Subgroups — C₃₁×#61979 #21518738

Order 7936.

2238 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3318	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
7	D₄×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3264	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3109	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#459	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂²×D₈×C₃₁	C₂²	1	4	yes	complemented
21	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#553	—	2	1	no	—
25	C₃₁×#553	C₂²	1	2	yes	complemented
26	C₃₁×#551	—	2	2	no	—
27	C₃₁×#550	—	2	1	no	—
28	C₃₁×#550	C₂²	1	2	yes	complemented
29	C₃₁×#546	—	2	1	no	—
30	C₃₁×#546	C₂²	1	2	yes	complemented
31	D₄²×C₃₁	—	2	1	no	—
32	D₄²×C₃₁	—	2	2	no	—
33	D₄²×C₃₁	C₂²	1	2	yes	—
34	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	D₄²×C₃₁	C₂²	1	4	yes	complemented
36	C₃₁×#535	—	2	2	no	—
37	C₃₁×#535	—	2	1	no	—
38	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#532	C₂²	1	2	yes	complemented
40	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
43	C₃₁×#529	—	2	1	no	—
44	C₃₁×#529	C₂²	1	2	yes	complemented
45	C₃₁×#525	—	2	2	no	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#496	C₂²	1	4	yes	complemented
51	C₃₁×#493	C₂²	1	2	yes	complemented
52	C₃₁×#490	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	complemented
54	C₃₁×#482	C₂²	1	2	yes	complemented
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#476	C₂²	1	2	yes	complemented
60	C₃₁×#476	C₂²	1	2	yes	complemented
61	C₃₁×#469	C₂²	1	4	yes	complemented
62	C₃₁×#466	C₂²	1	4	yes	complemented
63	C₃₁×#465	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#460	C₂²	1	2	yes	complemented
67	C₃₁×#460	C₂²	1	2	yes	complemented
68	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#459	C₂²	1	2	yes	complemented
70	C₃₁×#459	C₂²	1	2	yes	complemented
71	C₃₁×#459	C₂²	1	4	yes	complemented
72	C₃₁×#459	C₂²	1	2	yes	complemented
73	C₃₁×#459	C₂²	1	2	yes	complemented
74	C₃₁×#459	C₂²	1	4	yes	complemented
75	C₃₁×#459	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#450	C₂²	1	4	yes	complemented
78	C₃₁×#449	C₂²	1	2	yes	complemented
79	C₃₁×#447	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	4	yes	complemented
81	C₃₁×#447	C₂²	1	4	yes	complemented
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#442	C₂²	1	4	yes	complemented
84	C₃₁×#442	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#418	C₂²	1	2	yes	complemented
94	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
95	C₃₁×H(5,𝔽₂)	—	4	8	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	—	2	1	no	—
99	C₂×#41×C₃₁	—	2	1	no	—
100	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
101	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₃₁	—	2	1	no	—
103	C₂²×D₄×C₃₁	—	2	2	no	—
104	C₂²×D₄×C₃₁	—	2	4	no	—
105	C₂²×D₄×C₃₁	—	2	2	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	—	2	2	no	—
108	C₂²×D₄×C₃₁	—	2	1	no	—
109	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₃₁	—	2	2	no	—
113	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
114	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂×D₈×C₃₁	—	4	8	no	—
117	C₂×D₈×C₃₁	C₂³	1	2	yes	—
118	C₂×D₈×C₃₁	C₂³	1	4	yes	—
119	C₂×D₈×C₃₁	C₂³	1	4	yes	—
120	C₂×D₈×C₃₁	C₂³	1	4	yes	—
121	C₂×D₈×C₃₁	C₂³	1	4	yes	—
122	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
124	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×#127	—	2	1	no	—
127	C₃₁×#127	—	2	2	no	—
128	C₃₁×#127	—	2	1	no	—
129	C₃₁×#127	—	2	2	no	—
130	C₃₁×#127	C₂³	1	1	yes	characteristic
131	C₃₁×#127	C₂³	1	2	yes	—
132	C₃₁×#127	C₂³	1	4	yes	—
133	C₃₁×#127	C₂³	1	1	yes	characteristic
134	C₃₁×#127	C₂³	1	2	yes	—
135	C₃₁×#126	—	2	2	no	—
136	C₃₁×#126	—	2	2	no	—
137	C₃₁×#125	—	2	1	no	—
138	C₃₁×#125	C₂³	1	2	yes	—
139	C₃₁×#124	—	2	1	no	—
140	C₃₁×#124	—	2	1	no	—
141	C₃₁×#124	—	2	2	no	—
142	C₃₁×#124	—	2	1	no	—
143	C₃₁×#124	C₂³	1	2	yes	—
144	C₃₁×#123	—	2	2	no	—
145	C₃₁×#123	—	2	2	no	—
146	C₃₁×#123	—	2	2	no	—
147	C₃₁×#123	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	1	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	4	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	C₂³	1	2	yes	—
163	C₃₁×#121	C₂³	1	2	yes	—
164	C₃₁×#121	C₂³	1	4	yes	—
165	C₃₁×#121	C₂³	1	2	yes	—
166	C₃₁×#120	—	2	2	no	—
167	C₃₁×#120	—	2	2	no	—
168	C₃₁×#120	—	2	4	no	—
169	C₃₁×#120	—	2	4	no	—
170	C₃₁×#120	—	2	4	no	—
171	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
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	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	1	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
187	C₄×D₄×C₃₁	D₄	1	2	yes	—
188	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₃₁	C₂³	1	2	yes	—
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₄×D₄×C₃₁	C₂³	1	2	yes	—
192	C₄×D₄×C₃₁	C₂³	1	4	yes	—
193	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₃₁	C₂³	1	2	yes	—
195	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₃₁	C₂³	1	2	yes	—
197	C₃₁×#117	—	2	1	no	—
198	C₃₁×#117	—	2	2	no	—
199	C₃₁×#117	D₄	1	2	yes	—
200	C₃₁×#117	D₄	1	1	yes	characteristic
201	C₃₁×#117	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
206	C₂×C₄²×C₃₁	—	2	1	no	—
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×#106	C₂³	1	4	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	2	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	2	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃₁×#97	C₂³	1	4	yes	—
230	C₄×C₈×C₃₁	C₂³	1	2	yes	—
231	C₂⁴×C₃₁	—	2	2	no	—
232	C₂⁴×C₃₁	—	2	2	no	—
233	C₂⁴×C₃₁	—	2	4	no	—
234	#41×C₃₁	—	2	4	no	—
235	#41×C₃₁	—	2	2	no	—
236	#41×C₃₁	—	4	1	no	—
237	#41×C₃₁	—	4	8	no	—
238	#41×C₃₁	—	4	4	no	—
239	#41×C₃₁	—	4	8	no	—
240	#41×C₃₁	—	8	2	no	—
241	C₂×Q₈×C₃₁	—	2	1	no	—
242	C₂×Q₈×C₃₁	—	2	1	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₃₁	—	2	4	no	—
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	4	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	4	no	—
256	C₂×D₄×C₃₁	—	2	2	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	2	no	—
259	C₂×D₄×C₃₁	—	2	2	no	—
260	C₂×D₄×C₃₁	—	2	4	no	—
261	C₂×D₄×C₃₁	—	2	4	no	—
262	C₂×D₄×C₃₁	—	2	2	no	—
263	C₂×D₄×C₃₁	—	2	1	no	—
264	C₂×D₄×C₃₁	—	4	2	no	—
265	C₂×D₄×C₃₁	—	4	4	no	—
266	C₂×D₄×C₃₁	—	4	2	no	—
267	C₂×D₄×C₃₁	—	4	4	no	—
268	C₂×D₄×C₃₁	—	4	2	no	—
269	C₂×D₄×C₃₁	—	4	8	no	—
270	C₂×D₄×C₃₁	—	4	4	no	—
271	C₂×D₄×C₃₁	—	4	16	no	—
272	C₂×D₄×C₃₁	—	4	4	no	—
273	C₂×D₄×C₃₁	—	4	8	no	—
274	C₂×D₄×C₃₁	—	8	4	no	—
275	C₂×D₄×C₃₁	—	8	2	no	—
276	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
280	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	—	2	2	no	—
283	C₂²×C₄×C₃₁	—	2	1	no	—
284	C₂²×C₄×C₃₁	—	2	1	no	—
285	C₂²×C₄×C₃₁	—	2	1	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	4	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	8	4	no	—
292	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	SD₁₆×C₃₁	—	4	2	no	—
299	SD₁₆×C₃₁	—	4	4	no	—
300	D₈×C₃₁	—	2	4	no	—
301	D₈×C₃₁	—	2	8	no	—
302	D₈×C₃₁	—	4	4	no	—
303	D₈×C₃₁	—	4	4	no	—
304	D₈×C₃₁	—	4	4	no	—
305	M₁₆×C₃₁	—	4	2	no	—
306	C₂×C₈×C₃₁	—	4	4	no	—
307	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
308	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
309	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₃₁	—	2	1	no	—
311	C₄⋊C₄×C₃₁	—	2	2	no	—
312	C₄⋊C₄×C₃₁	—	2	2	no	—
313	C₄⋊C₄×C₃₁	—	2	1	no	—
314	C₄⋊C₄×C₃₁	—	2	1	no	—
315	C₄⋊C₄×C₃₁	—	2	2	no	—
316	C₄⋊C₄×C₃₁	—	2	2	no	—
317	C₄⋊C₄×C₃₁	—	2	1	no	—
318	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
326	C₂²⋊C₄×C₃₁	—	2	2	no	—
327	C₂²⋊C₄×C₃₁	—	2	1	no	—
328	C₂²⋊C₄×C₃₁	—	2	1	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	—	2	2	no	—
332	C₂²⋊C₄×C₃₁	—	2	2	no	—
333	C₂²⋊C₄×C₃₁	—	2	2	no	—
334	C₂²⋊C₄×C₃₁	—	2	1	no	—
335	C₂²⋊C₄×C₃₁	—	2	2	no	—
336	C₂²⋊C₄×C₃₁	—	2	2	no	—
337	C₂²⋊C₄×C₃₁	—	2	2	no	—
338	C₂²⋊C₄×C₃₁	—	2	4	no	—
339	C₂²⋊C₄×C₃₁	—	2	4	no	—
340	C₂²⋊C₄×C₃₁	—	2	2	no	—
341	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₄²×C₃₁	—	2	1	no	—
345	C₄²×C₃₁	—	2	1	no	—
346	C₄²×C₃₁	—	2	1	no	—
347	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₃₁	C₂×D₄	1	2	yes	—
350	C₄²×C₃₁	C₂×D₄	1	2	yes	—
351	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₄²×C₃₁	C₂⁴	1	2	yes	—
353	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
354	#61979	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂³×C₃₁	—	2	1	no	—
356	C₂³×C₃₁	—	2	2	no	—
357	C₂³×C₃₁	—	2	2	no	—
358	C₂³×C₃₁	—	2	4	no	—
359	C₂³×C₃₁	—	4	4	no	—
360	C₂³×C₃₁	—	4	4	no	—
361	C₂³×C₃₁	—	4	4	no	—
362	C₂³×C₃₁	—	4	8	no	—
363	C₂³×C₃₁	—	8	2	no	—
364	C₂³×C₃₁	—	8	4	no	—
365	C₂³×C₃₁	—	8	2	no	—
366	C₂³×C₃₁	—	8	4	no	—
367	C₂³×C₃₁	—	8	2	no	—
368	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
369	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
370	Q₈×C₃₁	—	2	2	no	—
371	Q₈×C₃₁	—	2	1	no	—
372	Q₈×C₃₁	—	2	1	no	—
373	Q₈×C₃₁	—	4	2	no	—
374	Q₈×C₃₁	—	8	1	no	—
375	D₄×C₃₁	—	2	4	no	—
376	D₄×C₃₁	—	2	2	no	—
377	D₄×C₃₁	—	2	4	no	—
378	D₄×C₃₁	—	2	2	no	—
379	D₄×C₃₁	—	2	1	no	—
380	D₄×C₃₁	—	2	2	no	—
381	D₄×C₃₁	—	2	4	no	—
382	D₄×C₃₁	—	2	2	no	—
383	D₄×C₃₁	—	4	4	no	—
384	D₄×C₃₁	—	4	4	no	—
385	D₄×C₃₁	—	4	2	no	—
386	D₄×C₃₁	—	4	8	no	—
387	D₄×C₃₁	—	4	2	no	—
388	D₄×C₃₁	—	4	4	no	—
389	D₄×C₃₁	—	4	4	no	—
390	D₄×C₃₁	—	4	8	no	—
391	D₄×C₃₁	—	4	2	no	—
392	D₄×C₃₁	—	4	4	no	—
393	D₄×C₃₁	—	4	2	no	—
394	D₄×C₃₁	—	4	4	no	—
395	D₄×C₃₁	—	8	2	no	—
396	D₄×C₃₁	—	8	4	no	—
397	D₄×C₃₁	—	8	4	no	—
398	D₄×C₃₁	—	8	2	no	—
399	D₄×C₃₁	—	8	1	no	—
400	D₄×C₃₁	—	8	2	no	—
401	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
402	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	complemented
403	C₂×C₄×C₃₁	—	2	4	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	4	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	1	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	1	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	1	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	4	2	no	—
417	C₂×C₄×C₃₁	—	4	8	no	—
418	C₂×C₄×C₃₁	—	4	2	no	—
419	C₂×C₄×C₃₁	—	4	4	no	—
420	C₂×C₄×C₃₁	—	4	2	no	—
421	C₂×C₄×C₃₁	—	4	4	no	—
422	C₂×C₄×C₃₁	—	8	2	no	—
423	C₂×C₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	—	8	2	no	—
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
434	C₈×C₃₁	—	2	2	no	—
435	C₈×C₃₁	—	2	4	no	—
436	C₈×C₃₁	—	2	2	no	—
437	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
438	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
439	#3399	C₂×C₃₁	1	2	yes	complemented
440	#3366	C₂×C₃₁	1	2	yes	complemented
441	#3318	C₂×C₃₁	1	4	yes	complemented
442	#3295	C₂×C₃₁	1	2	yes	complemented
443	D₄×D₈	C₂×C₃₁	1	2	yes	complemented
444	#3264	C₂×C₃₁	1	4	yes	complemented
445	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
446	#3247	C₂×C₃₁	1	2	yes	complemented
447	#3217	C₂×C₃₁	1	2	yes	complemented
448	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#3109	C₂×C₃₁	1	2	yes	complemented
450	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
451	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
452	C₂×#459	C₂×C₃₁	1	2	yes	complemented
453	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	1	no	—
457	C₂²×C₃₁	—	2	2	no	—
458	C₂²×C₃₁	—	2	1	no	—
459	C₂²×C₃₁	—	2	1	no	—
460	C₂²×C₃₁	—	4	1	no	—
461	C₂²×C₃₁	—	4	1	no	—
462	C₂²×C₃₁	—	4	2	no	—
463	C₂²×C₃₁	—	4	2	no	—
464	C₂²×C₃₁	—	4	4	no	—
465	C₂²×C₃₁	—	4	4	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	4	no	—
471	C₂²×C₃₁	—	8	8	no	—
472	C₂²×C₃₁	—	16	8	no	—
473	C₂²×C₃₁	—	16	4	no	—
474	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
475	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
476	C₄×C₃₁	—	2	1	no	—
477	C₄×C₃₁	—	2	2	no	—
478	C₄×C₃₁	—	2	1	no	—
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	2	1	no	—
482	C₄×C₃₁	—	4	1	no	—
483	C₄×C₃₁	—	4	2	no	—
484	C₄×C₃₁	—	4	1	no	—
485	C₄×C₃₁	—	4	1	no	—
486	C₄×C₃₁	—	4	2	no	—
487	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
488	C₄×C₃₁	#576	1	2	yes	—
489	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
490	C₄×C₃₁	#585	1	1	yes	characteristic
491	C₂×H(5,𝔽₂)	—	2	1	no	—
492	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
493	C₂²×D₈	C₂²×C₃₁	1	4	yes	complemented
494	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
495	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#553	—	2	1	no	—
498	#553	C₂²×C₃₁	1	2	yes	complemented
499	#551	—	2	2	no	—
500	#550	—	2	1	no	—
501	#550	C₂²×C₃₁	1	2	yes	complemented
502	#546	—	2	1	no	—
503	#546	C₂²×C₃₁	1	2	yes	complemented
504	D₄²	—	2	1	no	—
505	D₄²	—	2	2	no	—
506	D₄²	C₂²×C₃₁	1	2	yes	—
507	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
508	D₄²	C₂²×C₃₁	1	4	yes	complemented
509	#535	—	2	2	no	—
510	#535	—	2	1	no	—
511	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
512	#532	C₂²×C₃₁	1	2	yes	complemented
513	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
516	#529	—	2	1	no	—
517	#529	C₂²×C₃₁	1	2	yes	complemented
518	#525	—	2	2	no	—
519	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
520	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	C₂×C₄×D₄	—	2	1	no	—
522	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
523	#496	C₂²×C₃₁	1	4	yes	complemented
524	#493	C₂²×C₃₁	1	2	yes	complemented
525	#490	C₂²×C₃₁	1	4	yes	complemented
526	#486	C₂²×C₃₁	1	2	yes	complemented
527	#482	C₂²×C₃₁	1	2	yes	complemented
528	#481	C₂²×C₃₁	1	4	yes	complemented
529	#478	C₂²×C₃₁	1	4	yes	complemented
530	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
531	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#476	C₂²×C₃₁	1	2	yes	complemented
533	#476	C₂²×C₃₁	1	2	yes	complemented
534	#469	C₂²×C₃₁	1	4	yes	complemented
535	#466	C₂²×C₃₁	1	4	yes	complemented
536	#465	C₂²×C₃₁	1	4	yes	complemented
537	#463	C₂²×C₃₁	1	4	yes	complemented
538	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
539	#460	C₂²×C₃₁	1	2	yes	complemented
540	#460	C₂²×C₃₁	1	2	yes	complemented
541	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
542	#459	C₂²×C₃₁	1	2	yes	complemented
543	#459	C₂²×C₃₁	1	2	yes	complemented
544	#459	C₂²×C₃₁	1	4	yes	complemented
545	#459	C₂²×C₃₁	1	2	yes	complemented
546	#459	C₂²×C₃₁	1	2	yes	complemented
547	#459	C₂²×C₃₁	1	4	yes	complemented
548	#459	C₂²×C₃₁	1	2	yes	complemented
549	#459	C₂²×C₃₁	1	2	yes	complemented
550	#450	C₂²×C₃₁	1	4	yes	complemented
551	#449	C₂²×C₃₁	1	2	yes	complemented
552	#447	C₂²×C₃₁	1	4	yes	complemented
553	#447	C₂²×C₃₁	1	4	yes	complemented
554	#447	C₂²×C₃₁	1	4	yes	complemented
555	#446	C₂²×C₃₁	1	2	yes	complemented
556	#442	C₂²×C₃₁	1	4	yes	complemented
557	#442	C₂²×C₃₁	1	4	yes	complemented
558	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
559	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
560	#435	C₂²×C₃₁	1	4	yes	complemented
561	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
562	#432	C₂²×C₃₁	1	2	yes	complemented
563	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
566	#418	C₂²×C₃₁	1	2	yes	complemented
567	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
568	C₂×C₃₁	—	2	4	no	—
569	C₂×C₃₁	—	4	1	no	—
570	C₂×C₃₁	—	4	2	no	—
571	C₂×C₃₁	—	8	2	no	—
572	C₂×C₃₁	—	8	2	no	—
573	C₂×C₃₁	—	8	4	no	—
574	C₂×C₃₁	#3488	1	1	yes	characteristic
575	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
576	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
577	H(5,𝔽₂)	—	4	8	no	—
578	C₂×#41	—	2	2	no	—
579	C₂×#41	—	2	2	no	—
580	C₂×#41	—	2	1	no	—
581	C₂×#41	—	2	1	no	—
582	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
583	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	2	no	—
586	C₂²×D₄	—	2	4	no	—
587	C₂²×D₄	—	2	2	no	—
588	C₂²×D₄	—	2	1	no	—
589	C₂²×D₄	—	2	2	no	—
590	C₂²×D₄	—	2	1	no	—
591	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
592	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
593	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
594	C₂³×C₄	—	2	2	no	—
595	AGL(1,ℤ/8)	—	4	4	no	—
596	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
597	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
598	C₂×D₈	—	4	8	no	—
599	C₂×D₈	C₂³×C₃₁	1	2	yes	—
600	C₂×D₈	C₂³×C₃₁	1	4	yes	—
601	C₂×D₈	C₂³×C₃₁	1	4	yes	—
602	C₂×D₈	C₂³×C₃₁	1	4	yes	—
603	C₂×D₈	C₂³×C₃₁	1	4	yes	—
604	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
605	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
606	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
608	#127	—	2	1	no	—
609	#127	—	2	2	no	—
610	#127	—	2	1	no	—
611	#127	—	2	2	no	—
612	#127	C₂³×C₃₁	1	2	yes	—
613	#127	C₂³×C₃₁	1	1	yes	characteristic
614	#127	C₂³×C₃₁	1	2	yes	—
615	#127	C₂³×C₃₁	1	4	yes	—
616	#127	C₂³×C₃₁	1	1	yes	characteristic
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#125	—	2	1	no	—
620	#125	C₂³×C₃₁	1	2	yes	—
621	#124	—	2	1	no	—
622	#124	—	2	1	no	—
623	#124	—	2	2	no	—
624	#124	—	2	1	no	—
625	#124	C₂³×C₃₁	1	2	yes	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
634	#121	—	2	2	no	—
635	#121	—	2	2	no	—
636	#121	—	2	1	no	—
637	#121	—	2	1	no	—
638	#121	—	2	1	no	—
639	#121	—	2	2	no	—
640	#121	—	2	4	no	—
641	#121	—	2	2	no	—
642	#121	—	2	4	no	—
643	#121	—	2	2	no	—
644	#121	C₂³×C₃₁	1	2	yes	—
645	#121	C₂³×C₃₁	1	4	yes	—
646	#121	C₂³×C₃₁	1	2	yes	—
647	#121	C₂³×C₃₁	1	2	yes	—
648	#120	—	2	2	no	—
649	#120	—	2	2	no	—
650	#120	—	2	4	no	—
651	#120	—	2	4	no	—
652	#120	—	2	4	no	—
653	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
654	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
655	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
656	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	1	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
669	C₄×D₄	D₄×C₃₁	1	2	yes	—
670	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₃₁	1	2	yes	—
672	C₄×D₄	C₂³×C₃₁	1	2	yes	—
673	C₄×D₄	C₂³×C₃₁	1	2	yes	—
674	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₄×D₄	C₂³×C₃₁	1	2	yes	—
676	C₄×D₄	C₂³×C₃₁	1	4	yes	—
677	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	#117	—	2	1	no	—
680	#117	—	2	2	no	—
681	#117	D₄×C₃₁	1	2	yes	—
682	#117	D₄×C₃₁	1	1	yes	characteristic
683	#117	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄⋊C₄	—	2	1	no	—
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₂²⋊C₄	—	2	2	no	—
687	C₂×C₂²⋊C₄	—	2	2	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	#107	C₂³×C₃₁	1	2	yes	—
692	#106	C₂³×C₃₁	1	2	yes	—
693	#106	C₂³×C₃₁	1	4	yes	—
694	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
695	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
696	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
697	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
698	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
699	#103	C₂³×C₃₁	1	2	yes	—
700	#102	C₂³×C₃₁	1	2	yes	—
701	#102	C₂³×C₃₁	1	4	yes	—
702	#102	C₂³×C₃₁	1	4	yes	—
703	#102	C₂³×C₃₁	1	4	yes	—
704	#102	C₂³×C₃₁	1	4	yes	—
705	#102	C₂³×C₃₁	1	2	yes	—
706	#102	C₂³×C₃₁	1	2	yes	—
707	#102	C₂³×C₃₁	1	4	yes	—
708	#102	C₂³×C₃₁	1	4	yes	—
709	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
711	#97	C₂³×C₃₁	1	4	yes	—
712	C₄×C₈	C₂³×C₃₁	1	2	yes	—
713	C₃₁	#61979	1	1	yes	characteristic, direct product factor, Sylow
714	C₂⁴	—	2	2	no	—
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	4	no	—
717	#41	—	2	4	no	—
718	#41	—	2	2	no	—
719	#41	—	4	1	no	—
720	#41	—	4	8	no	—
721	#41	—	4	4	no	—
722	#41	—	4	8	no	—
723	#41	—	8	2	no	—
724	C₂×Q₈	—	2	1	no	—
725	C₂×Q₈	—	2	1	no	—
726	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
727	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	1	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	1	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	4	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	4	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	8	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	16	no	—
755	C₂×D₄	—	4	4	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	8	4	no	—
758	C₂×D₄	—	8	2	no	—
759	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
760	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
762	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
763	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
764	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	8	4	no	—
775	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
776	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
777	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
778	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
781	SD₁₆	—	4	2	no	—
782	SD₁₆	—	4	4	no	—
783	D₈	—	2	4	no	—
784	D₈	—	2	8	no	—
785	D₈	—	4	4	no	—
786	D₈	—	4	4	no	—
787	D₈	—	4	4	no	—
788	M₁₆	—	4	2	no	—
789	C₂×C₈	—	4	4	no	—
790	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
791	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
792	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
802	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
803	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
804	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
805	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
806	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	1	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
825	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
826	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	1	no	—
829	C₄²	—	2	1	no	—
830	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
831	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
832	C₄²	C₂×D₄×C₃₁	1	2	yes	—
833	C₄²	C₂×D₄×C₃₁	1	2	yes	—
834	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₄²	C₂⁴×C₃₁	1	2	yes	—
836	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₂³	—	2	1	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	4	4	no	—
842	C₂³	—	4	4	no	—
843	C₂³	—	4	4	no	—
844	C₂³	—	4	8	no	—
845	C₂³	—	8	2	no	—
846	C₂³	—	8	4	no	—
847	C₂³	—	8	2	no	—
848	C₂³	—	8	4	no	—
849	C₂³	—	8	2	no	—
850	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
851	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	1	no	—
854	Q₈	—	2	1	no	—
855	Q₈	—	4	2	no	—
856	Q₈	—	8	1	no	—
857	D₄	—	2	4	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	4	no	—
860	D₄	—	2	2	no	—
861	D₄	—	2	1	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	4	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	8	no	—
869	D₄	—	4	2	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	4	no	—
872	D₄	—	4	8	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	4	no	—
879	D₄	—	8	4	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	1	no	—
882	D₄	—	8	2	no	—
883	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
884	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	complemented
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
909	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
915	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
916	C₈	—	2	2	no	—
917	C₈	—	2	4	no	—
918	C₈	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	4	no	—
930	C₂²	—	4	4	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	8	8	no	—
937	C₂²	—	16	8	no	—
938	C₂²	—	16	4	no	—
939	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
940	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
953	C₄	C₃₁×#576	1	2	yes	—
954	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
955	C₄	C₃₁×#585	1	1	yes	characteristic
956	C₂	—	2	4	no	—
957	C₂	—	4	1	no	—
958	C₂	—	4	2	no	—
959	C₂	—	8	2	no	—
960	C₂	—	8	2	no	—
961	C₂	—	8	4	no	—
962	C₂	C₃₁×#3488	1	1	yes	characteristic
963	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
964	C₂	C₂×C₃₁×#576	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×#3498	C₂	semidirect
2. C₃₁×#3481	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3318	C₂	semidirect
6. C₃₁×#3295	C₂	semidirect
7. D₄×D₈×C₃₁	C₂	semidirect
8. C₃₁×#3264	C₂	semidirect
9. C₃₁×#3253	C₂	semidirect
10. C₃₁×#3247	C₂	semidirect
11. C₃₁×#3217	C₂	semidirect
12. C₃₁×#3205	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3106	C₂	semidirect
15. C₃₁×#3038	C₂	semidirect
16. C₂×C₃₁×#459	C₂	semidirect
17. C₃₁×#2990	C₂	semidirect
19. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂²×D₈×C₃₁	C₂²	semidirect
21. C₃₁×#559	C₂²	semidirect
22. C₃₁×#554	C₂²	semidirect
23. C₃₁×#554	C₂²	semidirect
25. C₃₁×#553	C₂²	semidirect
28. C₃₁×#550	C₂²	semidirect
30. C₃₁×#546	C₂²	semidirect
34. D₄²×C₃₁	C₂²	semidirect
35. D₄²×C₃₁	C₂²	semidirect
38. C₃₁×#532	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×#127	C₂²	semidirect
42. C₂×C₃₁×#127	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
47. C₄×#41×C₃₁	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#496	C₂²	semidirect
51. C₃₁×#493	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#476	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#476	C₂²	semidirect
61. C₃₁×#469	C₂²	semidirect
62. C₃₁×#466	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
66. C₃₁×#460	C₂²	semidirect
67. C₃₁×#460	C₂²	semidirect
68. C₃₁×#459	C₂²	semidirect
69. C₃₁×#459	C₂²	semidirect
70. C₃₁×#459	C₂²	semidirect
71. C₃₁×#459	C₂²	semidirect
72. C₃₁×#459	C₂²	semidirect
73. C₃₁×#459	C₂²	semidirect
74. C₃₁×#459	C₂²	semidirect
75. C₃₁×#459	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
77. C₃₁×#450	C₂²	semidirect
78. C₃₁×#449	C₂²	semidirect
79. C₃₁×#447	C₂²	semidirect
80. C₃₁×#447	C₂²	semidirect
81. C₃₁×#447	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₃₁×#442	C₂²	semidirect
84. C₃₁×#442	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×D₈×C₃₁	C₂²	semidirect
87. C₃₁×#435	C₂²	semidirect
88. C₈×D₄×C₃₁	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
93. C₃₁×#418	C₂²	semidirect
94. C₂×C₃₁×#102	C₂²	semidirect
354. #61979	C₃₁	direct (N × H)
401. D₄×C₃₁	AGL(1,ℤ/8)	semidirect
402. D₄×C₃₁	H(5,𝔽₂)	semidirect
437. #3498	C₂×C₃₁	semidirect
438. #3481	C₂×C₃₁	semidirect
439. #3399	C₂×C₃₁	semidirect
440. #3366	C₂×C₃₁	semidirect
441. #3318	C₂×C₃₁	semidirect
442. #3295	C₂×C₃₁	semidirect
443. D₄×D₈	C₂×C₃₁	semidirect
444. #3264	C₂×C₃₁	semidirect
445. #3253	C₂×C₃₁	semidirect
446. #3247	C₂×C₃₁	semidirect
447. #3217	C₂×C₃₁	semidirect
448. #3205	C₂×C₃₁	semidirect
449. #3109	C₂×C₃₁	semidirect
450. #3106	C₂×C₃₁	semidirect
451. #3038	C₂×C₃₁	semidirect
452. C₂×#459	C₂×C₃₁	semidirect
453. #2990	C₂×C₃₁	semidirect
492. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
493. C₂²×D₈	C₂²×C₃₁	semidirect
494. #559	C₂²×C₃₁	semidirect
495. #554	C₂²×C₃₁	semidirect
496. #554	C₂²×C₃₁	semidirect
498. #553	C₂²×C₃₁	semidirect
501. #550	C₂²×C₃₁	semidirect
503. #546	C₂²×C₃₁	semidirect
507. D₄²	C₂²×C₃₁	semidirect
508. D₄²	C₂²×C₃₁	semidirect
511. #532	C₂²×C₃₁	semidirect
512. #532	C₂²×C₃₁	semidirect
513. #532	C₂²×C₃₁	semidirect
514. C₂×#127	C₂²×C₃₁	semidirect
515. C₂×#127	C₂²×C₃₁	semidirect
517. #529	C₂²×C₃₁	semidirect
520. C₄×#41	C₂²×C₃₁	semidirect
522. C₂×C₄×D₄	C₂²×C₃₁	semidirect
523. #496	C₂²×C₃₁	semidirect
524. #493	C₂²×C₃₁	semidirect
525. #490	C₂²×C₃₁	semidirect
526. #486	C₂²×C₃₁	semidirect
527. #482	C₂²×C₃₁	semidirect
528. #481	C₂²×C₃₁	semidirect
529. #478	C₂²×C₃₁	semidirect
530. #477	C₂²×C₃₁	semidirect
531. #476	C₂²×C₃₁	semidirect
532. #476	C₂²×C₃₁	semidirect
533. #476	C₂²×C₃₁	semidirect
534. #469	C₂²×C₃₁	semidirect
535. #466	C₂²×C₃₁	semidirect
536. #465	C₂²×C₃₁	semidirect
537. #463	C₂²×C₃₁	semidirect
538. #460	C₂²×C₃₁	semidirect
539. #460	C₂²×C₃₁	semidirect
540. #460	C₂²×C₃₁	semidirect
541. #459	C₂²×C₃₁	semidirect
542. #459	C₂²×C₃₁	semidirect
543. #459	C₂²×C₃₁	semidirect
544. #459	C₂²×C₃₁	semidirect
545. #459	C₂²×C₃₁	semidirect
546. #459	C₂²×C₃₁	semidirect
547. #459	C₂²×C₃₁	semidirect
548. #459	C₂²×C₃₁	semidirect
549. #459	C₂²×C₃₁	semidirect
550. #450	C₂²×C₃₁	semidirect
551. #449	C₂²×C₃₁	semidirect
552. #447	C₂²×C₃₁	semidirect
553. #447	C₂²×C₃₁	semidirect
554. #447	C₂²×C₃₁	semidirect
555. #446	C₂²×C₃₁	semidirect
556. #442	C₂²×C₃₁	semidirect
557. #442	C₂²×C₃₁	semidirect
558. C₄×SD₁₆	C₂²×C₃₁	semidirect
559. C₄×D₈	C₂²×C₃₁	semidirect
560. #435	C₂²×C₃₁	semidirect
561. C₈×D₄	C₂²×C₃₁	semidirect
562. #432	C₂²×C₃₁	semidirect
563. #431	C₂²×C₃₁	semidirect
564. #423	C₂²×C₃₁	semidirect
565. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
566. #418	C₂²×C₃₁	semidirect
567. C₂×#102	C₂²×C₃₁	semidirect
713. C₃₁	#61979	direct (N × H)
883. D₄	C₃₁×AGL(1,ℤ/8)	semidirect
884. D₄	C₃₁×H(5,𝔽₂)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3498	2
C₃₁×#3481	2
C₃₁×#3399	2
C₃₁×#3366	2
C₃₁×#3318	2
C₃₁×#3295	2
D₄×D₈×C₃₁	2
C₃₁×#3264	2
C₃₁×#3253	2
C₃₁×#3247	2
C₃₁×#3217	2
C₃₁×#3205	2
C₃₁×#3109	2
C₃₁×#3106	2
C₃₁×#3038	2
C₂×C₃₁×#459	2
C₃₁×#2990	2
#61979	31

Subgroups — C31×#61979 #21518738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61979 #21518738