Subgroups — C₃₁×#60875 #21517634

Order 7936.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3458	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3235	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3228	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#555	—	2	1	no	—
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#553	—	2	1	no	—
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#546	—	2	2	no	—
30	C₃₁×#544	—	2	1	no	—
31	C₃₁×#544	—	2	1	no	—
32	C₃₁×#544	C₂²	1	1	yes	characteristic
33	C₃₁×#544	C₂²	1	1	yes	characteristic
34	C₃₁×#544	C₂²	1	1	yes	characteristic
35	C₃₁×#544	C₂²	1	1	yes	characteristic
36	C₃₁×#544	C₂²	1	1	yes	characteristic
37	C₃₁×#544	C₂²	1	2	yes	complemented
38	C₃₁×#544	C₂²	1	2	yes	complemented
39	C₃₁×#543	—	2	2	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#540	C₂²	1	2	yes	—
42	C₃₁×#535	C₂²	1	1	yes	characteristic
43	C₃₁×#533	—	2	2	no	—
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	—	2	1	no	—
46	C₃₁×#533	C₂²	1	2	yes	complemented
47	C₃₁×#533	C₂²	1	2	yes	complemented
48	C₃₁×#532	C₂²	1	2	yes	—
49	C₃₁×#529	C₂²	1	2	yes	—
50	C₃₁×#525	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
52	C₃₁×#520	C₂²	1	1	yes	characteristic
53	C₃₁×#518	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#501	C₂²	1	2	yes	complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#501	C₂²	1	2	yes	complemented
61	C₃₁×#500	C₂²	1	2	yes	complemented
62	C₃₁×#499	C₂²	1	2	yes	complemented
63	C₃₁×#499	C₂²	1	2	yes	complemented
64	C₃₁×#498	C₂²	1	2	yes	complemented
65	C₃₁×#490	C₂²	1	2	yes	complemented
66	C₃₁×#490	C₂²	1	2	yes	complemented
67	C₃₁×#489	C₂²	1	2	yes	complemented
68	C₃₁×#489	C₂²	1	2	yes	complemented
69	C₃₁×#488	C₂²	1	2	yes	complemented
70	C₃₁×#488	C₂²	1	2	yes	complemented
71	C₃₁×#486	C₂²	1	2	yes	complemented
72	C₃₁×#486	C₂²	1	2	yes	complemented
73	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#485	C₂²	1	2	yes	complemented
77	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#482	C₂²	1	2	yes	—
80	C₃₁×#482	C₂²	1	2	yes	—
81	C₃₁×#482	C₂²	1	2	yes	—
82	C₃₁×#482	C₂²	1	2	yes	—
83	C₃₁×#482	C₂²	1	2	yes	—
84	C₃₁×#482	C₂²	1	2	yes	—
85	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#482	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#482	C₂²	1	2	yes	complemented
88	C₃₁×#482	C₂²	1	2	yes	complemented
89	C₃₁×#481	C₂²	1	2	yes	—
90	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#480	C₂²	1	2	yes	—
92	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#479	C₂²	1	2	yes	complemented
94	C₃₁×#479	C₂²	1	2	yes	complemented
95	C₃₁×#478	C₂²	1	2	yes	complemented
96	C₃₁×#478	C₂²	1	2	yes	complemented
97	C₃₁×#478	C₂²	1	2	yes	complemented
98	C₃₁×#478	C₂²	1	2	yes	complemented
99	C₃₁×#478	C₂²	1	2	yes	complemented
100	C₃₁×#478	C₂²	1	2	yes	complemented
101	C₃₁×#477	C₂²	1	2	yes	complemented
102	C₃₁×#476	C₂²	1	2	yes	complemented
103	C₃₁×#476	C₂²	1	2	yes	complemented
104	C₃₁×#476	C₂²	1	2	yes	complemented
105	C₃₁×#475	C₂²	1	2	yes	complemented
106	C₃₁×#474	C₂²	1	2	yes	complemented
107	C₃₁×#474	C₂²	1	2	yes	complemented
108	C₃₁×#474	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#433	C₂²	1	2	yes	complemented
111	C₃₁×#432	C₂²	1	2	yes	complemented
112	C₃₁×#431	C₂²	1	2	yes	complemented
113	C₃₁×#428	C₂²	1	1	yes	characteristic
114	C₃₁×#428	C₂²	1	1	yes	characteristic
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	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
120	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
121	C₃₁×#424	C₂²	1	1	yes	characteristic
122	C₃₁×#424	C₂²	1	1	yes	characteristic
123	C₃₁×#418	C₂²	1	1	yes	characteristic
124	C₃₁×#418	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₃₁×#407	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₃₁×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	—	2	1	no	—
145	C₃₁×C₄⋊Q₈	—	2	1	no	—
146	C₃₁×C₄⋊Q₈	—	2	1	no	—
147	C₃₁×C₄⋊Q₈	—	2	1	no	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	—	2	1	no	—
151	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×#127	C₂³	1	2	yes	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#125	—	2	1	no	—
160	C₃₁×#125	—	2	1	no	—
161	C₃₁×#125	—	2	1	no	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	C₂³	1	2	yes	—
167	C₃₁×#125	C₂³	1	2	yes	—
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#123	—	2	1	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₃₁×#121	—	2	1	no	—
196	C₃₁×#121	—	2	1	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	1	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	C₂³	1	2	yes	—
203	C₃₁×#121	C₂³	1	1	yes	characteristic
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	1	yes	characteristic
206	C₃₁×#120	—	2	1	no	—
207	C₃₁×#120	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	2	no	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×D₄×C₃₁	—	2	1	no	—
214	C₄×D₄×C₃₁	—	2	1	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₃₁×#117	—	2	1	no	—
224	C₃₁×#117	—	2	1	no	—
225	C₃₁×#117	—	2	1	no	—
226	C₃₁×#117	—	2	1	no	—
227	C₃₁×#117	—	2	1	no	—
228	C₃₁×#117	—	2	2	no	—
229	C₃₁×#117	D₄	1	2	yes	—
230	C₃₁×#117	D₄	1	1	yes	characteristic
231	C₃₁×#117	D₄	1	1	yes	characteristic
232	C₃₁×#117	C₂³	1	1	yes	characteristic
233	C₃₁×#117	C₂³	1	1	yes	characteristic
234	C₃₁×#117	C₂³	1	1	yes	characteristic
235	C₃₁×#117	C₂³	1	2	yes	—
236	C₃₁×#117	C₂³	1	1	yes	characteristic
237	C₃₁×#117	C₂³	1	1	yes	characteristic
238	C₃₁×#117	C₂³	1	2	yes	—
239	C₃₁×#117	C₂³	1	1	yes	characteristic
240	C₃₁×#117	C₂³	1	1	yes	characteristic
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
251	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
255	C₂×C₄²×C₃₁	—	2	1	no	—
256	C₂×C₄²×C₃₁	—	2	1	no	—
257	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
258	C₃₁×#107	C₂³	1	2	yes	—
259	C₃₁×#107	C₂³	1	2	yes	—
260	C₃₁×#107	C₂³	1	1	yes	characteristic
261	C₃₁×#107	C₂³	1	1	yes	characteristic
262	C₃₁×#107	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×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	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×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#102	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	1	no	—
313	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
314	#41×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	8	4	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₃₁	—	2	1	no	—
324	C₂×D₄×C₃₁	—	2	1	no	—
325	C₂×D₄×C₃₁	—	2	2	no	—
326	C₂×D₄×C₃₁	—	2	1	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	8	2	no	—
334	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
335	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	—	2	2	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	M₁₆×C₃₁	—	2	2	no	—
356	M₁₆×C₃₁	—	2	2	no	—
357	C₂×C₈×C₃₁	—	2	2	no	—
358	C₂×C₈×C₃₁	—	2	2	no	—
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	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	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₃₁	—	2	1	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	1	no	—
406	C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	1	no	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	C₂×D₄	1	2	yes	—
435	C₄²×C₃₁	C₂⁴	1	2	yes	—
436	C₄²×C₃₁	C₂⁴	1	2	yes	—
437	#60875	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂³×C₃₁	—	2	2	no	—
439	C₂³×C₃₁	—	2	2	no	—
440	C₂³×C₃₁	—	2	1	no	—
441	C₂³×C₃₁	—	4	1	no	—
442	C₂³×C₃₁	—	4	1	no	—
443	C₂³×C₃₁	—	4	2	no	—
444	C₂³×C₃₁	—	8	1	no	—
445	C₂³×C₃₁	—	8	1	no	—
446	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₃₁	—	2	1	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	8	2	no	—
452	Q₈×C₃₁	—	8	2	no	—
453	Q₈×C₃₁	—	8	2	no	—
454	Q₈×C₃₁	—	8	2	no	—
455	Q₈×C₃₁	—	8	2	no	—
456	D₄×C₃₁	—	2	2	no	—
457	D₄×C₃₁	—	2	2	no	—
458	D₄×C₃₁	—	2	1	no	—
459	D₄×C₃₁	—	2	1	no	—
460	D₄×C₃₁	—	4	4	no	—
461	D₄×C₃₁	—	4	2	no	—
462	D₄×C₃₁	—	4	2	no	—
463	D₄×C₃₁	—	4	2	no	—
464	D₄×C₃₁	—	8	2	no	—
465	D₄×C₃₁	—	8	2	no	—
466	D₄×C₃₁	—	8	1	no	—
467	D₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	4	2	no	—
486	C₂×C₄×C₃₁	—	4	2	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	8	2	no	—
489	C₂×C₄×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	—	8	2	no	—
491	C₂×C₄×C₃₁	—	8	1	no	—
492	C₂×C₄×C₃₁	—	8	1	no	—
493	C₂×C₄×C₃₁	—	8	1	no	—
494	C₂×C₄×C₃₁	—	8	1	no	—
495	C₂×C₄×C₃₁	—	8	1	no	—
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
504	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
505	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
506	C₈×C₃₁	—	2	1	no	—
507	C₈×C₃₁	—	2	1	no	—
508	C₈×C₃₁	—	2	1	no	—
509	C₈×C₃₁	—	2	1	no	—
510	C₈×C₃₁	—	2	2	no	—
511	C₈×C₃₁	—	2	2	no	—
512	#3494	C₂×C₃₁	1	1	yes	characteristic
513	#3458	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3244	C₂×C₃₁	1	2	yes	complemented
515	#3243	C₂×C₃₁	1	2	yes	complemented
516	#3241	C₂×C₃₁	1	2	yes	complemented
517	#3241	C₂×C₃₁	1	2	yes	complemented
518	#3240	C₂×C₃₁	1	2	yes	complemented
519	#3235	C₂×C₃₁	1	2	yes	complemented
520	#3233	C₂×C₃₁	1	2	yes	complemented
521	#3228	C₂×C₃₁	1	2	yes	complemented
522	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3136	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3093	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
529	C₂×#482	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
535	C₂²×C₃₁	—	2	1	no	—
536	C₂²×C₃₁	—	2	1	no	—
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	1	no	—
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	1	no	—
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	4	2	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	2	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	2	no	—
549	C₂²×C₃₁	—	8	2	no	—
550	C₂²×C₃₁	—	16	2	no	—
551	C₂²×C₃₁	#536	1	2	yes	—
552	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₃₁	—	2	2	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	2	2	no	—
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	4	1	no	—
560	C₄×C₃₁	—	4	2	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	#536	1	2	yes	—
570	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
571	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
572	#555	—	2	1	no	—
573	#553	—	2	1	no	—
574	#553	—	2	1	no	—
575	#551	—	2	2	no	—
576	#547	—	2	1	no	—
577	#546	—	2	2	no	—
578	#544	—	2	1	no	—
579	#544	—	2	1	no	—
580	#544	C₂²×C₃₁	1	1	yes	characteristic
581	#544	C₂²×C₃₁	1	1	yes	characteristic
582	#544	C₂²×C₃₁	1	1	yes	characteristic
583	#544	C₂²×C₃₁	1	1	yes	characteristic
584	#544	C₂²×C₃₁	1	1	yes	characteristic
585	#544	C₂²×C₃₁	1	2	yes	complemented
586	#544	C₂²×C₃₁	1	2	yes	complemented
587	#543	—	2	2	no	—
588	#542	C₂²×C₃₁	1	2	yes	—
589	#540	C₂²×C₃₁	1	2	yes	—
590	#535	C₂²×C₃₁	1	1	yes	characteristic
591	#533	—	2	2	no	—
592	#533	—	2	1	no	—
593	#533	—	2	1	no	—
594	#533	C₂²×C₃₁	1	2	yes	complemented
595	#533	C₂²×C₃₁	1	2	yes	complemented
596	#532	C₂²×C₃₁	1	2	yes	—
597	#529	C₂²×C₃₁	1	2	yes	—
598	#525	C₂²×C₃₁	1	1	yes	characteristic
599	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
600	#520	C₂²×C₃₁	1	1	yes	characteristic
601	#518	C₂²×C₃₁	1	1	yes	characteristic
602	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
603	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
605	#501	C₂²×C₃₁	1	2	yes	complemented
606	#501	C₂²×C₃₁	1	2	yes	complemented
607	#501	C₂²×C₃₁	1	2	yes	complemented
608	#501	C₂²×C₃₁	1	2	yes	complemented
609	#500	C₂²×C₃₁	1	2	yes	complemented
610	#499	C₂²×C₃₁	1	2	yes	complemented
611	#499	C₂²×C₃₁	1	2	yes	complemented
612	#498	C₂²×C₃₁	1	2	yes	complemented
613	#490	C₂²×C₃₁	1	2	yes	complemented
614	#490	C₂²×C₃₁	1	2	yes	complemented
615	#489	C₂²×C₃₁	1	2	yes	complemented
616	#489	C₂²×C₃₁	1	2	yes	complemented
617	#488	C₂²×C₃₁	1	2	yes	complemented
618	#488	C₂²×C₃₁	1	2	yes	complemented
619	#486	C₂²×C₃₁	1	2	yes	complemented
620	#486	C₂²×C₃₁	1	2	yes	complemented
621	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#485	C₂²×C₃₁	1	2	yes	complemented
624	#485	C₂²×C₃₁	1	2	yes	complemented
625	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#482	C₂²×C₃₁	1	2	yes	—
628	#482	C₂²×C₃₁	1	2	yes	—
629	#482	C₂²×C₃₁	1	2	yes	—
630	#482	C₂²×C₃₁	1	2	yes	—
631	#482	C₂²×C₃₁	1	2	yes	—
632	#482	C₂²×C₃₁	1	2	yes	—
633	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#482	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#482	C₂²×C₃₁	1	2	yes	complemented
636	#482	C₂²×C₃₁	1	2	yes	complemented
637	#481	C₂²×C₃₁	1	2	yes	—
638	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#480	C₂²×C₃₁	1	2	yes	—
640	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#479	C₂²×C₃₁	1	2	yes	complemented
642	#479	C₂²×C₃₁	1	2	yes	complemented
643	#478	C₂²×C₃₁	1	2	yes	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	#478	C₂²×C₃₁	1	2	yes	complemented
649	#477	C₂²×C₃₁	1	2	yes	complemented
650	#476	C₂²×C₃₁	1	2	yes	complemented
651	#476	C₂²×C₃₁	1	2	yes	complemented
652	#476	C₂²×C₃₁	1	2	yes	complemented
653	#475	C₂²×C₃₁	1	2	yes	complemented
654	#474	C₂²×C₃₁	1	2	yes	complemented
655	#474	C₂²×C₃₁	1	2	yes	complemented
656	#474	C₂²×C₃₁	1	2	yes	complemented
657	#433	C₂²×C₃₁	1	2	yes	complemented
658	#433	C₂²×C₃₁	1	2	yes	complemented
659	#432	C₂²×C₃₁	1	2	yes	complemented
660	#431	C₂²×C₃₁	1	2	yes	complemented
661	#428	C₂²×C₃₁	1	1	yes	characteristic
662	#428	C₂²×C₃₁	1	1	yes	characteristic
663	#428	C₂²×C₃₁	1	1	yes	characteristic
664	#428	C₂²×C₃₁	1	1	yes	characteristic
665	#427	C₂²×C₃₁	1	1	yes	characteristic
666	#427	C₂²×C₃₁	1	1	yes	characteristic
667	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
668	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
669	#424	C₂²×C₃₁	1	1	yes	characteristic
670	#424	C₂²×C₃₁	1	1	yes	characteristic
671	#418	C₂²×C₃₁	1	1	yes	characteristic
672	#418	C₂²×C₃₁	1	1	yes	characteristic
673	#417	C₂²×C₃₁	1	1	yes	characteristic
674	#417	C₂²×C₃₁	1	1	yes	characteristic
675	#416	C₂²×C₃₁	1	1	yes	characteristic
676	#416	C₂²×C₃₁	1	1	yes	characteristic
677	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
678	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
679	#407	C₂²×C₃₁	1	1	yes	characteristic
680	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
681	#405	C₂²×C₃₁	1	1	yes	characteristic
682	#405	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×C₃₁	—	2	2	no	—
684	C₂×C₃₁	—	4	1	no	—
685	C₂×C₃₁	—	4	1	no	—
686	C₂×C₃₁	—	8	1	no	—
687	C₂×C₃₁	—	8	2	no	—
688	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
689	C₂×C₃₁	#3584	1	1	yes	characteristic
690	C₂×C₃₁	#3585	1	1	yes	characteristic
691	C₂×#41	—	2	2	no	—
692	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
693	C₂²×D₄	—	2	1	no	—
694	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	—	2	2	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	—	2	1	no	—
707	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
709	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
710	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
711	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	#127	C₂³×C₃₁	1	2	yes	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#125	—	2	1	no	—
716	#125	—	2	1	no	—
717	#125	—	2	1	no	—
718	#125	—	2	1	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	1	no	—
722	#125	C₂³×C₃₁	1	2	yes	—
723	#125	C₂³×C₃₁	1	2	yes	—
724	#125	C₂³×C₃₁	1	2	yes	—
725	#125	C₂³×C₃₁	1	2	yes	—
726	#125	C₂³×C₃₁	1	2	yes	—
727	#124	—	2	2	no	—
728	#124	—	2	2	no	—
729	#124	C₂³×C₃₁	1	2	yes	—
730	#123	—	2	1	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
750	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
751	#121	—	2	1	no	—
752	#121	—	2	1	no	—
753	#121	—	2	2	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	2	no	—
757	#121	—	2	2	no	—
758	#121	C₂³×C₃₁	1	2	yes	—
759	#121	C₂³×C₃₁	1	2	yes	—
760	#121	C₂³×C₃₁	1	1	yes	characteristic
761	#121	C₂³×C₃₁	1	1	yes	characteristic
762	#120	—	2	1	no	—
763	#120	—	2	2	no	—
764	C₄×Q₈	—	2	2	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	—	2	2	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	C₂³×C₃₁	1	2	yes	—
777	C₄×D₄	C₂³×C₃₁	1	2	yes	—
778	C₄×D₄	C₂³×C₃₁	1	2	yes	—
779	#117	—	2	1	no	—
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	—	2	2	no	—
785	#117	D₄×C₃₁	1	2	yes	—
786	#117	D₄×C₃₁	1	1	yes	characteristic
787	#117	D₄×C₃₁	1	1	yes	characteristic
788	#117	C₂³×C₃₁	1	2	yes	—
789	#117	C₂³×C₃₁	1	1	yes	characteristic
790	#117	C₂³×C₃₁	1	1	yes	characteristic
791	#117	C₂³×C₃₁	1	1	yes	characteristic
792	#117	C₂³×C₃₁	1	1	yes	characteristic
793	#117	C₂³×C₃₁	1	2	yes	—
794	#117	C₂³×C₃₁	1	1	yes	characteristic
795	#117	C₂³×C₃₁	1	1	yes	characteristic
796	#117	C₂³×C₃₁	1	1	yes	characteristic
797	#117	C₂³×C₃₁	1	2	yes	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
800	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	—	2	1	no	—
807	C₂×C₂²⋊C₄	—	2	1	no	—
808	C₂×C₂²⋊C₄	—	2	1	no	—
809	C₂×C₂²⋊C₄	—	2	2	no	—
810	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
811	C₂×C₄²	—	2	1	no	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
814	#107	C₂³×C₃₁	1	2	yes	—
815	#107	C₂³×C₃₁	1	2	yes	—
816	#107	C₂³×C₃₁	1	1	yes	characteristic
817	#107	C₂³×C₃₁	1	1	yes	characteristic
818	#107	C₂³×C₃₁	1	1	yes	characteristic
819	#107	C₂³×C₃₁	1	1	yes	characteristic
820	#107	C₂³×C₃₁	1	2	yes	—
821	#107	C₂³×C₃₁	1	2	yes	—
822	#107	C₂³×C₃₁	1	2	yes	—
823	#107	C₂³×C₃₁	1	2	yes	—
824	#106	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	2	yes	—
826	#106	C₂³×C₃₁	1	1	yes	characteristic
827	#106	C₂³×C₃₁	1	1	yes	characteristic
828	#106	C₂³×C₃₁	1	1	yes	characteristic
829	#106	C₂³×C₃₁	1	1	yes	characteristic
830	#106	C₂³×C₃₁	1	2	yes	—
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
835	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	1	yes	characteristic
839	#103	C₂³×C₃₁	1	1	yes	characteristic
840	#103	C₂³×C₃₁	1	1	yes	characteristic
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#102	C₂³×C₃₁	1	2	yes	—
845	#102	C₂³×C₃₁	1	2	yes	—
846	#102	C₂³×C₃₁	1	2	yes	—
847	#102	C₂³×C₃₁	1	2	yes	—
848	#102	C₂³×C₃₁	1	1	yes	characteristic
849	#102	C₂³×C₃₁	1	1	yes	characteristic
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	#102	C₂³×C₃₁	1	1	yes	characteristic
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
864	#97	C₂³×C₃₁	1	2	yes	—
865	#97	C₂³×C₃₁	1	2	yes	—
866	C₄×C₈	C₂³×C₃₁	1	2	yes	—
867	C₄×C₈	C₂³×C₃₁	1	2	yes	—
868	C₃₁	#60875	1	1	yes	characteristic, direct product factor, Sylow
869	C₂⁴	—	2	1	no	—
870	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	8	4	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	8	2	no	—
891	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
892	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
905	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
908	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
912	M₁₆	—	2	2	no	—
913	M₁₆	—	2	2	no	—
914	C₂×C₈	—	2	2	no	—
915	C₂×C₈	—	2	2	no	—
916	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
919	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
920	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	C₂×D₄×C₃₁	1	2	yes	—
991	C₄²	C₂×D₄×C₃₁	1	2	yes	—
992	C₄²	C₂⁴×C₃₁	1	2	yes	—
993	C₄²	C₂⁴×C₃₁	1	2	yes	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	4	1	no	—
998	C₂³	—	4	1	no	—
999	C₂³	—	4	2	no	—
1000	C₂³	—	8	1	no	—
1001	C₂³	—	8	1	no	—
1002	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1004	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	8	2	no	—
1009	Q₈	—	8	2	no	—
1010	Q₈	—	8	2	no	—
1011	Q₈	—	8	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	1	no	—
1023	D₄	—	8	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	—	8	1	no	—
1048	C₂×C₄	—	8	1	no	—
1049	C₂×C₄	—	8	1	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	8	1	no	—
1052	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1055	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1058	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1059	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1060	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1061	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	8	2	no	—
1083	C₂²	—	16	2	no	—
1084	C₂²	C₃₁×#536	1	2	yes	—
1085	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	C₃₁×#536	1	2	yes	—
1103	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1104	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1105	C₂	—	2	2	no	—
1106	C₂	—	4	1	no	—
1107	C₂	—	4	1	no	—
1108	C₂	—	8	2	no	—
1109	C₂	—	8	1	no	—
1110	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
1111	C₂	C₃₁×#3584	1	1	yes	characteristic
1112	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3458	C₂	semidirect
3. C₃₁×#3244	C₂	semidirect
4. C₃₁×#3243	C₂	semidirect
5. C₃₁×#3241	C₂	semidirect
6. C₃₁×#3241	C₂	semidirect
7. C₃₁×#3240	C₂	semidirect
8. C₃₁×#3235	C₂	semidirect
9. C₃₁×#3233	C₂	semidirect
10. C₃₁×#3228	C₂	semidirect
11. C₃₁×#3164	C₂	semidirect
12. C₃₁×#3163	C₂	semidirect
13. C₃₁×#3136	C₂	semidirect
14. C₃₁×#3136	C₂	semidirect
15. C₃₁×#3094	C₂	semidirect
16. C₃₁×#3093	C₂	semidirect
17. C₃₁×#3091	C₂	semidirect
18. C₂×C₃₁×#482	C₂	semidirect
19. C₃₁×#3084	C₂	semidirect
20. C₃₁×#3083	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3081	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
37. C₃₁×#544	C₂²	semidirect
38. C₃₁×#544	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
47. C₃₁×#533	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#501	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#501	C₂²	semidirect
61. C₃₁×#500	C₂²	semidirect
62. C₃₁×#499	C₂²	semidirect
63. C₃₁×#499	C₂²	semidirect
64. C₃₁×#498	C₂²	semidirect
65. C₃₁×#490	C₂²	semidirect
66. C₃₁×#490	C₂²	semidirect
67. C₃₁×#489	C₂²	semidirect
68. C₃₁×#489	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
70. C₃₁×#488	C₂²	semidirect
71. C₃₁×#486	C₂²	semidirect
72. C₃₁×#486	C₂²	semidirect
73. C₃₁×#485	C₂²	semidirect
74. C₃₁×#485	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
76. C₃₁×#485	C₂²	semidirect
77. C₃₁×#484	C₂²	semidirect
78. C₃₁×#483	C₂²	semidirect
85. C₃₁×#482	C₂²	semidirect
86. C₃₁×#482	C₂²	semidirect
87. C₃₁×#482	C₂²	semidirect
88. C₃₁×#482	C₂²	semidirect
90. C₃₁×#481	C₂²	semidirect
92. C₃₁×#480	C₂²	semidirect
93. C₃₁×#479	C₂²	semidirect
94. C₃₁×#479	C₂²	semidirect
95. C₃₁×#478	C₂²	semidirect
96. C₃₁×#478	C₂²	semidirect
97. C₃₁×#478	C₂²	semidirect
98. C₃₁×#478	C₂²	semidirect
99. C₃₁×#478	C₂²	semidirect
100. C₃₁×#478	C₂²	semidirect
101. C₃₁×#477	C₂²	semidirect
102. C₃₁×#476	C₂²	semidirect
103. C₃₁×#476	C₂²	semidirect
104. C₃₁×#476	C₂²	semidirect
105. C₃₁×#475	C₂²	semidirect
106. C₃₁×#474	C₂²	semidirect
107. C₃₁×#474	C₂²	semidirect
108. C₃₁×#474	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#433	C₂²	semidirect
111. C₃₁×#432	C₂²	semidirect
112. C₃₁×#431	C₂²	semidirect
437. #60875	C₃₁	direct (N × H)
513. #3458	C₂×C₃₁	semidirect
514. #3244	C₂×C₃₁	semidirect
515. #3243	C₂×C₃₁	semidirect
516. #3241	C₂×C₃₁	semidirect
517. #3241	C₂×C₃₁	semidirect
518. #3240	C₂×C₃₁	semidirect
519. #3235	C₂×C₃₁	semidirect
520. #3233	C₂×C₃₁	semidirect
521. #3228	C₂×C₃₁	semidirect
522. #3164	C₂×C₃₁	semidirect
523. #3163	C₂×C₃₁	semidirect
524. #3136	C₂×C₃₁	semidirect
525. #3136	C₂×C₃₁	semidirect
526. #3094	C₂×C₃₁	semidirect
527. #3093	C₂×C₃₁	semidirect
528. #3091	C₂×C₃₁	semidirect
529. C₂×#482	C₂×C₃₁	semidirect
530. #3084	C₂×C₃₁	semidirect
531. #3083	C₂×C₃₁	semidirect
532. #3081	C₂×C₃₁	semidirect
533. #3081	C₂×C₃₁	semidirect
534. #2924	C₂×C₃₁	semidirect
585. #544	C₂²×C₃₁	semidirect
586. #544	C₂²×C₃₁	semidirect
594. #533	C₂²×C₃₁	semidirect
595. #533	C₂²×C₃₁	semidirect
605. #501	C₂²×C₃₁	semidirect
606. #501	C₂²×C₃₁	semidirect
607. #501	C₂²×C₃₁	semidirect
608. #501	C₂²×C₃₁	semidirect
609. #500	C₂²×C₃₁	semidirect
610. #499	C₂²×C₃₁	semidirect
611. #499	C₂²×C₃₁	semidirect
612. #498	C₂²×C₃₁	semidirect
613. #490	C₂²×C₃₁	semidirect
614. #490	C₂²×C₃₁	semidirect
615. #489	C₂²×C₃₁	semidirect
616. #489	C₂²×C₃₁	semidirect
617. #488	C₂²×C₃₁	semidirect
618. #488	C₂²×C₃₁	semidirect
619. #486	C₂²×C₃₁	semidirect
620. #486	C₂²×C₃₁	semidirect
621. #485	C₂²×C₃₁	semidirect
622. #485	C₂²×C₃₁	semidirect
623. #485	C₂²×C₃₁	semidirect
624. #485	C₂²×C₃₁	semidirect
625. #484	C₂²×C₃₁	semidirect
626. #483	C₂²×C₃₁	semidirect
633. #482	C₂²×C₃₁	semidirect
634. #482	C₂²×C₃₁	semidirect
635. #482	C₂²×C₃₁	semidirect
636. #482	C₂²×C₃₁	semidirect
638. #481	C₂²×C₃₁	semidirect
640. #480	C₂²×C₃₁	semidirect
641. #479	C₂²×C₃₁	semidirect
642. #479	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. #478	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. #474	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
656. #474	C₂²×C₃₁	semidirect
657. #433	C₂²×C₃₁	semidirect
658. #433	C₂²×C₃₁	semidirect
659. #432	C₂²×C₃₁	semidirect
660. #431	C₂²×C₃₁	semidirect
868. C₃₁	#60875	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×#3494	2
C₃₁×#3458	2
C₃₁×#3244	2
C₃₁×#3243	2
C₃₁×#3241	2
C₃₁×#3240	2
C₃₁×#3235	2
C₃₁×#3233	2
C₃₁×#3228	2
C₃₁×#3164	2
C₃₁×#3163	2
C₃₁×#3136	2
C₃₁×#3094	2
C₃₁×#3093	2
C₃₁×#3091	2
C₂×C₃₁×#482	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3081	2
C₃₁×#2924	2
#60875	31

Subgroups — C31×#60875 #21517634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60875 #21517634