Subgroups — C₂×C₃₁×#3118 #21517306

Order 7936.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3118	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#447	C₂	1	1	yes	maximal, characteristic
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	C₂³×D₄×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×#542	—	2	4	no	—
23	C₃₁×#542	C₂²	1	8	yes	complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃₁×#126	—	2	1	no	—
26	C₂×C₃₁×#124	—	2	1	no	—
27	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×#123	—	2	1	no	—
29	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₃₁×#518	—	2	4	no	—
33	C₃₁×#518	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₃₁	—	2	1	no	—
36	C₂×C₄×D₄×C₃₁	—	2	1	no	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
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, complemented
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
45	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
46	C₃₁×#485	C₂²	1	8	yes	complemented
47	C₃₁×#482	C₂²	1	8	yes	complemented
48	C₃₁×#476	C₂²	1	8	yes	complemented
49	C₃₁×#474	C₂²	1	8	yes	complemented
50	C₃₁×#463	C₂²	1	8	yes	complemented
51	C₃₁×#463	C₂²	1	8	yes	complemented
52	C₃₁×#450	C₂²	1	8	yes	complemented
53	C₃₁×#447	C₂²	1	8	yes	—
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, complemented
60	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
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, complemented
72	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
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, complemented
76	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₃₁	—	2	1	no	—
78	C₂²×Q₈×C₃₁	—	2	1	no	—
79	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₃₁	—	2	4	no	—
81	C₂²×D₄×C₃₁	—	2	4	no	—
82	C₂²×D₄×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	—	2	1	no	—
84	C₂²×D₄×C₃₁	—	2	2	no	—
85	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
95	C₂×SD₁₆×C₃₁	—	2	4	no	—
96	C₂×SD₁₆×C₃₁	—	2	4	no	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	—	2	4	no	—
100	C₂×D₈×C₃₁	—	2	4	no	—
101	C₂×D₈×C₃₁	C₂³	1	4	yes	—
102	C₂×D₈×C₃₁	C₂³	1	4	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	complemented
109	C₃₁×#126	—	2	8	no	—
110	C₃₁×#124	—	2	8	no	—
111	C₃₁×#124	—	2	2	no	—
112	C₃₁×#124	C₂³	1	4	yes	complemented
113	C₃₁×#123	—	2	8	no	—
114	C₃₁×C₂²⋊Q₈	—	2	2	no	—
115	C₃₁×C₂²⋊Q₈	—	2	8	no	—
116	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
117	C₃₁×#121	—	2	2	no	—
118	C₃₁×#121	C₂³	1	4	yes	—
119	C₄×Q₈×C₃₁	—	2	2	no	—
120	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
121	C₄×D₄×C₃₁	—	2	8	no	—
122	C₄×D₄×C₃₁	—	2	8	no	—
123	C₄×D₄×C₃₁	—	2	2	no	—
124	C₄×D₄×C₃₁	—	2	2	no	—
125	C₄×D₄×C₃₁	—	2	2	no	—
126	C₄×D₄×C₃₁	—	2	2	no	—
127	C₄×D₄×C₃₁	—	2	2	no	—
128	C₄×D₄×C₃₁	C₂³	1	4	yes	—
129	C₄×D₄×C₃₁	C₂³	1	4	yes	—
130	C₄×D₄×C₃₁	C₂³	1	4	yes	—
131	C₄×D₄×C₃₁	C₂³	1	4	yes	—
132	C₄×D₄×C₃₁	C₂³	1	4	yes	complemented
133	C₃₁×#117	—	2	2	no	—
134	C₃₁×#117	D₄	1	4	yes	—
135	C₃₁×#117	C₂³	1	4	yes	—
136	C₃₁×#117	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
138	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
139	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
140	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
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	8	no	—
157	C₂×C₂²⋊C₄×C₃₁	—	2	8	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	complemented
165	C₃₁×#107	C₂³	1	4	yes	complemented
166	C₃₁×#106	C₂³	1	4	yes	complemented
167	C₃₁×#106	C₂³	1	4	yes	complemented
168	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
169	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
170	C₃₁×#103	C₂³	1	4	yes	complemented
171	C₃₁×#103	C₂³	1	4	yes	complemented
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	complemented
177	C₃₁×#102	C₂³	1	4	yes	complemented
178	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₃₁×#97	C₂³	1	4	yes	complemented
181	C₄×C₈×C₃₁	C₂³	1	4	yes	complemented
182	C₂⁴×C₃₁	—	2	8	no	—
183	C₂⁴×C₃₁	—	2	1	no	—
184	C₂⁴×C₃₁	—	2	1	no	—
185	C₂⁴×C₃₁	—	2	4	no	—
186	C₂⁴×C₃₁	—	2	1	no	—
187	C₂⁴×C₃₁	—	8	2	no	—
188	C₂⁴×C₃₁	—	8	2	no	—
189	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₃₁	—	2	1	no	—
191	C₂×Q₈×C₃₁	—	2	4	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	8	2	no	—
195	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
196	C₂×D₄×C₃₁	—	2	8	no	—
197	C₂×D₄×C₃₁	—	2	16	no	—
198	C₂×D₄×C₃₁	—	2	8	no	—
199	C₂×D₄×C₃₁	—	2	8	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
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	2	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	8	2	no	—
210	C₂×D₄×C₃₁	#41	1	4	yes	—
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	2	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	1	no	—
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	4	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	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	8	2	no	—
228	C₂²×C₄×C₃₁	—	8	2	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	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	SD₁₆×C₃₁	—	2	8	no	—
241	SD₁₆×C₃₁	—	2	8	no	—
242	D₈×C₃₁	—	2	8	no	—
243	D₈×C₃₁	—	2	8	no	—
244	C₂×C₈×C₃₁	—	2	2	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	C₂⁴	1	2	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	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	2	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	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×#3118	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₃₁	—	2	16	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	2	4	no	—
287	C₂³×C₃₁	—	2	4	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	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	—	4	2	no	—
300	C₂³×C₃₁	—	8	4	no	—
301	C₂³×C₃₁	—	8	4	no	—
302	C₂³×C₃₁	—	8	16	no	—
303	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
304	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₃₁	—	2	2	no	—
306	Q₈×C₃₁	—	2	2	no	—
307	Q₈×C₃₁	—	4	2	no	—
308	Q₈×C₃₁	—	8	4	no	—
309	D₄×C₃₁	—	2	16	no	—
310	D₄×C₃₁	—	2	4	no	—
311	D₄×C₃₁	—	2	4	no	—
312	D₄×C₃₁	—	2	2	no	—
313	D₄×C₃₁	—	2	2	no	—
314	D₄×C₃₁	—	2	2	no	—
315	D₄×C₃₁	—	2	2	no	—
316	D₄×C₃₁	—	4	2	no	—
317	D₄×C₃₁	—	8	4	no	—
318	D₄×C₃₁	C₂×#41	1	4	yes	—
319	D₄×C₃₁	C₂×#41	1	4	yes	—
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	4	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	—	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	—	4	2	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	—	8	4	no	—
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	2	yes	—
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
350	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
351	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
352	C₈×C₃₁	—	2	2	no	—
353	C₈×C₃₁	—	2	2	no	—
354	C₈×C₃₁	—	2	2	no	—
355	C₈×C₃₁	—	2	2	no	—
356	C₂×#542	C₂×C₃₁	1	1	yes	characteristic, complemented
357	C₂×#518	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#3118	C₂×C₃₁	1	16	yes	direct product factor
359	C₂×#485	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂×#482	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂×#474	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
364	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂×#450	C₂×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#447	C₂×C₃₁	1	1	yes	characteristic
367	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
368	C₂×#440	C₂×C₃₁	1	1	yes	characteristic, complemented
369	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
370	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
371	C₂×#433	C₂×C₃₁	1	1	yes	characteristic, complemented
372	C₂²×C₃₁	—	2	2	no	—
373	C₂²×C₃₁	—	2	4	no	—
374	C₂²×C₃₁	—	2	4	no	—
375	C₂²×C₃₁	—	2	2	no	—
376	C₂²×C₃₁	—	2	2	no	—
377	C₂²×C₃₁	—	4	4	no	—
378	C₂²×C₃₁	—	4	8	no	—
379	C₂²×C₃₁	—	4	8	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	—	4	2	no	—
386	C₂²×C₃₁	—	4	2	no	—
387	C₂²×C₃₁	—	8	16	no	—
388	C₂²×C₃₁	—	8	4	no	—
389	C₂²×C₃₁	#525	1	2	yes	—
390	C₂²×C₃₁	#576	1	2	yes	—
391	C₂²×C₃₁	#577	1	2	yes	—
392	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	—	2	2	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	2	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	2	no	—
402	C₄×C₃₁	—	4	2	no	—
403	C₄×C₃₁	#525	1	2	yes	—
404	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
405	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
406	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
407	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
408	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
410	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
411	#542	—	2	4	no	—
412	#542	C₂²×C₃₁	1	8	yes	complemented
413	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
414	C₂×#126	—	2	1	no	—
415	C₂×#124	—	2	1	no	—
416	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
417	C₂×#123	—	2	1	no	—
418	C₂×C₂²⋊Q₈	—	2	1	no	—
419	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
420	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
421	#518	—	2	4	no	—
422	#518	C₂²×C₃₁	1	8	yes	complemented
423	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	C₂×C₄×D₄	—	2	1	no	—
425	C₂×C₄×D₄	—	2	1	no	—
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×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
431	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
433	C₂²×C₂²⋊C₄	—	2	1	no	—
434	C₂²×C₂²⋊C₄	—	2	1	no	—
435	#485	C₂²×C₃₁	1	8	yes	complemented
436	#482	C₂²×C₃₁	1	8	yes	complemented
437	#476	C₂²×C₃₁	1	8	yes	complemented
438	#474	C₂²×C₃₁	1	8	yes	complemented
439	#463	C₂²×C₃₁	1	8	yes	complemented
440	#463	C₂²×C₃₁	1	8	yes	complemented
441	#450	C₂²×C₃₁	1	8	yes	complemented
442	#447	C₂²×C₃₁	1	8	yes	—
443	#442	C₂²×C₃₁	1	8	yes	complemented
444	#440	C₂²×C₃₁	1	8	yes	complemented
445	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
446	C₄×D₈	C₂²×C₃₁	1	8	yes	complemented
447	#433	C₂²×C₃₁	1	8	yes	complemented
448	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
455	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
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×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
462	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
463	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	C₂×C₃₁	—	4	2	no	—
467	C₂×C₃₁	—	4	4	no	—
468	C₂×C₃₁	—	4	4	no	—
469	C₂×C₃₁	—	8	2	no	—
470	C₂×C₃₁	#3118	1	4	yes	direct product factor
471	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
472	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
473	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
474	C₂⁵	—	2	1	no	—
475	C₂²×Q₈	—	2	1	no	—
476	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
477	C₂²×D₄	—	2	4	no	—
478	C₂²×D₄	—	2	4	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	2	no	—
482	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
484	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	complemented
506	#126	—	2	8	no	—
507	#124	—	2	8	no	—
508	#124	—	2	2	no	—
509	#124	C₂³×C₃₁	1	4	yes	complemented
510	#123	—	2	8	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	8	no	—
513	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
514	#121	—	2	2	no	—
515	#121	C₂³×C₃₁	1	4	yes	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
518	C₄×D₄	—	2	8	no	—
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	C₂³×C₃₁	1	4	yes	—
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	complemented
530	#117	—	2	2	no	—
531	#117	D₄×C₃₁	1	4	yes	—
532	#117	C₂³×C₃₁	1	4	yes	—
533	#117	C₂³×C₃₁	1	4	yes	—
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	D₄×C₃₁	1	1	yes	characteristic
538	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	—	2	1	no	—
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	8	no	—
554	C₂×C₂²⋊C₄	—	2	8	no	—
555	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
561	#107	C₂³×C₃₁	1	4	yes	complemented
562	#107	C₂³×C₃₁	1	4	yes	complemented
563	#106	C₂³×C₃₁	1	4	yes	complemented
564	#106	C₂³×C₃₁	1	4	yes	complemented
565	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
566	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
567	#103	C₂³×C₃₁	1	4	yes	complemented
568	#103	C₂³×C₃₁	1	4	yes	complemented
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	#102	C₂³×C₃₁	1	4	yes	complemented
574	#102	C₂³×C₃₁	1	4	yes	complemented
575	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
577	#97	C₂³×C₃₁	1	4	yes	complemented
578	C₄×C₈	C₂³×C₃₁	1	4	yes	complemented
579	C₃₁	C₂×#3118	1	1	yes	characteristic, direct product factor, Sylow
580	C₂⁴	—	2	8	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	—	2	1	no	—
583	C₂⁴	—	2	4	no	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	8	2	no	—
586	C₂⁴	—	8	2	no	—
587	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	8	2	no	—
593	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	16	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	8	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	8	2	no	—
608	C₂×D₄	#41×C₃₁	1	4	yes	—
609	C₂×D₄	#41×C₃₁	1	4	yes	—
610	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
612	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	1	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	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
658	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
659	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
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	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
674	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	C₂×D₄×C₃₁	1	2	yes	—
678	C₄²	C₂×D₄×C₃₁	1	2	yes	—
679	C₄²	C₂⁴×C₃₁	1	2	yes	—
680	C₄²	C₂⁴×C₃₁	1	2	yes	—
681	C₂³	—	2	16	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	16	no	—
700	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
701	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	4	2	no	—
705	Q₈	—	8	4	no	—
706	D₄	—	2	16	no	—
707	D₄	—	2	4	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	4	2	no	—
714	D₄	—	8	4	no	—
715	D₄	C₂×#41×C₃₁	1	4	yes	—
716	D₄	C₂×#41×C₃₁	1	4	yes	—
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	4	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	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
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	2	yes	—
743	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
744	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
746	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
747	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
748	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	2	no	—
752	C₈	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	4	4	no	—
759	C₂²	—	4	8	no	—
760	C₂²	—	4	8	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	16	no	—
769	C₂²	—	8	4	no	—
770	C₂²	C₃₁×#525	1	2	yes	—
771	C₂²	C₃₁×#576	1	2	yes	—
772	C₂²	C₃₁×#577	1	2	yes	—
773	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	C₃₁×#525	1	2	yes	—
785	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
786	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
787	C₂	—	4	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	4	4	no	—
790	C₂	—	8	2	no	—
791	C₂	C₃₁×#3118	1	4	yes	direct product factor
792	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
793	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
794	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×#447	C₂
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×#542	C₂	semidirect
2. C₂×C₃₁×#518	C₂	semidirect
3. C₃₁×#3118	C₂	direct (N × H)
4. C₂×C₃₁×#485	C₂	semidirect
5. C₂×C₃₁×#482	C₂	semidirect
6. C₂×C₃₁×#476	C₂	semidirect
7. C₂×C₃₁×#474	C₂	semidirect
8. C₂×C₃₁×#463	C₂	semidirect
9. C₂×C₃₁×#463	C₂	semidirect
10. C₂×C₃₁×#450	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×#542	C₂²	semidirect
24. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₃₁×#124	C₂²	semidirect
33. C₃₁×#518	C₂²	semidirect
34. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
41. C₂×C₄×D₄×C₃₁	C₂²	semidirect
46. C₃₁×#485	C₂²	semidirect
47. C₃₁×#482	C₂²	semidirect
48. C₃₁×#476	C₂²	semidirect
49. C₃₁×#474	C₂²	semidirect
50. C₃₁×#463	C₂²	semidirect
51. C₃₁×#463	C₂²	semidirect
52. C₃₁×#450	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
59. C₂×C₃₁×#107	C₂²	semidirect
60. C₂×C₃₁×#107	C₂²	semidirect
61. C₂×C₃₁×#106	C₂²	semidirect
62. C₂×C₃₁×#106	C₂²	semidirect
63. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
64. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
65. C₂×C₃₁×#103	C₂²	semidirect
66. C₂×C₃₁×#103	C₂²	semidirect
71. C₂×C₃₁×#102	C₂²	semidirect
72. C₂×C₃₁×#102	C₂²	semidirect
75. C₂×C₃₁×#97	C₂²	semidirect
76. C₂×C₄×C₈×C₃₁	C₂²	semidirect
108. C₃₁×C₄⋊Q₈	C₂³	semidirect
112. C₃₁×#124	C₂³	semidirect
120. C₄×Q₈×C₃₁	C₂³	semidirect
132. C₄×D₄×C₃₁	C₂³	semidirect
164. C₃₁×#107	C₂³	semidirect
165. C₃₁×#107	C₂³	semidirect
166. C₃₁×#106	C₂³	semidirect
167. C₃₁×#106	C₂³	semidirect
168. C₃₁×C₄⋊C₈	C₂³	semidirect
169. C₃₁×C₄⋊C₈	C₂³	semidirect
170. C₃₁×#103	C₂³	semidirect
171. C₃₁×#103	C₂³	semidirect
176. C₃₁×#102	C₂³	semidirect
177. C₃₁×#102	C₂³	semidirect
180. C₃₁×#97	C₂³	semidirect
181. C₄×C₈×C₃₁	C₂³	semidirect
283. C₂×#3118	C₃₁	direct (N × H)
356. C₂×#542	C₂×C₃₁	semidirect
357. C₂×#518	C₂×C₃₁	semidirect
358. #3118	C₂×C₃₁	direct (N × H)
359. C₂×#485	C₂×C₃₁	semidirect
360. C₂×#482	C₂×C₃₁	semidirect
361. C₂×#476	C₂×C₃₁	semidirect
362. C₂×#474	C₂×C₃₁	semidirect
363. C₂×#463	C₂×C₃₁	semidirect
364. C₂×#463	C₂×C₃₁	semidirect
365. C₂×#450	C₂×C₃₁	semidirect
367. C₂×#442	C₂×C₃₁	semidirect
368. C₂×#440	C₂×C₃₁	semidirect
369. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
370. C₂×C₄×D₈	C₂×C₃₁	semidirect
371. C₂×#433	C₂×C₃₁	semidirect
412. #542	C₂²×C₃₁	semidirect
413. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
416. C₂×#124	C₂²×C₃₁	semidirect
422. #518	C₂²×C₃₁	semidirect
423. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
430. C₂×C₄×D₄	C₂²×C₃₁	semidirect
435. #485	C₂²×C₃₁	semidirect
436. #482	C₂²×C₃₁	semidirect
437. #476	C₂²×C₃₁	semidirect
438. #474	C₂²×C₃₁	semidirect
439. #463	C₂²×C₃₁	semidirect
440. #463	C₂²×C₃₁	semidirect
441. #450	C₂²×C₃₁	semidirect
443. #442	C₂²×C₃₁	semidirect
444. #440	C₂²×C₃₁	semidirect
445. C₄×SD₁₆	C₂²×C₃₁	semidirect
446. C₄×D₈	C₂²×C₃₁	semidirect
447. #433	C₂²×C₃₁	semidirect
448. C₂×#107	C₂²×C₃₁	semidirect
449. C₂×#107	C₂²×C₃₁	semidirect
450. C₂×#106	C₂²×C₃₁	semidirect
451. C₂×#106	C₂²×C₃₁	semidirect
452. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
453. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
454. C₂×#103	C₂²×C₃₁	semidirect
455. C₂×#103	C₂²×C₃₁	semidirect
460. C₂×#102	C₂²×C₃₁	semidirect
461. C₂×#102	C₂²×C₃₁	semidirect
464. C₂×#97	C₂²×C₃₁	semidirect
465. C₂×C₄×C₈	C₂²×C₃₁	semidirect
470. C₂×C₃₁	#3118	direct (N × H)
505. C₄⋊Q₈	C₂³×C₃₁	semidirect
509. #124	C₂³×C₃₁	semidirect
517. C₄×Q₈	C₂³×C₃₁	semidirect
529. C₄×D₄	C₂³×C₃₁	semidirect
561. #107	C₂³×C₃₁	semidirect
562. #107	C₂³×C₃₁	semidirect
563. #106	C₂³×C₃₁	semidirect
564. #106	C₂³×C₃₁	semidirect
565. C₄⋊C₈	C₂³×C₃₁	semidirect
566. C₄⋊C₈	C₂³×C₃₁	semidirect
567. #103	C₂³×C₃₁	semidirect
568. #103	C₂³×C₃₁	semidirect
573. #102	C₂³×C₃₁	semidirect
574. #102	C₂³×C₃₁	semidirect
577. #97	C₂³×C₃₁	semidirect
578. C₄×C₈	C₂³×C₃₁	semidirect
579. C₃₁	C₂×#3118	direct (N × H)
791. C₂	C₃₁×#3118	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×#542	2
C₂×C₃₁×#518	2
C₃₁×#3118	2
C₂×C₃₁×#485	2
C₂×C₃₁×#482	2
C₂×C₃₁×#476	2
C₂×C₃₁×#474	2
C₂×C₃₁×#463	2
C₂×C₃₁×#450	2
C₂×C₃₁×#447	2
C₂×C₃₁×#442	2
C₂×C₃₁×#440	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₄×D₈×C₃₁	2
C₂×C₃₁×#433	2
C₂×#3118	31

Subgroups — C2×C31×#3118 #21517306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3118 #21517306