Subgroups — C₂×#2481×C₁₃₁ #45720545

Order 33536.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2481×C₁₃₁	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#400×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#397×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#396×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#388×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#387×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#387×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#386×C₁₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂×#386×C₁₃₁	C₂	1	1	yes	maximal, characteristic
13	C₂×#386×C₁₃₁	C₂	1	1	yes	maximal, characteristic
14	C₂×#385×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×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	C₂×#126×C₁₃₁	—	2	8	no	—
22	C₂×#126×C₁₃₁	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₁₃₁	—	2	8	no	—
24	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
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	8	yes	complemented
33	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊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×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
44	#400×C₁₃₁	C₂²	1	8	yes	complemented
45	#400×C₁₃₁	C₂²	1	8	yes	complemented
46	#397×C₁₃₁	C₂²	1	8	yes	complemented
47	#396×C₁₃₁	C₂²	1	8	yes	complemented
48	#388×C₁₃₁	C₂²	1	8	yes	complemented
49	#387×C₁₃₁	C₂²	1	8	yes	complemented
50	#387×C₁₃₁	C₂²	1	8	yes	complemented
51	#386×C₁₃₁	C₂²	1	8	yes	—
52	#386×C₁₃₁	C₂²	1	8	yes	—
53	#386×C₁₃₁	C₂²	1	8	yes	—
54	#385×C₁₃₁	C₂²	1	8	yes	complemented
55	#380×C₁₃₁	C₂²	1	8	yes	complemented
56	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	8	yes	complemented
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	1	yes	characteristic
69	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
70	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₁	—	2	4	no	—
72	C₂²×D₄×C₁₃₁	—	2	4	no	—
73	C₂²×D₄×C₁₃₁	—	2	4	no	—
74	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃₁	—	2	4	no	—
76	C₂³×C₄×C₁₃₁	—	2	4	no	—
77	C₂³×C₄×C₁₃₁	—	2	4	no	—
78	C₂³×C₄×C₁₃₁	—	2	4	no	—
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	—	4	2	no	—
83	C₂³×C₄×C₁₃₁	—	4	2	no	—
84	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
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	4	yes	—
95	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
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	1	yes	characteristic
100	#126×C₁₃₁	—	2	32	no	—
101	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
102	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
103	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
104	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
105	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
106	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
107	C₂×C₄⋊C₄×C₁₃₁	—	2	32	no	—
108	C₂×C₄⋊C₄×C₁₃₁	—	4	2	no	—
109	C₂×C₄⋊C₄×C₁₃₁	D₄	1	8	yes	complemented
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
119	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
120	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₁₃₁	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
126	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
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	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₁	—	2	4	no	—
137	C₂×C₄²×C₁₃₁	—	4	2	no	—
138	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
140	#95×C₁₃₁	C₂³	1	4	yes	—
141	#95×C₁₃₁	C₂³	1	4	yes	—
142	#95×C₁₃₁	C₂³	1	4	yes	—
143	#95×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	C₂⁴×C₁₃₁	—	2	2	no	—
153	C₂⁴×C₁₃₁	—	2	2	no	—
154	C₂⁴×C₁₃₁	—	2	2	no	—
155	C₂⁴×C₁₃₁	—	2	2	no	—
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	#41	1	4	yes	—
164	C₂⁴×C₁₃₁	#41	1	4	yes	—
165	C₂⁴×C₁₃₁	#41	1	4	yes	—
166	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
167	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
168	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
169	C₂×D₄×C₁₃₁	—	2	8	no	—
170	C₂×D₄×C₁₃₁	—	2	8	no	—
171	C₂×D₄×C₁₃₁	—	2	8	no	—
172	C₂×D₄×C₁₃₁	—	4	16	no	—
173	C₂²×C₄×C₁₃₁	—	2	32	no	—
174	C₂²×C₄×C₁₃₁	—	2	2	no	—
175	C₂²×C₄×C₁₃₁	—	2	8	no	—
176	C₂²×C₄×C₁₃₁	—	2	2	no	—
177	C₂²×C₄×C₁₃₁	—	2	2	no	—
178	C₂²×C₄×C₁₃₁	—	2	2	no	—
179	C₂²×C₄×C₁₃₁	—	2	2	no	—
180	C₂²×C₄×C₁₃₁	—	2	2	no	—
181	C₂²×C₄×C₁₃₁	—	2	2	no	—
182	C₂²×C₄×C₁₃₁	—	2	2	no	—
183	C₂²×C₄×C₁₃₁	—	2	8	no	—
184	C₂²×C₄×C₁₃₁	—	2	8	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	2	no	—
196	C₂²×C₄×C₁₃₁	—	2	2	no	—
197	C₂²×C₄×C₁₃₁	—	2	2	no	—
198	C₂²×C₄×C₁₃₁	—	2	2	no	—
199	C₂²×C₄×C₁₃₁	—	2	8	no	—
200	C₂²×C₄×C₁₃₁	—	2	8	no	—
201	C₂²×C₄×C₁₃₁	—	2	2	no	—
202	C₂²×C₄×C₁₃₁	—	2	2	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	8	no	—
215	C₂²×C₄×C₁₃₁	—	2	8	no	—
216	C₂²×C₄×C₁₃₁	—	4	4	no	—
217	C₂²×C₄×C₁₃₁	—	4	4	no	—
218	C₂²×C₄×C₁₃₁	—	4	16	no	—
219	C₂²×C₄×C₁₃₁	—	4	16	no	—
220	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
221	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
224	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₁₃₁	—	2	8	no	—
238	C₄⋊C₄×C₁₃₁	—	2	8	no	—
239	C₄⋊C₄×C₁₃₁	—	2	8	no	—
240	C₄⋊C₄×C₁₃₁	—	2	8	no	—
241	C₄⋊C₄×C₁₃₁	—	2	8	no	—
242	C₄⋊C₄×C₁₃₁	—	2	8	no	—
243	C₄⋊C₄×C₁₃₁	—	4	4	no	—
244	C₄⋊C₄×C₁₃₁	C₂×D₄	1	16	yes	complemented
245	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
250	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
251	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
252	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
253	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
254	C₄²×C₁₃₁	—	2	8	no	—
255	C₄²×C₁₃₁	—	4	4	no	—
256	C₂³×C₁₃₁	—	2	8	no	—
257	C₂³×C₁₃₁	—	2	8	no	—
258	C₂³×C₁₃₁	—	2	8	no	—
259	C₂³×C₁₃₁	—	2	8	no	—
260	C₂³×C₁₃₁	—	2	8	no	—
261	C₂³×C₁₃₁	—	2	8	no	—
262	C₂³×C₁₃₁	—	2	2	no	—
263	C₂³×C₁₃₁	—	2	2	no	—
264	C₂³×C₁₃₁	—	2	2	no	—
265	C₂³×C₁₃₁	—	2	2	no	—
266	C₂³×C₁₃₁	—	2	2	no	—
267	C₂³×C₁₃₁	—	2	2	no	—
268	C₂³×C₁₃₁	—	2	2	no	—
269	C₂³×C₁₃₁	—	2	2	no	—
270	C₂³×C₁₃₁	—	2	2	no	—
271	C₂³×C₁₃₁	—	2	2	no	—
272	C₂³×C₁₃₁	—	2	2	no	—
273	C₂³×C₁₃₁	—	4	4	no	—
274	C₂³×C₁₃₁	—	4	4	no	—
275	C₂³×C₁₃₁	—	4	4	no	—
276	C₂³×C₁₃₁	—	4	4	no	—
277	C₂³×C₁₃₁	—	4	4	no	—
278	C₂³×C₁₃₁	—	4	4	no	—
279	C₂³×C₁₃₁	—	4	4	no	—
280	C₂³×C₁₃₁	#126	1	16	yes	complemented
281	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
282	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
283	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
284	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
285	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
286	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
287	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
288	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
289	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
290	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
291	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
292	D₄×C₁₃₁	—	4	16	no	—
293	C₂×C₄×C₁₃₁	—	2	32	no	—
294	C₂×C₄×C₁₃₁	—	2	8	no	—
295	C₂×C₄×C₁₃₁	—	2	8	no	—
296	C₂×C₄×C₁₃₁	—	2	8	no	—
297	C₂×C₄×C₁₃₁	—	2	8	no	—
298	C₂×C₄×C₁₃₁	—	2	2	no	—
299	C₂×C₄×C₁₃₁	—	2	2	no	—
300	C₂×C₄×C₁₃₁	—	2	2	no	—
301	C₂×C₄×C₁₃₁	—	2	2	no	—
302	C₂×C₄×C₁₃₁	—	2	2	no	—
303	C₂×C₄×C₁₃₁	—	2	2	no	—
304	C₂×C₄×C₁₃₁	—	2	2	no	—
305	C₂×C₄×C₁₃₁	—	2	2	no	—
306	C₂×C₄×C₁₃₁	—	2	2	no	—
307	C₂×C₄×C₁₃₁	—	2	2	no	—
308	C₂×C₄×C₁₃₁	—	2	2	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	—	4	16	no	—
334	C₂×C₄×C₁₃₁	—	4	16	no	—
335	C₂×C₄×C₁₃₁	—	4	4	no	—
336	C₂×C₄×C₁₃₁	—	4	4	no	—
337	C₂×C₄×C₁₃₁	—	4	4	no	—
338	C₂×C₄×C₁₃₁	—	4	4	no	—
339	C₂×C₄×C₁₃₁	—	4	4	no	—
340	C₂×C₄×C₁₃₁	—	4	4	no	—
341	C₂×C₄×C₁₃₁	—	4	4	no	—
342	C₂×C₄×C₁₃₁	—	4	4	no	—
343	C₂×C₄×C₁₃₁	—	4	4	no	—
344	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
346	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
347	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
348	C₂²×C₁₃₁	—	2	4	no	—
349	C₂²×C₁₃₁	—	2	4	no	—
350	C₂²×C₁₃₁	—	2	4	no	—
351	C₂²×C₁₃₁	—	2	4	no	—
352	C₂²×C₁₃₁	—	2	4	no	—
353	C₂²×C₁₃₁	—	2	4	no	—
354	C₂²×C₁₃₁	—	2	32	no	—
355	C₂²×C₁₃₁	—	4	2	no	—
356	C₂²×C₁₃₁	—	4	2	no	—
357	C₂²×C₁₃₁	—	4	2	no	—
358	C₂²×C₁₃₁	—	4	2	no	—
359	C₂²×C₁₃₁	—	4	2	no	—
360	C₂²×C₁₃₁	—	4	2	no	—
361	C₂²×C₁₃₁	—	4	2	no	—
362	C₂²×C₁₃₁	—	8	8	no	—
363	C₂²×C₁₃₁	#525	1	4	yes	—
364	C₂²×C₁₃₁	C₂×#126	1	4	yes	—
365	C₂²×C₁₃₁	C₂×#126	1	8	yes	complemented
366	C₂²×C₁₃₁	#539	1	4	yes	—
367	C₂²×C₁₃₁	#546	1	4	yes	—
368	C₂²×C₁₃₁	#548	1	4	yes	—
369	C₂²×C₁₃₁	#552	1	4	yes	—
370	C₂²×C₁₃₁	#553	1	4	yes	—
371	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
372	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
373	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₄×C₁₃₁	—	2	4	no	—
379	C₄×C₁₃₁	—	2	4	no	—
380	C₄×C₁₃₁	—	2	4	no	—
381	C₄×C₁₃₁	—	2	4	no	—
382	C₄×C₁₃₁	—	4	2	no	—
383	C₄×C₁₃₁	—	4	2	no	—
384	C₄×C₁₃₁	—	4	2	no	—
385	C₄×C₁₃₁	—	4	2	no	—
386	C₄×C₁₃₁	—	4	2	no	—
387	C₄×C₁₃₁	—	4	2	no	—
388	C₄×C₁₃₁	—	4	2	no	—
389	C₄×C₁₃₁	—	4	2	no	—
390	C₄×C₁₃₁	—	4	2	no	—
391	C₂×C₁₃₁	—	2	8	no	—
392	C₂×C₁₃₁	—	8	2	no	—
393	C₂×C₁₃₁	#2481	1	8	yes	direct product factor
394	C₂×C₁₃₁	C₂×#525	1	1	yes	characteristic
395	C₂×C₁₃₁	C₂²×#126	1	1	yes	characteristic
396	C₂×C₁₃₁	C₂×#539	1	1	yes	characteristic
397	C₂×C₁₃₁	C₂×#546	1	1	yes	characteristic
398	C₂×C₁₃₁	C₂×#548	1	1	yes	characteristic
399	C₂×C₁₃₁	C₂×#552	1	1	yes	characteristic
400	C₂×C₁₃₁	C₂×#553	1	1	yes	characteristic
401	C₂×#2481	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₁₃₁	C₂×#2481	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²×#126	C₂×C₁₃₁	1	1	yes	characteristic, complemented
404	C₂³×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
405	#2481	C₂×C₁₃₁	1	16	yes	direct product factor
406	C₂×#400	C₂×C₁₃₁	1	1	yes	characteristic, complemented
407	C₂×#400	C₂×C₁₃₁	1	1	yes	characteristic, complemented
408	C₂×#397	C₂×C₁₃₁	1	1	yes	characteristic, complemented
409	C₂×#396	C₂×C₁₃₁	1	1	yes	characteristic, complemented
410	C₂×#388	C₂×C₁₃₁	1	1	yes	characteristic, complemented
411	C₂×#387	C₂×C₁₃₁	1	1	yes	characteristic, complemented
412	C₂×#387	C₂×C₁₃₁	1	1	yes	characteristic, complemented
413	C₂×#386	C₂×C₁₃₁	1	1	yes	characteristic
414	C₂×#386	C₂×C₁₃₁	1	1	yes	characteristic
415	C₂×#386	C₂×C₁₃₁	1	1	yes	characteristic
416	C₂×#385	C₂×C₁₃₁	1	1	yes	characteristic, complemented
417	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
418	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
419	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
420	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
422	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
423	C₂×#126	—	2	8	no	—
424	C₂×#126	C₂²×C₁₃₁	1	8	yes	complemented
425	C₂²×C₄⋊C₄	—	2	8	no	—
426	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
427	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
429	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
432	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	8	yes	complemented
435	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
439	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
440	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
444	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
445	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
446	#400	C₂²×C₁₃₁	1	8	yes	complemented
447	#400	C₂²×C₁₃₁	1	8	yes	complemented
448	#397	C₂²×C₁₃₁	1	8	yes	complemented
449	#396	C₂²×C₁₃₁	1	8	yes	complemented
450	#388	C₂²×C₁₃₁	1	8	yes	complemented
451	#387	C₂²×C₁₃₁	1	8	yes	complemented
452	#387	C₂²×C₁₃₁	1	8	yes	complemented
453	#386	C₂²×C₁₃₁	1	8	yes	—
454	#386	C₂²×C₁₃₁	1	8	yes	—
455	#386	C₂²×C₁₃₁	1	8	yes	—
456	#385	C₂²×C₁₃₁	1	8	yes	complemented
457	#380	C₂²×C₁₃₁	1	8	yes	complemented
458	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	8	yes	complemented
459	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
460	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
461	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
462	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
463	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
464	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
465	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
466	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
467	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
468	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
469	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
470	C₂×#95	C₂²×C₁₃₁	1	1	yes	characteristic
471	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
472	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
473	C₂²×D₄	—	2	4	no	—
474	C₂²×D₄	—	2	4	no	—
475	C₂²×D₄	—	2	4	no	—
476	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
477	C₂³×C₄	—	2	4	no	—
478	C₂³×C₄	—	2	4	no	—
479	C₂³×C₄	—	2	4	no	—
480	C₂³×C₄	—	2	4	no	—
481	C₂³×C₄	—	2	4	no	—
482	C₂³×C₄	—	2	4	no	—
483	C₂³×C₄	—	2	4	no	—
484	C₂³×C₄	—	4	2	no	—
485	C₂³×C₄	—	4	2	no	—
486	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
495	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
497	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
498	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
502	#126	—	2	32	no	—
503	C₂×C₄⋊C₄	—	2	4	no	—
504	C₂×C₄⋊C₄	—	2	4	no	—
505	C₂×C₄⋊C₄	—	2	4	no	—
506	C₂×C₄⋊C₄	—	2	4	no	—
507	C₂×C₄⋊C₄	—	2	4	no	—
508	C₂×C₄⋊C₄	—	2	4	no	—
509	C₂×C₄⋊C₄	—	2	32	no	—
510	C₂×C₄⋊C₄	—	4	2	no	—
511	C₂×C₄⋊C₄	D₄×C₁₃₁	1	8	yes	complemented
512	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
520	C₂×C₂²⋊C₄	—	2	4	no	—
521	C₂×C₂²⋊C₄	—	2	4	no	—
522	C₂×C₂²⋊C₄	—	2	4	no	—
523	C₂×C₂²⋊C₄	—	2	4	no	—
524	C₂×C₂²⋊C₄	—	2	4	no	—
525	C₂×C₂²⋊C₄	—	2	4	no	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	C₂×C₂²⋊C₄	—	4	2	no	—
528	C₂×C₂²⋊C₄	—	4	2	no	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
538	C₂×C₄²	—	2	4	no	—
539	C₂×C₄²	—	4	2	no	—
540	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
541	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
542	#95	C₂³×C₁₃₁	1	4	yes	—
543	#95	C₂³×C₁₃₁	1	4	yes	—
544	#95	C₂³×C₁₃₁	1	4	yes	—
545	#95	C₂³×C₁₃₁	1	4	yes	—
546	#95	C₂³×C₁₃₁	1	4	yes	—
547	#95	C₂³×C₁₃₁	1	4	yes	—
548	#95	C₂³×C₁₃₁	1	4	yes	—
549	#95	C₂³×C₁₃₁	1	4	yes	—
550	#95	C₂³×C₁₃₁	1	4	yes	—
551	#95	C₂³×C₁₃₁	1	4	yes	—
552	#95	C₂³×C₁₃₁	1	4	yes	—
553	#95	C₂³×C₁₃₁	1	4	yes	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	2	no	—
563	C₂⁴	—	2	2	no	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	#41×C₁₃₁	1	4	yes	—
566	C₂⁴	#41×C₁₃₁	1	4	yes	—
567	C₂⁴	#41×C₁₃₁	1	4	yes	—
568	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
569	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
570	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	2	8	no	—
573	C₂×D₄	—	2	8	no	—
574	C₂×D₄	—	4	16	no	—
575	C₂²×C₄	—	2	32	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	8	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
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	8	no	—
602	C₂²×C₄	—	2	8	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	2	no	—
610	C₂²×C₄	—	2	2	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	8	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	—	4	16	no	—
621	C₂²×C₄	—	4	16	no	—
622	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
623	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
624	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
625	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
639	C₄⋊C₄	—	2	8	no	—
640	C₄⋊C₄	—	2	8	no	—
641	C₄⋊C₄	—	2	8	no	—
642	C₄⋊C₄	—	2	8	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	8	no	—
645	C₄⋊C₄	—	4	4	no	—
646	C₄⋊C₄	C₂×D₄×C₁₃₁	1	16	yes	complemented
647	C₂²⋊C₄	—	2	8	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₄²	—	2	8	no	—
657	C₄²	—	4	4	no	—
658	C₂³	—	2	8	no	—
659	C₂³	—	2	8	no	—
660	C₂³	—	2	8	no	—
661	C₂³	—	2	8	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	8	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	4	no	—
678	C₂³	—	4	4	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	4	no	—
682	C₂³	#126×C₁₃₁	1	16	yes	complemented
683	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
684	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
685	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
686	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
687	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
688	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
689	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
690	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
691	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
692	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
693	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
694	D₄	—	4	16	no	—
695	C₂×C₄	—	2	32	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	8	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	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	—	4	16	no	—
736	C₂×C₄	—	4	16	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
747	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
748	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
749	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
750	C₂²	—	2	32	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	8	no	—
765	C₂²	#525×C₁₃₁	1	4	yes	—
766	C₂²	C₂×#126×C₁₃₁	1	4	yes	—
767	C₂²	C₂×#126×C₁₃₁	1	8	yes	complemented
768	C₂²	#539×C₁₃₁	1	4	yes	—
769	C₂²	#546×C₁₃₁	1	4	yes	—
770	C₂²	#548×C₁₃₁	1	4	yes	—
771	C₂²	#552×C₁₃₁	1	4	yes	—
772	C₂²	#553×C₁₃₁	1	4	yes	—
773	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
774	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
775	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
776	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
778	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
779	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
780	C₄	—	2	4	no	—
781	C₄	—	2	4	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	4	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₂	—	2	8	no	—
794	C₂	—	8	2	no	—
795	C₂	#2481×C₁₃₁	1	8	yes	direct product factor
796	C₂	C₂×#525×C₁₃₁	1	1	yes	characteristic
797	C₂	C₂²×#126×C₁₃₁	1	1	yes	characteristic
798	C₂	C₂×#539×C₁₃₁	1	1	yes	characteristic
799	C₂	C₂×#546×C₁₃₁	1	1	yes	characteristic
800	C₂	C₂×#548×C₁₃₁	1	1	yes	characteristic
801	C₂	C₂×#552×C₁₃₁	1	1	yes	characteristic
802	C₂	C₂×#553×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×#126×C₁₃₁	C₂	semidirect
2. C₂³×C₄⋊C₄×C₁₃₁	C₂	semidirect
3. #2481×C₁₃₁	C₂	direct (N × H)
4. C₂×#400×C₁₃₁	C₂	semidirect
5. C₂×#400×C₁₃₁	C₂	semidirect
6. C₂×#397×C₁₃₁	C₂	semidirect
7. C₂×#396×C₁₃₁	C₂	semidirect
8. C₂×#388×C₁₃₁	C₂	semidirect
9. C₂×#387×C₁₃₁	C₂	semidirect
10. C₂×#387×C₁₃₁	C₂	semidirect
14. C₂×#385×C₁₃₁	C₂	semidirect
15. C₂×#380×C₁₃₁	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
22. C₂×#126×C₁₃₁	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
44. #400×C₁₃₁	C₂²	semidirect
45. #400×C₁₃₁	C₂²	semidirect
46. #397×C₁₃₁	C₂²	semidirect
47. #396×C₁₃₁	C₂²	semidirect
48. #388×C₁₃₁	C₂²	semidirect
49. #387×C₁₃₁	C₂²	semidirect
50. #387×C₁₃₁	C₂²	semidirect
54. #385×C₁₃₁	C₂²	semidirect
55. #380×C₁₃₁	C₂²	semidirect
56. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
109. C₂×C₄⋊C₄×C₁₃₁	D₄	semidirect
244. C₄⋊C₄×C₁₃₁	C₂×D₄	semidirect
280. C₂³×C₁₃₁	#126	semidirect
365. C₂²×C₁₃₁	C₂×#126	semidirect
393. C₂×C₁₃₁	#2481	direct (N × H)
401. C₂×#2481	C₁₃₁	direct (N × H)
402. C₁₃₁	C₂×#2481	direct (N × H)
403. C₂²×#126	C₂×C₁₃₁	semidirect
404. C₂³×C₄⋊C₄	C₂×C₁₃₁	semidirect
405. #2481	C₂×C₁₃₁	direct (N × H)
406. C₂×#400	C₂×C₁₃₁	semidirect
407. C₂×#400	C₂×C₁₃₁	semidirect
408. C₂×#397	C₂×C₁₃₁	semidirect
409. C₂×#396	C₂×C₁₃₁	semidirect
410. C₂×#388	C₂×C₁₃₁	semidirect
411. C₂×#387	C₂×C₁₃₁	semidirect
412. C₂×#387	C₂×C₁₃₁	semidirect
416. C₂×#385	C₂×C₁₃₁	semidirect
417. C₂×#380	C₂×C₁₃₁	semidirect
418. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
424. C₂×#126	C₂²×C₁₃₁	semidirect
434. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
446. #400	C₂²×C₁₃₁	semidirect
447. #400	C₂²×C₁₃₁	semidirect
448. #397	C₂²×C₁₃₁	semidirect
449. #396	C₂²×C₁₃₁	semidirect
450. #388	C₂²×C₁₃₁	semidirect
451. #387	C₂²×C₁₃₁	semidirect
452. #387	C₂²×C₁₃₁	semidirect
456. #385	C₂²×C₁₃₁	semidirect
457. #380	C₂²×C₁₃₁	semidirect
458. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
511. C₂×C₄⋊C₄	D₄×C₁₃₁	semidirect
646. C₄⋊C₄	C₂×D₄×C₁₃₁	semidirect
682. C₂³	#126×C₁₃₁	semidirect
767. C₂²	C₂×#126×C₁₃₁	semidirect
795. C₂	#2481×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×#126×C₁₃₁	2
C₂³×C₄⋊C₄×C₁₃₁	2
#2481×C₁₃₁	2
C₂×#400×C₁₃₁	2
C₂×#397×C₁₃₁	2
C₂×#396×C₁₃₁	2
C₂×#388×C₁₃₁	2
C₂×#387×C₁₃₁	2
C₂×#386×C₁₃₁	2
C₂×#385×C₁₃₁	2
C₂×#380×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
C₂×#2481	131

Subgroups — C2×#2481×C131 #45720545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2481×C₁₃₁ #45720545