Subgroups — C₃₁×#61336 #21518095

Order 7936.

1792 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×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#489	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×#3079	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2943	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	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
27	C₃₁×#559	C₂²	1	2	yes	—
28	C₃₁×#559	C₂²	1	2	yes	—
29	Q₈²×C₃₁	C₂²	1	2	yes	complemented
30	C₃₁×#557	C₂²	1	2	yes	complemented
31	C₃₁×#556	C₂²	1	2	yes	—
32	C₃₁×#556	C₂²	1	2	yes	—
33	C₃₁×#554	—	2	2	no	—
34	C₃₁×#554	C₂²	1	2	yes	complemented
35	C₃₁×#551	—	2	2	no	—
36	C₃₁×#551	—	2	2	no	—
37	D₄×Q₈×C₃₁	—	2	2	no	—
38	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
39	C₃₁×#544	—	2	1	no	—
40	C₃₁×#544	—	2	1	no	—
41	C₃₁×#544	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#535	C₂²	1	1	yes	characteristic
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	—	2	1	no	—
53	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
54	C₃₁×#520	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	1	yes	characteristic
56	C₃₁×#519	C₂²	1	1	yes	characteristic
57	C₃₁×#518	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
59	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#491	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	2	yes	—
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#489	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	2	yes	—
67	C₃₁×#489	C₂²	1	2	yes	complemented
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#488	C₂²	1	2	yes	complemented
70	C₃₁×#487	C₂²	1	2	yes	complemented
71	C₃₁×#486	C₂²	1	2	yes	—
72	C₃₁×#479	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#477	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	2	yes	complemented
78	C₃₁×#476	C₂²	1	2	yes	—
79	C₃₁×#476	C₂²	1	2	yes	complemented
80	C₃₁×#475	C₂²	1	2	yes	complemented
81	C₃₁×#475	C₂²	1	2	yes	complemented
82	C₃₁×#474	C₂²	1	2	yes	—
83	C₃₁×#474	C₂²	1	2	yes	complemented
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#464	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	complemented
92	C₃₁×#462	C₂²	1	2	yes	complemented
93	C₃₁×#461	C₂²	1	2	yes	complemented
94	C₃₁×#460	C₂²	1	2	yes	—
95	C₃₁×#459	C₂²	1	2	yes	—
96	C₃₁×#446	C₂²	1	2	yes	complemented
97	C₃₁×#446	C₂²	1	2	yes	complemented
98	C₃₁×#446	C₂²	1	2	yes	complemented
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#441	C₂²	1	2	yes	complemented
105	C₃₁×#441	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
115	C₄×D₈×C₃₁	C₂²	1	2	yes	—
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#428	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×#423	C₂²	1	1	yes	characteristic
122	C₃₁×#419	C₂²	1	1	yes	characteristic
123	C₃₁×#418	C₂²	1	1	yes	characteristic
124	C₃₁×#417	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#416	C₂²	1	1	yes	characteristic
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	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	C₂×C₃₁×#97	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	—	2	2	no	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₃₁×#137	—	2	4	no	—
142	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
143	C₃₁×#135	—	2	4	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	2	no	—
160	C₃₁×C₄⋊Q₈	—	2	2	no	—
161	C₃₁×C₄⋊Q₈	—	2	2	no	—
162	C₃₁×C₄⋊Q₈	—	2	1	no	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₃₁×#127	C₂³	1	2	yes	—
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×#125	—	2	1	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	D₄	1	1	yes	characteristic
181	C₃₁×#125	D₄	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	2	yes	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	—	2	1	no	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#124	C₂³	1	2	yes	—
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	D₄	1	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	2	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	2	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×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	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	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×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	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×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	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×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
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×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	1	yes	characteristic
310	C₃₁×#97	C₂³	1	1	yes	characteristic
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₃₁×#97	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	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	2	2	no	—
319	#41×C₃₁	#41	1	4	yes	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	8	2	no	—
328	C₂×Q₈×C₃₁	—	8	4	no	—
329	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	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	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	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	Q₁₆×C₃₁	—	2	2	no	—
361	Q₁₆×C₃₁	—	2	4	no	—
362	SD₁₆×C₃₁	—	2	2	no	—
363	SD₁₆×C₃₁	—	2	4	no	—
364	SD₁₆×C₃₁	—	2	2	no	—
365	SD₁₆×C₃₁	—	2	4	no	—
366	D₈×C₃₁	—	2	2	no	—
367	D₈×C₃₁	—	2	4	no	—
368	M₁₆×C₃₁	—	2	2	no	—
369	M₁₆×C₃₁	—	2	2	no	—
370	C₂×C₈×C₃₁	—	2	2	no	—
371	C₂×C₈×C₃₁	—	2	2	no	—
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	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	1	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	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	2	yes	—
447	C₄²×C₃₁	C₂⁴	1	2	yes	—
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	#61336	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	4	2	no	—
455	C₂³×C₃₁	—	8	1	no	—
456	C₂³×C₃₁	—	8	1	no	—
457	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₃₁	—	2	1	no	—
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	4	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	8	2	no	—
468	Q₈×C₃₁	—	8	2	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	Q₈×C₃₁	C₂×#41	1	2	yes	—
471	D₄×C₃₁	—	2	4	no	—
472	D₄×C₃₁	—	2	2	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	4	2	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	C₂×#41	1	2	yes	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	4	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	4	1	no	—
493	C₂×C₄×C₃₁	—	4	1	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	8	1	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	8	1	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	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	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
516	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
517	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	—	2	2	no	—
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	1	no	—
524	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3377	C₂×C₃₁	1	2	yes	complemented
527	#3376	C₂×C₃₁	1	2	yes	complemented
528	#3375	C₂×C₃₁	1	2	yes	complemented
529	#3373	C₂×C₃₁	1	2	yes	complemented
530	#3371	C₂×C₃₁	1	2	yes	complemented
531	#3370	C₂×C₃₁	1	2	yes	complemented
532	#3369	C₂×C₃₁	1	2	yes	complemented
533	#3367	C₂×C₃₁	1	2	yes	complemented
534	#3137	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
536	C₂×#489	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3045	C₂×C₃₁	1	1	yes	characteristic
542	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#2943	C₂×C₃₁	1	1	yes	characteristic, complemented
547	C₂²×C₃₁	—	2	1	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	2	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	2	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	—	2	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	2	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×#137	C₂²×C₃₁	1	1	yes	characteristic
582	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
583	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
584	#559	C₂²×C₃₁	1	2	yes	—
585	#559	C₂²×C₃₁	1	2	yes	—
586	Q₈²	C₂²×C₃₁	1	2	yes	complemented
587	#557	C₂²×C₃₁	1	2	yes	complemented
588	#556	C₂²×C₃₁	1	2	yes	—
589	#556	C₂²×C₃₁	1	2	yes	—
590	#554	—	2	2	no	—
591	#554	C₂²×C₃₁	1	2	yes	complemented
592	#551	—	2	2	no	—
593	#551	—	2	2	no	—
594	D₄×Q₈	—	2	2	no	—
595	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
596	#544	—	2	1	no	—
597	#544	—	2	1	no	—
598	#544	C₂²×C₃₁	1	1	yes	characteristic
599	#544	C₂²×C₃₁	1	1	yes	characteristic
600	#542	—	2	1	no	—
601	#542	—	2	1	no	—
602	#536	C₂²×C₃₁	1	1	yes	characteristic
603	#535	C₂²×C₃₁	1	1	yes	characteristic
604	#533	—	2	1	no	—
605	#533	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×C₄⋊Q₈	—	2	1	no	—
607	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
608	#529	—	2	1	no	—
609	#529	—	2	1	no	—
610	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
611	#520	C₂²×C₃₁	1	1	yes	characteristic
612	#520	C₂²×C₃₁	1	1	yes	characteristic
613	#519	C₂²×C₃₁	1	1	yes	characteristic
614	#518	C₂²×C₃₁	1	1	yes	characteristic
615	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
616	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
617	#491	C₂²×C₃₁	1	2	yes	complemented
618	#490	C₂²×C₃₁	1	2	yes	—
619	#489	C₂²×C₃₁	1	2	yes	—
620	#489	C₂²×C₃₁	1	2	yes	—
621	#489	C₂²×C₃₁	1	2	yes	—
622	#489	C₂²×C₃₁	1	2	yes	—
623	#489	C₂²×C₃₁	1	2	yes	—
624	#489	C₂²×C₃₁	1	2	yes	complemented
625	#488	C₂²×C₃₁	1	2	yes	—
626	#488	C₂²×C₃₁	1	2	yes	complemented
627	#487	C₂²×C₃₁	1	2	yes	complemented
628	#486	C₂²×C₃₁	1	2	yes	—
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	#477	C₂²×C₃₁	1	2	yes	complemented
634	#477	C₂²×C₃₁	1	2	yes	complemented
635	#476	C₂²×C₃₁	1	2	yes	—
636	#476	C₂²×C₃₁	1	2	yes	complemented
637	#475	C₂²×C₃₁	1	2	yes	complemented
638	#475	C₂²×C₃₁	1	2	yes	complemented
639	#474	C₂²×C₃₁	1	2	yes	—
640	#474	C₂²×C₃₁	1	2	yes	complemented
641	#464	C₂²×C₃₁	1	2	yes	—
642	#464	C₂²×C₃₁	1	2	yes	—
643	#464	C₂²×C₃₁	1	2	yes	—
644	#464	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	complemented
649	#462	C₂²×C₃₁	1	2	yes	complemented
650	#461	C₂²×C₃₁	1	2	yes	complemented
651	#460	C₂²×C₃₁	1	2	yes	—
652	#459	C₂²×C₃₁	1	2	yes	—
653	#446	C₂²×C₃₁	1	2	yes	complemented
654	#446	C₂²×C₃₁	1	2	yes	complemented
655	#446	C₂²×C₃₁	1	2	yes	complemented
656	#446	C₂²×C₃₁	1	2	yes	complemented
657	#442	C₂²×C₃₁	1	2	yes	—
658	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#441	C₂²×C₃₁	1	2	yes	complemented
662	#441	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#440	C₂²×C₃₁	1	2	yes	—
664	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#440	C₂²×C₃₁	1	2	yes	complemented
666	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
670	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
671	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
672	C₄×D₈	C₂²×C₃₁	1	2	yes	—
673	#428	C₂²×C₃₁	1	1	yes	characteristic
674	#428	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	#423	C₂²×C₃₁	1	1	yes	characteristic
679	#419	C₂²×C₃₁	1	1	yes	characteristic
680	#418	C₂²×C₃₁	1	1	yes	characteristic
681	#417	C₂²×C₃₁	1	1	yes	characteristic
682	#417	C₂²×C₃₁	1	1	yes	characteristic
683	#416	C₂²×C₃₁	1	1	yes	characteristic
684	#416	C₂²×C₃₁	1	1	yes	characteristic
685	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
686	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×#102	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	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
692	C₂×C₃₁	—	2	2	no	—
693	C₂×C₃₁	—	4	2	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	#3585	1	1	yes	characteristic
698	C₂×C₃₁	#3586	1	1	yes	characteristic
699	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
701	C₂²×Q₈	—	2	2	no	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
705	#137	—	2	4	no	—
706	AGL(1,ℤ/8)	—	2	4	no	—
707	#135	—	2	4	no	—
708	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×D₈	C₂³×C₃₁	1	2	yes	—
716	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
718	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	2	no	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
729	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
731	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
732	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
734	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
735	#127	C₂³×C₃₁	1	2	yes	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	1	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	D₄×C₃₁	1	1	yes	characteristic
745	#125	D₄×C₃₁	1	1	yes	characteristic
746	#125	C₂³×C₃₁	1	2	yes	—
747	#125	C₂³×C₃₁	1	2	yes	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	1	no	—
751	#124	—	2	1	no	—
752	#124	C₂³×C₃₁	1	2	yes	—
753	#124	C₂³×C₃₁	1	2	yes	—
754	#124	C₂³×C₃₁	1	2	yes	—
755	#124	C₂³×C₃₁	1	2	yes	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	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	1	no	—
765	C₂²⋊Q₈	—	2	1	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	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	2	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	1	yes	characteristic
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
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	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₃₁	1	2	yes	—
807	C₄×D₄	C₂³×C₃₁	1	2	yes	—
808	C₄×D₄	C₂³×C₃₁	1	2	yes	—
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	—	2	2	no	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	C₂³×C₃₁	1	1	yes	characteristic
818	#117	C₂³×C₃₁	1	1	yes	characteristic
819	#117	C₂³×C₃₁	1	1	yes	characteristic
820	#117	C₂³×C₃₁	1	1	yes	characteristic
821	C₂×C₄⋊C₄	—	2	1	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	2	2	no	—
825	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	—	2	1	no	—
828	C₂×C₂²⋊C₄	—	2	1	no	—
829	C₂×C₂²⋊C₄	—	2	2	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	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	#107	C₂³×C₃₁	1	2	yes	—
837	#106	C₂³×C₃₁	1	1	yes	characteristic
838	#106	C₂³×C₃₁	1	1	yes	characteristic
839	#106	C₂³×C₃₁	1	2	yes	—
840	#106	C₂³×C₃₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	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	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
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	#97	C₂³×C₃₁	1	1	yes	characteristic
872	#97	C₂³×C₃₁	1	1	yes	characteristic
873	#97	C₂³×C₃₁	1	1	yes	characteristic
874	#97	C₂³×C₃₁	1	1	yes	characteristic
875	#97	C₂³×C₃₁	1	2	yes	—
876	#97	C₂³×C₃₁	1	2	yes	—
877	C₄×C₈	C₂³×C₃₁	1	2	yes	—
878	C₄×C₈	C₂³×C₃₁	1	2	yes	—
879	C₃₁	#61336	1	1	yes	characteristic, direct product factor, Sylow
880	C₂⁴	—	2	1	no	—
881	#41	—	2	2	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	#41×C₃₁	1	4	yes	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	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	—	2	2	no	—
892	C₂×Q₈	—	8	2	no	—
893	C₂×Q₈	—	8	4	no	—
894	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
895	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
896	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
897	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
898	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
907	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	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	Q₁₆	—	2	2	no	—
926	Q₁₆	—	2	4	no	—
927	SD₁₆	—	2	2	no	—
928	SD₁₆	—	2	4	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	2	4	no	—
931	D₈	—	2	2	no	—
932	D₈	—	2	4	no	—
933	M₁₆	—	2	2	no	—
934	M₁₆	—	2	2	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
940	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
941	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	—	2	2	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	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	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	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	1	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	C₂×D₄×C₃₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₃₁	1	2	yes	—
1012	C₄²	C₂⁴×C₃₁	1	2	yes	—
1013	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	4	2	no	—
1019	C₂³	—	8	1	no	—
1020	C₂³	—	8	1	no	—
1021	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	Q₈	—	2	1	no	—
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	4	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	2	no	—
1034	Q₈	C₂×#41×C₃₁	1	2	yes	—
1035	D₄	—	2	4	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	C₂×#41×C₃₁	1	2	yes	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	8	1	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	1	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	—	8	1	no	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1079	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1080	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1081	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	2	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	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	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	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	2	no	—
1124	C₂	—	8	2	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
1127	C₂	C₃₁×#3585	1	1	yes	characteristic
1128	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×#3045	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×#3503	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3375	C₂	semidirect
6. C₃₁×#3373	C₂	semidirect
7. C₃₁×#3371	C₂	semidirect
8. C₃₁×#3370	C₂	semidirect
9. C₃₁×#3369	C₂	semidirect
10. C₃₁×#3367	C₂	semidirect
11. C₃₁×#3137	C₂	semidirect
12. C₃₁×#3136	C₂	semidirect
13. C₂×C₃₁×#489	C₂	semidirect
14. C₃₁×#3082	C₂	semidirect
15. C₃₁×#3081	C₂	semidirect
16. C₃₁×#3079	C₂	semidirect
17. C₃₁×#3046	C₂	semidirect
19. C₃₁×#3040	C₂	semidirect
20. C₃₁×#2961	C₂	semidirect
21. C₃₁×#2947	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₃₁×#2943	C₂	semidirect
29. Q₈²×C₃₁	C₂²	semidirect
30. C₃₁×#557	C₂²	semidirect
34. C₃₁×#554	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
60. C₃₁×#491	C₂²	semidirect
67. C₃₁×#489	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
70. C₃₁×#487	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#475	C₂²	semidirect
83. C₃₁×#474	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
91. C₃₁×#463	C₂²	semidirect
92. C₃₁×#462	C₂²	semidirect
93. C₃₁×#461	C₂²	semidirect
96. C₃₁×#446	C₂²	semidirect
97. C₃₁×#446	C₂²	semidirect
98. C₃₁×#446	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
101. C₃₁×#442	C₂²	semidirect
102. C₃₁×#442	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#441	C₂²	semidirect
105. C₃₁×#441	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₃₁×#440	C₂²	semidirect
110. C₃₁×#440	C₂²	semidirect
111. C₃₁×#440	C₂²	semidirect
112. C₄×Q₁₆×C₃₁	C₂²	semidirect
114. C₄×SD₁₆×C₃₁	C₂²	semidirect
450. #61336	C₃₁	direct (N × H)
524. #3510	C₂×C₃₁	semidirect
525. #3503	C₂×C₃₁	semidirect
526. #3377	C₂×C₃₁	semidirect
527. #3376	C₂×C₃₁	semidirect
528. #3375	C₂×C₃₁	semidirect
529. #3373	C₂×C₃₁	semidirect
530. #3371	C₂×C₃₁	semidirect
531. #3370	C₂×C₃₁	semidirect
532. #3369	C₂×C₃₁	semidirect
533. #3367	C₂×C₃₁	semidirect
534. #3137	C₂×C₃₁	semidirect
535. #3136	C₂×C₃₁	semidirect
536. C₂×#489	C₂×C₃₁	semidirect
537. #3082	C₂×C₃₁	semidirect
538. #3081	C₂×C₃₁	semidirect
539. #3079	C₂×C₃₁	semidirect
540. #3046	C₂×C₃₁	semidirect
542. #3040	C₂×C₃₁	semidirect
543. #2961	C₂×C₃₁	semidirect
544. #2947	C₂×C₃₁	semidirect
545. #2946	C₂×C₃₁	semidirect
546. #2943	C₂×C₃₁	semidirect
586. Q₈²	C₂²×C₃₁	semidirect
587. #557	C₂²×C₃₁	semidirect
591. #554	C₂²×C₃₁	semidirect
595. D₄×Q₈	C₂²×C₃₁	semidirect
617. #491	C₂²×C₃₁	semidirect
624. #489	C₂²×C₃₁	semidirect
626. #488	C₂²×C₃₁	semidirect
627. #487	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
633. #477	C₂²×C₃₁	semidirect
634. #477	C₂²×C₃₁	semidirect
636. #476	C₂²×C₃₁	semidirect
637. #475	C₂²×C₃₁	semidirect
638. #475	C₂²×C₃₁	semidirect
640. #474	C₂²×C₃₁	semidirect
644. #464	C₂²×C₃₁	semidirect
648. #463	C₂²×C₃₁	semidirect
649. #462	C₂²×C₃₁	semidirect
650. #461	C₂²×C₃₁	semidirect
653. #446	C₂²×C₃₁	semidirect
654. #446	C₂²×C₃₁	semidirect
655. #446	C₂²×C₃₁	semidirect
656. #446	C₂²×C₃₁	semidirect
658. #442	C₂²×C₃₁	semidirect
659. #442	C₂²×C₃₁	semidirect
660. #441	C₂²×C₃₁	semidirect
661. #441	C₂²×C₃₁	semidirect
662. #441	C₂²×C₃₁	semidirect
664. #440	C₂²×C₃₁	semidirect
665. #440	C₂²×C₃₁	semidirect
666. #440	C₂²×C₃₁	semidirect
667. #440	C₂²×C₃₁	semidirect
668. #440	C₂²×C₃₁	semidirect
669. C₄×Q₁₆	C₂²×C₃₁	semidirect
671. C₄×SD₁₆	C₂²×C₃₁	semidirect
879. C₃₁	#61336	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×#3503	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3137	2
C₃₁×#3136	2
C₂×C₃₁×#489	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3079	2
C₃₁×#3046	2
C₃₁×#3045	2
C₃₁×#3040	2
C₃₁×#2961	2
C₃₁×#2947	2
C₃₁×#2946	2
C₃₁×#2943	2
#61336	31

Subgroups — C31×#61336 #21518095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61336 #21518095