Subgroups — C₃₁×#60703 #21517462

Order 7936.

1910 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3179	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3178	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3175	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3173	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#137	C₂²	1	2	yes	—
17	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
19	C₃₁×#542	—	2	2	no	—
20	C₃₁×#542	—	2	2	no	—
21	C₃₁×#542	C₂²	1	4	yes	—
22	C₃₁×#542	C₂²	1	4	yes	—
23	C₃₁×#542	C₂²	1	2	yes	complemented
24	C₃₁×#542	C₂²	1	2	yes	complemented
25	C₃₁×#541	C₂²	1	2	yes	complemented
26	C₃₁×#540	C₂²	1	2	yes	complemented
27	C₃₁×#539	—	2	1	no	—
28	C₃₁×#539	—	2	1	no	—
29	C₃₁×#538	—	2	1	no	—
30	C₃₁×#538	—	2	1	no	—
31	C₃₁×#533	C₂²	1	1	yes	characteristic
32	C₃₁×#532	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃₁×#529	—	2	2	no	—
35	C₃₁×#529	—	2	2	no	—
36	C₂×C₃₁×#126	—	2	1	no	—
37	C₂×C₃₁×#124	—	2	1	no	—
38	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
39	C₃₁×#525	C₂²	1	2	yes	—
40	C₂×C₃₁×#123	—	2	1	no	—
41	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
44	C₄×#41×C₃₁	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	complemented
49	C₃₁×#500	C₂²	1	2	yes	complemented
50	C₃₁×#498	C₂²	1	2	yes	complemented
51	C₃₁×#497	C₂²	1	2	yes	complemented
52	C₃₁×#496	C₂²	1	2	yes	complemented
53	C₃₁×#495	C₂²	1	4	yes	complemented
54	C₃₁×#489	C₂²	1	2	yes	complemented
55	C₃₁×#489	C₂²	1	2	yes	complemented
56	C₃₁×#489	C₂²	1	4	yes	complemented
57	C₃₁×#488	C₂²	1	4	yes	complemented
58	C₃₁×#487	C₂²	1	2	yes	complemented
59	C₃₁×#486	C₂²	1	2	yes	complemented
60	C₃₁×#470	C₂²	1	4	yes	complemented
61	C₃₁×#469	C₂²	1	4	yes	—
62	C₃₁×#468	C₂²	1	4	yes	—
63	C₃₁×#468	C₂²	1	4	yes	complemented
64	C₃₁×#467	C₂²	1	4	yes	complemented
65	C₃₁×#466	C₂²	1	4	yes	—
66	C₃₁×#465	C₂²	1	4	yes	—
67	C₃₁×#465	C₂²	1	4	yes	complemented
68	C₃₁×#442	C₂²	1	4	yes	complemented
69	C₃₁×#441	C₂²	1	4	yes	complemented
70	C₃₁×#440	C₂²	1	4	yes	complemented
71	C₃₁×#440	C₂²	1	4	yes	complemented
72	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
75	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
76	C₃₁×#428	C₂²	1	2	yes	—
77	C₃₁×#428	C₂²	1	2	yes	—
78	C₃₁×#419	C₂²	1	2	yes	—
79	C₃₁×#418	C₂²	1	2	yes	—
80	C₃₁×#417	C₂²	1	2	yes	—
81	C₃₁×#417	C₂²	1	2	yes	—
82	C₃₁×#405	C₂²	1	4	yes	complemented
83	C₃₁×#405	C₂²	1	4	yes	complemented
84	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
85	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
87	C₂×#41×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	—	2	1	no	—
89	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	—	2	1	no	—
91	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	—	2	1	no	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×#137	—	2	8	no	—
95	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
96	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	C₂³	1	4	yes	—
100	C₂×M₁₆×C₃₁	—	2	8	no	—
101	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
105	C₃₁×C₄⋊Q₈	—	2	1	no	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×#127	C₂³	1	1	yes	characteristic
113	C₃₁×#126	—	2	4	no	—
114	C₃₁×#126	—	2	4	no	—
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#126	—	2	2	no	—
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	C₂³	1	2	yes	—
122	C₃₁×#124	—	2	4	no	—
123	C₃₁×#124	—	2	4	no	—
124	C₃₁×#124	—	2	2	no	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	1	no	—
127	C₃₁×#124	—	2	1	no	—
128	C₃₁×#124	C₂³	1	2	yes	—
129	C₃₁×#124	C₂³	1	2	yes	—
130	C₃₁×#124	C₂³	1	2	yes	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	4	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	1	no	—
140	C₃₁×C₂²⋊Q₈	—	2	1	no	—
141	C₃₁×C₂²⋊Q₈	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	4	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	1	no	—
150	C₃₁×#121	—	2	1	no	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	C₂³	1	4	yes	—
154	C₃₁×#121	C₂³	1	2	yes	—
155	C₃₁×#121	C₂³	1	2	yes	—
156	C₃₁×#120	—	2	2	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	1	no	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
161	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₄×D₄×C₃₁	C₂³	1	4	yes	—
172	C₄×D₄×C₃₁	C₂³	1	2	yes	—
173	C₃₁×#117	—	2	2	no	—
174	C₃₁×#117	D₄	1	2	yes	—
175	C₃₁×#117	D₄	1	2	yes	—
176	C₃₁×#117	C₂³	1	2	yes	—
177	C₃₁×#117	C₂³	1	2	yes	—
178	C₃₁×#117	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	—	2	1	no	—
194	C₂×C₄²×C₃₁	—	2	2	no	—
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₃₁×#107	C₂³	1	4	yes	—
198	C₃₁×#107	C₂³	1	4	yes	—
199	C₃₁×#106	C₂³	1	4	yes	—
200	C₃₁×#106	C₂³	1	4	yes	—
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	4	yes	—
203	C₃₁×#103	C₂³	1	4	yes	—
204	C₃₁×#103	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×#102	C₂³	1	4	yes	—
208	C₃₁×#102	C₂³	1	4	yes	—
209	C₃₁×#97	C₂³	1	4	yes	—
210	C₃₁×#97	C₂³	1	2	yes	—
211	C₃₁×#97	C₂³	1	2	yes	—
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	C₄×C₈×C₃₁	C₂³	1	2	yes	—
214	C₄×C₈×C₃₁	C₂³	1	2	yes	—
215	C₂⁴×C₃₁	—	2	1	no	—
216	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
217	#41×C₃₁	—	2	4	no	—
218	#41×C₃₁	—	2	4	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	1	no	—
221	C₂×Q₈×C₃₁	—	2	1	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	2	no	—
224	C₂×Q₈×C₃₁	—	2	4	no	—
225	C₂×Q₈×C₃₁	—	8	2	no	—
226	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₃₁	—	2	2	no	—
229	C₂×D₄×C₃₁	—	2	2	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	4	no	—
232	C₂×D₄×C₃₁	—	2	1	no	—
233	C₂×D₄×C₃₁	—	2	1	no	—
234	C₂×D₄×C₃₁	—	2	1	no	—
235	C₂×D₄×C₃₁	—	2	4	no	—
236	C₂×D₄×C₃₁	—	8	2	no	—
237	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	—	2	4	no	—
240	C₂²×C₄×C₃₁	—	2	1	no	—
241	C₂²×C₄×C₃₁	—	2	1	no	—
242	C₂²×C₄×C₃₁	—	2	1	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	4	no	—
247	C₂²×C₄×C₃₁	—	8	2	no	—
248	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	Q₁₆×C₃₁	—	2	8	no	—
257	SD₁₆×C₃₁	—	2	8	no	—
258	SD₁₆×C₃₁	—	2	8	no	—
259	D₈×C₃₁	—	2	8	no	—
260	M₁₆×C₃₁	—	2	4	no	—
261	M₁₆×C₃₁	—	2	8	no	—
262	M₁₆×C₃₁	#41	1	8	yes	—
263	C₂×C₈×C₃₁	—	2	8	no	—
264	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
265	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₃₁	—	2	4	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	2	no	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	—	2	2	no	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	2	no	—
303	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
308	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₄²×C₃₁	—	2	2	no	—
311	C₄²×C₃₁	—	2	2	no	—
312	C₄²×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	—	2	4	no	—
314	C₄²×C₃₁	C₂×D₄	1	2	yes	—
315	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₃₁	C₂⁴	1	2	yes	—
318	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
320	#60703	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₃₁	—	2	2	no	—
322	C₂³×C₃₁	—	2	2	no	—
323	C₂³×C₃₁	—	2	2	no	—
324	C₂³×C₃₁	—	4	1	no	—
325	C₂³×C₃₁	—	4	1	no	—
326	C₂³×C₃₁	—	4	2	no	—
327	C₂³×C₃₁	—	4	2	no	—
328	C₂³×C₃₁	—	4	2	no	—
329	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
330	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₃₁	—	2	2	no	—
332	Q₈×C₃₁	—	2	4	no	—
333	Q₈×C₃₁	—	2	2	no	—
334	Q₈×C₃₁	—	4	2	no	—
335	Q₈×C₃₁	—	8	1	no	—
336	Q₈×C₃₁	—	8	1	no	—
337	Q₈×C₃₁	—	8	2	no	—
338	Q₈×C₃₁	—	8	2	no	—
339	D₄×C₃₁	—	2	2	no	—
340	D₄×C₃₁	—	2	4	no	—
341	D₄×C₃₁	—	2	2	no	—
342	D₄×C₃₁	—	4	4	no	—
343	D₄×C₃₁	—	4	2	no	—
344	D₄×C₃₁	—	8	1	no	—
345	D₄×C₃₁	—	8	1	no	—
346	D₄×C₃₁	—	8	2	no	—
347	D₄×C₃₁	—	8	2	no	—
348	D₄×C₃₁	—	8	4	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	4	no	—
351	C₂×C₄×C₃₁	—	2	2	no	—
352	C₂×C₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	4	1	no	—
360	C₂×C₄×C₃₁	—	4	1	no	—
361	C₂×C₄×C₃₁	—	4	1	no	—
362	C₂×C₄×C₃₁	—	4	1	no	—
363	C₂×C₄×C₃₁	—	4	2	no	—
364	C₂×C₄×C₃₁	—	4	2	no	—
365	C₂×C₄×C₃₁	—	4	2	no	—
366	C₂×C₄×C₃₁	—	4	4	no	—
367	C₂×C₄×C₃₁	—	8	2	no	—
368	C₂×C₄×C₃₁	—	8	2	no	—
369	C₂×C₄×C₃₁	—	8	4	no	—
370	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
379	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
380	C₈×C₃₁	—	2	4	no	—
381	C₈×C₃₁	C₂×#41	1	8	yes	—
382	#3455	C₂×C₃₁	1	1	yes	characteristic, complemented
383	C₂×#542	C₂×C₃₁	1	1	yes	characteristic, complemented
384	#3179	C₂×C₃₁	1	4	yes	complemented
385	#3178	C₂×C₃₁	1	4	yes	complemented
386	#3175	C₂×C₃₁	1	4	yes	complemented
387	#3173	C₂×C₃₁	1	4	yes	complemented
388	#3165	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3153	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
391	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
392	#3056	C₂×C₃₁	1	2	yes	complemented
393	#3055	C₂×C₃₁	1	2	yes	complemented
394	C₄×#137	C₂×C₃₁	1	2	yes	complemented
395	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
396	#2873	C₂×C₃₁	1	1	yes	characteristic, complemented
397	C₂²×C₃₁	—	2	1	no	—
398	C₂²×C₃₁	—	2	1	no	—
399	C₂²×C₃₁	—	2	2	no	—
400	C₂²×C₃₁	—	2	2	no	—
401	C₂²×C₃₁	—	2	2	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	4	2	no	—
404	C₂²×C₃₁	—	4	2	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	—	4	2	no	—
408	C₂²×C₃₁	—	8	2	no	—
409	C₂²×C₃₁	—	8	4	no	—
410	C₂²×C₃₁	#532	1	2	yes	—
411	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₃₁	—	2	2	no	—
413	C₄×C₃₁	—	2	1	no	—
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	2	no	—
416	C₄×C₃₁	—	2	1	no	—
417	C₄×C₃₁	—	2	1	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	4	2	no	—
420	C₄×C₃₁	—	4	2	no	—
421	C₄×C₃₁	—	4	2	no	—
422	C₄×C₃₁	—	4	2	no	—
423	C₄×C₃₁	—	4	2	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	#532	1	2	yes	—
426	C₄×C₃₁	C₂²×#41	1	2	yes	—
427	C₂×#137	C₂²×C₃₁	1	2	yes	—
428	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
429	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
430	#542	—	2	2	no	—
431	#542	—	2	2	no	—
432	#542	C₂²×C₃₁	1	4	yes	—
433	#542	C₂²×C₃₁	1	4	yes	—
434	#542	C₂²×C₃₁	1	2	yes	complemented
435	#542	C₂²×C₃₁	1	2	yes	complemented
436	#541	C₂²×C₃₁	1	2	yes	complemented
437	#540	C₂²×C₃₁	1	2	yes	complemented
438	#539	—	2	1	no	—
439	#539	—	2	1	no	—
440	#538	—	2	1	no	—
441	#538	—	2	1	no	—
442	#533	C₂²×C₃₁	1	1	yes	characteristic
443	#532	C₂²×C₃₁	1	1	yes	characteristic
444	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
445	#529	—	2	2	no	—
446	#529	—	2	2	no	—
447	C₂×#126	—	2	1	no	—
448	C₂×#124	—	2	1	no	—
449	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
450	#525	C₂²×C₃₁	1	2	yes	—
451	C₂×#123	—	2	1	no	—
452	C₂×C₂²⋊Q₈	—	2	1	no	—
453	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
455	C₄×#41	C₂²×C₃₁	1	2	yes	—
456	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
459	#501	C₂²×C₃₁	1	4	yes	complemented
460	#500	C₂²×C₃₁	1	2	yes	complemented
461	#498	C₂²×C₃₁	1	2	yes	complemented
462	#497	C₂²×C₃₁	1	2	yes	complemented
463	#496	C₂²×C₃₁	1	2	yes	complemented
464	#495	C₂²×C₃₁	1	4	yes	complemented
465	#489	C₂²×C₃₁	1	2	yes	complemented
466	#489	C₂²×C₃₁	1	2	yes	complemented
467	#489	C₂²×C₃₁	1	4	yes	complemented
468	#488	C₂²×C₃₁	1	4	yes	complemented
469	#487	C₂²×C₃₁	1	2	yes	complemented
470	#486	C₂²×C₃₁	1	2	yes	complemented
471	#470	C₂²×C₃₁	1	4	yes	complemented
472	#469	C₂²×C₃₁	1	4	yes	—
473	#468	C₂²×C₃₁	1	4	yes	—
474	#468	C₂²×C₃₁	1	4	yes	complemented
475	#467	C₂²×C₃₁	1	4	yes	complemented
476	#466	C₂²×C₃₁	1	4	yes	—
477	#465	C₂²×C₃₁	1	4	yes	—
478	#465	C₂²×C₃₁	1	4	yes	complemented
479	#442	C₂²×C₃₁	1	4	yes	complemented
480	#441	C₂²×C₃₁	1	4	yes	complemented
481	#440	C₂²×C₃₁	1	4	yes	complemented
482	#440	C₂²×C₃₁	1	4	yes	complemented
483	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
484	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
485	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
486	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
487	#428	C₂²×C₃₁	1	2	yes	—
488	#428	C₂²×C₃₁	1	2	yes	—
489	#419	C₂²×C₃₁	1	2	yes	—
490	#418	C₂²×C₃₁	1	2	yes	—
491	#417	C₂²×C₃₁	1	2	yes	—
492	#417	C₂²×C₃₁	1	2	yes	—
493	#405	C₂²×C₃₁	1	4	yes	complemented
494	#405	C₂²×C₃₁	1	4	yes	complemented
495	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
496	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
497	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
498	C₂×C₃₁	—	2	2	no	—
499	C₂×C₃₁	—	4	2	no	—
500	C₂×C₃₁	—	8	2	no	—
501	C₂×C₃₁	—	8	2	no	—
502	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
503	C₂×C₃₁	#3585	1	1	yes	characteristic
504	C₂×C₃₁	#3586	1	1	yes	characteristic
505	C₂×#41	C₂³×C₃₁	1	2	yes	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
512	#137	—	2	8	no	—
513	AGL(1,ℤ/8)	—	2	8	no	—
514	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
517	C₂×D₈	C₂³×C₃₁	1	4	yes	—
518	C₂×M₁₆	—	2	8	no	—
519	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
520	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
521	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
522	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
526	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
530	#127	C₂³×C₃₁	1	1	yes	characteristic
531	#126	—	2	4	no	—
532	#126	—	2	4	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#125	—	2	2	no	—
538	#125	—	2	2	no	—
539	#125	C₂³×C₃₁	1	2	yes	—
540	#124	—	2	4	no	—
541	#124	—	2	4	no	—
542	#124	—	2	2	no	—
543	#124	—	2	2	no	—
544	#124	—	2	1	no	—
545	#124	—	2	1	no	—
546	#124	C₂³×C₃₁	1	2	yes	—
547	#124	C₂³×C₃₁	1	2	yes	—
548	#124	C₂³×C₃₁	1	2	yes	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	4	no	—
553	#123	—	2	4	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
564	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
566	#121	—	2	2	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	C₂³×C₃₁	1	4	yes	—
572	#121	C₂³×C₃₁	1	2	yes	—
573	#121	C₂³×C₃₁	1	2	yes	—
574	#120	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
579	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
580	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	C₂³×C₃₁	1	4	yes	—
589	C₄×D₄	C₂³×C₃₁	1	2	yes	—
590	C₄×D₄	C₂³×C₃₁	1	2	yes	—
591	#117	—	2	2	no	—
592	#117	D₄×C₃₁	1	2	yes	—
593	#117	D₄×C₃₁	1	2	yes	—
594	#117	C₂³×C₃₁	1	2	yes	—
595	#117	C₂³×C₃₁	1	2	yes	—
596	#117	C₂³×C₃₁	1	2	yes	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
601	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	—	2	2	no	—
613	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
615	#107	C₂³×C₃₁	1	4	yes	—
616	#107	C₂³×C₃₁	1	4	yes	—
617	#106	C₂³×C₃₁	1	4	yes	—
618	#106	C₂³×C₃₁	1	4	yes	—
619	#103	C₂³×C₃₁	1	4	yes	—
620	#103	C₂³×C₃₁	1	4	yes	—
621	#103	C₂³×C₃₁	1	4	yes	—
622	#103	C₂³×C₃₁	1	4	yes	—
623	#102	C₂³×C₃₁	1	4	yes	—
624	#102	C₂³×C₃₁	1	4	yes	—
625	#102	C₂³×C₃₁	1	4	yes	—
626	#102	C₂³×C₃₁	1	4	yes	—
627	#97	C₂³×C₃₁	1	4	yes	—
628	#97	C₂³×C₃₁	1	2	yes	—
629	#97	C₂³×C₃₁	1	2	yes	—
630	C₄×C₈	C₂³×C₃₁	1	4	yes	—
631	C₄×C₈	C₂³×C₃₁	1	2	yes	—
632	C₄×C₈	C₂³×C₃₁	1	2	yes	—
633	C₃₁	#60703	1	1	yes	characteristic, direct product factor, Sylow
634	C₂⁴	—	2	1	no	—
635	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	8	2	no	—
645	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	8	2	no	—
656	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
657	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	8	2	no	—
667	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
675	Q₁₆	—	2	8	no	—
676	SD₁₆	—	2	8	no	—
677	SD₁₆	—	2	8	no	—
678	D₈	—	2	8	no	—
679	M₁₆	—	2	4	no	—
680	M₁₆	—	2	8	no	—
681	M₁₆	#41×C₃₁	1	8	yes	—
682	C₂×C₈	—	2	8	no	—
683	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
684	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
703	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
704	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
726	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
727	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
728	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	4	no	—
733	C₄²	C₂×D₄×C₃₁	1	2	yes	—
734	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
736	C₄²	C₂⁴×C₃₁	1	2	yes	—
737	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
748	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
749	Q₈	—	2	2	no	—
750	Q₈	—	2	4	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	8	1	no	—
754	Q₈	—	8	1	no	—
755	Q₈	—	8	2	no	—
756	Q₈	—	8	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	2	no	—
762	D₄	—	8	1	no	—
763	D₄	—	8	1	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	2	no	—
766	D₄	—	8	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	4	no	—
788	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
797	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
798	C₈	—	2	4	no	—
799	C₈	C₂×#41×C₃₁	1	8	yes	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	4	no	—
813	C₂²	C₃₁×#532	1	2	yes	—
814	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	C₃₁×#532	1	2	yes	—
829	C₄	C₂²×#41×C₃₁	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
835	C₂	C₃₁×#3585	1	1	yes	characteristic
836	C₂	C₃₁×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3455	C₂	semidirect
2. C₂×C₃₁×#542	C₂	semidirect
3. C₃₁×#3179	C₂	semidirect
4. C₃₁×#3178	C₂	semidirect
5. C₃₁×#3175	C₂	semidirect
6. C₃₁×#3173	C₂	semidirect
7. C₃₁×#3165	C₂	semidirect
8. C₃₁×#3153	C₂	semidirect
9. C₃₁×#3141	C₂	semidirect
10. C₃₁×#3140	C₂	semidirect
11. C₃₁×#3056	C₂	semidirect
12. C₃₁×#3055	C₂	semidirect
13. C₄×C₃₁×#137	C₂	semidirect
14. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
15. C₃₁×#2873	C₂	semidirect
23. C₃₁×#542	C₂²	semidirect
24. C₃₁×#542	C₂²	semidirect
25. C₃₁×#541	C₂²	semidirect
26. C₃₁×#540	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#500	C₂²	semidirect
50. C₃₁×#498	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
52. C₃₁×#496	C₂²	semidirect
53. C₃₁×#495	C₂²	semidirect
54. C₃₁×#489	C₂²	semidirect
55. C₃₁×#489	C₂²	semidirect
56. C₃₁×#489	C₂²	semidirect
57. C₃₁×#488	C₂²	semidirect
58. C₃₁×#487	C₂²	semidirect
59. C₃₁×#486	C₂²	semidirect
60. C₃₁×#470	C₂²	semidirect
63. C₃₁×#468	C₂²	semidirect
64. C₃₁×#467	C₂²	semidirect
67. C₃₁×#465	C₂²	semidirect
68. C₃₁×#442	C₂²	semidirect
69. C₃₁×#441	C₂²	semidirect
70. C₃₁×#440	C₂²	semidirect
71. C₃₁×#440	C₂²	semidirect
72. C₄×Q₁₆×C₃₁	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₄×SD₁₆×C₃₁	C₂²	semidirect
75. C₄×D₈×C₃₁	C₂²	semidirect
82. C₃₁×#405	C₂²	semidirect
83. C₃₁×#405	C₂²	semidirect
320. #60703	C₃₁	direct (N × H)
382. #3455	C₂×C₃₁	semidirect
383. C₂×#542	C₂×C₃₁	semidirect
384. #3179	C₂×C₃₁	semidirect
385. #3178	C₂×C₃₁	semidirect
386. #3175	C₂×C₃₁	semidirect
387. #3173	C₂×C₃₁	semidirect
388. #3165	C₂×C₃₁	semidirect
389. #3153	C₂×C₃₁	semidirect
390. #3141	C₂×C₃₁	semidirect
391. #3140	C₂×C₃₁	semidirect
392. #3056	C₂×C₃₁	semidirect
393. #3055	C₂×C₃₁	semidirect
394. C₄×#137	C₂×C₃₁	semidirect
395. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
396. #2873	C₂×C₃₁	semidirect
434. #542	C₂²×C₃₁	semidirect
435. #542	C₂²×C₃₁	semidirect
436. #541	C₂²×C₃₁	semidirect
437. #540	C₂²×C₃₁	semidirect
459. #501	C₂²×C₃₁	semidirect
460. #500	C₂²×C₃₁	semidirect
461. #498	C₂²×C₃₁	semidirect
462. #497	C₂²×C₃₁	semidirect
463. #496	C₂²×C₃₁	semidirect
464. #495	C₂²×C₃₁	semidirect
465. #489	C₂²×C₃₁	semidirect
466. #489	C₂²×C₃₁	semidirect
467. #489	C₂²×C₃₁	semidirect
468. #488	C₂²×C₃₁	semidirect
469. #487	C₂²×C₃₁	semidirect
470. #486	C₂²×C₃₁	semidirect
471. #470	C₂²×C₃₁	semidirect
474. #468	C₂²×C₃₁	semidirect
475. #467	C₂²×C₃₁	semidirect
478. #465	C₂²×C₃₁	semidirect
479. #442	C₂²×C₃₁	semidirect
480. #441	C₂²×C₃₁	semidirect
481. #440	C₂²×C₃₁	semidirect
482. #440	C₂²×C₃₁	semidirect
483. C₄×Q₁₆	C₂²×C₃₁	semidirect
484. C₄×SD₁₆	C₂²×C₃₁	semidirect
485. C₄×SD₁₆	C₂²×C₃₁	semidirect
486. C₄×D₈	C₂²×C₃₁	semidirect
493. #405	C₂²×C₃₁	semidirect
494. #405	C₂²×C₃₁	semidirect
633. C₃₁	#60703	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3455	2
C₂×C₃₁×#542	2
C₃₁×#3179	2
C₃₁×#3178	2
C₃₁×#3175	2
C₃₁×#3173	2
C₃₁×#3165	2
C₃₁×#3153	2
C₃₁×#3141	2
C₃₁×#3140	2
C₃₁×#3056	2
C₃₁×#3055	2
C₄×C₃₁×#137	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₃₁×#2873	2
#60703	31

Subgroups — C31×#60703 #21517462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60703 #21517462