Subgroups — C₁₃₁×#26080 #45711964

Order 33536.

674 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3163×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3083×C₁₃₁	C₂	1	2	yes	maximal
3	#2912×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2089×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2061×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1951×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1945×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1860×C₁₃₁	C₂	1	2	yes	maximal
9	#1846×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1815×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	#1764×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
13	#544×C₁₃₁	C₂²	1	2	yes	—
14	#520×C₁₃₁	C₂²	1	2	yes	—
15	#501×C₁₃₁	—	2	2	no	—
16	#499×C₁₃₁	—	2	1	no	—
17	#498×C₁₃₁	—	2	1	no	—
18	#479×C₁₃₁	—	2	2	no	—
19	#478×C₁₃₁	—	2	2	no	—
20	#477×C₁₃₁	—	2	2	no	—
21	#474×C₁₃₁	—	2	2	no	—
22	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
23	#428×C₁₃₁	—	2	2	no	—
24	#428×C₁₃₁	C₂²	1	2	yes	—
25	#428×C₁₃₁	C₂²	1	2	yes	—
26	#428×C₁₃₁	C₂²	1	2	yes	—
27	#427×C₁₃₁	—	2	1	no	—
28	#427×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#106×C₁₃₁	—	2	1	no	—
31	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×#106×C₁₃₁	C₂²	1	1	yes	characteristic
33	#424×C₁₃₁	C₂²	1	2	yes	—
34	C₂×#104×C₁₃₁	C₂²	1	1	yes	characteristic
35	#417×C₁₃₁	C₂²	1	2	yes	—
36	#416×C₁₃₁	C₂²	1	1	yes	characteristic
37	#405×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
39	#382×C₁₃₁	C₂²	1	2	yes	—
40	#343×C₁₃₁	C₂²	1	2	yes	—
41	#343×C₁₃₁	C₂²	1	2	yes	—
42	#341×C₁₃₁	C₂²	1	1	yes	characteristic
43	#339×C₁₃₁	C₂²	1	1	yes	characteristic
44	#339×C₁₃₁	C₂²	1	2	yes	—
45	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
46	#131×C₁₃₁	—	2	2	no	—
47	#131×C₁₃₁	Q₈	1	4	yes	complemented
48	C₂×M₁₆×C₁₃₁	—	2	1	no	—
49	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
50	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	—	2	1	no	—
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
56	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
57	#125×C₁₃₁	—	2	2	no	—
58	#125×C₁₃₁	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₁	—	4	2	no	—
60	C₄×Q₈×C₁₃₁	—	2	2	no	—
61	C₄×D₄×C₁₃₁	—	2	2	no	—
62	C₄×D₄×C₁₃₁	—	4	2	no	—
63	#117×C₁₃₁	—	2	2	no	—
64	#117×C₁₃₁	C₂³	1	1	yes	characteristic
65	#117×C₁₃₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
70	#108×C₁₃₁	—	2	2	no	—
71	#107×C₁₃₁	—	2	2	no	—
72	#107×C₁₃₁	—	2	2	no	—
73	#107×C₁₃₁	—	2	2	no	—
74	#107×C₁₃₁	—	2	2	no	—
75	#107×C₁₃₁	—	2	2	no	—
76	#107×C₁₃₁	D₄	1	2	yes	—
77	#106×C₁₃₁	—	2	1	no	—
78	#106×C₁₃₁	—	2	1	no	—
79	#106×C₁₃₁	—	2	1	no	—
80	#106×C₁₃₁	—	2	1	no	—
81	#106×C₁₃₁	—	2	2	no	—
82	#106×C₁₃₁	—	2	2	no	—
83	#106×C₁₃₁	—	2	2	no	—
84	#106×C₁₃₁	D₄	1	1	yes	characteristic
85	#106×C₁₃₁	D₄	1	1	yes	characteristic
86	C₄⋊C₈×C₁₃₁	—	2	2	no	—
87	C₄⋊C₈×C₁₃₁	—	2	2	no	—
88	#104×C₁₃₁	Q₈	1	4	yes	complemented
89	#103×C₁₃₁	—	2	2	no	—
90	#103×C₁₃₁	D₄	1	2	yes	—
91	#102×C₁₃₁	—	2	2	no	—
92	#102×C₁₃₁	D₄	1	2	yes	—
93	#97×C₁₃₁	—	2	1	no	—
94	C₄×C₈×C₁₃₁	—	2	1	no	—
95	C₄×C₈×C₁₃₁	—	2	2	no	—
96	#95×C₁₃₁	—	4	2	no	—
97	#41×C₁₃₁	—	2	1	no	—
98	#41×C₁₃₁	—	2	1	no	—
99	#41×C₁₃₁	C₂×Q₈	1	2	yes	—
100	#41×C₁₃₁	C₂×Q₈	1	2	yes	—
101	C₂×Q₈×C₁₃₁	—	4	2	no	—
102	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₁₃₁	—	2	1	no	—
104	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₁	—	2	1	no	—
106	C₂²×C₄×C₁₃₁	—	2	1	no	—
107	C₂²×C₄×C₁₃₁	—	2	2	no	—
108	C₂²×C₄×C₁₃₁	—	2	2	no	—
109	C₂²×C₄×C₁₃₁	—	4	2	no	—
110	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₃₁	—	2	1	no	—
112	M₁₆×C₁₃₁	—	2	1	no	—
113	M₁₆×C₁₃₁	—	2	4	no	—
114	M₁₆×C₁₃₁	—	2	2	no	—
115	M₁₆×C₁₃₁	—	2	2	no	—
116	M₁₆×C₁₃₁	C₂×Q₈	1	2	yes	—
117	M₁₆×C₁₃₁	C₂×Q₈	1	2	yes	—
118	C₂×C₈×C₁₃₁	—	2	1	no	—
119	C₂×C₈×C₁₃₁	—	2	1	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	—	2	4	no	—
123	C₂×C₈×C₁₃₁	—	2	2	no	—
124	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
128	C₂×C₈×C₁₃₁	#41	1	2	yes	—
129	C₄⋊C₄×C₁₃₁	—	2	2	no	—
130	C₄⋊C₄×C₁₃₁	—	2	2	no	—
131	C₄⋊C₄×C₁₃₁	—	2	2	no	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	4	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	2	no	—
135	C₄⋊C₄×C₁₃₁	—	4	2	no	—
136	C₄⋊C₄×C₁₃₁	—	4	2	no	—
137	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
141	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
142	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
143	C₄²×C₁₃₁	—	2	1	no	—
144	C₄²×C₁₃₁	—	2	2	no	—
145	C₄²×C₁₃₁	—	2	1	no	—
146	C₄²×C₁₃₁	—	4	2	no	—
147	C₄²×C₁₃₁	C₂×Q₈	1	2	yes	—
148	C₂³×C₁₃₁	—	2	1	no	—
149	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
150	Q₈×C₁₃₁	—	2	1	no	—
151	Q₈×C₁₃₁	—	16	2	no	—
152	Q₈×C₁₃₁	C₄⋊Q₈	1	2	yes	—
153	D₄×C₁₃₁	—	2	2	no	—
154	D₄×C₁₃₁	—	2	2	no	—
155	D₄×C₁₃₁	—	2	1	no	—
156	D₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₃₁	—	2	1	no	—
158	C₂×C₄×C₁₃₁	—	2	2	no	—
159	C₂×C₄×C₁₃₁	—	2	2	no	—
160	C₂×C₄×C₁₃₁	—	2	2	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	2	2	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	4	2	no	—
165	C₂×C₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	4	2	no	—
167	C₂×C₄×C₁₃₁	—	8	2	no	—
168	C₂×C₄×C₁₃₁	—	8	2	no	—
169	C₂×C₄×C₁₃₁	—	16	2	no	—
170	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
176	C₈×C₁₃₁	—	2	2	no	—
177	C₈×C₁₃₁	—	2	2	no	—
178	C₈×C₁₃₁	—	2	2	no	—
179	C₈×C₁₃₁	—	4	2	no	—
180	C₈×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
181	C₈×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
182	C₂²×C₁₃₁	—	2	2	no	—
183	C₂²×C₁₃₁	—	2	2	no	—
184	C₂²×C₁₃₁	—	4	2	no	—
185	C₂²×C₁₃₁	#544	1	1	yes	characteristic
186	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
187	C₂²×C₁₃₁	#554	1	1	yes	characteristic
188	C₄×C₁₃₁	—	2	2	no	—
189	C₄×C₁₃₁	—	4	2	no	—
190	C₄×C₁₃₁	—	4	2	no	—
191	C₄×C₁₃₁	—	4	2	no	—
192	C₄×C₁₃₁	—	4	2	no	—
193	C₄×C₁₃₁	—	8	2	no	—
194	C₄×C₁₃₁	—	8	2	no	—
195	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
196	C₄×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
197	C₄×C₁₃₁	#547	1	1	yes	characteristic
198	C₄×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
199	C₂×C₁₃₁	—	2	1	no	—
200	C₂×C₁₃₁	—	2	1	no	—
201	C₂×C₁₃₁	—	4	2	no	—
202	C₂×C₁₃₁	#2440	1	1	yes	characteristic
203	C₂×C₁₃₁	#3290	1	2	yes	—
204	#26080	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₁	#26080	1	1	yes	characteristic, direct product factor, Sylow
206	#3163	C₂×C₁₃₁	1	1	yes	characteristic, complemented
207	#3083	C₂×C₁₃₁	1	2	yes	—
208	#2912	C₂×C₁₃₁	1	1	yes	characteristic
209	#2089	C₂×C₁₃₁	1	2	yes	complemented
210	#2061	C₂×C₁₃₁	1	2	yes	complemented
211	#1951	C₂×C₁₃₁	1	1	yes	characteristic, complemented
212	#1945	C₂×C₁₃₁	1	1	yes	characteristic, complemented
213	#1860	C₂×C₁₃₁	1	2	yes	—
214	#1846	C₂×C₁₃₁	1	1	yes	characteristic, complemented
215	#1815	C₂×C₁₃₁	1	1	yes	characteristic
216	#1764	C₂×C₁₃₁	1	1	yes	characteristic
217	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
218	#544	C₂²×C₁₃₁	1	2	yes	—
219	#520	C₂²×C₁₃₁	1	2	yes	—
220	#501	—	2	2	no	—
221	#499	—	2	1	no	—
222	#498	—	2	1	no	—
223	#479	—	2	2	no	—
224	#478	—	2	2	no	—
225	#477	—	2	2	no	—
226	#474	—	2	2	no	—
227	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
228	#428	—	2	2	no	—
229	#428	C₂²×C₁₃₁	1	2	yes	—
230	#428	C₂²×C₁₃₁	1	2	yes	—
231	#428	C₂²×C₁₃₁	1	2	yes	—
232	#427	—	2	1	no	—
233	#427	C₂²×C₁₃₁	1	1	yes	characteristic
234	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
235	C₂×#106	—	2	1	no	—
236	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
237	C₂×#106	C₂²×C₁₃₁	1	1	yes	characteristic
238	#424	C₂²×C₁₃₁	1	2	yes	—
239	C₂×#104	C₂²×C₁₃₁	1	1	yes	characteristic
240	#417	C₂²×C₁₃₁	1	2	yes	—
241	#416	C₂²×C₁₃₁	1	1	yes	characteristic
242	#405	C₂²×C₁₃₁	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
244	#382	C₂²×C₁₃₁	1	2	yes	—
245	#343	C₂²×C₁₃₁	1	2	yes	—
246	#343	C₂²×C₁₃₁	1	2	yes	—
247	#341	C₂²×C₁₃₁	1	1	yes	characteristic
248	#339	C₂²×C₁₃₁	1	1	yes	characteristic
249	#339	C₂²×C₁₃₁	1	2	yes	—
250	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
251	#131	—	2	2	no	—
252	#131	Q₈×C₁₃₁	1	4	yes	complemented
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
255	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	#125	—	2	2	no	—
263	#125	—	2	2	no	—
264	C₂²⋊Q₈	—	4	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	—	4	2	no	—
268	#117	—	2	2	no	—
269	#117	C₂³×C₁₃₁	1	2	yes	—
270	#117	C₂³×C₁₃₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
274	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
275	#108	—	2	2	no	—
276	#107	—	2	2	no	—
277	#107	—	2	2	no	—
278	#107	—	2	2	no	—
279	#107	—	2	2	no	—
280	#107	—	2	2	no	—
281	#107	D₄×C₁₃₁	1	2	yes	—
282	#106	—	2	1	no	—
283	#106	—	2	1	no	—
284	#106	—	2	1	no	—
285	#106	—	2	1	no	—
286	#106	—	2	2	no	—
287	#106	—	2	2	no	—
288	#106	—	2	2	no	—
289	#106	D₄×C₁₃₁	1	1	yes	characteristic
290	#106	D₄×C₁₃₁	1	1	yes	characteristic
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	#104	Q₈×C₁₃₁	1	4	yes	complemented
294	#103	—	2	2	no	—
295	#103	D₄×C₁₃₁	1	2	yes	—
296	#102	—	2	2	no	—
297	#102	D₄×C₁₃₁	1	2	yes	—
298	#97	—	2	1	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	—	2	2	no	—
301	#95	—	4	2	no	—
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	C₂×Q₈×C₁₃₁	1	2	yes	—
305	#41	C₂×Q₈×C₁₃₁	1	2	yes	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	1	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	C₂×Q₈×C₁₃₁	1	2	yes	—
322	M₁₆	C₂×Q₈×C₁₃₁	1	2	yes	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
332	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
333	C₂×C₈	#41×C₁₃₁	1	2	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
343	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
344	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	2	no	—
352	C₄²	C₂×Q₈×C₁₃₁	1	2	yes	—
353	C₂³	—	2	1	no	—
354	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	16	2	no	—
357	Q₈	C₄⋊Q₈×C₁₃₁	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	16	2	no	—
375	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
380	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	2	no	—
385	C₈	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
386	C₈	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	#544×C₁₃₁	1	1	yes	characteristic
391	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
392	C₂²	#554×C₁₃₁	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
401	C₄	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
402	C₄	#547×C₁₃₁	1	1	yes	characteristic
403	C₄	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	4	2	no	—
407	C₂	#2440×C₁₃₁	1	1	yes	characteristic
408	C₂	#3290×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#41×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3163×C₁₃₁	C₂	semidirect
4. #2089×C₁₃₁	C₂	semidirect
5. #2061×C₁₃₁	C₂	semidirect
6. #1951×C₁₃₁	C₂	semidirect
7. #1945×C₁₃₁	C₂	semidirect
9. #1846×C₁₃₁	C₂	semidirect
47. #131×C₁₃₁	Q₈	semidirect
88. #104×C₁₃₁	Q₈	semidirect
204. #26080	C₁₃₁	direct (N × H)
205. C₁₃₁	#26080	direct (N × H)
206. #3163	C₂×C₁₃₁	semidirect
209. #2089	C₂×C₁₃₁	semidirect
210. #2061	C₂×C₁₃₁	semidirect
211. #1951	C₂×C₁₃₁	semidirect
212. #1945	C₂×C₁₃₁	semidirect
214. #1846	C₂×C₁₃₁	semidirect
252. #131	Q₈×C₁₃₁	semidirect
293. #104	Q₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3163×C₁₃₁	2
#3083×C₁₃₁	2
#2912×C₁₃₁	2
#2089×C₁₃₁	2
#2061×C₁₃₁	2
#1951×C₁₃₁	2
#1945×C₁₃₁	2
#1860×C₁₃₁	2
#1846×C₁₃₁	2
#1815×C₁₃₁	2
#1764×C₁₃₁	2
#26080	131

Subgroups — C131×#26080 #45711964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#26080 #45711964