Subgroups — C₃₁×#62583 #21519342

Order 7936.

1978 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3308	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3306	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3238	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#489	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×2₋¹⁺⁴	—	2	1	no	—
19	C₃₁×#559	C₂²	1	1	yes	characteristic
20	C₃₁×#556	C₂²	1	1	yes	characteristic
21	C₃₁×#555	—	2	1	no	—
22	C₃₁×#551	—	2	2	no	—
23	D₄×Q₈×C₃₁	—	2	1	no	—
24	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
26	C₃₁×#548	C₂²	1	2	yes	—
27	C₃₁×#547	—	2	1	no	—
28	C₃₁×#547	—	2	2	no	—
29	C₃₁×#547	C₂²	1	2	yes	—
30	C₃₁×#547	C₂²	1	4	yes	complemented
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#546	C₂²	1	2	yes	—
33	D₄²×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#542	—	2	1	no	—
35	C₃₁×#538	—	2	2	no	—
36	C₃₁×#536	—	2	2	no	—
37	C₃₁×#536	—	2	1	no	—
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#532	C₂²	1	2	yes	complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#529	C₂²	1	1	yes	characteristic
44	C₃₁×#529	C₂²	1	2	yes	—
45	C₂×C₃₁×#124	C₂²	1	2	yes	—
46	C₃₁×#518	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#496	C₂²	1	1	yes	characteristic
51	C₃₁×#496	C₂²	1	2	yes	complemented
52	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#489	C₂²	1	4	yes	—
54	C₃₁×#489	C₂²	1	1	yes	characteristic
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#489	C₂²	1	4	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#489	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#487	C₂²	1	2	yes	complemented
61	C₃₁×#486	C₂²	1	2	yes	—
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#483	C₂²	1	4	yes	complemented
64	C₃₁×#481	C₂²	1	2	yes	—
65	C₃₁×#480	C₂²	1	4	yes	—
66	C₃₁×#477	C₂²	1	4	yes	complemented
67	C₃₁×#476	C₂²	1	4	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#474	C₂²	1	2	yes	—
70	C₃₁×#469	C₂²	1	2	yes	—
71	C₃₁×#468	C₂²	1	2	yes	complemented
72	C₃₁×#466	C₂²	1	4	yes	—
73	C₃₁×#465	C₂²	1	4	yes	complemented
74	C₃₁×#463	C₂²	1	4	yes	—
75	C₃₁×#463	C₂²	1	4	yes	complemented
76	C₃₁×#461	C₂²	1	2	yes	complemented
77	C₃₁×#459	C₂²	1	2	yes	—
78	C₃₁×#449	C₂²	1	4	yes	complemented
79	C₃₁×#448	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	4	yes	—
81	C₃₁×#446	C₂²	1	2	yes	complemented
82	C₃₁×#442	C₂²	1	4	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×D₈×C₃₁	C₂²	1	2	yes	—
86	C₃₁×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₃₁	C₂²	1	2	yes	—
88	C₃₁×#432	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#417	C₂²	1	4	yes	complemented
91	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
92	C₂×C₃₁×#102	C₂²	1	4	yes	—
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
95	C₃₁×2₋¹⁺⁴	—	4	8	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	4	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	—	2	1	no	—
100	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	—	2	2	no	—
103	C₂²×Q₈×C₃₁	—	2	2	no	—
104	C₂²×Q₈×C₃₁	—	2	1	no	—
105	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×D₈×C₃₁	C₂³	1	2	yes	—
111	C₂×D₈×C₃₁	C₂³	1	4	yes	—
112	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
113	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	—	2	2	no	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	—	2	1	no	—
118	C₃₁×C₄⋊Q₈	—	2	2	no	—
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₃₁×#127	C₂³	1	1	yes	characteristic
125	C₃₁×#127	C₂³	1	1	yes	characteristic
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	1	no	—
129	C₃₁×#125	C₂³	1	1	yes	characteristic
130	C₃₁×#124	—	2	1	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	—	2	1	no	—
136	C₃₁×#124	C₂³	1	2	yes	—
137	C₃₁×#124	C₂³	1	2	yes	—
138	C₃₁×#124	C₂³	1	1	yes	characteristic
139	C₃₁×#124	C₂³	1	2	yes	—
140	C₃₁×#123	—	2	1	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×#123	—	2	4	no	—
145	C₃₁×#123	—	2	4	no	—
146	C₃₁×#123	—	2	4	no	—
147	C₃₁×C₂²⋊Q₈	—	2	1	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	4	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	—	2	4	no	—
152	C₃₁×C₂²⋊Q₈	—	2	2	no	—
153	C₃₁×C₂²⋊Q₈	—	2	2	no	—
154	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	1	no	—
158	C₃₁×#121	—	2	1	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	1	no	—
161	C₃₁×#121	—	2	1	no	—
162	C₃₁×#121	—	2	2	no	—
163	C₃₁×#121	C₂³	1	4	yes	—
164	C₃₁×#121	C₂³	1	2	yes	—
165	C₃₁×#121	C₂³	1	2	yes	—
166	C₃₁×#121	C₂³	1	1	yes	characteristic
167	C₃₁×#120	—	2	2	no	—
168	C₃₁×#120	—	2	2	no	—
169	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	1	no	—
181	C₄×D₄×C₃₁	—	2	2	no	—
182	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
183	C₄×D₄×C₃₁	D₄	1	2	yes	—
184	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₃₁	C₂³	1	2	yes	—
186	C₄×D₄×C₃₁	C₂³	1	4	yes	—
187	C₄×D₄×C₃₁	C₂³	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₃₁×#117	—	2	1	no	—
191	C₃₁×#117	—	2	1	no	—
192	C₃₁×#117	—	2	2	no	—
193	C₃₁×#117	D₄	1	2	yes	—
194	C₃₁×#117	D₄	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
202	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#107	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
210	C₃₁×#103	C₂³	1	2	yes	—
211	C₃₁×#103	C₂³	1	4	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#102	C₂³	1	2	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₃₁×#97	C₂³	1	1	yes	characteristic
225	C₃₁×#97	C₂³	1	2	yes	—
226	C₃₁×#97	C₂³	1	4	yes	—
227	C₃₁×#97	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₂⁴×C₃₁	—	2	2	no	—
230	#41×C₃₁	—	2	4	no	—
231	#41×C₃₁	—	4	8	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	16	no	—
235	#41×C₃₁	—	4	8	no	—
236	C₂×Q₈×C₃₁	—	2	4	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	4	8	no	—
242	C₂×Q₈×C₃₁	—	4	4	no	—
243	C₂×Q₈×C₃₁	—	4	4	no	—
244	C₂×Q₈×C₃₁	—	4	8	no	—
245	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	—	2	1	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	2	2	no	—
258	C₂×D₄×C₃₁	—	4	4	no	—
259	C₂×D₄×C₃₁	—	4	4	no	—
260	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
264	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	4	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	1	no	—
269	C₂²×C₄×C₃₁	—	2	4	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	2	no	—
272	C₂²×C₄×C₃₁	—	2	2	no	—
273	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	SD₁₆×C₃₁	—	4	4	no	—
280	SD₁₆×C₃₁	—	4	2	no	—
281	D₈×C₃₁	—	4	4	no	—
282	D₈×C₃₁	—	4	2	no	—
283	M₁₆×C₃₁	—	4	2	no	—
284	C₂×C₈×C₃₁	—	4	4	no	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	1	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	1	no	—
314	C₂²⋊C₄×C₃₁	—	2	1	no	—
315	C₂²⋊C₄×C₃₁	—	2	1	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	1	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	—	2	4	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
330	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	1	no	—
333	C₄²×C₃₁	C₂×D₄	1	2	yes	—
334	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₃₁	C₂×D₄	1	2	yes	—
337	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₄²×C₃₁	C₂⁴	1	2	yes	—
340	#62583	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	—	2	2	no	—
343	C₂³×C₃₁	—	2	2	no	—
344	C₂³×C₃₁	—	4	4	no	—
345	C₂³×C₃₁	—	8	2	no	—
346	C₂³×C₃₁	—	8	2	no	—
347	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
349	Q₈×C₃₁	—	2	2	no	—
350	Q₈×C₃₁	—	2	2	no	—
351	Q₈×C₃₁	—	2	4	no	—
352	Q₈×C₃₁	—	4	4	no	—
353	Q₈×C₃₁	—	4	2	no	—
354	Q₈×C₃₁	—	4	8	no	—
355	Q₈×C₃₁	—	4	4	no	—
356	Q₈×C₃₁	—	8	2	no	—
357	D₄×C₃₁	—	2	4	no	—
358	D₄×C₃₁	—	2	2	no	—
359	D₄×C₃₁	—	2	2	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	4	no	—
362	D₄×C₃₁	—	4	2	no	—
363	D₄×C₃₁	—	4	2	no	—
364	D₄×C₃₁	—	4	4	no	—
365	D₄×C₃₁	—	4	4	no	—
366	D₄×C₃₁	—	4	8	no	—
367	D₄×C₃₁	—	4	2	no	—
368	D₄×C₃₁	—	8	1	no	—
369	D₄×C₃₁	—	8	2	no	—
370	D₄×C₃₁	—	8	1	no	—
371	D₄×C₃₁	—	8	2	no	—
372	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
373	C₂×C₄×C₃₁	—	2	4	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	4	2	no	—
384	C₂×C₄×C₃₁	—	4	1	no	—
385	C₂×C₄×C₃₁	—	4	8	no	—
386	C₂×C₄×C₃₁	—	4	4	no	—
387	C₂×C₄×C₃₁	—	4	8	no	—
388	C₂×C₄×C₃₁	—	4	2	no	—
389	C₂×C₄×C₃₁	—	4	4	no	—
390	C₂×C₄×C₃₁	—	8	2	no	—
391	C₂×C₄×C₃₁	—	8	2	no	—
392	C₂×C₄×C₃₁	—	8	2	no	—
393	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
402	C₈×C₃₁	—	2	2	no	—
403	C₈×C₃₁	—	2	4	no	—
404	C₈×C₃₁	—	2	2	no	—
405	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3373	C₂×C₃₁	1	2	yes	complemented
408	#3367	C₂×C₃₁	1	2	yes	complemented
409	#3308	C₂×C₃₁	1	4	yes	complemented
410	#3306	C₂×C₃₁	1	4	yes	complemented
411	#3298	C₂×C₃₁	1	2	yes	complemented
412	#3294	C₂×C₃₁	1	2	yes	complemented
413	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3238	C₂×C₃₁	1	2	yes	complemented
415	#3214	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3213	C₂×C₃₁	1	2	yes	complemented
417	#3180	C₂×C₃₁	1	2	yes	complemented
418	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
420	C₂×#489	C₂×C₃₁	1	2	yes	complemented
421	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
422	C₂²×C₃₁	—	2	2	no	—
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	1	no	—
426	C₂²×C₃₁	—	2	1	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	2	no	—
429	C₂²×C₃₁	—	4	1	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	1	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	1	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	16	4	no	—
437	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
438	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₃₁	—	2	1	no	—
440	C₄×C₃₁	—	2	2	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	1	no	—
443	C₄×C₃₁	—	2	2	no	—
444	C₄×C₃₁	—	2	1	no	—
445	C₄×C₃₁	—	2	2	no	—
446	C₄×C₃₁	—	4	1	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	4	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	—	4	1	no	—
452	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
453	C₄×C₃₁	#585	1	2	yes	—
454	C₂×2₋¹⁺⁴	—	2	1	no	—
455	#559	C₂²×C₃₁	1	1	yes	characteristic
456	#556	C₂²×C₃₁	1	1	yes	characteristic
457	#555	—	2	1	no	—
458	#551	—	2	2	no	—
459	D₄×Q₈	—	2	1	no	—
460	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
461	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
462	#548	C₂²×C₃₁	1	2	yes	—
463	#547	—	2	1	no	—
464	#547	—	2	2	no	—
465	#547	C₂²×C₃₁	1	2	yes	—
466	#547	C₂²×C₃₁	1	4	yes	complemented
467	#546	—	2	1	no	—
468	#546	C₂²×C₃₁	1	2	yes	—
469	D₄²	C₂²×C₃₁	1	1	yes	characteristic
470	#542	—	2	1	no	—
471	#538	—	2	2	no	—
472	#536	—	2	2	no	—
473	#536	—	2	1	no	—
474	#532	C₂²×C₃₁	1	1	yes	characteristic
475	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
476	#532	C₂²×C₃₁	1	2	yes	complemented
477	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
478	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	#529	C₂²×C₃₁	1	1	yes	characteristic
480	#529	C₂²×C₃₁	1	2	yes	—
481	C₂×#124	C₂²×C₃₁	1	2	yes	—
482	#518	—	2	1	no	—
483	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
484	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
485	#501	C₂²×C₃₁	1	2	yes	complemented
486	#496	C₂²×C₃₁	1	1	yes	characteristic
487	#496	C₂²×C₃₁	1	2	yes	complemented
488	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	#489	C₂²×C₃₁	1	4	yes	—
490	#489	C₂²×C₃₁	1	1	yes	characteristic
491	#489	C₂²×C₃₁	1	2	yes	—
492	#489	C₂²×C₃₁	1	4	yes	complemented
493	#489	C₂²×C₃₁	1	2	yes	complemented
494	#489	C₂²×C₃₁	1	2	yes	complemented
495	#489	C₂²×C₃₁	1	2	yes	complemented
496	#487	C₂²×C₃₁	1	2	yes	complemented
497	#486	C₂²×C₃₁	1	2	yes	—
498	#484	C₂²×C₃₁	1	2	yes	complemented
499	#483	C₂²×C₃₁	1	4	yes	complemented
500	#481	C₂²×C₃₁	1	2	yes	—
501	#480	C₂²×C₃₁	1	4	yes	—
502	#477	C₂²×C₃₁	1	4	yes	complemented
503	#476	C₂²×C₃₁	1	4	yes	complemented
504	#475	C₂²×C₃₁	1	2	yes	complemented
505	#474	C₂²×C₃₁	1	2	yes	—
506	#469	C₂²×C₃₁	1	2	yes	—
507	#468	C₂²×C₃₁	1	2	yes	complemented
508	#466	C₂²×C₃₁	1	4	yes	—
509	#465	C₂²×C₃₁	1	4	yes	complemented
510	#463	C₂²×C₃₁	1	4	yes	—
511	#463	C₂²×C₃₁	1	4	yes	complemented
512	#461	C₂²×C₃₁	1	2	yes	complemented
513	#459	C₂²×C₃₁	1	2	yes	—
514	#449	C₂²×C₃₁	1	4	yes	complemented
515	#448	C₂²×C₃₁	1	4	yes	complemented
516	#447	C₂²×C₃₁	1	4	yes	—
517	#446	C₂²×C₃₁	1	2	yes	complemented
518	#442	C₂²×C₃₁	1	4	yes	complemented
519	#440	C₂²×C₃₁	1	4	yes	complemented
520	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
521	C₄×D₈	C₂²×C₃₁	1	2	yes	—
522	#435	C₂²×C₃₁	1	4	yes	complemented
523	C₈×D₄	C₂²×C₃₁	1	2	yes	—
524	#432	C₂²×C₃₁	1	2	yes	complemented
525	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
526	#417	C₂²×C₃₁	1	4	yes	complemented
527	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
528	C₂×#102	C₂²×C₃₁	1	4	yes	—
529	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
530	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
531	C₂×C₃₁	—	2	4	no	—
532	C₂×C₃₁	—	4	1	no	—
533	C₂×C₃₁	—	8	2	no	—
534	C₂×C₃₁	—	8	2	no	—
535	C₂×C₃₁	—	8	1	no	—
536	C₂×C₃₁	#3500	1	1	yes	characteristic
537	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂×C₃₁	#3586	1	1	yes	characteristic
539	2₋¹⁺⁴	—	4	8	no	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	2	4	no	—
542	C₂×#41	—	2	2	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
545	C₂×#41	C₂³×C₃₁	1	2	yes	—
546	C₂²×Q₈	—	2	2	no	—
547	C₂²×Q₈	—	2	2	no	—
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
554	C₂×D₈	C₂³×C₃₁	1	2	yes	—
555	C₂×D₈	C₂³×C₃₁	1	4	yes	—
556	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
557	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	2	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
568	#127	C₂³×C₃₁	1	1	yes	characteristic
569	#127	C₂³×C₃₁	1	1	yes	characteristic
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#126	—	2	1	no	—
573	#125	C₂³×C₃₁	1	1	yes	characteristic
574	#124	—	2	1	no	—
575	#124	—	2	2	no	—
576	#124	—	2	2	no	—
577	#124	—	2	2	no	—
578	#124	—	2	2	no	—
579	#124	—	2	1	no	—
580	#124	C₂³×C₃₁	1	1	yes	characteristic
581	#124	C₂³×C₃₁	1	2	yes	—
582	#124	C₂³×C₃₁	1	2	yes	—
583	#124	C₂³×C₃₁	1	2	yes	—
584	#123	—	2	1	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	4	no	—
589	#123	—	2	4	no	—
590	#123	—	2	4	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	4	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	#121	—	2	2	no	—
601	#121	—	2	1	no	—
602	#121	—	2	1	no	—
603	#121	—	2	2	no	—
604	#121	—	2	1	no	—
605	#121	—	2	1	no	—
606	#121	—	2	2	no	—
607	#121	C₂³×C₃₁	1	2	yes	—
608	#121	C₂³×C₃₁	1	1	yes	characteristic
609	#121	C₂³×C₃₁	1	4	yes	—
610	#121	C₂³×C₃₁	1	2	yes	—
611	#120	—	2	2	no	—
612	#120	—	2	2	no	—
613	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
615	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
627	C₄×D₄	D₄×C₃₁	1	2	yes	—
628	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₃₁	1	2	yes	—
630	C₄×D₄	C₂³×C₃₁	1	2	yes	—
631	C₄×D₄	C₂³×C₃₁	1	4	yes	—
632	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₃₁	1	2	yes	—
634	#117	—	2	1	no	—
635	#117	—	2	1	no	—
636	#117	—	2	2	no	—
637	#117	D₄×C₃₁	1	2	yes	—
638	#117	D₄×C₃₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₂²⋊C₄	—	2	2	no	—
644	C₂×C₂²⋊C₄	—	2	2	no	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	#107	C₂³×C₃₁	1	2	yes	—
649	#107	C₂³×C₃₁	1	4	yes	—
650	#106	C₂³×C₃₁	1	2	yes	—
651	#106	C₂³×C₃₁	1	4	yes	—
652	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
653	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
654	#103	C₂³×C₃₁	1	2	yes	—
655	#103	C₂³×C₃₁	1	4	yes	—
656	#103	C₂³×C₃₁	1	4	yes	—
657	#103	C₂³×C₃₁	1	4	yes	—
658	#103	C₂³×C₃₁	1	4	yes	—
659	#102	C₂³×C₃₁	1	2	yes	—
660	#102	C₂³×C₃₁	1	4	yes	—
661	#102	C₂³×C₃₁	1	4	yes	—
662	#102	C₂³×C₃₁	1	4	yes	—
663	#102	C₂³×C₃₁	1	4	yes	—
664	#102	C₂³×C₃₁	1	2	yes	—
665	#102	C₂³×C₃₁	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
667	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
668	#97	C₂³×C₃₁	1	1	yes	characteristic
669	#97	C₂³×C₃₁	1	2	yes	—
670	#97	C₂³×C₃₁	1	4	yes	—
671	#97	C₂³×C₃₁	1	1	yes	characteristic
672	C₄×C₈	C₂³×C₃₁	1	2	yes	—
673	C₃₁	#62583	1	1	yes	characteristic, direct product factor, Sylow
674	C₂⁴	—	2	2	no	—
675	#41	—	2	4	no	—
676	#41	—	4	8	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	4	16	no	—
680	#41	—	4	8	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	4	8	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	4	no	—
689	C₂×Q₈	—	4	8	no	—
690	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
691	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
709	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
721	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	2	no	—
726	D₈	—	4	4	no	—
727	D₈	—	4	2	no	—
728	M₁₆	—	4	2	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
774	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
775	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	1	no	—
778	C₄²	C₂×D₄×C₃₁	1	2	yes	—
779	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₃₁	1	2	yes	—
782	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
783	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₃₁	1	2	yes	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	8	2	no	—
790	C₂³	—	8	2	no	—
791	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
792	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	8	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	8	2	no	—
801	D₄	—	2	4	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	4	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	1	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	2	no	—
816	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	4	no	—
848	C₈	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	16	4	no	—
864	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
865	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	4	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
880	C₄	C₃₁×#585	1	2	yes	—
881	C₂	—	2	4	no	—
882	C₂	—	4	1	no	—
883	C₂	—	8	1	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₃₁×#3500	1	1	yes	characteristic
887	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
888	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3514	C₂	semidirect
2. C₃₁×#3499	C₂	semidirect
3. C₃₁×#3373	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3308	C₂	semidirect
6. C₃₁×#3306	C₂	semidirect
7. C₃₁×#3298	C₂	semidirect
8. C₃₁×#3294	C₂	semidirect
9. C₃₁×#3239	C₂	semidirect
10. C₃₁×#3238	C₂	semidirect
11. C₃₁×#3214	C₂	semidirect
12. C₃₁×#3213	C₂	semidirect
13. C₃₁×#3180	C₂	semidirect
14. C₃₁×#3171	C₂	semidirect
15. C₃₁×#3141	C₂	semidirect
16. C₂×C₃₁×#489	C₂	semidirect
17. C₃₁×#2970	C₂	semidirect
25. D₄×Q₈×C₃₁	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
51. C₃₁×#496	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
56. C₃₁×#489	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#487	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
63. C₃₁×#483	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#476	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
75. C₃₁×#463	C₂²	semidirect
76. C₃₁×#461	C₂²	semidirect
78. C₃₁×#449	C₂²	semidirect
79. C₃₁×#448	C₂²	semidirect
81. C₃₁×#446	C₂²	semidirect
82. C₃₁×#442	C₂²	semidirect
83. C₃₁×#440	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₃₁×#435	C₂²	semidirect
88. C₃₁×#432	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#417	C₂²	semidirect
91. C₂×C₃₁×#103	C₂²	semidirect
93. C₄×M₁₆×C₃₁	C₂²	semidirect
94. C₂×C₃₁×#97	C₂²	semidirect
340. #62583	C₃₁	direct (N × H)
405. #3514	C₂×C₃₁	semidirect
406. #3499	C₂×C₃₁	semidirect
407. #3373	C₂×C₃₁	semidirect
408. #3367	C₂×C₃₁	semidirect
409. #3308	C₂×C₃₁	semidirect
410. #3306	C₂×C₃₁	semidirect
411. #3298	C₂×C₃₁	semidirect
412. #3294	C₂×C₃₁	semidirect
413. #3239	C₂×C₃₁	semidirect
414. #3238	C₂×C₃₁	semidirect
415. #3214	C₂×C₃₁	semidirect
416. #3213	C₂×C₃₁	semidirect
417. #3180	C₂×C₃₁	semidirect
418. #3171	C₂×C₃₁	semidirect
419. #3141	C₂×C₃₁	semidirect
420. C₂×#489	C₂×C₃₁	semidirect
421. #2970	C₂×C₃₁	semidirect
461. D₄×Q₈	C₂²×C₃₁	semidirect
466. #547	C₂²×C₃₁	semidirect
475. #532	C₂²×C₃₁	semidirect
476. #532	C₂²×C₃₁	semidirect
477. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
484. #501	C₂²×C₃₁	semidirect
485. #501	C₂²×C₃₁	semidirect
487. #496	C₂²×C₃₁	semidirect
488. #490	C₂²×C₃₁	semidirect
492. #489	C₂²×C₃₁	semidirect
493. #489	C₂²×C₃₁	semidirect
494. #489	C₂²×C₃₁	semidirect
495. #489	C₂²×C₃₁	semidirect
496. #487	C₂²×C₃₁	semidirect
498. #484	C₂²×C₃₁	semidirect
499. #483	C₂²×C₃₁	semidirect
502. #477	C₂²×C₃₁	semidirect
503. #476	C₂²×C₃₁	semidirect
504. #475	C₂²×C₃₁	semidirect
507. #468	C₂²×C₃₁	semidirect
509. #465	C₂²×C₃₁	semidirect
511. #463	C₂²×C₃₁	semidirect
512. #461	C₂²×C₃₁	semidirect
514. #449	C₂²×C₃₁	semidirect
515. #448	C₂²×C₃₁	semidirect
517. #446	C₂²×C₃₁	semidirect
518. #442	C₂²×C₃₁	semidirect
519. #440	C₂²×C₃₁	semidirect
520. C₄×SD₁₆	C₂²×C₃₁	semidirect
522. #435	C₂²×C₃₁	semidirect
524. #432	C₂²×C₃₁	semidirect
525. #432	C₂²×C₃₁	semidirect
526. #417	C₂²×C₃₁	semidirect
527. C₂×#103	C₂²×C₃₁	semidirect
529. C₄×M₁₆	C₂²×C₃₁	semidirect
530. C₂×#97	C₂²×C₃₁	semidirect
673. C₃₁	#62583	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×#3514	2
C₃₁×#3499	2
C₃₁×#3373	2
C₃₁×#3367	2
C₃₁×#3308	2
C₃₁×#3306	2
C₃₁×#3298	2
C₃₁×#3294	2
C₃₁×#3239	2
C₃₁×#3238	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3180	2
C₃₁×#3171	2
C₃₁×#3141	2
C₂×C₃₁×#489	2
C₃₁×#2970	2
#62583	31

Subgroups — C31×#62583 #21519342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62583 #21519342