Subgroups — C₃₁×#60782 #21517541

Order 7936.

2208 conjugacy classes of subgroups.

The subgroup lattice has 894 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×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3212	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3211	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3210	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3147	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3131	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3035	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	2	yes	—
17	C₂×C₃₁×#135	C₂²	1	8	yes	complemented
18	C₃₁×#533	C₂²	1	1	yes	characteristic
19	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
21	C₃₁×#532	—	2	1	no	—
22	C₃₁×#532	—	2	1	no	—
23	C₃₁×#532	—	2	1	no	—
24	C₃₁×#532	—	2	1	no	—
25	C₃₁×#532	C₂²	1	2	yes	—
26	C₃₁×#532	C₂²	1	2	yes	—
27	C₃₁×#532	C₂²	1	2	yes	—
28	C₃₁×#532	C₂²	1	2	yes	—
29	C₃₁×#532	C₂²	1	1	yes	characteristic
30	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
34	C₃₁×#529	—	2	1	no	—
35	C₃₁×#529	—	2	1	no	—
36	C₃₁×#529	—	2	1	no	—
37	C₃₁×#529	—	2	1	no	—
38	C₃₁×#529	C₂²	1	2	yes	—
39	C₃₁×#529	C₂²	1	2	yes	complemented
40	C₂×C₃₁×#124	C₂²	1	2	yes	—
41	C₃₁×#525	—	2	1	no	—
42	C₃₁×#525	—	2	1	no	—
43	C₃₁×#525	C₂²	1	2	yes	—
44	C₂×C₃₁×#121	—	2	1	no	—
45	C₂×C₃₁×#121	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	—	2	1	no	—
48	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₃₁	—	2	1	no	—
50	C₂×C₄×D₄×C₃₁	—	2	1	no	—
51	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
52	C₃₁×#495	C₂²	1	8	yes	complemented
53	C₃₁×#494	C₂²	1	2	yes	complemented
54	C₃₁×#493	C₂²	1	2	yes	complemented
55	C₃₁×#492	C₂²	1	2	yes	complemented
56	C₃₁×#492	C₂²	1	2	yes	complemented
57	C₃₁×#488	C₂²	1	8	yes	complemented
58	C₃₁×#487	C₂²	1	2	yes	complemented
59	C₃₁×#487	C₂²	1	2	yes	complemented
60	C₃₁×#486	C₂²	1	2	yes	complemented
61	C₃₁×#486	C₂²	1	2	yes	complemented
62	C₃₁×#464	C₂²	1	8	yes	complemented
63	C₃₁×#463	C₂²	1	8	yes	complemented
64	C₃₁×#462	C₂²	1	4	yes	complemented
65	C₃₁×#461	C₂²	1	4	yes	complemented
66	C₃₁×#460	C₂²	1	4	yes	complemented
67	C₃₁×#459	C₂²	1	4	yes	complemented
68	C₃₁×#452	C₂²	1	8	yes	complemented
69	C₃₁×#451	C₂²	1	4	yes	—
70	C₃₁×#450	C₂²	1	4	yes	—
71	C₃₁×#449	C₂²	1	8	yes	complemented
72	C₃₁×#448	C₂²	1	4	yes	—
73	C₃₁×#447	C₂²	1	4	yes	—
74	C₃₁×#431	C₂²	1	1	yes	characteristic
75	C₃₁×#431	C₂²	1	1	yes	characteristic
76	C₃₁×#431	C₂²	1	2	yes	—
77	C₃₁×#431	C₂²	1	2	yes	complemented
78	C₃₁×#431	C₂²	1	2	yes	complemented
79	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
80	C₃₁×#416	C₂²	1	8	yes	complemented
81	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	complemented
83	C₂×#41×C₃₁	—	2	1	no	—
84	C₂×#41×C₃₁	—	2	1	no	—
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	2	no	—
87	C₂×#41×C₃₁	—	4	8	no	—
88	C₂×#41×C₃₁	C₂³	1	4	yes	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂×#41×C₃₁	C₂³	1	4	yes	—
91	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	—	2	2	no	—
93	C₂²×D₄×C₃₁	—	2	1	no	—
94	C₂²×D₄×C₃₁	—	2	1	no	—
95	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
96	C₂³×C₄×C₃₁	—	2	2	no	—
97	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
98	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
100	C₃₁×#135	—	4	16	no	—
101	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
104	C₂×D₈×C₃₁	C₂³	1	8	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×#127	—	2	1	no	—
114	C₃₁×#127	—	2	1	no	—
115	C₃₁×#127	C₂³	1	2	yes	—
116	C₃₁×#127	C₂³	1	2	yes	—
117	C₃₁×#127	C₂³	1	1	yes	characteristic
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#125	—	2	1	no	—
121	C₃₁×#125	—	2	1	no	—
122	C₃₁×#125	C₂³	1	2	yes	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	—	2	2	no	—
125	C₃₁×#124	—	2	1	no	—
126	C₃₁×#124	—	2	1	no	—
127	C₃₁×#124	C₂³	1	4	yes	—
128	C₃₁×#124	C₂³	1	4	yes	—
129	C₃₁×#124	C₂³	1	2	yes	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	2	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	1	no	—
150	C₃₁×#121	—	2	1	no	—
151	C₃₁×#121	C₂³	1	2	yes	—
152	C₃₁×#121	C₂³	1	2	yes	—
153	C₃₁×#120	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	—	2	1	no	—
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	2	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	2	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	1	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	C₂³	1	2	yes	—
179	C₄×D₄×C₃₁	C₂³	1	2	yes	—
180	C₃₁×#117	—	2	1	no	—
181	C₃₁×#117	—	2	1	no	—
182	C₃₁×#117	—	2	2	no	—
183	C₃₁×#117	—	2	2	no	—
184	C₃₁×#117	—	2	2	no	—
185	C₃₁×#117	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
187	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
189	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
190	C₂×C₄²×C₃₁	—	2	2	no	—
191	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
204	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
205	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
206	C₃₁×#103	C₂³	1	8	yes	—
207	C₃₁×#103	C₂³	1	8	yes	—
208	C₃₁×#102	C₂³	1	8	yes	—
209	C₃₁×#102	C₂³	1	8	yes	—
210	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₄×C₈×C₃₁	C₂³	1	2	yes	—
214	C₄×C₈×C₃₁	C₂³	1	2	yes	—
215	C₄×C₈×C₃₁	C₂³	1	4	yes	—
216	C₂⁴×C₃₁	—	2	2	no	—
217	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
218	#41×C₃₁	—	2	8	no	—
219	#41×C₃₁	—	2	16	no	—
220	#41×C₃₁	—	4	8	no	—
221	#41×C₃₁	—	4	4	no	—
222	#41×C₃₁	—	4	8	no	—
223	#41×C₃₁	—	4	8	no	—
224	#41×C₃₁	—	4	4	no	—
225	C₂×Q₈×C₃₁	—	2	1	no	—
226	C₂×Q₈×C₃₁	—	2	1	no	—
227	C₂×Q₈×C₃₁	—	2	2	no	—
228	C₂×Q₈×C₃₁	—	4	4	no	—
229	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
230	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	2	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	4	no	—
236	C₂×D₄×C₃₁	—	2	1	no	—
237	C₂×D₄×C₃₁	—	2	1	no	—
238	C₂×D₄×C₃₁	—	2	2	no	—
239	C₂×D₄×C₃₁	—	2	2	no	—
240	C₂×D₄×C₃₁	—	2	2	no	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	4	4	no	—
244	C₂×D₄×C₃₁	—	4	4	no	—
245	C₂×D₄×C₃₁	—	4	8	no	—
246	C₂×D₄×C₃₁	—	4	4	no	—
247	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
248	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₃₁	—	2	4	no	—
250	C₂²×C₄×C₃₁	—	2	4	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	4	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	4	no	—
257	C₂²×C₄×C₃₁	—	4	2	no	—
258	C₂²×C₄×C₃₁	—	4	8	no	—
259	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₃₁	—	4	8	no	—
278	SD₁₆×C₃₁	—	4	8	no	—
279	SD₁₆×C₃₁	—	4	8	no	—
280	D₈×C₃₁	—	4	8	no	—
281	C₂×C₈×C₃₁	—	2	8	no	—
282	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
283	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	1	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²⋊C₄×C₃₁	—	2	2	no	—
301	C₂²⋊C₄×C₃₁	—	2	2	no	—
302	C₂²⋊C₄×C₃₁	—	2	2	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	—	2	2	no	—
314	C₄²×C₃₁	—	2	2	no	—
315	C₄²×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
332	#60782	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂³×C₃₁	—	2	2	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	4	no	—
337	C₂³×C₃₁	—	4	1	no	—
338	C₂³×C₃₁	—	4	4	no	—
339	C₂³×C₃₁	—	4	4	no	—
340	C₂³×C₃₁	—	4	4	no	—
341	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₃₁	—	2	4	no	—
345	Q₈×C₃₁	—	2	8	no	—
346	Q₈×C₃₁	—	4	4	no	—
347	Q₈×C₃₁	—	4	2	no	—
348	Q₈×C₃₁	—	4	2	no	—
349	D₄×C₃₁	—	2	4	no	—
350	D₄×C₃₁	—	2	8	no	—
351	D₄×C₃₁	—	4	4	no	—
352	D₄×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	4	8	no	—
354	D₄×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	4	8	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	4	4	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	2	no	—
361	D₄×C₃₁	—	4	4	no	—
362	D₄×C₃₁	—	4	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	4	no	—
380	C₂×C₄×C₃₁	—	4	1	no	—
381	C₂×C₄×C₃₁	—	4	1	no	—
382	C₂×C₄×C₃₁	—	4	1	no	—
383	C₂×C₄×C₃₁	—	4	8	no	—
384	C₂×C₄×C₃₁	—	4	4	no	—
385	C₂×C₄×C₃₁	—	4	4	no	—
386	C₂×C₄×C₃₁	—	4	8	no	—
387	C₂×C₄×C₃₁	—	4	4	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	#135	1	4	yes	complemented
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
402	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
403	C₈×C₃₁	—	2	4	no	—
404	C₈×C₃₁	—	2	4	no	—
405	#3444	C₂×C₃₁	1	1	yes	characteristic, complemented
406	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3212	C₂×C₃₁	1	4	yes	complemented
408	#3211	C₂×C₃₁	1	4	yes	complemented
409	#3210	C₂×C₃₁	1	2	yes	complemented
410	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3207	C₂×C₃₁	1	2	yes	complemented
413	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#3147	C₂×C₃₁	1	2	yes	complemented
416	#3131	C₂×C₃₁	1	2	yes	complemented
417	#3035	C₂×C₃₁	1	4	yes	complemented
418	#3002	C₂×C₃₁	1	4	yes	complemented
419	C₂×#431	C₂×C₃₁	1	1	yes	characteristic, complemented
420	C₂²×C₃₁	—	2	1	no	—
421	C₂²×C₃₁	—	2	1	no	—
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	1	no	—
426	C₂²×C₃₁	—	2	1	no	—
427	C₂²×C₃₁	—	4	4	no	—
428	C₂²×C₃₁	—	4	4	no	—
429	C₂²×C₃₁	—	4	2	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	4	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	4	4	no	—
434	C₂²×C₃₁	—	8	8	no	—
435	C₂²×C₃₁	#535	1	2	yes	—
436	C₂²×C₃₁	C₂×#135	1	2	yes	—
437	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	1	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	1	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	1	no	—
445	C₄×C₃₁	—	4	4	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	—	4	2	no	—
449	C₄×C₃₁	#535	1	2	yes	—
450	C₄×C₃₁	C₂×#135	1	2	yes	—
451	C₄×C₃₁	C₂×#135	1	2	yes	—
452	C₄×C₃₁	#575	1	2	yes	—
453	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
454	C₂²×#41	C₂²×C₃₁	1	2	yes	—
455	C₂×#135	C₂²×C₃₁	1	8	yes	complemented
456	#533	C₂²×C₃₁	1	1	yes	characteristic
457	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	#532	—	2	1	no	—
460	#532	—	2	1	no	—
461	#532	—	2	1	no	—
462	#532	—	2	1	no	—
463	#532	C₂²×C₃₁	1	2	yes	—
464	#532	C₂²×C₃₁	1	2	yes	—
465	#532	C₂²×C₃₁	1	2	yes	—
466	#532	C₂²×C₃₁	1	2	yes	—
467	#532	C₂²×C₃₁	1	1	yes	characteristic
468	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
469	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
471	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
472	#529	—	2	1	no	—
473	#529	—	2	1	no	—
474	#529	—	2	1	no	—
475	#529	—	2	1	no	—
476	#529	C₂²×C₃₁	1	2	yes	—
477	#529	C₂²×C₃₁	1	2	yes	complemented
478	C₂×#124	C₂²×C₃₁	1	2	yes	—
479	#525	—	2	1	no	—
480	#525	—	2	1	no	—
481	#525	C₂²×C₃₁	1	2	yes	—
482	C₂×#121	—	2	1	no	—
483	C₂×#121	—	2	1	no	—
484	C₄×#41	—	2	1	no	—
485	C₄×#41	—	2	1	no	—
486	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
487	C₂×C₄×D₄	—	2	1	no	—
488	C₂×C₄×D₄	—	2	1	no	—
489	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
490	#495	C₂²×C₃₁	1	8	yes	complemented
491	#494	C₂²×C₃₁	1	2	yes	complemented
492	#493	C₂²×C₃₁	1	2	yes	complemented
493	#492	C₂²×C₃₁	1	2	yes	complemented
494	#492	C₂²×C₃₁	1	2	yes	complemented
495	#488	C₂²×C₃₁	1	8	yes	complemented
496	#487	C₂²×C₃₁	1	2	yes	complemented
497	#487	C₂²×C₃₁	1	2	yes	complemented
498	#486	C₂²×C₃₁	1	2	yes	complemented
499	#486	C₂²×C₃₁	1	2	yes	complemented
500	#464	C₂²×C₃₁	1	8	yes	complemented
501	#463	C₂²×C₃₁	1	8	yes	complemented
502	#462	C₂²×C₃₁	1	4	yes	complemented
503	#461	C₂²×C₃₁	1	4	yes	complemented
504	#460	C₂²×C₃₁	1	4	yes	complemented
505	#459	C₂²×C₃₁	1	4	yes	complemented
506	#452	C₂²×C₃₁	1	8	yes	complemented
507	#451	C₂²×C₃₁	1	4	yes	—
508	#450	C₂²×C₃₁	1	4	yes	—
509	#449	C₂²×C₃₁	1	8	yes	complemented
510	#448	C₂²×C₃₁	1	4	yes	—
511	#447	C₂²×C₃₁	1	4	yes	—
512	#431	C₂²×C₃₁	1	1	yes	characteristic
513	#431	C₂²×C₃₁	1	1	yes	characteristic
514	#431	C₂²×C₃₁	1	2	yes	—
515	#431	C₂²×C₃₁	1	2	yes	complemented
516	#431	C₂²×C₃₁	1	2	yes	complemented
517	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
518	#416	C₂²×C₃₁	1	8	yes	complemented
519	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
520	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	complemented
521	C₂×C₃₁	—	2	2	no	—
522	C₂×C₃₁	—	2	2	no	—
523	C₂×C₃₁	—	4	1	no	—
524	C₂×C₃₁	—	8	2	no	—
525	C₂×C₃₁	—	8	4	no	—
526	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
527	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
528	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	2	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	4	8	no	—
534	C₂×#41	C₂³×C₃₁	1	2	yes	—
535	C₂×#41	C₂³×C₃₁	1	4	yes	—
536	C₂×#41	C₂³×C₃₁	1	4	yes	—
537	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
538	C₂²×D₄	—	2	2	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
542	C₂³×C₄	—	2	2	no	—
543	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
544	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
546	#135	—	4	16	no	—
547	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	—
548	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
549	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
550	C₂×D₈	C₂³×C₃₁	1	8	yes	—
551	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
559	#127	—	2	1	no	—
560	#127	—	2	1	no	—
561	#127	C₂³×C₃₁	1	2	yes	—
562	#127	C₂³×C₃₁	1	2	yes	—
563	#127	C₂³×C₃₁	1	1	yes	characteristic
564	#126	—	2	2	no	—
565	#126	—	2	2	no	—
566	#125	—	2	1	no	—
567	#125	—	2	1	no	—
568	#125	C₂³×C₃₁	1	2	yes	—
569	#124	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	—	2	1	no	—
572	#124	—	2	1	no	—
573	#124	C₂³×C₃₁	1	4	yes	—
574	#124	C₂³×C₃₁	1	4	yes	—
575	#124	C₂³×C₃₁	1	2	yes	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	—	2	1	no	—
596	#121	—	2	1	no	—
597	#121	C₂³×C₃₁	1	2	yes	—
598	#121	C₂³×C₃₁	1	2	yes	—
599	#120	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
605	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	C₂³×C₃₁	1	2	yes	—
625	C₄×D₄	C₂³×C₃₁	1	2	yes	—
626	#117	—	2	1	no	—
627	#117	—	2	1	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	C₂³×C₃₁	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₂²⋊C₄	—	2	2	no	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
638	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
639	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
640	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
641	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
642	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
649	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
650	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
651	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
652	#103	C₂³×C₃₁	1	8	yes	—
653	#103	C₂³×C₃₁	1	8	yes	—
654	#102	C₂³×C₃₁	1	8	yes	—
655	#102	C₂³×C₃₁	1	8	yes	—
656	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
659	C₄×C₈	C₂³×C₃₁	1	2	yes	—
660	C₄×C₈	C₂³×C₃₁	1	2	yes	—
661	C₄×C₈	C₂³×C₃₁	1	4	yes	—
662	C₃₁	#60782	1	1	yes	characteristic, direct product factor, Sylow
663	C₂⁴	—	2	2	no	—
664	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
665	#41	—	2	8	no	—
666	#41	—	2	16	no	—
667	#41	—	4	8	no	—
668	#41	—	4	4	no	—
669	#41	—	4	8	no	—
670	#41	—	4	8	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
677	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	—	4	8	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
695	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
719	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
724	Q₁₆	—	4	8	no	—
725	SD₁₆	—	4	8	no	—
726	SD₁₆	—	4	8	no	—
727	D₈	—	4	8	no	—
728	C₂×C₈	—	2	8	no	—
729	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
730	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
772	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
777	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	4	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	4	no	—
786	C₂³	—	4	4	no	—
787	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
788	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
789	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
790	Q₈	—	2	4	no	—
791	Q₈	—	2	8	no	—
792	Q₈	—	4	4	no	—
793	Q₈	—	4	2	no	—
794	Q₈	—	4	2	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	8	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	C₃₁×#135	1	4	yes	complemented
836	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
847	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
848	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
849	C₈	—	2	4	no	—
850	C₈	—	2	4	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	4	4	no	—
859	C₂²	—	4	4	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	8	8	no	—
866	C₂²	C₃₁×#535	1	2	yes	—
867	C₂²	C₂×C₃₁×#135	1	2	yes	—
868	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	4	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	C₃₁×#535	1	2	yes	—
881	C₄	C₂×C₃₁×#135	1	2	yes	—
882	C₄	C₂×C₃₁×#135	1	2	yes	—
883	C₄	C₃₁×#575	1	2	yes	—
884	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	4	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
891	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
892	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×#532	C₂	semidirect
3. C₃₁×#3212	C₂	semidirect
4. C₃₁×#3211	C₂	semidirect
5. C₃₁×#3210	C₂	semidirect
6. C₃₁×#3209	C₂	semidirect
7. C₃₁×#3208	C₂	semidirect
8. C₃₁×#3207	C₂	semidirect
9. C₃₁×#3206	C₂	semidirect
10. C₃₁×#3205	C₂	semidirect
11. C₃₁×#3147	C₂	semidirect
12. C₃₁×#3131	C₂	semidirect
13. C₃₁×#3035	C₂	semidirect
14. C₃₁×#3002	C₂	semidirect
15. C₂×C₃₁×#431	C₂	semidirect
17. C₂×C₃₁×#135	C₂²	semidirect
19. C₃₁×#533	C₂²	semidirect
20. C₃₁×#533	C₂²	semidirect
30. C₃₁×#532	C₂²	semidirect
31. C₃₁×#532	C₂²	semidirect
39. C₃₁×#529	C₂²	semidirect
48. C₄×#41×C₃₁	C₂²	semidirect
52. C₃₁×#495	C₂²	semidirect
53. C₃₁×#494	C₂²	semidirect
54. C₃₁×#493	C₂²	semidirect
55. C₃₁×#492	C₂²	semidirect
56. C₃₁×#492	C₂²	semidirect
57. C₃₁×#488	C₂²	semidirect
58. C₃₁×#487	C₂²	semidirect
59. C₃₁×#487	C₂²	semidirect
60. C₃₁×#486	C₂²	semidirect
61. C₃₁×#486	C₂²	semidirect
62. C₃₁×#464	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#462	C₂²	semidirect
65. C₃₁×#461	C₂²	semidirect
66. C₃₁×#460	C₂²	semidirect
67. C₃₁×#459	C₂²	semidirect
68. C₃₁×#452	C₂²	semidirect
71. C₃₁×#449	C₂²	semidirect
77. C₃₁×#431	C₂²	semidirect
78. C₃₁×#431	C₂²	semidirect
79. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
80. C₃₁×#416	C₂²	semidirect
82. C₂×C₄×C₈×C₃₁	C₂²	semidirect
332. #60782	C₃₁	direct (N × H)
389. C₂×C₄×C₃₁	#135	semidirect
405. #3444	C₂×C₃₁	semidirect
406. C₂×#532	C₂×C₃₁	semidirect
407. #3212	C₂×C₃₁	semidirect
408. #3211	C₂×C₃₁	semidirect
409. #3210	C₂×C₃₁	semidirect
410. #3209	C₂×C₃₁	semidirect
411. #3208	C₂×C₃₁	semidirect
412. #3207	C₂×C₃₁	semidirect
413. #3206	C₂×C₃₁	semidirect
414. #3205	C₂×C₃₁	semidirect
415. #3147	C₂×C₃₁	semidirect
416. #3131	C₂×C₃₁	semidirect
417. #3035	C₂×C₃₁	semidirect
418. #3002	C₂×C₃₁	semidirect
419. C₂×#431	C₂×C₃₁	semidirect
455. C₂×#135	C₂²×C₃₁	semidirect
457. #533	C₂²×C₃₁	semidirect
458. #533	C₂²×C₃₁	semidirect
468. #532	C₂²×C₃₁	semidirect
469. #532	C₂²×C₃₁	semidirect
477. #529	C₂²×C₃₁	semidirect
486. C₄×#41	C₂²×C₃₁	semidirect
490. #495	C₂²×C₃₁	semidirect
491. #494	C₂²×C₃₁	semidirect
492. #493	C₂²×C₃₁	semidirect
493. #492	C₂²×C₃₁	semidirect
494. #492	C₂²×C₃₁	semidirect
495. #488	C₂²×C₃₁	semidirect
496. #487	C₂²×C₃₁	semidirect
497. #487	C₂²×C₃₁	semidirect
498. #486	C₂²×C₃₁	semidirect
499. #486	C₂²×C₃₁	semidirect
500. #464	C₂²×C₃₁	semidirect
501. #463	C₂²×C₃₁	semidirect
502. #462	C₂²×C₃₁	semidirect
503. #461	C₂²×C₃₁	semidirect
504. #460	C₂²×C₃₁	semidirect
505. #459	C₂²×C₃₁	semidirect
506. #452	C₂²×C₃₁	semidirect
509. #449	C₂²×C₃₁	semidirect
515. #431	C₂²×C₃₁	semidirect
516. #431	C₂²×C₃₁	semidirect
517. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
518. #416	C₂²×C₃₁	semidirect
520. C₂×C₄×C₈	C₂²×C₃₁	semidirect
662. C₃₁	#60782	direct (N × H)
835. C₂×C₄	C₃₁×#135	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×#532	2
C₃₁×#3212	2
C₃₁×#3211	2
C₃₁×#3210	2
C₃₁×#3209	2
C₃₁×#3208	2
C₃₁×#3207	2
C₃₁×#3206	2
C₃₁×#3205	2
C₃₁×#3147	2
C₃₁×#3131	2
C₃₁×#3035	2
C₃₁×#3002	2
C₂×C₃₁×#431	2
#60782	31

Subgroups — C31×#60782 #21517541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60782 #21517541