Subgroups — C₃₁×#62179 #21518938

Order 7936.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	2	yes	—
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	C₂²	1	2	yes	complemented
34	C₃₁×#551	—	2	2	no	—
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	—	2	1	no	—
38	C₃₁×#547	C₂²	1	2	yes	complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	complemented
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#542	C₂²	1	2	yes	complemented
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#536	—	2	2	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃₁×#124	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#498	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#488	C₂²	1	2	yes	complemented
63	C₃₁×#486	C₂²	1	1	yes	characteristic
64	C₃₁×#486	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#481	C₂²	1	2	yes	complemented
74	C₃₁×#481	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#476	C₂²	1	1	yes	characteristic
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	2	yes	—
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#476	C₂²	1	2	yes	complemented
87	C₃₁×#476	C₂²	1	2	yes	complemented
88	C₃₁×#475	C₂²	1	2	yes	complemented
89	C₃₁×#475	C₂²	1	2	yes	complemented
90	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#470	C₂²	1	2	yes	complemented
95	C₃₁×#469	C₂²	1	2	yes	—
96	C₃₁×#469	C₂²	1	2	yes	complemented
97	C₃₁×#468	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	1	yes	characteristic
103	C₃₁×#463	C₂²	1	2	yes	complemented
104	C₃₁×#463	C₂²	1	2	yes	complemented
105	C₃₁×#460	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#452	C₂²	1	1	yes	characteristic
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	1	yes	characteristic
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₃₁×#427	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#417	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	—	2	2	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×#127	C₂³	1	1	yes	characteristic
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	1	no	—
168	C₃₁×#126	D₄	1	2	yes	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	D₄	1	1	yes	characteristic
173	C₃₁×#125	C₂³	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	D₄	1	1	yes	characteristic
184	C₃₁×#124	C₂³	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	C₂³	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#106	C₂³	1	1	yes	characteristic
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	1	yes	characteristic
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	4	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	4	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	4	2	no	—
338	C₂×D₄×C₃₁	—	8	2	no	—
339	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
358	Q₁₆×C₃₁	—	4	1	no	—
359	SD₁₆×C₃₁	—	2	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	2	no	—
362	D₈×C₃₁	—	2	2	no	—
363	D₈×C₃₁	—	4	2	no	—
364	M₁₆×C₃₁	—	4	2	no	—
365	M₁₆×C₃₁	—	4	2	no	—
366	C₂×C₈×C₃₁	—	4	2	no	—
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	2	yes	—
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	#62179	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	2	1	no	—
446	C₂³×C₃₁	—	2	2	no	—
447	C₂³×C₃₁	—	4	4	no	—
448	C₂³×C₃₁	—	8	2	no	—
449	C₂³×C₃₁	—	8	2	no	—
450	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
451	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	8	2	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	1	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	4	4	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	8	1	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	2	no	—
478	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	4	1	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	4	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	8	1	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
513	C₈×C₃₁	—	2	1	no	—
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	2	no	—
517	C₈×C₃₁	—	2	2	no	—
518	C₈×C₃₁	—	2	1	no	—
519	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
522	Q₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3354	C₂×C₃₁	1	2	yes	complemented
527	#3348	C₂×C₃₁	1	2	yes	complemented
528	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3323	C₂×C₃₁	1	2	yes	complemented
531	#3306	C₂×C₃₁	1	2	yes	complemented
532	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3263	C₂×C₃₁	1	2	yes	complemented
534	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3244	C₂×C₃₁	1	2	yes	complemented
536	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3118	C₂×C₃₁	1	2	yes	complemented
538	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3081	C₂×C₃₁	1	2	yes	complemented
540	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	2	no	—
547	C₂²×C₃₁	—	2	1	no	—
548	C₂²×C₃₁	—	2	2	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	16	4	no	—
558	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	2	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	1	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	#577	1	2	yes	—
576	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
577	C₄×C₃₁	#585	1	1	yes	characteristic
578	#563	—	2	2	no	—
579	#559	C₂²×C₃₁	1	1	yes	characteristic
580	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
581	#556	C₂²×C₃₁	1	1	yes	characteristic
582	#555	C₂²×C₃₁	1	1	yes	characteristic
583	#555	C₂²×C₃₁	1	2	yes	—
584	#554	C₂²×C₃₁	1	1	yes	characteristic
585	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	#552	—	2	1	no	—
587	#552	C₂²×C₃₁	1	2	yes	complemented
588	#551	—	2	2	no	—
589	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
590	#548	—	2	1	no	—
591	#547	—	2	1	no	—
592	#547	C₂²×C₃₁	1	2	yes	complemented
593	#546	—	2	1	no	—
594	#546	C₂²×C₃₁	1	2	yes	—
595	D₄²	C₂²×C₃₁	1	1	yes	characteristic
596	#544	—	2	1	no	—
597	#544	C₂²×C₃₁	1	2	yes	complemented
598	#542	—	2	1	no	—
599	#542	C₂²×C₃₁	1	2	yes	—
600	#542	C₂²×C₃₁	1	2	yes	complemented
601	#538	—	2	2	no	—
602	#536	—	2	2	no	—
603	#532	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#529	—	2	1	no	—
606	#529	C₂²×C₃₁	1	1	yes	characteristic
607	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	C₂×#124	—	2	1	no	—
609	#518	C₂²×C₃₁	1	2	yes	—
610	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
611	#501	C₂²×C₃₁	1	2	yes	complemented
612	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#498	C₂²×C₃₁	1	2	yes	complemented
614	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#489	C₂²×C₃₁	1	2	yes	complemented
616	#488	C₂²×C₃₁	1	2	yes	complemented
617	#486	C₂²×C₃₁	1	1	yes	characteristic
618	#486	C₂²×C₃₁	1	1	yes	characteristic
619	#485	C₂²×C₃₁	1	2	yes	complemented
620	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#485	C₂²×C₃₁	1	2	yes	complemented
622	#483	C₂²×C₃₁	1	2	yes	complemented
623	#482	C₂²×C₃₁	1	2	yes	—
624	#482	C₂²×C₃₁	1	2	yes	complemented
625	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#481	C₂²×C₃₁	1	2	yes	—
627	#481	C₂²×C₃₁	1	2	yes	complemented
628	#481	C₂²×C₃₁	1	2	yes	complemented
629	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#478	C₂²×C₃₁	1	1	yes	characteristic
631	#478	C₂²×C₃₁	1	2	yes	—
632	#478	C₂²×C₃₁	1	2	yes	complemented
633	#478	C₂²×C₃₁	1	2	yes	complemented
634	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#476	C₂²×C₃₁	1	1	yes	characteristic
637	#476	C₂²×C₃₁	1	1	yes	characteristic
638	#476	C₂²×C₃₁	1	2	yes	—
639	#476	C₂²×C₃₁	1	2	yes	complemented
640	#476	C₂²×C₃₁	1	2	yes	complemented
641	#476	C₂²×C₃₁	1	2	yes	complemented
642	#475	C₂²×C₃₁	1	2	yes	complemented
643	#475	C₂²×C₃₁	1	2	yes	complemented
644	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#474	C₂²×C₃₁	1	2	yes	—
646	#474	C₂²×C₃₁	1	2	yes	complemented
647	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#470	C₂²×C₃₁	1	2	yes	complemented
649	#469	C₂²×C₃₁	1	2	yes	—
650	#469	C₂²×C₃₁	1	2	yes	complemented
651	#468	C₂²×C₃₁	1	2	yes	complemented
652	#465	C₂²×C₃₁	1	2	yes	—
653	#465	C₂²×C₃₁	1	2	yes	complemented
654	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#464	C₂²×C₃₁	1	2	yes	complemented
656	#463	C₂²×C₃₁	1	1	yes	characteristic
657	#463	C₂²×C₃₁	1	2	yes	complemented
658	#463	C₂²×C₃₁	1	2	yes	complemented
659	#460	C₂²×C₃₁	1	1	yes	characteristic
660	#459	C₂²×C₃₁	1	1	yes	characteristic
661	#452	C₂²×C₃₁	1	1	yes	characteristic
662	#450	C₂²×C₃₁	1	2	yes	—
663	#449	C₂²×C₃₁	1	1	yes	characteristic
664	#447	C₂²×C₃₁	1	2	yes	—
665	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#442	C₂²×C₃₁	1	2	yes	—
668	#440	C₂²×C₃₁	1	2	yes	complemented
669	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
675	#436	C₂²×C₃₁	1	1	yes	characteristic
676	#436	C₂²×C₃₁	1	2	yes	complemented
677	#435	C₂²×C₃₁	1	2	yes	complemented
678	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
679	#433	C₂²×C₃₁	1	2	yes	complemented
680	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#428	C₂²×C₃₁	1	2	yes	complemented
682	#428	C₂²×C₃₁	1	2	yes	complemented
683	#427	C₂²×C₃₁	1	2	yes	complemented
684	#424	C₂²×C₃₁	1	2	yes	complemented
685	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#418	C₂²×C₃₁	1	2	yes	—
687	#417	C₂²×C₃₁	1	2	yes	—
688	C₂×#102	C₂²×C₃₁	1	2	yes	—
689	C₂×C₃₁	—	4	1	no	—
690	C₂×C₃₁	—	4	2	no	—
691	C₂×C₃₁	—	4	2	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	—	8	2	no	—
694	C₂×C₃₁	#3489	1	1	yes	characteristic
695	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
696	C₂×C₃₁	#3585	1	1	yes	characteristic
697	C₂×#41	—	2	2	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
700	C₂²×Q₈	—	2	1	no	—
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×D₄	—	2	1	no	—
703	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
704	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₃₁	1	2	yes	—
710	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
713	C₄⋊Q₈	—	2	2	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
724	#127	C₂³×C₃₁	1	1	yes	characteristic
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	1	no	—
730	#126	D₄×C₃₁	1	2	yes	—
731	#125	—	2	1	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	D₄×C₃₁	1	1	yes	characteristic
735	#125	C₂³×C₃₁	1	1	yes	characteristic
736	#125	C₂³×C₃₁	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	1	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	1	no	—
745	#124	D₄×C₃₁	1	1	yes	characteristic
746	#124	C₂³×C₃₁	1	1	yes	characteristic
747	#124	C₂³×C₃₁	1	2	yes	—
748	#123	—	2	2	no	—
749	#123	—	2	1	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	D₄×C₃₁	1	2	yes	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	D₄×C₃₁	1	1	yes	characteristic
777	#121	C₂³×C₃₁	1	1	yes	characteristic
778	#121	C₂³×C₃₁	1	2	yes	—
779	#121	C₂³×C₃₁	1	2	yes	—
780	#121	C₂³×C₃₁	1	2	yes	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₃₁	1	2	yes	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	C₂³×C₃₁	1	1	yes	characteristic
813	#117	C₂³×C₃₁	1	2	yes	—
814	#117	C₂³×C₃₁	1	2	yes	—
815	#117	C₂³×C₃₁	1	2	yes	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₂²⋊C₄	—	2	2	no	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
825	#107	C₂³×C₃₁	1	2	yes	—
826	#107	C₂³×C₃₁	1	2	yes	—
827	#107	C₂³×C₃₁	1	2	yes	—
828	#107	C₂³×C₃₁	1	1	yes	characteristic
829	#107	C₂³×C₃₁	1	1	yes	characteristic
830	#106	C₂³×C₃₁	1	1	yes	characteristic
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	2	yes	—
834	#106	C₂³×C₃₁	1	2	yes	—
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	#106	C₂³×C₃₁	1	1	yes	characteristic
838	#106	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#102	C₂³×C₃₁	1	1	yes	characteristic
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	#97	C₂³×C₃₁	1	2	yes	—
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₃₁	1	2	yes	—
874	C₃₁	#62179	1	1	yes	characteristic, direct product factor, Sylow
875	C₂⁴	—	2	2	no	—
876	#41	—	2	2	no	—
877	#41	—	4	1	no	—
878	#41	—	8	2	no	—
879	#41	—	8	4	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	—	8	2	no	—
888	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	8	2	no	—
902	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
904	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
905	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
921	Q₁₆	—	4	1	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	4	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	2	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
935	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1002	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₃₁	1	2	yes	—
1005	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	8	2	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1013	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	2	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	—	8	2	no	—
1022	Q₈	—	8	1	no	—
1023	Q₈	—	8	1	no	—
1024	Q₈	—	8	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	1	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	2	no	—
1040	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	16	4	no	—
1097	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₃₁×#577	1	2	yes	—
1115	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1116	C₄	C₃₁×#585	1	1	yes	characteristic
1117	C₂	—	4	2	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₃₁×#3489	1	1	yes	characteristic
1123	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1124	C₂	C₃₁×#3585	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3544	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. Q₈×SD₁₆×C₃₁	C₂	semidirect
5. C₃₁×#3375	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3354	C₂	semidirect
9. C₃₁×#3348	C₂	semidirect
10. C₃₁×#3340	C₂	semidirect
11. C₃₁×#3325	C₂	semidirect
12. C₃₁×#3323	C₂	semidirect
13. C₃₁×#3306	C₂	semidirect
14. C₃₁×#3295	C₂	semidirect
15. C₃₁×#3263	C₂	semidirect
16. C₃₁×#3251	C₂	semidirect
17. C₃₁×#3244	C₂	semidirect
18. C₃₁×#3227	C₂	semidirect
19. C₃₁×#3118	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3079	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
26. Q₈²×C₃₁	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
33. C₃₁×#552	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
43. C₃₁×#544	C₂²	semidirect
46. C₃₁×#542	C₂²	semidirect
50. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#498	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
73. C₃₁×#481	C₂²	semidirect
74. C₃₁×#481	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#475	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#470	C₂²	semidirect
96. C₃₁×#469	C₂²	semidirect
97. C₃₁×#468	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
103. C₃₁×#463	C₂²	semidirect
104. C₃₁×#463	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₃₁×#427	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
443. #62179	C₃₁	direct (N × H)
519. #3544	C₂×C₃₁	semidirect
520. #3514	C₂×C₃₁	semidirect
521. #3384	C₂×C₃₁	semidirect
522. Q₈×SD₁₆	C₂×C₃₁	semidirect
523. #3375	C₂×C₃₁	semidirect
524. #3361	C₂×C₃₁	semidirect
525. #3356	C₂×C₃₁	semidirect
526. #3354	C₂×C₃₁	semidirect
527. #3348	C₂×C₃₁	semidirect
528. #3340	C₂×C₃₁	semidirect
529. #3325	C₂×C₃₁	semidirect
530. #3323	C₂×C₃₁	semidirect
531. #3306	C₂×C₃₁	semidirect
532. #3295	C₂×C₃₁	semidirect
533. #3263	C₂×C₃₁	semidirect
534. #3251	C₂×C₃₁	semidirect
535. #3244	C₂×C₃₁	semidirect
536. #3227	C₂×C₃₁	semidirect
537. #3118	C₂×C₃₁	semidirect
538. #3102	C₂×C₃₁	semidirect
539. #3081	C₂×C₃₁	semidirect
540. #3079	C₂×C₃₁	semidirect
541. #2993	C₂×C₃₁	semidirect
580. Q₈²	C₂²×C₃₁	semidirect
585. #554	C₂²×C₃₁	semidirect
587. #552	C₂²×C₃₁	semidirect
592. #547	C₂²×C₃₁	semidirect
597. #544	C₂²×C₃₁	semidirect
600. #542	C₂²×C₃₁	semidirect
604. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
607. #529	C₂²×C₃₁	semidirect
611. #501	C₂²×C₃₁	semidirect
612. #498	C₂²×C₃₁	semidirect
613. #498	C₂²×C₃₁	semidirect
614. #498	C₂²×C₃₁	semidirect
615. #489	C₂²×C₃₁	semidirect
616. #488	C₂²×C₃₁	semidirect
619. #485	C₂²×C₃₁	semidirect
620. #485	C₂²×C₃₁	semidirect
621. #485	C₂²×C₃₁	semidirect
622. #483	C₂²×C₃₁	semidirect
624. #482	C₂²×C₃₁	semidirect
625. #482	C₂²×C₃₁	semidirect
627. #481	C₂²×C₃₁	semidirect
628. #481	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
632. #478	C₂²×C₃₁	semidirect
633. #478	C₂²×C₃₁	semidirect
634. #477	C₂²×C₃₁	semidirect
635. #477	C₂²×C₃₁	semidirect
639. #476	C₂²×C₃₁	semidirect
640. #476	C₂²×C₃₁	semidirect
641. #476	C₂²×C₃₁	semidirect
642. #475	C₂²×C₃₁	semidirect
643. #475	C₂²×C₃₁	semidirect
644. #475	C₂²×C₃₁	semidirect
646. #474	C₂²×C₃₁	semidirect
647. #474	C₂²×C₃₁	semidirect
648. #470	C₂²×C₃₁	semidirect
650. #469	C₂²×C₃₁	semidirect
651. #468	C₂²×C₃₁	semidirect
653. #465	C₂²×C₃₁	semidirect
654. #464	C₂²×C₃₁	semidirect
655. #464	C₂²×C₃₁	semidirect
657. #463	C₂²×C₃₁	semidirect
658. #463	C₂²×C₃₁	semidirect
665. #446	C₂²×C₃₁	semidirect
666. C₈×Q₈	C₂²×C₃₁	semidirect
668. #440	C₂²×C₃₁	semidirect
669. C₄×Q₁₆	C₂²×C₃₁	semidirect
672. C₄×SD₁₆	C₂²×C₃₁	semidirect
674. C₄×D₈	C₂²×C₃₁	semidirect
676. #436	C₂²×C₃₁	semidirect
677. #435	C₂²×C₃₁	semidirect
679. #433	C₂²×C₃₁	semidirect
680. #431	C₂²×C₃₁	semidirect
681. #428	C₂²×C₃₁	semidirect
682. #428	C₂²×C₃₁	semidirect
683. #427	C₂²×C₃₁	semidirect
684. #424	C₂²×C₃₁	semidirect
685. #423	C₂²×C₃₁	semidirect
874. C₃₁	#62179	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×#3544	2
C₃₁×#3514	2
C₃₁×#3384	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3375	2
C₃₁×#3361	2
C₃₁×#3356	2
C₃₁×#3354	2
C₃₁×#3348	2
C₃₁×#3340	2
C₃₁×#3325	2
C₃₁×#3323	2
C₃₁×#3306	2
C₃₁×#3295	2
C₃₁×#3263	2
C₃₁×#3251	2
C₃₁×#3244	2
C₃₁×#3227	2
C₃₁×#3118	2
C₃₁×#3102	2
C₃₁×#3081	2
C₃₁×#3079	2
C₃₁×#2993	2
#62179	31

Subgroups — C31×#62179 #21518938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62179 #21518938