Subgroups — #28403985

Order 14464.

1160 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299223	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299191	C₂	1	2	yes	maximal, complemented
3	#20299190	C₂	1	2	yes	maximal, complemented
4	#20299189	C₂	1	2	yes	maximal, complemented
5	#20299186	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299182	C₂	1	2	yes	maximal, complemented
7	#20299180	C₂	1	2	yes	maximal, complemented
8	#20299158	C₂	1	2	yes	maximal, complemented
9	#20299156	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299134	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299131	C₂	1	2	yes	maximal, complemented
12	#20299129	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299127	C₂	1	2	yes	maximal, complemented
14	#20299108	C₂	1	2	yes	maximal, complemented
15	#20299106	C₂	1	2	yes	maximal, complemented
16	#20299104	C₂	1	2	yes	maximal, complemented
17	C₂×#16813582	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₁₁₃	C₂	1	2	yes	maximal, complemented
19	#538×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268646	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
23	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
26	#16813617	C₂²	1	2	yes	complemented
27	#16813616	C₂²	1	2	yes	complemented
28	#16813615	C₂²	1	2	yes	complemented
29	#16813615	C₂²	1	2	yes	complemented
30	#16813615	C₂²	1	2	yes	complemented
31	#16813614	C₂²	1	2	yes	complemented
32	#16813613	C₂²	1	1	yes	characteristic, complemented
33	#16813613	C₂²	1	1	yes	characteristic, complemented
34	#16813612	C₂²	1	2	yes	complemented
35	#16813611	C₂²	1	1	yes	characteristic, complemented
36	#16813609	C₂²	1	1	yes	characteristic, complemented
37	#16813608	C₂²	1	2	yes	complemented
38	#16813607	C₂²	1	2	yes	complemented
39	#16813606	C₂²	1	2	yes	complemented
40	#16813606	C₂²	1	2	yes	complemented
41	#16813605	C₂²	1	2	yes	complemented
42	#16813604	C₂²	1	2	yes	complemented
43	#16813604	C₂²	1	2	yes	complemented
44	#16813604	C₂²	1	2	yes	complemented
45	#16813604	C₂²	1	2	yes	complemented
46	#16813604	C₂²	1	2	yes	complemented
47	#16813603	C₂²	1	2	yes	complemented
48	#16813603	C₂²	1	2	yes	complemented
49	#16813602	C₂²	1	2	yes	complemented
50	#16813601	C₂²	1	2	yes	complemented
51	#16813601	C₂²	1	1	yes	characteristic, complemented
52	#16813600	C₂²	1	2	yes	complemented
53	#16813600	C₂²	1	2	yes	complemented
54	#16813600	C₂²	1	2	yes	complemented
55	#16813599	C₂²	1	2	yes	complemented
56	#16813599	C₂²	1	2	yes	complemented
57	#16813598	C₂²	1	2	yes	complemented
58	#16813596	C₂²	1	1	yes	characteristic
59	#16813595	C₂²	1	2	yes	—
60	#16813595	C₂²	1	2	yes	—
61	#16813595	C₂²	1	2	yes	complemented
62	#16813594	C₂²	1	2	yes	—
63	#16813594	C₂²	1	2	yes	complemented
64	#16813593	C₂²	1	2	yes	—
65	#16813593	C₂²	1	2	yes	—
66	#16813592	C₂²	1	2	yes	complemented
67	#16813591	C₂²	1	2	yes	complemented
68	#16813590	C₂²	1	2	yes	complemented
69	#16813590	C₂²	1	2	yes	complemented
70	#16813590	C₂²	1	2	yes	complemented
71	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
72	#16813587	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₄₅₂	C₂²	1	2	yes	complemented
74	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
75	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
76	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
77	#16813584	C₂²	1	2	yes	complemented
78	#16813584	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
81	#16813582	C₂²	1	2	yes	complemented
82	#16813582	C₂²	1	2	yes	complemented
83	#16813582	C₂²	1	2	yes	complemented
84	#16813582	C₂²	1	2	yes	complemented
85	#16813582	C₂²	1	2	yes	complemented
86	#16813582	C₂²	1	2	yes	complemented
87	#16813582	C₂²	1	2	yes	complemented
88	#16813580	C₂²	1	2	yes	complemented
89	#16813578	C₂²	1	2	yes	complemented
90	#16813578	C₂²	1	2	yes	complemented
91	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
93	C₂×#14268624	C₂²	1	1	yes	characteristic
94	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
98	#126×C₁₁₃	C₂²	1	2	yes	complemented
99	#124×C₁₁₃	C₂²	1	2	yes	complemented
100	#123×C₁₁₃	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
102	#121×C₁₁₃	C₂²	1	1	yes	characteristic
103	#121×C₁₁₃	C₂²	1	2	yes	complemented
104	#120×C₁₁₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₁₃	C₂³	1	2	yes	—
108	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
109	#14268646	—	4	4	no	—
110	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
111	C₂×Dic₂₂₆	C₂³	1	2	yes	—
112	C₂×D₄₅₂	C₂³	1	2	yes	—
113	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
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	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
122	D₄×D₁₁₃	—	2	8	no	—
123	C₂²×Dic₁₁₃	—	4	2	no	—
124	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
126	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
127	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
128	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
129	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
130	C₂×C₄×D₁₁₃	—	4	2	no	—
131	C₂×C₄×D₁₁₃	—	4	4	no	—
132	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
133	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
134	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
138	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
139	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
140	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
141	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
142	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
144	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
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	#14268626	C₂³	1	2	yes	—
150	#14268626	C₂³	1	2	yes	—
151	#14268626	C₂³	1	2	yes	—
152	#14268626	C₂³	1	2	yes	—
153	#14268626	C₂³	1	2	yes	—
154	#14268626	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₁₃	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	#14268624	C₂³	1	2	yes	—
167	#14268624	C₂³	1	2	yes	—
168	#14268624	C₂³	1	2	yes	—
169	#14268624	C₂³	1	2	yes	—
170	#14268624	C₂³	1	2	yes	—
171	#14268624	C₂³	1	2	yes	—
172	C₄×Dic₁₁₃	C₂³	1	2	yes	—
173	C₄×Dic₁₁₃	C₂³	1	2	yes	—
174	C₄×Dic₁₁₃	C₂³	1	2	yes	—
175	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
176	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
177	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
178	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
179	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
180	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
182	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
184	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
185	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
192	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
199	C₄²×C₁₁₃	C₂³	1	2	yes	—
200	C₂³×C₁₁₃	—	2	2	no	—
201	C₂³×C₁₁₃	—	4	1	no	—
202	C₂³×C₁₁₃	—	4	1	no	—
203	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
204	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
205	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×D₁₁₃	—	2	4	no	—
207	C₂²×D₁₁₃	—	4	1	no	—
208	C₂²×D₁₁₃	—	4	2	no	—
209	C₂²×D₁₁₃	—	4	1	no	—
210	C₂²×D₁₁₃	—	4	2	no	—
211	C₂²×D₁₁₃	#41	1	4	yes	complemented
212	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
213	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
214	Q₈×C₁₁₃	—	4	1	no	—
215	D₄×C₁₁₃	—	2	4	no	—
216	D₄×C₁₁₃	—	4	1	no	—
217	D₄×C₁₁₃	—	4	2	no	—
218	D₄×C₁₁₃	—	4	2	no	—
219	C₂×C₄×C₁₁₃	—	4	1	no	—
220	C₂×C₄×C₁₁₃	—	4	2	no	—
221	C₂×C₄×C₁₁₃	—	4	1	no	—
222	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
223	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
224	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
225	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
228	C₂²⋊D₁₁₃	—	2	4	no	—
229	C₂²⋊D₁₁₃	—	2	4	no	—
230	C₂²⋊D₁₁₃	—	2	4	no	—
231	C₂²⋊D₁₁₃	—	2	4	no	—
232	C₂²⋊D₁₁₃	—	4	2	no	—
233	C₂²⋊D₁₁₃	—	4	2	no	—
234	C₂²⋊D₁₁₃	—	4	2	no	—
235	C₂×Dic₁₁₃	—	2	2	no	—
236	C₂×Dic₁₁₃	—	2	2	no	—
237	C₂×Dic₁₁₃	—	2	4	no	—
238	C₂×Dic₁₁₃	—	2	4	no	—
239	C₂×Dic₁₁₃	—	4	1	no	—
240	C₂×Dic₁₁₃	—	4	2	no	—
241	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
242	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
246	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
248	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
249	D₄₅₂	—	2	4	no	—
250	D₄₅₂	—	4	1	no	—
251	C₄×D₁₁₃	—	2	4	no	—
252	C₄×D₁₁₃	—	2	4	no	—
253	C₄×D₁₁₃	—	2	4	no	—
254	C₄×D₁₁₃	—	4	2	no	—
255	C₄×D₁₁₃	—	4	2	no	—
256	C₄×D₁₁₃	—	4	2	no	—
257	C₄×D₁₁₃	—	4	2	no	—
258	Dic₂₂₆	—	4	1	no	—
259	Dic₂₂₆	—	4	2	no	—
260	C₂²×C₁₁₃	—	2	1	no	—
261	C₂²×C₁₁₃	—	2	1	no	—
262	C₂²×C₁₁₃	—	2	2	no	—
263	C₂²×C₁₁₃	—	2	2	no	—
264	C₂²×C₁₁₃	—	2	2	no	—
265	C₂²×C₁₁₃	—	2	2	no	—
266	C₂²×C₁₁₃	—	2	2	no	—
267	C₂²×C₁₁₃	—	2	2	no	—
268	C₂²×C₁₁₃	—	4	4	no	—
269	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
270	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
271	C₂×D₁₁₃	—	2	2	no	—
272	C₂×D₁₁₃	—	2	2	no	—
273	C₂×D₁₁₃	—	2	2	no	—
274	C₂×D₁₁₃	—	2	2	no	—
275	C₂×D₁₁₃	—	2	2	no	—
276	C₂×D₁₁₃	—	4	4	no	—
277	C₂×D₁₁₃	—	4	8	no	—
278	C₂×D₁₁₃	C₂×#41	1	4	yes	—
279	C₄×C₁₁₃	—	2	2	no	—
280	C₄×C₁₁₃	—	2	2	no	—
281	C₄×C₁₁₃	—	2	2	no	—
282	C₄×C₁₁₃	—	2	1	no	—
283	C₄×C₁₁₃	—	2	2	no	—
284	C₄×C₁₁₃	—	2	1	no	—
285	Dic₁₁₃	—	2	2	no	—
286	Dic₁₁₃	—	2	1	no	—
287	Dic₁₁₃	—	2	1	no	—
288	Dic₁₁₃	—	2	2	no	—
289	Dic₁₁₃	—	2	2	no	—
290	Dic₁₁₃	—	2	1	no	—
291	Dic₁₁₃	—	2	2	no	—
292	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
293	C₂×C₁₁₃	—	2	2	no	—
294	C₂×C₁₁₃	—	4	2	no	—
295	C₂×C₁₁₃	—	4	2	no	—
296	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
297	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₁₁₃	#585	1	1	yes	characteristic
299	D₁₁₃	—	2	4	no	—
300	D₁₁₃	—	4	2	no	—
301	#3459	—	113	1	no	maximal, Sylow
302	C₁₁₃	#3459	1	1	yes	characteristic, complemented, Sylow
303	#543	—	113	1	no	—
304	#539	—	113	2	no	—
305	#539	—	113	2	no	—
306	#539	—	113	2	no	—
307	#538	—	113	2	no	—
308	#538	—	113	2	no	—
309	#538	—	113	1	no	—
310	#538	D₁₁₃	1	1	yes	characteristic, complemented
311	#534	—	113	1	no	—
312	#534	—	113	2	no	—
313	#529	—	113	2	no	—
314	#529	—	113	2	no	—
315	#529	—	113	1	no	—
316	#529	—	113	1	no	—
317	#525	—	113	2	no	—
318	#525	—	113	2	no	—
319	#525	—	113	2	no	—
320	C₂×C₄×D₄	—	113	2	no	—
321	C₂×C₄×D₄	—	113	1	no	—
322	C₂×#41	—	113	2	no	—
323	C₂²×D₄	—	113	1	no	—
324	C₂²×D₄	—	113	2	no	—
325	C₂³×C₄	—	113	1	no	—
326	C₂³×C₄	—	113	1	no	—
327	C₂³×C₄	—	113	2	no	—
328	#126	—	113	2	no	—
329	#126	—	113	2	no	—
330	#126	—	113	2	no	—
331	#126	—	113	2	no	—
332	#126	—	113	2	no	—
333	#126	C₂×D₁₁₃	1	2	yes	complemented
334	#125	—	113	2	no	—
335	#125	—	113	1	no	—
336	#125	—	113	1	no	—
337	#125	—	113	2	no	—
338	#124	—	113	1	no	—
339	#124	—	113	1	no	—
340	#124	—	113	2	no	—
341	#124	C₂×D₁₁₃	1	2	yes	complemented
342	#123	—	113	2	no	—
343	#123	—	113	2	no	—
344	#123	—	113	2	no	—
345	#123	—	113	2	no	—
346	#123	—	113	2	no	—
347	#123	—	113	2	no	—
348	#123	—	113	2	no	—
349	#123	—	113	2	no	—
350	#123	—	113	2	no	—
351	#123	—	113	2	no	—
352	#123	—	113	2	no	—
353	#123	C₂×D₁₁₃	1	2	yes	complemented
354	C₂²⋊Q₈	—	113	2	no	—
355	C₂²⋊Q₈	—	113	2	no	—
356	C₂²⋊Q₈	—	113	1	no	—
357	C₂²⋊Q₈	—	113	2	no	—
358	C₂²⋊Q₈	—	113	2	no	—
359	C₂²⋊Q₈	—	113	2	no	—
360	C₂²⋊Q₈	—	113	2	no	—
361	C₂²⋊Q₈	—	113	2	no	—
362	C₂²⋊Q₈	—	113	2	no	—
363	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
364	#121	—	113	2	no	—
365	#121	—	113	2	no	—
366	#121	—	113	2	no	—
367	#121	—	113	2	no	—
368	#121	—	113	1	no	—
369	#121	—	113	2	no	—
370	#121	—	113	2	no	—
371	#121	—	113	2	no	—
372	#121	C₂×D₁₁₃	1	1	yes	characteristic
373	#121	C₂×D₁₁₃	1	2	yes	complemented
374	#120	—	113	2	no	—
375	#120	—	113	2	no	—
376	#120	—	113	2	no	—
377	#120	—	113	2	no	—
378	#120	—	113	2	no	—
379	#120	C₂×D₁₁₃	1	2	yes	complemented
380	C₄×Q₈	—	113	1	no	—
381	C₄×Q₈	—	113	1	no	—
382	C₄×D₄	—	113	2	no	—
383	C₄×D₄	—	113	1	no	—
384	C₄×D₄	—	113	2	no	—
385	C₄×D₄	—	113	2	no	—
386	C₄×D₄	—	113	2	no	—
387	C₄×D₄	—	113	2	no	—
388	C₄×D₄	—	113	1	no	—
389	C₄×D₄	—	113	2	no	—
390	C₄×D₄	—	113	2	no	—
391	C₄×D₄	—	113	2	no	—
392	C₄×D₄	—	113	2	no	—
393	C₄×D₄	—	113	2	no	—
394	C₄×D₄	—	113	2	no	—
395	C₄×D₄	—	113	2	no	—
396	C₄×D₄	—	113	2	no	—
397	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
398	#117	—	113	2	no	—
399	#117	—	113	2	no	—
400	#117	—	113	2	no	—
401	C₂×C₄⋊C₄	—	113	1	no	—
402	C₂×C₄⋊C₄	—	113	2	no	—
403	C₂×C₂²⋊C₄	—	113	1	no	—
404	C₂×C₂²⋊C₄	—	113	2	no	—
405	C₂×C₂²⋊C₄	—	113	2	no	—
406	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
407	C₂×C₄²	—	113	1	no	—
408	C₂×C₄²	—	113	2	no	—
409	C₂⁴	—	113	1	no	—
410	C₂⁴	—	113	2	no	—
411	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
412	#41	—	452	4	no	—
413	C₂×Q₈	—	113	1	no	—
414	C₂×Q₈	—	113	2	no	—
415	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
416	C₂×D₄	—	113	2	no	—
417	C₂×D₄	—	113	2	no	—
418	C₂×D₄	—	113	2	no	—
419	C₂×D₄	—	113	2	no	—
420	C₂×D₄	—	113	2	no	—
421	C₂×D₄	—	113	2	no	—
422	C₂×D₄	—	113	2	no	—
423	C₂×D₄	—	113	1	no	—
424	C₂×D₄	—	113	2	no	—
425	C₂×D₄	—	226	8	no	—
426	C₂×D₄	—	226	4	no	—
427	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
428	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
430	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
431	C₂²×C₄	—	113	1	no	—
432	C₂²×C₄	—	113	2	no	—
433	C₂²×C₄	—	113	1	no	—
434	C₂²×C₄	—	113	1	no	—
435	C₂²×C₄	—	113	2	no	—
436	C₂²×C₄	—	113	2	no	—
437	C₂²×C₄	—	113	2	no	—
438	C₂²×C₄	—	113	2	no	—
439	C₂²×C₄	—	113	2	no	—
440	C₂²×C₄	—	113	2	no	—
441	C₂²×C₄	—	113	2	no	—
442	C₂²×C₄	—	113	2	no	—
443	C₂²×C₄	—	113	2	no	—
444	C₂²×C₄	—	452	2	no	—
445	C₂²×C₄	—	452	4	no	—
446	C₂²×C₄	—	452	2	no	—
447	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
450	C₄⋊C₄	—	113	2	no	—
451	C₄⋊C₄	—	113	2	no	—
452	C₄⋊C₄	—	113	2	no	—
453	C₄⋊C₄	—	113	2	no	—
454	C₄⋊C₄	—	113	2	no	—
455	C₄⋊C₄	—	113	2	no	—
456	C₄⋊C₄	—	113	2	no	—
457	C₄⋊C₄	—	113	2	no	—
458	C₄⋊C₄	—	113	2	no	—
459	C₄⋊C₄	—	113	2	no	—
460	C₄⋊C₄	—	113	2	no	—
461	C₄⋊C₄	—	113	1	no	—
462	C₄⋊C₄	—	113	2	no	—
463	C₄⋊C₄	—	113	2	no	—
464	C₄⋊C₄	—	113	1	no	—
465	C₄⋊C₄	—	113	2	no	—
466	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
467	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
468	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
470	C₂²⋊C₄	—	113	2	no	—
471	C₂²⋊C₄	—	113	2	no	—
472	C₂²⋊C₄	—	113	2	no	—
473	C₂²⋊C₄	—	113	2	no	—
474	C₂²⋊C₄	—	113	2	no	—
475	C₂²⋊C₄	—	113	2	no	—
476	C₂²⋊C₄	—	113	2	no	—
477	C₂²⋊C₄	—	113	2	no	—
478	C₂²⋊C₄	—	113	2	no	—
479	C₂²⋊C₄	—	113	2	no	—
480	C₂²⋊C₄	—	113	2	no	—
481	C₂²⋊C₄	—	113	2	no	—
482	C₂²⋊C₄	—	113	2	no	—
483	C₂²⋊C₄	—	113	2	no	—
484	C₂²⋊C₄	—	113	2	no	—
485	C₂²⋊C₄	—	113	2	no	—
486	C₂²⋊C₄	—	113	2	no	—
487	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
494	C₄²	—	113	2	no	—
495	C₄²	—	113	1	no	—
496	C₄²	—	113	1	no	—
497	C₄²	—	113	2	no	—
498	C₄²	—	113	2	no	—
499	C₄²	—	113	1	no	—
500	C₄²	—	113	1	no	—
501	C₄²	C₂²×D₁₁₃	1	2	yes	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	113	4	no	—
506	C₂³	—	113	2	no	—
507	C₂³	—	113	2	no	—
508	C₂³	—	452	1	no	—
509	C₂³	—	452	2	no	—
510	C₂³	—	452	1	no	—
511	C₂³	—	452	2	no	—
512	C₂³	—	226	4	no	—
513	C₂³	C₂³×D₁₁₃	1	2	yes	—
514	C₂³	C₂³×D₁₁₃	1	2	yes	—
515	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
516	Q₈	—	4	1	no	—
517	Q₈	—	452	2	no	—
518	Q₈	—	452	1	no	—
519	D₄	—	2	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	2	no	—
523	D₄	—	452	1	no	—
524	D₄	—	452	2	no	—
525	D₄	—	452	2	no	—
526	D₄	—	452	2	no	—
527	D₄	—	226	4	no	—
528	D₄	—	226	4	no	—
529	D₄	—	226	4	no	—
530	D₄	—	226	4	no	—
531	D₄	—	226	4	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	113	1	no	—
536	C₂×C₄	—	113	2	no	—
537	C₂×C₄	—	113	1	no	—
538	C₂×C₄	—	113	2	no	—
539	C₂×C₄	—	113	1	no	—
540	C₂×C₄	—	113	1	no	—
541	C₂×C₄	—	113	2	no	—
542	C₂×C₄	—	113	2	no	—
543	C₂×C₄	—	452	2	no	—
544	C₂×C₄	—	452	2	no	—
545	C₂×C₄	—	452	2	no	—
546	C₂×C₄	—	452	2	no	—
547	C₂×C₄	—	452	2	no	—
548	C₂×C₄	—	452	1	no	—
549	C₂×C₄	—	226	4	no	—
550	C₂×C₄	—	226	4	no	—
551	C₂×C₄	—	226	4	no	—
552	C₂×C₄	—	226	2	no	—
553	C₂×C₄	—	226	4	no	—
554	C₂×C₄	—	226	4	no	—
555	C₂×C₄	—	226	2	no	—
556	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
559	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
560	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
561	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	113	4	no	—
572	C₂²	—	452	4	no	—
573	C₂²	—	452	8	no	—
574	C₂²	—	226	2	no	—
575	C₂²	—	226	2	no	—
576	C₂²	—	226	2	no	—
577	C₂²	—	226	2	no	—
578	C₂²	—	226	2	no	—
579	C₂²	#41×D₁₁₃	1	2	yes	—
580	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	113	2	no	—
588	C₄	—	226	2	no	—
589	C₄	—	226	1	no	—
590	C₄	—	226	1	no	—
591	C₄	—	226	1	no	—
592	C₄	—	226	2	no	—
593	C₄	—	226	2	no	—
594	C₄	—	226	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	452	2	no	—
599	C₂	—	226	4	no	—
600	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
601	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
602	C₂	#20299433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#538×C₁₁₃	C₂
hypercenter	#538	D₁₁₃
hypocenter	C₁₁₃	#3459
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #20299223	C₂	semidirect
2. #20299191	C₂	semidirect
3. #20299190	C₂	semidirect
4. #20299189	C₂	semidirect
5. #20299186	C₂	semidirect
6. #20299182	C₂	semidirect
7. #20299180	C₂	semidirect
8. #20299158	C₂	semidirect
9. #20299156	C₂	semidirect
10. #20299134	C₂	semidirect
11. #20299131	C₂	semidirect
12. #20299129	C₂	semidirect
13. #20299127	C₂	semidirect
14. #20299108	C₂	semidirect
15. #20299106	C₂	semidirect
16. #20299104	C₂	semidirect
17. C₂×#16813582	C₂	semidirect
18. C₄×D₄×D₁₁₃	C₂	semidirect
19. #538×C₁₁₃	C₂	semidirect
20. C₂×#14268646	C₂²	semidirect
23. C₂³×Dic₁₁₃	C₂²	semidirect
25. C₂²×C₄×D₁₁₃	C₂²	semidirect
26. #16813617	C₂²	semidirect
27. #16813616	C₂²	semidirect
28. #16813615	C₂²	semidirect
29. #16813615	C₂²	semidirect
30. #16813615	C₂²	semidirect
31. #16813614	C₂²	semidirect
32. #16813613	C₂²	semidirect
33. #16813613	C₂²	semidirect
34. #16813612	C₂²	semidirect
35. #16813611	C₂²	semidirect
36. #16813609	C₂²	semidirect
37. #16813608	C₂²	semidirect
38. #16813607	C₂²	semidirect
39. #16813606	C₂²	semidirect
40. #16813606	C₂²	semidirect
41. #16813605	C₂²	semidirect
42. #16813604	C₂²	semidirect
43. #16813604	C₂²	semidirect
44. #16813604	C₂²	semidirect
45. #16813604	C₂²	semidirect
46. #16813604	C₂²	semidirect
47. #16813603	C₂²	semidirect
48. #16813603	C₂²	semidirect
49. #16813602	C₂²	semidirect
50. #16813601	C₂²	semidirect
51. #16813601	C₂²	semidirect
52. #16813600	C₂²	semidirect
53. #16813600	C₂²	semidirect
54. #16813600	C₂²	semidirect
55. #16813599	C₂²	semidirect
56. #16813599	C₂²	semidirect
57. #16813598	C₂²	semidirect
61. #16813595	C₂²	semidirect
63. #16813594	C₂²	semidirect
66. #16813592	C₂²	semidirect
67. #16813591	C₂²	semidirect
68. #16813590	C₂²	semidirect
69. #16813590	C₂²	semidirect
70. #16813590	C₂²	semidirect
71. Q₈×Dic₁₁₃	C₂²	semidirect
72. #16813587	C₂²	semidirect
73. C₄×D₄₅₂	C₂²	semidirect
74. D₄×Dic₁₁₃	C₂²	semidirect
75. D₄×Dic₁₁₃	C₂²	semidirect
76. D₄×Dic₁₁₃	C₂²	semidirect
77. #16813584	C₂²	semidirect
78. #16813584	C₂²	semidirect
79. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
80. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
81. #16813582	C₂²	semidirect
82. #16813582	C₂²	semidirect
83. #16813582	C₂²	semidirect
84. #16813582	C₂²	semidirect
85. #16813582	C₂²	semidirect
86. #16813582	C₂²	semidirect
87. #16813582	C₂²	semidirect
88. #16813580	C₂²	semidirect
89. #16813578	C₂²	semidirect
90. #16813578	C₂²	semidirect
91. C₂×#14268626	C₂²	semidirect
92. C₄⋊C₄×D₁₁₃	C₂²	semidirect
95. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
96. C₂×C₄×Dic₁₁₃	C₂²	semidirect
97. C₄²×D₁₁₃	C₂²	semidirect
98. #126×C₁₁₃	C₂²	semidirect
99. #124×C₁₁₃	C₂²	semidirect
100. #123×C₁₁₃	C₂²	semidirect
101. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
103. #121×C₁₁₃	C₂²	semidirect
104. #120×C₁₁₃	C₂²	semidirect
105. C₄×D₄×C₁₁₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
211. C₂²×D₁₁₃	#41	semidirect
302. C₁₁₃	#3459	semidirect
310. #538	D₁₁₃	semidirect
333. #126	C₂×D₁₁₃	semidirect
341. #124	C₂×D₁₁₃	semidirect
353. #123	C₂×D₁₁₃	semidirect
363. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
373. #121	C₂×D₁₁₃	semidirect
379. #120	C₂×D₁₁₃	semidirect
397. C₄×D₄	C₂×D₁₁₃	semidirect
406. C₂×C₂²⋊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
#20299223	2
#20299191	2
#20299190	2
#20299189	2
#20299186	2
#20299182	2
#20299180	2
#20299158	2
#20299156	2
#20299134	2
#20299131	2
#20299129	2
#20299127	2
#20299108	2
#20299106	2
#20299104	2
C₂×#16813582	2
C₄×D₄×D₁₁₃	2
#538×C₁₁₃	2
#3459	113