Subgroups — #28405256

Order 14464.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299349	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299346	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299344	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299338	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299332	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299320	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299311	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299301	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299292	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299284	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299280	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299277	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299273	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299272	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299219	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299219	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299218	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299211	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299207	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299199	C₂	1	1	yes	maximal, characteristic, complemented
22	#20299196	C₂	1	1	yes	maximal, characteristic, complemented
23	#20299195	C₂	1	1	yes	maximal, characteristic, complemented
24	#20299191	C₂	1	1	yes	maximal, characteristic, complemented
25	#20299188	C₂	1	1	yes	maximal, characteristic, complemented
26	#20299187	C₂	1	1	yes	maximal, characteristic, complemented
27	#20299184	C₂	1	1	yes	maximal, characteristic, complemented
28	#20299135	C₂	1	1	yes	maximal, characteristic, complemented
29	#20299131	C₂	1	1	yes	maximal, characteristic, complemented
30	#20299126	C₂	1	1	yes	maximal, characteristic, complemented
31	#552×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
32	#16813622	C₂²	1	1	yes	characteristic, complemented
33	#16813621	C₂²	1	1	yes	characteristic, complemented
34	#16813620	C₂²	1	1	yes	characteristic, complemented
35	#16813618	C₂²	1	1	yes	characteristic
36	#16813617	C₂²	1	1	yes	characteristic
37	#16813617	C₂²	1	1	yes	characteristic
38	#16813617	C₂²	1	1	yes	characteristic
39	#16813617	C₂²	1	1	yes	characteristic
40	#16813617	C₂²	1	1	yes	characteristic
41	#16813617	C₂²	1	1	yes	characteristic
42	#16813617	C₂²	1	1	yes	characteristic
43	#16813617	C₂²	1	1	yes	characteristic
44	#16813617	C₂²	1	1	yes	characteristic, complemented
45	#16813617	C₂²	1	1	yes	characteristic, complemented
46	#16813617	C₂²	1	1	yes	characteristic, complemented
47	#16813617	C₂²	1	1	yes	characteristic, complemented
48	#16813616	C₂²	1	1	yes	characteristic
49	#16813616	C₂²	1	1	yes	characteristic
50	#16813616	C₂²	1	1	yes	characteristic, complemented
51	#16813615	C₂²	1	1	yes	characteristic
52	#16813615	C₂²	1	1	yes	characteristic
53	#16813615	C₂²	1	1	yes	characteristic, complemented
54	#16813613	C₂²	1	1	yes	characteristic, complemented
55	#16813613	C₂²	1	1	yes	characteristic, complemented
56	#16813613	C₂²	1	1	yes	characteristic, complemented
57	#16813613	C₂²	1	1	yes	characteristic, complemented
58	#16813612	C₂²	1	1	yes	characteristic, complemented
59	#16813612	C₂²	1	1	yes	characteristic, complemented
60	#16813612	C₂²	1	1	yes	characteristic, complemented
61	#16813612	C₂²	1	1	yes	characteristic, complemented
62	#16813612	C₂²	1	1	yes	characteristic, complemented
63	#16813611	C₂²	1	1	yes	characteristic
64	#16813611	C₂²	1	1	yes	characteristic
65	#16813610	C₂²	1	1	yes	characteristic
66	#16813610	C₂²	1	1	yes	characteristic
67	#16813610	C₂²	1	1	yes	characteristic, complemented
68	#16813608	C₂²	1	1	yes	characteristic
69	#16813608	C₂²	1	1	yes	characteristic
70	#16813608	C₂²	1	1	yes	characteristic
71	#16813608	C₂²	1	1	yes	characteristic
72	#16813608	C₂²	1	1	yes	characteristic
73	#16813608	C₂²	1	1	yes	characteristic, complemented
74	#16813608	C₂²	1	1	yes	characteristic, complemented
75	#16813607	C₂²	1	1	yes	characteristic
76	#16813607	C₂²	1	1	yes	characteristic
77	#16813607	C₂²	1	1	yes	characteristic
78	#16813607	C₂²	1	1	yes	characteristic
79	#16813607	C₂²	1	1	yes	characteristic
80	#16813607	C₂²	1	1	yes	characteristic
81	#16813607	C₂²	1	1	yes	characteristic
82	#16813607	C₂²	1	1	yes	characteristic
83	#16813607	C₂²	1	1	yes	characteristic, complemented
84	#16813607	C₂²	1	1	yes	characteristic, complemented
85	#16813607	C₂²	1	1	yes	characteristic, complemented
86	#16813605	C₂²	1	1	yes	characteristic
87	#16813605	C₂²	1	1	yes	characteristic
88	#16813605	C₂²	1	1	yes	characteristic, complemented
89	#16813604	C₂²	1	1	yes	characteristic
90	#16813604	C₂²	1	1	yes	characteristic
91	#16813604	C₂²	1	1	yes	characteristic
92	#16813604	C₂²	1	1	yes	characteristic
93	#16813604	C₂²	1	1	yes	characteristic
94	#16813604	C₂²	1	1	yes	characteristic, complemented
95	#16813604	C₂²	1	1	yes	characteristic, complemented
96	#16813603	C₂²	1	1	yes	characteristic
97	#16813602	C₂²	1	1	yes	characteristic
98	#16813602	C₂²	1	1	yes	characteristic
99	#16813601	C₂²	1	1	yes	characteristic
100	#16813601	C₂²	1	1	yes	characteristic, complemented
101	#16813600	C₂²	1	1	yes	characteristic
102	#16813600	C₂²	1	1	yes	characteristic
103	#16813600	C₂²	1	1	yes	characteristic
104	#16813600	C₂²	1	1	yes	characteristic
105	#16813600	C₂²	1	1	yes	characteristic, complemented
106	#16813600	C₂²	1	1	yes	characteristic, complemented
107	#16813600	C₂²	1	1	yes	characteristic, complemented
108	#16813600	C₂²	1	1	yes	characteristic, complemented
109	#16813600	C₂²	1	1	yes	characteristic, complemented
110	#16813600	C₂²	1	1	yes	characteristic, complemented
111	#16813599	C₂²	1	1	yes	characteristic
112	#16813598	C₂²	1	1	yes	characteristic, complemented
113	#16813597	C₂²	1	1	yes	characteristic
114	#16813597	C₂²	1	1	yes	characteristic
115	#16813597	C₂²	1	1	yes	characteristic
116	#16813597	C₂²	1	1	yes	characteristic
117	#16813597	C₂²	1	1	yes	characteristic
118	#16813597	C₂²	1	1	yes	characteristic
119	#16813597	C₂²	1	1	yes	characteristic, complemented
120	#16813596	C₂²	1	1	yes	characteristic
121	#16813596	C₂²	1	1	yes	characteristic
122	#16813596	C₂²	1	1	yes	characteristic
123	#16813596	C₂²	1	1	yes	characteristic
124	#16813596	C₂²	1	1	yes	characteristic, complemented
125	#16813595	C₂²	1	1	yes	characteristic
126	#16813595	C₂²	1	1	yes	characteristic
127	#16813595	C₂²	1	1	yes	characteristic
128	#16813595	C₂²	1	1	yes	characteristic
129	#16813595	C₂²	1	1	yes	characteristic, complemented
130	#16813593	C₂²	1	1	yes	characteristic
131	#16813592	C₂²	1	1	yes	characteristic
132	#16813592	C₂²	1	1	yes	characteristic
133	#16813592	C₂²	1	1	yes	characteristic
134	#16813590	C₂²	1	1	yes	characteristic
135	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
137	#16813587	C₂²	1	1	yes	characteristic, complemented
138	#16813587	C₂²	1	1	yes	characteristic, complemented
139	#16813587	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
141	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
142	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
143	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
144	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
145	#16813584	C₂²	1	1	yes	characteristic
146	#16813584	C₂²	1	1	yes	characteristic
147	#16813584	C₂²	1	1	yes	characteristic
148	#16813584	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
153	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
154	#16813582	C₂²	1	1	yes	characteristic
155	#16813582	C₂²	1	1	yes	characteristic
156	#16813582	C₂²	1	1	yes	characteristic
157	#16813580	C₂²	1	1	yes	characteristic
158	#16813580	C₂²	1	1	yes	characteristic, complemented
159	#16813580	C₂²	1	1	yes	characteristic, complemented
160	#16813579	C₂²	1	1	yes	characteristic
161	#16813579	C₂²	1	1	yes	characteristic
162	#16813579	C₂²	1	1	yes	characteristic
163	#16813579	C₂²	1	1	yes	characteristic, complemented
164	#16813579	C₂²	1	1	yes	characteristic, complemented
165	#16813578	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
167	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
168	C₂×#14268624	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
171	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₁₃	C₂²	1	1	yes	characteristic
173	#126×C₁₁₃	C₂²	1	1	yes	characteristic
174	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
175	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
176	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
177	#123×C₁₁₃	C₂²	1	1	yes	characteristic
178	#123×C₁₁₃	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
180	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
183	#117×C₁₁₃	C₂²	1	1	yes	characteristic
184	#117×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	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
189	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
190	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
191	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
192	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
193	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
194	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
195	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
196	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
197	C₂×D₄₅₂	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×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₁₃	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	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
234	#14268626	C₂³	1	1	yes	characteristic
235	#14268626	C₂³	1	1	yes	characteristic
236	#14268626	C₂³	1	1	yes	characteristic
237	#14268626	C₂³	1	1	yes	characteristic
238	#14268626	C₂³	1	1	yes	characteristic
239	#14268626	C₂³	1	1	yes	characteristic
240	#14268626	C₂³	1	1	yes	characteristic
241	#14268626	C₂³	1	1	yes	characteristic
242	#14268626	C₂³	1	1	yes	characteristic
243	#14268626	C₂³	1	1	yes	characteristic
244	#14268626	C₂³	1	1	yes	characteristic
245	#14268626	C₂³	1	1	yes	characteristic
246	#14268626	C₂³	1	1	yes	characteristic
247	#14268626	C₂³	1	1	yes	characteristic
248	#14268626	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	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
262	#14268624	C₂³	1	1	yes	characteristic
263	#14268624	C₂³	1	1	yes	characteristic
264	#14268624	C₂³	1	1	yes	characteristic
265	#14268624	C₂³	1	1	yes	characteristic
266	#14268624	C₂³	1	1	yes	characteristic
267	#14268624	C₂³	1	1	yes	characteristic
268	#14268624	C₂³	1	1	yes	characteristic
269	#14268624	C₂³	1	1	yes	characteristic
270	#14268624	C₂³	1	1	yes	characteristic
271	#14268624	C₂³	1	1	yes	characteristic
272	#14268624	C₂³	1	1	yes	characteristic
273	#14268624	C₂³	1	1	yes	characteristic
274	#14268624	C₂³	1	1	yes	characteristic
275	#14268624	C₂³	1	1	yes	characteristic
276	#14268624	C₂³	1	1	yes	characteristic
277	#14268624	C₂³	1	1	yes	characteristic
278	#14268624	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	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
297	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
298	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
299	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
300	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
301	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
302	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
303	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
304	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
305	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
307	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
308	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
309	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
310	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
311	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
312	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
313	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
314	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
315	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
316	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
329	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
337	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
338	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
339	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
340	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
341	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
342	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
343	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
344	C₂²×D₁₁₃	—	4	1	no	—
345	C₂²×D₁₁₃	—	4	1	no	—
346	C₂²×D₁₁₃	—	4	1	no	—
347	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
348	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
349	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
350	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
352	Q₈×C₁₁₃	—	4	1	no	—
353	D₄×C₁₁₃	—	4	1	no	—
354	C₂×C₄×C₁₁₃	—	4	1	no	—
355	C₂×C₄×C₁₁₃	—	4	1	no	—
356	C₂×C₄×C₁₁₃	—	4	1	no	—
357	C₂×C₄×C₁₁₃	—	4	1	no	—
358	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
371	C₂²⋊D₁₁₃	—	4	1	no	—
372	C₂²⋊D₁₁₃	—	4	1	no	—
373	C₂²⋊D₁₁₃	—	4	1	no	—
374	C₂²⋊D₁₁₃	—	4	1	no	—
375	C₂²⋊D₁₁₃	—	4	1	no	—
376	C₂²⋊D₁₁₃	—	4	1	no	—
377	C₂²⋊D₁₁₃	—	4	1	no	—
378	C₂²⋊D₁₁₃	—	4	1	no	—
379	C₂×Dic₁₁₃	—	4	1	no	—
380	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
391	D₄₅₂	—	4	1	no	—
392	D₄₅₂	—	4	1	no	—
393	D₄₅₂	—	4	1	no	—
394	D₄₅₂	—	4	1	no	—
395	D₄₅₂	—	4	1	no	—
396	D₄₅₂	—	4	1	no	—
397	D₄₅₂	—	4	1	no	—
398	D₄₅₂	—	4	1	no	—
399	D₄₅₂	—	4	1	no	—
400	C₄×D₁₁₃	—	4	1	no	—
401	C₄×D₁₁₃	—	4	1	no	—
402	C₄×D₁₁₃	—	4	1	no	—
403	C₄×D₁₁₃	—	4	1	no	—
404	C₄×D₁₁₃	—	4	1	no	—
405	C₄×D₁₁₃	—	4	1	no	—
406	C₄×D₁₁₃	—	4	1	no	—
407	C₄×D₁₁₃	—	4	1	no	—
408	C₄×D₁₁₃	—	4	1	no	—
409	C₄×D₁₁₃	—	4	1	no	—
410	C₄×D₁₁₃	—	4	1	no	—
411	C₄×D₁₁₃	—	4	1	no	—
412	C₄×D₁₁₃	—	4	1	no	—
413	Dic₂₂₆	—	4	1	no	—
414	Dic₂₂₆	—	4	1	no	—
415	Dic₂₂₆	—	4	1	no	—
416	Dic₂₂₆	—	4	1	no	—
417	Dic₂₂₆	—	4	1	no	—
418	C₂²×C₁₁₃	—	2	1	no	—
419	C₂²×C₁₁₃	—	2	1	no	—
420	C₂²×C₁₁₃	—	2	1	no	—
421	C₂²×C₁₁₃	—	2	1	no	—
422	C₂²×C₁₁₃	—	2	1	no	—
423	C₂²×C₁₁₃	—	2	1	no	—
424	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
425	C₂×D₁₁₃	—	2	1	no	—
426	C₂×D₁₁₃	—	2	1	no	—
427	C₂×D₁₁₃	—	2	1	no	—
428	C₂×D₁₁₃	—	2	1	no	—
429	C₂×D₁₁₃	—	2	1	no	—
430	C₂×D₁₁₃	—	2	1	no	—
431	C₂×D₁₁₃	—	2	1	no	—
432	C₂×D₁₁₃	—	2	1	no	—
433	C₂×D₁₁₃	—	2	1	no	—
434	C₂×D₁₁₃	—	2	1	no	—
435	C₂×D₁₁₃	—	2	1	no	—
436	C₂×D₁₁₃	—	2	1	no	—
437	C₂×D₁₁₃	—	2	1	no	—
438	C₂×D₁₁₃	—	2	1	no	—
439	C₂×D₁₁₃	—	2	1	no	—
440	C₂×D₁₁₃	—	8	2	no	—
441	C₄×C₁₁₃	—	2	1	no	—
442	C₄×C₁₁₃	—	2	1	no	—
443	C₄×C₁₁₃	—	2	1	no	—
444	C₄×C₁₁₃	—	2	1	no	—
445	C₄×C₁₁₃	—	2	1	no	—
446	C₄×C₁₁₃	—	2	1	no	—
447	C₄×C₁₁₃	—	2	1	no	—
448	C₄×C₁₁₃	—	2	1	no	—
449	C₄×C₁₁₃	—	2	1	no	—
450	C₄×C₁₁₃	—	2	1	no	—
451	C₄×C₁₁₃	—	2	1	no	—
452	C₄×C₁₁₃	—	2	1	no	—
453	C₄×C₁₁₃	—	2	1	no	—
454	Dic₁₁₃	—	2	1	no	—
455	Dic₁₁₃	—	2	1	no	—
456	Dic₁₁₃	—	2	1	no	—
457	Dic₁₁₃	—	2	1	no	—
458	Dic₁₁₃	—	2	1	no	—
459	Dic₁₁₃	—	2	1	no	—
460	Dic₁₁₃	—	2	1	no	—
461	Dic₁₁₃	—	2	1	no	—
462	Dic₁₁₃	—	2	1	no	—
463	Dic₁₁₃	—	2	1	no	—
464	Dic₁₁₃	—	2	1	no	—
465	C₂×C₁₁₃	—	4	1	no	—
466	C₂×C₁₁₃	—	4	1	no	—
467	C₂×C₁₁₃	#585	1	1	yes	characteristic
468	C₂×C₁₁₃	#585	1	1	yes	characteristic
469	C₂×C₁₁₃	#585	1	1	yes	characteristic
470	D₁₁₃	—	4	1	no	—
471	D₁₁₃	—	4	1	no	—
472	D₁₁₃	—	4	1	no	—
473	D₁₁₃	—	4	1	no	—
474	D₁₁₃	—	4	1	no	—
475	#3566	—	113	1	no	maximal, Sylow
476	C₁₁₃	#3566	1	1	yes	characteristic, complemented, Sylow
477	#563	—	113	1	no	—
478	#562	—	113	1	no	—
479	#562	—	113	1	no	—
480	#560	—	113	1	no	—
481	#559	—	113	1	no	—
482	#556	—	113	1	no	—
483	#555	—	113	1	no	—
484	#553	—	113	1	no	—
485	#553	—	113	1	no	—
486	#553	—	113	1	no	—
487	#552	—	113	1	no	—
488	#552	—	113	1	no	—
489	#552	D₁₁₃	1	1	yes	characteristic, complemented
490	#551	—	113	1	no	—
491	#551	—	113	1	no	—
492	#551	—	113	1	no	—
493	#542	—	113	1	no	—
494	#542	—	113	1	no	—
495	#542	—	113	1	no	—
496	#541	—	113	1	no	—
497	#541	—	113	1	no	—
498	#540	—	113	1	no	—
499	#539	—	113	1	no	—
500	#539	—	113	1	no	—
501	#539	—	113	1	no	—
502	#538	—	113	1	no	—
503	#538	—	113	1	no	—
504	#538	—	113	1	no	—
505	#529	—	113	1	no	—
506	#529	—	113	1	no	—
507	#529	—	113	1	no	—
508	C₄⋊Q₈	—	113	1	no	—
509	C₄⋊Q₈	—	113	1	no	—
510	C₄⋊Q₈	—	113	1	no	—
511	#127	—	113	1	no	—
512	#126	—	113	1	no	—
513	#126	—	113	1	no	—
514	#126	—	113	1	no	—
515	#126	—	113	1	no	—
516	#126	—	113	1	no	—
517	#126	—	113	1	no	—
518	#126	—	113	1	no	—
519	#126	—	113	1	no	—
520	#126	—	113	1	no	—
521	#126	—	113	1	no	—
522	#126	—	113	1	no	—
523	#126	—	113	1	no	—
524	#126	—	113	1	no	—
525	#126	—	113	1	no	—
526	#126	—	113	1	no	—
527	#126	—	113	1	no	—
528	#126	—	113	1	no	—
529	#126	—	113	1	no	—
530	#126	C₂×D₁₁₃	1	1	yes	characteristic
531	#126	C₂×D₁₁₃	1	1	yes	characteristic
532	#125	—	113	1	no	—
533	#125	—	113	1	no	—
534	#125	—	113	1	no	—
535	#125	—	113	1	no	—
536	#125	—	113	1	no	—
537	#125	—	113	1	no	—
538	#125	—	113	1	no	—
539	#125	—	113	1	no	—
540	#125	—	113	1	no	—
541	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
542	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
543	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
544	#124	—	113	1	no	—
545	#124	—	113	1	no	—
546	#124	—	113	1	no	—
547	#124	—	113	1	no	—
548	#124	—	113	1	no	—
549	#124	—	113	1	no	—
550	#124	—	113	1	no	—
551	#124	—	113	1	no	—
552	#124	—	113	1	no	—
553	#124	—	113	1	no	—
554	#124	—	113	1	no	—
555	#124	—	113	1	no	—
556	#123	—	113	1	no	—
557	#123	—	113	1	no	—
558	#123	—	113	1	no	—
559	#123	—	113	1	no	—
560	#123	—	113	1	no	—
561	#123	—	113	1	no	—
562	#123	—	113	1	no	—
563	#123	—	113	1	no	—
564	#123	—	113	1	no	—
565	#123	—	113	1	no	—
566	#123	—	113	1	no	—
567	#123	—	113	1	no	—
568	#123	—	113	1	no	—
569	#123	—	113	1	no	—
570	#123	—	113	1	no	—
571	#123	—	113	1	no	—
572	#123	—	113	1	no	—
573	#123	—	113	1	no	—
574	#123	—	113	1	no	—
575	#123	—	113	1	no	—
576	#123	—	113	1	no	—
577	#123	—	113	1	no	—
578	#123	C₂×D₁₁₃	1	1	yes	characteristic
579	#123	C₂×D₁₁₃	1	1	yes	characteristic
580	C₂²⋊Q₈	—	113	1	no	—
581	C₂²⋊Q₈	—	113	1	no	—
582	C₂²⋊Q₈	—	113	1	no	—
583	C₂²⋊Q₈	—	113	1	no	—
584	C₂²⋊Q₈	—	113	1	no	—
585	C₂²⋊Q₈	—	113	1	no	—
586	C₂²⋊Q₈	—	113	1	no	—
587	C₂²⋊Q₈	—	113	1	no	—
588	C₂²⋊Q₈	—	113	1	no	—
589	C₂²⋊Q₈	—	113	1	no	—
590	C₂²⋊Q₈	—	113	1	no	—
591	C₂²⋊Q₈	—	113	1	no	—
592	C₂²⋊Q₈	—	113	1	no	—
593	C₂²⋊Q₈	—	113	1	no	—
594	C₂²⋊Q₈	—	113	1	no	—
595	C₂²⋊Q₈	—	113	1	no	—
596	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
597	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
598	#121	—	113	1	no	—
599	#121	—	113	1	no	—
600	#121	—	113	1	no	—
601	#121	—	113	1	no	—
602	#121	—	113	1	no	—
603	#121	—	113	1	no	—
604	#121	—	113	1	no	—
605	#121	—	113	1	no	—
606	#121	—	113	1	no	—
607	#121	—	113	1	no	—
608	#121	—	113	1	no	—
609	#121	—	113	1	no	—
610	#121	—	113	1	no	—
611	#121	—	113	1	no	—
612	#121	—	113	1	no	—
613	#121	—	113	1	no	—
614	#121	—	113	1	no	—
615	#121	—	113	1	no	—
616	#120	—	113	1	no	—
617	#120	—	113	1	no	—
618	#120	—	113	1	no	—
619	#120	—	113	1	no	—
620	C₄×Q₈	—	113	1	no	—
621	C₄×Q₈	—	113	1	no	—
622	C₄×Q₈	—	113	1	no	—
623	C₄×Q₈	—	113	1	no	—
624	C₄×Q₈	—	113	1	no	—
625	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
626	C₄×D₄	—	113	1	no	—
627	C₄×D₄	—	113	1	no	—
628	C₄×D₄	—	113	1	no	—
629	C₄×D₄	—	113	1	no	—
630	C₄×D₄	—	113	1	no	—
631	C₄×D₄	—	113	1	no	—
632	C₄×D₄	—	113	1	no	—
633	C₄×D₄	—	113	1	no	—
634	C₄×D₄	—	113	1	no	—
635	C₄×D₄	—	113	1	no	—
636	C₄×D₄	—	113	1	no	—
637	C₄×D₄	—	113	1	no	—
638	C₄×D₄	—	113	1	no	—
639	C₄×D₄	—	113	1	no	—
640	C₄×D₄	—	113	1	no	—
641	C₄×D₄	—	113	1	no	—
642	C₄×D₄	—	113	1	no	—
643	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
644	#117	—	113	1	no	—
645	#117	—	113	1	no	—
646	#117	—	113	1	no	—
647	#117	—	113	1	no	—
648	#117	—	113	1	no	—
649	#117	—	113	1	no	—
650	#117	—	113	1	no	—
651	#117	—	113	1	no	—
652	#117	—	113	1	no	—
653	#117	C₂×D₁₁₃	1	1	yes	characteristic
654	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
655	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
656	C₂×C₄⋊C₄	—	113	1	no	—
657	C₂×C₄⋊C₄	—	113	1	no	—
658	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
659	C₂×C₂²⋊C₄	—	113	1	no	—
660	C₂×C₂²⋊C₄	—	113	1	no	—
661	C₂×C₂²⋊C₄	—	113	1	no	—
662	C₂×C₄²	—	113	1	no	—
663	C₂⁴	—	113	1	no	—
664	C₂×Q₈	—	113	1	no	—
665	C₂×Q₈	—	113	1	no	—
666	C₂×Q₈	—	113	1	no	—
667	C₂×Q₈	—	113	1	no	—
668	C₂×Q₈	—	113	1	no	—
669	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
670	C₂×D₄	—	113	1	no	—
671	C₂×D₄	—	113	1	no	—
672	C₂×D₄	—	113	1	no	—
673	C₂×D₄	—	113	1	no	—
674	C₂×D₄	—	113	1	no	—
675	C₂×D₄	—	113	1	no	—
676	C₂×D₄	—	113	1	no	—
677	C₂×D₄	—	113	1	no	—
678	C₂×D₄	—	113	1	no	—
679	C₂×D₄	—	113	1	no	—
680	C₂×D₄	—	113	1	no	—
681	C₂×D₄	—	113	1	no	—
682	C₂×D₄	—	113	1	no	—
683	C₂×D₄	—	113	1	no	—
684	C₂×D₄	—	113	1	no	—
685	C₂×D₄	—	113	1	no	—
686	C₂×D₄	—	113	1	no	—
687	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
688	C₂²×C₄	—	113	1	no	—
689	C₂²×C₄	—	113	1	no	—
690	C₂²×C₄	—	113	1	no	—
691	C₂²×C₄	—	113	1	no	—
692	C₂²×C₄	—	113	1	no	—
693	C₂²×C₄	—	113	1	no	—
694	C₂²×C₄	—	113	1	no	—
695	C₂²×C₄	—	113	1	no	—
696	C₂²×C₄	—	113	1	no	—
697	C₂²×C₄	—	113	1	no	—
698	C₂²×C₄	—	113	1	no	—
699	C₂²×C₄	—	113	1	no	—
700	C₂²×C₄	—	113	1	no	—
701	C₂²×C₄	—	113	1	no	—
702	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
706	C₄⋊C₄	—	113	1	no	—
707	C₄⋊C₄	—	113	1	no	—
708	C₄⋊C₄	—	113	1	no	—
709	C₄⋊C₄	—	113	1	no	—
710	C₄⋊C₄	—	113	1	no	—
711	C₄⋊C₄	—	113	1	no	—
712	C₄⋊C₄	—	113	1	no	—
713	C₄⋊C₄	—	113	1	no	—
714	C₄⋊C₄	—	113	1	no	—
715	C₄⋊C₄	—	113	1	no	—
716	C₄⋊C₄	—	113	1	no	—
717	C₄⋊C₄	—	113	1	no	—
718	C₄⋊C₄	—	113	1	no	—
719	C₄⋊C₄	—	113	1	no	—
720	C₄⋊C₄	—	113	1	no	—
721	C₄⋊C₄	—	113	1	no	—
722	C₄⋊C₄	—	113	1	no	—
723	C₄⋊C₄	—	113	1	no	—
724	C₄⋊C₄	—	113	1	no	—
725	C₄⋊C₄	—	113	1	no	—
726	C₄⋊C₄	—	113	1	no	—
727	C₄⋊C₄	—	113	1	no	—
728	C₄⋊C₄	—	113	1	no	—
729	C₄⋊C₄	—	113	1	no	—
730	C₄⋊C₄	—	113	1	no	—
731	C₄⋊C₄	—	113	1	no	—
732	C₄⋊C₄	—	113	1	no	—
733	C₄⋊C₄	—	113	1	no	—
734	C₄⋊C₄	—	113	1	no	—
735	C₄⋊C₄	—	113	1	no	—
736	C₄⋊C₄	—	113	1	no	—
737	C₄⋊C₄	—	113	1	no	—
738	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
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	—	113	1	no	—
764	C₂²⋊C₄	—	113	1	no	—
765	C₂²⋊C₄	—	113	1	no	—
766	C₂²⋊C₄	—	113	1	no	—
767	C₂²⋊C₄	—	113	1	no	—
768	C₂²⋊C₄	—	113	1	no	—
769	C₂²⋊C₄	—	113	1	no	—
770	C₂²⋊C₄	—	113	1	no	—
771	C₂²⋊C₄	—	113	1	no	—
772	C₂²⋊C₄	—	113	1	no	—
773	C₂²⋊C₄	—	113	1	no	—
774	C₂²⋊C₄	—	113	1	no	—
775	C₂²⋊C₄	—	113	1	no	—
776	C₂²⋊C₄	—	113	1	no	—
777	C₂²⋊C₄	—	113	1	no	—
778	C₂²⋊C₄	—	113	1	no	—
779	C₂²⋊C₄	—	113	1	no	—
780	C₂²⋊C₄	—	113	1	no	—
781	C₂²⋊C₄	—	113	1	no	—
782	C₂²⋊C₄	—	113	1	no	—
783	C₂²⋊C₄	—	113	1	no	—
784	C₂²⋊C₄	—	113	1	no	—
785	C₂²⋊C₄	—	113	1	no	—
786	C₂²⋊C₄	—	113	1	no	—
787	C₂²⋊C₄	—	113	1	no	—
788	C₂²⋊C₄	—	113	1	no	—
789	C₂²⋊C₄	—	113	1	no	—
790	C₂²⋊C₄	—	113	1	no	—
791	C₂²⋊C₄	—	113	1	no	—
792	C₂²⋊C₄	—	113	1	no	—
793	C₂²⋊C₄	—	113	1	no	—
794	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
802	C₄²	—	113	1	no	—
803	C₄²	—	113	1	no	—
804	C₄²	—	113	1	no	—
805	C₄²	—	113	1	no	—
806	C₄²	—	113	1	no	—
807	C₄²	—	113	1	no	—
808	C₄²	—	113	1	no	—
809	C₄²	—	113	1	no	—
810	C₄²	—	113	1	no	—
811	C₄²	—	113	1	no	—
812	C₄²	—	113	1	no	—
813	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
814	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
815	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
816	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
817	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
818	C₂³	—	113	1	no	—
819	C₂³	—	113	1	no	—
820	C₂³	—	113	1	no	—
821	C₂³	—	113	1	no	—
822	C₂³	—	113	1	no	—
823	C₂³	—	452	1	no	—
824	C₂³	—	452	1	no	—
825	C₂³	—	452	1	no	—
826	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
827	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
828	Q₈	—	4	1	no	—
829	Q₈	—	452	1	no	—
830	Q₈	—	452	1	no	—
831	Q₈	—	452	1	no	—
832	Q₈	—	452	1	no	—
833	Q₈	—	452	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	452	1	no	—
836	D₄	—	452	1	no	—
837	D₄	—	452	1	no	—
838	D₄	—	452	1	no	—
839	D₄	—	452	1	no	—
840	D₄	—	452	1	no	—
841	D₄	—	452	1	no	—
842	D₄	—	452	1	no	—
843	D₄	—	452	1	no	—
844	D₄	—	452	1	no	—
845	D₄	—	452	1	no	—
846	D₄	—	452	1	no	—
847	D₄	—	452	1	no	—
848	D₄	—	452	1	no	—
849	D₄	—	452	1	no	—
850	D₄	—	452	1	no	—
851	D₄	—	452	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	113	1	no	—
857	C₂×C₄	—	113	1	no	—
858	C₂×C₄	—	113	1	no	—
859	C₂×C₄	—	113	1	no	—
860	C₂×C₄	—	113	1	no	—
861	C₂×C₄	—	113	1	no	—
862	C₂×C₄	—	113	1	no	—
863	C₂×C₄	—	113	1	no	—
864	C₂×C₄	—	113	1	no	—
865	C₂×C₄	—	113	1	no	—
866	C₂×C₄	—	113	1	no	—
867	C₂×C₄	—	452	1	no	—
868	C₂×C₄	—	452	1	no	—
869	C₂×C₄	—	452	1	no	—
870	C₂×C₄	—	452	1	no	—
871	C₂×C₄	—	452	1	no	—
872	C₂×C₄	—	452	1	no	—
873	C₂×C₄	—	452	1	no	—
874	C₂×C₄	—	452	1	no	—
875	C₂×C₄	—	452	1	no	—
876	C₂×C₄	—	452	1	no	—
877	C₂×C₄	—	452	1	no	—
878	C₂×C₄	—	452	1	no	—
879	C₂×C₄	—	452	1	no	—
880	C₂×C₄	—	452	1	no	—
881	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
882	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
883	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	904	2	no	—
901	C₂²	—	226	1	no	—
902	C₂²	—	226	1	no	—
903	C₂²	—	226	1	no	—
904	C₂²	—	226	1	no	—
905	C₂²	—	226	1	no	—
906	C₂²	—	226	1	no	—
907	C₂²	—	226	1	no	—
908	C₂²	—	226	1	no	—
909	C₂²	—	226	1	no	—
910	C₂²	—	226	1	no	—
911	C₂²	—	226	1	no	—
912	C₂²	—	226	1	no	—
913	C₂²	—	226	1	no	—
914	C₂²	—	226	1	no	—
915	C₂²	—	226	1	no	—
916	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	226	1	no	—
931	C₄	—	226	1	no	—
932	C₄	—	226	1	no	—
933	C₄	—	226	1	no	—
934	C₄	—	226	1	no	—
935	C₄	—	226	1	no	—
936	C₄	—	226	1	no	—
937	C₄	—	226	1	no	—
938	C₄	—	226	1	no	—
939	C₄	—	226	1	no	—
940	C₄	—	226	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	452	1	no	—
944	C₂	—	452	1	no	—
945	C₂	—	452	1	no	—
946	C₂	—	452	1	no	—
947	C₂	—	452	1	no	—
948	C₂	#20299434	1	1	yes	characteristic
949	C₂	#20299434	1	1	yes	characteristic
950	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#552×C₁₁₃	C₂
hypercenter	#552	D₁₁₃
hypocenter	C₁₁₃	#3566
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #20299349	C₂	semidirect
2. #20299346	C₂	semidirect
3. #20299344	C₂	semidirect
4. #20299338	C₂	semidirect
5. #20299332	C₂	semidirect
6. #20299320	C₂	semidirect
7. #20299311	C₂	semidirect
8. #20299301	C₂	semidirect
9. #20299296	C₂	semidirect
10. #20299292	C₂	semidirect
11. #20299284	C₂	semidirect
12. #20299280	C₂	semidirect
13. #20299277	C₂	semidirect
14. #20299273	C₂	semidirect
15. #20299272	C₂	semidirect
16. #20299219	C₂	semidirect
17. #20299219	C₂	semidirect
18. #20299218	C₂	semidirect
19. #20299211	C₂	semidirect
20. #20299207	C₂	semidirect
21. #20299199	C₂	semidirect
22. #20299196	C₂	semidirect
23. #20299195	C₂	semidirect
24. #20299191	C₂	semidirect
25. #20299188	C₂	semidirect
26. #20299187	C₂	semidirect
27. #20299184	C₂	semidirect
28. #20299135	C₂	semidirect
29. #20299131	C₂	semidirect
30. #20299126	C₂	semidirect
31. #552×C₁₁₃	C₂	semidirect
32. #16813622	C₂²	semidirect
33. #16813621	C₂²	semidirect
34. #16813620	C₂²	semidirect
44. #16813617	C₂²	semidirect
45. #16813617	C₂²	semidirect
46. #16813617	C₂²	semidirect
47. #16813617	C₂²	semidirect
50. #16813616	C₂²	semidirect
53. #16813615	C₂²	semidirect
54. #16813613	C₂²	semidirect
55. #16813613	C₂²	semidirect
56. #16813613	C₂²	semidirect
57. #16813613	C₂²	semidirect
58. #16813612	C₂²	semidirect
59. #16813612	C₂²	semidirect
60. #16813612	C₂²	semidirect
61. #16813612	C₂²	semidirect
62. #16813612	C₂²	semidirect
67. #16813610	C₂²	semidirect
73. #16813608	C₂²	semidirect
74. #16813608	C₂²	semidirect
83. #16813607	C₂²	semidirect
84. #16813607	C₂²	semidirect
85. #16813607	C₂²	semidirect
88. #16813605	C₂²	semidirect
94. #16813604	C₂²	semidirect
95. #16813604	C₂²	semidirect
100. #16813601	C₂²	semidirect
105. #16813600	C₂²	semidirect
106. #16813600	C₂²	semidirect
107. #16813600	C₂²	semidirect
108. #16813600	C₂²	semidirect
109. #16813600	C₂²	semidirect
110. #16813600	C₂²	semidirect
112. #16813598	C₂²	semidirect
119. #16813597	C₂²	semidirect
124. #16813596	C₂²	semidirect
129. #16813595	C₂²	semidirect
135. C₄×Dic₂₂₆	C₂²	semidirect
136. C₄×Dic₂₂₆	C₂²	semidirect
137. #16813587	C₂²	semidirect
138. #16813587	C₂²	semidirect
139. #16813587	C₂²	semidirect
143. C₄×D₄₅₂	C₂²	semidirect
144. C₄×D₄₅₂	C₂²	semidirect
148. #16813584	C₂²	semidirect
151. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
152. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
153. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
158. #16813580	C₂²	semidirect
159. #16813580	C₂²	semidirect
163. #16813579	C₂²	semidirect
164. #16813579	C₂²	semidirect
166. C₄⋊C₄×D₁₁₃	C₂²	semidirect
167. C₄⋊C₄×D₁₁₃	C₂²	semidirect
171. C₄²×D₁₁₃	C₂²	semidirect
174. #125×C₁₁₃	C₂²	semidirect
175. #125×C₁₁₃	C₂²	semidirect
176. #125×C₁₁₃	C₂²	semidirect
180. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
181. C₄×Q₈×C₁₁₃	C₂²	semidirect
184. #117×C₁₁₃	C₂²	semidirect
185. #117×C₁₁₃	C₂²	semidirect
186. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
476. C₁₁₃	#3566	semidirect
489. #552	D₁₁₃	semidirect
541. #125	C₂×D₁₁₃	semidirect
542. #125	C₂×D₁₁₃	semidirect
543. #125	C₂×D₁₁₃	semidirect
597. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
625. C₄×Q₈	C₂×D₁₁₃	semidirect
654. #117	C₂×D₁₁₃	semidirect
655. #117	C₂×D₁₁₃	semidirect
658. 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
#20299349	2
#20299346	2
#20299344	2
#20299338	2
#20299332	2
#20299320	2
#20299311	2
#20299301	2
#20299296	2
#20299292	2
#20299284	2
#20299280	2
#20299277	2
#20299273	2
#20299272	2
#20299219	2
#20299218	2
#20299211	2
#20299207	2
#20299199	2
#20299196	2
#20299195	2
#20299191	2
#20299188	2
#20299187	2
#20299184	2
#20299135	2
#20299131	2
#20299126	2
#552×C₁₁₃	2
#3566	113