Subgroups — C₃₁×#61939 #21518698

Order 7936.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1008 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×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3400	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3219	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#559	C₂²	1	2	yes	—
22	C₃₁×#559	C₂²	1	2	yes	—
23	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#557	C₂²	1	2	yes	complemented
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#556	C₂²	1	2	yes	complemented
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#555	—	2	1	no	—
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#553	—	2	2	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#550	C₂²	1	2	yes	—
35	C₃₁×#547	—	2	1	no	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#541	—	2	1	no	—
39	C₃₁×#541	—	2	2	no	—
40	C₃₁×#541	C₂²	1	2	yes	—
41	C₃₁×#538	—	2	1	no	—
42	C₃₁×#538	—	2	1	no	—
43	C₃₁×#535	C₂²	1	2	yes	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#529	C₂²	1	1	yes	characteristic
48	C₃₁×#525	—	2	2	no	—
49	C₃₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	2	yes	—
52	C₃₁×#497	C₂²	1	2	yes	complemented
53	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#496	C₂²	1	2	yes	—
55	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#495	C₂²	1	2	yes	—
57	C₃₁×#492	C₂²	1	2	yes	—
58	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#490	C₂²	1	2	yes	—
60	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	2	yes	complemented
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#486	C₂²	1	2	yes	—
65	C₃₁×#484	C₂²	1	2	yes	—
66	C₃₁×#483	C₂²	1	1	yes	characteristic
67	C₃₁×#480	C₂²	1	1	yes	characteristic
68	C₃₁×#479	C₂²	1	2	yes	complemented
69	C₃₁×#478	C₂²	1	2	yes	—
70	C₃₁×#478	C₂²	1	2	yes	complemented
71	C₃₁×#477	C₂²	1	2	yes	complemented
72	C₃₁×#474	C₂²	1	2	yes	—
73	C₃₁×#474	C₂²	1	2	yes	complemented
74	C₃₁×#464	C₂²	1	2	yes	—
75	C₃₁×#464	C₂²	1	2	yes	—
76	C₃₁×#464	C₂²	1	2	yes	—
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	—
80	C₃₁×#463	C₂²	1	2	yes	—
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#462	C₂²	1	2	yes	complemented
84	C₃₁×#462	C₂²	1	2	yes	complemented
85	C₃₁×#461	C₂²	1	2	yes	—
86	C₃₁×#461	C₂²	1	2	yes	complemented
87	C₃₁×#460	C₂²	1	2	yes	—
88	C₃₁×#460	C₂²	1	2	yes	—
89	C₃₁×#460	C₂²	1	2	yes	—
90	C₃₁×#460	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#452	C₂²	1	2	yes	—
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	1	yes	characteristic
97	C₃₁×#449	C₂²	1	2	yes	—
98	C₃₁×#447	C₂²	1	1	yes	characteristic
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#446	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#446	C₂²	1	2	yes	complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#441	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₃₁×#440	C₂²	1	2	yes	complemented
110	C₃₁×#440	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
114	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
115	C₃₁×#433	C₂²	1	2	yes	—
116	C₃₁×#433	C₂²	1	2	yes	—
117	C₃₁×#432	C₂²	1	1	yes	characteristic
118	C₃₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	—	2	1	no	—
123	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×D₈×C₃₁	C₂³	1	2	yes	—
134	C₂×D₈×C₃₁	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	—	2	1	no	—
138	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₃₁×#127	C₂³	1	2	yes	—
146	C₃₁×#127	C₂³	1	2	yes	—
147	C₃₁×#127	C₂³	1	1	yes	characteristic
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	2	no	—
151	C₃₁×#126	—	2	2	no	—
152	C₃₁×#126	—	2	2	no	—
153	C₃₁×#126	—	2	2	no	—
154	C₃₁×#126	—	2	2	no	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	1	no	—
157	C₃₁×#125	—	2	2	no	—
158	C₃₁×#125	—	2	2	no	—
159	C₃₁×#125	—	2	2	no	—
160	C₃₁×#125	—	2	2	no	—
161	C₃₁×#125	—	2	2	no	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	D₄	1	2	yes	—
165	C₃₁×#125	C₂³	1	1	yes	characteristic
166	C₃₁×#125	C₂³	1	2	yes	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	2	no	—
170	C₃₁×#124	C₂³	1	1	yes	characteristic
171	C₃₁×#124	C₂³	1	2	yes	—
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#123	—	2	1	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	1	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
190	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
191	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	1	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	C₂³	1	1	yes	characteristic
201	C₃₁×#120	—	2	2	no	—
202	C₃₁×#120	—	2	2	no	—
203	C₄×Q₈×C₃₁	—	2	1	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	—	2	2	no	—
206	C₄×Q₈×C₃₁	—	2	1	no	—
207	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₃₁×#117	—	2	1	no	—
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	—	2	2	no	—
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
241	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
243	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#107	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
251	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×#97	C₂³	1	1	yes	characteristic
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	8	4	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
287	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
289	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
290	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂×D₄×C₃₁	—	2	2	no	—
293	C₂×D₄×C₃₁	—	2	1	no	—
294	C₂×D₄×C₃₁	—	2	1	no	—
295	C₂×D₄×C₃₁	—	2	1	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	4	2	no	—
302	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	1	no	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	2	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	2	no	—
313	C₂²×C₄×C₃₁	—	8	2	no	—
314	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
317	Q₁₆×C₃₁	—	4	2	no	—
318	Q₁₆×C₃₁	—	4	2	no	—
319	Q₁₆×C₃₁	—	4	2	no	—
320	SD₁₆×C₃₁	—	4	2	no	—
321	SD₁₆×C₃₁	—	4	2	no	—
322	SD₁₆×C₃₁	—	4	2	no	—
323	SD₁₆×C₃₁	—	4	2	no	—
324	SD₁₆×C₃₁	—	4	2	no	—
325	SD₁₆×C₃₁	—	4	2	no	—
326	SD₁₆×C₃₁	—	4	2	no	—
327	D₈×C₃₁	—	4	2	no	—
328	D₈×C₃₁	—	4	2	no	—
329	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	1	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	1	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	1	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	1	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	1	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	2	no	—
392	C₄²×C₃₁	—	2	1	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₃₁	C₂⁴	1	2	yes	—
399	C₄²×C₃₁	C₂⁴	1	2	yes	—
400	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	#61939	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	2	2	no	—
406	C₂³×C₃₁	—	4	2	no	—
407	C₂³×C₃₁	—	8	1	no	—
408	C₂³×C₃₁	—	8	1	no	—
409	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₃₁	—	2	2	no	—
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	2	2	no	—
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	4	1	no	—
416	Q₈×C₃₁	—	4	1	no	—
417	Q₈×C₃₁	—	4	2	no	—
418	Q₈×C₃₁	—	8	1	no	—
419	Q₈×C₃₁	—	8	2	no	—
420	D₄×C₃₁	—	2	2	no	—
421	D₄×C₃₁	—	2	2	no	—
422	D₄×C₃₁	—	2	2	no	—
423	D₄×C₃₁	—	2	2	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	4	2	no	—
426	D₄×C₃₁	—	4	2	no	—
427	D₄×C₃₁	—	4	4	no	—
428	D₄×C₃₁	—	8	1	no	—
429	D₄×C₃₁	—	8	2	no	—
430	D₄×C₃₁	—	8	2	no	—
431	D₄×C₃₁	—	8	2	no	—
432	D₄×C₃₁	—	8	2	no	—
433	D₄×C₃₁	—	8	1	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	1	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	1	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	4	1	no	—
443	C₂×C₄×C₃₁	—	4	1	no	—
444	C₂×C₄×C₃₁	—	4	2	no	—
445	C₂×C₄×C₃₁	—	4	4	no	—
446	C₂×C₄×C₃₁	—	4	4	no	—
447	C₂×C₄×C₃₁	—	8	2	no	—
448	C₂×C₄×C₃₁	—	8	2	no	—
449	C₂×C₄×C₃₁	—	8	2	no	—
450	C₂×C₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	—	8	1	no	—
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
462	C₈×C₃₁	—	2	2	no	—
463	C₈×C₃₁	—	2	2	no	—
464	C₈×C₃₁	—	2	2	no	—
465	C₈×C₃₁	—	2	2	no	—
466	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3402	C₂×C₃₁	1	2	yes	complemented
469	#3401	C₂×C₃₁	1	2	yes	complemented
470	#3400	C₂×C₃₁	1	2	yes	complemented
471	#3397	C₂×C₃₁	1	2	yes	complemented
472	#3377	C₂×C₃₁	1	2	yes	complemented
473	#3375	C₂×C₃₁	1	2	yes	complemented
474	#3370	C₂×C₃₁	1	2	yes	complemented
475	#3368	C₂×C₃₁	1	2	yes	complemented
476	#3224	C₂×C₃₁	1	2	yes	complemented
477	#3222	C₂×C₃₁	1	2	yes	complemented
478	#3219	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#3124	C₂×C₃₁	1	2	yes	complemented
481	#3120	C₂×C₃₁	1	2	yes	complemented
482	#3114	C₂×C₃₁	1	1	yes	characteristic, complemented
483	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
485	C₂²×C₃₁	—	2	1	no	—
486	C₂²×C₃₁	—	2	1	no	—
487	C₂²×C₃₁	—	2	1	no	—
488	C₂²×C₃₁	—	4	2	no	—
489	C₂²×C₃₁	—	4	2	no	—
490	C₂²×C₃₁	—	4	1	no	—
491	C₂²×C₃₁	—	4	1	no	—
492	C₂²×C₃₁	—	4	2	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	4	1	no	—
497	C₂²×C₃₁	—	8	4	no	—
498	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
499	C₄×C₃₁	—	2	1	no	—
500	C₄×C₃₁	—	2	1	no	—
501	C₄×C₃₁	—	2	2	no	—
502	C₄×C₃₁	—	2	2	no	—
503	C₄×C₃₁	—	2	1	no	—
504	C₄×C₃₁	—	2	1	no	—
505	C₄×C₃₁	—	2	2	no	—
506	C₄×C₃₁	—	2	2	no	—
507	C₄×C₃₁	—	2	1	no	—
508	C₄×C₃₁	—	4	2	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	1	no	—
511	C₄×C₃₁	—	4	1	no	—
512	C₄×C₃₁	—	4	2	no	—
513	C₄×C₃₁	—	4	2	no	—
514	C₄×C₃₁	—	4	1	no	—
515	C₄×C₃₁	#585	1	2	yes	—
516	#563	—	2	2	no	—
517	#559	C₂²×C₃₁	1	2	yes	—
518	#559	C₂²×C₃₁	1	2	yes	—
519	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	#557	C₂²×C₃₁	1	2	yes	complemented
522	#556	—	2	1	no	—
523	#556	C₂²×C₃₁	1	2	yes	—
524	#556	C₂²×C₃₁	1	2	yes	complemented
525	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
526	#555	—	2	1	no	—
527	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#553	—	2	2	no	—
529	#552	—	2	1	no	—
530	#550	C₂²×C₃₁	1	2	yes	—
531	#547	—	2	1	no	—
532	#544	—	2	1	no	—
533	#542	C₂²×C₃₁	1	2	yes	—
534	#541	—	2	1	no	—
535	#541	—	2	2	no	—
536	#541	C₂²×C₃₁	1	2	yes	—
537	#538	—	2	1	no	—
538	#538	—	2	1	no	—
539	#535	C₂²×C₃₁	1	2	yes	—
540	#533	C₂²×C₃₁	1	1	yes	characteristic
541	#533	C₂²×C₃₁	1	1	yes	characteristic
542	#532	C₂²×C₃₁	1	1	yes	characteristic
543	#529	C₂²×C₃₁	1	1	yes	characteristic
544	#525	—	2	2	no	—
545	#520	C₂²×C₃₁	1	2	yes	—
546	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
547	#497	C₂²×C₃₁	1	2	yes	—
548	#497	C₂²×C₃₁	1	2	yes	complemented
549	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	#496	C₂²×C₃₁	1	2	yes	—
551	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
552	#495	C₂²×C₃₁	1	2	yes	—
553	#492	C₂²×C₃₁	1	2	yes	—
554	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
555	#490	C₂²×C₃₁	1	2	yes	—
556	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
557	#489	C₂²×C₃₁	1	2	yes	—
558	#489	C₂²×C₃₁	1	2	yes	complemented
559	#488	C₂²×C₃₁	1	2	yes	—
560	#486	C₂²×C₃₁	1	2	yes	—
561	#484	C₂²×C₃₁	1	2	yes	—
562	#483	C₂²×C₃₁	1	1	yes	characteristic
563	#480	C₂²×C₃₁	1	1	yes	characteristic
564	#479	C₂²×C₃₁	1	2	yes	complemented
565	#478	C₂²×C₃₁	1	2	yes	—
566	#478	C₂²×C₃₁	1	2	yes	complemented
567	#477	C₂²×C₃₁	1	2	yes	complemented
568	#474	C₂²×C₃₁	1	2	yes	—
569	#474	C₂²×C₃₁	1	2	yes	complemented
570	#464	C₂²×C₃₁	1	2	yes	—
571	#464	C₂²×C₃₁	1	2	yes	—
572	#464	C₂²×C₃₁	1	2	yes	—
573	#464	C₂²×C₃₁	1	2	yes	complemented
574	#464	C₂²×C₃₁	1	2	yes	complemented
575	#463	C₂²×C₃₁	1	2	yes	—
576	#463	C₂²×C₃₁	1	2	yes	—
577	#463	C₂²×C₃₁	1	2	yes	complemented
578	#463	C₂²×C₃₁	1	2	yes	complemented
579	#462	C₂²×C₃₁	1	2	yes	complemented
580	#462	C₂²×C₃₁	1	2	yes	complemented
581	#461	C₂²×C₃₁	1	2	yes	—
582	#461	C₂²×C₃₁	1	2	yes	complemented
583	#460	C₂²×C₃₁	1	2	yes	—
584	#460	C₂²×C₃₁	1	2	yes	—
585	#460	C₂²×C₃₁	1	2	yes	—
586	#460	C₂²×C₃₁	1	2	yes	complemented
587	#459	C₂²×C₃₁	1	2	yes	—
588	#452	C₂²×C₃₁	1	2	yes	—
589	#452	C₂²×C₃₁	1	2	yes	—
590	#452	C₂²×C₃₁	1	2	yes	—
591	#450	C₂²×C₃₁	1	2	yes	—
592	#450	C₂²×C₃₁	1	1	yes	characteristic
593	#449	C₂²×C₃₁	1	2	yes	—
594	#447	C₂²×C₃₁	1	1	yes	characteristic
595	#446	C₂²×C₃₁	1	2	yes	complemented
596	#446	C₂²×C₃₁	1	2	yes	complemented
597	#446	C₂²×C₃₁	1	2	yes	complemented
598	#446	C₂²×C₃₁	1	2	yes	complemented
599	#442	C₂²×C₃₁	1	2	yes	—
600	#441	C₂²×C₃₁	1	2	yes	complemented
601	#440	C₂²×C₃₁	1	2	yes	—
602	#440	C₂²×C₃₁	1	2	yes	—
603	#440	C₂²×C₃₁	1	2	yes	—
604	#440	C₂²×C₃₁	1	2	yes	complemented
605	#440	C₂²×C₃₁	1	2	yes	complemented
606	#440	C₂²×C₃₁	1	2	yes	complemented
607	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
608	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
609	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
610	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
611	#433	C₂²×C₃₁	1	2	yes	—
612	#433	C₂²×C₃₁	1	2	yes	—
613	#432	C₂²×C₃₁	1	1	yes	characteristic
614	#432	C₂²×C₃₁	1	1	yes	characteristic
615	C₂×C₃₁	—	4	1	no	—
616	C₂×C₃₁	—	8	2	no	—
617	C₂×C₃₁	—	8	1	no	—
618	C₂×C₃₁	—	8	2	no	—
619	C₂×C₃₁	#3487	1	1	yes	characteristic
620	C₂×C₃₁	#3585	1	1	yes	characteristic
621	C₂×C₃₁	#3586	1	1	yes	characteristic
622	C₂×#41	—	2	2	no	—
623	C₂×#41	C₂³×C₃₁	1	2	yes	—
624	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂³×C₄	—	2	1	no	—
626	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
627	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
636	C₂×D₈	C₂³×C₃₁	1	2	yes	—
637	C₂×D₈	C₂³×C₃₁	1	2	yes	—
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
642	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
646	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
648	#127	C₂³×C₃₁	1	1	yes	characteristic
649	#127	C₂³×C₃₁	1	2	yes	—
650	#127	C₂³×C₃₁	1	2	yes	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	1	no	—
660	#125	—	2	2	no	—
661	#125	—	2	2	no	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	1	no	—
666	#125	—	2	1	no	—
667	#125	D₄×C₃₁	1	2	yes	—
668	#125	C₂³×C₃₁	1	1	yes	characteristic
669	#125	C₂³×C₃₁	1	2	yes	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	C₂³×C₃₁	1	1	yes	characteristic
674	#124	C₂³×C₃₁	1	2	yes	—
675	#124	C₂³×C₃₁	1	2	yes	—
676	#124	C₂³×C₃₁	1	2	yes	—
677	#124	C₂³×C₃₁	1	2	yes	—
678	#123	—	2	1	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
692	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
693	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
694	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
695	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
696	#121	—	2	1	no	—
697	#121	—	2	1	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	C₂³×C₃₁	1	1	yes	characteristic
704	#120	—	2	2	no	—
705	#120	—	2	2	no	—
706	C₄×Q₈	—	2	1	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	2	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
711	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
712	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
714	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
715	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
716	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
717	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
718	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	C₂³×C₃₁	1	2	yes	—
730	C₄×D₄	C₂³×C₃₁	1	2	yes	—
731	C₄×D₄	C₂³×C₃₁	1	2	yes	—
732	C₄×D₄	C₂³×C₃₁	1	2	yes	—
733	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₃₁	1	2	yes	—
735	#117	—	2	1	no	—
736	#117	—	2	2	no	—
737	#117	—	2	2	no	—
738	#117	—	2	2	no	—
739	#117	—	2	1	no	—
740	#117	—	2	1	no	—
741	#117	C₂³×C₃₁	1	2	yes	—
742	C₂×C₄⋊C₄	—	2	2	no	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	—	2	1	no	—
746	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
747	#107	C₂³×C₃₁	1	2	yes	—
748	#107	C₂³×C₃₁	1	2	yes	—
749	#107	C₂³×C₃₁	1	2	yes	—
750	#106	C₂³×C₃₁	1	2	yes	—
751	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
753	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
754	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
755	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
756	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#103	C₂³×C₃₁	1	2	yes	—
760	#103	C₂³×C₃₁	1	2	yes	—
761	#103	C₂³×C₃₁	1	2	yes	—
762	#103	C₂³×C₃₁	1	2	yes	—
763	#103	C₂³×C₃₁	1	2	yes	—
764	#102	C₂³×C₃₁	1	2	yes	—
765	#102	C₂³×C₃₁	1	2	yes	—
766	#102	C₂³×C₃₁	1	2	yes	—
767	#102	C₂³×C₃₁	1	2	yes	—
768	#102	C₂³×C₃₁	1	2	yes	—
769	#102	C₂³×C₃₁	1	2	yes	—
770	#102	C₂³×C₃₁	1	2	yes	—
771	#102	C₂³×C₃₁	1	2	yes	—
772	#102	C₂³×C₃₁	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
776	#97	C₂³×C₃₁	1	1	yes	characteristic
777	#97	C₂³×C₃₁	1	1	yes	characteristic
778	#97	C₂³×C₃₁	1	2	yes	—
779	#97	C₂³×C₃₁	1	2	yes	—
780	#97	C₂³×C₃₁	1	2	yes	—
781	C₄×C₈	C₂³×C₃₁	1	2	yes	—
782	C₄×C₈	C₂³×C₃₁	1	2	yes	—
783	C₃₁	#61939	1	1	yes	characteristic, direct product factor, Sylow
784	C₂⁴	—	2	1	no	—
785	#41	—	4	2	no	—
786	#41	—	4	2	no	—
787	#41	—	8	4	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
791	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
792	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
794	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
807	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
808	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	8	2	no	—
818	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
821	Q₁₆	—	4	2	no	—
822	Q₁₆	—	4	2	no	—
823	Q₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	SD₁₆	—	4	2	no	—
830	SD₁₆	—	4	2	no	—
831	D₈	—	4	2	no	—
832	D₈	—	4	2	no	—
833	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
834	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
835	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
836	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
860	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
865	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
869	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	1	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₂²⋊C₄	—	2	1	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	1	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₄²	C₂⁴×C₃₁	1	2	yes	—
903	C₄²	C₂⁴×C₃₁	1	2	yes	—
904	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	8	1	no	—
911	C₂³	—	8	1	no	—
912	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
913	Q₈	—	2	2	no	—
914	Q₈	—	2	2	no	—
915	Q₈	—	2	2	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	2	no	—
918	Q₈	—	4	1	no	—
919	Q₈	—	4	1	no	—
920	Q₈	—	4	2	no	—
921	Q₈	—	8	1	no	—
922	Q₈	—	8	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	4	2	no	—
929	D₄	—	4	2	no	—
930	D₄	—	4	4	no	—
931	D₄	—	8	1	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	2	no	—
934	D₄	—	8	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	—	8	1	no	—
955	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
956	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
960	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
964	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
965	C₈	—	2	2	no	—
966	C₈	—	2	2	no	—
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	8	4	no	—
982	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	C₃₁×#585	1	2	yes	—
1000	C₂	—	4	1	no	—
1001	C₂	—	8	2	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	1	no	—
1004	C₂	C₃₁×#3487	1	1	yes	characteristic
1005	C₂	C₃₁×#3585	1	1	yes	characteristic
1006	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3555	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3400	C₂	semidirect
6. C₃₁×#3397	C₂	semidirect
7. C₃₁×#3377	C₂	semidirect
8. C₃₁×#3375	C₂	semidirect
9. C₃₁×#3370	C₂	semidirect
10. C₃₁×#3368	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3222	C₂	semidirect
13. C₃₁×#3219	C₂	semidirect
14. C₃₁×#3216	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3120	C₂	semidirect
17. C₃₁×#3114	C₂	semidirect
18. C₃₁×#3110	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
23. Q₈²×C₃₁	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
25. C₃₁×#557	C₂²	semidirect
28. C₃₁×#556	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
52. C₃₁×#497	C₂²	semidirect
53. C₃₁×#497	C₂²	semidirect
55. C₃₁×#496	C₂²	semidirect
58. C₃₁×#491	C₂²	semidirect
60. C₃₁×#490	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
68. C₃₁×#479	C₂²	semidirect
70. C₃₁×#478	C₂²	semidirect
71. C₃₁×#477	C₂²	semidirect
73. C₃₁×#474	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#462	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
86. C₃₁×#461	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#446	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
104. C₃₁×#441	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₃₁×#440	C₂²	semidirect
110. C₃₁×#440	C₂²	semidirect
111. C₄×Q₁₆×C₃₁	C₂²	semidirect
112. C₄×Q₁₆×C₃₁	C₂²	semidirect
113. C₄×SD₁₆×C₃₁	C₂²	semidirect
114. C₄×D₈×C₃₁	C₂²	semidirect
402. #61939	C₃₁	direct (N × H)
466. #3555	C₂×C₃₁	semidirect
467. #3506	C₂×C₃₁	semidirect
468. #3402	C₂×C₃₁	semidirect
469. #3401	C₂×C₃₁	semidirect
470. #3400	C₂×C₃₁	semidirect
471. #3397	C₂×C₃₁	semidirect
472. #3377	C₂×C₃₁	semidirect
473. #3375	C₂×C₃₁	semidirect
474. #3370	C₂×C₃₁	semidirect
475. #3368	C₂×C₃₁	semidirect
476. #3224	C₂×C₃₁	semidirect
477. #3222	C₂×C₃₁	semidirect
478. #3219	C₂×C₃₁	semidirect
479. #3216	C₂×C₃₁	semidirect
480. #3124	C₂×C₃₁	semidirect
481. #3120	C₂×C₃₁	semidirect
482. #3114	C₂×C₃₁	semidirect
483. #3110	C₂×C₃₁	semidirect
484. #2987	C₂×C₃₁	semidirect
519. Q₈²	C₂²×C₃₁	semidirect
520. #557	C₂²×C₃₁	semidirect
521. #557	C₂²×C₃₁	semidirect
524. #556	C₂²×C₃₁	semidirect
525. #556	C₂²×C₃₁	semidirect
527. #554	C₂²×C₃₁	semidirect
548. #497	C₂²×C₃₁	semidirect
549. #497	C₂²×C₃₁	semidirect
551. #496	C₂²×C₃₁	semidirect
554. #491	C₂²×C₃₁	semidirect
556. #490	C₂²×C₃₁	semidirect
558. #489	C₂²×C₃₁	semidirect
564. #479	C₂²×C₃₁	semidirect
566. #478	C₂²×C₃₁	semidirect
567. #477	C₂²×C₃₁	semidirect
569. #474	C₂²×C₃₁	semidirect
573. #464	C₂²×C₃₁	semidirect
574. #464	C₂²×C₃₁	semidirect
577. #463	C₂²×C₃₁	semidirect
578. #463	C₂²×C₃₁	semidirect
579. #462	C₂²×C₃₁	semidirect
580. #462	C₂²×C₃₁	semidirect
582. #461	C₂²×C₃₁	semidirect
586. #460	C₂²×C₃₁	semidirect
595. #446	C₂²×C₃₁	semidirect
596. #446	C₂²×C₃₁	semidirect
597. #446	C₂²×C₃₁	semidirect
598. #446	C₂²×C₃₁	semidirect
600. #441	C₂²×C₃₁	semidirect
604. #440	C₂²×C₃₁	semidirect
605. #440	C₂²×C₃₁	semidirect
606. #440	C₂²×C₃₁	semidirect
607. C₄×Q₁₆	C₂²×C₃₁	semidirect
608. C₄×Q₁₆	C₂²×C₃₁	semidirect
609. C₄×SD₁₆	C₂²×C₃₁	semidirect
610. C₄×D₈	C₂²×C₃₁	semidirect
783. C₃₁	#61939	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×#3506	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3400	2
C₃₁×#3397	2
C₃₁×#3377	2
C₃₁×#3375	2
C₃₁×#3370	2
C₃₁×#3368	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3219	2
C₃₁×#3216	2
C₃₁×#3124	2
C₃₁×#3120	2
C₃₁×#3114	2
C₃₁×#3110	2
C₃₁×#2987	2
#61939	31

Subgroups — C31×#61939 #21518698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61939 #21518698