Subgroups — C₃₁×#62190 #21518949

Order 7936.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	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×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3346	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×#3322	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#556	C₂²	1	1	yes	characteristic
26	C₃₁×#555	C₂²	1	2	yes	—
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#551	—	2	2	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	—	2	2	no	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#540	C₂²	1	2	yes	complemented
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#537	—	2	1	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#532	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×#498	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	—
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#480	C₂²	1	2	yes	—
72	C₃₁×#480	C₂²	1	1	yes	characteristic
73	C₃₁×#480	C₂²	1	1	yes	characteristic
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×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	—
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#477	C₂²	1	2	yes	complemented
82	C₃₁×#477	C₂²	1	2	yes	complemented
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#474	C₂²	1	1	yes	characteristic
87	C₃₁×#474	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#474	C₂²	1	2	yes	—
90	C₃₁×#474	C₂²	1	1	yes	characteristic
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#469	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	—
97	C₃₁×#468	C₂²	1	2	yes	complemented
98	C₃₁×#466	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	2	yes	—
101	C₃₁×#463	C₂²	1	2	yes	—
102	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	2	yes	complemented
105	C₃₁×#459	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#449	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	1	yes	characteristic
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×#442	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×D₈×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	2	yes	—
122	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#435	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	—
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#417	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
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	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
160	C₃₁×#127	C₂³	1	1	yes	characteristic
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	D₄	1	2	yes	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	D₄	1	1	yes	characteristic
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	D₄	1	1	yes	characteristic
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	D₄	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
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	D₄	1	1	yes	characteristic
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
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	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
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	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	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	—	2	2	no	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
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	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
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	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	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	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	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	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×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	4	1	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	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	8	2	no	—
359	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
363	SD₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	4	2	no	—
365	D₈×C₃₁	—	2	2	no	—
366	D₈×C₃₁	—	2	2	no	—
367	D₈×C₃₁	—	4	1	no	—
368	D₈×C₃₁	—	4	1	no	—
369	M₁₆×C₃₁	—	4	2	no	—
370	M₁₆×C₃₁	—	4	2	no	—
371	C₂×C₈×C₃₁	—	4	2	no	—
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	1	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	1	yes	characteristic
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	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	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	#62190	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	—	2	1	no	—
449	C₂³×C₃₁	—	4	2	no	—
450	C₂³×C₃₁	—	4	2	no	—
451	C₂³×C₃₁	—	8	1	no	—
452	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	4	2	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	1	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	2	no	—
473	D₄×C₃₁	—	4	4	no	—
474	D₄×C₃₁	—	8	1	no	—
475	D₄×C₃₁	—	8	1	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	8	1	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	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	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	4	1	no	—
496	C₂×C₄×C₃₁	—	4	4	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	1	no	—
503	C₂×C₄×C₃₁	—	8	1	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	—	8	1	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	1	no	—
521	C₈×C₃₁	—	2	2	no	—
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	2	no	—
524	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
527	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3357	C₂×C₃₁	1	2	yes	complemented
531	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3346	C₂×C₃₁	1	2	yes	complemented
533	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3322	C₂×C₃₁	1	2	yes	complemented
536	#3319	C₂×C₃₁	1	2	yes	complemented
537	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3257	C₂×C₃₁	1	2	yes	complemented
539	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3243	C₂×C₃₁	1	2	yes	complemented
541	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3119	C₂×C₃₁	1	2	yes	complemented
543	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3083	C₂×C₃₁	1	2	yes	complemented
545	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
547	C₂²×C₃₁	—	2	1	no	—
548	C₂²×C₃₁	—	2	2	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	8	4	no	—
566	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	2	2	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	1	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	2	no	—
582	C₄×C₃₁	#576	1	2	yes	—
583	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
584	C₄×C₃₁	#585	1	1	yes	characteristic
585	#562	—	2	2	no	—
586	#556	C₂²×C₃₁	1	1	yes	characteristic
587	#555	C₂²×C₃₁	1	2	yes	—
588	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
589	#554	C₂²×C₃₁	1	2	yes	—
590	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	#553	C₂²×C₃₁	1	2	yes	—
592	#552	—	2	1	no	—
593	#552	—	2	1	no	—
594	#551	—	2	2	no	—
595	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
596	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#548	—	2	1	no	—
598	#548	—	2	1	no	—
599	#547	C₂²×C₃₁	1	1	yes	characteristic
600	#547	C₂²×C₃₁	1	1	yes	characteristic
601	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#546	C₂²×C₃₁	1	2	yes	—
603	#544	C₂²×C₃₁	1	2	yes	complemented
604	#542	—	2	2	no	—
605	#542	C₂²×C₃₁	1	2	yes	—
606	#540	C₂²×C₃₁	1	2	yes	complemented
607	#539	—	2	2	no	—
608	#537	—	2	1	no	—
609	#536	—	2	1	no	—
610	#533	C₂²×C₃₁	1	1	yes	characteristic
611	#533	C₂²×C₃₁	1	1	yes	characteristic
612	#532	C₂²×C₃₁	1	1	yes	characteristic
613	#529	C₂²×C₃₁	1	1	yes	characteristic
614	#525	—	2	1	no	—
615	C₂×C₂²⋊Q₈	—	2	1	no	—
616	#520	C₂²×C₃₁	1	2	yes	—
617	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
618	#501	C₂²×C₃₁	1	2	yes	complemented
619	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#500	C₂²×C₃₁	1	2	yes	complemented
621	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#489	C₂²×C₃₁	1	2	yes	—
623	#488	C₂²×C₃₁	1	2	yes	—
624	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#485	C₂²×C₃₁	1	2	yes	—
627	#485	C₂²×C₃₁	1	2	yes	—
628	#485	C₂²×C₃₁	1	2	yes	complemented
629	#484	C₂²×C₃₁	1	2	yes	complemented
630	#482	C₂²×C₃₁	1	2	yes	—
631	#481	C₂²×C₃₁	1	2	yes	complemented
632	#480	C₂²×C₃₁	1	2	yes	—
633	#480	C₂²×C₃₁	1	1	yes	characteristic
634	#480	C₂²×C₃₁	1	1	yes	characteristic
635	#480	C₂²×C₃₁	1	2	yes	complemented
636	#479	C₂²×C₃₁	1	2	yes	complemented
637	#479	C₂²×C₃₁	1	2	yes	complemented
638	#479	C₂²×C₃₁	1	2	yes	complemented
639	#478	C₂²×C₃₁	1	2	yes	—
640	#478	C₂²×C₃₁	1	2	yes	—
641	#478	C₂²×C₃₁	1	2	yes	—
642	#477	C₂²×C₃₁	1	2	yes	complemented
643	#477	C₂²×C₃₁	1	2	yes	complemented
644	#476	C₂²×C₃₁	1	1	yes	characteristic
645	#476	C₂²×C₃₁	1	1	yes	characteristic
646	#476	C₂²×C₃₁	1	2	yes	complemented
647	#474	C₂²×C₃₁	1	1	yes	characteristic
648	#474	C₂²×C₃₁	1	1	yes	characteristic
649	#474	C₂²×C₃₁	1	1	yes	characteristic
650	#474	C₂²×C₃₁	1	2	yes	—
651	#474	C₂²×C₃₁	1	1	yes	characteristic
652	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#474	C₂²×C₃₁	1	2	yes	complemented
654	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#469	C₂²×C₃₁	1	2	yes	—
656	#468	C₂²×C₃₁	1	2	yes	—
657	#468	C₂²×C₃₁	1	2	yes	—
658	#468	C₂²×C₃₁	1	2	yes	complemented
659	#466	C₂²×C₃₁	1	2	yes	—
660	#465	C₂²×C₃₁	1	2	yes	complemented
661	#463	C₂²×C₃₁	1	2	yes	—
662	#463	C₂²×C₃₁	1	2	yes	—
663	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#460	C₂²×C₃₁	1	2	yes	complemented
666	#459	C₂²×C₃₁	1	1	yes	characteristic
667	#459	C₂²×C₃₁	1	1	yes	characteristic
668	#449	C₂²×C₃₁	1	2	yes	—
669	#449	C₂²×C₃₁	1	2	yes	—
670	#447	C₂²×C₃₁	1	1	yes	characteristic
671	#447	C₂²×C₃₁	1	1	yes	characteristic
672	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	#442	C₂²×C₃₁	1	2	yes	—
675	#440	C₂²×C₃₁	1	2	yes	complemented
676	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
677	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
679	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₃₁	1	2	yes	—
682	#436	C₂²×C₃₁	1	2	yes	—
683	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#435	C₂²×C₃₁	1	2	yes	—
685	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#433	C₂²×C₃₁	1	2	yes	complemented
687	#431	C₂²×C₃₁	1	1	yes	characteristic
688	#428	C₂²×C₃₁	1	2	yes	—
689	#428	C₂²×C₃₁	1	2	yes	complemented
690	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
691	#424	C₂²×C₃₁	1	2	yes	complemented
692	#423	C₂²×C₃₁	1	1	yes	characteristic
693	#418	C₂²×C₃₁	1	2	yes	—
694	#417	C₂²×C₃₁	1	2	yes	—
695	#416	C₂²×C₃₁	1	2	yes	—
696	C₂×C₃₁	—	4	2	no	—
697	C₂×C₃₁	—	4	1	no	—
698	C₂×C₃₁	—	4	2	no	—
699	C₂×C₃₁	—	8	1	no	—
700	C₂×C₃₁	—	8	1	no	—
701	C₂×C₃₁	—	8	1	no	—
702	C₂×C₃₁	#3489	1	1	yes	characteristic
703	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
704	C₂×C₃₁	#3586	1	1	yes	characteristic
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	C₂³×C₃₁	1	2	yes	—
709	C₂²×Q₈	—	2	1	no	—
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
712	C₂³×C₄	—	2	1	no	—
713	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
722	C₄⋊Q₈	—	2	2	no	—
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
730	#127	C₂³×C₃₁	1	1	yes	characteristic
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	D₄×C₃₁	1	2	yes	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	D₄×C₃₁	1	1	yes	characteristic
739	#125	C₂³×C₃₁	1	2	yes	—
740	#125	C₂³×C₃₁	1	2	yes	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	D₄×C₃₁	1	1	yes	characteristic
747	#124	C₂³×C₃₁	1	2	yes	—
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	—	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	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₃₁	1	1	yes	characteristic
786	#121	C₂³×C₃₁	1	1	yes	characteristic
787	#121	C₂³×C₃₁	1	1	yes	characteristic
788	#121	C₂³×C₃₁	1	2	yes	—
789	#121	C₂³×C₃₁	1	2	yes	—
790	#121	C₂³×C₃₁	1	2	yes	—
791	#120	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	C₂³×C₃₁	1	2	yes	—
814	C₄×D₄	C₂³×C₃₁	1	2	yes	—
815	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
816	#117	—	2	1	no	—
817	#117	—	2	2	no	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	C₂³×C₃₁	1	2	yes	—
822	#117	C₂³×C₃₁	1	2	yes	—
823	#117	C₂³×C₃₁	1	2	yes	—
824	C₂×C₄⋊C₄	—	2	2	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
829	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
833	#107	C₂³×C₃₁	1	1	yes	characteristic
834	#107	C₂³×C₃₁	1	2	yes	—
835	#107	C₂³×C₃₁	1	2	yes	—
836	#107	C₂³×C₃₁	1	2	yes	—
837	#107	C₂³×C₃₁	1	2	yes	—
838	#107	C₂³×C₃₁	1	1	yes	characteristic
839	#107	C₂³×C₃₁	1	2	yes	—
840	#107	C₂³×C₃₁	1	1	yes	characteristic
841	#107	C₂³×C₃₁	1	1	yes	characteristic
842	#107	C₂³×C₃₁	1	2	yes	—
843	#106	C₂³×C₃₁	1	2	yes	—
844	#106	C₂³×C₃₁	1	2	yes	—
845	#106	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	2	yes	—
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
852	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
853	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	1	yes	characteristic
861	#102	C₂³×C₃₁	1	2	yes	—
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	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	1	yes	characteristic
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	#97	C₂³×C₃₁	1	2	yes	—
879	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₃₁	1	2	yes	—
882	C₃₁	#62190	1	1	yes	characteristic, direct product factor, Sylow
883	C₂⁴	—	2	1	no	—
884	#41	—	2	4	no	—
885	#41	—	4	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	2	no	—
888	#41	—	8	2	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	8	2	no	—
896	C₂×Q₈	—	8	2	no	—
897	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
898	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	4	1	no	—
910	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
911	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
912	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	8	2	no	—
930	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	D₈	—	2	2	no	—
937	D₈	—	2	2	no	—
938	D₈	—	4	1	no	—
939	D₈	—	4	1	no	—
940	M₁₆	—	4	2	no	—
941	M₁₆	—	4	2	no	—
942	C₂×C₈	—	4	2	no	—
943	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
946	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₃₁	1	2	yes	—
1014	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1023	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	—	8	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	8	1	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	1	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	1	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	8	4	no	—
1113	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1114	C₄	—	2	2	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	C₃₁×#576	1	2	yes	—
1130	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1131	C₄	C₃₁×#585	1	1	yes	characteristic
1132	C₂	—	4	1	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	4	2	no	—
1135	C₂	—	8	1	no	—
1136	C₂	—	8	1	no	—
1137	C₂	—	8	1	no	—
1138	C₂	C₃₁×#3489	1	1	yes	characteristic
1139	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1140	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3547	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. Q₈×D₈×C₃₁	C₂	semidirect
5. C₃₁×#3367	C₂	semidirect
6. C₃₁×#3360	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3354	C₂	semidirect
9. C₃₁×#3346	C₂	semidirect
10. C₃₁×#3334	C₂	semidirect
11. C₃₁×#3330	C₂	semidirect
12. C₃₁×#3322	C₂	semidirect
13. C₃₁×#3319	C₂	semidirect
14. C₃₁×#3303	C₂	semidirect
15. C₃₁×#3257	C₂	semidirect
16. C₃₁×#3254	C₂	semidirect
17. C₃₁×#3243	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3119	C₂	semidirect
20. C₃₁×#3100	C₂	semidirect
21. C₃₁×#3083	C₂	semidirect
22. C₃₁×#3077	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
27. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
40. C₃₁×#547	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
45. C₃₁×#540	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
82. C₃₁×#477	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
97. C₃₁×#468	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
102. C₃₁×#461	C₂²	semidirect
103. C₃₁×#461	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₂×C₃₁×#107	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
444. #62190	C₃₁	direct (N × H)
524. #3547	C₂×C₃₁	semidirect
525. #3520	C₂×C₃₁	semidirect
526. #3384	C₂×C₃₁	semidirect
527. Q₈×D₈	C₂×C₃₁	semidirect
528. #3367	C₂×C₃₁	semidirect
529. #3360	C₂×C₃₁	semidirect
530. #3357	C₂×C₃₁	semidirect
531. #3354	C₂×C₃₁	semidirect
532. #3346	C₂×C₃₁	semidirect
533. #3334	C₂×C₃₁	semidirect
534. #3330	C₂×C₃₁	semidirect
535. #3322	C₂×C₃₁	semidirect
536. #3319	C₂×C₃₁	semidirect
537. #3303	C₂×C₃₁	semidirect
538. #3257	C₂×C₃₁	semidirect
539. #3254	C₂×C₃₁	semidirect
540. #3243	C₂×C₃₁	semidirect
541. #3231	C₂×C₃₁	semidirect
542. #3119	C₂×C₃₁	semidirect
543. #3100	C₂×C₃₁	semidirect
544. #3083	C₂×C₃₁	semidirect
545. #3077	C₂×C₃₁	semidirect
546. #2993	C₂×C₃₁	semidirect
588. #555	C₂²×C₃₁	semidirect
590. #554	C₂²×C₃₁	semidirect
596. D₄×Q₈	C₂²×C₃₁	semidirect
601. #547	C₂²×C₃₁	semidirect
603. #544	C₂²×C₃₁	semidirect
606. #540	C₂²×C₃₁	semidirect
618. #501	C₂²×C₃₁	semidirect
619. #500	C₂²×C₃₁	semidirect
620. #500	C₂²×C₃₁	semidirect
621. #498	C₂²×C₃₁	semidirect
624. #487	C₂²×C₃₁	semidirect
625. #487	C₂²×C₃₁	semidirect
628. #485	C₂²×C₃₁	semidirect
629. #484	C₂²×C₃₁	semidirect
631. #481	C₂²×C₃₁	semidirect
635. #480	C₂²×C₃₁	semidirect
636. #479	C₂²×C₃₁	semidirect
637. #479	C₂²×C₃₁	semidirect
638. #479	C₂²×C₃₁	semidirect
642. #477	C₂²×C₃₁	semidirect
643. #477	C₂²×C₃₁	semidirect
646. #476	C₂²×C₃₁	semidirect
652. #474	C₂²×C₃₁	semidirect
653. #474	C₂²×C₃₁	semidirect
654. #474	C₂²×C₃₁	semidirect
658. #468	C₂²×C₃₁	semidirect
660. #465	C₂²×C₃₁	semidirect
663. #461	C₂²×C₃₁	semidirect
664. #461	C₂²×C₃₁	semidirect
665. #460	C₂²×C₃₁	semidirect
672. #446	C₂²×C₃₁	semidirect
673. C₈×Q₈	C₂²×C₃₁	semidirect
675. #440	C₂²×C₃₁	semidirect
676. C₄×SD₁₆	C₂²×C₃₁	semidirect
683. #436	C₂²×C₃₁	semidirect
685. C₈×D₄	C₂²×C₃₁	semidirect
686. #433	C₂²×C₃₁	semidirect
689. #428	C₂²×C₃₁	semidirect
690. C₂×#107	C₂²×C₃₁	semidirect
691. #424	C₂²×C₃₁	semidirect
882. C₃₁	#62190	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×#3547	2
C₃₁×#3520	2
C₃₁×#3384	2
Q₈×D₈×C₃₁	2
C₃₁×#3367	2
C₃₁×#3360	2
C₃₁×#3357	2
C₃₁×#3354	2
C₃₁×#3346	2
C₃₁×#3334	2
C₃₁×#3330	2
C₃₁×#3322	2
C₃₁×#3319	2
C₃₁×#3303	2
C₃₁×#3257	2
C₃₁×#3254	2
C₃₁×#3243	2
C₃₁×#3231	2
C₃₁×#3119	2
C₃₁×#3100	2
C₃₁×#3083	2
C₃₁×#3077	2
C₃₁×#2993	2
#62190	31

Subgroups — C31×#62190 #21518949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62190 #21518949