Subgroups — C₂×#2450×C₁₃₁ #45720553

Order 33536.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 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	#2450×C₁₃₁	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#398×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#396×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#393×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#391×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#387×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#386×C₁₃₁	C₂	1	1	yes	maximal, characteristic
11	C₂×#386×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂×#385×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#385×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#385×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#95×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₁₃₁	—	2	8	no	—
24	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	8	yes	complemented
25	C₂×C₄×D₄×C₁₃₁	—	2	8	no	—
26	C₂×C₄×D₄×C₁₃₁	C₂²	1	8	yes	—
27	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
44	#400×C₁₃₁	C₂²	1	8	yes	complemented
45	#398×C₁₃₁	C₂²	1	8	yes	complemented
46	#396×C₁₃₁	C₂²	1	8	yes	complemented
47	#393×C₁₃₁	C₂²	1	8	yes	complemented
48	#391×C₁₃₁	C₂²	1	8	yes	complemented
49	#387×C₁₃₁	C₂²	1	8	yes	complemented
50	#386×C₁₃₁	C₂²	1	8	yes	—
51	#386×C₁₃₁	C₂²	1	8	yes	—
52	#385×C₁₃₁	C₂²	1	8	yes	complemented
53	#385×C₁₃₁	C₂²	1	8	yes	complemented
54	#385×C₁₃₁	C₂²	1	8	yes	complemented
55	#380×C₁₃₁	C₂²	1	8	yes	complemented
56	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
57	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
58	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
59	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
60	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
61	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
62	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
63	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
64	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
65	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
66	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
67	C₂×#95×C₁₃₁	C₂²	1	1	yes	characteristic
68	C₂×#95×C₁₃₁	C₂²	1	8	yes	complemented
69	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
70	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃₁	—	2	4	no	—
72	C₂²×Q₈×C₁₃₁	—	2	4	no	—
73	C₂²×Q₈×C₁₃₁	—	4	2	no	—
74	C₂²×Q₈×C₁₃₁	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃₁	—	2	4	no	—
76	C₂²×D₄×C₁₃₁	—	2	4	no	—
77	C₂²×D₄×C₁₃₁	Q₈	1	8	yes	complemented
78	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃₁	—	2	4	no	—
80	C₂³×C₄×C₁₃₁	—	2	4	no	—
81	C₂³×C₄×C₁₃₁	—	2	4	no	—
82	C₂³×C₄×C₁₃₁	—	2	4	no	—
83	C₂³×C₄×C₁₃₁	—	2	4	no	—
84	C₂³×C₄×C₁₃₁	—	2	4	no	—
85	C₂³×C₄×C₁₃₁	—	2	4	no	—
86	C₂³×C₄×C₁₃₁	—	4	2	no	—
87	C₂³×C₄×C₁₃₁	—	4	2	no	—
88	C₂³×C₄×C₁₃₁	—	4	2	no	—
89	C₂³×C₄×C₁₃₁	—	4	2	no	—
90	C₂³×C₄×C₁₃₁	—	4	2	no	—
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	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
108	C₂²⋊Q₈×C₁₃₁	—	2	32	no	—
109	C₄×D₄×C₁₃₁	—	2	32	no	—
110	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
111	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
112	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
113	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
114	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
115	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
116	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
117	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
118	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
127	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
131	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
132	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
133	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	8	yes	—
134	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃₁	—	2	4	no	—
143	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
144	#95×C₁₃₁	C₂³	1	4	yes	—
145	#95×C₁₃₁	C₂³	1	4	yes	—
146	#95×C₁₃₁	C₂³	1	4	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	4	yes	—
149	#95×C₁₃₁	C₂³	1	4	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	4	yes	—
152	#95×C₁₃₁	C₂³	1	4	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	#95×C₁₃₁	C₂³	1	4	yes	—
155	#95×C₁₃₁	C₂³	1	4	yes	—
156	C₂⁴×C₁₃₁	—	2	2	no	—
157	C₂⁴×C₁₃₁	—	2	2	no	—
158	C₂⁴×C₁₃₁	—	2	2	no	—
159	C₂⁴×C₁₃₁	—	2	2	no	—
160	C₂⁴×C₁₃₁	—	2	2	no	—
161	C₂⁴×C₁₃₁	—	2	2	no	—
162	C₂⁴×C₁₃₁	—	2	2	no	—
163	C₂⁴×C₁₃₁	—	2	2	no	—
164	C₂⁴×C₁₃₁	—	2	2	no	—
165	C₂⁴×C₁₃₁	—	2	2	no	—
166	C₂⁴×C₁₃₁	C₂×D₄	1	4	yes	—
167	C₂⁴×C₁₃₁	C₂×Q₈	1	4	yes	—
168	C₂⁴×C₁₃₁	C₂×Q₈	1	4	yes	—
169	C₂⁴×C₁₃₁	#41	1	4	yes	—
170	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
171	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
172	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₁₃₁	—	2	8	no	—
174	C₂×Q₈×C₁₃₁	—	2	8	no	—
175	C₂×Q₈×C₁₃₁	—	4	4	no	—
176	C₂×Q₈×C₁₃₁	—	4	16	no	—
177	C₂×D₄×C₁₃₁	—	2	32	no	—
178	C₂×D₄×C₁₃₁	—	2	8	no	—
179	C₂×D₄×C₁₃₁	—	2	8	no	—
180	C₂×D₄×C₁₃₁	C₂×Q₈	1	16	yes	complemented
181	C₂²×C₄×C₁₃₁	—	2	2	no	—
182	C₂²×C₄×C₁₃₁	—	2	2	no	—
183	C₂²×C₄×C₁₃₁	—	2	2	no	—
184	C₂²×C₄×C₁₃₁	—	2	2	no	—
185	C₂²×C₄×C₁₃₁	—	2	2	no	—
186	C₂²×C₄×C₁₃₁	—	2	2	no	—
187	C₂²×C₄×C₁₃₁	—	2	2	no	—
188	C₂²×C₄×C₁₃₁	—	2	2	no	—
189	C₂²×C₄×C₁₃₁	—	2	2	no	—
190	C₂²×C₄×C₁₃₁	—	2	2	no	—
191	C₂²×C₄×C₁₃₁	—	2	2	no	—
192	C₂²×C₄×C₁₃₁	—	2	2	no	—
193	C₂²×C₄×C₁₃₁	—	2	2	no	—
194	C₂²×C₄×C₁₃₁	—	2	2	no	—
195	C₂²×C₄×C₁₃₁	—	2	8	no	—
196	C₂²×C₄×C₁₃₁	—	2	8	no	—
197	C₂²×C₄×C₁₃₁	—	2	2	no	—
198	C₂²×C₄×C₁₃₁	—	2	2	no	—
199	C₂²×C₄×C₁₃₁	—	2	2	no	—
200	C₂²×C₄×C₁₃₁	—	2	2	no	—
201	C₂²×C₄×C₁₃₁	—	2	2	no	—
202	C₂²×C₄×C₁₃₁	—	2	8	no	—
203	C₂²×C₄×C₁₃₁	—	2	2	no	—
204	C₂²×C₄×C₁₃₁	—	2	2	no	—
205	C₂²×C₄×C₁₃₁	—	2	2	no	—
206	C₂²×C₄×C₁₃₁	—	2	2	no	—
207	C₂²×C₄×C₁₃₁	—	2	2	no	—
208	C₂²×C₄×C₁₃₁	—	2	2	no	—
209	C₂²×C₄×C₁₃₁	—	2	2	no	—
210	C₂²×C₄×C₁₃₁	—	2	2	no	—
211	C₂²×C₄×C₁₃₁	—	2	2	no	—
212	C₂²×C₄×C₁₃₁	—	2	2	no	—
213	C₂²×C₄×C₁₃₁	—	2	2	no	—
214	C₂²×C₄×C₁₃₁	—	2	2	no	—
215	C₂²×C₄×C₁₃₁	—	2	2	no	—
216	C₂²×C₄×C₁₃₁	—	2	2	no	—
217	C₂²×C₄×C₁₃₁	—	2	2	no	—
218	C₂²×C₄×C₁₃₁	—	2	8	no	—
219	C₂²×C₄×C₁₃₁	—	2	8	no	—
220	C₂²×C₄×C₁₃₁	—	2	8	no	—
221	C₂²×C₄×C₁₃₁	—	2	8	no	—
222	C₂²×C₄×C₁₃₁	—	4	4	no	—
223	C₂²×C₄×C₁₃₁	—	4	4	no	—
224	C₂²×C₄×C₁₃₁	—	4	4	no	—
225	C₂²×C₄×C₁₃₁	—	4	4	no	—
226	C₂²×C₄×C₁₃₁	—	4	4	no	—
227	C₂²×C₄×C₁₃₁	—	4	16	no	—
228	C₂²×C₄×C₁₃₁	—	4	16	no	—
229	C₂²×C₄×C₁₃₁	—	4	16	no	—
230	C₂²×C₄×C₁₃₁	—	4	16	no	—
231	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃₁	C₂×Q₈	1	4	yes	—
234	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
235	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
236	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₁₃₁	—	2	8	no	—
250	C₄⋊C₄×C₁₃₁	—	2	8	no	—
251	C₄⋊C₄×C₁₃₁	—	2	8	no	—
252	C₄⋊C₄×C₁₃₁	—	2	8	no	—
253	C₄⋊C₄×C₁₃₁	—	2	8	no	—
254	C₄⋊C₄×C₁₃₁	—	4	4	no	—
255	C₄⋊C₄×C₁₃₁	—	4	4	no	—
256	C₄⋊C₄×C₁₃₁	—	4	4	no	—
257	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
258	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
262	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₁	C₂×D₄	1	16	yes	—
265	C₄²×C₁₃₁	—	2	8	no	—
266	C₂³×C₁₃₁	—	2	8	no	—
267	C₂³×C₁₃₁	—	2	8	no	—
268	C₂³×C₁₃₁	—	2	8	no	—
269	C₂³×C₁₃₁	—	2	8	no	—
270	C₂³×C₁₃₁	—	2	8	no	—
271	C₂³×C₁₃₁	—	2	8	no	—
272	C₂³×C₁₃₁	—	2	2	no	—
273	C₂³×C₁₃₁	—	2	2	no	—
274	C₂³×C₁₃₁	—	2	2	no	—
275	C₂³×C₁₃₁	—	2	2	no	—
276	C₂³×C₁₃₁	—	2	8	no	—
277	C₂³×C₁₃₁	—	2	8	no	—
278	C₂³×C₁₃₁	—	2	8	no	—
279	C₂³×C₁₃₁	—	2	2	no	—
280	C₂³×C₁₃₁	—	2	2	no	—
281	C₂³×C₁₃₁	—	2	2	no	—
282	C₂³×C₁₃₁	—	2	2	no	—
283	C₂³×C₁₃₁	—	2	2	no	—
284	C₂³×C₁₃₁	—	2	2	no	—
285	C₂³×C₁₃₁	—	4	4	no	—
286	C₂³×C₁₃₁	—	4	4	no	—
287	C₂³×C₁₃₁	—	4	4	no	—
288	C₂³×C₁₃₁	—	4	4	no	—
289	C₂³×C₁₃₁	C₂²⋊Q₈	1	16	yes	—
290	C₂³×C₁₃₁	C₂²×D₄	1	4	yes	—
291	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
292	C₂³×C₁₃₁	C₂²×Q₈	1	4	yes	—
293	C₂³×C₁₃₁	C₂²×Q₈	1	4	yes	—
294	C₂³×C₁₃₁	C₂²×Q₈	1	2	yes	—
295	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
296	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
297	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
298	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
299	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
300	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
301	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
302	Q₈×C₁₃₁	—	4	16	no	—
303	D₄×C₁₃₁	—	2	32	no	—
304	C₂×C₄×C₁₃₁	—	2	8	no	—
305	C₂×C₄×C₁₃₁	—	2	8	no	—
306	C₂×C₄×C₁₃₁	—	2	8	no	—
307	C₂×C₄×C₁₃₁	—	2	8	no	—
308	C₂×C₄×C₁₃₁	—	2	8	no	—
309	C₂×C₄×C₁₃₁	—	2	2	no	—
310	C₂×C₄×C₁₃₁	—	2	2	no	—
311	C₂×C₄×C₁₃₁	—	2	2	no	—
312	C₂×C₄×C₁₃₁	—	2	2	no	—
313	C₂×C₄×C₁₃₁	—	2	2	no	—
314	C₂×C₄×C₁₃₁	—	2	2	no	—
315	C₂×C₄×C₁₃₁	—	2	2	no	—
316	C₂×C₄×C₁₃₁	—	2	2	no	—
317	C₂×C₄×C₁₃₁	—	2	2	no	—
318	C₂×C₄×C₁₃₁	—	2	2	no	—
319	C₂×C₄×C₁₃₁	—	2	2	no	—
320	C₂×C₄×C₁₃₁	—	2	2	no	—
321	C₂×C₄×C₁₃₁	—	2	2	no	—
322	C₂×C₄×C₁₃₁	—	2	2	no	—
323	C₂×C₄×C₁₃₁	—	2	2	no	—
324	C₂×C₄×C₁₃₁	—	2	2	no	—
325	C₂×C₄×C₁₃₁	—	2	2	no	—
326	C₂×C₄×C₁₃₁	—	2	2	no	—
327	C₂×C₄×C₁₃₁	—	2	2	no	—
328	C₂×C₄×C₁₃₁	—	2	2	no	—
329	C₂×C₄×C₁₃₁	—	2	2	no	—
330	C₂×C₄×C₁₃₁	—	2	2	no	—
331	C₂×C₄×C₁₃₁	—	2	2	no	—
332	C₂×C₄×C₁₃₁	—	2	2	no	—
333	C₂×C₄×C₁₃₁	—	2	2	no	—
334	C₂×C₄×C₁₃₁	—	2	2	no	—
335	C₂×C₄×C₁₃₁	—	2	2	no	—
336	C₂×C₄×C₁₃₁	—	2	2	no	—
337	C₂×C₄×C₁₃₁	—	2	2	no	—
338	C₂×C₄×C₁₃₁	—	2	2	no	—
339	C₂×C₄×C₁₃₁	—	2	2	no	—
340	C₂×C₄×C₁₃₁	—	2	2	no	—
341	C₂×C₄×C₁₃₁	—	2	2	no	—
342	C₂×C₄×C₁₃₁	—	2	2	no	—
343	C₂×C₄×C₁₃₁	—	4	16	no	—
344	C₂×C₄×C₁₃₁	—	4	16	no	—
345	C₂×C₄×C₁₃₁	—	4	16	no	—
346	C₂×C₄×C₁₃₁	—	4	16	no	—
347	C₂×C₄×C₁₃₁	—	4	4	no	—
348	C₂×C₄×C₁₃₁	—	4	4	no	—
349	C₂×C₄×C₁₃₁	—	4	4	no	—
350	C₂×C₄×C₁₃₁	—	4	4	no	—
351	C₂×C₄×C₁₃₁	—	4	4	no	—
352	C₂×C₄×C₁₃₁	—	4	4	no	—
353	C₂×C₄×C₁₃₁	—	4	4	no	—
354	C₂×C₄×C₁₃₁	—	4	4	no	—
355	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₁₃₁	C₂²×Q₈	1	4	yes	—
358	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
359	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
360	C₂²×C₁₃₁	—	2	4	no	—
361	C₂²×C₁₃₁	—	2	4	no	—
362	C₂²×C₁₃₁	—	2	4	no	—
363	C₂²×C₁₃₁	—	2	4	no	—
364	C₂²×C₁₃₁	—	2	4	no	—
365	C₂²×C₁₃₁	—	2	4	no	—
366	C₂²×C₁₃₁	—	2	32	no	—
367	C₂²×C₁₃₁	—	2	4	no	—
368	C₂²×C₁₃₁	—	2	4	no	—
369	C₂²×C₁₃₁	—	2	4	no	—
370	C₂²×C₁₃₁	—	4	2	no	—
371	C₂²×C₁₃₁	—	4	2	no	—
372	C₂²×C₁₃₁	—	4	2	no	—
373	C₂²×C₁₃₁	—	4	2	no	—
374	C₂²×C₁₃₁	—	4	16	no	—
375	C₂²×C₁₃₁	C₂×C₂²⋊Q₈	1	8	yes	—
376	C₂²×C₁₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
377	C₂²×C₁₃₁	#529	1	4	yes	—
378	C₂²×C₁₃₁	#538	1	4	yes	—
379	C₂²×C₁₃₁	#546	1	4	yes	—
380	C₂²×C₁₃₁	#546	1	4	yes	—
381	C₂²×C₁₃₁	#554	1	4	yes	—
382	C₂²×C₁₃₁	#554	1	4	yes	—
383	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
384	C₂²×C₁₃₁	C₂³×Q₈	1	1	yes	characteristic
385	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
386	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
387	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
390	C₄×C₁₃₁	—	2	4	no	—
391	C₄×C₁₃₁	—	2	4	no	—
392	C₄×C₁₃₁	—	2	4	no	—
393	C₄×C₁₃₁	—	2	4	no	—
394	C₄×C₁₃₁	—	2	4	no	—
395	C₄×C₁₃₁	—	4	2	no	—
396	C₄×C₁₃₁	—	4	2	no	—
397	C₄×C₁₃₁	—	4	2	no	—
398	C₄×C₁₃₁	—	4	2	no	—
399	C₄×C₁₃₁	—	4	2	no	—
400	C₄×C₁₃₁	—	4	2	no	—
401	C₄×C₁₃₁	—	4	2	no	—
402	C₄×C₁₃₁	—	4	2	no	—
403	C₂×C₁₃₁	—	2	8	no	—
404	C₂×C₁₃₁	—	4	4	no	—
405	C₂×C₁₃₁	#2450	1	8	yes	direct product factor
406	C₂×C₁₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
407	C₂×C₁₃₁	C₂×#529	1	1	yes	characteristic
408	C₂×C₁₃₁	C₂×#538	1	1	yes	characteristic
409	C₂×C₁₃₁	C₂×#546	1	1	yes	characteristic
410	C₂×C₁₃₁	C₂×#546	1	1	yes	characteristic
411	C₂×C₁₃₁	C₂×#554	1	1	yes	characteristic
412	C₂×C₁₃₁	C₂×#554	1	1	yes	characteristic
413	C₂×#2450	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₁₃₁	C₂×#2450	1	1	yes	characteristic, direct product factor, Sylow
415	C₂²×C₂²⋊Q₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
416	C₂²×C₄×D₄	C₂×C₁₃₁	1	1	yes	characteristic
417	#2450	C₂×C₁₃₁	1	16	yes	direct product factor
418	C₂×#400	C₂×C₁₃₁	1	1	yes	characteristic, complemented
419	C₂×#398	C₂×C₁₃₁	1	1	yes	characteristic, complemented
420	C₂×#396	C₂×C₁₃₁	1	1	yes	characteristic, complemented
421	C₂×#393	C₂×C₁₃₁	1	1	yes	characteristic, complemented
422	C₂×#391	C₂×C₁₃₁	1	1	yes	characteristic, complemented
423	C₂×#387	C₂×C₁₃₁	1	1	yes	characteristic, complemented
424	C₂×#386	C₂×C₁₃₁	1	1	yes	characteristic
425	C₂×#386	C₂×C₁₃₁	1	1	yes	characteristic
426	C₂×#385	C₂×C₁₃₁	1	1	yes	characteristic, complemented
427	C₂×#385	C₂×C₁₃₁	1	1	yes	characteristic, complemented
428	C₂×#385	C₂×C₁₃₁	1	1	yes	characteristic, complemented
429	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
430	C₂²×#95	C₂×C₁₃₁	1	1	yes	characteristic, complemented
431	C₂³×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
432	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
433	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
434	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
435	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
436	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
437	C₂×C₂²⋊Q₈	—	2	8	no	—
438	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	8	yes	complemented
439	C₂×C₄×D₄	—	2	8	no	—
440	C₂×C₄×D₄	C₂²×C₁₃₁	1	8	yes	—
441	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
443	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
445	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
446	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
447	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
448	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
450	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
457	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
458	#400	C₂²×C₁₃₁	1	8	yes	complemented
459	#398	C₂²×C₁₃₁	1	8	yes	complemented
460	#396	C₂²×C₁₃₁	1	8	yes	complemented
461	#393	C₂²×C₁₃₁	1	8	yes	complemented
462	#391	C₂²×C₁₃₁	1	8	yes	complemented
463	#387	C₂²×C₁₃₁	1	8	yes	complemented
464	#386	C₂²×C₁₃₁	1	8	yes	—
465	#386	C₂²×C₁₃₁	1	8	yes	—
466	#385	C₂²×C₁₃₁	1	8	yes	complemented
467	#385	C₂²×C₁₃₁	1	8	yes	complemented
468	#385	C₂²×C₁₃₁	1	8	yes	complemented
469	#380	C₂²×C₁₃₁	1	8	yes	complemented
470	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
471	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
472	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
473	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
474	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
475	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
476	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
477	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
478	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
479	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
480	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
481	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
482	C₂×#95	C₂²×C₁₃₁	1	8	yes	complemented
483	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
484	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
485	C₂²×Q₈	—	2	4	no	—
486	C₂²×Q₈	—	2	4	no	—
487	C₂²×Q₈	—	4	2	no	—
488	C₂²×Q₈	C₂³×C₁₃₁	1	4	yes	—
489	C₂²×D₄	—	2	4	no	—
490	C₂²×D₄	—	2	4	no	—
491	C₂²×D₄	Q₈×C₁₃₁	1	8	yes	complemented
492	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
493	C₂³×C₄	—	2	4	no	—
494	C₂³×C₄	—	2	4	no	—
495	C₂³×C₄	—	2	4	no	—
496	C₂³×C₄	—	2	4	no	—
497	C₂³×C₄	—	2	4	no	—
498	C₂³×C₄	—	2	4	no	—
499	C₂³×C₄	—	2	4	no	—
500	C₂³×C₄	—	4	2	no	—
501	C₂³×C₄	—	4	2	no	—
502	C₂³×C₄	—	4	2	no	—
503	C₂³×C₄	—	4	2	no	—
504	C₂³×C₄	—	4	2	no	—
505	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
514	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
515	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
516	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
522	C₂²⋊Q₈	—	2	32	no	—
523	C₄×D₄	—	2	32	no	—
524	C₂×C₄⋊C₄	—	2	4	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	4	no	—
527	C₂×C₄⋊C₄	—	2	4	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	—	4	2	no	—
530	C₂×C₄⋊C₄	—	4	2	no	—
531	C₂×C₄⋊C₄	—	4	2	no	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₂²⋊C₄	—	2	4	no	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	4	2	no	—
545	C₂×C₂²⋊C₄	—	4	2	no	—
546	C₂×C₂²⋊C₄	—	4	2	no	—
547	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	8	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
556	C₂×C₄²	—	2	4	no	—
557	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
558	#95	C₂³×C₁₃₁	1	4	yes	—
559	#95	C₂³×C₁₃₁	1	4	yes	—
560	#95	C₂³×C₁₃₁	1	4	yes	—
561	#95	C₂³×C₁₃₁	1	4	yes	—
562	#95	C₂³×C₁₃₁	1	4	yes	—
563	#95	C₂³×C₁₃₁	1	4	yes	—
564	#95	C₂³×C₁₃₁	1	4	yes	—
565	#95	C₂³×C₁₃₁	1	4	yes	—
566	#95	C₂³×C₁₃₁	1	4	yes	—
567	#95	C₂³×C₁₃₁	1	4	yes	—
568	#95	C₂³×C₁₃₁	1	4	yes	—
569	#95	C₂³×C₁₃₁	1	4	yes	—
570	C₂⁴	—	2	2	no	—
571	C₂⁴	—	2	2	no	—
572	C₂⁴	—	2	2	no	—
573	C₂⁴	—	2	2	no	—
574	C₂⁴	—	2	2	no	—
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	2	2	no	—
577	C₂⁴	—	2	2	no	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	—	2	2	no	—
580	C₂⁴	C₂×D₄×C₁₃₁	1	4	yes	—
581	C₂⁴	C₂×Q₈×C₁₃₁	1	4	yes	—
582	C₂⁴	C₂×Q₈×C₁₃₁	1	4	yes	—
583	C₂⁴	#41×C₁₃₁	1	4	yes	—
584	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
585	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
586	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
587	C₂×Q₈	—	2	8	no	—
588	C₂×Q₈	—	2	8	no	—
589	C₂×Q₈	—	4	4	no	—
590	C₂×Q₈	—	4	16	no	—
591	C₂×D₄	—	2	32	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	8	no	—
594	C₂×D₄	C₂×Q₈×C₁₃₁	1	16	yes	complemented
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	8	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	8	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	4	4	no	—
639	C₂²×C₄	—	4	4	no	—
640	C₂²×C₄	—	4	4	no	—
641	C₂²×C₄	—	4	16	no	—
642	C₂²×C₄	—	4	16	no	—
643	C₂²×C₄	—	4	16	no	—
644	C₂²×C₄	—	4	16	no	—
645	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
646	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
647	C₂²×C₄	C₂×Q₈×C₁₃₁	1	4	yes	—
648	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
649	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
650	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
663	C₄⋊C₄	—	2	8	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	8	no	—
667	C₄⋊C₄	—	2	8	no	—
668	C₄⋊C₄	—	4	4	no	—
669	C₄⋊C₄	—	4	4	no	—
670	C₄⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	8	no	—
673	C₂²⋊C₄	—	2	8	no	—
674	C₂²⋊C₄	—	2	8	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₂²⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	—	4	4	no	—
678	C₂²⋊C₄	C₂×D₄×C₁₃₁	1	16	yes	—
679	C₄²	—	2	8	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	8	no	—
682	C₂³	—	2	8	no	—
683	C₂³	—	2	8	no	—
684	C₂³	—	2	8	no	—
685	C₂³	—	2	8	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	8	no	—
691	C₂³	—	2	8	no	—
692	C₂³	—	2	8	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	4	4	no	—
701	C₂³	—	4	4	no	—
702	C₂³	—	4	4	no	—
703	C₂³	C₂²⋊Q₈×C₁₃₁	1	16	yes	—
704	C₂³	C₂²×D₄×C₁₃₁	1	4	yes	—
705	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
706	C₂³	C₂²×Q₈×C₁₃₁	1	4	yes	—
707	C₂³	C₂²×Q₈×C₁₃₁	1	4	yes	—
708	C₂³	C₂²×Q₈×C₁₃₁	1	2	yes	—
709	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
710	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
711	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
712	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
713	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
714	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
715	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
716	Q₈	—	4	16	no	—
717	D₄	—	2	32	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	4	16	no	—
758	C₂×C₄	—	4	16	no	—
759	C₂×C₄	—	4	16	no	—
760	C₂×C₄	—	4	16	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
771	C₂×C₄	C₂²×Q₈×C₁₃₁	1	4	yes	—
772	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
773	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	32	no	—
781	C₂²	—	2	4	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	16	no	—
789	C₂²	C₂×C₂²⋊Q₈×C₁₃₁	1	8	yes	—
790	C₂²	C₂×C₂²⋊Q₈×C₁₃₁	1	4	yes	—
791	C₂²	#529×C₁₃₁	1	4	yes	—
792	C₂²	#538×C₁₃₁	1	4	yes	—
793	C₂²	#546×C₁₃₁	1	4	yes	—
794	C₂²	#546×C₁₃₁	1	4	yes	—
795	C₂²	#554×C₁₃₁	1	4	yes	—
796	C₂²	#554×C₁₃₁	1	4	yes	—
797	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
798	C₂²	C₂³×Q₈×C₁₃₁	1	1	yes	characteristic
799	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
800	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
801	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
802	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
803	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	4	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	4	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₂	—	2	8	no	—
818	C₂	—	4	4	no	—
819	C₂	#2450×C₁₃₁	1	8	yes	direct product factor
820	C₂	C₂²×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
821	C₂	C₂×#529×C₁₃₁	1	1	yes	characteristic
822	C₂	C₂×#538×C₁₃₁	1	1	yes	characteristic
823	C₂	C₂×#546×C₁₃₁	1	1	yes	characteristic
824	C₂	C₂×#546×C₁₃₁	1	1	yes	characteristic
825	C₂	C₂×#554×C₁₃₁	1	1	yes	characteristic
826	C₂	C₂×#554×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂³×D₄×C₁₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×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. #2450×C₁₃₁	C₂	direct (N × H)
4. C₂×#400×C₁₃₁	C₂	semidirect
5. C₂×#398×C₁₃₁	C₂	semidirect
6. C₂×#396×C₁₃₁	C₂	semidirect
7. C₂×#393×C₁₃₁	C₂	semidirect
8. C₂×#391×C₁₃₁	C₂	semidirect
9. C₂×#387×C₁₃₁	C₂	semidirect
12. C₂×#385×C₁₃₁	C₂	semidirect
13. C₂×#385×C₁₃₁	C₂	semidirect
14. C₂×#385×C₁₃₁	C₂	semidirect
15. C₂×#380×C₁₃₁	C₂	semidirect
16. C₂²×#95×C₁₃₁	C₂	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
44. #400×C₁₃₁	C₂²	semidirect
45. #398×C₁₃₁	C₂²	semidirect
46. #396×C₁₃₁	C₂²	semidirect
47. #393×C₁₃₁	C₂²	semidirect
48. #391×C₁₃₁	C₂²	semidirect
49. #387×C₁₃₁	C₂²	semidirect
52. #385×C₁₃₁	C₂²	semidirect
53. #385×C₁₃₁	C₂²	semidirect
54. #385×C₁₃₁	C₂²	semidirect
55. #380×C₁₃₁	C₂²	semidirect
68. C₂×#95×C₁₃₁	C₂²	semidirect
77. C₂²×D₄×C₁₃₁	Q₈	semidirect
180. C₂×D₄×C₁₃₁	C₂×Q₈	semidirect
405. C₂×C₁₃₁	#2450	direct (N × H)
413. C₂×#2450	C₁₃₁	direct (N × H)
414. C₁₃₁	C₂×#2450	direct (N × H)
415. C₂²×C₂²⋊Q₈	C₂×C₁₃₁	semidirect
417. #2450	C₂×C₁₃₁	direct (N × H)
418. C₂×#400	C₂×C₁₃₁	semidirect
419. C₂×#398	C₂×C₁₃₁	semidirect
420. C₂×#396	C₂×C₁₃₁	semidirect
421. C₂×#393	C₂×C₁₃₁	semidirect
422. C₂×#391	C₂×C₁₃₁	semidirect
423. C₂×#387	C₂×C₁₃₁	semidirect
426. C₂×#385	C₂×C₁₃₁	semidirect
427. C₂×#385	C₂×C₁₃₁	semidirect
428. C₂×#385	C₂×C₁₃₁	semidirect
429. C₂×#380	C₂×C₁₃₁	semidirect
430. C₂²×#95	C₂×C₁₃₁	semidirect
438. C₂×C₂²⋊Q₈	C₂²×C₁₃₁	semidirect
458. #400	C₂²×C₁₃₁	semidirect
459. #398	C₂²×C₁₃₁	semidirect
460. #396	C₂²×C₁₃₁	semidirect
461. #393	C₂²×C₁₃₁	semidirect
462. #391	C₂²×C₁₃₁	semidirect
463. #387	C₂²×C₁₃₁	semidirect
466. #385	C₂²×C₁₃₁	semidirect
467. #385	C₂²×C₁₃₁	semidirect
468. #385	C₂²×C₁₃₁	semidirect
469. #380	C₂²×C₁₃₁	semidirect
482. C₂×#95	C₂²×C₁₃₁	semidirect
491. C₂²×D₄	Q₈×C₁₃₁	semidirect
594. C₂×D₄	C₂×Q₈×C₁₃₁	semidirect
819. C₂	#2450×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×C₂²⋊Q₈×C₁₃₁	2
C₂²×C₄×D₄×C₁₃₁	2
#2450×C₁₃₁	2
C₂×#400×C₁₃₁	2
C₂×#398×C₁₃₁	2
C₂×#396×C₁₃₁	2
C₂×#393×C₁₃₁	2
C₂×#391×C₁₃₁	2
C₂×#387×C₁₃₁	2
C₂×#386×C₁₃₁	2
C₂×#385×C₁₃₁	2
C₂×#380×C₁₃₁	2
C₂²×#95×C₁₃₁	2
C₂×#2450	131

Subgroups — C2×#2450×C131 #45720553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2450×C₁₃₁ #45720553