Subgroups — C₃₁×#61343 #21518102

Order 7936.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1130 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×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3041	C₂	1	1	yes	maximal, characteristic
19	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2949	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#559	C₂²	1	2	yes	complemented
28	C₃₁×#559	C₂²	1	2	yes	complemented
29	C₃₁×#556	C₂²	1	2	yes	complemented
30	C₃₁×#556	C₂²	1	2	yes	complemented
31	C₃₁×#554	—	2	1	no	—
32	C₃₁×#554	—	2	1	no	—
33	C₃₁×#554	—	2	1	no	—
34	C₃₁×#554	C₂²	1	2	yes	complemented
35	C₃₁×#554	C₂²	1	2	yes	complemented
36	C₃₁×#554	C₂²	1	2	yes	complemented
37	C₃₁×#551	—	2	2	no	—
38	C₃₁×#551	—	2	2	no	—
39	D₄×Q₈×C₃₁	—	2	1	no	—
40	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
41	C₃₁×#544	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#543	—	2	2	no	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#536	C₂²	1	1	yes	characteristic
47	C₃₁×#535	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	—	2	1	no	—
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
54	C₃₁×#519	C₂²	1	1	yes	characteristic
55	C₃₁×#518	C₂²	1	1	yes	characteristic
56	C₃₁×#518	C₂²	1	1	yes	characteristic
57	C₃₁×#518	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#491	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#489	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	2	yes	complemented
64	C₃₁×#489	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×#488	C₂²	1	2	yes	complemented
69	C₃₁×#488	C₂²	1	2	yes	complemented
70	C₃₁×#487	C₂²	1	2	yes	complemented
71	C₃₁×#486	C₂²	1	2	yes	complemented
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#477	C₂²	1	2	yes	complemented
82	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#476	C₂²	1	2	yes	complemented
84	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#475	C₂²	1	2	yes	complemented
86	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#474	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#463	C₂²	1	2	yes	—
94	C₃₁×#463	C₂²	1	2	yes	complemented
95	C₃₁×#463	C₂²	1	2	yes	complemented
96	C₃₁×#461	C₂²	1	2	yes	complemented
97	C₃₁×#461	C₂²	1	2	yes	complemented
98	C₃₁×#459	C₂²	1	2	yes	—
99	C₃₁×#459	C₂²	1	2	yes	—
100	C₃₁×#446	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#446	C₂²	1	2	yes	complemented
103	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#442	C₂²	1	2	yes	—
106	C₃₁×#442	C₂²	1	2	yes	complemented
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₃₁×#440	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
113	C₄×D₈×C₃₁	C₂²	1	2	yes	—
114	C₄×D₈×C₃₁	C₂²	1	2	yes	—
115	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
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	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	C₃₁×#419	C₂²	1	1	yes	characteristic
123	C₃₁×#419	C₂²	1	1	yes	characteristic
124	C₃₁×#418	C₂²	1	1	yes	characteristic
125	C₃₁×#418	C₂²	1	1	yes	characteristic
126	C₃₁×#418	C₂²	1	1	yes	characteristic
127	C₃₁×#417	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
132	C₃₁×#405	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₃₁	—	2	2	no	—
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	—	2	1	no	—
141	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
142	C₂×SD₁₆×C₃₁	—	2	4	no	—
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	—	2	4	no	—
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	2	yes	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#125	—	2	1	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	D₄	1	1	yes	characteristic
171	C₃₁×#125	D₄	1	1	yes	characteristic
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#125	C₂³	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	1	yes	characteristic
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	1	yes	characteristic
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	1	no	—
266	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	—	2	1	no	—
316	C₂⁴×C₃₁	—	2	1	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	8	4	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	#41	1	4	yes	—
340	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
341	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	8	2	no	—
357	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
360	SD₁₆×C₃₁	—	2	4	no	—
361	SD₁₆×C₃₁	—	2	4	no	—
362	SD₁₆×C₃₁	—	2	4	no	—
363	D₈×C₃₁	—	2	4	no	—
364	D₈×C₃₁	—	2	4	no	—
365	D₈×C₃₁	—	2	4	no	—
366	M₁₆×C₃₁	—	2	2	no	—
367	M₁₆×C₃₁	—	2	2	no	—
368	C₂×C₈×C₃₁	—	2	2	no	—
369	C₂×C₈×C₃₁	—	2	2	no	—
370	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	1	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	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	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
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	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	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	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	C₄²×C₃₁	C₂⁴	1	2	yes	—
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	#61343	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₃₁	—	2	2	no	—
450	C₂³×C₃₁	—	2	4	no	—
451	C₂³×C₃₁	—	2	2	no	—
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	4	2	no	—
454	C₂³×C₃₁	—	8	1	no	—
455	C₂³×C₃₁	—	8	1	no	—
456	C₂³×C₃₁	—	8	1	no	—
457	C₂³×C₃₁	—	8	1	no	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	Q₈×C₃₁	—	4	2	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	8	1	no	—
468	Q₈×C₃₁	—	8	2	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	D₄×C₃₁	—	2	4	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	4	2	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	C₂×#41	1	4	yes	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	4	1	no	—
491	C₂×C₄×C₃₁	—	4	1	no	—
492	C₂×C₄×C₃₁	—	4	4	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	8	1	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	—	8	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	8	1	no	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	C₂×#41	1	2	yes	—
515	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
516	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
517	C₈×C₃₁	—	2	1	no	—
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	2	no	—
523	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3376	C₂×C₃₁	1	2	yes	complemented
526	#3376	C₂×C₃₁	1	2	yes	complemented
527	#3373	C₂×C₃₁	1	2	yes	complemented
528	#3370	C₂×C₃₁	1	2	yes	complemented
529	#3370	C₂×C₃₁	1	2	yes	complemented
530	#3367	C₂×C₃₁	1	2	yes	complemented
531	#3361	C₂×C₃₁	1	2	yes	complemented
532	#3360	C₂×C₃₁	1	2	yes	complemented
533	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3042	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3041	C₂×C₃₁	1	1	yes	characteristic
541	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#2962	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2949	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
545	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	1	no	—
548	C₂²×C₃₁	—	2	4	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	2	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	8	4	no	—
558	C₂²×C₃₁	—	16	2	no	—
559	C₂²×C₃₁	#548	1	2	yes	—
560	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	2	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	#548	1	2	yes	—
579	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
580	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
581	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
582	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
583	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
584	#559	C₂²×C₃₁	1	2	yes	complemented
585	#559	C₂²×C₃₁	1	2	yes	complemented
586	#556	C₂²×C₃₁	1	2	yes	complemented
587	#556	C₂²×C₃₁	1	2	yes	complemented
588	#554	—	2	1	no	—
589	#554	—	2	1	no	—
590	#554	—	2	1	no	—
591	#554	C₂²×C₃₁	1	2	yes	complemented
592	#554	C₂²×C₃₁	1	2	yes	complemented
593	#554	C₂²×C₃₁	1	2	yes	complemented
594	#551	—	2	2	no	—
595	#551	—	2	2	no	—
596	D₄×Q₈	—	2	1	no	—
597	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
598	#544	C₂²×C₃₁	1	1	yes	characteristic
599	#544	C₂²×C₃₁	1	1	yes	characteristic
600	#543	—	2	2	no	—
601	#542	—	2	1	no	—
602	#542	—	2	1	no	—
603	#536	C₂²×C₃₁	1	1	yes	characteristic
604	#535	C₂²×C₃₁	1	1	yes	characteristic
605	#533	C₂²×C₃₁	1	1	yes	characteristic
606	#533	C₂²×C₃₁	1	1	yes	characteristic
607	#529	—	2	1	no	—
608	#529	—	2	1	no	—
609	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
610	C₂×C₂²⋊Q₈	—	2	2	no	—
611	#519	C₂²×C₃₁	1	1	yes	characteristic
612	#518	C₂²×C₃₁	1	1	yes	characteristic
613	#518	C₂²×C₃₁	1	1	yes	characteristic
614	#518	C₂²×C₃₁	1	1	yes	characteristic
615	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
617	#491	C₂²×C₃₁	1	2	yes	complemented
618	#490	C₂²×C₃₁	1	2	yes	complemented
619	#489	C₂²×C₃₁	1	2	yes	complemented
620	#489	C₂²×C₃₁	1	2	yes	complemented
621	#489	C₂²×C₃₁	1	2	yes	complemented
622	#489	C₂²×C₃₁	1	2	yes	complemented
623	#488	C₂²×C₃₁	1	2	yes	complemented
624	#488	C₂²×C₃₁	1	2	yes	complemented
625	#488	C₂²×C₃₁	1	2	yes	complemented
626	#488	C₂²×C₃₁	1	2	yes	complemented
627	#487	C₂²×C₃₁	1	2	yes	complemented
628	#486	C₂²×C₃₁	1	2	yes	complemented
629	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	#479	C₂²×C₃₁	1	2	yes	complemented
632	#479	C₂²×C₃₁	1	2	yes	complemented
633	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#478	C₂²×C₃₁	1	2	yes	complemented
636	#478	C₂²×C₃₁	1	2	yes	complemented
637	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#477	C₂²×C₃₁	1	2	yes	complemented
639	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#476	C₂²×C₃₁	1	2	yes	complemented
641	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#475	C₂²×C₃₁	1	2	yes	complemented
643	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#474	C₂²×C₃₁	1	2	yes	complemented
645	#463	C₂²×C₃₁	1	2	yes	—
646	#463	C₂²×C₃₁	1	2	yes	—
647	#463	C₂²×C₃₁	1	2	yes	—
648	#463	C₂²×C₃₁	1	2	yes	—
649	#463	C₂²×C₃₁	1	2	yes	—
650	#463	C₂²×C₃₁	1	2	yes	—
651	#463	C₂²×C₃₁	1	2	yes	complemented
652	#463	C₂²×C₃₁	1	2	yes	complemented
653	#461	C₂²×C₃₁	1	2	yes	complemented
654	#461	C₂²×C₃₁	1	2	yes	complemented
655	#459	C₂²×C₃₁	1	2	yes	—
656	#459	C₂²×C₃₁	1	2	yes	—
657	#446	C₂²×C₃₁	1	2	yes	complemented
658	#446	C₂²×C₃₁	1	2	yes	complemented
659	#446	C₂²×C₃₁	1	2	yes	complemented
660	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
661	#442	C₂²×C₃₁	1	2	yes	—
662	#442	C₂²×C₃₁	1	2	yes	—
663	#442	C₂²×C₃₁	1	2	yes	complemented
664	#440	C₂²×C₃₁	1	2	yes	complemented
665	#440	C₂²×C₃₁	1	2	yes	complemented
666	#440	C₂²×C₃₁	1	2	yes	complemented
667	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
668	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
669	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
670	C₄×D₈	C₂²×C₃₁	1	2	yes	—
671	C₄×D₈	C₂²×C₃₁	1	2	yes	—
672	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
673	#428	C₂²×C₃₁	1	1	yes	characteristic
674	#427	C₂²×C₃₁	1	1	yes	characteristic
675	#427	C₂²×C₃₁	1	1	yes	characteristic
676	#424	C₂²×C₃₁	1	1	yes	characteristic
677	#424	C₂²×C₃₁	1	1	yes	characteristic
678	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
679	#419	C₂²×C₃₁	1	1	yes	characteristic
680	#419	C₂²×C₃₁	1	1	yes	characteristic
681	#418	C₂²×C₃₁	1	1	yes	characteristic
682	#418	C₂²×C₃₁	1	1	yes	characteristic
683	#418	C₂²×C₃₁	1	1	yes	characteristic
684	#417	C₂²×C₃₁	1	1	yes	characteristic
685	#416	C₂²×C₃₁	1	1	yes	characteristic
686	#416	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
688	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
689	#405	C₂²×C₃₁	1	1	yes	characteristic
690	#405	C₂²×C₃₁	1	1	yes	characteristic
691	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
692	C₂×C₃₁	—	2	2	no	—
693	C₂×C₃₁	—	4	4	no	—
694	C₂×C₃₁	—	8	1	no	—
695	C₂×C₃₁	—	8	2	no	—
696	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
697	C₂×C₃₁	#3584	1	1	yes	characteristic
698	C₂×C₃₁	#3585	1	1	yes	characteristic
699	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
700	C₂²×Q₈	—	2	2	no	—
701	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
703	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	AGL(1,ℤ/8)	—	2	4	no	—
706	C₂×SD₁₆	—	2	4	no	—
707	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×D₈	—	2	4	no	—
711	C₂×D₈	C₂³×C₃₁	1	2	yes	—
712	C₂×D₈	C₂³×C₃₁	1	2	yes	—
713	C₂×D₈	C₂³×C₃₁	1	2	yes	—
714	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
716	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
726	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
727	#127	C₂³×C₃₁	1	2	yes	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	—	2	1	no	—
734	#125	D₄×C₃₁	1	1	yes	characteristic
735	#125	D₄×C₃₁	1	1	yes	characteristic
736	#125	C₂³×C₃₁	1	1	yes	characteristic
737	#125	C₂³×C₃₁	1	1	yes	characteristic
738	#125	C₂³×C₃₁	1	2	yes	—
739	#125	C₂³×C₃₁	1	2	yes	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	1	no	—
743	#124	—	2	1	no	—
744	#124	C₂³×C₃₁	1	2	yes	—
745	#124	C₂³×C₃₁	1	2	yes	—
746	#124	C₂³×C₃₁	1	2	yes	—
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	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	2	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
774	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#120	—	2	2	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
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×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×D₄	—	2	1	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	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	2	yes	—
806	C₄×D₄	C₂³×C₃₁	1	2	yes	—
807	C₄×D₄	C₂³×C₃₁	1	2	yes	—
808	C₄×D₄	C₂³×C₃₁	1	2	yes	—
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	C₂³×C₃₁	1	1	yes	characteristic
815	#117	C₂³×C₃₁	1	1	yes	characteristic
816	#117	C₂³×C₃₁	1	1	yes	characteristic
817	#117	C₂³×C₃₁	1	1	yes	characteristic
818	#117	C₂³×C₃₁	1	1	yes	characteristic
819	C₂×C₄⋊C₄	—	2	2	no	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₄²	—	2	1	no	—
830	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
831	#107	C₂³×C₃₁	1	1	yes	characteristic
832	#107	C₂³×C₃₁	1	1	yes	characteristic
833	#107	C₂³×C₃₁	1	1	yes	characteristic
834	#107	C₂³×C₃₁	1	1	yes	characteristic
835	#107	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	1	yes	characteristic
838	#106	C₂³×C₃₁	1	1	yes	characteristic
839	#106	C₂³×C₃₁	1	1	yes	characteristic
840	#106	C₂³×C₃₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	C₂³×C₃₁	1	1	yes	characteristic
854	#103	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	1	yes	characteristic
865	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
873	#97	C₂³×C₃₁	1	2	yes	—
874	#97	C₂³×C₃₁	1	2	yes	—
875	#97	C₂³×C₃₁	1	2	yes	—
876	C₄×C₈	C₂³×C₃₁	1	2	yes	—
877	C₄×C₈	C₂³×C₃₁	1	2	yes	—
878	C₄×C₈	C₂³×C₃₁	1	2	yes	—
879	C₃₁	#61343	1	1	yes	characteristic, direct product factor, Sylow
880	C₂⁴	—	2	1	no	—
881	C₂⁴	—	2	1	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	8	4	no	—
892	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
893	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	1	no	—
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	2	no	—
904	C₂×D₄	#41×C₃₁	1	4	yes	—
905	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
906	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	8	2	no	—
922	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
925	SD₁₆	—	2	4	no	—
926	SD₁₆	—	2	4	no	—
927	SD₁₆	—	2	4	no	—
928	D₈	—	2	4	no	—
929	D₈	—	2	4	no	—
930	D₈	—	2	4	no	—
931	M₁₆	—	2	2	no	—
932	M₁₆	—	2	2	no	—
933	C₂×C₈	—	2	2	no	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
936	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
939	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	2	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	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1008	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₃₁	1	2	yes	—
1011	C₄²	C₂⁴×C₃₁	1	2	yes	—
1012	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	4	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	4	2	no	—
1018	C₂³	—	8	1	no	—
1019	C₂³	—	8	1	no	—
1020	C₂³	—	8	1	no	—
1021	C₂³	—	8	1	no	—
1022	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	4	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	1	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	2	no	—
1034	D₄	—	2	4	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	C₂×#41×C₃₁	1	4	yes	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	1	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	1	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1078	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1079	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1080	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	8	4	no	—
1099	C₂²	—	16	2	no	—
1100	C₂²	C₃₁×#548	1	2	yes	—
1101	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	C₃₁×#548	1	2	yes	—
1120	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1121	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1122	C₂	—	2	2	no	—
1123	C₂	—	4	4	no	—
1124	C₂	—	8	2	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
1127	C₂	C₃₁×#3584	1	1	yes	characteristic
1128	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3041	C₂
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×#3510	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3370	C₂	semidirect
8. C₃₁×#3367	C₂	semidirect
9. C₃₁×#3361	C₂	semidirect
10. C₃₁×#3360	C₂	semidirect
11. C₃₁×#3140	C₂	semidirect
12. C₃₁×#3137	C₂	semidirect
13. C₃₁×#3136	C₂	semidirect
14. C₃₁×#3082	C₂	semidirect
15. C₃₁×#3081	C₂	semidirect
16. C₃₁×#3076	C₂	semidirect
17. C₃₁×#3042	C₂	semidirect
19. C₂×C₃₁×#463	C₂	semidirect
20. C₃₁×#2962	C₂	semidirect
21. C₃₁×#2949	C₂	semidirect
22. C₃₁×#2948	C₂	semidirect
23. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
30. C₃₁×#556	C₂²	semidirect
34. C₃₁×#554	C₂²	semidirect
35. C₃₁×#554	C₂²	semidirect
36. C₃₁×#554	C₂²	semidirect
40. D₄×Q₈×C₃₁	C₂²	semidirect
60. C₃₁×#491	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
63. C₃₁×#489	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#488	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
68. C₃₁×#488	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
70. C₃₁×#487	C₂²	semidirect
71. C₃₁×#486	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
82. C₃₁×#476	C₂²	semidirect
83. C₃₁×#476	C₂²	semidirect
84. C₃₁×#475	C₂²	semidirect
85. C₃₁×#475	C₂²	semidirect
86. C₃₁×#474	C₂²	semidirect
87. C₃₁×#474	C₂²	semidirect
94. C₃₁×#463	C₂²	semidirect
95. C₃₁×#463	C₂²	semidirect
96. C₃₁×#461	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
100. C₃₁×#446	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
103. C₈×Q₈×C₃₁	C₂²	semidirect
106. C₃₁×#442	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₃₁×#440	C₂²	semidirect
110. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
112. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×D₈×C₃₁	C₂²	semidirect
448. #61343	C₃₁	direct (N × H)
523. #3510	C₂×C₃₁	semidirect
524. #3501	C₂×C₃₁	semidirect
525. #3376	C₂×C₃₁	semidirect
526. #3376	C₂×C₃₁	semidirect
527. #3373	C₂×C₃₁	semidirect
528. #3370	C₂×C₃₁	semidirect
529. #3370	C₂×C₃₁	semidirect
530. #3367	C₂×C₃₁	semidirect
531. #3361	C₂×C₃₁	semidirect
532. #3360	C₂×C₃₁	semidirect
533. #3140	C₂×C₃₁	semidirect
534. #3137	C₂×C₃₁	semidirect
535. #3136	C₂×C₃₁	semidirect
536. #3082	C₂×C₃₁	semidirect
537. #3081	C₂×C₃₁	semidirect
538. #3076	C₂×C₃₁	semidirect
539. #3042	C₂×C₃₁	semidirect
541. C₂×#463	C₂×C₃₁	semidirect
542. #2962	C₂×C₃₁	semidirect
543. #2949	C₂×C₃₁	semidirect
544. #2948	C₂×C₃₁	semidirect
545. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
584. #559	C₂²×C₃₁	semidirect
585. #559	C₂²×C₃₁	semidirect
586. #556	C₂²×C₃₁	semidirect
587. #556	C₂²×C₃₁	semidirect
591. #554	C₂²×C₃₁	semidirect
592. #554	C₂²×C₃₁	semidirect
593. #554	C₂²×C₃₁	semidirect
597. D₄×Q₈	C₂²×C₃₁	semidirect
617. #491	C₂²×C₃₁	semidirect
618. #490	C₂²×C₃₁	semidirect
619. #489	C₂²×C₃₁	semidirect
620. #489	C₂²×C₃₁	semidirect
621. #489	C₂²×C₃₁	semidirect
622. #489	C₂²×C₃₁	semidirect
623. #488	C₂²×C₃₁	semidirect
624. #488	C₂²×C₃₁	semidirect
625. #488	C₂²×C₃₁	semidirect
626. #488	C₂²×C₃₁	semidirect
627. #487	C₂²×C₃₁	semidirect
628. #486	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
631. #479	C₂²×C₃₁	semidirect
632. #479	C₂²×C₃₁	semidirect
633. #478	C₂²×C₃₁	semidirect
634. #478	C₂²×C₃₁	semidirect
635. #478	C₂²×C₃₁	semidirect
636. #478	C₂²×C₃₁	semidirect
637. #477	C₂²×C₃₁	semidirect
638. #477	C₂²×C₃₁	semidirect
639. #476	C₂²×C₃₁	semidirect
640. #476	C₂²×C₃₁	semidirect
641. #475	C₂²×C₃₁	semidirect
642. #475	C₂²×C₃₁	semidirect
643. #474	C₂²×C₃₁	semidirect
644. #474	C₂²×C₃₁	semidirect
651. #463	C₂²×C₃₁	semidirect
652. #463	C₂²×C₃₁	semidirect
653. #461	C₂²×C₃₁	semidirect
654. #461	C₂²×C₃₁	semidirect
657. #446	C₂²×C₃₁	semidirect
658. #446	C₂²×C₃₁	semidirect
659. #446	C₂²×C₃₁	semidirect
660. C₈×Q₈	C₂²×C₃₁	semidirect
663. #442	C₂²×C₃₁	semidirect
664. #440	C₂²×C₃₁	semidirect
665. #440	C₂²×C₃₁	semidirect
666. #440	C₂²×C₃₁	semidirect
667. C₄×SD₁₆	C₂²×C₃₁	semidirect
668. C₄×SD₁₆	C₂²×C₃₁	semidirect
669. C₄×SD₁₆	C₂²×C₃₁	semidirect
672. C₄×D₈	C₂²×C₃₁	semidirect
879. C₃₁	#61343	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×#3501	2
C₃₁×#3376	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3367	2
C₃₁×#3361	2
C₃₁×#3360	2
C₃₁×#3140	2
C₃₁×#3137	2
C₃₁×#3136	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3076	2
C₃₁×#3042	2
C₃₁×#3041	2
C₂×C₃₁×#463	2
C₃₁×#2962	2
C₃₁×#2949	2
C₃₁×#2948	2
C₄×C₃₁×AGL(1,ℤ/8)	2
#61343	31

Subgroups — C31×#61343 #21518102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61343 #21518102