Subgroups — #28404277

Order 14464.

1124 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299308	C₂	1	2	yes	maximal, complemented
2	#20299303	C₂	1	2	yes	maximal, complemented
3	#20299298	C₂	1	2	yes	maximal, complemented
4	#20299292	C₂	1	2	yes	maximal, complemented
5	#20299289	C₂	1	2	yes	maximal, complemented
6	#20299287	C₂	1	2	yes	maximal, complemented
7	#20299253	C₂	1	2	yes	maximal, complemented
8	#20299249	C₂	1	2	yes	maximal, complemented
9	#20299226	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299190	C₂	1	4	yes	maximal, complemented
11	#20299176	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299110	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299107	C₂	1	4	yes	maximal, complemented
14	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₁₁₃	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	C₂×#14268647	C₂²	1	4	yes	—
20	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
22	#16813622	C₂²	1	2	yes	complemented
23	#16813621	C₂²	1	2	yes	complemented
24	#16813616	C₂²	1	4	yes	complemented
25	#16813615	C₂²	1	4	yes	complemented
26	#16813614	C₂²	1	4	yes	complemented
27	#16813614	C₂²	1	2	yes	complemented
28	#16813613	C₂²	1	2	yes	complemented
29	#16813612	C₂²	1	4	yes	complemented
30	#16813607	C₂²	1	4	yes	—
31	#16813606	C₂²	1	2	yes	—
32	#16813605	C₂²	1	4	yes	complemented
33	#16813604	C₂²	1	4	yes	—
34	#16813604	C₂²	1	4	yes	complemented
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	#16813601	C₂²	1	4	yes	complemented
40	#16813600	C₂²	1	4	yes	—
41	#16813600	C₂²	1	4	yes	complemented
42	#16813599	C₂²	1	4	yes	—
43	#16813598	C₂²	1	1	yes	characteristic
44	#16813598	C₂²	1	1	yes	characteristic
45	#16813598	C₂²	1	2	yes	complemented
46	#16813597	C₂²	1	1	yes	characteristic
47	#16813597	C₂²	1	1	yes	characteristic
48	#16813596	C₂²	1	2	yes	complemented
49	#16813595	C₂²	1	4	yes	—
50	#16813594	C₂²	1	4	yes	—
51	#16813593	C₂²	1	1	yes	characteristic
52	#16813593	C₂²	1	1	yes	characteristic
53	#16813593	C₂²	1	2	yes	complemented
54	#16813592	C₂²	1	2	yes	—
55	#16813590	C₂²	1	2	yes	—
56	#16813587	C₂²	1	2	yes	complemented
57	C₄×D₄₅₂	C₂²	1	2	yes	—
58	C₄×D₄₅₂	C₂²	1	4	yes	—
59	C₄×D₄₅₂	C₂²	1	2	yes	—
60	#16813584	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
64	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
65	#16813581	C₂²	1	1	yes	characteristic
66	#16813580	C₂²	1	2	yes	complemented
67	#16813579	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
69	C₂×#14268626	C₂²	1	2	yes	—
70	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
73	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
74	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
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	#14268647	—	4	8	no	—
86	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₂₆	C₂³	1	4	yes	—
88	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
89	C₂×D₄₅₂	C₂³	1	2	yes	—
90	C₂×D₄₅₂	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	2	yes	—
94	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
95	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄×D₁₁₃	—	2	4	no	—
98	C₂×C₄×D₁₁₃	—	4	4	no	—
99	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
105	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
106	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
107	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
108	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
109	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
112	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
113	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
114	#14268626	C₂³	1	4	yes	—
115	#14268626	C₂³	1	4	yes	—
116	#14268626	C₂³	1	4	yes	—
117	#14268626	C₂³	1	4	yes	—
118	#14268626	C₂³	1	4	yes	—
119	#14268626	C₂³	1	2	yes	—
120	#14268626	C₂³	1	2	yes	—
121	#14268626	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
123	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
126	#14268624	C₂³	1	2	yes	—
127	#14268624	C₂³	1	2	yes	—
128	#14268624	C₂³	1	4	yes	—
129	#14268624	C₂³	1	2	yes	—
130	#14268624	C₂³	1	2	yes	—
131	#14268624	C₂³	1	4	yes	—
132	#14268624	C₂³	1	2	yes	—
133	#14268624	C₂³	1	2	yes	—
134	C₄×Dic₁₁₃	C₂³	1	4	yes	—
135	C₄×Dic₁₁₃	C₂³	1	2	yes	—
136	#41×C₁₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
139	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
143	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
151	C₄²×C₁₁₃	C₂³	1	4	yes	—
152	C₄²×C₁₁₃	C₂³	1	2	yes	—
153	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×D₁₁₃	—	2	2	no	—
156	C₂²×D₁₁₃	—	2	2	no	—
157	C₂²×D₁₁₃	—	2	2	no	—
158	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
159	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₁₁₃	—	2	2	no	—
162	D₄×C₁₁₃	—	2	4	no	—
163	D₄×C₁₁₃	—	2	2	no	—
164	C₂×C₄×C₁₁₃	—	2	4	no	—
165	C₂×C₄×C₁₁₃	—	4	2	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	#41	1	4	yes	complemented
168	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
171	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₁₁₃	—	2	4	no	—
175	C₂²⋊D₁₁₃	—	2	4	no	—
176	C₂²⋊D₁₁₃	—	2	4	no	—
177	C₂²⋊D₁₁₃	—	4	4	no	—
178	C₂×Dic₁₁₃	—	2	2	no	—
179	C₂×Dic₁₁₃	—	4	2	no	—
180	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
186	D₄₅₂	—	2	4	no	—
187	D₄₅₂	—	2	4	no	—
188	D₄₅₂	—	2	2	no	—
189	C₄×D₁₁₃	—	2	8	no	—
190	C₄×D₁₁₃	—	2	2	no	—
191	C₄×D₁₁₃	—	2	2	no	—
192	C₄×D₁₁₃	—	2	2	no	—
193	C₄×D₁₁₃	—	2	2	no	—
194	C₄×D₁₁₃	—	2	4	no	—
195	C₄×D₁₁₃	—	4	4	no	—
196	C₄×D₁₁₃	—	4	4	no	—
197	Dic₂₂₆	—	2	2	no	—
198	Dic₂₂₆	—	4	4	no	—
199	C₂²×C₁₁₃	—	2	1	no	—
200	C₂²×C₁₁₃	—	2	1	no	—
201	C₂²×C₁₁₃	—	2	2	no	—
202	C₂²×C₁₁₃	—	2	2	no	—
203	C₂²×C₁₁₃	—	2	2	no	—
204	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
205	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₁₁₃	—	2	8	no	—
207	C₂×D₁₁₃	—	2	1	no	—
208	C₂×D₁₁₃	—	2	1	no	—
209	C₂×D₁₁₃	—	2	1	no	—
210	C₂×D₁₁₃	—	2	1	no	—
211	C₂×D₁₁₃	—	2	2	no	—
212	C₂×D₁₁₃	—	2	2	no	—
213	C₂×D₁₁₃	—	2	2	no	—
214	C₂×D₁₁₃	H(5,𝔽₂)	1	2	yes	—
215	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
216	C₄×C₁₁₃	—	2	2	no	—
217	C₄×C₁₁₃	—	2	2	no	—
218	C₄×C₁₁₃	—	2	4	no	—
219	C₄×C₁₁₃	—	2	2	no	—
220	C₄×C₁₁₃	C₂×#41	1	2	yes	—
221	C₄×C₁₁₃	C₂×#41	1	2	yes	—
222	Dic₁₁₃	—	2	2	no	—
223	Dic₁₁₃	—	2	1	no	—
224	Dic₁₁₃	—	2	1	no	—
225	Dic₁₁₃	—	2	2	no	—
226	Dic₁₁₃	—	2	4	no	—
227	Dic₁₁₃	—	2	2	no	—
228	C₂×C₁₁₃	—	2	2	no	—
229	C₂×C₁₁₃	—	4	2	no	—
230	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
231	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
233	D₁₁₃	—	2	2	no	—
234	D₁₁₃	—	2	2	no	—
235	D₁₁₃	—	4	2	no	—
236	#3492	—	113	1	no	maximal, Sylow
237	C₁₁₃	#3492	1	1	yes	characteristic, complemented, Sylow
238	#554	—	113	2	no	—
239	#554	—	113	2	no	—
240	#553	—	113	2	no	—
241	#553	—	113	2	no	—
242	#552	—	113	2	no	—
243	#552	—	113	2	no	—
244	#547	—	113	2	no	—
245	#547	—	113	2	no	—
246	#544	—	113	1	no	—
247	#539	—	113	4	no	—
248	#537	—	113	1	no	—
249	#525	—	113	1	no	—
250	#525	—	113	4	no	—
251	#525	—	113	1	no	—
252	#520	—	113	1	no	—
253	#520	D₁₁₃	1	1	yes	characteristic, complemented
254	C₂²×C₄⋊C₄	—	113	1	no	—
255	C₂×#41	—	113	4	no	—
256	C₂×#41	—	113	1	no	—
257	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
258	C₂³×C₄	—	113	2	no	—
259	C₂³×C₄	—	113	1	no	—
260	C₄⋊Q₈	—	113	2	no	—
261	C₄⋊Q₈	—	113	2	no	—
262	#126	—	113	4	no	—
263	#126	—	113	4	no	—
264	#125	—	113	4	no	—
265	#125	—	113	2	no	—
266	#125	—	113	4	no	—
267	#125	—	113	2	no	—
268	#123	—	113	2	no	—
269	#123	—	113	4	no	—
270	#123	—	113	4	no	—
271	#123	—	113	2	no	—
272	#123	—	113	4	no	—
273	#123	—	113	4	no	—
274	C₂²⋊Q₈	—	113	1	no	—
275	C₂²⋊Q₈	—	113	1	no	—
276	C₂²⋊Q₈	—	113	2	no	—
277	C₂²⋊Q₈	—	113	2	no	—
278	C₂²⋊Q₈	—	113	4	no	—
279	C₂²⋊Q₈	—	113	4	no	—
280	C₂²⋊Q₈	—	113	1	no	—
281	C₂²⋊Q₈	—	113	1	no	—
282	C₂²⋊Q₈	—	113	4	no	—
283	C₂²⋊Q₈	—	113	4	no	—
284	#121	—	113	4	no	—
285	#121	—	113	1	no	—
286	#121	—	113	1	no	—
287	#121	—	113	2	no	—
288	#121	—	113	2	no	—
289	#121	—	113	1	no	—
290	#121	—	113	1	no	—
291	#121	—	113	4	no	—
292	#120	—	113	2	no	—
293	#120	—	113	2	no	—
294	C₄×Q₈	—	113	2	no	—
295	C₄×Q₈	C₂×D₁₁₃	1	2	yes	complemented
296	C₄×D₄	—	113	4	no	—
297	C₄×D₄	—	113	2	no	—
298	C₄×D₄	—	113	4	no	—
299	C₄×D₄	—	113	2	no	—
300	C₄×D₄	—	113	2	no	—
301	C₄×D₄	—	113	2	no	—
302	C₄×D₄	—	113	4	no	—
303	C₄×D₄	—	113	2	no	—
304	C₄×D₄	C₂×D₁₁₃	1	4	yes	—
305	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
306	#117	—	113	1	no	—
307	#117	—	113	2	no	—
308	#117	—	113	4	no	—
309	#117	C₂×D₁₁₃	1	1	yes	characteristic
310	#117	C₂×D₁₁₃	1	2	yes	complemented
311	C₂×C₄⋊C₄	—	113	2	no	—
312	C₂×C₄⋊C₄	—	113	1	no	—
313	C₂×C₄⋊C₄	—	113	2	no	—
314	C₂×C₄⋊C₄	—	113	2	no	—
315	C₂×C₄⋊C₄	—	113	2	no	—
316	C₂×C₄⋊C₄	—	113	2	no	—
317	C₂×C₄⋊C₄	—	113	2	no	—
318	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
320	C₂⁴	—	113	1	no	—
321	#41	—	2	4	no	—
322	#41	—	452	8	no	—
323	#41	—	226	4	no	—
324	C₂×Q₈	—	113	4	no	—
325	C₂×Q₈	—	113	1	no	—
326	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
327	C₂×D₄	—	113	4	no	—
328	C₂×D₄	—	113	2	no	—
329	C₂×D₄	—	113	2	no	—
330	C₂×D₄	—	113	2	no	—
331	C₂×D₄	—	113	2	no	—
332	C₂×D₄	—	113	1	no	—
333	C₂×D₄	—	113	2	no	—
334	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
335	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
336	C₂²×C₄	—	113	2	no	—
337	C₂²×C₄	—	113	1	no	—
338	C₂²×C₄	—	113	4	no	—
339	C₂²×C₄	—	113	4	no	—
340	C₂²×C₄	—	113	4	no	—
341	C₂²×C₄	—	113	1	no	—
342	C₂²×C₄	—	113	1	no	—
343	C₂²×C₄	—	113	1	no	—
344	C₂²×C₄	—	113	1	no	—
345	C₂²×C₄	—	113	2	no	—
346	C₂²×C₄	—	452	4	no	—
347	C₂²×C₄	—	226	4	no	—
348	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
349	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
350	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
351	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
352	C₄⋊C₄	—	113	2	no	—
353	C₄⋊C₄	—	113	2	no	—
354	C₄⋊C₄	—	113	4	no	—
355	C₄⋊C₄	—	113	4	no	—
356	C₄⋊C₄	—	113	1	no	—
357	C₄⋊C₄	—	113	4	no	—
358	C₄⋊C₄	—	113	1	no	—
359	C₄⋊C₄	—	113	4	no	—
360	C₄⋊C₄	—	113	4	no	—
361	C₄⋊C₄	—	113	2	no	—
362	C₄⋊C₄	—	113	2	no	—
363	C₄⋊C₄	—	113	4	no	—
364	C₄⋊C₄	—	113	4	no	—
365	C₄⋊C₄	—	113	2	no	—
366	C₄⋊C₄	—	113	2	no	—
367	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
368	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
369	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
371	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
372	C₂²⋊C₄	—	113	2	no	—
373	C₂²⋊C₄	—	113	4	no	—
374	C₂²⋊C₄	—	113	2	no	—
375	C₂²⋊C₄	—	113	2	no	—
376	C₂²⋊C₄	—	113	2	no	—
377	C₂²⋊C₄	—	113	2	no	—
378	C₂²⋊C₄	—	113	4	no	—
379	C₂²⋊C₄	—	113	2	no	—
380	C₂²⋊C₄	—	113	2	no	—
381	C₂²⋊C₄	—	113	4	no	—
382	C₂²⋊C₄	—	113	2	no	—
383	C₂²⋊C₄	—	113	2	no	—
384	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
386	C₄²	—	113	4	no	—
387	C₄²	—	113	2	no	—
388	C₄²	C₂²×D₁₁₃	1	4	yes	—
389	C₄²	C₂²×D₁₁₃	1	2	yes	—
390	C₂³	—	113	1	no	—
391	C₂³	—	113	1	no	—
392	C₂³	—	113	2	no	—
393	C₂³	—	226	2	no	—
394	C₂³	—	226	2	no	—
395	C₂³	—	226	2	no	—
396	C₂³	C₂³×D₁₁₃	1	2	yes	—
397	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	452	4	no	—
400	Q₈	—	226	2	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	2	no	—
403	D₄	—	452	4	no	—
404	D₄	—	226	4	no	—
405	D₄	—	226	4	no	—
406	D₄	—	226	4	no	—
407	D₄	—	226	4	no	—
408	D₄	—	226	4	no	—
409	D₄	—	226	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	113	2	no	—
414	C₂×C₄	—	113	2	no	—
415	C₂×C₄	—	113	2	no	—
416	C₂×C₄	—	113	1	no	—
417	C₂×C₄	—	113	1	no	—
418	C₂×C₄	—	113	4	no	—
419	C₂×C₄	—	452	4	no	—
420	C₂×C₄	—	452	4	no	—
421	C₂×C₄	—	452	2	no	—
422	C₂×C₄	—	226	8	no	—
423	C₂×C₄	—	226	2	no	—
424	C₂×C₄	—	226	2	no	—
425	C₂×C₄	—	226	2	no	—
426	C₂×C₄	—	226	2	no	—
427	C₂×C₄	—	226	2	no	—
428	C₂×C₄	—	226	4	no	—
429	C₂×C₄	#14268647	1	4	yes	complemented
430	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
431	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
432	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
433	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
434	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	113	2	no	—
442	C₂²	—	113	2	no	—
443	C₂²	—	226	8	no	—
444	C₂²	—	226	2	no	—
445	C₂²	—	226	2	no	—
446	C₂²	—	226	2	no	—
447	C₂²	—	226	1	no	—
448	C₂²	—	226	1	no	—
449	C₂²	—	226	1	no	—
450	C₂²	—	226	1	no	—
451	C₂²	C₂×#14268647	1	2	yes	—
452	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	226	1	no	—
458	C₄	—	226	1	no	—
459	C₄	—	226	2	no	—
460	C₄	—	226	4	no	—
461	C₄	—	226	2	no	—
462	C₄	—	226	2	no	—
463	C₄	C₂×#14268647	1	2	yes	—
464	C₄	C₂×#14268647	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	4	2	no	—
467	C₂	—	452	2	no	—
468	C₂	—	226	2	no	—
469	C₂	—	226	2	no	—
470	C₂	C₂²×#14268647	1	1	yes	characteristic
471	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
472	C₂	2₋¹⁺⁴×D₁₁₃	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	#3492
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. #20299308	C₂	semidirect
2. #20299303	C₂	semidirect
3. #20299298	C₂	semidirect
4. #20299292	C₂	semidirect
5. #20299289	C₂	semidirect
6. #20299287	C₂	semidirect
7. #20299253	C₂	semidirect
8. #20299249	C₂	semidirect
9. #20299226	C₂	semidirect
10. #20299190	C₂	semidirect
11. #20299176	C₂	semidirect
12. #20299110	C₂	semidirect
13. #20299107	C₂	semidirect
14. #20299105	C₂	semidirect
15. #20299079	C₂	semidirect
16. C₂×C₄⋊C₄×D₁₁₃	C₂	semidirect
17. #520×C₁₁₃	C₂	semidirect
22. #16813622	C₂²	semidirect
23. #16813621	C₂²	semidirect
24. #16813616	C₂²	semidirect
25. #16813615	C₂²	semidirect
26. #16813614	C₂²	semidirect
27. #16813614	C₂²	semidirect
28. #16813613	C₂²	semidirect
29. #16813612	C₂²	semidirect
32. #16813605	C₂²	semidirect
34. #16813604	C₂²	semidirect
38. #16813601	C₂²	semidirect
39. #16813601	C₂²	semidirect
41. #16813600	C₂²	semidirect
45. #16813598	C₂²	semidirect
48. #16813596	C₂²	semidirect
53. #16813593	C₂²	semidirect
56. #16813587	C₂²	semidirect
60. #16813584	C₂²	semidirect
66. #16813580	C₂²	semidirect
74. 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
167. C₂×C₄×C₁₁₃	#41	semidirect
237. C₁₁₃	#3492	semidirect
253. #520	D₁₁₃	semidirect
295. C₄×Q₈	C₂×D₁₁₃	semidirect
305. C₄×D₄	C₂×D₁₁₃	semidirect
310. #117	C₂×D₁₁₃	semidirect
319. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
429. C₂×C₄	#14268647	semidirect

Maximal subgroups

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

subgroup	index
#20299308	2
#20299303	2
#20299298	2
#20299292	2
#20299289	2
#20299287	2
#20299253	2
#20299249	2
#20299226	2
#20299190	2
#20299176	2
#20299110	2
#20299107	2
#20299105	2
#20299079	2
C₂×C₄⋊C₄×D₁₁₃	2
#520×C₁₁₃	2
#3492	113