Subgroups — C₂×#1990×C₁₃₁ #45707200

Order 33536.

1550 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#384×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1990×C₁₃₁	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₃₁	C₂	1	4	yes	maximal
6	C₂³×Q₈×C₁₃₁	—	2	1	no	—
7	C₂³×C₈×C₁₃₁	C₂²	1	2	yes	—
8	C₂×C₄⋊Q₈×C₁₃₁	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₁₃₁	—	2	4	no	—
10	C₂×C₄⋊Q₈×C₁₃₁	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₁₃₁	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₃₁	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₃₁	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃₁	—	2	4	no	—
19	C₂×C₄×C₈×C₁₃₁	C₂²	1	4	yes	—
20	#384×C₁₃₁	—	2	2	no	—
21	#384×C₁₃₁	C₂²	1	4	yes	—
22	#340×C₁₃₁	C₂²	1	16	yes	—
23	C₂²×Q₈×C₁₃₁	—	2	8	no	—
24	C₂²×Q₈×C₁₃₁	—	2	4	no	—
25	C₂²×Q₈×C₁₃₁	—	4	4	no	—
26	C₂²×Q₈×C₁₃₁	—	4	4	no	—
27	C₂³×C₄×C₁₃₁	—	2	2	no	—
28	C₂³×C₄×C₁₃₁	—	2	2	no	—
29	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₁	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₁₃₁	—	2	4	no	—
33	C₂²×C₈×C₁₃₁	—	2	4	no	—
34	C₂²×C₈×C₁₃₁	Q₈	1	8	yes	complemented
35	C₂²×C₈×C₁₃₁	C₂³	1	4	yes	—
36	C₄⋊Q₈×C₁₃₁	—	2	16	no	—
37	C₄⋊Q₈×C₁₃₁	—	2	8	no	—
38	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	16	yes	complemented
39	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
40	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₁	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	4	4	no	—
49	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
52	C₂×C₄²×C₁₃₁	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
54	C₂×C₄²×C₁₃₁	D₄	1	4	yes	—
55	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
56	C₄×C₈×C₁₃₁	—	2	8	no	—
57	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
58	C₂×Q₈×C₁₃₁	—	2	16	no	—
59	C₂×Q₈×C₁₃₁	—	4	32	no	—
60	C₂×Q₈×C₁₃₁	—	4	8	no	—
61	C₂×Q₈×C₁₃₁	—	4	8	no	—
62	C₂²×C₄×C₁₃₁	—	2	8	no	—
63	C₂²×C₄×C₁₃₁	—	2	4	no	—
64	C₂²×C₄×C₁₃₁	—	2	4	no	—
65	C₂²×C₄×C₁₃₁	—	4	4	no	—
66	C₂²×C₄×C₁₃₁	—	4	4	no	—
67	C₂²×C₄×C₁₃₁	—	4	4	no	—
68	C₂²×C₄×C₁₃₁	—	4	4	no	—
69	C₂²×C₄×C₁₃₁	—	4	4	no	—
70	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
71	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	4	yes	—
72	C₂²×C₄×C₁₃₁	D₈	1	4	yes	—
73	C₂²×C₄×C₁₃₁	SD₁₆	1	4	yes	—
74	C₂²×C₄×C₁₃₁	SD₁₆	1	4	yes	—
75	C₂²×C₄×C₁₃₁	Q₁₆	1	4	yes	—
76	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₃₁	C₂×Q₈	1	4	yes	—
82	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
83	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
84	C₂×C₈×C₁₃₁	—	2	16	no	—
85	C₂×C₈×C₁₃₁	—	2	4	no	—
86	C₂×C₈×C₁₃₁	—	2	4	no	—
87	C₂×C₈×C₁₃₁	C₂×Q₈	1	8	yes	complemented
88	C₄⋊C₄×C₁₃₁	—	2	16	no	—
89	C₄⋊C₄×C₁₃₁	—	2	8	no	—
90	C₄⋊C₄×C₁₃₁	—	2	4	no	—
91	C₄⋊C₄×C₁₃₁	—	2	8	no	—
92	C₄⋊C₄×C₁₃₁	—	4	4	no	—
93	C₄⋊C₄×C₁₃₁	—	4	8	no	—
94	C₄⋊C₄×C₁₃₁	—	4	8	no	—
95	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
96	C₄²×C₁₃₁	C₂²⋊C₄	1	8	yes	—
97	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
98	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
99	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
100	C₂³×C₁₃₁	#124	1	2	yes	—
101	C₂³×C₁₃₁	C₄⋊Q₈	1	2	yes	—
102	C₂³×C₁₃₁	C₂×D₈	1	2	yes	—
103	C₂³×C₁₃₁	C₂×SD₁₆	1	2	yes	—
104	C₂³×C₁₃₁	C₂×SD₁₆	1	2	yes	—
105	C₂³×C₁₃₁	C₂×Q₁₆	1	2	yes	—
106	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
107	Q₈×C₁₃₁	—	4	32	no	—
108	C₂×C₄×C₁₃₁	—	2	8	no	—
109	C₂×C₄×C₁₃₁	—	4	4	no	—
110	C₂×C₄×C₁₃₁	—	4	4	no	—
111	C₂×C₄×C₁₃₁	—	4	16	no	—
112	C₂×C₄×C₁₃₁	—	4	4	no	—
113	C₂×C₄×C₁₃₁	—	4	4	no	—
114	C₂×C₄×C₁₃₁	—	4	4	no	—
115	C₂×C₄×C₁₃₁	—	8	8	no	—
116	C₂×C₄×C₁₃₁	#102	1	16	yes	—
117	C₂×C₄×C₁₃₁	#103	1	16	yes	—
118	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
119	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
120	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
121	C₂×C₄×C₁₃₁	C₄×Q₈	1	8	yes	—
122	C₂×C₄×C₁₃₁	C₂²⋊Q₈	1	8	yes	—
123	C₂×C₄×C₁₃₁	#124	1	2	yes	—
124	C₂×C₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
125	C₂×C₄×C₁₃₁	C₂×D₈	1	4	yes	—
126	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	4	yes	—
127	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	4	yes	—
128	C₂×C₄×C₁₃₁	C₂×Q₁₆	1	4	yes	—
129	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₁	C₂²×Q₈	1	2	yes	—
132	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
133	C₈×C₁₃₁	—	2	8	no	—
134	C₂²×C₁₃₁	#391	1	4	yes	—
135	C₂²×C₁₃₁	C₂×#102	1	4	yes	—
136	C₂²×C₁₃₁	C₂×#103	1	4	yes	—
137	C₂²×C₁₃₁	#486	1	4	yes	—
138	C₂²×C₁₃₁	#487	1	4	yes	—
139	C₂²×C₁₃₁	#498	1	4	yes	—
140	C₂²×C₁₃₁	#500	1	4	yes	—
141	C₂²×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
143	C₂²×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
144	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
145	C₂²×C₁₃₁	C₂²×SD₁₆	1	1	yes	characteristic
146	C₂²×C₁₃₁	C₂²×SD₁₆	1	1	yes	characteristic
147	C₂²×C₁₃₁	C₂²×Q₁₆	1	1	yes	characteristic
148	C₄×C₁₃₁	—	4	8	no	—
149	C₄×C₁₃₁	—	8	4	no	—
150	C₄×C₁₃₁	#391	1	4	yes	—
151	C₄×C₁₃₁	C₂×#102	1	8	yes	—
152	C₄×C₁₃₁	C₂×#103	1	8	yes	—
153	C₄×C₁₃₁	C₂×C₄×Q₈	1	2	yes	—
154	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
155	C₂×C₁₃₁	#1990	1	8	yes	direct product factor
156	C₂×C₁₃₁	C₂×#391	1	1	yes	characteristic
157	C₂×C₁₃₁	C₂²×#102	1	1	yes	characteristic
158	C₂×C₁₃₁	C₂²×#103	1	1	yes	characteristic
159	C₂×C₁₃₁	C₂×#486	1	1	yes	characteristic
160	C₂×C₁₃₁	C₂×#487	1	1	yes	characteristic
161	C₂×C₁₃₁	C₂×#498	1	1	yes	characteristic
162	C₂×C₁₃₁	C₂×#500	1	1	yes	characteristic
163	C₂×#1990	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₁₃₁	C₂×#1990	1	1	yes	characteristic, direct product factor, Sylow
165	C₂²×C₄⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic
166	C₂²×C₄×C₈	C₂×C₁₃₁	1	1	yes	characteristic
167	C₂×#384	C₂×C₁₃₁	1	1	yes	characteristic
168	#1990	C₂×C₁₃₁	1	8	yes	direct product factor
169	C₂×#340	C₂×C₁₃₁	1	4	yes	—
170	C₂³×Q₈	—	2	1	no	—
171	C₂³×C₈	C₂²×C₁₃₁	1	2	yes	—
172	C₂×C₄⋊Q₈	—	2	2	no	—
173	C₂×C₄⋊Q₈	—	2	4	no	—
174	C₂×C₄⋊Q₈	C₄×C₁₃₁	1	8	yes	complemented
175	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	4	yes	—
176	C₂²×C₄⋊C₄	—	2	1	no	—
177	C₂²×C₄⋊C₄	—	2	1	no	—
178	C₂²×C₄⋊C₄	—	2	1	no	—
179	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
181	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
182	C₂×C₄×C₈	—	2	4	no	—
183	C₂×C₄×C₈	C₂²×C₁₃₁	1	4	yes	—
184	#384	—	2	2	no	—
185	#384	C₂²×C₁₃₁	1	4	yes	—
186	#340	C₂²×C₁₃₁	1	16	yes	—
187	C₂²×Q₈	—	2	8	no	—
188	C₂²×Q₈	—	2	4	no	—
189	C₂²×Q₈	—	4	4	no	—
190	C₂²×Q₈	—	4	4	no	—
191	C₂³×C₄	—	2	2	no	—
192	C₂³×C₄	—	2	2	no	—
193	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
194	C₂³×C₄	D₄×C₁₃₁	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
196	C₂²×C₈	—	2	4	no	—
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	Q₈×C₁₃₁	1	8	yes	complemented
199	C₂²×C₈	C₂³×C₁₃₁	1	4	yes	—
200	C₄⋊Q₈	—	2	16	no	—
201	C₄⋊Q₈	—	2	8	no	—
202	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	16	yes	complemented
203	C₂×C₄⋊C₄	—	2	8	no	—
204	C₂×C₄⋊C₄	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	8	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	4	4	no	—
212	C₂×C₄⋊C₄	—	4	4	no	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
216	C₂×C₄²	C₂×C₄×C₁₃₁	1	4	yes	—
217	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
218	C₂×C₄²	D₄×C₁₃₁	1	4	yes	—
219	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
220	C₄×C₈	—	2	8	no	—
221	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
222	C₂×Q₈	—	2	16	no	—
223	C₂×Q₈	—	4	32	no	—
224	C₂×Q₈	—	4	8	no	—
225	C₂×Q₈	—	4	8	no	—
226	C₂²×C₄	—	2	8	no	—
227	C₂²×C₄	—	2	4	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	4	4	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	—	4	4	no	—
233	C₂²×C₄	—	4	4	no	—
234	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
235	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	4	yes	—
236	C₂²×C₄	D₈×C₁₃₁	1	4	yes	—
237	C₂²×C₄	SD₁₆×C₁₃₁	1	4	yes	—
238	C₂²×C₄	SD₁₆×C₁₃₁	1	4	yes	—
239	C₂²×C₄	Q₁₆×C₁₃₁	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
241	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
243	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
244	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
245	C₂²×C₄	C₂×Q₈×C₁₃₁	1	4	yes	—
246	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
247	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
248	C₂×C₈	—	2	16	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	C₂×Q₈×C₁₃₁	1	8	yes	complemented
252	C₄⋊C₄	—	2	16	no	—
253	C₄⋊C₄	—	2	8	no	—
254	C₄⋊C₄	—	2	4	no	—
255	C₄⋊C₄	—	2	8	no	—
256	C₄⋊C₄	—	4	4	no	—
257	C₄⋊C₄	—	4	8	no	—
258	C₄⋊C₄	—	4	8	no	—
259	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
260	C₄²	C₂²⋊C₄×C₁₃₁	1	8	yes	—
261	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
262	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
263	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
264	C₂³	#124×C₁₃₁	1	2	yes	—
265	C₂³	C₄⋊Q₈×C₁₃₁	1	2	yes	—
266	C₂³	C₂×D₈×C₁₃₁	1	2	yes	—
267	C₂³	C₂×SD₁₆×C₁₃₁	1	2	yes	—
268	C₂³	C₂×SD₁₆×C₁₃₁	1	2	yes	—
269	C₂³	C₂×Q₁₆×C₁₃₁	1	2	yes	—
270	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
271	Q₈	—	4	32	no	—
272	C₂×C₄	—	2	8	no	—
273	C₂×C₄	—	4	16	no	—
274	C₂×C₄	—	4	4	no	—
275	C₂×C₄	—	4	4	no	—
276	C₂×C₄	—	4	4	no	—
277	C₂×C₄	—	4	4	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	8	8	no	—
280	C₂×C₄	#102×C₁₃₁	1	16	yes	—
281	C₂×C₄	#103×C₁₃₁	1	16	yes	—
282	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
283	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
284	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
285	C₂×C₄	C₄×Q₈×C₁₃₁	1	8	yes	—
286	C₂×C₄	C₂²⋊Q₈×C₁₃₁	1	8	yes	—
287	C₂×C₄	#124×C₁₃₁	1	2	yes	—
288	C₂×C₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
289	C₂×C₄	C₂×D₈×C₁₃₁	1	4	yes	—
290	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	4	yes	—
291	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	4	yes	—
292	C₂×C₄	C₂×Q₁₆×C₁₃₁	1	4	yes	—
293	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
294	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
295	C₂×C₄	C₂²×Q₈×C₁₃₁	1	2	yes	—
296	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
297	C₈	—	2	8	no	—
298	C₂²	#391×C₁₃₁	1	4	yes	—
299	C₂²	C₂×#102×C₁₃₁	1	4	yes	—
300	C₂²	C₂×#103×C₁₃₁	1	4	yes	—
301	C₂²	#486×C₁₃₁	1	4	yes	—
302	C₂²	#487×C₁₃₁	1	4	yes	—
303	C₂²	#498×C₁₃₁	1	4	yes	—
304	C₂²	#500×C₁₃₁	1	4	yes	—
305	C₂²	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
306	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
307	C₂²	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
308	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
309	C₂²	C₂²×SD₁₆×C₁₃₁	1	1	yes	characteristic
310	C₂²	C₂²×SD₁₆×C₁₃₁	1	1	yes	characteristic
311	C₂²	C₂²×Q₁₆×C₁₃₁	1	1	yes	characteristic
312	C₄	—	4	8	no	—
313	C₄	—	8	4	no	—
314	C₄	#391×C₁₃₁	1	4	yes	—
315	C₄	C₂×#102×C₁₃₁	1	8	yes	—
316	C₄	C₂×#103×C₁₃₁	1	8	yes	—
317	C₄	C₂×C₄×Q₈×C₁₃₁	1	2	yes	—
318	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	2	yes	—
319	C₂	#1990×C₁₃₁	1	8	yes	direct product factor
320	C₂	C₂×#391×C₁₃₁	1	1	yes	characteristic
321	C₂	C₂²×#102×C₁₃₁	1	1	yes	characteristic
322	C₂	C₂²×#103×C₁₃₁	1	1	yes	characteristic
323	C₂	C₂×#486×C₁₃₁	1	1	yes	characteristic
324	C₂	C₂×#487×C₁₃₁	1	1	yes	characteristic
325	C₂	C₂×#498×C₁₃₁	1	1	yes	characteristic
326	C₂	C₂×#500×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₁ ◁ C₂²×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1990×C₁₃₁	C₂	direct (N × H)
10. C₂×C₄⋊Q₈×C₁₃₁	C₄	semidirect
34. C₂²×C₈×C₁₃₁	Q₈	semidirect
38. C₄⋊Q₈×C₁₃₁	C₂×C₄	semidirect
87. C₂×C₈×C₁₃₁	C₂×Q₈	semidirect
155. C₂×C₁₃₁	#1990	direct (N × H)
163. C₂×#1990	C₁₃₁	direct (N × H)
164. C₁₃₁	C₂×#1990	direct (N × H)
168. #1990	C₂×C₁₃₁	direct (N × H)
174. C₂×C₄⋊Q₈	C₄×C₁₃₁	semidirect
198. C₂²×C₈	Q₈×C₁₃₁	semidirect
202. C₄⋊Q₈	C₂×C₄×C₁₃₁	semidirect
251. C₂×C₈	C₂×Q₈×C₁₃₁	semidirect
319. C₂	#1990×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₁₃₁	2
C₂²×C₄×C₈×C₁₃₁	2
C₂×#384×C₁₃₁	2
#1990×C₁₃₁	2
C₂×#340×C₁₃₁	2
C₂×#1990	131

Subgroups — C2×#1990×C131 #45707200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1990×C₁₃₁ #45707200