Subgroups — C₃₁×#61061 #21517820

Order 7936.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3278	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3277	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3271	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3270	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3004	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
23	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#578	—	2	8	no	—
25	C₂×C₃₁×#137	—	2	8	no	—
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#137	C₂²	1	4	yes	—
29	C₂×C₃₁×#137	C₂²	1	4	yes	—
30	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
32	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
33	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
36	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
39	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
42	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#550	—	2	2	no	—
44	C₃₁×#550	C₂²	1	4	yes	—
45	D₄×Q₈×C₃₁	—	2	2	no	—
46	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
47	C₃₁×#548	—	2	2	no	—
48	C₃₁×#548	—	2	2	no	—
49	C₃₁×#548	C₂²	1	4	yes	—
50	C₃₁×#548	C₂²	1	4	yes	complemented
51	C₃₁×#536	—	2	2	no	—
52	C₃₁×#536	C₂²	1	1	yes	characteristic
53	C₃₁×#536	C₂²	1	1	yes	characteristic
54	C₃₁×#535	—	2	2	no	—
55	C₃₁×#535	C₂²	1	1	yes	characteristic
56	C₃₁×#535	C₂²	1	1	yes	characteristic
57	C₃₁×#525	—	2	2	no	—
58	C₃₁×#525	—	2	2	no	—
59	C₃₁×#525	C₂²	1	1	yes	characteristic
60	C₃₁×#525	C₂²	1	1	yes	characteristic
61	C₃₁×#525	C₂²	1	1	yes	characteristic
62	C₃₁×#519	C₂²	1	1	yes	characteristic
63	C₃₁×#519	C₂²	1	1	yes	characteristic
64	C₃₁×#497	C₂²	1	2	yes	complemented
65	C₃₁×#496	C₂²	1	2	yes	complemented
66	C₃₁×#495	C₂²	1	2	yes	complemented
67	C₃₁×#492	C₂²	1	2	yes	complemented
68	C₃₁×#470	C₂²	1	2	yes	complemented
69	C₃₁×#469	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	4	yes	complemented
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#465	C₂²	1	4	yes	complemented
74	C₃₁×#464	C₂²	1	4	yes	complemented
75	C₃₁×#464	C₂²	1	4	yes	complemented
76	C₃₁×#462	C₂²	1	4	yes	complemented
77	C₃₁×#460	C₂²	1	4	yes	complemented
78	C₃₁×#452	C₂²	1	4	yes	—
79	C₃₁×#452	C₂²	1	4	yes	complemented
80	C₃₁×#451	C₂²	1	4	yes	complemented
81	C₃₁×#451	C₂²	1	4	yes	complemented
82	C₃₁×#449	C₂²	1	4	yes	—
83	C₃₁×#449	C₂²	1	4	yes	complemented
84	C₃₁×#448	C₂²	1	4	yes	complemented
85	C₃₁×#448	C₂²	1	4	yes	complemented
86	C₃₁×#441	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
88	C₃₁×#436	C₂²	1	4	yes	complemented
89	C₃₁×#435	C₂²	1	4	yes	complemented
90	C₃₁×#427	C₂²	1	1	yes	characteristic
91	C₃₁×#424	C₂²	1	1	yes	characteristic
92	C₃₁×#419	C₂²	1	1	yes	characteristic
93	C₃₁×#419	C₂²	1	1	yes	characteristic
94	C₃₁×#419	C₂²	1	1	yes	characteristic
95	C₃₁×#418	C₂²	1	1	yes	characteristic
96	C₃₁×#416	C₂²	1	1	yes	characteristic
97	C₃₁×#416	C₂²	1	1	yes	characteristic
98	C₃₁×#408	C₂²	1	1	yes	characteristic
99	C₃₁×#407	C₂²	1	1	yes	characteristic
100	C₃₁×#405	C₂²	1	1	yes	characteristic
101	C₃₁×2₋¹⁺⁴	—	2	4	no	—
102	C₃₁×2₋¹⁺⁴	—	2	4	no	—
103	C₃₁×2₋¹⁺⁴	—	4	2	no	—
104	C₃₁×2₋¹⁺⁴	—	4	2	no	—
105	C₂×#41×C₃₁	—	2	2	no	—
106	C₂×#41×C₃₁	—	2	2	no	—
107	C₂×#41×C₃₁	—	2	1	no	—
108	C₂×#41×C₃₁	—	2	1	no	—
109	C₂×#41×C₃₁	—	2	2	no	—
110	C₂×#41×C₃₁	—	2	4	no	—
111	C₂×#41×C₃₁	—	4	2	no	—
112	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
113	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
114	C₂×#41×C₃₁	C₂³	1	4	yes	—
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂×#41×C₃₁	C₂³	1	2	yes	—
117	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₃₁	—	2	1	no	—
119	C₂²×Q₈×C₃₁	—	2	1	no	—
120	C₂²×Q₈×C₃₁	—	2	1	no	—
121	C₂²×Q₈×C₃₁	—	2	2	no	—
122	C₂²×Q₈×C₃₁	—	2	4	no	—
123	C₂²×Q₈×C₃₁	—	4	2	no	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
127	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
128	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₃₁	—	2	1	no	—
131	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	—	2	1	no	—
133	C₂³×C₄×C₃₁	—	2	1	no	—
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₃₁×#137	—	2	4	no	—
136	C₃₁×#137	—	2	4	no	—
137	C₃₁×#137	—	2	16	no	—
138	C₃₁×#137	—	2	16	no	—
139	C₃₁×#137	—	2	8	no	—
140	C₃₁×#137	—	2	8	no	—
141	C₃₁×#137	—	4	2	no	—
142	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
143	C₃₁×#135	—	2	8	no	—
144	C₃₁×#135	—	2	4	no	—
145	C₂×Q₁₆×C₃₁	—	2	4	no	—
146	C₂×Q₁₆×C₃₁	—	2	8	no	—
147	C₂×Q₁₆×C₃₁	D₄	1	8	yes	complemented
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
150	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	—	2	4	no	—
156	C₂×SD₁₆×C₃₁	—	2	4	no	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×D₈×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#131	—	2	4	no	—
169	C₂×M₁₆×C₃₁	—	2	4	no	—
170	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
174	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
175	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
177	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₃₁×C₄⋊Q₈	—	2	1	no	—
179	C₃₁×C₄⋊Q₈	—	2	4	no	—
180	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₃₁×#127	—	2	4	no	—
182	C₃₁×#127	—	2	1	no	—
183	C₃₁×#127	C₂³	1	2	yes	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	4	no	—
187	C₃₁×#124	—	2	4	no	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	4	no	—
196	C₃₁×C₂²⋊Q₈	—	2	4	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	4	no	—
199	C₃₁×C₂²⋊Q₈	—	2	4	no	—
200	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×#121	—	2	4	no	—
205	C₃₁×#121	—	2	4	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	4	no	—
208	C₃₁×#121	—	2	4	no	—
209	C₃₁×#121	D₄	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	4	yes	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#120	—	2	1	no	—
214	C₃₁×#120	—	2	1	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	D₄	1	2	yes	—
218	C₄×Q₈×C₃₁	—	2	2	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
222	C₄×D₄×C₃₁	—	2	4	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	4	no	—
226	C₄×D₄×C₃₁	—	2	4	no	—
227	C₄×D₄×C₃₁	—	2	4	no	—
228	C₄×D₄×C₃₁	C₂³	1	4	yes	—
229	C₃₁×#117	—	2	2	no	—
230	C₃₁×#117	—	2	2	no	—
231	C₃₁×#117	C₂³	1	1	yes	characteristic
232	C₃₁×#117	C₂³	1	1	yes	characteristic
233	C₃₁×#117	C₂³	1	1	yes	characteristic
234	C₃₁×#107	C₂³	1	2	yes	—
235	C₃₁×#106	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
237	C₃₁×#103	C₂³	1	2	yes	—
238	C₃₁×#103	C₂³	1	2	yes	—
239	C₃₁×#103	C₂³	1	4	yes	—
240	C₃₁×#103	C₂³	1	4	yes	—
241	C₃₁×#103	C₂³	1	4	yes	—
242	C₃₁×#102	C₂³	1	2	yes	—
243	C₃₁×#102	C₂³	1	2	yes	—
244	C₃₁×#102	C₂³	1	4	yes	—
245	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
246	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₃₁×#97	C₂³	1	2	yes	—
248	C₄×C₈×C₃₁	C₂³	1	2	yes	—
249	C₂⁴×C₃₁	—	2	1	no	—
250	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
251	#41×C₃₁	—	2	2	no	—
252	#41×C₃₁	—	2	2	no	—
253	#41×C₃₁	—	2	4	no	—
254	#41×C₃₁	—	2	4	no	—
255	#41×C₃₁	—	2	8	no	—
256	#41×C₃₁	—	2	2	no	—
257	#41×C₃₁	—	2	2	no	—
258	#41×C₃₁	—	2	2	no	—
259	#41×C₃₁	—	2	2	no	—
260	#41×C₃₁	—	4	4	no	—
261	#41×C₃₁	—	4	2	no	—
262	#41×C₃₁	—	4	2	no	—
263	#41×C₃₁	—	4	8	no	—
264	#41×C₃₁	—	4	8	no	—
265	#41×C₃₁	—	4	8	no	—
266	#41×C₃₁	—	4	4	no	—
267	#41×C₃₁	—	4	4	no	—
268	C₂×Q₈×C₃₁	—	2	1	no	—
269	C₂×Q₈×C₃₁	—	2	1	no	—
270	C₂×Q₈×C₃₁	—	2	2	no	—
271	C₂×Q₈×C₃₁	—	2	4	no	—
272	C₂×Q₈×C₃₁	—	2	1	no	—
273	C₂×Q₈×C₃₁	—	2	2	no	—
274	C₂×Q₈×C₃₁	—	2	2	no	—
275	C₂×Q₈×C₃₁	—	2	2	no	—
276	C₂×Q₈×C₃₁	—	2	4	no	—
277	C₂×Q₈×C₃₁	—	2	4	no	—
278	C₂×Q₈×C₃₁	—	2	8	no	—
279	C₂×Q₈×C₃₁	—	2	2	no	—
280	C₂×Q₈×C₃₁	—	2	2	no	—
281	C₂×Q₈×C₃₁	—	4	4	no	—
282	C₂×Q₈×C₃₁	—	4	4	no	—
283	C₂×Q₈×C₃₁	—	4	2	no	—
284	C₂×Q₈×C₃₁	—	4	2	no	—
285	C₂×Q₈×C₃₁	—	4	8	no	—
286	C₂×Q₈×C₃₁	—	4	4	no	—
287	C₂×Q₈×C₃₁	—	4	4	no	—
288	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
289	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
290	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	1	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	4	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	4	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	1	no	—
306	C₂×D₄×C₃₁	—	2	4	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	4	4	no	—
309	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
312	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
314	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	—	2	1	no	—
316	C₂²×C₄×C₃₁	—	2	1	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	2	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	4	no	—
321	C₂²×C₄×C₃₁	—	2	2	no	—
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	1	no	—
325	C₂²×C₄×C₃₁	—	2	4	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	1	no	—
328	C₂²×C₄×C₃₁	—	4	4	no	—
329	C₂²×C₄×C₃₁	—	4	4	no	—
330	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	Q₁₆×C₃₁	—	2	8	no	—
336	Q₁₆×C₃₁	—	2	4	no	—
337	Q₁₆×C₃₁	—	2	4	no	—
338	Q₁₆×C₃₁	—	2	2	no	—
339	Q₁₆×C₃₁	—	4	2	no	—
340	Q₁₆×C₃₁	C₂×D₄	1	8	yes	—
341	Q₁₆×C₃₁	C₂×D₄	1	8	yes	—
342	SD₁₆×C₃₁	—	2	8	no	—
343	SD₁₆×C₃₁	—	2	4	no	—
344	SD₁₆×C₃₁	—	2	4	no	—
345	SD₁₆×C₃₁	—	2	4	no	—
346	SD₁₆×C₃₁	—	2	4	no	—
347	SD₁₆×C₃₁	—	2	2	no	—
348	SD₁₆×C₃₁	—	2	2	no	—
349	SD₁₆×C₃₁	—	4	2	no	—
350	SD₁₆×C₃₁	—	4	2	no	—
351	D₈×C₃₁	—	2	2	no	—
352	D₈×C₃₁	—	4	2	no	—
353	M₁₆×C₃₁	—	2	2	no	—
354	M₁₆×C₃₁	—	2	2	no	—
355	M₁₆×C₃₁	—	2	4	no	—
356	M₁₆×C₃₁	—	2	4	no	—
357	M₁₆×C₃₁	—	2	4	no	—
358	C₂×C₈×C₃₁	—	2	2	no	—
359	C₂×C₈×C₃₁	—	2	4	no	—
360	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₃₁	—	2	4	no	—
367	C₄⋊C₄×C₃₁	—	2	4	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	4	no	—
370	C₄⋊C₄×C₃₁	—	2	4	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
374	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
376	C₂²⋊C₄×C₃₁	—	2	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	4	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	4	no	—
383	C₂²⋊C₄×C₃₁	—	2	4	no	—
384	C₂²⋊C₄×C₃₁	—	2	4	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
389	C₄²×C₃₁	—	2	4	no	—
390	C₄²×C₃₁	—	2	4	no	—
391	C₄²×C₃₁	—	2	1	no	—
392	C₄²×C₃₁	—	2	1	no	—
393	C₄²×C₃₁	C₂⁴	1	2	yes	—
394	#61061	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂³×C₃₁	—	2	2	no	—
396	C₂³×C₃₁	—	2	1	no	—
397	C₂³×C₃₁	—	2	2	no	—
398	C₂³×C₃₁	—	2	1	no	—
399	C₂³×C₃₁	—	4	2	no	—
400	C₂³×C₃₁	—	4	2	no	—
401	C₂³×C₃₁	—	8	2	no	—
402	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
403	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
404	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
405	Q₈×C₃₁	—	2	4	no	—
406	Q₈×C₃₁	—	2	4	no	—
407	Q₈×C₃₁	—	2	2	no	—
408	Q₈×C₃₁	—	2	2	no	—
409	Q₈×C₃₁	—	2	2	no	—
410	Q₈×C₃₁	—	2	2	no	—
411	Q₈×C₃₁	—	2	1	no	—
412	Q₈×C₃₁	—	2	1	no	—
413	Q₈×C₃₁	—	2	1	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	2	1	no	—
416	Q₈×C₃₁	—	4	8	no	—
417	Q₈×C₃₁	—	4	4	no	—
418	Q₈×C₃₁	—	4	4	no	—
419	Q₈×C₃₁	—	4	2	no	—
420	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
421	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
422	D₄×C₃₁	—	2	4	no	—
423	D₄×C₃₁	—	2	2	no	—
424	D₄×C₃₁	—	2	1	no	—
425	D₄×C₃₁	—	2	1	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	1	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	1	no	—
430	D₄×C₃₁	—	4	4	no	—
431	D₄×C₃₁	—	4	8	no	—
432	D₄×C₃₁	—	4	4	no	—
433	D₄×C₃₁	—	4	4	no	—
434	D₄×C₃₁	—	4	4	no	—
435	D₄×C₃₁	—	4	2	no	—
436	D₄×C₃₁	—	4	2	no	—
437	D₄×C₃₁	—	4	2	no	—
438	D₄×C₃₁	—	8	4	no	—
439	D₄×C₃₁	—	8	4	no	—
440	D₄×C₃₁	—	8	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	4	no	—
443	C₂×C₄×C₃₁	—	2	4	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	4	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	1	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	1	no	—
456	C₂×C₄×C₃₁	—	4	8	no	—
457	C₂×C₄×C₃₁	—	4	4	no	—
458	C₂×C₄×C₃₁	—	4	4	no	—
459	C₂×C₄×C₃₁	—	4	8	no	—
460	C₂×C₄×C₃₁	—	4	4	no	—
461	C₂×C₄×C₃₁	—	4	4	no	—
462	C₂×C₄×C₃₁	—	4	2	no	—
463	C₂×C₄×C₃₁	—	4	2	no	—
464	C₂×C₄×C₃₁	—	4	2	no	—
465	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
466	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
471	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
472	C₈×C₃₁	—	2	2	no	—
473	C₈×C₃₁	—	2	2	no	—
474	C₈×C₃₁	—	2	2	no	—
475	C₈×C₃₁	C₂²×D₄	1	2	yes	—
476	C₈×C₃₁	C₂²×D₄	1	2	yes	—
477	C₂×#578	C₂×C₃₁	1	1	yes	characteristic, complemented
478	C₂²×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#3487	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#3486	C₂×C₃₁	1	1	yes	characteristic, complemented
481	#3278	C₂×C₃₁	1	4	yes	complemented
482	#3277	C₂×C₃₁	1	4	yes	complemented
483	#3271	C₂×C₃₁	1	4	yes	complemented
484	#3270	C₂×C₃₁	1	4	yes	complemented
485	#3154	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3057	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3054	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#3043	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
491	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
492	#3005	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#3004	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#2950	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#2930	C₂×C₃₁	1	1	yes	characteristic, complemented
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	2	no	—
498	C₂²×C₃₁	—	2	4	no	—
499	C₂²×C₃₁	—	2	2	no	—
500	C₂²×C₃₁	—	2	2	no	—
501	C₂²×C₃₁	—	2	2	no	—
502	C₂²×C₃₁	—	4	4	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	4	2	no	—
505	C₂²×C₃₁	—	4	4	no	—
506	C₂²×C₃₁	—	4	1	no	—
507	C₂²×C₃₁	—	4	1	no	—
508	C₂²×C₃₁	—	4	2	no	—
509	C₂²×C₃₁	—	8	4	no	—
510	C₂²×C₃₁	D₄²	1	2	yes	—
511	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
512	C₄×C₃₁	—	2	4	no	—
513	C₄×C₃₁	—	2	2	no	—
514	C₄×C₃₁	—	2	4	no	—
515	C₄×C₃₁	—	2	4	no	—
516	C₄×C₃₁	—	2	2	no	—
517	C₄×C₃₁	—	4	2	no	—
518	C₄×C₃₁	—	4	2	no	—
519	C₄×C₃₁	—	4	1	no	—
520	C₄×C₃₁	—	4	1	no	—
521	C₄×C₃₁	—	4	2	no	—
522	C₄×C₃₁	D₄²	1	2	yes	—
523	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
527	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
528	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
529	#578	—	2	8	no	—
530	C₂×#137	—	2	8	no	—
531	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
532	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
533	C₂×#137	C₂²×C₃₁	1	4	yes	—
534	C₂×#137	C₂²×C₃₁	1	4	yes	—
535	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
536	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
537	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
538	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
539	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
541	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
542	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
543	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
544	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
545	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
546	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
547	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
548	#550	—	2	2	no	—
549	#550	C₂²×C₃₁	1	4	yes	—
550	D₄×Q₈	—	2	2	no	—
551	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
552	#548	—	2	2	no	—
553	#548	—	2	2	no	—
554	#548	C₂²×C₃₁	1	4	yes	—
555	#548	C₂²×C₃₁	1	4	yes	complemented
556	#536	—	2	2	no	—
557	#536	C₂²×C₃₁	1	1	yes	characteristic
558	#536	C₂²×C₃₁	1	1	yes	characteristic
559	#535	—	2	2	no	—
560	#535	C₂²×C₃₁	1	1	yes	characteristic
561	#535	C₂²×C₃₁	1	1	yes	characteristic
562	#525	—	2	2	no	—
563	#525	—	2	2	no	—
564	#525	C₂²×C₃₁	1	1	yes	characteristic
565	#525	C₂²×C₃₁	1	1	yes	characteristic
566	#525	C₂²×C₃₁	1	1	yes	characteristic
567	#519	C₂²×C₃₁	1	1	yes	characteristic
568	#519	C₂²×C₃₁	1	1	yes	characteristic
569	#497	C₂²×C₃₁	1	2	yes	complemented
570	#496	C₂²×C₃₁	1	2	yes	complemented
571	#495	C₂²×C₃₁	1	2	yes	complemented
572	#492	C₂²×C₃₁	1	2	yes	complemented
573	#470	C₂²×C₃₁	1	2	yes	complemented
574	#469	C₂²×C₃₁	1	2	yes	complemented
575	#468	C₂²×C₃₁	1	2	yes	complemented
576	#468	C₂²×C₃₁	1	4	yes	complemented
577	#468	C₂²×C₃₁	1	2	yes	complemented
578	#465	C₂²×C₃₁	1	4	yes	complemented
579	#464	C₂²×C₃₁	1	4	yes	complemented
580	#464	C₂²×C₃₁	1	4	yes	complemented
581	#462	C₂²×C₃₁	1	4	yes	complemented
582	#460	C₂²×C₃₁	1	4	yes	complemented
583	#452	C₂²×C₃₁	1	4	yes	—
584	#452	C₂²×C₃₁	1	4	yes	complemented
585	#451	C₂²×C₃₁	1	4	yes	complemented
586	#451	C₂²×C₃₁	1	4	yes	complemented
587	#449	C₂²×C₃₁	1	4	yes	—
588	#449	C₂²×C₃₁	1	4	yes	complemented
589	#448	C₂²×C₃₁	1	4	yes	complemented
590	#448	C₂²×C₃₁	1	4	yes	complemented
591	#441	C₂²×C₃₁	1	4	yes	complemented
592	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
593	#436	C₂²×C₃₁	1	4	yes	complemented
594	#435	C₂²×C₃₁	1	4	yes	complemented
595	#427	C₂²×C₃₁	1	1	yes	characteristic
596	#424	C₂²×C₃₁	1	1	yes	characteristic
597	#419	C₂²×C₃₁	1	1	yes	characteristic
598	#419	C₂²×C₃₁	1	1	yes	characteristic
599	#419	C₂²×C₃₁	1	1	yes	characteristic
600	#418	C₂²×C₃₁	1	1	yes	characteristic
601	#416	C₂²×C₃₁	1	1	yes	characteristic
602	#416	C₂²×C₃₁	1	1	yes	characteristic
603	#408	C₂²×C₃₁	1	1	yes	characteristic
604	#407	C₂²×C₃₁	1	1	yes	characteristic
605	#405	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×C₃₁	—	2	2	no	—
607	C₂×C₃₁	—	4	2	no	—
608	C₂×C₃₁	—	4	2	no	—
609	C₂×C₃₁	—	8	1	no	—
610	C₂×C₃₁	—	8	1	no	—
611	C₂×C₃₁	—	8	2	no	—
612	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
613	C₂×C₃₁	#3586	1	2	yes	—
614	2₋¹⁺⁴	—	2	4	no	—
615	2₋¹⁺⁴	—	2	4	no	—
616	2₋¹⁺⁴	—	4	2	no	—
617	2₋¹⁺⁴	—	4	2	no	—
618	C₂×#41	—	2	2	no	—
619	C₂×#41	—	2	2	no	—
620	C₂×#41	—	2	1	no	—
621	C₂×#41	—	2	1	no	—
622	C₂×#41	—	2	2	no	—
623	C₂×#41	—	2	4	no	—
624	C₂×#41	—	4	2	no	—
625	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×#41	C₂³×C₃₁	1	4	yes	—
628	C₂×#41	C₂³×C₃₁	1	2	yes	—
629	C₂×#41	C₂³×C₃₁	1	2	yes	—
630	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
631	C₂²×Q₈	—	2	1	no	—
632	C₂²×Q₈	—	2	1	no	—
633	C₂²×Q₈	—	2	1	no	—
634	C₂²×Q₈	—	2	2	no	—
635	C₂²×Q₈	—	2	4	no	—
636	C₂²×Q₈	—	4	2	no	—
637	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
638	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
639	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
640	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
641	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
642	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
643	C₂²×D₄	—	2	1	no	—
644	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
645	C₂³×C₄	—	2	1	no	—
646	C₂³×C₄	—	2	1	no	—
647	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
648	#137	—	2	4	no	—
649	#137	—	2	4	no	—
650	#137	—	2	16	no	—
651	#137	—	2	16	no	—
652	#137	—	2	8	no	—
653	#137	—	2	8	no	—
654	#137	—	4	2	no	—
655	AGL(1,ℤ/8)	—	4	2	no	—
656	#135	—	2	8	no	—
657	#135	—	2	4	no	—
658	C₂×Q₁₆	—	2	4	no	—
659	C₂×Q₁₆	—	2	8	no	—
660	C₂×Q₁₆	D₄×C₃₁	1	8	yes	complemented
661	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
662	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
663	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
667	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
668	C₂×SD₁₆	—	2	4	no	—
669	C₂×SD₁₆	—	2	4	no	—
670	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
671	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
674	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
675	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
679	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
680	C₂×D₈	C₂³×C₃₁	1	2	yes	—
681	#131	—	2	4	no	—
682	C₂×M₁₆	—	2	4	no	—
683	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
684	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
685	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
687	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
690	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	—	2	4	no	—
693	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	#127	—	2	4	no	—
695	#127	—	2	1	no	—
696	#127	C₂³×C₃₁	1	2	yes	—
697	#124	—	2	1	no	—
698	#124	—	2	1	no	—
699	#124	—	2	4	no	—
700	#124	—	2	4	no	—
701	#124	C₂³×C₃₁	1	2	yes	—
702	#124	C₂³×C₃₁	1	2	yes	—
703	#123	—	2	2	no	—
704	#123	—	2	1	no	—
705	#123	—	2	1	no	—
706	#123	—	2	2	no	—
707	#123	D₄×C₃₁	1	2	yes	—
708	C₂²⋊Q₈	—	2	4	no	—
709	C₂²⋊Q₈	—	2	4	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	4	no	—
712	C₂²⋊Q₈	—	2	4	no	—
713	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
714	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
715	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
716	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
717	#121	—	2	4	no	—
718	#121	—	2	4	no	—
719	#121	—	2	2	no	—
720	#121	—	2	4	no	—
721	#121	—	2	4	no	—
722	#121	D₄×C₃₁	1	2	yes	—
723	#121	C₂³×C₃₁	1	2	yes	—
724	#121	C₂³×C₃₁	1	2	yes	—
725	#121	C₂³×C₃₁	1	4	yes	—
726	#120	—	2	1	no	—
727	#120	—	2	1	no	—
728	#120	—	2	2	no	—
729	#120	—	2	2	no	—
730	#120	D₄×C₃₁	1	2	yes	—
731	C₄×Q₈	—	2	2	no	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
734	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
735	C₄×D₄	—	2	4	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	4	no	—
739	C₄×D₄	—	2	4	no	—
740	C₄×D₄	—	2	4	no	—
741	C₄×D₄	C₂³×C₃₁	1	4	yes	—
742	#117	—	2	2	no	—
743	#117	—	2	2	no	—
744	#117	C₂³×C₃₁	1	1	yes	characteristic
745	#117	C₂³×C₃₁	1	1	yes	characteristic
746	#117	C₂³×C₃₁	1	1	yes	characteristic
747	#107	C₂³×C₃₁	1	2	yes	—
748	#106	C₂³×C₃₁	1	2	yes	—
749	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
750	#103	C₂³×C₃₁	1	2	yes	—
751	#103	C₂³×C₃₁	1	2	yes	—
752	#103	C₂³×C₃₁	1	4	yes	—
753	#103	C₂³×C₃₁	1	4	yes	—
754	#103	C₂³×C₃₁	1	4	yes	—
755	#102	C₂³×C₃₁	1	2	yes	—
756	#102	C₂³×C₃₁	1	2	yes	—
757	#102	C₂³×C₃₁	1	4	yes	—
758	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
759	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
760	#97	C₂³×C₃₁	1	2	yes	—
761	C₄×C₈	C₂³×C₃₁	1	2	yes	—
762	C₃₁	#61061	1	1	yes	characteristic, direct product factor, Sylow
763	C₂⁴	—	2	1	no	—
764	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
765	#41	—	2	2	no	—
766	#41	—	2	2	no	—
767	#41	—	2	4	no	—
768	#41	—	2	4	no	—
769	#41	—	2	8	no	—
770	#41	—	2	2	no	—
771	#41	—	2	2	no	—
772	#41	—	2	2	no	—
773	#41	—	2	2	no	—
774	#41	—	4	4	no	—
775	#41	—	4	2	no	—
776	#41	—	4	2	no	—
777	#41	—	4	8	no	—
778	#41	—	4	8	no	—
779	#41	—	4	8	no	—
780	#41	—	4	4	no	—
781	#41	—	4	4	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	4	no	—
791	C₂×Q₈	—	2	4	no	—
792	C₂×Q₈	—	2	8	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	4	4	no	—
796	C₂×Q₈	—	4	4	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	2	no	—
799	C₂×Q₈	—	4	8	no	—
800	C₂×Q₈	—	4	4	no	—
801	C₂×Q₈	—	4	4	no	—
802	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
803	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
804	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
805	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
806	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
807	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
809	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	4	4	no	—
823	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
824	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
825	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
826	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
827	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
828	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	—	4	4	no	—
844	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
849	Q₁₆	—	2	8	no	—
850	Q₁₆	—	2	4	no	—
851	Q₁₆	—	2	4	no	—
852	Q₁₆	—	2	2	no	—
853	Q₁₆	—	4	2	no	—
854	Q₁₆	C₂×D₄×C₃₁	1	8	yes	—
855	Q₁₆	C₂×D₄×C₃₁	1	8	yes	—
856	SD₁₆	—	2	8	no	—
857	SD₁₆	—	2	4	no	—
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	2	4	no	—
860	SD₁₆	—	2	4	no	—
861	SD₁₆	—	2	2	no	—
862	SD₁₆	—	2	2	no	—
863	SD₁₆	—	4	2	no	—
864	SD₁₆	—	4	2	no	—
865	D₈	—	2	2	no	—
866	D₈	—	4	2	no	—
867	M₁₆	—	2	2	no	—
868	M₁₆	—	2	2	no	—
869	M₁₆	—	2	4	no	—
870	M₁₆	—	2	4	no	—
871	M₁₆	—	2	4	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	4	no	—
874	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
875	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
876	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
877	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
878	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₄⋊C₄	—	2	4	no	—
881	C₄⋊C₄	—	2	4	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
887	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
888	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
889	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
901	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
902	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
903	C₄²	—	2	4	no	—
904	C₄²	—	2	4	no	—
905	C₄²	—	2	1	no	—
906	C₄²	—	2	1	no	—
907	C₄²	C₂⁴×C₃₁	1	2	yes	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	4	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	8	2	no	—
915	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
916	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
917	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
918	Q₈	—	2	4	no	—
919	Q₈	—	2	4	no	—
920	Q₈	—	2	2	no	—
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	1	no	—
925	Q₈	—	2	1	no	—
926	Q₈	—	2	1	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	1	no	—
929	Q₈	—	4	8	no	—
930	Q₈	—	4	4	no	—
931	Q₈	—	4	4	no	—
932	Q₈	—	4	2	no	—
933	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
934	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
935	D₄	—	2	4	no	—
936	D₄	—	2	2	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	1	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	1	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	1	no	—
943	D₄	—	4	4	no	—
944	D₄	—	4	8	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	4	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	2	no	—
951	D₄	—	8	4	no	—
952	D₄	—	8	4	no	—
953	D₄	—	8	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	4	no	—
956	C₂×C₄	—	2	4	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	4	8	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
979	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
983	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
984	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	C₂²×D₄×C₃₁	1	2	yes	—
989	C₈	C₂²×D₄×C₃₁	1	2	yes	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	4	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	4	4	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	4	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	D₄²×C₃₁	1	2	yes	—
1005	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1006	C₄	—	2	2	no	—
1007	C₄	—	2	4	no	—
1008	C₄	—	2	4	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	4	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	D₄²×C₃₁	1	2	yes	—
1017	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1018	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1019	C₂	—	2	2	no	—
1020	C₂	—	4	2	no	—
1021	C₂	—	4	2	no	—
1022	C₂	—	8	2	no	—
1023	C₂	—	8	1	no	—
1024	C₂	—	8	1	no	—
1025	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1026	C₂	C₃₁×#3586	1	2	yes	—

	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 ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#578	C₂	semidirect
2. C₂²×C₃₁×#137	C₂	semidirect
3. C₃₁×#3487	C₂	semidirect
4. C₃₁×#3486	C₂	semidirect
5. C₃₁×#3278	C₂	semidirect
6. C₃₁×#3277	C₂	semidirect
7. C₃₁×#3271	C₂	semidirect
8. C₃₁×#3270	C₂	semidirect
9. C₃₁×#3154	C₂	semidirect
10. C₃₁×#3057	C₂	semidirect
11. C₃₁×#3054	C₂	semidirect
12. C₃₁×#3044	C₂	semidirect
13. C₃₁×#3043	C₂	semidirect
14. C₃₁×#3011	C₂	semidirect
15. C₃₁×#3010	C₂	semidirect
16. C₃₁×#3005	C₂	semidirect
17. C₃₁×#3004	C₂	semidirect
18. C₃₁×#2950	C₂	semidirect
19. C₃₁×#2930	C₂	semidirect
31. C₂×C₃₁×#137	C₂²	semidirect
32. C₂×C₃₁×#137	C₂²	semidirect
35. C₂×C₃₁×#135	C₂²	semidirect
38. C₂²×Q₁₆×C₃₁	C₂²	semidirect
46. D₄×Q₈×C₃₁	C₂²	semidirect
50. C₃₁×#548	C₂²	semidirect
64. C₃₁×#497	C₂²	semidirect
65. C₃₁×#496	C₂²	semidirect
66. C₃₁×#495	C₂²	semidirect
67. C₃₁×#492	C₂²	semidirect
68. C₃₁×#470	C₂²	semidirect
69. C₃₁×#469	C₂²	semidirect
70. C₃₁×#468	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#465	C₂²	semidirect
74. C₃₁×#464	C₂²	semidirect
75. C₃₁×#464	C₂²	semidirect
76. C₃₁×#462	C₂²	semidirect
77. C₃₁×#460	C₂²	semidirect
79. C₃₁×#452	C₂²	semidirect
80. C₃₁×#451	C₂²	semidirect
81. C₃₁×#451	C₂²	semidirect
83. C₃₁×#449	C₂²	semidirect
84. C₃₁×#448	C₂²	semidirect
85. C₃₁×#448	C₂²	semidirect
86. C₃₁×#441	C₂²	semidirect
87. C₄×Q₁₆×C₃₁	C₂²	semidirect
88. C₃₁×#436	C₂²	semidirect
89. C₃₁×#435	C₂²	semidirect
147. C₂×Q₁₆×C₃₁	D₄	semidirect
394. #61061	C₃₁	direct (N × H)
477. C₂×#578	C₂×C₃₁	semidirect
478. C₂²×#137	C₂×C₃₁	semidirect
479. #3487	C₂×C₃₁	semidirect
480. #3486	C₂×C₃₁	semidirect
481. #3278	C₂×C₃₁	semidirect
482. #3277	C₂×C₃₁	semidirect
483. #3271	C₂×C₃₁	semidirect
484. #3270	C₂×C₃₁	semidirect
485. #3154	C₂×C₃₁	semidirect
486. #3057	C₂×C₃₁	semidirect
487. #3054	C₂×C₃₁	semidirect
488. #3044	C₂×C₃₁	semidirect
489. #3043	C₂×C₃₁	semidirect
490. #3011	C₂×C₃₁	semidirect
491. #3010	C₂×C₃₁	semidirect
492. #3005	C₂×C₃₁	semidirect
493. #3004	C₂×C₃₁	semidirect
494. #2950	C₂×C₃₁	semidirect
495. #2930	C₂×C₃₁	semidirect
536. C₂×#137	C₂²×C₃₁	semidirect
537. C₂×#137	C₂²×C₃₁	semidirect
540. C₂×#135	C₂²×C₃₁	semidirect
543. C₂²×Q₁₆	C₂²×C₃₁	semidirect
551. D₄×Q₈	C₂²×C₃₁	semidirect
555. #548	C₂²×C₃₁	semidirect
569. #497	C₂²×C₃₁	semidirect
570. #496	C₂²×C₃₁	semidirect
571. #495	C₂²×C₃₁	semidirect
572. #492	C₂²×C₃₁	semidirect
573. #470	C₂²×C₃₁	semidirect
574. #469	C₂²×C₃₁	semidirect
575. #468	C₂²×C₃₁	semidirect
576. #468	C₂²×C₃₁	semidirect
577. #468	C₂²×C₃₁	semidirect
578. #465	C₂²×C₃₁	semidirect
579. #464	C₂²×C₃₁	semidirect
580. #464	C₂²×C₃₁	semidirect
581. #462	C₂²×C₃₁	semidirect
582. #460	C₂²×C₃₁	semidirect
584. #452	C₂²×C₃₁	semidirect
585. #451	C₂²×C₃₁	semidirect
586. #451	C₂²×C₃₁	semidirect
588. #449	C₂²×C₃₁	semidirect
589. #448	C₂²×C₃₁	semidirect
590. #448	C₂²×C₃₁	semidirect
591. #441	C₂²×C₃₁	semidirect
592. C₄×Q₁₆	C₂²×C₃₁	semidirect
593. #436	C₂²×C₃₁	semidirect
594. #435	C₂²×C₃₁	semidirect
660. C₂×Q₁₆	D₄×C₃₁	semidirect
762. C₃₁	#61061	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#578	2
C₂²×C₃₁×#137	2
C₃₁×#3487	2
C₃₁×#3486	2
C₃₁×#3278	2
C₃₁×#3277	2
C₃₁×#3271	2
C₃₁×#3270	2
C₃₁×#3154	2
C₃₁×#3057	2
C₃₁×#3054	2
C₃₁×#3044	2
C₃₁×#3043	2
C₃₁×#3011	2
C₃₁×#3010	2
C₃₁×#3005	2
C₃₁×#3004	2
C₃₁×#2950	2
C₃₁×#2930	2
#61061	31

Subgroups — C31×#61061 #21517820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61061 #21517820