Subgroups — #28404286

Order 14464.

1040 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299320	C₂	1	2	yes	maximal, complemented
2	#20299315	C₂	1	2	yes	maximal, complemented
3	#20299311	C₂	1	2	yes	maximal, complemented
4	#20299310	C₂	1	2	yes	maximal, complemented
5	#20299299	C₂	1	2	yes	maximal, complemented
6	#20299297	C₂	1	2	yes	maximal, complemented
7	#20299281	C₂	1	2	yes	maximal, complemented
8	#20299280	C₂	1	2	yes	maximal, complemented
9	#20299227	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299188	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299185	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299181	C₂	1	2	yes	maximal, complemented
13	#20299175	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299132	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299125	C₂	1	2	yes	maximal, complemented
16	#20299106	C₂	1	2	yes	maximal, complemented
17	#20299077	C₂	1	2	yes	maximal, complemented
18	C₂×#16813579	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268646	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
22	#16813621	C₂²	1	2	yes	complemented
23	#16813620	C₂²	1	2	yes	complemented
24	#16813617	C₂²	1	2	yes	—
25	#16813617	C₂²	1	2	yes	—
26	#16813617	C₂²	1	2	yes	—
27	#16813617	C₂²	1	2	yes	complemented
28	#16813616	C₂²	1	2	yes	—
29	#16813616	C₂²	1	2	yes	complemented
30	#16813615	C₂²	1	2	yes	complemented
31	#16813614	C₂²	1	1	yes	characteristic, complemented
32	#16813612	C₂²	1	2	yes	complemented
33	#16813612	C₂²	1	2	yes	complemented
34	#16813612	C₂²	1	2	yes	complemented
35	#16813611	C₂²	1	2	yes	—
36	#16813610	C₂²	1	2	yes	—
37	#16813610	C₂²	1	1	yes	characteristic, complemented
38	#16813608	C₂²	1	2	yes	—
39	#16813608	C₂²	1	2	yes	—
40	#16813608	C₂²	1	2	yes	complemented
41	#16813607	C₂²	1	2	yes	—
42	#16813607	C₂²	1	2	yes	—
43	#16813606	C₂²	1	2	yes	—
44	#16813605	C₂²	1	2	yes	—
45	#16813605	C₂²	1	2	yes	—
46	#16813601	C₂²	1	1	yes	characteristic
47	#16813600	C₂²	1	2	yes	—
48	#16813600	C₂²	1	2	yes	—
49	#16813600	C₂²	1	2	yes	complemented
50	#16813599	C₂²	1	2	yes	—
51	#16813599	C₂²	1	2	yes	complemented
52	#16813597	C₂²	1	2	yes	—
53	#16813596	C₂²	1	2	yes	—
54	#16813596	C₂²	1	1	yes	characteristic
55	#16813595	C₂²	1	2	yes	—
56	#16813595	C₂²	1	2	yes	—
57	#16813595	C₂²	1	2	yes	—
58	#16813595	C₂²	1	2	yes	complemented
59	#16813594	C₂²	1	2	yes	—
60	#16813594	C₂²	1	2	yes	—
61	#16813594	C₂²	1	2	yes	complemented
62	#16813592	C₂²	1	2	yes	—
63	#16813590	C₂²	1	2	yes	—
64	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
65	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
66	#16813587	C₂²	1	2	yes	complemented
67	#16813587	C₂²	1	2	yes	complemented
68	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₁₁₃	C₂²	1	2	yes	—
70	#16813584	C₂²	1	2	yes	—
71	#16813584	C₂²	1	2	yes	—
72	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
74	#16813582	C₂²	1	2	yes	—
75	#16813582	C₂²	1	2	yes	—
76	#16813582	C₂²	1	2	yes	—
77	#16813582	C₂²	1	2	yes	complemented
78	#16813582	C₂²	1	2	yes	complemented
79	#16813580	C₂²	1	2	yes	complemented
80	#16813579	C₂²	1	2	yes	—
81	#16813579	C₂²	1	2	yes	—
82	#16813579	C₂²	1	2	yes	—
83	#16813579	C₂²	1	2	yes	—
84	#16813579	C₂²	1	2	yes	complemented
85	#16813579	C₂²	1	2	yes	complemented
86	#16813578	C₂²	1	2	yes	—
87	#16813578	C₂²	1	2	yes	complemented
88	#16813578	C₂²	1	2	yes	complemented
89	C₂×#14268626	C₂²	1	1	yes	characteristic
90	C₂×#14268626	C₂²	1	1	yes	characteristic
91	C₂×#14268626	C₂²	1	2	yes	complemented
92	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
93	C₂×#14268624	C₂²	1	1	yes	characteristic
94	C₂×#14268624	C₂²	1	1	yes	characteristic
95	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
96	#126×C₁₁₃	C₂²	1	2	yes	complemented
97	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₁₁₃	C₂²	1	2	yes	—
100	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
101	#121×C₁₁₃	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
104	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
105	#117×C₁₁₃	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
107	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
108	#14268646	—	2	8	no	—
109	C₂×Dic₂₂₆	C₂³	1	2	yes	—
110	C₂×Dic₂₂₆	C₂³	1	2	yes	—
111	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
112	C₂×D₄₅₂	C₂³	1	2	yes	—
113	C₂×D₄₅₂	C₂³	1	2	yes	—
114	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
120	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
121	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
122	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
123	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
124	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₁₃	—	2	4	no	—
126	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
127	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
128	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
129	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
130	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
131	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
132	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
133	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
135	#14268626	C₂³	1	2	yes	—
136	#14268626	C₂³	1	2	yes	—
137	#14268626	C₂³	1	2	yes	—
138	#14268626	C₂³	1	2	yes	—
139	#14268626	C₂³	1	2	yes	—
140	#14268626	C₂³	1	2	yes	—
141	#14268626	C₂³	1	2	yes	—
142	#14268626	C₂³	1	2	yes	—
143	#14268626	C₂³	1	2	yes	—
144	#14268626	C₂³	1	2	yes	—
145	#14268626	C₂³	1	2	yes	—
146	#14268626	C₂³	1	2	yes	—
147	#14268626	C₂³	1	2	yes	—
148	#14268626	C₂³	1	2	yes	—
149	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
150	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
151	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
152	#14268624	C₂³	1	2	yes	—
153	#14268624	C₂³	1	2	yes	—
154	#14268624	C₂³	1	2	yes	—
155	#14268624	C₂³	1	2	yes	—
156	#14268624	C₂³	1	2	yes	—
157	#14268624	C₂³	1	2	yes	—
158	#14268624	C₂³	1	2	yes	—
159	#14268624	C₂³	1	2	yes	—
160	#14268624	C₂³	1	2	yes	—
161	#14268624	C₂³	1	2	yes	—
162	#14268624	C₂³	1	2	yes	—
163	#14268624	C₂³	1	2	yes	—
164	#14268624	C₂³	1	2	yes	—
165	#14268624	C₂³	1	2	yes	—
166	C₄×Dic₁₁₃	C₂³	1	2	yes	—
167	C₄×Dic₁₁₃	C₂³	1	2	yes	—
168	C₄×Dic₁₁₃	C₂³	1	2	yes	—
169	C₄×Dic₁₁₃	C₂³	1	2	yes	—
170	C₄×Dic₁₁₃	C₂³	1	2	yes	—
171	C₄×Dic₁₁₃	C₂³	1	2	yes	—
172	C₄×Dic₁₁₃	C₂³	1	2	yes	—
173	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
174	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
175	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
180	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
181	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
182	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
183	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
184	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
191	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
192	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
193	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
194	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
195	C₄²×C₁₁₃	C₂³	1	2	yes	—
196	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
197	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
198	C₂²×D₁₁₃	—	2	2	no	—
199	C₂²×D₁₁₃	—	4	1	no	—
200	C₂²×D₁₁₃	—	4	1	no	—
201	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
202	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
203	Q₈×C₁₁₃	—	4	1	no	—
204	D₄×C₁₁₃	—	2	4	no	—
205	D₄×C₁₁₃	—	4	1	no	—
206	C₂×C₄×C₁₁₃	—	2	2	no	—
207	C₂×C₄×C₁₁₃	—	4	1	no	—
208	C₂×C₄×C₁₁₃	—	4	1	no	—
209	C₂×C₄×C₁₁₃	—	4	2	no	—
210	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
217	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
218	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
219	C₂²⋊D₁₁₃	—	2	4	no	—
220	C₂²⋊D₁₁₃	—	2	4	no	—
221	C₂²⋊D₁₁₃	—	4	2	no	—
222	C₂²⋊D₁₁₃	—	4	2	no	—
223	C₂²⋊D₁₁₃	—	4	2	no	—
224	C₂×Dic₁₁₃	—	2	4	no	—
225	C₂×Dic₁₁₃	—	4	1	no	—
226	C₂×Dic₁₁₃	—	4	1	no	—
227	C₂×Dic₁₁₃	—	4	2	no	—
228	C₂×Dic₁₁₃	#41	1	4	yes	—
229	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
230	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
231	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
232	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
233	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
234	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
235	D₄₅₂	—	4	1	no	—
236	D₄₅₂	—	4	2	no	—
237	D₄₅₂	—	4	2	no	—
238	C₄×D₁₁₃	—	2	4	no	—
239	C₄×D₁₁₃	—	2	4	no	—
240	C₄×D₁₁₃	—	2	4	no	—
241	C₄×D₁₁₃	—	4	2	no	—
242	C₄×D₁₁₃	—	4	2	no	—
243	Dic₂₂₆	—	2	4	no	—
244	Dic₂₂₆	—	4	1	no	—
245	Dic₂₂₆	—	4	2	no	—
246	C₂²×C₁₁₃	—	2	1	no	—
247	C₂²×C₁₁₃	—	2	1	no	—
248	C₂²×C₁₁₃	—	2	2	no	—
249	C₂²×C₁₁₃	—	2	2	no	—
250	C₂²×C₁₁₃	—	2	2	no	—
251	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
252	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
253	C₂×D₁₁₃	—	2	2	no	—
254	C₂×D₁₁₃	—	2	2	no	—
255	C₂×D₁₁₃	—	2	2	no	—
256	C₂×D₁₁₃	—	2	2	no	—
257	C₂×D₁₁₃	—	2	2	no	—
258	C₂×D₁₁₃	—	2	2	no	—
259	C₂×D₁₁₃	—	4	4	no	—
260	C₄×C₁₁₃	—	2	2	no	—
261	C₄×C₁₁₃	—	2	1	no	—
262	C₄×C₁₁₃	—	2	1	no	—
263	C₄×C₁₁₃	—	2	1	no	—
264	C₄×C₁₁₃	—	2	2	no	—
265	C₄×C₁₁₃	—	2	1	no	—
266	C₄×C₁₁₃	—	2	2	no	—
267	C₄×C₁₁₃	—	2	1	no	—
268	C₄×C₁₁₃	—	2	1	no	—
269	Dic₁₁₃	—	2	2	no	—
270	Dic₁₁₃	—	2	2	no	—
271	Dic₁₁₃	—	2	2	no	—
272	Dic₁₁₃	—	2	2	no	—
273	Dic₁₁₃	—	2	2	no	—
274	Dic₁₁₃	C₂×#41	1	4	yes	—
275	C₂×C₁₁₃	—	2	2	no	—
276	C₂×C₁₁₃	—	4	2	no	—
277	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
278	C₂×C₁₁₃	#585	1	1	yes	characteristic
279	C₂×C₁₁₃	#585	1	1	yes	characteristic
280	D₁₁₃	—	4	2	no	—
281	D₁₁₃	—	4	2	no	—
282	#3493	—	113	1	no	maximal, Sylow
283	C₁₁₃	#3493	1	1	yes	characteristic, complemented, Sylow
284	#556	—	113	2	no	—
285	#556	—	113	2	no	—
286	#555	—	113	2	no	—
287	#555	—	113	2	no	—
288	#553	—	113	2	no	—
289	#553	—	113	2	no	—
290	#552	—	113	2	no	—
291	#552	—	113	2	no	—
292	#544	—	113	1	no	—
293	#538	—	113	1	no	—
294	#538	—	113	1	no	—
295	#538	—	113	2	no	—
296	#537	—	113	1	no	—
297	#529	—	113	2	no	—
298	#529	—	113	1	no	—
299	#529	D₁₁₃	1	1	yes	characteristic, complemented
300	#525	—	113	2	no	—
301	#520	—	113	2	no	—
302	C₂×#117	—	113	1	no	—
303	C₂×#41	—	113	2	no	—
304	C₂³×C₄	—	113	1	no	—
305	C₄⋊Q₈	—	113	2	no	—
306	C₄⋊Q₈	—	113	2	no	—
307	#126	—	113	2	no	—
308	#126	—	113	2	no	—
309	#126	—	113	2	no	—
310	#126	—	113	2	no	—
311	#126	—	113	2	no	—
312	#126	—	113	2	no	—
313	#126	—	113	2	no	—
314	#126	C₂×D₁₁₃	1	2	yes	complemented
315	#125	—	113	2	no	—
316	#125	—	113	2	no	—
317	#125	—	113	2	no	—
318	#125	—	113	1	no	—
319	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
320	#124	—	113	2	no	—
321	#124	—	113	2	no	—
322	#124	—	113	2	no	—
323	#124	—	113	2	no	—
324	#124	—	113	1	no	—
325	#124	—	113	2	no	—
326	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
327	#123	—	113	2	no	—
328	#123	—	113	2	no	—
329	#123	—	113	2	no	—
330	#123	—	113	2	no	—
331	#123	—	113	2	no	—
332	#123	C₂×D₁₁₃	1	2	yes	—
333	C₂²⋊Q₈	—	113	1	no	—
334	C₂²⋊Q₈	—	113	2	no	—
335	C₂²⋊Q₈	—	113	2	no	—
336	C₂²⋊Q₈	—	113	2	no	—
337	C₂²⋊Q₈	—	113	2	no	—
338	C₂²⋊Q₈	—	113	2	no	—
339	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
340	#121	—	113	2	no	—
341	#121	—	113	2	no	—
342	#121	—	113	2	no	—
343	#121	—	113	1	no	—
344	#121	—	113	2	no	—
345	#121	—	113	2	no	—
346	#121	—	113	2	no	—
347	#121	—	113	2	no	—
348	#121	—	113	2	no	—
349	#121	—	113	2	no	—
350	#121	C₂×D₁₁₃	1	1	yes	characteristic
351	#120	—	113	2	no	—
352	#120	—	113	2	no	—
353	C₄×Q₈	—	113	2	no	—
354	C₄×Q₈	—	113	2	no	—
355	C₄×Q₈	—	113	2	no	—
356	C₄×Q₈	—	113	1	no	—
357	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
358	C₄×D₄	—	113	2	no	—
359	C₄×D₄	—	113	2	no	—
360	C₄×D₄	—	113	2	no	—
361	C₄×D₄	—	113	2	no	—
362	C₄×D₄	—	113	2	no	—
363	C₄×D₄	—	113	2	no	—
364	C₄×D₄	—	113	2	no	—
365	C₄×D₄	—	113	2	no	—
366	C₄×D₄	—	113	2	no	—
367	C₄×D₄	—	113	2	no	—
368	C₄×D₄	—	113	1	no	—
369	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
370	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
371	#117	—	113	2	no	—
372	#117	—	113	2	no	—
373	#117	—	113	2	no	—
374	#117	—	113	2	no	—
375	#117	—	113	2	no	—
376	#117	—	113	2	no	—
377	#117	—	113	2	no	—
378	#117	—	113	2	no	—
379	#117	—	113	2	no	—
380	#117	—	113	2	no	—
381	#117	C₂×D₁₁₃	1	2	yes	complemented
382	C₂×C₄⋊C₄	—	113	1	no	—
383	C₂×C₄⋊C₄	—	113	1	no	—
384	C₂×C₄⋊C₄	—	113	2	no	—
385	C₂×C₄⋊C₄	—	113	2	no	—
386	C₂×C₂²⋊C₄	—	113	1	no	—
387	C₂×C₂²⋊C₄	—	113	1	no	—
388	C₂×C₄²	—	113	1	no	—
389	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
390	C₂⁴	—	113	1	no	—
391	#41	—	226	8	no	—
392	C₂×Q₈	—	113	1	no	—
393	C₂×Q₈	—	113	2	no	—
394	C₂×Q₈	—	113	2	no	—
395	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
396	C₂×D₄	—	113	2	no	—
397	C₂×D₄	—	113	2	no	—
398	C₂×D₄	—	113	2	no	—
399	C₂×D₄	—	113	2	no	—
400	C₂×D₄	—	113	2	no	—
401	C₂×D₄	—	113	2	no	—
402	C₂×D₄	—	113	2	no	—
403	C₂×D₄	—	113	1	no	—
404	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
405	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
406	C₂²×C₄	—	113	1	no	—
407	C₂²×C₄	—	113	1	no	—
408	C₂²×C₄	—	113	1	no	—
409	C₂²×C₄	—	113	2	no	—
410	C₂²×C₄	—	113	2	no	—
411	C₂²×C₄	—	113	2	no	—
412	C₂²×C₄	—	113	2	no	—
413	C₂²×C₄	—	113	2	no	—
414	C₂²×C₄	—	113	2	no	—
415	C₂²×C₄	—	113	2	no	—
416	C₂²×C₄	—	226	4	no	—
417	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
421	C₄⋊C₄	—	113	2	no	—
422	C₄⋊C₄	—	113	2	no	—
423	C₄⋊C₄	—	113	2	no	—
424	C₄⋊C₄	—	113	2	no	—
425	C₄⋊C₄	—	113	2	no	—
426	C₄⋊C₄	—	113	2	no	—
427	C₄⋊C₄	—	113	2	no	—
428	C₄⋊C₄	—	113	2	no	—
429	C₄⋊C₄	—	113	2	no	—
430	C₄⋊C₄	—	113	2	no	—
431	C₄⋊C₄	—	113	2	no	—
432	C₄⋊C₄	—	113	2	no	—
433	C₄⋊C₄	—	113	2	no	—
434	C₄⋊C₄	—	113	2	no	—
435	C₄⋊C₄	—	113	2	no	—
436	C₄⋊C₄	—	113	1	no	—
437	C₄⋊C₄	—	113	2	no	—
438	C₄⋊C₄	—	113	1	no	—
439	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
440	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
441	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
442	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
443	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
444	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
445	C₂²⋊C₄	—	113	2	no	—
446	C₂²⋊C₄	—	113	2	no	—
447	C₂²⋊C₄	—	113	2	no	—
448	C₂²⋊C₄	—	113	2	no	—
449	C₂²⋊C₄	—	113	2	no	—
450	C₂²⋊C₄	—	113	2	no	—
451	C₂²⋊C₄	—	113	2	no	—
452	C₂²⋊C₄	—	113	2	no	—
453	C₂²⋊C₄	—	113	2	no	—
454	C₂²⋊C₄	—	113	2	no	—
455	C₂²⋊C₄	—	113	2	no	—
456	C₂²⋊C₄	—	113	2	no	—
457	C₂²⋊C₄	—	113	2	no	—
458	C₂²⋊C₄	—	113	2	no	—
459	C₂²⋊C₄	—	113	2	no	—
460	C₂²⋊C₄	—	113	2	no	—
461	C₂²⋊C₄	—	113	2	no	—
462	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
463	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
464	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
465	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
467	C₄²	—	113	2	no	—
468	C₄²	—	113	2	no	—
469	C₄²	—	113	2	no	—
470	C₄²	—	113	2	no	—
471	C₄²	—	113	2	no	—
472	C₄²	—	113	2	no	—
473	C₄²	—	113	2	no	—
474	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
475	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
476	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
477	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
478	C₄²	C₂²×D₁₁₃	1	2	yes	—
479	C₂³	—	113	2	no	—
480	C₂³	—	113	2	no	—
481	C₂³	—	452	1	no	—
482	C₂³	—	452	1	no	—
483	C₂³	—	226	2	no	—
484	C₂³	C₂³×D₁₁₃	1	2	yes	—
485	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
486	Q₈	—	4	1	no	—
487	Q₈	—	452	1	no	—
488	Q₈	—	452	2	no	—
489	Q₈	—	226	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	1	no	—
492	D₄	—	452	2	no	—
493	D₄	—	452	1	no	—
494	D₄	—	452	2	no	—
495	D₄	—	452	2	no	—
496	D₄	—	452	2	no	—
497	D₄	—	452	2	no	—
498	D₄	—	226	4	no	—
499	D₄	—	226	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	113	4	no	—
505	C₂×C₄	—	113	2	no	—
506	C₂×C₄	—	113	2	no	—
507	C₂×C₄	—	113	2	no	—
508	C₂×C₄	—	113	2	no	—
509	C₂×C₄	—	113	2	no	—
510	C₂×C₄	—	113	2	no	—
511	C₂×C₄	—	452	2	no	—
512	C₂×C₄	—	452	2	no	—
513	C₂×C₄	—	452	1	no	—
514	C₂×C₄	—	452	2	no	—
515	C₂×C₄	—	452	1	no	—
516	C₂×C₄	—	226	4	no	—
517	C₂×C₄	—	226	4	no	—
518	C₂×C₄	—	226	4	no	—
519	C₂×C₄	—	226	4	no	—
520	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
524	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
525	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
526	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	452	4	no	—
535	C₂²	—	226	2	no	—
536	C₂²	—	226	2	no	—
537	C₂²	—	226	2	no	—
538	C₂²	—	226	2	no	—
539	C₂²	—	226	2	no	—
540	C₂²	—	226	2	no	—
541	C₂²	#41×D₁₁₃	1	2	yes	—
542	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	113	4	no	—
553	C₄	—	226	2	no	—
554	C₄	—	226	2	no	—
555	C₄	—	226	2	no	—
556	C₄	—	226	2	no	—
557	C₄	—	226	2	no	—
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	452	2	no	—
561	C₂	—	452	2	no	—
562	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
563	C₂	#20299434	1	1	yes	characteristic
564	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#529×C₁₁₃	C₂
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3493
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #20299320	C₂	semidirect
2. #20299315	C₂	semidirect
3. #20299311	C₂	semidirect
4. #20299310	C₂	semidirect
5. #20299299	C₂	semidirect
6. #20299297	C₂	semidirect
7. #20299281	C₂	semidirect
8. #20299280	C₂	semidirect
9. #20299227	C₂	semidirect
10. #20299188	C₂	semidirect
11. #20299185	C₂	semidirect
12. #20299181	C₂	semidirect
13. #20299175	C₂	semidirect
14. #20299132	C₂	semidirect
15. #20299125	C₂	semidirect
16. #20299106	C₂	semidirect
17. #20299077	C₂	semidirect
18. C₂×#16813579	C₂	semidirect
19. #529×C₁₁₃	C₂	semidirect
22. #16813621	C₂²	semidirect
23. #16813620	C₂²	semidirect
27. #16813617	C₂²	semidirect
29. #16813616	C₂²	semidirect
30. #16813615	C₂²	semidirect
31. #16813614	C₂²	semidirect
32. #16813612	C₂²	semidirect
33. #16813612	C₂²	semidirect
34. #16813612	C₂²	semidirect
37. #16813610	C₂²	semidirect
40. #16813608	C₂²	semidirect
49. #16813600	C₂²	semidirect
51. #16813599	C₂²	semidirect
58. #16813595	C₂²	semidirect
61. #16813594	C₂²	semidirect
64. C₄×Dic₂₂₆	C₂²	semidirect
65. C₄×Dic₂₂₆	C₂²	semidirect
66. #16813587	C₂²	semidirect
67. #16813587	C₂²	semidirect
68. C₄×D₄₅₂	C₂²	semidirect
73. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
77. #16813582	C₂²	semidirect
78. #16813582	C₂²	semidirect
79. #16813580	C₂²	semidirect
84. #16813579	C₂²	semidirect
85. #16813579	C₂²	semidirect
87. #16813578	C₂²	semidirect
88. #16813578	C₂²	semidirect
91. C₂×#14268626	C₂²	semidirect
92. C₄⋊C₄×D₁₁₃	C₂²	semidirect
96. #126×C₁₁₃	C₂²	semidirect
97. #125×C₁₁₃	C₂²	semidirect
98. #124×C₁₁₃	C₂²	semidirect
102. C₄×Q₈×C₁₁₃	C₂²	semidirect
104. C₄×D₄×C₁₁₃	C₂²	semidirect
105. #117×C₁₁₃	C₂²	semidirect
283. C₁₁₃	#3493	semidirect
299. #529	D₁₁₃	semidirect
314. #126	C₂×D₁₁₃	semidirect
319. #125	C₂×D₁₁₃	semidirect
326. #124	C₂×D₁₁₃	semidirect
357. C₄×Q₈	C₂×D₁₁₃	semidirect
370. C₄×D₄	C₂×D₁₁₃	semidirect
381. #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
#20299320	2
#20299315	2
#20299311	2
#20299310	2
#20299299	2
#20299297	2
#20299281	2
#20299280	2
#20299227	2
#20299188	2
#20299185	2
#20299181	2
#20299175	2
#20299132	2
#20299125	2
#20299106	2
#20299077	2
C₂×#16813579	2
#529×C₁₁₃	2
#3493	113