Subgroups — C₃₁×#62180 #21518939

Order 7936.

1748 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	2	yes	—
30	C₃₁×#554	C₂²	1	2	yes	complemented
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#551	—	2	2	no	—
33	D₄×Q₈×C₃₁	—	2	1	no	—
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#542	C₂²	1	2	yes	complemented
45	C₃₁×#541	—	2	1	no	—
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃₁×#124	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#500	C₂²	1	2	yes	complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#488	C₂²	1	2	yes	complemented
63	C₃₁×#486	C₂²	1	1	yes	characteristic
64	C₃₁×#486	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	—
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#477	C₂²	1	2	yes	complemented
81	C₃₁×#477	C₂²	1	2	yes	complemented
82	C₃₁×#476	C₂²	1	2	yes	—
83	C₃₁×#476	C₂²	1	2	yes	complemented
84	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#474	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#474	C₂²	1	2	yes	—
90	C₃₁×#474	C₂²	1	2	yes	complemented
91	C₃₁×#474	C₂²	1	2	yes	complemented
92	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#474	C₂²	1	2	yes	complemented
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	complemented
97	C₃₁×#468	C₂²	1	2	yes	complemented
98	C₃₁×#467	C₂²	1	2	yes	complemented
99	C₃₁×#466	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	1	yes	characteristic
103	C₃₁×#463	C₂²	1	2	yes	complemented
104	C₃₁×#463	C₂²	1	2	yes	complemented
105	C₃₁×#460	C₂²	1	1	yes	characteristic
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#452	C₂²	1	1	yes	characteristic
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	1	yes	characteristic
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₃₁×#427	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#417	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×#127	C₂³	1	1	yes	characteristic
163	C₃₁×#126	—	2	2	no	—
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×#126	—	2	1	no	—
169	C₃₁×#126	D₄	1	2	yes	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	D₄	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	1	yes	characteristic
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	D₄	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	1	yes	characteristic
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
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	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#120	—	2	2	no	—
221	C₃₁×#120	—	2	2	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	—	2	2	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	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
291	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	—	2	4	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	4	2	no	—
339	C₂×D₄×C₃₁	—	8	2	no	—
340	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	—	2	2	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	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	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
359	Q₁₆×C₃₁	—	4	1	no	—
360	SD₁₆×C₃₁	—	2	2	no	—
361	SD₁₆×C₃₁	—	4	1	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	D₈×C₃₁	—	2	2	no	—
364	D₈×C₃₁	—	4	2	no	—
365	M₁₆×C₃₁	—	4	2	no	—
366	M₁₆×C₃₁	—	4	2	no	—
367	C₂×C₈×C₃₁	—	4	2	no	—
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
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	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	2	yes	—
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	#62180	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂³×C₃₁	—	2	1	no	—
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	2	2	no	—
448	C₂³×C₃₁	—	4	4	no	—
449	C₂³×C₃₁	—	8	2	no	—
450	C₂³×C₃₁	—	8	2	no	—
451	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
452	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₃₁	—	2	2	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	4	2	no	—
459	Q₈×C₃₁	—	4	2	no	—
460	Q₈×C₃₁	—	4	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	2	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	2	no	—
470	D₄×C₃₁	—	4	2	no	—
471	D₄×C₃₁	—	4	4	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	8	1	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	2	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
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	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	1	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	4	1	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	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	2	no	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	2	no	—
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	2	no	—
520	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
523	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3357	C₂×C₃₁	1	2	yes	complemented
527	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3347	C₂×C₃₁	1	2	yes	complemented
529	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3322	C₂×C₃₁	1	2	yes	complemented
532	#3314	C₂×C₃₁	1	2	yes	complemented
533	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3262	C₂×C₃₁	1	2	yes	complemented
535	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3243	C₂×C₃₁	1	2	yes	complemented
537	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3118	C₂×C₃₁	1	2	yes	complemented
539	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3081	C₂×C₃₁	1	2	yes	complemented
541	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	2	2	no	—
547	C₂²×C₃₁	—	2	2	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	2	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	2	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	2	no	—
558	C₂²×C₃₁	—	16	4	no	—
559	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	1	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	2	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	#576	1	2	yes	—
577	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
578	C₄×C₃₁	#585	1	1	yes	characteristic
579	#563	—	2	2	no	—
580	#559	C₂²×C₃₁	1	1	yes	characteristic
581	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#556	C₂²×C₃₁	1	1	yes	characteristic
583	#556	C₂²×C₃₁	1	1	yes	characteristic
584	#555	C₂²×C₃₁	1	2	yes	—
585	#554	C₂²×C₃₁	1	2	yes	complemented
586	#553	C₂²×C₃₁	1	2	yes	complemented
587	#551	—	2	2	no	—
588	D₄×Q₈	—	2	1	no	—
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	#548	—	2	1	no	—
593	#547	C₂²×C₃₁	1	1	yes	characteristic
594	#546	—	2	1	no	—
595	#546	C₂²×C₃₁	1	2	yes	—
596	D₄²	C₂²×C₃₁	1	1	yes	characteristic
597	#544	C₂²×C₃₁	1	2	yes	complemented
598	#542	C₂²×C₃₁	1	2	yes	—
599	#542	C₂²×C₃₁	1	2	yes	complemented
600	#541	—	2	1	no	—
601	#539	—	2	2	no	—
602	#538	—	2	2	no	—
603	#536	—	2	1	no	—
604	#532	C₂²×C₃₁	1	1	yes	characteristic
605	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#529	—	2	1	no	—
607	#529	C₂²×C₃₁	1	1	yes	characteristic
608	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	C₂×#124	—	2	1	no	—
610	#518	C₂²×C₃₁	1	2	yes	—
611	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
612	#501	C₂²×C₃₁	1	2	yes	complemented
613	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#500	C₂²×C₃₁	1	2	yes	complemented
616	#489	C₂²×C₃₁	1	2	yes	complemented
617	#488	C₂²×C₃₁	1	2	yes	complemented
618	#486	C₂²×C₃₁	1	1	yes	characteristic
619	#486	C₂²×C₃₁	1	1	yes	characteristic
620	#485	C₂²×C₃₁	1	2	yes	complemented
621	#485	C₂²×C₃₁	1	2	yes	complemented
622	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#484	C₂²×C₃₁	1	2	yes	complemented
624	#482	C₂²×C₃₁	1	2	yes	—
625	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#482	C₂²×C₃₁	1	2	yes	complemented
627	#480	C₂²×C₃₁	1	2	yes	—
628	#480	C₂²×C₃₁	1	2	yes	complemented
629	#480	C₂²×C₃₁	1	2	yes	complemented
630	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	#478	C₂²×C₃₁	1	1	yes	characteristic
632	#478	C₂²×C₃₁	1	2	yes	—
633	#478	C₂²×C₃₁	1	2	yes	complemented
634	#478	C₂²×C₃₁	1	2	yes	complemented
635	#477	C₂²×C₃₁	1	2	yes	complemented
636	#477	C₂²×C₃₁	1	2	yes	complemented
637	#476	C₂²×C₃₁	1	2	yes	—
638	#476	C₂²×C₃₁	1	2	yes	complemented
639	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#474	C₂²×C₃₁	1	1	yes	characteristic
643	#474	C₂²×C₃₁	1	1	yes	characteristic
644	#474	C₂²×C₃₁	1	2	yes	—
645	#474	C₂²×C₃₁	1	2	yes	complemented
646	#474	C₂²×C₃₁	1	2	yes	complemented
647	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#474	C₂²×C₃₁	1	2	yes	complemented
649	#469	C₂²×C₃₁	1	2	yes	complemented
650	#468	C₂²×C₃₁	1	2	yes	—
651	#468	C₂²×C₃₁	1	2	yes	complemented
652	#468	C₂²×C₃₁	1	2	yes	complemented
653	#467	C₂²×C₃₁	1	2	yes	complemented
654	#466	C₂²×C₃₁	1	2	yes	—
655	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#464	C₂²×C₃₁	1	2	yes	complemented
657	#463	C₂²×C₃₁	1	1	yes	characteristic
658	#463	C₂²×C₃₁	1	2	yes	complemented
659	#463	C₂²×C₃₁	1	2	yes	complemented
660	#460	C₂²×C₃₁	1	1	yes	characteristic
661	#459	C₂²×C₃₁	1	1	yes	characteristic
662	#452	C₂²×C₃₁	1	1	yes	characteristic
663	#450	C₂²×C₃₁	1	2	yes	—
664	#449	C₂²×C₃₁	1	1	yes	characteristic
665	#447	C₂²×C₃₁	1	2	yes	—
666	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#442	C₂²×C₃₁	1	2	yes	complemented
669	#440	C₂²×C₃₁	1	2	yes	—
670	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
674	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
675	C₄×D₈	C₂²×C₃₁	1	2	yes	—
676	#436	C₂²×C₃₁	1	1	yes	characteristic
677	#436	C₂²×C₃₁	1	2	yes	complemented
678	#435	C₂²×C₃₁	1	2	yes	complemented
679	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
680	#433	C₂²×C₃₁	1	2	yes	complemented
681	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#428	C₂²×C₃₁	1	2	yes	complemented
683	#428	C₂²×C₃₁	1	2	yes	complemented
684	#427	C₂²×C₃₁	1	2	yes	complemented
685	#424	C₂²×C₃₁	1	2	yes	complemented
686	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#418	C₂²×C₃₁	1	2	yes	—
688	#417	C₂²×C₃₁	1	2	yes	—
689	C₂×#102	C₂²×C₃₁	1	2	yes	—
690	C₂×C₃₁	—	4	1	no	—
691	C₂×C₃₁	—	4	2	no	—
692	C₂×C₃₁	—	4	2	no	—
693	C₂×C₃₁	—	8	1	no	—
694	C₂×C₃₁	—	8	2	no	—
695	C₂×C₃₁	#3489	1	1	yes	characteristic
696	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
697	C₂×C₃₁	#3586	1	1	yes	characteristic
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
701	C₂²×Q₈	—	2	1	no	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×D₄	—	2	1	no	—
705	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×D₈	C₂³×C₃₁	1	2	yes	—
712	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
725	#127	C₂³×C₃₁	1	1	yes	characteristic
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	1	no	—
732	#126	D₄×C₃₁	1	2	yes	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	D₄×C₃₁	1	1	yes	characteristic
737	#125	C₂³×C₃₁	1	1	yes	characteristic
738	#125	C₂³×C₃₁	1	2	yes	—
739	#124	—	2	1	no	—
740	#124	—	2	1	no	—
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	1	no	—
747	#124	D₄×C₃₁	1	1	yes	characteristic
748	#124	C₂³×C₃₁	1	1	yes	characteristic
749	#124	C₂³×C₃₁	1	2	yes	—
750	#123	—	2	1	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	D₄×C₃₁	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	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	D₄×C₃₁	1	1	yes	characteristic
770	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	D₄×C₃₁	1	1	yes	characteristic
779	#121	C₂³×C₃₁	1	1	yes	characteristic
780	#121	C₂³×C₃₁	1	2	yes	—
781	#121	C₂³×C₃₁	1	2	yes	—
782	#121	C₂³×C₃₁	1	2	yes	—
783	#120	—	2	2	no	—
784	#120	—	2	2	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	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	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	2	yes	—
806	C₄×D₄	C₂³×C₃₁	1	2	yes	—
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₃₁	1	2	yes	—
809	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	C₂³×C₃₁	1	1	yes	characteristic
815	#117	C₂³×C₃₁	1	2	yes	—
816	#117	C₂³×C₃₁	1	2	yes	—
817	#117	C₂³×C₃₁	1	2	yes	—
818	C₂×C₄⋊C₄	—	2	1	no	—
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
826	#107	C₂³×C₃₁	1	1	yes	characteristic
827	#107	C₂³×C₃₁	1	2	yes	—
828	#107	C₂³×C₃₁	1	2	yes	—
829	#107	C₂³×C₃₁	1	2	yes	—
830	#107	C₂³×C₃₁	1	2	yes	—
831	#107	C₂³×C₃₁	1	2	yes	—
832	#107	C₂³×C₃₁	1	2	yes	—
833	#107	C₂³×C₃₁	1	1	yes	characteristic
834	#107	C₂³×C₃₁	1	2	yes	—
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	#106	C₂³×C₃₁	1	2	yes	—
838	#106	C₂³×C₃₁	1	1	yes	characteristic
839	#106	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	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	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
846	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	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	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	2	yes	—
859	#102	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
871	#97	C₂³×C₃₁	1	2	yes	—
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₃₁	1	2	yes	—
875	C₃₁	#62180	1	1	yes	characteristic, direct product factor, Sylow
876	C₂⁴	—	2	2	no	—
877	#41	—	2	2	no	—
878	#41	—	4	1	no	—
879	#41	—	8	2	no	—
880	#41	—	8	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	8	2	no	—
888	C₂×Q₈	—	8	2	no	—
889	C₂×Q₈	—	8	2	no	—
890	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×D₄	—	2	4	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	8	2	no	—
904	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
905	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
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	2	no	—
910	C₂²×C₄	—	2	2	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	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
923	Q₁₆	—	4	1	no	—
924	SD₁₆	—	2	2	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	2	no	—
927	D₈	—	2	2	no	—
928	D₈	—	4	2	no	—
929	M₁₆	—	4	2	no	—
930	M₁₆	—	4	2	no	—
931	C₂×C₈	—	4	2	no	—
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
937	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	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	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₃₁	1	2	yes	—
1007	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	4	4	no	—
1012	C₂³	—	8	2	no	—
1013	C₂³	—	8	2	no	—
1014	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1015	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	—	8	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	8	1	no	—
1039	D₄	—	8	2	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	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	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	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	—	8	1	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	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	C₂²×D₄×C₃₁	1	2	yes	—
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	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	16	4	no	—
1099	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	C₃₁×#576	1	2	yes	—
1117	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1118	C₄	C₃₁×#585	1	1	yes	characteristic
1119	C₂	—	4	2	no	—
1120	C₂	—	4	1	no	—
1121	C₂	—	4	2	no	—
1122	C₂	—	8	2	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₃₁×#3489	1	1	yes	characteristic
1125	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1126	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3552	C₂	semidirect
2. C₃₁×#3514	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. Q₈×D₈×C₃₁	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3365	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3353	C₂	semidirect
9. C₃₁×#3347	C₂	semidirect
10. C₃₁×#3342	C₂	semidirect
11. C₃₁×#3324	C₂	semidirect
12. C₃₁×#3322	C₂	semidirect
13. C₃₁×#3314	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3262	C₂	semidirect
16. C₃₁×#3251	C₂	semidirect
17. C₃₁×#3243	C₂	semidirect
18. C₃₁×#3226	C₂	semidirect
19. C₃₁×#3118	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3079	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
26. C₃₁×#557	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
44. C₃₁×#542	C₂²	semidirect
50. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#500	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
83. C₃₁×#476	C₂²	semidirect
84. C₃₁×#475	C₂²	semidirect
85. C₃₁×#475	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
90. C₃₁×#474	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
96. C₃₁×#468	C₂²	semidirect
97. C₃₁×#468	C₂²	semidirect
98. C₃₁×#467	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
103. C₃₁×#463	C₂²	semidirect
104. C₃₁×#463	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₃₁×#427	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
444. #62180	C₃₁	direct (N × H)
520. #3552	C₂×C₃₁	semidirect
521. #3514	C₂×C₃₁	semidirect
522. #3386	C₂×C₃₁	semidirect
523. Q₈×D₈	C₂×C₃₁	semidirect
524. #3373	C₂×C₃₁	semidirect
525. #3365	C₂×C₃₁	semidirect
526. #3357	C₂×C₃₁	semidirect
527. #3353	C₂×C₃₁	semidirect
528. #3347	C₂×C₃₁	semidirect
529. #3342	C₂×C₃₁	semidirect
530. #3324	C₂×C₃₁	semidirect
531. #3322	C₂×C₃₁	semidirect
532. #3314	C₂×C₃₁	semidirect
533. #3294	C₂×C₃₁	semidirect
534. #3262	C₂×C₃₁	semidirect
535. #3251	C₂×C₃₁	semidirect
536. #3243	C₂×C₃₁	semidirect
537. #3226	C₂×C₃₁	semidirect
538. #3118	C₂×C₃₁	semidirect
539. #3102	C₂×C₃₁	semidirect
540. #3081	C₂×C₃₁	semidirect
541. #3079	C₂×C₃₁	semidirect
542. #2993	C₂×C₃₁	semidirect
581. #557	C₂²×C₃₁	semidirect
585. #554	C₂²×C₃₁	semidirect
586. #553	C₂²×C₃₁	semidirect
590. D₄×Q₈	C₂²×C₃₁	semidirect
597. #544	C₂²×C₃₁	semidirect
599. #542	C₂²×C₃₁	semidirect
605. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
608. #529	C₂²×C₃₁	semidirect
612. #501	C₂²×C₃₁	semidirect
613. #500	C₂²×C₃₁	semidirect
614. #500	C₂²×C₃₁	semidirect
615. #500	C₂²×C₃₁	semidirect
616. #489	C₂²×C₃₁	semidirect
617. #488	C₂²×C₃₁	semidirect
620. #485	C₂²×C₃₁	semidirect
621. #485	C₂²×C₃₁	semidirect
622. #485	C₂²×C₃₁	semidirect
623. #484	C₂²×C₃₁	semidirect
625. #482	C₂²×C₃₁	semidirect
626. #482	C₂²×C₃₁	semidirect
628. #480	C₂²×C₃₁	semidirect
629. #480	C₂²×C₃₁	semidirect
630. #479	C₂²×C₃₁	semidirect
633. #478	C₂²×C₃₁	semidirect
634. #478	C₂²×C₃₁	semidirect
635. #477	C₂²×C₃₁	semidirect
636. #477	C₂²×C₃₁	semidirect
638. #476	C₂²×C₃₁	semidirect
639. #475	C₂²×C₃₁	semidirect
640. #475	C₂²×C₃₁	semidirect
641. #475	C₂²×C₃₁	semidirect
645. #474	C₂²×C₃₁	semidirect
646. #474	C₂²×C₃₁	semidirect
647. #474	C₂²×C₃₁	semidirect
648. #474	C₂²×C₃₁	semidirect
649. #469	C₂²×C₃₁	semidirect
651. #468	C₂²×C₃₁	semidirect
652. #468	C₂²×C₃₁	semidirect
653. #467	C₂²×C₃₁	semidirect
655. #464	C₂²×C₃₁	semidirect
656. #464	C₂²×C₃₁	semidirect
658. #463	C₂²×C₃₁	semidirect
659. #463	C₂²×C₃₁	semidirect
666. #446	C₂²×C₃₁	semidirect
667. C₈×Q₈	C₂²×C₃₁	semidirect
668. #442	C₂²×C₃₁	semidirect
670. C₄×Q₁₆	C₂²×C₃₁	semidirect
672. C₄×SD₁₆	C₂²×C₃₁	semidirect
673. C₄×SD₁₆	C₂²×C₃₁	semidirect
677. #436	C₂²×C₃₁	semidirect
678. #435	C₂²×C₃₁	semidirect
680. #433	C₂²×C₃₁	semidirect
681. #431	C₂²×C₃₁	semidirect
682. #428	C₂²×C₃₁	semidirect
683. #428	C₂²×C₃₁	semidirect
684. #427	C₂²×C₃₁	semidirect
685. #424	C₂²×C₃₁	semidirect
686. #423	C₂²×C₃₁	semidirect
875. C₃₁	#62180	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×#3552	2
C₃₁×#3514	2
C₃₁×#3386	2
Q₈×D₈×C₃₁	2
C₃₁×#3373	2
C₃₁×#3365	2
C₃₁×#3357	2
C₃₁×#3353	2
C₃₁×#3347	2
C₃₁×#3342	2
C₃₁×#3324	2
C₃₁×#3322	2
C₃₁×#3314	2
C₃₁×#3294	2
C₃₁×#3262	2
C₃₁×#3251	2
C₃₁×#3243	2
C₃₁×#3226	2
C₃₁×#3118	2
C₃₁×#3102	2
C₃₁×#3081	2
C₃₁×#3079	2
C₃₁×#2993	2
#62180	31

Subgroups — C31×#62180 #21518939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62180 #21518939