Subgroups — #28404516

Order 14464.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299333	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299307	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299297	C₂	1	2	yes	maximal, complemented
4	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299289	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299272	C₂	1	2	yes	maximal, complemented
7	#20299272	C₂	1	2	yes	maximal, complemented
8	#20299249	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299244	C₂	1	2	yes	maximal, complemented
10	#20299236	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299236	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×D₄₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299220	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299203	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299195	C₂	1	2	yes	maximal, complemented
16	#20299181	C₂	1	2	yes	maximal, complemented
17	#20299135	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299126	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299107	C₂	1	2	yes	maximal, complemented
20	C₂×#16813607	C₂	1	2	yes	maximal, complemented
21	#20299070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#520×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268647	C₂²	1	2	yes	complemented
25	C₂²×D₄₅₂	C₂²	1	2	yes	—
26	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
29	#16813621	C₂²	1	1	yes	characteristic, complemented
30	#16813619	C₂²	1	1	yes	characteristic
31	#16813617	C₂²	1	1	yes	characteristic, complemented
32	#16813617	C₂²	1	2	yes	complemented
33	#16813617	C₂²	1	2	yes	complemented
34	#16813616	C₂²	1	2	yes	complemented
35	#16813616	C₂²	1	2	yes	complemented
36	#16813615	C₂²	1	1	yes	characteristic, complemented
37	#16813614	C₂²	1	1	yes	characteristic, complemented
38	#16813613	C₂²	1	1	yes	characteristic, complemented
39	#16813612	C₂²	1	2	yes	complemented
40	#16813612	C₂²	1	1	yes	characteristic, complemented
41	#16813611	C₂²	1	1	yes	characteristic, complemented
42	#16813611	C₂²	1	1	yes	characteristic, complemented
43	#16813610	C₂²	1	2	yes	complemented
44	#16813610	C₂²	1	2	yes	complemented
45	#16813608	C₂²	1	1	yes	characteristic, complemented
46	#16813607	C₂²	1	2	yes	—
47	#16813607	C₂²	1	1	yes	characteristic
48	#16813607	C₂²	1	2	yes	complemented
49	#16813607	C₂²	1	2	yes	complemented
50	#16813607	C₂²	1	2	yes	complemented
51	#16813607	C₂²	1	2	yes	complemented
52	#16813607	C₂²	1	2	yes	complemented
53	#16813607	C₂²	1	2	yes	complemented
54	#16813607	C₂²	1	2	yes	complemented
55	#16813607	C₂²	1	2	yes	complemented
56	#16813605	C₂²	1	2	yes	complemented
57	#16813605	C₂²	1	2	yes	complemented
58	#16813605	C₂²	1	2	yes	complemented
59	#16813604	C₂²	1	1	yes	characteristic, complemented
60	#16813601	C₂²	1	2	yes	complemented
61	#16813600	C₂²	1	1	yes	characteristic, complemented
62	#16813600	C₂²	1	2	yes	complemented
63	#16813600	C₂²	1	2	yes	complemented
64	#16813599	C₂²	1	2	yes	complemented
65	#16813599	C₂²	1	2	yes	complemented
66	#16813598	C₂²	1	1	yes	characteristic, complemented
67	#16813598	C₂²	1	1	yes	characteristic, complemented
68	#16813597	C₂²	1	1	yes	characteristic
69	#16813597	C₂²	1	1	yes	characteristic
70	#16813596	C₂²	1	2	yes	—
71	#16813596	C₂²	1	2	yes	complemented
72	#16813596	C₂²	1	1	yes	characteristic, complemented
73	#16813596	C₂²	1	1	yes	characteristic, complemented
74	#16813595	C₂²	1	1	yes	characteristic
75	#16813595	C₂²	1	2	yes	complemented
76	#16813595	C₂²	1	2	yes	complemented
77	#16813594	C₂²	1	2	yes	complemented
78	#16813594	C₂²	1	2	yes	complemented
79	#16813592	C₂²	1	2	yes	—
80	#16813592	C₂²	1	2	yes	—
81	#16813590	C₂²	1	2	yes	complemented
82	#16813590	C₂²	1	2	yes	complemented
83	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
85	C₄×D₄₅₂	C₂²	1	2	yes	complemented
86	C₄×D₄₅₂	C₂²	1	2	yes	complemented
87	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
89	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
90	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
91	#16813584	C₂²	1	1	yes	characteristic, complemented
92	#16813584	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	#16813582	C₂²	1	2	yes	complemented
99	#16813582	C₂²	1	2	yes	complemented
100	#16813580	C₂²	1	1	yes	characteristic, complemented
101	#16813579	C₂²	1	2	yes	complemented
102	#16813579	C₂²	1	2	yes	complemented
103	#16813579	C₂²	1	1	yes	characteristic, complemented
104	C₂×#14268626	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
106	C₂×#14268624	C₂²	1	2	yes	complemented
107	C₂×#14268624	C₂²	1	2	yes	complemented
108	C₂×#14268624	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
119	#117×C₁₁₃	C₂²	1	2	yes	complemented
120	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
123	C₂³×D₁₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₁₃	C₂³	1	2	yes	—
125	#14268647	—	4	4	no	—
126	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₂₆	C₂³	1	2	yes	—
128	C₂×D₄₅₂	—	4	4	no	—
129	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
130	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×D₄₅₂	C₂³	1	2	yes	—
134	C₂×D₄₅₂	C₂³	1	2	yes	—
135	C₂×D₄₅₂	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
142	D₄×D₁₁₃	—	2	4	no	—
143	D₄×D₁₁₃	—	2	4	no	—
144	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
145	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁₃	—	4	4	no	—
147	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
156	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	1	yes	characteristic
163	#14268626	C₂³	1	2	yes	—
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	2	yes	—
166	#14268626	C₂³	1	1	yes	characteristic
167	#14268626	C₂³	1	1	yes	characteristic
168	#14268626	C₂³	1	2	yes	—
169	#14268626	C₂³	1	2	yes	—
170	#14268626	C₂³	1	2	yes	—
171	#14268626	C₂³	1	1	yes	characteristic
172	#14268626	C₂³	1	1	yes	characteristic
173	#14268626	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
178	#14268624	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	2	yes	—
180	#14268624	C₂³	1	2	yes	—
181	#14268624	C₂³	1	2	yes	—
182	#14268624	C₂³	1	1	yes	characteristic
183	#14268624	C₂³	1	1	yes	characteristic
184	#14268624	C₂³	1	1	yes	characteristic
185	#14268624	C₂³	1	2	yes	—
186	#14268624	C₂³	1	2	yes	—
187	#14268624	C₂³	1	2	yes	—
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	2	yes	—
190	#14268624	C₂³	1	2	yes	—
191	#14268624	C₂³	1	2	yes	—
192	#14268624	C₂³	1	2	yes	—
193	#14268624	C₂³	1	1	yes	characteristic
194	#14268624	C₂³	1	2	yes	—
195	#14268624	C₂³	1	2	yes	—
196	#14268624	C₂³	1	1	yes	characteristic
197	#14268624	C₂³	1	2	yes	—
198	#14268624	C₂³	1	2	yes	—
199	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₁₃	C₂³	1	2	yes	—
203	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
204	#41×C₁₁₃	—	2	4	no	—
205	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
207	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
224	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
225	C₄²×C₁₁₃	C₂³	1	2	yes	—
226	C₄²×C₁₁₃	C₂³	1	2	yes	—
227	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
228	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
230	C₂²×D₁₁₃	—	2	4	no	—
231	C₂²×D₁₁₃	—	2	4	no	—
232	C₂²×D₁₁₃	—	2	4	no	—
233	C₂²×D₁₁₃	—	4	2	no	—
234	C₂²×D₁₁₃	—	4	2	no	—
235	C₂²×D₁₁₃	—	4	2	no	—
236	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
238	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
239	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
240	Q₈×C₁₁₃	—	2	2	no	—
241	D₄×C₁₁₃	—	2	4	no	—
242	D₄×C₁₁₃	#41	1	4	yes	complemented
243	C₂×C₄×C₁₁₃	—	2	4	no	—
244	C₂×C₄×C₁₁₃	—	2	2	no	—
245	C₂×C₄×C₁₁₃	—	4	2	no	—
246	C₂×C₄×C₁₁₃	—	4	2	no	—
247	C₂×C₄×C₁₁₃	—	4	2	no	—
248	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₁₃	—	2	4	no	—
258	C₂²⋊D₁₁₃	—	2	4	no	—
259	C₂²⋊D₁₁₃	—	2	2	no	—
260	C₂²⋊D₁₁₃	—	4	1	no	—
261	C₂²⋊D₁₁₃	—	4	2	no	—
262	C₂²⋊D₁₁₃	—	4	2	no	—
263	C₂×Dic₁₁₃	—	4	2	no	—
264	C₂×Dic₁₁₃	—	4	2	no	—
265	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
271	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
273	D₄₅₂	—	2	2	no	—
274	D₄₅₂	—	2	4	no	—
275	D₄₅₂	—	2	2	no	—
276	D₄₅₂	—	2	2	no	—
277	D₄₅₂	—	4	2	no	—
278	D₄₅₂	—	4	2	no	—
279	D₄₅₂	—	4	2	no	—
280	C₄×D₁₁₃	—	2	2	no	—
281	C₄×D₁₁₃	—	2	4	no	—
282	C₄×D₁₁₃	—	2	2	no	—
283	C₄×D₁₁₃	—	2	2	no	—
284	C₄×D₁₁₃	—	4	2	no	—
285	C₄×D₁₁₃	—	4	2	no	—
286	C₄×D₁₁₃	—	4	1	no	—
287	C₄×D₁₁₃	—	4	2	no	—
288	C₄×D₁₁₃	—	4	2	no	—
289	Dic₂₂₆	—	4	1	no	—
290	Dic₂₂₆	—	4	2	no	—
291	C₂²×C₁₁₃	—	2	2	no	—
292	C₂²×C₁₁₃	—	2	2	no	—
293	C₂²×C₁₁₃	—	2	1	no	—
294	C₂²×C₁₁₃	—	2	1	no	—
295	C₂²×C₁₁₃	—	2	1	no	—
296	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
297	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
298	C₂×D₁₁₃	—	2	1	no	—
299	C₂×D₁₁₃	—	2	1	no	—
300	C₂×D₁₁₃	—	2	1	no	—
301	C₂×D₁₁₃	—	2	2	no	—
302	C₂×D₁₁₃	—	2	2	no	—
303	C₂×D₁₁₃	—	2	2	no	—
304	C₂×D₁₁₃	—	2	2	no	—
305	C₂×D₁₁₃	—	2	1	no	—
306	C₂×D₁₁₃	—	2	2	no	—
307	C₂×D₁₁₃	—	2	2	no	—
308	C₂×D₁₁₃	—	2	1	no	—
309	C₂×D₁₁₃	—	4	8	no	—
310	C₂×D₁₁₃	—	8	4	no	—
311	C₂×D₁₁₃	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₁₁₃	—	2	1	no	—
313	C₄×C₁₁₃	—	2	2	no	—
314	C₄×C₁₁₃	—	2	2	no	—
315	C₄×C₁₁₃	—	2	1	no	—
316	C₄×C₁₁₃	—	2	2	no	—
317	C₄×C₁₁₃	—	2	1	no	—
318	C₄×C₁₁₃	—	2	1	no	—
319	C₄×C₁₁₃	—	2	1	no	—
320	C₄×C₁₁₃	C₂×#41	1	2	yes	—
321	Dic₁₁₃	—	2	1	no	—
322	Dic₁₁₃	—	2	1	no	—
323	Dic₁₁₃	—	2	1	no	—
324	Dic₁₁₃	—	2	2	no	—
325	Dic₁₁₃	—	2	1	no	—
326	Dic₁₁₃	—	2	1	no	—
327	Dic₁₁₃	—	2	1	no	—
328	Dic₁₁₃	—	2	2	no	—
329	C₂×C₁₁₃	—	2	4	no	—
330	C₂×C₁₁₃	—	4	1	no	—
331	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
332	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₁₁₃	#585	1	1	yes	characteristic
334	D₁₁₃	—	2	2	no	—
335	D₁₁₃	—	4	2	no	—
336	D₁₁₃	—	4	2	no	—
337	D₁₁₃	—	4	1	no	—
338	#3513	—	113	1	no	maximal, Sylow
339	C₁₁₃	#3513	1	1	yes	characteristic, complemented, Sylow
340	#559	—	113	1	no	—
341	#554	—	113	1	no	—
342	#553	—	113	2	no	—
343	#553	—	113	1	no	—
344	#552	—	113	1	no	—
345	#551	—	113	2	no	—
346	#551	—	113	2	no	—
347	#547	—	113	1	no	—
348	#546	—	113	1	no	—
349	#546	—	113	1	no	—
350	#546	—	113	2	no	—
351	D₄²	—	113	1	no	—
352	#542	—	113	1	no	—
353	#540	—	113	1	no	—
354	#539	—	113	2	no	—
355	#538	—	113	2	no	—
356	#529	—	113	1	no	—
357	#529	—	113	1	no	—
358	#525	—	113	2	no	—
359	C₂×#123	—	113	2	no	—
360	#520	D₁₁₃	1	1	yes	characteristic, complemented
361	#518	—	113	1	no	—
362	C₂×C₄×D₄	—	113	1	no	—
363	C₂×#41	—	113	2	no	—
364	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
365	C₂²×D₄	—	113	1	no	—
366	C₂²×D₄	—	113	1	no	—
367	C₂²×D₄	—	113	2	no	—
368	C₂³×C₄	—	113	2	no	—
369	C₄⋊Q₈	—	113	1	no	—
370	#127	—	113	1	no	—
371	#126	—	113	2	no	—
372	#126	—	113	1	no	—
373	#126	—	113	2	no	—
374	#126	—	113	1	no	—
375	#126	—	113	2	no	—
376	#126	—	113	2	no	—
377	#125	—	113	1	no	—
378	#125	—	113	1	no	—
379	#125	—	113	2	no	—
380	#125	—	113	1	no	—
381	#124	—	113	1	no	—
382	#124	—	113	1	no	—
383	#124	—	113	1	no	—
384	#124	—	113	2	no	—
385	#124	—	113	2	no	—
386	#123	—	113	2	no	—
387	#123	—	113	2	no	—
388	#123	—	113	2	no	—
389	#123	—	113	1	no	—
390	#123	—	113	2	no	—
391	#123	—	113	2	no	—
392	#123	—	113	2	no	—
393	#123	—	113	2	no	—
394	#123	—	113	2	no	—
395	#123	—	113	2	no	—
396	#123	—	113	2	no	—
397	#123	—	113	2	no	—
398	#123	—	113	2	no	—
399	#123	—	113	1	no	—
400	C₂²⋊Q₈	—	113	1	no	—
401	C₂²⋊Q₈	—	113	1	no	—
402	C₂²⋊Q₈	—	113	2	no	—
403	C₂²⋊Q₈	—	113	2	no	—
404	C₂²⋊Q₈	—	113	1	no	—
405	C₂²⋊Q₈	—	113	2	no	—
406	C₂²⋊Q₈	—	113	2	no	—
407	C₂²⋊Q₈	—	113	2	no	—
408	#121	—	113	2	no	—
409	#121	—	113	2	no	—
410	#121	—	113	2	no	—
411	#121	—	113	2	no	—
412	#121	—	113	1	no	—
413	#121	—	113	1	no	—
414	#121	—	113	1	no	—
415	#121	—	113	1	no	—
416	#121	—	113	2	no	—
417	#121	—	113	1	no	—
418	#121	—	113	2	no	—
419	#120	—	113	2	no	—
420	#120	—	113	2	no	—
421	#120	—	113	2	no	—
422	#120	—	113	2	no	—
423	C₄×Q₈	—	113	1	no	—
424	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
425	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
426	C₄×D₄	—	113	1	no	—
427	C₄×D₄	—	113	1	no	—
428	C₄×D₄	—	113	2	no	—
429	C₄×D₄	—	113	2	no	—
430	C₄×D₄	—	113	2	no	—
431	C₄×D₄	—	113	1	no	—
432	C₄×D₄	—	113	1	no	—
433	C₄×D₄	—	113	1	no	—
434	C₄×D₄	—	113	1	no	—
435	C₄×D₄	—	113	2	no	—
436	C₄×D₄	—	113	2	no	—
437	C₄×D₄	—	113	1	no	—
438	C₄×D₄	—	113	1	no	—
439	C₄×D₄	—	113	2	no	—
440	C₄×D₄	—	113	1	no	—
441	C₄×D₄	—	113	2	no	—
442	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
443	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
444	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
445	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
446	#117	—	113	1	no	—
447	#117	—	113	1	no	—
448	#117	—	113	2	no	—
449	#117	—	113	2	no	—
450	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
451	#117	C₂×D₁₁₃	1	2	yes	complemented
452	C₂×C₄⋊C₄	—	113	2	no	—
453	C₂×C₄⋊C₄	—	113	1	no	—
454	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
455	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
456	C₂×C₂²⋊C₄	—	113	2	no	—
457	C₂×C₂²⋊C₄	—	113	2	no	—
458	C₂×C₂²⋊C₄	—	113	2	no	—
459	C₂×C₂²⋊C₄	—	113	2	no	—
460	C₂×C₂²⋊C₄	—	113	2	no	—
461	C₂×C₄²	—	113	1	no	—
462	C₂⁴	—	113	2	no	—
463	C₂⁴	—	113	2	no	—
464	#41	—	2	4	no	—
465	#41	—	452	4	no	—
466	C₂×Q₈	—	113	1	no	—
467	C₂×Q₈	—	113	2	no	—
468	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
469	C₂×D₄	—	113	1	no	—
470	C₂×D₄	—	113	2	no	—
471	C₂×D₄	—	113	2	no	—
472	C₂×D₄	—	113	2	no	—
473	C₂×D₄	—	113	2	no	—
474	C₂×D₄	—	113	1	no	—
475	C₂×D₄	—	113	2	no	—
476	C₂×D₄	—	113	2	no	—
477	C₂×D₄	—	113	2	no	—
478	C₂×D₄	—	113	1	no	—
479	C₂×D₄	—	113	1	no	—
480	C₂×D₄	—	113	2	no	—
481	C₂×D₄	—	113	1	no	—
482	C₂×D₄	—	452	4	no	—
483	C₂×D₄	—	226	4	no	—
484	C₂×D₄	—	226	4	no	—
485	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
486	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
487	C₂²×C₄	—	113	2	no	—
488	C₂²×C₄	—	113	2	no	—
489	C₂²×C₄	—	113	1	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	1	no	—
495	C₂²×C₄	—	113	1	no	—
496	C₂²×C₄	—	113	2	no	—
497	C₂²×C₄	—	113	1	no	—
498	C₂²×C₄	—	452	4	no	—
499	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
500	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
503	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
504	C₄⋊C₄	—	113	1	no	—
505	C₄⋊C₄	—	113	2	no	—
506	C₄⋊C₄	—	113	1	no	—
507	C₄⋊C₄	—	113	2	no	—
508	C₄⋊C₄	—	113	2	no	—
509	C₄⋊C₄	—	113	2	no	—
510	C₄⋊C₄	—	113	1	no	—
511	C₄⋊C₄	—	113	1	no	—
512	C₄⋊C₄	—	113	1	no	—
513	C₄⋊C₄	—	113	2	no	—
514	C₄⋊C₄	—	113	2	no	—
515	C₄⋊C₄	—	113	2	no	—
516	C₄⋊C₄	—	113	1	no	—
517	C₄⋊C₄	—	113	1	no	—
518	C₄⋊C₄	—	113	2	no	—
519	C₄⋊C₄	—	113	1	no	—
520	C₄⋊C₄	—	113	1	no	—
521	C₄⋊C₄	—	113	1	no	—
522	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
529	C₂²⋊C₄	—	113	2	no	—
530	C₂²⋊C₄	—	113	2	no	—
531	C₂²⋊C₄	—	113	1	no	—
532	C₂²⋊C₄	—	113	1	no	—
533	C₂²⋊C₄	—	113	2	no	—
534	C₂²⋊C₄	—	113	1	no	—
535	C₂²⋊C₄	—	113	1	no	—
536	C₂²⋊C₄	—	113	1	no	—
537	C₂²⋊C₄	—	113	1	no	—
538	C₂²⋊C₄	—	113	2	no	—
539	C₂²⋊C₄	—	113	2	no	—
540	C₂²⋊C₄	—	113	2	no	—
541	C₂²⋊C₄	—	113	2	no	—
542	C₂²⋊C₄	—	113	2	no	—
543	C₂²⋊C₄	—	113	2	no	—
544	C₂²⋊C₄	—	113	2	no	—
545	C₂²⋊C₄	—	113	2	no	—
546	C₂²⋊C₄	—	113	2	no	—
547	C₂²⋊C₄	—	113	2	no	—
548	C₂²⋊C₄	—	113	1	no	—
549	C₂²⋊C₄	—	113	2	no	—
550	C₂²⋊C₄	—	113	1	no	—
551	C₂²⋊C₄	—	113	2	no	—
552	C₂²⋊C₄	—	113	2	no	—
553	C₂²⋊C₄	—	113	2	no	—
554	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
558	C₄²	—	113	1	no	—
559	C₄²	—	113	1	no	—
560	C₄²	—	113	1	no	—
561	C₄²	—	113	2	no	—
562	C₄²	—	113	1	no	—
563	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
564	C₄²	C₂²×D₁₁₃	1	2	yes	—
565	C₄²	C₂²×D₁₁₃	1	2	yes	—
566	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
567	C₂³	—	113	1	no	—
568	C₂³	—	113	1	no	—
569	C₂³	—	113	2	no	—
570	C₂³	—	113	2	no	—
571	C₂³	—	452	2	no	—
572	C₂³	—	452	2	no	—
573	C₂³	—	452	2	no	—
574	C₂³	—	226	4	no	—
575	C₂³	—	226	4	no	—
576	C₂³	—	226	4	no	—
577	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
578	C₂³	C₂³×D₁₁₃	1	2	yes	—
579	Q₈	—	2	2	no	—
580	Q₈	—	452	2	no	—
581	Q₈	—	452	1	no	—
582	D₄	—	2	4	no	—
583	D₄	—	452	2	no	—
584	D₄	—	452	2	no	—
585	D₄	—	452	2	no	—
586	D₄	—	452	2	no	—
587	D₄	—	452	2	no	—
588	D₄	—	452	1	no	—
589	D₄	—	226	2	no	—
590	D₄	—	226	4	no	—
591	D₄	—	226	2	no	—
592	D₄	—	226	4	no	—
593	D₄	—	226	4	no	—
594	D₄	—	226	2	no	—
595	D₄	—	226	2	no	—
596	D₄	#14268647	1	4	yes	complemented
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	113	1	no	—
603	C₂×C₄	—	113	1	no	—
604	C₂×C₄	—	113	1	no	—
605	C₂×C₄	—	113	1	no	—
606	C₂×C₄	—	113	1	no	—
607	C₂×C₄	—	113	2	no	—
608	C₂×C₄	—	113	1	no	—
609	C₂×C₄	—	113	2	no	—
610	C₂×C₄	—	452	2	no	—
611	C₂×C₄	—	452	2	no	—
612	C₂×C₄	—	452	2	no	—
613	C₂×C₄	—	452	2	no	—
614	C₂×C₄	—	452	1	no	—
615	C₂×C₄	—	452	2	no	—
616	C₂×C₄	—	452	2	no	—
617	C₂×C₄	—	226	2	no	—
618	C₂×C₄	—	226	4	no	—
619	C₂×C₄	—	226	2	no	—
620	C₂×C₄	—	226	2	no	—
621	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
624	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
626	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
627	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	113	2	no	—
636	C₂²	—	904	4	no	—
637	C₂²	—	452	8	no	—
638	C₂²	—	226	1	no	—
639	C₂²	—	226	2	no	—
640	C₂²	—	226	2	no	—
641	C₂²	—	226	2	no	—
642	C₂²	—	226	2	no	—
643	C₂²	—	226	1	no	—
644	C₂²	—	226	2	no	—
645	C₂²	—	226	2	no	—
646	C₂²	—	226	1	no	—
647	C₂²	—	226	1	no	—
648	C₂²	—	226	1	no	—
649	C₂²	C₂×#14268647	1	4	yes	—
650	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	226	1	no	—
660	C₄	—	226	1	no	—
661	C₄	—	226	1	no	—
662	C₄	—	226	2	no	—
663	C₄	—	226	1	no	—
664	C₄	—	226	2	no	—
665	C₄	—	226	1	no	—
666	C₄	—	226	1	no	—
667	C₄	C₂×#14268647	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	452	1	no	—
671	C₂	—	452	2	no	—
672	C₂	—	452	2	no	—
673	C₂	—	226	2	no	—
674	C₂	C₂²×#14268647	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
676	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	#3513
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. #20299333	C₂	semidirect
2. #20299307	C₂	semidirect
3. #20299297	C₂	semidirect
4. #20299296	C₂	semidirect
5. #20299289	C₂	semidirect
6. #20299272	C₂	semidirect
7. #20299272	C₂	semidirect
8. #20299249	C₂	semidirect
9. #20299244	C₂	semidirect
10. #20299236	C₂	semidirect
11. #20299236	C₂	semidirect
12. D₄×D₄₅₂	C₂	semidirect
13. #20299220	C₂	semidirect
14. #20299203	C₂	semidirect
15. #20299195	C₂	semidirect
16. #20299181	C₂	semidirect
17. #20299135	C₂	semidirect
18. #20299126	C₂	semidirect
19. #20299107	C₂	semidirect
20. C₂×#16813607	C₂	semidirect
21. #20299070	C₂	semidirect
22. C₄×D₄×D₁₁₃	C₂	semidirect
23. #520×C₁₁₃	C₂	semidirect
24. C₂×#14268647	C₂²	semidirect
28. C₂²×C₄×D₁₁₃	C₂²	semidirect
29. #16813621	C₂²	semidirect
31. #16813617	C₂²	semidirect
32. #16813617	C₂²	semidirect
33. #16813617	C₂²	semidirect
34. #16813616	C₂²	semidirect
35. #16813616	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813614	C₂²	semidirect
38. #16813613	C₂²	semidirect
39. #16813612	C₂²	semidirect
40. #16813612	C₂²	semidirect
41. #16813611	C₂²	semidirect
42. #16813611	C₂²	semidirect
43. #16813610	C₂²	semidirect
44. #16813610	C₂²	semidirect
45. #16813608	C₂²	semidirect
48. #16813607	C₂²	semidirect
49. #16813607	C₂²	semidirect
50. #16813607	C₂²	semidirect
51. #16813607	C₂²	semidirect
52. #16813607	C₂²	semidirect
53. #16813607	C₂²	semidirect
54. #16813607	C₂²	semidirect
55. #16813607	C₂²	semidirect
56. #16813605	C₂²	semidirect
57. #16813605	C₂²	semidirect
58. #16813605	C₂²	semidirect
59. #16813604	C₂²	semidirect
60. #16813601	C₂²	semidirect
61. #16813600	C₂²	semidirect
62. #16813600	C₂²	semidirect
63. #16813600	C₂²	semidirect
64. #16813599	C₂²	semidirect
65. #16813599	C₂²	semidirect
66. #16813598	C₂²	semidirect
67. #16813598	C₂²	semidirect
71. #16813596	C₂²	semidirect
72. #16813596	C₂²	semidirect
73. #16813596	C₂²	semidirect
75. #16813595	C₂²	semidirect
76. #16813595	C₂²	semidirect
77. #16813594	C₂²	semidirect
78. #16813594	C₂²	semidirect
81. #16813590	C₂²	semidirect
82. #16813590	C₂²	semidirect
83. C₄×Dic₂₂₆	C₂²	semidirect
85. C₄×D₄₅₂	C₂²	semidirect
86. C₄×D₄₅₂	C₂²	semidirect
87. C₄×D₄₅₂	C₂²	semidirect
88. C₄×D₄₅₂	C₂²	semidirect
91. #16813584	C₂²	semidirect
92. #16813584	C₂²	semidirect
93. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
94. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
95. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
96. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
97. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
98. #16813582	C₂²	semidirect
99. #16813582	C₂²	semidirect
100. #16813580	C₂²	semidirect
101. #16813579	C₂²	semidirect
102. #16813579	C₂²	semidirect
103. #16813579	C₂²	semidirect
104. C₂×#14268626	C₂²	semidirect
105. C₄⋊C₄×D₁₁₃	C₂²	semidirect
106. C₂×#14268624	C₂²	semidirect
107. C₂×#14268624	C₂²	semidirect
108. C₂×#14268624	C₂²	semidirect
109. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
110. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
111. C₄²×D₁₁₃	C₂²	semidirect
113. C₄×Q₈×C₁₁₃	C₂²	semidirect
114. C₄×Q₈×C₁₁₃	C₂²	semidirect
117. C₄×D₄×C₁₁₃	C₂²	semidirect
118. C₄×D₄×C₁₁₃	C₂²	semidirect
119. #117×C₁₁₃	C₂²	semidirect
120. #117×C₁₁₃	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
242. D₄×C₁₁₃	#41	semidirect
339. C₁₁₃	#3513	semidirect
360. #520	D₁₁₃	semidirect
424. C₄×Q₈	C₂×D₁₁₃	semidirect
425. C₄×Q₈	C₂×D₁₁₃	semidirect
444. C₄×D₄	C₂×D₁₁₃	semidirect
445. C₄×D₄	C₂×D₁₁₃	semidirect
450. #117	C₂×D₁₁₃	semidirect
451. #117	C₂×D₁₁₃	semidirect
454. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
455. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
596. D₄	#14268647	semidirect

Maximal subgroups

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

subgroup	index
#20299333	2
#20299307	2
#20299297	2
#20299296	2
#20299289	2
#20299272	2
#20299249	2
#20299244	2
#20299236	2
D₄×D₄₅₂	2
#20299220	2
#20299203	2
#20299195	2
#20299181	2
#20299135	2
#20299126	2
#20299107	2
C₂×#16813607	2
#20299070	2
C₄×D₄×D₁₁₃	2
#520×C₁₁₃	2
#3513	113