Subgroups — #28404287

Order 14464.

1040 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299321	C₂	1	2	yes	maximal, complemented
2	#20299316	C₂	1	2	yes	maximal, complemented
3	#20299313	C₂	1	2	yes	maximal, complemented
4	#20299311	C₂	1	2	yes	maximal, complemented
5	#20299298	C₂	1	2	yes	maximal, complemented
6	#20299296	C₂	1	2	yes	maximal, complemented
7	#20299289	C₂	1	2	yes	maximal, complemented
8	#20299283	C₂	1	2	yes	maximal, complemented
9	#20299226	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299181	C₂	1	4	yes	maximal, complemented
11	#20299176	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299128	C₂	1	4	yes	maximal, complemented
13	#20299110	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16813580	C₂	1	1	yes	maximal, characteristic, complemented
17	#520×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268647	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
20	#16813622	C₂²	1	2	yes	complemented
21	#16813621	C₂²	1	2	yes	complemented
22	#16813617	C₂²	1	4	yes	—
23	#16813617	C₂²	1	4	yes	complemented
24	#16813616	C₂²	1	4	yes	—
25	#16813615	C₂²	1	4	yes	complemented
26	#16813614	C₂²	1	2	yes	complemented
27	#16813613	C₂²	1	2	yes	complemented
28	#16813612	C₂²	1	4	yes	complemented
29	#16813610	C₂²	1	4	yes	—
30	#16813608	C₂²	1	4	yes	—
31	#16813608	C₂²	1	4	yes	complemented
32	#16813607	C₂²	1	4	yes	—
33	#16813606	C₂²	1	2	yes	—
34	#16813605	C₂²	1	4	yes	—
35	#16813603	C₂²	1	2	yes	—
36	#16813602	C₂²	1	1	yes	characteristic
37	#16813602	C₂²	1	1	yes	characteristic
38	#16813601	C₂²	1	2	yes	complemented
39	#16813599	C₂²	1	4	yes	—
40	#16813598	C₂²	1	1	yes	characteristic
41	#16813598	C₂²	1	1	yes	characteristic
42	#16813598	C₂²	1	2	yes	complemented
43	#16813597	C₂²	1	1	yes	characteristic
44	#16813597	C₂²	1	1	yes	characteristic
45	#16813596	C₂²	1	4	yes	—
46	#16813596	C₂²	1	2	yes	complemented
47	#16813595	C₂²	1	4	yes	—
48	#16813594	C₂²	1	4	yes	—
49	#16813593	C₂²	1	1	yes	characteristic
50	#16813593	C₂²	1	1	yes	characteristic
51	#16813593	C₂²	1	2	yes	complemented
52	#16813592	C₂²	1	2	yes	—
53	#16813590	C₂²	1	2	yes	—
54	C₄×Dic₂₂₆	C₂²	1	4	yes	complemented
55	#16813587	C₂²	1	2	yes	complemented
56	C₄×D₄₅₂	C₂²	1	2	yes	—
57	C₄×D₄₅₂	C₂²	1	2	yes	—
58	#16813584	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
63	#16813581	C₂²	1	1	yes	characteristic
64	#16813581	C₂²	1	4	yes	complemented
65	#16813580	C₂²	1	2	yes	—
66	#16813580	C₂²	1	2	yes	—
67	#16813580	C₂²	1	2	yes	—
68	#16813580	C₂²	1	2	yes	—
69	#16813580	C₂²	1	2	yes	complemented
70	#16813579	C₂²	1	4	yes	complemented
71	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
73	C₂×#14268624	C₂²	1	2	yes	—
74	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
75	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
76	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	complemented
77	C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
78	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
79	#117×C₁₁₃	C₂²	1	1	yes	characteristic
80	#117×C₁₁₃	C₂²	1	2	yes	complemented
81	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
83	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
84	#14268647	—	2	4	no	—
85	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₂₆	C₂³	1	4	yes	—
87	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
88	C₂×D₄₅₂	C₂³	1	2	yes	—
89	C₂×D₄₅₂	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
94	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	—	2	4	no	—
97	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
105	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
106	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
108	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
109	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
110	#14268626	C₂³	1	4	yes	—
111	#14268626	C₂³	1	2	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	2	yes	—
114	#14268626	C₂³	1	4	yes	—
115	#14268626	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	#14268624	C₂³	1	2	yes	—
123	#14268624	C₂³	1	4	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	2	yes	—
126	#14268624	C₂³	1	2	yes	—
127	#14268624	C₂³	1	2	yes	—
128	#14268624	C₂³	1	2	yes	—
129	#14268624	C₂³	1	2	yes	—
130	C₄×Dic₁₁₃	C₂³	1	4	yes	—
131	C₄×Dic₁₁₃	C₂³	1	4	yes	—
132	C₄×Dic₁₁₃	C₂³	1	4	yes	—
133	C₄×Dic₁₁₃	C₂³	1	2	yes	—
134	#41×C₁₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
137	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
141	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
147	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
149	C₄²×C₁₁₃	C₂³	1	4	yes	—
150	C₄²×C₁₁₃	C₂³	1	2	yes	—
151	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
152	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×D₁₁₃	—	2	2	no	—
154	C₂²×D₁₁₃	—	4	1	no	—
155	C₂²×D₁₁₃	—	4	1	no	—
156	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
159	Q₈×C₁₁₃	—	2	2	no	—
160	D₄×C₁₁₃	—	2	4	no	—
161	D₄×C₁₁₃	—	2	2	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	4	2	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	#41	1	4	yes	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₁₁₃	—	2	4	no	—
173	C₂²⋊D₁₁₃	—	4	2	no	—
174	C₂²⋊D₁₁₃	—	4	4	no	—
175	C₂²⋊D₁₁₃	—	4	2	no	—
176	C₂×Dic₁₁₃	—	2	2	no	—
177	C₂×Dic₁₁₃	—	4	2	no	—
178	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
184	D₄₅₂	—	2	2	no	—
185	D₄₅₂	—	4	2	no	—
186	D₄₅₂	—	4	2	no	—
187	C₄×D₁₁₃	—	2	2	no	—
188	C₄×D₁₁₃	—	2	2	no	—
189	C₄×D₁₁₃	—	2	2	no	—
190	C₄×D₁₁₃	—	2	2	no	—
191	C₄×D₁₁₃	—	2	4	no	—
192	C₄×D₁₁₃	—	4	4	no	—
193	Dic₂₂₆	—	2	2	no	—
194	Dic₂₂₆	—	4	4	no	—
195	C₂²×C₁₁₃	—	2	1	no	—
196	C₂²×C₁₁₃	—	2	1	no	—
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	—	2	2	no	—
199	C₂²×C₁₁₃	—	2	2	no	—
200	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
201	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₁₃	—	2	1	no	—
203	C₂×D₁₁₃	—	2	1	no	—
204	C₂×D₁₁₃	—	2	2	no	—
205	C₂×D₁₁₃	—	2	2	no	—
206	C₂×D₁₁₃	—	2	1	no	—
207	C₂×D₁₁₃	—	2	1	no	—
208	C₂×D₁₁₃	—	2	2	no	—
209	C₂×D₁₁₃	—	2	1	no	—
210	C₂×D₁₁₃	—	2	1	no	—
211	C₂×D₁₁₃	—	4	4	no	—
212	C₄×C₁₁₃	—	2	2	no	—
213	C₄×C₁₁₃	—	2	2	no	—
214	C₄×C₁₁₃	—	2	4	no	—
215	C₄×C₁₁₃	—	2	2	no	—
216	C₄×C₁₁₃	C₂×#41	1	2	yes	—
217	C₄×C₁₁₃	C₂×#41	1	2	yes	—
218	Dic₁₁₃	—	2	2	no	—
219	Dic₁₁₃	—	2	1	no	—
220	Dic₁₁₃	—	2	1	no	—
221	Dic₁₁₃	—	2	2	no	—
222	Dic₁₁₃	—	2	4	no	—
223	Dic₁₁₃	—	2	2	no	—
224	C₂×C₁₁₃	—	2	2	no	—
225	C₂×C₁₁₃	—	4	2	no	—
226	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
227	C₂×C₁₁₃	#585	1	1	yes	characteristic
228	C₂×C₁₁₃	#585	1	1	yes	characteristic
229	D₁₁₃	—	4	2	no	—
230	D₁₁₃	—	4	1	no	—
231	D₁₁₃	—	4	1	no	—
232	#3493	—	113	1	no	maximal, Sylow
233	C₁₁₃	#3493	1	1	yes	characteristic, complemented, Sylow
234	#556	—	113	2	no	—
235	#556	—	113	2	no	—
236	#555	—	113	2	no	—
237	#555	—	113	2	no	—
238	#553	—	113	2	no	—
239	#553	—	113	2	no	—
240	#552	—	113	2	no	—
241	#552	—	113	2	no	—
242	#544	—	113	1	no	—
243	#538	—	113	4	no	—
244	#537	—	113	1	no	—
245	#529	—	113	4	no	—
246	#525	—	113	1	no	—
247	#525	—	113	1	no	—
248	#520	—	113	1	no	—
249	#520	D₁₁₃	1	1	yes	characteristic, complemented
250	C₂×#117	—	113	1	no	—
251	C₂×#41	—	113	1	no	—
252	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
253	C₂³×C₄	—	113	1	no	—
254	C₄⋊Q₈	—	113	2	no	—
255	C₄⋊Q₈	—	113	2	no	—
256	#126	—	113	4	no	—
257	#126	—	113	4	no	—
258	#126	—	113	4	no	—
259	#126	—	113	4	no	—
260	#125	—	113	4	no	—
261	#125	—	113	2	no	—
262	#125	—	113	2	no	—
263	#124	—	113	4	no	—
264	#124	—	113	4	no	—
265	#124	—	113	4	no	—
266	#123	—	113	2	no	—
267	#123	—	113	4	no	—
268	#123	—	113	4	no	—
269	#123	—	113	2	no	—
270	C₂²⋊Q₈	—	113	1	no	—
271	C₂²⋊Q₈	—	113	1	no	—
272	C₂²⋊Q₈	—	113	2	no	—
273	C₂²⋊Q₈	—	113	2	no	—
274	C₂²⋊Q₈	—	113	1	no	—
275	C₂²⋊Q₈	—	113	1	no	—
276	C₂²⋊Q₈	—	113	4	no	—
277	#121	—	113	1	no	—
278	#121	—	113	1	no	—
279	#121	—	113	4	no	—
280	#121	—	113	2	no	—
281	#121	—	113	2	no	—
282	#121	—	113	4	no	—
283	#121	—	113	1	no	—
284	#121	—	113	1	no	—
285	#121	—	113	4	no	—
286	#120	—	113	2	no	—
287	#120	—	113	2	no	—
288	C₄×Q₈	—	113	2	no	—
289	C₄×Q₈	—	113	4	no	—
290	C₄×Q₈	C₂×D₁₁₃	1	2	yes	complemented
291	C₄×D₄	—	113	4	no	—
292	C₄×D₄	—	113	2	no	—
293	C₄×D₄	—	113	2	no	—
294	C₄×D₄	—	113	4	no	—
295	C₄×D₄	—	113	2	no	—
296	C₄×D₄	—	113	2	no	—
297	C₄×D₄	—	113	2	no	—
298	C₄×D₄	C₂×D₁₁₃	1	4	yes	—
299	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
300	#117	—	113	1	no	—
301	#117	—	113	4	no	—
302	#117	—	113	2	no	—
303	#117	—	113	2	no	—
304	#117	—	113	2	no	—
305	#117	—	113	2	no	—
306	#117	—	113	2	no	—
307	#117	—	113	4	no	—
308	#117	C₂×D₁₁₃	1	1	yes	characteristic
309	#117	C₂×D₁₁₃	1	2	yes	complemented
310	C₂×C₄⋊C₄	—	113	1	no	—
311	C₂×C₄⋊C₄	—	113	2	no	—
312	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
314	C₂×C₂²⋊C₄	—	113	2	no	—
315	C₂×C₄²	—	113	2	no	—
316	C₂⁴	—	113	1	no	—
317	#41	—	2	4	no	—
318	#41	—	226	4	no	—
319	C₂×Q₈	—	113	4	no	—
320	C₂×Q₈	—	113	1	no	—
321	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
322	C₂×D₄	—	113	2	no	—
323	C₂×D₄	—	113	2	no	—
324	C₂×D₄	—	113	4	no	—
325	C₂×D₄	—	113	2	no	—
326	C₂×D₄	—	113	2	no	—
327	C₂×D₄	—	113	2	no	—
328	C₂×D₄	—	113	1	no	—
329	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
330	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
331	C₂²×C₄	—	113	2	no	—
332	C₂²×C₄	—	113	1	no	—
333	C₂²×C₄	—	113	4	no	—
334	C₂²×C₄	—	113	2	no	—
335	C₂²×C₄	—	113	1	no	—
336	C₂²×C₄	—	113	1	no	—
337	C₂²×C₄	—	113	1	no	—
338	C₂²×C₄	—	113	1	no	—
339	C₂²×C₄	—	226	4	no	—
340	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
341	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
342	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
343	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
344	C₄⋊C₄	—	113	1	no	—
345	C₄⋊C₄	—	113	2	no	—
346	C₄⋊C₄	—	113	2	no	—
347	C₄⋊C₄	—	113	4	no	—
348	C₄⋊C₄	—	113	1	no	—
349	C₄⋊C₄	—	113	2	no	—
350	C₄⋊C₄	—	113	2	no	—
351	C₄⋊C₄	—	113	4	no	—
352	C₄⋊C₄	—	113	4	no	—
353	C₄⋊C₄	—	113	2	no	—
354	C₄⋊C₄	—	113	2	no	—
355	C₄⋊C₄	—	113	4	no	—
356	C₄⋊C₄	—	113	4	no	—
357	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
359	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
361	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
362	C₂²⋊C₄	—	113	2	no	—
363	C₂²⋊C₄	—	113	2	no	—
364	C₂²⋊C₄	—	113	4	no	—
365	C₂²⋊C₄	—	113	2	no	—
366	C₂²⋊C₄	—	113	4	no	—
367	C₂²⋊C₄	—	113	4	no	—
368	C₂²⋊C₄	—	113	2	no	—
369	C₂²⋊C₄	—	113	4	no	—
370	C₂²⋊C₄	—	113	4	no	—
371	C₂²⋊C₄	—	113	2	no	—
372	C₂²⋊C₄	—	113	2	no	—
373	C₂²⋊C₄	—	113	2	no	—
374	C₂²⋊C₄	—	113	2	no	—
375	C₂²⋊C₄	—	113	2	no	—
376	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
378	C₄²	—	113	4	no	—
379	C₄²	—	113	4	no	—
380	C₄²	—	113	4	no	—
381	C₄²	—	113	2	no	—
382	C₄²	C₂²×D₁₁₃	1	4	yes	—
383	C₄²	C₂²×D₁₁₃	1	2	yes	—
384	C₂³	—	113	1	no	—
385	C₂³	—	113	1	no	—
386	C₂³	—	113	2	no	—
387	C₂³	—	452	1	no	—
388	C₂³	—	452	1	no	—
389	C₂³	—	226	2	no	—
390	C₂³	C₂³×D₁₁₃	1	2	yes	—
391	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	452	4	no	—
394	Q₈	—	226	2	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	452	2	no	—
398	D₄	—	452	2	no	—
399	D₄	—	452	2	no	—
400	D₄	—	452	4	no	—
401	D₄	—	452	2	no	—
402	D₄	—	226	4	no	—
403	D₄	—	226	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	113	1	no	—
408	C₂×C₄	—	113	1	no	—
409	C₂×C₄	—	113	2	no	—
410	C₂×C₄	—	113	2	no	—
411	C₂×C₄	—	113	4	no	—
412	C₂×C₄	—	113	2	no	—
413	C₂×C₄	—	452	4	no	—
414	C₂×C₄	—	452	2	no	—
415	C₂×C₄	—	226	2	no	—
416	C₂×C₄	—	226	2	no	—
417	C₂×C₄	—	226	2	no	—
418	C₂×C₄	—	226	2	no	—
419	C₂×C₄	—	226	2	no	—
420	C₂×C₄	—	226	4	no	—
421	C₂×C₄	#14268647	1	4	yes	—
422	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
423	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
424	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
425	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
426	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	452	4	no	—
434	C₂²	—	226	1	no	—
435	C₂²	—	226	1	no	—
436	C₂²	—	226	2	no	—
437	C₂²	—	226	2	no	—
438	C₂²	—	226	1	no	—
439	C₂²	—	226	1	no	—
440	C₂²	—	226	2	no	—
441	C₂²	—	226	1	no	—
442	C₂²	—	226	1	no	—
443	C₂²	C₂×#14268647	1	2	yes	—
444	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	226	1	no	—
450	C₄	—	226	1	no	—
451	C₄	—	226	2	no	—
452	C₄	—	226	2	no	—
453	C₄	—	226	4	no	—
454	C₄	—	226	2	no	—
455	C₄	C₂×#14268647	1	2	yes	—
456	C₄	C₂×#14268647	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	452	1	no	—
460	C₂	—	452	1	no	—
461	C₂	—	452	2	no	—
462	C₂	C₂²×#14268647	1	1	yes	characteristic
463	C₂	#20299433	1	1	yes	characteristic
464	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#520×C₁₁₃	C₂
hypercenter	#520	D₁₁₃
hypocenter	C₁₁₃	#3493
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #20299321	C₂	semidirect
2. #20299316	C₂	semidirect
3. #20299313	C₂	semidirect
4. #20299311	C₂	semidirect
5. #20299298	C₂	semidirect
6. #20299296	C₂	semidirect
7. #20299289	C₂	semidirect
8. #20299283	C₂	semidirect
9. #20299226	C₂	semidirect
10. #20299181	C₂	semidirect
11. #20299176	C₂	semidirect
12. #20299128	C₂	semidirect
13. #20299110	C₂	semidirect
14. #20299105	C₂	semidirect
15. #20299079	C₂	semidirect
16. C₂×#16813580	C₂	semidirect
17. #520×C₁₁₃	C₂	semidirect
20. #16813622	C₂²	semidirect
21. #16813621	C₂²	semidirect
23. #16813617	C₂²	semidirect
25. #16813615	C₂²	semidirect
26. #16813614	C₂²	semidirect
27. #16813613	C₂²	semidirect
28. #16813612	C₂²	semidirect
31. #16813608	C₂²	semidirect
38. #16813601	C₂²	semidirect
42. #16813598	C₂²	semidirect
46. #16813596	C₂²	semidirect
51. #16813593	C₂²	semidirect
54. C₄×Dic₂₂₆	C₂²	semidirect
55. #16813587	C₂²	semidirect
58. #16813584	C₂²	semidirect
62. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
64. #16813581	C₂²	semidirect
69. #16813580	C₂²	semidirect
70. #16813579	C₂²	semidirect
72. C₄⋊C₄×D₁₁₃	C₂²	semidirect
76. C₄×Q₈×C₁₁₃	C₂²	semidirect
78. C₄×D₄×C₁₁₃	C₂²	semidirect
80. #117×C₁₁₃	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
233. C₁₁₃	#3493	semidirect
249. #520	D₁₁₃	semidirect
290. C₄×Q₈	C₂×D₁₁₃	semidirect
299. C₄×D₄	C₂×D₁₁₃	semidirect
309. #117	C₂×D₁₁₃	semidirect
313. 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
#20299321	2
#20299316	2
#20299313	2
#20299311	2
#20299298	2
#20299296	2
#20299289	2
#20299283	2
#20299226	2
#20299181	2
#20299176	2
#20299128	2
#20299110	2
#20299105	2
#20299079	2
C₂×#16813580	2
#520×C₁₁₃	2
#3493	113