Subgroups — C₃₁×#62019 #21518778

Order 7936.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3558	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
8	D₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3043	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
21	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
24	C₃₁×#562	—	2	1	no	—
25	C₃₁×H(3,𝔽₄)	—	2	1	no	—
26	C₃₁×#559	C₂²	1	2	yes	—
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#552	—	2	2	no	—
33	C₃₁×#552	C₂²	1	2	yes	complemented
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
36	C₃₁×#548	C₂²	1	2	yes	—
37	C₃₁×#546	—	2	2	no	—
38	C₃₁×#546	C₂²	1	2	yes	—
39	D₄²×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#541	—	2	2	no	—
42	C₃₁×#541	C₂²	1	2	yes	complemented
43	C₃₁×#538	—	2	2	no	—
44	C₃₁×#538	—	2	1	no	—
45	C₃₁×#535	C₂²	1	2	yes	—
46	C₃₁×#534	—	2	1	no	—
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₃₁×#519	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#497	C₂²	1	2	yes	complemented
56	C₃₁×#497	C₂²	1	2	yes	complemented
57	C₃₁×#492	C₂²	1	2	yes	—
58	C₃₁×#490	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#482	C₂²	1	2	yes	—
63	C₃₁×#480	C₂²	1	2	yes	complemented
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	complemented
66	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#476	C₂²	1	2	yes	complemented
69	C₃₁×#475	C₂²	1	2	yes	complemented
70	C₃₁×#470	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#467	C₂²	1	2	yes	complemented
73	C₃₁×#465	C₂²	1	2	yes	—
74	C₃₁×#465	C₂²	1	2	yes	complemented
75	C₃₁×#465	C₂²	1	2	yes	complemented
76	C₃₁×#464	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#464	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	2	yes	complemented
83	C₃₁×#464	C₂²	1	2	yes	complemented
84	C₃₁×#462	C₂²	1	2	yes	complemented
85	C₃₁×#461	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
90	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#460	C₂²	1	2	yes	complemented
92	C₃₁×#452	C₂²	1	2	yes	complemented
93	C₃₁×#452	C₂²	1	2	yes	complemented
94	C₃₁×#451	C₂²	1	2	yes	complemented
95	C₃₁×#451	C₂²	1	2	yes	complemented
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#450	C₂²	1	2	yes	complemented
98	C₃₁×#450	C₂²	1	2	yes	complemented
99	C₃₁×#448	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#418	C₂²	1	2	yes	complemented
116	C₃₁×#416	C₂²	1	2	yes	complemented
117	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	—	2	2	no	—
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₃₁×#137	—	4	4	no	—
128	C₂×Q₁₆×C₃₁	—	4	2	no	—
129	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₃₁	—	4	2	no	—
134	C₂×SD₁₆×C₃₁	—	4	4	no	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
147	C₃₁×C₄⋊Q₈	—	2	1	no	—
148	C₃₁×C₄⋊Q₈	—	2	1	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×#127	C₂³	1	2	yes	—
155	C₃₁×#127	C₂³	1	1	yes	characteristic
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	D₄	1	2	yes	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	1	no	—
169	C₃₁×#125	D₄	1	1	yes	characteristic
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	1	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	D₄	1	1	yes	characteristic
179	C₃₁×#124	C₂³	1	2	yes	—
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	D₄	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	D₄	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
210	C₃₁×#120	—	2	2	no	—
211	C₃₁×#120	—	2	2	no	—
212	C₃₁×#120	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	2	no	—
215	C₄×Q₈×C₃₁	—	2	2	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	C₂³	1	2	yes	—
244	C₃₁×#117	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₄²×C₃₁	—	2	1	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#106	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	C₂⁴×C₃₁	—	2	2	no	—
286	#41×C₃₁	—	4	2	no	—
287	#41×C₃₁	—	4	2	no	—
288	#41×C₃₁	—	8	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	2	no	—
291	C₂×Q₈×C₃₁	—	2	1	no	—
292	C₂×Q₈×C₃₁	—	2	1	no	—
293	C₂×Q₈×C₃₁	—	2	1	no	—
294	C₂×Q₈×C₃₁	—	2	2	no	—
295	C₂×Q₈×C₃₁	—	2	4	no	—
296	C₂×Q₈×C₃₁	—	4	1	no	—
297	C₂×Q₈×C₃₁	—	4	2	no	—
298	C₂×Q₈×C₃₁	—	4	1	no	—
299	C₂×Q₈×C₃₁	—	4	1	no	—
300	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	1	no	—
310	C₂×D₄×C₃₁	—	2	1	no	—
311	C₂×D₄×C₃₁	—	2	1	no	—
312	C₂×D₄×C₃₁	—	2	2	no	—
313	C₂×D₄×C₃₁	—	2	2	no	—
314	C₂×D₄×C₃₁	—	4	1	no	—
315	C₂×D₄×C₃₁	—	4	2	no	—
316	C₂×D₄×C₃₁	—	4	1	no	—
317	C₂×D₄×C₃₁	—	4	2	no	—
318	C₂×D₄×C₃₁	—	8	4	no	—
319	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
322	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₃₁	—	2	1	no	—
324	C₂²×C₄×C₃₁	—	2	1	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	1	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
334	Q₁₆×C₃₁	—	2	4	no	—
335	Q₁₆×C₃₁	—	4	2	no	—
336	Q₁₆×C₃₁	—	4	2	no	—
337	Q₁₆×C₃₁	—	4	2	no	—
338	SD₁₆×C₃₁	—	2	4	no	—
339	SD₁₆×C₃₁	—	2	4	no	—
340	SD₁₆×C₃₁	—	4	2	no	—
341	SD₁₆×C₃₁	—	4	2	no	—
342	SD₁₆×C₃₁	—	4	2	no	—
343	SD₁₆×C₃₁	—	4	2	no	—
344	SD₁₆×C₃₁	—	4	2	no	—
345	SD₁₆×C₃₁	—	4	2	no	—
346	M₁₆×C₃₁	—	4	2	no	—
347	C₂×C₈×C₃₁	—	4	1	no	—
348	C₂×C₈×C₃₁	—	4	2	no	—
349	C₂×C₈×C₃₁	—	4	1	no	—
350	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
351	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
352	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
353	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	1	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
400	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄²×C₃₁	—	2	1	no	—
406	C₄²×C₃₁	—	2	1	no	—
407	C₄²×C₃₁	—	2	1	no	—
408	C₄²×C₃₁	—	2	1	no	—
409	C₄²×C₃₁	—	2	2	no	—
410	C₄²×C₃₁	—	2	2	no	—
411	C₄²×C₃₁	—	2	2	no	—
412	C₄²×C₃₁	—	2	2	no	—
413	C₄²×C₃₁	—	2	2	no	—
414	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₃₁	C₂⁴	1	2	yes	—
417	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
419	#62019	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
420	C₂³×C₃₁	—	2	2	no	—
421	C₂³×C₃₁	—	2	2	no	—
422	C₂³×C₃₁	—	4	2	no	—
423	C₂³×C₃₁	—	8	1	no	—
424	C₂³×C₃₁	—	8	2	no	—
425	C₂³×C₃₁	—	8	2	no	—
426	C₂³×C₃₁	—	8	1	no	—
427	C₂³×C₃₁	—	8	2	no	—
428	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
429	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
430	Q₈×C₃₁	—	2	1	no	—
431	Q₈×C₃₁	—	2	2	no	—
432	Q₈×C₃₁	—	2	1	no	—
433	Q₈×C₃₁	—	2	2	no	—
434	Q₈×C₃₁	—	2	1	no	—
435	Q₈×C₃₁	—	2	2	no	—
436	Q₈×C₃₁	—	2	2	no	—
437	Q₈×C₃₁	—	4	1	no	—
438	Q₈×C₃₁	—	4	4	no	—
439	Q₈×C₃₁	—	4	2	no	—
440	Q₈×C₃₁	—	4	2	no	—
441	Q₈×C₃₁	—	8	1	no	—
442	Q₈×C₃₁	—	8	1	no	—
443	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
444	D₄×C₃₁	—	2	4	no	—
445	D₄×C₃₁	—	2	2	no	—
446	D₄×C₃₁	—	2	2	no	—
447	D₄×C₃₁	—	2	2	no	—
448	D₄×C₃₁	—	2	2	no	—
449	D₄×C₃₁	—	4	1	no	—
450	D₄×C₃₁	—	4	4	no	—
451	D₄×C₃₁	—	8	1	no	—
452	D₄×C₃₁	—	8	2	no	—
453	D₄×C₃₁	—	8	2	no	—
454	D₄×C₃₁	—	8	1	no	—
455	D₄×C₃₁	—	8	2	no	—
456	D₄×C₃₁	—	8	1	no	—
457	D₄×C₃₁	—	8	2	no	—
458	D₄×C₃₁	—	8	2	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	4	1	no	—
473	C₂×C₄×C₃₁	—	4	2	no	—
474	C₂×C₄×C₃₁	—	4	4	no	—
475	C₂×C₄×C₃₁	—	4	2	no	—
476	C₂×C₄×C₃₁	—	8	2	no	—
477	C₂×C₄×C₃₁	—	8	2	no	—
478	C₂×C₄×C₃₁	—	8	2	no	—
479	C₂×C₄×C₃₁	—	8	1	no	—
480	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
489	C₈×C₃₁	—	2	2	no	—
490	C₈×C₃₁	—	2	2	no	—
491	C₈×C₃₁	—	2	2	no	—
492	C₈×C₃₁	—	2	2	no	—
493	#3558	C₂×C₃₁	1	1	yes	characteristic
494	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3400	C₂×C₃₁	1	2	yes	complemented
496	#3371	C₂×C₃₁	1	2	yes	complemented
497	#3311	C₂×C₃₁	1	2	yes	complemented
498	#3310	C₂×C₃₁	1	2	yes	complemented
499	#3300	C₂×C₃₁	1	2	yes	complemented
500	D₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
501	#3270	C₂×C₃₁	1	2	yes	complemented
502	#3266	C₂×C₃₁	1	2	yes	complemented
503	#3258	C₂×C₃₁	1	2	yes	complemented
504	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
505	#3222	C₂×C₃₁	1	2	yes	complemented
506	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3121	C₂×C₃₁	1	2	yes	complemented
508	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3043	C₂×C₃₁	1	2	yes	complemented
510	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
512	C₂²×C₃₁	—	2	1	no	—
513	C₂²×C₃₁	—	2	1	no	—
514	C₂²×C₃₁	—	2	2	no	—
515	C₂²×C₃₁	—	2	2	no	—
516	C₂²×C₃₁	—	2	2	no	—
517	C₂²×C₃₁	—	4	2	no	—
518	C₂²×C₃₁	—	4	2	no	—
519	C₂²×C₃₁	—	4	2	no	—
520	C₂²×C₃₁	—	4	2	no	—
521	C₂²×C₃₁	—	4	2	no	—
522	C₂²×C₃₁	—	4	2	no	—
523	C₂²×C₃₁	—	16	2	no	—
524	C₂²×C₃₁	—	16	4	no	—
525	C₂²×C₃₁	#577	1	2	yes	—
526	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
527	C₄×C₃₁	—	2	1	no	—
528	C₄×C₃₁	—	2	1	no	—
529	C₄×C₃₁	—	2	2	no	—
530	C₄×C₃₁	—	2	2	no	—
531	C₄×C₃₁	—	2	1	no	—
532	C₄×C₃₁	—	2	2	no	—
533	C₄×C₃₁	—	2	1	no	—
534	C₄×C₃₁	—	2	1	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	1	no	—
541	C₄×C₃₁	—	4	1	no	—
542	C₄×C₃₁	—	4	2	no	—
543	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	C₄×C₃₁	#585	1	1	yes	characteristic
545	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
546	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
548	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
549	#562	—	2	1	no	—
550	H(3,𝔽₄)	—	2	1	no	—
551	#559	C₂²×C₃₁	1	2	yes	—
552	#557	—	2	1	no	—
553	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
555	#556	—	2	1	no	—
556	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
557	#552	—	2	2	no	—
558	#552	C₂²×C₃₁	1	2	yes	complemented
559	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
561	#548	C₂²×C₃₁	1	2	yes	—
562	#546	—	2	2	no	—
563	#546	C₂²×C₃₁	1	2	yes	—
564	D₄²	C₂²×C₃₁	1	2	yes	—
565	#542	C₂²×C₃₁	1	2	yes	—
566	#541	—	2	2	no	—
567	#541	C₂²×C₃₁	1	2	yes	complemented
568	#538	—	2	2	no	—
569	#538	—	2	1	no	—
570	#535	C₂²×C₃₁	1	2	yes	—
571	#534	—	2	1	no	—
572	#533	—	2	1	no	—
573	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#532	C₂²×C₃₁	1	1	yes	characteristic
575	#529	—	2	1	no	—
576	#529	C₂²×C₃₁	1	1	yes	characteristic
577	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
578	#519	C₂²×C₃₁	1	2	yes	complemented
579	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
580	#497	C₂²×C₃₁	1	2	yes	complemented
581	#497	C₂²×C₃₁	1	2	yes	complemented
582	#492	C₂²×C₃₁	1	2	yes	—
583	#490	C₂²×C₃₁	1	2	yes	—
584	#489	C₂²×C₃₁	1	2	yes	complemented
585	#488	C₂²×C₃₁	1	2	yes	complemented
586	#485	C₂²×C₃₁	1	2	yes	complemented
587	#482	C₂²×C₃₁	1	2	yes	—
588	#480	C₂²×C₃₁	1	2	yes	complemented
589	#479	C₂²×C₃₁	1	2	yes	complemented
590	#478	C₂²×C₃₁	1	2	yes	complemented
591	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#476	C₂²×C₃₁	1	2	yes	complemented
594	#475	C₂²×C₃₁	1	2	yes	complemented
595	#470	C₂²×C₃₁	1	2	yes	complemented
596	#468	C₂²×C₃₁	1	2	yes	—
597	#467	C₂²×C₃₁	1	2	yes	complemented
598	#465	C₂²×C₃₁	1	2	yes	—
599	#465	C₂²×C₃₁	1	2	yes	complemented
600	#465	C₂²×C₃₁	1	2	yes	complemented
601	#464	C₂²×C₃₁	1	2	yes	complemented
602	#464	C₂²×C₃₁	1	2	yes	complemented
603	#464	C₂²×C₃₁	1	2	yes	complemented
604	#464	C₂²×C₃₁	1	2	yes	complemented
605	#464	C₂²×C₃₁	1	2	yes	complemented
606	#464	C₂²×C₃₁	1	2	yes	complemented
607	#464	C₂²×C₃₁	1	2	yes	complemented
608	#464	C₂²×C₃₁	1	2	yes	complemented
609	#462	C₂²×C₃₁	1	2	yes	complemented
610	#461	C₂²×C₃₁	1	2	yes	complemented
611	#461	C₂²×C₃₁	1	2	yes	complemented
612	#460	C₂²×C₃₁	1	2	yes	—
613	#460	C₂²×C₃₁	1	2	yes	—
614	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#460	C₂²×C₃₁	1	2	yes	complemented
617	#452	C₂²×C₃₁	1	2	yes	complemented
618	#452	C₂²×C₃₁	1	2	yes	complemented
619	#451	C₂²×C₃₁	1	2	yes	complemented
620	#451	C₂²×C₃₁	1	2	yes	complemented
621	#450	C₂²×C₃₁	1	2	yes	—
622	#450	C₂²×C₃₁	1	2	yes	complemented
623	#450	C₂²×C₃₁	1	2	yes	complemented
624	#448	C₂²×C₃₁	1	2	yes	—
625	#448	C₂²×C₃₁	1	2	yes	complemented
626	#446	C₂²×C₃₁	1	2	yes	complemented
627	#441	C₂²×C₃₁	1	2	yes	complemented
628	#440	C₂²×C₃₁	1	2	yes	complemented
629	#440	C₂²×C₃₁	1	2	yes	complemented
630	#440	C₂²×C₃₁	1	2	yes	complemented
631	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
632	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
633	#435	C₂²×C₃₁	1	2	yes	complemented
634	#435	C₂²×C₃₁	1	2	yes	complemented
635	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
636	#433	C₂²×C₃₁	1	2	yes	complemented
637	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#424	C₂²×C₃₁	1	2	yes	complemented
639	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#418	C₂²×C₃₁	1	2	yes	complemented
641	#416	C₂²×C₃₁	1	2	yes	complemented
642	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
644	C₂×C₃₁	—	2	2	no	—
645	C₂×C₃₁	—	4	2	no	—
646	C₂×C₃₁	—	8	2	no	—
647	C₂×C₃₁	—	8	2	no	—
648	C₂×C₃₁	#3488	1	1	yes	characteristic
649	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
650	C₂×C₃₁	#3586	1	1	yes	characteristic
651	C₂×#41	—	2	1	no	—
652	C₂×#41	C₂³×C₃₁	1	2	yes	—
653	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
654	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
655	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
656	C₂²×D₄	—	2	2	no	—
657	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
659	#137	—	4	4	no	—
660	C₂×Q₁₆	—	4	2	no	—
661	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
662	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
663	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
665	C₂×SD₁₆	—	4	2	no	—
666	C₂×SD₁₆	—	4	4	no	—
667	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
676	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
678	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
683	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
684	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
686	#127	C₂³×C₃₁	1	1	yes	characteristic
687	#127	C₂³×C₃₁	1	2	yes	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#126	—	2	2	no	—
693	#126	D₄×C₃₁	1	2	yes	—
694	#125	—	2	1	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	1	no	—
701	#125	D₄×C₃₁	1	1	yes	characteristic
702	#125	C₂³×C₃₁	1	2	yes	—
703	#124	—	2	2	no	—
704	#124	—	2	1	no	—
705	#124	—	2	2	no	—
706	#124	—	2	2	no	—
707	#124	—	2	1	no	—
708	#124	—	2	1	no	—
709	#124	—	2	1	no	—
710	#124	D₄×C₃₁	1	1	yes	characteristic
711	#124	C₂³×C₃₁	1	2	yes	—
712	#124	C₂³×C₃₁	1	2	yes	—
713	#124	C₂³×C₃₁	1	2	yes	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	D₄×C₃₁	1	2	yes	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
727	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
728	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
731	#121	—	2	2	no	—
732	#121	—	2	1	no	—
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	D₄×C₃₁	1	1	yes	characteristic
738	#121	C₂³×C₃₁	1	2	yes	—
739	#121	C₂³×C₃₁	1	2	yes	—
740	#120	—	2	2	no	—
741	#120	—	2	2	no	—
742	#120	—	2	2	no	—
743	#120	—	2	2	no	—
744	#120	—	2	2	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	C₂³×C₃₁	1	2	yes	—
768	C₄×D₄	C₂³×C₃₁	1	2	yes	—
769	C₄×D₄	C₂³×C₃₁	1	2	yes	—
770	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
771	#117	—	2	1	no	—
772	#117	—	2	2	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	C₂³×C₃₁	1	2	yes	—
776	#117	C₂³×C₃₁	1	2	yes	—
777	C₂×C₄⋊C₄	—	2	1	no	—
778	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
779	C₂×C₂²⋊C₄	—	2	1	no	—
780	C₂×C₂²⋊C₄	—	2	1	no	—
781	C₂×C₂²⋊C₄	—	2	2	no	—
782	C₂×C₄²	—	2	1	no	—
783	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
784	#107	C₂³×C₃₁	1	2	yes	—
785	#107	C₂³×C₃₁	1	2	yes	—
786	#106	C₂³×C₃₁	1	2	yes	—
787	#106	C₂³×C₃₁	1	2	yes	—
788	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
789	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
790	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
792	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
793	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
794	#103	C₂³×C₃₁	1	2	yes	—
795	#103	C₂³×C₃₁	1	2	yes	—
796	#103	C₂³×C₃₁	1	2	yes	—
797	#103	C₂³×C₃₁	1	2	yes	—
798	#103	C₂³×C₃₁	1	2	yes	—
799	#103	C₂³×C₃₁	1	2	yes	—
800	#103	C₂³×C₃₁	1	2	yes	—
801	#103	C₂³×C₃₁	1	2	yes	—
802	#102	C₂³×C₃₁	1	2	yes	—
803	#102	C₂³×C₃₁	1	2	yes	—
804	#102	C₂³×C₃₁	1	2	yes	—
805	#102	C₂³×C₃₁	1	2	yes	—
806	#102	C₂³×C₃₁	1	2	yes	—
807	#102	C₂³×C₃₁	1	2	yes	—
808	#102	C₂³×C₃₁	1	2	yes	—
809	#102	C₂³×C₃₁	1	2	yes	—
810	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
811	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
813	#97	C₂³×C₃₁	1	2	yes	—
814	#97	C₂³×C₃₁	1	2	yes	—
815	C₄×C₈	C₂³×C₃₁	1	2	yes	—
816	C₃₁	#62019	1	1	yes	characteristic, direct product factor, Sylow
817	C₂⁴	—	2	1	no	—
818	C₂⁴	—	2	2	no	—
819	#41	—	4	2	no	—
820	#41	—	4	2	no	—
821	#41	—	8	2	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	2	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	4	no	—
829	C₂×Q₈	—	4	1	no	—
830	C₂×Q₈	—	4	2	no	—
831	C₂×Q₈	—	4	1	no	—
832	C₂×Q₈	—	4	1	no	—
833	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
834	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
835	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
836	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	1	no	—
843	C₂×D₄	—	2	1	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	4	1	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	1	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	8	4	no	—
852	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
853	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
854	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
855	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
864	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
867	Q₁₆	—	2	4	no	—
868	Q₁₆	—	4	2	no	—
869	Q₁₆	—	4	2	no	—
870	Q₁₆	—	4	2	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	2	4	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	SD₁₆	—	4	2	no	—
876	SD₁₆	—	4	2	no	—
877	SD₁₆	—	4	2	no	—
878	SD₁₆	—	4	2	no	—
879	M₁₆	—	4	2	no	—
880	C₂×C₈	—	4	1	no	—
881	C₂×C₈	—	4	2	no	—
882	C₂×C₈	—	4	1	no	—
883	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
885	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
886	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
910	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
911	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
913	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
915	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
934	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
935	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
936	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
937	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
938	C₄²	—	2	1	no	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₄²	C₂⁴×C₃₁	1	2	yes	—
950	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	4	2	no	—
955	C₂³	—	8	1	no	—
956	C₂³	—	8	2	no	—
957	C₂³	—	8	2	no	—
958	C₂³	—	8	1	no	—
959	C₂³	—	8	2	no	—
960	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
961	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
962	Q₈	—	2	1	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	1	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	2	1	no	—
967	Q₈	—	2	2	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	4	1	no	—
970	Q₈	—	4	4	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	1	no	—
975	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
976	D₄	—	2	4	no	—
977	D₄	—	2	2	no	—
978	D₄	—	2	2	no	—
979	D₄	—	2	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	4	no	—
983	D₄	—	8	1	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	D₄	—	8	1	no	—
987	D₄	—	8	2	no	—
988	D₄	—	8	1	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	1	no	—
1012	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1014	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1017	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1018	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1020	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	2	2	no	—
1024	C₈	—	2	2	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	16	2	no	—
1037	C₂²	—	16	4	no	—
1038	C₂²	C₃₁×#577	1	2	yes	—
1039	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	2	no	—
1056	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1057	C₄	C₃₁×#585	1	1	yes	characteristic
1058	C₂	—	2	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	—	8	2	no	—
1061	C₂	—	8	2	no	—
1062	C₂	C₃₁×#3488	1	1	yes	characteristic
1063	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1064	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3558	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
2. C₃₁×#3523	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3371	C₂	semidirect
5. C₃₁×#3311	C₂	semidirect
6. C₃₁×#3310	C₂	semidirect
7. C₃₁×#3300	C₂	semidirect
8. D₄×SD₁₆×C₃₁	C₂	semidirect
9. C₃₁×#3270	C₂	semidirect
10. C₃₁×#3266	C₂	semidirect
11. C₃₁×#3258	C₂	semidirect
12. C₃₁×#3246	C₂	semidirect
13. C₃₁×#3222	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3112	C₂	semidirect
17. C₃₁×#3043	C₂	semidirect
18. C₂×C₃₁×#464	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
20. C₂×C₃₁×#137	C₂²	semidirect
21. C₂²×Q₁₆×C₃₁	C₂²	semidirect
23. C₂²×SD₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
33. C₃₁×#552	C₂²	semidirect
34. D₄×Q₈×C₃₁	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#541	C₂²	semidirect
48. C₃₁×#533	C₂²	semidirect
53. C₃₁×#519	C₂²	semidirect
54. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
55. C₃₁×#497	C₂²	semidirect
56. C₃₁×#497	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
63. C₃₁×#480	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
65. C₃₁×#478	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#476	C₂²	semidirect
69. C₃₁×#475	C₂²	semidirect
70. C₃₁×#470	C₂²	semidirect
72. C₃₁×#467	C₂²	semidirect
74. C₃₁×#465	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
76. C₃₁×#464	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#464	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
83. C₃₁×#464	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
85. C₃₁×#461	C₂²	semidirect
86. C₃₁×#461	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
92. C₃₁×#452	C₂²	semidirect
93. C₃₁×#452	C₂²	semidirect
94. C₃₁×#451	C₂²	semidirect
95. C₃₁×#451	C₂²	semidirect
97. C₃₁×#450	C₂²	semidirect
98. C₃₁×#450	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
110. C₈×D₄×C₃₁	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
112. C₃₁×#432	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
114. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
115. C₃₁×#418	C₂²	semidirect
116. C₃₁×#416	C₂²	semidirect
117. C₂×C₃₁×#103	C₂²	semidirect
419. #62019	C₃₁	direct (N × H)
494. #3523	C₂×C₃₁	semidirect
495. #3400	C₂×C₃₁	semidirect
496. #3371	C₂×C₃₁	semidirect
497. #3311	C₂×C₃₁	semidirect
498. #3310	C₂×C₃₁	semidirect
499. #3300	C₂×C₃₁	semidirect
500. D₄×SD₁₆	C₂×C₃₁	semidirect
501. #3270	C₂×C₃₁	semidirect
502. #3266	C₂×C₃₁	semidirect
503. #3258	C₂×C₃₁	semidirect
504. #3246	C₂×C₃₁	semidirect
505. #3222	C₂×C₃₁	semidirect
506. #3215	C₂×C₃₁	semidirect
507. #3121	C₂×C₃₁	semidirect
508. #3112	C₂×C₃₁	semidirect
509. #3043	C₂×C₃₁	semidirect
510. C₂×#464	C₂×C₃₁	semidirect
511. #2992	C₂×C₃₁	semidirect
545. C₂×#137	C₂²×C₃₁	semidirect
546. C₂²×Q₁₆	C₂²×C₃₁	semidirect
548. C₂²×SD₁₆	C₂²×C₃₁	semidirect
553. #557	C₂²×C₃₁	semidirect
554. #557	C₂²×C₃₁	semidirect
556. #556	C₂²×C₃₁	semidirect
558. #552	C₂²×C₃₁	semidirect
559. D₄×Q₈	C₂²×C₃₁	semidirect
560. D₄×Q₈	C₂²×C₃₁	semidirect
567. #541	C₂²×C₃₁	semidirect
573. #533	C₂²×C₃₁	semidirect
578. #519	C₂²×C₃₁	semidirect
579. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
580. #497	C₂²×C₃₁	semidirect
581. #497	C₂²×C₃₁	semidirect
584. #489	C₂²×C₃₁	semidirect
585. #488	C₂²×C₃₁	semidirect
586. #485	C₂²×C₃₁	semidirect
588. #480	C₂²×C₃₁	semidirect
589. #479	C₂²×C₃₁	semidirect
590. #478	C₂²×C₃₁	semidirect
591. #477	C₂²×C₃₁	semidirect
592. #477	C₂²×C₃₁	semidirect
593. #476	C₂²×C₃₁	semidirect
594. #475	C₂²×C₃₁	semidirect
595. #470	C₂²×C₃₁	semidirect
597. #467	C₂²×C₃₁	semidirect
599. #465	C₂²×C₃₁	semidirect
600. #465	C₂²×C₃₁	semidirect
601. #464	C₂²×C₃₁	semidirect
602. #464	C₂²×C₃₁	semidirect
603. #464	C₂²×C₃₁	semidirect
604. #464	C₂²×C₃₁	semidirect
605. #464	C₂²×C₃₁	semidirect
606. #464	C₂²×C₃₁	semidirect
607. #464	C₂²×C₃₁	semidirect
608. #464	C₂²×C₃₁	semidirect
609. #462	C₂²×C₃₁	semidirect
610. #461	C₂²×C₃₁	semidirect
611. #461	C₂²×C₃₁	semidirect
614. #460	C₂²×C₃₁	semidirect
615. #460	C₂²×C₃₁	semidirect
616. #460	C₂²×C₃₁	semidirect
617. #452	C₂²×C₃₁	semidirect
618. #452	C₂²×C₃₁	semidirect
619. #451	C₂²×C₃₁	semidirect
620. #451	C₂²×C₃₁	semidirect
622. #450	C₂²×C₃₁	semidirect
623. #450	C₂²×C₃₁	semidirect
625. #448	C₂²×C₃₁	semidirect
626. #446	C₂²×C₃₁	semidirect
627. #441	C₂²×C₃₁	semidirect
628. #440	C₂²×C₃₁	semidirect
629. #440	C₂²×C₃₁	semidirect
630. #440	C₂²×C₃₁	semidirect
631. C₄×Q₁₆	C₂²×C₃₁	semidirect
632. C₄×SD₁₆	C₂²×C₃₁	semidirect
633. #435	C₂²×C₃₁	semidirect
634. #435	C₂²×C₃₁	semidirect
635. C₈×D₄	C₂²×C₃₁	semidirect
636. #433	C₂²×C₃₁	semidirect
637. #432	C₂²×C₃₁	semidirect
638. #424	C₂²×C₃₁	semidirect
639. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
640. #418	C₂²×C₃₁	semidirect
641. #416	C₂²×C₃₁	semidirect
642. C₂×#103	C₂²×C₃₁	semidirect
816. C₃₁	#62019	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×#3558	2
C₃₁×#3523	2
C₃₁×#3400	2
C₃₁×#3371	2
C₃₁×#3311	2
C₃₁×#3310	2
C₃₁×#3300	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3270	2
C₃₁×#3266	2
C₃₁×#3258	2
C₃₁×#3246	2
C₃₁×#3222	2
C₃₁×#3215	2
C₃₁×#3121	2
C₃₁×#3112	2
C₃₁×#3043	2
C₂×C₃₁×#464	2
C₃₁×#2992	2
#62019	31

Subgroups — C31×#62019 #21518778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62019 #21518778