Subgroups — C₃₁×#60923 #21517682

Order 7936.

1812 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3460	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3260	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3258	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3254	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3246	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3082	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3057	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3043	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
20	C₂×C₃₁×#131	C₂²	1	2	yes	—
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#552	—	2	2	no	—
26	C₃₁×#552	—	2	2	no	—
27	C₃₁×#544	C₂²	1	1	yes	characteristic
28	C₃₁×#542	—	2	1	no	—
29	C₃₁×#542	C₂²	1	2	yes	—
30	C₃₁×#541	C₂²	1	4	yes	complemented
31	C₃₁×#540	—	2	1	no	—
32	C₃₁×#540	C₂²	1	2	yes	—
33	C₃₁×#538	—	2	2	no	—
34	C₃₁×#537	C₂²	1	1	yes	characteristic
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#535	C₂²	1	1	yes	characteristic
37	C₃₁×#535	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	1	yes	characteristic
39	C₃₁×#533	C₂²	1	2	yes	complemented
40	C₃₁×#533	C₂²	1	2	yes	complemented
41	C₃₁×#532	—	2	1	no	—
42	C₃₁×#532	C₂²	1	2	yes	—
43	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₃₁×#529	—	2	1	no	—
45	C₃₁×#529	C₂²	1	2	yes	—
46	C₃₁×#525	—	2	2	no	—
47	C₃₁×#519	C₂²	1	2	yes	—
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#479	C₂²	1	2	yes	complemented
52	C₃₁×#479	C₂²	1	4	yes	complemented
53	C₃₁×#479	C₂²	1	4	yes	complemented
54	C₃₁×#478	C₂²	1	4	yes	—
55	C₃₁×#478	C₂²	1	2	yes	complemented
56	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#477	C₂²	1	4	yes	complemented
58	C₃₁×#476	C₂²	1	2	yes	—
59	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#475	C₂²	1	4	yes	complemented
62	C₃₁×#474	C₂²	1	2	yes	—
63	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#470	C₂²	1	4	yes	complemented
65	C₃₁×#468	C₂²	1	4	yes	—
66	C₃₁×#468	C₂²	1	4	yes	—
67	C₃₁×#468	C₂²	1	4	yes	complemented
68	C₃₁×#467	C₂²	1	4	yes	complemented
69	C₃₁×#465	C₂²	1	4	yes	—
70	C₃₁×#465	C₂²	1	4	yes	—
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#464	C₂²	1	4	yes	—
73	C₃₁×#464	C₂²	1	4	yes	—
74	C₃₁×#462	C₂²	1	2	yes	complemented
75	C₃₁×#462	C₂²	1	2	yes	complemented
76	C₃₁×#461	C₂²	1	2	yes	—
77	C₃₁×#461	C₂²	1	2	yes	—
78	C₃₁×#461	C₂²	1	4	yes	—
79	C₃₁×#461	C₂²	1	2	yes	complemented
80	C₃₁×#461	C₂²	1	2	yes	complemented
81	C₃₁×#460	C₂²	1	4	yes	—
82	C₃₁×#460	C₂²	1	4	yes	—
83	C₃₁×#428	C₂²	1	2	yes	—
84	C₃₁×#427	C₂²	1	2	yes	—
85	C₃₁×#424	C₂²	1	2	yes	—
86	C₃₁×#424	C₂²	1	4	yes	complemented
87	C₃₁×#423	C₂²	1	1	yes	characteristic
88	C₃₁×#423	C₂²	1	2	yes	complemented
89	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
91	C₃₁×#419	C₂²	1	2	yes	—
92	C₃₁×#418	C₂²	1	2	yes	—
93	C₃₁×#416	C₂²	1	2	yes	—
94	C₂×C₃₁×#103	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	—	2	1	no	—
101	C₃₁×#137	—	4	4	no	—
102	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₃₁	—	4	4	no	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
107	C₃₁×#131	—	4	4	no	—
108	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
109	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
111	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
112	C₃₁×C₄⋊Q₈	—	2	2	no	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×#127	—	2	1	no	—
122	C₃₁×#127	C₂³	1	2	yes	—
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#126	—	2	4	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#125	—	2	1	no	—
128	C₃₁×#125	—	2	4	no	—
129	C₃₁×#125	—	2	4	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	2	no	—
132	C₃₁×#125	C₂³	1	2	yes	—
133	C₃₁×#125	C₂³	1	2	yes	—
134	C₃₁×#124	—	2	1	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	—	2	2	no	—
137	C₃₁×#124	—	2	2	no	—
138	C₃₁×#124	C₂³	1	2	yes	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	2	no	—
143	C₃₁×#123	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	1	no	—
158	C₃₁×#121	—	2	1	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	2	no	—
161	C₃₁×#121	C₂³	1	2	yes	—
162	C₃₁×#121	C₂³	1	2	yes	—
163	C₃₁×#121	C₂³	1	2	yes	—
164	C₃₁×#120	—	2	2	no	—
165	C₃₁×#120	—	2	2	no	—
166	C₄×Q₈×C₃₁	—	2	2	no	—
167	C₄×Q₈×C₃₁	—	2	2	no	—
168	C₄×Q₈×C₃₁	—	2	1	no	—
169	C₄×Q₈×C₃₁	—	2	1	no	—
170	C₄×Q₈×C₃₁	—	2	2	no	—
171	C₄×Q₈×C₃₁	—	2	2	no	—
172	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
175	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
176	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	—	2	1	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	D₄	1	2	yes	—
185	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
186	C₄×D₄×C₃₁	D₄	1	2	yes	—
187	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₃₁×#117	—	2	2	no	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	—	2	4	no	—
195	C₃₁×#117	—	2	1	no	—
196	C₃₁×#117	—	2	2	no	—
197	C₃₁×#117	C₂³	1	2	yes	—
198	C₃₁×#117	C₂³	1	1	yes	characteristic
199	C₃₁×#117	C₂³	1	1	yes	characteristic
200	C₃₁×#117	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	2	yes	—
212	C₃₁×#106	C₂³	1	2	yes	—
213	C₃₁×#106	C₂³	1	4	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
218	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
219	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
220	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	4	yes	—
222	C₃₁×#103	C₂³	1	4	yes	—
223	C₃₁×#103	C₂³	1	2	yes	—
224	C₃₁×#103	C₂³	1	2	yes	—
225	C₃₁×#103	C₂³	1	4	yes	—
226	C₃₁×#103	C₂³	1	4	yes	—
227	C₃₁×#102	C₂³	1	2	yes	—
228	C₃₁×#102	C₂³	1	2	yes	—
229	C₃₁×#102	C₂³	1	4	yes	—
230	C₃₁×#102	C₂³	1	4	yes	—
231	C₂⁴×C₃₁	—	2	1	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	2	2	no	—
234	#41×C₃₁	—	2	2	no	—
235	#41×C₃₁	—	2	2	no	—
236	#41×C₃₁	—	8	4	no	—
237	C₂×Q₈×C₃₁	—	2	1	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	2	4	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	1	no	—
261	C₂²×C₄×C₃₁	—	2	1	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	8	2	no	—
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	Q₁₆×C₃₁	—	4	4	no	—
274	SD₁₆×C₃₁	—	4	4	no	—
275	SD₁₆×C₃₁	—	4	4	no	—
276	SD₁₆×C₃₁	—	4	4	no	—
277	M₁₆×C₃₁	—	2	4	no	—
278	M₁₆×C₃₁	—	4	4	no	—
279	C₂×C₈×C₃₁	—	2	4	no	—
280	C₂×C₈×C₃₁	—	4	4	no	—
281	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
282	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	4	no	—
302	C₄⋊C₄×C₃₁	—	2	4	no	—
303	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	1	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	2	no	—
325	C₂²⋊C₄×C₃₁	—	2	2	no	—
326	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	—	2	1	no	—
330	C₄²×C₃₁	—	2	1	no	—
331	C₄²×C₃₁	—	2	1	no	—
332	C₄²×C₃₁	—	2	4	no	—
333	C₄²×C₃₁	—	2	4	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₃₁	C₂×D₄	1	2	yes	—
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₄²×C₃₁	C₂⁴	1	2	yes	—
342	#60923	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₃₁	—	2	2	no	—
344	C₂³×C₃₁	—	2	1	no	—
345	C₂³×C₃₁	—	4	2	no	—
346	C₂³×C₃₁	—	8	1	no	—
347	C₂³×C₃₁	—	8	1	no	—
348	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
349	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₃₁	—	2	2	no	—
351	Q₈×C₃₁	—	2	4	no	—
352	Q₈×C₃₁	—	2	1	no	—
353	Q₈×C₃₁	—	2	4	no	—
354	Q₈×C₃₁	—	2	1	no	—
355	Q₈×C₃₁	—	4	2	no	—
356	Q₈×C₃₁	—	4	4	no	—
357	Q₈×C₃₁	—	4	2	no	—
358	Q₈×C₃₁	—	8	2	no	—
359	D₄×C₃₁	—	2	4	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	2	no	—
362	D₄×C₃₁	—	2	1	no	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	2	1	no	—
365	D₄×C₃₁	—	4	2	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	—	8	2	no	—
368	D₄×C₃₁	—	8	2	no	—
369	D₄×C₃₁	—	8	2	no	—
370	D₄×C₃₁	—	8	2	no	—
371	D₄×C₃₁	—	8	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	4	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	4	1	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	4	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	—	4	4	no	—
388	C₂×C₄×C₃₁	—	4	2	no	—
389	C₂×C₄×C₃₁	—	8	1	no	—
390	C₂×C₄×C₃₁	—	8	2	no	—
391	C₂×C₄×C₃₁	—	8	1	no	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
401	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
402	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
403	C₈×C₃₁	—	2	2	no	—
404	C₈×C₃₁	—	2	2	no	—
405	C₈×C₃₁	—	2	4	no	—
406	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3460	C₂×C₃₁	1	1	yes	characteristic
408	#3260	C₂×C₃₁	1	4	yes	complemented
409	#3258	C₂×C₃₁	1	4	yes	complemented
410	#3254	C₂×C₃₁	1	2	yes	complemented
411	#3252	C₂×C₃₁	1	2	yes	complemented
412	#3248	C₂×C₃₁	1	2	yes	complemented
413	#3246	C₂×C₃₁	1	2	yes	complemented
414	#3082	C₂×C₃₁	1	2	yes	complemented
415	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#3063	C₂×C₃₁	1	2	yes	complemented
418	#3057	C₂×C₃₁	1	2	yes	complemented
419	#3043	C₂×C₃₁	1	2	yes	complemented
420	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₂×#461	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#2906	C₂×C₃₁	1	1	yes	characteristic, complemented
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	2	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	2	2	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	—	4	2	no	—
430	C₂²×C₃₁	—	4	1	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	1	no	—
434	C₂²×C₃₁	—	8	4	no	—
435	C₂²×C₃₁	#537	1	2	yes	—
436	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
437	C₄×C₃₁	—	2	1	no	—
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	2	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	4	1	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	4	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	2	no	—
450	C₄×C₃₁	#537	1	2	yes	—
451	C₄×C₃₁	#577	1	2	yes	—
452	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂×#137	C₂²×C₃₁	1	2	yes	—
455	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
456	C₂×#131	C₂²×C₃₁	1	2	yes	—
457	#557	—	2	1	no	—
458	#557	—	2	1	no	—
459	#556	—	2	1	no	—
460	#556	—	2	1	no	—
461	#552	—	2	2	no	—
462	#552	—	2	2	no	—
463	#544	C₂²×C₃₁	1	1	yes	characteristic
464	#542	—	2	1	no	—
465	#542	C₂²×C₃₁	1	2	yes	—
466	#541	C₂²×C₃₁	1	4	yes	complemented
467	#540	—	2	1	no	—
468	#540	C₂²×C₃₁	1	2	yes	—
469	#538	—	2	2	no	—
470	#537	C₂²×C₃₁	1	1	yes	characteristic
471	#536	C₂²×C₃₁	1	2	yes	—
472	#535	C₂²×C₃₁	1	1	yes	characteristic
473	#535	C₂²×C₃₁	1	1	yes	characteristic
474	#533	C₂²×C₃₁	1	1	yes	characteristic
475	#533	C₂²×C₃₁	1	2	yes	complemented
476	#533	C₂²×C₃₁	1	2	yes	complemented
477	#532	—	2	1	no	—
478	#532	C₂²×C₃₁	1	2	yes	—
479	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
480	#529	—	2	1	no	—
481	#529	C₂²×C₃₁	1	2	yes	—
482	#525	—	2	2	no	—
483	#519	C₂²×C₃₁	1	2	yes	—
484	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
485	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
486	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
487	#479	C₂²×C₃₁	1	2	yes	complemented
488	#479	C₂²×C₃₁	1	4	yes	complemented
489	#479	C₂²×C₃₁	1	4	yes	complemented
490	#478	C₂²×C₃₁	1	4	yes	—
491	#478	C₂²×C₃₁	1	2	yes	complemented
492	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
493	#477	C₂²×C₃₁	1	4	yes	complemented
494	#476	C₂²×C₃₁	1	2	yes	—
495	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#475	C₂²×C₃₁	1	4	yes	complemented
498	#474	C₂²×C₃₁	1	2	yes	—
499	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#470	C₂²×C₃₁	1	4	yes	complemented
501	#468	C₂²×C₃₁	1	4	yes	—
502	#468	C₂²×C₃₁	1	4	yes	—
503	#468	C₂²×C₃₁	1	4	yes	complemented
504	#467	C₂²×C₃₁	1	4	yes	complemented
505	#465	C₂²×C₃₁	1	4	yes	—
506	#465	C₂²×C₃₁	1	4	yes	—
507	#465	C₂²×C₃₁	1	4	yes	complemented
508	#464	C₂²×C₃₁	1	4	yes	—
509	#464	C₂²×C₃₁	1	4	yes	—
510	#462	C₂²×C₃₁	1	2	yes	complemented
511	#462	C₂²×C₃₁	1	2	yes	complemented
512	#461	C₂²×C₃₁	1	2	yes	—
513	#461	C₂²×C₃₁	1	2	yes	—
514	#461	C₂²×C₃₁	1	4	yes	—
515	#461	C₂²×C₃₁	1	2	yes	complemented
516	#461	C₂²×C₃₁	1	2	yes	complemented
517	#460	C₂²×C₃₁	1	4	yes	—
518	#460	C₂²×C₃₁	1	4	yes	—
519	#428	C₂²×C₃₁	1	2	yes	—
520	#427	C₂²×C₃₁	1	2	yes	—
521	#424	C₂²×C₃₁	1	2	yes	—
522	#424	C₂²×C₃₁	1	4	yes	complemented
523	#423	C₂²×C₃₁	1	1	yes	characteristic
524	#423	C₂²×C₃₁	1	2	yes	complemented
525	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
527	#419	C₂²×C₃₁	1	2	yes	—
528	#418	C₂²×C₃₁	1	2	yes	—
529	#416	C₂²×C₃₁	1	2	yes	—
530	C₂×#103	C₂²×C₃₁	1	2	yes	—
531	C₂×C₃₁	—	2	2	no	—
532	C₂×C₃₁	—	4	2	no	—
533	C₂×C₃₁	—	8	1	no	—
534	C₂×C₃₁	—	8	2	no	—
535	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
536	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
537	C₂×C₃₁	#3586	1	1	yes	characteristic
538	C₂×#41	—	2	2	no	—
539	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
542	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂³×C₄	—	2	1	no	—
544	#137	—	4	4	no	—
545	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
546	C₂×SD₁₆	—	4	4	no	—
547	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
548	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
550	#131	—	4	4	no	—
551	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
552	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
553	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
554	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
555	C₄⋊Q₈	—	2	2	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	#127	—	2	1	no	—
565	#127	C₂³×C₃₁	1	2	yes	—
566	#126	—	2	2	no	—
567	#126	—	2	4	no	—
568	#126	—	2	4	no	—
569	#126	—	2	2	no	—
570	#125	—	2	1	no	—
571	#125	—	2	4	no	—
572	#125	—	2	4	no	—
573	#125	—	2	2	no	—
574	#125	—	2	2	no	—
575	#125	C₂³×C₃₁	1	2	yes	—
576	#125	C₂³×C₃₁	1	2	yes	—
577	#124	—	2	1	no	—
578	#124	—	2	2	no	—
579	#124	—	2	2	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₃₁	1	2	yes	—
582	#123	—	2	4	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
595	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
596	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
597	#121	—	2	2	no	—
598	#121	—	2	1	no	—
599	#121	—	2	2	no	—
600	#121	—	2	1	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	C₂³×C₃₁	1	2	yes	—
605	#121	C₂³×C₃₁	1	2	yes	—
606	#121	C₂³×C₃₁	1	2	yes	—
607	#120	—	2	2	no	—
608	#120	—	2	2	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	2	no	—
614	C₄×Q₈	—	2	2	no	—
615	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
616	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
620	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₃₁	1	2	yes	—
628	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
629	C₄×D₄	D₄×C₃₁	1	2	yes	—
630	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₃₁	1	2	yes	—
632	C₄×D₄	C₂³×C₃₁	1	2	yes	—
633	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
635	#117	—	2	2	no	—
636	#117	—	2	2	no	—
637	#117	—	2	4	no	—
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	C₂³×C₃₁	1	1	yes	characteristic
641	#117	C₂³×C₃₁	1	2	yes	—
642	#117	C₂³×C₃₁	1	1	yes	characteristic
643	#117	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
651	#107	C₂³×C₃₁	1	2	yes	—
652	#107	C₂³×C₃₁	1	2	yes	—
653	#107	C₂³×C₃₁	1	4	yes	—
654	#106	C₂³×C₃₁	1	2	yes	—
655	#106	C₂³×C₃₁	1	2	yes	—
656	#106	C₂³×C₃₁	1	4	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
658	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
659	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
660	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
661	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
662	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
663	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
664	#103	C₂³×C₃₁	1	4	yes	—
665	#103	C₂³×C₃₁	1	4	yes	—
666	#103	C₂³×C₃₁	1	2	yes	—
667	#103	C₂³×C₃₁	1	2	yes	—
668	#103	C₂³×C₃₁	1	4	yes	—
669	#103	C₂³×C₃₁	1	4	yes	—
670	#102	C₂³×C₃₁	1	2	yes	—
671	#102	C₂³×C₃₁	1	2	yes	—
672	#102	C₂³×C₃₁	1	4	yes	—
673	#102	C₂³×C₃₁	1	4	yes	—
674	C₃₁	#60923	1	1	yes	characteristic, direct product factor, Sylow
675	C₂⁴	—	2	1	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	—	2	2	no	—
680	#41	—	8	4	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
688	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
700	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
702	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	8	2	no	—
711	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
717	Q₁₆	—	4	4	no	—
718	SD₁₆	—	4	4	no	—
719	SD₁₆	—	4	4	no	—
720	SD₁₆	—	4	4	no	—
721	M₁₆	—	2	4	no	—
722	M₁₆	—	4	4	no	—
723	C₂×C₈	—	2	4	no	—
724	C₂×C₈	—	4	4	no	—
725	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
726	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
727	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
750	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₃₁	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₃₁	1	2	yes	—
781	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
782	C₄²	C₂×D₄×C₃₁	1	2	yes	—
783	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₄²	C₂⁴×C₃₁	1	2	yes	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	1	no	—
790	C₂³	—	8	1	no	—
791	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
792	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	2	4	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	D₄	—	2	4	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	1	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	8	1	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
844	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
845	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	2	no	—
848	C₈	—	2	4	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	8	4	no	—
861	C₂²	C₃₁×#537	1	2	yes	—
862	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	4	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	C₃₁×#537	1	2	yes	—
877	C₄	C₃₁×#577	1	2	yes	—
878	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
879	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	8	2	no	—
883	C₂	—	8	1	no	—
884	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
885	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
886	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×#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3260	C₂	semidirect
4. C₃₁×#3258	C₂	semidirect
5. C₃₁×#3254	C₂	semidirect
6. C₃₁×#3252	C₂	semidirect
7. C₃₁×#3248	C₂	semidirect
8. C₃₁×#3246	C₂	semidirect
9. C₃₁×#3082	C₂	semidirect
10. C₃₁×#3077	C₂	semidirect
11. C₃₁×#3076	C₂	semidirect
12. C₃₁×#3063	C₂	semidirect
13. C₃₁×#3057	C₂	semidirect
14. C₃₁×#3043	C₂	semidirect
15. C₃₁×#3039	C₂	semidirect
16. C₂×C₃₁×#461	C₂	semidirect
17. C₃₁×#2906	C₂	semidirect
30. C₃₁×#541	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
40. C₃₁×#533	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
52. C₃₁×#479	C₂²	semidirect
53. C₃₁×#479	C₂²	semidirect
55. C₃₁×#478	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#475	C₂²	semidirect
61. C₃₁×#475	C₂²	semidirect
63. C₃₁×#474	C₂²	semidirect
64. C₃₁×#470	C₂²	semidirect
67. C₃₁×#468	C₂²	semidirect
68. C₃₁×#467	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
74. C₃₁×#462	C₂²	semidirect
75. C₃₁×#462	C₂²	semidirect
79. C₃₁×#461	C₂²	semidirect
80. C₃₁×#461	C₂²	semidirect
86. C₃₁×#424	C₂²	semidirect
88. C₃₁×#423	C₂²	semidirect
90. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
342. #60923	C₃₁	direct (N × H)
406. #3509	C₂×C₃₁	semidirect
408. #3260	C₂×C₃₁	semidirect
409. #3258	C₂×C₃₁	semidirect
410. #3254	C₂×C₃₁	semidirect
411. #3252	C₂×C₃₁	semidirect
412. #3248	C₂×C₃₁	semidirect
413. #3246	C₂×C₃₁	semidirect
414. #3082	C₂×C₃₁	semidirect
415. #3077	C₂×C₃₁	semidirect
416. #3076	C₂×C₃₁	semidirect
417. #3063	C₂×C₃₁	semidirect
418. #3057	C₂×C₃₁	semidirect
419. #3043	C₂×C₃₁	semidirect
420. #3039	C₂×C₃₁	semidirect
421. C₂×#461	C₂×C₃₁	semidirect
422. #2906	C₂×C₃₁	semidirect
466. #541	C₂²×C₃₁	semidirect
475. #533	C₂²×C₃₁	semidirect
476. #533	C₂²×C₃₁	semidirect
487. #479	C₂²×C₃₁	semidirect
488. #479	C₂²×C₃₁	semidirect
489. #479	C₂²×C₃₁	semidirect
491. #478	C₂²×C₃₁	semidirect
492. #477	C₂²×C₃₁	semidirect
493. #477	C₂²×C₃₁	semidirect
495. #476	C₂²×C₃₁	semidirect
496. #475	C₂²×C₃₁	semidirect
497. #475	C₂²×C₃₁	semidirect
499. #474	C₂²×C₃₁	semidirect
500. #470	C₂²×C₃₁	semidirect
503. #468	C₂²×C₃₁	semidirect
504. #467	C₂²×C₃₁	semidirect
507. #465	C₂²×C₃₁	semidirect
510. #462	C₂²×C₃₁	semidirect
511. #462	C₂²×C₃₁	semidirect
515. #461	C₂²×C₃₁	semidirect
516. #461	C₂²×C₃₁	semidirect
522. #424	C₂²×C₃₁	semidirect
524. #423	C₂²×C₃₁	semidirect
526. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
674. C₃₁	#60923	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×#3509	2
C₃₁×#3460	2
C₃₁×#3260	2
C₃₁×#3258	2
C₃₁×#3254	2
C₃₁×#3252	2
C₃₁×#3248	2
C₃₁×#3246	2
C₃₁×#3082	2
C₃₁×#3077	2
C₃₁×#3076	2
C₃₁×#3063	2
C₃₁×#3057	2
C₃₁×#3043	2
C₃₁×#3039	2
C₂×C₃₁×#461	2
C₃₁×#2906	2
#60923	31

Subgroups — C31×#60923 #21517682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60923 #21517682