Subgroups — C₂×C₃₁×#3401 #21518157

Order 7936.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#496	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
24	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#559	—	2	4	no	—
27	C₃₁×#559	C₂²	1	8	yes	complemented
28	C₃₁×#556	—	2	4	no	—
29	C₃₁×#556	C₂²	1	8	yes	complemented
30	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#126	—	2	1	no	—
33	C₂×C₃₁×#126	—	2	1	no	—
34	C₂×C₃₁×#124	—	2	1	no	—
35	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#123	—	2	1	no	—
40	C₂×C₃₁×#123	—	2	1	no	—
41	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	—	2	1	no	—
47	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#117	—	2	1	no	—
51	C₃₁×#497	C₂²	1	8	yes	complemented
52	C₃₁×#496	C₂²	1	8	yes	—
53	C₃₁×#495	C₂²	1	8	yes	complemented
54	C₃₁×#464	C₂²	1	8	yes	complemented
55	C₃₁×#464	C₂²	1	8	yes	complemented
56	C₃₁×#463	C₂²	1	8	yes	complemented
57	C₃₁×#463	C₂²	1	8	yes	complemented
58	C₃₁×#461	C₂²	1	8	yes	complemented
59	C₃₁×#460	C₂²	1	8	yes	complemented
60	C₃₁×#446	C₂²	1	8	yes	complemented
61	C₃₁×#442	C₂²	1	8	yes	complemented
62	C₃₁×#441	C₂²	1	8	yes	complemented
63	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
64	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
75	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₃₁	—	2	1	no	—
82	C₂²×D₄×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	—	2	1	no	—
87	C₂³×C₄×C₃₁	—	2	1	no	—
88	C₂³×C₄×C₃₁	—	2	1	no	—
89	C₂×Q₁₆×C₃₁	—	2	4	no	—
90	C₂×Q₁₆×C₃₁	—	4	2	no	—
91	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₃₁	—	2	4	no	—
94	C₂×SD₁₆×C₃₁	—	4	2	no	—
95	C₂×SD₁₆×C₃₁	—	4	2	no	—
96	C₂×SD₁₆×C₃₁	—	4	2	no	—
97	C₂×SD₁₆×C₃₁	—	4	2	no	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×D₈×C₃₁	—	2	4	no	—
104	C₂×D₈×C₃₁	—	4	2	no	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₂×D₈×C₃₁	C₂³	1	4	yes	—
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	—	2	2	no	—
112	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₃₁×#127	—	2	2	no	—
114	C₃₁×#127	C₂³	1	4	yes	—
115	C₃₁×#126	—	2	8	no	—
116	C₃₁×#126	—	2	8	no	—
117	C₃₁×#124	—	2	8	no	—
118	C₃₁×#124	—	2	2	no	—
119	C₃₁×#124	—	2	2	no	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	C₂³	1	4	yes	—
123	C₃₁×#124	C₂³	1	4	yes	—
124	C₃₁×#124	C₂³	1	4	yes	—
125	C₃₁×#124	C₂³	1	4	yes	—
126	C₃₁×#123	—	2	8	no	—
127	C₃₁×#123	—	2	8	no	—
128	C₃₁×C₂²⋊Q₈	—	2	8	no	—
129	C₄×Q₈×C₃₁	—	2	2	no	—
130	C₄×Q₈×C₃₁	—	2	2	no	—
131	C₄×Q₈×C₃₁	—	2	2	no	—
132	C₄×Q₈×C₃₁	D₄	1	4	yes	—
133	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
134	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
135	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
136	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
137	C₄×D₄×C₃₁	—	2	8	no	—
138	C₄×D₄×C₃₁	—	2	2	no	—
139	C₄×D₄×C₃₁	—	2	2	no	—
140	C₄×D₄×C₃₁	—	2	2	no	—
141	C₄×D₄×C₃₁	C₂³	1	4	yes	—
142	C₄×D₄×C₃₁	C₂³	1	4	yes	—
143	C₄×D₄×C₃₁	C₂³	1	4	yes	—
144	C₃₁×#117	—	2	8	no	—
145	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
146	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
147	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
148	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
149	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
150	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
166	C₂×C₄²×C₃₁	—	2	1	no	—
167	C₂×C₄²×C₃₁	—	2	1	no	—
168	C₂×C₄²×C₃₁	—	2	1	no	—
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
172	C₃₁×#106	C₂³	1	4	yes	—
173	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
174	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
175	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
176	C₃₁×#103	C₂³	1	4	yes	—
177	C₃₁×#103	C₂³	1	4	yes	—
178	C₃₁×#103	C₂³	1	4	yes	—
179	C₃₁×#102	C₂³	1	4	yes	—
180	C₃₁×#102	C₂³	1	4	yes	—
181	C₃₁×#102	C₂³	1	4	yes	—
182	C₃₁×#97	C₂³	1	4	yes	—
183	C₃₁×#97	C₂³	1	4	yes	—
184	C₄×C₈×C₃₁	C₂³	1	4	yes	—
185	C₂⁴×C₃₁	—	2	1	no	—
186	C₂⁴×C₃₁	—	2	1	no	—
187	C₂⁴×C₃₁	—	2	1	no	—
188	C₂×Q₈×C₃₁	—	2	1	no	—
189	C₂×Q₈×C₃₁	—	2	1	no	—
190	C₂×Q₈×C₃₁	—	2	1	no	—
191	C₂×Q₈×C₃₁	—	2	2	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	2	2	no	—
195	C₂×Q₈×C₃₁	—	2	2	no	—
196	C₂×Q₈×C₃₁	—	2	2	no	—
197	C₂×Q₈×C₃₁	—	4	2	no	—
198	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
199	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
200	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
201	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
202	C₂×D₄×C₃₁	—	2	1	no	—
203	C₂×D₄×C₃₁	—	2	1	no	—
204	C₂×D₄×C₃₁	—	2	1	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	4	4	no	—
214	C₂×D₄×C₃₁	—	8	2	no	—
215	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	—	2	1	no	—
219	C₂²×C₄×C₃₁	—	2	1	no	—
220	C₂²×C₄×C₃₁	—	2	1	no	—
221	C₂²×C₄×C₃₁	—	2	1	no	—
222	C₂²×C₄×C₃₁	—	2	1	no	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	4	4	no	—
227	C₂²×C₄×C₃₁	—	8	2	no	—
228	C₂²×C₄×C₃₁	—	8	2	no	—
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₃₁	—	2	8	no	—
237	Q₁₆×C₃₁	—	4	4	no	—
238	SD₁₆×C₃₁	—	2	8	no	—
239	SD₁₆×C₃₁	—	4	4	no	—
240	SD₁₆×C₃₁	—	4	4	no	—
241	SD₁₆×C₃₁	—	4	4	no	—
242	SD₁₆×C₃₁	—	4	4	no	—
243	D₈×C₃₁	—	2	8	no	—
244	D₈×C₃₁	—	4	4	no	—
245	C₂×C₈×C₃₁	—	2	2	no	—
246	C₂×C₈×C₃₁	—	2	2	no	—
247	C₂×C₈×C₃₁	—	2	2	no	—
248	C₂×C₈×C₃₁	#41	1	4	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
251	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	—	2	4	no	—
277	C₄²×C₃₁	—	2	4	no	—
278	C₄²×C₃₁	—	2	4	no	—
279	C₄²×C₃₁	C₂×D₄	1	2	yes	—
280	C₄²×C₃₁	C₂×D₄	1	2	yes	—
281	C₄²×C₃₁	C₂×D₄	1	2	yes	—
282	C₄²×C₃₁	C₂⁴	1	2	yes	—
283	C₄²×C₃₁	C₂⁴	1	2	yes	—
284	C₄²×C₃₁	C₂⁴	1	2	yes	—
285	C₂×#3401	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	4	2	no	—
290	C₂³×C₃₁	—	4	2	no	—
291	C₂³×C₃₁	—	4	2	no	—
292	C₂³×C₃₁	—	4	2	no	—
293	C₂³×C₃₁	—	4	2	no	—
294	C₂³×C₃₁	—	4	2	no	—
295	C₂³×C₃₁	—	4	2	no	—
296	C₂³×C₃₁	—	4	2	no	—
297	C₂³×C₃₁	—	4	2	no	—
298	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₃₁	—	2	2	no	—
300	Q₈×C₃₁	—	2	2	no	—
301	Q₈×C₃₁	—	2	2	no	—
302	Q₈×C₃₁	—	2	2	no	—
303	Q₈×C₃₁	—	2	2	no	—
304	Q₈×C₃₁	—	2	2	no	—
305	Q₈×C₃₁	—	4	4	no	—
306	Q₈×C₃₁	—	4	2	no	—
307	Q₈×C₃₁	—	4	2	no	—
308	Q₈×C₃₁	—	4	2	no	—
309	D₄×C₃₁	—	2	2	no	—
310	D₄×C₃₁	—	2	2	no	—
311	D₄×C₃₁	—	2	2	no	—
312	D₄×C₃₁	—	2	2	no	—
313	D₄×C₃₁	—	2	2	no	—
314	D₄×C₃₁	—	2	2	no	—
315	D₄×C₃₁	—	4	8	no	—
316	D₄×C₃₁	—	4	2	no	—
317	D₄×C₃₁	—	4	2	no	—
318	D₄×C₃₁	—	4	2	no	—
319	D₄×C₃₁	—	8	4	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	4	8	no	—
332	C₂×C₄×C₃₁	—	4	2	no	—
333	C₂×C₄×C₃₁	—	4	2	no	—
334	C₂×C₄×C₃₁	—	4	2	no	—
335	C₂×C₄×C₃₁	—	4	2	no	—
336	C₂×C₄×C₃₁	—	4	2	no	—
337	C₂×C₄×C₃₁	—	8	4	no	—
338	C₂×C₄×C₃₁	—	8	4	no	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
347	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
349	C₈×C₃₁	—	2	2	no	—
350	C₈×C₃₁	—	2	2	no	—
351	C₈×C₃₁	—	2	2	no	—
352	C₈×C₃₁	C₂×#41	1	4	yes	—
353	C₂×#559	C₂×C₃₁	1	1	yes	characteristic, complemented
354	C₂×#556	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#3401	C₂×C₃₁	1	16	yes	direct product factor
356	C₂×#497	C₂×C₃₁	1	1	yes	characteristic, complemented
357	C₂×#496	C₂×C₃₁	1	1	yes	characteristic
358	C₂×#495	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
364	C₂×#461	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂×#446	C₂×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
367	C₂×#441	C₂×C₃₁	1	1	yes	characteristic, complemented
368	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	8	4	no	—
379	C₂²×C₃₁	—	8	4	no	—
380	C₂²×C₃₁	—	8	4	no	—
381	C₂²×C₃₁	#550	1	2	yes	—
382	C₂²×C₃₁	#575	1	2	yes	—
383	C₂²×C₃₁	#577	1	2	yes	—
384	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₃₁	—	2	2	no	—
386	C₄×C₃₁	—	2	2	no	—
387	C₄×C₃₁	—	2	2	no	—
388	C₄×C₃₁	—	2	2	no	—
389	C₄×C₃₁	—	2	2	no	—
390	C₄×C₃₁	—	2	2	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	2	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	2	no	—
396	C₄×C₃₁	#550	1	2	yes	—
397	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
398	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
400	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
401	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
402	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
403	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
404	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
406	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
407	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
408	#559	—	2	4	no	—
409	#559	C₂²×C₃₁	1	8	yes	complemented
410	#556	—	2	4	no	—
411	#556	C₂²×C₃₁	1	8	yes	complemented
412	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
413	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
414	C₂×#126	—	2	1	no	—
415	C₂×#126	—	2	1	no	—
416	C₂×#124	—	2	1	no	—
417	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
418	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
419	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
420	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×#123	—	2	1	no	—
422	C₂×#123	—	2	1	no	—
423	C₂×C₂²⋊Q₈	—	2	1	no	—
424	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
428	C₂×C₄×D₄	—	2	1	no	—
429	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×#117	—	2	1	no	—
433	#497	C₂²×C₃₁	1	8	yes	complemented
434	#496	C₂²×C₃₁	1	8	yes	—
435	#495	C₂²×C₃₁	1	8	yes	complemented
436	#464	C₂²×C₃₁	1	8	yes	complemented
437	#464	C₂²×C₃₁	1	8	yes	complemented
438	#463	C₂²×C₃₁	1	8	yes	complemented
439	#463	C₂²×C₃₁	1	8	yes	complemented
440	#461	C₂²×C₃₁	1	8	yes	complemented
441	#460	C₂²×C₃₁	1	8	yes	complemented
442	#446	C₂²×C₃₁	1	8	yes	complemented
443	#442	C₂²×C₃₁	1	8	yes	complemented
444	#441	C₂²×C₃₁	1	8	yes	complemented
445	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
446	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
455	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
456	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
457	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×C₃₁	—	8	2	no	—
460	C₂×C₃₁	—	8	2	no	—
461	C₂×C₃₁	—	8	2	no	—
462	C₂×C₃₁	#3401	1	4	yes	direct product factor
463	C₂×C₃₁	C₂×#550	1	1	yes	characteristic
464	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
465	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
466	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
467	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂×Q₁₆	—	2	4	no	—
479	C₂×Q₁₆	—	4	2	no	—
480	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
481	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
482	C₂×SD₁₆	—	2	4	no	—
483	C₂×SD₁₆	—	4	2	no	—
484	C₂×SD₁₆	—	4	2	no	—
485	C₂×SD₁₆	—	4	2	no	—
486	C₂×SD₁₆	—	4	2	no	—
487	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
488	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
491	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
492	C₂×D₈	—	2	4	no	—
493	C₂×D₈	—	4	2	no	—
494	C₂×D₈	C₂³×C₃₁	1	4	yes	—
495	C₂×D₈	C₂³×C₃₁	1	4	yes	—
496	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
502	#127	—	2	2	no	—
503	#127	C₂³×C₃₁	1	4	yes	—
504	#126	—	2	8	no	—
505	#126	—	2	8	no	—
506	#124	—	2	8	no	—
507	#124	—	2	2	no	—
508	#124	—	2	2	no	—
509	#124	—	2	2	no	—
510	#124	—	2	2	no	—
511	#124	C₂³×C₃₁	1	4	yes	—
512	#124	C₂³×C₃₁	1	4	yes	—
513	#124	C₂³×C₃₁	1	4	yes	—
514	#124	C₂³×C₃₁	1	4	yes	—
515	#123	—	2	8	no	—
516	#123	—	2	8	no	—
517	C₂²⋊Q₈	—	2	8	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	D₄×C₃₁	1	4	yes	—
522	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
524	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
525	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	C₂³×C₃₁	1	4	yes	—
531	C₄×D₄	C₂³×C₃₁	1	4	yes	—
532	C₄×D₄	C₂³×C₃₁	1	4	yes	—
533	#117	—	2	8	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
540	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
541	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
561	#106	C₂³×C₃₁	1	4	yes	—
562	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
563	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
564	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
565	#103	C₂³×C₃₁	1	4	yes	—
566	#103	C₂³×C₃₁	1	4	yes	—
567	#103	C₂³×C₃₁	1	4	yes	—
568	#102	C₂³×C₃₁	1	4	yes	—
569	#102	C₂³×C₃₁	1	4	yes	—
570	#102	C₂³×C₃₁	1	4	yes	—
571	#97	C₂³×C₃₁	1	4	yes	—
572	#97	C₂³×C₃₁	1	4	yes	—
573	C₄×C₈	C₂³×C₃₁	1	4	yes	—
574	C₃₁	C₂×#3401	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	4	2	no	—
588	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
589	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	8	2	no	—
605	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
606	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
607	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
626	Q₁₆	—	2	8	no	—
627	Q₁₆	—	4	4	no	—
628	SD₁₆	—	2	8	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	no	—
631	SD₁₆	—	4	4	no	—
632	SD₁₆	—	4	4	no	—
633	D₈	—	2	8	no	—
634	D₈	—	4	4	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	#41×C₃₁	1	4	yes	—
639	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
640	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
641	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
642	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
652	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
653	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	C₂×D₄×C₃₁	1	2	yes	—
670	C₄²	C₂×D₄×C₃₁	1	2	yes	—
671	C₄²	C₂×D₄×C₃₁	1	2	yes	—
672	C₄²	C₂⁴×C₃₁	1	2	yes	—
673	C₄²	C₂⁴×C₃₁	1	2	yes	—
674	C₄²	C₂⁴×C₃₁	1	2	yes	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	4	4	no	—
695	Q₈	—	4	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	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	—	4	8	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	—	8	4	no	—
728	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
736	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
737	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×#41×C₃₁	1	4	yes	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	8	4	no	—
752	C₂²	—	8	4	no	—
753	C₂²	—	8	4	no	—
754	C₂²	C₃₁×#550	1	2	yes	—
755	C₂²	C₃₁×#575	1	2	yes	—
756	C₂²	C₃₁×#577	1	2	yes	—
757	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	C₃₁×#550	1	2	yes	—
770	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
771	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂	—	8	2	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	C₃₁×#3401	1	4	yes	direct product factor
776	C₂	C₂×C₃₁×#550	1	1	yes	characteristic
777	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
778	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#559	C₂	semidirect
2. C₂×C₃₁×#556	C₂	semidirect
3. C₃₁×#3401	C₂	direct (N × H)
4. C₂×C₃₁×#497	C₂	semidirect
6. C₂×C₃₁×#495	C₂	semidirect
7. C₂×C₃₁×#464	C₂	semidirect
8. C₂×C₃₁×#464	C₂	semidirect
9. C₂×C₃₁×#460	C₂	semidirect
10. C₂×C₃₁×#463	C₂	semidirect
11. C₂×C₃₁×#463	C₂	semidirect
12. C₂×C₃₁×#461	C₂	semidirect
13. C₂×C₃₁×#446	C₂	semidirect
14. C₂×C₃₁×#442	C₂	semidirect
15. C₂×C₃₁×#441	C₂	semidirect
16. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
53. C₃₁×#495	C₂²	semidirect
54. C₃₁×#464	C₂²	semidirect
55. C₃₁×#464	C₂²	semidirect
56. C₃₁×#463	C₂²	semidirect
57. C₃₁×#463	C₂²	semidirect
58. C₃₁×#461	C₂²	semidirect
59. C₃₁×#460	C₂²	semidirect
60. C₃₁×#446	C₂²	semidirect
61. C₃₁×#442	C₂²	semidirect
62. C₃₁×#441	C₂²	semidirect
63. C₄×SD₁₆×C₃₁	C₂²	semidirect
285. C₂×#3401	C₃₁	direct (N × H)
353. C₂×#559	C₂×C₃₁	semidirect
354. C₂×#556	C₂×C₃₁	semidirect
355. #3401	C₂×C₃₁	direct (N × H)
356. C₂×#497	C₂×C₃₁	semidirect
358. C₂×#495	C₂×C₃₁	semidirect
359. C₂×#464	C₂×C₃₁	semidirect
360. C₂×#464	C₂×C₃₁	semidirect
361. C₂×#460	C₂×C₃₁	semidirect
362. C₂×#463	C₂×C₃₁	semidirect
363. C₂×#463	C₂×C₃₁	semidirect
364. C₂×#461	C₂×C₃₁	semidirect
365. C₂×#446	C₂×C₃₁	semidirect
366. C₂×#442	C₂×C₃₁	semidirect
367. C₂×#441	C₂×C₃₁	semidirect
368. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
409. #559	C₂²×C₃₁	semidirect
411. #556	C₂²×C₃₁	semidirect
433. #497	C₂²×C₃₁	semidirect
435. #495	C₂²×C₃₁	semidirect
436. #464	C₂²×C₃₁	semidirect
437. #464	C₂²×C₃₁	semidirect
438. #463	C₂²×C₃₁	semidirect
439. #463	C₂²×C₃₁	semidirect
440. #461	C₂²×C₃₁	semidirect
441. #460	C₂²×C₃₁	semidirect
442. #446	C₂²×C₃₁	semidirect
443. #442	C₂²×C₃₁	semidirect
444. #441	C₂²×C₃₁	semidirect
445. C₄×SD₁₆	C₂²×C₃₁	semidirect
462. C₂×C₃₁	#3401	direct (N × H)
574. C₃₁	C₂×#3401	direct (N × H)
775. C₂	C₃₁×#3401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#559	2
C₂×C₃₁×#556	2
C₃₁×#3401	2
C₂×C₃₁×#497	2
C₂×C₃₁×#496	2
C₂×C₃₁×#495	2
C₂×C₃₁×#464	2
C₂×C₃₁×#460	2
C₂×C₃₁×#463	2
C₂×C₃₁×#461	2
C₂×C₃₁×#446	2
C₂×C₃₁×#442	2
C₂×C₃₁×#441	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×#3401	31

Subgroups — C2×C31×#3401 #21518157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3401 #21518157