Subgroups — C₃₁×#62188 #21518947

Order 7936.

1756 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3351	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3260	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	C₂²	1	2	yes	complemented
31	C₃₁×#555	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#553	C₂²	1	2	yes	—
36	C₃₁×#552	C₂²	1	2	yes	complemented
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#546	—	2	2	no	—
40	D₄²×C₃₁	C₂²	1	1	yes	characteristic
41	D₄²×C₃₁	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#541	—	2	2	no	—
45	C₃₁×#541	—	2	1	no	—
46	C₃₁×#541	C₂²	1	2	yes	complemented
47	C₃₁×#540	C₂²	1	2	yes	—
48	C₃₁×#538	—	2	2	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×#121	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×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×#499	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#486	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#481	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#476	C₂²	1	1	yes	characteristic
86	C₃₁×#476	C₂²	1	1	yes	characteristic
87	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#476	C₂²	1	2	yes	complemented
89	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#474	C₂²	1	1	yes	characteristic
91	C₃₁×#474	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#474	C₂²	1	2	yes	complemented
94	C₃₁×#468	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#468	C₂²	1	2	yes	complemented
97	C₃₁×#468	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic
101	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#461	C₂²	1	2	yes	complemented
103	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	2	yes	complemented
105	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#460	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	1	yes	characteristic
108	C₃₁×#450	C₂²	1	1	yes	characteristic
109	C₃₁×#450	C₂²	1	2	yes	—
110	C₃₁×#450	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×#440	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	2	yes	complemented
122	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
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×#418	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	C₂²×D₄×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	—	2	2	no	—
139	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×#127	C₂³	1	1	yes	characteristic
162	C₃₁×#127	C₂³	1	2	yes	—
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	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	D₄	1	2	yes	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	D₄	1	1	yes	characteristic
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	D₄	1	1	yes	characteristic
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	D₄	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#120	—	2	2	no	—
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	2	yes	—
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×#106	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	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	1	yes	characteristic
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	2	yes	—
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	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	1	no	—
313	C₂⁴×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	#41×C₃₁	—	8	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₃₁	—	2	2	no	—
325	C₂×D₄×C₃₁	—	2	4	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	4	2	no	—
336	C₂×D₄×C₃₁	—	4	1	no	—
337	C₂×D₄×C₃₁	—	8	2	no	—
338	C₂×D₄×C₃₁	—	8	4	no	—
339	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	8	2	no	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
358	SD₁₆×C₃₁	—	2	2	no	—
359	SD₁₆×C₃₁	—	2	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	2	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	SD₁₆×C₃₁	—	4	1	no	—
364	M₁₆×C₃₁	—	4	2	no	—
365	M₁₆×C₃₁	—	4	2	no	—
366	C₂×C₈×C₃₁	—	4	2	no	—
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
372	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₂²⋊C₄×C₃₁	—	2	2	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	1	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	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
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	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	2	yes	—
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	#62188	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	2	2	no	—
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	4	2	no	—
448	C₂³×C₃₁	—	4	4	no	—
449	C₂³×C₃₁	—	4	2	no	—
450	C₂³×C₃₁	—	8	1	no	—
451	C₂³×C₃₁	—	8	2	no	—
452	C₂³×C₃₁	—	8	2	no	—
453	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	4	2	no	—
461	Q₈×C₃₁	—	8	1	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	4	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	4	4	no	—
475	D₄×C₃₁	—	4	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	1	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	4	1	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	8	1	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	1	no	—
518	C₈×C₃₁	—	2	2	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	2	no	—
521	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3519	C₂×C₃₁	1	1	yes	characteristic
523	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3351	C₂×C₃₁	1	2	yes	complemented
529	#3350	C₂×C₃₁	1	2	yes	complemented
530	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3324	C₂×C₃₁	1	2	yes	complemented
533	#3310	C₂×C₃₁	1	2	yes	complemented
534	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3260	C₂×C₃₁	1	2	yes	complemented
536	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3241	C₂×C₃₁	1	2	yes	complemented
538	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3123	C₂×C₃₁	1	2	yes	complemented
540	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3081	C₂×C₃₁	1	2	yes	complemented
542	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	2	no	—
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	2	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	8	4	no	—
560	C₂²×C₃₁	—	16	4	no	—
561	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	1	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	#577	1	2	yes	—
579	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
580	C₄×C₃₁	#585	1	1	yes	characteristic
581	#563	—	2	2	no	—
582	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#557	—	2	1	no	—
584	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	#556	—	2	1	no	—
586	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#556	C₂²×C₃₁	1	2	yes	complemented
588	#555	C₂²×C₃₁	1	1	yes	characteristic
589	#554	C₂²×C₃₁	1	1	yes	characteristic
590	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	#553	—	2	1	no	—
592	#553	C₂²×C₃₁	1	2	yes	—
593	#552	C₂²×C₃₁	1	2	yes	complemented
594	#550	C₂²×C₃₁	1	1	yes	characteristic
595	#546	—	2	1	no	—
596	#546	—	2	2	no	—
597	D₄²	C₂²×C₃₁	1	1	yes	characteristic
598	D₄²	C₂²×C₃₁	1	2	yes	—
599	#544	C₂²×C₃₁	1	2	yes	complemented
600	#542	—	2	1	no	—
601	#541	—	2	2	no	—
602	#541	—	2	1	no	—
603	#541	C₂²×C₃₁	1	2	yes	complemented
604	#540	C₂²×C₃₁	1	2	yes	—
605	#538	—	2	2	no	—
606	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#532	C₂²×C₃₁	1	1	yes	characteristic
609	#529	C₂²×C₃₁	1	1	yes	characteristic
610	#525	—	2	1	no	—
611	C₂×#121	—	2	1	no	—
612	#518	C₂²×C₃₁	1	2	yes	—
613	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
614	#501	C₂²×C₃₁	1	2	yes	complemented
615	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#499	C₂²×C₃₁	1	2	yes	complemented
617	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#490	C₂²×C₃₁	1	2	yes	complemented
619	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#486	C₂²×C₃₁	1	2	yes	complemented
621	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#485	C₂²×C₃₁	1	2	yes	complemented
623	#485	C₂²×C₃₁	1	2	yes	complemented
624	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#482	C₂²×C₃₁	1	2	yes	complemented
627	#482	C₂²×C₃₁	1	2	yes	complemented
628	#482	C₂²×C₃₁	1	2	yes	complemented
629	#482	C₂²×C₃₁	1	2	yes	complemented
630	#481	C₂²×C₃₁	1	2	yes	complemented
631	#480	C₂²×C₃₁	1	2	yes	complemented
632	#479	C₂²×C₃₁	1	2	yes	complemented
633	#479	C₂²×C₃₁	1	2	yes	complemented
634	#478	C₂²×C₃₁	1	2	yes	—
635	#478	C₂²×C₃₁	1	2	yes	—
636	#478	C₂²×C₃₁	1	2	yes	complemented
637	#478	C₂²×C₃₁	1	2	yes	complemented
638	#478	C₂²×C₃₁	1	2	yes	complemented
639	#478	C₂²×C₃₁	1	2	yes	complemented
640	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#476	C₂²×C₃₁	1	1	yes	characteristic
643	#476	C₂²×C₃₁	1	1	yes	characteristic
644	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#476	C₂²×C₃₁	1	2	yes	complemented
646	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#474	C₂²×C₃₁	1	1	yes	characteristic
648	#474	C₂²×C₃₁	1	2	yes	—
649	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#474	C₂²×C₃₁	1	2	yes	complemented
651	#468	C₂²×C₃₁	1	2	yes	complemented
652	#468	C₂²×C₃₁	1	2	yes	complemented
653	#468	C₂²×C₃₁	1	2	yes	complemented
654	#468	C₂²×C₃₁	1	2	yes	complemented
655	#465	C₂²×C₃₁	1	2	yes	complemented
656	#465	C₂²×C₃₁	1	2	yes	complemented
657	#461	C₂²×C₃₁	1	1	yes	characteristic
658	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#461	C₂²×C₃₁	1	2	yes	complemented
660	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#460	C₂²×C₃₁	1	2	yes	complemented
662	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#460	C₂²×C₃₁	1	2	yes	complemented
664	#450	C₂²×C₃₁	1	1	yes	characteristic
665	#450	C₂²×C₃₁	1	1	yes	characteristic
666	#450	C₂²×C₃₁	1	2	yes	—
667	#450	C₂²×C₃₁	1	2	yes	—
668	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#440	C₂²×C₃₁	1	2	yes	—
671	#440	C₂²×C₃₁	1	2	yes	complemented
672	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
675	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#436	C₂²×C₃₁	1	2	yes	complemented
679	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#435	C₂²×C₃₁	1	2	yes	complemented
681	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#433	C₂²×C₃₁	1	2	yes	complemented
683	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#428	C₂²×C₃₁	1	2	yes	complemented
685	#428	C₂²×C₃₁	1	2	yes	complemented
686	#427	C₂²×C₃₁	1	2	yes	complemented
687	#424	C₂²×C₃₁	1	2	yes	complemented
688	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#418	C₂²×C₃₁	1	2	yes	—
690	#418	C₂²×C₃₁	1	2	yes	—
691	C₂×#102	C₂²×C₃₁	1	2	yes	—
692	C₂×C₃₁	—	4	1	no	—
693	C₂×C₃₁	—	4	2	no	—
694	C₂×C₃₁	—	4	2	no	—
695	C₂×C₃₁	—	8	1	no	—
696	C₂×C₃₁	—	8	2	no	—
697	C₂×C₃₁	#3489	1	1	yes	characteristic
698	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
699	C₂×C₃₁	#3585	1	1	yes	characteristic
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂²×D₄	—	2	1	no	—
703	C₂²×D₄	—	2	2	no	—
704	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
705	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
706	C₂³×C₄	—	2	1	no	—
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	2	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	2	no	—
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	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
726	#127	C₂³×C₃₁	1	1	yes	characteristic
727	#127	C₂³×C₃₁	1	2	yes	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	D₄×C₃₁	1	2	yes	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	2	no	—
739	#125	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	1	no	—
743	#125	D₄×C₃₁	1	1	yes	characteristic
744	#125	C₂³×C₃₁	1	2	yes	—
745	#125	C₂³×C₃₁	1	2	yes	—
746	#125	C₂³×C₃₁	1	2	yes	—
747	#124	—	2	1	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	1	no	—
751	#124	D₄×C₃₁	1	1	yes	characteristic
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	D₄×C₃₁	1	2	yes	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	D₄×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	#120	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	2	yes	—
812	C₄×D₄	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	C₂³×C₃₁	1	2	yes	—
818	#117	C₂³×C₃₁	1	2	yes	—
819	#117	C₂³×C₃₁	1	2	yes	—
820	#117	C₂³×C₃₁	1	2	yes	—
821	C₂×C₄⋊C₄	—	2	1	no	—
822	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
834	#106	C₂³×C₃₁	1	1	yes	characteristic
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	2	yes	—
838	#106	C₂³×C₃₁	1	2	yes	—
839	#106	C₂³×C₃₁	1	1	yes	characteristic
840	#106	C₂³×C₃₁	1	1	yes	characteristic
841	#106	C₂³×C₃₁	1	2	yes	—
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	C₂³×C₃₁	1	1	yes	characteristic
854	#103	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
870	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
873	#97	C₂³×C₃₁	1	2	yes	—
874	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₃₁	1	2	yes	—
877	C₃₁	#62188	1	1	yes	characteristic, direct product factor, Sylow
878	C₂⁴	—	2	1	no	—
879	C₂⁴	—	2	2	no	—
880	#41	—	8	2	no	—
881	#41	—	8	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	1	no	—
903	C₂×D₄	—	8	2	no	—
904	C₂×D₄	—	8	4	no	—
905	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
907	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
908	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	8	2	no	—
920	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
924	SD₁₆	—	2	2	no	—
925	SD₁₆	—	2	2	no	—
926	SD₁₆	—	4	1	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	4	2	no	—
932	C₂×C₈	—	4	2	no	—
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	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
938	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	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	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	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	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	2	yes	—
1008	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	4	4	no	—
1014	C₂³	—	4	2	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	2	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1019	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	4	2	no	—
1026	Q₈	—	8	1	no	—
1027	Q₈	—	8	1	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	1	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	1	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	4	1	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1079	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	8	4	no	—
1102	C₂²	—	16	4	no	—
1103	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₃₁×#577	1	2	yes	—
1121	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1122	C₄	C₃₁×#585	1	1	yes	characteristic
1123	C₂	—	4	1	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	2	no	—
1128	C₂	C₃₁×#3489	1	1	yes	characteristic
1129	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1130	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×#3519	C₂
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×#3555	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3381	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3362	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3351	C₂	semidirect
9. C₃₁×#3350	C₂	semidirect
10. C₃₁×#3340	C₂	semidirect
11. C₃₁×#3324	C₂	semidirect
12. C₃₁×#3324	C₂	semidirect
13. C₃₁×#3310	C₂	semidirect
14. C₃₁×#3295	C₂	semidirect
15. C₃₁×#3260	C₂	semidirect
16. C₃₁×#3254	C₂	semidirect
17. C₃₁×#3241	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3123	C₂	semidirect
20. C₃₁×#3101	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3077	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
25. Q₈²×C₃₁	C₂²	semidirect
27. C₃₁×#557	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
30. C₃₁×#556	C₂²	semidirect
33. C₃₁×#554	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
46. C₃₁×#541	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#499	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#486	C₂²	semidirect
63. C₃₁×#486	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#483	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#481	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#477	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#476	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#468	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
96. C₃₁×#468	C₂²	semidirect
97. C₃₁×#468	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
101. C₃₁×#461	C₂²	semidirect
102. C₃₁×#461	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#460	C₂²	semidirect
106. C₃₁×#460	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	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
443. #62188	C₃₁	direct (N × H)
521. #3555	C₂×C₃₁	semidirect
523. #3385	C₂×C₃₁	semidirect
524. #3381	C₂×C₃₁	semidirect
525. #3368	C₂×C₃₁	semidirect
526. #3362	C₂×C₃₁	semidirect
527. #3357	C₂×C₃₁	semidirect
528. #3351	C₂×C₃₁	semidirect
529. #3350	C₂×C₃₁	semidirect
530. #3340	C₂×C₃₁	semidirect
531. #3324	C₂×C₃₁	semidirect
532. #3324	C₂×C₃₁	semidirect
533. #3310	C₂×C₃₁	semidirect
534. #3295	C₂×C₃₁	semidirect
535. #3260	C₂×C₃₁	semidirect
536. #3254	C₂×C₃₁	semidirect
537. #3241	C₂×C₃₁	semidirect
538. #3228	C₂×C₃₁	semidirect
539. #3123	C₂×C₃₁	semidirect
540. #3101	C₂×C₃₁	semidirect
541. #3081	C₂×C₃₁	semidirect
542. #3077	C₂×C₃₁	semidirect
543. #2993	C₂×C₃₁	semidirect
582. Q₈²	C₂²×C₃₁	semidirect
584. #557	C₂²×C₃₁	semidirect
586. #556	C₂²×C₃₁	semidirect
587. #556	C₂²×C₃₁	semidirect
590. #554	C₂²×C₃₁	semidirect
593. #552	C₂²×C₃₁	semidirect
599. #544	C₂²×C₃₁	semidirect
603. #541	C₂²×C₃₁	semidirect
606. #533	C₂²×C₃₁	semidirect
607. #533	C₂²×C₃₁	semidirect
614. #501	C₂²×C₃₁	semidirect
615. #500	C₂²×C₃₁	semidirect
616. #499	C₂²×C₃₁	semidirect
617. #498	C₂²×C₃₁	semidirect
618. #490	C₂²×C₃₁	semidirect
619. #486	C₂²×C₃₁	semidirect
620. #486	C₂²×C₃₁	semidirect
621. #486	C₂²×C₃₁	semidirect
622. #485	C₂²×C₃₁	semidirect
623. #485	C₂²×C₃₁	semidirect
624. #483	C₂²×C₃₁	semidirect
625. #483	C₂²×C₃₁	semidirect
626. #482	C₂²×C₃₁	semidirect
627. #482	C₂²×C₃₁	semidirect
628. #482	C₂²×C₃₁	semidirect
629. #482	C₂²×C₃₁	semidirect
630. #481	C₂²×C₃₁	semidirect
631. #480	C₂²×C₃₁	semidirect
632. #479	C₂²×C₃₁	semidirect
633. #479	C₂²×C₃₁	semidirect
636. #478	C₂²×C₃₁	semidirect
637. #478	C₂²×C₃₁	semidirect
638. #478	C₂²×C₃₁	semidirect
639. #478	C₂²×C₃₁	semidirect
640. #477	C₂²×C₃₁	semidirect
641. #477	C₂²×C₃₁	semidirect
644. #476	C₂²×C₃₁	semidirect
645. #476	C₂²×C₃₁	semidirect
646. #476	C₂²×C₃₁	semidirect
649. #474	C₂²×C₃₁	semidirect
650. #474	C₂²×C₃₁	semidirect
651. #468	C₂²×C₃₁	semidirect
652. #468	C₂²×C₃₁	semidirect
653. #468	C₂²×C₃₁	semidirect
654. #468	C₂²×C₃₁	semidirect
655. #465	C₂²×C₃₁	semidirect
656. #465	C₂²×C₃₁	semidirect
658. #461	C₂²×C₃₁	semidirect
659. #461	C₂²×C₃₁	semidirect
660. #460	C₂²×C₃₁	semidirect
661. #460	C₂²×C₃₁	semidirect
662. #460	C₂²×C₃₁	semidirect
663. #460	C₂²×C₃₁	semidirect
668. #446	C₂²×C₃₁	semidirect
669. C₈×Q₈	C₂²×C₃₁	semidirect
671. #440	C₂²×C₃₁	semidirect
675. C₄×SD₁₆	C₂²×C₃₁	semidirect
676. C₄×SD₁₆	C₂²×C₃₁	semidirect
677. C₄×SD₁₆	C₂²×C₃₁	semidirect
678. #436	C₂²×C₃₁	semidirect
679. #436	C₂²×C₃₁	semidirect
680. #435	C₂²×C₃₁	semidirect
681. C₈×D₄	C₂²×C₃₁	semidirect
682. #433	C₂²×C₃₁	semidirect
683. #431	C₂²×C₃₁	semidirect
684. #428	C₂²×C₃₁	semidirect
685. #428	C₂²×C₃₁	semidirect
686. #427	C₂²×C₃₁	semidirect
687. #424	C₂²×C₃₁	semidirect
688. #423	C₂²×C₃₁	semidirect
877. C₃₁	#62188	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×#3555	2
C₃₁×#3519	2
C₃₁×#3385	2
C₃₁×#3381	2
C₃₁×#3368	2
C₃₁×#3362	2
C₃₁×#3357	2
C₃₁×#3351	2
C₃₁×#3350	2
C₃₁×#3340	2
C₃₁×#3324	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3260	2
C₃₁×#3254	2
C₃₁×#3241	2
C₃₁×#3228	2
C₃₁×#3123	2
C₃₁×#3101	2
C₃₁×#3081	2
C₃₁×#3077	2
C₃₁×#2993	2
#62188	31

Subgroups — C31×#62188 #21518947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62188 #21518947