Subgroups — #28404259

Order 14464.

1328 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299277	C₂	1	4	yes	maximal, complemented
2	#20299272	C₂	1	4	yes	maximal, complemented
3	#20299244	C₂	1	4	yes	maximal, complemented
4	#20299238	C₂	1	4	yes	maximal, complemented
5	#20299224	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299181	C₂	1	4	yes	maximal, complemented
7	#20299157	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299107	C₂	1	4	yes	maximal, complemented
9	C₂×#16813592	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16813590	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299071	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂²⋊C₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#518×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂⁴×D₁₁₃	C₂²	1	1	yes	characteristic
15	C₂×#14268647	C₂²	1	4	yes	complemented
16	C₂²×D₄₅₂	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
19	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
20	#16813617	C₂²	1	4	yes	complemented
21	#16813616	C₂²	1	4	yes	complemented
22	#16813610	C₂²	1	4	yes	complemented
23	#16813608	C₂²	1	4	yes	complemented
24	#16813607	C₂²	1	4	yes	complemented
25	#16813607	C₂²	1	4	yes	complemented
26	#16813605	C₂²	1	2	yes	complemented
27	#16813605	C₂²	1	4	yes	complemented
28	#16813604	C₂²	1	4	yes	complemented
29	#16813603	C₂²	1	2	yes	complemented
30	#16813601	C₂²	1	4	yes	complemented
31	#16813600	C₂²	1	4	yes	complemented
32	#16813599	C₂²	1	4	yes	complemented
33	#16813599	C₂²	1	4	yes	complemented
34	#16813596	C₂²	1	4	yes	complemented
35	#16813595	C₂²	1	4	yes	complemented
36	#16813595	C₂²	1	4	yes	complemented
37	#16813594	C₂²	1	4	yes	complemented
38	#16813592	C₂²	1	4	yes	—
39	#16813592	C₂²	1	2	yes	complemented
40	#16813592	C₂²	1	2	yes	complemented
41	#16813591	C₂²	1	2	yes	complemented
42	#16813590	C₂²	1	4	yes	—
43	#16813590	C₂²	1	2	yes	complemented
44	#16813590	C₂²	1	2	yes	complemented
45	#16813590	C₂²	1	2	yes	complemented
46	C₄×D₄₅₂	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
49	#16813582	C₂²	1	4	yes	complemented
50	#16813579	C₂²	1	4	yes	complemented
51	#16813578	C₂²	1	2	yes	complemented
52	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
54	C₂×#14268624	C₂²	1	2	yes	complemented
55	C₂×#14268624	C₂²	1	2	yes	complemented
56	C₂×#14268624	C₂²	1	2	yes	complemented
57	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
58	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
59	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
60	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
61	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
62	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
63	#117×C₁₁₃	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
67	C₂³×D₁₁₃	—	2	4	no	—
68	C₂³×D₁₁₃	—	4	4	no	—
69	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
70	C₂³×D₁₁₃	C₂³	1	2	yes	—
71	C₂³×D₁₁₃	C₂³	1	2	yes	—
72	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
73	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
74	#14268647	—	4	8	no	—
75	C₂×Dic₂₂₆	C₂³	1	4	yes	complemented
76	C₂×D₄₅₂	—	4	4	no	—
77	C₂×D₄₅₂	C₂³	1	4	yes	—
78	C₂×D₄₅₂	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
80	C₂×C₂²⋊D₁₁₃	—	4	4	no	—
81	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
83	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	complemented
86	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
88	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
89	C₂×C₄×D₁₁₃	—	4	4	no	—
90	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
91	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	4	yes	complemented
93	C₄⋊Dic₁₁₃	C₂³	1	4	yes	complemented
94	#14268626	C₂³	1	4	yes	complemented
95	#14268626	C₂³	1	4	yes	complemented
96	#14268626	C₂³	1	4	yes	complemented
97	#14268626	C₂³	1	4	yes	complemented
98	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
100	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
101	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
102	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	complemented
103	#14268624	C₂³	1	4	yes	—
104	#14268624	C₂³	1	4	yes	—
105	#14268624	C₂³	1	4	yes	—
106	#14268624	C₂³	1	4	yes	—
107	#14268624	C₂³	1	4	yes	—
108	#14268624	C₂³	1	4	yes	—
109	#14268624	C₂³	1	4	yes	complemented
110	#14268624	C₂³	1	4	yes	complemented
111	C₄×Dic₁₁₃	C₂³	1	4	yes	complemented
112	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
113	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₁₃	—	2	4	no	—
115	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
116	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
117	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	complemented
121	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	complemented
122	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
126	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	complemented
127	C₄²×C₁₁₃	C₂³	1	4	yes	complemented
128	C₂³×C₁₁₃	—	2	2	no	—
129	C₂³×C₁₁₃	—	4	2	no	—
130	C₂³×C₁₁₃	—	4	2	no	—
131	C₂³×C₁₁₃	#41	1	4	yes	complemented
132	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
133	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
134	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
135	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
136	C₂²×D₁₁₃	—	2	2	no	—
137	C₂²×D₁₁₃	—	2	4	no	—
138	C₂²×D₁₁₃	—	2	4	no	—
139	C₂²×D₁₁₃	—	2	4	no	—
140	C₂²×D₁₁₃	—	2	2	no	—
141	C₂²×D₁₁₃	—	2	2	no	—
142	C₂²×D₁₁₃	—	2	4	no	—
143	C₂²×D₁₁₃	—	2	4	no	—
144	C₂²×D₁₁₃	—	4	2	no	—
145	C₂²×D₁₁₃	—	4	2	no	—
146	C₂²×D₁₁₃	—	4	2	no	—
147	C₂²×D₁₁₃	—	4	2	no	—
148	C₂²×D₁₁₃	—	4	16	no	—
149	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
150	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
151	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
152	D₄×C₁₁₃	—	2	4	no	—
153	D₄×C₁₁₃	—	2	4	no	—
154	C₂×C₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	4	4	no	—
158	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
161	C₂²⋊D₁₁₃	—	2	4	no	—
162	C₂²⋊D₁₁₃	—	2	4	no	—
163	C₂²⋊D₁₁₃	—	2	8	no	—
164	C₂²⋊D₁₁₃	—	4	4	no	—
165	C₂²⋊D₁₁₃	—	4	4	no	—
166	C₂×Dic₁₁₃	—	2	2	no	—
167	C₂×Dic₁₁₃	—	4	2	no	—
168	C₂×Dic₁₁₃	—	4	2	no	—
169	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
170	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
171	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
172	D₄₅₂	—	2	8	no	—
173	D₄₅₂	—	4	4	no	—
174	C₄×D₁₁₃	—	2	8	no	—
175	C₄×D₁₁₃	—	4	4	no	—
176	C₄×D₁₁₃	—	4	4	no	—
177	Dic₂₂₆	—	4	4	no	—
178	C₂²×C₁₁₃	—	2	2	no	—
179	C₂²×C₁₁₃	—	2	2	no	—
180	C₂²×C₁₁₃	—	2	2	no	—
181	C₂²×C₁₁₃	—	2	2	no	—
182	C₂²×C₁₁₃	—	2	4	no	—
183	C₂²×C₁₁₃	—	4	4	no	—
184	C₂²×C₁₁₃	—	8	2	no	—
185	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
186	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
187	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
188	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
189	C₂×D₁₁₃	—	2	8	no	—
190	C₂×D₁₁₃	—	2	2	no	—
191	C₂×D₁₁₃	—	2	2	no	—
192	C₂×D₁₁₃	—	2	2	no	—
193	C₂×D₁₁₃	—	2	2	no	—
194	C₂×D₁₁₃	—	2	4	no	—
195	C₂×D₁₁₃	—	2	2	no	—
196	C₂×D₁₁₃	—	2	2	no	—
197	C₂×D₁₁₃	—	4	8	no	—
198	C₂×D₁₁₃	—	4	8	no	—
199	C₂×D₁₁₃	—	4	4	no	—
200	C₂×D₁₁₃	—	8	2	no	—
201	C₂×D₁₁₃	H(5,𝔽₂)	1	4	yes	—
202	C₄×C₁₁₃	—	2	2	no	—
203	C₄×C₁₁₃	—	2	4	no	—
204	C₄×C₁₁₃	—	2	4	no	—
205	Dic₁₁₃	—	2	2	no	—
206	Dic₁₁₃	—	2	4	no	—
207	Dic₁₁₃	—	2	4	no	—
208	C₂×C₁₁₃	—	2	2	no	—
209	C₂×C₁₁₃	—	2	2	no	—
210	C₂×C₁₁₃	—	2	2	no	—
211	C₂×C₁₁₃	—	4	2	no	—
212	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
213	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
214	D₁₁₃	—	2	4	no	—
215	D₁₁₃	—	4	2	no	—
216	D₁₁₃	—	4	2	no	—
217	#3490	—	113	1	no	maximal, Sylow
218	C₁₁₃	#3490	1	1	yes	characteristic, complemented, Sylow
219	#551	—	113	4	no	—
220	#551	—	113	4	no	—
221	#546	—	113	4	no	—
222	#546	—	113	4	no	—
223	#543	—	113	1	no	—
224	#538	—	113	4	no	—
225	#534	—	113	1	no	—
226	#525	—	113	4	no	—
227	C₂×#120	—	113	1	no	—
228	C₂×#120	—	113	1	no	—
229	#518	—	113	1	no	—
230	#518	D₁₁₃	1	1	yes	characteristic, complemented
231	C₂²×C₂²⋊C₄	—	113	1	no	—
232	C₂⁵	—	113	1	no	—
233	C₂×#41	—	113	4	no	—
234	C₂²×D₄	—	113	2	no	—
235	C₂²×D₄	—	113	1	no	—
236	C₂²×D₄	—	113	2	no	—
237	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
238	C₂³×C₄	—	113	2	no	—
239	#126	—	113	4	no	—
240	#126	—	113	4	no	—
241	#124	—	113	4	no	—
242	#124	—	113	4	no	—
243	#123	—	113	2	no	—
244	#123	—	113	2	no	—
245	#123	—	113	4	no	—
246	#123	—	113	4	no	—
247	#123	—	113	4	no	—
248	#123	—	113	4	no	—
249	C₂²⋊Q₈	—	113	4	no	—
250	C₂²⋊Q₈	—	113	4	no	—
251	C₂²⋊Q₈	—	113	4	no	—
252	C₂²⋊Q₈	—	113	4	no	—
253	#121	—	113	4	no	—
254	#121	—	113	4	no	—
255	#121	—	113	4	no	—
256	#121	—	113	4	no	—
257	#120	—	113	2	no	—
258	#120	—	113	2	no	—
259	#120	—	113	4	no	—
260	#120	—	113	2	no	—
261	#120	—	113	2	no	—
262	#120	—	113	2	no	—
263	#120	—	113	4	no	—
264	#120	—	113	2	no	—
265	C₄×D₄	—	113	4	no	—
266	C₄×D₄	—	113	4	no	—
267	C₄×D₄	—	113	4	no	—
268	C₄×D₄	—	113	4	no	—
269	C₄×D₄	C₂×D₁₁₃	1	4	yes	complemented
270	C₄×D₄	C₂×D₁₁₃	1	4	yes	complemented
271	#117	—	113	2	no	—
272	#117	—	113	4	no	—
273	#117	C₂×D₁₁₃	1	2	yes	complemented
274	C₂×C₂²⋊C₄	—	113	1	no	—
275	C₂×C₂²⋊C₄	—	113	1	no	—
276	C₂×C₂²⋊C₄	—	113	2	no	—
277	C₂×C₂²⋊C₄	—	113	2	no	—
278	C₂×C₂²⋊C₄	—	113	2	no	—
279	C₂×C₂²⋊C₄	—	113	4	no	—
280	C₂×C₂²⋊C₄	—	113	4	no	—
281	C₂×C₂²⋊C₄	—	113	2	no	—
282	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
285	C₂⁴	—	113	1	no	—
286	C₂⁴	—	113	1	no	—
287	C₂⁴	—	113	2	no	—
288	C₂⁴	—	113	2	no	—
289	C₂⁴	—	113	1	no	—
290	C₂⁴	—	452	4	no	—
291	C₂⁴	—	226	4	no	—
292	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
293	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
294	#41	—	452	8	no	—
295	C₂×Q₈	—	113	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	113	4	no	—
298	C₂×D₄	—	113	4	no	—
299	C₂×D₄	—	113	2	no	—
300	C₂×D₄	—	113	2	no	—
301	C₂×D₄	—	113	4	no	—
302	C₂×D₄	—	113	4	no	—
303	C₂×D₄	—	113	4	no	—
304	C₂×D₄	—	452	4	no	—
305	C₂×D₄	—	452	4	no	—
306	C₂×D₄	—	226	4	no	—
307	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
308	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
309	C₂²×C₄	—	113	2	no	—
310	C₂²×C₄	—	113	2	no	—
311	C₂²×C₄	—	113	1	no	—
312	C₂²×C₄	—	113	4	no	—
313	C₂²×C₄	—	113	4	no	—
314	C₂²×C₄	—	113	4	no	—
315	C₂²×C₄	—	452	4	no	—
316	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
318	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
319	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	complemented
320	C₄⋊C₄	—	113	4	no	—
321	C₄⋊C₄	—	113	4	no	—
322	C₄⋊C₄	—	113	4	no	—
323	C₄⋊C₄	—	113	4	no	—
324	C₄⋊C₄	—	113	4	no	—
325	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	complemented
326	C₂²⋊C₄	—	113	2	no	—
327	C₂²⋊C₄	—	113	2	no	—
328	C₂²⋊C₄	—	113	2	no	—
329	C₂²⋊C₄	—	113	2	no	—
330	C₂²⋊C₄	—	113	4	no	—
331	C₂²⋊C₄	—	113	4	no	—
332	C₂²⋊C₄	—	113	4	no	—
333	C₂²⋊C₄	—	113	4	no	—
334	C₂²⋊C₄	—	113	4	no	—
335	C₂²⋊C₄	—	113	4	no	—
336	C₂²⋊C₄	—	113	4	no	—
337	C₂²⋊C₄	—	113	4	no	—
338	C₂²⋊C₄	—	113	4	no	—
339	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
340	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
341	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
342	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	complemented
344	C₄²	—	113	4	no	—
345	C₄²	C₂²×D₁₁₃	1	4	yes	complemented
346	C₂³	—	2	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	113	2	no	—
350	C₂³	—	113	2	no	—
351	C₂³	—	113	2	no	—
352	C₂³	—	452	2	no	—
353	C₂³	—	452	2	no	—
354	C₂³	—	452	2	no	—
355	C₂³	—	452	2	no	—
356	C₂³	—	452	16	no	—
357	C₂³	—	226	4	no	—
358	C₂³	—	226	4	no	—
359	C₂³	—	226	4	no	—
360	C₂³	—	226	2	no	—
361	C₂³	—	226	2	no	—
362	C₂³	—	226	4	no	—
363	C₂³	—	226	4	no	—
364	C₂³	—	226	2	no	—
365	C₂³	#14268647	1	4	yes	complemented
366	C₂³	C₂³×D₁₁₃	1	2	yes	—
367	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
368	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
369	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
370	Q₈	—	452	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	452	4	no	—
374	D₄	—	452	4	no	—
375	D₄	—	452	4	no	—
376	D₄	—	226	8	no	—
377	D₄	—	226	8	no	—
378	D₄	—	226	4	no	—
379	D₄	—	226	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	113	2	no	—
385	C₂×C₄	—	113	4	no	—
386	C₂×C₄	—	113	4	no	—
387	C₂×C₄	—	452	4	no	—
388	C₂×C₄	—	452	4	no	—
389	C₂×C₄	—	452	2	no	—
390	C₂×C₄	—	452	2	no	—
391	C₂×C₄	—	226	8	no	—
392	C₂×C₄	—	226	2	no	—
393	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
394	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
395	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	113	4	no	—
404	C₂²	—	904	2	no	—
405	C₂²	—	452	4	no	—
406	C₂²	—	452	8	no	—
407	C₂²	—	452	8	no	—
408	C₂²	—	226	8	no	—
409	C₂²	—	226	2	no	—
410	C₂²	—	226	2	no	—
411	C₂²	—	226	4	no	—
412	C₂²	—	226	2	no	—
413	C₂²	—	226	2	no	—
414	C₂²	—	226	2	no	—
415	C₂²	—	226	2	no	—
416	C₂²	C₂×#14268647	1	2	yes	—
417	C₂²	C₂×#14268647	1	2	yes	—
418	C₂²	C₂×#14268647	1	2	yes	—
419	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	4	no	—
422	C₄	—	2	4	no	—
423	C₄	—	226	2	no	—
424	C₄	—	226	4	no	—
425	C₄	—	226	4	no	—
426	C₂	—	2	2	no	—
427	C₂	—	2	2	no	—
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	452	2	no	—
431	C₂	—	452	2	no	—
432	C₂	—	226	4	no	—
433	C₂	C₂²×#14268647	1	1	yes	characteristic
434	C₂	H(5,𝔽₂)×D₁₁₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#518×C₁₁₃	C₂
hypercenter	#518	D₁₁₃
hypocenter	C₁₁₃	#3490
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #20299277	C₂	semidirect
2. #20299272	C₂	semidirect
3. #20299244	C₂	semidirect
4. #20299238	C₂	semidirect
5. #20299224	C₂	semidirect
6. #20299181	C₂	semidirect
7. #20299157	C₂	semidirect
8. #20299107	C₂	semidirect
9. C₂×#16813592	C₂	semidirect
10. C₂×#16813590	C₂	semidirect
11. #20299071	C₂	semidirect
12. C₂×C₂²⋊C₄×D₁₁₃	C₂	semidirect
13. #518×C₁₁₃	C₂	semidirect
15. C₂×#14268647	C₂²	semidirect
16. C₂²×D₄₅₂	C₂²	semidirect
18. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
19. C₂²×C₄×D₁₁₃	C₂²	semidirect
20. #16813617	C₂²	semidirect
21. #16813616	C₂²	semidirect
22. #16813610	C₂²	semidirect
23. #16813608	C₂²	semidirect
24. #16813607	C₂²	semidirect
25. #16813607	C₂²	semidirect
26. #16813605	C₂²	semidirect
27. #16813605	C₂²	semidirect
28. #16813604	C₂²	semidirect
29. #16813603	C₂²	semidirect
30. #16813601	C₂²	semidirect
31. #16813600	C₂²	semidirect
32. #16813599	C₂²	semidirect
33. #16813599	C₂²	semidirect
34. #16813596	C₂²	semidirect
35. #16813595	C₂²	semidirect
36. #16813595	C₂²	semidirect
37. #16813594	C₂²	semidirect
39. #16813592	C₂²	semidirect
40. #16813592	C₂²	semidirect
41. #16813591	C₂²	semidirect
43. #16813590	C₂²	semidirect
44. #16813590	C₂²	semidirect
45. #16813590	C₂²	semidirect
46. C₄×D₄₅₂	C₂²	semidirect
47. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
48. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
49. #16813582	C₂²	semidirect
50. #16813579	C₂²	semidirect
51. #16813578	C₂²	semidirect
54. C₂×#14268624	C₂²	semidirect
55. C₂×#14268624	C₂²	semidirect
56. C₂×#14268624	C₂²	semidirect
57. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
58. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
59. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
61. C₄×D₄×C₁₁₃	C₂²	semidirect
62. C₄×D₄×C₁₁₃	C₂²	semidirect
63. #117×C₁₁₃	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
75. C₂×Dic₂₂₆	C₂³	semidirect
85. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
92. C₂×C₄×D₁₁₃	C₂³	semidirect
93. C₄⋊Dic₁₁₃	C₂³	semidirect
94. #14268626	C₂³	semidirect
95. #14268626	C₂³	semidirect
96. #14268626	C₂³	semidirect
97. #14268626	C₂³	semidirect
102. C₂²⋊Dic₁₁₃	C₂³	semidirect
109. #14268624	C₂³	semidirect
110. #14268624	C₂³	semidirect
111. C₄×Dic₁₁₃	C₂³	semidirect
120. C₂²×C₄×C₁₁₃	C₂³	semidirect
121. C₄⋊C₄×C₁₁₃	C₂³	semidirect
126. C₂²⋊C₄×C₁₁₃	C₂³	semidirect
127. C₄²×C₁₁₃	C₂³	semidirect
131. C₂³×C₁₁₃	#41	semidirect
218. C₁₁₃	#3490	semidirect
230. #518	D₁₁₃	semidirect
269. C₄×D₄	C₂×D₁₁₃	semidirect
270. C₄×D₄	C₂×D₁₁₃	semidirect
273. #117	C₂×D₁₁₃	semidirect
284. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
319. C₂²×C₄	C₂²×D₁₁₃	semidirect
325. C₄⋊C₄	C₂²×D₁₁₃	semidirect
343. C₂²⋊C₄	C₂²×D₁₁₃	semidirect
345. C₄²	C₂²×D₁₁₃	semidirect
365. C₂³	#14268647	semidirect

Maximal subgroups

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

subgroup	index
#20299277	2
#20299272	2
#20299244	2
#20299238	2
#20299224	2
#20299181	2
#20299157	2
#20299107	2
C₂×#16813592	2
C₂×#16813590	2
#20299071	2
C₂×C₂²⋊C₄×D₁₁₃	2
#518×C₁₁₃	2
#3490	113