Subgroups — #28404417

Order 14464.

1140 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299332	C₂	1	2	yes	maximal, complemented
2	#20299331	C₂	1	2	yes	maximal, complemented
3	#20299319	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299316	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299312	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299311	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299297	C₂	1	2	yes	maximal, complemented
8	#20299293	C₂	1	2	yes	maximal, complemented
9	#20299267	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299266	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299250	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299247	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299183	C₂	1	2	yes	maximal, complemented
14	#20299181	C₂	1	2	yes	maximal, complemented
15	#20299163	C₂	1	2	yes	maximal, complemented
16	#20299150	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299143	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299111	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299109	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299108	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299077	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#525×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14268646	C₂²	1	2	yes	—
27	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
30	#16813621	C₂²	1	1	yes	characteristic, complemented
31	#16813621	C₂²	1	1	yes	characteristic, complemented
32	#16813620	C₂²	1	1	yes	characteristic, complemented
33	#16813618	C₂²	1	2	yes	—
34	#16813618	C₂²	1	2	yes	—
35	#16813618	C₂²	1	1	yes	characteristic, complemented
36	#16813617	C₂²	1	2	yes	complemented
37	#16813616	C₂²	1	2	yes	complemented
38	#16813615	C₂²	1	2	yes	complemented
39	#16813615	C₂²	1	2	yes	complemented
40	#16813612	C₂²	1	2	yes	complemented
41	#16813610	C₂²	1	2	yes	complemented
42	#16813609	C₂²	1	2	yes	complemented
43	#16813608	C₂²	1	2	yes	—
44	#16813608	C₂²	1	2	yes	—
45	#16813608	C₂²	1	2	yes	complemented
46	#16813608	C₂²	1	2	yes	complemented
47	#16813608	C₂²	1	2	yes	complemented
48	#16813607	C₂²	1	2	yes	complemented
49	#16813607	C₂²	1	2	yes	complemented
50	#16813605	C₂²	1	2	yes	complemented
51	#16813605	C₂²	1	2	yes	complemented
52	#16813604	C₂²	1	2	yes	complemented
53	#16813604	C₂²	1	2	yes	complemented
54	#16813603	C₂²	1	2	yes	complemented
55	#16813602	C₂²	1	1	yes	characteristic, complemented
56	#16813601	C₂²	1	1	yes	characteristic
57	#16813601	C₂²	1	1	yes	characteristic, complemented
58	#16813599	C₂²	1	2	yes	—
59	#16813598	C₂²	1	1	yes	characteristic, complemented
60	#16813597	C₂²	1	1	yes	characteristic, complemented
61	#16813596	C₂²	1	1	yes	characteristic
62	#16813596	C₂²	1	2	yes	complemented
63	#16813596	C₂²	1	1	yes	characteristic, complemented
64	#16813595	C₂²	1	2	yes	—
65	#16813595	C₂²	1	2	yes	—
66	#16813595	C₂²	1	2	yes	complemented
67	#16813594	C₂²	1	2	yes	—
68	#16813594	C₂²	1	2	yes	—
69	#16813594	C₂²	1	2	yes	—
70	#16813594	C₂²	1	2	yes	complemented
71	#16813593	C₂²	1	2	yes	complemented
72	#16813593	C₂²	1	1	yes	characteristic, complemented
73	#16813592	C₂²	1	2	yes	—
74	#16813591	C₂²	1	2	yes	—
75	#16813590	C₂²	1	2	yes	—
76	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
78	#16813587	C₂²	1	1	yes	characteristic, complemented
79	#16813587	C₂²	1	2	yes	complemented
80	#16813587	C₂²	1	2	yes	complemented
81	D₄×Dic₁₁₃	C₂²	1	2	yes	—
82	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
83	#16813584	C₂²	1	2	yes	complemented
84	#16813584	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
96	#16813582	C₂²	1	2	yes	—
97	#16813582	C₂²	1	2	yes	complemented
98	#16813582	C₂²	1	2	yes	complemented
99	#16813582	C₂²	1	2	yes	complemented
100	#16813581	C₂²	1	1	yes	characteristic, complemented
101	#16813580	C₂²	1	1	yes	characteristic, complemented
102	#16813580	C₂²	1	1	yes	characteristic, complemented
103	#16813579	C₂²	1	2	yes	complemented
104	#16813578	C₂²	1	2	yes	—
105	#16813578	C₂²	1	2	yes	complemented
106	C₂×#14268626	C₂²	1	1	yes	characteristic
107	C₂×#14268626	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
109	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
110	C₂×#14268624	C₂²	1	1	yes	characteristic
111	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
112	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
113	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
114	#123×C₁₁₃	C₂²	1	2	yes	complemented
115	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₁₃	C₂²	1	1	yes	characteristic
118	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	#120×C₁₁₃	C₂²	1	2	yes	—
120	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
121	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
122	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
124	#14268648	—	4	2	no	—
125	#14268647	—	4	2	no	—
126	#14268646	—	2	8	no	—
127	#14268646	—	4	2	no	—
128	C₂×Dic₂₂₆	C₂³	1	2	yes	—
129	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₂₆	C₂³	1	2	yes	—
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×D₄₅₂	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
135	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
146	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
147	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
150	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₁₃	—	4	2	no	—
152	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
160	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
163	#14268626	C₂³	1	1	yes	characteristic
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	1	yes	characteristic
166	#14268626	C₂³	1	1	yes	characteristic
167	#14268626	C₂³	1	1	yes	characteristic
168	#14268626	C₂³	1	2	yes	—
169	#14268626	C₂³	1	2	yes	—
170	#14268626	C₂³	1	2	yes	—
171	#14268626	C₂³	1	2	yes	—
172	#14268626	C₂³	1	2	yes	—
173	#14268626	C₂³	1	2	yes	—
174	#14268626	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
184	#14268624	C₂³	1	1	yes	characteristic
185	#14268624	C₂³	1	1	yes	characteristic
186	#14268624	C₂³	1	1	yes	characteristic
187	#14268624	C₂³	1	1	yes	characteristic
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	2	yes	—
190	#14268624	C₂³	1	2	yes	—
191	#14268624	C₂³	1	2	yes	—
192	#14268624	C₂³	1	2	yes	—
193	#14268624	C₂³	1	2	yes	—
194	#14268624	C₂³	1	2	yes	—
195	#14268624	C₂³	1	2	yes	—
196	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₁₃	C₂³	1	2	yes	—
201	C₄×Dic₁₁₃	C₂³	1	2	yes	—
202	C₄×Dic₁₁₃	C₂³	1	2	yes	—
203	C₄×Dic₁₁₃	C₂³	1	2	yes	—
204	C₄×Dic₁₁₃	C₂³	1	2	yes	—
205	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
206	#41×C₁₁₃	—	4	2	no	—
207	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
209	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
211	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₁₃	—	4	2	no	—
213	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
218	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
229	C₄²×C₁₁₃	C₂³	1	2	yes	—
230	C₂³×C₁₁₃	—	2	2	no	—
231	C₂³×C₁₁₃	—	4	1	no	—
232	C₂³×C₁₁₃	—	4	1	no	—
233	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
236	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₁₃	—	2	2	no	—
238	C₂²×D₁₁₃	—	4	1	no	—
239	C₂²×D₁₁₃	—	4	1	no	—
240	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
243	Q₈×C₁₁₃	—	2	2	no	—
244	D₄×C₁₁₃	—	2	4	no	—
245	D₄×C₁₁₃	—	2	2	no	—
246	D₄×C₁₁₃	—	4	2	no	—
247	D₄×C₁₁₃	—	4	2	no	—
248	C₂×C₄×C₁₁₃	—	2	2	no	—
249	C₂×C₄×C₁₁₃	—	2	2	no	—
250	C₂×C₄×C₁₁₃	—	2	2	no	—
251	C₂×C₄×C₁₁₃	—	4	1	no	—
252	C₂×C₄×C₁₁₃	—	4	1	no	—
253	C₂×C₄×C₁₁₃	—	4	1	no	—
254	C₂×C₄×C₁₁₃	—	4	2	no	—
255	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₁₁₃	—	2	4	no	—
263	C₂²⋊D₁₁₃	—	2	2	no	—
264	C₂²⋊D₁₁₃	—	2	2	no	—
265	C₂²⋊D₁₁₃	—	2	2	no	—
266	C₂²⋊D₁₁₃	—	2	2	no	—
267	C₂²⋊D₁₁₃	—	2	4	no	—
268	C₂²⋊D₁₁₃	—	4	2	no	—
269	C₂²⋊D₁₁₃	—	4	2	no	—
270	C₂²⋊D₁₁₃	—	4	2	no	—
271	C₂²⋊D₁₁₃	—	4	2	no	—
272	C₂²⋊D₁₁₃	—	4	2	no	—
273	C₂×Dic₁₁₃	—	2	4	no	—
274	C₂×Dic₁₁₃	—	4	1	no	—
275	C₂×Dic₁₁₃	—	4	1	no	—
276	C₂×Dic₁₁₃	—	4	2	no	—
277	C₂×Dic₁₁₃	#41	1	4	yes	complemented
278	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
279	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
281	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
285	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
287	D₄₅₂	—	2	2	no	—
288	D₄₅₂	—	4	2	no	—
289	D₄₅₂	—	4	2	no	—
290	C₄×D₁₁₃	—	2	2	no	—
291	C₄×D₁₁₃	—	2	2	no	—
292	C₄×D₁₁₃	—	2	4	no	—
293	C₄×D₁₁₃	—	4	1	no	—
294	C₄×D₁₁₃	—	4	1	no	—
295	C₄×D₁₁₃	—	4	2	no	—
296	C₄×D₁₁₃	—	4	2	no	—
297	Dic₂₂₆	—	2	2	no	—
298	Dic₂₂₆	—	2	4	no	—
299	Dic₂₂₆	—	4	2	no	—
300	C₂²×C₁₁₃	—	2	1	no	—
301	C₂²×C₁₁₃	—	2	1	no	—
302	C₂²×C₁₁₃	—	2	2	no	—
303	C₂²×C₁₁₃	—	2	1	no	—
304	C₂²×C₁₁₃	—	2	1	no	—
305	C₂²×C₁₁₃	—	2	2	no	—
306	C₂²×C₁₁₃	—	2	1	no	—
307	C₂²×C₁₁₃	—	2	1	no	—
308	C₂²×C₁₁₃	—	2	2	no	—
309	C₂²×C₁₁₃	—	2	1	no	—
310	C₂²×C₁₁₃	—	2	1	no	—
311	C₂²×C₁₁₃	—	4	4	no	—
312	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
313	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
314	C₂×D₁₁₃	—	2	2	no	—
315	C₂×D₁₁₃	—	2	1	no	—
316	C₂×D₁₁₃	—	2	1	no	—
317	C₂×D₁₁₃	—	2	1	no	—
318	C₂×D₁₁₃	—	2	1	no	—
319	C₂×D₁₁₃	—	2	2	no	—
320	C₂×D₁₁₃	—	2	1	no	—
321	C₂×D₁₁₃	—	2	2	no	—
322	C₂×D₁₁₃	—	2	1	no	—
323	C₂×D₁₁₃	—	4	4	no	—
324	C₄×C₁₁₃	—	2	2	no	—
325	C₄×C₁₁₃	—	2	1	no	—
326	C₄×C₁₁₃	—	2	1	no	—
327	C₄×C₁₁₃	—	2	2	no	—
328	C₄×C₁₁₃	—	2	1	no	—
329	C₄×C₁₁₃	—	2	2	no	—
330	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
331	Dic₁₁₃	—	2	2	no	—
332	Dic₁₁₃	—	2	2	no	—
333	Dic₁₁₃	—	2	1	no	—
334	Dic₁₁₃	—	2	1	no	—
335	Dic₁₁₃	—	2	1	no	—
336	Dic₁₁₃	—	2	2	no	—
337	Dic₁₁₃	—	2	1	no	—
338	Dic₁₁₃	C₂×#41	1	2	yes	—
339	Dic₁₁₃	C₂×#41	1	2	yes	—
340	C₂×C₁₁₃	—	2	2	no	—
341	C₂×C₁₁₃	—	4	2	no	—
342	C₂×C₁₁₃	—	4	1	no	—
343	C₂×C₁₁₃	—	4	1	no	—
344	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
345	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₁₃	#585	1	1	yes	characteristic
347	D₁₁₃	—	4	2	no	—
348	D₁₁₃	—	4	1	no	—
349	D₁₁₃	—	4	1	no	—
350	#3506	—	113	1	no	maximal, Sylow
351	C₁₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
352	#559	—	113	2	no	—
353	#559	—	113	2	no	—
354	#556	—	113	1	no	—
355	#556	—	113	1	no	—
356	#555	—	113	1	no	—
357	#555	—	113	1	no	—
358	#553	—	113	2	no	—
359	#553	—	113	2	no	—
360	#550	—	113	1	no	—
361	#550	—	113	1	no	—
362	#547	—	113	1	no	—
363	#547	—	113	1	no	—
364	#538	—	113	2	no	—
365	#538	—	113	2	no	—
366	#535	—	113	2	no	—
367	#533	—	113	1	no	—
368	#532	—	113	1	no	—
369	#525	—	113	1	no	—
370	#525	—	113	1	no	—
371	#525	—	113	1	no	—
372	#525	D₁₁₃	1	1	yes	characteristic, complemented
373	#520	—	113	2	no	—
374	C₂×C₄×D₄	—	113	1	no	—
375	C₂×#41	—	113	1	no	—
376	C₂×#41	—	113	1	no	—
377	C₂×#41	—	113	2	no	—
378	C₂×#41	—	113	1	no	—
379	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
380	C₂²×D₄	—	113	1	no	—
381	C₂³×C₄	—	113	1	no	—
382	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
383	C₄⋊Q₈	—	113	1	no	—
384	C₄⋊Q₈	—	113	1	no	—
385	C₄⋊Q₈	—	113	1	no	—
386	#127	—	113	1	no	—
387	#127	—	113	2	no	—
388	#127	—	113	2	no	—
389	#126	—	113	2	no	—
390	#126	—	113	2	no	—
391	#126	—	113	2	no	—
392	#126	—	113	2	no	—
393	#125	—	113	2	no	—
394	#124	—	113	2	no	—
395	#124	—	113	2	no	—
396	#124	—	113	2	no	—
397	#124	—	113	2	no	—
398	#124	—	113	2	no	—
399	#124	—	113	2	no	—
400	#124	—	113	2	no	—
401	#123	—	113	2	no	—
402	#123	—	113	2	no	—
403	#123	—	113	2	no	—
404	#123	—	113	2	no	—
405	#123	—	113	2	no	—
406	#123	—	113	2	no	—
407	#123	—	113	2	no	—
408	#123	C₂×D₁₁₃	1	2	yes	complemented
409	C₂²⋊Q₈	—	113	1	no	—
410	C₂²⋊Q₈	—	113	1	no	—
411	C₂²⋊Q₈	—	113	1	no	—
412	C₂²⋊Q₈	—	113	1	no	—
413	C₂²⋊Q₈	—	113	2	no	—
414	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
416	#121	—	113	1	no	—
417	#121	—	113	2	no	—
418	#121	—	113	2	no	—
419	#121	—	113	2	no	—
420	#121	—	113	2	no	—
421	#121	—	113	2	no	—
422	#121	—	113	1	no	—
423	#121	—	113	1	no	—
424	#121	—	113	2	no	—
425	#121	—	113	1	no	—
426	#121	—	113	2	no	—
427	#121	—	113	2	no	—
428	#121	—	113	2	no	—
429	#121	C₂×D₁₁₃	1	1	yes	characteristic
430	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
431	#120	—	113	2	no	—
432	#120	—	113	2	no	—
433	#120	—	113	2	no	—
434	#120	C₂×D₁₁₃	1	2	yes	—
435	C₄×Q₈	—	113	1	no	—
436	C₄×Q₈	—	113	2	no	—
437	C₄×Q₈	—	113	1	no	—
438	C₄×Q₈	—	113	2	no	—
439	C₄×Q₈	—	113	2	no	—
440	C₄×D₄	—	113	2	no	—
441	C₄×D₄	—	113	1	no	—
442	C₄×D₄	—	113	1	no	—
443	C₄×D₄	—	113	1	no	—
444	C₄×D₄	—	113	1	no	—
445	C₄×D₄	—	113	1	no	—
446	C₄×D₄	—	113	1	no	—
447	C₄×D₄	—	113	1	no	—
448	C₄×D₄	—	113	1	no	—
449	C₄×D₄	—	113	1	no	—
450	C₄×D₄	—	113	2	no	—
451	C₄×D₄	—	113	2	no	—
452	C₄×D₄	—	113	2	no	—
453	C₄×D₄	—	113	2	no	—
454	C₄×D₄	—	113	1	no	—
455	C₄×D₄	—	113	2	no	—
456	C₄×D₄	—	113	2	no	—
457	C₄×D₄	—	113	2	no	—
458	C₄×D₄	—	113	2	no	—
459	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
460	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
461	#117	—	113	1	no	—
462	#117	—	113	1	no	—
463	#117	—	113	1	no	—
464	#117	—	113	2	no	—
465	#117	—	113	2	no	—
466	#117	—	113	2	no	—
467	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
468	C₂×C₄⋊C₄	—	113	1	no	—
469	C₂×C₄⋊C₄	—	113	2	no	—
470	C₂×C₄⋊C₄	—	113	2	no	—
471	C₂×C₂²⋊C₄	—	113	1	no	—
472	C₂×C₂²⋊C₄	—	113	1	no	—
473	C₂×C₄²	—	113	1	no	—
474	C₂⁴	—	113	1	no	—
475	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
476	#41	—	4	2	no	—
477	#41	—	452	2	no	—
478	#41	—	452	2	no	—
479	#41	—	452	2	no	—
480	#41	—	226	8	no	—
481	C₂×Q₈	—	113	2	no	—
482	C₂×Q₈	—	113	2	no	—
483	C₂×Q₈	—	113	1	no	—
484	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
485	C₂×D₄	—	113	2	no	—
486	C₂×D₄	—	113	2	no	—
487	C₂×D₄	—	113	2	no	—
488	C₂×D₄	—	113	2	no	—
489	C₂×D₄	—	113	2	no	—
490	C₂×D₄	—	113	2	no	—
491	C₂×D₄	—	113	1	no	—
492	C₂×D₄	—	113	1	no	—
493	C₂×D₄	—	113	1	no	—
494	C₂×D₄	—	113	1	no	—
495	C₂×D₄	—	113	2	no	—
496	C₂×D₄	—	113	2	no	—
497	C₂×D₄	—	113	2	no	—
498	C₂×D₄	—	113	1	no	—
499	C₂×D₄	—	226	4	no	—
500	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
501	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
502	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
503	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	113	1	no	—
506	C₂²×C₄	—	113	1	no	—
507	C₂²×C₄	—	113	1	no	—
508	C₂²×C₄	—	113	2	no	—
509	C₂²×C₄	—	113	2	no	—
510	C₂²×C₄	—	113	2	no	—
511	C₂²×C₄	—	113	2	no	—
512	C₂²×C₄	—	113	1	no	—
513	C₂²×C₄	—	113	1	no	—
514	C₂²×C₄	—	113	2	no	—
515	C₂²×C₄	—	113	1	no	—
516	C₂²×C₄	—	113	1	no	—
517	C₂²×C₄	—	452	2	no	—
518	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
519	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
520	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
523	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
525	C₄⋊C₄	—	113	1	no	—
526	C₄⋊C₄	—	113	1	no	—
527	C₄⋊C₄	—	113	2	no	—
528	C₄⋊C₄	—	113	1	no	—
529	C₄⋊C₄	—	113	1	no	—
530	C₄⋊C₄	—	113	2	no	—
531	C₄⋊C₄	—	113	2	no	—
532	C₄⋊C₄	—	113	2	no	—
533	C₄⋊C₄	—	113	2	no	—
534	C₄⋊C₄	—	113	1	no	—
535	C₄⋊C₄	—	113	1	no	—
536	C₄⋊C₄	—	113	2	no	—
537	C₄⋊C₄	—	113	2	no	—
538	C₄⋊C₄	—	113	2	no	—
539	C₄⋊C₄	—	113	2	no	—
540	C₄⋊C₄	—	113	2	no	—
541	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
542	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
545	C₂²⋊C₄	—	113	1	no	—
546	C₂²⋊C₄	—	113	1	no	—
547	C₂²⋊C₄	—	113	1	no	—
548	C₂²⋊C₄	—	113	1	no	—
549	C₂²⋊C₄	—	113	2	no	—
550	C₂²⋊C₄	—	113	2	no	—
551	C₂²⋊C₄	—	113	2	no	—
552	C₂²⋊C₄	—	113	2	no	—
553	C₂²⋊C₄	—	113	2	no	—
554	C₂²⋊C₄	—	113	1	no	—
555	C₂²⋊C₄	—	113	1	no	—
556	C₂²⋊C₄	—	113	1	no	—
557	C₂²⋊C₄	—	113	1	no	—
558	C₂²⋊C₄	—	113	2	no	—
559	C₂²⋊C₄	—	113	2	no	—
560	C₂²⋊C₄	—	113	2	no	—
561	C₂²⋊C₄	—	113	2	no	—
562	C₂²⋊C₄	—	113	2	no	—
563	C₂²⋊C₄	—	113	2	no	—
564	C₂²⋊C₄	—	113	2	no	—
565	C₂²⋊C₄	—	113	2	no	—
566	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
567	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
568	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
569	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
571	C₄²	—	113	1	no	—
572	C₄²	—	113	1	no	—
573	C₄²	—	113	1	no	—
574	C₄²	—	113	1	no	—
575	C₄²	—	113	2	no	—
576	C₄²	—	113	2	no	—
577	C₄²	—	113	2	no	—
578	C₄²	—	113	2	no	—
579	C₄²	—	113	2	no	—
580	C₄²	C₂²×D₁₁₃	1	2	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	113	1	no	—
585	C₂³	—	113	1	no	—
586	C₂³	—	113	2	no	—
587	C₂³	—	452	1	no	—
588	C₂³	—	452	1	no	—
589	C₂³	—	226	2	no	—
590	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
591	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
592	C₂³	C₂³×D₁₁₃	1	2	yes	—
593	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
594	Q₈	—	2	2	no	—
595	Q₈	—	452	2	no	—
596	Q₈	—	226	4	no	—
597	Q₈	—	226	2	no	—
598	D₄	—	2	4	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	452	2	no	—
603	D₄	—	452	2	no	—
604	D₄	—	452	2	no	—
605	D₄	—	452	2	no	—
606	D₄	—	452	2	no	—
607	D₄	—	452	2	no	—
608	D₄	—	452	2	no	—
609	D₄	—	226	2	no	—
610	D₄	—	226	2	no	—
611	D₄	—	226	2	no	—
612	D₄	—	226	2	no	—
613	D₄	—	226	4	no	—
614	D₄	—	226	4	no	—
615	D₄	—	226	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	113	4	no	—
624	C₂×C₄	—	113	1	no	—
625	C₂×C₄	—	113	1	no	—
626	C₂×C₄	—	113	2	no	—
627	C₂×C₄	—	113	1	no	—
628	C₂×C₄	—	113	2	no	—
629	C₂×C₄	—	113	1	no	—
630	C₂×C₄	—	113	1	no	—
631	C₂×C₄	—	113	1	no	—
632	C₂×C₄	—	113	2	no	—
633	C₂×C₄	—	452	1	no	—
634	C₂×C₄	—	452	1	no	—
635	C₂×C₄	—	452	2	no	—
636	C₂×C₄	—	452	2	no	—
637	C₂×C₄	—	452	1	no	—
638	C₂×C₄	—	452	2	no	—
639	C₂×C₄	—	452	1	no	—
640	C₂×C₄	—	226	4	no	—
641	C₂×C₄	—	226	4	no	—
642	C₂×C₄	—	226	2	no	—
643	C₂×C₄	—	226	2	no	—
644	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
645	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
648	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
649	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	452	4	no	—
664	C₂²	—	226	2	no	—
665	C₂²	—	226	1	no	—
666	C₂²	—	226	1	no	—
667	C₂²	—	226	2	no	—
668	C₂²	—	226	1	no	—
669	C₂²	—	226	1	no	—
670	C₂²	—	226	2	no	—
671	C₂²	—	226	1	no	—
672	C₂²	—	226	1	no	—
673	C₂²	#41×D₁₁₃	1	2	yes	—
674	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	113	2	no	—
682	C₄	—	113	2	no	—
683	C₄	—	226	2	no	—
684	C₄	—	226	1	no	—
685	C₄	—	226	1	no	—
686	C₄	—	226	2	no	—
687	C₄	—	226	1	no	—
688	C₄	—	226	1	no	—
689	C₄	—	226	2	no	—
690	C₄	#16813667	1	2	yes	—
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	452	1	no	—
696	C₂	—	452	1	no	—
697	C₂	—	452	2	no	—
698	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
699	C₂	C₂×#16813667	1	1	yes	characteristic
700	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#525×C₁₁₃	C₂
hypercenter	#525	D₁₁₃
hypocenter	C₁₁₃	#3506
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #20299332	C₂	semidirect
2. #20299331	C₂	semidirect
3. #20299319	C₂	semidirect
4. #20299316	C₂	semidirect
5. #20299312	C₂	semidirect
6. #20299311	C₂	semidirect
7. #20299297	C₂	semidirect
8. #20299293	C₂	semidirect
9. #20299267	C₂	semidirect
10. #20299266	C₂	semidirect
11. #20299250	C₂	semidirect
12. #20299247	C₂	semidirect
13. #20299183	C₂	semidirect
14. #20299181	C₂	semidirect
15. #20299163	C₂	semidirect
16. #20299150	C₂	semidirect
17. #20299143	C₂	semidirect
18. #20299111	C₂	semidirect
19. #20299109	C₂	semidirect
20. #20299108	C₂	semidirect
21. #20299077	C₂	semidirect
22. C₂×C₄×C₂²⋊D₁₁₃	C₂	semidirect
23. #525×C₁₁₃	C₂	semidirect
24. C₂×#14268648	C₂²	semidirect
25. C₂×#14268647	C₂²	semidirect
27. C₂×#14268646	C₂²	semidirect
30. #16813621	C₂²	semidirect
31. #16813621	C₂²	semidirect
32. #16813620	C₂²	semidirect
35. #16813618	C₂²	semidirect
36. #16813617	C₂²	semidirect
37. #16813616	C₂²	semidirect
38. #16813615	C₂²	semidirect
39. #16813615	C₂²	semidirect
40. #16813612	C₂²	semidirect
41. #16813610	C₂²	semidirect
42. #16813609	C₂²	semidirect
45. #16813608	C₂²	semidirect
46. #16813608	C₂²	semidirect
47. #16813608	C₂²	semidirect
48. #16813607	C₂²	semidirect
49. #16813607	C₂²	semidirect
50. #16813605	C₂²	semidirect
51. #16813605	C₂²	semidirect
52. #16813604	C₂²	semidirect
53. #16813604	C₂²	semidirect
54. #16813603	C₂²	semidirect
55. #16813602	C₂²	semidirect
57. #16813601	C₂²	semidirect
59. #16813598	C₂²	semidirect
60. #16813597	C₂²	semidirect
62. #16813596	C₂²	semidirect
63. #16813596	C₂²	semidirect
66. #16813595	C₂²	semidirect
70. #16813594	C₂²	semidirect
71. #16813593	C₂²	semidirect
72. #16813593	C₂²	semidirect
76. Q₈×Dic₁₁₃	C₂²	semidirect
77. C₄×Dic₂₂₆	C₂²	semidirect
78. #16813587	C₂²	semidirect
79. #16813587	C₂²	semidirect
80. #16813587	C₂²	semidirect
82. D₄×Dic₁₁₃	C₂²	semidirect
83. #16813584	C₂²	semidirect
84. #16813584	C₂²	semidirect
94. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
95. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
97. #16813582	C₂²	semidirect
98. #16813582	C₂²	semidirect
99. #16813582	C₂²	semidirect
100. #16813581	C₂²	semidirect
101. #16813580	C₂²	semidirect
102. #16813580	C₂²	semidirect
103. #16813579	C₂²	semidirect
105. #16813578	C₂²	semidirect
107. C₂×#14268626	C₂²	semidirect
108. C₄⋊C₄×D₁₁₃	C₂²	semidirect
112. C₂×#41×C₁₁₃	C₂²	semidirect
114. #123×C₁₁₃	C₂²	semidirect
116. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
118. #121×C₁₁₃	C₂²	semidirect
121. C₄×D₄×C₁₁₃	C₂²	semidirect
122. #117×C₁₁₃	C₂²	semidirect
277. C₂×Dic₁₁₃	#41	semidirect
351. C₁₁₃	#3506	semidirect
372. #525	D₁₁₃	semidirect
379. C₂×#41	C₂×D₁₁₃	semidirect
408. #123	C₂×D₁₁₃	semidirect
415. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
430. #121	C₂×D₁₁₃	semidirect
460. C₄×D₄	C₂×D₁₁₃	semidirect
467. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299332	2
#20299331	2
#20299319	2
#20299316	2
#20299312	2
#20299311	2
#20299297	2
#20299293	2
#20299267	2
#20299266	2
#20299250	2
#20299247	2
#20299183	2
#20299181	2
#20299163	2
#20299150	2
#20299143	2
#20299111	2
#20299109	2
#20299108	2
#20299077	2
C₂×C₄×C₂²⋊D₁₁₃	2
#525×C₁₁₃	2
#3506	113