Subgroups — C₃₁×#61998 #21518757

Order 7936.

1840 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3393	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3327	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3277	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3276	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3104	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3037	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	4	yes	—
19	C₂×C₃₁×#137	C₂²	1	2	yes	—
20	C₃₁×#557	C₂²	1	1	yes	characteristic
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	C₂²	1	2	yes	—
23	C₃₁×#556	C₂²	1	1	yes	characteristic
24	C₃₁×#555	—	2	1	no	—
25	C₃₁×#554	—	2	1	no	—
26	C₃₁×#553	—	2	2	no	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#548	C₂²	1	2	yes	—
31	C₃₁×#548	C₂²	1	4	yes	—
32	C₃₁×#547	—	2	1	no	—
33	C₃₁×#547	C₂²	1	2	yes	—
34	C₃₁×#547	C₂²	1	1	yes	characteristic
35	C₃₁×#542	—	2	2	no	—
36	C₃₁×#537	—	2	1	no	—
37	C₃₁×#533	—	2	1	no	—
38	C₃₁×#533	C₂²	1	2	yes	—
39	C₃₁×#533	C₂²	1	1	yes	characteristic
40	C₃₁×#532	C₂²	1	2	yes	—
41	C₃₁×#532	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#529	C₂²	1	2	yes	—
45	C₃₁×#520	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
50	C₃₁×#495	C₂²	1	4	yes	—
51	C₃₁×#494	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	—
53	C₃₁×#487	C₂²	1	2	yes	—
54	C₃₁×#484	C₂²	1	4	yes	—
55	C₃₁×#482	C₂²	1	2	yes	—
56	C₃₁×#479	C₂²	1	4	yes	—
57	C₃₁×#477	C₂²	1	1	yes	characteristic
58	C₃₁×#477	C₂²	1	2	yes	—
59	C₃₁×#476	C₂²	1	1	yes	characteristic
60	C₃₁×#474	C₂²	1	2	yes	—
61	C₃₁×#470	C₂²	1	4	yes	—
62	C₃₁×#468	C₂²	1	4	yes	—
63	C₃₁×#468	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	—
65	C₃₁×#464	C₂²	1	4	yes	—
66	C₃₁×#464	C₂²	1	4	yes	—
67	C₃₁×#462	C₂²	1	2	yes	—
68	C₃₁×#462	C₂²	1	2	yes	—
69	C₃₁×#462	C₂²	1	2	yes	—
70	C₃₁×#462	C₂²	1	2	yes	—
71	C₃₁×#461	C₂²	1	2	yes	—
72	C₃₁×#461	C₂²	1	2	yes	—
73	C₃₁×#461	C₂²	1	2	yes	—
74	C₃₁×#460	C₂²	1	1	yes	characteristic
75	C₃₁×#460	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	1	yes	characteristic
77	C₃₁×#452	C₂²	1	4	yes	—
78	C₃₁×#451	C₂²	1	4	yes	—
79	C₃₁×#451	C₂²	1	4	yes	—
80	C₃₁×#449	C₂²	1	2	yes	—
81	C₃₁×#449	C₂²	1	4	yes	—
82	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
86	C₄×D₈×C₃₁	C₂²	1	2	yes	—
87	C₃₁×#436	C₂²	1	2	yes	—
88	C₃₁×#436	C₂²	1	4	yes	—
89	C₃₁×#431	C₂²	1	2	yes	—
90	C₃₁×#431	C₂²	1	1	yes	characteristic
91	C₃₁×#423	C₂²	1	2	yes	—
92	C₃₁×#423	C₂²	1	1	yes	characteristic
93	C₃₁×#419	C₂²	1	2	yes	—
94	C₃₁×#417	C₂²	1	4	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
102	C₃₁×#137	—	4	8	no	—
103	C₃₁×#137	—	4	4	no	—
104	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×D₈×C₃₁	C₂³	1	2	yes	—
111	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
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	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₃₁×#127	C₂³	1	1	yes	characteristic
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#125	—	2	2	no	—
128	C₃₁×#125	—	2	2	no	—
129	C₃₁×#125	—	2	1	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	C₂³	1	2	yes	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#124	—	2	4	no	—
134	C₃₁×#124	—	2	1	no	—
135	C₃₁×#124	C₂³	1	4	yes	—
136	C₃₁×#124	C₂³	1	2	yes	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	1	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	4	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	4	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	1	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₄×Q₈×C₃₁	—	2	1	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	2	no	—
163	C₄×Q₈×C₃₁	—	2	1	no	—
164	C₄×Q₈×C₃₁	—	2	2	no	—
165	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	4	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
183	C₄×D₄×C₃₁	D₄	1	2	yes	—
184	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₃₁	C₂³	1	2	yes	—
186	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₃₁×#117	—	2	1	no	—
190	C₃₁×#117	—	2	2	no	—
191	C₃₁×#117	—	2	1	no	—
192	C₃₁×#117	—	2	2	no	—
193	C₃₁×#117	—	2	2	no	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	—	2	2	no	—
196	C₃₁×#117	D₄	1	1	yes	characteristic
197	C₃₁×#117	D₄	1	2	yes	—
198	C₃₁×#117	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
202	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₃₁	—	2	2	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#103	C₂³	1	4	yes	—
221	C₃₁×#103	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	4	yes	—
230	#41×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	4	2	no	—
232	#41×C₃₁	—	4	1	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	4	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	4	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	4	2	no	—
243	C₂×Q₈×C₃₁	—	4	2	no	—
244	C₂×Q₈×C₃₁	—	4	2	no	—
245	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	4	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	—	2	1	no	—
255	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
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	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	4	no	—
267	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	—	2	8	no	—
274	Q₁₆×C₃₁	—	4	4	no	—
275	Q₁₆×C₃₁	—	4	4	no	—
276	SD₁₆×C₃₁	—	2	4	no	—
277	SD₁₆×C₃₁	—	4	4	no	—
278	SD₁₆×C₃₁	—	4	4	no	—
279	D₈×C₃₁	—	4	2	no	—
280	M₁₆×C₃₁	—	4	4	no	—
281	M₁₆×C₃₁	—	4	2	no	—
282	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
284	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	4	no	—
305	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	1	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	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	4	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	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	4	no	—
336	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂×D₄	1	2	yes	—
339	C₄²×C₃₁	C₂×D₄	1	2	yes	—
340	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₄²×C₃₁	C₂⁴	1	2	yes	—
342	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
343	#61998	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₃₁	—	2	1	no	—
345	C₂³×C₃₁	—	2	2	no	—
346	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
347	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₃₁	—	2	2	no	—
349	Q₈×C₃₁	—	2	1	no	—
350	Q₈×C₃₁	—	2	2	no	—
351	Q₈×C₃₁	—	2	4	no	—
352	Q₈×C₃₁	—	2	2	no	—
353	Q₈×C₃₁	—	2	4	no	—
354	Q₈×C₃₁	—	4	4	no	—
355	Q₈×C₃₁	—	4	2	no	—
356	Q₈×C₃₁	—	4	2	no	—
357	Q₈×C₃₁	—	8	2	no	—
358	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
359	D₄×C₃₁	—	2	2	no	—
360	D₄×C₃₁	—	2	2	no	—
361	D₄×C₃₁	—	2	1	no	—
362	D₄×C₃₁	—	2	1	no	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	4	2	no	—
365	D₄×C₃₁	—	4	2	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	—	4	4	no	—
368	D₄×C₃₁	—	4	4	no	—
369	D₄×C₃₁	—	4	2	no	—
370	D₄×C₃₁	—	8	4	no	—
371	C₂×C₄×C₃₁	—	2	1	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	1	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	4	no	—
385	C₂×C₄×C₃₁	—	4	2	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	—	4	4	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	—	4	2	no	—
390	C₂×C₄×C₃₁	—	4	4	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	—	8	4	no	—
393	C₂×C₄×C₃₁	—	8	2	no	—
394	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
403	C₈×C₃₁	—	2	2	no	—
404	C₈×C₃₁	—	2	4	no	—
405	C₈×C₃₁	—	2	2	no	—
406	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3393	C₂×C₃₁	1	2	yes	complemented
409	#3364	C₂×C₃₁	1	2	yes	complemented
410	#3330	C₂×C₃₁	1	2	yes	complemented
411	#3327	C₂×C₃₁	1	4	yes	complemented
412	#3277	C₂×C₃₁	1	4	yes	complemented
413	#3276	C₂×C₃₁	1	2	yes	complemented
414	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#3252	C₂×C₃₁	1	2	yes	complemented
416	#3212	C₂×C₃₁	1	2	yes	complemented
417	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3104	C₂×C₃₁	1	2	yes	complemented
420	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
421	#3037	C₂×C₃₁	1	2	yes	complemented
422	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	1	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	2	2	no	—
428	C₂²×C₃₁	—	2	1	no	—
429	C₂²×C₃₁	—	4	1	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	2	no	—
432	C₂²×C₃₁	—	4	1	no	—
433	C₂²×C₃₁	—	4	1	no	—
434	C₂²×C₃₁	—	4	2	no	—
435	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
436	C₄×C₃₁	—	2	1	no	—
437	C₄×C₃₁	—	2	2	no	—
438	C₄×C₃₁	—	2	2	no	—
439	C₄×C₃₁	—	2	1	no	—
440	C₄×C₃₁	—	2	2	no	—
441	C₄×C₃₁	—	2	2	no	—
442	C₄×C₃₁	—	2	1	no	—
443	C₄×C₃₁	—	4	2	no	—
444	C₄×C₃₁	—	4	4	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	#575	1	2	yes	—
450	C₄×C₃₁	#578	1	2	yes	—
451	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₄×C₃₁	#585	1	1	yes	characteristic
453	C₂×#137	C₂²×C₃₁	1	4	yes	—
454	C₂×#137	C₂²×C₃₁	1	2	yes	—
455	#557	C₂²×C₃₁	1	1	yes	characteristic
456	#556	—	2	1	no	—
457	#556	C₂²×C₃₁	1	2	yes	—
458	#556	C₂²×C₃₁	1	1	yes	characteristic
459	#555	—	2	1	no	—
460	#554	—	2	1	no	—
461	#553	—	2	2	no	—
462	#552	—	2	2	no	—
463	#552	C₂²×C₃₁	1	2	yes	—
464	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
465	#548	C₂²×C₃₁	1	2	yes	—
466	#548	C₂²×C₃₁	1	4	yes	—
467	#547	—	2	1	no	—
468	#547	C₂²×C₃₁	1	2	yes	—
469	#547	C₂²×C₃₁	1	1	yes	characteristic
470	#542	—	2	2	no	—
471	#537	—	2	1	no	—
472	#533	—	2	1	no	—
473	#533	C₂²×C₃₁	1	2	yes	—
474	#533	C₂²×C₃₁	1	1	yes	characteristic
475	#532	C₂²×C₃₁	1	2	yes	—
476	#532	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
478	#529	—	2	2	no	—
479	#529	C₂²×C₃₁	1	2	yes	—
480	#520	—	2	1	no	—
481	C₄×#41	—	2	1	no	—
482	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
483	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
484	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
485	#495	C₂²×C₃₁	1	4	yes	—
486	#494	C₂²×C₃₁	1	2	yes	—
487	#488	C₂²×C₃₁	1	4	yes	—
488	#487	C₂²×C₃₁	1	2	yes	—
489	#484	C₂²×C₃₁	1	4	yes	—
490	#482	C₂²×C₃₁	1	2	yes	—
491	#479	C₂²×C₃₁	1	4	yes	—
492	#477	C₂²×C₃₁	1	1	yes	characteristic
493	#477	C₂²×C₃₁	1	2	yes	—
494	#476	C₂²×C₃₁	1	1	yes	characteristic
495	#474	C₂²×C₃₁	1	2	yes	—
496	#470	C₂²×C₃₁	1	4	yes	—
497	#468	C₂²×C₃₁	1	4	yes	—
498	#468	C₂²×C₃₁	1	4	yes	—
499	#464	C₂²×C₃₁	1	4	yes	—
500	#464	C₂²×C₃₁	1	4	yes	—
501	#464	C₂²×C₃₁	1	4	yes	—
502	#462	C₂²×C₃₁	1	2	yes	—
503	#462	C₂²×C₃₁	1	2	yes	—
504	#462	C₂²×C₃₁	1	2	yes	—
505	#462	C₂²×C₃₁	1	2	yes	—
506	#461	C₂²×C₃₁	1	2	yes	—
507	#461	C₂²×C₃₁	1	2	yes	—
508	#461	C₂²×C₃₁	1	2	yes	—
509	#460	C₂²×C₃₁	1	1	yes	characteristic
510	#460	C₂²×C₃₁	1	2	yes	—
511	#459	C₂²×C₃₁	1	1	yes	characteristic
512	#452	C₂²×C₃₁	1	4	yes	—
513	#451	C₂²×C₃₁	1	4	yes	—
514	#451	C₂²×C₃₁	1	4	yes	—
515	#449	C₂²×C₃₁	1	4	yes	—
516	#449	C₂²×C₃₁	1	2	yes	—
517	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
518	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
519	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
520	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
521	C₄×D₈	C₂²×C₃₁	1	2	yes	—
522	#436	C₂²×C₃₁	1	2	yes	—
523	#436	C₂²×C₃₁	1	4	yes	—
524	#431	C₂²×C₃₁	1	2	yes	—
525	#431	C₂²×C₃₁	1	1	yes	characteristic
526	#423	C₂²×C₃₁	1	2	yes	—
527	#423	C₂²×C₃₁	1	1	yes	characteristic
528	#419	C₂²×C₃₁	1	2	yes	—
529	#417	C₂²×C₃₁	1	4	yes	—
530	C₂×C₃₁	—	4	2	no	—
531	C₂×C₃₁	—	4	1	no	—
532	C₂×C₃₁	—	8	1	no	—
533	C₂×C₃₁	—	8	2	no	—
534	C₂×C₃₁	#3488	1	1	yes	characteristic
535	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
536	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
537	C₂×#41	—	2	1	no	—
538	C₂×#41	—	2	1	no	—
539	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
541	C₂×#41	C₂³×C₃₁	1	4	yes	—
542	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
543	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
544	#137	—	4	8	no	—
545	#137	—	4	4	no	—
546	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
547	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
548	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
551	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
552	C₂×D₈	C₂³×C₃₁	1	2	yes	—
553	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
554	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
555	C₄⋊Q₈	—	2	1	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	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	#127	C₂³×C₃₁	1	1	yes	characteristic
565	#126	—	2	2	no	—
566	#126	—	2	4	no	—
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#125	—	2	2	no	—
570	#125	—	2	2	no	—
571	#125	—	2	1	no	—
572	#125	—	2	2	no	—
573	#125	C₂³×C₃₁	1	2	yes	—
574	#124	—	2	2	no	—
575	#124	—	2	4	no	—
576	#124	—	2	1	no	—
577	#124	C₂³×C₃₁	1	2	yes	—
578	#124	C₂³×C₃₁	1	4	yes	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	4	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
592	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
593	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	4	no	—
597	#121	—	2	2	no	—
598	#121	—	2	1	no	—
599	#121	—	2	2	no	—
600	#121	C₂³×C₃₁	1	2	yes	—
601	#121	C₂³×C₃₁	1	2	yes	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
610	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
611	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
612	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
614	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
625	C₄×D₄	D₄×C₃₁	1	2	yes	—
626	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₃₁	1	2	yes	—
629	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₃₁	1	2	yes	—
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	—	2	1	no	—
634	#117	—	2	2	no	—
635	#117	—	2	2	no	—
636	#117	—	2	1	no	—
637	#117	—	2	2	no	—
638	#117	D₄×C₃₁	1	1	yes	characteristic
639	#117	D₄×C₃₁	1	2	yes	—
640	#117	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×C₄⋊C₄	—	2	2	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
646	C₂×C₄²	—	2	2	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
649	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
650	#107	C₂³×C₃₁	1	2	yes	—
651	#107	C₂³×C₃₁	1	4	yes	—
652	#106	C₂³×C₃₁	1	2	yes	—
653	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
654	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
655	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
656	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
658	#103	C₂³×C₃₁	1	4	yes	—
659	#103	C₂³×C₃₁	1	4	yes	—
660	#103	C₂³×C₃₁	1	4	yes	—
661	#103	C₂³×C₃₁	1	2	yes	—
662	#103	C₂³×C₃₁	1	4	yes	—
663	#103	C₂³×C₃₁	1	4	yes	—
664	#102	C₂³×C₃₁	1	2	yes	—
665	#102	C₂³×C₃₁	1	4	yes	—
666	#102	C₂³×C₃₁	1	2	yes	—
667	#102	C₂³×C₃₁	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
670	C₄×C₈	C₂³×C₃₁	1	2	yes	—
671	C₄×C₈	C₂³×C₃₁	1	4	yes	—
672	C₃₁	#61998	1	1	yes	characteristic, direct product factor, Sylow
673	#41	—	2	2	no	—
674	#41	—	4	2	no	—
675	#41	—	4	1	no	—
676	#41	—	4	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
699	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
700	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
701	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
711	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
716	Q₁₆	—	2	8	no	—
717	Q₁₆	—	4	4	no	—
718	Q₁₆	—	4	4	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	4	4	no	—
721	SD₁₆	—	4	4	no	—
722	D₈	—	4	2	no	—
723	M₁₆	—	4	4	no	—
724	M₁₆	—	4	2	no	—
725	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
726	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
727	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
751	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	4	no	—
779	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₃₁	1	2	yes	—
782	C₄²	C₂×D₄×C₃₁	1	2	yes	—
783	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₃₁	1	2	yes	—
785	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
789	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	4	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	8	2	no	—
800	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	4	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	2	no	—
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	2	yes	—
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	1	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	C₂³×D₄×C₃₁	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	4	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	C₃₁×#575	1	2	yes	—
875	C₄	C₃₁×#578	1	2	yes	—
876	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
877	C₄	C₃₁×#585	1	1	yes	characteristic
878	C₂	—	4	2	no	—
879	C₂	—	4	1	no	—
880	C₂	—	8	1	no	—
881	C₂	—	8	2	no	—
882	C₂	C₃₁×#3488	1	1	yes	characteristic
883	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
884	C₂	C₂×C₃₁×#578	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3393	C₂	semidirect
4. C₃₁×#3364	C₂	semidirect
5. C₃₁×#3330	C₂	semidirect
6. C₃₁×#3327	C₂	semidirect
7. C₃₁×#3277	C₂	semidirect
8. C₃₁×#3276	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3252	C₂	semidirect
11. C₃₁×#3212	C₂	semidirect
12. C₃₁×#3209	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3104	C₂	semidirect
15. C₃₁×#3039	C₂	semidirect
16. C₃₁×#3037	C₂	semidirect
17. C₃₁×#2991	C₂	semidirect
343. #61998	C₃₁	direct (N × H)
406. #3511	C₂×C₃₁	semidirect
407. #3482	C₂×C₃₁	semidirect
408. #3393	C₂×C₃₁	semidirect
409. #3364	C₂×C₃₁	semidirect
410. #3330	C₂×C₃₁	semidirect
411. #3327	C₂×C₃₁	semidirect
412. #3277	C₂×C₃₁	semidirect
413. #3276	C₂×C₃₁	semidirect
414. #3254	C₂×C₃₁	semidirect
415. #3252	C₂×C₃₁	semidirect
416. #3212	C₂×C₃₁	semidirect
417. #3209	C₂×C₃₁	semidirect
418. #3106	C₂×C₃₁	semidirect
419. #3104	C₂×C₃₁	semidirect
420. #3039	C₂×C₃₁	semidirect
421. #3037	C₂×C₃₁	semidirect
422. #2991	C₂×C₃₁	semidirect
672. C₃₁	#61998	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×#3511	2
C₃₁×#3482	2
C₃₁×#3393	2
C₃₁×#3364	2
C₃₁×#3330	2
C₃₁×#3327	2
C₃₁×#3277	2
C₃₁×#3276	2
C₃₁×#3254	2
C₃₁×#3252	2
C₃₁×#3212	2
C₃₁×#3209	2
C₃₁×#3106	2
C₃₁×#3104	2
C₃₁×#3039	2
C₃₁×#3037	2
C₃₁×#2991	2
#61998	31

Subgroups — C31×#61998 #21518757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61998 #21518757