Subgroups — C₃₁×#60927 #21517686

Order 7936.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3256	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic
17	C₃₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
30	C₃₁×#559	—	2	1	no	—
31	C₃₁×#559	—	2	1	no	—
32	C₃₁×#556	—	2	1	no	—
33	C₃₁×#556	—	2	1	no	—
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#551	—	2	2	no	—
36	C₃₁×#544	C₂²	1	1	yes	characteristic
37	C₃₁×#542	—	2	1	no	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#542	C₂²	1	2	yes	—
40	C₃₁×#542	C₂²	1	2	yes	complemented
41	C₃₁×#541	—	2	1	no	—
42	C₃₁×#541	C₂²	1	2	yes	complemented
43	C₃₁×#539	—	2	2	no	—
44	C₃₁×#537	C₂²	1	1	yes	characteristic
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#536	C₂²	1	1	yes	characteristic
47	C₃₁×#536	C₂²	1	1	yes	characteristic
48	C₃₁×#535	C₂²	1	1	yes	characteristic
49	C₃₁×#533	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#533	C₂²	1	2	yes	complemented
52	C₃₁×#529	—	2	2	no	—
53	C₃₁×#529	—	2	1	no	—
54	C₃₁×#529	C₂²	1	2	yes	—
55	C₃₁×#529	C₂²	1	2	yes	—
56	C₃₁×#529	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
58	C₃₁×#519	C₂²	1	1	yes	characteristic
59	C₃₁×#518	C₂²	1	1	yes	characteristic
60	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
63	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#479	C₂²	1	2	yes	complemented
68	C₃₁×#479	C₂²	1	2	yes	complemented
69	C₃₁×#478	C₂²	1	2	yes	—
70	C₃₁×#478	C₂²	1	2	yes	—
71	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#477	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	2	yes	—
77	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#475	C₂²	1	2	yes	complemented
81	C₃₁×#474	C₂²	1	2	yes	—
82	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#470	C₂²	1	2	yes	complemented
84	C₃₁×#470	C₂²	1	2	yes	complemented
85	C₃₁×#470	C₂²	1	2	yes	complemented
86	C₃₁×#469	C₂²	1	2	yes	—
87	C₃₁×#468	C₂²	1	2	yes	—
88	C₃₁×#468	C₂²	1	2	yes	—
89	C₃₁×#468	C₂²	1	2	yes	—
90	C₃₁×#468	C₂²	1	2	yes	complemented
91	C₃₁×#467	C₂²	1	2	yes	complemented
92	C₃₁×#467	C₂²	1	2	yes	complemented
93	C₃₁×#467	C₂²	1	2	yes	complemented
94	C₃₁×#466	C₂²	1	2	yes	—
95	C₃₁×#465	C₂²	1	2	yes	—
96	C₃₁×#465	C₂²	1	2	yes	—
97	C₃₁×#465	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#464	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#464	C₂²	1	2	yes	—
103	C₃₁×#464	C₂²	1	2	yes	—
104	C₃₁×#464	C₂²	1	2	yes	—
105	C₃₁×#464	C₂²	1	2	yes	complemented
106	C₃₁×#464	C₂²	1	2	yes	complemented
107	C₃₁×#463	C₂²	1	2	yes	—
108	C₃₁×#463	C₂²	1	2	yes	—
109	C₃₁×#463	C₂²	1	2	yes	—
110	C₃₁×#463	C₂²	1	2	yes	—
111	C₃₁×#462	C₂²	1	2	yes	complemented
112	C₃₁×#462	C₂²	1	2	yes	complemented
113	C₃₁×#461	C₂²	1	2	yes	—
114	C₃₁×#461	C₂²	1	2	yes	—
115	C₃₁×#428	C₂²	1	1	yes	characteristic
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#427	C₂²	1	1	yes	characteristic
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₃₁×#424	C₂²	1	1	yes	characteristic
120	C₃₁×#424	C₂²	1	1	yes	characteristic
121	C₃₁×#424	C₂²	1	2	yes	complemented
122	C₃₁×#424	C₂²	1	2	yes	complemented
123	C₃₁×#423	C₂²	1	1	yes	characteristic
124	C₃₁×#423	C₂²	1	2	yes	complemented
125	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
127	C₃₁×#419	C₂²	1	1	yes	characteristic
128	C₃₁×#419	C₂²	1	1	yes	characteristic
129	C₃₁×#419	C₂²	1	1	yes	characteristic
130	C₃₁×#418	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₃₁×#416	C₂²	1	1	yes	characteristic
133	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₃₁×#137	—	4	2	no	—
141	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
142	C₂×Q₁₆×C₃₁	—	4	2	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	—	4	2	no	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×#131	—	4	2	no	—
153	C₃₁×#131	—	4	2	no	—
154	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	—	2	1	no	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	—	2	1	no	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×#127	—	2	1	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	1	yes	characteristic
184	C₃₁×#125	C₂³	1	1	yes	characteristic
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#124	C₂³	1	2	yes	—
195	C₃₁×#124	C₂³	1	2	yes	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	—	2	2	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	1	no	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	2	yes	—
225	C₃₁×#120	—	2	2	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	—	2	2	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	1	no	—
233	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	D₄	1	2	yes	—
249	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
250	C₄×D₄×C₃₁	D₄	1	2	yes	—
251	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	C₂³	1	1	yes	characteristic
263	C₃₁×#117	C₂³	1	1	yes	characteristic
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₃₁×#117	C₂³	1	1	yes	characteristic
266	C₃₁×#117	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	—	2	1	no	—
274	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	1	yes	characteristic
278	C₃₁×#107	C₂³	1	1	yes	characteristic
279	C₃₁×#107	C₂³	1	1	yes	characteristic
280	C₃₁×#107	C₂³	1	2	yes	—
281	C₃₁×#107	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	1	yes	characteristic
283	C₃₁×#106	C₂³	1	1	yes	characteristic
284	C₃₁×#106	C₂³	1	1	yes	characteristic
285	C₃₁×#106	C₂³	1	1	yes	characteristic
286	C₃₁×#106	C₂³	1	2	yes	—
287	C₃₁×#106	C₂³	1	2	yes	—
288	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
293	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
294	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
295	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
296	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
297	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	1	yes	characteristic
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	1	yes	characteristic
303	C₃₁×#103	C₂³	1	1	yes	characteristic
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	C₂³	1	2	yes	—
306	C₃₁×#103	C₂³	1	2	yes	—
307	C₃₁×#103	C₂³	1	2	yes	—
308	C₃₁×#103	C₂³	1	2	yes	—
309	C₃₁×#103	C₂³	1	2	yes	—
310	C₃₁×#102	C₂³	1	2	yes	—
311	C₃₁×#102	C₂³	1	2	yes	—
312	C₃₁×#102	C₂³	1	1	yes	characteristic
313	C₃₁×#102	C₂³	1	1	yes	characteristic
314	C₃₁×#102	C₂³	1	1	yes	characteristic
315	C₃₁×#102	C₂³	1	1	yes	characteristic
316	C₃₁×#102	C₂³	1	2	yes	—
317	C₃₁×#102	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	1	no	—
319	#41×C₃₁	—	2	2	no	—
320	#41×C₃₁	—	2	2	no	—
321	#41×C₃₁	—	2	2	no	—
322	#41×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	2	2	no	—
329	C₂×Q₈×C₃₁	—	2	2	no	—
330	C₂×Q₈×C₃₁	—	2	2	no	—
331	C₂×Q₈×C₃₁	—	2	2	no	—
332	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	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	2	no	—
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₃₁	—	4	2	no	—
362	Q₁₆×C₃₁	—	4	2	no	—
363	Q₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	4	2	no	—
365	SD₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	D₈×C₃₁	—	4	2	no	—
369	M₁₆×C₃₁	—	2	2	no	—
370	M₁₆×C₃₁	—	2	2	no	—
371	M₁₆×C₃₁	—	4	2	no	—
372	M₁₆×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	—	2	2	no	—
374	C₂×C₈×C₃₁	—	2	2	no	—
375	C₂×C₈×C₃₁	—	4	2	no	—
376	C₂×C₈×C₃₁	—	4	2	no	—
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	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	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	1	no	—
449	C₄²×C₃₁	—	2	1	no	—
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂×D₄	1	2	yes	—
452	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₃₁	C₂×D₄	1	2	yes	—
454	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	2	yes	—
456	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
457	#60927	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂³×C₃₁	—	2	1	no	—
459	C₂³×C₃₁	—	2	2	no	—
460	C₂³×C₃₁	—	4	2	no	—
461	C₂³×C₃₁	—	8	1	no	—
462	C₂³×C₃₁	—	8	1	no	—
463	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
464	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	Q₈×C₃₁	—	2	2	no	—
466	Q₈×C₃₁	—	2	2	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	2	2	no	—
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	4	2	no	—
473	Q₈×C₃₁	—	4	2	no	—
474	Q₈×C₃₁	—	8	1	no	—
475	Q₈×C₃₁	—	8	2	no	—
476	Q₈×C₃₁	—	8	1	no	—
477	D₄×C₃₁	—	2	4	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	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	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	4	1	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	1	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	4	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	1	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	1	no	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
521	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
522	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	—	2	1	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	2	no	—
528	C₈×C₃₁	—	2	2	no	—
529	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3461	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3263	C₂×C₃₁	1	2	yes	complemented
532	#3262	C₂×C₃₁	1	2	yes	complemented
533	#3258	C₂×C₃₁	1	2	yes	complemented
534	#3258	C₂×C₃₁	1	2	yes	complemented
535	#3256	C₂×C₃₁	1	2	yes	complemented
536	#3252	C₂×C₃₁	1	2	yes	complemented
537	#3250	C₂×C₃₁	1	2	yes	complemented
538	#3248	C₂×C₃₁	1	2	yes	complemented
539	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3062	C₂×C₃₁	1	1	yes	characteristic
545	#3059	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3042	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
550	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#2906	C₂×C₃₁	1	1	yes	characteristic, complemented
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	1	no	—
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	16	2	no	—
564	C₂²×C₃₁	#537	1	2	yes	—
565	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	2	1	no	—
570	C₄×C₃₁	—	2	2	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	—	4	1	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	1	no	—
581	C₄×C₃₁	—	4	2	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	#537	1	2	yes	—
584	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
586	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
587	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
588	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
589	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
590	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
591	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
592	#559	—	2	1	no	—
593	#559	—	2	1	no	—
594	#556	—	2	1	no	—
595	#556	—	2	1	no	—
596	#551	—	2	2	no	—
597	#551	—	2	2	no	—
598	#544	C₂²×C₃₁	1	1	yes	characteristic
599	#542	—	2	1	no	—
600	#542	C₂²×C₃₁	1	2	yes	—
601	#542	C₂²×C₃₁	1	2	yes	—
602	#542	C₂²×C₃₁	1	2	yes	complemented
603	#541	—	2	1	no	—
604	#541	C₂²×C₃₁	1	2	yes	complemented
605	#539	—	2	2	no	—
606	#537	C₂²×C₃₁	1	1	yes	characteristic
607	#536	C₂²×C₃₁	1	1	yes	characteristic
608	#536	C₂²×C₃₁	1	1	yes	characteristic
609	#536	C₂²×C₃₁	1	1	yes	characteristic
610	#535	C₂²×C₃₁	1	1	yes	characteristic
611	#533	—	2	1	no	—
612	#533	C₂²×C₃₁	1	1	yes	characteristic
613	#533	C₂²×C₃₁	1	2	yes	complemented
614	#529	—	2	2	no	—
615	#529	—	2	1	no	—
616	#529	C₂²×C₃₁	1	2	yes	—
617	#529	C₂²×C₃₁	1	2	yes	—
618	#529	C₂²×C₃₁	1	2	yes	complemented
619	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
620	#519	C₂²×C₃₁	1	1	yes	characteristic
621	#518	C₂²×C₃₁	1	1	yes	characteristic
622	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
623	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
624	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
625	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#479	C₂²×C₃₁	1	2	yes	complemented
628	#479	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	2	yes	—
632	#478	C₂²×C₃₁	1	2	yes	—
633	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#477	C₂²×C₃₁	1	2	yes	complemented
637	#477	C₂²×C₃₁	1	2	yes	complemented
638	#476	C₂²×C₃₁	1	2	yes	—
639	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#475	C₂²×C₃₁	1	2	yes	complemented
642	#475	C₂²×C₃₁	1	2	yes	complemented
643	#474	C₂²×C₃₁	1	2	yes	—
644	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#470	C₂²×C₃₁	1	2	yes	complemented
646	#470	C₂²×C₃₁	1	2	yes	complemented
647	#470	C₂²×C₃₁	1	2	yes	complemented
648	#469	C₂²×C₃₁	1	2	yes	—
649	#468	C₂²×C₃₁	1	2	yes	—
650	#468	C₂²×C₃₁	1	2	yes	—
651	#468	C₂²×C₃₁	1	2	yes	—
652	#468	C₂²×C₃₁	1	2	yes	complemented
653	#467	C₂²×C₃₁	1	2	yes	complemented
654	#467	C₂²×C₃₁	1	2	yes	complemented
655	#467	C₂²×C₃₁	1	2	yes	complemented
656	#466	C₂²×C₃₁	1	2	yes	—
657	#465	C₂²×C₃₁	1	2	yes	—
658	#465	C₂²×C₃₁	1	2	yes	—
659	#465	C₂²×C₃₁	1	2	yes	—
660	#465	C₂²×C₃₁	1	2	yes	complemented
661	#464	C₂²×C₃₁	1	2	yes	—
662	#464	C₂²×C₃₁	1	2	yes	—
663	#464	C₂²×C₃₁	1	2	yes	—
664	#464	C₂²×C₃₁	1	2	yes	—
665	#464	C₂²×C₃₁	1	2	yes	—
666	#464	C₂²×C₃₁	1	2	yes	—
667	#464	C₂²×C₃₁	1	2	yes	complemented
668	#464	C₂²×C₃₁	1	2	yes	complemented
669	#463	C₂²×C₃₁	1	2	yes	—
670	#463	C₂²×C₃₁	1	2	yes	—
671	#463	C₂²×C₃₁	1	2	yes	—
672	#463	C₂²×C₃₁	1	2	yes	—
673	#462	C₂²×C₃₁	1	2	yes	complemented
674	#462	C₂²×C₃₁	1	2	yes	complemented
675	#461	C₂²×C₃₁	1	2	yes	—
676	#461	C₂²×C₃₁	1	2	yes	—
677	#428	C₂²×C₃₁	1	1	yes	characteristic
678	#428	C₂²×C₃₁	1	1	yes	characteristic
679	#427	C₂²×C₃₁	1	1	yes	characteristic
680	#427	C₂²×C₃₁	1	1	yes	characteristic
681	#424	C₂²×C₃₁	1	1	yes	characteristic
682	#424	C₂²×C₃₁	1	1	yes	characteristic
683	#424	C₂²×C₃₁	1	2	yes	complemented
684	#424	C₂²×C₃₁	1	2	yes	complemented
685	#423	C₂²×C₃₁	1	1	yes	characteristic
686	#423	C₂²×C₃₁	1	2	yes	complemented
687	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
688	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
689	#419	C₂²×C₃₁	1	1	yes	characteristic
690	#419	C₂²×C₃₁	1	1	yes	characteristic
691	#419	C₂²×C₃₁	1	1	yes	characteristic
692	#418	C₂²×C₃₁	1	1	yes	characteristic
693	#416	C₂²×C₃₁	1	1	yes	characteristic
694	#416	C₂²×C₃₁	1	1	yes	characteristic
695	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
697	C₂×C₃₁	—	2	2	no	—
698	C₂×C₃₁	—	4	2	no	—
699	C₂×C₃₁	—	8	1	no	—
700	C₂×C₃₁	—	8	2	no	—
701	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
702	C₂×C₃₁	#3584	1	1	yes	characteristic
703	C₂×C₃₁	#3586	1	1	yes	characteristic
704	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
709	#137	—	4	2	no	—
710	AGL(1,ℤ/8)	—	4	2	no	—
711	C₂×Q₁₆	—	4	2	no	—
712	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×SD₁₆	—	4	2	no	—
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×D₈	C₂³×C₃₁	1	2	yes	—
721	#131	—	4	2	no	—
722	#131	—	4	2	no	—
723	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
727	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
730	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
735	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
738	#127	—	2	1	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#125	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	C₂³×C₃₁	1	1	yes	characteristic
752	#125	C₂³×C₃₁	1	1	yes	characteristic
753	#125	C₂³×C₃₁	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	1	no	—
761	#124	—	2	1	no	—
762	#124	C₂³×C₃₁	1	2	yes	—
763	#124	C₂³×C₃₁	1	2	yes	—
764	#124	C₂³×C₃₁	1	2	yes	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	C₂³×C₃₁	1	2	yes	—
792	#121	C₂³×C₃₁	1	2	yes	—
793	#121	C₂³×C₃₁	1	2	yes	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
803	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
806	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	D₄×C₃₁	1	2	yes	—
818	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
819	C₄×D₄	D₄×C₃₁	1	2	yes	—
820	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	2	yes	—
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	—	2	2	no	—
831	#117	C₂³×C₃₁	1	1	yes	characteristic
832	#117	C₂³×C₃₁	1	1	yes	characteristic
833	#117	C₂³×C₃₁	1	1	yes	characteristic
834	#117	C₂³×C₃₁	1	1	yes	characteristic
835	#117	C₂³×C₃₁	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	1	yes	characteristic
846	#107	C₂³×C₃₁	1	1	yes	characteristic
847	#107	C₂³×C₃₁	1	1	yes	characteristic
848	#107	C₂³×C₃₁	1	1	yes	characteristic
849	#107	C₂³×C₃₁	1	2	yes	—
850	#107	C₂³×C₃₁	1	2	yes	—
851	#106	C₂³×C₃₁	1	1	yes	characteristic
852	#106	C₂³×C₃₁	1	1	yes	characteristic
853	#106	C₂³×C₃₁	1	1	yes	characteristic
854	#106	C₂³×C₃₁	1	1	yes	characteristic
855	#106	C₂³×C₃₁	1	2	yes	—
856	#106	C₂³×C₃₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	1	yes	characteristic
870	#103	C₂³×C₃₁	1	1	yes	characteristic
871	#103	C₂³×C₃₁	1	1	yes	characteristic
872	#103	C₂³×C₃₁	1	1	yes	characteristic
873	#103	C₂³×C₃₁	1	2	yes	—
874	#103	C₂³×C₃₁	1	2	yes	—
875	#103	C₂³×C₃₁	1	2	yes	—
876	#103	C₂³×C₃₁	1	2	yes	—
877	#103	C₂³×C₃₁	1	2	yes	—
878	#103	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	1	yes	characteristic
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	C₃₁	#60927	1	1	yes	characteristic, direct product factor, Sylow
888	C₂⁴	—	2	1	no	—
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
905	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
914	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
931	Q₁₆	—	4	2	no	—
932	Q₁₆	—	4	2	no	—
933	Q₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	D₈	—	4	2	no	—
939	M₁₆	—	2	2	no	—
940	M₁₆	—	2	2	no	—
941	M₁₆	—	4	2	no	—
942	M₁₆	—	4	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	2	2	no	—
945	C₂×C₈	—	4	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
950	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	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	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1022	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1024	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₃₁	1	2	yes	—
1026	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	1	no	—
1032	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1033	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	1	no	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	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	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	C₂²×D₄×C₃₁	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1089	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1090	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1091	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	2	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	16	2	no	—
1110	C₂²	C₃₁×#537	1	2	yes	—
1111	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	C₃₁×#537	1	2	yes	—
1130	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1131	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1132	C₂	—	2	2	no	—
1133	C₂	—	4	2	no	—
1134	C₂	—	8	2	no	—
1135	C₂	—	8	1	no	—
1136	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
1137	C₂	C₃₁×#3584	1	1	yes	characteristic
1138	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3062	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3510	C₂	semidirect
2. C₃₁×#3461	C₂	semidirect
3. C₃₁×#3263	C₂	semidirect
4. C₃₁×#3262	C₂	semidirect
5. C₃₁×#3258	C₂	semidirect
6. C₃₁×#3258	C₂	semidirect
7. C₃₁×#3256	C₂	semidirect
8. C₃₁×#3252	C₂	semidirect
9. C₃₁×#3250	C₂	semidirect
10. C₃₁×#3248	C₂	semidirect
11. C₃₁×#3082	C₂	semidirect
12. C₃₁×#3081	C₂	semidirect
13. C₃₁×#3078	C₂	semidirect
14. C₃₁×#3076	C₂	semidirect
15. C₃₁×#3063	C₂	semidirect
17. C₃₁×#3059	C₂	semidirect
18. C₃₁×#3057	C₂	semidirect
19. C₃₁×#3044	C₂	semidirect
20. C₃₁×#3042	C₂	semidirect
21. C₃₁×#3040	C₂	semidirect
22. C₂×C₃₁×#464	C₂	semidirect
23. C₃₁×#2906	C₂	semidirect
40. C₃₁×#542	C₂²	semidirect
42. C₃₁×#541	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
63. C₃₁×#479	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#479	C₂²	semidirect
68. C₃₁×#479	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#477	C₂²	semidirect
74. C₃₁×#477	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
82. C₃₁×#474	C₂²	semidirect
83. C₃₁×#470	C₂²	semidirect
84. C₃₁×#470	C₂²	semidirect
85. C₃₁×#470	C₂²	semidirect
90. C₃₁×#468	C₂²	semidirect
91. C₃₁×#467	C₂²	semidirect
92. C₃₁×#467	C₂²	semidirect
93. C₃₁×#467	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
105. C₃₁×#464	C₂²	semidirect
106. C₃₁×#464	C₂²	semidirect
111. C₃₁×#462	C₂²	semidirect
112. C₃₁×#462	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
124. C₃₁×#423	C₂²	semidirect
126. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
457. #60927	C₃₁	direct (N × H)
529. #3510	C₂×C₃₁	semidirect
530. #3461	C₂×C₃₁	semidirect
531. #3263	C₂×C₃₁	semidirect
532. #3262	C₂×C₃₁	semidirect
533. #3258	C₂×C₃₁	semidirect
534. #3258	C₂×C₃₁	semidirect
535. #3256	C₂×C₃₁	semidirect
536. #3252	C₂×C₃₁	semidirect
537. #3250	C₂×C₃₁	semidirect
538. #3248	C₂×C₃₁	semidirect
539. #3082	C₂×C₃₁	semidirect
540. #3081	C₂×C₃₁	semidirect
541. #3078	C₂×C₃₁	semidirect
542. #3076	C₂×C₃₁	semidirect
543. #3063	C₂×C₃₁	semidirect
545. #3059	C₂×C₃₁	semidirect
546. #3057	C₂×C₃₁	semidirect
547. #3044	C₂×C₃₁	semidirect
548. #3042	C₂×C₃₁	semidirect
549. #3040	C₂×C₃₁	semidirect
550. C₂×#464	C₂×C₃₁	semidirect
551. #2906	C₂×C₃₁	semidirect
602. #542	C₂²×C₃₁	semidirect
604. #541	C₂²×C₃₁	semidirect
613. #533	C₂²×C₃₁	semidirect
618. #529	C₂²×C₃₁	semidirect
625. #479	C₂²×C₃₁	semidirect
626. #479	C₂²×C₃₁	semidirect
627. #479	C₂²×C₃₁	semidirect
628. #479	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
633. #478	C₂²×C₃₁	semidirect
634. #478	C₂²×C₃₁	semidirect
635. #477	C₂²×C₃₁	semidirect
636. #477	C₂²×C₃₁	semidirect
637. #477	C₂²×C₃₁	semidirect
639. #476	C₂²×C₃₁	semidirect
640. #475	C₂²×C₃₁	semidirect
641. #475	C₂²×C₃₁	semidirect
642. #475	C₂²×C₃₁	semidirect
644. #474	C₂²×C₃₁	semidirect
645. #470	C₂²×C₃₁	semidirect
646. #470	C₂²×C₃₁	semidirect
647. #470	C₂²×C₃₁	semidirect
652. #468	C₂²×C₃₁	semidirect
653. #467	C₂²×C₃₁	semidirect
654. #467	C₂²×C₃₁	semidirect
655. #467	C₂²×C₃₁	semidirect
660. #465	C₂²×C₃₁	semidirect
667. #464	C₂²×C₃₁	semidirect
668. #464	C₂²×C₃₁	semidirect
673. #462	C₂²×C₃₁	semidirect
674. #462	C₂²×C₃₁	semidirect
683. #424	C₂²×C₃₁	semidirect
684. #424	C₂²×C₃₁	semidirect
686. #423	C₂²×C₃₁	semidirect
688. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
887. C₃₁	#60927	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×#3510	2
C₃₁×#3461	2
C₃₁×#3263	2
C₃₁×#3262	2
C₃₁×#3258	2
C₃₁×#3256	2
C₃₁×#3252	2
C₃₁×#3250	2
C₃₁×#3248	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3078	2
C₃₁×#3076	2
C₃₁×#3063	2
C₃₁×#3062	2
C₃₁×#3059	2
C₃₁×#3057	2
C₃₁×#3044	2
C₃₁×#3042	2
C₃₁×#3040	2
C₂×C₃₁×#464	2
C₃₁×#2906	2
#60927	31

Subgroups — C31×#60927 #21517686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60927 #21517686