Subgroups — C₃₁×#60702 #21517461

Order 7936.

2008 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3183	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3172	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3168	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
16	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
21	C₃₁×#533	C₂²	1	1	yes	characteristic
22	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#532	C₂²	1	1	yes	characteristic
25	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#529	—	2	1	no	—
28	C₃₁×#529	—	2	1	no	—
29	C₃₁×#529	—	2	1	no	—
30	C₃₁×#529	—	2	1	no	—
31	C₃₁×#529	—	2	1	no	—
32	C₃₁×#529	—	2	1	no	—
33	C₃₁×#529	—	2	1	no	—
34	C₃₁×#529	—	2	1	no	—
35	C₃₁×#529	C₂²	1	2	yes	—
36	C₃₁×#529	C₂²	1	2	yes	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₃₁×#529	C₂²	1	2	yes	—
39	C₃₁×#529	C₂²	1	2	yes	complemented
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#126	—	2	1	no	—
42	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
44	C₃₁×#525	—	2	1	no	—
45	C₃₁×#525	—	2	1	no	—
46	C₃₁×#525	C₂²	1	2	yes	—
47	C₂×C₃₁×#123	—	2	1	no	—
48	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
50	C₄×#41×C₃₁	—	2	1	no	—
51	C₄×#41×C₃₁	—	2	1	no	—
52	C₄×#41×C₃₁	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₃₁	—	2	1	no	—
55	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×#117	—	2	1	no	—
57	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
58	C₃₁×#501	C₂²	1	2	yes	complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#499	C₂²	1	4	yes	complemented
61	C₃₁×#497	C₂²	1	2	yes	complemented
62	C₃₁×#496	C₂²	1	2	yes	complemented
63	C₃₁×#495	C₂²	1	4	yes	complemented
64	C₃₁×#491	C₂²	1	2	yes	complemented
65	C₃₁×#490	C₂²	1	2	yes	complemented
66	C₃₁×#489	C₂²	1	2	yes	complemented
67	C₃₁×#489	C₂²	1	2	yes	complemented
68	C₃₁×#488	C₂²	1	4	yes	complemented
69	C₃₁×#488	C₂²	1	4	yes	complemented
70	C₃₁×#470	C₂²	1	4	yes	complemented
71	C₃₁×#469	C₂²	1	4	yes	—
72	C₃₁×#468	C₂²	1	4	yes	—
73	C₃₁×#468	C₂²	1	4	yes	complemented
74	C₃₁×#467	C₂²	1	4	yes	complemented
75	C₃₁×#466	C₂²	1	4	yes	—
76	C₃₁×#465	C₂²	1	4	yes	—
77	C₃₁×#465	C₂²	1	4	yes	complemented
78	C₃₁×#442	C₂²	1	4	yes	complemented
79	C₃₁×#441	C₂²	1	4	yes	complemented
80	C₃₁×#440	C₂²	1	4	yes	complemented
81	C₃₁×#440	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
85	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
86	C₃₁×#428	C₂²	1	2	yes	—
87	C₃₁×#428	C₂²	1	2	yes	—
88	C₃₁×#419	C₂²	1	2	yes	—
89	C₃₁×#418	C₂²	1	2	yes	—
90	C₃₁×#417	C₂²	1	2	yes	—
91	C₃₁×#417	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
95	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
96	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
97	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
98	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	complemented
99	C₂×#41×C₃₁	—	2	1	no	—
100	C₂×#41×C₃₁	—	2	1	no	—
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	—	2	1	no	—
106	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×#137	—	2	8	no	—
110	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂×D₈×C₃₁	C₂³	1	4	yes	—
115	C₂×M₁₆×C₃₁	—	2	8	no	—
116	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
117	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
118	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×#127	C₂³	1	1	yes	characteristic
124	C₃₁×#126	—	2	2	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#126	—	2	2	no	—
127	C₃₁×#126	—	2	2	no	—
128	C₃₁×#126	—	2	2	no	—
129	C₃₁×#126	—	2	2	no	—
130	C₃₁×#125	—	2	1	no	—
131	C₃₁×#125	—	2	1	no	—
132	C₃₁×#125	—	2	1	no	—
133	C₃₁×#125	—	2	1	no	—
134	C₃₁×#125	C₂³	1	2	yes	—
135	C₃₁×#125	C₂³	1	2	yes	—
136	C₃₁×#125	C₂³	1	2	yes	—
137	C₃₁×#124	—	2	1	no	—
138	C₃₁×#124	—	2	1	no	—
139	C₃₁×#124	—	2	1	no	—
140	C₃₁×#124	—	2	1	no	—
141	C₃₁×#124	C₂³	1	2	yes	—
142	C₃₁×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
149	C₃₁×#123	—	2	2	no	—
150	C₃₁×#123	—	2	2	no	—
151	C₃₁×C₂²⋊Q₈	—	2	1	no	—
152	C₃₁×C₂²⋊Q₈	—	2	1	no	—
153	C₃₁×C₂²⋊Q₈	—	2	1	no	—
154	C₃₁×C₂²⋊Q₈	—	2	1	no	—
155	C₃₁×C₂²⋊Q₈	—	2	1	no	—
156	C₃₁×C₂²⋊Q₈	—	2	1	no	—
157	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×#121	—	2	1	no	—
162	C₃₁×#121	—	2	1	no	—
163	C₃₁×#121	—	2	1	no	—
164	C₃₁×#121	—	2	1	no	—
165	C₃₁×#121	—	2	1	no	—
166	C₃₁×#121	—	2	1	no	—
167	C₃₁×#121	C₂³	1	2	yes	—
168	C₃₁×#121	C₂³	1	2	yes	—
169	C₃₁×#121	C₂³	1	2	yes	—
170	C₃₁×#121	C₂³	1	2	yes	—
171	C₃₁×#120	—	2	2	no	—
172	C₄×Q₈×C₃₁	—	2	1	no	—
173	C₄×Q₈×C₃₁	—	2	1	no	—
174	C₄×Q₈×C₃₁	—	2	1	no	—
175	C₄×Q₈×C₃₁	—	2	1	no	—
176	C₄×Q₈×C₃₁	—	2	1	no	—
177	C₄×Q₈×C₃₁	—	2	1	no	—
178	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
179	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
180	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
181	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	2	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	2	no	—
187	C₄×D₄×C₃₁	—	2	2	no	—
188	C₄×D₄×C₃₁	—	2	2	no	—
189	C₄×D₄×C₃₁	—	2	2	no	—
190	C₄×D₄×C₃₁	—	2	2	no	—
191	C₄×D₄×C₃₁	—	2	2	no	—
192	C₄×D₄×C₃₁	—	2	1	no	—
193	C₄×D₄×C₃₁	—	2	1	no	—
194	C₄×D₄×C₃₁	—	2	1	no	—
195	C₄×D₄×C₃₁	—	2	1	no	—
196	C₄×D₄×C₃₁	—	2	1	no	—
197	C₄×D₄×C₃₁	—	2	1	no	—
198	C₄×D₄×C₃₁	C₂³	1	2	yes	—
199	C₄×D₄×C₃₁	C₂³	1	2	yes	—
200	C₄×D₄×C₃₁	C₂³	1	2	yes	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#117	—	2	1	no	—
203	C₃₁×#117	—	2	1	no	—
204	C₃₁×#117	—	2	2	no	—
205	C₃₁×#117	—	2	2	no	—
206	C₃₁×#117	—	2	2	no	—
207	C₃₁×#117	—	2	2	no	—
208	C₃₁×#117	—	2	2	no	—
209	C₃₁×#117	—	2	2	no	—
210	C₃₁×#117	—	2	2	no	—
211	C₃₁×#117	C₂³	1	2	yes	—
212	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
213	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
214	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
215	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
216	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
219	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
220	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
221	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
222	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
223	C₂×C₄²×C₃₁	—	2	1	no	—
224	C₂×C₄²×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
229	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
230	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
237	C₃₁×#107	C₂³	1	4	yes	—
238	C₃₁×#107	C₂³	1	4	yes	—
239	C₃₁×#106	C₂³	1	4	yes	—
240	C₃₁×#106	C₂³	1	4	yes	—
241	C₃₁×#103	C₂³	1	4	yes	—
242	C₃₁×#103	C₂³	1	4	yes	—
243	C₃₁×#103	C₂³	1	4	yes	—
244	C₃₁×#103	C₂³	1	4	yes	—
245	C₃₁×#102	C₂³	1	4	yes	—
246	C₃₁×#102	C₂³	1	4	yes	—
247	C₃₁×#102	C₂³	1	4	yes	—
248	C₃₁×#102	C₂³	1	4	yes	—
249	C₃₁×#97	C₂³	1	4	yes	—
250	C₃₁×#97	C₂³	1	2	yes	—
251	C₃₁×#97	C₂³	1	2	yes	—
252	C₄×C₈×C₃₁	C₂³	1	4	yes	—
253	C₄×C₈×C₃₁	C₂³	1	2	yes	—
254	C₄×C₈×C₃₁	C₂³	1	2	yes	—
255	C₂⁴×C₃₁	—	2	1	no	—
256	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
257	#41×C₃₁	—	2	4	no	—
258	#41×C₃₁	—	2	4	no	—
259	#41×C₃₁	—	4	4	no	—
260	#41×C₃₁	—	4	4	no	—
261	C₂×Q₈×C₃₁	—	2	1	no	—
262	C₂×Q₈×C₃₁	—	2	1	no	—
263	C₂×Q₈×C₃₁	—	2	1	no	—
264	C₂×Q₈×C₃₁	—	2	4	no	—
265	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
266	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
267	C₂×D₄×C₃₁	—	2	2	no	—
268	C₂×D₄×C₃₁	—	2	2	no	—
269	C₂×D₄×C₃₁	—	2	2	no	—
270	C₂×D₄×C₃₁	—	2	2	no	—
271	C₂×D₄×C₃₁	—	2	2	no	—
272	C₂×D₄×C₃₁	—	2	1	no	—
273	C₂×D₄×C₃₁	—	2	1	no	—
274	C₂×D₄×C₃₁	—	2	1	no	—
275	C₂×D₄×C₃₁	—	2	4	no	—
276	C₂×D₄×C₃₁	—	4	4	no	—
277	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
278	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₃₁	—	2	4	no	—
280	C₂²×C₄×C₃₁	—	2	1	no	—
281	C₂²×C₄×C₃₁	—	2	1	no	—
282	C₂²×C₄×C₃₁	—	2	1	no	—
283	C₂²×C₄×C₃₁	—	2	2	no	—
284	C₂²×C₄×C₃₁	—	2	2	no	—
285	C₂²×C₄×C₃₁	—	2	2	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	4	2	no	—
289	C₂²×C₄×C₃₁	—	4	2	no	—
290	C₂²×C₄×C₃₁	—	4	4	no	—
291	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	Q₁₆×C₃₁	—	2	8	no	—
310	SD₁₆×C₃₁	—	2	8	no	—
311	SD₁₆×C₃₁	—	2	8	no	—
312	D₈×C₃₁	—	2	8	no	—
313	M₁₆×C₃₁	—	2	4	no	—
314	M₁₆×C₃₁	—	2	8	no	—
315	M₁₆×C₃₁	#41	1	8	yes	complemented
316	C₂×C₈×C₃₁	—	2	8	no	—
317	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
318	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	1	no	—
328	C₄⋊C₄×C₃₁	—	2	1	no	—
329	C₄⋊C₄×C₃₁	—	2	1	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	1	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
341	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	2	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₄²×C₃₁	—	2	2	no	—
363	C₄²×C₃₁	—	2	2	no	—
364	C₄²×C₃₁	—	2	2	no	—
365	C₄²×C₃₁	—	2	2	no	—
366	C₄²×C₃₁	—	2	2	no	—
367	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
383	#60702	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂³×C₃₁	—	2	2	no	—
385	C₂³×C₃₁	—	2	2	no	—
386	C₂³×C₃₁	—	2	2	no	—
387	C₂³×C₃₁	—	2	2	no	—
388	C₂³×C₃₁	—	4	1	no	—
389	C₂³×C₃₁	—	4	2	no	—
390	C₂³×C₃₁	—	4	2	no	—
391	C₂³×C₃₁	—	4	2	no	—
392	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	Q₈×C₃₁	—	2	2	no	—
396	Q₈×C₃₁	—	2	4	no	—
397	Q₈×C₃₁	—	2	2	no	—
398	Q₈×C₃₁	—	4	2	no	—
399	Q₈×C₃₁	—	4	2	no	—
400	Q₈×C₃₁	—	4	2	no	—
401	D₄×C₃₁	—	2	2	no	—
402	D₄×C₃₁	—	2	4	no	—
403	D₄×C₃₁	—	2	2	no	—
404	D₄×C₃₁	—	4	2	no	—
405	D₄×C₃₁	—	4	2	no	—
406	D₄×C₃₁	—	4	4	no	—
407	D₄×C₃₁	—	4	4	no	—
408	D₄×C₃₁	—	4	4	no	—
409	D₄×C₃₁	—	4	4	no	—
410	D₄×C₃₁	—	4	4	no	—
411	D₄×C₃₁	—	4	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	4	1	no	—
429	C₂×C₄×C₃₁	—	4	1	no	—
430	C₂×C₄×C₃₁	—	4	1	no	—
431	C₂×C₄×C₃₁	—	4	1	no	—
432	C₂×C₄×C₃₁	—	4	1	no	—
433	C₂×C₄×C₃₁	—	4	1	no	—
434	C₂×C₄×C₃₁	—	4	1	no	—
435	C₂×C₄×C₃₁	—	4	4	no	—
436	C₂×C₄×C₃₁	—	4	4	no	—
437	C₂×C₄×C₃₁	—	4	2	no	—
438	C₂×C₄×C₃₁	—	4	2	no	—
439	C₂×C₄×C₃₁	—	4	2	no	—
440	C₂×C₄×C₃₁	—	4	4	no	—
441	C₂×C₄×C₃₁	—	4	4	no	—
442	C₂×C₄×C₃₁	—	4	4	no	—
443	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
455	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
456	C₈×C₃₁	—	2	4	no	—
457	C₈×C₃₁	C₂×#41	1	8	yes	—
458	#3444	C₂×C₃₁	1	1	yes	characteristic, complemented
459	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#3183	C₂×C₃₁	1	4	yes	complemented
461	#3181	C₂×C₃₁	1	2	yes	complemented
462	#3180	C₂×C₃₁	1	2	yes	complemented
463	#3172	C₂×C₃₁	1	2	yes	complemented
464	#3171	C₂×C₃₁	1	2	yes	complemented
465	#3168	C₂×C₃₁	1	4	yes	complemented
466	#3166	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#3153	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3142	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#3056	C₂×C₃₁	1	2	yes	complemented
471	#3055	C₂×C₃₁	1	2	yes	complemented
472	C₄×#137	C₂×C₃₁	1	2	yes	complemented
473	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
474	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
475	C₂²×C₃₁	—	2	1	no	—
476	C₂²×C₃₁	—	2	1	no	—
477	C₂²×C₃₁	—	2	1	no	—
478	C₂²×C₃₁	—	2	1	no	—
479	C₂²×C₃₁	—	2	1	no	—
480	C₂²×C₃₁	—	2	1	no	—
481	C₂²×C₃₁	—	2	1	no	—
482	C₂²×C₃₁	—	4	4	no	—
483	C₂²×C₃₁	—	4	2	no	—
484	C₂²×C₃₁	—	4	2	no	—
485	C₂²×C₃₁	—	4	2	no	—
486	C₂²×C₃₁	—	4	2	no	—
487	C₂²×C₃₁	—	4	2	no	—
488	C₂²×C₃₁	—	4	2	no	—
489	C₂²×C₃₁	—	8	4	no	—
490	C₂²×C₃₁	#532	1	2	yes	—
491	C₂²×C₃₁	#575	1	2	yes	—
492	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₃₁	—	2	1	no	—
494	C₄×C₃₁	—	2	1	no	—
495	C₄×C₃₁	—	2	1	no	—
496	C₄×C₃₁	—	2	1	no	—
497	C₄×C₃₁	—	2	1	no	—
498	C₄×C₃₁	—	2	1	no	—
499	C₄×C₃₁	—	2	1	no	—
500	C₄×C₃₁	—	2	1	no	—
501	C₄×C₃₁	—	2	1	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	2	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	2	no	—
506	C₄×C₃₁	—	4	2	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	#532	1	2	yes	—
509	C₄×C₃₁	#575	1	2	yes	—
510	C₄×C₃₁	C₂²×#41	1	2	yes	—
511	C₂×#137	C₂²×C₃₁	1	2	yes	—
512	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
513	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
514	#533	C₂²×C₃₁	1	1	yes	characteristic
515	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
517	#532	C₂²×C₃₁	1	1	yes	characteristic
518	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
519	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
520	#529	—	2	1	no	—
521	#529	—	2	1	no	—
522	#529	—	2	1	no	—
523	#529	—	2	1	no	—
524	#529	—	2	1	no	—
525	#529	—	2	1	no	—
526	#529	—	2	1	no	—
527	#529	—	2	1	no	—
528	#529	C₂²×C₃₁	1	2	yes	—
529	#529	C₂²×C₃₁	1	2	yes	—
530	#529	C₂²×C₃₁	1	2	yes	—
531	#529	C₂²×C₃₁	1	2	yes	—
532	#529	C₂²×C₃₁	1	2	yes	complemented
533	#529	C₂²×C₃₁	1	2	yes	complemented
534	C₂×#126	—	2	1	no	—
535	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
536	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
537	#525	—	2	1	no	—
538	#525	—	2	1	no	—
539	#525	C₂²×C₃₁	1	2	yes	—
540	C₂×#123	—	2	1	no	—
541	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
542	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
543	C₄×#41	—	2	1	no	—
544	C₄×#41	—	2	1	no	—
545	C₄×#41	C₂²×C₃₁	1	2	yes	—
546	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
547	C₂×C₄×D₄	—	2	1	no	—
548	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×#117	—	2	1	no	—
550	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
551	#501	C₂²×C₃₁	1	2	yes	complemented
552	#501	C₂²×C₃₁	1	2	yes	complemented
553	#499	C₂²×C₃₁	1	4	yes	complemented
554	#497	C₂²×C₃₁	1	2	yes	complemented
555	#496	C₂²×C₃₁	1	2	yes	complemented
556	#495	C₂²×C₃₁	1	4	yes	complemented
557	#491	C₂²×C₃₁	1	2	yes	complemented
558	#490	C₂²×C₃₁	1	2	yes	complemented
559	#489	C₂²×C₃₁	1	2	yes	complemented
560	#489	C₂²×C₃₁	1	2	yes	complemented
561	#488	C₂²×C₃₁	1	4	yes	complemented
562	#488	C₂²×C₃₁	1	4	yes	complemented
563	#470	C₂²×C₃₁	1	4	yes	complemented
564	#469	C₂²×C₃₁	1	4	yes	—
565	#468	C₂²×C₃₁	1	4	yes	—
566	#468	C₂²×C₃₁	1	4	yes	complemented
567	#467	C₂²×C₃₁	1	4	yes	complemented
568	#466	C₂²×C₃₁	1	4	yes	—
569	#465	C₂²×C₃₁	1	4	yes	—
570	#465	C₂²×C₃₁	1	4	yes	complemented
571	#442	C₂²×C₃₁	1	4	yes	complemented
572	#441	C₂²×C₃₁	1	4	yes	complemented
573	#440	C₂²×C₃₁	1	4	yes	complemented
574	#440	C₂²×C₃₁	1	4	yes	complemented
575	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
576	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
577	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
578	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
579	#428	C₂²×C₃₁	1	2	yes	—
580	#428	C₂²×C₃₁	1	2	yes	—
581	#419	C₂²×C₃₁	1	2	yes	—
582	#418	C₂²×C₃₁	1	2	yes	—
583	#417	C₂²×C₃₁	1	2	yes	—
584	#417	C₂²×C₃₁	1	2	yes	—
585	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
586	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
587	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
588	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
589	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
590	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
591	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	complemented
592	C₂×C₃₁	—	2	2	no	—
593	C₂×C₃₁	—	2	2	no	—
594	C₂×C₃₁	—	4	1	no	—
595	C₂×C₃₁	—	8	2	no	—
596	C₂×C₃₁	—	8	2	no	—
597	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
598	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
599	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	C₂³×C₃₁	1	2	yes	—
603	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₂²×D₄	—	2	1	no	—
605	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
606	C₂³×C₄	—	2	1	no	—
607	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
608	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
610	#137	—	2	8	no	—
611	AGL(1,ℤ/8)	—	2	8	no	—
612	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
613	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
614	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
615	C₂×D₈	C₂³×C₃₁	1	4	yes	—
616	C₂×M₁₆	—	2	8	no	—
617	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
618	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
619	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
620	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
621	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	#127	C₂³×C₃₁	1	1	yes	characteristic
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#125	—	2	1	no	—
632	#125	—	2	1	no	—
633	#125	—	2	1	no	—
634	#125	—	2	1	no	—
635	#125	C₂³×C₃₁	1	2	yes	—
636	#125	C₂³×C₃₁	1	2	yes	—
637	#125	C₂³×C₃₁	1	2	yes	—
638	#124	—	2	1	no	—
639	#124	—	2	1	no	—
640	#124	—	2	1	no	—
641	#124	—	2	1	no	—
642	#124	C₂³×C₃₁	1	2	yes	—
643	#124	C₂³×C₃₁	1	2	yes	—
644	#124	C₂³×C₃₁	1	2	yes	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	1	no	—
658	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
659	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
660	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
661	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
662	#121	—	2	1	no	—
663	#121	—	2	1	no	—
664	#121	—	2	1	no	—
665	#121	—	2	1	no	—
666	#121	—	2	1	no	—
667	#121	—	2	1	no	—
668	#121	C₂³×C₃₁	1	2	yes	—
669	#121	C₂³×C₃₁	1	2	yes	—
670	#121	C₂³×C₃₁	1	2	yes	—
671	#121	C₂³×C₃₁	1	2	yes	—
672	#120	—	2	2	no	—
673	C₄×Q₈	—	2	1	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	—	2	1	no	—
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
680	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
681	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
682	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	C₂³×C₃₁	1	2	yes	—
700	C₄×D₄	C₂³×C₃₁	1	2	yes	—
701	C₄×D₄	C₂³×C₃₁	1	2	yes	—
702	C₄×D₄	C₂³×C₃₁	1	2	yes	—
703	#117	—	2	1	no	—
704	#117	—	2	1	no	—
705	#117	—	2	2	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	—	2	2	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	—	2	2	no	—
712	#117	C₂³×C₃₁	1	2	yes	—
713	C₂×C₄⋊C₄	—	2	1	no	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	—	2	1	no	—
720	C₂×C₂²⋊C₄	—	2	1	no	—
721	C₂×C₂²⋊C₄	—	2	1	no	—
722	C₂×C₂²⋊C₄	—	2	1	no	—
723	C₂×C₂²⋊C₄	—	2	1	no	—
724	C₂×C₄²	—	2	1	no	—
725	C₂×C₄²	—	2	2	no	—
726	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
727	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
730	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
731	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
738	#107	C₂³×C₃₁	1	4	yes	—
739	#107	C₂³×C₃₁	1	4	yes	—
740	#106	C₂³×C₃₁	1	4	yes	—
741	#106	C₂³×C₃₁	1	4	yes	—
742	#103	C₂³×C₃₁	1	4	yes	—
743	#103	C₂³×C₃₁	1	4	yes	—
744	#103	C₂³×C₃₁	1	4	yes	—
745	#103	C₂³×C₃₁	1	4	yes	—
746	#102	C₂³×C₃₁	1	4	yes	—
747	#102	C₂³×C₃₁	1	4	yes	—
748	#102	C₂³×C₃₁	1	4	yes	—
749	#102	C₂³×C₃₁	1	4	yes	—
750	#97	C₂³×C₃₁	1	4	yes	—
751	#97	C₂³×C₃₁	1	2	yes	—
752	#97	C₂³×C₃₁	1	2	yes	—
753	C₄×C₈	C₂³×C₃₁	1	4	yes	—
754	C₄×C₈	C₂³×C₃₁	1	2	yes	—
755	C₄×C₈	C₂³×C₃₁	1	2	yes	—
756	C₃₁	#60702	1	1	yes	characteristic, direct product factor, Sylow
757	C₂⁴	—	2	1	no	—
758	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
759	#41	—	2	4	no	—
760	#41	—	2	4	no	—
761	#41	—	4	4	no	—
762	#41	—	4	4	no	—
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	4	no	—
767	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
768	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	4	4	no	—
779	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	4	no	—
793	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
800	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
801	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
804	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
805	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
806	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
807	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
811	Q₁₆	—	2	8	no	—
812	SD₁₆	—	2	8	no	—
813	SD₁₆	—	2	8	no	—
814	D₈	—	2	8	no	—
815	M₁₆	—	2	4	no	—
816	M₁₆	—	2	8	no	—
817	M₁₆	#41×C₃₁	1	8	yes	complemented
818	C₂×C₈	—	2	8	no	—
819	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
820	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
870	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
871	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
874	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
875	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
878	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
879	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
880	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
881	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	4	1	no	—
890	C₂³	—	4	2	no	—
891	C₂³	—	4	2	no	—
892	C₂³	—	4	2	no	—
893	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
894	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
895	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
896	Q₈	—	2	2	no	—
897	Q₈	—	2	4	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	4	2	no	—
902	D₄	—	2	2	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	4	2	no	—
906	D₄	—	4	2	no	—
907	D₄	—	4	4	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	4	no	—
944	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
953	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
955	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
956	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
957	C₈	—	2	4	no	—
958	C₈	C₂×#41×C₃₁	1	8	yes	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	8	4	no	—
974	C₂²	C₃₁×#532	1	2	yes	—
975	C₂²	C₃₁×#575	1	2	yes	—
976	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	C₃₁×#532	1	2	yes	—
993	C₄	C₃₁×#575	1	2	yes	—
994	C₄	C₂²×#41×C₃₁	1	2	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	2	2	no	—
997	C₂	—	4	1	no	—
998	C₂	—	8	2	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
1001	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1002	C₂	C₂×C₃₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3444	C₂	semidirect
2. C₂×C₃₁×#529	C₂	semidirect
3. C₃₁×#3183	C₂	semidirect
4. C₃₁×#3181	C₂	semidirect
5. C₃₁×#3180	C₂	semidirect
6. C₃₁×#3172	C₂	semidirect
7. C₃₁×#3171	C₂	semidirect
8. C₃₁×#3168	C₂	semidirect
9. C₃₁×#3166	C₂	semidirect
10. C₃₁×#3153	C₂	semidirect
11. C₃₁×#3142	C₂	semidirect
12. C₃₁×#3140	C₂	semidirect
13. C₃₁×#3056	C₂	semidirect
14. C₃₁×#3055	C₂	semidirect
15. C₄×C₃₁×#137	C₂	semidirect
16. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
17. C₂×C₄×M₁₆×C₃₁	C₂	semidirect
22. C₃₁×#533	C₂²	semidirect
23. C₃₁×#533	C₂²	semidirect
25. C₃₁×#532	C₂²	semidirect
26. C₃₁×#532	C₂²	semidirect
39. C₃₁×#529	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
58. C₃₁×#501	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#499	C₂²	semidirect
61. C₃₁×#497	C₂²	semidirect
62. C₃₁×#496	C₂²	semidirect
63. C₃₁×#495	C₂²	semidirect
64. C₃₁×#491	C₂²	semidirect
65. C₃₁×#490	C₂²	semidirect
66. C₃₁×#489	C₂²	semidirect
67. C₃₁×#489	C₂²	semidirect
68. C₃₁×#488	C₂²	semidirect
69. C₃₁×#488	C₂²	semidirect
70. C₃₁×#470	C₂²	semidirect
73. C₃₁×#468	C₂²	semidirect
74. C₃₁×#467	C₂²	semidirect
77. C₃₁×#465	C₂²	semidirect
78. C₃₁×#442	C₂²	semidirect
79. C₃₁×#441	C₂²	semidirect
80. C₃₁×#440	C₂²	semidirect
81. C₃₁×#440	C₂²	semidirect
82. C₄×Q₁₆×C₃₁	C₂²	semidirect
83. C₄×SD₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×D₈×C₃₁	C₂²	semidirect
95. C₄×M₁₆×C₃₁	C₂²	semidirect
96. C₄×M₁₆×C₃₁	C₂²	semidirect
97. C₂×C₃₁×#97	C₂²	semidirect
98. C₂×C₄×C₈×C₃₁	C₂²	semidirect
315. M₁₆×C₃₁	#41	semidirect
383. #60702	C₃₁	direct (N × H)
458. #3444	C₂×C₃₁	semidirect
459. C₂×#529	C₂×C₃₁	semidirect
460. #3183	C₂×C₃₁	semidirect
461. #3181	C₂×C₃₁	semidirect
462. #3180	C₂×C₃₁	semidirect
463. #3172	C₂×C₃₁	semidirect
464. #3171	C₂×C₃₁	semidirect
465. #3168	C₂×C₃₁	semidirect
466. #3166	C₂×C₃₁	semidirect
467. #3153	C₂×C₃₁	semidirect
468. #3142	C₂×C₃₁	semidirect
469. #3140	C₂×C₃₁	semidirect
470. #3056	C₂×C₃₁	semidirect
471. #3055	C₂×C₃₁	semidirect
472. C₄×#137	C₂×C₃₁	semidirect
473. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
474. C₂×C₄×M₁₆	C₂×C₃₁	semidirect
515. #533	C₂²×C₃₁	semidirect
516. #533	C₂²×C₃₁	semidirect
518. #532	C₂²×C₃₁	semidirect
519. #532	C₂²×C₃₁	semidirect
532. #529	C₂²×C₃₁	semidirect
533. #529	C₂²×C₃₁	semidirect
551. #501	C₂²×C₃₁	semidirect
552. #501	C₂²×C₃₁	semidirect
553. #499	C₂²×C₃₁	semidirect
554. #497	C₂²×C₃₁	semidirect
555. #496	C₂²×C₃₁	semidirect
556. #495	C₂²×C₃₁	semidirect
557. #491	C₂²×C₃₁	semidirect
558. #490	C₂²×C₃₁	semidirect
559. #489	C₂²×C₃₁	semidirect
560. #489	C₂²×C₃₁	semidirect
561. #488	C₂²×C₃₁	semidirect
562. #488	C₂²×C₃₁	semidirect
563. #470	C₂²×C₃₁	semidirect
566. #468	C₂²×C₃₁	semidirect
567. #467	C₂²×C₃₁	semidirect
570. #465	C₂²×C₃₁	semidirect
571. #442	C₂²×C₃₁	semidirect
572. #441	C₂²×C₃₁	semidirect
573. #440	C₂²×C₃₁	semidirect
574. #440	C₂²×C₃₁	semidirect
575. C₄×Q₁₆	C₂²×C₃₁	semidirect
576. C₄×SD₁₆	C₂²×C₃₁	semidirect
577. C₄×SD₁₆	C₂²×C₃₁	semidirect
578. C₄×D₈	C₂²×C₃₁	semidirect
588. C₄×M₁₆	C₂²×C₃₁	semidirect
589. C₄×M₁₆	C₂²×C₃₁	semidirect
590. C₂×#97	C₂²×C₃₁	semidirect
591. C₂×C₄×C₈	C₂²×C₃₁	semidirect
756. C₃₁	#60702	direct (N × H)
817. M₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3444	2
C₂×C₃₁×#529	2
C₃₁×#3183	2
C₃₁×#3181	2
C₃₁×#3180	2
C₃₁×#3172	2
C₃₁×#3171	2
C₃₁×#3168	2
C₃₁×#3166	2
C₃₁×#3153	2
C₃₁×#3142	2
C₃₁×#3140	2
C₃₁×#3056	2
C₃₁×#3055	2
C₄×C₃₁×#137	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₂×C₄×M₁₆×C₃₁	2
#60702	31

Subgroups — C31×#60702 #21517461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60702 #21517461