Subgroups — C₁₃₁×#22457 #45708341

Order 33536.

1294 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2950×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2884×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1976×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1905×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	#1812×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1796×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1757×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×2₋¹⁺⁴×C₁₃₁	C₂²	1	2	yes	—
10	#578×C₁₃₁	—	2	4	no	—
11	#578×C₁₃₁	—	2	4	no	—
12	C₂×#137×C₁₃₁	C₄	1	4	yes	complemented
13	C₂×#137×C₁₃₁	C₂²	1	2	yes	—
14	C₂×#135×C₁₃₁	C₄	1	2	yes	complemented
15	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂²×Q₁₆×C₁₃₁	C₄	1	2	yes	complemented
17	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
19	#519×C₁₃₁	C₂²	1	4	yes	—
20	#441×C₁₃₁	—	2	4	no	—
21	C₄×Q₁₆×C₁₃₁	—	2	4	no	—
22	#427×C₁₃₁	C₂²	1	2	yes	—
23	#421×C₁₃₁	C₂²	1	4	yes	—
24	#419×C₁₃₁	C₂²	1	4	yes	—
25	#413×C₁₃₁	C₂²	1	1	yes	characteristic
26	#410×C₁₃₁	—	2	8	no	—
27	#410×C₁₃₁	C₂²	1	4	yes	—
28	#410×C₁₃₁	C₂²	1	2	yes	—
29	#410×C₁₃₁	C₂²	1	1	yes	characteristic
30	#405×C₁₃₁	C₂²	1	2	yes	—
31	#344×C₁₃₁	C₂²	1	2	yes	—
32	H(3,ℤ/4)×C₁₃₁	C₂²	1	2	yes	—
33	2₋¹⁺⁴×C₁₃₁	—	2	8	no	—
34	2₋¹⁺⁴×C₁₃₁	—	4	4	no	—
35	C₂×#41×C₁₃₁	—	2	4	no	—
36	C₂×#41×C₁₃₁	—	2	2	no	—
37	C₂×#41×C₁₃₁	C₂×C₄	1	4	yes	—
38	C₂×#41×C₁₃₁	C₂³	1	2	yes	—
39	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃₁	—	2	2	no	—
41	C₂²×Q₈×C₁₃₁	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
43	#137×C₁₃₁	—	2	8	no	—
44	#137×C₁₃₁	—	2	16	no	—
45	#135×C₁₃₁	—	2	4	no	—
46	#135×C₁₃₁	—	2	4	no	—
47	#135×C₁₃₁	—	2	2	no	—
48	#135×C₁₃₁	—	2	2	no	—
49	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
50	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
51	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
53	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
54	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
55	C₂×Q₁₆×C₁₃₁	D₄	1	4	yes	—
56	C₂×Q₁₆×C₁₃₁	D₄	1	4	yes	—
57	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
58	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
59	C₂×D₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
60	#131×C₁₃₁	—	2	2	no	—
61	#131×C₁₃₁	—	2	2	no	—
62	C₂×M₁₆×C₁₃₁	C₂×C₄	1	2	yes	—
63	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
64	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₄×Q₈×C₁₃₁	—	2	8	no	—
68	C₄×Q₈×C₁₃₁	—	4	4	no	—
69	#117×C₁₃₁	—	2	8	no	—
70	#117×C₁₃₁	C₂³	1	4	yes	—
71	#117×C₁₃₁	C₂³	1	2	yes	—
72	#107×C₁₃₁	—	2	2	no	—
73	#106×C₁₃₁	—	2	2	no	—
74	#104×C₁₃₁	—	4	4	no	—
75	#103×C₁₃₁	—	2	8	no	—
76	#101×C₁₃₁	—	2	1	no	—
77	#100×C₁₃₁	—	2	1	no	—
78	#99×C₁₃₁	—	2	4	no	—
79	#99×C₁₃₁	—	2	8	no	—
80	#99×C₁₃₁	D₄	1	4	yes	—
81	#97×C₁₃₁	—	2	2	no	—
82	C₄×C₈×C₁₃₁	—	2	2	no	—
83	#41×C₁₃₁	—	2	2	no	—
84	#41×C₁₃₁	—	2	2	no	—
85	#41×C₁₃₁	—	2	8	no	—
86	#41×C₁₃₁	—	2	4	no	—
87	#41×C₁₃₁	—	2	4	no	—
88	#41×C₁₃₁	—	4	4	no	—
89	#41×C₁₃₁	—	4	16	no	—
90	#41×C₁₃₁	—	4	8	no	—
91	C₂×Q₈×C₁₃₁	—	2	4	no	—
92	C₂×Q₈×C₁₃₁	—	2	2	no	—
93	C₂×Q₈×C₁₃₁	—	2	4	no	—
94	C₂×Q₈×C₁₃₁	—	2	8	no	—
95	C₂×Q₈×C₁₃₁	—	4	4	no	—
96	C₂×Q₈×C₁₃₁	—	4	8	no	—
97	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
99	C₂×Q₈×C₁₃₁	C₂×D₄	1	8	yes	—
100	C₂×Q₈×C₁₃₁	#41	1	1	yes	characteristic
101	C₂×D₄×C₁₃₁	—	2	4	no	—
102	C₂×D₄×C₁₃₁	—	2	2	no	—
103	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
104	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₁₃₁	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₁	—	2	2	no	—
107	C₂²×C₄×C₁₃₁	—	2	4	no	—
108	C₂²×C₄×C₁₃₁	—	2	4	no	—
109	C₂²×C₄×C₁₃₁	—	2	2	no	—
110	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₁₃₁	—	2	8	no	—
113	Q₁₆×C₁₃₁	—	2	1	no	—
114	Q₁₆×C₁₃₁	—	2	1	no	—
115	Q₁₆×C₁₃₁	C₂²⋊C₄	1	4	yes	—
116	Q₁₆×C₁₃₁	C₂²⋊C₄	1	4	yes	—
117	Q₁₆×C₁₃₁	C₂²⋊C₄	1	8	yes	—
118	SD₁₆×C₁₃₁	—	2	8	no	—
119	SD₁₆×C₁₃₁	—	2	4	no	—
120	D₈×C₁₃₁	—	2	1	no	—
121	D₈×C₁₃₁	—	2	1	no	—
122	M₁₆×C₁₃₁	—	2	2	no	—
123	M₁₆×C₁₃₁	—	2	4	no	—
124	M₁₆×C₁₃₁	—	2	2	no	—
125	M₁₆×C₁₃₁	—	2	2	no	—
126	C₂×C₈×C₁₃₁	—	2	2	no	—
127	C₂×C₈×C₁₃₁	—	2	2	no	—
128	C₂×C₈×C₁₃₁	—	2	2	no	—
129	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₁₃₁	—	2	2	no	—
135	C₄⋊C₄×C₁₃₁	—	2	4	no	—
136	C₄⋊C₄×C₁₃₁	—	4	8	no	—
137	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
138	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
139	C₄²×C₁₃₁	—	2	2	no	—
140	C₄²×C₁₃₁	—	2	4	no	—
141	C₄²×C₁₃₁	—	4	8	no	—
142	C₂³×C₁₃₁	—	2	2	no	—
143	C₂³×C₁₃₁	C₄×D₄	1	2	yes	—
144	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₃₁	—	2	4	no	—
146	Q₈×C₁₃₁	—	2	8	no	—
147	Q₈×C₁₃₁	—	2	2	no	—
148	Q₈×C₁₃₁	—	2	2	no	—
149	Q₈×C₁₃₁	—	2	2	no	—
150	Q₈×C₁₃₁	—	4	8	no	—
151	Q₈×C₁₃₁	C₂×C₂²⋊C₄	1	8	yes	—
152	D₄×C₁₃₁	—	2	4	no	—
153	D₄×C₁₃₁	—	2	2	no	—
154	D₄×C₁₃₁	—	2	2	no	—
155	D₄×C₁₃₁	—	2	2	no	—
156	D₄×C₁₃₁	—	4	8	no	—
157	D₄×C₁₃₁	—	4	4	no	—
158	C₂×C₄×C₁₃₁	—	2	4	no	—
159	C₂×C₄×C₁₃₁	—	2	8	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	4	no	—
164	C₂×C₄×C₁₃₁	—	4	8	no	—
165	C₂×C₄×C₁₃₁	—	4	8	no	—
166	C₂×C₄×C₁₃₁	—	4	4	no	—
167	C₂×C₄×C₁₃₁	—	4	4	no	—
168	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
173	C₈×C₁₃₁	—	2	2	no	—
174	C₈×C₁₃₁	—	4	2	no	—
175	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂²×C₁₃₁	—	2	2	no	—
179	C₂²×C₁₃₁	—	4	1	no	—
180	C₂²×C₁₃₁	—	4	2	no	—
181	C₂²×C₁₃₁	—	4	2	no	—
182	C₂²×C₁₃₁	—	8	2	no	—
183	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₁₃₁	D₄²	1	2	yes	—
185	C₄×C₁₃₁	—	2	8	no	—
186	C₄×C₁₃₁	—	2	2	no	—
187	C₄×C₁₃₁	—	4	4	no	—
188	C₄×C₁₃₁	—	4	2	no	—
189	C₄×C₁₃₁	—	8	4	no	—
190	C₄×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₄×C₁₃₁	#518	1	1	yes	characteristic
192	C₄×C₁₃₁	#546	1	2	yes	—
193	C₂×C₁₃₁	—	2	2	no	—
194	C₂×C₁₃₁	—	2	1	no	—
195	C₂×C₁₃₁	—	4	2	no	—
196	C₂×C₁₃₁	—	8	2	no	—
197	C₂×C₁₃₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
198	#22457	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₁	#22457	1	1	yes	characteristic, direct product factor, Sylow
200	C₂×#578	C₂×C₁₃₁	1	1	yes	characteristic
201	#2950	C₂×C₁₃₁	1	2	yes	complemented
202	#2884	C₂×C₁₃₁	1	2	yes	complemented
203	#1976	C₂×C₁₃₁	1	2	yes	complemented
204	#1905	C₂×C₁₃₁	1	4	yes	complemented
205	#1812	C₂×C₁₃₁	1	1	yes	characteristic, complemented
206	#1796	C₂×C₁₃₁	1	2	yes	complemented
207	#1757	C₂×C₁₃₁	1	1	yes	characteristic, complemented
208	C₂×2₋¹⁺⁴	C₂²×C₁₃₁	1	2	yes	—
209	#578	—	2	4	no	—
210	#578	—	2	4	no	—
211	C₂×#137	C₄×C₁₃₁	1	4	yes	complemented
212	C₂×#137	C₂²×C₁₃₁	1	2	yes	—
213	C₂×#135	C₄×C₁₃₁	1	2	yes	complemented
214	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂²×Q₁₆	C₄×C₁₃₁	1	2	yes	complemented
216	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
218	#519	C₂²×C₁₃₁	1	4	yes	—
219	#441	—	2	4	no	—
220	C₄×Q₁₆	—	2	4	no	—
221	#427	C₂²×C₁₃₁	1	2	yes	—
222	#421	C₂²×C₁₃₁	1	4	yes	—
223	#419	C₂²×C₁₃₁	1	4	yes	—
224	#413	C₂²×C₁₃₁	1	1	yes	characteristic
225	#410	—	2	8	no	—
226	#410	C₂²×C₁₃₁	1	2	yes	—
227	#410	C₂²×C₁₃₁	1	4	yes	—
228	#410	C₂²×C₁₃₁	1	1	yes	characteristic
229	#405	C₂²×C₁₃₁	1	2	yes	—
230	#344	C₂²×C₁₃₁	1	2	yes	—
231	H(3,ℤ/4)	C₂²×C₁₃₁	1	2	yes	—
232	2₋¹⁺⁴	—	2	8	no	—
233	2₋¹⁺⁴	—	4	4	no	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	C₂×C₄×C₁₃₁	1	4	yes	—
237	C₂×#41	C₂³×C₁₃₁	1	2	yes	—
238	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	C₂×C₄×C₁₃₁	1	4	yes	—
241	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
242	#137	—	2	8	no	—
243	#137	—	2	16	no	—
244	#135	—	2	4	no	—
245	#135	—	2	4	no	—
246	#135	—	2	2	no	—
247	#135	—	2	2	no	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×Q₁₆	—	2	4	no	—
250	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
251	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
252	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
253	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
254	C₂×Q₁₆	D₄×C₁₃₁	1	4	yes	—
255	C₂×Q₁₆	D₄×C₁₃₁	1	4	yes	—
256	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
257	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
258	C₂×D₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
259	#131	—	2	2	no	—
260	#131	—	2	2	no	—
261	C₂×M₁₆	C₂×C₄×C₁₃₁	1	2	yes	—
262	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
263	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
264	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
266	C₄×Q₈	—	2	8	no	—
267	C₄×Q₈	—	4	4	no	—
268	#117	—	2	8	no	—
269	#117	C₂³×C₁₃₁	1	4	yes	—
270	#117	C₂³×C₁₃₁	1	2	yes	—
271	#107	—	2	2	no	—
272	#106	—	2	2	no	—
273	#104	—	4	4	no	—
274	#103	—	2	8	no	—
275	#101	—	2	1	no	—
276	#100	—	2	1	no	—
277	#99	—	2	4	no	—
278	#99	—	2	8	no	—
279	#99	D₄×C₁₃₁	1	4	yes	—
280	#97	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	8	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	4	4	no	—
288	#41	—	4	16	no	—
289	#41	—	4	8	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	8	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	8	no	—
296	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
297	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
298	C₂×Q₈	C₂×D₄×C₁₃₁	1	8	yes	—
299	C₂×Q₈	#41×C₁₃₁	1	1	yes	characteristic
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
303	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
304	C₂×D₄	#41×C₁₃₁	1	1	yes	characteristic
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
311	Q₁₆	—	2	8	no	—
312	Q₁₆	—	2	1	no	—
313	Q₁₆	—	2	1	no	—
314	Q₁₆	C₂²⋊C₄×C₁₃₁	1	4	yes	—
315	Q₁₆	C₂²⋊C₄×C₁₃₁	1	4	yes	—
316	Q₁₆	C₂²⋊C₄×C₁₃₁	1	8	yes	—
317	SD₁₆	—	2	8	no	—
318	SD₁₆	—	2	4	no	—
319	D₈	—	2	1	no	—
320	D₈	—	2	1	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
330	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	4	8	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	4	8	no	—
341	C₂³	—	2	2	no	—
342	C₂³	C₄×D₄×C₁₃₁	1	2	yes	—
343	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	2	8	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	8	no	—
350	Q₈	C₂×C₂²⋊C₄×C₁₃₁	1	8	yes	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
368	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
370	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
371	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
375	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
376	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
383	C₂²	D₄²×C₁₃₁	1	2	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	4	no	—
389	C₄	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
390	C₄	#518×C₁₃₁	1	1	yes	characteristic
391	C₄	#546×C₁₃₁	1	2	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	2	1	no	—
394	C₂	—	4	2	no	—
395	C₂	—	8	2	no	—
396	C₂	D₄×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₁	D₄×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#578×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2950×C₁₃₁	C₂	semidirect
3. #2884×C₁₃₁	C₂	semidirect
4. #1976×C₁₃₁	C₂	semidirect
5. #1905×C₁₃₁	C₂	semidirect
6. #1812×C₁₃₁	C₂	semidirect
7. #1796×C₁₃₁	C₂	semidirect
8. #1757×C₁₃₁	C₂	semidirect
12. C₂×#137×C₁₃₁	C₄	semidirect
14. C₂×#135×C₁₃₁	C₄	semidirect
16. C₂²×Q₁₆×C₁₃₁	C₄	semidirect
198. #22457	C₁₃₁	direct (N × H)
199. C₁₃₁	#22457	direct (N × H)
201. #2950	C₂×C₁₃₁	semidirect
202. #2884	C₂×C₁₃₁	semidirect
203. #1976	C₂×C₁₃₁	semidirect
204. #1905	C₂×C₁₃₁	semidirect
205. #1812	C₂×C₁₃₁	semidirect
206. #1796	C₂×C₁₃₁	semidirect
207. #1757	C₂×C₁₃₁	semidirect
211. C₂×#137	C₄×C₁₃₁	semidirect
213. C₂×#135	C₄×C₁₃₁	semidirect
215. C₂²×Q₁₆	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₁₃₁	2
#2950×C₁₃₁	2
#2884×C₁₃₁	2
#1976×C₁₃₁	2
#1905×C₁₃₁	2
#1812×C₁₃₁	2
#1796×C₁₃₁	2
#1757×C₁₃₁	2
#22457	131

Subgroups — C131×#22457 #45708341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22457 #45708341