Subgroups — C₂×C₃₁×#3119 #21517307

Order 7936.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3119	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#540	—	2	4	no	—
23	C₃₁×#540	C₂²	1	8	yes	complemented
24	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#123	—	2	1	no	—
27	C₂×C₃₁×#123	—	2	1	no	—
28	C₂×C₃₁×#121	—	2	1	no	—
29	C₂×C₃₁×#121	—	2	1	no	—
30	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₃₁×#520	—	2	4	no	—
33	C₃₁×#520	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₃₁	—	2	1	no	—
37	C₂×C₄×D₄×C₃₁	—	2	1	no	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#117	—	2	1	no	—
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#481	C₂²	1	8	yes	complemented
47	C₃₁×#480	C₂²	1	8	yes	complemented
48	C₃₁×#479	C₂²	1	8	yes	complemented
49	C₃₁×#478	C₂²	1	8	yes	complemented
50	C₃₁×#460	C₂²	1	8	yes	complemented
51	C₃₁×#459	C₂²	1	8	yes	complemented
52	C₃₁×#449	C₂²	1	8	yes	complemented
53	C₃₁×#449	C₂²	1	8	yes	complemented
54	C₃₁×#442	C₂²	1	8	yes	complemented
55	C₃₁×#440	C₂²	1	8	yes	complemented
56	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
57	C₄×D₈×C₃₁	C₂²	1	8	yes	complemented
58	C₃₁×#433	C₂²	1	8	yes	complemented
59	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
63	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
66	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
68	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×C₂²⋊C₈	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	C₂×#41×C₃₁	—	2	4	no	—
78	C₂×#41×C₃₁	—	2	4	no	—
79	C₂×#41×C₃₁	—	2	2	no	—
80	C₂×#41×C₃₁	C₂³	1	4	yes	—
81	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	—	2	1	no	—
84	C₂²×D₄×C₃₁	—	2	1	no	—
85	C₂²×D₄×C₃₁	—	2	1	no	—
86	C₂²×D₄×C₃₁	—	2	1	no	—
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	—	2	1	no	—
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂³×C₄×C₃₁	—	2	1	no	—
94	C₂³×C₄×C₃₁	—	2	1	no	—
95	C₂³×C₄×C₃₁	—	2	1	no	—
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₃₁	—	2	4	no	—
98	C₂×SD₁₆×C₃₁	—	2	4	no	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×D₈×C₃₁	—	2	4	no	—
102	C₂×D₈×C₃₁	—	2	4	no	—
103	C₂×D₈×C₃₁	C₂³	1	4	yes	—
104	C₂×D₈×C₃₁	C₂³	1	4	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×#127	—	2	2	no	—
110	C₃₁×#127	C₂³	1	4	yes	—
111	C₃₁×#125	—	2	2	no	—
112	C₃₁×#125	C₂³	1	4	yes	—
113	C₃₁×#123	—	2	8	no	—
114	C₃₁×#123	—	2	8	no	—
115	C₃₁×#121	—	2	2	no	—
116	C₃₁×#121	—	2	2	no	—
117	C₃₁×#121	—	2	8	no	—
118	C₃₁×#121	—	2	8	no	—
119	C₃₁×#121	C₂³	1	4	yes	—
120	C₃₁×#121	C₂³	1	4	yes	—
121	C₄×Q₈×C₃₁	—	2	2	no	—
122	C₄×Q₈×C₃₁	—	2	2	no	—
123	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
124	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
125	C₄×D₄×C₃₁	—	2	8	no	—
126	C₄×D₄×C₃₁	—	2	8	no	—
127	C₄×D₄×C₃₁	—	2	2	no	—
128	C₄×D₄×C₃₁	—	2	2	no	—
129	C₄×D₄×C₃₁	—	2	2	no	—
130	C₄×D₄×C₃₁	—	2	2	no	—
131	C₄×D₄×C₃₁	C₂³	1	4	yes	—
132	C₄×D₄×C₃₁	C₂³	1	4	yes	—
133	C₄×D₄×C₃₁	C₂³	1	4	yes	—
134	C₄×D₄×C₃₁	C₂³	1	4	yes	—
135	C₃₁×#117	—	2	8	no	—
136	C₃₁×#117	D₄	1	4	yes	—
137	C₃₁×#117	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
139	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
140	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
141	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
142	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
143	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
144	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
145	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₃₁	—	2	1	no	—
161	C₂×C₄²×C₃₁	—	2	1	no	—
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₃₁×#107	C₂³	1	4	yes	—
165	C₃₁×#107	C₂³	1	4	yes	—
166	C₃₁×#106	C₂³	1	4	yes	—
167	C₃₁×#106	C₂³	1	4	yes	—
168	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
169	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
170	C₃₁×#103	C₂³	1	4	yes	—
171	C₃₁×#103	C₂³	1	4	yes	—
172	C₃₁×#102	C₂³	1	4	yes	—
173	C₃₁×#102	C₂³	1	4	yes	—
174	C₃₁×#102	C₂³	1	4	yes	—
175	C₃₁×#102	C₂³	1	4	yes	—
176	C₃₁×#102	C₂³	1	4	yes	—
177	C₃₁×#102	C₂³	1	4	yes	—
178	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₃₁×#97	C₂³	1	4	yes	—
181	C₄×C₈×C₃₁	C₂³	1	4	yes	—
182	C₂⁴×C₃₁	—	2	1	no	—
183	C₂⁴×C₃₁	—	2	1	no	—
184	C₂⁴×C₃₁	—	2	1	no	—
185	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
186	#41×C₃₁	—	2	16	no	—
187	#41×C₃₁	—	2	8	no	—
188	#41×C₃₁	—	2	8	no	—
189	C₂×Q₈×C₃₁	—	2	1	no	—
190	C₂×Q₈×C₃₁	—	2	2	no	—
191	C₂×Q₈×C₃₁	#41	1	4	yes	—
192	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
193	C₂×D₄×C₃₁	—	2	8	no	—
194	C₂×D₄×C₃₁	—	2	4	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	4	no	—
197	C₂×D₄×C₃₁	—	2	1	no	—
198	C₂×D₄×C₃₁	—	2	1	no	—
199	C₂×D₄×C₃₁	—	2	1	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	2	no	—
203	C₂×D₄×C₃₁	—	2	2	no	—
204	C₂×D₄×C₃₁	—	2	2	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	8	2	no	—
208	C₂×D₄×C₃₁	—	8	2	no	—
209	C₂×D₄×C₃₁	—	8	2	no	—
210	C₂×D₄×C₃₁	—	8	2	no	—
211	C₂×D₄×C₃₁	#41	1	4	yes	—
212	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
214	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₃₁	—	2	8	no	—
216	C₂²×C₄×C₃₁	—	2	1	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	8	2	no	—
230	C₂²×C₄×C₃₁	—	8	2	no	—
231	C₂²×C₄×C₃₁	—	8	2	no	—
232	C₂²×C₄×C₃₁	—	8	2	no	—
233	C₂²×C₄×C₃₁	—	8	2	no	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	SD₁₆×C₃₁	—	2	8	no	—
243	SD₁₆×C₃₁	—	2	8	no	—
244	D₈×C₃₁	—	2	8	no	—
245	D₈×C₃₁	—	2	8	no	—
246	C₂×C₈×C₃₁	—	2	2	no	—
247	C₂×C₈×C₃₁	—	2	2	no	—
248	C₂×C₈×C₃₁	—	2	2	no	—
249	C₂×C₈×C₃₁	—	2	2	no	—
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	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
258	C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₄⋊C₄×C₃₁	—	2	4	no	—
260	C₄⋊C₄×C₃₁	—	2	4	no	—
261	C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂×D₄	1	4	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
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	C₂⁴	1	2	yes	—
282	C₄²×C₃₁	C₂⁴	1	2	yes	—
283	C₂×#3119	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₃₁	—	2	2	no	—
285	C₂³×C₃₁	—	2	4	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	2	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	—	4	2	no	—
299	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₃₁	—	2	4	no	—
302	Q₈×C₃₁	—	2	2	no	—
303	Q₈×C₃₁	C₂×#41	1	4	yes	—
304	D₄×C₃₁	—	2	16	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	2	2	no	—
309	D₄×C₃₁	—	2	2	no	—
310	D₄×C₃₁	—	2	2	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	4	2	no	—
313	D₄×C₃₁	—	8	4	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	4	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	C₂×#41	1	4	yes	—
318	C₂×C₄×C₃₁	—	2	16	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	4	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	4	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	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	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	—	8	4	no	—
340	C₂×C₄×C₃₁	—	8	4	no	—
341	C₂×C₄×C₃₁	—	8	4	no	—
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	2	yes	—
346	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
349	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
350	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
351	C₈×C₃₁	—	2	2	no	—
352	C₈×C₃₁	—	2	2	no	—
353	C₈×C₃₁	—	2	2	no	—
354	C₈×C₃₁	—	2	2	no	—
355	C₂×#540	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#3119	C₂×C₃₁	1	16	yes	direct product factor
358	C₂×#481	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂×#459	C₂×C₃₁	1	1	yes	characteristic, complemented
364	C₂×#449	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂×#449	C₂×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
367	C₂×#440	C₂×C₃₁	1	1	yes	characteristic, complemented
368	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
369	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
370	C₂×#433	C₂×C₃₁	1	1	yes	characteristic, complemented
371	C₂²×C₃₁	—	2	2	no	—
372	C₂²×C₃₁	—	2	4	no	—
373	C₂²×C₃₁	—	2	2	no	—
374	C₂²×C₃₁	—	2	2	no	—
375	C₂²×C₃₁	—	4	4	no	—
376	C₂²×C₃₁	—	4	8	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	4	2	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	—	4	2	no	—
381	C₂²×C₃₁	—	4	2	no	—
382	C₂²×C₃₁	—	4	2	no	—
383	C₂²×C₃₁	—	4	2	no	—
384	C₂²×C₃₁	—	4	2	no	—
385	C₂²×C₃₁	—	8	4	no	—
386	C₂²×C₃₁	—	8	4	no	—
387	C₂²×C₃₁	#525	1	2	yes	—
388	C₂²×C₃₁	#576	1	2	yes	—
389	C₂²×C₃₁	#577	1	2	yes	—
390	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₃₁	—	2	2	no	—
392	C₄×C₃₁	—	2	4	no	—
393	C₄×C₃₁	—	2	2	no	—
394	C₄×C₃₁	—	2	2	no	—
395	C₄×C₃₁	—	2	2	no	—
396	C₄×C₃₁	—	2	2	no	—
397	C₄×C₃₁	—	4	2	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	#525	1	2	yes	—
402	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
403	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
404	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
406	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
407	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
408	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
409	#540	—	2	4	no	—
410	#540	C₂²×C₃₁	1	8	yes	complemented
411	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
412	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
413	C₂×#123	—	2	1	no	—
414	C₂×#123	—	2	1	no	—
415	C₂×#121	—	2	1	no	—
416	C₂×#121	—	2	1	no	—
417	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
418	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
419	#520	—	2	4	no	—
420	#520	C₂²×C₃₁	1	8	yes	complemented
421	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
423	C₂×C₄×D₄	—	2	1	no	—
424	C₂×C₄×D₄	—	2	1	no	—
425	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
429	C₂×#117	—	2	1	no	—
430	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	—	2	1	no	—
432	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
433	#481	C₂²×C₃₁	1	8	yes	complemented
434	#480	C₂²×C₃₁	1	8	yes	complemented
435	#479	C₂²×C₃₁	1	8	yes	complemented
436	#478	C₂²×C₃₁	1	8	yes	complemented
437	#460	C₂²×C₃₁	1	8	yes	complemented
438	#459	C₂²×C₃₁	1	8	yes	complemented
439	#449	C₂²×C₃₁	1	8	yes	complemented
440	#449	C₂²×C₃₁	1	8	yes	complemented
441	#442	C₂²×C₃₁	1	8	yes	complemented
442	#440	C₂²×C₃₁	1	8	yes	complemented
443	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
444	C₄×D₈	C₂²×C₃₁	1	8	yes	complemented
445	#433	C₂²×C₃₁	1	8	yes	complemented
446	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
447	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
451	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×#103	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×#102	C₂²×C₃₁	1	1	yes	characteristic
457	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
461	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
463	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×C₃₁	—	4	2	no	—
465	C₂×C₃₁	—	4	4	no	—
466	C₂×C₃₁	—	8	2	no	—
467	C₂×C₃₁	—	8	2	no	—
468	C₂×C₃₁	#3119	1	4	yes	direct product factor
469	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
470	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
471	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
472	C₂×#41	—	2	4	no	—
473	C₂×#41	—	2	4	no	—
474	C₂×#41	—	2	2	no	—
475	C₂×#41	C₂³×C₃₁	1	4	yes	—
476	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂×SD₁₆	—	2	4	no	—
493	C₂×SD₁₆	—	2	4	no	—
494	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
496	C₂×D₈	—	2	4	no	—
497	C₂×D₈	—	2	4	no	—
498	C₂×D₈	C₂³×C₃₁	1	4	yes	—
499	C₂×D₈	C₂³×C₃₁	1	4	yes	—
500	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
504	#127	—	2	2	no	—
505	#127	C₂³×C₃₁	1	4	yes	—
506	#125	—	2	2	no	—
507	#125	C₂³×C₃₁	1	4	yes	—
508	#123	—	2	8	no	—
509	#123	—	2	8	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	8	no	—
513	#121	—	2	8	no	—
514	#121	C₂³×C₃₁	1	4	yes	—
515	#121	C₂³×C₃₁	1	4	yes	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
519	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	C₂³×C₃₁	1	4	yes	—
527	C₄×D₄	C₂³×C₃₁	1	4	yes	—
528	C₄×D₄	C₂³×C₃₁	1	4	yes	—
529	C₄×D₄	C₂³×C₃₁	1	4	yes	—
530	#117	—	2	8	no	—
531	#117	D₄×C₃₁	1	4	yes	—
532	#117	C₂³×C₃₁	1	4	yes	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	8	no	—
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×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
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	D₄×C₃₁	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
555	C₂×C₄²	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
559	#107	C₂³×C₃₁	1	4	yes	—
560	#107	C₂³×C₃₁	1	4	yes	—
561	#106	C₂³×C₃₁	1	4	yes	—
562	#106	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	#102	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	#102	C₂³×C₃₁	1	4	yes	—
572	#102	C₂³×C₃₁	1	4	yes	—
573	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
574	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
575	#97	C₂³×C₃₁	1	4	yes	—
576	C₄×C₈	C₂³×C₃₁	1	4	yes	—
577	C₃₁	C₂×#3119	1	1	yes	characteristic, direct product factor, Sylow
578	C₂⁴	—	2	1	no	—
579	C₂⁴	—	2	1	no	—
580	C₂⁴	—	2	1	no	—
581	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
582	#41	—	2	16	no	—
583	#41	—	2	8	no	—
584	#41	—	2	8	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	#41×C₃₁	1	4	yes	—
588	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	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	—	8	2	no	—
604	C₂×D₄	—	8	2	no	—
605	C₂×D₄	—	8	2	no	—
606	C₂×D₄	—	8	2	no	—
607	C₂×D₄	#41×C₃₁	1	4	yes	—
608	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
609	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
610	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	8	2	no	—
626	C₂²×C₄	—	8	2	no	—
627	C₂²×C₄	—	8	2	no	—
628	C₂²×C₄	—	8	2	no	—
629	C₂²×C₄	—	8	2	no	—
630	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
638	SD₁₆	—	2	8	no	—
639	SD₁₆	—	2	8	no	—
640	D₈	—	2	8	no	—
641	D₈	—	2	8	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
647	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
648	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
649	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
660	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
661	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
672	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	C₂×D₄×C₃₁	1	2	yes	—
676	C₄²	C₂×D₄×C₃₁	1	2	yes	—
677	C₄²	C₂⁴×C₃₁	1	2	yes	—
678	C₄²	C₂⁴×C₃₁	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
695	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
696	Q₈	—	2	4	no	—
697	Q₈	—	2	2	no	—
698	Q₈	C₂×#41×C₃₁	1	4	yes	—
699	D₄	—	2	16	no	—
700	D₄	—	2	4	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	4	no	—
711	D₄	—	8	4	no	—
712	D₄	C₂×#41×C₃₁	1	4	yes	—
713	C₂×C₄	—	2	16	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	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	4	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	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
744	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
745	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	8	no	—
756	C₂²	—	4	2	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	4	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₃₁×#525	1	2	yes	—
767	C₂²	C₃₁×#576	1	2	yes	—
768	C₂²	C₃₁×#577	1	2	yes	—
769	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	4	no	—
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	C₃₁×#525	1	2	yes	—
781	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
782	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
783	C₂	—	4	2	no	—
784	C₂	—	4	4	no	—
785	C₂	—	8	2	no	—
786	C₂	—	8	2	no	—
787	C₂	C₃₁×#3119	1	4	yes	direct product factor
788	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
789	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
790	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#540	C₂	semidirect
2. C₂×C₃₁×#520	C₂	semidirect
3. C₃₁×#3119	C₂	direct (N × H)
4. C₂×C₃₁×#481	C₂	semidirect
5. C₂×C₃₁×#480	C₂	semidirect
6. C₂×C₃₁×#479	C₂	semidirect
7. C₂×C₃₁×#478	C₂	semidirect
8. C₂×C₃₁×#460	C₂	semidirect
9. C₂×C₃₁×#459	C₂	semidirect
10. C₂×C₃₁×#449	C₂	semidirect
11. C₂×C₃₁×#449	C₂	semidirect
12. C₂×C₃₁×#442	C₂	semidirect
13. C₂×C₃₁×#440	C₂	semidirect
14. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
15. C₂×C₄×D₈×C₃₁	C₂	semidirect
16. C₂×C₃₁×#433	C₂	semidirect
23. C₃₁×#540	C₂²	semidirect
33. C₃₁×#520	C₂²	semidirect
46. C₃₁×#481	C₂²	semidirect
47. C₃₁×#480	C₂²	semidirect
48. C₃₁×#479	C₂²	semidirect
49. C₃₁×#478	C₂²	semidirect
50. C₃₁×#460	C₂²	semidirect
51. C₃₁×#459	C₂²	semidirect
52. C₃₁×#449	C₂²	semidirect
53. C₃₁×#449	C₂²	semidirect
54. C₃₁×#442	C₂²	semidirect
55. C₃₁×#440	C₂²	semidirect
56. C₄×SD₁₆×C₃₁	C₂²	semidirect
57. C₄×D₈×C₃₁	C₂²	semidirect
58. C₃₁×#433	C₂²	semidirect
283. C₂×#3119	C₃₁	direct (N × H)
355. C₂×#540	C₂×C₃₁	semidirect
356. C₂×#520	C₂×C₃₁	semidirect
357. #3119	C₂×C₃₁	direct (N × H)
358. C₂×#481	C₂×C₃₁	semidirect
359. C₂×#480	C₂×C₃₁	semidirect
360. C₂×#479	C₂×C₃₁	semidirect
361. C₂×#478	C₂×C₃₁	semidirect
362. C₂×#460	C₂×C₃₁	semidirect
363. C₂×#459	C₂×C₃₁	semidirect
364. C₂×#449	C₂×C₃₁	semidirect
365. C₂×#449	C₂×C₃₁	semidirect
366. C₂×#442	C₂×C₃₁	semidirect
367. C₂×#440	C₂×C₃₁	semidirect
368. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
369. C₂×C₄×D₈	C₂×C₃₁	semidirect
370. C₂×#433	C₂×C₃₁	semidirect
410. #540	C₂²×C₃₁	semidirect
420. #520	C₂²×C₃₁	semidirect
433. #481	C₂²×C₃₁	semidirect
434. #480	C₂²×C₃₁	semidirect
435. #479	C₂²×C₃₁	semidirect
436. #478	C₂²×C₃₁	semidirect
437. #460	C₂²×C₃₁	semidirect
438. #459	C₂²×C₃₁	semidirect
439. #449	C₂²×C₃₁	semidirect
440. #449	C₂²×C₃₁	semidirect
441. #442	C₂²×C₃₁	semidirect
442. #440	C₂²×C₃₁	semidirect
443. C₄×SD₁₆	C₂²×C₃₁	semidirect
444. C₄×D₈	C₂²×C₃₁	semidirect
445. #433	C₂²×C₃₁	semidirect
468. C₂×C₃₁	#3119	direct (N × H)
577. C₃₁	C₂×#3119	direct (N × H)
787. C₂	C₃₁×#3119	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×#540	2
C₂×C₃₁×#520	2
C₃₁×#3119	2
C₂×C₃₁×#481	2
C₂×C₃₁×#480	2
C₂×C₃₁×#479	2
C₂×C₃₁×#478	2
C₂×C₃₁×#460	2
C₂×C₃₁×#459	2
C₂×C₃₁×#449	2
C₂×C₃₁×#442	2
C₂×C₃₁×#440	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₄×D₈×C₃₁	2
C₂×C₃₁×#433	2
C₂×#3119	31

Subgroups — C2×C31×#3119 #21517307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3119 #21517307