Subgroups — C₃₁×#60755 #21517514

Order 7936.

2194 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3449	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3204	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3203	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3201	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3198	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3092	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3005	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃₁×#137	C₂²	1	2	yes	—
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
22	C₃₁×#537	—	2	2	no	—
23	C₃₁×#537	—	2	2	no	—
24	C₃₁×#537	C₂²	1	4	yes	—
25	C₃₁×#537	C₂²	1	4	yes	complemented
26	C₃₁×#537	C₂²	1	2	yes	complemented
27	C₃₁×#537	C₂²	1	2	yes	complemented
28	C₃₁×#536	—	2	1	no	—
29	C₃₁×#536	C₂²	1	2	yes	complemented
30	C₃₁×#535	—	2	1	no	—
31	C₃₁×#535	C₂²	1	2	yes	complemented
32	C₃₁×#534	—	2	1	no	—
33	C₃₁×#534	—	2	1	no	—
34	C₃₁×#532	—	2	2	no	—
35	C₃₁×#525	—	2	2	no	—
36	C₃₁×#525	C₂²	1	2	yes	—
37	C₃₁×#525	C₂²	1	2	yes	—
38	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃₁×#121	—	2	1	no	—
42	C₂×C₃₁×#121	—	2	1	no	—
43	C₂×C₃₁×#121	—	2	1	no	—
44	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#485	C₂²	1	4	yes	complemented
49	C₃₁×#484	C₂²	1	4	yes	complemented
50	C₃₁×#484	C₂²	1	2	yes	complemented
51	C₃₁×#483	C₂²	1	4	yes	complemented
52	C₃₁×#483	C₂²	1	2	yes	complemented
53	C₃₁×#482	C₂²	1	4	yes	complemented
54	C₃₁×#481	C₂²	1	4	yes	complemented
55	C₃₁×#481	C₂²	1	2	yes	complemented
56	C₃₁×#480	C₂²	1	4	yes	complemented
57	C₃₁×#480	C₂²	1	2	yes	complemented
58	C₃₁×#470	C₂²	1	4	yes	complemented
59	C₃₁×#469	C₂²	1	4	yes	complemented
60	C₃₁×#468	C₂²	1	4	yes	complemented
61	C₃₁×#468	C₂²	1	4	yes	complemented
62	C₃₁×#467	C₂²	1	4	yes	complemented
63	C₃₁×#466	C₂²	1	4	yes	complemented
64	C₃₁×#465	C₂²	1	4	yes	complemented
65	C₃₁×#465	C₂²	1	4	yes	complemented
66	C₃₁×#452	C₂²	1	4	yes	complemented
67	C₃₁×#452	C₂²	1	4	yes	complemented
68	C₃₁×#452	C₂²	1	4	yes	complemented
69	C₃₁×#451	C₂²	1	2	yes	complemented
70	C₃₁×#450	C₂²	1	2	yes	complemented
71	C₃₁×#449	C₂²	1	4	yes	complemented
72	C₃₁×#449	C₂²	1	4	yes	complemented
73	C₃₁×#449	C₂²	1	4	yes	complemented
74	C₃₁×#448	C₂²	1	2	yes	complemented
75	C₃₁×#447	C₂²	1	2	yes	complemented
76	C₃₁×#428	C₂²	1	2	yes	complemented
77	C₃₁×#428	C₂²	1	2	yes	complemented
78	C₃₁×#419	C₂²	1	2	yes	complemented
79	C₃₁×#418	C₂²	1	2	yes	complemented
80	C₃₁×#417	C₂²	1	2	yes	—
81	C₃₁×#417	C₂²	1	2	yes	—
82	C₃₁×#408	C₂²	1	4	yes	complemented
83	C₃₁×#408	C₂²	1	4	yes	complemented
84	C₃₁×#407	C₂²	1	1	yes	characteristic
85	C₃₁×#407	C₂²	1	1	yes	characteristic
86	C₃₁×#407	C₂²	1	2	yes	complemented
87	C₂×#41×C₃₁	—	2	1	no	—
88	C₂×#41×C₃₁	—	2	1	no	—
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	—	4	4	no	—
91	C₂×#41×C₃₁	—	4	4	no	—
92	C₂×#41×C₃₁	—	4	4	no	—
93	C₂×#41×C₃₁	D₄	1	2	yes	—
94	C₂×#41×C₃₁	D₄	1	2	yes	—
95	C₂×#41×C₃₁	C₂³	1	2	yes	—
96	C₂×#41×C₃₁	C₂³	1	4	yes	—
97	C₂×#41×C₃₁	C₂³	1	2	yes	—
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂×#41×C₃₁	C₂³	1	2	yes	—
100	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
101	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	—	2	1	no	—
106	C₂²×D₄×C₃₁	—	2	1	no	—
107	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
108	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	—	2	1	no	—
113	C₂³×C₄×C₃₁	—	2	1	no	—
114	C₂³×C₄×C₃₁	—	2	1	no	—
115	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₃₁×#137	—	4	4	no	—
119	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
120	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
121	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
122	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
123	C₂×D₈×C₃₁	C₂³	1	4	yes	—
124	C₂×M₁₆×C₃₁	—	4	4	no	—
125	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
128	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
129	C₃₁×C₄⋊Q₈	—	2	2	no	—
130	C₃₁×#127	—	2	2	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×#123	—	2	2	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×#121	—	2	4	no	—
152	C₃₁×#121	—	2	4	no	—
153	C₃₁×#121	—	2	4	no	—
154	C₃₁×#121	—	2	4	no	—
155	C₃₁×#121	—	2	4	no	—
156	C₃₁×#121	—	2	4	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	—	2	2	no	—
159	C₃₁×#121	—	2	2	no	—
160	C₃₁×#121	—	2	2	no	—
161	C₃₁×#121	—	2	2	no	—
162	C₃₁×#121	—	2	2	no	—
163	C₃₁×#121	—	2	1	no	—
164	C₃₁×#121	—	2	1	no	—
165	C₃₁×#121	—	2	2	no	—
166	C₃₁×#121	C₂³	1	2	yes	—
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×#121	C₂³	1	4	yes	—
172	C₃₁×#121	C₂³	1	2	yes	—
173	C₃₁×#120	—	2	2	no	—
174	C₃₁×#120	—	2	2	no	—
175	C₃₁×#120	—	2	2	no	—
176	C₃₁×#120	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₃₁×#117	—	2	1	no	—
182	C₃₁×#117	—	2	1	no	—
183	C₃₁×#117	C₂³	1	2	yes	—
184	C₃₁×#117	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
186	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
187	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
188	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
199	C₂×C₄²×C₃₁	—	2	1	no	—
200	C₃₁×#107	C₂³	1	4	yes	—
201	C₃₁×#107	C₂³	1	4	yes	—
202	C₃₁×#106	C₂³	1	4	yes	—
203	C₃₁×#106	C₂³	1	4	yes	—
204	C₃₁×#103	C₂³	1	4	yes	—
205	C₃₁×#103	C₂³	1	4	yes	—
206	C₃₁×#103	C₂³	1	4	yes	—
207	C₃₁×#103	C₂³	1	4	yes	—
208	C₃₁×#102	C₂³	1	4	yes	—
209	C₃₁×#102	C₂³	1	4	yes	—
210	C₃₁×#102	C₂³	1	4	yes	—
211	C₃₁×#102	C₂³	1	4	yes	—
212	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
216	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
217	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
218	C₂⁴×C₃₁	—	2	1	no	—
219	C₂⁴×C₃₁	—	2	1	no	—
220	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
222	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
223	#41×C₃₁	—	2	4	no	—
224	#41×C₃₁	—	2	4	no	—
225	#41×C₃₁	—	4	4	no	—
226	#41×C₃₁	—	4	4	no	—
227	#41×C₃₁	—	4	2	no	—
228	#41×C₃₁	—	4	2	no	—
229	#41×C₃₁	—	4	2	no	—
230	#41×C₃₁	—	4	2	no	—
231	#41×C₃₁	—	4	2	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	4	2	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	8	no	—
237	#41×C₃₁	—	4	4	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	4	no	—
241	C₂×Q₈×C₃₁	—	4	2	no	—
242	C₂×Q₈×C₃₁	—	4	2	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	—	2	4	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	4	no	—
256	C₂×D₄×C₃₁	—	2	2	no	—
257	C₂×D₄×C₃₁	—	2	1	no	—
258	C₂×D₄×C₃₁	—	2	1	no	—
259	C₂×D₄×C₃₁	—	2	4	no	—
260	C₂×D₄×C₃₁	—	4	2	no	—
261	C₂×D₄×C₃₁	—	4	2	no	—
262	C₂×D₄×C₃₁	—	4	2	no	—
263	C₂×D₄×C₃₁	—	4	2	no	—
264	C₂×D₄×C₃₁	—	4	4	no	—
265	C₂×D₄×C₃₁	—	4	4	no	—
266	C₂×D₄×C₃₁	—	8	2	no	—
267	C₂×D₄×C₃₁	—	8	2	no	—
268	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	—	2	4	no	—
277	C₂²×C₄×C₃₁	—	2	4	no	—
278	C₂²×C₄×C₃₁	—	2	4	no	—
279	C₂²×C₄×C₃₁	—	2	1	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	1	no	—
284	C₂²×C₄×C₃₁	—	2	1	no	—
285	C₂²×C₄×C₃₁	—	2	4	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	—	4	4	no	—
290	C₂²×C₄×C₃₁	—	4	4	no	—
291	C₂²×C₄×C₃₁	—	8	2	no	—
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	2	yes	—
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	2	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	Q₁₆×C₃₁	—	4	4	no	—
305	SD₁₆×C₃₁	—	4	4	no	—
306	SD₁₆×C₃₁	—	4	4	no	—
307	D₈×C₃₁	—	4	4	no	—
308	M₁₆×C₃₁	—	2	4	no	—
309	M₁₆×C₃₁	—	2	4	no	—
310	M₁₆×C₃₁	—	4	4	no	—
311	C₂×C₈×C₃₁	—	4	4	no	—
312	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
313	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₃₁	—	2	4	no	—
315	C₄⋊C₄×C₃₁	—	2	1	no	—
316	C₄⋊C₄×C₃₁	—	2	1	no	—
317	C₄⋊C₄×C₃₁	—	2	2	no	—
318	C₄⋊C₄×C₃₁	—	2	4	no	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	1	no	—
321	C₄⋊C₄×C₃₁	—	2	1	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	C₂⁴	1	2	yes	—
327	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
328	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
329	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
334	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
339	C₂²⋊C₄×C₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₃₁	—	2	4	no	—
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₄²×C₃₁	—	2	2	no	—
347	C₄²×C₃₁	—	2	2	no	—
348	#60755	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	2	no	—
351	C₂³×C₃₁	—	2	2	no	—
352	C₂³×C₃₁	—	2	2	no	—
353	C₂³×C₃₁	—	2	2	no	—
354	C₂³×C₃₁	—	4	1	no	—
355	C₂³×C₃₁	—	4	1	no	—
356	C₂³×C₃₁	—	4	1	no	—
357	C₂³×C₃₁	—	4	1	no	—
358	C₂³×C₃₁	—	4	1	no	—
359	C₂³×C₃₁	—	4	1	no	—
360	C₂³×C₃₁	—	4	2	no	—
361	C₂³×C₃₁	—	4	2	no	—
362	C₂³×C₃₁	—	4	2	no	—
363	C₂³×C₃₁	—	4	2	no	—
364	C₂³×C₃₁	—	8	1	no	—
365	C₂³×C₃₁	—	8	1	no	—
366	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
368	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
369	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
371	Q₈×C₃₁	—	2	2	no	—
372	Q₈×C₃₁	—	2	4	no	—
373	Q₈×C₃₁	—	2	2	no	—
374	Q₈×C₃₁	—	4	2	no	—
375	Q₈×C₃₁	—	4	2	no	—
376	Q₈×C₃₁	—	4	2	no	—
377	Q₈×C₃₁	—	4	2	no	—
378	D₄×C₃₁	—	2	2	no	—
379	D₄×C₃₁	—	2	4	no	—
380	D₄×C₃₁	—	2	2	no	—
381	D₄×C₃₁	—	4	2	no	—
382	D₄×C₃₁	—	4	2	no	—
383	D₄×C₃₁	—	4	2	no	—
384	D₄×C₃₁	—	4	2	no	—
385	D₄×C₃₁	—	4	2	no	—
386	D₄×C₃₁	—	4	2	no	—
387	D₄×C₃₁	—	4	2	no	—
388	D₄×C₃₁	—	4	8	no	—
389	D₄×C₃₁	—	4	4	no	—
390	D₄×C₃₁	—	4	4	no	—
391	D₄×C₃₁	—	4	2	no	—
392	D₄×C₃₁	—	8	2	no	—
393	D₄×C₃₁	—	8	2	no	—
394	D₄×C₃₁	—	8	2	no	—
395	D₄×C₃₁	—	8	2	no	—
396	D₄×C₃₁	—	8	2	no	—
397	D₄×C₃₁	—	8	4	no	—
398	D₄×C₃₁	—	8	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	2	no	—
403	C₂×C₄×C₃₁	—	2	4	no	—
404	C₂×C₄×C₃₁	—	2	4	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	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	—	4	8	no	—
419	C₂×C₄×C₃₁	—	4	4	no	—
420	C₂×C₄×C₃₁	—	4	2	no	—
421	C₂×C₄×C₃₁	—	4	2	no	—
422	C₂×C₄×C₃₁	—	4	2	no	—
423	C₂×C₄×C₃₁	—	4	2	no	—
424	C₂×C₄×C₃₁	—	4	4	no	—
425	C₂×C₄×C₃₁	—	8	1	no	—
426	C₂×C₄×C₃₁	—	8	1	no	—
427	C₂×C₄×C₃₁	—	8	4	no	—
428	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
434	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
435	C₈×C₃₁	—	2	4	no	—
436	C₈×C₃₁	—	2	4	no	—
437	#3449	C₂×C₃₁	1	1	yes	characteristic, complemented
438	C₂×#537	C₂×C₃₁	1	1	yes	characteristic, complemented
439	#3204	C₂×C₃₁	1	4	yes	complemented
440	#3203	C₂×C₃₁	1	4	yes	complemented
441	#3201	C₂×C₃₁	1	4	yes	complemented
442	#3198	C₂×C₃₁	1	4	yes	complemented
443	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
444	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3092	C₂×C₃₁	1	2	yes	complemented
446	#3056	C₂×C₃₁	1	2	yes	complemented
447	#3055	C₂×C₃₁	1	2	yes	complemented
448	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#3006	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#3005	C₂×C₃₁	1	2	yes	complemented
451	#2879	C₂×C₃₁	1	1	yes	characteristic, complemented
452	C₂²×C₃₁	—	2	1	no	—
453	C₂²×C₃₁	—	2	1	no	—
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	1	no	—
456	C₂²×C₃₁	—	2	2	no	—
457	C₂²×C₃₁	—	2	1	no	—
458	C₂²×C₃₁	—	2	1	no	—
459	C₂²×C₃₁	—	2	2	no	—
460	C₂²×C₃₁	—	2	2	no	—
461	C₂²×C₃₁	—	2	1	no	—
462	C₂²×C₃₁	—	2	1	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	1	no	—
465	C₂²×C₃₁	—	2	2	no	—
466	C₂²×C₃₁	—	4	4	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	4	2	no	—
472	C₂²×C₃₁	—	4	2	no	—
473	C₂²×C₃₁	—	8	2	no	—
474	C₂²×C₃₁	—	8	2	no	—
475	C₂²×C₃₁	—	8	4	no	—
476	C₂²×C₃₁	—	8	4	no	—
477	C₂²×C₃₁	#534	1	2	yes	—
478	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	1	no	—
481	C₄×C₃₁	—	2	1	no	—
482	C₄×C₃₁	—	2	2	no	—
483	C₄×C₃₁	—	4	2	no	—
484	C₄×C₃₁	—	4	2	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	—	4	2	no	—
487	C₄×C₃₁	—	4	2	no	—
488	C₄×C₃₁	—	4	2	no	—
489	C₄×C₃₁	#534	1	2	yes	—
490	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
491	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
492	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
493	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
494	C₂×#137	C₂²×C₃₁	1	2	yes	—
495	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
496	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
497	#537	—	2	2	no	—
498	#537	—	2	2	no	—
499	#537	C₂²×C₃₁	1	4	yes	—
500	#537	C₂²×C₃₁	1	4	yes	complemented
501	#537	C₂²×C₃₁	1	2	yes	complemented
502	#537	C₂²×C₃₁	1	2	yes	complemented
503	#536	—	2	1	no	—
504	#536	C₂²×C₃₁	1	2	yes	complemented
505	#535	—	2	1	no	—
506	#535	C₂²×C₃₁	1	2	yes	complemented
507	#534	—	2	1	no	—
508	#534	—	2	1	no	—
509	#532	—	2	2	no	—
510	#525	—	2	2	no	—
511	#525	C₂²×C₃₁	1	2	yes	—
512	#525	C₂²×C₃₁	1	2	yes	—
513	C₂×C₂²⋊Q₈	—	2	1	no	—
514	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
515	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	C₂×#121	—	2	1	no	—
517	C₂×#121	—	2	1	no	—
518	C₂×#121	—	2	1	no	—
519	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
520	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
521	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
522	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
523	#485	C₂²×C₃₁	1	4	yes	complemented
524	#484	C₂²×C₃₁	1	4	yes	complemented
525	#484	C₂²×C₃₁	1	2	yes	complemented
526	#483	C₂²×C₃₁	1	4	yes	complemented
527	#483	C₂²×C₃₁	1	2	yes	complemented
528	#482	C₂²×C₃₁	1	4	yes	complemented
529	#481	C₂²×C₃₁	1	4	yes	complemented
530	#481	C₂²×C₃₁	1	2	yes	complemented
531	#480	C₂²×C₃₁	1	4	yes	complemented
532	#480	C₂²×C₃₁	1	2	yes	complemented
533	#470	C₂²×C₃₁	1	4	yes	complemented
534	#469	C₂²×C₃₁	1	4	yes	complemented
535	#468	C₂²×C₃₁	1	4	yes	complemented
536	#468	C₂²×C₃₁	1	4	yes	complemented
537	#467	C₂²×C₃₁	1	4	yes	complemented
538	#466	C₂²×C₃₁	1	4	yes	complemented
539	#465	C₂²×C₃₁	1	4	yes	complemented
540	#465	C₂²×C₃₁	1	4	yes	complemented
541	#452	C₂²×C₃₁	1	4	yes	complemented
542	#452	C₂²×C₃₁	1	4	yes	complemented
543	#452	C₂²×C₃₁	1	4	yes	complemented
544	#451	C₂²×C₃₁	1	2	yes	complemented
545	#450	C₂²×C₃₁	1	2	yes	complemented
546	#449	C₂²×C₃₁	1	4	yes	complemented
547	#449	C₂²×C₃₁	1	4	yes	complemented
548	#449	C₂²×C₃₁	1	4	yes	complemented
549	#448	C₂²×C₃₁	1	2	yes	complemented
550	#447	C₂²×C₃₁	1	2	yes	complemented
551	#428	C₂²×C₃₁	1	2	yes	complemented
552	#428	C₂²×C₃₁	1	2	yes	complemented
553	#419	C₂²×C₃₁	1	2	yes	complemented
554	#418	C₂²×C₃₁	1	2	yes	complemented
555	#417	C₂²×C₃₁	1	2	yes	—
556	#417	C₂²×C₃₁	1	2	yes	—
557	#408	C₂²×C₃₁	1	4	yes	complemented
558	#408	C₂²×C₃₁	1	4	yes	complemented
559	#407	C₂²×C₃₁	1	1	yes	characteristic
560	#407	C₂²×C₃₁	1	1	yes	characteristic
561	#407	C₂²×C₃₁	1	2	yes	complemented
562	C₂×C₃₁	—	2	2	no	—
563	C₂×C₃₁	—	4	2	no	—
564	C₂×C₃₁	—	4	1	no	—
565	C₂×C₃₁	—	4	2	no	—
566	C₂×C₃₁	—	4	1	no	—
567	C₂×C₃₁	—	8	2	no	—
568	C₂×C₃₁	—	8	2	no	—
569	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
570	C₂×C₃₁	#3585	1	1	yes	characteristic
571	C₂×C₃₁	#3586	1	1	yes	characteristic
572	C₂×#41	—	2	1	no	—
573	C₂×#41	—	2	1	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	4	4	no	—
576	C₂×#41	—	4	4	no	—
577	C₂×#41	—	4	4	no	—
578	C₂×#41	D₄×C₃₁	1	2	yes	—
579	C₂×#41	D₄×C₃₁	1	2	yes	—
580	C₂×#41	C₂³×C₃₁	1	2	yes	—
581	C₂×#41	C₂³×C₃₁	1	4	yes	—
582	C₂×#41	C₂³×C₃₁	1	2	yes	—
583	C₂×#41	C₂³×C₃₁	1	2	yes	—
584	C₂×#41	C₂³×C₃₁	1	2	yes	—
585	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
586	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
588	C₂²×D₄	—	2	1	no	—
589	C₂²×D₄	—	2	1	no	—
590	C₂²×D₄	—	2	1	no	—
591	C₂²×D₄	—	2	1	no	—
592	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
593	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
594	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₂³×C₄	—	2	1	no	—
598	C₂³×C₄	—	2	1	no	—
599	C₂³×C₄	—	2	1	no	—
600	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
603	#137	—	4	4	no	—
604	AGL(1,ℤ/8)	—	4	4	no	—
605	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
606	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
607	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
608	C₂×D₈	C₂³×C₃₁	1	4	yes	—
609	C₂×M₁₆	—	4	4	no	—
610	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
611	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
612	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
613	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
614	C₄⋊Q₈	—	2	2	no	—
615	#127	—	2	2	no	—
616	#124	—	2	2	no	—
617	#124	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	C₂²⋊Q₈	—	2	4	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	1	no	—
627	C₂²⋊Q₈	—	2	1	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
630	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
631	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
632	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
633	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
634	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
636	#121	—	2	4	no	—
637	#121	—	2	4	no	—
638	#121	—	2	4	no	—
639	#121	—	2	4	no	—
640	#121	—	2	4	no	—
641	#121	—	2	4	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	1	no	—
649	#121	—	2	1	no	—
650	#121	—	2	2	no	—
651	#121	C₂³×C₃₁	1	2	yes	—
652	#121	C₂³×C₃₁	1	2	yes	—
653	#121	C₂³×C₃₁	1	4	yes	—
654	#121	C₂³×C₃₁	1	2	yes	—
655	#121	C₂³×C₃₁	1	2	yes	—
656	#121	C₂³×C₃₁	1	2	yes	—
657	#121	C₂³×C₃₁	1	2	yes	—
658	#120	—	2	2	no	—
659	#120	—	2	2	no	—
660	#120	—	2	2	no	—
661	#120	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	#117	—	2	1	no	—
667	#117	—	2	1	no	—
668	#117	C₂³×C₃₁	1	2	yes	—
669	#117	C₂³×C₃₁	1	2	yes	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	—	2	2	no	—
672	C₂×C₄⋊C₄	—	2	1	no	—
673	C₂×C₄⋊C₄	—	2	1	no	—
674	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
677	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	#107	C₂³×C₃₁	1	4	yes	—
686	#107	C₂³×C₃₁	1	4	yes	—
687	#106	C₂³×C₃₁	1	4	yes	—
688	#106	C₂³×C₃₁	1	4	yes	—
689	#103	C₂³×C₃₁	1	4	yes	—
690	#103	C₂³×C₃₁	1	4	yes	—
691	#103	C₂³×C₃₁	1	4	yes	—
692	#103	C₂³×C₃₁	1	4	yes	—
693	#102	C₂³×C₃₁	1	4	yes	—
694	#102	C₂³×C₃₁	1	4	yes	—
695	#102	C₂³×C₃₁	1	4	yes	—
696	#102	C₂³×C₃₁	1	4	yes	—
697	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
698	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
699	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
700	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
701	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
702	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
703	C₃₁	#60755	1	1	yes	characteristic, direct product factor, Sylow
704	C₂⁴	—	2	1	no	—
705	C₂⁴	—	2	1	no	—
706	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
709	#41	—	2	4	no	—
710	#41	—	2	4	no	—
711	#41	—	4	4	no	—
712	#41	—	4	4	no	—
713	#41	—	4	2	no	—
714	#41	—	4	2	no	—
715	#41	—	4	2	no	—
716	#41	—	4	2	no	—
717	#41	—	4	2	no	—
718	#41	—	4	4	no	—
719	#41	—	4	4	no	—
720	#41	—	4	2	no	—
721	#41	—	4	4	no	—
722	#41	—	4	8	no	—
723	#41	—	4	4	no	—
724	C₂×Q₈	—	2	1	no	—
725	C₂×Q₈	—	2	1	no	—
726	C₂×Q₈	—	2	4	no	—
727	C₂×Q₈	—	4	2	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
730	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	4	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	4	no	—
751	C₂×D₄	—	4	4	no	—
752	C₂×D₄	—	8	2	no	—
753	C₂×D₄	—	8	2	no	—
754	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
755	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
756	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
757	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
758	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
759	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
760	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
761	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	4	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	—	4	4	no	—
777	C₂²×C₄	—	8	2	no	—
778	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	Q₁₆	—	4	4	no	—
791	SD₁₆	—	4	4	no	—
792	SD₁₆	—	4	4	no	—
793	D₈	—	4	4	no	—
794	M₁₆	—	2	4	no	—
795	M₁₆	—	2	4	no	—
796	M₁₆	—	4	4	no	—
797	C₂×C₈	—	4	4	no	—
798	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
799	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
814	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
815	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	4	1	no	—
840	C₂³	—	4	1	no	—
841	C₂³	—	4	1	no	—
842	C₂³	—	4	1	no	—
843	C₂³	—	4	1	no	—
844	C₂³	—	4	1	no	—
845	C₂³	—	4	2	no	—
846	C₂³	—	4	2	no	—
847	C₂³	—	4	2	no	—
848	C₂³	—	4	2	no	—
849	C₂³	—	8	1	no	—
850	C₂³	—	8	1	no	—
851	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
853	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
854	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
855	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
856	Q₈	—	2	2	no	—
857	Q₈	—	2	4	no	—
858	Q₈	—	2	2	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	4	2	no	—
861	Q₈	—	4	2	no	—
862	Q₈	—	4	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	4	no	—
865	D₄	—	2	2	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	2	no	—
870	D₄	—	4	2	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	2	no	—
873	D₄	—	4	8	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	2	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	2	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	4	no	—
883	D₄	—	8	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	4	no	—
889	C₂×C₄	—	2	4	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	4	8	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	4	2	no	—
908	C₂×C₄	—	4	2	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	8	1	no	—
911	C₂×C₄	—	8	1	no	—
912	C₂×C₄	—	8	4	no	—
913	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
916	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
917	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
918	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
919	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
920	C₈	—	2	4	no	—
921	C₈	—	2	4	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	4	4	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	8	2	no	—
944	C₂²	—	8	2	no	—
945	C₂²	—	8	4	no	—
946	C₂²	—	8	4	no	—
947	C₂²	C₃₁×#534	1	2	yes	—
948	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
949	C₄	—	2	2	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	C₃₁×#534	1	2	yes	—
960	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
961	C₂	—	2	2	no	—
962	C₂	—	4	2	no	—
963	C₂	—	4	1	no	—
964	C₂	—	4	1	no	—
965	C₂	—	4	2	no	—
966	C₂	—	8	2	no	—
967	C₂	—	8	2	no	—
968	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
969	C₂	C₃₁×#3585	1	1	yes	characteristic
970	C₂	C₃₁×#3586	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 ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3449	C₂	semidirect
2. C₂×C₃₁×#537	C₂	semidirect
3. C₃₁×#3204	C₂	semidirect
4. C₃₁×#3203	C₂	semidirect
5. C₃₁×#3201	C₂	semidirect
6. C₃₁×#3198	C₂	semidirect
7. C₃₁×#3095	C₂	semidirect
8. C₃₁×#3094	C₂	semidirect
9. C₃₁×#3092	C₂	semidirect
10. C₃₁×#3056	C₂	semidirect
11. C₃₁×#3055	C₂	semidirect
12. C₃₁×#3007	C₂	semidirect
13. C₃₁×#3006	C₂	semidirect
14. C₃₁×#3005	C₂	semidirect
15. C₃₁×#2879	C₂	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
21. C₂²×M₁₆×C₃₁	C₂²	semidirect
25. C₃₁×#537	C₂²	semidirect
26. C₃₁×#537	C₂²	semidirect
27. C₃₁×#537	C₂²	semidirect
29. C₃₁×#536	C₂²	semidirect
31. C₃₁×#535	C₂²	semidirect
40. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₃₁×#121	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
48. C₃₁×#485	C₂²	semidirect
49. C₃₁×#484	C₂²	semidirect
50. C₃₁×#484	C₂²	semidirect
51. C₃₁×#483	C₂²	semidirect
52. C₃₁×#483	C₂²	semidirect
53. C₃₁×#482	C₂²	semidirect
54. C₃₁×#481	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
57. C₃₁×#480	C₂²	semidirect
58. C₃₁×#470	C₂²	semidirect
59. C₃₁×#469	C₂²	semidirect
60. C₃₁×#468	C₂²	semidirect
61. C₃₁×#468	C₂²	semidirect
62. C₃₁×#467	C₂²	semidirect
63. C₃₁×#466	C₂²	semidirect
64. C₃₁×#465	C₂²	semidirect
65. C₃₁×#465	C₂²	semidirect
66. C₃₁×#452	C₂²	semidirect
67. C₃₁×#452	C₂²	semidirect
68. C₃₁×#452	C₂²	semidirect
69. C₃₁×#451	C₂²	semidirect
70. C₃₁×#450	C₂²	semidirect
71. C₃₁×#449	C₂²	semidirect
72. C₃₁×#449	C₂²	semidirect
73. C₃₁×#449	C₂²	semidirect
74. C₃₁×#448	C₂²	semidirect
75. C₃₁×#447	C₂²	semidirect
76. C₃₁×#428	C₂²	semidirect
77. C₃₁×#428	C₂²	semidirect
78. C₃₁×#419	C₂²	semidirect
79. C₃₁×#418	C₂²	semidirect
82. C₃₁×#408	C₂²	semidirect
83. C₃₁×#408	C₂²	semidirect
86. C₃₁×#407	C₂²	semidirect
348. #60755	C₃₁	direct (N × H)
437. #3449	C₂×C₃₁	semidirect
438. C₂×#537	C₂×C₃₁	semidirect
439. #3204	C₂×C₃₁	semidirect
440. #3203	C₂×C₃₁	semidirect
441. #3201	C₂×C₃₁	semidirect
442. #3198	C₂×C₃₁	semidirect
443. #3095	C₂×C₃₁	semidirect
444. #3094	C₂×C₃₁	semidirect
445. #3092	C₂×C₃₁	semidirect
446. #3056	C₂×C₃₁	semidirect
447. #3055	C₂×C₃₁	semidirect
448. #3007	C₂×C₃₁	semidirect
449. #3006	C₂×C₃₁	semidirect
450. #3005	C₂×C₃₁	semidirect
451. #2879	C₂×C₃₁	semidirect
493. C₂²×#41	C₂²×C₃₁	semidirect
496. C₂²×M₁₆	C₂²×C₃₁	semidirect
500. #537	C₂²×C₃₁	semidirect
501. #537	C₂²×C₃₁	semidirect
502. #537	C₂²×C₃₁	semidirect
504. #536	C₂²×C₃₁	semidirect
506. #535	C₂²×C₃₁	semidirect
515. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
520. C₂×#121	C₂²×C₃₁	semidirect
522. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
523. #485	C₂²×C₃₁	semidirect
524. #484	C₂²×C₃₁	semidirect
525. #484	C₂²×C₃₁	semidirect
526. #483	C₂²×C₃₁	semidirect
527. #483	C₂²×C₃₁	semidirect
528. #482	C₂²×C₃₁	semidirect
529. #481	C₂²×C₃₁	semidirect
530. #481	C₂²×C₃₁	semidirect
531. #480	C₂²×C₃₁	semidirect
532. #480	C₂²×C₃₁	semidirect
533. #470	C₂²×C₃₁	semidirect
534. #469	C₂²×C₃₁	semidirect
535. #468	C₂²×C₃₁	semidirect
536. #468	C₂²×C₃₁	semidirect
537. #467	C₂²×C₃₁	semidirect
538. #466	C₂²×C₃₁	semidirect
539. #465	C₂²×C₃₁	semidirect
540. #465	C₂²×C₃₁	semidirect
541. #452	C₂²×C₃₁	semidirect
542. #452	C₂²×C₃₁	semidirect
543. #452	C₂²×C₃₁	semidirect
544. #451	C₂²×C₃₁	semidirect
545. #450	C₂²×C₃₁	semidirect
546. #449	C₂²×C₃₁	semidirect
547. #449	C₂²×C₃₁	semidirect
548. #449	C₂²×C₃₁	semidirect
549. #448	C₂²×C₃₁	semidirect
550. #447	C₂²×C₃₁	semidirect
551. #428	C₂²×C₃₁	semidirect
552. #428	C₂²×C₃₁	semidirect
553. #419	C₂²×C₃₁	semidirect
554. #418	C₂²×C₃₁	semidirect
557. #408	C₂²×C₃₁	semidirect
558. #408	C₂²×C₃₁	semidirect
561. #407	C₂²×C₃₁	semidirect
703. C₃₁	#60755	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×#3449	2
C₂×C₃₁×#537	2
C₃₁×#3204	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3198	2
C₃₁×#3095	2
C₃₁×#3094	2
C₃₁×#3092	2
C₃₁×#3056	2
C₃₁×#3055	2
C₃₁×#3007	2
C₃₁×#3006	2
C₃₁×#3005	2
C₃₁×#2879	2
#60755	31

Subgroups — C31×#60755 #21517514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60755 #21517514