Subgroups — C₃₁×#61863 #21518622

Order 7936.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3380	C₂	1	2	yes	maximal, complemented
8	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#559	C₂²	1	2	yes	complemented
26	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	—	2	1	no	—
29	C₃₁×#554	—	2	2	no	—
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	2	yes	—
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#554	C₂²	1	2	yes	—
34	C₃₁×#554	C₂²	1	2	yes	complemented
35	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₃₁	—	2	1	no	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#548	—	2	1	no	—
41	C₃₁×#547	—	2	1	no	—
42	C₃₁×#544	C₂²	1	2	yes	—
43	C₃₁×#543	—	2	2	no	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#540	C₂²	1	2	yes	—
47	C₃₁×#539	—	2	2	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	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
54	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#501	C₂²	1	2	yes	complemented
59	C₃₁×#500	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#499	C₂²	1	2	yes	complemented
62	C₃₁×#499	C₂²	1	2	yes	complemented
63	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#490	C₂²	1	2	yes	complemented
65	C₃₁×#489	C₂²	1	2	yes	complemented
66	C₃₁×#488	C₂²	1	2	yes	complemented
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#486	C₂²	1	2	yes	complemented
69	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#485	C₂²	1	2	yes	—
72	C₃₁×#484	C₂²	1	1	yes	characteristic
73	C₃₁×#482	C₂²	1	2	yes	—
74	C₃₁×#482	C₂²	1	2	yes	—
75	C₃₁×#482	C₂²	1	2	yes	—
76	C₃₁×#481	C₂²	1	1	yes	characteristic
77	C₃₁×#480	C₂²	1	2	yes	—
78	C₃₁×#479	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	1	yes	characteristic
80	C₃₁×#478	C₂²	1	1	yes	characteristic
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	2	yes	complemented
84	C₃₁×#478	C₂²	1	2	yes	complemented
85	C₃₁×#478	C₂²	1	2	yes	complemented
86	C₃₁×#478	C₂²	1	2	yes	complemented
87	C₃₁×#478	C₂²	1	2	yes	complemented
88	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#477	C₂²	1	2	yes	complemented
90	C₃₁×#476	C₂²	1	2	yes	—
91	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#476	C₂²	1	2	yes	complemented
93	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#474	C₂²	1	1	yes	characteristic
95	C₃₁×#474	C₂²	1	1	yes	characteristic
96	C₃₁×#474	C₂²	1	2	yes	—
97	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#474	C₂²	1	2	yes	complemented
99	C₃₁×#474	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic
102	C₃₁×#463	C₂²	1	2	yes	—
103	C₃₁×#463	C₂²	1	2	yes	—
104	C₃₁×#459	C₂²	1	1	yes	characteristic
105	C₃₁×#459	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	2	yes	—
107	C₃₁×#459	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	1	yes	characteristic
109	C₃₁×#447	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#446	C₂²	1	2	yes	complemented
113	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
114	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
117	C₃₁×#442	C₂²	1	2	yes	—
118	C₃₁×#442	C₂²	1	2	yes	—
119	C₃₁×#442	C₂²	1	2	yes	—
120	C₃₁×#440	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
124	C₄×D₈×C₃₁	C₂²	1	2	yes	—
125	C₄×D₈×C₃₁	C₂²	1	2	yes	—
126	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
127	C₄×D₈×C₃₁	C₂²	1	2	yes	—
128	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₃₁	C₂²	1	2	yes	—
130	C₄×D₈×C₃₁	C₂²	1	2	yes	—
131	C₃₁×#433	C₂²	1	2	yes	—
132	C₃₁×#433	C₂²	1	2	yes	—
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₃₁	C₂³	1	2	yes	—
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₃₁×C₄⋊Q₈	—	2	1	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×#127	C₂³	1	1	yes	characteristic
159	C₃₁×#127	C₂³	1	2	yes	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	1	no	—
162	C₃₁×#125	—	2	2	no	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	D₄	1	2	yes	—
165	C₃₁×#125	C₂³	1	1	yes	characteristic
166	C₃₁×#125	C₂³	1	2	yes	—
167	C₃₁×#125	C₂³	1	2	yes	—
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	1	no	—
174	C₃₁×#124	C₂³	1	1	yes	characteristic
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	1	no	—
177	C₃₁×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	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	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	C₂³	1	2	yes	—
249	C₃₁×#117	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
260	C₃₁×#107	C₂³	1	2	yes	—
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#107	C₂³	1	2	yes	—
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	1	yes	characteristic
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#102	C₂³	1	1	yes	characteristic
287	C₃₁×#102	C₂³	1	2	yes	—
288	C₃₁×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₃₁	C₂³	1	2	yes	—
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	1	no	—
313	#41×C₃₁	—	8	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	2	no	—
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	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	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	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	8	2	no	—
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	SD₁₆×C₃₁	—	2	2	no	—
360	SD₁₆×C₃₁	—	2	2	no	—
361	D₈×C₃₁	—	2	4	no	—
362	D₈×C₃₁	—	2	2	no	—
363	D₈×C₃₁	—	2	4	no	—
364	D₈×C₃₁	—	2	2	no	—
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	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	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	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
437	C₄²×C₃₁	C₂⁴	1	2	yes	—
438	C₄²×C₃₁	C₂⁴	1	2	yes	—
439	#61863	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂³×C₃₁	—	2	4	no	—
441	C₂³×C₃₁	—	2	1	no	—
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	—	2	2	no	—
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	8	1	no	—
446	C₂³×C₃₁	—	8	1	no	—
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₃₁	—	2	2	no	—
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	4	2	no	—
453	Q₈×C₃₁	—	4	2	no	—
454	Q₈×C₃₁	—	4	2	no	—
455	Q₈×C₃₁	—	8	1	no	—
456	Q₈×C₃₁	—	8	2	no	—
457	Q₈×C₃₁	—	8	2	no	—
458	Q₈×C₃₁	—	8	2	no	—
459	D₄×C₃₁	—	2	4	no	—
460	D₄×C₃₁	—	2	1	no	—
461	D₄×C₃₁	—	2	1	no	—
462	D₄×C₃₁	—	2	1	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	4	2	no	—
467	D₄×C₃₁	—	8	1	no	—
468	D₄×C₃₁	—	8	2	no	—
469	D₄×C₃₁	—	8	2	no	—
470	D₄×C₃₁	—	8	1	no	—
471	D₄×C₃₁	—	8	2	no	—
472	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
473	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	4	1	no	—
486	C₂×C₄×C₃₁	—	4	2	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	4	2	no	—
489	C₂×C₄×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	—	8	2	no	—
491	C₂×C₄×C₃₁	—	8	2	no	—
492	C₂×C₄×C₃₁	—	8	1	no	—
493	C₂×C₄×C₃₁	—	8	1	no	—
494	C₂×C₄×C₃₁	—	8	2	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	1	no	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
510	C₈×C₃₁	—	2	2	no	—
511	C₈×C₃₁	—	2	1	no	—
512	C₈×C₃₁	—	2	2	no	—
513	C₈×C₃₁	—	2	1	no	—
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	1	no	—
516	#3554	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3389	C₂×C₃₁	1	2	yes	complemented
519	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3380	C₂×C₃₁	1	2	yes	complemented
523	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3370	C₂×C₃₁	1	2	yes	complemented
526	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3361	C₂×C₃₁	1	2	yes	complemented
529	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3243	C₂×C₃₁	1	2	yes	complemented
531	#3241	C₂×C₃₁	1	2	yes	complemented
532	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3122	C₂×C₃₁	1	2	yes	complemented
535	#3118	C₂×C₃₁	1	2	yes	complemented
536	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	2	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	8	4	no	—
555	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	2	no	—
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	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	#576	1	2	yes	—
573	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
574	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
575	#562	—	2	2	no	—
576	#559	C₂²×C₃₁	1	2	yes	complemented
577	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
579	#554	—	2	1	no	—
580	#554	—	2	2	no	—
581	#554	C₂²×C₃₁	1	1	yes	characteristic
582	#554	C₂²×C₃₁	1	2	yes	—
583	#554	C₂²×C₃₁	1	1	yes	characteristic
584	#554	C₂²×C₃₁	1	2	yes	—
585	#554	C₂²×C₃₁	1	2	yes	complemented
586	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	D₄×Q₈	—	2	1	no	—
588	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
589	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
590	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	#548	—	2	1	no	—
592	#547	—	2	1	no	—
593	#544	C₂²×C₃₁	1	2	yes	—
594	#543	—	2	2	no	—
595	#542	—	2	1	no	—
596	#542	C₂²×C₃₁	1	2	yes	—
597	#540	C₂²×C₃₁	1	2	yes	—
598	#539	—	2	2	no	—
599	#536	—	2	1	no	—
600	#533	C₂²×C₃₁	1	1	yes	characteristic
601	#533	C₂²×C₃₁	1	1	yes	characteristic
602	#532	C₂²×C₃₁	1	1	yes	characteristic
603	#529	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×C₂²⋊Q₈	—	2	1	no	—
605	C₂×C₂²⋊Q₈	—	2	1	no	—
606	#518	C₂²×C₃₁	1	2	yes	—
607	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
608	#501	C₂²×C₃₁	1	2	yes	complemented
609	#501	C₂²×C₃₁	1	2	yes	complemented
610	#500	C₂²×C₃₁	1	2	yes	complemented
611	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#499	C₂²×C₃₁	1	2	yes	complemented
613	#499	C₂²×C₃₁	1	2	yes	complemented
614	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#490	C₂²×C₃₁	1	2	yes	complemented
616	#489	C₂²×C₃₁	1	2	yes	complemented
617	#488	C₂²×C₃₁	1	2	yes	complemented
618	#488	C₂²×C₃₁	1	2	yes	complemented
619	#486	C₂²×C₃₁	1	2	yes	complemented
620	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#485	C₂²×C₃₁	1	2	yes	—
623	#484	C₂²×C₃₁	1	1	yes	characteristic
624	#482	C₂²×C₃₁	1	2	yes	—
625	#482	C₂²×C₃₁	1	2	yes	—
626	#482	C₂²×C₃₁	1	2	yes	—
627	#481	C₂²×C₃₁	1	1	yes	characteristic
628	#480	C₂²×C₃₁	1	2	yes	—
629	#479	C₂²×C₃₁	1	2	yes	complemented
630	#478	C₂²×C₃₁	1	1	yes	characteristic
631	#478	C₂²×C₃₁	1	1	yes	characteristic
632	#478	C₂²×C₃₁	1	2	yes	—
633	#478	C₂²×C₃₁	1	2	yes	—
634	#478	C₂²×C₃₁	1	2	yes	complemented
635	#478	C₂²×C₃₁	1	2	yes	complemented
636	#478	C₂²×C₃₁	1	2	yes	complemented
637	#478	C₂²×C₃₁	1	2	yes	complemented
638	#478	C₂²×C₃₁	1	2	yes	complemented
639	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#477	C₂²×C₃₁	1	2	yes	complemented
641	#476	C₂²×C₃₁	1	2	yes	—
642	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#476	C₂²×C₃₁	1	2	yes	complemented
644	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#474	C₂²×C₃₁	1	1	yes	characteristic
646	#474	C₂²×C₃₁	1	1	yes	characteristic
647	#474	C₂²×C₃₁	1	2	yes	—
648	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#474	C₂²×C₃₁	1	2	yes	complemented
650	#474	C₂²×C₃₁	1	2	yes	complemented
651	#463	C₂²×C₃₁	1	1	yes	characteristic
652	#463	C₂²×C₃₁	1	1	yes	characteristic
653	#463	C₂²×C₃₁	1	2	yes	—
654	#463	C₂²×C₃₁	1	2	yes	—
655	#459	C₂²×C₃₁	1	1	yes	characteristic
656	#459	C₂²×C₃₁	1	1	yes	characteristic
657	#459	C₂²×C₃₁	1	2	yes	—
658	#459	C₂²×C₃₁	1	2	yes	—
659	#450	C₂²×C₃₁	1	1	yes	characteristic
660	#447	C₂²×C₃₁	1	2	yes	—
661	#447	C₂²×C₃₁	1	1	yes	characteristic
662	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#446	C₂²×C₃₁	1	2	yes	complemented
664	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
668	#442	C₂²×C₃₁	1	2	yes	—
669	#442	C₂²×C₃₁	1	2	yes	—
670	#442	C₂²×C₃₁	1	2	yes	—
671	#440	C₂²×C₃₁	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
675	C₄×D₈	C₂²×C₃₁	1	2	yes	—
676	C₄×D₈	C₂²×C₃₁	1	2	yes	—
677	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×D₈	C₂²×C₃₁	1	2	yes	—
679	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₃₁	1	2	yes	—
681	C₄×D₈	C₂²×C₃₁	1	2	yes	—
682	#433	C₂²×C₃₁	1	2	yes	—
683	#433	C₂²×C₃₁	1	2	yes	—
684	#431	C₂²×C₃₁	1	1	yes	characteristic
685	#431	C₂²×C₃₁	1	1	yes	characteristic
686	C₂×C₃₁	—	4	1	no	—
687	C₂×C₃₁	—	4	2	no	—
688	C₂×C₃₁	—	4	2	no	—
689	C₂×C₃₁	—	8	2	no	—
690	C₂×C₃₁	—	8	1	no	—
691	C₂×C₃₁	#3486	1	1	yes	characteristic
692	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
693	C₂×C₃₁	#3584	1	1	yes	characteristic
694	C₂×#41	—	2	1	no	—
695	C₂×#41	—	2	1	no	—
696	C₂²×Q₈	—	2	1	no	—
697	C₂²×Q₈	—	2	1	no	—
698	C₂²×Q₈	—	2	1	no	—
699	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₂³×C₄	—	2	1	no	—
701	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×D₈	C₂³×C₃₁	1	2	yes	—
704	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×D₈	C₂³×C₃₁	1	2	yes	—
706	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
710	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
715	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
716	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
717	#127	C₂³×C₃₁	1	1	yes	characteristic
718	#127	C₂³×C₃₁	1	2	yes	—
719	#126	—	2	2	no	—
720	#126	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	D₄×C₃₁	1	2	yes	—
724	#125	C₂³×C₃₁	1	1	yes	characteristic
725	#125	C₂³×C₃₁	1	2	yes	—
726	#125	C₂³×C₃₁	1	2	yes	—
727	#125	C₂³×C₃₁	1	2	yes	—
728	#125	C₂³×C₃₁	1	2	yes	—
729	#124	—	2	1	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	1	no	—
733	#124	C₂³×C₃₁	1	1	yes	characteristic
734	#124	C₂³×C₃₁	1	2	yes	—
735	#123	—	2	1	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
767	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
768	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	C₂³×C₃₁	1	1	yes	characteristic
776	#121	C₂³×C₃₁	1	2	yes	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₃₁	1	2	yes	—
798	C₄×D₄	C₂³×C₃₁	1	2	yes	—
799	C₄×D₄	C₂³×C₃₁	1	2	yes	—
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	2	yes	—
806	#117	—	2	1	no	—
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	2	no	—
810	C₂×C₄⋊C₄	—	2	2	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	2	no	—
814	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	—	2	1	no	—
816	C₂×C₂²⋊C₄	—	2	2	no	—
817	C₂×C₂²⋊C₄	—	2	2	no	—
818	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
819	#107	C₂³×C₃₁	1	2	yes	—
820	#107	C₂³×C₃₁	1	2	yes	—
821	#107	C₂³×C₃₁	1	2	yes	—
822	#107	C₂³×C₃₁	1	1	yes	characteristic
823	#107	C₂³×C₃₁	1	2	yes	—
824	#107	C₂³×C₃₁	1	2	yes	—
825	#107	C₂³×C₃₁	1	1	yes	characteristic
826	#107	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	2	yes	—
828	#106	C₂³×C₃₁	1	1	yes	characteristic
829	#106	C₂³×C₃₁	1	1	yes	characteristic
830	#106	C₂³×C₃₁	1	2	yes	—
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	2	yes	—
833	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	1	yes	characteristic
844	#103	C₂³×C₃₁	1	2	yes	—
845	#102	C₂³×C₃₁	1	1	yes	characteristic
846	#102	C₂³×C₃₁	1	2	yes	—
847	#102	C₂³×C₃₁	1	1	yes	characteristic
848	#102	C₂³×C₃₁	1	2	yes	—
849	#102	C₂³×C₃₁	1	1	yes	characteristic
850	#102	C₂³×C₃₁	1	2	yes	—
851	#102	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	1	yes	characteristic
857	#102	C₂³×C₃₁	1	1	yes	characteristic
858	#102	C₂³×C₃₁	1	2	yes	—
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
864	#97	C₂³×C₃₁	1	2	yes	—
865	#97	C₂³×C₃₁	1	2	yes	—
866	C₄×C₈	C₂³×C₃₁	1	2	yes	—
867	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₃₁	1	2	yes	—
870	C₄×C₈	C₂³×C₃₁	1	2	yes	—
871	C₃₁	#61863	1	1	yes	characteristic, direct product factor, Sylow
872	C₂⁴	—	2	1	no	—
873	#41	—	8	2	no	—
874	#41	—	8	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	8	2	no	—
882	C₂×Q₈	—	8	2	no	—
883	C₂×Q₈	—	8	2	no	—
884	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
899	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
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	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	SD₁₆	—	2	2	no	—
920	SD₁₆	—	2	2	no	—
921	D₈	—	2	4	no	—
922	D₈	—	2	2	no	—
923	D₈	—	2	4	no	—
924	D₈	—	2	2	no	—
925	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
927	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
952	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄²	C₂⁴×C₃₁	1	2	yes	—
998	C₄²	C₂⁴×C₃₁	1	2	yes	—
999	C₂³	—	2	4	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	8	1	no	—
1005	C₂³	—	8	1	no	—
1006	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	1	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	4	2	no	—
1014	Q₈	—	8	1	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	—	8	2	no	—
1017	Q₈	—	8	2	no	—
1018	D₄	—	2	4	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	4	2	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	1	no	—
1030	D₄	—	8	2	no	—
1031	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1032	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	1	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1060	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1068	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1069	C₈	—	2	2	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	8	4	no	—
1091	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	C₃₁×#576	1	2	yes	—
1109	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1110	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1111	C₂	—	4	1	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	1	no	—
1115	C₂	—	8	2	no	—
1116	C₂	C₃₁×#3486	1	1	yes	characteristic
1117	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1118	C₂	C₃₁×#3584	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3554	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3384	C₂	semidirect
6. C₃₁×#3381	C₂	semidirect
7. C₃₁×#3380	C₂	semidirect
8. Q₈×D₈×C₃₁	C₂	semidirect
9. C₃₁×#3373	C₂	semidirect
10. C₃₁×#3370	C₂	semidirect
11. C₃₁×#3366	C₂	semidirect
12. C₃₁×#3361	C₂	semidirect
13. C₃₁×#3361	C₂	semidirect
14. C₃₁×#3358	C₂	semidirect
15. C₃₁×#3243	C₂	semidirect
16. C₃₁×#3241	C₂	semidirect
17. C₃₁×#3233	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3122	C₂	semidirect
20. C₃₁×#3118	C₂	semidirect
21. C₃₁×#3105	C₂	semidirect
22. C₃₁×#3100	C₂	semidirect
23. C₃₁×#2986	C₂	semidirect
25. C₃₁×#559	C₂²	semidirect
26. C₃₁×#559	C₂²	semidirect
27. C₃₁×#557	C₂²	semidirect
34. C₃₁×#554	C₂²	semidirect
35. C₃₁×#550	C₂²	semidirect
39. D₄×Q₈×C₃₁	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#501	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
61. C₃₁×#499	C₂²	semidirect
62. C₃₁×#499	C₂²	semidirect
63. C₃₁×#498	C₂²	semidirect
64. C₃₁×#490	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#488	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
68. C₃₁×#486	C₂²	semidirect
69. C₃₁×#486	C₂²	semidirect
70. C₃₁×#486	C₂²	semidirect
78. C₃₁×#479	C₂²	semidirect
83. C₃₁×#478	C₂²	semidirect
84. C₃₁×#478	C₂²	semidirect
85. C₃₁×#478	C₂²	semidirect
86. C₃₁×#478	C₂²	semidirect
87. C₃₁×#478	C₂²	semidirect
88. C₃₁×#477	C₂²	semidirect
89. C₃₁×#477	C₂²	semidirect
91. C₃₁×#476	C₂²	semidirect
92. C₃₁×#476	C₂²	semidirect
93. C₃₁×#475	C₂²	semidirect
97. C₃₁×#474	C₂²	semidirect
98. C₃₁×#474	C₂²	semidirect
99. C₃₁×#474	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₃₁×#446	C₂²	semidirect
113. C₃₁×#446	C₂²	semidirect
114. C₈×Q₈×C₃₁	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₈×Q₈×C₃₁	C₂²	semidirect
439. #61863	C₃₁	direct (N × H)
516. #3554	C₂×C₃₁	semidirect
517. #3501	C₂×C₃₁	semidirect
518. #3389	C₂×C₃₁	semidirect
519. #3386	C₂×C₃₁	semidirect
520. #3384	C₂×C₃₁	semidirect
521. #3381	C₂×C₃₁	semidirect
522. #3380	C₂×C₃₁	semidirect
523. Q₈×D₈	C₂×C₃₁	semidirect
524. #3373	C₂×C₃₁	semidirect
525. #3370	C₂×C₃₁	semidirect
526. #3366	C₂×C₃₁	semidirect
527. #3361	C₂×C₃₁	semidirect
528. #3361	C₂×C₃₁	semidirect
529. #3358	C₂×C₃₁	semidirect
530. #3243	C₂×C₃₁	semidirect
531. #3241	C₂×C₃₁	semidirect
532. #3233	C₂×C₃₁	semidirect
533. #3228	C₂×C₃₁	semidirect
534. #3122	C₂×C₃₁	semidirect
535. #3118	C₂×C₃₁	semidirect
536. #3105	C₂×C₃₁	semidirect
537. #3100	C₂×C₃₁	semidirect
538. #2986	C₂×C₃₁	semidirect
576. #559	C₂²×C₃₁	semidirect
577. #559	C₂²×C₃₁	semidirect
578. #557	C₂²×C₃₁	semidirect
585. #554	C₂²×C₃₁	semidirect
586. #550	C₂²×C₃₁	semidirect
590. D₄×Q₈	C₂²×C₃₁	semidirect
608. #501	C₂²×C₃₁	semidirect
609. #501	C₂²×C₃₁	semidirect
610. #500	C₂²×C₃₁	semidirect
611. #500	C₂²×C₃₁	semidirect
612. #499	C₂²×C₃₁	semidirect
613. #499	C₂²×C₃₁	semidirect
614. #498	C₂²×C₃₁	semidirect
615. #490	C₂²×C₃₁	semidirect
616. #489	C₂²×C₃₁	semidirect
617. #488	C₂²×C₃₁	semidirect
618. #488	C₂²×C₃₁	semidirect
619. #486	C₂²×C₃₁	semidirect
620. #486	C₂²×C₃₁	semidirect
621. #486	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
634. #478	C₂²×C₃₁	semidirect
635. #478	C₂²×C₃₁	semidirect
636. #478	C₂²×C₃₁	semidirect
637. #478	C₂²×C₃₁	semidirect
638. #478	C₂²×C₃₁	semidirect
639. #477	C₂²×C₃₁	semidirect
640. #477	C₂²×C₃₁	semidirect
642. #476	C₂²×C₃₁	semidirect
643. #476	C₂²×C₃₁	semidirect
644. #475	C₂²×C₃₁	semidirect
648. #474	C₂²×C₃₁	semidirect
649. #474	C₂²×C₃₁	semidirect
650. #474	C₂²×C₃₁	semidirect
662. #446	C₂²×C₃₁	semidirect
663. #446	C₂²×C₃₁	semidirect
664. #446	C₂²×C₃₁	semidirect
665. C₈×Q₈	C₂²×C₃₁	semidirect
666. C₈×Q₈	C₂²×C₃₁	semidirect
667. C₈×Q₈	C₂²×C₃₁	semidirect
871. C₃₁	#61863	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×#3554	2
C₃₁×#3501	2
C₃₁×#3389	2
C₃₁×#3386	2
C₃₁×#3384	2
C₃₁×#3381	2
C₃₁×#3380	2
Q₈×D₈×C₃₁	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3361	2
C₃₁×#3358	2
C₃₁×#3243	2
C₃₁×#3241	2
C₃₁×#3233	2
C₃₁×#3228	2
C₃₁×#3122	2
C₃₁×#3118	2
C₃₁×#3105	2
C₃₁×#3100	2
C₃₁×#2986	2
#61863	31

Subgroups — C31×#61863 #21518622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61863 #21518622