Subgroups — C₃₁×#61788 #21518547

Order 7936.

1846 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3198	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3096	C₂	1	4	yes	maximal, complemented
17	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×H(3,𝔽₄)	—	2	2	no	—
19	C₃₁×#556	C₂²	1	2	yes	complemented
20	C₃₁×#555	—	2	1	no	—
21	C₃₁×#555	C₂²	1	2	yes	—
22	C₃₁×#555	C₂²	1	2	yes	—
23	C₃₁×#555	C₂²	1	2	yes	complemented
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#548	—	2	2	no	—
27	C₃₁×#547	C₂²	1	2	yes	complemented
28	D₄²×C₃₁	—	2	1	no	—
29	D₄²×C₃₁	C₂²	1	2	yes	—
30	D₄²×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#542	—	2	2	no	—
32	C₃₁×#537	C₂²	1	2	yes	complemented
33	C₃₁×#535	—	2	2	no	—
34	C₃₁×#535	—	2	2	no	—
35	C₃₁×#535	C₂²	1	4	yes	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#532	—	2	1	no	—
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#520	C₂²	1	2	yes	complemented
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#500	C₂²	1	2	yes	complemented
45	C₃₁×#498	C₂²	1	2	yes	complemented
46	C₃₁×#486	C₂²	1	2	yes	—
47	C₃₁×#486	C₂²	1	2	yes	—
48	C₃₁×#485	C₂²	1	4	yes	complemented
49	C₃₁×#482	C₂²	1	4	yes	complemented
50	C₃₁×#482	C₂²	1	4	yes	complemented
51	C₃₁×#482	C₂²	1	4	yes	complemented
52	C₃₁×#482	C₂²	1	2	yes	complemented
53	C₃₁×#482	C₂²	1	2	yes	complemented
54	C₃₁×#481	C₂²	1	4	yes	complemented
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	4	yes	complemented
57	C₃₁×#480	C₂²	1	4	yes	complemented
58	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#476	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#476	C₂²	1	2	yes	complemented
64	C₃₁×#474	C₂²	1	2	yes	complemented
65	C₃₁×#474	C₂²	1	2	yes	complemented
66	C₃₁×#469	C₂²	1	4	yes	complemented
67	C₃₁×#468	C₂²	1	4	yes	complemented
68	C₃₁×#466	C₂²	1	4	yes	complemented
69	C₃₁×#465	C₂²	1	4	yes	complemented
70	C₃₁×#460	C₂²	1	1	yes	characteristic
71	C₃₁×#460	C₂²	1	1	yes	characteristic
72	C₃₁×#459	C₂²	1	1	yes	characteristic
73	C₃₁×#459	C₂²	1	1	yes	characteristic
74	C₃₁×#450	C₂²	1	4	yes	complemented
75	C₃₁×#449	C₂²	1	2	yes	complemented
76	C₃₁×#449	C₂²	1	2	yes	complemented
77	C₃₁×#447	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
79	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
80	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
81	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
82	C₃₁×#436	C₂²	1	2	yes	complemented
83	C₃₁×#436	C₂²	1	2	yes	complemented
84	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
85	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
86	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#428	C₂²	1	4	yes	complemented
89	C₃₁×#427	C₂²	1	4	yes	complemented
90	C₃₁×#418	C₂²	1	4	yes	complemented
91	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
92	C₃₁×#408	C₂²	1	4	yes	complemented
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	—	2	1	no	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	2	yes	—
98	C₂²×Q₈×C₃₁	—	2	1	no	—
99	C₂²×D₄×C₃₁	—	2	2	no	—
100	C₂²×D₄×C₃₁	—	2	2	no	—
101	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×#127	—	2	4	no	—
116	C₃₁×#127	D₄	1	1	yes	characteristic
117	C₃₁×#127	C₂³	1	1	yes	characteristic
118	C₃₁×#127	C₂³	1	1	yes	characteristic
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#124	—	2	4	no	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	—	2	4	no	—
124	C₃₁×#124	—	2	4	no	—
125	C₃₁×#124	—	2	4	no	—
126	C₃₁×#124	—	2	1	no	—
127	C₃₁×#124	—	2	1	no	—
128	C₃₁×#124	D₄	1	2	yes	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	2	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₃₁×#121	—	2	1	no	—
140	C₃₁×#121	—	2	1	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	D₄	1	2	yes	—
144	C₃₁×#121	D₄	1	2	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₃₁×#121	C₂³	1	2	yes	—
147	C₃₁×#121	C₂³	1	2	yes	—
148	C₃₁×#121	C₂³	1	4	yes	—
149	C₃₁×#121	C₂³	1	4	yes	—
150	C₃₁×#120	—	2	4	no	—
151	C₃₁×#120	—	2	4	no	—
152	C₃₁×#120	—	2	4	no	—
153	C₃₁×#120	—	2	4	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	4	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	1	no	—
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₄×D₄×C₃₁	C₂³	1	2	yes	—
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	C₂³	1	2	yes	—
171	C₃₁×#117	—	2	2	no	—
172	C₃₁×#117	—	2	2	no	—
173	C₃₁×#117	—	2	2	no	—
174	C₃₁×#117	—	2	1	no	—
175	C₃₁×#117	C₂³	1	4	yes	—
176	C₃₁×#117	C₂³	1	4	yes	—
177	C₃₁×#117	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄²×C₃₁	—	2	1	no	—
182	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₃₁×#107	C₂³	1	2	yes	—
184	C₃₁×#107	C₂³	1	4	yes	—
185	C₃₁×#107	C₂³	1	2	yes	—
186	C₃₁×#107	C₂³	1	4	yes	—
187	C₃₁×#106	C₂³	1	2	yes	—
188	C₃₁×#106	C₂³	1	4	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×#106	C₂³	1	4	yes	—
191	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	yes	—
197	C₃₁×#102	C₂³	1	2	yes	—
198	C₃₁×#102	C₂³	1	2	yes	—
199	C₃₁×#102	C₂³	1	4	yes	—
200	C₃₁×#102	C₂³	1	4	yes	—
201	C₃₁×#102	C₂³	1	2	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	4	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	2	yes	—
206	C₃₁×#102	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₄×C₈×C₃₁	C₂³	1	2	yes	—
212	C₄×C₈×C₃₁	C₂³	1	2	yes	—
213	C₂⁴×C₃₁	—	2	4	no	—
214	#41×C₃₁	—	4	2	no	—
215	#41×C₃₁	—	4	2	no	—
216	#41×C₃₁	—	4	1	no	—
217	#41×C₃₁	—	4	1	no	—
218	#41×C₃₁	—	8	2	no	—
219	#41×C₃₁	—	8	2	no	—
220	#41×C₃₁	—	8	4	no	—
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	1	no	—
224	C₂×Q₈×C₃₁	—	2	1	no	—
225	C₂×Q₈×C₃₁	—	8	2	no	—
226	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂×D₄×C₃₁	—	2	1	no	—
229	C₂×D₄×C₃₁	—	2	4	no	—
230	C₂×D₄×C₃₁	—	2	4	no	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	4	no	—
234	C₂×D₄×C₃₁	—	2	1	no	—
235	C₂×D₄×C₃₁	—	2	1	no	—
236	C₂×D₄×C₃₁	—	2	1	no	—
237	C₂×D₄×C₃₁	—	2	1	no	—
238	C₂×D₄×C₃₁	—	2	4	no	—
239	C₂×D₄×C₃₁	—	4	4	no	—
240	C₂×D₄×C₃₁	—	4	4	no	—
241	C₂×D₄×C₃₁	—	8	4	no	—
242	C₂×D₄×C₃₁	—	8	4	no	—
243	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
244	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
247	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	4	no	—
252	C₂²×C₄×C₃₁	—	2	1	no	—
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	1	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
261	SD₁₆×C₃₁	—	4	2	no	—
262	SD₁₆×C₃₁	—	4	2	no	—
263	D₈×C₃₁	—	4	2	no	—
264	D₈×C₃₁	—	4	2	no	—
265	M₁₆×C₃₁	—	4	4	no	—
266	C₂×C₈×C₃₁	—	4	4	no	—
267	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
268	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
269	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
270	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	1	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	4	no	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂²⋊C₄×C₃₁	—	2	1	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	1	no	—
292	C₂²⋊C₄×C₃₁	—	2	1	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	2	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
300	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
301	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
302	C₄²×C₃₁	—	2	1	no	—
303	C₄²×C₃₁	—	2	1	no	—
304	C₄²×C₃₁	—	2	1	no	—
305	C₄²×C₃₁	—	2	4	no	—
306	C₄²×C₃₁	—	2	4	no	—
307	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
311	#61788	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂³×C₃₁	—	2	1	no	—
313	C₂³×C₃₁	—	2	2	no	—
314	C₂³×C₃₁	—	2	2	no	—
315	C₂³×C₃₁	—	8	4	no	—
316	C₂³×C₃₁	—	8	4	no	—
317	C₂³×C₃₁	—	8	4	no	—
318	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
319	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₃₁	—	2	1	no	—
321	Q₈×C₃₁	—	2	1	no	—
322	Q₈×C₃₁	—	4	2	no	—
323	Q₈×C₃₁	—	4	4	no	—
324	Q₈×C₃₁	—	8	2	no	—
325	Q₈×C₃₁	—	8	1	no	—
326	Q₈×C₃₁	—	8	1	no	—
327	D₄×C₃₁	—	2	4	no	—
328	D₄×C₃₁	—	2	4	no	—
329	D₄×C₃₁	—	2	1	no	—
330	D₄×C₃₁	—	2	1	no	—
331	D₄×C₃₁	—	2	2	no	—
332	D₄×C₃₁	—	2	2	no	—
333	D₄×C₃₁	—	2	2	no	—
334	D₄×C₃₁	—	2	2	no	—
335	D₄×C₃₁	—	4	2	no	—
336	D₄×C₃₁	—	4	4	no	—
337	D₄×C₃₁	—	4	2	no	—
338	D₄×C₃₁	—	4	2	no	—
339	D₄×C₃₁	—	4	2	no	—
340	D₄×C₃₁	—	8	4	no	—
341	D₄×C₃₁	—	8	1	no	—
342	D₄×C₃₁	—	8	1	no	—
343	D₄×C₃₁	—	8	4	no	—
344	D₄×C₃₁	—	8	4	no	—
345	D₄×C₃₁	—	8	2	no	—
346	D₄×C₃₁	—	8	4	no	—
347	D₄×C₃₁	—	8	2	no	—
348	C₂×C₄×C₃₁	—	2	2	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	4	no	—
351	C₂×C₄×C₃₁	—	2	4	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	1	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	1	no	—
359	C₂×C₄×C₃₁	—	2	4	no	—
360	C₂×C₄×C₃₁	—	4	2	no	—
361	C₂×C₄×C₃₁	—	4	4	no	—
362	C₂×C₄×C₃₁	—	4	2	no	—
363	C₂×C₄×C₃₁	—	4	2	no	—
364	C₂×C₄×C₃₁	—	4	4	no	—
365	C₂×C₄×C₃₁	—	8	2	no	—
366	C₂×C₄×C₃₁	—	8	4	no	—
367	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
374	C₈×C₃₁	—	2	2	no	—
375	C₈×C₃₁	—	2	2	no	—
376	C₈×C₃₁	—	2	2	no	—
377	C₈×C₃₁	—	2	2	no	—
378	#3549	C₂×C₃₁	1	1	yes	characteristic, complemented
379	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#3357	C₂×C₃₁	1	2	yes	complemented
381	#3354	C₂×C₃₁	1	2	yes	complemented
382	#3341	C₂×C₃₁	1	2	yes	complemented
383	#3340	C₂×C₃₁	1	2	yes	complemented
384	#3325	C₂×C₃₁	1	2	yes	complemented
385	#3324	C₂×C₃₁	1	2	yes	complemented
386	#3295	C₂×C₃₁	1	2	yes	complemented
387	#3294	C₂×C₃₁	1	2	yes	complemented
388	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#3198	C₂×C₃₁	1	4	yes	complemented
391	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
392	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
393	#3096	C₂×C₃₁	1	4	yes	complemented
394	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
395	C₂²×C₃₁	—	2	1	no	—
396	C₂²×C₃₁	—	2	4	no	—
397	C₂²×C₃₁	—	2	1	no	—
398	C₂²×C₃₁	—	2	4	no	—
399	C₂²×C₃₁	—	2	1	no	—
400	C₂²×C₃₁	—	2	4	no	—
401	C₂²×C₃₁	—	4	1	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	4	2	no	—
404	C₂²×C₃₁	—	4	1	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	2	no	—
407	C₂²×C₃₁	—	4	2	no	—
408	C₂²×C₃₁	—	4	1	no	—
409	C₂²×C₃₁	—	4	2	no	—
410	C₂²×C₃₁	—	16	8	no	—
411	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₃₁	—	2	1	no	—
413	C₄×C₃₁	—	2	4	no	—
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	1	no	—
416	C₄×C₃₁	—	4	1	no	—
417	C₄×C₃₁	—	4	1	no	—
418	C₄×C₃₁	—	4	2	no	—
419	C₄×C₃₁	—	4	4	no	—
420	C₄×C₃₁	—	4	1	no	—
421	C₄×C₃₁	—	4	2	no	—
422	C₄×C₃₁	#576	1	2	yes	—
423	C₄×C₃₁	#577	1	2	yes	—
424	C₄×C₃₁	#585	1	1	yes	characteristic
425	C₄×C₃₁	#585	1	1	yes	characteristic
426	H(3,𝔽₄)	—	2	2	no	—
427	#556	C₂²×C₃₁	1	2	yes	complemented
428	#555	—	2	1	no	—
429	#555	C₂²×C₃₁	1	2	yes	—
430	#555	C₂²×C₃₁	1	2	yes	—
431	#555	C₂²×C₃₁	1	2	yes	complemented
432	#554	C₂²×C₃₁	1	2	yes	complemented
433	#553	—	2	2	no	—
434	#548	—	2	2	no	—
435	#547	C₂²×C₃₁	1	2	yes	complemented
436	D₄²	—	2	1	no	—
437	D₄²	C₂²×C₃₁	1	2	yes	—
438	D₄²	C₂²×C₃₁	1	2	yes	—
439	#542	—	2	2	no	—
440	#537	C₂²×C₃₁	1	2	yes	complemented
441	#535	—	2	2	no	—
442	#535	—	2	2	no	—
443	#535	C₂²×C₃₁	1	4	yes	—
444	#533	—	2	1	no	—
445	#532	—	2	1	no	—
446	#532	C₂²×C₃₁	1	1	yes	characteristic
447	#532	C₂²×C₃₁	1	1	yes	characteristic
448	#532	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#520	C₂²×C₃₁	1	2	yes	complemented
451	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
452	#500	C₂²×C₃₁	1	2	yes	complemented
453	#498	C₂²×C₃₁	1	2	yes	complemented
454	#486	C₂²×C₃₁	1	2	yes	—
455	#486	C₂²×C₃₁	1	2	yes	—
456	#485	C₂²×C₃₁	1	4	yes	complemented
457	#482	C₂²×C₃₁	1	4	yes	complemented
458	#482	C₂²×C₃₁	1	4	yes	complemented
459	#482	C₂²×C₃₁	1	4	yes	complemented
460	#482	C₂²×C₃₁	1	2	yes	complemented
461	#482	C₂²×C₃₁	1	2	yes	complemented
462	#481	C₂²×C₃₁	1	4	yes	complemented
463	#481	C₂²×C₃₁	1	4	yes	complemented
464	#480	C₂²×C₃₁	1	4	yes	complemented
465	#480	C₂²×C₃₁	1	4	yes	complemented
466	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
468	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
469	#476	C₂²×C₃₁	1	2	yes	complemented
470	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	#476	C₂²×C₃₁	1	2	yes	complemented
472	#474	C₂²×C₃₁	1	2	yes	complemented
473	#474	C₂²×C₃₁	1	2	yes	complemented
474	#469	C₂²×C₃₁	1	4	yes	complemented
475	#468	C₂²×C₃₁	1	4	yes	complemented
476	#466	C₂²×C₃₁	1	4	yes	complemented
477	#465	C₂²×C₃₁	1	4	yes	complemented
478	#460	C₂²×C₃₁	1	1	yes	characteristic
479	#460	C₂²×C₃₁	1	1	yes	characteristic
480	#459	C₂²×C₃₁	1	1	yes	characteristic
481	#459	C₂²×C₃₁	1	1	yes	characteristic
482	#450	C₂²×C₃₁	1	4	yes	complemented
483	#449	C₂²×C₃₁	1	2	yes	complemented
484	#449	C₂²×C₃₁	1	2	yes	complemented
485	#447	C₂²×C₃₁	1	4	yes	complemented
486	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
487	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
488	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
489	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
490	#436	C₂²×C₃₁	1	2	yes	complemented
491	#436	C₂²×C₃₁	1	2	yes	complemented
492	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
493	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
494	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
495	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	#428	C₂²×C₃₁	1	4	yes	complemented
497	#427	C₂²×C₃₁	1	4	yes	complemented
498	#418	C₂²×C₃₁	1	4	yes	complemented
499	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
500	#408	C₂²×C₃₁	1	4	yes	complemented
501	C₂×C₃₁	—	4	1	no	—
502	C₂×C₃₁	—	4	4	no	—
503	C₂×C₃₁	—	8	1	no	—
504	C₂×C₃₁	—	8	2	no	—
505	C₂×C₃₁	—	8	2	no	—
506	C₂×C₃₁	#3485	1	1	yes	characteristic
507	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
508	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	1	no	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
513	C₂×#41	C₂³×C₃₁	1	2	yes	—
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×D₄	—	2	2	no	—
516	C₂²×D₄	—	2	2	no	—
517	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
518	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
519	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
520	C₂×D₈	C₂³×C₃₁	1	2	yes	—
521	C₂×D₈	C₂³×C₃₁	1	2	yes	—
522	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
523	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
531	#127	—	2	4	no	—
532	#127	D₄×C₃₁	1	1	yes	characteristic
533	#127	C₂³×C₃₁	1	1	yes	characteristic
534	#127	C₂³×C₃₁	1	1	yes	characteristic
535	#126	—	2	4	no	—
536	#125	—	2	2	no	—
537	#124	—	2	4	no	—
538	#124	—	2	2	no	—
539	#124	—	2	4	no	—
540	#124	—	2	4	no	—
541	#124	—	2	4	no	—
542	#124	—	2	1	no	—
543	#124	—	2	1	no	—
544	#124	D₄×C₃₁	1	2	yes	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	2	no	—
554	#121	—	2	4	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	D₄×C₃₁	1	2	yes	—
560	#121	D₄×C₃₁	1	2	yes	—
561	#121	C₂³×C₃₁	1	2	yes	—
562	#121	C₂³×C₃₁	1	2	yes	—
563	#121	C₂³×C₃₁	1	4	yes	—
564	#121	C₂³×C₃₁	1	4	yes	—
565	#121	C₂³×C₃₁	1	4	yes	—
566	#120	—	2	4	no	—
567	#120	—	2	4	no	—
568	#120	—	2	4	no	—
569	#120	—	2	4	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	4	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
583	C₄×D₄	C₂³×C₃₁	1	2	yes	—
584	C₄×D₄	C₂³×C₃₁	1	2	yes	—
585	C₄×D₄	C₂³×C₃₁	1	2	yes	—
586	C₄×D₄	C₂³×C₃₁	1	2	yes	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	2	1	no	—
591	#117	C₂³×C₃₁	1	1	yes	characteristic
592	#117	C₂³×C₃₁	1	4	yes	—
593	#117	C₂³×C₃₁	1	4	yes	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
597	C₂×C₄²	—	2	1	no	—
598	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
599	#107	C₂³×C₃₁	1	2	yes	—
600	#107	C₂³×C₃₁	1	4	yes	—
601	#107	C₂³×C₃₁	1	2	yes	—
602	#107	C₂³×C₃₁	1	4	yes	—
603	#106	C₂³×C₃₁	1	2	yes	—
604	#106	C₂³×C₃₁	1	4	yes	—
605	#106	C₂³×C₃₁	1	2	yes	—
606	#106	C₂³×C₃₁	1	4	yes	—
607	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
610	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
611	#103	C₂³×C₃₁	1	2	yes	—
612	#103	C₂³×C₃₁	1	2	yes	—
613	#102	C₂³×C₃₁	1	2	yes	—
614	#102	C₂³×C₃₁	1	2	yes	—
615	#102	C₂³×C₃₁	1	4	yes	—
616	#102	C₂³×C₃₁	1	4	yes	—
617	#102	C₂³×C₃₁	1	2	yes	—
618	#102	C₂³×C₃₁	1	2	yes	—
619	#102	C₂³×C₃₁	1	4	yes	—
620	#102	C₂³×C₃₁	1	4	yes	—
621	#102	C₂³×C₃₁	1	2	yes	—
622	#102	C₂³×C₃₁	1	2	yes	—
623	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
624	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
627	C₄×C₈	C₂³×C₃₁	1	2	yes	—
628	C₄×C₈	C₂³×C₃₁	1	2	yes	—
629	C₃₁	#61788	1	1	yes	characteristic, direct product factor, Sylow
630	C₂⁴	—	2	4	no	—
631	#41	—	4	2	no	—
632	#41	—	4	2	no	—
633	#41	—	4	1	no	—
634	#41	—	4	1	no	—
635	#41	—	8	2	no	—
636	#41	—	8	2	no	—
637	#41	—	8	4	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	8	2	no	—
643	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
644	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	4	no	—
659	C₂×D₄	—	8	4	no	—
660	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
661	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
662	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
663	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
664	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
666	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
678	SD₁₆	—	4	2	no	—
679	SD₁₆	—	4	2	no	—
680	D₈	—	4	2	no	—
681	D₈	—	4	2	no	—
682	M₁₆	—	4	4	no	—
683	C₂×C₈	—	4	4	no	—
684	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
685	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
686	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
687	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
701	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
702	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
718	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
726	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
727	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂³	—	2	1	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	—	8	4	no	—
734	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
735	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	4	4	no	—
740	Q₈	—	8	2	no	—
741	Q₈	—	8	1	no	—
742	Q₈	—	8	1	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	4	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	2	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	2	no	—
750	D₄	—	2	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	2	no	—
762	D₄	—	8	4	no	—
763	D₄	—	8	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	4	no	—
783	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
789	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	16	8	no	—
810	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	4	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	1	no	—
821	C₄	C₃₁×#576	1	2	yes	—
822	C₄	C₃₁×#577	1	2	yes	—
823	C₄	C₃₁×#585	1	1	yes	characteristic
824	C₄	C₃₁×#585	1	1	yes	characteristic
825	C₂	—	4	4	no	—
826	C₂	—	4	1	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	1	no	—
830	C₂	C₃₁×#3485	1	1	yes	characteristic
831	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
832	C₂	C₂×C₃₁×#577	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3549	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3354	C₂	semidirect
5. C₃₁×#3341	C₂	semidirect
6. C₃₁×#3340	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3324	C₂	semidirect
9. C₃₁×#3295	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. C₃₁×#3227	C₂	semidirect
12. C₃₁×#3226	C₂	semidirect
13. C₃₁×#3198	C₂	semidirect
14. C₃₁×#3106	C₂	semidirect
15. C₃₁×#3106	C₂	semidirect
16. C₃₁×#3096	C₂	semidirect
17. C₃₁×#2979	C₂	semidirect
19. C₃₁×#556	C₂²	semidirect
23. C₃₁×#555	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
27. C₃₁×#547	C₂²	semidirect
32. C₃₁×#537	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₃₁×#520	C₂²	semidirect
43. C₄×#41×C₃₁	C₂²	semidirect
44. C₃₁×#500	C₂²	semidirect
45. C₃₁×#498	C₂²	semidirect
48. C₃₁×#485	C₂²	semidirect
49. C₃₁×#482	C₂²	semidirect
50. C₃₁×#482	C₂²	semidirect
51. C₃₁×#482	C₂²	semidirect
52. C₃₁×#482	C₂²	semidirect
53. C₃₁×#482	C₂²	semidirect
54. C₃₁×#481	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
57. C₃₁×#480	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#477	C₂²	semidirect
60. C₃₁×#476	C₂²	semidirect
61. C₃₁×#476	C₂²	semidirect
62. C₃₁×#476	C₂²	semidirect
63. C₃₁×#476	C₂²	semidirect
64. C₃₁×#474	C₂²	semidirect
65. C₃₁×#474	C₂²	semidirect
66. C₃₁×#469	C₂²	semidirect
67. C₃₁×#468	C₂²	semidirect
68. C₃₁×#466	C₂²	semidirect
69. C₃₁×#465	C₂²	semidirect
74. C₃₁×#450	C₂²	semidirect
75. C₃₁×#449	C₂²	semidirect
76. C₃₁×#449	C₂²	semidirect
77. C₃₁×#447	C₂²	semidirect
78. C₄×SD₁₆×C₃₁	C₂²	semidirect
79. C₄×SD₁₆×C₃₁	C₂²	semidirect
80. C₄×D₈×C₃₁	C₂²	semidirect
81. C₄×D₈×C₃₁	C₂²	semidirect
82. C₃₁×#436	C₂²	semidirect
83. C₃₁×#436	C₂²	semidirect
84. C₈×D₄×C₃₁	C₂²	semidirect
85. C₈×D₄×C₃₁	C₂²	semidirect
86. C₃₁×#431	C₂²	semidirect
87. C₃₁×#431	C₂²	semidirect
88. C₃₁×#428	C₂²	semidirect
89. C₃₁×#427	C₂²	semidirect
90. C₃₁×#418	C₂²	semidirect
91. C₂×C₃₁×#102	C₂²	semidirect
92. C₃₁×#408	C₂²	semidirect
311. #61788	C₃₁	direct (N × H)
378. #3549	C₂×C₃₁	semidirect
379. #3511	C₂×C₃₁	semidirect
380. #3357	C₂×C₃₁	semidirect
381. #3354	C₂×C₃₁	semidirect
382. #3341	C₂×C₃₁	semidirect
383. #3340	C₂×C₃₁	semidirect
384. #3325	C₂×C₃₁	semidirect
385. #3324	C₂×C₃₁	semidirect
386. #3295	C₂×C₃₁	semidirect
387. #3294	C₂×C₃₁	semidirect
388. #3227	C₂×C₃₁	semidirect
389. #3226	C₂×C₃₁	semidirect
390. #3198	C₂×C₃₁	semidirect
391. #3106	C₂×C₃₁	semidirect
392. #3106	C₂×C₃₁	semidirect
393. #3096	C₂×C₃₁	semidirect
394. #2979	C₂×C₃₁	semidirect
427. #556	C₂²×C₃₁	semidirect
431. #555	C₂²×C₃₁	semidirect
432. #554	C₂²×C₃₁	semidirect
435. #547	C₂²×C₃₁	semidirect
440. #537	C₂²×C₃₁	semidirect
449. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
450. #520	C₂²×C₃₁	semidirect
451. C₄×#41	C₂²×C₃₁	semidirect
452. #500	C₂²×C₃₁	semidirect
453. #498	C₂²×C₃₁	semidirect
456. #485	C₂²×C₃₁	semidirect
457. #482	C₂²×C₃₁	semidirect
458. #482	C₂²×C₃₁	semidirect
459. #482	C₂²×C₃₁	semidirect
460. #482	C₂²×C₃₁	semidirect
461. #482	C₂²×C₃₁	semidirect
462. #481	C₂²×C₃₁	semidirect
463. #481	C₂²×C₃₁	semidirect
464. #480	C₂²×C₃₁	semidirect
465. #480	C₂²×C₃₁	semidirect
466. #477	C₂²×C₃₁	semidirect
467. #477	C₂²×C₃₁	semidirect
468. #476	C₂²×C₃₁	semidirect
469. #476	C₂²×C₃₁	semidirect
470. #476	C₂²×C₃₁	semidirect
471. #476	C₂²×C₃₁	semidirect
472. #474	C₂²×C₃₁	semidirect
473. #474	C₂²×C₃₁	semidirect
474. #469	C₂²×C₃₁	semidirect
475. #468	C₂²×C₃₁	semidirect
476. #466	C₂²×C₃₁	semidirect
477. #465	C₂²×C₃₁	semidirect
482. #450	C₂²×C₃₁	semidirect
483. #449	C₂²×C₃₁	semidirect
484. #449	C₂²×C₃₁	semidirect
485. #447	C₂²×C₃₁	semidirect
486. C₄×SD₁₆	C₂²×C₃₁	semidirect
487. C₄×SD₁₆	C₂²×C₃₁	semidirect
488. C₄×D₈	C₂²×C₃₁	semidirect
489. C₄×D₈	C₂²×C₃₁	semidirect
490. #436	C₂²×C₃₁	semidirect
491. #436	C₂²×C₃₁	semidirect
492. C₈×D₄	C₂²×C₃₁	semidirect
493. C₈×D₄	C₂²×C₃₁	semidirect
494. #431	C₂²×C₃₁	semidirect
495. #431	C₂²×C₃₁	semidirect
496. #428	C₂²×C₃₁	semidirect
497. #427	C₂²×C₃₁	semidirect
498. #418	C₂²×C₃₁	semidirect
499. C₂×#102	C₂²×C₃₁	semidirect
500. #408	C₂²×C₃₁	semidirect
629. C₃₁	#61788	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×#3549	2
C₃₁×#3511	2
C₃₁×#3357	2
C₃₁×#3354	2
C₃₁×#3341	2
C₃₁×#3340	2
C₃₁×#3325	2
C₃₁×#3324	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3227	2
C₃₁×#3226	2
C₃₁×#3198	2
C₃₁×#3106	2
C₃₁×#3096	2
C₃₁×#2979	2
#61788	31

Subgroups — C31×#61788 #21518547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61788 #21518547