₄	—	53	1	no	—
895	C₂²×C₂²⋊C₄	—	53	2	no	—
896	C₂²×C₂²⋊C₄	—	53	8	no	—
897	C₂²×C₂²⋊C₄	—	53	2	no	—
898	C₂²×C₂²⋊C₄	—	53	8	no	—
899	C₂²×C₂²⋊C₄	—	53	4	no	—
900	C₂²×C₂²⋊C₄	—	53	4	no	—
901	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
902	C₅₃	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
903	C₂⁵	—	53	1	no	—
904	C₂⁵	—	53	1	no	—
905	C₂⁵	—	53	4	no	—
906	C₂⁵	—	53	1	no	—
907	C₂⁵	—	53	1	no	—
908	C₂⁵	—	53	4	no	—
909	C₂⁵	—	53	1	no	—
910	C₂⁵	—	53	1	no	—
911	C₂⁵	—	53	2	no	—
912	C₂⁵	—	106	8	no	—
913	C₂⁵	—	212	8	no	—
914	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
915	C₂×#41	—	53	4	no	—
916	C₂×#41	—	53	8	no	—
917	C₂×#41	—	53	4	no	—
918	C₂×#41	—	53	4	no	—
919	C₂×#41	—	53	8	no	—
920	C₂×#41	—	212	16	no	—
921	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
922	C₂²×Q₈	—	53	4	no	—
923	C₂²×D₄	—	53	2	no	—
924	C₂²×D₄	—	53	2	no	—
925	C₂²×D₄	—	53	4	no	—
926	C₂²×D₄	—	53	4	no	—
927	C₂²×D₄	—	53	4	no	—
928	C₂²×D₄	—	53	4	no	—
929	C₂²×D₄	—	53	8	no	—
930	C₂²×D₄	—	53	4	no	—
931	C₂²×D₄	—	53	4	no	—
932	C₂²×D₄	—	53	8	no	—
933	C₂²×D₄	—	53	8	no	—
934	C₂²×D₄	—	53	8	no	—
935	C₂²×D₄	—	53	4	no	—
936	C₂²×D₄	—	53	2	no	—
937	C₂²×D₄	—	53	4	no	—
938	C₂²×D₄	—	106	16	no	—
939	C₂²×D₄	—	212	16	no	—
940	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
941	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
942	C₂³×C₄	—	53	2	no	—
943	C₂³×C₄	—	53	2	no	—
944	C₂³×C₄	—	53	4	no	—
945	C₂³×C₄	—	53	2	no	—
946	C₂³×C₄	—	53	4	no	—
947	C₂³×C₄	—	53	4	no	—
948	C₂³×C₄	—	53	2	no	—
949	C₂³×C₄	—	53	4	no	—
950	C₂³×C₄	—	53	2	no	—
951	C₂³×C₄	—	53	4	no	—
952	C₂³×C₄	—	53	2	no	—
953	C₂³×C₄	—	53	8	no	—
954	C₂³×C₄	—	212	8	no	—
955	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
956	#126	—	53	8	no	—
957	#126	—	53	8	no	—
958	#126	—	53	8	no	—
959	#126	—	53	8	no	—
960	#126	—	53	8	no	—
961	#126	—	53	8	no	—
962	#126	—	53	8	no	—
963	#126	C₂²×D₅₃	1	8	yes	complemented
964	#124	—	53	8	no	—
965	#124	—	53	8	no	—
966	#124	—	53	8	no	—
967	#124	—	53	8	no	—
968	#124	—	53	8	no	—
969	#124	—	53	8	no	—
970	#124	—	53	8	no	—
971	#124	C₂²×D₅₃	1	8	yes	complemented
972	#123	—	53	8	no	—
973	#123	—	53	4	no	—
974	#123	—	53	8	no	—
975	#123	—	53	8	no	—
976	#123	—	53	4	no	—
977	#123	—	53	8	no	—
978	#123	—	53	8	no	—
979	#123	—	53	8	no	—
980	#123	—	53	8	no	—
981	#123	—	53	8	no	—
982	#123	—	53	8	no	—
983	#123	—	53	8	no	—
984	#123	—	53	4	no	—
985	#123	—	53	8	no	—
986	#123	—	53	8	no	—
987	#123	—	53	8	no	—
988	#123	—	53	8	no	—
989	#123	—	53	8	no	—
990	#123	—	53	8	no	—
991	#123	C₂²×D₅₃	1	8	yes	complemented
992	#123	C₂²×D₅₃	1	8	yes	complemented
993	#123	C₂²×D₅₃	1	4	yes	complemented
994	C₂²⋊Q₈	—	53	4	no	—
995	C₂²⋊Q₈	—	53	4	no	—
996	C₂²⋊Q₈	—	53	8	no	—
997	C₂²⋊Q₈	—	53	4	no	—
998	C₂²⋊Q₈	—	53	4	no	—
999	C₂²⋊Q₈	—	53	8	no	—
1000	C₂²⋊Q₈	—	53	8	no	—
1001	C₂²⋊Q₈	—	53	4	no	—
1002	C₂²⋊Q₈	—	53	8	no	—
1003	C₂²⋊Q₈	—	53	4	no	—
1004	C₂²⋊Q₈	—	53	8	no	—
1005	C₂²⋊Q₈	—	53	8	no	—
1006	C₂²⋊Q₈	—	53	8	no	—
1007	C₂²⋊Q₈	—	53	8	no	—
1008	C₂²⋊Q₈	—	53	8	no	—
1009	C₂²⋊Q₈	—	53	8	no	—
1010	C₂²⋊Q₈	—	53	8	no	—
1011	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1012	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1013	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1014	#121	—	53	8	no	—
1015	#121	—	53	8	no	—
1016	#121	—	53	8	no	—
1017	#121	—	53	8	no	—
1018	#121	—	53	4	no	—
1019	#121	—	53	4	no	—
1020	#121	—	53	8	no	—
1021	#121	—	53	4	no	—
1022	#121	—	53	4	no	—
1023	#121	—	53	8	no	—
1024	#121	—	53	4	no	—
1025	#121	—	53	4	no	—
1026	#121	—	53	8	no	—
1027	#121	—	53	8	no	—
1028	#121	—	53	8	no	—
1029	#121	—	53	8	no	—
1030	#121	—	53	8	no	—
1031	#121	C₂²×D₅₃	1	8	yes	complemented
1032	#121	C₂²×D₅₃	1	4	yes	complemented
1033	#121	C₂²×D₅₃	1	4	yes	complemented
1034	#120	—	53	4	no	—
1035	#120	—	53	4	no	—
1036	#120	—	53	8	no	—
1037	#120	—	53	4	no	—
1038	#120	—	53	8	no	—
1039	#120	—	53	4	no	—
1040	#120	—	53	4	no	—
1041	#120	—	53	8	no	—
1042	#120	—	53	8	no	—
1043	#120	—	53	8	no	—
1044	#120	—	53	8	no	—
1045	#120	—	53	4	no	—
1046	#120	—	53	8	no	—
1047	#120	—	53	4	no	—
1048	#120	—	53	8	no	—
1049	#120	—	53	8	no	—
1050	#120	—	53	4	no	—
1051	#120	—	53	8	no	—
1052	#120	—	53	8	no	—
1053	#120	—	53	8	no	—
1054	#120	—	53	4	no	—
1055	#120	—	53	8	no	—
1056	#120	C₂²×D₅₃	1	8	yes	—
1057	#120	C₂²×D₅₃	1	4	yes	complemented
1058	#120	C₂²×D₅₃	1	4	yes	complemented
1059	#120	C₂²×D₅₃	1	4	yes	complemented
1060	C₄×D₄	—	53	8	no	—
1061	C₄×D₄	—	53	8	no	—
1062	C₄×D₄	—	53	8	no	—
1063	C₄×D₄	—	53	8	no	—
1064	C₄×D₄	—	53	8	no	—
1065	C₄×D₄	—	53	8	no	—
1066	C₄×D₄	—	53	8	no	—
1067	C₄×D₄	—	53	8	no	—
1068	C₄×D₄	—	53	8	no	—
1069	C₄×D₄	—	53	8	no	—
1070	C₄×D₄	—	53	8	no	—
1071	C₄×D₄	—	53	8	no	—
1072	C₄×D₄	—	53	8	no	—
1073	C₄×D₄	—	53	8	no	—
1074	C₄×D₄	—	53	8	no	—
1075	C₄×D₄	—	53	8	no	—
1076	C₄×D₄	—	53	8	no	—
1077	C₄×D₄	—	53	8	no	—
1078	C₄×D₄	—	53	8	no	—
1079	C₄×D₄	—	53	8	no	—
1080	C₄×D₄	—	53	8	no	—
1081	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1082	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1083	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1084	#117	—	53	4	no	—
1085	#117	—	53	4	no	—
1086	#117	—	53	8	no	—
1087	#117	—	53	4	no	—
1088	#117	—	53	4	no	—
1089	#117	—	53	4	no	—
1090	#117	—	53	4	no	—
1091	#117	—	53	8	no	—
1092	#117	—	53	8	no	—
1093	#117	—	53	8	no	—
1094	#117	C₂²×D₅₃	1	4	yes	complemented
1095	#117	C₂²×D₅₃	1	4	yes	complemented
1096	C₂×C₄⋊C₄	—	53	8	no	—
1097	C₂×C₄⋊C₄	—	53	4	no	—
1098	C₂×C₄⋊C₄	—	53	4	no	—
1099	C₂×C₄⋊C₄	—	53	8	no	—
1100	C₂×C₂²⋊C₄	—	53	1	no	—
1101	C₂×C₂²⋊C₄	—	53	1	no	—
1102	C₂×C₂²⋊C₄	—	53	2	no	—
1103	C₂×C₂²⋊C₄	—	53	8	no	—
1104	C₂×C₂²⋊C₄	—	53	2	no	—
1105	C₂×C₂²⋊C₄	—	53	4	no	—
1106	C₂×C₂²⋊C₄	—	53	4	no	—
1107	C₂×C₂²⋊C₄	—	53	2	no	—
1108	C₂×C₂²⋊C₄	—	53	2	no	—
1109	C₂×C₂²⋊C₄	—	53	2	no	—
1110	C₂×C₂²⋊C₄	—	53	2	no	—
1111	C₂×C₂²⋊C₄	—	53	8	no	—
1112	C₂×C₂²⋊C₄	—	53	8	no	—
1113	C₂×C₂²⋊C₄	—	53	4	no	—
1114	C₂×C₂²⋊C₄	—	53	4	no	—
1115	C₂×C₂²⋊C₄	—	53	4	no	—
1116	C₂×C₂²⋊C₄	—	53	8	no	—
1117	C₂×C₂²⋊C₄	—	53	4	no	—
1118	C₂×C₂²⋊C₄	—	53	4	no	—
1119	C₂×C₂²⋊C₄	—	53	4	no	—
1120	C₂×C₂²⋊C₄	—	53	8	no	—
1121	C₂×C₂²⋊C₄	—	53	4	no	—
1122	C₂×C₂²⋊C₄	—	53	8	no	—
1123	C₂×C₂²⋊C₄	—	53	8	no	—
1124	C₂×C₂²⋊C₄	—	53	8	no	—
1125	C₂×C₂²⋊C₄	—	53	8	no	—
1126	C₂×C₂²⋊C₄	—	53	8	no	—
1127	C₂×C₂²⋊C₄	—	53	4	no	—
1128	C₂×C₂²⋊C₄	—	53	8	no	—
1129	C₂×C₂²⋊C₄	—	53	4	no	—
1130	C₂×C₂²⋊C₄	—	53	4	no	—
1131	C₂×C₂²⋊C₄	—	53	4	no	—
1132	C₂×C₂²⋊C₄	—	53	4	no	—
1133	C₂×C₂²⋊C₄	—	53	4	no	—
1134	C₂×C₂²⋊C₄	—	53	8	no	—
1135	C₂×C₂²⋊C₄	—	53	8	no	—
1136	C₂×C₂²⋊C₄	—	53	8	no	—
1137	C₂×C₂²⋊C₄	—	53	8	no	—
1138	C₂×C₂²⋊C₄	—	53	8	no	—
1139	C₂×C₂²⋊C₄	—	53	8	no	—
1140	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1141	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1142	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1143	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1144	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1145	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1146	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1147	C₂×C₄²	—	53	8	no	—
1148	C₂⁴	—	2	4	no	—
1149	C₂⁴	—	4	4	no	—
1150	C₂⁴	—	53	2	no	—
1151	C₂⁴	—	53	1	no	—
1152	C₂⁴	—	53	2	no	—
1153	C₂⁴	—	53	8	no	—
1154	C₂⁴	—	53	1	no	—
1155	C₂⁴	—	53	2	no	—
1156	C₂⁴	—	53	2	no	—
1157	C₂⁴	—	53	4	no	—
1158	C₂⁴	—	53	1	no	—
1159	C₂⁴	—	53	2	no	—
1160	C₂⁴	—	53	4	no	—
1161	C₂⁴	—	53	4	no	—
1162	C₂⁴	—	53	4	no	—
1163	C₂⁴	—	53	2	no	—
1164	C₂⁴	—	53	1	no	—
1165	C₂⁴	—	53	4	no	—
1166	C₂⁴	—	53	2	no	—
1167	C₂⁴	—	106	8	no	—
1168	C₂⁴	—	106	4	no	—
1169	C₂⁴	—	106	8	no	—
1170	C₂⁴	—	106	16	no	—
1171	C₂⁴	—	106	4	no	—
1172	C₂⁴	—	106	16	no	—
1173	C₂⁴	—	106	4	no	—
1174	C₂⁴	—	106	16	no	—
1175	C₂⁴	—	106	4	no	—
1176	C₂⁴	—	106	4	no	—
1177	C₂⁴	—	212	4	no	—
1178	C₂⁴	—	212	8	no	—
1179	C₂⁴	—	212	8	no	—
1180	C₂⁴	—	212	4	no	—
1181	C₂⁴	—	212	8	no	—
1182	C₂⁴	—	212	4	no	—
1183	C₂⁴	—	212	8	no	—
1184	C₂⁴	—	212	4	no	—
1185	C₂⁴	—	212	4	no	—
1186	C₂⁴	—	212	64	no	—
1187	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1188	C₂⁴	C₂³×D₅₃	1	4	yes	—
1189	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1190	C₂⁴	C₂³×D₅₃	1	2	yes	—
1191	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1192	#41	—	4	8	no	—
1193	#41	—	212	8	no	—
1194	#41	—	212	16	no	—
1195	#41	—	212	16	no	—
1196	#41	—	212	8	no	—
1197	#41	—	212	8	no	—
1198	C₂×Q₈	—	53	4	no	—
1199	C₂×Q₈	—	53	8	no	—
1200	C₂×Q₈	—	212	8	no	—
1201	C₂×Q₈	C₂³×D₅₃	1	4	yes	complemented
1202	C₂×D₄	—	2	8	no	—
1203	C₂×D₄	—	4	8	no	—
1204	C₂×D₄	—	53	4	no	—
1205	C₂×D₄	—	53	4	no	—
1206	C₂×D₄	—	53	4	no	—
1207	C₂×D₄	—	53	4	no	—
1208	C₂×D₄	—	53	8	no	—
1209	C₂×D₄	—	53	8	no	—
1210	C₂×D₄	—	53	8	no	—
1211	C₂×D₄	—	53	8	no	—
1212	C₂×D₄	—	53	8	no	—
1213	C₂×D₄	—	53	4	no	—
1214	C₂×D₄	—	53	4	no	—
1215	C₂×D₄	—	53	8	no	—
1216	C₂×D₄	—	53	8	no	—
1217	C₂×D₄	—	53	4	no	—
1218	C₂×D₄	—	106	8	no	—
1219	C₂×D₄	—	106	16	no	—
1220	C₂×D₄	—	106	16	no	—
1221	C₂×D₄	—	106	16	no	—
1222	C₂×D₄	—	106	16	no	—
1223	C₂×D₄	—	106	32	no	—
1224	C₂×D₄	—	106	8	no	—
1225	C₂×D₄	—	106	8	no	—
1226	C₂×D₄	—	212	8	no	—
1227	C₂×D₄	—	212	16	no	—
1228	C₂×D₄	—	212	8	no	—
1229	C₂×D₄	—	212	16	no	—
1230	C₂×D₄	—	212	16	no	—
1231	C₂×D₄	—	212	8	no	—
1232	C₂×D₄	—	212	8	no	—
1233	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1234	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1235	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1236	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1237	C₂×D₄	C₂³×D₅₃	1	4	yes	complemented
1238	C₂²×C₄	—	4	4	no	—
1239	C₂²×C₄	—	53	2	no	—
1240	C₂²×C₄	—	53	4	no	—
1241	C₂²×C₄	—	53	2	no	—
1242	C₂²×C₄	—	53	4	no	—
1243	C₂²×C₄	—	53	4	no	—
1244	C₂²×C₄	—	53	2	no	—
1245	C₂²×C₄	—	53	8	no	—
1246	C₂²×C₄	—	53	4	no	—
1247	C₂²×C₄	—	53	4	no	—
1248	C₂²×C₄	—	53	8	no	—
1249	C₂²×C₄	—	53	4	no	—
1250	C₂²×C₄	—	53	4	no	—
1251	C₂²×C₄	—	53	4	no	—
1252	C₂²×C₄	—	53	4	no	—
1253	C₂²×C₄	—	53	4	no	—
1254	C₂²×C₄	—	53	4	no	—
1255	C₂²×C₄	—	53	4	no	—
1256	C₂²×C₄	—	53	8	no	—
1257	C₂²×C₄	—	53	4	no	—
1258	C₂²×C₄	—	53	8	no	—
1259	C₂²×C₄	—	53	8	no	—
1260	C₂²×C₄	—	106	16	no	—
1261	C₂²×C₄	—	106	8	no	—
1262	C₂²×C₄	—	212	8	no	—
1263	C₂²×C₄	—	212	4	no	—
1264	C₂²×C₄	—	212	8	no	—
1265	C₂²×C₄	—	212	4	no	—
1266	C₂²×C₄	—	212	4	no	—
1267	C₂²×C₄	—	212	8	no	—
1268	C₂²×C₄	—	212	4	no	—
1269	C₂²×C₄	—	212	8	no	—
1270	C₂²×C₄	—	212	16	no	—
1271	C₂²×C₄	—	212	4	no	—
1272	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1273	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1274	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1275	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1276	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1277	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1278	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
1279	C₄⋊C₄	—	53	8	no	—
1280	C₄⋊C₄	—	53	8	no	—
1281	C₄⋊C₄	—	53	8	no	—
1282	C₄⋊C₄	—	53	8	no	—
1283	C₄⋊C₄	—	53	4	no	—
1284	C₄⋊C₄	—	53	8	no	—
1285	C₄⋊C₄	—	53	4	no	—
1286	C₄⋊C₄	—	53	8	no	—
1287	C₄⋊C₄	—	53	8	no	—
1288	C₄⋊C₄	—	53	8	no	—
1289	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1290	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1291	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1292	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1293	C₂²⋊C₄	—	53	4	no	—
1294	C₂²⋊C₄	—	53	4	no	—
1295	C₂²⋊C₄	—	53	8	no	—
1296	C₂²⋊C₄	—	53	4	no	—
1297	C₂²⋊C₄	—	53	8	no	—
1298	C₂²⋊C₄	—	53	4	no	—
1299	C₂²⋊C₄	—	53	8	no	—
1300	C₂²⋊C₄	—	53	8	no	—
1301	C₂²⋊C₄	—	53	8	no	—
1302	C₂²⋊C₄	—	53	8	no	—
1303	C₂²⋊C₄	—	53	8	no	—
1304	C₂²⋊C₄	—	53	8	no	—
1305	C₂²⋊C₄	—	53	8	no	—
1306	C₂²⋊C₄	—	53	8	no	—
1307	C₂²⋊C₄	—	53	8	no	—
1308	C₂²⋊C₄	—	53	8	no	—
1309	C₂²⋊C₄	—	53	8	no	—
1310	C₂²⋊C₄	—	53	8	no	—
1311	C₂²⋊C₄	—	53	8	no	—
1312	C₂²⋊C₄	—	53	8	no	—
1313	C₂²⋊C₄	—	53	8	no	—
1314	C₂²⋊C₄	—	53	8	no	—
1315	C₂²⋊C₄	—	53	8	no	—
1316	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1317	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1318	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1319	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1320	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1321	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1322	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1323	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1324	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1325	C₄²	—	53	8	no	—
1326	C₄²	—	53	8	no	—
1327	C₄²	—	53	8	no	—
1328	C₄²	C₂³×D₅₃	1	8	yes	complemented
1329	C₂³	—	2	2	no	—
1330	C₂³	—	2	4	no	—
1331	C₂³	—	2	8	no	—
1332	C₂³	—	2	2	no	—
1333	C₂³	—	2	8	no	—
1334	C₂³	—	2	4	no	—
1335	C₂³	—	4	2	no	—
1336	C₂³	—	4	4	no	—
1337	C₂³	—	4	2	no	—
1338	C₂³	—	4	4	no	—
1339	C₂³	—	4	16	no	—
1340	C₂³	—	53	1	no	—
1341	C₂³	—	53	8	no	—
1342	C₂³	—	53	4	no	—
1343	C₂³	—	53	8	no	—
1344	C₂³	—	53	2	no	—
1345	C₂³	—	53	1	no	—
1346	C₂³	—	53	2	no	—
1347	C₂³	—	53	4	no	—
1348	C₂³	—	53	8	no	—
1349	C₂³	—	53	2	no	—
1350	C₂³	—	53	4	no	—
1351	C₂³	—	106	4	no	—
1352	C₂³	—	106	4	no	—
1353	C₂³	—	106	4	no	—
1354	C₂³	—	106	4	no	—
1355	C₂³	—	106	8	no	—
1356	C₂³	—	106	4	no	—
1357	C₂³	—	106	4	no	—
1358	C₂³	—	106	8	no	—
1359	C₂³	—	106	16	no	—
1360	C₂³	—	106	8	no	—
1361	C₂³	—	106	8	no	—
1362	C₂³	—	106	8	no	—
1363	C₂³	—	106	8	no	—
1364	C₂³	—	106	8	no	—
1365	C₂³	—	106	4	no	—
1366	C₂³	—	106	8	no	—
1367	C₂³	—	106	4	no	—
1368	C₂³	—	106	32	no	—
1369	C₂³	—	106	2	no	—
1370	C₂³	—	106	4	no	—
1371	C₂³	—	106	4	no	—
1372	C₂³	—	106	8	no	—
1373	C₂³	—	106	2	no	—
1374	C₂³	—	106	8	no	—
1375	C₂³	—	424	16	no	—
1376	C₂³	—	212	4	no	—
1377	C₂³	—	212	8	no	—
1378	C₂³	—	212	2	no	—
1379	C₂³	—	212	4	no	—
1380	C₂³	—	212	2	no	—
1381	C₂³	—	212	4	no	—
1382	C₂³	—	212	4	no	—
1383	C₂³	—	212	4	no	—
1384	C₂³	—	212	4	no	—
1385	C₂³	—	212	16	no	—
1386	C₂³	—	212	16	no	—
1387	C₂³	—	212	64	no	—
1388	C₂³	—	212	16	no	—
1389	C₂³	—	212	64	no	—
1390	C₂³	—	212	16	no	—
1391	C₂³	—	212	16	no	—
1392	C₂³	#41×D₅₃	1	4	yes	complemented
1393	C₂³	C₂⁴×D₅₃	1	2	yes	—
1394	C₂³	C₂⁴×D₅₃	1	4	yes	—
1395	C₂³	C₂⁴×D₅₃	1	2	yes	—
1396	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1397	C₂³	C₂⁴×D₅₃	1	2	yes	—
1398	Q₈	—	4	4	no	—
1399	Q₈	—	212	4	no	—
1400	Q₈	—	212	8	no	—
1401	D₄	—	2	8	no	—
1402	D₄	—	2	8	no	—
1403	D₄	—	2	16	no	—
1404	D₄	—	4	8	no	—
1405	D₄	—	4	4	no	—
1406	D₄	—	106	8	no	—
1407	D₄	—	106	8	no	—
1408	D₄	—	106	16	no	—
1409	D₄	—	106	8	no	—
1410	D₄	—	106	8	no	—
1411	D₄	—	106	16	no	—
1412	D₄	—	106	8	no	—
1413	D₄	—	106	8	no	—
1414	D₄	—	106	16	no	—
1415	D₄	—	212	8	no	—
1416	D₄	—	212	4	no	—
1417	D₄	—	212	8	no	—
1418	D₄	—	212	8	no	—
1419	D₄	—	212	8	no	—
1420	C₂×C₄	—	2	4	no	—
1421	C₂×C₄	—	2	8	no	—
1422	C₂×C₄	—	4	2	no	—
1423	C₂×C₄	—	4	4	no	—
1424	C₂×C₄	—	4	2	no	—
1425	C₂×C₄	—	4	4	no	—
1426	C₂×C₄	—	4	8	no	—
1427	C₂×C₄	—	53	4	no	—
1428	C₂×C₄	—	53	4	no	—
1429	C₂×C₄	—	53	8	no	—
1430	C₂×C₄	—	53	4	no	—
1431	C₂×C₄	—	106	8	no	—
1432	C₂×C₄	—	106	8	no	—
1433	C₂×C₄	—	106	8	no	—
1434	C₂×C₄	—	106	8	no	—
1435	C₂×C₄	—	106	8	no	—
1436	C₂×C₄	—	106	8	no	—
1437	C₂×C₄	—	106	16	no	—
1438	C₂×C₄	—	106	4	no	—
1439	C₂×C₄	—	106	8	no	—
1440	C₂×C₄	—	212	4	no	—
1441	C₂×C₄	—	212	4	no	—
1442	C₂×C₄	—	212	4	no	—
1443	C₂×C₄	—	212	4	no	—
1444	C₂×C₄	—	212	8	no	—
1445	C₂×C₄	—	212	8	no	—
1446	C₂×C₄	—	212	8	no	—
1447	C₂×C₄	—	212	2	no	—
1448	C₂×C₄	—	212	4	no	—
1449	C₂×C₄	—	212	2	no	—
1450	C₂×C₄	—	212	4	no	—
1451	C₂×C₄	—	212	8	no	—
1452	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1453	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1454	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1455	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1456	C₂²	—	2	8	no	—
1457	C₂²	—	2	2	no	—
1458	C₂²	—	2	2	no	—
1459	C₂²	—	2	2	no	—
1460	C₂²	—	2	4	no	—
1461	C₂²	—	2	4	no	—
1462	C₂²	—	2	2	no	—
1463	C₂²	—	2	8	no	—
1464	C₂²	—	2	4	no	—
1465	C₂²	—	4	4	no	—
1466	C₂²	—	4	16	no	—
1467	C₂²	—	4	4	no	—
1468	C₂²	—	8	4	no	—
1469	C₂²	—	53	2	no	—
1470	C₂²	—	53	4	no	—
1471	C₂²	—	53	4	no	—
1472	C₂²	—	53	2	no	—
1473	C₂²	—	53	4	no	—
1474	C₂²	—	106	8	no	—
1475	C₂²	—	106	16	no	—
1476	C₂²	—	106	16	no	—
1477	C₂²	—	106	8	no	—
1478	C₂²	—	106	16	no	—
1479	C₂²	—	106	2	no	—
1480	C₂²	—	106	2	no	—
1481	C₂²	—	106	2	no	—
1482	C₂²	—	106	4	no	—
1483	C₂²	—	106	4	no	—
1484	C₂²	—	106	2	no	—
1485	C₂²	—	106	8	no	—
1486	C₂²	—	106	4	no	—
1487	C₂²	—	424	4	no	—
1488	C₂²	—	424	8	no	—
1489	C₂²	—	212	4	no	—
1490	C₂²	—	212	8	no	—
1491	C₂²	—	212	16	no	—
1492	C₂²	—	212	16	no	—
1493	C₂²	—	212	4	no	—
1494	C₂²	—	212	16	no	—
1495	C₂²	—	212	8	no	—
1496	C₂²	—	212	16	no	—
1497	C₂²	—	212	8	no	—
1498	C₂²	C₂×#41×D₅₃	1	4	yes	—
1499	C₂²	C₂×#41×D₅₃	1	2	yes	—
1500	C₂²	H(5,𝔽₂)×D₅₃	1	4	yes	—
1501	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1502	C₄	—	2	4	no	—
1503	C₄	—	2	4	no	—
1504	C₄	—	2	4	no	—
1505	C₄	—	2	8	no	—
1506	C₄	—	106	4	no	—
1507	C₄	—	106	4	no	—
1508	C₄	—	106	4	no	—
1509	C₄	—	106	8	no	—
1510	C₂	—	2	2	no	—
1511	C₂	—	2	4	no	—
1512	C₂	—	2	4	no	—
1513	C₂	—	4	2	no	—
1514	C₂	—	4	4	no	—
1515	C₂	—	53	4	no	—
1516	C₂	—	106	2	no	—
1517	C₂	—	106	4	no	—
1518	C₂	—	106	4	no	—
1519	C₂	—	212	4	no	—
1520	C₂	—	212	2	no	—
1521	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1522	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3490	C₂
hypercenter	#3490	D₅₃
hypocenter	C₅₃	C₂×#3490
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3490

Complements

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

N	H ≅ G/N	type
1. #20288405	C₂	semidirect
2. #20288404	C₂	semidirect
3. #20288403	C₂	semidirect
4. #20288402	C₂	semidirect
5. #20288401	C₂	semidirect
6. #20288400	C₂	semidirect
7. #20288399	C₂	semidirect
8. #20288398	C₂	semidirect
9. #20288397	C₂	semidirect
10. #551×D₅₃	C₂	semidirect
11. #546×D₅₃	C₂	semidirect
12. #543×D₅₃	C₂	semidirect
13. #538×D₅₃	C₂	semidirect
14. #534×D₅₃	C₂	semidirect
15. #525×D₅₃	C₂	semidirect
16. C₂×#120×D₅₃	C₂	semidirect
17. #518×D₅₃	C₂	semidirect
18. C₂²×C₂²⋊C₄×D₅₃	C₂	semidirect
19. C₅₃×#3490	C₂	semidirect
21. C₂×#41×D₅₃	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂³×C₄×D₅₃	C₂²	semidirect
25. #16811304	C₂²	semidirect
26. #16811303	C₂²	semidirect
27. #16811302	C₂²	semidirect
28. #16811302	C₂²	semidirect
29. #16811301	C₂²	semidirect
30. #16811300	C₂²	semidirect
31. #16811300	C₂²	semidirect
32. #16811299	C₂²	semidirect
33. #16811299	C₂²	semidirect
34. #16811298	C₂²	semidirect
35. #16811298	C₂²	semidirect
36. #16811297	C₂²	semidirect
37. #16811297	C₂²	semidirect
38. #16811296	C₂²	semidirect
39. #16811296	C₂²	semidirect
40. #16811270	C₂²	semidirect
41. #16811269	C₂²	semidirect
42. #16811268	C₂²	semidirect
43. #16811267	C₂²	semidirect
44. #16811266	C₂²	semidirect
45. #16811265	C₂²	semidirect
46. #16811265	C₂²	semidirect
47. #16811264	C₂²	semidirect
48. #16811263	C₂²	semidirect
49. #16811263	C₂²	semidirect
50. #16811262	C₂²	semidirect
51. #16811262	C₂²	semidirect
52. #16811261	C₂²	semidirect
53. #16811260	C₂²	semidirect
54. #16811260	C₂²	semidirect
55. #16811249	C₂²	semidirect
56. #16811249	C₂²	semidirect
57. #16811248	C₂²	semidirect
58. #16811248	C₂²	semidirect
59. #16811213	C₂²	semidirect
60. #16811212	C₂²	semidirect
61. #16811211	C₂²	semidirect
62. #16811210	C₂²	semidirect
63. #16811209	C₂²	semidirect
64. #16811208	C₂²	semidirect
65. #16811207	C₂²	semidirect
66. #16811206	C₂²	semidirect
67. #16811205	C₂²	semidirect
68. #16811185	C₂²	semidirect
69. #16811184	C₂²	semidirect
70. #16811183	C₂²	semidirect
71. #16811182	C₂²	semidirect
72. #16811181	C₂²	semidirect
73. #126×D₅₃	C₂²	semidirect
74. #124×D₅₃	C₂²	semidirect
75. #16811136	C₂²	semidirect
76. #16811136	C₂²	semidirect
77. #16811135	C₂²	semidirect
78. #16811134	C₂²	semidirect
79. #16811133	C₂²	semidirect
80. #16811133	C₂²	semidirect
81. #16811132	C₂²	semidirect
82. #16811132	C₂²	semidirect
83. #16811131	C₂²	semidirect
84. #16811130	C₂²	semidirect
85. #16811129	C₂²	semidirect
86. #123×D₅₃	C₂²	semidirect
87. #123×D₅₃	C₂²	semidirect
88. #123×D₅₃	C₂²	semidirect
89. C₂²⋊Q₈×D₅₃	C₂²	semidirect
90. C₂²⋊Q₈×D₅₃	C₂²	semidirect
91. C₂²⋊Q₈×D₅₃	C₂²	semidirect
92. #121×D₅₃	C₂²	semidirect
93. #121×D₅₃	C₂²	semidirect
94. #121×D₅₃	C₂²	semidirect
95. C₂×#13133187	C₂²	semidirect
96. C₂×#13133187	C₂²	semidirect
97. C₂×#13133186	C₂²	semidirect
98. C₂×#13133185	C₂²	semidirect
99. C₂×#13133185	C₂²	semidirect
101. #120×D₅₃	C₂²	semidirect
102. #120×D₅₃	C₂²	semidirect
103. #120×D₅₃	C₂²	semidirect
104. #120×D₅₃	C₂²	semidirect
105. #120×D₅₃	C₂²	semidirect
106. #120×D₅₃	C₂²	semidirect
107. #16811098	C₂²	semidirect
108. #16811097	C₂²	semidirect
109. #16811096	C₂²	semidirect
110. #16811096	C₂²	semidirect
111. #16811096	C₂²	semidirect
112. #16811095	C₂²	semidirect
113. #16811095	C₂²	semidirect
114. C₄×D₄×D₅₃	C₂²	semidirect
115. C₄×D₄×D₅₃	C₂²	semidirect
116. C₄×D₄×D₅₃	C₂²	semidirect
117. #117×D₅₃	C₂²	semidirect
118. #117×D₅₃	C₂²	semidirect
119. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
120. C₂²×#11719921	C₂²	semidirect
124. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
125. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
126. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
127. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
128. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
132. C₅₃×#551	C₂²	semidirect
133. C₅₃×#546	C₂²	semidirect
134. C₅₃×#543	C₂²	semidirect
135. C₅₃×#538	C₂²	semidirect
136. C₅₃×#534	C₂²	semidirect
137. C₅₃×#525	C₂²	semidirect
138. C₂×#120×C₅₃	C₂²	semidirect
139. C₅₃×#518	C₂²	semidirect
140. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
152. C₂×#11719949	C₂³	semidirect
153. C₂×#11719945	C₂³	semidirect
154. C₂×#11719945	C₂³	semidirect
155. C₂×#11719947	C₂³	semidirect
156. C₂×#11719947	C₂³	semidirect
158. C₂×Q₈×D₅₃	C₂³	semidirect
160. C₂²×D₂₁₂	C₂³	semidirect
163. C₂²×C₂²⋊D₅₃	C₂³	semidirect
164. C₂²×C₂²⋊D₅₃	C₂³	semidirect
173. C₂×D₄×D₅₃	C₂³	semidirect
174. C₂×D₄×D₅₃	C₂³	semidirect
175. C₂×D₄×D₅₃	C₂³	semidirect
176. C₂³×Dic₅₃	C₂³	semidirect
184. C₂²×C₄×D₅₃	C₂³	semidirect
185. C₂²×C₄×D₅₃	C₂³	semidirect
186. C₂²×C₄×D₅₃	C₂³	semidirect
187. C₂²×C₄×D₅₃	C₂³	semidirect
188. C₂²×C₄×D₅₃	C₂³	semidirect
189. #13133212	C₂³	semidirect
190. #13133212	C₂³	semidirect
191. #13133212	C₂³	semidirect
192. #13133211	C₂³	semidirect
193. #13133210	C₂³	semidirect
194. #13133210	C₂³	semidirect
195. #13133210	C₂³	semidirect
196. #13133206	C₂³	semidirect
197. #13133205	C₂³	semidirect
198. #13133204	C₂³	semidirect
199. #13133203	C₂³	semidirect
200. #13133203	C₂³	semidirect
201. #13133203	C₂³	semidirect
202. #13133203	C₂³	semidirect
203. #13133202	C₂³	semidirect
204. #13133202	C₂³	semidirect
205. #13133202	C₂³	semidirect
206. #13133202	C₂³	semidirect
207. #13133202	C₂³	semidirect
208. #13133201	C₂³	semidirect
209. #13133201	C₂³	semidirect
210. #13133201	C₂³	semidirect
211. #13133200	C₂³	semidirect
212. #13133200	C₂³	semidirect
213. #13133200	C₂³	semidirect
214. #13133199	C₂³	semidirect
215. #13133199	C₂³	semidirect
216. #13133199	C₂³	semidirect
217. #13133199	C₂³	semidirect
218. #13133199	C₂³	semidirect
219. #13133198	C₂³	semidirect
220. #13133198	C₂³	semidirect
221. #13133198	C₂³	semidirect
222. #13133197	C₂³	semidirect
223. #13133197	C₂³	semidirect
224. #13133197	C₂³	semidirect
225. #13133196	C₂³	semidirect
226. #13133196	C₂³	semidirect
227. #13133196	C₂³	semidirect
228. #13133195	C₂³	semidirect
229. #13133195	C₂³	semidirect
230. #13133195	C₂³	semidirect
231. #13133195	C₂³	semidirect
232. #13133194	C₂³	semidirect
233. #13133194	C₂³	semidirect
234. #13133194	C₂³	semidirect
235. #13133194	C₂³	semidirect
236. #13133193	C₂³	semidirect
237. #13133193	C₂³	semidirect
238. #13133193	C₂³	semidirect
239. #13133192	C₂³	semidirect
240. #13133192	C₂³	semidirect
241. #13133192	C₂³	semidirect
242. #13133191	C₂³	semidirect
243. #13133191	C₂³	semidirect
244. #13133191	C₂³	semidirect
245. #13133190	C₂³	semidirect
246. #13133190	C₂³	semidirect
247. #13133190	C₂³	semidirect
248. #13133190	C₂³	semidirect
249. #13133189	C₂³	semidirect
250. #13133189	C₂³	semidirect
251. #13133189	C₂³	semidirect
252. #13133189	C₂³	semidirect
253. #13133188	C₂³	semidirect
254. #13133188	C₂³	semidirect
255. #13133188	C₂³	semidirect
259. #13133187	C₂³	semidirect
260. #13133187	C₂³	semidirect
261. #13133187	C₂³	semidirect
262. #13133187	C₂³	semidirect
263. #13133187	C₂³	semidirect
264. #13133187	C₂³	semidirect
266. #13133186	C₂³	semidirect
267. #13133186	C₂³	semidirect
268. #13133186	C₂³	semidirect
272. #13133185	C₂³	semidirect
273. #13133185	C₂³	semidirect
274. #13133185	C₂³	semidirect
275. #13133185	C₂³	semidirect
276. #13133185	C₂³	semidirect
277. #13133185	C₂³	semidirect
278. C₄×D₂₁₂	C₂³	semidirect
279. C₄×D₂₁₂	C₂³	semidirect
280. C₄×D₂₁₂	C₂³	semidirect
281. D₄×Dic₅₃	C₂³	semidirect
282. D₄×Dic₅₃	C₂³	semidirect
283. D₄×Dic₅₃	C₂³	semidirect
284. #13133179	C₂³	semidirect
285. #13133179	C₂³	semidirect
286. #13133179	C₂³	semidirect
287. C₄×C₂²⋊D₅₃	C₂³	semidirect
288. C₄×C₂²⋊D₅₃	C₂³	semidirect
289. C₄×C₂²⋊D₅₃	C₂³	semidirect
290. C₄×C₂²⋊D₅₃	C₂³	semidirect
291. C₄×C₂²⋊D₅₃	C₂³	semidirect
292. C₄×C₂²⋊D₅₃	C₂³	semidirect
293. #13133177	C₂³	semidirect
294. #13133177	C₂³	semidirect
295. #13133177	C₂³	semidirect
296. #13133177	C₂³	semidirect
297. #13133177	C₂³	semidirect
298. #13133177	C₂³	semidirect
299. #13133176	C₂³	semidirect
300. #13133176	C₂³	semidirect
301. #13133175	C₂³	semidirect
302. #13133175	C₂³	semidirect
303. #13133175	C₂³	semidirect
304. #13133174	C₂³	semidirect
305. #13133174	C₂³	semidirect
306. #13133173	C₂³	semidirect
307. #13133173	C₂³	semidirect
308. #13133173	C₂³	semidirect
309. C₄⋊C₄×D₅₃	C₂³	semidirect
310. C₄⋊C₄×D₅₃	C₂³	semidirect
311. C₄⋊C₄×D₅₃	C₂³	semidirect
312. C₄⋊C₄×D₅₃	C₂³	semidirect
316. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
317. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
318. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
319. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
323. C₂×#11719921	C₂³	semidirect
324. C₂×#11719921	C₂³	semidirect
325. C₂×#11719921	C₂³	semidirect
326. C₂×#11719921	C₂³	semidirect
327. C₂×#11719921	C₂³	semidirect
328. C₂×#11719921	C₂³	semidirect
329. C₂×#11719921	C₂³	semidirect
341. C₂²⋊C₄×D₅₃	C₂³	semidirect
342. C₂²⋊C₄×D₅₃	C₂³	semidirect
343. C₂²⋊C₄×D₅₃	C₂³	semidirect
344. C₂²⋊C₄×D₅₃	C₂³	semidirect
345. C₂²⋊C₄×D₅₃	C₂³	semidirect
346. C₂²⋊C₄×D₅₃	C₂³	semidirect
347. C₂²⋊C₄×D₅₃	C₂³	semidirect
348. C₂²⋊C₄×D₅₃	C₂³	semidirect
349. C₂²⋊C₄×D₅₃	C₂³	semidirect
350. C₂²⋊C₄×D₅₃	C₂³	semidirect
351. C₂²⋊C₄×D₅₃	C₂³	semidirect
352. C₂²⋊C₄×D₅₃	C₂³	semidirect
353. C₄²×D₅₃	C₂³	semidirect
355. C₂×#41×C₅₃	C₂³	semidirect
357. C₂²×D₄×C₅₃	C₂³	semidirect
358. C₂³×C₄×C₅₃	C₂³	semidirect
359. #126×C₅₃	C₂³	semidirect
360. #124×C₅₃	C₂³	semidirect
361. #123×C₅₃	C₂³	semidirect
362. #123×C₅₃	C₂³	semidirect
363. #123×C₅₃	C₂³	semidirect
364. C₂²⋊Q₈×C₅₃	C₂³	semidirect
365. C₂²⋊Q₈×C₅₃	C₂³	semidirect
366. C₂²⋊Q₈×C₅₃	C₂³	semidirect
367. #121×C₅₃	C₂³	semidirect
368. #121×C₅₃	C₂³	semidirect
369. #121×C₅₃	C₂³	semidirect
371. #120×C₅₃	C₂³	semidirect
372. #120×C₅₃	C₂³	semidirect
373. #120×C₅₃	C₂³	semidirect
374. C₄×D₄×C₅₃	C₂³	semidirect
375. C₄×D₄×C₅₃	C₂³	semidirect
376. C₄×D₄×C₅₃	C₂³	semidirect
377. #117×C₅₃	C₂³	semidirect
378. #117×C₅₃	C₂³	semidirect
382. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
383. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
384. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
385. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
413. C₂³×D₅₃	#41	semidirect
431. C₂×Q₈×C₅₃	C₂⁴	semidirect
438. C₂×D₄×C₅₃	C₂⁴	semidirect
446. C₂²×C₄×C₅₃	C₂⁴	semidirect
459. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
467. C₂²×Dic₅₃	C₂⁴	semidirect
489. C₂×D₂₁₂	C₂⁴	semidirect
513. C₂×C₄×D₅₃	C₂⁴	semidirect
514. C₂×C₄×D₅₃	C₂⁴	semidirect
515. C₂×Dic₁₀₆	C₂⁴	semidirect
516. C₂×Dic₁₀₆	C₂⁴	semidirect
517. C₄⋊C₄×C₅₃	C₂⁴	semidirect
518. C₄⋊C₄×C₅₃	C₂⁴	semidirect
519. C₄⋊C₄×C₅₃	C₂⁴	semidirect
520. C₄⋊C₄×C₅₃	C₂⁴	semidirect
528. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
529. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
530. C₄²×C₅₃	C₂⁴	semidirect
538. C₂²⋊Dic₅₃	C₂⁴	semidirect
539. C₂²⋊Dic₅₃	C₂⁴	semidirect
550. #11719921	C₂⁴	semidirect
551. #11719921	C₂⁴	semidirect
552. #11719921	C₂⁴	semidirect
553. #11719921	C₂⁴	semidirect
554. C₄⋊Dic₅₃	C₂⁴	semidirect
555. C₄⋊Dic₅₃	C₂⁴	semidirect
556. C₄⋊Dic₅₃	C₂⁴	semidirect
557. C₄⋊Dic₅₃	C₂⁴	semidirect
558. #11719919	C₂⁴	semidirect
559. #11719919	C₂⁴	semidirect
560. #11719919	C₂⁴	semidirect
561. #11719919	C₂⁴	semidirect
562. #11719919	C₂⁴	semidirect
563. #11719919	C₂⁴	semidirect
564. C₄×Dic₅₃	C₂⁴	semidirect
565. C₄×Dic₅₃	C₂⁴	semidirect
566. C₄×Dic₅₃	C₂⁴	semidirect
578. C₂³×C₅₃	C₂×#41	semidirect
627. C₂²×D₅₃	C₂×#41	semidirect
628. C₂²×D₅₃	C₂×#41	semidirect
758. #3490	D₅₃	direct (N × H)
780. D₅₃	#3490	direct (N × H)
801. #551	C₂×D₅₃	semidirect
817. #546	C₂×D₅₃	semidirect
822. #543	C₂×D₅₃	semidirect
832. #538	C₂×D₅₃	semidirect
838. #534	C₂×D₅₃	semidirect
852. #525	C₂×D₅₃	semidirect
874. C₂×#120	C₂×D₅₃	semidirect
882. #518	C₂×D₅₃	semidirect
901. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
902. C₅₃	C₂×#3490	semidirect
921. C₂×#41	C₂²×D₅₃	semidirect
941. C₂²×D₄	C₂²×D₅₃	semidirect
955. C₂³×C₄	C₂²×D₅₃	semidirect
963. #126	C₂²×D₅₃	semidirect
971. #124	C₂²×D₅₃	semidirect
991. #123	C₂²×D₅₃	semidirect
992. #123	C₂²×D₅₃	semidirect
993. #123	C₂²×D₅₃	semidirect
1011. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1012. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1013. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1031. #121	C₂²×D₅₃	semidirect
1032. #121	C₂²×D₅₃	semidirect
1033. #121	C₂²×D₅₃	semidirect
1057. #120	C₂²×D₅₃	semidirect
1058. #120	C₂²×D₅₃	semidirect
1059. #120	C₂²×D₅₃	semidirect
1081. C₄×D₄	C₂²×D₅₃	semidirect
1082. C₄×D₄	C₂²×D₅₃	semidirect
1083. C₄×D₄	C₂²×D₅₃	semidirect
1094. #117	C₂²×D₅₃	semidirect
1095. #117	C₂²×D₅₃	semidirect
1143. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1144. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1145. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1146. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1201. C₂×Q₈	C₂³×D₅₃	semidirect
1237. C₂×D₄	C₂³×D₅₃	semidirect
1278. C₂²×C₄	C₂³×D₅₃	semidirect
1289. C₄⋊C₄	C₂³×D₅₃	semidirect
1290. C₄⋊C₄	C₂³×D₅₃	semidirect
1291. C₄⋊C₄	C₂³×D₅₃	semidirect
1292. C₄⋊C₄	C₂³×D₅₃	semidirect
1323. C₂²⋊C₄	C₂³×D₅₃	semidirect
1324. C₂²⋊C₄	C₂³×D₅₃	semidirect
1328. C₄²	C₂³×D₅₃	semidirect
1392. C₂³	#41×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288405	2
#20288404	2
#20288403	2
#20288402	2
#20288401	2
#20288400	2
#20288399	2
#20288398	2
#20288397	2
#551×D₅₃	2
#546×D₅₃	2
#543×D₅₃	2
#538×D₅₃	2
#534×D₅₃	2
#525×D₅₃	2
C₂×#120×D₅₃	2
#518×D₅₃	2
C₂²×C₂²⋊C₄×D₅₃	2
C₅₃×#3490	2
C₂×#3490	53

Subgroups — D53×#3490 #28291997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3490 #28291997