Subgroups — #28403982

Order 14464.

1160 conjugacy classes of subgroups.

The subgroup lattice has 616 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	#20299196	C₂	1	2	yes	maximal, complemented
3	#20299195	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299194	C₂	1	2	yes	maximal, complemented
5	#20299187	C₂	1	2	yes	maximal, complemented
6	#20299184	C₂	1	2	yes	maximal, complemented
7	#20299181	C₂	1	2	yes	maximal, complemented
8	#20299159	C₂	1	2	yes	maximal, complemented
9	#20299156	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299133	C₂	1	2	yes	maximal, complemented
11	#20299131	C₂	1	2	yes	maximal, complemented
12	#20299125	C₂	1	2	yes	maximal, complemented
13	#20299111	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299111	C₂	1	2	yes	maximal, complemented
15	#20299108	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299106	C₂	1	2	yes	maximal, complemented
17	C₂×#16813584	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₁₁₃	C₂	1	2	yes	maximal, complemented
19	#539×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
27	#16813617	C₂²	1	2	yes	complemented
28	#16813617	C₂²	1	2	yes	complemented
29	#16813617	C₂²	1	2	yes	complemented
30	#16813616	C₂²	1	2	yes	complemented
31	#16813615	C₂²	1	2	yes	complemented
32	#16813612	C₂²	1	2	yes	complemented
33	#16813612	C₂²	1	2	yes	complemented
34	#16813610	C₂²	1	2	yes	complemented
35	#16813608	C₂²	1	2	yes	complemented
36	#16813608	C₂²	1	2	yes	complemented
37	#16813607	C₂²	1	2	yes	complemented
38	#16813607	C₂²	1	2	yes	complemented
39	#16813607	C₂²	1	2	yes	complemented
40	#16813607	C₂²	1	2	yes	complemented
41	#16813607	C₂²	1	2	yes	complemented
42	#16813607	C₂²	1	2	yes	complemented
43	#16813605	C₂²	1	2	yes	complemented
44	#16813605	C₂²	1	2	yes	complemented
45	#16813604	C₂²	1	2	yes	complemented
46	#16813604	C₂²	1	2	yes	complemented
47	#16813602	C₂²	1	1	yes	characteristic, complemented
48	#16813602	C₂²	1	2	yes	complemented
49	#16813601	C₂²	1	1	yes	characteristic, complemented
50	#16813600	C₂²	1	2	yes	complemented
51	#16813600	C₂²	1	2	yes	complemented
52	#16813600	C₂²	1	2	yes	complemented
53	#16813599	C₂²	1	2	yes	complemented
54	#16813598	C₂²	1	1	yes	characteristic, complemented
55	#16813598	C₂²	1	2	yes	complemented
56	#16813597	C₂²	1	2	yes	—
57	#16813597	C₂²	1	2	yes	—
58	#16813597	C₂²	1	1	yes	characteristic, complemented
59	#16813596	C₂²	1	1	yes	characteristic
60	#16813596	C₂²	1	2	yes	complemented
61	#16813595	C₂²	1	2	yes	—
62	#16813595	C₂²	1	2	yes	—
63	#16813595	C₂²	1	2	yes	complemented
64	#16813594	C₂²	1	2	yes	—
65	#16813593	C₂²	1	1	yes	characteristic, complemented
66	#16813592	C₂²	1	2	yes	complemented
67	#16813592	C₂²	1	2	yes	complemented
68	#16813592	C₂²	1	2	yes	complemented
69	#16813592	C₂²	1	2	yes	complemented
70	#16813590	C₂²	1	2	yes	complemented
71	#16813590	C₂²	1	2	yes	complemented
72	#16813587	C₂²	1	2	yes	complemented
73	C₄×D₄₅₂	C₂²	1	2	yes	complemented
74	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
75	#16813584	C₂²	1	2	yes	complemented
76	#16813584	C₂²	1	2	yes	complemented
77	#16813584	C₂²	1	2	yes	complemented
78	#16813584	C₂²	1	2	yes	complemented
79	#16813584	C₂²	1	2	yes	complemented
80	#16813584	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₁₃	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	#16813580	C₂²	1	1	yes	characteristic, complemented
88	#16813580	C₂²	1	2	yes	complemented
89	#16813580	C₂²	1	1	yes	characteristic, complemented
90	#16813578	C₂²	1	2	yes	complemented
91	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
92	C₂×#14268624	C₂²	1	1	yes	characteristic
93	C₂×#14268624	C₂²	1	1	yes	characteristic, complemented
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	#125×C₁₁₃	C₂²	1	2	yes	complemented
100	#123×C₁₁₃	C₂²	1	2	yes	complemented
101	#123×C₁₁₃	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
104	#121×C₁₁₃	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₁₃	C₂³	1	2	yes	—
108	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
109	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
110	#14268648	—	4	2	no	—
111	#14268646	—	4	2	no	—
112	C₂×Dic₂₂₆	C₂³	1	2	yes	—
113	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
114	C₂×D₄₅₂	—	2	4	no	—
115	C₂×D₄₅₂	C₂³	1	2	yes	—
116	C₂×D₄₅₂	C₂³	1	2	yes	—
117	C₂×D₄₅₂	C₂³	1	2	yes	—
118	C₂×D₄₅₂	C₂³	1	2	yes	—
119	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
120	C₂×D₄₅₂	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
126	D₄×D₁₁₃	—	2	8	no	—
127	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
128	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
129	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₁₁₃	—	4	2	no	—
131	C₂×C₄×D₁₁₃	—	4	4	no	—
132	C₂×C₄×D₁₁₃	—	4	2	no	—
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	1	yes	characteristic
137	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
145	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₁₃	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	#14268626	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	#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	#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	#14268624	C₂³	1	2	yes	—
173	#14268624	C₂³	1	2	yes	—
174	#14268624	C₂³	1	2	yes	—
175	C₄×Dic₁₁₃	C₂³	1	2	yes	—
176	C₄×Dic₁₁₃	C₂³	1	2	yes	—
177	C₄×Dic₁₁₃	C₂³	1	2	yes	—
178	C₄×Dic₁₁₃	C₂³	1	2	yes	—
179	C₄×Dic₁₁₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
192	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
194	C₄⋊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	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
200	C₄²×C₁₁₃	C₂³	1	2	yes	—
201	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
202	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×D₁₁₃	—	2	2	no	—
204	C₂²×D₁₁₃	—	2	4	no	—
205	C₂²×D₁₁₃	—	4	1	no	—
206	C₂²×D₁₁₃	—	4	2	no	—
207	C₂²×D₁₁₃	—	4	1	no	—
208	C₂²×D₁₁₃	—	4	1	no	—
209	C₂²×D₁₁₃	—	4	2	no	—
210	C₂²×D₁₁₃	—	4	1	no	—
211	C₂²×D₁₁₃	#41	1	4	yes	complemented
212	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
215	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
216	Q₈×C₁₁₃	—	4	1	no	—
217	D₄×C₁₁₃	—	2	4	no	—
218	D₄×C₁₁₃	—	4	1	no	—
219	C₂×C₄×C₁₁₃	—	2	2	no	—
220	C₂×C₄×C₁₁₃	—	4	1	no	—
221	C₂×C₄×C₁₁₃	—	4	1	no	—
222	C₂×C₄×C₁₁₃	—	4	2	no	—
223	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
224	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
225	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
226	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
227	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
228	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
237	C₂×Dic₁₁₃	—	4	1	no	—
238	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
239	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
240	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
241	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
243	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
244	D₄₅₂	—	2	4	no	—
245	D₄₅₂	—	2	4	no	—
246	D₄₅₂	—	2	4	no	—
247	D₄₅₂	—	4	2	no	—
248	D₄₅₂	—	4	1	no	—
249	D₄₅₂	—	4	2	no	—
250	C₄×D₁₁₃	—	2	4	no	—
251	C₄×D₁₁₃	—	2	4	no	—
252	C₄×D₁₁₃	—	2	2	no	—
253	C₄×D₁₁₃	—	2	4	no	—
254	C₄×D₁₁₃	—	2	2	no	—
255	C₄×D₁₁₃	—	4	2	no	—
256	C₄×D₁₁₃	—	4	2	no	—
257	C₄×D₁₁₃	—	4	1	no	—
258	C₄×D₁₁₃	—	4	2	no	—
259	C₄×D₁₁₃	—	4	1	no	—
260	C₄×D₁₁₃	—	4	2	no	—
261	Dic₂₂₆	—	4	2	no	—
262	Dic₂₂₆	—	4	1	no	—
263	C₂²×C₁₁₃	—	2	1	no	—
264	C₂²×C₁₁₃	—	2	1	no	—
265	C₂²×C₁₁₃	—	2	2	no	—
266	C₂²×C₁₁₃	—	2	2	no	—
267	C₂²×C₁₁₃	—	2	2	no	—
268	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
269	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
270	C₂×D₁₁₃	—	2	2	no	—
271	C₂×D₁₁₃	—	2	2	no	—
272	C₂×D₁₁₃	—	2	1	no	—
273	C₂×D₁₁₃	—	2	1	no	—
274	C₂×D₁₁₃	—	2	2	no	—
275	C₂×D₁₁₃	—	2	1	no	—
276	C₂×D₁₁₃	—	2	2	no	—
277	C₂×D₁₁₃	—	2	1	no	—
278	C₂×D₁₁₃	—	2	1	no	—
279	C₂×D₁₁₃	—	2	2	no	—
280	C₂×D₁₁₃	—	2	1	no	—
281	C₂×D₁₁₃	—	4	4	no	—
282	C₂×D₁₁₃	—	4	8	no	—
283	C₂×D₁₁₃	—	4	4	no	—
284	C₂×D₁₁₃	C₂×#41	1	4	yes	—
285	C₄×C₁₁₃	—	2	2	no	—
286	C₄×C₁₁₃	—	2	2	no	—
287	C₄×C₁₁₃	—	2	1	no	—
288	C₄×C₁₁₃	—	2	2	no	—
289	C₄×C₁₁₃	—	2	2	no	—
290	C₄×C₁₁₃	—	2	1	no	—
291	C₄×C₁₁₃	—	2	2	no	—
292	Dic₁₁₃	—	2	2	no	—
293	Dic₁₁₃	—	2	2	no	—
294	Dic₁₁₃	—	2	1	no	—
295	Dic₁₁₃	—	2	2	no	—
296	Dic₁₁₃	—	2	2	no	—
297	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₁₁₃	—	2	2	no	—
299	C₂×C₁₁₃	—	4	2	no	—
300	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
301	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₁₁₃	#585	1	1	yes	characteristic
303	D₁₁₃	—	2	4	no	—
304	D₁₁₃	—	4	1	no	—
305	D₁₁₃	—	4	1	no	—
306	D₁₁₃	—	4	2	no	—
307	#3459	—	113	1	no	maximal, Sylow
308	C₁₁₃	#3459	1	1	yes	characteristic, complemented, Sylow
309	#543	—	113	1	no	—
310	#539	—	113	2	no	—
311	#539	—	113	2	no	—
312	#539	—	113	1	no	—
313	#539	D₁₁₃	1	1	yes	characteristic, complemented
314	#538	—	113	2	no	—
315	#538	—	113	2	no	—
316	#538	—	113	2	no	—
317	#534	—	113	2	no	—
318	#534	—	113	1	no	—
319	#529	—	113	2	no	—
320	#529	—	113	2	no	—
321	#529	—	113	2	no	—
322	#525	—	113	2	no	—
323	#525	—	113	2	no	—
324	#525	—	113	1	no	—
325	#525	—	113	1	no	—
326	C₂×C₄×D₄	—	113	2	no	—
327	C₂×C₄×D₄	—	113	1	no	—
328	C₂×#41	—	113	1	no	—
329	C₂×#41	—	113	1	no	—
330	C₂²×D₄	—	113	2	no	—
331	C₂²×D₄	—	113	1	no	—
332	C₂³×C₄	—	113	1	no	—
333	C₂³×C₄	—	113	1	no	—
334	C₂³×C₄	—	113	2	no	—
335	#126	—	113	2	no	—
336	#126	—	113	2	no	—
337	#126	—	113	2	no	—
338	#126	—	113	2	no	—
339	#126	—	113	2	no	—
340	#126	C₂×D₁₁₃	1	2	yes	complemented
341	#125	—	113	2	no	—
342	#125	—	113	2	no	—
343	#125	C₂×D₁₁₃	1	2	yes	complemented
344	#124	—	113	2	no	—
345	#124	—	113	2	no	—
346	#124	—	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	—	113	2	no	—
354	#123	—	113	2	no	—
355	#123	—	113	2	no	—
356	#123	—	113	2	no	—
357	#123	C₂×D₁₁₃	1	2	yes	complemented
358	#123	C₂×D₁₁₃	1	2	yes	complemented
359	C₂²⋊Q₈	—	113	1	no	—
360	C₂²⋊Q₈	—	113	2	no	—
361	C₂²⋊Q₈	—	113	1	no	—
362	C₂²⋊Q₈	—	113	2	no	—
363	C₂²⋊Q₈	—	113	1	no	—
364	C₂²⋊Q₈	—	113	2	no	—
365	C₂²⋊Q₈	—	113	2	no	—
366	C₂²⋊Q₈	—	113	2	no	—
367	C₂²⋊Q₈	—	113	2	no	—
368	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
369	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
370	#121	—	113	1	no	—
371	#121	—	113	2	no	—
372	#121	—	113	1	no	—
373	#121	—	113	2	no	—
374	#121	—	113	2	no	—
375	#121	—	113	1	no	—
376	#121	—	113	2	no	—
377	#121	—	113	2	no	—
378	#121	—	113	2	no	—
379	#121	—	113	2	no	—
380	#121	C₂×D₁₁₃	1	1	yes	characteristic
381	#120	—	113	2	no	—
382	#120	—	113	2	no	—
383	#120	—	113	2	no	—
384	#120	—	113	2	no	—
385	#120	—	113	2	no	—
386	#120	—	113	2	no	—
387	C₄×Q₈	—	113	2	no	—
388	C₄×D₄	—	113	2	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	—	113	2	no	—
398	C₄×D₄	—	113	2	no	—
399	C₄×D₄	—	113	2	no	—
400	C₄×D₄	—	113	2	no	—
401	C₄×D₄	—	113	2	no	—
402	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
403	#117	—	113	2	no	—
404	#117	—	113	1	no	—
405	#117	—	113	1	no	—
406	#117	—	113	2	no	—
407	C₂×C₄⋊C₄	—	113	2	no	—
408	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
409	C₂×C₂²⋊C₄	—	113	1	no	—
410	C₂×C₂²⋊C₄	—	113	1	no	—
411	C₂×C₂²⋊C₄	—	113	2	no	—
412	C₂×C₂²⋊C₄	—	113	2	no	—
413	C₂×C₄²	—	113	1	no	—
414	C₂×C₄²	—	113	2	no	—
415	C₂⁴	—	113	1	no	—
416	C₂⁴	—	113	2	no	—
417	C₂⁴	—	113	1	no	—
418	#41	—	452	2	no	—
419	#41	—	452	2	no	—
420	C₂×Q₈	—	113	2	no	—
421	C₂×Q₈	—	113	1	no	—
422	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
423	C₂×D₄	—	113	2	no	—
424	C₂×D₄	—	113	2	no	—
425	C₂×D₄	—	113	2	no	—
426	C₂×D₄	—	113	2	no	—
427	C₂×D₄	—	113	2	no	—
428	C₂×D₄	—	113	2	no	—
429	C₂×D₄	—	113	1	no	—
430	C₂×D₄	—	113	2	no	—
431	C₂×D₄	—	113	2	no	—
432	C₂×D₄	—	113	2	no	—
433	C₂×D₄	—	113	2	no	—
434	C₂×D₄	—	226	4	no	—
435	C₂×D₄	—	226	8	no	—
436	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
437	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
438	C₂²×C₄	—	113	1	no	—
439	C₂²×C₄	—	113	1	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	—	113	1	no	—
445	C₂²×C₄	—	113	1	no	—
446	C₂²×C₄	—	113	2	no	—
447	C₂²×C₄	—	113	2	no	—
448	C₂²×C₄	—	113	2	no	—
449	C₂²×C₄	—	113	1	no	—
450	C₂²×C₄	—	113	1	no	—
451	C₂²×C₄	—	113	2	no	—
452	C₂²×C₄	—	452	2	no	—
453	C₂²×C₄	—	452	4	no	—
454	C₂²×C₄	—	452	2	no	—
455	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
459	C₄⋊C₄	—	113	2	no	—
460	C₄⋊C₄	—	113	2	no	—
461	C₄⋊C₄	—	113	2	no	—
462	C₄⋊C₄	—	113	2	no	—
463	C₄⋊C₄	—	113	1	no	—
464	C₄⋊C₄	—	113	2	no	—
465	C₄⋊C₄	—	113	2	no	—
466	C₄⋊C₄	—	113	1	no	—
467	C₄⋊C₄	—	113	2	no	—
468	C₄⋊C₄	—	113	2	no	—
469	C₄⋊C₄	—	113	2	no	—
470	C₄⋊C₄	—	113	2	no	—
471	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
473	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
474	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
476	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	—	113	2	no	—
488	C₂²⋊C₄	—	113	2	no	—
489	C₂²⋊C₄	—	113	2	no	—
490	C₂²⋊C₄	—	113	2	no	—
491	C₂²⋊C₄	—	113	2	no	—
492	C₂²⋊C₄	—	113	2	no	—
493	C₂²⋊C₄	—	113	2	no	—
494	C₂²⋊C₄	—	113	2	no	—
495	C₂²⋊C₄	—	113	2	no	—
496	C₂²⋊C₄	—	113	2	no	—
497	C₂²⋊C₄	—	113	2	no	—
498	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
503	C₄²	—	113	2	no	—
504	C₄²	—	113	2	no	—
505	C₄²	—	113	2	no	—
506	C₄²	—	113	2	no	—
507	C₄²	—	113	2	no	—
508	C₄²	C₂²×D₁₁₃	1	2	yes	—
509	C₂³	—	113	4	no	—
510	C₂³	—	113	2	no	—
511	C₂³	—	113	1	no	—
512	C₂³	—	113	2	no	—
513	C₂³	—	113	1	no	—
514	C₂³	—	452	1	no	—
515	C₂³	—	452	1	no	—
516	C₂³	—	452	2	no	—
517	C₂³	—	452	1	no	—
518	C₂³	—	452	1	no	—
519	C₂³	—	452	2	no	—
520	C₂³	—	226	4	no	—
521	C₂³	—	226	2	no	—
522	C₂³	C₂³×D₁₁₃	1	2	yes	—
523	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
524	Q₈	—	4	1	no	—
525	Q₈	—	452	1	no	—
526	Q₈	—	452	2	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	1	no	—
529	D₄	—	452	1	no	—
530	D₄	—	452	2	no	—
531	D₄	—	452	2	no	—
532	D₄	—	452	2	no	—
533	D₄	—	452	2	no	—
534	D₄	—	452	2	no	—
535	D₄	—	226	4	no	—
536	D₄	—	226	4	no	—
537	D₄	—	226	4	no	—
538	D₄	—	226	4	no	—
539	D₄	—	226	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	113	1	no	—
545	C₂×C₄	—	113	2	no	—
546	C₂×C₄	—	113	2	no	—
547	C₂×C₄	—	113	2	no	—
548	C₂×C₄	—	113	1	no	—
549	C₂×C₄	—	113	2	no	—
550	C₂×C₄	—	452	2	no	—
551	C₂×C₄	—	452	2	no	—
552	C₂×C₄	—	452	1	no	—
553	C₂×C₄	—	452	1	no	—
554	C₂×C₄	—	452	2	no	—
555	C₂×C₄	—	452	2	no	—
556	C₂×C₄	—	452	1	no	—
557	C₂×C₄	—	226	4	no	—
558	C₂×C₄	—	226	2	no	—
559	C₂×C₄	—	226	2	no	—
560	C₂×C₄	—	226	4	no	—
561	C₂×C₄	—	226	4	no	—
562	C₂×C₄	—	226	2	no	—
563	C₂×C₄	—	226	4	no	—
564	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
565	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
566	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
567	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
568	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	113	4	no	—
577	C₂²	—	452	4	no	—
578	C₂²	—	452	4	no	—
579	C₂²	—	452	8	no	—
580	C₂²	—	226	1	no	—
581	C₂²	—	226	1	no	—
582	C₂²	—	226	2	no	—
583	C₂²	—	226	1	no	—
584	C₂²	—	226	2	no	—
585	C₂²	—	226	1	no	—
586	C₂²	—	226	1	no	—
587	C₂²	—	226	2	no	—
588	C₂²	—	226	1	no	—
589	C₂²	—	226	2	no	—
590	C₂²	—	226	2	no	—
591	C₂²	#41×D₁₁₃	1	2	yes	—
592	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	2	no	—
600	C₄	—	113	2	no	—
601	C₄	—	226	2	no	—
602	C₄	—	226	1	no	—
603	C₄	—	226	2	no	—
604	C₄	—	226	2	no	—
605	C₄	—	226	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	4	2	no	—
608	C₂	—	452	1	no	—
609	C₂	—	452	1	no	—
610	C₂	—	452	2	no	—
611	C₂	—	226	4	no	—
612	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
613	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
614	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#539×C₁₁₃	C₂
hypercenter	#539	D₁₁₃
hypocenter	C₁₁₃	#3459
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #20299223	C₂	semidirect
2. #20299196	C₂	semidirect
3. #20299195	C₂	semidirect
4. #20299194	C₂	semidirect
5. #20299187	C₂	semidirect
6. #20299184	C₂	semidirect
7. #20299181	C₂	semidirect
8. #20299159	C₂	semidirect
9. #20299156	C₂	semidirect
10. #20299133	C₂	semidirect
11. #20299131	C₂	semidirect
12. #20299125	C₂	semidirect
13. #20299111	C₂	semidirect
14. #20299111	C₂	semidirect
15. #20299108	C₂	semidirect
16. #20299106	C₂	semidirect
17. C₂×#16813584	C₂	semidirect
18. C₄×D₄×D₁₁₃	C₂	semidirect
19. #539×C₁₁₃	C₂	semidirect
20. C₂×#14268648	C₂²	semidirect
21. C₂×#14268646	C₂²	semidirect
25. C₂²×C₄×D₁₁₃	C₂²	semidirect
26. C₂²×C₄×D₁₁₃	C₂²	semidirect
27. #16813617	C₂²	semidirect
28. #16813617	C₂²	semidirect
29. #16813617	C₂²	semidirect
30. #16813616	C₂²	semidirect
31. #16813615	C₂²	semidirect
32. #16813612	C₂²	semidirect
33. #16813612	C₂²	semidirect
34. #16813610	C₂²	semidirect
35. #16813608	C₂²	semidirect
36. #16813608	C₂²	semidirect
37. #16813607	C₂²	semidirect
38. #16813607	C₂²	semidirect
39. #16813607	C₂²	semidirect
40. #16813607	C₂²	semidirect
41. #16813607	C₂²	semidirect
42. #16813607	C₂²	semidirect
43. #16813605	C₂²	semidirect
44. #16813605	C₂²	semidirect
45. #16813604	C₂²	semidirect
46. #16813604	C₂²	semidirect
47. #16813602	C₂²	semidirect
48. #16813602	C₂²	semidirect
49. #16813601	C₂²	semidirect
50. #16813600	C₂²	semidirect
51. #16813600	C₂²	semidirect
52. #16813600	C₂²	semidirect
53. #16813599	C₂²	semidirect
54. #16813598	C₂²	semidirect
55. #16813598	C₂²	semidirect
58. #16813597	C₂²	semidirect
60. #16813596	C₂²	semidirect
63. #16813595	C₂²	semidirect
65. #16813593	C₂²	semidirect
66. #16813592	C₂²	semidirect
67. #16813592	C₂²	semidirect
68. #16813592	C₂²	semidirect
69. #16813592	C₂²	semidirect
70. #16813590	C₂²	semidirect
71. #16813590	C₂²	semidirect
72. #16813587	C₂²	semidirect
73. C₄×D₄₅₂	C₂²	semidirect
74. D₄×Dic₁₁₃	C₂²	semidirect
75. #16813584	C₂²	semidirect
76. #16813584	C₂²	semidirect
77. #16813584	C₂²	semidirect
78. #16813584	C₂²	semidirect
79. #16813584	C₂²	semidirect
80. #16813584	C₂²	semidirect
81. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
82. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
83. #16813582	C₂²	semidirect
84. #16813582	C₂²	semidirect
85. #16813582	C₂²	semidirect
86. #16813582	C₂²	semidirect
87. #16813580	C₂²	semidirect
88. #16813580	C₂²	semidirect
89. #16813580	C₂²	semidirect
90. #16813578	C₂²	semidirect
91. C₄⋊C₄×D₁₁₃	C₂²	semidirect
93. C₂×#14268624	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. #125×C₁₁₃	C₂²	semidirect
100. #123×C₁₁₃	C₂²	semidirect
101. #123×C₁₁₃	C₂²	semidirect
102. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
103. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
105. C₄×D₄×C₁₁₃	C₂²	semidirect
106. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
211. C₂²×D₁₁₃	#41	semidirect
308. C₁₁₃	#3459	semidirect
313. #539	D₁₁₃	semidirect
340. #126	C₂×D₁₁₃	semidirect
343. #125	C₂×D₁₁₃	semidirect
357. #123	C₂×D₁₁₃	semidirect
358. #123	C₂×D₁₁₃	semidirect
368. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
369. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
402. C₄×D₄	C₂×D₁₁₃	semidirect
408. 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
#20299223	2
#20299196	2
#20299195	2
#20299194	2
#20299187	2
#20299184	2
#20299181	2
#20299159	2
#20299156	2
#20299133	2
#20299131	2
#20299125	2
#20299111	2
#20299108	2
#20299106	2
C₂×#16813584	2
C₄×D₄×D₁₁₃	2
#539×C₁₁₃	2
#3459	113