Subgroups — C₃₁×#60926 #21517685

Order 7936.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1168 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×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3256	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
30	C₃₁×#559	—	2	1	no	—
31	C₃₁×#559	—	2	1	no	—
32	C₃₁×#556	—	2	1	no	—
33	C₃₁×#556	—	2	1	no	—
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#551	—	2	2	no	—
36	C₃₁×#544	C₂²	1	1	yes	characteristic
37	C₃₁×#542	—	2	1	no	—
38	C₃₁×#542	C₂²	1	2	yes	complemented
39	C₃₁×#542	C₂²	1	2	yes	complemented
40	C₃₁×#542	C₂²	1	2	yes	complemented
41	C₃₁×#540	—	2	1	no	—
42	C₃₁×#540	C₂²	1	2	yes	complemented
43	C₃₁×#538	—	2	2	no	—
44	C₃₁×#537	C₂²	1	1	yes	characteristic
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#535	C₂²	1	1	yes	characteristic
47	C₃₁×#535	C₂²	1	1	yes	characteristic
48	C₃₁×#535	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#532	—	2	1	no	—
51	C₃₁×#532	C₂²	1	2	yes	complemented
52	C₃₁×#529	—	2	1	no	—
53	C₃₁×#529	C₂²	1	2	yes	complemented
54	C₃₁×#529	C₂²	1	2	yes	complemented
55	C₃₁×#529	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
57	C₃₁×#525	—	2	2	no	—
58	C₃₁×#519	C₂²	1	1	yes	characteristic
59	C₃₁×#518	C₂²	1	1	yes	characteristic
60	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
63	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#478	C₂²	1	2	yes	complemented
70	C₃₁×#478	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#477	C₂²	1	2	yes	complemented
75	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#476	C₂²	1	2	yes	complemented
78	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#474	C₂²	1	2	yes	complemented
83	C₃₁×#470	C₂²	1	2	yes	complemented
84	C₃₁×#469	C₂²	1	2	yes	—
85	C₃₁×#469	C₂²	1	2	yes	—
86	C₃₁×#469	C₂²	1	2	yes	complemented
87	C₃₁×#468	C₂²	1	2	yes	complemented
88	C₃₁×#468	C₂²	1	2	yes	complemented
89	C₃₁×#468	C₂²	1	2	yes	complemented
90	C₃₁×#468	C₂²	1	2	yes	complemented
91	C₃₁×#467	C₂²	1	2	yes	complemented
92	C₃₁×#466	C₂²	1	2	yes	—
93	C₃₁×#466	C₂²	1	2	yes	—
94	C₃₁×#466	C₂²	1	2	yes	complemented
95	C₃₁×#465	C₂²	1	2	yes	complemented
96	C₃₁×#465	C₂²	1	2	yes	complemented
97	C₃₁×#465	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#464	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	complemented
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#464	C₂²	1	2	yes	complemented
103	C₃₁×#463	C₂²	1	2	yes	—
104	C₃₁×#463	C₂²	1	2	yes	—
105	C₃₁×#463	C₂²	1	2	yes	—
106	C₃₁×#463	C₂²	1	2	yes	—
107	C₃₁×#463	C₂²	1	2	yes	—
108	C₃₁×#463	C₂²	1	2	yes	—
109	C₃₁×#463	C₂²	1	2	yes	complemented
110	C₃₁×#463	C₂²	1	2	yes	complemented
111	C₃₁×#460	C₂²	1	2	yes	complemented
112	C₃₁×#460	C₂²	1	2	yes	complemented
113	C₃₁×#459	C₂²	1	2	yes	—
114	C₃₁×#459	C₂²	1	2	yes	—
115	C₃₁×#428	C₂²	1	1	yes	characteristic
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#427	C₂²	1	1	yes	characteristic
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₃₁×#424	C₂²	1	1	yes	characteristic
120	C₃₁×#424	C₂²	1	1	yes	characteristic
121	C₃₁×#424	C₂²	1	2	yes	complemented
122	C₃₁×#424	C₂²	1	2	yes	complemented
123	C₃₁×#423	C₂²	1	1	yes	characteristic
124	C₃₁×#423	C₂²	1	2	yes	complemented
125	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
127	C₃₁×#419	C₂²	1	1	yes	characteristic
128	C₃₁×#418	C₂²	1	1	yes	characteristic
129	C₃₁×#418	C₂²	1	1	yes	characteristic
130	C₃₁×#418	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₃₁×#416	C₂²	1	1	yes	characteristic
133	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₃₁×#137	—	4	2	no	—
143	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	—	4	2	no	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×D₈×C₃₁	—	4	2	no	—
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×#131	—	4	2	no	—
155	C₃₁×#131	—	4	2	no	—
156	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	—	2	1	no	—
165	C₃₁×C₄⋊Q₈	—	2	1	no	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×#127	—	2	1	no	—
170	C₃₁×#127	—	2	1	no	—
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×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	C₂³	1	1	yes	characteristic
180	C₃₁×#125	C₂³	1	1	yes	characteristic
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	1	no	—
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#124	C₂³	1	2	yes	—
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	2	yes	—
225	C₃₁×#120	—	2	2	no	—
226	C₃₁×#120	—	2	2	no	—
227	C₃₁×#120	—	2	2	no	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	—	2	1	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	D₄	1	2	yes	—
249	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
250	C₄×D₄×C₃₁	D₄	1	2	yes	—
251	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	—	2	2	no	—
263	C₃₁×#117	C₂³	1	1	yes	characteristic
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₃₁×#117	C₂³	1	1	yes	characteristic
266	C₃₁×#117	C₂³	1	1	yes	characteristic
267	C₃₁×#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂×C₄²×C₃₁	—	2	1	no	—
274	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	1	yes	characteristic
278	C₃₁×#107	C₂³	1	1	yes	characteristic
279	C₃₁×#107	C₂³	1	1	yes	characteristic
280	C₃₁×#107	C₂³	1	2	yes	—
281	C₃₁×#107	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	1	yes	characteristic
283	C₃₁×#106	C₂³	1	1	yes	characteristic
284	C₃₁×#106	C₂³	1	1	yes	characteristic
285	C₃₁×#106	C₂³	1	1	yes	characteristic
286	C₃₁×#106	C₂³	1	2	yes	—
287	C₃₁×#106	C₂³	1	2	yes	—
288	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
293	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
294	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
295	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
296	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
297	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	1	yes	characteristic
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	1	yes	characteristic
303	C₃₁×#103	C₂³	1	1	yes	characteristic
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	1	yes	characteristic
309	C₃₁×#102	C₂³	1	1	yes	characteristic
310	C₃₁×#102	C₂³	1	1	yes	characteristic
311	C₃₁×#102	C₂³	1	1	yes	characteristic
312	C₃₁×#102	C₂³	1	2	yes	—
313	C₃₁×#102	C₂³	1	2	yes	—
314	C₃₁×#102	C₂³	1	2	yes	—
315	C₃₁×#102	C₂³	1	2	yes	—
316	C₃₁×#102	C₂³	1	2	yes	—
317	C₃₁×#102	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	1	no	—
319	C₂⁴×C₃₁	—	2	1	no	—
320	#41×C₃₁	—	2	2	no	—
321	#41×C₃₁	—	2	2	no	—
322	#41×C₃₁	—	2	2	no	—
323	#41×C₃₁	—	2	2	no	—
324	#41×C₃₁	—	8	4	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	—	2	1	no	—
328	C₂×Q₈×C₃₁	—	2	2	no	—
329	C₂×Q₈×C₃₁	—	2	2	no	—
330	C₂×Q₈×C₃₁	—	2	2	no	—
331	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	2	no	—
347	C₂×D₄×C₃₁	—	2	2	no	—
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	8	2	no	—
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	Q₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	4	2	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	2	no	—
374	D₈×C₃₁	—	4	2	no	—
375	D₈×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	4	2	no	—
377	M₁₆×C₃₁	—	2	2	no	—
378	M₁₆×C₃₁	—	2	2	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	M₁₆×C₃₁	—	4	2	no	—
381	C₂×C₈×C₃₁	—	2	2	no	—
382	C₂×C₈×C₃₁	—	2	2	no	—
383	C₂×C₈×C₃₁	—	4	2	no	—
384	C₂×C₈×C₃₁	—	4	2	no	—
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	—	2	1	no	—
452	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₃₁	C₂×D₄	1	2	yes	—
454	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₃₁	C₂×D₄	1	2	yes	—
456	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	C₄²×C₃₁	C₂⁴	1	2	yes	—
459	#60926	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
460	C₂³×C₃₁	—	2	2	no	—
461	C₂³×C₃₁	—	2	2	no	—
462	C₂³×C₃₁	—	2	1	no	—
463	C₂³×C₃₁	—	4	2	no	—
464	C₂³×C₃₁	—	4	2	no	—
465	C₂³×C₃₁	—	8	1	no	—
466	C₂³×C₃₁	—	8	1	no	—
467	C₂³×C₃₁	—	8	1	no	—
468	C₂³×C₃₁	—	8	1	no	—
469	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
470	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
471	Q₈×C₃₁	—	2	2	no	—
472	Q₈×C₃₁	—	2	2	no	—
473	Q₈×C₃₁	—	2	1	no	—
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	2	1	no	—
476	Q₈×C₃₁	—	4	2	no	—
477	Q₈×C₃₁	—	8	1	no	—
478	Q₈×C₃₁	—	8	1	no	—
479	Q₈×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	2	4	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	2	no	—
483	D₄×C₃₁	—	2	2	no	—
484	D₄×C₃₁	—	2	1	no	—
485	D₄×C₃₁	—	2	2	no	—
486	D₄×C₃₁	—	2	2	no	—
487	D₄×C₃₁	—	2	1	no	—
488	D₄×C₃₁	—	4	2	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	4	2	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	2	no	—
509	C₂×C₄×C₃₁	—	4	1	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	1	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	4	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	1	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	1	no	—
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
531	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
532	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	1	no	—
537	C₈×C₃₁	—	2	2	no	—
538	C₈×C₃₁	—	2	2	no	—
539	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3460	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3263	C₂×C₃₁	1	2	yes	complemented
542	#3262	C₂×C₃₁	1	2	yes	complemented
543	#3257	C₂×C₃₁	1	2	yes	complemented
544	#3257	C₂×C₃₁	1	2	yes	complemented
545	#3256	C₂×C₃₁	1	2	yes	complemented
546	#3251	C₂×C₃₁	1	2	yes	complemented
547	#3250	C₂×C₃₁	1	2	yes	complemented
548	#3247	C₂×C₃₁	1	2	yes	complemented
549	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3062	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3058	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3043	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3041	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
560	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#2906	C₂×C₃₁	1	1	yes	characteristic, complemented
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	1	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	2	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	2	no	—
576	C₂²×C₃₁	—	8	4	no	—
577	C₂²×C₃₁	—	16	2	no	—
578	C₂²×C₃₁	#537	1	2	yes	—
579	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	1	no	—
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	2	2	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	1	no	—
595	C₄×C₃₁	—	4	2	no	—
596	C₄×C₃₁	#537	1	2	yes	—
597	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
599	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
600	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
601	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
602	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
603	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
605	#559	—	2	1	no	—
606	#559	—	2	1	no	—
607	#556	—	2	1	no	—
608	#556	—	2	1	no	—
609	#551	—	2	2	no	—
610	#551	—	2	2	no	—
611	#544	C₂²×C₃₁	1	1	yes	characteristic
612	#542	—	2	1	no	—
613	#542	C₂²×C₃₁	1	2	yes	complemented
614	#542	C₂²×C₃₁	1	2	yes	complemented
615	#542	C₂²×C₃₁	1	2	yes	complemented
616	#540	—	2	1	no	—
617	#540	C₂²×C₃₁	1	2	yes	complemented
618	#538	—	2	2	no	—
619	#537	C₂²×C₃₁	1	1	yes	characteristic
620	#536	C₂²×C₃₁	1	1	yes	characteristic
621	#535	C₂²×C₃₁	1	1	yes	characteristic
622	#535	C₂²×C₃₁	1	1	yes	characteristic
623	#535	C₂²×C₃₁	1	1	yes	characteristic
624	#533	C₂²×C₃₁	1	1	yes	characteristic
625	#532	—	2	1	no	—
626	#532	C₂²×C₃₁	1	2	yes	complemented
627	#529	—	2	1	no	—
628	#529	C₂²×C₃₁	1	2	yes	complemented
629	#529	C₂²×C₃₁	1	2	yes	complemented
630	#529	C₂²×C₃₁	1	2	yes	complemented
631	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
632	#525	—	2	2	no	—
633	#519	C₂²×C₃₁	1	1	yes	characteristic
634	#518	C₂²×C₃₁	1	1	yes	characteristic
635	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
636	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
638	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#479	C₂²×C₃₁	1	2	yes	complemented
641	#479	C₂²×C₃₁	1	2	yes	complemented
642	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#478	C₂²×C₃₁	1	2	yes	complemented
645	#478	C₂²×C₃₁	1	2	yes	complemented
646	#478	C₂²×C₃₁	1	2	yes	complemented
647	#478	C₂²×C₃₁	1	2	yes	complemented
648	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#477	C₂²×C₃₁	1	2	yes	complemented
650	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#476	C₂²×C₃₁	1	2	yes	complemented
652	#476	C₂²×C₃₁	1	2	yes	complemented
653	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₃₁	1	2	yes	complemented
655	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#474	C₂²×C₃₁	1	2	yes	complemented
657	#474	C₂²×C₃₁	1	2	yes	complemented
658	#470	C₂²×C₃₁	1	2	yes	complemented
659	#469	C₂²×C₃₁	1	2	yes	—
660	#469	C₂²×C₃₁	1	2	yes	—
661	#469	C₂²×C₃₁	1	2	yes	complemented
662	#468	C₂²×C₃₁	1	2	yes	complemented
663	#468	C₂²×C₃₁	1	2	yes	complemented
664	#468	C₂²×C₃₁	1	2	yes	complemented
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#467	C₂²×C₃₁	1	2	yes	complemented
667	#466	C₂²×C₃₁	1	2	yes	—
668	#466	C₂²×C₃₁	1	2	yes	—
669	#466	C₂²×C₃₁	1	2	yes	complemented
670	#465	C₂²×C₃₁	1	2	yes	complemented
671	#465	C₂²×C₃₁	1	2	yes	complemented
672	#465	C₂²×C₃₁	1	2	yes	complemented
673	#465	C₂²×C₃₁	1	2	yes	complemented
674	#464	C₂²×C₃₁	1	2	yes	complemented
675	#464	C₂²×C₃₁	1	2	yes	complemented
676	#464	C₂²×C₃₁	1	2	yes	complemented
677	#464	C₂²×C₃₁	1	2	yes	complemented
678	#463	C₂²×C₃₁	1	2	yes	—
679	#463	C₂²×C₃₁	1	2	yes	—
680	#463	C₂²×C₃₁	1	2	yes	—
681	#463	C₂²×C₃₁	1	2	yes	—
682	#463	C₂²×C₃₁	1	2	yes	—
683	#463	C₂²×C₃₁	1	2	yes	—
684	#463	C₂²×C₃₁	1	2	yes	complemented
685	#463	C₂²×C₃₁	1	2	yes	complemented
686	#460	C₂²×C₃₁	1	2	yes	complemented
687	#460	C₂²×C₃₁	1	2	yes	complemented
688	#459	C₂²×C₃₁	1	2	yes	—
689	#459	C₂²×C₃₁	1	2	yes	—
690	#428	C₂²×C₃₁	1	1	yes	characteristic
691	#428	C₂²×C₃₁	1	1	yes	characteristic
692	#427	C₂²×C₃₁	1	1	yes	characteristic
693	#427	C₂²×C₃₁	1	1	yes	characteristic
694	#424	C₂²×C₃₁	1	1	yes	characteristic
695	#424	C₂²×C₃₁	1	1	yes	characteristic
696	#424	C₂²×C₃₁	1	2	yes	complemented
697	#424	C₂²×C₃₁	1	2	yes	complemented
698	#423	C₂²×C₃₁	1	1	yes	characteristic
699	#423	C₂²×C₃₁	1	2	yes	complemented
700	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
701	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
702	#419	C₂²×C₃₁	1	1	yes	characteristic
703	#418	C₂²×C₃₁	1	1	yes	characteristic
704	#418	C₂²×C₃₁	1	1	yes	characteristic
705	#418	C₂²×C₃₁	1	1	yes	characteristic
706	#416	C₂²×C₃₁	1	1	yes	characteristic
707	#416	C₂²×C₃₁	1	1	yes	characteristic
708	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
709	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
710	C₂×C₃₁	—	2	2	no	—
711	C₂×C₃₁	—	4	2	no	—
712	C₂×C₃₁	—	8	1	no	—
713	C₂×C₃₁	—	8	2	no	—
714	C₂×C₃₁	—	8	2	no	—
715	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
716	C₂×C₃₁	#3584	1	1	yes	characteristic
717	C₂×C₃₁	#3585	1	1	yes	characteristic
718	C₂×#41	—	2	2	no	—
719	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
721	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
723	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
724	C₂³×C₄	—	2	1	no	—
725	#137	—	4	2	no	—
726	AGL(1,ℤ/8)	—	4	2	no	—
727	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂×SD₁₆	—	4	2	no	—
729	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
733	C₂×D₈	—	4	2	no	—
734	C₂×D₈	C₂³×C₃₁	1	2	yes	—
735	C₂×D₈	C₂³×C₃₁	1	2	yes	—
736	C₂×D₈	C₂³×C₃₁	1	2	yes	—
737	#131	—	4	2	no	—
738	#131	—	4	2	no	—
739	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
744	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
746	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	—	2	1	no	—
749	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
752	#127	—	2	1	no	—
753	#127	—	2	1	no	—
754	#127	C₂³×C₃₁	1	2	yes	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	C₂³×C₃₁	1	1	yes	characteristic
763	#125	C₂³×C₃₁	1	1	yes	characteristic
764	#125	C₂³×C₃₁	1	2	yes	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	—	2	1	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	1	no	—
772	#124	—	2	1	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₃₁	1	2	yes	—
775	#124	C₂³×C₃₁	1	2	yes	—
776	#124	C₂³×C₃₁	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	C₂³×C₃₁	1	2	yes	—
804	#121	C₂³×C₃₁	1	2	yes	—
805	#121	C₂³×C₃₁	1	2	yes	—
806	#121	C₂³×C₃₁	1	2	yes	—
807	#121	C₂³×C₃₁	1	2	yes	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
816	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
820	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	D₄×C₃₁	1	2	yes	—
832	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
833	C₄×D₄	D₄×C₃₁	1	2	yes	—
834	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₃₁	1	2	yes	—
840	C₄×D₄	C₂³×C₃₁	1	2	yes	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	C₂³×C₃₁	1	1	yes	characteristic
847	#117	C₂³×C₃₁	1	1	yes	characteristic
848	#117	C₂³×C₃₁	1	1	yes	characteristic
849	#117	C₂³×C₃₁	1	1	yes	characteristic
850	#117	C₂³×C₃₁	1	2	yes	—
851	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
852	C₂×C₂²⋊C₄	—	2	1	no	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	2	no	—
856	C₂×C₄²	—	2	1	no	—
857	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
858	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
859	#107	C₂³×C₃₁	1	1	yes	characteristic
860	#107	C₂³×C₃₁	1	1	yes	characteristic
861	#107	C₂³×C₃₁	1	1	yes	characteristic
862	#107	C₂³×C₃₁	1	1	yes	characteristic
863	#107	C₂³×C₃₁	1	2	yes	—
864	#107	C₂³×C₃₁	1	2	yes	—
865	#106	C₂³×C₃₁	1	1	yes	characteristic
866	#106	C₂³×C₃₁	1	1	yes	characteristic
867	#106	C₂³×C₃₁	1	1	yes	characteristic
868	#106	C₂³×C₃₁	1	1	yes	characteristic
869	#106	C₂³×C₃₁	1	2	yes	—
870	#106	C₂³×C₃₁	1	2	yes	—
871	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄⋊C₈	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	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
881	#103	C₂³×C₃₁	1	2	yes	—
882	#103	C₂³×C₃₁	1	2	yes	—
883	#103	C₂³×C₃₁	1	1	yes	characteristic
884	#103	C₂³×C₃₁	1	1	yes	characteristic
885	#103	C₂³×C₃₁	1	1	yes	characteristic
886	#103	C₂³×C₃₁	1	1	yes	characteristic
887	#103	C₂³×C₃₁	1	2	yes	—
888	#103	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	2	yes	—
890	#102	C₂³×C₃₁	1	2	yes	—
891	#102	C₂³×C₃₁	1	1	yes	characteristic
892	#102	C₂³×C₃₁	1	1	yes	characteristic
893	#102	C₂³×C₃₁	1	1	yes	characteristic
894	#102	C₂³×C₃₁	1	1	yes	characteristic
895	#102	C₂³×C₃₁	1	2	yes	—
896	#102	C₂³×C₃₁	1	2	yes	—
897	#102	C₂³×C₃₁	1	2	yes	—
898	#102	C₂³×C₃₁	1	2	yes	—
899	#102	C₂³×C₃₁	1	2	yes	—
900	#102	C₂³×C₃₁	1	2	yes	—
901	C₃₁	#60926	1	1	yes	characteristic, direct product factor, Sylow
902	C₂⁴	—	2	1	no	—
903	C₂⁴	—	2	1	no	—
904	#41	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	8	4	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
917	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	8	2	no	—
947	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	Q₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	D₈	—	4	2	no	—
959	D₈	—	4	2	no	—
960	D₈	—	4	2	no	—
961	M₁₆	—	2	2	no	—
962	M₁₆	—	2	2	no	—
963	M₁₆	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	C₂×C₈	—	2	2	no	—
966	C₂×C₈	—	2	2	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
970	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1037	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1038	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1039	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1040	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₃₁	1	2	yes	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	1	no	—
1051	C₂³	—	8	1	no	—
1052	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1053	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	8	1	no	—
1061	Q₈	—	8	1	no	—
1062	Q₈	—	8	2	no	—
1063	D₄	—	2	4	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1113	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1114	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1115	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	8	4	no	—
1137	C₂²	—	16	2	no	—
1138	C₂²	C₃₁×#537	1	2	yes	—
1139	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	C₃₁×#537	1	2	yes	—
1157	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1158	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1159	C₂	—	2	2	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	—	8	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
1165	C₂	C₃₁×#3584	1	1	yes	characteristic
1166	C₂	C₃₁×#3585	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3510	C₂	semidirect
2. C₃₁×#3460	C₂	semidirect
3. C₃₁×#3263	C₂	semidirect
4. C₃₁×#3262	C₂	semidirect
5. C₃₁×#3257	C₂	semidirect
6. C₃₁×#3257	C₂	semidirect
7. C₃₁×#3256	C₂	semidirect
8. C₃₁×#3251	C₂	semidirect
9. C₃₁×#3250	C₂	semidirect
10. C₃₁×#3247	C₂	semidirect
11. C₃₁×#3082	C₂	semidirect
12. C₃₁×#3081	C₂	semidirect
13. C₃₁×#3077	C₂	semidirect
14. C₃₁×#3076	C₂	semidirect
15. C₃₁×#3063	C₂	semidirect
16. C₃₁×#3062	C₂	semidirect
17. C₃₁×#3058	C₂	semidirect
18. C₃₁×#3057	C₂	semidirect
19. C₃₁×#3043	C₂	semidirect
20. C₃₁×#3041	C₂	semidirect
21. C₃₁×#3040	C₂	semidirect
22. C₂×C₃₁×#463	C₂	semidirect
23. C₃₁×#2906	C₂	semidirect
38. C₃₁×#542	C₂²	semidirect
39. C₃₁×#542	C₂²	semidirect
40. C₃₁×#542	C₂²	semidirect
42. C₃₁×#540	C₂²	semidirect
51. C₃₁×#532	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
54. C₃₁×#529	C₂²	semidirect
55. C₃₁×#529	C₂²	semidirect
63. C₃₁×#479	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#478	C₂²	semidirect
70. C₃₁×#478	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#477	C₂²	semidirect
74. C₃₁×#477	C₂²	semidirect
75. C₃₁×#476	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
82. C₃₁×#474	C₂²	semidirect
83. C₃₁×#470	C₂²	semidirect
86. C₃₁×#469	C₂²	semidirect
87. C₃₁×#468	C₂²	semidirect
88. C₃₁×#468	C₂²	semidirect
89. C₃₁×#468	C₂²	semidirect
90. C₃₁×#468	C₂²	semidirect
91. C₃₁×#467	C₂²	semidirect
94. C₃₁×#466	C₂²	semidirect
95. C₃₁×#465	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
97. C₃₁×#465	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#464	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
102. C₃₁×#464	C₂²	semidirect
109. C₃₁×#463	C₂²	semidirect
110. C₃₁×#463	C₂²	semidirect
111. C₃₁×#460	C₂²	semidirect
112. C₃₁×#460	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
124. C₃₁×#423	C₂²	semidirect
126. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
459. #60926	C₃₁	direct (N × H)
539. #3510	C₂×C₃₁	semidirect
540. #3460	C₂×C₃₁	semidirect
541. #3263	C₂×C₃₁	semidirect
542. #3262	C₂×C₃₁	semidirect
543. #3257	C₂×C₃₁	semidirect
544. #3257	C₂×C₃₁	semidirect
545. #3256	C₂×C₃₁	semidirect
546. #3251	C₂×C₃₁	semidirect
547. #3250	C₂×C₃₁	semidirect
548. #3247	C₂×C₃₁	semidirect
549. #3082	C₂×C₃₁	semidirect
550. #3081	C₂×C₃₁	semidirect
551. #3077	C₂×C₃₁	semidirect
552. #3076	C₂×C₃₁	semidirect
553. #3063	C₂×C₃₁	semidirect
554. #3062	C₂×C₃₁	semidirect
555. #3058	C₂×C₃₁	semidirect
556. #3057	C₂×C₃₁	semidirect
557. #3043	C₂×C₃₁	semidirect
558. #3041	C₂×C₃₁	semidirect
559. #3040	C₂×C₃₁	semidirect
560. C₂×#463	C₂×C₃₁	semidirect
561. #2906	C₂×C₃₁	semidirect
613. #542	C₂²×C₃₁	semidirect
614. #542	C₂²×C₃₁	semidirect
615. #542	C₂²×C₃₁	semidirect
617. #540	C₂²×C₃₁	semidirect
626. #532	C₂²×C₃₁	semidirect
628. #529	C₂²×C₃₁	semidirect
629. #529	C₂²×C₃₁	semidirect
630. #529	C₂²×C₃₁	semidirect
638. #479	C₂²×C₃₁	semidirect
639. #479	C₂²×C₃₁	semidirect
640. #479	C₂²×C₃₁	semidirect
641. #479	C₂²×C₃₁	semidirect
642. #478	C₂²×C₃₁	semidirect
643. #478	C₂²×C₃₁	semidirect
644. #478	C₂²×C₃₁	semidirect
645. #478	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #477	C₂²×C₃₁	semidirect
649. #477	C₂²×C₃₁	semidirect
650. #476	C₂²×C₃₁	semidirect
651. #476	C₂²×C₃₁	semidirect
652. #476	C₂²×C₃₁	semidirect
653. #475	C₂²×C₃₁	semidirect
654. #475	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
656. #474	C₂²×C₃₁	semidirect
657. #474	C₂²×C₃₁	semidirect
658. #470	C₂²×C₃₁	semidirect
661. #469	C₂²×C₃₁	semidirect
662. #468	C₂²×C₃₁	semidirect
663. #468	C₂²×C₃₁	semidirect
664. #468	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
666. #467	C₂²×C₃₁	semidirect
669. #466	C₂²×C₃₁	semidirect
670. #465	C₂²×C₃₁	semidirect
671. #465	C₂²×C₃₁	semidirect
672. #465	C₂²×C₃₁	semidirect
673. #465	C₂²×C₃₁	semidirect
674. #464	C₂²×C₃₁	semidirect
675. #464	C₂²×C₃₁	semidirect
676. #464	C₂²×C₃₁	semidirect
677. #464	C₂²×C₃₁	semidirect
684. #463	C₂²×C₃₁	semidirect
685. #463	C₂²×C₃₁	semidirect
686. #460	C₂²×C₃₁	semidirect
687. #460	C₂²×C₃₁	semidirect
696. #424	C₂²×C₃₁	semidirect
697. #424	C₂²×C₃₁	semidirect
699. #423	C₂²×C₃₁	semidirect
701. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
901. C₃₁	#60926	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×#3460	2
C₃₁×#3263	2
C₃₁×#3262	2
C₃₁×#3257	2
C₃₁×#3256	2
C₃₁×#3251	2
C₃₁×#3250	2
C₃₁×#3247	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3077	2
C₃₁×#3076	2
C₃₁×#3063	2
C₃₁×#3062	2
C₃₁×#3058	2
C₃₁×#3057	2
C₃₁×#3043	2
C₃₁×#3041	2
C₃₁×#3040	2
C₂×C₃₁×#463	2
C₃₁×#2906	2
#60926	31

Subgroups — C31×#60926 #21517685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60926 #21517685