Subgroups — C₃₁×#60790 #21517549

Order 7936.

2188 conjugacy classes of subgroups.

The subgroup lattice has 876 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×#3219	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3218	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3216	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3214	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3150	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3135	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3035	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3002	C₂	1	4	yes	maximal, complemented
14	C₂×C₃₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₃₁	C₂²	1	2	yes	—
16	C₂×C₃₁×#135	C₂²	1	8	yes	complemented
17	C₃₁×#533	C₂²	1	1	yes	characteristic
18	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#532	—	2	1	no	—
21	C₃₁×#532	—	2	1	no	—
22	C₃₁×#532	—	2	1	no	—
23	C₃₁×#532	—	2	1	no	—
24	C₃₁×#532	C₂²	1	2	yes	—
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	1	yes	characteristic
29	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
33	C₃₁×#529	—	2	1	no	—
34	C₃₁×#529	—	2	1	no	—
35	C₃₁×#529	—	2	1	no	—
36	C₃₁×#529	—	2	1	no	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₃₁×#529	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#124	C₂²	1	2	yes	—
40	C₃₁×#525	—	2	1	no	—
41	C₃₁×#525	—	2	1	no	—
42	C₃₁×#525	C₂²	1	2	yes	—
43	C₂×C₃₁×#121	—	2	1	no	—
44	C₂×C₃₁×#121	—	2	1	no	—
45	C₄×#41×C₃₁	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	—	2	1	no	—
50	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	4	yes	complemented
52	C₃₁×#497	C₂²	1	4	yes	complemented
53	C₃₁×#496	C₂²	1	4	yes	complemented
54	C₃₁×#496	C₂²	1	4	yes	complemented
55	C₃₁×#491	C₂²	1	4	yes	complemented
56	C₃₁×#490	C₂²	1	4	yes	complemented
57	C₃₁×#489	C₂²	1	4	yes	complemented
58	C₃₁×#489	C₂²	1	4	yes	complemented
59	C₃₁×#464	C₂²	1	8	yes	complemented
60	C₃₁×#463	C₂²	1	8	yes	complemented
61	C₃₁×#462	C₂²	1	4	yes	complemented
62	C₃₁×#461	C₂²	1	4	yes	complemented
63	C₃₁×#460	C₂²	1	4	yes	complemented
64	C₃₁×#459	C₂²	1	4	yes	complemented
65	C₃₁×#452	C₂²	1	8	yes	complemented
66	C₃₁×#451	C₂²	1	4	yes	—
67	C₃₁×#450	C₂²	1	4	yes	—
68	C₃₁×#449	C₂²	1	8	yes	complemented
69	C₃₁×#448	C₂²	1	4	yes	—
70	C₃₁×#447	C₂²	1	4	yes	—
71	C₃₁×#432	C₂²	1	2	yes	—
72	C₃₁×#432	C₂²	1	2	yes	—
73	C₃₁×#432	C₂²	1	2	yes	complemented
74	C₃₁×#432	C₂²	1	2	yes	complemented
75	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
76	C₃₁×#416	C₂²	1	8	yes	complemented
77	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
78	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
79	C₂×#41×C₃₁	—	2	1	no	—
80	C₂×#41×C₃₁	—	2	1	no	—
81	C₂×#41×C₃₁	—	2	2	no	—
82	C₂×#41×C₃₁	—	2	2	no	—
83	C₂×#41×C₃₁	—	4	8	no	—
84	C₂×#41×C₃₁	C₂³	1	4	yes	—
85	C₂×#41×C₃₁	C₂³	1	2	yes	—
86	C₂×#41×C₃₁	C₂³	1	4	yes	—
87	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₃₁	—	2	2	no	—
89	C₂²×D₄×C₃₁	—	2	1	no	—
90	C₂²×D₄×C₃₁	—	2	1	no	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	—	2	2	no	—
93	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₃₁×#135	—	4	16	no	—
97	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
100	C₂×D₈×C₃₁	C₂³	1	8	yes	—
101	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
102	C₃₁×C₄⋊Q₈	—	2	1	no	—
103	C₃₁×C₄⋊Q₈	—	2	1	no	—
104	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₃₁×#127	—	2	1	no	—
110	C₃₁×#127	—	2	1	no	—
111	C₃₁×#127	C₂³	1	2	yes	—
112	C₃₁×#127	C₂³	1	2	yes	—
113	C₃₁×#127	C₂³	1	1	yes	characteristic
114	C₃₁×#126	—	2	2	no	—
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#125	—	2	1	no	—
117	C₃₁×#125	—	2	1	no	—
118	C₃₁×#125	C₂³	1	2	yes	—
119	C₃₁×#124	—	2	2	no	—
120	C₃₁×#124	—	2	2	no	—
121	C₃₁×#124	—	2	1	no	—
122	C₃₁×#124	—	2	1	no	—
123	C₃₁×#124	C₂³	1	4	yes	—
124	C₃₁×#124	C₂³	1	4	yes	—
125	C₃₁×#124	C₂³	1	2	yes	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	2	no	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	1	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	1	no	—
132	C₃₁×C₂²⋊Q₈	—	2	1	no	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	2	no	—
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	1	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	1	no	—
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	C₂³	1	2	yes	—
148	C₃₁×#121	C₂³	1	2	yes	—
149	C₃₁×#120	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×D₄×C₃₁	—	2	2	no	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	—	2	2	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
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	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₃₁×#117	—	2	1	no	—
177	C₃₁×#117	—	2	1	no	—
178	C₃₁×#117	—	2	2	no	—
179	C₃₁×#117	—	2	2	no	—
180	C₃₁×#117	—	2	2	no	—
181	C₃₁×#117	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
185	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
186	C₂×C₄²×C₃₁	—	2	2	no	—
187	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
199	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
200	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
201	C₃₁×#103	C₂³	1	8	yes	—
202	C₃₁×#103	C₂³	1	8	yes	—
203	C₃₁×#102	C₂³	1	8	yes	—
204	C₃₁×#102	C₂³	1	8	yes	—
205	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₃₁×#97	C₂³	1	4	yes	—
208	C₃₁×#97	C₂³	1	4	yes	—
209	C₂⁴×C₃₁	—	2	2	no	—
210	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
211	#41×C₃₁	—	2	8	no	—
212	#41×C₃₁	—	2	16	no	—
213	#41×C₃₁	—	4	8	no	—
214	#41×C₃₁	—	4	4	no	—
215	#41×C₃₁	—	4	4	no	—
216	#41×C₃₁	—	4	8	no	—
217	#41×C₃₁	—	4	8	no	—
218	C₂×Q₈×C₃₁	—	2	1	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	4	4	no	—
222	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
223	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₃₁	—	2	2	no	—
225	C₂×D₄×C₃₁	—	2	2	no	—
226	C₂×D₄×C₃₁	—	2	2	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	2	4	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	1	no	—
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	2	no	—
235	C₂×D₄×C₃₁	—	2	2	no	—
236	C₂×D₄×C₃₁	—	4	4	no	—
237	C₂×D₄×C₃₁	—	4	4	no	—
238	C₂×D₄×C₃₁	—	4	4	no	—
239	C₂×D₄×C₃₁	—	4	8	no	—
240	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
241	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	—	2	2	no	—
245	C₂²×C₄×C₃₁	—	2	2	no	—
246	C₂²×C₄×C₃₁	—	2	4	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	4	no	—
249	C₂²×C₄×C₃₁	—	4	2	no	—
250	C₂²×C₄×C₃₁	—	4	2	no	—
251	C₂²×C₄×C₃₁	—	4	8	no	—
252	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₃₁	—	4	8	no	—
271	SD₁₆×C₃₁	—	4	8	no	—
272	SD₁₆×C₃₁	—	4	8	no	—
273	D₈×C₃₁	—	4	8	no	—
274	C₂×C₈×C₃₁	—	2	8	no	—
275	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	—	2	1	no	—
283	C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
292	C₂²⋊C₄×C₃₁	—	2	2	no	—
293	C₂²⋊C₄×C₃₁	—	2	2	no	—
294	C₂²⋊C₄×C₃₁	—	2	2	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	4	no	—
297	C₂²⋊C₄×C₃₁	—	2	4	no	—
298	C₂²⋊C₄×C₃₁	—	2	4	no	—
299	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₄²×C₃₁	—	2	2	no	—
306	C₄²×C₃₁	—	2	2	no	—
307	C₄²×C₃₁	—	2	2	no	—
308	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
321	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
323	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
324	#60790	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	—	2	2	no	—
327	C₂³×C₃₁	—	2	2	no	—
328	C₂³×C₃₁	—	2	4	no	—
329	C₂³×C₃₁	—	4	1	no	—
330	C₂³×C₃₁	—	4	4	no	—
331	C₂³×C₃₁	—	4	4	no	—
332	C₂³×C₃₁	—	4	4	no	—
333	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₃₁	—	2	4	no	—
337	Q₈×C₃₁	—	2	8	no	—
338	Q₈×C₃₁	—	4	4	no	—
339	Q₈×C₃₁	—	4	2	no	—
340	Q₈×C₃₁	—	4	2	no	—
341	D₄×C₃₁	—	2	4	no	—
342	D₄×C₃₁	—	2	8	no	—
343	D₄×C₃₁	—	4	4	no	—
344	D₄×C₃₁	—	4	4	no	—
345	D₄×C₃₁	—	4	4	no	—
346	D₄×C₃₁	—	4	4	no	—
347	D₄×C₃₁	—	4	2	no	—
348	D₄×C₃₁	—	4	2	no	—
349	D₄×C₃₁	—	4	8	no	—
350	D₄×C₃₁	—	4	4	no	—
351	D₄×C₃₁	—	4	8	no	—
352	D₄×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	4	4	no	—
354	D₄×C₃₁	—	4	4	no	—
355	C₂×C₄×C₃₁	—	2	2	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	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	4	no	—
369	C₂×C₄×C₃₁	—	4	1	no	—
370	C₂×C₄×C₃₁	—	4	1	no	—
371	C₂×C₄×C₃₁	—	4	1	no	—
372	C₂×C₄×C₃₁	—	4	1	no	—
373	C₂×C₄×C₃₁	—	4	1	no	—
374	C₂×C₄×C₃₁	—	4	1	no	—
375	C₂×C₄×C₃₁	—	4	1	no	—
376	C₂×C₄×C₃₁	—	4	8	no	—
377	C₂×C₄×C₃₁	—	4	4	no	—
378	C₂×C₄×C₃₁	—	4	4	no	—
379	C₂×C₄×C₃₁	—	4	8	no	—
380	C₂×C₄×C₃₁	—	4	4	no	—
381	C₂×C₄×C₃₁	—	4	4	no	—
382	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	4	yes	—
394	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
395	C₈×C₃₁	—	2	8	no	—
396	#3444	C₂×C₃₁	1	1	yes	characteristic, complemented
397	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
398	#3219	C₂×C₃₁	1	4	yes	complemented
399	#3218	C₂×C₃₁	1	2	yes	complemented
400	#3217	C₂×C₃₁	1	2	yes	complemented
401	#3216	C₂×C₃₁	1	2	yes	complemented
402	#3215	C₂×C₃₁	1	2	yes	complemented
403	#3214	C₂×C₃₁	1	2	yes	complemented
404	#3213	C₂×C₃₁	1	2	yes	complemented
405	#3150	C₂×C₃₁	1	2	yes	complemented
406	#3135	C₂×C₃₁	1	2	yes	complemented
407	#3035	C₂×C₃₁	1	4	yes	complemented
408	#3002	C₂×C₃₁	1	4	yes	complemented
409	C₂×#432	C₂×C₃₁	1	1	yes	characteristic, complemented
410	C₂²×C₃₁	—	2	1	no	—
411	C₂²×C₃₁	—	2	1	no	—
412	C₂²×C₃₁	—	2	1	no	—
413	C₂²×C₃₁	—	2	1	no	—
414	C₂²×C₃₁	—	2	1	no	—
415	C₂²×C₃₁	—	2	1	no	—
416	C₂²×C₃₁	—	2	1	no	—
417	C₂²×C₃₁	—	4	4	no	—
418	C₂²×C₃₁	—	4	4	no	—
419	C₂²×C₃₁	—	4	2	no	—
420	C₂²×C₃₁	—	4	2	no	—
421	C₂²×C₃₁	—	4	2	no	—
422	C₂²×C₃₁	—	4	4	no	—
423	C₂²×C₃₁	—	4	4	no	—
424	C₂²×C₃₁	—	8	8	no	—
425	C₂²×C₃₁	#535	1	2	yes	—
426	C₂²×C₃₁	#575	1	2	yes	—
427	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₃₁	—	2	1	no	—
429	C₄×C₃₁	—	2	1	no	—
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	1	no	—
432	C₄×C₃₁	—	2	1	no	—
433	C₄×C₃₁	—	2	1	no	—
434	C₄×C₃₁	—	2	1	no	—
435	C₄×C₃₁	—	2	1	no	—
436	C₄×C₃₁	—	2	1	no	—
437	C₄×C₃₁	—	4	4	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₄×C₃₁	—	4	2	no	—
441	C₄×C₃₁	#535	1	2	yes	—
442	C₄×C₃₁	#575	1	2	yes	—
443	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₂²×#41	C₂²×C₃₁	1	2	yes	—
445	C₂×#135	C₂²×C₃₁	1	8	yes	complemented
446	#533	C₂²×C₃₁	1	1	yes	characteristic
447	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
448	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
449	#532	—	2	1	no	—
450	#532	—	2	1	no	—
451	#532	—	2	1	no	—
452	#532	—	2	1	no	—
453	#532	C₂²×C₃₁	1	2	yes	—
454	#532	C₂²×C₃₁	1	2	yes	—
455	#532	C₂²×C₃₁	1	2	yes	—
456	#532	C₂²×C₃₁	1	2	yes	—
457	#532	C₂²×C₃₁	1	1	yes	characteristic
458	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
461	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
462	#529	—	2	1	no	—
463	#529	—	2	1	no	—
464	#529	—	2	1	no	—
465	#529	—	2	1	no	—
466	#529	C₂²×C₃₁	1	2	yes	—
467	#529	C₂²×C₃₁	1	2	yes	complemented
468	C₂×#124	C₂²×C₃₁	1	2	yes	—
469	#525	—	2	1	no	—
470	#525	—	2	1	no	—
471	#525	C₂²×C₃₁	1	2	yes	—
472	C₂×#121	—	2	1	no	—
473	C₂×#121	—	2	1	no	—
474	C₄×#41	—	2	1	no	—
475	C₄×#41	—	2	1	no	—
476	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
477	C₂×C₄×D₄	—	2	1	no	—
478	C₂×C₄×D₄	—	2	1	no	—
479	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
480	#497	C₂²×C₃₁	1	4	yes	complemented
481	#497	C₂²×C₃₁	1	4	yes	complemented
482	#496	C₂²×C₃₁	1	4	yes	complemented
483	#496	C₂²×C₃₁	1	4	yes	complemented
484	#491	C₂²×C₃₁	1	4	yes	complemented
485	#490	C₂²×C₃₁	1	4	yes	complemented
486	#489	C₂²×C₃₁	1	4	yes	complemented
487	#489	C₂²×C₃₁	1	4	yes	complemented
488	#464	C₂²×C₃₁	1	8	yes	complemented
489	#463	C₂²×C₃₁	1	8	yes	complemented
490	#462	C₂²×C₃₁	1	4	yes	complemented
491	#461	C₂²×C₃₁	1	4	yes	complemented
492	#460	C₂²×C₃₁	1	4	yes	complemented
493	#459	C₂²×C₃₁	1	4	yes	complemented
494	#452	C₂²×C₃₁	1	8	yes	complemented
495	#451	C₂²×C₃₁	1	4	yes	—
496	#450	C₂²×C₃₁	1	4	yes	—
497	#449	C₂²×C₃₁	1	8	yes	complemented
498	#448	C₂²×C₃₁	1	4	yes	—
499	#447	C₂²×C₃₁	1	4	yes	—
500	#432	C₂²×C₃₁	1	2	yes	—
501	#432	C₂²×C₃₁	1	2	yes	—
502	#432	C₂²×C₃₁	1	2	yes	complemented
503	#432	C₂²×C₃₁	1	2	yes	complemented
504	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
505	#416	C₂²×C₃₁	1	8	yes	complemented
506	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
507	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
508	C₂×C₃₁	—	2	2	no	—
509	C₂×C₃₁	—	2	2	no	—
510	C₂×C₃₁	—	4	1	no	—
511	C₂×C₃₁	—	8	2	no	—
512	C₂×C₃₁	—	8	4	no	—
513	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
514	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
515	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
516	C₂×#41	—	2	1	no	—
517	C₂×#41	—	2	1	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	4	8	no	—
521	C₂×#41	C₂³×C₃₁	1	2	yes	—
522	C₂×#41	C₂³×C₃₁	1	4	yes	—
523	C₂×#41	C₂³×C₃₁	1	4	yes	—
524	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
525	C₂²×D₄	—	2	2	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
529	C₂³×C₄	—	2	2	no	—
530	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
531	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
533	#135	—	4	16	no	—
534	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	—
535	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
536	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
537	C₂×D₈	C₂³×C₃₁	1	8	yes	—
538	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
546	#127	—	2	1	no	—
547	#127	—	2	1	no	—
548	#127	C₂³×C₃₁	1	2	yes	—
549	#127	C₂³×C₃₁	1	2	yes	—
550	#127	C₂³×C₃₁	1	1	yes	characteristic
551	#126	—	2	2	no	—
552	#126	—	2	2	no	—
553	#125	—	2	1	no	—
554	#125	—	2	1	no	—
555	#125	C₂³×C₃₁	1	2	yes	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	1	no	—
559	#124	—	2	1	no	—
560	#124	C₂³×C₃₁	1	4	yes	—
561	#124	C₂³×C₃₁	1	4	yes	—
562	#124	C₂³×C₃₁	1	2	yes	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
571	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	1	no	—
584	#121	C₂³×C₃₁	1	2	yes	—
585	#121	C₂³×C₃₁	1	2	yes	—
586	#120	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
592	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	C₂³×C₃₁	1	2	yes	—
612	C₄×D₄	C₂³×C₃₁	1	2	yes	—
613	#117	—	2	1	no	—
614	#117	—	2	1	no	—
615	#117	—	2	2	no	—
616	#117	—	2	2	no	—
617	#117	—	2	2	no	—
618	#117	C₂³×C₃₁	1	2	yes	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	2	no	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₄²	—	2	2	no	—
624	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
625	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
626	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
627	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
628	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
629	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
636	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
637	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
638	#103	C₂³×C₃₁	1	8	yes	—
639	#103	C₂³×C₃₁	1	8	yes	—
640	#102	C₂³×C₃₁	1	8	yes	—
641	#102	C₂³×C₃₁	1	8	yes	—
642	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
643	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
644	#97	C₂³×C₃₁	1	4	yes	—
645	#97	C₂³×C₃₁	1	4	yes	—
646	C₃₁	#60790	1	1	yes	characteristic, direct product factor, Sylow
647	C₂⁴	—	2	2	no	—
648	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
649	#41	—	2	8	no	—
650	#41	—	2	16	no	—
651	#41	—	4	8	no	—
652	#41	—	4	4	no	—
653	#41	—	4	4	no	—
654	#41	—	4	8	no	—
655	#41	—	4	8	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	4	4	no	—
660	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
661	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
679	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	8	no	—
690	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	Q₁₆	—	4	8	no	—
709	SD₁₆	—	4	8	no	—
710	SD₁₆	—	4	8	no	—
711	D₈	—	4	8	no	—
712	C₂×C₈	—	2	8	no	—
713	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
751	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
752	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
755	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
758	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
759	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	4	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
771	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
773	Q₈	—	2	4	no	—
774	Q₈	—	2	8	no	—
775	Q₈	—	4	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	8	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
830	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
831	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
832	C₈	—	2	8	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	8	8	no	—
848	C₂²	C₃₁×#535	1	2	yes	—
849	C₂²	C₃₁×#575	1	2	yes	—
850	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	4	4	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	C₃₁×#535	1	2	yes	—
865	C₄	C₃₁×#575	1	2	yes	—
866	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
867	C₂	—	2	2	no	—
868	C₂	—	2	2	no	—
869	C₂	—	4	1	no	—
870	C₂	—	8	4	no	—
871	C₂	—	8	2	no	—
872	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
873	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
874	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×#3219	C₂	semidirect
4. C₃₁×#3218	C₂	semidirect
5. C₃₁×#3217	C₂	semidirect
6. C₃₁×#3216	C₂	semidirect
7. C₃₁×#3215	C₂	semidirect
8. C₃₁×#3214	C₂	semidirect
9. C₃₁×#3213	C₂	semidirect
10. C₃₁×#3150	C₂	semidirect
11. C₃₁×#3135	C₂	semidirect
12. C₃₁×#3035	C₂	semidirect
13. C₃₁×#3002	C₂	semidirect
14. C₂×C₃₁×#432	C₂	semidirect
16. C₂×C₃₁×#135	C₂²	semidirect
18. C₃₁×#533	C₂²	semidirect
19. C₃₁×#533	C₂²	semidirect
29. C₃₁×#532	C₂²	semidirect
30. C₃₁×#532	C₂²	semidirect
38. C₃₁×#529	C₂²	semidirect
47. C₄×#41×C₃₁	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
52. C₃₁×#497	C₂²	semidirect
53. C₃₁×#496	C₂²	semidirect
54. C₃₁×#496	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#464	C₂²	semidirect
60. C₃₁×#463	C₂²	semidirect
61. C₃₁×#462	C₂²	semidirect
62. C₃₁×#461	C₂²	semidirect
63. C₃₁×#460	C₂²	semidirect
64. C₃₁×#459	C₂²	semidirect
65. C₃₁×#452	C₂²	semidirect
68. C₃₁×#449	C₂²	semidirect
73. C₃₁×#432	C₂²	semidirect
74. C₃₁×#432	C₂²	semidirect
75. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
76. C₃₁×#416	C₂²	semidirect
78. C₂×C₃₁×#97	C₂²	semidirect
324. #60790	C₃₁	direct (N × H)
396. #3444	C₂×C₃₁	semidirect
397. C₂×#532	C₂×C₃₁	semidirect
398. #3219	C₂×C₃₁	semidirect
399. #3218	C₂×C₃₁	semidirect
400. #3217	C₂×C₃₁	semidirect
401. #3216	C₂×C₃₁	semidirect
402. #3215	C₂×C₃₁	semidirect
403. #3214	C₂×C₃₁	semidirect
404. #3213	C₂×C₃₁	semidirect
405. #3150	C₂×C₃₁	semidirect
406. #3135	C₂×C₃₁	semidirect
407. #3035	C₂×C₃₁	semidirect
408. #3002	C₂×C₃₁	semidirect
409. C₂×#432	C₂×C₃₁	semidirect
445. C₂×#135	C₂²×C₃₁	semidirect
447. #533	C₂²×C₃₁	semidirect
448. #533	C₂²×C₃₁	semidirect
458. #532	C₂²×C₃₁	semidirect
459. #532	C₂²×C₃₁	semidirect
467. #529	C₂²×C₃₁	semidirect
476. C₄×#41	C₂²×C₃₁	semidirect
480. #497	C₂²×C₃₁	semidirect
481. #497	C₂²×C₃₁	semidirect
482. #496	C₂²×C₃₁	semidirect
483. #496	C₂²×C₃₁	semidirect
484. #491	C₂²×C₃₁	semidirect
485. #490	C₂²×C₃₁	semidirect
486. #489	C₂²×C₃₁	semidirect
487. #489	C₂²×C₃₁	semidirect
488. #464	C₂²×C₃₁	semidirect
489. #463	C₂²×C₃₁	semidirect
490. #462	C₂²×C₃₁	semidirect
491. #461	C₂²×C₃₁	semidirect
492. #460	C₂²×C₃₁	semidirect
493. #459	C₂²×C₃₁	semidirect
494. #452	C₂²×C₃₁	semidirect
497. #449	C₂²×C₃₁	semidirect
502. #432	C₂²×C₃₁	semidirect
503. #432	C₂²×C₃₁	semidirect
504. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
505. #416	C₂²×C₃₁	semidirect
507. C₂×#97	C₂²×C₃₁	semidirect
646. C₃₁	#60790	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×#3444	2
C₂×C₃₁×#532	2
C₃₁×#3219	2
C₃₁×#3218	2
C₃₁×#3217	2
C₃₁×#3216	2
C₃₁×#3215	2
C₃₁×#3214	2
C₃₁×#3213	2
C₃₁×#3150	2
C₃₁×#3135	2
C₃₁×#3035	2
C₃₁×#3002	2
C₂×C₃₁×#432	2
#60790	31

Subgroups — C31×#60790 #21517549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60790 #21517549