Subgroups — C₃₁×#62201 #21518960

Order 7936.

1744 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×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3338	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#554	C₂²	1	2	yes	—
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#551	—	2	2	no	—
33	D₄×Q₈×C₃₁	—	2	1	no	—
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#542	C₂²	1	2	yes	complemented
45	C₃₁×#541	—	2	1	no	—
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#500	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#488	C₂²	1	2	yes	—
63	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	1	yes	characteristic
67	C₃₁×#484	C₂²	1	2	yes	—
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	2	yes	complemented
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	1	yes	characteristic
73	C₃₁×#480	C₂²	1	2	yes	—
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	1	yes	characteristic
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	1	yes	characteristic
80	C₃₁×#477	C₂²	1	2	yes	complemented
81	C₃₁×#477	C₂²	1	2	yes	complemented
82	C₃₁×#477	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	2	yes	complemented
84	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#474	C₂²	1	1	yes	characteristic
86	C₃₁×#474	C₂²	1	2	yes	—
87	C₃₁×#474	C₂²	1	2	yes	—
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#474	C₂²	1	1	yes	characteristic
90	C₃₁×#474	C₂²	1	1	yes	characteristic
91	C₃₁×#474	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#474	C₂²	1	2	yes	complemented
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#467	C₂²	1	2	yes	—
97	C₃₁×#467	C₂²	1	2	yes	complemented
98	C₃₁×#466	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	1	yes	characteristic
103	C₃₁×#463	C₂²	1	1	yes	characteristic
104	C₃₁×#463	C₂²	1	2	yes	—
105	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#440	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#107	C₂²	1	2	yes	—
129	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	—	2	1	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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	2	no	—
168	C₃₁×#126	—	2	1	no	—
169	C₃₁×#126	D₄	1	2	yes	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	D₄	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	1	yes	characteristic
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	D₄	1	1	yes	characteristic
182	C₃₁×#124	C₂³	1	1	yes	characteristic
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#123	—	2	1	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	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	D₄	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	D₄	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	1	yes	characteristic
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#120	—	2	2	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	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×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	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	2	yes	—
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	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	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	no	—
313	#41×C₃₁	—	2	4	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	—	2	2	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	1	no	—
335	C₂×D₄×C₃₁	—	4	1	no	—
336	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
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	2	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	8	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	2	no	—
359	SD₁₆×C₃₁	—	2	2	no	—
360	SD₁₆×C₃₁	—	4	2	no	—
361	SD₁₆×C₃₁	—	4	1	no	—
362	D₈×C₃₁	—	2	2	no	—
363	D₈×C₃₁	—	4	1	no	—
364	M₁₆×C₃₁	—	4	2	no	—
365	C₂×C₈×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	2	yes	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	2	yes	—
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	#62201	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂³×C₃₁	—	2	1	no	—
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	4	2	no	—
449	C₂³×C₃₁	—	4	2	no	—
450	C₂³×C₃₁	—	8	1	no	—
451	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
452	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₃₁	—	2	2	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	4	2	no	—
459	Q₈×C₃₁	—	4	2	no	—
460	Q₈×C₃₁	—	4	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	D₄×C₃₁	—	2	4	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	4	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	8	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	1	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	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	4	4	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	8	1	no	—
497	C₂×C₄×C₃₁	—	8	1	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	1	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	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
522	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3346	C₂×C₃₁	1	2	yes	complemented
527	#3338	C₂×C₃₁	1	2	yes	complemented
528	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3314	C₂×C₃₁	1	2	yes	complemented
531	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3297	C₂×C₃₁	1	2	yes	complemented
533	#3262	C₂×C₃₁	1	2	yes	complemented
534	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3243	C₂×C₃₁	1	2	yes	complemented
536	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3124	C₂×C₃₁	1	2	yes	complemented
538	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3083	C₂×C₃₁	1	2	yes	complemented
540	C₂×#474	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	2	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	8	4	no	—
557	C₂²×C₃₁	#578	1	2	yes	—
558	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	1	no	—
564	C₄×C₃₁	—	2	1	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	#576	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	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
580	#556	C₂²×C₃₁	1	1	yes	characteristic
581	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#554	C₂²×C₃₁	1	2	yes	—
583	#554	C₂²×C₃₁	1	2	yes	—
584	#553	C₂²×C₃₁	1	2	yes	—
585	#552	—	2	1	no	—
586	#551	—	2	2	no	—
587	D₄×Q₈	—	2	1	no	—
588	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
589	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#548	—	2	1	no	—
591	#548	—	2	1	no	—
592	#547	C₂²×C₃₁	1	1	yes	characteristic
593	#547	C₂²×C₃₁	1	1	yes	characteristic
594	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	#546	C₂²×C₃₁	1	2	yes	—
596	#544	C₂²×C₃₁	1	2	yes	complemented
597	#542	C₂²×C₃₁	1	2	yes	—
598	#542	C₂²×C₃₁	1	2	yes	complemented
599	#541	—	2	1	no	—
600	#539	—	2	2	no	—
601	#539	—	2	2	no	—
602	#536	—	2	1	no	—
603	#533	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
605	#529	C₂²×C₃₁	1	1	yes	characteristic
606	#529	C₂²×C₃₁	1	1	yes	characteristic
607	#525	—	2	1	no	—
608	C₂×C₂²⋊Q₈	—	2	1	no	—
609	#520	C₂²×C₃₁	1	2	yes	—
610	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
611	#501	C₂²×C₃₁	1	2	yes	complemented
612	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#500	C₂²×C₃₁	1	2	yes	complemented
614	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#489	C₂²×C₃₁	1	2	yes	—
616	#488	C₂²×C₃₁	1	2	yes	—
617	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
619	#485	C₂²×C₃₁	1	2	yes	complemented
620	#484	C₂²×C₃₁	1	1	yes	characteristic
621	#484	C₂²×C₃₁	1	2	yes	—
622	#484	C₂²×C₃₁	1	2	yes	—
623	#484	C₂²×C₃₁	1	2	yes	complemented
624	#484	C₂²×C₃₁	1	2	yes	complemented
625	#482	C₂²×C₃₁	1	2	yes	—
626	#481	C₂²×C₃₁	1	1	yes	characteristic
627	#480	C₂²×C₃₁	1	2	yes	—
628	#480	C₂²×C₃₁	1	2	yes	complemented
629	#479	C₂²×C₃₁	1	2	yes	complemented
630	#479	C₂²×C₃₁	1	2	yes	complemented
631	#478	C₂²×C₃₁	1	1	yes	characteristic
632	#478	C₂²×C₃₁	1	2	yes	—
633	#478	C₂²×C₃₁	1	1	yes	characteristic
634	#477	C₂²×C₃₁	1	2	yes	complemented
635	#477	C₂²×C₃₁	1	2	yes	complemented
636	#477	C₂²×C₃₁	1	2	yes	complemented
637	#477	C₂²×C₃₁	1	2	yes	complemented
638	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#474	C₂²×C₃₁	1	1	yes	characteristic
640	#474	C₂²×C₃₁	1	1	yes	characteristic
641	#474	C₂²×C₃₁	1	2	yes	—
642	#474	C₂²×C₃₁	1	2	yes	—
643	#474	C₂²×C₃₁	1	1	yes	characteristic
644	#474	C₂²×C₃₁	1	1	yes	characteristic
645	#474	C₂²×C₃₁	1	2	yes	—
646	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#474	C₂²×C₃₁	1	2	yes	complemented
648	#468	C₂²×C₃₁	1	2	yes	—
649	#468	C₂²×C₃₁	1	2	yes	complemented
650	#467	C₂²×C₃₁	1	2	yes	—
651	#467	C₂²×C₃₁	1	2	yes	complemented
652	#466	C₂²×C₃₁	1	2	yes	—
653	#465	C₂²×C₃₁	1	2	yes	—
654	#464	C₂²×C₃₁	1	2	yes	—
655	#464	C₂²×C₃₁	1	2	yes	complemented
656	#463	C₂²×C₃₁	1	1	yes	characteristic
657	#463	C₂²×C₃₁	1	1	yes	characteristic
658	#463	C₂²×C₃₁	1	2	yes	—
659	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#452	C₂²×C₃₁	1	2	yes	—
662	#450	C₂²×C₃₁	1	1	yes	characteristic
663	#449	C₂²×C₃₁	1	2	yes	—
664	#447	C₂²×C₃₁	1	1	yes	characteristic
665	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#440	C₂²×C₃₁	1	2	yes	—
668	#440	C₂²×C₃₁	1	2	yes	complemented
669	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
670	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×D₈	C₂²×C₃₁	1	2	yes	—
675	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#435	C₂²×C₃₁	1	2	yes	—
677	C₈×D₄	C₂²×C₃₁	1	2	yes	—
678	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#433	C₂²×C₃₁	1	2	yes	complemented
680	#431	C₂²×C₃₁	1	1	yes	characteristic
681	#428	C₂²×C₃₁	1	2	yes	complemented
682	C₂×#107	C₂²×C₃₁	1	2	yes	—
683	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
684	#424	C₂²×C₃₁	1	2	yes	complemented
685	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
686	#417	C₂²×C₃₁	1	2	yes	—
687	#416	C₂²×C₃₁	1	2	yes	—
688	C₂×#102	C₂²×C₃₁	1	2	yes	—
689	C₂×C₃₁	—	2	2	no	—
690	C₂×C₃₁	—	4	2	no	—
691	C₂×C₃₁	—	4	2	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	—	8	1	no	—
694	C₂×C₃₁	#3489	1	1	yes	characteristic
695	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
696	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	C₂³×C₃₁	1	2	yes	—
700	C₂²×Q₈	—	2	1	no	—
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
713	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	1	no	—
731	#126	D₄×C₃₁	1	2	yes	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	1	no	—
737	#125	D₄×C₃₁	1	1	yes	characteristic
738	#125	C₂³×C₃₁	1	1	yes	characteristic
739	#125	C₂³×C₃₁	1	2	yes	—
740	#124	—	2	1	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	D₄×C₃₁	1	1	yes	characteristic
744	#124	C₂³×C₃₁	1	1	yes	characteristic
745	#124	C₂³×C₃₁	1	2	yes	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	D₄×C₃₁	1	2	yes	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
772	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	D₄×C₃₁	1	1	yes	characteristic
780	#121	C₂³×C₃₁	1	1	yes	characteristic
781	#121	C₂³×C₃₁	1	2	yes	—
782	#121	C₂³×C₃₁	1	2	yes	—
783	#120	—	2	2	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
791	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
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	C₄×D₄	C₂³×C₃₁	1	2	yes	—
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	C₂³×C₃₁	1	2	yes	—
814	#117	C₂³×C₃₁	1	2	yes	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
821	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	2	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	2	yes	—
829	#107	C₂³×C₃₁	1	1	yes	characteristic
830	#107	C₂³×C₃₁	1	2	yes	—
831	#107	C₂³×C₃₁	1	2	yes	—
832	#107	C₂³×C₃₁	1	2	yes	—
833	#107	C₂³×C₃₁	1	2	yes	—
834	#107	C₂³×C₃₁	1	1	yes	characteristic
835	#107	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	2	yes	—
838	#106	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	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	2	yes	—
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	1	yes	characteristic
861	#102	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	1	yes	characteristic
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	#62201	1	1	yes	characteristic, direct product factor, Sylow
875	C₂⁴	—	2	1	no	—
876	#41	—	2	4	no	—
877	#41	—	4	2	no	—
878	#41	—	8	2	no	—
879	#41	—	8	2	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	—	8	2	no	—
888	C₂×Q₈	—	8	2	no	—
889	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
891	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
892	C₂×D₄	—	2	2	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	1	no	—
898	C₂×D₄	—	4	1	no	—
899	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
900	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
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	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	8	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	2	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	1	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	1	no	—
927	M₁₆	—	4	2	no	—
928	C₂×C₈	—	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	2	yes	—
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
936	C₄⋊C₄	—	2	2	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	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	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	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₃₁	1	2	yes	—
1006	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	2	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	8	1	no	—
1013	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1014	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	8	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	D₄	—	2	4	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	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	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	1	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	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	8	4	no	—
1096	C₂²	C₃₁×#578	1	2	yes	—
1097	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	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	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₃₁×#576	1	2	yes	—
1115	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1116	C₄	C₃₁×#585	1	1	yes	characteristic
1117	C₂	—	2	2	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	1	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₃₁×#3489	1	1	yes	characteristic
1123	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1124	C₂	C₂×C₃₁×#578	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×#3552	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. Q₈×D₈×C₃₁	C₂	semidirect
5. C₃₁×#3367	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3353	C₂	semidirect
8. C₃₁×#3346	C₂	semidirect
9. C₃₁×#3338	C₂	semidirect
10. C₃₁×#3334	C₂	semidirect
11. C₃₁×#3330	C₂	semidirect
12. C₃₁×#3314	C₂	semidirect
13. C₃₁×#3302	C₂	semidirect
14. C₃₁×#3297	C₂	semidirect
15. C₃₁×#3262	C₂	semidirect
16. C₃₁×#3248	C₂	semidirect
17. C₃₁×#3243	C₂	semidirect
18. C₃₁×#3230	C₂	semidirect
19. C₃₁×#3124	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3083	C₂	semidirect
22. C₂×C₃₁×#474	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
25. C₃₁×#557	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
40. C₃₁×#547	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
44. C₃₁×#542	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
69. C₃₁×#484	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
82. C₃₁×#477	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#475	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
97. C₃₁×#467	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
105. C₃₁×#462	C₂²	semidirect
106. C₃₁×#461	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
129. C₂×C₃₁×#107	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
444. #62201	C₃₁	direct (N × H)
519. #3552	C₂×C₃₁	semidirect
520. #3520	C₂×C₃₁	semidirect
521. #3386	C₂×C₃₁	semidirect
522. Q₈×D₈	C₂×C₃₁	semidirect
523. #3367	C₂×C₃₁	semidirect
524. #3364	C₂×C₃₁	semidirect
525. #3353	C₂×C₃₁	semidirect
526. #3346	C₂×C₃₁	semidirect
527. #3338	C₂×C₃₁	semidirect
528. #3334	C₂×C₃₁	semidirect
529. #3330	C₂×C₃₁	semidirect
530. #3314	C₂×C₃₁	semidirect
531. #3302	C₂×C₃₁	semidirect
532. #3297	C₂×C₃₁	semidirect
533. #3262	C₂×C₃₁	semidirect
534. #3248	C₂×C₃₁	semidirect
535. #3243	C₂×C₃₁	semidirect
536. #3230	C₂×C₃₁	semidirect
537. #3124	C₂×C₃₁	semidirect
538. #3105	C₂×C₃₁	semidirect
539. #3083	C₂×C₃₁	semidirect
540. C₂×#474	C₂×C₃₁	semidirect
541. #2994	C₂×C₃₁	semidirect
579. #557	C₂²×C₃₁	semidirect
581. #556	C₂²×C₃₁	semidirect
589. D₄×Q₈	C₂²×C₃₁	semidirect
594. #547	C₂²×C₃₁	semidirect
596. #544	C₂²×C₃₁	semidirect
598. #542	C₂²×C₃₁	semidirect
611. #501	C₂²×C₃₁	semidirect
612. #500	C₂²×C₃₁	semidirect
613. #500	C₂²×C₃₁	semidirect
614. #500	C₂²×C₃₁	semidirect
617. #487	C₂²×C₃₁	semidirect
618. #487	C₂²×C₃₁	semidirect
619. #485	C₂²×C₃₁	semidirect
623. #484	C₂²×C₃₁	semidirect
624. #484	C₂²×C₃₁	semidirect
628. #480	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
634. #477	C₂²×C₃₁	semidirect
635. #477	C₂²×C₃₁	semidirect
636. #477	C₂²×C₃₁	semidirect
637. #477	C₂²×C₃₁	semidirect
638. #475	C₂²×C₃₁	semidirect
646. #474	C₂²×C₃₁	semidirect
647. #474	C₂²×C₃₁	semidirect
649. #468	C₂²×C₃₁	semidirect
651. #467	C₂²×C₃₁	semidirect
655. #464	C₂²×C₃₁	semidirect
659. #462	C₂²×C₃₁	semidirect
660. #461	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
675. #436	C₂²×C₃₁	semidirect
678. C₈×D₄	C₂²×C₃₁	semidirect
679. #433	C₂²×C₃₁	semidirect
681. #428	C₂²×C₃₁	semidirect
683. C₂×#107	C₂²×C₃₁	semidirect
684. #424	C₂²×C₃₁	semidirect
874. C₃₁	#62201	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×#3552	2
C₃₁×#3520	2
C₃₁×#3386	2
Q₈×D₈×C₃₁	2
C₃₁×#3367	2
C₃₁×#3364	2
C₃₁×#3353	2
C₃₁×#3346	2
C₃₁×#3338	2
C₃₁×#3334	2
C₃₁×#3330	2
C₃₁×#3314	2
C₃₁×#3302	2
C₃₁×#3297	2
C₃₁×#3262	2
C₃₁×#3248	2
C₃₁×#3243	2
C₃₁×#3230	2
C₃₁×#3124	2
C₃₁×#3105	2
C₃₁×#3083	2
C₂×C₃₁×#474	2
C₃₁×#2994	2
#62201	31

Subgroups — C31×#62201 #21518960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62201 #21518960