Subgroups — #28292126

Order 13568.

7998 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288764	C₂	1	4	yes	maximal, complemented
2	#20288747	C₂	1	4	yes	maximal, complemented
3	#20288655	C₂	1	8	yes	maximal, complemented
4	#20288567	C₂	1	2	yes	maximal, complemented
5	#20288554	C₂	1	4	yes	maximal, complemented
6	#20288518	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288479	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288424	C₂	1	2	yes	maximal, complemented
9	#20288404	C₂	1	4	yes	maximal, complemented
10	#20288350	C₂	1	2	yes	maximal, complemented
11	#20288319	C₂	1	8	yes	maximal, complemented
12	#20288273	C₂	1	4	yes	maximal, complemented
13	D₄×#11719945	C₂	1	4	yes	maximal, complemented
14	#20288137	C₂	1	2	yes	maximal, complemented
15	#20288124	C₂	1	4	yes	maximal, complemented
16	#20288011	C₂	1	2	yes	maximal, complemented
17	C₂×#16811134	C₂	1	4	yes	maximal, complemented
18	C₄×#13133262	C₂	1	2	yes	maximal, complemented
19	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133262	C₂²	1	2	yes	—
21	C₂²×#11719945	C₂²	1	4	yes	complemented
22	#16811356	C₂²	1	8	yes	complemented
23	#16811343	C₂²	1	4	yes	complemented
24	#16811338	C₂²	1	4	yes	complemented
25	#16811332	C₂²	1	8	yes	complemented
26	#16811330	C₂²	1	4	yes	complemented
27	#16811328	C₂²	1	8	yes	complemented
28	#16811323	C₂²	1	8	yes	complemented
29	#16811322	C₂²	1	16	yes	complemented
30	#16811321	C₂²	1	8	yes	complemented
31	#16811319	C₂²	1	8	yes	complemented
32	#16811313	C₂²	1	8	yes	complemented
33	#16811308	C₂²	1	8	yes	complemented
34	#16811302	C₂²	1	16	yes	complemented
35	#16811299	C₂²	1	16	yes	complemented
36	#16811299	C₂²	1	16	yes	complemented
37	#16811294	C₂²	1	4	yes	complemented
38	D₄×Dic₁₀₆	C₂²	1	4	yes	complemented
39	#16811282	C₂²	1	8	yes	complemented
40	#16811278	C₂²	1	4	yes	complemented
41	#16811277	C₂²	1	4	yes	complemented
42	#16811274	C₂²	1	8	yes	complemented
43	#16811269	C₂²	1	8	yes	complemented
44	#16811268	C₂²	1	8	yes	complemented
45	#16811267	C₂²	1	8	yes	complemented
46	#16811267	C₂²	1	8	yes	complemented
47	#16811263	C₂²	1	16	yes	complemented
48	#16811263	C₂²	1	16	yes	complemented
49	D₄×D₂₁₂	C₂²	1	4	yes	complemented
50	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
51	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
52	#16811254	C₂²	1	2	yes	complemented
53	#16811249	C₂²	1	4	yes	complemented
54	#16811238	C₂²	1	8	yes	complemented
55	#16811224	C₂²	1	8	yes	complemented
56	#16811220	C₂²	1	8	yes	complemented
57	#16811215	C₂²	1	16	yes	complemented
58	#16811211	C₂²	1	8	yes	complemented
59	#16811211	C₂²	1	8	yes	complemented
60	#16811206	C₂²	1	16	yes	complemented
61	#16811204	C₂²	1	2	yes	complemented
62	#16811190	C₂²	1	4	yes	complemented
63	#16811185	C₂²	1	4	yes	complemented
64	#16811182	C₂²	1	8	yes	complemented
65	#16811180	C₂²	1	2	yes	complemented
66	#16811180	C₂²	1	2	yes	complemented
67	#16811180	C₂²	1	2	yes	complemented
68	#16811173	C₂²	1	2	yes	complemented
69	#16811173	C₂²	1	2	yes	complemented
70	#16811173	C₂²	1	2	yes	complemented
71	#16811170	C₂²	1	8	yes	complemented
72	#16811157	C₂²	1	4	yes	complemented
73	#16811157	C₂²	1	4	yes	complemented
74	#16811157	C₂²	1	4	yes	complemented
75	#16811157	C₂²	1	4	yes	complemented
76	#16811157	C₂²	1	4	yes	complemented
77	#16811157	C₂²	1	4	yes	complemented
78	#16811155	C₂²	1	8	yes	complemented
79	#16811153	C₂²	1	16	yes	complemented
80	#16811134	C₂²	1	4	yes	complemented
81	#16811134	C₂²	1	4	yes	complemented
82	#16811134	C₂²	1	4	yes	complemented
83	#16811134	C₂²	1	8	yes	complemented
84	#16811134	C₂²	1	8	yes	complemented
85	#16811134	C₂²	1	8	yes	complemented
86	#16811134	C₂²	1	8	yes	complemented
87	#16811134	C₂²	1	8	yes	complemented
88	#16811134	C₂²	1	8	yes	complemented
89	#16811134	C₂²	1	8	yes	complemented
90	#16811132	C₂²	1	16	yes	complemented
91	C₂×#13133200	C₂²	1	8	yes	complemented
92	C₂×#13133196	C₂²	1	4	yes	complemented
93	C₂×#13133196	C₂²	1	4	yes	complemented
94	C₂×#13133191	C₂²	1	4	yes	complemented
95	C₂×#13133191	C₂²	1	4	yes	complemented
96	C₂×#13133186	C₂²	1	8	yes	complemented
97	#16811104	C₂²	1	4	yes	complemented
98	#16811102	C₂²	1	8	yes	complemented
99	#16811098	C₂²	1	2	yes	—
100	#16811096	C₂²	1	8	yes	complemented
101	#16811095	C₂²	1	8	yes	complemented
102	C₄×#11719945	C₂²	1	4	yes	complemented
103	C₄×#11719945	C₂²	1	4	yes	complemented
104	C₄×#11719945	C₂²	1	4	yes	complemented
105	C₄×#11719947	C₂²	1	8	yes	complemented
106	C₂×C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
107	C₂×C₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
108	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
109	C₂×#13133176	C₂²	1	4	yes	complemented
110	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
111	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	complemented
112	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
113	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
115	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
116	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
118	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
119	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
121	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
122	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	complemented
124	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	#13133262	—	2	16	no	—
126	C₂×#11719945	—	4	16	no	—
127	C₂×#11719945	C₂³	1	4	yes	—
128	C₂×#11719945	C₂³	1	4	yes	—
129	C₂×#11719945	C₂³	1	8	yes	—
130	C₂×#11719945	C₂³	1	4	yes	—
131	C₂×#11719945	C₂³	1	8	yes	complemented
132	C₂×#11719945	C₂³	1	8	yes	complemented
133	C₂×#11719947	C₂³	1	8	yes	—
134	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
135	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
136	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
137	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
138	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
139	C₂×D₄×D₅₃	C₂³	1	8	yes	—
140	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
141	#13133217	C₂³	1	2	yes	complemented
142	#13133217	C₂³	1	2	yes	complemented
143	#13133217	C₂³	1	2	yes	complemented
144	#13133216	C₂³	1	8	yes	complemented
145	#13133214	C₂³	1	2	yes	complemented
146	#13133213	C₂³	1	8	yes	—
147	#13133212	C₂³	1	16	yes	complemented
148	#13133211	C₂³	1	8	yes	complemented
149	#13133211	C₂³	1	8	yes	complemented
150	#13133210	C₂³	1	16	yes	complemented
151	#13133210	C₂³	1	16	yes	complemented
152	#13133209	C₂³	1	4	yes	complemented
153	#13133209	C₂³	1	4	yes	complemented
154	#13133209	C₂³	1	4	yes	complemented
155	#13133208	C₂³	1	8	yes	complemented
156	#13133207	C₂³	1	16	yes	complemented
157	#13133205	C₂³	1	4	yes	complemented
158	#13133205	C₂³	1	4	yes	complemented
159	#13133205	C₂³	1	4	yes	complemented
160	#13133204	C₂³	1	8	yes	—
161	#13133203	C₂³	1	16	yes	complemented
162	#13133203	C₂³	1	16	yes	complemented
163	#13133202	C₂³	1	16	yes	complemented
164	#13133201	C₂³	1	16	yes	complemented
165	#13133200	C₂³	1	16	yes	—
166	#13133200	C₂³	1	8	yes	—
167	#13133200	C₂³	1	8	yes	—
168	#13133200	C₂³	1	8	yes	—
169	#13133200	C₂³	1	16	yes	complemented
170	#13133200	C₂³	1	16	yes	complemented
171	#13133199	C₂³	1	16	yes	complemented
172	#13133199	C₂³	1	16	yes	complemented
173	#13133198	C₂³	1	16	yes	—
174	#13133197	C₂³	1	8	yes	complemented
175	#13133196	C₂³	1	4	yes	—
176	#13133196	C₂³	1	4	yes	—
177	#13133196	C₂³	1	4	yes	—
178	#13133196	C₂³	1	8	yes	—
179	#13133196	C₂³	1	4	yes	—
180	#13133196	C₂³	1	4	yes	—
181	#13133196	C₂³	1	8	yes	—
182	#13133196	C₂³	1	4	yes	—
183	#13133196	C₂³	1	8	yes	complemented
184	#13133196	C₂³	1	8	yes	complemented
185	#13133196	C₂³	1	8	yes	complemented
186	#13133196	C₂³	1	8	yes	complemented
187	#13133195	C₂³	1	16	yes	complemented
188	#13133194	C₂³	1	16	yes	complemented
189	#13133194	C₂³	1	16	yes	complemented
190	#13133192	C₂³	1	8	yes	complemented
191	#13133191	C₂³	1	4	yes	—
192	#13133191	C₂³	1	8	yes	—
193	#13133191	C₂³	1	4	yes	—
194	#13133191	C₂³	1	4	yes	—
195	#13133191	C₂³	1	4	yes	—
196	#13133191	C₂³	1	8	yes	—
197	#13133191	C₂³	1	4	yes	—
198	#13133191	C₂³	1	4	yes	—
199	#13133191	C₂³	1	8	yes	complemented
200	#13133191	C₂³	1	8	yes	complemented
201	#13133191	C₂³	1	8	yes	complemented
202	#13133191	C₂³	1	8	yes	complemented
203	#13133190	C₂³	1	16	yes	complemented
204	#13133190	C₂³	1	16	yes	complemented
205	#13133189	C₂³	1	16	yes	—
206	#13133189	C₂³	1	16	yes	—
207	#13133188	C₂³	1	8	yes	—
208	#13133188	C₂³	1	8	yes	—
209	#13133187	C₂³	1	16	yes	complemented
210	#13133186	C₂³	1	16	yes	—
211	#13133186	C₂³	1	16	yes	—
212	#13133186	C₂³	1	8	yes	—
213	#13133186	C₂³	1	16	yes	—
214	#13133185	C₂³	1	16	yes	—
215	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
216	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
217	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
218	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
219	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
220	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
221	#13133182	C₂³	1	8	yes	complemented
222	C₄×D₂₁₂	C₂³	1	4	yes	complemented
223	C₄×D₂₁₂	C₂³	1	4	yes	complemented
224	C₄×D₂₁₂	C₂³	1	4	yes	complemented
225	C₄×D₂₁₂	C₂³	1	4	yes	complemented
226	C₄×D₂₁₂	C₂³	1	4	yes	complemented
227	C₄×D₂₁₂	C₂³	1	4	yes	complemented
228	D₄×Dic₅₃	C₂³	1	8	yes	—
229	D₄×Dic₅₃	C₂³	1	8	yes	—
230	#13133179	C₂³	1	8	yes	complemented
231	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
232	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
233	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
234	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
235	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
236	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
237	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	—
238	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
239	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
240	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
241	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
242	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
243	#13133177	C₂³	1	16	yes	complemented
244	#13133177	C₂³	1	16	yes	complemented
245	#13133176	C₂³	1	4	yes	—
246	#13133176	C₂³	1	8	yes	—
247	#13133176	C₂³	1	4	yes	—
248	#13133176	C₂³	1	4	yes	—
249	#13133176	C₂³	1	8	yes	complemented
250	#13133176	C₂³	1	8	yes	complemented
251	#13133175	C₂³	1	8	yes	complemented
252	#13133174	C₂³	1	8	yes	complemented
253	#13133174	C₂³	1	8	yes	complemented
254	#13133174	C₂³	1	8	yes	complemented
255	#13133173	C₂³	1	16	yes	complemented
256	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
257	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
258	C₂×#11719919	C₂³	1	8	yes	complemented
259	C₂×#11719919	C₂³	1	8	yes	complemented
260	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
261	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
262	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
263	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	—
264	C₂×#11719921	C₂³	1	8	yes	complemented
265	C₂×#11719921	C₂³	1	8	yes	complemented
266	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
267	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
268	C₄²×D₅₃	C₂³	1	8	yes	complemented
269	C₂⁵×C₅₃	C₂³	1	2	yes	—
270	C₂²×D₄×C₅₃	—	2	8	no	—
271	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
272	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
273	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
274	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₅₃	—	4	8	no	—
277	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
280	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
282	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
283	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
284	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
285	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
286	C₂³×C₄×C₅₃	C₂³	1	4	yes	—
287	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
288	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
289	C₄×D₄×C₅₃	C₂³	1	4	yes	—
290	C₄×D₄×C₅₃	C₂³	1	8	yes	—
291	C₄×D₄×C₅₃	C₂³	1	4	yes	—
292	C₄×D₄×C₅₃	C₂³	1	4	yes	—
293	C₄×D₄×C₅₃	C₂³	1	4	yes	—
294	C₄×D₄×C₅₃	C₂³	1	4	yes	—
295	C₄×D₄×C₅₃	C₂³	1	8	yes	—
296	C₄×D₄×C₅₃	C₂³	1	4	yes	—
297	C₄×D₄×C₅₃	C₂³	1	8	yes	—
298	C₄×D₄×C₅₃	C₂³	1	4	yes	—
299	C₄×D₄×C₅₃	C₂³	1	8	yes	—
300	C₄×D₄×C₅₃	C₂³	1	4	yes	—
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
305	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
311	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
312	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
315	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
316	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
317	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
320	C₂⁴×C₅₃	—	2	8	no	—
321	C₂⁴×C₅₃	—	4	4	no	—
322	C₂⁴×C₅₃	—	4	4	no	—
323	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
325	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
326	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
327	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
328	C₂³×D₅₃	C₂⁴	1	8	yes	—
329	C₂×D₄×C₅₃	—	2	8	no	—
330	C₂×D₄×C₅₃	—	2	16	no	—
331	C₂×D₄×C₅₃	—	2	16	no	—
332	C₂×D₄×C₅₃	—	2	4	no	—
333	C₂×D₄×C₅₃	#41	1	8	yes	complemented
334	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
335	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
336	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
337	C₂²×C₄×C₅₃	—	2	4	no	—
338	C₂²×C₄×C₅₃	—	2	4	no	—
339	C₂²×C₄×C₅₃	—	2	16	no	—
340	C₂²×C₄×C₅₃	—	4	4	no	—
341	C₂²×C₄×C₅₃	—	4	8	no	—
342	C₂²×C₄×C₅₃	—	4	4	no	—
343	C₂²×C₄×C₅₃	—	4	8	no	—
344	C₂²×C₄×C₅₃	—	4	4	no	—
345	C₂²×C₄×C₅₃	—	4	4	no	—
346	C₂²×C₄×C₅₃	—	4	4	no	—
347	C₂²×C₄×C₅₃	—	4	8	no	—
348	C₂²×C₄×C₅₃	—	4	2	no	—
349	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
368	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
370	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
371	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
372	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₂²⋊D₅₃	—	2	32	no	—
376	C₂×C₂²⋊D₅₃	—	4	16	no	—
377	C₂×C₂²⋊D₅₃	—	4	16	no	—
378	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
379	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
380	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
381	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
382	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
383	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
384	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
385	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
386	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
387	#11719947	—	2	32	no	—
388	D₄×D₅₃	—	2	32	no	—
389	#11719945	—	2	16	no	—
390	#11719945	—	2	16	no	—
391	#11719945	—	4	16	no	—
392	#11719945	—	4	16	no	—
393	#11719945	—	4	16	no	—
394	#11719945	—	4	8	no	—
395	C₂×D₂₁₂	—	4	8	no	—
396	C₂×D₂₁₂	C₂⁴	1	4	yes	—
397	C₂×D₂₁₂	C₂⁴	1	4	yes	—
398	C₂×D₂₁₂	C₂⁴	1	4	yes	—
399	C₂×D₂₁₂	C₂⁴	1	8	yes	—
400	C₂×C₄×D₅₃	—	4	16	no	—
401	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
402	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
403	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
404	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
405	C₂×Dic₁₀₆	—	4	8	no	—
406	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
407	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
408	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
409	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
410	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
411	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
412	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
417	C₄²×C₅₃	C₂⁴	1	2	yes	—
418	C₄²×C₅₃	C₂⁴	1	2	yes	—
419	C₄²×C₅₃	C₂⁴	1	2	yes	—
420	C₄²×C₅₃	C₂⁴	1	2	yes	—
421	C₄²×C₅₃	C₂⁴	1	2	yes	—
422	C₄²×C₅₃	C₂⁴	1	2	yes	—
423	C₄²×C₅₃	C₂⁴	1	2	yes	—
424	C₄²×C₅₃	C₂⁴	1	2	yes	—
425	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
426	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
427	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
428	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
429	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
430	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
431	#11719921	C₂⁴	1	8	yes	—
432	#11719921	C₂⁴	1	16	yes	—
433	#11719921	C₂⁴	1	8	yes	—
434	#11719921	C₂⁴	1	8	yes	—
435	#11719921	C₂⁴	1	16	yes	—
436	#11719921	C₂⁴	1	8	yes	—
437	#11719921	C₂⁴	1	8	yes	—
438	#11719921	C₂⁴	1	8	yes	—
439	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
440	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
441	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
442	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
443	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
444	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
445	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
446	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
447	#11719919	C₂⁴	1	16	yes	—
448	#11719919	C₂⁴	1	8	yes	—
449	#11719919	C₂⁴	1	8	yes	—
450	#11719919	C₂⁴	1	16	yes	—
451	#11719919	C₂⁴	1	8	yes	—
452	#11719919	C₂⁴	1	8	yes	—
453	#11719919	C₂⁴	1	8	yes	—
454	#11719919	C₂⁴	1	8	yes	—
455	C₄×Dic₅₃	C₂⁴	1	8	yes	—
456	C₄×Dic₅₃	C₂⁴	1	8	yes	—
457	C₄×Dic₅₃	C₂⁴	1	8	yes	—
458	C₄×Dic₅₃	C₂⁴	1	16	yes	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	2	no	—
461	C₂³×C₅₃	—	2	2	no	—
462	C₂³×C₅₃	—	2	8	no	—
463	C₂³×C₅₃	—	2	8	no	—
464	C₂³×C₅₃	—	2	4	no	—
465	C₂³×C₅₃	—	2	8	no	—
466	C₂³×C₅₃	—	2	8	no	—
467	C₂³×C₅₃	—	4	2	no	—
468	C₂³×C₅₃	—	4	4	no	—
469	C₂³×C₅₃	—	4	2	no	—
470	C₂³×C₅₃	—	4	2	no	—
471	C₂³×C₅₃	—	4	4	no	—
472	C₂³×C₅₃	—	4	2	no	—
473	C₂³×C₅₃	—	4	32	no	—
474	C₂³×C₅₃	C₂×#41	1	8	yes	complemented
475	C₂³×C₅₃	C₂⁵	1	4	yes	—
476	C₂³×C₅₃	C₂⁵	1	4	yes	—
477	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
478	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
479	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
480	C₂²×D₅₃	—	2	16	no	—
481	C₂²×D₅₃	—	4	8	no	—
482	C₂²×D₅₃	—	4	8	no	—
483	C₂²×D₅₃	C₂⁵	1	8	yes	—
484	D₄×C₅₃	—	2	16	no	—
485	D₄×C₅₃	—	2	8	no	—
486	D₄×C₅₃	C₂×#41	1	16	yes	complemented
487	C₂×C₄×C₅₃	—	2	2	no	—
488	C₂×C₄×C₅₃	—	2	8	no	—
489	C₂×C₄×C₅₃	—	2	2	no	—
490	C₂×C₄×C₅₃	—	2	4	no	—
491	C₂×C₄×C₅₃	—	2	4	no	—
492	C₂×C₄×C₅₃	—	2	4	no	—
493	C₂×C₄×C₅₃	—	2	8	no	—
494	C₂×C₄×C₅₃	—	2	8	no	—
495	C₂×C₄×C₅₃	—	2	8	no	—
496	C₂×C₄×C₅₃	—	2	8	no	—
497	C₂×C₄×C₅₃	—	2	2	no	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	2	no	—
500	C₂×C₄×C₅₃	—	2	2	no	—
501	C₂×C₄×C₅₃	—	4	2	no	—
502	C₂×C₄×C₅₃	—	4	4	no	—
503	C₂×C₄×C₅₃	—	4	4	no	—
504	C₂×C₄×C₅₃	—	4	4	no	—
505	C₂×C₄×C₅₃	—	4	2	no	—
506	C₂×C₄×C₅₃	—	4	4	no	—
507	C₂×C₄×C₅₃	—	4	4	no	—
508	C₂×C₄×C₅₃	—	4	1	no	—
509	C₂×C₄×C₅₃	—	4	2	no	—
510	C₂×C₄×C₅₃	—	4	1	no	—
511	C₂×C₄×C₅₃	C₂×#41	1	4	yes	complemented
512	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	complemented
513	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
514	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
515	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
516	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
517	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
518	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
519	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
520	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
521	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
522	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
523	C₂²⋊D₅₃	—	2	16	no	—
524	C₂²⋊D₅₃	—	2	32	no	—
525	C₂²⋊D₅₃	—	2	16	no	—
526	C₂²⋊D₅₃	—	2	16	no	—
527	C₂²⋊D₅₃	—	4	16	no	—
528	C₂²⋊D₅₃	—	4	16	no	—
529	C₂×Dic₅₃	—	2	16	no	—
530	C₂×Dic₅₃	—	4	8	no	—
531	C₂×Dic₅₃	—	4	8	no	—
532	C₂×Dic₅₃	C₂⁵	1	8	yes	—
533	C₂×Dic₅₃	C₂⁵	1	8	yes	—
534	C₂×Dic₅₃	C₂⁵	1	8	yes	—
535	D₂₁₂	—	2	8	no	—
536	D₂₁₂	—	2	8	no	—
537	D₂₁₂	—	4	8	no	—
538	D₂₁₂	—	4	4	no	—
539	C₄×D₅₃	—	2	16	no	—
540	C₄×D₅₃	—	2	16	no	—
541	C₄×D₅₃	—	4	16	no	—
542	C₄×D₅₃	—	4	8	no	—
543	Dic₁₀₆	—	2	8	no	—
544	Dic₁₀₆	—	2	8	no	—
545	Dic₁₀₆	—	4	8	no	—
546	Dic₁₀₆	—	4	4	no	—
547	#62773	—	53	1	no	maximal, Sylow
548	C₂²×C₅₃	—	2	8	no	—
549	C₂²×C₅₃	—	2	1	no	—
550	C₂²×C₅₃	—	2	1	no	—
551	C₂²×C₅₃	—	2	4	no	—
552	C₂²×C₅₃	—	2	1	no	—
553	C₂²×C₅₃	—	2	1	no	—
554	C₂²×C₅₃	—	2	4	no	—
555	C₂²×C₅₃	—	2	1	no	—
556	C₂²×C₅₃	—	2	1	no	—
557	C₂²×C₅₃	—	2	4	no	—
558	C₂²×C₅₃	—	2	4	no	—
559	C₂²×C₅₃	—	2	4	no	—
560	C₂²×C₅₃	—	4	8	no	—
561	C₂²×C₅₃	—	4	16	no	—
562	C₂²×C₅₃	—	4	16	no	—
563	C₂²×C₅₃	—	4	8	no	—
564	C₂²×C₅₃	C₂²×#41	1	8	yes	—
565	C₂²×C₅₃	C₂²×#41	1	2	yes	—
566	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
567	C₂²×C₅₃	#585	1	2	yes	—
568	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
569	C₂×D₅₃	—	2	8	no	—
570	C₂×D₅₃	—	2	8	no	—
571	C₂×D₅₃	—	2	8	no	—
572	C₂×D₅₃	—	8	16	no	—
573	C₄×C₅₃	—	2	2	no	—
574	C₄×C₅₃	—	2	4	no	—
575	C₄×C₅₃	—	2	4	no	—
576	C₄×C₅₃	—	2	1	no	—
577	C₄×C₅₃	—	2	1	no	—
578	C₄×C₅₃	—	2	2	no	—
579	C₄×C₅₃	—	2	2	no	—
580	C₄×C₅₃	C₂²×#41	1	4	yes	—
581	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
582	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
583	Dic₅₃	—	2	8	no	—
584	Dic₅₃	—	2	8	no	—
585	Dic₅₃	—	2	8	no	—
586	#3520	—	53	4	no	—
587	#3519	—	53	4	no	—
588	#3513	—	53	8	no	—
589	#3506	—	53	2	no	—
590	#3505	—	53	4	no	—
591	#3501	—	53	1	no	—
592	#3496	—	53	1	no	—
593	#3492	—	53	2	no	—
594	#3490	—	53	4	no	—
595	#3484	—	53	2	no	—
596	#3481	—	53	8	no	—
597	#3475	—	53	4	no	—
598	D₄×#41	—	53	4	no	—
599	#3460	—	53	2	no	—
600	#3459	—	53	4	no	—
601	#3444	—	53	2	no	—
602	C₂×#525	—	53	4	no	—
603	C₄×H(5,𝔽₂)	—	53	2	no	—
604	C₂²×C₄×D₄	D₅₃	1	1	yes	characteristic, complemented
605	C₂×C₅₃	—	2	8	no	—
606	C₂×C₅₃	—	2	2	no	—
607	C₂×C₅₃	—	2	2	no	—
608	C₂×C₅₃	—	2	2	no	—
609	C₂×C₅₃	—	4	4	no	—
610	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
611	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
613	D₅₃	—	4	8	no	—
614	C₂×H(5,𝔽₂)	—	53	2	no	—
615	C₂²×#41	—	53	4	no	—
616	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
617	C₂⁴×C₄	C₂×D₅₃	1	2	yes	complemented
618	#559	—	53	8	no	—
619	#556	—	53	4	no	—
620	#555	—	53	4	no	—
621	#554	—	53	4	no	—
622	#554	—	53	8	no	—
623	#554	—	53	8	no	—
624	#553	—	53	8	no	—
625	#553	—	53	16	no	—
626	#553	—	53	8	no	—
627	#553	—	53	8	no	—
628	#552	—	53	8	no	—
629	#552	—	53	8	no	—
630	#551	—	53	16	no	—
631	#551	—	53	16	no	—
632	#551	—	53	16	no	—
633	#550	—	53	4	no	—
634	D₄×Q₈	—	53	4	no	—
635	#548	—	53	8	no	—
636	#547	—	53	4	no	—
637	#547	—	53	4	no	—
638	#547	—	53	8	no	—
639	#546	—	53	8	no	—
640	#546	—	53	8	no	—
641	#546	—	53	8	no	—
642	#546	—	53	8	no	—
643	#546	—	53	16	no	—
644	#546	—	53	16	no	—
645	D₄²	—	53	8	no	—
646	D₄²	—	53	8	no	—
647	D₄²	—	53	4	no	—
648	#544	—	53	2	no	—
649	#543	—	53	4	no	—
650	#542	—	53	8	no	—
651	#540	—	53	8	no	—
652	#539	—	53	16	no	—
653	#539	—	53	8	no	—
654	#538	—	53	16	no	—
655	#538	—	53	8	no	—
656	#538	—	53	8	no	—
657	#537	—	53	2	no	—
658	#535	—	53	4	no	—
659	#534	—	53	8	no	—
660	#534	—	53	4	no	—
661	#533	—	53	2	no	—
662	#533	—	53	2	no	—
663	#533	—	53	2	no	—
664	#532	—	53	8	no	—
665	#532	—	53	2	no	—
666	#532	—	53	2	no	—
667	#532	—	53	2	no	—
668	#529	—	53	16	no	—
669	#529	—	53	8	no	—
670	#529	—	53	4	no	—
671	#529	—	53	4	no	—
672	#529	—	53	4	no	—
673	#529	—	53	4	no	—
674	#529	—	53	4	no	—
675	#529	—	53	4	no	—
676	#525	—	53	4	no	—
677	#525	—	53	8	no	—
678	#525	—	53	8	no	—
679	#525	—	53	8	no	—
680	#525	—	53	8	no	—
681	#525	—	53	8	no	—
682	#525	—	53	8	no	—
683	#525	—	53	8	no	—
684	#525	—	53	4	no	—
685	#525	—	53	4	no	—
686	#525	—	53	16	no	—
687	C₂×#123	—	53	8	no	—
688	C₂×C₂²⋊Q₈	—	53	4	no	—
689	C₂×C₂²⋊Q₈	—	53	4	no	—
690	C₂×#121	—	53	4	no	—
691	C₂×#121	—	53	4	no	—
692	C₂×#120	—	53	8	no	—
693	#520	—	53	8	no	—
694	#520	—	53	4	no	—
695	#518	—	53	2	no	—
696	#518	—	53	8	no	—
697	#518	—	53	8	no	—
698	C₄×#41	—	53	8	no	—
699	C₄×#41	—	53	4	no	—
700	C₄×#41	—	53	4	no	—
701	C₄×#41	—	53	4	no	—
702	C₂×C₄×D₄	—	53	8	no	—
703	C₂×C₄×D₄	—	53	8	no	—
704	C₂×C₄×D₄	—	53	8	no	—
705	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
706	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
707	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
708	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
709	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
710	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
711	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
712	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
713	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
714	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
715	C₂×#117	—	53	4	no	—
716	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
717	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	complemented
718	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
719	C₅₃	#62773	1	1	yes	characteristic, complemented, Sylow
720	C₂⁵	C₂²×D₅₃	1	2	yes	—
721	H(5,𝔽₂)	—	106	16	no	—
722	C₂×#41	—	53	8	no	—
723	C₂×#41	—	53	4	no	—
724	C₂×#41	—	53	4	no	—
725	C₂×#41	—	53	4	no	—
726	C₂×#41	—	53	8	no	—
727	C₂×#41	—	53	8	no	—
728	C₂×#41	—	53	8	no	—
729	C₂×#41	—	212	16	no	—
730	C₂²×Q₈	—	53	4	no	—
731	C₂²×D₄	—	2	8	no	—
732	C₂²×D₄	—	53	8	no	—
733	C₂²×D₄	—	53	8	no	—
734	C₂²×D₄	—	53	8	no	—
735	C₂²×D₄	—	53	8	no	—
736	C₂²×D₄	—	53	4	no	—
737	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
738	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
739	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
740	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
741	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
742	C₂³×C₄	—	4	8	no	—
743	C₂³×C₄	—	53	8	no	—
744	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
745	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
746	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
747	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
748	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
749	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
750	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
751	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
752	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
753	C₂³×C₄	C₂²×D₅₃	1	4	yes	—
754	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
755	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
756	C₄⋊Q₈	—	53	8	no	—
757	C₄⋊Q₈	—	53	2	no	—
758	C₄⋊Q₈	—	53	2	no	—
759	C₄⋊Q₈	—	53	2	no	—
760	#127	—	53	8	no	—
761	#127	—	53	2	no	—
762	#126	—	53	16	no	—
763	#126	—	53	16	no	—
764	#126	—	53	16	no	—
765	#126	—	53	8	no	—
766	#126	—	53	8	no	—
767	#125	—	53	16	no	—
768	#125	—	53	8	no	—
769	#125	—	53	4	no	—
770	#125	—	53	4	no	—
771	#125	—	53	4	no	—
772	#124	—	53	8	no	—
773	#124	—	53	16	no	—
774	#124	—	53	16	no	—
775	#124	—	53	4	no	—
776	#124	—	53	4	no	—
777	#124	—	53	4	no	—
778	#123	—	53	16	no	—
779	#123	—	53	8	no	—
780	#123	—	53	16	no	—
781	#123	—	53	16	no	—
782	#123	—	53	16	no	—
783	#123	—	53	8	no	—
784	#123	—	53	8	no	—
785	#123	—	53	16	no	—
786	#123	—	53	16	no	—
787	#123	—	53	16	no	—
788	#123	—	53	16	no	—
789	C₂²⋊Q₈	—	53	4	no	—
790	C₂²⋊Q₈	—	53	4	no	—
791	C₂²⋊Q₈	—	53	8	no	—
792	C₂²⋊Q₈	—	53	8	no	—
793	C₂²⋊Q₈	—	53	8	no	—
794	C₂²⋊Q₈	—	53	8	no	—
795	C₂²⋊Q₈	—	53	8	no	—
796	C₂²⋊Q₈	—	53	8	no	—
797	C₂²⋊Q₈	—	53	4	no	—
798	C₂²⋊Q₈	—	53	4	no	—
799	C₂²⋊Q₈	—	53	4	no	—
800	C₂²⋊Q₈	—	53	4	no	—
801	C₂²⋊Q₈	—	53	16	no	—
802	C₂²⋊Q₈	—	53	8	no	—
803	C₂²⋊Q₈	—	53	16	no	—
804	C₂²⋊Q₈	—	53	16	no	—
805	#121	—	53	16	no	—
806	#121	—	53	16	no	—
807	#121	—	53	8	no	—
808	#121	—	53	8	no	—
809	#121	—	53	4	no	—
810	#121	—	53	4	no	—
811	#121	—	53	8	no	—
812	#121	—	53	8	no	—
813	#121	—	53	8	no	—
814	#121	—	53	8	no	—
815	#121	—	53	8	no	—
816	#121	—	53	8	no	—
817	#121	—	53	4	no	—
818	#121	—	53	4	no	—
819	#121	—	53	4	no	—
820	#121	—	53	4	no	—
821	#121	—	53	8	no	—
822	#121	—	53	16	no	—
823	#121	—	53	16	no	—
824	#120	—	53	8	no	—
825	#120	—	53	16	no	—
826	#120	—	53	16	no	—
827	#120	—	53	16	no	—
828	#120	—	53	16	no	—
829	#120	—	53	16	no	—
830	C₄×Q₈	—	53	8	no	—
831	C₄×Q₈	—	53	4	no	—
832	C₄×Q₈	—	53	4	no	—
833	C₄×Q₈	—	53	4	no	—
834	C₄×Q₈	—	53	4	no	—
835	C₄×Q₈	—	53	4	no	—
836	C₄×Q₈	—	53	4	no	—
837	C₄×D₄	—	53	8	no	—
838	C₄×D₄	—	53	8	no	—
839	C₄×D₄	—	53	8	no	—
840	C₄×D₄	—	53	8	no	—
841	C₄×D₄	—	53	16	no	—
842	C₄×D₄	—	53	16	no	—
843	C₄×D₄	—	53	16	no	—
844	C₄×D₄	—	53	16	no	—
845	C₄×D₄	—	53	16	no	—
846	C₄×D₄	—	53	16	no	—
847	C₄×D₄	—	53	8	no	—
848	C₄×D₄	—	53	8	no	—
849	C₄×D₄	—	53	8	no	—
850	C₄×D₄	—	53	8	no	—
851	C₄×D₄	—	53	8	no	—
852	C₄×D₄	—	53	16	no	—
853	C₄×D₄	—	53	16	no	—
854	C₄×D₄	—	53	4	no	—
855	C₄×D₄	—	53	4	no	—
856	C₄×D₄	—	53	4	no	—
857	C₄×D₄	—	53	4	no	—
858	C₄×D₄	—	53	4	no	—
859	C₄×D₄	—	53	4	no	—
860	C₄×D₄	C₂²×D₅₃	1	4	yes	—
861	C₄×D₄	C₂²×D₅₃	1	4	yes	—
862	C₄×D₄	C₂²×D₅₃	1	4	yes	—
863	C₄×D₄	C₂²×D₅₃	1	4	yes	—
864	C₄×D₄	C₂²×D₅₃	1	8	yes	—
865	C₄×D₄	C₂²×D₅₃	1	4	yes	—
866	C₄×D₄	C₂²×D₅₃	1	8	yes	—
867	C₄×D₄	C₂²×D₅₃	1	4	yes	—
868	C₄×D₄	C₂²×D₅₃	1	8	yes	—
869	C₄×D₄	C₂²×D₅₃	1	4	yes	—
870	C₄×D₄	C₂²×D₅₃	1	8	yes	—
871	C₄×D₄	C₂²×D₅₃	1	4	yes	—
872	#117	—	53	4	no	—
873	#117	—	53	8	no	—
874	#117	—	53	8	no	—
875	#117	—	53	8	no	—
876	#117	—	53	4	no	—
877	#117	—	53	4	no	—
878	#117	—	53	8	no	—
879	#117	—	53	16	no	—
880	#117	—	53	8	no	—
881	#117	—	53	8	no	—
882	#117	—	53	8	no	—
883	C₂×C₄⋊C₄	—	53	4	no	—
884	C₂×C₄⋊C₄	—	53	4	no	—
885	C₂×C₄⋊C₄	—	53	8	no	—
886	C₂×C₄⋊C₄	—	53	8	no	—
887	C₂×C₄⋊C₄	—	53	8	no	—
888	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
891	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
892	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
893	C₂×C₂²⋊C₄	—	53	8	no	—
894	C₂×C₂²⋊C₄	—	53	8	no	—
895	C₂×C₂²⋊C₄	—	53	8	no	—
896	C₂×C₂²⋊C₄	—	53	8	no	—
897	C₂×C₂²⋊C₄	—	53	8	no	—
898	C₂×C₂²⋊C₄	—	53	16	no	—
899	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
900	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
901	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
902	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
903	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
904	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
905	C₂×C₄²	—	53	8	no	—
906	C₂×C₄²	—	53	8	no	—
907	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
908	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
909	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
910	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
911	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
912	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
913	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
914	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
915	C₂⁴	—	2	8	no	—
916	C₂⁴	—	4	4	no	—
917	C₂⁴	—	4	4	no	—
918	C₂⁴	—	53	8	no	—
919	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
920	C₂⁴	C₂³×D₅₃	1	4	yes	—
921	C₂⁴	C₂³×D₅₃	1	4	yes	—
922	C₂⁴	C₂³×D₅₃	1	2	yes	—
923	C₂⁴	C₂³×D₅₃	1	2	yes	—
924	#41	—	106	32	no	—
925	#41	—	106	16	no	—
926	#41	—	106	16	no	—
927	#41	—	212	16	no	—
928	#41	—	212	8	no	—
929	#41	—	212	16	no	—
930	#41	—	212	16	no	—
931	C₂×Q₈	—	53	4	no	—
932	C₂×Q₈	—	53	4	no	—
933	C₂×Q₈	—	53	4	no	—
934	C₂×Q₈	—	53	8	no	—
935	C₂×Q₈	—	212	8	no	—
936	C₂×D₄	—	2	8	no	—
937	C₂×D₄	—	2	16	no	—
938	C₂×D₄	—	2	16	no	—
939	C₂×D₄	—	2	4	no	—
940	C₂×D₄	—	53	8	no	—
941	C₂×D₄	—	53	16	no	—
942	C₂×D₄	—	53	8	no	—
943	C₂×D₄	—	53	8	no	—
944	C₂×D₄	—	53	16	no	—
945	C₂×D₄	—	53	16	no	—
946	C₂×D₄	—	53	4	no	—
947	C₂×D₄	—	53	4	no	—
948	C₂×D₄	—	53	4	no	—
949	C₂×D₄	—	53	8	no	—
950	C₂×D₄	—	106	32	no	—
951	C₂×D₄	—	106	32	no	—
952	C₂×D₄	—	212	8	no	—
953	C₂×D₄	—	212	16	no	—
954	C₂×D₄	—	212	16	no	—
955	C₂×D₄	#11719945	1	8	yes	complemented
956	C₂×D₄	C₂³×D₅₃	1	8	yes	—
957	C₂×D₄	C₂³×D₅₃	1	4	yes	—
958	C₂×D₄	C₂³×D₅₃	1	4	yes	—
959	C₂²×C₄	—	2	4	no	—
960	C₂²×C₄	—	2	4	no	—
961	C₂²×C₄	—	2	16	no	—
962	C₂²×C₄	—	4	4	no	—
963	C₂²×C₄	—	4	8	no	—
964	C₂²×C₄	—	4	4	no	—
965	C₂²×C₄	—	4	8	no	—
966	C₂²×C₄	—	4	4	no	—
967	C₂²×C₄	—	4	4	no	—
968	C₂²×C₄	—	4	8	no	—
969	C₂²×C₄	—	4	4	no	—
970	C₂²×C₄	—	4	2	no	—
971	C₂²×C₄	—	53	8	no	—
972	C₂²×C₄	—	53	8	no	—
973	C₂²×C₄	—	53	8	no	—
974	C₂²×C₄	—	53	8	no	—
975	C₂²×C₄	—	53	8	no	—
976	C₂²×C₄	—	53	8	no	—
977	C₂²×C₄	—	53	16	no	—
978	C₂²×C₄	—	212	16	no	—
979	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
980	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
981	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
982	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
983	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
984	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
985	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
986	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
987	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
988	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
989	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
990	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
991	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
992	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
993	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
994	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
995	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
996	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
997	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
998	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
999	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1000	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1001	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1002	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1003	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1004	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1005	C₄⋊C₄	—	53	4	no	—
1006	C₄⋊C₄	—	53	4	no	—
1007	C₄⋊C₄	—	53	4	no	—
1008	C₄⋊C₄	—	53	16	no	—
1009	C₄⋊C₄	—	53	8	no	—
1010	C₄⋊C₄	—	53	8	no	—
1011	C₄⋊C₄	—	53	8	no	—
1012	C₄⋊C₄	—	53	8	no	—
1013	C₄⋊C₄	—	53	16	no	—
1014	C₄⋊C₄	—	53	4	no	—
1015	C₄⋊C₄	—	53	8	no	—
1016	C₄⋊C₄	—	53	8	no	—
1017	C₄⋊C₄	—	53	8	no	—
1018	C₄⋊C₄	—	53	8	no	—
1019	C₄⋊C₄	—	53	4	no	—
1020	C₄⋊C₄	—	53	4	no	—
1021	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1022	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1023	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1024	C₂²⋊C₄	—	53	8	no	—
1025	C₂²⋊C₄	—	53	8	no	—
1026	C₂²⋊C₄	—	53	16	no	—
1027	C₂²⋊C₄	—	53	8	no	—
1028	C₂²⋊C₄	—	53	16	no	—
1029	C₂²⋊C₄	—	53	16	no	—
1030	C₂²⋊C₄	—	53	16	no	—
1031	C₂²⋊C₄	—	53	8	no	—
1032	C₂²⋊C₄	—	53	8	no	—
1033	C₂²⋊C₄	—	53	8	no	—
1034	C₂²⋊C₄	—	53	16	no	—
1035	C₂²⋊C₄	—	53	8	no	—
1036	C₂²⋊C₄	—	53	8	no	—
1037	C₂²⋊C₄	—	53	8	no	—
1038	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1039	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1040	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1041	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1042	C₄²	—	53	16	no	—
1043	C₄²	—	53	8	no	—
1044	C₄²	—	53	8	no	—
1045	C₄²	—	53	8	no	—
1046	C₄²	C₂³×D₅₃	1	2	yes	—
1047	C₄²	C₂³×D₅₃	1	2	yes	—
1048	C₄²	C₂³×D₅₃	1	2	yes	—
1049	C₄²	C₂³×D₅₃	1	2	yes	—
1050	C₄²	C₂³×D₅₃	1	2	yes	—
1051	C₄²	C₂³×D₅₃	1	2	yes	—
1052	C₄²	C₂³×D₅₃	1	2	yes	—
1053	C₄²	C₂³×D₅₃	1	2	yes	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	8	no	—
1058	C₂³	—	2	8	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	8	no	—
1061	C₂³	—	2	8	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	2	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	4	no	—
1067	C₂³	—	4	2	no	—
1068	C₂³	—	4	32	no	—
1069	C₂³	—	53	8	no	—
1070	C₂³	—	106	16	no	—
1071	C₂³	—	212	8	no	—
1072	C₂³	—	212	8	no	—
1073	C₂³	C₂×#11719945	1	8	yes	complemented
1074	C₂³	C₂⁴×D₅₃	1	4	yes	—
1075	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1076	C₂³	C₂⁴×D₅₃	1	4	yes	—
1077	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1078	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1079	Q₈	—	106	8	no	—
1080	Q₈	—	106	8	no	—
1081	Q₈	—	212	8	no	—
1082	Q₈	—	212	4	no	—
1083	D₄	—	2	16	no	—
1084	D₄	—	2	8	no	—
1085	D₄	—	106	16	no	—
1086	D₄	—	106	32	no	—
1087	D₄	—	106	16	no	—
1088	D₄	—	106	16	no	—
1089	D₄	—	106	8	no	—
1090	D₄	—	106	8	no	—
1091	D₄	—	212	8	no	—
1092	D₄	—	212	4	no	—
1093	D₄	—	212	16	no	—
1094	D₄	—	212	16	no	—
1095	D₄	C₂×#11719945	1	16	yes	complemented
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	8	no	—
1099	C₂×C₄	—	2	4	no	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	2	4	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	8	no	—
1107	C₂×C₄	—	2	8	no	—
1108	C₂×C₄	—	2	8	no	—
1109	C₂×C₄	—	2	8	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	53	8	no	—
1121	C₂×C₄	—	53	8	no	—
1122	C₂×C₄	—	53	8	no	—
1123	C₂×C₄	—	106	16	no	—
1124	C₂×C₄	—	106	16	no	—
1125	C₂×C₄	—	106	16	no	—
1126	C₂×C₄	—	212	16	no	—
1127	C₂×C₄	—	212	8	no	—
1128	C₂×C₄	—	212	8	no	—
1129	C₂×C₄	—	212	8	no	—
1130	C₂×C₄	C₂×#11719945	1	4	yes	complemented
1131	C₂×C₄	#13133262	1	4	yes	complemented
1132	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1133	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1134	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1135	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1136	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1137	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1138	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1139	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1140	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1141	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1142	C₂²	—	2	8	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	4	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	4	no	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	4	8	no	—
1155	C₂²	—	4	16	no	—
1156	C₂²	—	4	16	no	—
1157	C₂²	—	4	8	no	—
1158	C₂²	—	106	8	no	—
1159	C₂²	—	106	8	no	—
1160	C₂²	—	106	8	no	—
1161	C₂²	—	424	16	no	—
1162	C₂²	C₂²×#11719945	1	2	yes	—
1163	C₂²	C₂²×#11719945	1	8	yes	—
1164	C₂²	C₂×#13133262	1	2	yes	—
1165	C₂²	#16811459	1	2	yes	—
1166	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1167	C₄	—	2	2	no	—
1168	C₄	—	2	1	no	—
1169	C₄	—	2	1	no	—
1170	C₄	—	2	4	no	—
1171	C₄	—	2	4	no	—
1172	C₄	—	2	2	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	106	8	no	—
1175	C₄	—	106	8	no	—
1176	C₄	—	106	8	no	—
1177	C₄	C₂²×#11719945	1	4	yes	—
1178	C₄	C₂×#13133262	1	2	yes	—
1179	C₄	C₂×#13133262	1	2	yes	—
1180	C₂	—	2	2	no	—
1181	C₂	—	2	2	no	—
1182	C₂	—	2	2	no	—
1183	C₂	—	2	8	no	—
1184	C₂	—	4	4	no	—
1185	C₂	—	212	8	no	—
1186	C₂	C₂³×#11719945	1	1	yes	characteristic
1187	C₂	C₂²×#13133262	1	1	yes	characteristic
1188	C₂	C₂×#16811459	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×C₄×D₄×C₅₃	C₂
hypercenter	C₂²×C₄×D₄	D₅₃
hypocenter	C₅₃	#62773
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20288764	C₂	semidirect
2. #20288747	C₂	semidirect
3. #20288655	C₂	semidirect
4. #20288567	C₂	semidirect
5. #20288554	C₂	semidirect
6. #20288518	C₂	semidirect
7. #20288479	C₂	semidirect
8. #20288424	C₂	semidirect
9. #20288404	C₂	semidirect
10. #20288350	C₂	semidirect
11. #20288319	C₂	semidirect
12. #20288273	C₂	semidirect
13. D₄×#11719945	C₂	semidirect
14. #20288137	C₂	semidirect
15. #20288124	C₂	semidirect
16. #20288011	C₂	semidirect
17. C₂×#16811134	C₂	semidirect
18. C₄×#13133262	C₂	semidirect
19. C₂²×C₄×D₄×C₅₃	C₂	semidirect
21. C₂²×#11719945	C₂²	semidirect
22. #16811356	C₂²	semidirect
23. #16811343	C₂²	semidirect
24. #16811338	C₂²	semidirect
25. #16811332	C₂²	semidirect
26. #16811330	C₂²	semidirect
27. #16811328	C₂²	semidirect
28. #16811323	C₂²	semidirect
29. #16811322	C₂²	semidirect
30. #16811321	C₂²	semidirect
31. #16811319	C₂²	semidirect
32. #16811313	C₂²	semidirect
33. #16811308	C₂²	semidirect
34. #16811302	C₂²	semidirect
35. #16811299	C₂²	semidirect
36. #16811299	C₂²	semidirect
37. #16811294	C₂²	semidirect
38. D₄×Dic₁₀₆	C₂²	semidirect
39. #16811282	C₂²	semidirect
40. #16811278	C₂²	semidirect
41. #16811277	C₂²	semidirect
42. #16811274	C₂²	semidirect
43. #16811269	C₂²	semidirect
44. #16811268	C₂²	semidirect
45. #16811267	C₂²	semidirect
46. #16811267	C₂²	semidirect
47. #16811263	C₂²	semidirect
48. #16811263	C₂²	semidirect
49. D₄×D₂₁₂	C₂²	semidirect
50. D₄×C₂²⋊D₅₃	C₂²	semidirect
51. D₄×C₂²⋊D₅₃	C₂²	semidirect
52. #16811254	C₂²	semidirect
53. #16811249	C₂²	semidirect
54. #16811238	C₂²	semidirect
55. #16811224	C₂²	semidirect
56. #16811220	C₂²	semidirect
57. #16811215	C₂²	semidirect
58. #16811211	C₂²	semidirect
59. #16811211	C₂²	semidirect
60. #16811206	C₂²	semidirect
61. #16811204	C₂²	semidirect
62. #16811190	C₂²	semidirect
63. #16811185	C₂²	semidirect
64. #16811182	C₂²	semidirect
65. #16811180	C₂²	semidirect
66. #16811180	C₂²	semidirect
67. #16811180	C₂²	semidirect
68. #16811173	C₂²	semidirect
69. #16811173	C₂²	semidirect
70. #16811173	C₂²	semidirect
71. #16811170	C₂²	semidirect
72. #16811157	C₂²	semidirect
73. #16811157	C₂²	semidirect
74. #16811157	C₂²	semidirect
75. #16811157	C₂²	semidirect
76. #16811157	C₂²	semidirect
77. #16811157	C₂²	semidirect
78. #16811155	C₂²	semidirect
79. #16811153	C₂²	semidirect
80. #16811134	C₂²	semidirect
81. #16811134	C₂²	semidirect
82. #16811134	C₂²	semidirect
83. #16811134	C₂²	semidirect
84. #16811134	C₂²	semidirect
85. #16811134	C₂²	semidirect
86. #16811134	C₂²	semidirect
87. #16811134	C₂²	semidirect
88. #16811134	C₂²	semidirect
89. #16811134	C₂²	semidirect
90. #16811132	C₂²	semidirect
91. C₂×#13133200	C₂²	semidirect
92. C₂×#13133196	C₂²	semidirect
93. C₂×#13133196	C₂²	semidirect
94. C₂×#13133191	C₂²	semidirect
95. C₂×#13133191	C₂²	semidirect
96. C₂×#13133186	C₂²	semidirect
97. #16811104	C₂²	semidirect
98. #16811102	C₂²	semidirect
100. #16811096	C₂²	semidirect
101. #16811095	C₂²	semidirect
102. C₄×#11719945	C₂²	semidirect
103. C₄×#11719945	C₂²	semidirect
104. C₄×#11719945	C₂²	semidirect
105. C₄×#11719947	C₂²	semidirect
106. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
107. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
108. C₄×D₄×D₅₃	C₂²	semidirect
109. C₂×#13133176	C₂²	semidirect
111. C₂⁴×C₄×C₅₃	C₂²	semidirect
114. C₂×C₄×D₄×C₅₃	C₂²	semidirect
115. C₂×C₄×D₄×C₅₃	C₂²	semidirect
116. C₂×C₄×D₄×C₅₃	C₂²	semidirect
117. C₂×C₄×D₄×C₅₃	C₂²	semidirect
118. C₂×C₄×D₄×C₅₃	C₂²	semidirect
119. C₂×C₄×D₄×C₅₃	C₂²	semidirect
120. C₂×C₄×D₄×C₅₃	C₂²	semidirect
121. C₂×C₄×D₄×C₅₃	C₂²	semidirect
122. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
123. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
124. C₂²×C₄²×C₅₃	C₂²	semidirect
131. C₂×#11719945	C₂³	semidirect
132. C₂×#11719945	C₂³	semidirect
134. C₂²×Dic₁₀₆	C₂³	semidirect
135. C₂²×D₂₁₂	C₂³	semidirect
140. C₂²×C₄×D₅₃	C₂³	semidirect
141. #13133217	C₂³	semidirect
142. #13133217	C₂³	semidirect
143. #13133217	C₂³	semidirect
144. #13133216	C₂³	semidirect
145. #13133214	C₂³	semidirect
147. #13133212	C₂³	semidirect
148. #13133211	C₂³	semidirect
149. #13133211	C₂³	semidirect
150. #13133210	C₂³	semidirect
151. #13133210	C₂³	semidirect
152. #13133209	C₂³	semidirect
153. #13133209	C₂³	semidirect
154. #13133209	C₂³	semidirect
155. #13133208	C₂³	semidirect
156. #13133207	C₂³	semidirect
157. #13133205	C₂³	semidirect
158. #13133205	C₂³	semidirect
159. #13133205	C₂³	semidirect
161. #13133203	C₂³	semidirect
162. #13133203	C₂³	semidirect
163. #13133202	C₂³	semidirect
164. #13133201	C₂³	semidirect
169. #13133200	C₂³	semidirect
170. #13133200	C₂³	semidirect
171. #13133199	C₂³	semidirect
172. #13133199	C₂³	semidirect
174. #13133197	C₂³	semidirect
183. #13133196	C₂³	semidirect
184. #13133196	C₂³	semidirect
185. #13133196	C₂³	semidirect
186. #13133196	C₂³	semidirect
187. #13133195	C₂³	semidirect
188. #13133194	C₂³	semidirect
189. #13133194	C₂³	semidirect
190. #13133192	C₂³	semidirect
199. #13133191	C₂³	semidirect
200. #13133191	C₂³	semidirect
201. #13133191	C₂³	semidirect
202. #13133191	C₂³	semidirect
203. #13133190	C₂³	semidirect
204. #13133190	C₂³	semidirect
209. #13133187	C₂³	semidirect
215. C₄×Dic₁₀₆	C₂³	semidirect
216. C₄×Dic₁₀₆	C₂³	semidirect
217. C₄×Dic₁₀₆	C₂³	semidirect
218. C₄×Dic₁₀₆	C₂³	semidirect
219. C₄×Dic₁₀₆	C₂³	semidirect
220. C₄×Dic₁₀₆	C₂³	semidirect
221. #13133182	C₂³	semidirect
222. C₄×D₂₁₂	C₂³	semidirect
223. C₄×D₂₁₂	C₂³	semidirect
224. C₄×D₂₁₂	C₂³	semidirect
225. C₄×D₂₁₂	C₂³	semidirect
226. C₄×D₂₁₂	C₂³	semidirect
227. C₄×D₂₁₂	C₂³	semidirect
230. #13133179	C₂³	semidirect
239. C₄×C₂²⋊D₅₃	C₂³	semidirect
240. C₄×C₂²⋊D₅₃	C₂³	semidirect
241. C₄×C₂²⋊D₅₃	C₂³	semidirect
242. C₄×C₂²⋊D₅₃	C₂³	semidirect
243. #13133177	C₂³	semidirect
244. #13133177	C₂³	semidirect
249. #13133176	C₂³	semidirect
250. #13133176	C₂³	semidirect
251. #13133175	C₂³	semidirect
252. #13133174	C₂³	semidirect
253. #13133174	C₂³	semidirect
254. #13133174	C₂³	semidirect
255. #13133173	C₂³	semidirect
256. C₂×C₄⋊Dic₅₃	C₂³	semidirect
257. C₂×C₄⋊Dic₅₃	C₂³	semidirect
258. C₂×#11719919	C₂³	semidirect
259. C₂×#11719919	C₂³	semidirect
260. C₄⋊C₄×D₅₃	C₂³	semidirect
264. C₂×#11719921	C₂³	semidirect
265. C₂×#11719921	C₂³	semidirect
266. C₂²⋊C₄×D₅₃	C₂³	semidirect
267. C₂×C₄×Dic₅₃	C₂³	semidirect
268. C₄²×D₅₃	C₂³	semidirect
333. C₂×D₄×C₅₃	#41	semidirect
474. C₂³×C₅₃	C₂×#41	semidirect
486. D₄×C₅₃	C₂×#41	semidirect
511. C₂×C₄×C₅₃	C₂×#41	semidirect
512. C₂×C₄×C₅₃	H(5,𝔽₂)	semidirect
604. C₂²×C₄×D₄	D₅₃	semidirect
617. C₂⁴×C₄	C₂×D₅₃	semidirect
707. C₂×C₄×D₄	C₂×D₅₃	semidirect
708. C₂×C₄×D₄	C₂×D₅₃	semidirect
709. C₂×C₄×D₄	C₂×D₅₃	semidirect
710. C₂×C₄×D₄	C₂×D₅₃	semidirect
711. C₂×C₄×D₄	C₂×D₅₃	semidirect
712. C₂×C₄×D₄	C₂×D₅₃	semidirect
713. C₂×C₄×D₄	C₂×D₅₃	semidirect
714. C₂×C₄×D₄	C₂×D₅₃	semidirect
716. C₂²×C₄⋊C₄	C₂×D₅₃	semidirect
717. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
718. C₂²×C₄²	C₂×D₅₃	semidirect
719. C₅₃	#62773	semidirect
955. C₂×D₄	#11719945	semidirect
1073. C₂³	C₂×#11719945	semidirect
1095. D₄	C₂×#11719945	semidirect
1130. C₂×C₄	C₂×#11719945	semidirect
1131. C₂×C₄	#13133262	semidirect

Maximal subgroups

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

subgroup	index
#20288764	2
#20288747	2
#20288655	2
#20288567	2
#20288554	2
#20288518	2
#20288479	2
#20288424	2
#20288404	2
#20288350	2
#20288319	2
#20288273	2
D₄×#11719945	2
#20288137	2
#20288124	2
#20288011	2
C₂×#16811134	2
C₄×#13133262	2
C₂²×C₄×D₄×C₅₃	2
#62773	53