Subgroups — #28404203

Order 14464.

1900 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813667	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299238	C₂	1	4	yes	maximal, complemented
4	#20299235	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊D₁₁₃	C₂	1	4	yes	maximal, complemented
6	#20299230	C₂	1	4	yes	maximal, complemented
7	#20299163	C₂	1	2	yes	maximal, complemented
8	#20299160	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299158	C₂	1	2	yes	maximal, complemented
10	#20299157	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299104	C₂	1	2	yes	maximal, complemented
12	C₂×#16813591	C₂	1	1	yes	maximal, characteristic, complemented
13	#120×D₁₁₃	C₂	1	2	yes	maximal, complemented
14	#20299071	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#120×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
17	#16813667	—	2	8	no	—
18	C₂×#14268647	C₂²	1	2	yes	complemented
19	C₂×#14268646	C₂²	1	2	yes	complemented
20	C₂×#14268646	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₁₃	—	2	8	no	—
22	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
27	C₂²×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
28	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₁₃	C₂²	1	4	yes	complemented
33	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
34	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
35	#16813618	C₂²	1	4	yes	complemented
36	#16813608	C₂²	1	4	yes	complemented
37	#16813606	C₂²	1	2	yes	complemented
38	#16813606	C₂²	1	2	yes	complemented
39	#16813605	C₂²	1	2	yes	complemented
40	#16813604	C₂²	1	4	yes	complemented
41	#16813603	C₂²	1	2	yes	complemented
42	#16813599	C₂²	1	4	yes	complemented
43	#16813596	C₂²	1	4	yes	complemented
44	#16813595	C₂²	1	4	yes	complemented
45	#16813595	C₂²	1	4	yes	complemented
46	#16813594	C₂²	1	4	yes	complemented
47	#16813594	C₂²	1	4	yes	complemented
48	#16813594	C₂²	1	4	yes	complemented
49	#16813593	C₂²	1	4	yes	complemented
50	#16813592	C₂²	1	2	yes	complemented
51	#16813592	C₂²	1	4	yes	complemented
52	#16813592	C₂²	1	2	yes	complemented
53	#16813591	C₂²	1	2	yes	complemented
54	#16813591	C₂²	1	2	yes	complemented
55	#16813591	C₂²	1	4	yes	complemented
56	#16813591	C₂²	1	2	yes	complemented
57	#16813590	C₂²	1	2	yes	complemented
58	#16813590	C₂²	1	4	yes	complemented
59	#16813590	C₂²	1	4	yes	complemented
60	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
62	#16813582	C₂²	1	4	yes	complemented
63	#16813582	C₂²	1	4	yes	complemented
64	#16813578	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
67	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
68	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
69	C₂⁵×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
70	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
71	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	complemented
72	#120×C₁₁₃	C₂²	1	2	yes	complemented
73	#120×C₁₁₃	C₂²	1	2	yes	complemented
74	#120×C₁₁₃	C₂²	1	4	yes	complemented
75	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
77	C₂³×D₁₁₃	—	2	4	no	—
78	C₂³×D₁₁₃	—	4	4	no	—
79	C₂³×D₁₁₃	C₂³	1	4	yes	—
80	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
81	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
82	C₂³×D₁₁₃	C₂³	1	2	yes	complemented
83	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic, complemented
84	#14268647	—	2	8	no	—
85	#14268646	—	2	8	no	—
86	#14268646	—	2	8	no	—
87	C₂×Dic₂₂₆	C₂³	1	2	yes	complemented
88	C₂×D₄₅₂	C₂³	1	2	yes	complemented
89	C₂×D₄₅₂	C₂³	1	4	yes	complemented
90	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
91	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
92	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
93	C₂×C₂²⋊D₁₁₃	—	2	16	no	—
94	C₂×C₂²⋊D₁₁₃	—	2	16	no	—
95	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
96	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
97	C₂×C₂²⋊D₁₁₃	—	4	4	no	—
98	C₂×C₂²⋊D₁₁₃	D₄	1	8	yes	complemented
99	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
102	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
103	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
104	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
107	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	complemented
108	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	complemented
109	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	complemented
110	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	complemented
111	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	complemented
112	D₄×D₁₁₃	—	2	8	no	—
113	D₄×D₁₁₃	—	2	8	no	—
114	D₄×D₁₁₃	—	4	8	no	—
115	C₂²×Dic₁₁₃	—	2	4	no	—
116	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
117	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
118	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
119	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic, complemented
120	C₂²×Dic₁₁₃	C₂³	1	2	yes	complemented
121	C₂²×Dic₁₁₃	C₂³	1	2	yes	complemented
122	C₂×C₄×D₁₁₃	C₂³	1	2	yes	complemented
123	C₂×C₄×D₁₁₃	C₂³	1	2	yes	complemented
124	C₂×C₄×D₁₁₃	C₂³	1	4	yes	complemented
125	C₄⋊Dic₁₁₃	C₂³	1	4	yes	complemented
126	#14268626	C₂³	1	4	yes	complemented
127	#14268626	C₂³	1	4	yes	complemented
128	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	complemented
131	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	complemented
132	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	complemented
133	#14268624	C₂³	1	4	yes	complemented
134	#14268624	C₂³	1	4	yes	complemented
135	#14268624	C₂³	1	4	yes	complemented
136	#14268624	C₂³	1	4	yes	complemented
137	C₄×Dic₁₁₃	C₂³	1	4	yes	complemented
138	C₂⁴×C₁₁₃	—	2	4	no	—
139	C₂⁴×C₁₁₃	—	4	4	no	—
140	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
141	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
142	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
143	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
144	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
145	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic, complemented
146	C₂×D₄×C₁₁₃	—	2	4	no	—
147	C₂×D₄×C₁₁₃	—	4	4	no	—
148	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
149	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂×D₄×C₁₁₃	C₂³	1	2	yes	complemented
151	C₂×D₄×C₁₁₃	C₂³	1	4	yes	complemented
152	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic, complemented
153	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	complemented
154	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
156	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	complemented
157	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	complemented
158	C₂³×C₁₁₃	—	2	2	no	—
159	C₂³×C₁₁₃	—	2	4	no	—
160	C₂³×C₁₁₃	—	2	4	no	—
161	C₂³×C₁₁₃	—	2	4	no	—
162	C₂³×C₁₁₃	—	2	2	no	—
163	C₂³×C₁₁₃	—	2	4	no	—
164	C₂³×C₁₁₃	—	2	4	no	—
165	C₂³×C₁₁₃	—	2	2	no	—
166	C₂³×C₁₁₃	—	4	2	no	—
167	C₂³×C₁₁₃	—	4	2	no	—
168	C₂³×C₁₁₃	—	4	2	no	—
169	C₂³×C₁₁₃	—	4	2	no	—
170	C₂³×C₁₁₃	—	4	2	no	—
171	C₂³×C₁₁₃	—	4	16	no	—
172	C₂³×C₁₁₃	C₂×D₄	1	4	yes	complemented
173	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
174	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
175	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
176	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
177	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
178	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
179	C₂²×D₁₁₃	—	2	2	no	—
180	C₂²×D₁₁₃	—	2	8	no	—
181	C₂²×D₁₁₃	—	2	2	no	—
182	C₂²×D₁₁₃	—	2	8	no	—
183	C₂²×D₁₁₃	—	2	4	no	—
184	C₂²×D₁₁₃	—	4	2	no	—
185	C₂²×D₁₁₃	—	4	4	no	—
186	C₂²×D₁₁₃	—	4	2	no	—
187	C₂²×D₁₁₃	—	4	4	no	—
188	C₂²×D₁₁₃	—	4	2	no	—
189	C₂²×D₁₁₃	—	4	16	no	—
190	C₂²×D₁₁₃	C₂×D₄	1	4	yes	complemented
191	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
192	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
193	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
194	D₄×C₁₁₃	—	2	4	no	—
195	D₄×C₁₁₃	—	2	4	no	—
196	D₄×C₁₁₃	—	2	8	no	—
197	D₄×C₁₁₃	—	4	4	no	—
198	C₂×C₄×C₁₁₃	—	2	2	no	—
199	C₂×C₄×C₁₁₃	—	4	2	no	—
200	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
201	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
202	C₂²⋊D₁₁₃	—	2	4	no	—
203	C₂²⋊D₁₁₃	—	2	4	no	—
204	C₂²⋊D₁₁₃	—	2	4	no	—
205	C₂²⋊D₁₁₃	—	2	4	no	—
206	C₂²⋊D₁₁₃	—	2	8	no	—
207	C₂²⋊D₁₁₃	—	2	4	no	—
208	C₂²⋊D₁₁₃	—	2	8	no	—
209	C₂²⋊D₁₁₃	—	2	4	no	—
210	C₂²⋊D₁₁₃	—	2	8	no	—
211	C₂²⋊D₁₁₃	—	4	4	no	—
212	C₂²⋊D₁₁₃	—	4	4	no	—
213	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
214	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
215	C₂×Dic₁₁₃	—	2	2	no	—
216	C₂×Dic₁₁₃	—	2	2	no	—
217	C₂×Dic₁₁₃	—	2	8	no	—
218	C₂×Dic₁₁₃	—	2	4	no	—
219	C₂×Dic₁₁₃	—	4	2	no	—
220	C₂×Dic₁₁₃	C₂×D₄	1	4	yes	complemented
221	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
222	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
223	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
224	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
225	D₄₅₂	—	2	4	no	—
226	D₄₅₂	—	4	4	no	—
227	C₄×D₁₁₃	—	2	4	no	—
228	C₄×D₁₁₃	—	2	4	no	—
229	C₄×D₁₁₃	—	4	4	no	—
230	Dic₂₂₆	—	2	4	no	—
231	C₂²×C₁₁₃	—	2	8	no	—
232	C₂²×C₁₁₃	—	2	2	no	—
233	C₂²×C₁₁₃	—	2	2	no	—
234	C₂²×C₁₁₃	—	2	2	no	—
235	C₂²×C₁₁₃	—	2	2	no	—
236	C₂²×C₁₁₃	—	2	2	no	—
237	C₂²×C₁₁₃	—	2	2	no	—
238	C₂²×C₁₁₃	—	2	2	no	—
239	C₂²×C₁₁₃	—	2	2	no	—
240	C₂²×C₁₁₃	—	2	4	no	—
241	C₂²×C₁₁₃	—	2	2	no	—
242	C₂²×C₁₁₃	—	4	4	no	—
243	C₂²×C₁₁₃	—	4	8	no	—
244	C₂²×C₁₁₃	—	4	8	no	—
245	C₂²×C₁₁₃	—	4	4	no	—
246	C₂²×C₁₁₃	—	8	2	no	—
247	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
248	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
249	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
250	C₂²×C₁₁₃	H(5,𝔽₂)	1	4	yes	complemented
251	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
252	C₂×D₁₁₃	—	2	4	no	—
253	C₂×D₁₁₃	—	2	2	no	—
254	C₂×D₁₁₃	—	2	2	no	—
255	C₂×D₁₁₃	—	2	4	no	—
256	C₂×D₁₁₃	—	2	4	no	—
257	C₂×D₁₁₃	—	4	4	no	—
258	C₂×D₁₁₃	—	4	16	no	—
259	C₂×D₁₁₃	—	4	4	no	—
260	C₂×D₁₁₃	—	8	4	no	—
261	C₂×D₁₁₃	—	8	2	no	—
262	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
263	C₄×C₁₁₃	—	2	2	no	—
264	C₄×C₁₁₃	—	2	4	no	—
265	Dic₁₁₃	—	2	2	no	—
266	Dic₁₁₃	—	2	2	no	—
267	Dic₁₁₃	—	2	4	no	—
268	Dic₁₁₃	C₂²×D₄	1	4	yes	—
269	C₂×C₁₁₃	—	2	2	no	—
270	C₂×C₁₁₃	—	2	4	no	—
271	C₂×C₁₁₃	—	2	2	no	—
272	C₂×C₁₁₃	—	2	2	no	—
273	C₂×C₁₁₃	—	4	2	no	—
274	C₂×C₁₁₃	—	4	2	no	—
275	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
276	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
277	D₁₁₃	—	2	4	no	—
278	D₁₁₃	—	4	2	no	—
279	D₁₁₃	—	4	2	no	—
280	#3484	—	113	1	no	maximal, Sylow
281	C₁₁₃	#3484	1	1	yes	characteristic, complemented, Sylow
282	C₂×H(5,𝔽₂)	—	113	1	no	—
283	C₂³×D₄	—	113	1	no	—
284	#546	—	113	4	no	—
285	#546	—	113	4	no	—
286	D₄²	—	113	4	no	—
287	D₄²	—	113	4	no	—
288	#535	—	113	2	no	—
289	#534	—	113	1	no	—
290	#534	—	113	2	no	—
291	#534	—	113	1	no	—
292	#525	—	113	2	no	—
293	C₂×#120	—	113	1	no	—
294	C₂×#120	—	113	2	no	—
295	C₂×#120	D₁₁₃	1	1	yes	characteristic, complemented
296	#518	—	113	1	no	—
297	C₂⁵	—	113	1	no	—
298	C₂⁵	C₂×D₁₁₃	1	1	yes	characteristic, complemented
299	H(5,𝔽₂)	—	226	8	no	—
300	C₂×#41	—	113	2	no	—
301	C₂×#41	—	113	2	no	—
302	C₂×#41	—	113	2	no	—
303	C₂²×D₄	—	113	1	no	—
304	C₂²×D₄	—	113	2	no	—
305	C₂²×D₄	—	113	1	no	—
306	C₂²×D₄	—	113	1	no	—
307	C₂²×D₄	—	113	1	no	—
308	C₂²×D₄	—	113	1	no	—
309	C₂²×D₄	—	113	4	no	—
310	C₂²×D₄	—	113	4	no	—
311	C₂²×D₄	—	113	2	no	—
312	C₂²×D₄	—	113	4	no	—
313	C₂²×D₄	—	113	2	no	—
314	C₂²×D₄	—	113	2	no	—
315	C₂²×D₄	—	226	8	no	—
316	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
317	C₂²×D₄	C₂×D₁₁₃	1	2	yes	complemented
318	C₂³×C₄	—	113	1	no	—
319	#127	—	113	4	no	—
320	#124	—	113	4	no	—
321	#123	—	113	2	no	—
322	#123	—	113	2	no	—
323	#123	—	113	2	no	—
324	#123	—	113	4	no	—
325	#123	—	113	2	no	—
326	C₂²⋊Q₈	—	113	4	no	—
327	#121	—	113	4	no	—
328	#121	—	113	4	no	—
329	#121	—	113	4	no	—
330	#121	—	113	4	no	—
331	#121	—	113	4	no	—
332	#121	—	113	4	no	—
333	#121	—	113	4	no	—
334	#120	—	113	2	no	—
335	#120	—	113	2	no	—
336	#120	—	113	4	no	—
337	#120	—	113	2	no	—
338	#120	—	113	2	no	—
339	#120	—	113	4	no	—
340	#120	—	113	4	no	—
341	#120	—	113	2	no	—
342	#120	—	113	4	no	—
343	#120	—	113	2	no	—
344	#120	C₂×D₁₁₃	1	2	yes	complemented
345	#120	C₂×D₁₁₃	1	2	yes	complemented
346	#120	C₂×D₁₁₃	1	4	yes	complemented
347	C₄×D₄	—	113	4	no	—
348	C₄×D₄	—	113	4	no	—
349	C₄×D₄	—	113	4	no	—
350	C₄×D₄	—	113	4	no	—
351	#117	—	113	2	no	—
352	C₂×C₂²⋊C₄	—	113	1	no	—
353	C₂×C₂²⋊C₄	—	113	2	no	—
354	C₂×C₂²⋊C₄	—	113	2	no	—
355	C₂×C₂²⋊C₄	—	113	4	no	—
356	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
357	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	4	4	no	—
360	C₂⁴	—	113	1	no	—
361	C₂⁴	—	113	1	no	—
362	C₂⁴	—	113	2	no	—
363	C₂⁴	—	113	1	no	—
364	C₂⁴	—	113	4	no	—
365	C₂⁴	—	452	4	no	—
366	C₂⁴	—	226	4	no	—
367	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
368	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
369	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
370	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
371	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
372	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic, complemented
373	#41	—	226	8	no	—
374	#41	—	226	8	no	—
375	#41	—	226	8	no	—
376	C₂×Q₈	—	113	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	113	8	no	—
380	C₂×D₄	—	113	2	no	—
381	C₂×D₄	—	113	2	no	—
382	C₂×D₄	—	113	4	no	—
383	C₂×D₄	—	113	4	no	—
384	C₂×D₄	—	113	4	no	—
385	C₂×D₄	—	113	2	no	—
386	C₂×D₄	—	113	2	no	—
387	C₂×D₄	—	113	2	no	—
388	C₂×D₄	—	113	4	no	—
389	C₂×D₄	—	113	2	no	—
390	C₂×D₄	—	113	2	no	—
391	C₂×D₄	—	113	4	no	—
392	C₂×D₄	—	113	2	no	—
393	C₂×D₄	—	113	4	no	—
394	C₂×D₄	—	113	2	no	—
395	C₂×D₄	—	452	8	no	—
396	C₂×D₄	—	452	4	no	—
397	C₂×D₄	—	226	4	no	—
398	C₂×D₄	—	226	8	no	—
399	C₂×D₄	—	226	8	no	—
400	C₂×D₄	—	226	16	no	—
401	C₂×D₄	—	226	16	no	—
402	C₂×D₄	—	226	8	no	—
403	C₂×D₄	—	226	4	no	—
404	C₂×D₄	—	226	4	no	—
405	C₂×D₄	—	226	4	no	—
406	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
407	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
408	C₂×D₄	C₂²×D₁₁₃	1	2	yes	complemented
409	C₂×D₄	C₂²×D₁₁₃	1	4	yes	complemented
410	C₂²×C₄	—	113	1	no	—
411	C₂²×C₄	—	113	2	no	—
412	C₂²×C₄	—	113	1	no	—
413	C₂²×C₄	—	113	2	no	—
414	C₂²×C₄	—	113	4	no	—
415	C₂²×C₄	—	113	1	no	—
416	C₂²×C₄	—	113	4	no	—
417	C₂²×C₄	—	113	2	no	—
418	C₂²×C₄	—	113	2	no	—
419	C₂²×C₄	—	226	4	no	—
420	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic, complemented
421	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	complemented
422	C₄⋊C₄	—	113	4	no	—
423	C₄⋊C₄	—	113	4	no	—
424	C₄⋊C₄	—	113	4	no	—
425	C₂²⋊C₄	—	113	2	no	—
426	C₂²⋊C₄	—	113	4	no	—
427	C₂²⋊C₄	—	113	2	no	—
428	C₂²⋊C₄	—	113	4	no	—
429	C₂²⋊C₄	—	113	4	no	—
430	C₂²⋊C₄	—	113	4	no	—
431	C₂²⋊C₄	—	113	4	no	—
432	C₂²⋊C₄	—	113	4	no	—
433	C₂²⋊C₄	—	113	4	no	—
434	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
436	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	complemented
437	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	complemented
438	C₄²	—	113	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	16	no	—
453	C₂³	—	113	4	no	—
454	C₂³	—	113	2	no	—
455	C₂³	—	113	2	no	—
456	C₂³	—	113	2	no	—
457	C₂³	—	452	2	no	—
458	C₂³	—	452	4	no	—
459	C₂³	—	452	16	no	—
460	C₂³	—	452	2	no	—
461	C₂³	—	452	4	no	—
462	C₂³	—	452	2	no	—
463	C₂³	—	226	4	no	—
464	C₂³	—	226	8	no	—
465	C₂³	—	226	2	no	—
466	C₂³	—	226	2	no	—
467	C₂³	—	226	8	no	—
468	C₂³	D₄×D₁₁₃	1	4	yes	complemented
469	C₂³	C₂³×D₁₁₃	1	2	yes	—
470	C₂³	C₂³×D₁₁₃	1	2	yes	—
471	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
472	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
473	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
474	C₂³	C₂³×D₁₁₃	1	2	yes	—
475	Q₈	—	226	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	8	no	—
479	D₄	—	4	4	no	—
480	D₄	—	113	8	no	—
481	D₄	—	113	8	no	—
482	D₄	—	452	4	no	—
483	D₄	—	452	4	no	—
484	D₄	—	452	4	no	—
485	D₄	—	226	4	no	—
486	D₄	—	226	8	no	—
487	D₄	—	226	4	no	—
488	D₄	—	226	8	no	—
489	D₄	—	226	4	no	—
490	D₄	—	226	4	no	—
491	D₄	—	226	4	no	—
492	D₄	—	226	4	no	—
493	D₄	—	226	4	no	—
494	D₄	—	226	8	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	113	4	no	—
498	C₂×C₄	—	113	2	no	—
499	C₂×C₄	—	113	4	no	—
500	C₂×C₄	—	113	2	no	—
501	C₂×C₄	—	113	2	no	—
502	C₂×C₄	—	452	4	no	—
503	C₂×C₄	—	452	2	no	—
504	C₂×C₄	—	226	4	no	—
505	C₂×C₄	—	226	4	no	—
506	C₂×C₄	—	226	8	no	—
507	C₂×C₄	—	226	4	no	—
508	C₂×C₄	—	226	2	no	—
509	C₂×C₄	—	226	2	no	—
510	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
511	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
512	C₂²	—	2	8	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	8	no	—
525	C₂²	—	4	8	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	113	4	no	—
529	C₂²	—	904	2	no	—
530	C₂²	—	904	4	no	—
531	C₂²	—	452	4	no	—
532	C₂²	—	452	16	no	—
533	C₂²	—	452	4	no	—
534	C₂²	—	226	2	no	—
535	C₂²	—	226	2	no	—
536	C₂²	—	226	4	no	—
537	C₂²	—	226	4	no	—
538	C₂²	—	226	4	no	—
539	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
540	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
541	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
542	C₂²	#16813667	1	4	yes	complemented
543	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
544	C₄	—	2	2	no	—
545	C₄	—	2	4	no	—
546	C₄	—	113	4	no	—
547	C₄	—	226	2	no	—
548	C₄	—	226	2	no	—
549	C₄	—	226	4	no	—
550	C₂	—	2	2	no	—
551	C₂	—	2	4	no	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	4	2	no	—
556	C₂	—	452	2	no	—
557	C₂	—	452	2	no	—
558	C₂	—	226	4	no	—
559	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
560	C₂	C₂×#16813667	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#120×C₁₁₃	C₂
hypercenter	C₂×#120	D₁₁₃
hypocenter	C₁₁₃	#3484
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂×#16813667	C₂	semidirect
2. C₂³×C₂²⋊D₁₁₃	C₂	semidirect
3. #20299238	C₂	semidirect
4. #20299235	C₂	semidirect
5. D₄×C₂²⋊D₁₁₃	C₂	semidirect
6. #20299230	C₂	semidirect
7. #20299163	C₂	semidirect
8. #20299160	C₂	semidirect
9. #20299158	C₂	semidirect
10. #20299157	C₂	semidirect
11. #20299104	C₂	semidirect
12. C₂×#16813591	C₂	semidirect
13. #120×D₁₁₃	C₂	semidirect
14. #20299071	C₂	semidirect
15. C₂×#120×C₁₁₃	C₂	semidirect
16. C₂⁴×D₁₁₃	C₂²	semidirect
18. C₂×#14268647	C₂²	semidirect
19. C₂×#14268646	C₂²	semidirect
20. C₂×#14268646	C₂²	semidirect
23. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
24. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
25. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
26. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
27. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
28. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
29. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
30. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
31. C₂×D₄×D₁₁₃	C₂²	semidirect
32. C₂×D₄×D₁₁₃	C₂²	semidirect
33. C₂×D₄×D₁₁₃	C₂²	semidirect
34. C₂³×Dic₁₁₃	C₂²	semidirect
35. #16813618	C₂²	semidirect
36. #16813608	C₂²	semidirect
37. #16813606	C₂²	semidirect
38. #16813606	C₂²	semidirect
39. #16813605	C₂²	semidirect
40. #16813604	C₂²	semidirect
41. #16813603	C₂²	semidirect
42. #16813599	C₂²	semidirect
43. #16813596	C₂²	semidirect
44. #16813595	C₂²	semidirect
45. #16813595	C₂²	semidirect
46. #16813594	C₂²	semidirect
47. #16813594	C₂²	semidirect
48. #16813594	C₂²	semidirect
49. #16813593	C₂²	semidirect
50. #16813592	C₂²	semidirect
51. #16813592	C₂²	semidirect
52. #16813592	C₂²	semidirect
53. #16813591	C₂²	semidirect
54. #16813591	C₂²	semidirect
55. #16813591	C₂²	semidirect
56. #16813591	C₂²	semidirect
57. #16813590	C₂²	semidirect
58. #16813590	C₂²	semidirect
59. #16813590	C₂²	semidirect
60. D₄×Dic₁₁₃	C₂²	semidirect
61. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
62. #16813582	C₂²	semidirect
63. #16813582	C₂²	semidirect
64. #16813578	C₂²	semidirect
65. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
66. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
67. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
68. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
69. C₂⁵×C₁₁₃	C₂²	semidirect
70. C₂²×D₄×C₁₁₃	C₂²	semidirect
71. C₂²×D₄×C₁₁₃	C₂²	semidirect
72. #120×C₁₁₃	C₂²	semidirect
73. #120×C₁₁₃	C₂²	semidirect
74. #120×C₁₁₃	C₂²	semidirect
75. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
76. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
82. C₂³×D₁₁₃	C₂³	semidirect
83. C₂³×D₁₁₃	C₂³	semidirect
87. C₂×Dic₂₂₆	C₂³	semidirect
88. C₂×D₄₅₂	C₂³	semidirect
89. C₂×D₄₅₂	C₂³	semidirect
98. C₂×C₂²⋊D₁₁₃	D₄	semidirect
107. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
108. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
109. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
110. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
111. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
119. C₂²×Dic₁₁₃	C₂³	semidirect
120. C₂²×Dic₁₁₃	C₂³	semidirect
121. C₂²×Dic₁₁₃	C₂³	semidirect
122. C₂×C₄×D₁₁₃	C₂³	semidirect
123. C₂×C₄×D₁₁₃	C₂³	semidirect
124. C₂×C₄×D₁₁₃	C₂³	semidirect
125. C₄⋊Dic₁₁₃	C₂³	semidirect
126. #14268626	C₂³	semidirect
127. #14268626	C₂³	semidirect
130. C₂²⋊Dic₁₁₃	C₂³	semidirect
131. C₂²⋊Dic₁₁₃	C₂³	semidirect
132. C₂²⋊Dic₁₁₃	C₂³	semidirect
133. #14268624	C₂³	semidirect
134. #14268624	C₂³	semidirect
135. #14268624	C₂³	semidirect
136. #14268624	C₂³	semidirect
137. C₄×Dic₁₁₃	C₂³	semidirect
145. C₂⁴×C₁₁₃	C₂³	semidirect
150. C₂×D₄×C₁₁₃	C₂³	semidirect
151. C₂×D₄×C₁₁₃	C₂³	semidirect
152. C₂²×C₄×C₁₁₃	C₂³	semidirect
153. C₂²×C₄×C₁₁₃	C₂³	semidirect
156. C₂²⋊C₄×C₁₁₃	C₂³	semidirect
157. C₂²⋊C₄×C₁₁₃	C₂³	semidirect
172. C₂³×C₁₁₃	C₂×D₄	semidirect
190. C₂²×D₁₁₃	C₂×D₄	semidirect
213. C₂²⋊D₁₁₃	C₂×D₄	semidirect
214. C₂²⋊D₁₁₃	C₂×D₄	semidirect
220. C₂×Dic₁₁₃	C₂×D₄	semidirect
250. C₂²×C₁₁₃	H(5,𝔽₂)	semidirect
281. C₁₁₃	#3484	semidirect
295. C₂×#120	D₁₁₃	semidirect
298. C₂⁵	C₂×D₁₁₃	semidirect
316. C₂²×D₄	C₂×D₁₁₃	semidirect
317. C₂²×D₄	C₂×D₁₁₃	semidirect
344. #120	C₂×D₁₁₃	semidirect
345. #120	C₂×D₁₁₃	semidirect
346. #120	C₂×D₁₁₃	semidirect
356. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
357. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
372. C₂⁴	C₂²×D₁₁₃	semidirect
408. C₂×D₄	C₂²×D₁₁₃	semidirect
409. C₂×D₄	C₂²×D₁₁₃	semidirect
420. C₂²×C₄	C₂²×D₁₁₃	semidirect
421. C₂²×C₄	C₂²×D₁₁₃	semidirect
436. C₂²⋊C₄	C₂²×D₁₁₃	semidirect
437. C₂²⋊C₄	C₂²×D₁₁₃	semidirect
468. C₂³	D₄×D₁₁₃	semidirect
542. C₂²	#16813667	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813667	2
C₂³×C₂²⋊D₁₁₃	2
#20299238	2
#20299235	2
D₄×C₂²⋊D₁₁₃	2
#20299230	2
#20299163	2
#20299160	2
#20299158	2
#20299157	2
#20299104	2
C₂×#16813591	2
#120×D₁₁₃	2
#20299071	2
C₂×#120×C₁₁₃	2
#3484	113