Subgroups — #28404407

Order 14464.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299297	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299297	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299291	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299291	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299284	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299280	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299277	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299276	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299273	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299272	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299257	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299254	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299240	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299237	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299196	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299191	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299187	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299180	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299156	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299156	C₂	1	1	yes	maximal, characteristic, complemented
22	#20299131	C₂	1	1	yes	maximal, characteristic, complemented
23	#20299126	C₂	1	1	yes	maximal, characteristic, complemented
24	#20299107	C₂	1	1	yes	maximal, characteristic, complemented
25	#20299106	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#16813600	C₂	1	1	yes	maximal, characteristic, complemented
27	#121×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#20299070	C₂	1	1	yes	maximal, characteristic, complemented
29	#20299070	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
31	#553×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
34	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
37	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
41	#16813617	C₂²	1	1	yes	characteristic, complemented
42	#16813617	C₂²	1	1	yes	characteristic, complemented
43	#16813617	C₂²	1	1	yes	characteristic, complemented
44	#16813617	C₂²	1	1	yes	characteristic, complemented
45	#16813616	C₂²	1	1	yes	characteristic, complemented
46	#16813616	C₂²	1	1	yes	characteristic, complemented
47	#16813615	C₂²	1	1	yes	characteristic, complemented
48	#16813615	C₂²	1	1	yes	characteristic, complemented
49	#16813615	C₂²	1	1	yes	characteristic, complemented
50	#16813615	C₂²	1	1	yes	characteristic, complemented
51	#16813613	C₂²	1	1	yes	characteristic, complemented
52	#16813612	C₂²	1	1	yes	characteristic, complemented
53	#16813612	C₂²	1	1	yes	characteristic, complemented
54	#16813612	C₂²	1	1	yes	characteristic, complemented
55	#16813612	C₂²	1	1	yes	characteristic, complemented
56	#16813610	C₂²	1	1	yes	characteristic, complemented
57	#16813609	C₂²	1	1	yes	characteristic, complemented
58	#16813608	C₂²	1	1	yes	characteristic, complemented
59	#16813608	C₂²	1	1	yes	characteristic, complemented
60	#16813608	C₂²	1	1	yes	characteristic, complemented
61	#16813608	C₂²	1	1	yes	characteristic, complemented
62	#16813607	C₂²	1	1	yes	characteristic
63	#16813607	C₂²	1	1	yes	characteristic
64	#16813607	C₂²	1	1	yes	characteristic, complemented
65	#16813607	C₂²	1	1	yes	characteristic, complemented
66	#16813607	C₂²	1	1	yes	characteristic, complemented
67	#16813607	C₂²	1	1	yes	characteristic, complemented
68	#16813607	C₂²	1	1	yes	characteristic, complemented
69	#16813607	C₂²	1	1	yes	characteristic, complemented
70	#16813605	C₂²	1	1	yes	characteristic, complemented
71	#16813605	C₂²	1	1	yes	characteristic, complemented
72	#16813604	C₂²	1	1	yes	characteristic
73	#16813604	C₂²	1	1	yes	characteristic
74	#16813604	C₂²	1	1	yes	characteristic, complemented
75	#16813604	C₂²	1	1	yes	characteristic, complemented
76	#16813604	C₂²	1	1	yes	characteristic, complemented
77	#16813604	C₂²	1	1	yes	characteristic, complemented
78	#16813603	C₂²	1	1	yes	characteristic, complemented
79	#16813603	C₂²	1	1	yes	characteristic, complemented
80	#16813602	C₂²	1	1	yes	characteristic, complemented
81	#16813601	C₂²	1	1	yes	characteristic, complemented
82	#16813600	C₂²	1	1	yes	characteristic, complemented
83	#16813600	C₂²	1	1	yes	characteristic, complemented
84	#16813600	C₂²	1	1	yes	characteristic, complemented
85	#16813600	C₂²	1	1	yes	characteristic, complemented
86	#16813600	C₂²	1	1	yes	characteristic, complemented
87	#16813600	C₂²	1	1	yes	characteristic, complemented
88	#16813600	C₂²	1	1	yes	characteristic, complemented
89	#16813600	C₂²	1	1	yes	characteristic, complemented
90	#16813600	C₂²	1	1	yes	characteristic, complemented
91	#16813600	C₂²	1	1	yes	characteristic, complemented
92	#16813599	C₂²	1	1	yes	characteristic, complemented
93	#16813599	C₂²	1	1	yes	characteristic, complemented
94	#16813597	C₂²	1	1	yes	characteristic
95	#16813597	C₂²	1	1	yes	characteristic, complemented
96	#16813596	C₂²	1	1	yes	characteristic, complemented
97	#16813596	C₂²	1	1	yes	characteristic, complemented
98	#16813596	C₂²	1	1	yes	characteristic, complemented
99	#16813595	C₂²	1	1	yes	characteristic
100	#16813595	C₂²	1	1	yes	characteristic
101	#16813595	C₂²	1	1	yes	characteristic, complemented
102	#16813595	C₂²	1	1	yes	characteristic, complemented
103	#16813594	C₂²	1	1	yes	characteristic, complemented
104	#16813594	C₂²	1	1	yes	characteristic, complemented
105	#16813594	C₂²	1	1	yes	characteristic, complemented
106	#16813594	C₂²	1	1	yes	characteristic, complemented
107	#16813594	C₂²	1	1	yes	characteristic, complemented
108	#16813594	C₂²	1	1	yes	characteristic, complemented
109	#16813594	C₂²	1	1	yes	characteristic, complemented
110	#16813594	C₂²	1	1	yes	characteristic, complemented
111	#16813593	C₂²	1	1	yes	characteristic
112	#16813592	C₂²	1	1	yes	characteristic
113	#16813592	C₂²	1	1	yes	characteristic
114	#16813592	C₂²	1	1	yes	characteristic, complemented
115	#16813592	C₂²	1	1	yes	characteristic, complemented
116	#16813590	C₂²	1	1	yes	characteristic
117	#16813590	C₂²	1	1	yes	characteristic
118	#16813590	C₂²	1	1	yes	characteristic, complemented
119	#16813590	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
121	#16813587	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
123	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
124	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
125	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
126	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
127	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
128	#16813584	C₂²	1	1	yes	characteristic
129	#16813584	C₂²	1	1	yes	characteristic, complemented
130	#16813584	C₂²	1	1	yes	characteristic, complemented
131	#16813584	C₂²	1	1	yes	characteristic, complemented
132	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
133	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
134	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
135	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
137	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
139	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
140	#16813582	C₂²	1	1	yes	characteristic
141	#16813582	C₂²	1	1	yes	characteristic, complemented
142	#16813582	C₂²	1	1	yes	characteristic, complemented
143	#16813582	C₂²	1	1	yes	characteristic, complemented
144	#16813582	C₂²	1	1	yes	characteristic, complemented
145	#16813582	C₂²	1	1	yes	characteristic, complemented
146	#16813582	C₂²	1	1	yes	characteristic, complemented
147	#16813582	C₂²	1	1	yes	characteristic, complemented
148	#16813580	C₂²	1	1	yes	characteristic, complemented
149	#16813580	C₂²	1	1	yes	characteristic, complemented
150	#16813580	C₂²	1	1	yes	characteristic, complemented
151	#16813579	C₂²	1	1	yes	characteristic, complemented
152	#16813579	C₂²	1	1	yes	characteristic, complemented
153	#16813579	C₂²	1	1	yes	characteristic, complemented
154	#16813579	C₂²	1	1	yes	characteristic, complemented
155	#16813578	C₂²	1	1	yes	characteristic, complemented
156	#16813578	C₂²	1	1	yes	characteristic, complemented
157	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
158	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
160	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
161	C₂×#14268624	C₂²	1	1	yes	characteristic
162	C₂×#14268624	C₂²	1	1	yes	characteristic
163	C₂×#14268624	C₂²	1	1	yes	characteristic, complemented
164	C₂×#14268624	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
173	#126×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
174	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
175	#123×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
177	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
178	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
179	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
180	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
185	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
188	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
189	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
190	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
191	#14268647	—	4	2	no	—
192	#14268646	—	4	2	no	—
193	C₂×Dic₂₂₆	—	4	2	no	—
194	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
195	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
196	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
197	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
198	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
199	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
200	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
201	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
202	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
203	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
216	D₄×D₁₁₃	—	2	4	no	—
217	D₄×D₁₁₃	—	2	4	no	—
218	D₄×D₁₁₃	—	2	4	no	—
219	D₄×D₁₁₃	—	4	2	no	—
220	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
221	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
224	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
225	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₁₃	—	4	2	no	—
227	C₂×C₄×D₁₁₃	—	4	2	no	—
228	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
249	#14268626	C₂³	1	1	yes	characteristic
250	#14268626	C₂³	1	1	yes	characteristic
251	#14268626	C₂³	1	1	yes	characteristic
252	#14268626	C₂³	1	1	yes	characteristic
253	#14268626	C₂³	1	1	yes	characteristic
254	#14268626	C₂³	1	1	yes	characteristic
255	#14268626	C₂³	1	1	yes	characteristic
256	#14268626	C₂³	1	1	yes	characteristic
257	#14268626	C₂³	1	1	yes	characteristic
258	#14268626	C₂³	1	1	yes	characteristic
259	#14268626	C₂³	1	1	yes	characteristic
260	#14268626	C₂³	1	1	yes	characteristic
261	#14268626	C₂³	1	1	yes	characteristic
262	#14268626	C₂³	1	1	yes	characteristic
263	#14268626	C₂³	1	1	yes	characteristic
264	#14268626	C₂³	1	1	yes	characteristic
265	#14268626	C₂³	1	1	yes	characteristic
266	#14268626	C₂³	1	1	yes	characteristic
267	#14268626	C₂³	1	1	yes	characteristic
268	#14268626	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
279	#14268624	C₂³	1	1	yes	characteristic
280	#14268624	C₂³	1	1	yes	characteristic
281	#14268624	C₂³	1	1	yes	characteristic
282	#14268624	C₂³	1	1	yes	characteristic
283	#14268624	C₂³	1	1	yes	characteristic
284	#14268624	C₂³	1	1	yes	characteristic
285	#14268624	C₂³	1	1	yes	characteristic
286	#14268624	C₂³	1	1	yes	characteristic
287	#14268624	C₂³	1	1	yes	characteristic
288	#14268624	C₂³	1	1	yes	characteristic
289	#14268624	C₂³	1	1	yes	characteristic
290	#14268624	C₂³	1	1	yes	characteristic
291	#14268624	C₂³	1	1	yes	characteristic
292	#14268624	C₂³	1	1	yes	characteristic
293	#14268624	C₂³	1	1	yes	characteristic
294	#14268624	C₂³	1	1	yes	characteristic
295	#14268624	C₂³	1	1	yes	characteristic
296	#14268624	C₂³	1	1	yes	characteristic
297	#14268624	C₂³	1	1	yes	characteristic
298	#14268624	C₂³	1	1	yes	characteristic
299	#14268624	C₂³	1	1	yes	characteristic
300	#14268624	C₂³	1	1	yes	characteristic
301	#14268624	C₂³	1	1	yes	characteristic
302	#14268624	C₂³	1	1	yes	characteristic
303	#14268624	C₂³	1	1	yes	characteristic
304	#14268624	C₂³	1	1	yes	characteristic
305	#14268624	C₂³	1	1	yes	characteristic
306	#14268624	C₂³	1	1	yes	characteristic
307	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
313	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
314	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
315	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
320	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
325	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
326	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
327	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
348	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
349	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
350	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
351	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
354	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₁₃	—	2	2	no	—
356	C₂²×D₁₁₃	—	2	2	no	—
357	C₂²×D₁₁₃	—	2	2	no	—
358	C₂²×D₁₁₃	—	4	1	no	—
359	C₂²×D₁₁₃	—	4	1	no	—
360	C₂²×D₁₁₃	—	4	1	no	—
361	C₂²×D₁₁₃	—	4	1	no	—
362	C₂²×D₁₁₃	—	4	1	no	—
363	C₂²×D₁₁₃	—	4	1	no	—
364	C₂²×D₁₁₃	—	4	1	no	—
365	C₂²×D₁₁₃	—	4	1	no	—
366	C₂²×D₁₁₃	#41	1	4	yes	complemented
367	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
368	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
370	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
371	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
372	D₄×C₁₁₃	—	2	2	no	—
373	D₄×C₁₁₃	—	2	2	no	—
374	D₄×C₁₁₃	—	2	2	no	—
375	D₄×C₁₁₃	—	4	1	no	—
376	D₄×C₁₁₃	—	4	1	no	—
377	D₄×C₁₁₃	—	4	1	no	—
378	C₂×C₄×C₁₁₃	—	4	1	no	—
379	C₂×C₄×C₁₁₃	—	4	1	no	—
380	C₂×C₄×C₁₁₃	—	4	1	no	—
381	C₂×C₄×C₁₁₃	—	4	1	no	—
382	C₂×C₄×C₁₁₃	—	4	1	no	—
383	C₂×C₄×C₁₁₃	—	4	1	no	—
384	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
395	C₂²⋊D₁₁₃	—	2	2	no	—
396	C₂²⋊D₁₁₃	—	2	2	no	—
397	C₂²⋊D₁₁₃	—	2	2	no	—
398	C₂²⋊D₁₁₃	—	2	2	no	—
399	C₂²⋊D₁₁₃	—	2	2	no	—
400	C₂²⋊D₁₁₃	—	2	2	no	—
401	C₂²⋊D₁₁₃	—	2	2	no	—
402	C₂²⋊D₁₁₃	—	2	2	no	—
403	C₂²⋊D₁₁₃	—	4	1	no	—
404	C₂²⋊D₁₁₃	—	4	1	no	—
405	C₂²⋊D₁₁₃	—	4	1	no	—
406	C₂²⋊D₁₁₃	—	4	1	no	—
407	C₂×Dic₁₁₃	—	2	2	no	—
408	C₂×Dic₁₁₃	—	2	2	no	—
409	C₂×Dic₁₁₃	—	4	1	no	—
410	C₂×Dic₁₁₃	—	4	1	no	—
411	C₂×Dic₁₁₃	—	4	1	no	—
412	C₂×Dic₁₁₃	—	4	1	no	—
413	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
424	D₄₅₂	—	2	2	no	—
425	D₄₅₂	—	2	2	no	—
426	D₄₅₂	—	2	2	no	—
427	D₄₅₂	—	4	1	no	—
428	D₄₅₂	—	4	1	no	—
429	D₄₅₂	—	4	1	no	—
430	C₄×D₁₁₃	—	2	2	no	—
431	C₄×D₁₁₃	—	2	2	no	—
432	C₄×D₁₁₃	—	2	2	no	—
433	C₄×D₁₁₃	—	2	2	no	—
434	C₄×D₁₁₃	—	2	2	no	—
435	C₄×D₁₁₃	—	2	2	no	—
436	C₄×D₁₁₃	—	4	1	no	—
437	C₄×D₁₁₃	—	4	1	no	—
438	C₄×D₁₁₃	—	4	1	no	—
439	C₄×D₁₁₃	—	4	1	no	—
440	C₄×D₁₁₃	—	4	1	no	—
441	C₄×D₁₁₃	—	4	1	no	—
442	C₄×D₁₁₃	—	4	1	no	—
443	C₄×D₁₁₃	—	4	1	no	—
444	C₄×D₁₁₃	—	4	1	no	—
445	Dic₂₂₆	—	2	2	no	—
446	Dic₂₂₆	—	2	2	no	—
447	Dic₂₂₆	—	4	1	no	—
448	Dic₂₂₆	—	4	1	no	—
449	C₂²×C₁₁₃	—	2	1	no	—
450	C₂²×C₁₁₃	—	2	1	no	—
451	C₂²×C₁₁₃	—	2	1	no	—
452	C₂²×C₁₁₃	—	2	1	no	—
453	C₂²×C₁₁₃	—	2	1	no	—
454	C₂²×C₁₁₃	—	2	1	no	—
455	C₂²×C₁₁₃	—	2	1	no	—
456	C₂²×C₁₁₃	—	2	1	no	—
457	C₂²×C₁₁₃	—	2	1	no	—
458	C₂²×C₁₁₃	—	2	1	no	—
459	C₂²×C₁₁₃	—	2	1	no	—
460	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
461	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
462	C₂×D₁₁₃	—	2	1	no	—
463	C₂×D₁₁₃	—	2	1	no	—
464	C₂×D₁₁₃	—	2	1	no	—
465	C₂×D₁₁₃	—	2	1	no	—
466	C₂×D₁₁₃	—	2	1	no	—
467	C₂×D₁₁₃	—	2	1	no	—
468	C₂×D₁₁₃	—	2	1	no	—
469	C₂×D₁₁₃	—	2	1	no	—
470	C₂×D₁₁₃	—	2	1	no	—
471	C₂×D₁₁₃	—	2	1	no	—
472	C₂×D₁₁₃	—	2	1	no	—
473	C₂×D₁₁₃	—	2	1	no	—
474	C₂×D₁₁₃	—	2	1	no	—
475	C₂×D₁₁₃	—	4	4	no	—
476	C₂×D₁₁₃	—	4	4	no	—
477	C₂×D₁₁₃	—	8	2	no	—
478	C₂×D₁₁₃	—	8	2	no	—
479	C₂×D₁₁₃	C₂×#41	1	2	yes	—
480	C₂×D₁₁₃	C₂×#41	1	2	yes	—
481	C₄×C₁₁₃	—	2	1	no	—
482	C₄×C₁₁₃	—	2	1	no	—
483	C₄×C₁₁₃	—	2	1	no	—
484	C₄×C₁₁₃	—	2	1	no	—
485	C₄×C₁₁₃	—	2	1	no	—
486	C₄×C₁₁₃	—	2	1	no	—
487	C₄×C₁₁₃	—	2	1	no	—
488	C₄×C₁₁₃	—	2	1	no	—
489	C₄×C₁₁₃	—	2	1	no	—
490	C₄×C₁₁₃	—	2	1	no	—
491	C₄×C₁₁₃	—	2	1	no	—
492	Dic₁₁₃	—	2	1	no	—
493	Dic₁₁₃	—	2	1	no	—
494	Dic₁₁₃	—	2	1	no	—
495	Dic₁₁₃	—	2	1	no	—
496	Dic₁₁₃	—	2	1	no	—
497	Dic₁₁₃	—	2	1	no	—
498	Dic₁₁₃	—	2	1	no	—
499	Dic₁₁₃	—	2	1	no	—
500	Dic₁₁₃	—	2	1	no	—
501	Dic₁₁₃	—	2	1	no	—
502	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₁₁₃	—	2	2	no	—
504	C₂×C₁₁₃	—	4	1	no	—
505	C₂×C₁₁₃	—	4	1	no	—
506	C₂×C₁₁₃	—	4	1	no	—
507	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
508	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂×C₁₁₃	#585	1	1	yes	characteristic
510	D₁₁₃	—	2	2	no	—
511	D₁₁₃	—	2	2	no	—
512	D₁₁₃	—	4	1	no	—
513	D₁₁₃	—	4	1	no	—
514	D₁₁₃	—	4	1	no	—
515	#3505	—	113	1	no	maximal, Sylow
516	C₁₁₃	#3505	1	1	yes	characteristic, complemented, Sylow
517	#553	—	113	1	no	—
518	#553	—	113	1	no	—
519	#553	—	113	1	no	—
520	#553	—	113	1	no	—
521	#553	—	113	1	no	—
522	#553	D₁₁₃	1	1	yes	characteristic, complemented
523	#552	—	113	1	no	—
524	#552	—	113	1	no	—
525	#551	—	113	1	no	—
526	#551	—	113	1	no	—
527	#551	—	113	1	no	—
528	#551	—	113	1	no	—
529	#548	—	113	1	no	—
530	#548	—	113	1	no	—
531	#546	—	113	1	no	—
532	#546	—	113	1	no	—
533	#539	—	113	1	no	—
534	#539	—	113	1	no	—
535	#538	—	113	1	no	—
536	#538	—	113	1	no	—
537	#534	—	113	1	no	—
538	#534	—	113	1	no	—
539	#529	—	113	1	no	—
540	#529	—	113	1	no	—
541	#525	—	113	1	no	—
542	#525	—	113	1	no	—
543	C₂×C₂²⋊Q₈	—	113	1	no	—
544	C₂×#121	—	113	1	no	—
545	#518	—	113	1	no	—
546	#518	—	113	1	no	—
547	C₂×C₄×D₄	—	113	1	no	—
548	C₂×#41	—	113	1	no	—
549	C₂×#41	—	113	1	no	—
550	C₂²×Q₈	—	113	1	no	—
551	C₂²×D₄	—	113	1	no	—
552	C₂²×D₄	—	113	1	no	—
553	C₂²×D₄	—	113	1	no	—
554	C₂²×D₄	—	113	1	no	—
555	C₂³×C₄	—	113	1	no	—
556	C₂³×C₄	—	113	1	no	—
557	#126	—	113	1	no	—
558	#126	—	113	1	no	—
559	#126	—	113	1	no	—
560	#126	—	113	1	no	—
561	#126	—	113	1	no	—
562	#126	—	113	1	no	—
563	#126	—	113	1	no	—
564	#126	—	113	1	no	—
565	#126	—	113	1	no	—
566	#126	—	113	1	no	—
567	#126	C₂×D₁₁₃	1	1	yes	characteristic, complemented
568	#126	C₂×D₁₁₃	1	1	yes	characteristic, complemented
569	#125	—	113	1	no	—
570	#125	—	113	1	no	—
571	#125	—	113	1	no	—
572	#125	—	113	1	no	—
573	#125	—	113	1	no	—
574	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
575	#124	—	113	1	no	—
576	#124	—	113	1	no	—
577	#124	—	113	1	no	—
578	#124	—	113	1	no	—
579	#124	—	113	1	no	—
580	#124	—	113	1	no	—
581	#123	—	113	1	no	—
582	#123	—	113	1	no	—
583	#123	—	113	1	no	—
584	#123	—	113	1	no	—
585	#123	—	113	1	no	—
586	#123	—	113	1	no	—
587	#123	—	113	1	no	—
588	#123	—	113	1	no	—
589	#123	—	113	1	no	—
590	#123	—	113	1	no	—
591	#123	—	113	1	no	—
592	#123	—	113	1	no	—
593	#123	—	113	1	no	—
594	#123	—	113	1	no	—
595	#123	—	113	1	no	—
596	#123	—	113	1	no	—
597	#123	—	113	1	no	—
598	#123	—	113	1	no	—
599	#123	C₂×D₁₁₃	1	1	yes	characteristic, complemented
600	#123	C₂×D₁₁₃	1	1	yes	characteristic, complemented
601	C₂²⋊Q₈	—	113	1	no	—
602	C₂²⋊Q₈	—	113	1	no	—
603	C₂²⋊Q₈	—	113	1	no	—
604	C₂²⋊Q₈	—	113	1	no	—
605	C₂²⋊Q₈	—	113	1	no	—
606	C₂²⋊Q₈	—	113	1	no	—
607	C₂²⋊Q₈	—	113	1	no	—
608	C₂²⋊Q₈	—	113	1	no	—
609	C₂²⋊Q₈	—	113	1	no	—
610	C₂²⋊Q₈	—	113	1	no	—
611	C₂²⋊Q₈	—	113	1	no	—
612	C₂²⋊Q₈	—	113	1	no	—
613	C₂²⋊Q₈	—	113	1	no	—
614	C₂²⋊Q₈	—	113	1	no	—
615	#121	—	113	1	no	—
616	#121	—	113	1	no	—
617	#121	—	113	1	no	—
618	#121	—	113	1	no	—
619	#121	—	113	1	no	—
620	#121	—	113	1	no	—
621	#121	—	113	1	no	—
622	#121	—	113	1	no	—
623	#121	—	113	1	no	—
624	#121	—	113	1	no	—
625	#121	—	113	1	no	—
626	#121	—	113	1	no	—
627	#121	—	113	1	no	—
628	#121	—	113	1	no	—
629	#121	—	113	1	no	—
630	#121	—	113	1	no	—
631	#121	—	113	1	no	—
632	#121	—	113	1	no	—
633	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
634	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
635	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
636	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
637	#120	—	113	1	no	—
638	#120	—	113	1	no	—
639	#120	—	113	1	no	—
640	#120	—	113	1	no	—
641	#120	—	113	1	no	—
642	#120	—	113	1	no	—
643	#120	—	113	1	no	—
644	#120	—	113	1	no	—
645	C₄×Q₈	—	113	1	no	—
646	C₄×Q₈	—	113	1	no	—
647	C₄×D₄	—	113	1	no	—
648	C₄×D₄	—	113	1	no	—
649	C₄×D₄	—	113	1	no	—
650	C₄×D₄	—	113	1	no	—
651	C₄×D₄	—	113	1	no	—
652	C₄×D₄	—	113	1	no	—
653	C₄×D₄	—	113	1	no	—
654	C₄×D₄	—	113	1	no	—
655	C₄×D₄	—	113	1	no	—
656	C₄×D₄	—	113	1	no	—
657	C₄×D₄	—	113	1	no	—
658	C₄×D₄	—	113	1	no	—
659	C₄×D₄	—	113	1	no	—
660	C₄×D₄	—	113	1	no	—
661	C₄×D₄	—	113	1	no	—
662	C₄×D₄	—	113	1	no	—
663	C₄×D₄	—	113	1	no	—
664	C₄×D₄	—	113	1	no	—
665	C₄×D₄	—	113	1	no	—
666	C₄×D₄	—	113	1	no	—
667	C₄×D₄	—	113	1	no	—
668	C₄×D₄	—	113	1	no	—
669	C₄×D₄	—	113	1	no	—
670	C₄×D₄	—	113	1	no	—
671	C₄×D₄	—	113	1	no	—
672	C₄×D₄	—	113	1	no	—
673	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
674	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
675	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
676	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
677	#117	—	113	1	no	—
678	#117	—	113	1	no	—
679	#117	—	113	1	no	—
680	#117	—	113	1	no	—
681	#117	—	113	1	no	—
682	#117	—	113	1	no	—
683	#117	—	113	1	no	—
684	#117	—	113	1	no	—
685	#117	—	113	1	no	—
686	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
687	C₂×C₄⋊C₄	—	113	1	no	—
688	C₂×C₄⋊C₄	—	113	1	no	—
689	C₂×C₄⋊C₄	—	113	1	no	—
690	C₂×C₄⋊C₄	—	113	1	no	—
691	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
692	C₂×C₂²⋊C₄	—	113	1	no	—
693	C₂×C₂²⋊C₄	—	113	1	no	—
694	C₂×C₂²⋊C₄	—	113	1	no	—
695	C₂×C₂²⋊C₄	—	113	1	no	—
696	C₂×C₂²⋊C₄	—	113	1	no	—
697	C₂×C₂²⋊C₄	—	113	1	no	—
698	C₂×C₂²⋊C₄	—	113	1	no	—
699	C₂×C₂²⋊C₄	—	113	1	no	—
700	C₂×C₂²⋊C₄	—	113	1	no	—
701	C₂×C₂²⋊C₄	—	113	1	no	—
702	C₂×C₄²	—	113	1	no	—
703	C₂⁴	—	113	1	no	—
704	C₂⁴	—	113	1	no	—
705	C₂⁴	—	113	1	no	—
706	C₂⁴	—	113	1	no	—
707	#41	—	452	2	no	—
708	#41	—	452	2	no	—
709	C₂×Q₈	—	113	1	no	—
710	C₂×Q₈	—	113	1	no	—
711	C₂×Q₈	—	113	1	no	—
712	C₂×Q₈	—	113	1	no	—
713	C₂×Q₈	—	452	2	no	—
714	C₂×D₄	—	113	1	no	—
715	C₂×D₄	—	113	1	no	—
716	C₂×D₄	—	113	1	no	—
717	C₂×D₄	—	113	1	no	—
718	C₂×D₄	—	113	1	no	—
719	C₂×D₄	—	113	1	no	—
720	C₂×D₄	—	113	1	no	—
721	C₂×D₄	—	113	1	no	—
722	C₂×D₄	—	113	1	no	—
723	C₂×D₄	—	113	1	no	—
724	C₂×D₄	—	113	1	no	—
725	C₂×D₄	—	113	1	no	—
726	C₂×D₄	—	113	1	no	—
727	C₂×D₄	—	113	1	no	—
728	C₂×D₄	—	113	1	no	—
729	C₂×D₄	—	113	1	no	—
730	C₂×D₄	—	113	1	no	—
731	C₂×D₄	—	113	1	no	—
732	C₂×D₄	—	452	2	no	—
733	C₂×D₄	—	226	4	no	—
734	C₂×D₄	—	226	4	no	—
735	C₂×D₄	—	226	4	no	—
736	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
737	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
738	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
739	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
742	C₂²×C₄	—	113	1	no	—
743	C₂²×C₄	—	113	1	no	—
744	C₂²×C₄	—	113	1	no	—
745	C₂²×C₄	—	113	1	no	—
746	C₂²×C₄	—	113	1	no	—
747	C₂²×C₄	—	113	1	no	—
748	C₂²×C₄	—	113	1	no	—
749	C₂²×C₄	—	113	1	no	—
750	C₂²×C₄	—	113	1	no	—
751	C₂²×C₄	—	113	1	no	—
752	C₂²×C₄	—	113	1	no	—
753	C₂²×C₄	—	113	1	no	—
754	C₂²×C₄	—	113	1	no	—
755	C₂²×C₄	—	113	1	no	—
756	C₂²×C₄	—	113	1	no	—
757	C₂²×C₄	—	113	1	no	—
758	C₂²×C₄	—	113	1	no	—
759	C₂²×C₄	—	113	1	no	—
760	C₂²×C₄	—	113	1	no	—
761	C₂²×C₄	—	113	1	no	—
762	C₂²×C₄	—	113	1	no	—
763	C₂²×C₄	—	452	2	no	—
764	C₂²×C₄	—	452	2	no	—
765	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
771	C₄⋊C₄	—	113	1	no	—
772	C₄⋊C₄	—	113	1	no	—
773	C₄⋊C₄	—	113	1	no	—
774	C₄⋊C₄	—	113	1	no	—
775	C₄⋊C₄	—	113	1	no	—
776	C₄⋊C₄	—	113	1	no	—
777	C₄⋊C₄	—	113	1	no	—
778	C₄⋊C₄	—	113	1	no	—
779	C₄⋊C₄	—	113	1	no	—
780	C₄⋊C₄	—	113	1	no	—
781	C₄⋊C₄	—	113	1	no	—
782	C₄⋊C₄	—	113	1	no	—
783	C₄⋊C₄	—	113	1	no	—
784	C₄⋊C₄	—	113	1	no	—
785	C₄⋊C₄	—	113	1	no	—
786	C₄⋊C₄	—	113	1	no	—
787	C₄⋊C₄	—	113	1	no	—
788	C₄⋊C₄	—	113	1	no	—
789	C₄⋊C₄	—	113	1	no	—
790	C₄⋊C₄	—	113	1	no	—
791	C₄⋊C₄	—	113	1	no	—
792	C₄⋊C₄	—	113	1	no	—
793	C₄⋊C₄	—	113	1	no	—
794	C₄⋊C₄	—	113	1	no	—
795	C₄⋊C₄	—	113	1	no	—
796	C₄⋊C₄	—	113	1	no	—
797	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
802	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
803	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
804	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
806	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
807	C₂²⋊C₄	—	113	1	no	—
808	C₂²⋊C₄	—	113	1	no	—
809	C₂²⋊C₄	—	113	1	no	—
810	C₂²⋊C₄	—	113	1	no	—
811	C₂²⋊C₄	—	113	1	no	—
812	C₂²⋊C₄	—	113	1	no	—
813	C₂²⋊C₄	—	113	1	no	—
814	C₂²⋊C₄	—	113	1	no	—
815	C₂²⋊C₄	—	113	1	no	—
816	C₂²⋊C₄	—	113	1	no	—
817	C₂²⋊C₄	—	113	1	no	—
818	C₂²⋊C₄	—	113	1	no	—
819	C₂²⋊C₄	—	113	1	no	—
820	C₂²⋊C₄	—	113	1	no	—
821	C₂²⋊C₄	—	113	1	no	—
822	C₂²⋊C₄	—	113	1	no	—
823	C₂²⋊C₄	—	113	1	no	—
824	C₂²⋊C₄	—	113	1	no	—
825	C₂²⋊C₄	—	113	1	no	—
826	C₂²⋊C₄	—	113	1	no	—
827	C₂²⋊C₄	—	113	1	no	—
828	C₂²⋊C₄	—	113	1	no	—
829	C₂²⋊C₄	—	113	1	no	—
830	C₂²⋊C₄	—	113	1	no	—
831	C₂²⋊C₄	—	113	1	no	—
832	C₂²⋊C₄	—	113	1	no	—
833	C₂²⋊C₄	—	113	1	no	—
834	C₂²⋊C₄	—	113	1	no	—
835	C₂²⋊C₄	—	113	1	no	—
836	C₂²⋊C₄	—	113	1	no	—
837	C₂²⋊C₄	—	113	1	no	—
838	C₂²⋊C₄	—	113	1	no	—
839	C₂²⋊C₄	—	113	1	no	—
840	C₂²⋊C₄	—	113	1	no	—
841	C₂²⋊C₄	—	113	1	no	—
842	C₂²⋊C₄	—	113	1	no	—
843	C₂²⋊C₄	—	113	1	no	—
844	C₂²⋊C₄	—	113	1	no	—
845	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
850	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
851	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
852	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
853	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
854	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
855	C₄²	—	113	1	no	—
856	C₄²	—	113	1	no	—
857	C₄²	—	113	1	no	—
858	C₄²	—	113	1	no	—
859	C₄²	—	113	1	no	—
860	C₄²	—	113	1	no	—
861	C₄²	—	113	1	no	—
862	C₄²	—	113	1	no	—
863	C₄²	—	113	1	no	—
864	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
865	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
866	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
867	C₂³	—	113	4	no	—
868	C₂³	—	113	1	no	—
869	C₂³	—	113	1	no	—
870	C₂³	—	113	1	no	—
871	C₂³	—	113	1	no	—
872	C₂³	—	113	1	no	—
873	C₂³	—	452	1	no	—
874	C₂³	—	452	1	no	—
875	C₂³	—	452	1	no	—
876	C₂³	—	452	1	no	—
877	C₂³	—	452	1	no	—
878	C₂³	—	452	1	no	—
879	C₂³	—	452	1	no	—
880	C₂³	—	452	1	no	—
881	C₂³	—	226	2	no	—
882	C₂³	—	226	2	no	—
883	C₂³	—	226	2	no	—
884	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
885	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
886	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
887	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
888	Q₈	—	452	1	no	—
889	Q₈	—	452	1	no	—
890	Q₈	—	226	2	no	—
891	Q₈	—	226	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	452	1	no	—
899	D₄	—	452	1	no	—
900	D₄	—	452	1	no	—
901	D₄	—	452	1	no	—
902	D₄	—	452	1	no	—
903	D₄	—	452	1	no	—
904	D₄	—	452	1	no	—
905	D₄	—	226	2	no	—
906	D₄	—	226	2	no	—
907	D₄	—	226	2	no	—
908	D₄	—	226	2	no	—
909	D₄	—	226	2	no	—
910	D₄	—	226	2	no	—
911	D₄	—	226	2	no	—
912	D₄	—	226	2	no	—
913	D₄	—	226	2	no	—
914	D₄	—	226	2	no	—
915	D₄	—	226	2	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	113	1	no	—
923	C₂×C₄	—	113	1	no	—
924	C₂×C₄	—	113	1	no	—
925	C₂×C₄	—	113	1	no	—
926	C₂×C₄	—	113	1	no	—
927	C₂×C₄	—	113	1	no	—
928	C₂×C₄	—	113	1	no	—
929	C₂×C₄	—	113	1	no	—
930	C₂×C₄	—	113	1	no	—
931	C₂×C₄	—	113	1	no	—
932	C₂×C₄	—	113	1	no	—
933	C₂×C₄	—	452	1	no	—
934	C₂×C₄	—	452	1	no	—
935	C₂×C₄	—	452	1	no	—
936	C₂×C₄	—	452	1	no	—
937	C₂×C₄	—	452	1	no	—
938	C₂×C₄	—	452	1	no	—
939	C₂×C₄	—	452	1	no	—
940	C₂×C₄	—	452	1	no	—
941	C₂×C₄	—	452	1	no	—
942	C₂×C₄	—	452	1	no	—
943	C₂×C₄	—	452	1	no	—
944	C₂×C₄	—	452	1	no	—
945	C₂×C₄	—	452	1	no	—
946	C₂×C₄	—	226	2	no	—
947	C₂×C₄	—	226	2	no	—
948	C₂×C₄	—	226	2	no	—
949	C₂×C₄	—	226	2	no	—
950	C₂×C₄	—	226	2	no	—
951	C₂×C₄	—	226	2	no	—
952	C₂×C₄	—	226	2	no	—
953	C₂×C₄	—	226	2	no	—
954	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	113	2	no	—
977	C₂²	—	113	2	no	—
978	C₂²	—	904	2	no	—
979	C₂²	—	904	2	no	—
980	C₂²	—	452	4	no	—
981	C₂²	—	452	4	no	—
982	C₂²	—	226	1	no	—
983	C₂²	—	226	1	no	—
984	C₂²	—	226	1	no	—
985	C₂²	—	226	1	no	—
986	C₂²	—	226	1	no	—
987	C₂²	—	226	1	no	—
988	C₂²	—	226	1	no	—
989	C₂²	—	226	1	no	—
990	C₂²	—	226	1	no	—
991	C₂²	—	226	1	no	—
992	C₂²	—	226	1	no	—
993	C₂²	—	226	1	no	—
994	C₂²	—	226	1	no	—
995	C₂²	#41×D₁₁₃	1	2	yes	—
996	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	113	2	no	—
1009	C₄	—	226	1	no	—
1010	C₄	—	226	1	no	—
1011	C₄	—	226	1	no	—
1012	C₄	—	226	1	no	—
1013	C₄	—	226	1	no	—
1014	C₄	—	226	1	no	—
1015	C₄	—	226	1	no	—
1016	C₄	—	226	1	no	—
1017	C₄	—	226	1	no	—
1018	C₄	—	226	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	452	1	no	—
1024	C₂	—	452	1	no	—
1025	C₂	—	452	1	no	—
1026	C₂	—	226	2	no	—
1027	C₂	—	226	2	no	—
1028	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
1029	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
1030	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#553×C₁₁₃	C₂
hypercenter	#553	D₁₁₃
hypocenter	C₁₁₃	#3505
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #20299297	C₂	semidirect
2. #20299297	C₂	semidirect
3. #20299296	C₂	semidirect
4. #20299291	C₂	semidirect
5. #20299291	C₂	semidirect
6. #20299284	C₂	semidirect
7. #20299280	C₂	semidirect
8. #20299277	C₂	semidirect
9. #20299276	C₂	semidirect
10. #20299273	C₂	semidirect
11. #20299272	C₂	semidirect
12. #20299257	C₂	semidirect
13. #20299254	C₂	semidirect
14. #20299240	C₂	semidirect
15. #20299237	C₂	semidirect
16. #20299196	C₂	semidirect
17. #20299191	C₂	semidirect
18. #20299187	C₂	semidirect
19. #20299180	C₂	semidirect
20. #20299156	C₂	semidirect
21. #20299156	C₂	semidirect
22. #20299131	C₂	semidirect
23. #20299126	C₂	semidirect
24. #20299107	C₂	semidirect
25. #20299106	C₂	semidirect
26. C₂×#16813600	C₂	semidirect
27. #121×D₁₁₃	C₂	semidirect
28. #20299070	C₂	semidirect
29. #20299070	C₂	semidirect
30. C₄×D₄×D₁₁₃	C₂	semidirect
31. #553×C₁₁₃	C₂	semidirect
32. C₂×#14268647	C₂²	semidirect
33. C₂×#14268646	C₂²	semidirect
34. C₂²×Dic₂₂₆	C₂²	semidirect
38. C₂×D₄×D₁₁₃	C₂²	semidirect
40. C₂²×C₄×D₁₁₃	C₂²	semidirect
41. #16813617	C₂²	semidirect
42. #16813617	C₂²	semidirect
43. #16813617	C₂²	semidirect
44. #16813617	C₂²	semidirect
45. #16813616	C₂²	semidirect
46. #16813616	C₂²	semidirect
47. #16813615	C₂²	semidirect
48. #16813615	C₂²	semidirect
49. #16813615	C₂²	semidirect
50. #16813615	C₂²	semidirect
51. #16813613	C₂²	semidirect
52. #16813612	C₂²	semidirect
53. #16813612	C₂²	semidirect
54. #16813612	C₂²	semidirect
55. #16813612	C₂²	semidirect
56. #16813610	C₂²	semidirect
57. #16813609	C₂²	semidirect
58. #16813608	C₂²	semidirect
59. #16813608	C₂²	semidirect
60. #16813608	C₂²	semidirect
61. #16813608	C₂²	semidirect
64. #16813607	C₂²	semidirect
65. #16813607	C₂²	semidirect
66. #16813607	C₂²	semidirect
67. #16813607	C₂²	semidirect
68. #16813607	C₂²	semidirect
69. #16813607	C₂²	semidirect
70. #16813605	C₂²	semidirect
71. #16813605	C₂²	semidirect
74. #16813604	C₂²	semidirect
75. #16813604	C₂²	semidirect
76. #16813604	C₂²	semidirect
77. #16813604	C₂²	semidirect
78. #16813603	C₂²	semidirect
79. #16813603	C₂²	semidirect
80. #16813602	C₂²	semidirect
81. #16813601	C₂²	semidirect
82. #16813600	C₂²	semidirect
83. #16813600	C₂²	semidirect
84. #16813600	C₂²	semidirect
85. #16813600	C₂²	semidirect
86. #16813600	C₂²	semidirect
87. #16813600	C₂²	semidirect
88. #16813600	C₂²	semidirect
89. #16813600	C₂²	semidirect
90. #16813600	C₂²	semidirect
91. #16813600	C₂²	semidirect
92. #16813599	C₂²	semidirect
93. #16813599	C₂²	semidirect
95. #16813597	C₂²	semidirect
96. #16813596	C₂²	semidirect
97. #16813596	C₂²	semidirect
98. #16813596	C₂²	semidirect
101. #16813595	C₂²	semidirect
102. #16813595	C₂²	semidirect
103. #16813594	C₂²	semidirect
104. #16813594	C₂²	semidirect
105. #16813594	C₂²	semidirect
106. #16813594	C₂²	semidirect
107. #16813594	C₂²	semidirect
108. #16813594	C₂²	semidirect
109. #16813594	C₂²	semidirect
110. #16813594	C₂²	semidirect
114. #16813592	C₂²	semidirect
115. #16813592	C₂²	semidirect
118. #16813590	C₂²	semidirect
119. #16813590	C₂²	semidirect
120. C₄×Dic₂₂₆	C₂²	semidirect
121. #16813587	C₂²	semidirect
123. C₄×D₄₅₂	C₂²	semidirect
124. C₄×D₄₅₂	C₂²	semidirect
125. D₄×Dic₁₁₃	C₂²	semidirect
126. D₄×Dic₁₁₃	C₂²	semidirect
127. D₄×Dic₁₁₃	C₂²	semidirect
129. #16813584	C₂²	semidirect
130. #16813584	C₂²	semidirect
131. #16813584	C₂²	semidirect
133. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
134. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
135. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
136. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
137. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
138. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
139. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
141. #16813582	C₂²	semidirect
142. #16813582	C₂²	semidirect
143. #16813582	C₂²	semidirect
144. #16813582	C₂²	semidirect
145. #16813582	C₂²	semidirect
146. #16813582	C₂²	semidirect
147. #16813582	C₂²	semidirect
148. #16813580	C₂²	semidirect
149. #16813580	C₂²	semidirect
150. #16813580	C₂²	semidirect
151. #16813579	C₂²	semidirect
152. #16813579	C₂²	semidirect
153. #16813579	C₂²	semidirect
154. #16813579	C₂²	semidirect
155. #16813578	C₂²	semidirect
156. #16813578	C₂²	semidirect
157. C₂×#14268626	C₂²	semidirect
158. C₂×#14268626	C₂²	semidirect
159. C₄⋊C₄×D₁₁₃	C₂²	semidirect
160. C₄⋊C₄×D₁₁₃	C₂²	semidirect
163. C₂×#14268624	C₂²	semidirect
164. C₂×#14268624	C₂²	semidirect
166. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
167. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
168. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
169. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
170. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
171. C₄²×D₁₁₃	C₂²	semidirect
172. #126×C₁₁₃	C₂²	semidirect
173. #126×C₁₁₃	C₂²	semidirect
174. #125×C₁₁₃	C₂²	semidirect
175. #123×C₁₁₃	C₂²	semidirect
176. #123×C₁₁₃	C₂²	semidirect
177. #121×C₁₁₃	C₂²	semidirect
178. #121×C₁₁₃	C₂²	semidirect
179. #121×C₁₁₃	C₂²	semidirect
180. #121×C₁₁₃	C₂²	semidirect
181. C₄×D₄×C₁₁₃	C₂²	semidirect
182. C₄×D₄×C₁₁₃	C₂²	semidirect
183. C₄×D₄×C₁₁₃	C₂²	semidirect
184. C₄×D₄×C₁₁₃	C₂²	semidirect
185. #117×C₁₁₃	C₂²	semidirect
186. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
366. C₂²×D₁₁₃	#41	semidirect
516. C₁₁₃	#3505	semidirect
522. #553	D₁₁₃	semidirect
567. #126	C₂×D₁₁₃	semidirect
568. #126	C₂×D₁₁₃	semidirect
574. #125	C₂×D₁₁₃	semidirect
599. #123	C₂×D₁₁₃	semidirect
600. #123	C₂×D₁₁₃	semidirect
633. #121	C₂×D₁₁₃	semidirect
634. #121	C₂×D₁₁₃	semidirect
635. #121	C₂×D₁₁₃	semidirect
636. #121	C₂×D₁₁₃	semidirect
673. C₄×D₄	C₂×D₁₁₃	semidirect
674. C₄×D₄	C₂×D₁₁₃	semidirect
675. C₄×D₄	C₂×D₁₁₃	semidirect
676. C₄×D₄	C₂×D₁₁₃	semidirect
686. #117	C₂×D₁₁₃	semidirect
691. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299297	2
#20299296	2
#20299291	2
#20299284	2
#20299280	2
#20299277	2
#20299276	2
#20299273	2
#20299272	2
#20299257	2
#20299254	2
#20299240	2
#20299237	2
#20299196	2
#20299191	2
#20299187	2
#20299180	2
#20299156	2
#20299131	2
#20299126	2
#20299107	2
#20299106	2
C₂×#16813600	2
#121×D₁₁₃	2
#20299070	2
C₄×D₄×D₁₁₃	2
#553×C₁₁₃	2
#3505	113