Subgroups — C₃₁×#60893 #21517652

Order 7936.

1672 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3461	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3243	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3242	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3238	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3237	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3230	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3164	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3098	C₂	1	2	yes	maximal
12	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₃₁	—	2	1	no	—
19	C₃₁×#557	—	2	1	no	—
20	C₃₁×#554	—	2	2	no	—
21	C₃₁×#554	—	2	1	no	—
22	D₄×Q₈×C₃₁	—	2	2	no	—
23	D₄×Q₈×C₃₁	—	2	1	no	—
24	C₃₁×#544	C₂²	1	2	yes	—
25	C₃₁×#544	C₂²	1	1	yes	characteristic
26	C₃₁×#544	C₂²	1	4	yes	—
27	C₃₁×#542	—	2	1	no	—
28	C₃₁×#542	C₂²	1	2	yes	—
29	C₃₁×#541	—	2	1	no	—
30	C₃₁×#541	C₂²	1	2	yes	—
31	C₃₁×#539	—	2	2	no	—
32	C₃₁×#537	C₂²	1	1	yes	characteristic
33	C₃₁×#536	C₂²	1	1	yes	characteristic
34	C₃₁×#536	C₂²	1	1	yes	characteristic
35	C₃₁×#533	—	2	1	no	—
36	C₃₁×#533	C₂²	1	2	yes	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	2	yes	—
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
41	C₃₁×#529	—	2	2	no	—
42	C₃₁×#529	—	2	1	no	—
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₃₁×#520	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	—
49	C₃₁×#501	C₂²	1	4	yes	—
50	C₃₁×#500	C₂²	1	4	yes	—
51	C₃₁×#499	C₂²	1	4	yes	—
52	C₃₁×#491	C₂²	1	4	yes	—
53	C₃₁×#489	C₂²	1	4	yes	—
54	C₃₁×#488	C₂²	1	4	yes	—
55	C₃₁×#487	C₂²	1	4	yes	—
56	C₃₁×#485	C₂²	1	4	yes	—
57	C₃₁×#485	C₂²	1	4	yes	—
58	C₃₁×#485	C₂²	1	4	yes	—
59	C₃₁×#484	C₂²	1	4	yes	—
60	C₃₁×#484	C₂²	1	4	yes	—
61	C₃₁×#483	C₂²	1	4	yes	—
62	C₃₁×#482	C₂²	1	4	yes	—
63	C₃₁×#480	C₂²	1	4	yes	—
64	C₃₁×#479	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	4	yes	—
66	C₃₁×#478	C₂²	1	2	yes	—
67	C₃₁×#477	C₂²	1	1	yes	characteristic
68	C₃₁×#477	C₂²	1	2	yes	—
69	C₃₁×#477	C₂²	1	2	yes	—
70	C₃₁×#477	C₂²	1	2	yes	—
71	C₃₁×#477	C₂²	1	2	yes	—
72	C₃₁×#477	C₂²	1	4	yes	—
73	C₃₁×#476	C₂²	1	1	yes	characteristic
74	C₃₁×#476	C₂²	1	2	yes	—
75	C₃₁×#475	C₂²	1	1	yes	characteristic
76	C₃₁×#475	C₂²	1	2	yes	—
77	C₃₁×#475	C₂²	1	2	yes	—
78	C₃₁×#474	C₂²	1	1	yes	characteristic
79	C₃₁×#474	C₂²	1	2	yes	—
80	C₃₁×#433	C₂²	1	4	yes	—
81	C₃₁×#432	C₂²	1	2	yes	—
82	C₃₁×#431	C₂²	1	2	yes	—
83	C₃₁×#428	C₂²	1	2	yes	—
84	C₃₁×#428	C₂²	1	2	yes	—
85	C₃₁×#427	C₂²	1	2	yes	—
86	C₂×C₃₁×#107	C₂²	1	2	yes	—
87	C₃₁×#423	C₂²	1	1	yes	characteristic
88	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₃₁×#419	C₂²	1	2	yes	—
90	C₃₁×#417	C₂²	1	2	yes	—
91	C₃₁×#416	C₂²	1	2	yes	—
92	C₂×C₃₁×#103	C₂²	1	2	yes	—
93	C₃₁×#408	C₂²	1	2	yes	—
94	C₃₁×#405	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	—	2	1	no	—
98	C₂²×Q₈×C₃₁	—	2	2	no	—
99	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
102	C₃₁×C₄⋊Q₈	—	2	1	no	—
103	C₃₁×C₄⋊Q₈	—	2	1	no	—
104	C₃₁×C₄⋊Q₈	—	2	4	no	—
105	C₃₁×C₄⋊Q₈	—	2	2	no	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#126	—	2	2	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	—	2	1	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	—	2	4	no	—
126	C₃₁×#125	—	2	2	no	—
127	C₃₁×#125	C₂³	1	2	yes	—
128	C₃₁×#125	C₂³	1	4	yes	—
129	C₃₁×#125	C₂³	1	2	yes	—
130	C₃₁×#124	—	2	1	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	C₂³	1	2	yes	—
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	1	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	1	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	1	no	—
144	C₃₁×C₂²⋊Q₈	—	2	1	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	4	no	—
148	C₃₁×C₂²⋊Q₈	—	2	4	no	—
149	C₃₁×C₂²⋊Q₈	—	2	4	no	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×#121	—	2	2	no	—
154	C₃₁×#121	—	2	1	no	—
155	C₃₁×#121	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	—	2	2	no	—
157	C₄×Q₈×C₃₁	—	2	1	no	—
158	C₄×Q₈×C₃₁	—	2	1	no	—
159	C₄×Q₈×C₃₁	—	2	2	no	—
160	C₄×Q₈×C₃₁	—	2	1	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	2	no	—
164	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×D₄×C₃₁	—	2	4	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
176	C₄×D₄×C₃₁	D₄	1	2	yes	—
177	C₄×D₄×C₃₁	D₄	1	2	yes	—
178	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
179	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₃₁×#117	—	2	2	no	—
182	C₃₁×#117	—	2	1	no	—
183	C₃₁×#117	—	2	2	no	—
184	C₃₁×#117	C₂³	1	2	yes	—
185	C₃₁×#117	C₂³	1	1	yes	characteristic
186	C₃₁×#117	C₂³	1	4	yes	—
187	C₃₁×#117	C₂³	1	1	yes	characteristic
188	C₃₁×#117	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
190	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
195	C₂×C₄²×C₃₁	—	2	1	no	—
196	C₂×C₄²×C₃₁	—	2	1	no	—
197	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₃₁×#107	C₂³	1	4	yes	—
200	C₃₁×#107	C₂³	1	4	yes	—
201	C₃₁×#107	C₂³	1	2	yes	—
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₃₁×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	#41×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	2	2	no	—
230	#41×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	2	no	—
232	C₂×Q₈×C₃₁	—	2	1	no	—
233	C₂×Q₈×C₃₁	—	2	1	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	4	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	8	2	no	—
242	C₂×Q₈×C₃₁	—	8	4	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₃₁	—	2	1	no	—
252	C₂²×C₄×C₃₁	—	2	1	no	—
253	C₂²×C₄×C₃₁	—	2	4	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	1	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	1	no	—
258	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	M₁₆×C₃₁	—	2	4	no	—
265	C₂×C₈×C₃₁	—	2	4	no	—
266	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
267	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
268	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	2	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	1	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	4	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²⋊C₄×C₃₁	—	2	2	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	1	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	1	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
317	C₄²×C₃₁	—	2	2	no	—
318	C₄²×C₃₁	—	2	1	no	—
319	C₄²×C₃₁	—	2	1	no	—
320	C₄²×C₃₁	—	2	1	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	4	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₃₁	C₂×D₄	1	2	yes	—
326	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₃₁	C₂×D₄	1	2	yes	—
328	C₄²×C₃₁	C₂⁴	1	2	yes	—
329	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
331	#60893	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂³×C₃₁	—	2	1	no	—
333	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₃₁	—	2	2	no	—
336	Q₈×C₃₁	—	2	2	no	—
337	Q₈×C₃₁	—	2	2	no	—
338	Q₈×C₃₁	—	2	1	no	—
339	Q₈×C₃₁	—	2	1	no	—
340	Q₈×C₃₁	—	4	4	no	—
341	Q₈×C₃₁	—	4	2	no	—
342	Q₈×C₃₁	—	4	2	no	—
343	Q₈×C₃₁	—	4	2	no	—
344	Q₈×C₃₁	—	8	2	no	—
345	Q₈×C₃₁	—	8	2	no	—
346	Q₈×C₃₁	—	8	4	no	—
347	D₄×C₃₁	—	2	4	no	—
348	D₄×C₃₁	—	2	2	no	—
349	D₄×C₃₁	—	2	1	no	—
350	D₄×C₃₁	—	2	1	no	—
351	D₄×C₃₁	—	4	2	no	—
352	D₄×C₃₁	—	8	2	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	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	1	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	1	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	4	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	4	1	no	—
366	C₂×C₄×C₃₁	—	4	2	no	—
367	C₂×C₄×C₃₁	—	4	2	no	—
368	C₂×C₄×C₃₁	—	4	2	no	—
369	C₂×C₄×C₃₁	—	4	2	no	—
370	C₂×C₄×C₃₁	—	8	1	no	—
371	C₂×C₄×C₃₁	—	8	1	no	—
372	C₂×C₄×C₃₁	—	8	2	no	—
373	C₂×C₄×C₃₁	—	8	4	no	—
374	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
383	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
384	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
385	C₈×C₃₁	—	2	2	no	—
386	C₈×C₃₁	—	2	2	no	—
387	C₈×C₃₁	—	2	4	no	—
388	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3461	C₂×C₃₁	1	1	yes	characteristic
390	#3243	C₂×C₃₁	1	4	yes	complemented
391	#3242	C₂×C₃₁	1	4	yes	complemented
392	#3238	C₂×C₃₁	1	2	yes	complemented
393	#3237	C₂×C₃₁	1	2	yes	complemented
394	#3233	C₂×C₃₁	1	2	yes	complemented
395	#3230	C₂×C₃₁	1	2	yes	complemented
396	#3164	C₂×C₃₁	1	2	yes	complemented
397	#3137	C₂×C₃₁	1	2	yes	complemented
398	#3098	C₂×C₃₁	1	2	yes	—
399	#3097	C₂×C₃₁	1	2	yes	complemented
400	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
402	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
403	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
405	C₂²×C₃₁	—	2	1	no	—
406	C₂²×C₃₁	—	2	1	no	—
407	C₂²×C₃₁	—	2	2	no	—
408	C₂²×C₃₁	—	2	2	no	—
409	C₂²×C₃₁	—	2	2	no	—
410	C₂²×C₃₁	—	4	1	no	—
411	C₂²×C₃₁	—	4	1	no	—
412	C₂²×C₃₁	—	4	1	no	—
413	C₂²×C₃₁	#536	1	2	yes	—
414	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₃₁	—	2	1	no	—
416	C₄×C₃₁	—	2	1	no	—
417	C₄×C₃₁	—	2	2	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	2	1	no	—
420	C₄×C₃₁	—	2	2	no	—
421	C₄×C₃₁	—	4	4	no	—
422	C₄×C₃₁	—	4	2	no	—
423	C₄×C₃₁	—	4	2	no	—
424	C₄×C₃₁	—	4	1	no	—
425	C₄×C₃₁	—	4	1	no	—
426	C₄×C₃₁	—	4	2	no	—
427	C₄×C₃₁	—	4	1	no	—
428	C₄×C₃₁	—	4	2	no	—
429	C₄×C₃₁	#536	1	2	yes	—
430	C₄×C₃₁	#578	1	2	yes	—
431	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	Q₈²	—	2	1	no	—
434	#557	—	2	1	no	—
435	#554	—	2	2	no	—
436	#554	—	2	1	no	—
437	D₄×Q₈	—	2	2	no	—
438	D₄×Q₈	—	2	1	no	—
439	#544	C₂²×C₃₁	1	2	yes	—
440	#544	C₂²×C₃₁	1	1	yes	characteristic
441	#544	C₂²×C₃₁	1	4	yes	—
442	#542	—	2	1	no	—
443	#542	C₂²×C₃₁	1	2	yes	—
444	#541	—	2	1	no	—
445	#541	C₂²×C₃₁	1	2	yes	—
446	#539	—	2	2	no	—
447	#537	C₂²×C₃₁	1	1	yes	characteristic
448	#536	C₂²×C₃₁	1	1	yes	characteristic
449	#536	C₂²×C₃₁	1	1	yes	characteristic
450	#533	—	2	1	no	—
451	#533	C₂²×C₃₁	1	2	yes	—
452	#533	C₂²×C₃₁	1	1	yes	characteristic
453	#533	C₂²×C₃₁	1	2	yes	—
454	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
455	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
456	#529	—	2	2	no	—
457	#529	—	2	1	no	—
458	#529	C₂²×C₃₁	1	2	yes	—
459	#520	C₂²×C₃₁	1	2	yes	—
460	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
461	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
463	#501	C₂²×C₃₁	1	4	yes	—
464	#501	C₂²×C₃₁	1	4	yes	—
465	#500	C₂²×C₃₁	1	4	yes	—
466	#499	C₂²×C₃₁	1	4	yes	—
467	#491	C₂²×C₃₁	1	4	yes	—
468	#489	C₂²×C₃₁	1	4	yes	—
469	#488	C₂²×C₃₁	1	4	yes	—
470	#487	C₂²×C₃₁	1	4	yes	—
471	#485	C₂²×C₃₁	1	4	yes	—
472	#485	C₂²×C₃₁	1	4	yes	—
473	#485	C₂²×C₃₁	1	4	yes	—
474	#484	C₂²×C₃₁	1	4	yes	—
475	#484	C₂²×C₃₁	1	4	yes	—
476	#483	C₂²×C₃₁	1	4	yes	—
477	#482	C₂²×C₃₁	1	4	yes	—
478	#480	C₂²×C₃₁	1	4	yes	—
479	#479	C₂²×C₃₁	1	2	yes	—
480	#479	C₂²×C₃₁	1	4	yes	—
481	#478	C₂²×C₃₁	1	2	yes	—
482	#477	C₂²×C₃₁	1	2	yes	—
483	#477	C₂²×C₃₁	1	2	yes	—
484	#477	C₂²×C₃₁	1	4	yes	—
485	#477	C₂²×C₃₁	1	1	yes	characteristic
486	#477	C₂²×C₃₁	1	2	yes	—
487	#477	C₂²×C₃₁	1	2	yes	—
488	#476	C₂²×C₃₁	1	1	yes	characteristic
489	#476	C₂²×C₃₁	1	2	yes	—
490	#475	C₂²×C₃₁	1	1	yes	characteristic
491	#475	C₂²×C₃₁	1	2	yes	—
492	#475	C₂²×C₃₁	1	2	yes	—
493	#474	C₂²×C₃₁	1	1	yes	characteristic
494	#474	C₂²×C₃₁	1	2	yes	—
495	#433	C₂²×C₃₁	1	4	yes	—
496	#432	C₂²×C₃₁	1	2	yes	—
497	#431	C₂²×C₃₁	1	2	yes	—
498	#428	C₂²×C₃₁	1	2	yes	—
499	#428	C₂²×C₃₁	1	2	yes	—
500	#427	C₂²×C₃₁	1	2	yes	—
501	C₂×#107	C₂²×C₃₁	1	2	yes	—
502	#423	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
504	#419	C₂²×C₃₁	1	2	yes	—
505	#417	C₂²×C₃₁	1	2	yes	—
506	#416	C₂²×C₃₁	1	2	yes	—
507	C₂×#103	C₂²×C₃₁	1	2	yes	—
508	#408	C₂²×C₃₁	1	2	yes	—
509	#405	C₂²×C₃₁	1	2	yes	—
510	C₂×C₃₁	—	2	2	no	—
511	C₂×C₃₁	—	4	2	no	—
512	C₂×C₃₁	—	8	1	no	—
513	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
514	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
515	C₂×C₃₁	#3585	1	1	yes	characteristic
516	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
517	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	—	2	2	no	—
520	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
522	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	4	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
536	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	1	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	4	no	—
547	#125	—	2	2	no	—
548	#125	C₂³×C₃₁	1	2	yes	—
549	#125	C₂³×C₃₁	1	2	yes	—
550	#125	C₂³×C₃₁	1	4	yes	—
551	#124	—	2	1	no	—
552	#124	—	2	2	no	—
553	#124	C₂³×C₃₁	1	2	yes	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
574	#121	—	2	2	no	—
575	#121	—	2	1	no	—
576	#121	C₂³×C₃₁	1	2	yes	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
588	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
589	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
597	C₄×D₄	D₄×C₃₁	1	2	yes	—
598	C₄×D₄	D₄×C₃₁	1	2	yes	—
599	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
602	#117	—	2	2	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	#117	C₂³×C₃₁	1	1	yes	characteristic
606	#117	C₂³×C₃₁	1	2	yes	—
607	#117	C₂³×C₃₁	1	4	yes	—
608	#117	C₂³×C₃₁	1	1	yes	characteristic
609	#117	C₂³×C₃₁	1	2	yes	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
620	#107	C₂³×C₃₁	1	4	yes	—
621	#107	C₂³×C₃₁	1	4	yes	—
622	#107	C₂³×C₃₁	1	2	yes	—
623	#107	C₂³×C₃₁	1	2	yes	—
624	#107	C₂³×C₃₁	1	4	yes	—
625	#107	C₂³×C₃₁	1	4	yes	—
626	#106	C₂³×C₃₁	1	2	yes	—
627	#106	C₂³×C₃₁	1	2	yes	—
628	#106	C₂³×C₃₁	1	4	yes	—
629	#106	C₂³×C₃₁	1	4	yes	—
630	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
631	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
632	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
633	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
634	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
635	#103	C₂³×C₃₁	1	4	yes	—
636	#103	C₂³×C₃₁	1	4	yes	—
637	#103	C₂³×C₃₁	1	2	yes	—
638	#103	C₂³×C₃₁	1	2	yes	—
639	#103	C₂³×C₃₁	1	4	yes	—
640	#103	C₂³×C₃₁	1	4	yes	—
641	#103	C₂³×C₃₁	1	4	yes	—
642	#102	C₂³×C₃₁	1	2	yes	—
643	#102	C₂³×C₃₁	1	2	yes	—
644	#102	C₂³×C₃₁	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
647	#97	C₂³×C₃₁	1	4	yes	—
648	C₄×C₈	C₂³×C₃₁	1	4	yes	—
649	C₃₁	#60893	1	1	yes	characteristic, direct product factor, Sylow
650	#41	—	2	2	no	—
651	#41	—	2	2	no	—
652	#41	—	2	2	no	—
653	#41	—	2	2	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	8	2	no	—
664	C₂×Q₈	—	8	4	no	—
665	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
666	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
672	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
686	M₁₆	—	2	4	no	—
687	C₂×C₈	—	2	4	no	—
688	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
689	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
690	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
722	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
737	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
738	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	2	no	—
746	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₃₁	1	2	yes	—
748	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₃₁	1	2	yes	—
750	C₄²	C₂⁴×C₃₁	1	2	yes	—
751	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₂³	—	2	1	no	—
754	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
755	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	4	4	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	4	2	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	2	no	—
767	Q₈	—	8	4	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	1	no	—
792	C₂×C₄	—	8	1	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	—	8	4	no	—
795	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
803	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
804	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
805	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	2	4	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₃₁×#536	1	2	yes	—
818	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
819	C₄	—	2	2	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	4	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	1	no	—
833	C₄	C₃₁×#536	1	2	yes	—
834	C₄	C₃₁×#578	1	2	yes	—
835	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
836	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
837	C₂	—	2	2	no	—
838	C₂	—	4	2	no	—
839	C₂	—	8	1	no	—
840	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
841	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
842	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3243	C₂	semidirect
4. C₃₁×#3242	C₂	semidirect
5. C₃₁×#3238	C₂	semidirect
6. C₃₁×#3237	C₂	semidirect
7. C₃₁×#3233	C₂	semidirect
8. C₃₁×#3230	C₂	semidirect
9. C₃₁×#3164	C₂	semidirect
10. C₃₁×#3137	C₂	semidirect
12. C₃₁×#3097	C₂	semidirect
13. C₃₁×#3079	C₂	semidirect
14. C₃₁×#3078	C₂	semidirect
15. C₃₁×#3076	C₂	semidirect
16. C₂×C₃₁×#477	C₂	semidirect
17. C₃₁×#2925	C₂	semidirect
331. #60893	C₃₁	direct (N × H)
388. #3503	C₂×C₃₁	semidirect
390. #3243	C₂×C₃₁	semidirect
391. #3242	C₂×C₃₁	semidirect
392. #3238	C₂×C₃₁	semidirect
393. #3237	C₂×C₃₁	semidirect
394. #3233	C₂×C₃₁	semidirect
395. #3230	C₂×C₃₁	semidirect
396. #3164	C₂×C₃₁	semidirect
397. #3137	C₂×C₃₁	semidirect
399. #3097	C₂×C₃₁	semidirect
400. #3079	C₂×C₃₁	semidirect
401. #3078	C₂×C₃₁	semidirect
402. #3076	C₂×C₃₁	semidirect
403. C₂×#477	C₂×C₃₁	semidirect
404. #2925	C₂×C₃₁	semidirect
649. C₃₁	#60893	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×#3503	2
C₃₁×#3461	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3238	2
C₃₁×#3237	2
C₃₁×#3233	2
C₃₁×#3230	2
C₃₁×#3164	2
C₃₁×#3137	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3079	2
C₃₁×#3078	2
C₃₁×#3076	2
C₂×C₃₁×#477	2
C₃₁×#2925	2
#60893	31

Subgroups — C31×#60893 #21517652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60893 #21517652