Subgroups — #28292708

Order 13568.

9494 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	#20288869	C₂	1	4	yes	maximal, complemented
2	#20288867	C₂	1	4	yes	maximal, complemented
3	#20288865	C₂	1	8	yes	maximal, complemented
4	#20288864	C₂	1	8	yes	maximal, complemented
5	#20288403	C₂	1	2	yes	maximal, complemented
6	#20288402	C₂	1	2	yes	maximal, complemented
7	#20288400	C₂	1	2	yes	maximal, complemented
8	#20288398	C₂	1	4	yes	maximal, complemented
9	#20288397	C₂	1	8	yes	maximal, complemented
10	#20288350	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288347	C₂	1	2	yes	maximal, complemented
12	#20288346	C₂	1	2	yes	maximal, complemented
13	#20288344	C₂	1	4	yes	maximal, complemented
14	#20288343	C₂	1	8	yes	maximal, complemented
15	C₂²×#13133185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#120×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁵×D₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13133262	C₂²	1	4	yes	complemented
21	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
23	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
24	#16811366	C₂²	1	4	yes	complemented
25	#16811365	C₂²	1	4	yes	complemented
26	#16811363	C₂²	1	4	yes	complemented
27	#16811361	C₂²	1	8	yes	complemented
28	#16811361	C₂²	1	8	yes	complemented
29	#16811360	C₂²	1	4	yes	complemented
30	#16811304	C₂²	1	8	yes	complemented
31	#16811303	C₂²	1	4	yes	complemented
32	#16811302	C₂²	1	8	yes	complemented
33	#16811302	C₂²	1	8	yes	complemented
34	#16811301	C₂²	1	4	yes	complemented
35	#16811300	C₂²	1	8	yes	complemented
36	#16811299	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	#16811267	C₂²	1	8	yes	complemented
45	#16811265	C₂²	1	8	yes	complemented
46	#16811263	C₂²	1	8	yes	complemented
47	#16811263	C₂²	1	8	yes	complemented
48	#16811262	C₂²	1	8	yes	complemented
49	#16811262	C₂²	1	8	yes	complemented
50	#16811262	C₂²	1	8	yes	complemented
51	#16811261	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	#16811260	C₂²	1	8	yes	complemented
56	#16811260	C₂²	1	8	yes	complemented
57	#16811258	C₂²	1	4	yes	complemented
58	#16811257	C₂²	1	8	yes	complemented
59	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
60	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
61	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
62	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
63	#16811255	C₂²	1	4	yes	complemented
64	#16811255	C₂²	1	8	yes	complemented
65	#16811255	C₂²	1	8	yes	complemented
66	#16811249	C₂²	1	2	yes	complemented
67	#16811248	C₂²	1	4	yes	complemented
68	#16811213	C₂²	1	4	yes	complemented
69	#16811210	C₂²	1	8	yes	complemented
70	#16811210	C₂²	1	4	yes	complemented
71	#16811209	C₂²	1	8	yes	complemented
72	#16811208	C₂²	1	8	yes	complemented
73	#16811207	C₂²	1	8	yes	complemented
74	#16811206	C₂²	1	8	yes	complemented
75	#16811206	C₂²	1	8	yes	complemented
76	#16811205	C₂²	1	8	yes	complemented
77	#16811205	C₂²	1	8	yes	complemented
78	#16811190	C₂²	1	2	yes	complemented
79	#16811189	C₂²	1	8	yes	complemented
80	#16811188	C₂²	1	8	yes	complemented
81	#16811188	C₂²	1	4	yes	complemented
82	#16811187	C₂²	1	4	yes	complemented
83	#16811186	C₂²	1	8	yes	complemented
84	#16811185	C₂²	1	4	yes	complemented
85	#16811184	C₂²	1	4	yes	complemented
86	#16811183	C₂²	1	8	yes	complemented
87	#16811183	C₂²	1	8	yes	complemented
88	#16811182	C₂²	1	2	yes	complemented
89	#16811182	C₂²	1	2	yes	complemented
90	#16811182	C₂²	1	4	yes	complemented
91	#16811182	C₂²	1	4	yes	complemented
92	#16811182	C₂²	1	2	yes	complemented
93	#16811181	C₂²	1	4	yes	complemented
94	#16811181	C₂²	1	8	yes	complemented
95	#16811134	C₂²	1	2	yes	complemented
96	#16811133	C₂²	1	8	yes	complemented
97	#16811132	C₂²	1	8	yes	complemented
98	#16811131	C₂²	1	4	yes	complemented
99	#16811130	C₂²	1	4	yes	complemented
100	#16811129	C₂²	1	8	yes	complemented
101	C₂×#13133187	C₂²	1	2	yes	complemented
102	C₂×#13133187	C₂²	1	4	yes	complemented
103	C₂×#13133186	C₂²	1	2	yes	complemented
104	C₂×#13133186	C₂²	1	2	yes	complemented
105	C₂×#13133185	C₂²	1	2	yes	complemented
106	C₂×#13133185	C₂²	1	2	yes	complemented
107	C₂×#13133185	C₂²	1	2	yes	complemented
108	C₂×#13133185	C₂²	1	8	yes	complemented
109	C₂×#13133185	C₂²	1	8	yes	complemented
110	C₂×#13133185	C₂²	1	4	yes	complemented
111	C₂×#13133185	C₂²	1	2	yes	complemented
112	C₂×#13133185	C₂²	1	2	yes	complemented
113	C₂×#13133185	C₂²	1	4	yes	complemented
114	#120×D₅₃	C₂²	1	8	yes	complemented
115	#120×D₅₃	C₂²	1	8	yes	complemented
116	#120×D₅₃	C₂²	1	8	yes	complemented
117	#120×D₅₃	C₂²	1	8	yes	complemented
118	#120×D₅₃	C₂²	1	4	yes	complemented
119	#16811098	C₂²	1	2	yes	complemented
120	#16811098	C₂²	1	1	yes	characteristic, complemented
121	#16811096	C₂²	1	2	yes	complemented
122	#16811096	C₂²	1	4	yes	complemented
123	#16811095	C₂²	1	8	yes	complemented
124	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂²×#11719921	C₂²	1	2	yes	complemented
126	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
128	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#546	C₂²	1	8	yes	complemented
131	D₄²×C₅₃	C₂²	1	8	yes	complemented
132	C₅₃×#535	C₂²	1	2	yes	complemented
133	C₅₃×#534	C₂²	1	2	yes	complemented
134	C₅₃×#534	C₂²	1	2	yes	complemented
135	C₅₃×#525	C₂²	1	2	yes	complemented
136	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
137	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
138	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₅₃	—	4	8	no	—
140	C₂⁴×D₅₃	—	4	4	no	—
141	C₂⁴×D₅₃	C₂³	1	4	yes	—
142	C₂⁴×D₅₃	C₂³	1	2	yes	—
143	C₂⁴×D₅₃	C₂³	1	2	yes	—
144	C₂⁴×D₅₃	C₂³	1	2	yes	—
145	C₂⁴×D₅₃	C₂³	1	4	yes	—
146	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
147	#13133262	—	4	16	no	—
148	#13133262	—	4	4	no	—
149	C₂×#11719945	C₂³	1	8	yes	complemented
150	C₂×#11719945	C₂³	1	2	yes	complemented
151	C₂×#11719947	C₂³	1	8	yes	complemented
152	C₂×#11719947	C₂³	1	4	yes	complemented
153	C₂×#11719947	C₂³	1	8	yes	complemented
154	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
155	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
156	C₂²×C₂²⋊D₅₃	—	4	8	no	—
157	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
158	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
159	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
160	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
161	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
162	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
163	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
164	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
165	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
166	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
167	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
168	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
169	C₂×D₄×D₅₃	—	4	16	no	—
170	C₂×D₄×D₅₃	—	4	8	no	—
171	C₂×D₄×D₅₃	C₂³	1	8	yes	—
172	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
173	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
174	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
175	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
176	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
177	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
178	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
179	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
180	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
181	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
182	#13133213	C₂³	1	8	yes	complemented
183	#13133213	C₂³	1	8	yes	complemented
184	#13133213	C₂³	1	4	yes	complemented
185	#13133212	C₂³	1	8	yes	complemented
186	#13133212	C₂³	1	8	yes	complemented
187	#13133212	C₂³	1	8	yes	complemented
188	#13133211	C₂³	1	8	yes	complemented
189	#13133210	C₂³	1	8	yes	complemented
190	#13133210	C₂³	1	8	yes	complemented
191	#13133206	C₂³	1	8	yes	complemented
192	#13133205	C₂³	1	8	yes	complemented
193	#13133204	C₂³	1	4	yes	complemented
194	#13133204	C₂³	1	8	yes	complemented
195	#13133203	C₂³	1	8	yes	complemented
196	#13133203	C₂³	1	8	yes	complemented
197	#13133203	C₂³	1	8	yes	complemented
198	#13133203	C₂³	1	8	yes	complemented
199	#13133203	C₂³	1	8	yes	complemented
200	#13133202	C₂³	1	8	yes	complemented
201	#13133202	C₂³	1	8	yes	complemented
202	#13133202	C₂³	1	8	yes	complemented
203	#13133201	C₂³	1	8	yes	complemented
204	#13133201	C₂³	1	8	yes	complemented
205	#13133201	C₂³	1	8	yes	complemented
206	#13133200	C₂³	1	4	yes	complemented
207	#13133200	C₂³	1	4	yes	complemented
208	#13133200	C₂³	1	8	yes	complemented
209	#13133200	C₂³	1	8	yes	complemented
210	#13133199	C₂³	1	8	yes	complemented
211	#13133199	C₂³	1	8	yes	complemented
212	#13133199	C₂³	1	8	yes	complemented
213	#13133199	C₂³	1	8	yes	complemented
214	#13133198	C₂³	1	4	yes	complemented
215	#13133198	C₂³	1	8	yes	complemented
216	#13133198	C₂³	1	4	yes	complemented
217	#13133198	C₂³	1	4	yes	complemented
218	#13133198	C₂³	1	8	yes	complemented
219	#13133197	C₂³	1	8	yes	complemented
220	#13133196	C₂³	1	4	yes	complemented
221	#13133196	C₂³	1	8	yes	complemented
222	#13133195	C₂³	1	8	yes	complemented
223	#13133195	C₂³	1	8	yes	complemented
224	#13133194	C₂³	1	8	yes	complemented
225	#13133194	C₂³	1	8	yes	complemented
226	#13133194	C₂³	1	8	yes	complemented
227	#13133193	C₂³	1	8	yes	complemented
228	#13133192	C₂³	1	8	yes	complemented
229	#13133191	C₂³	1	8	yes	complemented
230	#13133191	C₂³	1	8	yes	complemented
231	#13133191	C₂³	1	8	yes	complemented
232	#13133191	C₂³	1	4	yes	complemented
233	#13133190	C₂³	1	8	yes	complemented
234	#13133190	C₂³	1	8	yes	complemented
235	#13133190	C₂³	1	8	yes	complemented
236	#13133190	C₂³	1	8	yes	complemented
237	#13133190	C₂³	1	8	yes	complemented
238	#13133189	C₂³	1	8	yes	complemented
239	#13133189	C₂³	1	8	yes	complemented
240	#13133189	C₂³	1	8	yes	complemented
241	#13133189	C₂³	1	8	yes	complemented
242	#13133189	C₂³	1	8	yes	complemented
243	#13133189	C₂³	1	8	yes	complemented
244	#13133189	C₂³	1	8	yes	complemented
245	#13133189	C₂³	1	8	yes	complemented
246	#13133189	C₂³	1	8	yes	complemented
247	#13133189	C₂³	1	8	yes	complemented
248	#13133188	C₂³	1	8	yes	complemented
249	#13133188	C₂³	1	8	yes	complemented
250	#13133188	C₂³	1	8	yes	complemented
251	#13133188	C₂³	1	8	yes	complemented
252	#13133187	C₂³	1	8	yes	—
253	#13133187	C₂³	1	8	yes	—
254	#13133187	C₂³	1	8	yes	complemented
255	#13133187	C₂³	1	4	yes	complemented
256	#13133187	C₂³	1	8	yes	complemented
257	#13133187	C₂³	1	4	yes	complemented
258	#13133187	C₂³	1	8	yes	complemented
259	#13133187	C₂³	1	8	yes	complemented
260	#13133187	C₂³	1	8	yes	complemented
261	#13133186	C₂³	1	8	yes	—
262	#13133186	C₂³	1	4	yes	complemented
263	#13133186	C₂³	1	4	yes	complemented
264	#13133186	C₂³	1	8	yes	complemented
265	#13133186	C₂³	1	4	yes	complemented
266	#13133186	C₂³	1	8	yes	complemented
267	#13133186	C₂³	1	4	yes	complemented
268	#13133185	C₂³	1	8	yes	—
269	#13133185	C₂³	1	4	yes	—
270	#13133185	C₂³	1	8	yes	—
271	#13133185	C₂³	1	8	yes	—
272	#13133185	C₂³	1	8	yes	—
273	#13133185	C₂³	1	4	yes	—
274	#13133185	C₂³	1	8	yes	complemented
275	#13133185	C₂³	1	4	yes	complemented
276	#13133185	C₂³	1	4	yes	complemented
277	#13133185	C₂³	1	4	yes	complemented
278	#13133185	C₂³	1	4	yes	complemented
279	#13133185	C₂³	1	8	yes	complemented
280	#13133185	C₂³	1	8	yes	complemented
281	#13133185	C₂³	1	4	yes	complemented
282	#13133185	C₂³	1	4	yes	complemented
283	#13133185	C₂³	1	8	yes	complemented
284	#13133185	C₂³	1	4	yes	complemented
285	#13133185	C₂³	1	8	yes	complemented
286	#13133185	C₂³	1	4	yes	complemented
287	#13133185	C₂³	1	4	yes	complemented
288	#13133185	C₂³	1	8	yes	complemented
289	#13133185	C₂³	1	8	yes	complemented
290	#13133185	C₂³	1	8	yes	complemented
291	#13133185	C₂³	1	4	yes	complemented
292	#13133185	C₂³	1	4	yes	complemented
293	C₄×D₂₁₂	C₂³	1	8	yes	complemented
294	D₄×Dic₅₃	C₂³	1	8	yes	complemented
295	D₄×Dic₅₃	C₂³	1	8	yes	complemented
296	D₄×Dic₅₃	C₂³	1	8	yes	complemented
297	D₄×Dic₅₃	C₂³	1	8	yes	complemented
298	#13133179	C₂³	1	8	yes	complemented
299	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
300	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
301	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
302	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
303	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
304	#13133177	C₂³	1	8	yes	complemented
305	#13133177	C₂³	1	8	yes	complemented
306	#13133177	C₂³	1	8	yes	complemented
307	#13133177	C₂³	1	8	yes	complemented
308	#13133177	C₂³	1	8	yes	complemented
309	#13133176	C₂³	1	2	yes	complemented
310	#13133176	C₂³	1	4	yes	complemented
311	#13133175	C₂³	1	8	yes	complemented
312	#13133174	C₂³	1	8	yes	complemented
313	#13133173	C₂³	1	8	yes	complemented
314	#13133173	C₂³	1	4	yes	complemented
315	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
316	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
317	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
318	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
319	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
320	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
321	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
322	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
323	C₂×#11719921	C₂³	1	4	yes	—
324	C₂×#11719921	C₂³	1	4	yes	complemented
325	C₂×#11719921	C₂³	1	8	yes	complemented
326	C₂×#11719921	C₂³	1	4	yes	complemented
327	C₂×#11719921	C₂³	1	4	yes	complemented
328	C₂×#11719921	C₂³	1	4	yes	complemented
329	C₂×#11719921	C₂³	1	4	yes	complemented
330	C₂×#11719921	C₂³	1	4	yes	complemented
331	C₂×#11719921	C₂³	1	8	yes	complemented
332	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
333	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
334	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
335	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
336	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
337	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
338	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
339	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
340	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
341	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic, complemented
342	H(5,𝔽₂)×C₅₃	—	4	4	no	—
343	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
344	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
345	C₂²×D₄×C₅₃	—	4	4	no	—
346	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
348	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
350	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
351	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
352	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
353	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
354	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
355	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
356	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
357	#127×C₅₃	C₂³	1	4	yes	complemented
358	#124×C₅₃	C₂³	1	4	yes	complemented
359	#123×C₅₃	C₂³	1	4	yes	complemented
360	#123×C₅₃	C₂³	1	4	yes	complemented
361	#123×C₅₃	C₂³	1	4	yes	complemented
362	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
363	#121×C₅₃	C₂³	1	4	yes	complemented
364	#121×C₅₃	C₂³	1	8	yes	complemented
365	#121×C₅₃	C₂³	1	8	yes	complemented
366	#121×C₅₃	C₂³	1	8	yes	complemented
367	#120×C₅₃	C₂³	1	8	yes	—
368	#120×C₅₃	C₂³	1	4	yes	complemented
369	#120×C₅₃	C₂³	1	4	yes	complemented
370	#120×C₅₃	C₂³	1	4	yes	complemented
371	#120×C₅₃	C₂³	1	4	yes	complemented
372	#120×C₅₃	C₂³	1	8	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	#117×C₅₃	C₂³	1	2	yes	complemented
377	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
378	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
379	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
380	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
381	C₂⁴×C₅₃	—	2	4	no	—
382	C₂⁴×C₅₃	—	4	4	no	—
383	C₂⁴×C₅₃	—	4	2	no	—
384	C₂⁴×C₅₃	—	4	4	no	—
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
387	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
389	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
392	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂⁴×C₅₃	C₂⁴	1	2	yes	complemented
394	C₂³×D₅₃	—	2	8	no	—
395	C₂³×D₅₃	—	2	16	no	—
396	C₂³×D₅₃	—	2	8	no	—
397	C₂³×D₅₃	—	4	8	no	—
398	C₂³×D₅₃	—	4	8	no	—
399	C₂³×D₅₃	—	4	8	no	—
400	C₂³×D₅₃	—	4	8	no	—
401	C₂³×D₅₃	—	4	8	no	—
402	C₂³×D₅₃	—	4	8	no	—
403	C₂³×D₅₃	—	4	8	no	—
404	C₂³×D₅₃	—	4	4	no	—
405	C₂³×D₅₃	—	4	4	no	—
406	C₂³×D₅₃	—	4	4	no	—
407	C₂³×D₅₃	—	4	8	no	—
408	C₂³×D₅₃	—	4	4	no	—
409	C₂³×D₅₃	—	4	64	no	—
410	C₂³×D₅₃	C₂⁴	1	2	yes	—
411	C₂³×D₅₃	C₂⁴	1	2	yes	—
412	C₂³×D₅₃	C₂⁴	1	4	yes	—
413	C₂³×D₅₃	C₂⁴	1	4	yes	—
414	C₂³×D₅₃	C₂⁴	1	4	yes	—
415	C₂³×D₅₃	C₂⁴	1	4	yes	—
416	C₂³×D₅₃	C₂⁴	1	2	yes	—
417	C₂³×D₅₃	C₂⁴	1	8	yes	—
418	C₂³×D₅₃	C₂⁴	1	2	yes	—
419	C₂³×D₅₃	C₂⁴	1	2	yes	—
420	C₂³×D₅₃	C₂⁴	1	2	yes	—
421	C₂³×D₅₃	C₂⁴	1	2	yes	—
422	C₂³×D₅₃	C₂⁴	1	2	yes	complemented
423	#41×C₅₃	—	4	8	no	—
424	#41×C₅₃	—	4	4	no	—
425	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	complemented
426	C₂×D₄×C₅₃	—	2	4	no	—
427	C₂×D₄×C₅₃	—	2	4	no	—
428	C₂×D₄×C₅₃	—	2	8	no	—
429	C₂×D₄×C₅₃	—	4	2	no	—
430	C₂×D₄×C₅₃	—	4	2	no	—
431	C₂×D₄×C₅₃	—	4	16	no	—
432	C₂×D₄×C₅₃	—	4	4	no	—
433	C₂×D₄×C₅₃	—	4	8	no	—
434	C₂×D₄×C₅₃	—	4	8	no	—
435	C₂×D₄×C₅₃	—	4	8	no	—
436	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
437	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
438	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
439	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
440	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
441	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
442	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
443	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
444	C₂×D₄×C₅₃	C₂⁴	1	8	yes	complemented
445	C₂×D₄×C₅₃	C₂⁴	1	4	yes	complemented
446	C₂×D₄×C₅₃	C₂⁴	1	2	yes	complemented
447	C₂²×C₄×C₅₃	—	4	2	no	—
448	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
452	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
453	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
454	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	complemented
455	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
456	C₂×C₂²⋊D₅₃	—	2	8	no	—
457	C₂×C₂²⋊D₅₃	—	2	16	no	—
458	C₂×C₂²⋊D₅₃	—	4	4	no	—
459	C₂×C₂²⋊D₅₃	—	4	8	no	—
460	C₂×C₂²⋊D₅₃	—	4	8	no	—
461	C₂×C₂²⋊D₅₃	—	4	8	no	—
462	C₂×C₂²⋊D₅₃	—	4	16	no	—
463	C₂×C₂²⋊D₅₃	—	4	8	no	—
464	C₂×C₂²⋊D₅₃	—	4	16	no	—
465	C₂×C₂²⋊D₅₃	—	4	8	no	—
466	C₂×C₂²⋊D₅₃	—	4	4	no	—
467	C₂×C₂²⋊D₅₃	—	4	8	no	—
468	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
469	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
470	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
471	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
472	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
473	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
474	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
475	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
476	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
477	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
478	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
479	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
480	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	complemented
481	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
482	C₂²×Dic₅₃	—	4	4	no	—
483	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
484	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
485	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
486	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
487	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
488	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
489	C₂²×Dic₅₃	C₂⁴	1	2	yes	complemented
490	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
491	#11719947	—	4	16	no	—
492	#11719947	—	4	8	no	—
493	#11719947	—	4	16	no	—
494	D₄×D₅₃	—	2	32	no	—
495	D₄×D₅₃	—	4	16	no	—
496	D₄×D₅₃	—	4	16	no	—
497	D₄×D₅₃	—	4	16	no	—
498	D₄×D₅₃	—	4	16	no	—
499	D₄×D₅₃	—	4	16	no	—
500	D₄×D₅₃	—	4	16	no	—
501	D₄×D₅₃	—	4	8	no	—
502	#11719945	—	4	16	no	—
503	#11719945	—	4	4	no	—
504	C₂×D₂₁₂	—	4	8	no	—
505	C₂×D₂₁₂	—	4	4	no	—
506	C₂×D₂₁₂	C₂⁴	1	8	yes	—
507	C₂×D₂₁₂	C₂⁴	1	8	yes	—
508	C₂×D₂₁₂	C₂⁴	1	8	yes	—
509	C₂×D₂₁₂	C₂⁴	1	2	yes	complemented
510	C₂×C₄×D₅₃	—	4	8	no	—
511	C₂×C₄×D₅₃	—	4	4	no	—
512	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
513	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
514	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
515	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
516	C₂×C₄×D₅₃	C₂⁴	1	4	yes	complemented
517	C₂×Dic₁₀₆	C₂⁴	1	8	yes	complemented
518	C₂×Dic₁₀₆	C₂⁴	1	2	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	8	yes	—
524	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
525	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
526	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
527	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
528	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
529	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
530	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
531	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
532	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
533	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
534	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
535	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
536	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
537	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
538	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
539	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
540	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	complemented
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	—
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	8	yes	complemented
557	#11719919	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	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
563	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
564	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
565	C₂³×C₅₃	—	2	4	no	—
566	C₂³×C₅₃	—	2	2	no	—
567	C₂³×C₅₃	—	2	8	no	—
568	C₂³×C₅₃	—	2	8	no	—
569	C₂³×C₅₃	—	2	2	no	—
570	C₂³×C₅₃	—	2	8	no	—
571	C₂³×C₅₃	—	2	2	no	—
572	C₂³×C₅₃	—	2	4	no	—
573	C₂³×C₅₃	—	2	2	no	—
574	C₂³×C₅₃	—	4	2	no	—
575	C₂³×C₅₃	—	4	4	no	—
576	C₂³×C₅₃	—	4	2	no	—
577	C₂³×C₅₃	—	4	2	no	—
578	C₂³×C₅₃	—	4	4	no	—
579	C₂³×C₅₃	—	4	2	no	—
580	C₂³×C₅₃	—	4	4	no	—
581	C₂³×C₅₃	—	4	4	no	—
582	C₂³×C₅₃	—	4	4	no	—
583	C₂³×C₅₃	—	4	2	no	—
584	C₂³×C₅₃	—	4	16	no	—
585	C₂³×C₅₃	—	8	8	no	—
586	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
587	C₂³×C₅₃	C₂⁵	1	2	yes	—
588	C₂³×C₅₃	C₂⁵	1	4	yes	—
589	C₂³×C₅₃	C₂⁵	1	2	yes	—
590	C₂³×C₅₃	C₂⁵	1	2	yes	—
591	C₂³×C₅₃	C₂⁵	1	2	yes	—
592	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
593	C₂³×C₅₃	C₂⁵	1	2	yes	—
594	C₂²×D₅₃	—	2	4	no	—
595	C₂²×D₅₃	—	2	8	no	—
596	C₂²×D₅₃	—	2	4	no	—
597	C₂²×D₅₃	—	2	8	no	—
598	C₂²×D₅₃	—	2	8	no	—
599	C₂²×D₅₃	—	2	8	no	—
600	C₂²×D₅₃	—	2	4	no	—
601	C₂²×D₅₃	—	2	4	no	—
602	C₂²×D₅₃	—	2	8	no	—
603	C₂²×D₅₃	—	2	8	no	—
604	C₂²×D₅₃	—	2	8	no	—
605	C₂²×D₅₃	—	2	8	no	—
606	C₂²×D₅₃	—	2	8	no	—
607	C₂²×D₅₃	—	2	16	no	—
608	C₂²×D₅₃	—	4	2	no	—
609	C₂²×D₅₃	—	4	2	no	—
610	C₂²×D₅₃	—	4	2	no	—
611	C₂²×D₅₃	—	4	4	no	—
612	C₂²×D₅₃	—	4	4	no	—
613	C₂²×D₅₃	—	4	4	no	—
614	C₂²×D₅₃	—	4	4	no	—
615	C₂²×D₅₃	—	4	4	no	—
616	C₂²×D₅₃	—	4	2	no	—
617	C₂²×D₅₃	—	4	2	no	—
618	C₂²×D₅₃	—	4	2	no	—
619	C₂²×D₅₃	—	4	4	no	—
620	C₂²×D₅₃	—	4	4	no	—
621	C₂²×D₅₃	—	4	4	no	—
622	C₂²×D₅₃	—	4	8	no	—
623	C₂²×D₅₃	—	4	8	no	—
624	C₂²×D₅₃	—	4	4	no	—
625	C₂²×D₅₃	—	4	2	no	—
626	C₂²×D₅₃	—	4	64	no	—
627	C₂²×D₅₃	—	4	32	no	—
628	C₂²×D₅₃	—	4	32	no	—
629	C₂²×D₅₃	—	4	32	no	—
630	C₂²×D₅₃	—	4	64	no	—
631	C₂²×D₅₃	—	8	16	no	—
632	C₂²×D₅₃	H(5,𝔽₂)	1	8	yes	complemented
633	C₂²×D₅₃	C₂⁵	1	4	yes	—
634	C₂²×D₅₃	C₂⁵	1	4	yes	—
635	C₂²×D₅₃	C₂⁵	1	4	yes	—
636	Q₈×C₅₃	—	4	2	no	—
637	D₄×C₅₃	—	2	16	no	—
638	D₄×C₅₃	—	2	8	no	—
639	D₄×C₅₃	—	2	8	no	—
640	D₄×C₅₃	—	2	8	no	—
641	D₄×C₅₃	—	2	8	no	—
642	D₄×C₅₃	—	4	8	no	—
643	D₄×C₅₃	—	4	8	no	—
644	D₄×C₅₃	—	4	4	no	—
645	D₄×C₅₃	—	4	4	no	—
646	D₄×C₅₃	—	4	4	no	—
647	D₄×C₅₃	—	4	2	no	—
648	C₂×C₄×C₅₃	—	2	4	no	—
649	C₂×C₄×C₅₃	—	2	2	no	—
650	C₂×C₄×C₅₃	—	2	2	no	—
651	C₂×C₄×C₅₃	—	4	4	no	—
652	C₂×C₄×C₅₃	—	4	4	no	—
653	C₂×C₄×C₅₃	—	4	4	no	—
654	C₂×C₄×C₅₃	—	4	2	no	—
655	C₂×C₄×C₅₃	—	4	4	no	—
656	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
657	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
658	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
659	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
660	C₂²⋊D₅₃	—	2	8	no	—
661	C₂²⋊D₅₃	—	2	16	no	—
662	C₂²⋊D₅₃	—	2	8	no	—
663	C₂²⋊D₅₃	—	2	16	no	—
664	C₂²⋊D₅₃	—	2	16	no	—
665	C₂²⋊D₅₃	—	2	16	no	—
666	C₂²⋊D₅₃	—	4	8	no	—
667	C₂²⋊D₅₃	—	4	8	no	—
668	C₂²⋊D₅₃	—	4	8	no	—
669	C₂²⋊D₅₃	—	4	8	no	—
670	C₂²⋊D₅₃	—	4	4	no	—
671	C₂²⋊D₅₃	—	4	8	no	—
672	C₂²⋊D₅₃	—	4	8	no	—
673	C₂²⋊D₅₃	—	4	8	no	—
674	C₂×Dic₅₃	—	2	4	no	—
675	C₂×Dic₅₃	—	2	8	no	—
676	C₂×Dic₅₃	—	4	4	no	—
677	C₂×Dic₅₃	—	4	4	no	—
678	C₂×Dic₅₃	—	4	8	no	—
679	C₂×Dic₅₃	—	4	2	no	—
680	C₂×Dic₅₃	—	4	4	no	—
681	C₂×Dic₅₃	—	4	4	no	—
682	C₂×Dic₅₃	C₂⁵	1	4	yes	—
683	C₂×Dic₅₃	C₂⁵	1	8	yes	—
684	C₂×Dic₅₃	C₂⁵	1	8	yes	—
685	D₂₁₂	—	2	16	no	—
686	D₂₁₂	—	4	8	no	—
687	D₂₁₂	—	4	8	no	—
688	D₂₁₂	—	4	2	no	—
689	C₄×D₅₃	—	2	16	no	—
690	C₄×D₅₃	—	4	8	no	—
691	C₄×D₅₃	—	4	8	no	—
692	C₄×D₅₃	—	4	4	no	—
693	C₄×D₅₃	—	4	8	no	—
694	Dic₁₀₆	—	4	8	no	—
695	Dic₁₀₆	—	4	2	no	—
696	#62817	—	53	1	no	maximal, Sylow
697	C₂²×C₅₃	—	2	8	no	—
698	C₂²×C₅₃	—	2	2	no	—
699	C₂²×C₅₃	—	2	2	no	—
700	C₂²×C₅₃	—	2	4	no	—
701	C₂²×C₅₃	—	2	2	no	—
702	C₂²×C₅₃	—	2	4	no	—
703	C₂²×C₅₃	—	2	8	no	—
704	C₂²×C₅₃	—	2	2	no	—
705	C₂²×C₅₃	—	2	4	no	—
706	C₂²×C₅₃	—	2	4	no	—
707	C₂²×C₅₃	—	2	4	no	—
708	C₂²×C₅₃	—	2	2	no	—
709	C₂²×C₅₃	—	2	2	no	—
710	C₂²×C₅₃	—	4	4	no	—
711	C₂²×C₅₃	—	4	16	no	—
712	C₂²×C₅₃	—	4	4	no	—
713	C₂²×C₅₃	—	8	4	no	—
714	C₂²×C₅₃	—	8	2	no	—
715	C₂²×C₅₃	—	8	8	no	—
716	C₂²×C₅₃	—	8	2	no	—
717	C₂²×C₅₃	—	16	2	no	—
718	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
719	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
720	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
721	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
722	C₂×D₅₃	—	2	16	no	—
723	C₂×D₅₃	—	2	4	no	—
724	C₂×D₅₃	—	2	4	no	—
725	C₂×D₅₃	—	2	8	no	—
726	C₂×D₅₃	—	2	4	no	—
727	C₂×D₅₃	—	2	4	no	—
728	C₂×D₅₃	—	2	4	no	—
729	C₂×D₅₃	—	2	4	no	—
730	C₂×D₅₃	—	4	8	no	—
731	C₂×D₅₃	—	4	8	no	—
732	C₂×D₅₃	—	4	16	no	—
733	C₂×D₅₃	—	4	16	no	—
734	C₂×D₅₃	—	4	16	no	—
735	C₂×D₅₃	—	4	16	no	—
736	C₂×D₅₃	—	4	8	no	—
737	C₂×D₅₃	—	4	8	no	—
738	C₂×D₅₃	—	4	8	no	—
739	C₂×D₅₃	—	8	16	no	—
740	C₂×D₅₃	—	8	4	no	—
741	C₂×D₅₃	—	16	2	no	—
742	C₂×D₅₃	C₂×H(5,𝔽₂)	1	8	yes	—
743	C₄×C₅₃	—	2	8	no	—
744	C₄×C₅₃	—	2	2	no	—
745	C₄×C₅₃	—	2	4	no	—
746	C₄×C₅₃	—	2	2	no	—
747	Dic₅₃	—	2	8	no	—
748	Dic₅₃	—	2	4	no	—
749	Dic₅₃	—	2	8	no	—
750	#3532	—	53	8	no	—
751	#3532	—	53	8	no	—
752	#3532	—	53	4	no	—
753	#3532	—	53	4	no	—
754	#3490	—	53	8	no	—
755	#3490	—	53	2	no	—
756	#3490	—	53	4	no	—
757	#3490	—	53	2	no	—
758	#3490	—	53	2	no	—
759	#3484	—	53	2	no	—
760	#3484	—	53	1	no	—
761	#3484	—	53	8	no	—
762	#3484	—	53	2	no	—
763	#3484	—	53	4	no	—
764	#3484	D₅₃	1	1	yes	characteristic, complemented
765	C₂²×#120	—	53	1	no	—
766	C₂²×#120	—	53	2	no	—
767	C₂×C₅₃	—	2	4	no	—
768	C₂×C₅₃	—	2	4	no	—
769	C₂×C₅₃	—	2	2	no	—
770	C₂×C₅₃	—	4	2	no	—
771	C₂×C₅₃	—	4	4	no	—
772	C₂×C₅₃	—	4	2	no	—
773	C₂×C₅₃	—	4	2	no	—
774	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
775	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
776	D₅₃	—	2	8	no	—
777	D₅₃	—	4	4	no	—
778	D₅₃	—	4	4	no	—
779	C₂⁶	—	53	1	no	—
780	C₂×H(5,𝔽₂)	—	53	1	no	—
781	C₂×H(5,𝔽₂)	—	53	4	no	—
782	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
783	C₂³×D₄	—	53	2	no	—
784	C₂³×D₄	—	53	2	no	—
785	C₂³×D₄	—	53	4	no	—
786	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
787	H(3,𝔽₄)	—	53	4	no	—
788	H(3,𝔽₄)	—	53	4	no	—
789	#560	—	53	4	no	—
790	#560	—	53	4	no	—
791	#560	—	53	8	no	—
792	#560	—	53	8	no	—
793	#551	—	53	4	no	—
794	#551	—	53	8	no	—
795	#551	—	53	8	no	—
796	#551	—	53	4	no	—
797	#551	—	53	8	no	—
798	#551	—	53	8	no	—
799	#551	—	53	8	no	—
800	#551	—	53	8	no	—
801	#551	—	53	8	no	—
802	#551	—	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	—	53	8	no	—
818	#546	—	53	8	no	—
819	#546	—	53	8	no	—
820	#546	C₂×D₅₃	1	8	yes	complemented
821	D₄²	—	53	8	no	—
822	D₄²	—	53	8	no	—
823	D₄²	—	53	8	no	—
824	D₄²	—	53	8	no	—
825	D₄²	—	53	4	no	—
826	D₄²	—	53	8	no	—
827	D₄²	—	53	8	no	—
828	D₄²	—	53	8	no	—
829	D₄²	—	53	4	no	—
830	D₄²	C₂×D₅₃	1	8	yes	complemented
831	#543	—	53	4	no	—
832	#543	—	53	2	no	—
833	#538	—	53	8	no	—
834	#538	—	53	8	no	—
835	#538	—	53	4	no	—
836	#538	—	53	8	no	—
837	#538	—	53	8	no	—
838	#538	—	53	8	no	—
839	#538	—	53	4	no	—
840	#538	—	53	8	no	—
841	#538	—	53	8	no	—
842	#538	—	53	8	no	—
843	#535	—	53	4	no	—
844	#535	—	53	2	no	—
845	#535	—	53	8	no	—
846	#535	—	53	8	no	—
847	#535	—	53	4	no	—
848	#535	—	53	8	no	—
849	#535	C₂×D₅₃	1	2	yes	complemented
850	#534	—	53	2	no	—
851	#534	—	53	2	no	—
852	#534	—	53	2	no	—
853	#534	—	53	4	no	—
854	#534	—	53	4	no	—
855	#534	—	53	4	no	—
856	#534	—	53	4	no	—
857	#534	—	53	8	no	—
858	#534	—	53	8	no	—
859	#534	—	53	8	no	—
860	#534	—	53	4	no	—
861	#534	C₂×D₅₃	1	2	yes	complemented
862	#534	C₂×D₅₃	1	2	yes	complemented
863	#525	—	53	4	no	—
864	#525	—	53	2	no	—
865	#525	—	53	4	no	—
866	#525	—	53	8	no	—
867	#525	—	53	8	no	—
868	#525	—	53	8	no	—
869	#525	C₂×D₅₃	1	2	yes	complemented
870	C₂×#120	—	53	2	no	—
871	C₂×#120	—	53	2	no	—
872	C₂×#120	—	53	2	no	—
873	C₂×#120	—	53	2	no	—
874	C₂×#120	—	53	2	no	—
875	C₂×#120	—	53	8	no	—
876	C₂×#120	—	53	2	no	—
877	C₂×#120	—	53	2	no	—
878	C₂×#120	—	53	8	no	—
879	C₂×#120	—	53	4	no	—
880	C₂×#120	—	53	4	no	—
881	C₂×#120	—	53	8	no	—
882	C₂×#120	—	53	8	no	—
883	C₂×#120	—	53	8	no	—
884	C₂×#120	—	53	8	no	—
885	C₂×#120	—	53	4	no	—
886	C₂×#120	—	53	2	no	—
887	C₂×#120	—	53	4	no	—
888	C₂×#120	C₂×D₅₃	1	2	yes	complemented
889	C₂×#120	C₂×D₅₃	1	2	yes	complemented
890	#518	—	53	1	no	—
891	#518	—	53	2	no	—
892	#518	—	53	8	no	—
893	#518	—	53	2	no	—
894	#518	—	53	4	no	—
895	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
896	C₂²×C₂²⋊C₄	—	53	1	no	—
897	C₂²×C₂²⋊C₄	—	53	2	no	—
898	C₂²×C₂²⋊C₄	—	53	2	no	—
899	C₂²×C₂²⋊C₄	—	53	4	no	—
900	C₅₃	#62817	1	1	yes	characteristic, complemented, Sylow
901	C₂⁵	—	53	4	no	—
902	C₂⁵	—	53	2	no	—
903	C₂⁵	—	53	2	no	—
904	C₂⁵	—	53	2	no	—
905	C₂⁵	—	53	4	no	—
906	C₂⁵	—	53	2	no	—
907	C₂⁵	—	212	4	no	—
908	C₂⁵	—	212	8	no	—
909	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
910	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic, complemented
911	H(5,𝔽₂)	—	4	4	no	—
912	H(5,𝔽₂)	—	212	4	no	—
913	H(5,𝔽₂)	—	212	16	no	—
914	C₂×#41	—	53	4	no	—
915	C₂×#41	—	53	8	no	—
916	C₂×#41	—	53	8	no	—
917	C₂×#41	—	53	2	no	—
918	C₂×#41	—	53	8	no	—
919	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
920	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
921	C₂²×D₄	—	4	4	no	—
922	C₂²×D₄	—	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	2	no	—
932	C₂²×D₄	—	53	4	no	—
933	C₂²×D₄	—	53	8	no	—
934	C₂²×D₄	—	53	8	no	—
935	C₂²×D₄	—	53	8	no	—
936	C₂²×D₄	—	53	8	no	—
937	C₂²×D₄	—	53	8	no	—
938	C₂²×D₄	—	53	8	no	—
939	C₂²×D₄	—	53	8	no	—
940	C₂²×D₄	—	53	4	no	—
941	C₂²×D₄	—	53	8	no	—
942	C₂²×D₄	—	53	2	no	—
943	C₂²×D₄	—	53	4	no	—
944	C₂²×D₄	—	212	8	no	—
945	C₂²×D₄	—	212	16	no	—
946	C₂²×D₄	—	212	8	no	—
947	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
948	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
949	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
950	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
951	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
952	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
953	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
954	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
955	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
956	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
957	C₂³×C₄	—	53	2	no	—
958	C₂³×C₄	—	53	2	no	—
959	C₂³×C₄	—	53	4	no	—
960	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
961	#127	—	53	4	no	—
962	#127	—	53	8	no	—
963	#127	—	53	8	no	—
964	#127	C₂²×D₅₃	1	4	yes	complemented
965	#126	—	53	8	no	—
966	#126	—	53	8	no	—
967	#126	—	53	8	no	—
968	#126	—	53	8	no	—
969	#126	—	53	8	no	—
970	#126	—	53	8	no	—
971	#124	—	53	8	no	—
972	#124	—	53	4	no	—
973	#124	—	53	8	no	—
974	#124	—	53	8	no	—
975	#124	—	53	8	no	—
976	#124	—	53	8	no	—
977	#124	—	53	8	no	—
978	#124	—	53	8	no	—
979	#124	—	53	8	no	—
980	#124	C₂²×D₅₃	1	4	yes	complemented
981	#123	—	53	4	no	—
982	#123	—	53	8	no	—
983	#123	—	53	4	no	—
984	#123	—	53	4	no	—
985	#123	—	53	8	no	—
986	#123	—	53	4	no	—
987	#123	—	53	4	no	—
988	#123	—	53	8	no	—
989	#123	—	53	8	no	—
990	#123	—	53	8	no	—
991	#123	—	53	8	no	—
992	#123	—	53	8	no	—
993	#123	—	53	8	no	—
994	#123	—	53	8	no	—
995	#123	—	53	8	no	—
996	#123	—	53	8	no	—
997	#123	—	53	8	no	—
998	#123	—	53	8	no	—
999	#123	—	53	8	no	—
1000	#123	C₂²×D₅₃	1	4	yes	complemented
1001	#123	C₂²×D₅₃	1	4	yes	complemented
1002	#123	C₂²×D₅₃	1	4	yes	complemented
1003	C₂²⋊Q₈	—	53	8	no	—
1004	C₂²⋊Q₈	—	53	4	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	—	53	8	no	—
1012	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1013	#121	—	53	8	no	—
1014	#121	—	53	8	no	—
1015	#121	—	53	8	no	—
1016	#121	—	53	8	no	—
1017	#121	—	53	8	no	—
1018	#121	—	53	8	no	—
1019	#121	—	53	8	no	—
1020	#121	—	53	8	no	—
1021	#121	—	53	8	no	—
1022	#121	—	53	8	no	—
1023	#121	—	53	8	no	—
1024	#121	—	53	8	no	—
1025	#121	—	53	8	no	—
1026	#121	—	53	8	no	—
1027	#121	—	53	4	no	—
1028	#121	—	53	8	no	—
1029	#121	—	53	8	no	—
1030	#121	—	53	8	no	—
1031	#121	—	53	8	no	—
1032	#121	—	53	8	no	—
1033	#121	—	53	8	no	—
1034	#121	—	53	8	no	—
1035	#121	—	53	8	no	—
1036	#121	—	53	8	no	—
1037	#121	C₂²×D₅₃	1	8	yes	complemented
1038	#121	C₂²×D₅₃	1	8	yes	complemented
1039	#121	C₂²×D₅₃	1	8	yes	complemented
1040	#121	C₂²×D₅₃	1	4	yes	complemented
1041	#120	—	53	4	no	—
1042	#120	—	53	4	no	—
1043	#120	—	53	8	no	—
1044	#120	—	53	4	no	—
1045	#120	—	53	8	no	—
1046	#120	—	53	4	no	—
1047	#120	—	53	8	no	—
1048	#120	—	53	4	no	—
1049	#120	—	53	4	no	—
1050	#120	—	53	4	no	—
1051	#120	—	53	4	no	—
1052	#120	—	53	4	no	—
1053	#120	—	53	8	no	—
1054	#120	—	53	4	no	—
1055	#120	—	53	8	no	—
1056	#120	—	53	8	no	—
1057	#120	—	53	8	no	—
1058	#120	—	53	8	no	—
1059	#120	—	53	8	no	—
1060	#120	—	53	8	no	—
1061	#120	—	53	8	no	—
1062	#120	—	53	4	no	—
1063	#120	—	53	4	no	—
1064	#120	—	53	4	no	—
1065	#120	—	53	4	no	—
1066	#120	—	53	8	no	—
1067	#120	—	53	4	no	—
1068	#120	—	53	4	no	—
1069	#120	—	53	4	no	—
1070	#120	—	53	8	no	—
1071	#120	—	53	8	no	—
1072	#120	—	53	8	no	—
1073	#120	—	53	4	no	—
1074	#120	—	53	8	no	—
1075	#120	—	53	4	no	—
1076	#120	—	53	8	no	—
1077	#120	—	53	8	no	—
1078	#120	—	53	8	no	—
1079	#120	—	53	8	no	—
1080	#120	—	53	8	no	—
1081	#120	—	53	8	no	—
1082	#120	C₂²×D₅₃	1	8	yes	—
1083	#120	C₂²×D₅₃	1	4	yes	complemented
1084	#120	C₂²×D₅₃	1	4	yes	complemented
1085	#120	C₂²×D₅₃	1	4	yes	complemented
1086	#120	C₂²×D₅₃	1	8	yes	complemented
1087	#120	C₂²×D₅₃	1	4	yes	complemented
1088	#120	C₂²×D₅₃	1	4	yes	complemented
1089	C₄×D₄	—	53	8	no	—
1090	C₄×D₄	—	53	8	no	—
1091	C₄×D₄	—	53	8	no	—
1092	C₄×D₄	—	53	8	no	—
1093	C₄×D₄	—	53	8	no	—
1094	C₄×D₄	—	53	8	no	—
1095	C₄×D₄	—	53	8	no	—
1096	C₄×D₄	—	53	8	no	—
1097	C₄×D₄	—	53	8	no	—
1098	C₄×D₄	—	53	8	no	—
1099	C₄×D₄	—	53	8	no	—
1100	C₄×D₄	—	53	8	no	—
1101	C₄×D₄	—	53	8	no	—
1102	C₄×D₄	—	53	8	no	—
1103	C₄×D₄	—	53	8	no	—
1104	C₄×D₄	—	53	8	no	—
1105	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1106	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1107	#117	—	53	2	no	—
1108	#117	—	53	4	no	—
1109	#117	—	53	8	no	—
1110	#117	—	53	4	no	—
1111	#117	—	53	8	no	—
1112	#117	—	53	8	no	—
1113	#117	C₂²×D₅₃	1	2	yes	complemented
1114	C₂×C₂²⋊C₄	—	53	2	no	—
1115	C₂×C₂²⋊C₄	—	53	2	no	—
1116	C₂×C₂²⋊C₄	—	53	2	no	—
1117	C₂×C₂²⋊C₄	—	53	8	no	—
1118	C₂×C₂²⋊C₄	—	53	4	no	—
1119	C₂×C₂²⋊C₄	—	53	4	no	—
1120	C₂×C₂²⋊C₄	—	53	2	no	—
1121	C₂×C₂²⋊C₄	—	53	4	no	—
1122	C₂×C₂²⋊C₄	—	53	4	no	—
1123	C₂×C₂²⋊C₄	—	53	4	no	—
1124	C₂×C₂²⋊C₄	—	53	4	no	—
1125	C₂×C₂²⋊C₄	—	53	8	no	—
1126	C₂×C₂²⋊C₄	—	53	4	no	—
1127	C₂×C₂²⋊C₄	—	53	4	no	—
1128	C₂×C₂²⋊C₄	—	53	4	no	—
1129	C₂×C₂²⋊C₄	—	53	4	no	—
1130	C₂×C₂²⋊C₄	—	53	8	no	—
1131	C₂×C₂²⋊C₄	—	53	8	no	—
1132	C₂×C₂²⋊C₄	—	53	8	no	—
1133	C₂×C₂²⋊C₄	—	53	8	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	4	no	—
1138	C₂×C₂²⋊C₄	—	53	8	no	—
1139	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1140	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1141	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1142	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1143	C₂⁴	—	2	4	no	—
1144	C₂⁴	—	4	4	no	—
1145	C₂⁴	—	4	2	no	—
1146	C₂⁴	—	4	4	no	—
1147	C₂⁴	—	53	2	no	—
1148	C₂⁴	—	53	2	no	—
1149	C₂⁴	—	53	2	no	—
1150	C₂⁴	—	53	4	no	—
1151	C₂⁴	—	53	4	no	—
1152	C₂⁴	—	53	4	no	—
1153	C₂⁴	—	53	4	no	—
1154	C₂⁴	—	53	2	no	—
1155	C₂⁴	—	53	2	no	—
1156	C₂⁴	—	53	8	no	—
1157	C₂⁴	—	53	2	no	—
1158	C₂⁴	—	53	2	no	—
1159	C₂⁴	—	53	2	no	—
1160	C₂⁴	—	106	8	no	—
1161	C₂⁴	—	106	16	no	—
1162	C₂⁴	—	106	8	no	—
1163	C₂⁴	—	212	4	no	—
1164	C₂⁴	—	212	4	no	—
1165	C₂⁴	—	212	4	no	—
1166	C₂⁴	—	212	8	no	—
1167	C₂⁴	—	212	8	no	—
1168	C₂⁴	—	212	8	no	—
1169	C₂⁴	—	212	4	no	—
1170	C₂⁴	—	212	8	no	—
1171	C₂⁴	—	212	8	no	—
1172	C₂⁴	—	212	8	no	—
1173	C₂⁴	—	212	8	no	—
1174	C₂⁴	—	212	8	no	—
1175	C₂⁴	—	212	64	no	—
1176	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1177	C₂⁴	C₂³×D₅₃	1	4	yes	—
1178	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1179	C₂⁴	C₂³×D₅₃	1	2	yes	—
1180	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1181	C₂⁴	C₂³×D₅₃	1	4	yes	—
1182	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1183	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1184	C₂⁴	C₂³×D₅₃	1	2	yes	complemented
1185	#41	—	4	4	no	—
1186	#41	—	4	8	no	—
1187	#41	—	212	4	no	—
1188	#41	—	212	16	no	—
1189	#41	—	212	16	no	—
1190	#41	—	212	8	no	—
1191	#41	—	212	16	no	—
1192	C₂×Q₈	—	53	2	no	—
1193	C₂×Q₈	—	53	8	no	—
1194	C₂×Q₈	C₂³×D₅₃	1	2	yes	complemented
1195	C₂×D₄	—	2	4	no	—
1196	C₂×D₄	—	2	4	no	—
1197	C₂×D₄	—	2	8	no	—
1198	C₂×D₄	—	4	2	no	—
1199	C₂×D₄	—	4	2	no	—
1200	C₂×D₄	—	4	16	no	—
1201	C₂×D₄	—	4	8	no	—
1202	C₂×D₄	—	4	8	no	—
1203	C₂×D₄	—	4	4	no	—
1204	C₂×D₄	—	4	8	no	—
1205	C₂×D₄	—	53	8	no	—
1206	C₂×D₄	—	53	8	no	—
1207	C₂×D₄	—	53	8	no	—
1208	C₂×D₄	—	53	8	no	—
1209	C₂×D₄	—	53	4	no	—
1210	C₂×D₄	—	53	4	no	—
1211	C₂×D₄	—	53	8	no	—
1212	C₂×D₄	—	53	8	no	—
1213	C₂×D₄	—	53	8	no	—
1214	C₂×D₄	—	53	8	no	—
1215	C₂×D₄	—	53	8	no	—
1216	C₂×D₄	—	53	8	no	—
1217	C₂×D₄	—	53	8	no	—
1218	C₂×D₄	—	53	4	no	—
1219	C₂×D₄	—	53	8	no	—
1220	C₂×D₄	—	53	8	no	—
1221	C₂×D₄	—	53	8	no	—
1222	C₂×D₄	—	53	2	no	—
1223	C₂×D₄	—	106	32	no	—
1224	C₂×D₄	—	106	16	no	—
1225	C₂×D₄	—	106	8	no	—
1226	C₂×D₄	—	212	4	no	—
1227	C₂×D₄	—	212	8	no	—
1228	C₂×D₄	—	212	16	no	—
1229	C₂×D₄	—	212	8	no	—
1230	C₂×D₄	—	212	4	no	—
1231	C₂×D₄	—	212	16	no	—
1232	C₂×D₄	—	212	16	no	—
1233	C₂×D₄	—	212	16	no	—
1234	C₂×D₄	—	212	8	no	—
1235	C₂×D₄	—	212	16	no	—
1236	C₂×D₄	—	212	16	no	—
1237	C₂×D₄	—	212	8	no	—
1238	C₂×D₄	—	212	8	no	—
1239	C₂×D₄	—	212	4	no	—
1240	C₂×D₄	—	212	8	no	—
1241	C₂×D₄	—	212	8	no	—
1242	C₂×D₄	—	212	16	no	—
1243	C₂×D₄	—	212	8	no	—
1244	C₂×D₄	—	212	16	no	—
1245	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1246	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1247	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1248	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1249	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1250	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1251	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1252	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1253	C₂×D₄	C₂³×D₅₃	1	2	yes	complemented
1254	C₂×D₄	C₂³×D₅₃	1	4	yes	complemented
1255	C₂×D₄	C₂³×D₅₃	1	8	yes	complemented
1256	C₂²×C₄	—	4	2	no	—
1257	C₂²×C₄	—	53	4	no	—
1258	C₂²×C₄	—	53	2	no	—
1259	C₂²×C₄	—	53	4	no	—
1260	C₂²×C₄	—	53	4	no	—
1261	C₂²×C₄	—	53	4	no	—
1262	C₂²×C₄	—	53	8	no	—
1263	C₂²×C₄	—	53	2	no	—
1264	C₂²×C₄	—	53	4	no	—
1265	C₂²×C₄	—	53	8	no	—
1266	C₂²×C₄	—	53	8	no	—
1267	C₂²×C₄	—	53	8	no	—
1268	C₂²×C₄	—	53	4	no	—
1269	C₂²×C₄	—	53	8	no	—
1270	C₂²×C₄	—	212	4	no	—
1271	C₂²×C₄	—	212	8	no	—
1272	C₂²×C₄	—	212	4	no	—
1273	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1274	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1275	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1276	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1277	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1278	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1279	C₂²×C₄	C₂³×D₅₃	1	2	yes	complemented
1280	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1281	C₄⋊C₄	—	53	8	no	—
1282	C₄⋊C₄	—	53	8	no	—
1283	C₄⋊C₄	—	53	8	no	—
1284	C₄⋊C₄	—	53	8	no	—
1285	C₄⋊C₄	—	53	8	no	—
1286	C₄⋊C₄	—	53	4	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	C₂²⋊C₄	—	53	8	no	—
1292	C₂²⋊C₄	—	53	4	no	—
1293	C₂²⋊C₄	—	53	4	no	—
1294	C₂²⋊C₄	—	53	4	no	—
1295	C₂²⋊C₄	—	53	4	no	—
1296	C₂²⋊C₄	—	53	4	no	—
1297	C₂²⋊C₄	—	53	4	no	—
1298	C₂²⋊C₄	—	53	8	no	—
1299	C₂²⋊C₄	—	53	8	no	—
1300	C₂²⋊C₄	—	53	8	no	—
1301	C₂²⋊C₄	—	53	8	no	—
1302	C₂²⋊C₄	—	53	4	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	8	yes	—
1320	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1321	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1322	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1323	C₄²	—	53	4	no	—
1324	C₄²	—	53	8	no	—
1325	C₄²	—	53	8	no	—
1326	C₄²	C₂³×D₅₃	1	4	yes	complemented
1327	C₂³	—	2	4	no	—
1328	C₂³	—	2	2	no	—
1329	C₂³	—	2	8	no	—
1330	C₂³	—	2	8	no	—
1331	C₂³	—	2	2	no	—
1332	C₂³	—	2	8	no	—
1333	C₂³	—	2	2	no	—
1334	C₂³	—	2	4	no	—
1335	C₂³	—	2	2	no	—
1336	C₂³	—	4	2	no	—
1337	C₂³	—	4	4	no	—
1338	C₂³	—	4	2	no	—
1339	C₂³	—	4	4	no	—
1340	C₂³	—	4	4	no	—
1341	C₂³	—	4	2	no	—
1342	C₂³	—	4	4	no	—
1343	C₂³	—	4	2	no	—
1344	C₂³	—	4	2	no	—
1345	C₂³	—	4	4	no	—
1346	C₂³	—	4	16	no	—
1347	C₂³	—	8	8	no	—
1348	C₂³	—	53	4	no	—
1349	C₂³	—	53	8	no	—
1350	C₂³	—	53	4	no	—
1351	C₂³	—	53	4	no	—
1352	C₂³	—	106	8	no	—
1353	C₂³	—	106	16	no	—
1354	C₂³	—	106	8	no	—
1355	C₂³	—	106	8	no	—
1356	C₂³	—	106	8	no	—
1357	C₂³	—	106	8	no	—
1358	C₂³	—	106	8	no	—
1359	C₂³	—	106	4	no	—
1360	C₂³	—	106	4	no	—
1361	C₂³	—	106	8	no	—
1362	C₂³	—	106	4	no	—
1363	C₂³	—	106	8	no	—
1364	C₂³	—	106	8	no	—
1365	C₂³	—	106	4	no	—
1366	C₂³	—	424	16	no	—
1367	C₂³	—	212	4	no	—
1368	C₂³	—	212	2	no	—
1369	C₂³	—	212	4	no	—
1370	C₂³	—	212	8	no	—
1371	C₂³	—	212	8	no	—
1372	C₂³	—	212	4	no	—
1373	C₂³	—	212	4	no	—
1374	C₂³	—	212	2	no	—
1375	C₂³	—	212	4	no	—
1376	C₂³	—	212	2	no	—
1377	C₂³	—	212	2	no	—
1378	C₂³	—	212	4	no	—
1379	C₂³	—	212	2	no	—
1380	C₂³	—	212	4	no	—
1381	C₂³	—	212	4	no	—
1382	C₂³	—	212	2	no	—
1383	C₂³	—	212	4	no	—
1384	C₂³	—	212	2	no	—
1385	C₂³	—	212	32	no	—
1386	C₂³	—	212	32	no	—
1387	C₂³	—	212	64	no	—
1388	C₂³	—	212	64	no	—
1389	C₂³	—	212	32	no	—
1390	C₂³	#13133262	1	4	yes	complemented
1391	C₂³	C₂⁴×D₅₃	1	2	yes	—
1392	C₂³	C₂⁴×D₅₃	1	4	yes	—
1393	C₂³	C₂⁴×D₅₃	1	2	yes	—
1394	C₂³	C₂⁴×D₅₃	1	2	yes	—
1395	C₂³	C₂⁴×D₅₃	1	2	yes	—
1396	C₂³	C₂⁴×D₅₃	1	2	yes	—
1397	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1398	Q₈	—	4	2	no	—
1399	Q₈	—	212	8	no	—
1400	Q₈	—	212	2	no	—
1401	D₄	—	2	16	no	—
1402	D₄	—	2	8	no	—
1403	D₄	—	2	8	no	—
1404	D₄	—	2	8	no	—
1405	D₄	—	2	8	no	—
1406	D₄	—	4	4	no	—
1407	D₄	—	4	4	no	—
1408	D₄	—	4	2	no	—
1409	D₄	—	4	4	no	—
1410	D₄	—	4	8	no	—
1411	D₄	—	4	8	no	—
1412	D₄	—	106	16	no	—
1413	D₄	—	106	16	no	—
1414	D₄	—	106	16	no	—
1415	D₄	—	106	16	no	—
1416	D₄	—	106	16	no	—
1417	D₄	—	106	8	no	—
1418	D₄	—	106	8	no	—
1419	D₄	—	212	8	no	—
1420	D₄	—	212	8	no	—
1421	D₄	—	212	2	no	—
1422	D₄	—	212	8	no	—
1423	D₄	—	212	8	no	—
1424	D₄	—	212	8	no	—
1425	D₄	—	212	8	no	—
1426	D₄	—	212	8	no	—
1427	D₄	—	212	8	no	—
1428	D₄	—	212	8	no	—
1429	D₄	—	212	4	no	—
1430	C₂×C₄	—	2	2	no	—
1431	C₂×C₄	—	2	2	no	—
1432	C₂×C₄	—	2	4	no	—
1433	C₂×C₄	—	4	4	no	—
1434	C₂×C₄	—	4	4	no	—
1435	C₂×C₄	—	4	4	no	—
1436	C₂×C₄	—	4	2	no	—
1437	C₂×C₄	—	4	4	no	—
1438	C₂×C₄	—	53	8	no	—
1439	C₂×C₄	—	53	8	no	—
1440	C₂×C₄	—	53	4	no	—
1441	C₂×C₄	—	106	16	no	—
1442	C₂×C₄	—	106	8	no	—
1443	C₂×C₄	—	106	4	no	—
1444	C₂×C₄	—	212	8	no	—
1445	C₂×C₄	—	212	8	no	—
1446	C₂×C₄	—	212	8	no	—
1447	C₂×C₄	—	212	4	no	—
1448	C₂×C₄	—	212	4	no	—
1449	C₂×C₄	—	212	4	no	—
1450	C₂×C₄	—	212	4	no	—
1451	C₂×C₄	—	212	8	no	—
1452	C₂×C₄	—	212	4	no	—
1453	C₂×C₄	—	212	2	no	—
1454	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1455	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1456	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1457	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1458	C₂²	—	2	8	no	—
1459	C₂²	—	2	4	no	—
1460	C₂²	—	2	2	no	—
1461	C₂²	—	2	2	no	—
1462	C₂²	—	2	2	no	—
1463	C₂²	—	2	4	no	—
1464	C₂²	—	2	8	no	—
1465	C₂²	—	2	4	no	—
1466	C₂²	—	2	4	no	—
1467	C₂²	—	2	2	no	—
1468	C₂²	—	2	4	no	—
1469	C₂²	—	2	2	no	—
1470	C₂²	—	2	2	no	—
1471	C₂²	—	4	4	no	—
1472	C₂²	—	4	16	no	—
1473	C₂²	—	4	4	no	—
1474	C₂²	—	8	8	no	—
1475	C₂²	—	8	2	no	—
1476	C₂²	—	8	2	no	—
1477	C₂²	—	8	4	no	—
1478	C₂²	—	16	2	no	—
1479	C₂²	—	53	8	no	—
1480	C₂²	—	848	2	no	—
1481	C₂²	—	106	16	no	—
1482	C₂²	—	106	4	no	—
1483	C₂²	—	106	4	no	—
1484	C₂²	—	106	8	no	—
1485	C₂²	—	106	4	no	—
1486	C₂²	—	106	4	no	—
1487	C₂²	—	106	4	no	—
1488	C₂²	—	106	4	no	—
1489	C₂²	—	424	4	no	—
1490	C₂²	—	424	16	no	—
1491	C₂²	—	212	8	no	—
1492	C₂²	—	212	16	no	—
1493	C₂²	—	212	16	no	—
1494	C₂²	—	212	16	no	—
1495	C₂²	—	212	8	no	—
1496	C₂²	—	212	8	no	—
1497	C₂²	—	212	8	no	—
1498	C₂²	—	212	16	no	—
1499	C₂²	—	212	8	no	—
1500	C₂²	H(5,𝔽₂)×D₅₃	1	4	yes	—
1501	C₂²	C₂×#13133262	1	2	yes	—
1502	C₂²	C₂×#13133262	1	4	yes	—
1503	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1504	C₄	—	2	8	no	—
1505	C₄	—	2	2	no	—
1506	C₄	—	2	2	no	—
1507	C₄	—	2	4	no	—
1508	C₄	—	106	8	no	—
1509	C₄	—	106	8	no	—
1510	C₄	—	106	4	no	—
1511	C₂	—	2	4	no	—
1512	C₂	—	2	2	no	—
1513	C₂	—	2	4	no	—
1514	C₂	—	4	2	no	—
1515	C₂	—	4	2	no	—
1516	C₂	—	4	2	no	—
1517	C₂	—	4	4	no	—
1518	C₂	—	106	8	no	—
1519	C₂	—	212	4	no	—
1520	C₂	—	212	4	no	—
1521	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—
1522	C₂	C₂²×#13133262	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3484	C₂
hypercenter	#3484	D₅₃
hypocenter	C₅₃	#62817
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3484

Complements

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

N	H ≅ G/N	type
1. #20288869	C₂	semidirect
2. #20288867	C₂	semidirect
3. #20288865	C₂	semidirect
4. #20288864	C₂	semidirect
5. #20288403	C₂	semidirect
6. #20288402	C₂	semidirect
7. #20288400	C₂	semidirect
8. #20288398	C₂	semidirect
9. #20288397	C₂	semidirect
10. #20288350	C₂	semidirect
11. #20288347	C₂	semidirect
12. #20288346	C₂	semidirect
13. #20288344	C₂	semidirect
14. #20288343	C₂	semidirect
15. C₂²×#13133185	C₂	semidirect
16. C₂×#120×D₅₃	C₂	semidirect
17. C₅₃×#3484	C₂	semidirect
18. C₂⁵×D₅₃	C₂²	semidirect
19. C₂×#13133262	C₂²	semidirect
20. C₂×#13133262	C₂²	semidirect
21. C₂³×C₂²⋊D₅₃	C₂²	semidirect
22. C₂²×D₄×D₅₃	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. #16811366	C₂²	semidirect
25. #16811365	C₂²	semidirect
26. #16811363	C₂²	semidirect
27. #16811361	C₂²	semidirect
28. #16811361	C₂²	semidirect
29. #16811360	C₂²	semidirect
30. #16811304	C₂²	semidirect
31. #16811303	C₂²	semidirect
32. #16811302	C₂²	semidirect
33. #16811302	C₂²	semidirect
34. #16811301	C₂²	semidirect
35. #16811300	C₂²	semidirect
36. #16811299	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. #16811267	C₂²	semidirect
45. #16811265	C₂²	semidirect
46. #16811263	C₂²	semidirect
47. #16811263	C₂²	semidirect
48. #16811262	C₂²	semidirect
49. #16811262	C₂²	semidirect
50. #16811262	C₂²	semidirect
51. #16811261	C₂²	semidirect
52. #16811261	C₂²	semidirect
53. #16811260	C₂²	semidirect
54. #16811260	C₂²	semidirect
55. #16811260	C₂²	semidirect
56. #16811260	C₂²	semidirect
57. #16811258	C₂²	semidirect
58. #16811257	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. #16811249	C₂²	semidirect
67. #16811248	C₂²	semidirect
68. #16811213	C₂²	semidirect
69. #16811210	C₂²	semidirect
70. #16811210	C₂²	semidirect
71. #16811209	C₂²	semidirect
72. #16811208	C₂²	semidirect
73. #16811207	C₂²	semidirect
74. #16811206	C₂²	semidirect
75. #16811206	C₂²	semidirect
76. #16811205	C₂²	semidirect
77. #16811205	C₂²	semidirect
78. #16811190	C₂²	semidirect
79. #16811189	C₂²	semidirect
80. #16811188	C₂²	semidirect
81. #16811188	C₂²	semidirect
82. #16811187	C₂²	semidirect
83. #16811186	C₂²	semidirect
84. #16811185	C₂²	semidirect
85. #16811184	C₂²	semidirect
86. #16811183	C₂²	semidirect
87. #16811183	C₂²	semidirect
88. #16811182	C₂²	semidirect
89. #16811182	C₂²	semidirect
90. #16811182	C₂²	semidirect
91. #16811182	C₂²	semidirect
92. #16811182	C₂²	semidirect
93. #16811181	C₂²	semidirect
94. #16811181	C₂²	semidirect
95. #16811134	C₂²	semidirect
96. #16811133	C₂²	semidirect
97. #16811132	C₂²	semidirect
98. #16811131	C₂²	semidirect
99. #16811130	C₂²	semidirect
100. #16811129	C₂²	semidirect
101. C₂×#13133187	C₂²	semidirect
102. C₂×#13133187	C₂²	semidirect
103. C₂×#13133186	C₂²	semidirect
104. C₂×#13133186	C₂²	semidirect
105. C₂×#13133185	C₂²	semidirect
106. C₂×#13133185	C₂²	semidirect
107. C₂×#13133185	C₂²	semidirect
108. C₂×#13133185	C₂²	semidirect
109. C₂×#13133185	C₂²	semidirect
110. C₂×#13133185	C₂²	semidirect
111. C₂×#13133185	C₂²	semidirect
112. C₂×#13133185	C₂²	semidirect
113. C₂×#13133185	C₂²	semidirect
114. #120×D₅₃	C₂²	semidirect
115. #120×D₅₃	C₂²	semidirect
116. #120×D₅₃	C₂²	semidirect
117. #120×D₅₃	C₂²	semidirect
118. #120×D₅₃	C₂²	semidirect
119. #16811098	C₂²	semidirect
120. #16811098	C₂²	semidirect
121. #16811096	C₂²	semidirect
122. #16811096	C₂²	semidirect
123. #16811095	C₂²	semidirect
124. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
125. C₂²×#11719921	C₂²	semidirect
126. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
127. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
128. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
129. C₂³×D₄×C₅₃	C₂²	semidirect
130. C₅₃×#546	C₂²	semidirect
131. D₄²×C₅₃	C₂²	semidirect
132. C₅₃×#535	C₂²	semidirect
133. C₅₃×#534	C₂²	semidirect
134. C₅₃×#534	C₂²	semidirect
135. C₅₃×#525	C₂²	semidirect
136. C₂×#120×C₅₃	C₂²	semidirect
137. C₂×#120×C₅₃	C₂²	semidirect
138. C₅₃×#518	C₂²	semidirect
146. C₂⁴×D₅₃	C₂³	semidirect
149. C₂×#11719945	C₂³	semidirect
150. C₂×#11719945	C₂³	semidirect
151. C₂×#11719947	C₂³	semidirect
152. C₂×#11719947	C₂³	semidirect
153. C₂×#11719947	C₂³	semidirect
154. C₂²×D₂₁₂	C₂³	semidirect
155. C₂²×D₂₁₂	C₂³	semidirect
159. C₂²×C₂²⋊D₅₃	C₂³	semidirect
160. C₂²×C₂²⋊D₅₃	C₂³	semidirect
161. C₂²×C₂²⋊D₅₃	C₂³	semidirect
162. C₂²×C₂²⋊D₅₃	C₂³	semidirect
163. C₂²×C₂²⋊D₅₃	C₂³	semidirect
164. C₂²×C₂²⋊D₅₃	C₂³	semidirect
165. C₂²×C₂²⋊D₅₃	C₂³	semidirect
166. C₂²×C₂²⋊D₅₃	C₂³	semidirect
167. C₂²×C₂²⋊D₅₃	C₂³	semidirect
168. C₂²×C₂²⋊D₅₃	C₂³	semidirect
172. C₂×D₄×D₅₃	C₂³	semidirect
173. C₂×D₄×D₅₃	C₂³	semidirect
174. C₂×D₄×D₅₃	C₂³	semidirect
175. C₂×D₄×D₅₃	C₂³	semidirect
176. C₂×D₄×D₅₃	C₂³	semidirect
177. C₂×D₄×D₅₃	C₂³	semidirect
178. C₂×D₄×D₅₃	C₂³	semidirect
179. C₂³×Dic₅₃	C₂³	semidirect
180. C₂²×C₄×D₅₃	C₂³	semidirect
181. C₂²×C₄×D₅₃	C₂³	semidirect
182. #13133213	C₂³	semidirect
183. #13133213	C₂³	semidirect
184. #13133213	C₂³	semidirect
185. #13133212	C₂³	semidirect
186. #13133212	C₂³	semidirect
187. #13133212	C₂³	semidirect
188. #13133211	C₂³	semidirect
189. #13133210	C₂³	semidirect
190. #13133210	C₂³	semidirect
191. #13133206	C₂³	semidirect
192. #13133205	C₂³	semidirect
193. #13133204	C₂³	semidirect
194. #13133204	C₂³	semidirect
195. #13133203	C₂³	semidirect
196. #13133203	C₂³	semidirect
197. #13133203	C₂³	semidirect
198. #13133203	C₂³	semidirect
199. #13133203	C₂³	semidirect
200. #13133202	C₂³	semidirect
201. #13133202	C₂³	semidirect
202. #13133202	C₂³	semidirect
203. #13133201	C₂³	semidirect
204. #13133201	C₂³	semidirect
205. #13133201	C₂³	semidirect
206. #13133200	C₂³	semidirect
207. #13133200	C₂³	semidirect
208. #13133200	C₂³	semidirect
209. #13133200	C₂³	semidirect
210. #13133199	C₂³	semidirect
211. #13133199	C₂³	semidirect
212. #13133199	C₂³	semidirect
213. #13133199	C₂³	semidirect
214. #13133198	C₂³	semidirect
215. #13133198	C₂³	semidirect
216. #13133198	C₂³	semidirect
217. #13133198	C₂³	semidirect
218. #13133198	C₂³	semidirect
219. #13133197	C₂³	semidirect
220. #13133196	C₂³	semidirect
221. #13133196	C₂³	semidirect
222. #13133195	C₂³	semidirect
223. #13133195	C₂³	semidirect
224. #13133194	C₂³	semidirect
225. #13133194	C₂³	semidirect
226. #13133194	C₂³	semidirect
227. #13133193	C₂³	semidirect
228. #13133192	C₂³	semidirect
229. #13133191	C₂³	semidirect
230. #13133191	C₂³	semidirect
231. #13133191	C₂³	semidirect
232. #13133191	C₂³	semidirect
233. #13133190	C₂³	semidirect
234. #13133190	C₂³	semidirect
235. #13133190	C₂³	semidirect
236. #13133190	C₂³	semidirect
237. #13133190	C₂³	semidirect
238. #13133189	C₂³	semidirect
239. #13133189	C₂³	semidirect
240. #13133189	C₂³	semidirect
241. #13133189	C₂³	semidirect
242. #13133189	C₂³	semidirect
243. #13133189	C₂³	semidirect
244. #13133189	C₂³	semidirect
245. #13133189	C₂³	semidirect
246. #13133189	C₂³	semidirect
247. #13133189	C₂³	semidirect
248. #13133188	C₂³	semidirect
249. #13133188	C₂³	semidirect
250. #13133188	C₂³	semidirect
251. #13133188	C₂³	semidirect
254. #13133187	C₂³	semidirect
255. #13133187	C₂³	semidirect
256. #13133187	C₂³	semidirect
257. #13133187	C₂³	semidirect
258. #13133187	C₂³	semidirect
259. #13133187	C₂³	semidirect
260. #13133187	C₂³	semidirect
262. #13133186	C₂³	semidirect
263. #13133186	C₂³	semidirect
264. #13133186	C₂³	semidirect
265. #13133186	C₂³	semidirect
266. #13133186	C₂³	semidirect
267. #13133186	C₂³	semidirect
274. #13133185	C₂³	semidirect
275. #13133185	C₂³	semidirect
276. #13133185	C₂³	semidirect
277. #13133185	C₂³	semidirect
278. #13133185	C₂³	semidirect
279. #13133185	C₂³	semidirect
280. #13133185	C₂³	semidirect
281. #13133185	C₂³	semidirect
282. #13133185	C₂³	semidirect
283. #13133185	C₂³	semidirect
284. #13133185	C₂³	semidirect
285. #13133185	C₂³	semidirect
286. #13133185	C₂³	semidirect
287. #13133185	C₂³	semidirect
288. #13133185	C₂³	semidirect
289. #13133185	C₂³	semidirect
290. #13133185	C₂³	semidirect
291. #13133185	C₂³	semidirect
292. #13133185	C₂³	semidirect
293. C₄×D₂₁₂	C₂³	semidirect
294. D₄×Dic₅₃	C₂³	semidirect
295. D₄×Dic₅₃	C₂³	semidirect
296. D₄×Dic₅₃	C₂³	semidirect
297. D₄×Dic₅₃	C₂³	semidirect
298. #13133179	C₂³	semidirect
299. C₄×C₂²⋊D₅₃	C₂³	semidirect
300. C₄×C₂²⋊D₅₃	C₂³	semidirect
301. C₄×C₂²⋊D₅₃	C₂³	semidirect
302. C₄×C₂²⋊D₅₃	C₂³	semidirect
303. C₄×C₂²⋊D₅₃	C₂³	semidirect
304. #13133177	C₂³	semidirect
305. #13133177	C₂³	semidirect
306. #13133177	C₂³	semidirect
307. #13133177	C₂³	semidirect
308. #13133177	C₂³	semidirect
309. #13133176	C₂³	semidirect
310. #13133176	C₂³	semidirect
311. #13133175	C₂³	semidirect
312. #13133174	C₂³	semidirect
313. #13133173	C₂³	semidirect
314. #13133173	C₂³	semidirect
317. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
318. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
319. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
320. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
321. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
322. C₂×C₂²⋊Dic₅₃	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
330. C₂×#11719921	C₂³	semidirect
331. C₂×#11719921	C₂³	semidirect
333. C₂²⋊C₄×D₅₃	C₂³	semidirect
334. C₂²⋊C₄×D₅₃	C₂³	semidirect
335. C₂²⋊C₄×D₅₃	C₂³	semidirect
336. C₂²⋊C₄×D₅₃	C₂³	semidirect
337. C₂²⋊C₄×D₅₃	C₂³	semidirect
338. C₂²⋊C₄×D₅₃	C₂³	semidirect
339. C₂²⋊C₄×D₅₃	C₂³	semidirect
341. C₂⁵×C₅₃	C₂³	semidirect
343. C₂×#41×C₅₃	C₂³	semidirect
344. C₂×#41×C₅₃	C₂³	semidirect
349. C₂²×D₄×C₅₃	C₂³	semidirect
350. C₂²×D₄×C₅₃	C₂³	semidirect
351. C₂²×D₄×C₅₃	C₂³	semidirect
352. C₂²×D₄×C₅₃	C₂³	semidirect
353. C₂²×D₄×C₅₃	C₂³	semidirect
354. C₂²×D₄×C₅₃	C₂³	semidirect
355. C₂²×D₄×C₅₃	C₂³	semidirect
356. C₂³×C₄×C₅₃	C₂³	semidirect
357. #127×C₅₃	C₂³	semidirect
358. #124×C₅₃	C₂³	semidirect
359. #123×C₅₃	C₂³	semidirect
360. #123×C₅₃	C₂³	semidirect
361. #123×C₅₃	C₂³	semidirect
362. C₂²⋊Q₈×C₅₃	C₂³	semidirect
363. #121×C₅₃	C₂³	semidirect
364. #121×C₅₃	C₂³	semidirect
365. #121×C₅₃	C₂³	semidirect
366. #121×C₅₃	C₂³	semidirect
368. #120×C₅₃	C₂³	semidirect
369. #120×C₅₃	C₂³	semidirect
370. #120×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. #117×C₅₃	C₂³	semidirect
378. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
379. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
380. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
393. C₂⁴×C₅₃	C₂⁴	semidirect
422. C₂³×D₅₃	C₂⁴	semidirect
425. C₂×Q₈×C₅₃	C₂⁴	semidirect
444. C₂×D₄×C₅₃	C₂⁴	semidirect
445. C₂×D₄×C₅₃	C₂⁴	semidirect
446. C₂×D₄×C₅₃	C₂⁴	semidirect
453. C₂²×C₄×C₅₃	C₂⁴	semidirect
454. C₂²×C₄×C₅₃	C₂⁴	semidirect
455. C₂²×C₄×C₅₃	C₂⁴	semidirect
479. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
480. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
481. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
488. C₂²×Dic₅₃	C₂⁴	semidirect
489. C₂²×Dic₅₃	C₂⁴	semidirect
490. C₂²×Dic₅₃	C₂⁴	semidirect
509. C₂×D₂₁₂	C₂⁴	semidirect
515. C₂×C₄×D₅₃	C₂⁴	semidirect
516. C₂×C₄×D₅₃	C₂⁴	semidirect
517. C₂×Dic₁₀₆	C₂⁴	semidirect
518. C₂×Dic₁₀₆	C₂⁴	semidirect
519. C₄⋊C₄×C₅₃	C₂⁴	semidirect
520. C₄⋊C₄×C₅₃	C₂⁴	semidirect
525. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
526. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
527. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
528. C₄²×C₅₃	C₂⁴	semidirect
537. C₂²⋊Dic₅₃	C₂⁴	semidirect
538. C₂²⋊Dic₅₃	C₂⁴	semidirect
539. C₂²⋊Dic₅₃	C₂⁴	semidirect
540. C₂²⋊Dic₅₃	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. #11719919	C₂⁴	semidirect
558. #11719919	C₂⁴	semidirect
559. #11719919	C₂⁴	semidirect
560. #11719919	C₂⁴	semidirect
561. #11719919	C₂⁴	semidirect
562. C₄×Dic₅₃	C₂⁴	semidirect
563. C₄×Dic₅₃	C₂⁴	semidirect
564. C₄×Dic₅₃	C₂⁴	semidirect
586. C₂³×C₅₃	H(5,𝔽₂)	semidirect
632. C₂²×D₅₃	H(5,𝔽₂)	semidirect
764. #3484	D₅₃	semidirect
782. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
786. C₂³×D₄	C₂×D₅₃	semidirect
820. #546	C₂×D₅₃	semidirect
830. D₄²	C₂×D₅₃	semidirect
849. #535	C₂×D₅₃	semidirect
861. #534	C₂×D₅₃	semidirect
862. #534	C₂×D₅₃	semidirect
869. #525	C₂×D₅₃	semidirect
888. C₂×#120	C₂×D₅₃	semidirect
889. C₂×#120	C₂×D₅₃	semidirect
895. #518	C₂×D₅₃	semidirect
900. C₅₃	#62817	semidirect
910. C₂⁵	C₂²×D₅₃	semidirect
919. C₂×#41	C₂²×D₅₃	semidirect
920. C₂×#41	C₂²×D₅₃	semidirect
950. C₂²×D₄	C₂²×D₅₃	semidirect
951. C₂²×D₄	C₂²×D₅₃	semidirect
952. C₂²×D₄	C₂²×D₅₃	semidirect
953. C₂²×D₄	C₂²×D₅₃	semidirect
954. C₂²×D₄	C₂²×D₅₃	semidirect
955. C₂²×D₄	C₂²×D₅₃	semidirect
956. C₂²×D₄	C₂²×D₅₃	semidirect
960. C₂³×C₄	C₂²×D₅₃	semidirect
964. #127	C₂²×D₅₃	semidirect
980. #124	C₂²×D₅₃	semidirect
1000. #123	C₂²×D₅₃	semidirect
1001. #123	C₂²×D₅₃	semidirect
1002. #123	C₂²×D₅₃	semidirect
1012. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1037. #121	C₂²×D₅₃	semidirect
1038. #121	C₂²×D₅₃	semidirect
1039. #121	C₂²×D₅₃	semidirect
1040. #121	C₂²×D₅₃	semidirect
1083. #120	C₂²×D₅₃	semidirect
1084. #120	C₂²×D₅₃	semidirect
1085. #120	C₂²×D₅₃	semidirect
1086. #120	C₂²×D₅₃	semidirect
1087. #120	C₂²×D₅₃	semidirect
1088. #120	C₂²×D₅₃	semidirect
1105. C₄×D₄	C₂²×D₅₃	semidirect
1106. C₄×D₄	C₂²×D₅₃	semidirect
1113. #117	C₂²×D₅₃	semidirect
1140. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1141. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1142. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1184. C₂⁴	C₂³×D₅₃	semidirect
1194. C₂×Q₈	C₂³×D₅₃	semidirect
1253. C₂×D₄	C₂³×D₅₃	semidirect
1254. C₂×D₄	C₂³×D₅₃	semidirect
1255. C₂×D₄	C₂³×D₅₃	semidirect
1278. C₂²×C₄	C₂³×D₅₃	semidirect
1279. C₂²×C₄	C₂³×D₅₃	semidirect
1280. C₂²×C₄	C₂³×D₅₃	semidirect
1289. C₄⋊C₄	C₂³×D₅₃	semidirect
1290. C₄⋊C₄	C₂³×D₅₃	semidirect
1320. C₂²⋊C₄	C₂³×D₅₃	semidirect
1321. C₂²⋊C₄	C₂³×D₅₃	semidirect
1322. C₂²⋊C₄	C₂³×D₅₃	semidirect
1326. C₄²	C₂³×D₅₃	semidirect
1390. C₂³	#13133262	semidirect

Maximal subgroups

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

subgroup	index
#20288869	2
#20288867	2
#20288865	2
#20288864	2
#20288403	2
#20288402	2
#20288400	2
#20288398	2
#20288397	2
#20288350	2
#20288347	2
#20288346	2
#20288344	2
#20288343	2
C₂²×#13133185	2
C₂×#120×D₅₃	2
C₅₃×#3484	2
#62817	53