Subgroups — C₃₁×#60579 #21517338

Order 7936.

2214 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3123	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3118	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3110	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3105	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3101	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3042	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3003	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2949	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#554	—	2	1	no	—
23	C₃₁×#552	—	2	2	no	—
24	C₃₁×#552	—	2	1	no	—
25	C₃₁×#552	—	2	1	no	—
26	C₃₁×#551	—	2	2	no	—
27	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#542	C₂²	1	2	yes	complemented
29	C₃₁×#541	C₂²	1	2	yes	complemented
30	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#533	C₂²	1	2	yes	complemented
32	C₃₁×#529	C₂²	1	2	yes	complemented
33	C₃₁×#525	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#518	—	2	2	no	—
38	C₃₁×#518	—	2	1	no	—
39	C₃₁×#518	—	2	1	no	—
40	C₃₁×#518	C₂²	1	2	yes	—
41	C₃₁×#518	C₂²	1	4	yes	—
42	C₃₁×#518	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₃₁	—	2	1	no	—
44	C₂×C₄×D₄×C₃₁	—	2	1	no	—
45	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
47	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₃₁	—	2	2	no	—
50	C₃₁×#485	C₂²	1	2	yes	complemented
51	C₃₁×#485	C₂²	1	4	yes	complemented
52	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#484	C₂²	1	2	yes	complemented
54	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#483	C₂²	1	2	yes	complemented
56	C₃₁×#482	C₂²	1	2	yes	complemented
57	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#478	C₂²	1	4	yes	complemented
60	C₃₁×#478	C₂²	1	4	yes	complemented
61	C₃₁×#476	C₂²	1	4	yes	complemented
62	C₃₁×#474	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#461	C₂²	1	4	yes	complemented
66	C₃₁×#461	C₂²	1	4	yes	complemented
67	C₃₁×#450	C₂²	1	2	yes	—
68	C₃₁×#450	C₂²	1	2	yes	—
69	C₃₁×#450	C₂²	1	2	yes	—
70	C₃₁×#450	C₂²	1	4	yes	—
71	C₃₁×#450	C₂²	1	2	yes	—
72	C₃₁×#447	C₂²	1	2	yes	—
73	C₃₁×#447	C₂²	1	2	yes	—
74	C₃₁×#442	C₂²	1	4	yes	complemented
75	C₃₁×#440	C₂²	1	4	yes	complemented
76	C₃₁×#440	C₂²	1	4	yes	complemented
77	C₃₁×#440	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
81	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
82	C₃₁×#433	C₂²	1	4	yes	complemented
83	C₃₁×#432	C₂²	1	2	yes	complemented
84	C₃₁×#431	C₂²	1	2	yes	complemented
85	C₃₁×#428	C₂²	1	2	yes	complemented
86	C₃₁×#427	C₂²	1	2	yes	complemented
87	C₃₁×#424	C₂²	1	2	yes	complemented
88	C₃₁×#419	C₂²	1	2	yes	complemented
89	C₃₁×#418	C₂²	1	2	yes	—
90	C₃₁×#416	C₂²	1	2	yes	complemented
91	C₂×C₃₁×#102	C₂²	1	2	yes	—
92	C₃₁×#407	C₂²	1	1	yes	characteristic
93	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₃₁×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₃₁	—	2	8	no	—
99	C₂²×D₄×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
104	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
105	C₂³×C₄×C₃₁	—	2	2	no	—
106	C₂³×C₄×C₃₁	—	2	2	no	—
107	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
109	C₂×SD₁₆×C₃₁	—	2	8	no	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
113	C₂×D₈×C₃₁	C₂³	1	4	yes	—
114	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
115	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
118	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#126	—	2	2	no	—
121	C₃₁×#126	—	2	2	no	—
122	C₃₁×#126	—	2	2	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	—	2	1	no	—
126	C₃₁×#125	—	2	2	no	—
127	C₃₁×#125	C₂³	1	2	yes	complemented
128	C₃₁×#124	—	2	2	no	—
129	C₃₁×#124	C₂³	1	2	yes	complemented
130	C₃₁×#123	—	2	1	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	1	no	—
138	C₃₁×C₂²⋊Q₈	—	2	1	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
145	C₃₁×#121	C₂³	1	1	yes	characteristic
146	C₃₁×#121	C₂³	1	1	yes	characteristic
147	C₃₁×#120	—	2	1	no	—
148	C₄×Q₈×C₃₁	—	2	1	no	—
149	C₄×Q₈×C₃₁	—	2	1	no	—
150	C₄×Q₈×C₃₁	—	2	2	no	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
152	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
153	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
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	4	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	4	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	C₂³	1	4	yes	—
169	C₄×D₄×C₃₁	C₂³	1	4	yes	—
170	C₄×D₄×C₃₁	C₂³	1	4	yes	—
171	C₄×D₄×C₃₁	C₂³	1	4	yes	—
172	C₄×D₄×C₃₁	C₂³	1	2	yes	complemented
173	C₃₁×#117	—	2	1	no	—
174	C₃₁×#117	—	2	1	no	—
175	C₃₁×#117	—	2	2	no	—
176	C₃₁×#117	—	2	1	no	—
177	C₃₁×#117	—	2	2	no	—
178	C₃₁×#117	—	2	2	no	—
179	C₃₁×#117	D₄	1	1	yes	characteristic
180	C₃₁×#117	D₄	1	2	yes	—
181	C₃₁×#117	D₄	1	1	yes	characteristic
182	C₃₁×#117	C₂³	1	2	yes	—
183	C₃₁×#117	C₂³	1	1	yes	characteristic
184	C₃₁×#117	C₂³	1	2	yes	—
185	C₃₁×#117	C₂³	1	1	yes	characteristic
186	C₃₁×#117	C₂³	1	1	yes	characteristic
187	C₃₁×#117	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
189	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
190	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
201	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
202	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
203	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
206	C₃₁×#107	C₂³	1	2	yes	complemented
207	C₃₁×#107	C₂³	1	2	yes	complemented
208	C₃₁×#107	C₂³	1	4	yes	complemented
209	C₃₁×#106	C₂³	1	2	yes	complemented
210	C₃₁×#106	C₂³	1	2	yes	complemented
211	C₃₁×#106	C₂³	1	4	yes	complemented
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
213	C₃₁×C₄⋊C₈	C₂³	1	4	yes	complemented
214	C₃₁×#103	C₂³	1	2	yes	complemented
215	C₃₁×#103	C₂³	1	2	yes	complemented
216	C₃₁×#103	C₂³	1	4	yes	complemented
217	C₃₁×#103	C₂³	1	4	yes	complemented
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	2	yes	complemented
223	C₃₁×#102	C₂³	1	2	yes	complemented
224	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₃₁×#97	C₂³	1	4	yes	complemented
230	C₄×C₈×C₃₁	C₂³	1	4	yes	complemented
231	C₂⁴×C₃₁	—	2	8	no	—
232	C₂⁴×C₃₁	—	2	2	no	—
233	C₂⁴×C₃₁	—	2	2	no	—
234	C₂⁴×C₃₁	—	2	2	no	—
235	C₂⁴×C₃₁	—	8	2	no	—
236	C₂⁴×C₃₁	—	8	2	no	—
237	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
238	#41×C₃₁	—	2	4	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₃₁	—	2	8	no	—
245	C₂×D₄×C₃₁	—	2	8	no	—
246	C₂×D₄×C₃₁	—	2	8	no	—
247	C₂×D₄×C₃₁	—	2	8	no	—
248	C₂×D₄×C₃₁	—	2	8	no	—
249	C₂×D₄×C₃₁	—	2	1	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	4	no	—
256	C₂×D₄×C₃₁	#41	1	8	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	2	1	no	—
261	C₂²×C₄×C₃₁	—	2	1	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	4	no	—
266	C₂²×C₄×C₃₁	—	2	4	no	—
267	C₂²×C₄×C₃₁	—	2	4	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	8	4	no	—
271	C₂²×C₄×C₃₁	—	8	4	no	—
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	SD₁₆×C₃₁	—	2	8	no	—
281	SD₁₆×C₃₁	—	2	8	no	—
282	SD₁₆×C₃₁	—	2	8	no	—
283	D₈×C₃₁	—	2	8	no	—
284	M₁₆×C₃₁	—	2	4	no	—
285	C₂×C₈×C₃₁	—	2	4	no	—
286	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
288	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	1	no	—
320	C₂²⋊C₄×C₃₁	—	2	1	no	—
321	C₂²⋊C₄×C₃₁	—	2	1	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	—	2	1	no	—
327	C₂²⋊C₄×C₃₁	—	2	2	no	—
328	C₂²⋊C₄×C₃₁	—	2	2	no	—
329	C₂²⋊C₄×C₃₁	—	2	1	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	—	2	2	no	—
338	C₄²×C₃₁	—	2	2	no	—
339	C₄²×C₃₁	—	2	2	no	—
340	C₄²×C₃₁	—	2	1	no	—
341	C₄²×C₃₁	C₂×D₄	1	2	yes	—
342	C₄²×C₃₁	C₂×D₄	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	2	yes	—
344	C₄²×C₃₁	C₂⁴	1	2	yes	—
345	#60579	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂³×C₃₁	—	2	8	no	—
347	C₂³×C₃₁	—	2	8	no	—
348	C₂³×C₃₁	—	2	2	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	4	no	—
351	C₂³×C₃₁	—	2	8	no	—
352	C₂³×C₃₁	—	2	1	no	—
353	C₂³×C₃₁	—	4	1	no	—
354	C₂³×C₃₁	—	4	4	no	—
355	C₂³×C₃₁	—	4	4	no	—
356	C₂³×C₃₁	—	8	2	no	—
357	C₂³×C₃₁	—	8	2	no	—
358	C₂³×C₃₁	—	8	2	no	—
359	C₂³×C₃₁	—	8	2	no	—
360	C₂³×C₃₁	—	8	16	no	—
361	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
362	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₃₁	—	2	4	no	—
365	Q₈×C₃₁	—	2	2	no	—
366	Q₈×C₃₁	—	4	2	no	—
367	Q₈×C₃₁	—	8	2	no	—
368	D₄×C₃₁	—	2	8	no	—
369	D₄×C₃₁	—	2	8	no	—
370	D₄×C₃₁	—	2	8	no	—
371	D₄×C₃₁	—	2	4	no	—
372	D₄×C₃₁	—	2	2	no	—
373	D₄×C₃₁	—	4	2	no	—
374	D₄×C₃₁	—	4	2	no	—
375	D₄×C₃₁	—	8	1	no	—
376	D₄×C₃₁	C₂×#41	1	8	yes	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	4	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	—	4	2	no	—
393	C₂×C₄×C₃₁	—	4	2	no	—
394	C₂×C₄×C₃₁	—	4	2	no	—
395	C₂×C₄×C₃₁	—	8	2	no	—
396	C₂×C₄×C₃₁	—	8	4	no	—
397	C₂×C₄×C₃₁	—	8	4	no	—
398	C₂×C₄×C₃₁	—	8	4	no	—
399	C₂×C₄×C₃₁	—	8	4	no	—
400	C₂×C₄×C₃₁	—	8	1	no	—
401	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
409	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
410	C₈×C₃₁	—	2	2	no	—
411	C₈×C₃₁	—	2	2	no	—
412	C₈×C₃₁	—	2	4	no	—
413	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
414	C₂×#518	C₂×C₃₁	1	1	yes	characteristic, complemented
415	#3123	C₂×C₃₁	1	4	yes	complemented
416	#3118	C₂×C₃₁	1	4	yes	complemented
417	#3114	C₂×C₃₁	1	2	yes	complemented
418	#3110	C₂×C₃₁	1	2	yes	complemented
419	#3105	C₂×C₃₁	1	2	yes	complemented
420	#3101	C₂×C₃₁	1	2	yes	complemented
421	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
423	#3081	C₂×C₃₁	1	2	yes	complemented
424	#3042	C₂×C₃₁	1	2	yes	complemented
425	#3003	C₂×C₃₁	1	1	yes	characteristic
426	C₂×#450	C₂×C₃₁	1	1	yes	characteristic, complemented
427	#2949	C₂×C₃₁	1	2	yes	complemented
428	#2946	C₂×C₃₁	1	2	yes	complemented
429	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
430	C₂²×C₃₁	—	2	1	no	—
431	C₂²×C₃₁	—	2	1	no	—
432	C₂²×C₃₁	—	2	1	no	—
433	C₂²×C₃₁	—	2	1	no	—
434	C₂²×C₃₁	—	2	1	no	—
435	C₂²×C₃₁	—	2	1	no	—
436	C₂²×C₃₁	—	2	8	no	—
437	C₂²×C₃₁	—	2	1	no	—
438	C₂²×C₃₁	—	4	4	no	—
439	C₂²×C₃₁	—	4	16	no	—
440	C₂²×C₃₁	—	4	4	no	—
441	C₂²×C₃₁	—	4	4	no	—
442	C₂²×C₃₁	—	4	1	no	—
443	C₂²×C₃₁	—	4	1	no	—
444	C₂²×C₃₁	—	4	1	no	—
445	C₂²×C₃₁	—	8	8	no	—
446	C₂²×C₃₁	—	8	8	no	—
447	C₂²×C₃₁	#525	1	2	yes	—
448	C₂²×C₃₁	#577	1	2	yes	—
449	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
450	C₄×C₃₁	—	2	2	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	1	no	—
453	C₄×C₃₁	—	2	1	no	—
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	2	2	no	—
456	C₄×C₃₁	—	4	2	no	—
457	C₄×C₃₁	—	4	2	no	—
458	C₄×C₃₁	—	4	1	no	—
459	C₄×C₃₁	—	4	1	no	—
460	C₄×C₃₁	—	4	2	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	—	4	1	no	—
463	C₄×C₃₁	#525	1	2	yes	—
464	C₄×C₃₁	C₂²×#41	1	2	yes	—
465	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
466	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
467	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
468	#556	—	2	1	no	—
469	#554	—	2	1	no	—
470	#552	—	2	2	no	—
471	#552	—	2	1	no	—
472	#552	—	2	1	no	—
473	#551	—	2	2	no	—
474	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	#542	C₂²×C₃₁	1	2	yes	complemented
476	#541	C₂²×C₃₁	1	2	yes	complemented
477	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
478	#533	C₂²×C₃₁	1	2	yes	complemented
479	#529	C₂²×C₃₁	1	2	yes	complemented
480	#525	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
482	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
483	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
484	#518	—	2	2	no	—
485	#518	—	2	1	no	—
486	#518	—	2	1	no	—
487	#518	C₂²×C₃₁	1	2	yes	—
488	#518	C₂²×C₃₁	1	4	yes	—
489	#518	C₂²×C₃₁	1	2	yes	—
490	C₂×C₄×D₄	—	2	1	no	—
491	C₂×C₄×D₄	—	2	1	no	—
492	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
493	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
494	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
495	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
496	C₂²×C₂²⋊C₄	—	2	2	no	—
497	#485	C₂²×C₃₁	1	2	yes	complemented
498	#485	C₂²×C₃₁	1	4	yes	complemented
499	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#484	C₂²×C₃₁	1	2	yes	complemented
501	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
502	#483	C₂²×C₃₁	1	2	yes	complemented
503	#482	C₂²×C₃₁	1	2	yes	complemented
504	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
505	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
506	#478	C₂²×C₃₁	1	4	yes	complemented
507	#478	C₂²×C₃₁	1	4	yes	complemented
508	#476	C₂²×C₃₁	1	4	yes	complemented
509	#474	C₂²×C₃₁	1	4	yes	complemented
510	#463	C₂²×C₃₁	1	4	yes	complemented
511	#463	C₂²×C₃₁	1	4	yes	complemented
512	#461	C₂²×C₃₁	1	4	yes	complemented
513	#461	C₂²×C₃₁	1	4	yes	complemented
514	#450	C₂²×C₃₁	1	2	yes	—
515	#450	C₂²×C₃₁	1	2	yes	—
516	#450	C₂²×C₃₁	1	2	yes	—
517	#450	C₂²×C₃₁	1	4	yes	—
518	#450	C₂²×C₃₁	1	2	yes	—
519	#447	C₂²×C₃₁	1	2	yes	—
520	#447	C₂²×C₃₁	1	2	yes	—
521	#442	C₂²×C₃₁	1	4	yes	complemented
522	#440	C₂²×C₃₁	1	4	yes	complemented
523	#440	C₂²×C₃₁	1	4	yes	complemented
524	#440	C₂²×C₃₁	1	4	yes	complemented
525	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
526	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
527	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
528	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
529	#433	C₂²×C₃₁	1	4	yes	complemented
530	#432	C₂²×C₃₁	1	2	yes	complemented
531	#431	C₂²×C₃₁	1	2	yes	complemented
532	#428	C₂²×C₃₁	1	2	yes	complemented
533	#427	C₂²×C₃₁	1	2	yes	complemented
534	#424	C₂²×C₃₁	1	2	yes	complemented
535	#419	C₂²×C₃₁	1	2	yes	complemented
536	#418	C₂²×C₃₁	1	2	yes	—
537	#416	C₂²×C₃₁	1	2	yes	complemented
538	C₂×#102	C₂²×C₃₁	1	2	yes	—
539	#407	C₂²×C₃₁	1	1	yes	characteristic
540	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
541	#405	C₂²×C₃₁	1	2	yes	complemented
542	C₂×C₃₁	—	2	2	no	—
543	C₂×C₃₁	—	2	2	no	—
544	C₂×C₃₁	—	4	1	no	—
545	C₂×C₃₁	—	4	8	no	—
546	C₂×C₃₁	—	8	1	no	—
547	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
548	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
549	C₂×C₃₁	#3585	1	1	yes	characteristic
550	C₂⁵	—	2	1	no	—
551	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
553	C₂²×D₄	—	2	8	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
558	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
559	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
560	C₂³×C₄	—	2	2	no	—
561	C₂³×C₄	—	2	2	no	—
562	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
563	AGL(1,ℤ/8)	—	2	8	no	—
564	C₂×SD₁₆	—	2	8	no	—
565	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
568	C₂×D₈	C₂³×C₃₁	1	4	yes	—
569	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
570	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
573	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
574	#126	—	2	2	no	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#125	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	—	2	1	no	—
581	#125	—	2	2	no	—
582	#125	C₂³×C₃₁	1	2	yes	complemented
583	#124	—	2	2	no	—
584	#124	C₂³×C₃₁	1	2	yes	complemented
585	#123	—	2	1	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	C₂²⋊Q₈	—	2	1	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	#121	C₂³×C₃₁	1	1	yes	characteristic
601	#121	C₂³×C₃₁	1	1	yes	characteristic
602	#120	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
607	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
608	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	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	4	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	4	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	C₂³×C₃₁	1	4	yes	—
624	C₄×D₄	C₂³×C₃₁	1	4	yes	—
625	C₄×D₄	C₂³×C₃₁	1	4	yes	—
626	C₄×D₄	C₂³×C₃₁	1	4	yes	—
627	C₄×D₄	C₂³×C₃₁	1	2	yes	complemented
628	#117	—	2	1	no	—
629	#117	—	2	1	no	—
630	#117	—	2	2	no	—
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	D₄×C₃₁	1	1	yes	characteristic
635	#117	D₄×C₃₁	1	2	yes	—
636	#117	D₄×C₃₁	1	1	yes	characteristic
637	#117	C₂³×C₃₁	1	2	yes	—
638	#117	C₂³×C₃₁	1	2	yes	—
639	#117	C₂³×C₃₁	1	1	yes	characteristic
640	#117	C₂³×C₃₁	1	1	yes	characteristic
641	#117	C₂³×C₃₁	1	1	yes	characteristic
642	#117	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	—	2	4	no	—
655	C₂×C₂²⋊C₄	—	2	4	no	—
656	C₂×C₂²⋊C₄	—	2	4	no	—
657	C₂×C₂²⋊C₄	—	2	4	no	—
658	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
661	#107	C₂³×C₃₁	1	2	yes	complemented
662	#107	C₂³×C₃₁	1	2	yes	complemented
663	#107	C₂³×C₃₁	1	4	yes	complemented
664	#106	C₂³×C₃₁	1	2	yes	complemented
665	#106	C₂³×C₃₁	1	2	yes	complemented
666	#106	C₂³×C₃₁	1	4	yes	complemented
667	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
668	C₄⋊C₈	C₂³×C₃₁	1	4	yes	complemented
669	#103	C₂³×C₃₁	1	2	yes	complemented
670	#103	C₂³×C₃₁	1	2	yes	complemented
671	#103	C₂³×C₃₁	1	4	yes	complemented
672	#103	C₂³×C₃₁	1	4	yes	complemented
673	#102	C₂³×C₃₁	1	4	yes	—
674	#102	C₂³×C₃₁	1	4	yes	—
675	#102	C₂³×C₃₁	1	4	yes	—
676	#102	C₂³×C₃₁	1	4	yes	—
677	#102	C₂³×C₃₁	1	2	yes	complemented
678	#102	C₂³×C₃₁	1	2	yes	complemented
679	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
680	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
681	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
684	#97	C₂³×C₃₁	1	4	yes	complemented
685	C₄×C₈	C₂³×C₃₁	1	4	yes	complemented
686	C₃₁	#60579	1	1	yes	characteristic, direct product factor, Sylow
687	C₂⁴	—	2	8	no	—
688	C₂⁴	—	2	2	no	—
689	C₂⁴	—	2	2	no	—
690	C₂⁴	—	2	2	no	—
691	C₂⁴	—	8	2	no	—
692	C₂⁴	—	8	2	no	—
693	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
694	#41	—	2	4	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
699	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂×D₄	—	2	8	no	—
701	C₂×D₄	—	2	8	no	—
702	C₂×D₄	—	2	8	no	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	#41×C₃₁	1	8	yes	—
713	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	8	4	no	—
727	C₂²×C₄	—	8	4	no	—
728	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
736	SD₁₆	—	2	8	no	—
737	SD₁₆	—	2	8	no	—
738	SD₁₆	—	2	8	no	—
739	D₈	—	2	8	no	—
740	M₁₆	—	2	4	no	—
741	C₂×C₈	—	2	4	no	—
742	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
743	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
744	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
762	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
764	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
765	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
768	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
769	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	1	no	—
797	C₄²	C₂×D₄×C₃₁	1	2	yes	—
798	C₄²	C₂×D₄×C₃₁	1	2	yes	—
799	C₄²	C₂⁴×C₃₁	1	2	yes	—
800	C₄²	C₂⁴×C₃₁	1	2	yes	—
801	C₂³	—	2	8	no	—
802	C₂³	—	2	8	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	8	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	4	4	no	—
811	C₂³	—	8	2	no	—
812	C₂³	—	8	2	no	—
813	C₂³	—	8	2	no	—
814	C₂³	—	8	2	no	—
815	C₂³	—	8	16	no	—
816	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
817	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	8	2	no	—
823	D₄	—	2	8	no	—
824	D₄	—	2	8	no	—
825	D₄	—	2	8	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	2	no	—
830	D₄	—	8	1	no	—
831	D₄	C₂×#41×C₃₁	1	8	yes	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	—	8	4	no	—
852	C₂×C₄	—	8	4	no	—
853	C₂×C₄	—	8	4	no	—
854	C₂×C₄	—	8	4	no	—
855	C₂×C₄	—	8	1	no	—
856	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
862	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
863	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
864	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
865	C₈	—	2	2	no	—
866	C₈	—	2	2	no	—
867	C₈	—	2	4	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	8	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	4	16	no	—
878	C₂²	—	4	4	no	—
879	C₂²	—	4	4	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	8	8	no	—
884	C₂²	—	8	8	no	—
885	C₂²	C₃₁×#525	1	2	yes	—
886	C₂²	C₃₁×#577	1	2	yes	—
887	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	C₃₁×#525	1	2	yes	—
902	C₄	C₂²×#41×C₃₁	1	2	yes	—
903	C₂	—	2	2	no	—
904	C₂	—	2	2	no	—
905	C₂	—	4	1	no	—
906	C₂	—	4	8	no	—
907	C₂	—	8	1	no	—
908	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
909	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
910	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×#3003	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₂×C₃₁×#518	C₂	semidirect
3. C₃₁×#3123	C₂	semidirect
4. C₃₁×#3118	C₂	semidirect
5. C₃₁×#3114	C₂	semidirect
6. C₃₁×#3110	C₂	semidirect
7. C₃₁×#3105	C₂	semidirect
8. C₃₁×#3101	C₂	semidirect
9. C₃₁×#3095	C₂	semidirect
10. C₃₁×#3091	C₂	semidirect
11. C₃₁×#3081	C₂	semidirect
12. C₃₁×#3042	C₂	semidirect
14. C₂×C₃₁×#450	C₂	semidirect
15. C₃₁×#2949	C₂	semidirect
16. C₃₁×#2946	C₂	semidirect
17. C₃₁×#2924	C₂	semidirect
27. C₃₁×#544	C₂²	semidirect
28. C₃₁×#542	C₂²	semidirect
29. C₃₁×#541	C₂²	semidirect
30. C₃₁×#536	C₂²	semidirect
31. C₃₁×#533	C₂²	semidirect
32. C₃₁×#529	C₂²	semidirect
35. C₃₁×#520	C₂²	semidirect
36. C₃₁×#519	C₂²	semidirect
50. C₃₁×#485	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
52. C₃₁×#484	C₂²	semidirect
53. C₃₁×#484	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
55. C₃₁×#483	C₂²	semidirect
56. C₃₁×#482	C₂²	semidirect
57. C₃₁×#481	C₂²	semidirect
58. C₃₁×#480	C₂²	semidirect
59. C₃₁×#478	C₂²	semidirect
60. C₃₁×#478	C₂²	semidirect
61. C₃₁×#476	C₂²	semidirect
62. C₃₁×#474	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#461	C₂²	semidirect
66. C₃₁×#461	C₂²	semidirect
74. C₃₁×#442	C₂²	semidirect
75. C₃₁×#440	C₂²	semidirect
76. C₃₁×#440	C₂²	semidirect
77. C₃₁×#440	C₂²	semidirect
78. C₄×SD₁₆×C₃₁	C₂²	semidirect
79. C₄×SD₁₆×C₃₁	C₂²	semidirect
80. C₄×SD₁₆×C₃₁	C₂²	semidirect
81. C₄×D₈×C₃₁	C₂²	semidirect
82. C₃₁×#433	C₂²	semidirect
83. C₃₁×#432	C₂²	semidirect
84. C₃₁×#431	C₂²	semidirect
85. C₃₁×#428	C₂²	semidirect
86. C₃₁×#427	C₂²	semidirect
87. C₃₁×#424	C₂²	semidirect
88. C₃₁×#419	C₂²	semidirect
90. C₃₁×#416	C₂²	semidirect
94. C₃₁×#405	C₂²	semidirect
117. C₃₁×C₄⋊Q₈	C₂³	semidirect
118. C₃₁×C₄⋊Q₈	C₂³	semidirect
127. C₃₁×#125	C₂³	semidirect
129. C₃₁×#124	C₂³	semidirect
151. C₄×Q₈×C₃₁	C₂³	semidirect
152. C₄×Q₈×C₃₁	C₂³	semidirect
153. C₄×Q₈×C₃₁	C₂³	semidirect
172. C₄×D₄×C₃₁	C₂³	semidirect
206. C₃₁×#107	C₂³	semidirect
207. C₃₁×#107	C₂³	semidirect
208. C₃₁×#107	C₂³	semidirect
209. C₃₁×#106	C₂³	semidirect
210. C₃₁×#106	C₂³	semidirect
211. C₃₁×#106	C₂³	semidirect
212. C₃₁×C₄⋊C₈	C₂³	semidirect
213. C₃₁×C₄⋊C₈	C₂³	semidirect
214. C₃₁×#103	C₂³	semidirect
215. C₃₁×#103	C₂³	semidirect
216. C₃₁×#103	C₂³	semidirect
217. C₃₁×#103	C₂³	semidirect
222. C₃₁×#102	C₂³	semidirect
223. C₃₁×#102	C₂³	semidirect
229. C₃₁×#97	C₂³	semidirect
230. C₄×C₈×C₃₁	C₂³	semidirect
345. #60579	C₃₁	direct (N × H)
413. #3495	C₂×C₃₁	semidirect
414. C₂×#518	C₂×C₃₁	semidirect
415. #3123	C₂×C₃₁	semidirect
416. #3118	C₂×C₃₁	semidirect
417. #3114	C₂×C₃₁	semidirect
418. #3110	C₂×C₃₁	semidirect
419. #3105	C₂×C₃₁	semidirect
420. #3101	C₂×C₃₁	semidirect
421. #3095	C₂×C₃₁	semidirect
422. #3091	C₂×C₃₁	semidirect
423. #3081	C₂×C₃₁	semidirect
424. #3042	C₂×C₃₁	semidirect
426. C₂×#450	C₂×C₃₁	semidirect
427. #2949	C₂×C₃₁	semidirect
428. #2946	C₂×C₃₁	semidirect
429. #2924	C₂×C₃₁	semidirect
474. #544	C₂²×C₃₁	semidirect
475. #542	C₂²×C₃₁	semidirect
476. #541	C₂²×C₃₁	semidirect
477. #536	C₂²×C₃₁	semidirect
478. #533	C₂²×C₃₁	semidirect
479. #529	C₂²×C₃₁	semidirect
482. #520	C₂²×C₃₁	semidirect
483. #519	C₂²×C₃₁	semidirect
497. #485	C₂²×C₃₁	semidirect
498. #485	C₂²×C₃₁	semidirect
499. #484	C₂²×C₃₁	semidirect
500. #484	C₂²×C₃₁	semidirect
501. #483	C₂²×C₃₁	semidirect
502. #483	C₂²×C₃₁	semidirect
503. #482	C₂²×C₃₁	semidirect
504. #481	C₂²×C₃₁	semidirect
505. #480	C₂²×C₃₁	semidirect
506. #478	C₂²×C₃₁	semidirect
507. #478	C₂²×C₃₁	semidirect
508. #476	C₂²×C₃₁	semidirect
509. #474	C₂²×C₃₁	semidirect
510. #463	C₂²×C₃₁	semidirect
511. #463	C₂²×C₃₁	semidirect
512. #461	C₂²×C₃₁	semidirect
513. #461	C₂²×C₃₁	semidirect
521. #442	C₂²×C₃₁	semidirect
522. #440	C₂²×C₃₁	semidirect
523. #440	C₂²×C₃₁	semidirect
524. #440	C₂²×C₃₁	semidirect
525. C₄×SD₁₆	C₂²×C₃₁	semidirect
526. C₄×SD₁₆	C₂²×C₃₁	semidirect
527. C₄×SD₁₆	C₂²×C₃₁	semidirect
528. C₄×D₈	C₂²×C₃₁	semidirect
529. #433	C₂²×C₃₁	semidirect
530. #432	C₂²×C₃₁	semidirect
531. #431	C₂²×C₃₁	semidirect
532. #428	C₂²×C₃₁	semidirect
533. #427	C₂²×C₃₁	semidirect
534. #424	C₂²×C₃₁	semidirect
535. #419	C₂²×C₃₁	semidirect
537. #416	C₂²×C₃₁	semidirect
541. #405	C₂²×C₃₁	semidirect
572. C₄⋊Q₈	C₂³×C₃₁	semidirect
573. C₄⋊Q₈	C₂³×C₃₁	semidirect
582. #125	C₂³×C₃₁	semidirect
584. #124	C₂³×C₃₁	semidirect
606. C₄×Q₈	C₂³×C₃₁	semidirect
607. C₄×Q₈	C₂³×C₃₁	semidirect
608. C₄×Q₈	C₂³×C₃₁	semidirect
627. C₄×D₄	C₂³×C₃₁	semidirect
661. #107	C₂³×C₃₁	semidirect
662. #107	C₂³×C₃₁	semidirect
663. #107	C₂³×C₃₁	semidirect
664. #106	C₂³×C₃₁	semidirect
665. #106	C₂³×C₃₁	semidirect
666. #106	C₂³×C₃₁	semidirect
667. C₄⋊C₈	C₂³×C₃₁	semidirect
668. C₄⋊C₈	C₂³×C₃₁	semidirect
669. #103	C₂³×C₃₁	semidirect
670. #103	C₂³×C₃₁	semidirect
671. #103	C₂³×C₃₁	semidirect
672. #103	C₂³×C₃₁	semidirect
677. #102	C₂³×C₃₁	semidirect
678. #102	C₂³×C₃₁	semidirect
684. #97	C₂³×C₃₁	semidirect
685. C₄×C₈	C₂³×C₃₁	semidirect
686. C₃₁	#60579	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×#3495	2
C₂×C₃₁×#518	2
C₃₁×#3123	2
C₃₁×#3118	2
C₃₁×#3114	2
C₃₁×#3110	2
C₃₁×#3105	2
C₃₁×#3101	2
C₃₁×#3095	2
C₃₁×#3091	2
C₃₁×#3081	2
C₃₁×#3042	2
C₃₁×#3003	2
C₂×C₃₁×#450	2
C₃₁×#2949	2
C₃₁×#2946	2
C₃₁×#2924	2
#60579	31

Subgroups — C31×#60579 #21517338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60579 #21517338