Subgroups — C₁₃₁×#35010 #45720894

Order 33536.

2930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2855×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2848×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2627×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2626×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2579×C₁₃₁	C₂	1	4	yes	maximal, complemented
8	#2564×C₁₃₁	C₂	1	4	yes	maximal, complemented
9	#2487×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	#2417×C₁₃₁	C₂	1	4	yes	maximal, complemented
11	#2409×C₁₃₁	C₂	1	2	yes	maximal, complemented
12	#2315×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	#2308×C₁₃₁	C₂	1	2	yes	maximal
14	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
20	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₁₃₁	—	2	8	no	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
33	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
39	#400×C₁₃₁	C₂²	1	4	yes	complemented
40	#399×C₁₃₁	C₂²	1	4	yes	complemented
41	#398×C₁₃₁	C₂²	1	8	yes	complemented
42	#396×C₁₃₁	C₂²	1	8	yes	complemented
43	#395×C₁₃₁	C₂²	1	4	yes	complemented
44	#393×C₁₃₁	C₂²	1	4	yes	complemented
45	#391×C₁₃₁	C₂²	1	4	yes	complemented
46	#389×C₁₃₁	C₂²	1	4	yes	complemented
47	#387×C₁₃₁	C₂²	1	8	yes	complemented
48	#386×C₁₃₁	C₂²	1	4	yes	—
49	#386×C₁₃₁	C₂²	1	8	yes	—
50	#386×C₁₃₁	C₂²	1	4	yes	—
51	#385×C₁₃₁	C₂²	1	4	yes	—
52	#385×C₁₃₁	C₂²	1	4	yes	—
53	#385×C₁₃₁	C₂²	1	4	yes	complemented
54	#385×C₁₃₁	C₂²	1	8	yes	complemented
55	#385×C₁₃₁	C₂²	1	4	yes	complemented
56	#381×C₁₃₁	C₂²	1	4	yes	—
57	#380×C₁₃₁	C₂²	1	2	yes	—
58	#380×C₁₃₁	C₂²	1	2	yes	—
59	#380×C₁₃₁	C₂²	1	2	yes	complemented
60	#380×C₁₃₁	C₂²	1	4	yes	complemented
61	#380×C₁₃₁	C₂²	1	2	yes	complemented
62	#380×C₁₃₁	C₂²	1	8	yes	complemented
63	#379×C₁₃₁	C₂²	1	4	yes	—
64	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
65	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₁	—	2	4	no	—
68	C₂²×Q₈×C₁₃₁	—	4	4	no	—
69	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃₁	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃₁	—	2	4	no	—
72	C₂²×D₄×C₁₃₁	—	2	4	no	—
73	C₂²×D₄×C₁₃₁	Q₈	1	8	yes	complemented
74	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃₁	—	2	4	no	—
77	C₂³×C₄×C₁₃₁	—	4	4	no	—
78	C₂³×C₄×C₁₃₁	—	4	4	no	—
79	C₂³×C₄×C₁₃₁	D₄	1	8	yes	—
80	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
94	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
95	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
96	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
97	C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
98	C₂²⋊Q₈×C₁₃₁	—	4	8	no	—
99	C₄×D₄×C₁₃₁	—	2	8	no	—
100	C₄×D₄×C₁₃₁	—	2	8	no	—
101	C₄×D₄×C₁₃₁	—	2	8	no	—
102	C₄×D₄×C₁₃₁	—	2	8	no	—
103	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
104	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
105	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
106	C₂×C₄⋊C₄×C₁₃₁	—	4	4	no	—
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	8	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	8	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
118	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
131	C₂×C₄²×C₁₃₁	—	2	4	no	—
132	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
134	#95×C₁₃₁	C₂³	1	8	yes	—
135	#95×C₁₃₁	C₂³	1	8	yes	—
136	#95×C₁₃₁	C₂³	1	8	yes	—
137	#95×C₁₃₁	C₂³	1	4	yes	—
138	#95×C₁₃₁	C₂³	1	8	yes	—
139	#95×C₁₃₁	C₂³	1	4	yes	—
140	C₂⁴×C₁₃₁	—	2	2	no	—
141	C₂⁴×C₁₃₁	—	2	2	no	—
142	C₂⁴×C₁₃₁	—	4	2	no	—
143	C₂⁴×C₁₃₁	—	4	2	no	—
144	C₂⁴×C₁₃₁	—	4	2	no	—
145	C₂⁴×C₁₃₁	—	4	2	no	—
146	C₂⁴×C₁₃₁	C₂×D₄	1	4	yes	—
147	C₂⁴×C₁₃₁	C₂×Q₈	1	4	yes	—
148	C₂⁴×C₁₃₁	C₂×Q₈	1	4	yes	complemented
149	C₂⁴×C₁₃₁	#41	1	4	yes	—
150	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
151	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
153	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₁₃₁	—	2	4	no	—
155	C₂×Q₈×C₁₃₁	—	2	4	no	—
156	C₂×Q₈×C₁₃₁	—	2	8	no	—
157	C₂×Q₈×C₁₃₁	—	4	4	no	—
158	C₂×Q₈×C₁₃₁	—	4	16	no	—
159	C₂×D₄×C₁₃₁	—	2	32	no	—
160	C₂×D₄×C₁₃₁	—	2	4	no	—
161	C₂×D₄×C₁₃₁	—	2	4	no	—
162	C₂×D₄×C₁₃₁	—	2	4	no	—
163	C₂×D₄×C₁₃₁	—	2	4	no	—
164	C₂×D₄×C₁₃₁	C₂×Q₈	1	8	yes	—
165	C₂×D₄×C₁₃₁	C₂×Q₈	1	8	yes	complemented
166	C₂²×C₄×C₁₃₁	—	2	2	no	—
167	C₂²×C₄×C₁₃₁	—	2	2	no	—
168	C₂²×C₄×C₁₃₁	—	2	4	no	—
169	C₂²×C₄×C₁₃₁	—	2	4	no	—
170	C₂²×C₄×C₁₃₁	—	2	4	no	—
171	C₂²×C₄×C₁₃₁	—	2	2	no	—
172	C₂²×C₄×C₁₃₁	—	2	4	no	—
173	C₂²×C₄×C₁₃₁	—	2	2	no	—
174	C₂²×C₄×C₁₃₁	—	2	4	no	—
175	C₂²×C₄×C₁₃₁	—	2	8	no	—
176	C₂²×C₄×C₁₃₁	—	2	4	no	—
177	C₂²×C₄×C₁₃₁	—	2	4	no	—
178	C₂²×C₄×C₁₃₁	—	2	8	no	—
179	C₂²×C₄×C₁₃₁	—	4	16	no	—
180	C₂²×C₄×C₁₃₁	—	4	2	no	—
181	C₂²×C₄×C₁₃₁	—	4	2	no	—
182	C₂²×C₄×C₁₃₁	—	4	2	no	—
183	C₂²×C₄×C₁₃₁	—	4	4	no	—
184	C₂²×C₄×C₁₃₁	—	4	2	no	—
185	C₂²×C₄×C₁₃₁	—	4	4	no	—
186	C₂²×C₄×C₁₃₁	—	4	2	no	—
187	C₂²×C₄×C₁₃₁	—	4	4	no	—
188	C₂²×C₄×C₁₃₁	—	4	4	no	—
189	C₂²×C₄×C₁₃₁	—	4	4	no	—
190	C₂²×C₄×C₁₃₁	—	4	16	no	—
191	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
195	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
197	C₂²×C₄×C₁₃₁	C₂×Q₈	1	4	yes	complemented
198	C₂²×C₄×C₁₃₁	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₁₃₁	—	2	4	no	—
209	C₄⋊C₄×C₁₃₁	—	2	4	no	—
210	C₄⋊C₄×C₁₃₁	—	2	4	no	—
211	C₄⋊C₄×C₁₃₁	—	2	4	no	—
212	C₄⋊C₄×C₁₃₁	—	2	8	no	—
213	C₄⋊C₄×C₁₃₁	—	2	8	no	—
214	C₄⋊C₄×C₁₃₁	—	2	8	no	—
215	C₄⋊C₄×C₁₃₁	—	4	4	no	—
216	C₄⋊C₄×C₁₃₁	—	4	8	no	—
217	C₄⋊C₄×C₁₃₁	—	4	8	no	—
218	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
219	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
220	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
221	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
222	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
223	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
224	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
225	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₁	—	4	8	no	—
227	C₂²⋊C₄×C₁₃₁	—	4	8	no	—
228	C₄²×C₁₃₁	—	2	4	no	—
229	C₄²×C₁₃₁	—	2	4	no	—
230	C₂³×C₁₃₁	—	2	2	no	—
231	C₂³×C₁₃₁	—	2	2	no	—
232	C₂³×C₁₃₁	—	2	2	no	—
233	C₂³×C₁₃₁	—	2	2	no	—
234	C₂³×C₁₃₁	—	2	2	no	—
235	C₂³×C₁₃₁	—	2	2	no	—
236	C₂³×C₁₃₁	—	2	8	no	—
237	C₂³×C₁₃₁	—	2	2	no	—
238	C₂³×C₁₃₁	—	2	2	no	—
239	C₂³×C₁₃₁	—	2	4	no	—
240	C₂³×C₁₃₁	—	2	4	no	—
241	C₂³×C₁₃₁	—	4	4	no	—
242	C₂³×C₁₃₁	—	4	4	no	—
243	C₂³×C₁₃₁	—	4	8	no	—
244	C₂³×C₁₃₁	—	4	8	no	—
245	C₂³×C₁₃₁	—	4	8	no	—
246	C₂³×C₁₃₁	—	4	4	no	—
247	C₂³×C₁₃₁	—	4	4	no	—
248	C₂³×C₁₃₁	—	4	8	no	—
249	C₂³×C₁₃₁	C₂²⋊Q₈	1	16	yes	complemented
250	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
251	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
252	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
253	C₂³×C₁₃₁	C₂²×Q₈	1	4	yes	—
254	C₂³×C₁₃₁	C₂²×Q₈	1	2	yes	—
255	C₂³×C₁₃₁	C₂²×Q₈	1	2	yes	—
256	C₂³×C₁₃₁	C₂²×Q₈	1	2	yes	—
257	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
258	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
259	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
260	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
261	Q₈×C₁₃₁	—	4	8	no	—
262	Q₈×C₁₃₁	—	4	8	no	—
263	D₄×C₁₃₁	—	2	16	no	—
264	D₄×C₁₃₁	—	2	16	no	—
265	C₂×C₄×C₁₃₁	—	2	8	no	—
266	C₂×C₄×C₁₃₁	—	2	2	no	—
267	C₂×C₄×C₁₃₁	—	2	2	no	—
268	C₂×C₄×C₁₃₁	—	2	2	no	—
269	C₂×C₄×C₁₃₁	—	2	2	no	—
270	C₂×C₄×C₁₃₁	—	2	2	no	—
271	C₂×C₄×C₁₃₁	—	2	8	no	—
272	C₂×C₄×C₁₃₁	—	2	8	no	—
273	C₂×C₄×C₁₃₁	—	2	8	no	—
274	C₂×C₄×C₁₃₁	—	2	2	no	—
275	C₂×C₄×C₁₃₁	—	2	4	no	—
276	C₂×C₄×C₁₃₁	—	2	2	no	—
277	C₂×C₄×C₁₃₁	—	2	4	no	—
278	C₂×C₄×C₁₃₁	—	2	8	no	—
279	C₂×C₄×C₁₃₁	—	2	8	no	—
280	C₂×C₄×C₁₃₁	—	2	8	no	—
281	C₂×C₄×C₁₃₁	—	2	4	no	—
282	C₂×C₄×C₁₃₁	—	2	8	no	—
283	C₂×C₄×C₁₃₁	—	2	8	no	—
284	C₂×C₄×C₁₃₁	—	2	4	no	—
285	C₂×C₄×C₁₃₁	—	4	4	no	—
286	C₂×C₄×C₁₃₁	—	4	4	no	—
287	C₂×C₄×C₁₃₁	—	4	4	no	—
288	C₂×C₄×C₁₃₁	—	4	8	no	—
289	C₂×C₄×C₁₃₁	—	4	8	no	—
290	C₂×C₄×C₁₃₁	—	4	4	no	—
291	C₂×C₄×C₁₃₁	—	4	4	no	—
292	C₂×C₄×C₁₃₁	—	4	8	no	—
293	C₂×C₄×C₁₃₁	—	4	8	no	—
294	C₂×C₄×C₁₃₁	—	8	8	no	—
295	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₁₃₁	C₂²×Q₈	1	4	yes	—
300	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
301	C₂²×C₁₃₁	—	2	2	no	—
302	C₂²×C₁₃₁	—	2	2	no	—
303	C₂²×C₁₃₁	—	2	2	no	—
304	C₂²×C₁₃₁	—	2	2	no	—
305	C₂²×C₁₃₁	—	2	2	no	—
306	C₂²×C₁₃₁	—	2	2	no	—
307	C₂²×C₁₃₁	—	2	4	no	—
308	C₂²×C₁₃₁	—	2	4	no	—
309	C₂²×C₁₃₁	—	2	4	no	—
310	C₂²×C₁₃₁	—	2	4	no	—
311	C₂²×C₁₃₁	—	2	4	no	—
312	C₂²×C₁₃₁	—	2	4	no	—
313	C₂²×C₁₃₁	—	2	4	no	—
314	C₂²×C₁₃₁	—	2	8	no	—
315	C₂²×C₁₃₁	—	4	16	no	—
316	C₂²×C₁₃₁	—	4	16	no	—
317	C₂²×C₁₃₁	—	4	2	no	—
318	C₂²×C₁₃₁	—	4	2	no	—
319	C₂²×C₁₃₁	—	4	4	no	—
320	C₂²×C₁₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
321	C₂²×C₁₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
322	C₂²×C₁₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
323	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
324	C₂²×C₁₃₁	C₂³×Q₈	1	1	yes	characteristic
325	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₁₃₁	#585	1	2	yes	—
328	C₄×C₁₃₁	—	2	4	no	—
329	C₄×C₁₃₁	—	2	2	no	—
330	C₄×C₁₃₁	—	2	2	no	—
331	C₄×C₁₃₁	—	2	2	no	—
332	C₄×C₁₃₁	—	4	2	no	—
333	C₄×C₁₃₁	—	4	4	no	—
334	C₄×C₁₃₁	—	4	2	no	—
335	C₄×C₁₃₁	—	4	4	no	—
336	C₄×C₁₃₁	—	4	8	no	—
337	C₄×C₁₃₁	#534	1	4	yes	—
338	C₂×C₁₃₁	—	2	4	no	—
339	C₂×C₁₃₁	—	2	4	no	—
340	C₂×C₁₃₁	—	2	4	no	—
341	C₂×C₁₃₁	—	4	4	no	—
342	C₂×C₁₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
343	C₂×C₁₃₁	C₂×#534	1	1	yes	characteristic
344	C₂×C₁₃₁	#3449	1	1	yes	characteristic
345	C₂×C₁₃₁	#3501	1	2	yes	—
346	C₂×C₁₃₁	#3505	1	2	yes	—
347	#35010	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₁₃₁	#35010	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²×C₂²⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
350	C₂²×C₄×D₄	C₂×C₁₃₁	1	1	yes	characteristic
351	#2855	C₂×C₁₃₁	1	2	yes	complemented
352	#2848	C₂×C₁₃₁	1	2	yes	complemented
353	#2627	C₂×C₁₃₁	1	2	yes	complemented
354	#2626	C₂×C₁₃₁	1	2	yes	complemented
355	#2579	C₂×C₁₃₁	1	4	yes	complemented
356	#2564	C₂×C₁₃₁	1	4	yes	complemented
357	#2487	C₂×C₁₃₁	1	2	yes	complemented
358	#2417	C₂×C₁₃₁	1	4	yes	complemented
359	#2409	C₂×C₁₃₁	1	2	yes	complemented
360	#2315	C₂×C₁₃₁	1	2	yes	complemented
361	#2308	C₂×C₁₃₁	1	2	yes	—
362	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
363	C₂³×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
364	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
365	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
366	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
367	C₂×C₂²⋊Q₈	—	2	8	no	—
368	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
369	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	—
370	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	complemented
371	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	2	yes	complemented
372	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	4	yes	complemented
373	C₂×C₄×D₄	—	2	8	no	—
374	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₁₃₁	1	2	yes	—
378	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
380	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
381	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
382	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
383	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
384	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
385	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
387	#400	C₂²×C₁₃₁	1	4	yes	complemented
388	#399	C₂²×C₁₃₁	1	4	yes	complemented
389	#398	C₂²×C₁₃₁	1	8	yes	complemented
390	#396	C₂²×C₁₃₁	1	8	yes	complemented
391	#395	C₂²×C₁₃₁	1	4	yes	complemented
392	#393	C₂²×C₁₃₁	1	4	yes	complemented
393	#391	C₂²×C₁₃₁	1	4	yes	complemented
394	#389	C₂²×C₁₃₁	1	4	yes	complemented
395	#387	C₂²×C₁₃₁	1	8	yes	complemented
396	#386	C₂²×C₁₃₁	1	8	yes	—
397	#386	C₂²×C₁₃₁	1	4	yes	—
398	#386	C₂²×C₁₃₁	1	4	yes	—
399	#385	C₂²×C₁₃₁	1	4	yes	—
400	#385	C₂²×C₁₃₁	1	4	yes	—
401	#385	C₂²×C₁₃₁	1	8	yes	complemented
402	#385	C₂²×C₁₃₁	1	4	yes	complemented
403	#385	C₂²×C₁₃₁	1	4	yes	complemented
404	#381	C₂²×C₁₃₁	1	4	yes	—
405	#380	C₂²×C₁₃₁	1	2	yes	—
406	#380	C₂²×C₁₃₁	1	2	yes	—
407	#380	C₂²×C₁₃₁	1	8	yes	complemented
408	#380	C₂²×C₁₃₁	1	2	yes	complemented
409	#380	C₂²×C₁₃₁	1	4	yes	complemented
410	#380	C₂²×C₁₃₁	1	2	yes	complemented
411	#379	C₂²×C₁₃₁	1	4	yes	—
412	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
413	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
414	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
415	C₂²×Q₈	—	2	4	no	—
416	C₂²×Q₈	—	4	4	no	—
417	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
418	C₂²×Q₈	C₂³×C₁₃₁	1	2	yes	—
419	C₂²×D₄	—	2	4	no	—
420	C₂²×D₄	—	2	4	no	—
421	C₂²×D₄	Q₈×C₁₃₁	1	8	yes	complemented
422	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
423	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
424	C₂³×C₄	—	2	4	no	—
425	C₂³×C₄	—	4	4	no	—
426	C₂³×C₄	—	4	4	no	—
427	C₂³×C₄	D₄×C₁₃₁	1	8	yes	—
428	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
429	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
436	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
437	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
438	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
439	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
442	C₂²⋊Q₈	—	2	8	no	—
443	C₂²⋊Q₈	—	2	8	no	—
444	C₂²⋊Q₈	—	2	8	no	—
445	C₂²⋊Q₈	—	2	8	no	—
446	C₂²⋊Q₈	—	4	8	no	—
447	C₄×D₄	—	2	8	no	—
448	C₄×D₄	—	2	8	no	—
449	C₄×D₄	—	2	8	no	—
450	C₄×D₄	—	2	8	no	—
451	C₂×C₄⋊C₄	—	2	4	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	—	2	8	no	—
454	C₂×C₄⋊C₄	—	4	4	no	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	8	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	8	yes	—
465	C₂×C₂²⋊C₄	—	2	4	no	—
466	C₂×C₂²⋊C₄	—	2	8	no	—
467	C₂×C₂²⋊C₄	—	2	8	no	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
479	C₂×C₄²	—	2	4	no	—
480	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
481	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
482	#95	C₂³×C₁₃₁	1	4	yes	—
483	#95	C₂³×C₁₃₁	1	4	yes	—
484	#95	C₂³×C₁₃₁	1	8	yes	—
485	#95	C₂³×C₁₃₁	1	8	yes	—
486	#95	C₂³×C₁₃₁	1	8	yes	—
487	#95	C₂³×C₁₃₁	1	8	yes	—
488	C₂⁴	—	2	2	no	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	4	2	no	—
491	C₂⁴	—	4	2	no	—
492	C₂⁴	—	4	2	no	—
493	C₂⁴	—	4	2	no	—
494	C₂⁴	C₂×D₄×C₁₃₁	1	4	yes	—
495	C₂⁴	C₂×Q₈×C₁₃₁	1	4	yes	—
496	C₂⁴	C₂×Q₈×C₁₃₁	1	4	yes	complemented
497	C₂⁴	#41×C₁₃₁	1	4	yes	—
498	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
499	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
501	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	8	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	16	no	—
507	C₂×D₄	—	2	32	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	C₂×Q₈×C₁₃₁	1	8	yes	—
513	C₂×D₄	C₂×Q₈×C₁₃₁	1	8	yes	complemented
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	8	no	—
527	C₂²×C₄	—	4	16	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	16	no	—
539	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
540	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
541	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
542	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
543	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
545	C₂²×C₄	C₂×Q₈×C₁₃₁	1	4	yes	complemented
546	C₂²×C₄	C₂⁴×C₁₃₁	1	8	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	8	no	—
565	C₄⋊C₄	—	4	8	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	2	4	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	8	no	—
571	C₂²⋊C₄	—	2	8	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	4	8	no	—
575	C₂²⋊C₄	—	4	8	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	8	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	4	4	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	8	no	—
592	C₂³	—	4	8	no	—
593	C₂³	—	4	8	no	—
594	C₂³	—	4	4	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	4	no	—
597	C₂³	C₂²⋊Q₈×C₁₃₁	1	16	yes	complemented
598	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
599	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
600	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
601	C₂³	C₂²×Q₈×C₁₃₁	1	4	yes	—
602	C₂³	C₂²×Q₈×C₁₃₁	1	2	yes	—
603	C₂³	C₂²×Q₈×C₁₃₁	1	2	yes	—
604	C₂³	C₂²×Q₈×C₁₃₁	1	2	yes	—
605	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
606	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
607	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
608	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
609	Q₈	—	4	8	no	—
610	Q₈	—	4	8	no	—
611	D₄	—	2	16	no	—
612	D₄	—	2	16	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	8	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	4	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	8	no	—
639	C₂×C₄	—	4	8	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	8	no	—
642	C₂×C₄	—	8	8	no	—
643	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
644	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
645	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
646	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
647	C₂×C₄	C₂²×Q₈×C₁₃₁	1	4	yes	—
648	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	2	4	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	8	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	4	16	no	—
664	C₂²	—	4	16	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	C₂×C₂²⋊Q₈×C₁₃₁	1	4	yes	—
669	C₂²	C₂×C₂²⋊Q₈×C₁₃₁	1	4	yes	—
670	C₂²	C₂×C₂²⋊Q₈×C₁₃₁	1	4	yes	—
671	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
672	C₂²	C₂³×Q₈×C₁₃₁	1	1	yes	characteristic
673	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
674	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
675	C₂²	#585×C₁₃₁	1	2	yes	—
676	C₄	—	2	4	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	8	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	4	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	4	no	—
685	C₄	#534×C₁₃₁	1	4	yes	—
686	C₂	—	2	4	no	—
687	C₂	—	2	4	no	—
688	C₂	—	2	4	no	—
689	C₂	—	4	4	no	—
690	C₂	C₂²×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
691	C₂	C₂×#534×C₁₃₁	1	1	yes	characteristic
692	C₂	#3449×C₁₃₁	1	1	yes	characteristic
693	C₂	#3501×C₁₃₁	1	2	yes	—
694	C₂	#3505×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂³×D₄×C₁₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊Q₈×C₁₃₁	C₂	semidirect
3. #2855×C₁₃₁	C₂	semidirect
4. #2848×C₁₃₁	C₂	semidirect
5. #2627×C₁₃₁	C₂	semidirect
6. #2626×C₁₃₁	C₂	semidirect
7. #2579×C₁₃₁	C₂	semidirect
8. #2564×C₁₃₁	C₂	semidirect
9. #2487×C₁₃₁	C₂	semidirect
10. #2417×C₁₃₁	C₂	semidirect
11. #2409×C₁₃₁	C₂	semidirect
12. #2315×C₁₃₁	C₂	semidirect
14. C₂×#380×C₁₃₁	C₂	semidirect
15. C₂³×Q₈×C₁₃₁	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
31. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
39. #400×C₁₃₁	C₂²	semidirect
40. #399×C₁₃₁	C₂²	semidirect
41. #398×C₁₃₁	C₂²	semidirect
42. #396×C₁₃₁	C₂²	semidirect
43. #395×C₁₃₁	C₂²	semidirect
44. #393×C₁₃₁	C₂²	semidirect
45. #391×C₁₃₁	C₂²	semidirect
46. #389×C₁₃₁	C₂²	semidirect
47. #387×C₁₃₁	C₂²	semidirect
53. #385×C₁₃₁	C₂²	semidirect
54. #385×C₁₃₁	C₂²	semidirect
55. #385×C₁₃₁	C₂²	semidirect
59. #380×C₁₃₁	C₂²	semidirect
60. #380×C₁₃₁	C₂²	semidirect
61. #380×C₁₃₁	C₂²	semidirect
62. #380×C₁₃₁	C₂²	semidirect
64. C₂×#95×C₁₃₁	C₂²	semidirect
73. C₂²×D₄×C₁₃₁	Q₈	semidirect
148. C₂⁴×C₁₃₁	C₂×Q₈	semidirect
165. C₂×D₄×C₁₃₁	C₂×Q₈	semidirect
197. C₂²×C₄×C₁₃₁	C₂×Q₈	semidirect
249. C₂³×C₁₃₁	C₂²⋊Q₈	semidirect
347. #35010	C₁₃₁	direct (N × H)
348. C₁₃₁	#35010	direct (N × H)
349. C₂²×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
351. #2855	C₂×C₁₃₁	semidirect
352. #2848	C₂×C₁₃₁	semidirect
353. #2627	C₂×C₁₃₁	semidirect
354. #2626	C₂×C₁₃₁	semidirect
355. #2579	C₂×C₁₃₁	semidirect
356. #2564	C₂×C₁₃₁	semidirect
357. #2487	C₂×C₁₃₁	semidirect
358. #2417	C₂×C₁₃₁	semidirect
359. #2409	C₂×C₁₃₁	semidirect
360. #2315	C₂×C₁₃₁	semidirect
362. C₂×#380	C₂×C₁₃₁	semidirect
363. C₂³×Q₈	C₂²×C₁₃₁	semidirect
370. C₂×C₂²⋊Q₈	C₂²×C₁₃₁	semidirect
371. C₂×C₂²⋊Q₈	C₂²×C₁₃₁	semidirect
372. C₂×C₂²⋊Q₈	C₂²×C₁₃₁	semidirect
379. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
380. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
381. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
387. #400	C₂²×C₁₃₁	semidirect
388. #399	C₂²×C₁₃₁	semidirect
389. #398	C₂²×C₁₃₁	semidirect
390. #396	C₂²×C₁₃₁	semidirect
391. #395	C₂²×C₁₃₁	semidirect
392. #393	C₂²×C₁₃₁	semidirect
393. #391	C₂²×C₁₃₁	semidirect
394. #389	C₂²×C₁₃₁	semidirect
395. #387	C₂²×C₁₃₁	semidirect
401. #385	C₂²×C₁₃₁	semidirect
402. #385	C₂²×C₁₃₁	semidirect
403. #385	C₂²×C₁₃₁	semidirect
407. #380	C₂²×C₁₃₁	semidirect
408. #380	C₂²×C₁₃₁	semidirect
409. #380	C₂²×C₁₃₁	semidirect
410. #380	C₂²×C₁₃₁	semidirect
412. C₂×#95	C₂²×C₁₃₁	semidirect
421. C₂²×D₄	Q₈×C₁₃₁	semidirect
496. C₂⁴	C₂×Q₈×C₁₃₁	semidirect
513. C₂×D₄	C₂×Q₈×C₁₃₁	semidirect
545. C₂²×C₄	C₂×Q₈×C₁₃₁	semidirect
597. C₂³	C₂²⋊Q₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₁₃₁	2
C₂²×C₄×D₄×C₁₃₁	2
#2855×C₁₃₁	2
#2848×C₁₃₁	2
#2627×C₁₃₁	2
#2626×C₁₃₁	2
#2579×C₁₃₁	2
#2564×C₁₃₁	2
#2487×C₁₃₁	2
#2417×C₁₃₁	2
#2409×C₁₃₁	2
#2315×C₁₃₁	2
#2308×C₁₃₁	2
C₂×#380×C₁₃₁	2
#35010	131

Subgroups — C131×#35010 #45720894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#35010 #45720894