Subgroups — C₃₁×#61502 #21518261

Order 7936.

1788 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3524	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
19	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	2	yes	—
21	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
22	C₃₁×#559	—	2	2	no	—
23	C₃₁×#559	C₂²	1	2	yes	—
24	C₃₁×#557	C₂²	1	2	yes	—
25	C₃₁×#555	—	2	2	no	—
26	C₃₁×#555	C₂²	1	2	yes	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#552	C₂²	1	2	yes	—
31	C₃₁×#550	C₂²	1	2	yes	—
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#548	C₂²	1	2	yes	—
34	C₃₁×#542	—	2	2	no	—
35	C₃₁×#542	C₂²	1	2	yes	—
36	C₃₁×#540	—	2	2	no	—
37	C₃₁×#540	C₂²	1	2	yes	—
38	C₃₁×#529	—	2	2	no	—
39	C₃₁×#529	—	2	2	no	—
40	C₃₁×#529	C₂²	1	2	yes	—
41	C₃₁×#529	C₂²	1	1	yes	characteristic
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₃₁×#519	C₂²	1	2	yes	—
44	C₄×#41×C₃₁	C₂²	1	2	yes	—
45	C₃₁×#501	C₂²	1	2	yes	—
46	C₃₁×#499	C₂²	1	1	yes	characteristic
47	C₃₁×#496	C₂²	1	2	yes	—
48	C₃₁×#495	C₂²	1	1	yes	characteristic
49	C₃₁×#488	C₂²	1	2	yes	—
50	C₃₁×#488	C₂²	1	2	yes	—
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	2	yes	—
53	C₃₁×#485	C₂²	1	2	yes	—
54	C₃₁×#482	C₂²	1	2	yes	—
55	C₃₁×#482	C₂²	1	2	yes	—
56	C₃₁×#481	C₂²	1	2	yes	—
57	C₃₁×#480	C₂²	1	2	yes	—
58	C₃₁×#479	C₂²	1	2	yes	—
59	C₃₁×#479	C₂²	1	2	yes	—
60	C₃₁×#478	C₂²	1	2	yes	—
61	C₃₁×#478	C₂²	1	2	yes	—
62	C₃₁×#477	C₂²	1	2	yes	—
63	C₃₁×#475	C₂²	1	2	yes	—
64	C₃₁×#469	C₂²	1	2	yes	—
65	C₃₁×#468	C₂²	1	2	yes	—
66	C₃₁×#467	C₂²	1	1	yes	characteristic
67	C₃₁×#466	C₂²	1	1	yes	characteristic
68	C₃₁×#466	C₂²	1	2	yes	—
69	C₃₁×#465	C₂²	1	2	yes	—
70	C₃₁×#465	C₂²	1	2	yes	—
71	C₃₁×#464	C₂²	1	2	yes	—
72	C₃₁×#464	C₂²	1	2	yes	—
73	C₃₁×#464	C₂²	1	2	yes	—
74	C₃₁×#463	C₂²	1	2	yes	—
75	C₃₁×#460	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#451	C₂²	1	2	yes	—
79	C₃₁×#449	C₂²	1	2	yes	—
80	C₃₁×#449	C₂²	1	2	yes	—
81	C₃₁×#449	C₂²	1	2	yes	—
82	C₃₁×#448	C₂²	1	2	yes	—
83	C₃₁×#446	C₂²	1	1	yes	characteristic
84	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
85	C₃₁×#442	C₂²	1	2	yes	—
86	C₃₁×#441	C₂²	1	2	yes	—
87	C₃₁×#441	C₂²	1	2	yes	—
88	C₃₁×#440	C₂²	1	2	yes	—
89	C₃₁×#440	C₂²	1	2	yes	—
90	C₃₁×#440	C₂²	1	2	yes	—
91	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
92	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
94	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
95	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
96	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
97	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
98	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
99	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
102	C₃₁×#436	C₂²	1	1	yes	characteristic
103	C₃₁×#435	C₂²	1	2	yes	—
104	C₈×D₄×C₃₁	C₂²	1	2	yes	—
105	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₃₁×#433	C₂²	1	2	yes	—
107	C₃₁×#432	C₂²	1	1	yes	characteristic
108	C₃₁×#428	C₂²	1	2	yes	—
109	C₃₁×#427	C₂²	1	1	yes	characteristic
110	C₃₁×#416	C₂²	1	2	yes	—
111	C₃₁×#416	C₂²	1	2	yes	—
112	C₂×C₃₁×#103	C₂²	1	2	yes	—
113	C₃₁×#405	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂×#41×C₃₁	C₂³	1	2	yes	—
117	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
118	C₃₁×#137	—	2	8	no	—
119	C₃₁×#135	—	2	4	no	—
120	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×#127	—	2	2	no	—
137	C₃₁×#127	C₂³	1	2	yes	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	D₄	1	2	yes	—
143	C₃₁×#125	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	—	2	2	no	—
146	C₃₁×#125	D₄	1	1	yes	characteristic
147	C₃₁×#125	C₂³	1	2	yes	—
148	C₃₁×#125	C₂³	1	2	yes	—
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	—	2	2	no	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#124	—	2	2	no	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#124	D₄	1	1	yes	characteristic
156	C₃₁×#124	C₂³	1	2	yes	—
157	C₃₁×#124	C₂³	1	2	yes	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	D₄	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
171	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×#121	—	2	2	no	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	2	no	—
177	C₃₁×#121	—	2	2	no	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	D₄	1	1	yes	characteristic
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#121	C₂³	1	2	yes	—
184	C₃₁×#121	C₂³	1	2	yes	—
185	C₃₁×#121	C₂³	1	2	yes	—
186	C₄×Q₈×C₃₁	—	2	2	no	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	—	2	2	no	—
189	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
190	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
193	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
194	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
195	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	2	no	—
198	C₄×D₄×C₃₁	—	2	2	no	—
199	C₄×D₄×C₃₁	—	2	2	no	—
200	C₄×D₄×C₃₁	—	2	2	no	—
201	C₄×D₄×C₃₁	—	2	2	no	—
202	C₄×D₄×C₃₁	—	2	2	no	—
203	C₄×D₄×C₃₁	—	2	2	no	—
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	C₂³	1	2	yes	—
207	C₄×D₄×C₃₁	C₂³	1	2	yes	—
208	C₄×D₄×C₃₁	C₂³	1	2	yes	—
209	C₄×D₄×C₃₁	C₂³	1	2	yes	—
210	C₄×D₄×C₃₁	C₂³	1	2	yes	—
211	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×#117	—	2	2	no	—
213	C₃₁×#117	—	2	2	no	—
214	C₃₁×#117	—	2	2	no	—
215	C₃₁×#117	—	2	2	no	—
216	C₃₁×#117	—	2	2	no	—
217	C₃₁×#117	—	2	2	no	—
218	C₃₁×#117	—	2	2	no	—
219	C₃₁×#117	C₂³	1	2	yes	—
220	C₃₁×#117	C₂³	1	2	yes	—
221	C₃₁×#117	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
223	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
224	C₂×C₄²×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	2	yes	—
229	C₃₁×#107	C₂³	1	1	yes	characteristic
230	C₃₁×#107	C₂³	1	1	yes	characteristic
231	C₃₁×#107	C₂³	1	2	yes	—
232	C₃₁×#106	C₂³	1	2	yes	—
233	C₃₁×#106	C₂³	1	2	yes	—
234	C₃₁×#106	C₂³	1	2	yes	—
235	C₃₁×#106	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
239	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
240	C₃₁×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#103	C₂³	1	2	yes	—
245	C₃₁×#103	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#102	C₂³	1	2	yes	—
249	C₃₁×#102	C₂³	1	2	yes	—
250	C₃₁×#102	C₂³	1	2	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₃₁×#97	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	2	yes	—
266	#41×C₃₁	—	2	4	no	—
267	#41×C₃₁	—	2	4	no	—
268	#41×C₃₁	—	4	2	no	—
269	#41×C₃₁	—	4	2	no	—
270	C₂×Q₈×C₃₁	—	2	2	no	—
271	C₂×Q₈×C₃₁	—	2	2	no	—
272	C₂×Q₈×C₃₁	—	2	4	no	—
273	C₂×Q₈×C₃₁	—	4	2	no	—
274	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
288	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	—	2	2	no	—
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
301	Q₁₆×C₃₁	—	2	4	no	—
302	Q₁₆×C₃₁	—	4	1	no	—
303	Q₁₆×C₃₁	#41	1	4	yes	—
304	SD₁₆×C₃₁	—	2	4	no	—
305	SD₁₆×C₃₁	—	2	4	no	—
306	SD₁₆×C₃₁	—	2	4	no	—
307	SD₁₆×C₃₁	—	4	2	no	—
308	D₈×C₃₁	—	2	2	no	—
309	D₈×C₃₁	—	4	2	no	—
310	D₈×C₃₁	—	4	1	no	—
311	M₁₆×C₃₁	—	2	4	no	—
312	C₂×C₈×C₃₁	—	2	2	no	—
313	C₂×C₈×C₃₁	—	4	2	no	—
314	C₂×C₈×C₃₁	—	4	1	no	—
315	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
319	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	2	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	—	2	2	no	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	—	2	2	no	—
371	C₄²×C₃₁	—	2	2	no	—
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄²×C₃₁	C₂⁴	1	2	yes	—
379	#61502	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	2	no	—
382	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	2	2	no	—
386	Q₈×C₃₁	—	2	2	no	—
387	Q₈×C₃₁	—	4	1	no	—
388	Q₈×C₃₁	—	4	4	no	—
389	Q₈×C₃₁	—	8	2	no	—
390	Q₈×C₃₁	C₂×#41	1	4	yes	—
391	D₄×C₃₁	—	2	2	no	—
392	D₄×C₃₁	—	2	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	4	1	no	—
396	D₄×C₃₁	—	4	2	no	—
397	D₄×C₃₁	—	4	4	no	—
398	D₄×C₃₁	—	4	4	no	—
399	D₄×C₃₁	—	8	2	no	—
400	D₄×C₃₁	—	8	2	no	—
401	D₄×C₃₁	—	8	2	no	—
402	D₄×C₃₁	—	8	2	no	—
403	D₄×C₃₁	—	8	2	no	—
404	D₄×C₃₁	—	8	2	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	1	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	4	1	no	—
416	C₂×C₄×C₃₁	—	4	1	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	4	4	no	—
419	C₂×C₄×C₃₁	—	4	4	no	—
420	C₂×C₄×C₃₁	—	8	2	no	—
421	C₂×C₄×C₃₁	—	8	2	no	—
422	C₂×C₄×C₃₁	—	8	2	no	—
423	C₂×C₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	—	8	2	no	—
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
434	C₈×C₃₁	—	2	1	no	—
435	C₈×C₃₁	—	2	2	no	—
436	C₈×C₃₁	—	2	1	no	—
437	C₈×C₃₁	—	2	2	no	—
438	C₈×C₃₁	—	2	1	no	—
439	C₈×C₃₁	C₂×#41	1	2	yes	—
440	#3524	C₂×C₃₁	1	2	yes	complemented
441	#3403	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#3390	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#3365	C₂×C₃₁	1	2	yes	complemented
444	#3355	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3348	C₂×C₃₁	1	2	yes	complemented
446	#3305	C₂×C₃₁	1	2	yes	complemented
447	#3301	C₂×C₃₁	1	2	yes	complemented
448	#3300	C₂×C₃₁	1	2	yes	complemented
449	#3277	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#3271	C₂×C₃₁	1	2	yes	complemented
451	#3179	C₂×C₃₁	1	2	yes	complemented
452	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#3121	C₂×C₃₁	1	2	yes	complemented
454	#3119	C₂×C₃₁	1	2	yes	complemented
455	#3111	C₂×C₃₁	1	2	yes	complemented
456	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#2947	C₂×C₃₁	1	2	yes	complemented
458	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
459	C₂²×C₃₁	—	2	1	no	—
460	C₂²×C₃₁	—	2	1	no	—
461	C₂²×C₃₁	—	2	2	no	—
462	C₂²×C₃₁	—	2	2	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	1	no	—
465	C₂²×C₃₁	—	4	2	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
472	C₄×C₃₁	—	2	1	no	—
473	C₄×C₃₁	—	2	1	no	—
474	C₄×C₃₁	—	2	1	no	—
475	C₄×C₃₁	—	2	1	no	—
476	C₄×C₃₁	—	2	2	no	—
477	C₄×C₃₁	—	2	2	no	—
478	C₄×C₃₁	—	2	1	no	—
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	4	no	—
481	C₄×C₃₁	—	4	2	no	—
482	C₄×C₃₁	—	4	2	no	—
483	C₄×C₃₁	—	4	2	no	—
484	C₄×C₃₁	—	4	2	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
487	C₄×C₃₁	#585	1	1	yes	characteristic
488	C₂×#137	C₂²×C₃₁	1	2	yes	—
489	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
490	#559	—	2	2	no	—
491	#559	C₂²×C₃₁	1	2	yes	—
492	#557	C₂²×C₃₁	1	2	yes	—
493	#555	—	2	2	no	—
494	#555	C₂²×C₃₁	1	2	yes	—
495	#553	—	2	2	no	—
496	#553	C₂²×C₃₁	1	2	yes	—
497	#552	—	2	2	no	—
498	#552	C₂²×C₃₁	1	2	yes	—
499	#550	C₂²×C₃₁	1	2	yes	—
500	#548	C₂²×C₃₁	1	2	yes	—
501	#548	C₂²×C₃₁	1	2	yes	—
502	#542	—	2	2	no	—
503	#542	C₂²×C₃₁	1	2	yes	—
504	#540	—	2	2	no	—
505	#540	C₂²×C₃₁	1	2	yes	—
506	#529	—	2	2	no	—
507	#529	—	2	2	no	—
508	#529	C₂²×C₃₁	1	2	yes	—
509	#529	C₂²×C₃₁	1	1	yes	characteristic
510	#520	C₂²×C₃₁	1	2	yes	—
511	#519	C₂²×C₃₁	1	2	yes	—
512	C₄×#41	C₂²×C₃₁	1	2	yes	—
513	#501	C₂²×C₃₁	1	2	yes	—
514	#499	C₂²×C₃₁	1	1	yes	characteristic
515	#496	C₂²×C₃₁	1	2	yes	—
516	#495	C₂²×C₃₁	1	1	yes	characteristic
517	#488	C₂²×C₃₁	1	2	yes	—
518	#488	C₂²×C₃₁	1	2	yes	—
519	#486	C₂²×C₃₁	1	2	yes	—
520	#485	C₂²×C₃₁	1	2	yes	—
521	#485	C₂²×C₃₁	1	2	yes	—
522	#482	C₂²×C₃₁	1	2	yes	—
523	#482	C₂²×C₃₁	1	2	yes	—
524	#481	C₂²×C₃₁	1	2	yes	—
525	#480	C₂²×C₃₁	1	2	yes	—
526	#479	C₂²×C₃₁	1	2	yes	—
527	#479	C₂²×C₃₁	1	2	yes	—
528	#478	C₂²×C₃₁	1	2	yes	—
529	#478	C₂²×C₃₁	1	2	yes	—
530	#477	C₂²×C₃₁	1	2	yes	—
531	#475	C₂²×C₃₁	1	2	yes	—
532	#469	C₂²×C₃₁	1	2	yes	—
533	#468	C₂²×C₃₁	1	2	yes	—
534	#467	C₂²×C₃₁	1	1	yes	characteristic
535	#466	C₂²×C₃₁	1	1	yes	characteristic
536	#466	C₂²×C₃₁	1	2	yes	—
537	#465	C₂²×C₃₁	1	2	yes	—
538	#465	C₂²×C₃₁	1	2	yes	—
539	#464	C₂²×C₃₁	1	2	yes	—
540	#464	C₂²×C₃₁	1	2	yes	—
541	#464	C₂²×C₃₁	1	2	yes	—
542	#463	C₂²×C₃₁	1	2	yes	—
543	#460	C₂²×C₃₁	1	2	yes	—
544	#459	C₂²×C₃₁	1	2	yes	—
545	#452	C₂²×C₃₁	1	2	yes	—
546	#451	C₂²×C₃₁	1	2	yes	—
547	#449	C₂²×C₃₁	1	2	yes	—
548	#449	C₂²×C₃₁	1	2	yes	—
549	#449	C₂²×C₃₁	1	2	yes	—
550	#448	C₂²×C₃₁	1	2	yes	—
551	#446	C₂²×C₃₁	1	1	yes	characteristic
552	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
553	#442	C₂²×C₃₁	1	2	yes	—
554	#441	C₂²×C₃₁	1	2	yes	—
555	#441	C₂²×C₃₁	1	2	yes	—
556	#440	C₂²×C₃₁	1	2	yes	—
557	#440	C₂²×C₃₁	1	2	yes	—
558	#440	C₂²×C₃₁	1	2	yes	—
559	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
561	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
562	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
563	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
565	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
566	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
567	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
568	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
569	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
570	#436	C₂²×C₃₁	1	1	yes	characteristic
571	#435	C₂²×C₃₁	1	2	yes	—
572	C₈×D₄	C₂²×C₃₁	1	2	yes	—
573	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
574	#433	C₂²×C₃₁	1	2	yes	—
575	#432	C₂²×C₃₁	1	1	yes	characteristic
576	#428	C₂²×C₃₁	1	2	yes	—
577	#427	C₂²×C₃₁	1	1	yes	characteristic
578	#416	C₂²×C₃₁	1	2	yes	—
579	#416	C₂²×C₃₁	1	2	yes	—
580	C₂×#103	C₂²×C₃₁	1	2	yes	—
581	#405	C₂²×C₃₁	1	2	yes	—
582	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
583	C₂×C₃₁	—	4	1	no	—
584	C₂×C₃₁	—	4	2	no	—
585	C₂×C₃₁	—	8	2	no	—
586	C₂×C₃₁	—	8	2	no	—
587	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
588	C₂×C₃₁	#3584	1	1	yes	characteristic
589	C₂×C₃₁	#3584	1	1	yes	characteristic
590	C₂×#41	C₂³×C₃₁	1	2	yes	—
591	C₂×#41	C₂³×C₃₁	1	2	yes	—
592	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
593	#137	—	2	8	no	—
594	#135	—	2	4	no	—
595	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
596	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
602	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×D₈	C₂³×C₃₁	1	2	yes	—
605	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
606	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
609	C₄⋊Q₈	—	2	2	no	—
610	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
611	#127	—	2	2	no	—
612	#127	C₂³×C₃₁	1	2	yes	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	D₄×C₃₁	1	2	yes	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	—	2	2	no	—
621	#125	D₄×C₃₁	1	1	yes	characteristic
622	#125	C₂³×C₃₁	1	2	yes	—
623	#125	C₂³×C₃₁	1	2	yes	—
624	#124	—	2	2	no	—
625	#124	—	2	2	no	—
626	#124	—	2	2	no	—
627	#124	—	2	2	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	D₄×C₃₁	1	1	yes	characteristic
631	#124	C₂³×C₃₁	1	2	yes	—
632	#124	C₂³×C₃₁	1	2	yes	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	D₄×C₃₁	1	2	yes	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
646	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	D₄×C₃₁	1	1	yes	characteristic
657	#121	C₂³×C₃₁	1	2	yes	—
658	#121	C₂³×C₃₁	1	2	yes	—
659	#121	C₂³×C₃₁	1	2	yes	—
660	#121	C₂³×C₃₁	1	2	yes	—
661	C₄×Q₈	—	2	2	no	—
662	C₄×Q₈	—	2	2	no	—
663	C₄×Q₈	—	2	2	no	—
664	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
665	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
666	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
667	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
668	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
669	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
670	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	C₂³×C₃₁	1	2	yes	—
682	C₄×D₄	C₂³×C₃₁	1	2	yes	—
683	C₄×D₄	C₂³×C₃₁	1	2	yes	—
684	C₄×D₄	C₂³×C₃₁	1	2	yes	—
685	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₃₁	1	2	yes	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	C₂³×C₃₁	1	2	yes	—
695	#117	C₂³×C₃₁	1	2	yes	—
696	#117	C₂³×C₃₁	1	2	yes	—
697	C₂×C₄⋊C₄	—	2	2	no	—
698	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
699	C₂×C₄²	—	2	2	no	—
700	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
701	#107	C₂³×C₃₁	1	1	yes	characteristic
702	#107	C₂³×C₃₁	1	1	yes	characteristic
703	#107	C₂³×C₃₁	1	2	yes	—
704	#107	C₂³×C₃₁	1	1	yes	characteristic
705	#107	C₂³×C₃₁	1	1	yes	characteristic
706	#107	C₂³×C₃₁	1	2	yes	—
707	#106	C₂³×C₃₁	1	2	yes	—
708	#106	C₂³×C₃₁	1	2	yes	—
709	#106	C₂³×C₃₁	1	2	yes	—
710	#106	C₂³×C₃₁	1	2	yes	—
711	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
714	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
715	#103	C₂³×C₃₁	1	2	yes	—
716	#103	C₂³×C₃₁	1	2	yes	—
717	#103	C₂³×C₃₁	1	2	yes	—
718	#103	C₂³×C₃₁	1	2	yes	—
719	#103	C₂³×C₃₁	1	2	yes	—
720	#103	C₂³×C₃₁	1	2	yes	—
721	#103	C₂³×C₃₁	1	2	yes	—
722	#103	C₂³×C₃₁	1	2	yes	—
723	#102	C₂³×C₃₁	1	2	yes	—
724	#102	C₂³×C₃₁	1	2	yes	—
725	#102	C₂³×C₃₁	1	2	yes	—
726	#102	C₂³×C₃₁	1	2	yes	—
727	#102	C₂³×C₃₁	1	2	yes	—
728	#102	C₂³×C₃₁	1	2	yes	—
729	#102	C₂³×C₃₁	1	2	yes	—
730	#102	C₂³×C₃₁	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
734	#97	C₂³×C₃₁	1	2	yes	—
735	#97	C₂³×C₃₁	1	2	yes	—
736	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₃₁	1	2	yes	—
741	C₃₁	#61502	1	1	yes	characteristic, direct product factor, Sylow
742	#41	—	2	4	no	—
743	#41	—	2	4	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	4	2	no	—
750	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
751	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
752	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
764	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
777	Q₁₆	—	2	4	no	—
778	Q₁₆	—	4	1	no	—
779	Q₁₆	#41×C₃₁	1	4	yes	—
780	SD₁₆	—	2	4	no	—
781	SD₁₆	—	2	4	no	—
782	SD₁₆	—	2	4	no	—
783	SD₁₆	—	4	2	no	—
784	D₈	—	2	2	no	—
785	D₈	—	4	2	no	—
786	D₈	—	4	1	no	—
787	M₁₆	—	2	4	no	—
788	C₂×C₈	—	2	2	no	—
789	C₂×C₈	—	4	2	no	—
790	C₂×C₈	—	4	1	no	—
791	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
796	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
812	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
813	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
839	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
840	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
851	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
852	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
853	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
854	C₄²	C₂⁴×C₃₁	1	2	yes	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
858	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	2	2	no	—
862	Q₈	—	4	1	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	8	2	no	—
865	Q₈	C₂×#41×C₃₁	1	4	yes	—
866	D₄	—	2	2	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	8	2	no	—
875	D₄	—	8	2	no	—
876	D₄	—	8	2	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	—	8	2	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
905	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
908	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
909	C₈	—	2	1	no	—
910	C₈	—	2	2	no	—
911	C₈	—	2	1	no	—
912	C₈	—	2	2	no	—
913	C₈	—	2	1	no	—
914	C₈	C₂×#41×C₃₁	1	2	yes	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
928	C₄	—	2	1	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	4	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
943	C₄	C₃₁×#585	1	1	yes	characteristic
944	C₂	—	4	2	no	—
945	C₂	—	4	1	no	—
946	C₂	—	8	2	no	—
947	C₂	—	8	2	no	—
948	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
949	C₂	C₃₁×#3584	1	1	yes	characteristic
950	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3524	C₂	semidirect
2. C₃₁×#3403	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3365	C₂	semidirect
5. C₃₁×#3355	C₂	semidirect
6. C₃₁×#3348	C₂	semidirect
7. C₃₁×#3305	C₂	semidirect
8. C₃₁×#3301	C₂	semidirect
9. C₃₁×#3300	C₂	semidirect
10. C₃₁×#3277	C₂	semidirect
11. C₃₁×#3271	C₂	semidirect
12. C₃₁×#3179	C₂	semidirect
13. C₃₁×#3168	C₂	semidirect
14. C₃₁×#3121	C₂	semidirect
15. C₃₁×#3119	C₂	semidirect
16. C₃₁×#3111	C₂	semidirect
17. C₃₁×#2966	C₂	semidirect
18. C₃₁×#2947	C₂	semidirect
19. C₄×C₃₁×#135	C₂	semidirect
379. #61502	C₃₁	direct (N × H)
440. #3524	C₂×C₃₁	semidirect
441. #3403	C₂×C₃₁	semidirect
442. #3390	C₂×C₃₁	semidirect
443. #3365	C₂×C₃₁	semidirect
444. #3355	C₂×C₃₁	semidirect
445. #3348	C₂×C₃₁	semidirect
446. #3305	C₂×C₃₁	semidirect
447. #3301	C₂×C₃₁	semidirect
448. #3300	C₂×C₃₁	semidirect
449. #3277	C₂×C₃₁	semidirect
450. #3271	C₂×C₃₁	semidirect
451. #3179	C₂×C₃₁	semidirect
452. #3168	C₂×C₃₁	semidirect
453. #3121	C₂×C₃₁	semidirect
454. #3119	C₂×C₃₁	semidirect
455. #3111	C₂×C₃₁	semidirect
456. #2966	C₂×C₃₁	semidirect
457. #2947	C₂×C₃₁	semidirect
458. C₄×#135	C₂×C₃₁	semidirect
741. C₃₁	#61502	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×#3524	2
C₃₁×#3403	2
C₃₁×#3390	2
C₃₁×#3365	2
C₃₁×#3355	2
C₃₁×#3348	2
C₃₁×#3305	2
C₃₁×#3301	2
C₃₁×#3300	2
C₃₁×#3277	2
C₃₁×#3271	2
C₃₁×#3179	2
C₃₁×#3168	2
C₃₁×#3121	2
C₃₁×#3119	2
C₃₁×#3111	2
C₃₁×#2966	2
C₃₁×#2947	2
C₄×C₃₁×#135	2
#61502	31

Subgroups — C31×#61502 #21518261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61502 #21518261