Subgroups — C₁₃₁×#24645 #45710529

Order 33536.

848 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#462×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#440×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2547×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2356×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2056×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2015×C₁₃₁	C₂	1	2	yes	maximal
7	#1983×C₁₃₁	C₂	1	2	yes	maximal
8	#1960×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1940×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1928×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1804×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₃₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	#462×C₁₃₁	—	2	4	no	—
19	#440×C₁₃₁	—	2	4	no	—
20	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
27	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
30	#397×C₁₃₁	—	2	1	no	—
31	#397×C₁₃₁	—	2	1	no	—
32	#391×C₁₃₁	C₂²	1	2	yes	—
33	#391×C₁₃₁	C₂²	1	2	yes	—
34	#387×C₁₃₁	—	2	2	no	—
35	#383×C₁₃₁	—	2	1	no	—
36	#382×C₁₃₁	C₂²	1	1	yes	characteristic
37	#380×C₁₃₁	—	2	2	no	—
38	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
40	#376×C₁₃₁	—	2	1	no	—
41	#340×C₁₃₁	C₂²	1	2	yes	—
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₁	—	2	1	no	—
47	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
48	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
49	C₂×Q₁₆×C₁₃₁	—	4	2	no	—
50	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
51	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
52	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
57	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
58	#124×C₁₃₁	—	2	4	no	—
59	#124×C₁₃₁	—	4	2	no	—
60	C₄×Q₈×C₁₃₁	—	2	2	no	—
61	C₄×Q₈×C₁₃₁	D₄	1	4	yes	—
62	C₄×D₄×C₁₃₁	—	2	2	no	—
63	C₄×D₄×C₁₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₁	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
74	C₂×C₄²×C₁₃₁	—	2	1	no	—
75	C₂×C₄²×C₁₃₁	—	2	2	no	—
76	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	#107×C₁₃₁	—	2	2	no	—
79	C₄⋊C₈×C₁₃₁	—	2	2	no	—
80	C₄⋊C₈×C₁₃₁	—	4	2	no	—
81	#103×C₁₃₁	—	2	2	no	—
82	#103×C₁₃₁	—	2	4	no	—
83	#103×C₁₃₁	—	2	4	no	—
84	#103×C₁₃₁	—	4	2	no	—
85	#102×C₁₃₁	—	2	2	no	—
86	#102×C₁₃₁	—	4	2	no	—
87	#97×C₁₃₁	—	2	2	no	—
88	#95×C₁₃₁	—	2	2	no	—
89	#95×C₁₃₁	—	2	2	no	—
90	#95×C₁₃₁	—	2	2	no	—
91	#95×C₁₃₁	—	2	2	no	—
92	#95×C₁₃₁	—	2	1	no	—
93	#95×C₁₃₁	—	2	2	no	—
94	#95×C₁₃₁	—	2	1	no	—
95	#95×C₁₃₁	D₄	1	1	yes	characteristic
96	#95×C₁₃₁	D₄	1	1	yes	characteristic
97	C₂⁴×C₁₃₁	—	2	1	no	—
98	C₂×Q₈×C₁₃₁	—	2	1	no	—
99	C₂×Q₈×C₁₃₁	—	2	2	no	—
100	C₂×Q₈×C₁₃₁	—	2	1	no	—
101	C₂×Q₈×C₁₃₁	—	2	1	no	—
102	C₂×Q₈×C₁₃₁	—	2	2	no	—
103	C₂×Q₈×C₁₃₁	—	2	2	no	—
104	C₂×Q₈×C₁₃₁	—	2	2	no	—
105	C₂×Q₈×C₁₃₁	—	2	1	no	—
106	C₂×Q₈×C₁₃₁	—	2	1	no	—
107	C₂×Q₈×C₁₃₁	—	2	2	no	—
108	C₂×Q₈×C₁₃₁	—	2	2	no	—
109	C₂×Q₈×C₁₃₁	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃₁	—	2	1	no	—
111	C₂×D₄×C₁₃₁	—	2	1	no	—
112	C₂×D₄×C₁₃₁	—	2	1	no	—
113	C₂×D₄×C₁₃₁	—	2	1	no	—
114	C₂×D₄×C₁₃₁	—	2	1	no	—
115	C₂×D₄×C₁₃₁	#41	1	2	yes	—
116	C₂²×C₄×C₁₃₁	—	2	1	no	—
117	C₂²×C₄×C₁₃₁	—	2	1	no	—
118	C₂²×C₄×C₁₃₁	—	2	2	no	—
119	C₂²×C₄×C₁₃₁	—	2	1	no	—
120	C₂²×C₄×C₁₃₁	—	2	2	no	—
121	C₂²×C₄×C₁₃₁	—	4	4	no	—
122	C₂²×C₄×C₁₃₁	—	4	2	no	—
123	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
128	Q₁₆×C₁₃₁	—	4	8	no	—
129	SD₁₆×C₁₃₁	—	2	8	no	—
130	C₂×C₈×C₁₃₁	—	2	1	no	—
131	C₂×C₈×C₁₃₁	—	2	1	no	—
132	C₂×C₈×C₁₃₁	—	2	1	no	—
133	C₂×C₈×C₁₃₁	—	2	2	no	—
134	C₂×C₈×C₁₃₁	—	2	2	no	—
135	C₂×C₈×C₁₃₁	—	2	1	no	—
136	C₂×C₈×C₁₃₁	—	2	1	no	—
137	C₂×C₈×C₁₃₁	—	2	2	no	—
138	C₂×C₈×C₁₃₁	#41	1	2	yes	—
139	C₄⋊C₄×C₁₃₁	—	2	4	no	—
140	C₄⋊C₄×C₁₃₁	—	2	1	no	—
141	C₄⋊C₄×C₁₃₁	—	2	1	no	—
142	C₄⋊C₄×C₁₃₁	—	2	2	no	—
143	C₄⋊C₄×C₁₃₁	—	2	1	no	—
144	C₄⋊C₄×C₁₃₁	—	2	2	no	—
145	C₄⋊C₄×C₁₃₁	—	4	2	no	—
146	C₄⋊C₄×C₁₃₁	—	4	2	no	—
147	C₄⋊C₄×C₁₃₁	—	4	2	no	—
148	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
150	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
151	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
152	C₄²×C₁₃₁	—	2	4	no	—
153	C₄²×C₁₃₁	—	2	2	no	—
154	C₄²×C₁₃₁	—	2	2	no	—
155	C₄²×C₁₃₁	—	4	4	no	—
156	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃₁	#41	1	2	yes	—
158	C₂³×C₁₃₁	—	2	2	no	—
159	C₂³×C₁₃₁	—	4	1	no	—
160	C₂³×C₁₃₁	—	4	1	no	—
161	C₂³×C₁₃₁	—	4	2	no	—
162	C₂³×C₁₃₁	—	4	2	no	—
163	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃₁	—	2	2	no	—
165	Q₈×C₁₃₁	—	2	2	no	—
166	Q₈×C₁₃₁	—	4	1	no	—
167	Q₈×C₁₃₁	—	4	1	no	—
168	Q₈×C₁₃₁	—	4	2	no	—
169	Q₈×C₁₃₁	—	4	2	no	—
170	Q₈×C₁₃₁	—	4	2	no	—
171	Q₈×C₁₃₁	—	4	2	no	—
172	D₄×C₁₃₁	—	2	2	no	—
173	D₄×C₁₃₁	—	2	2	no	—
174	D₄×C₁₃₁	—	4	1	no	—
175	D₄×C₁₃₁	—	4	1	no	—
176	C₂×C₄×C₁₃₁	—	2	2	no	—
177	C₂×C₄×C₁₃₁	—	2	2	no	—
178	C₂×C₄×C₁₃₁	—	2	2	no	—
179	C₂×C₄×C₁₃₁	—	2	2	no	—
180	C₂×C₄×C₁₃₁	—	2	2	no	—
181	C₂×C₄×C₁₃₁	—	2	2	no	—
182	C₂×C₄×C₁₃₁	—	2	2	no	—
183	C₂×C₄×C₁₃₁	—	2	2	no	—
184	C₂×C₄×C₁₃₁	—	2	2	no	—
185	C₂×C₄×C₁₃₁	—	2	2	no	—
186	C₂×C₄×C₁₃₁	—	4	1	no	—
187	C₂×C₄×C₁₃₁	—	4	1	no	—
188	C₂×C₄×C₁₃₁	—	4	2	no	—
189	C₂×C₄×C₁₃₁	—	4	1	no	—
190	C₂×C₄×C₁₃₁	—	4	2	no	—
191	C₂×C₄×C₁₃₁	—	4	2	no	—
192	C₂×C₄×C₁₃₁	—	4	2	no	—
193	C₂×C₄×C₁₃₁	—	4	2	no	—
194	C₂×C₄×C₁₃₁	—	4	2	no	—
195	C₂×C₄×C₁₃₁	—	4	2	no	—
196	C₂×C₄×C₁₃₁	—	4	2	no	—
197	C₂×C₄×C₁₃₁	—	8	4	no	—
198	C₂×C₄×C₁₃₁	#121	1	2	yes	—
199	C₂×C₄×C₁₃₁	#121	1	2	yes	—
200	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
206	C₈×C₁₃₁	—	2	2	no	—
207	C₈×C₁₃₁	—	4	1	no	—
208	C₈×C₁₃₁	—	4	2	no	—
209	C₂²×C₁₃₁	—	4	2	no	—
210	C₂²×C₁₃₁	—	4	4	no	—
211	C₂²×C₁₃₁	—	8	2	no	—
212	C₂²×C₁₃₁	—	8	1	no	—
213	C₂²×C₁₃₁	—	8	1	no	—
214	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
215	C₂²×C₁₃₁	#546	1	1	yes	characteristic
216	C₂²×C₁₃₁	#550	1	1	yes	characteristic
217	C₂²×C₁₃₁	#575	1	2	yes	—
218	C₂²×C₁₃₁	#578	1	2	yes	—
219	C₄×C₁₃₁	—	2	2	no	—
220	C₄×C₁₃₁	—	2	2	no	—
221	C₄×C₁₃₁	—	4	2	no	—
222	C₄×C₁₃₁	—	4	2	no	—
223	C₄×C₁₃₁	—	4	2	no	—
224	C₄×C₁₃₁	—	4	2	no	—
225	C₄×C₁₃₁	—	8	2	no	—
226	C₄×C₁₃₁	—	8	2	no	—
227	C₄×C₁₃₁	—	8	1	no	—
228	C₄×C₁₃₁	#525	1	1	yes	characteristic
229	C₄×C₁₃₁	#535	1	1	yes	characteristic
230	C₄×C₁₃₁	#553	1	1	yes	characteristic
231	C₄×C₁₃₁	#555	1	1	yes	characteristic
232	C₂×C₁₃₁	—	8	2	no	—
233	C₂×C₁₃₁	#2414	1	1	yes	characteristic
234	C₂×C₁₃₁	#3040	1	1	yes	characteristic
235	C₂×C₁₃₁	#3044	1	1	yes	characteristic
236	C₂×C₁₃₁	#3315	1	2	yes	—
237	C₂×C₁₃₁	#3402	1	2	yes	—
238	#24645	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₃₁	#24645	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×#462	C₂×C₁₃₁	1	1	yes	characteristic, complemented
241	C₂×#440	C₂×C₁₃₁	1	1	yes	characteristic
242	#2547	C₂×C₁₃₁	1	1	yes	characteristic
243	#2356	C₂×C₁₃₁	1	1	yes	characteristic, complemented
244	#2056	C₂×C₁₃₁	1	2	yes	complemented
245	#2015	C₂×C₁₃₁	1	2	yes	—
246	#1983	C₂×C₁₃₁	1	2	yes	—
247	#1960	C₂×C₁₃₁	1	1	yes	characteristic, complemented
248	#1940	C₂×C₁₃₁	1	1	yes	characteristic, complemented
249	#1928	C₂×C₁₃₁	1	2	yes	complemented
250	#1804	C₂×C₁₃₁	1	1	yes	characteristic
251	C₂²×Q₁₆	C₂²×C₁₃₁	1	2	yes	—
252	C₂²×SD₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
254	C₂×#124	C₂²×C₁₃₁	1	2	yes	—
255	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
257	#462	—	2	4	no	—
258	#440	—	2	4	no	—
259	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
262	C₂×#103	C₂²×C₁₃₁	1	1	yes	characteristic
263	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
264	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
265	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
266	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
267	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
268	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
269	#397	—	2	1	no	—
270	#397	—	2	1	no	—
271	#391	C₂²×C₁₃₁	1	2	yes	—
272	#391	C₂²×C₁₃₁	1	2	yes	—
273	#387	—	2	2	no	—
274	#383	—	2	1	no	—
275	#382	C₂²×C₁₃₁	1	1	yes	characteristic
276	#380	—	2	2	no	—
277	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
278	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
279	#376	—	2	1	no	—
280	#340	C₂²×C₁₃₁	1	2	yes	—
281	#336	C₂²×C₁₃₁	1	2	yes	—
282	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
283	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×Q₁₆	—	2	4	no	—
287	C₂×Q₁₆	—	4	2	no	—
288	C₂×Q₁₆	—	4	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	#124	—	2	4	no	—
298	#124	—	4	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	D₄×C₁₃₁	1	4	yes	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	D₄×C₁₃₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
317	#107	—	2	2	no	—
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	4	2	no	—
320	#103	—	2	2	no	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	—	4	2	no	—
324	#102	—	2	2	no	—
325	#102	—	4	2	no	—
326	#97	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	1	no	—
333	#95	—	2	2	no	—
334	#95	D₄×C₁₃₁	1	1	yes	characteristic
335	#95	D₄×C₁₃₁	1	1	yes	characteristic
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	C₂×D₄×C₁₃₁	1	2	yes	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	#41×C₁₃₁	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
367	Q₁₆	—	4	8	no	—
368	SD₁₆	—	2	8	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	#41×C₁₃₁	1	2	yes	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₄²	—	2	4	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	4	4	no	—
395	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
396	C₄²	#41×C₁₃₁	1	2	yes	—
397	C₂³	—	2	2	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	4	no	—
437	C₂×C₄	#121×C₁₃₁	1	2	yes	—
438	C₂×C₄	#121×C₁₃₁	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
443	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
444	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	1	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	2	no	—
453	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
454	C₂²	#546×C₁₃₁	1	1	yes	characteristic
455	C₂²	#550×C₁₃₁	1	1	yes	characteristic
456	C₂²	#575×C₁₃₁	1	2	yes	—
457	C₂²	#578×C₁₃₁	1	2	yes	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	2	no	—
467	C₄	#525×C₁₃₁	1	1	yes	characteristic
468	C₄	#535×C₁₃₁	1	1	yes	characteristic
469	C₄	#553×C₁₃₁	1	1	yes	characteristic
470	C₄	#555×C₁₃₁	1	1	yes	characteristic
471	C₂	—	8	2	no	—
472	C₂	#2414×C₁₃₁	1	1	yes	characteristic
473	C₂	#3040×C₁₃₁	1	1	yes	characteristic
474	C₂	#3044×C₁₃₁	1	1	yes	characteristic
475	C₂	#3315×C₁₃₁	1	2	yes	—
476	C₂	#3402×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄×C₄⋊C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#462×C₁₃₁	C₂	semidirect
4. #2356×C₁₃₁	C₂	semidirect
5. #2056×C₁₃₁	C₂	semidirect
8. #1960×C₁₃₁	C₂	semidirect
9. #1940×C₁₃₁	C₂	semidirect
10. #1928×C₁₃₁	C₂	semidirect
238. #24645	C₁₃₁	direct (N × H)
239. C₁₃₁	#24645	direct (N × H)
240. C₂×#462	C₂×C₁₃₁	semidirect
243. #2356	C₂×C₁₃₁	semidirect
244. #2056	C₂×C₁₃₁	semidirect
247. #1960	C₂×C₁₃₁	semidirect
248. #1940	C₂×C₁₃₁	semidirect
249. #1928	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#462×C₁₃₁	2
C₂×#440×C₁₃₁	2
#2547×C₁₃₁	2
#2356×C₁₃₁	2
#2056×C₁₃₁	2
#2015×C₁₃₁	2
#1983×C₁₃₁	2
#1960×C₁₃₁	2
#1940×C₁₃₁	2
#1928×C₁₃₁	2
#1804×C₁₃₁	2
#24645	131

Subgroups — C131×#24645 #45710529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#24645 #45710529