Subgroups — C₃₁×#61501 #21518260

Order 7936.

1800 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3521	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
22	C₃₁×#556	C₂²	1	2	yes	complemented
23	C₃₁×#556	C₂²	1	2	yes	complemented
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	C₂²	1	2	yes	—
29	C₃₁×#551	—	2	2	no	—
30	C₃₁×#551	—	2	2	no	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#546	C₂²	1	2	yes	—
33	C₃₁×#546	C₂²	1	2	yes	complemented
34	C₃₁×#542	C₂²	1	2	yes	—
35	C₃₁×#541	C₂²	1	2	yes	complemented
36	C₃₁×#539	—	2	2	no	—
37	C₃₁×#538	—	2	2	no	—
38	C₃₁×#529	—	2	2	no	—
39	C₃₁×#529	C₂²	1	1	yes	characteristic
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#126	—	2	2	no	—
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₃₁×#518	C₂²	1	2	yes	complemented
44	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
45	C₃₁×#501	C₂²	1	2	yes	complemented
46	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#497	C₂²	1	2	yes	complemented
48	C₃₁×#495	C₂²	1	1	yes	characteristic
49	C₃₁×#488	C₂²	1	2	yes	complemented
50	C₃₁×#488	C₂²	1	2	yes	complemented
51	C₃₁×#487	C₂²	1	2	yes	complemented
52	C₃₁×#485	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	2	yes	complemented
54	C₃₁×#484	C₂²	1	2	yes	complemented
55	C₃₁×#483	C₂²	1	2	yes	complemented
56	C₃₁×#482	C₂²	1	2	yes	—
57	C₃₁×#482	C₂²	1	2	yes	complemented
58	C₃₁×#479	C₂²	1	2	yes	complemented
59	C₃₁×#479	C₂²	1	2	yes	complemented
60	C₃₁×#478	C₂²	1	2	yes	complemented
61	C₃₁×#478	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	2	yes	complemented
63	C₃₁×#474	C₂²	1	2	yes	complemented
64	C₃₁×#470	C₂²	1	2	yes	complemented
65	C₃₁×#468	C₂²	1	2	yes	—
66	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#467	C₂²	1	2	yes	complemented
68	C₃₁×#466	C₂²	1	1	yes	characteristic
69	C₃₁×#465	C₂²	1	2	yes	—
70	C₃₁×#465	C₂²	1	2	yes	complemented
71	C₃₁×#464	C₂²	1	2	yes	complemented
72	C₃₁×#463	C₂²	1	2	yes	—
73	C₃₁×#463	C₂²	1	2	yes	—
74	C₃₁×#463	C₂²	1	2	yes	—
75	C₃₁×#462	C₂²	1	2	yes	complemented
76	C₃₁×#461	C₂²	1	2	yes	complemented
77	C₃₁×#452	C₂²	1	2	yes	—
78	C₃₁×#452	C₂²	1	2	yes	—
79	C₃₁×#452	C₂²	1	2	yes	complemented
80	C₃₁×#450	C₂²	1	2	yes	complemented
81	C₃₁×#449	C₂²	1	2	yes	—
82	C₃₁×#447	C₂²	1	2	yes	—
83	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
84	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#442	C₂²	1	2	yes	—
86	C₃₁×#442	C₂²	1	2	yes	—
87	C₃₁×#441	C₂²	1	2	yes	complemented
88	C₃₁×#440	C₂²	1	2	yes	complemented
89	C₃₁×#440	C₂²	1	2	yes	complemented
90	C₃₁×#440	C₂²	1	2	yes	complemented
91	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
92	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
93	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
95	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
96	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
98	C₄×D₈×C₃₁	C₂²	1	2	yes	—
99	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
102	C₃₁×#436	C₂²	1	1	yes	characteristic
103	C₃₁×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₃₁×#433	C₂²	1	2	yes	complemented
107	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#428	C₂²	1	2	yes	complemented
109	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
110	C₃₁×#416	C₂²	1	2	yes	—
111	C₃₁×#416	C₂²	1	2	yes	complemented
112	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
113	C₃₁×#405	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₃₁	C₂³	1	2	yes	—
116	C₂×#41×C₃₁	C₂³	1	2	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
119	C₃₁×#135	—	2	4	no	—
120	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×#126	—	2	2	no	—
137	C₃₁×#126	—	2	2	no	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	D₄	1	2	yes	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	D₄	1	1	yes	characteristic
151	C₃₁×#125	C₂³	1	2	yes	—
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#124	D₄	1	1	yes	characteristic
156	C₃₁×#124	C₂³	1	2	yes	—
157	C₃₁×#124	C₂³	1	2	yes	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	D₄	1	2	yes	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
173	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×#121	—	2	2	no	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	D₄	1	1	yes	characteristic
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#121	C₂³	1	2	yes	—
184	C₃₁×#120	—	2	2	no	—
185	C₃₁×#120	—	2	2	no	—
186	C₄×Q₈×C₃₁	—	2	2	no	—
187	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
188	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
189	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
190	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₃₁	—	2	2	no	—
193	C₄×D₄×C₃₁	—	2	2	no	—
194	C₄×D₄×C₃₁	—	2	2	no	—
195	C₄×D₄×C₃₁	—	2	2	no	—
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	2	no	—
198	C₄×D₄×C₃₁	—	2	2	no	—
199	C₄×D₄×C₃₁	—	2	2	no	—
200	C₄×D₄×C₃₁	C₂³	1	2	yes	—
201	C₄×D₄×C₃₁	C₂³	1	2	yes	—
202	C₄×D₄×C₃₁	C₂³	1	2	yes	—
203	C₄×D₄×C₃₁	C₂³	1	2	yes	—
204	C₄×D₄×C₃₁	C₂³	1	2	yes	—
205	C₄×D₄×C₃₁	C₂³	1	2	yes	—
206	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#117	—	2	2	no	—
209	C₃₁×#117	—	2	2	no	—
210	C₃₁×#117	—	2	2	no	—
211	C₃₁×#117	—	2	2	no	—
212	C₃₁×#117	—	2	2	no	—
213	C₃₁×#117	C₂³	1	2	yes	—
214	C₃₁×#117	C₂³	1	2	yes	—
215	C₃₁×#117	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
217	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
218	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
219	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
221	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
224	C₂×C₄²×C₃₁	—	2	2	no	—
225	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₃₁×#107	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	1	yes	characteristic
228	C₃₁×#107	C₂³	1	2	yes	—
229	C₃₁×#107	C₂³	1	1	yes	characteristic
230	C₃₁×#107	C₂³	1	1	yes	characteristic
231	C₃₁×#107	C₂³	1	2	yes	—
232	C₃₁×#106	C₂³	1	2	yes	—
233	C₃₁×#106	C₂³	1	2	yes	—
234	C₃₁×#106	C₂³	1	2	yes	—
235	C₃₁×#106	C₂³	1	2	yes	—
236	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
239	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
240	C₃₁×#103	C₂³	1	2	yes	—
241	C₃₁×#103	C₂³	1	2	yes	—
242	C₃₁×#103	C₂³	1	2	yes	—
243	C₃₁×#103	C₂³	1	2	yes	—
244	C₃₁×#103	C₂³	1	2	yes	—
245	C₃₁×#103	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#102	C₂³	1	2	yes	—
249	C₃₁×#102	C₂³	1	2	yes	—
250	C₃₁×#102	C₂³	1	2	yes	—
251	C₃₁×#102	C₂³	1	2	yes	—
252	C₃₁×#102	C₂³	1	2	yes	—
253	C₃₁×#102	C₂³	1	2	yes	—
254	C₃₁×#102	C₂³	1	2	yes	—
255	C₃₁×#102	C₂³	1	2	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₃₁×#97	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	2	yes	—
266	C₂⁴×C₃₁	—	2	2	no	—
267	#41×C₃₁	—	2	4	no	—
268	#41×C₃₁	—	2	4	no	—
269	#41×C₃₁	—	4	2	no	—
270	#41×C₃₁	—	4	2	no	—
271	C₂×Q₈×C₃₁	—	2	2	no	—
272	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×D₄×C₃₁	—	2	4	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	2	no	—
278	C₂×D₄×C₃₁	—	2	2	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	4	2	no	—
282	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	2	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
299	Q₁₆×C₃₁	—	2	2	no	—
300	Q₁₆×C₃₁	—	4	1	no	—
301	Q₁₆×C₃₁	—	4	2	no	—
302	SD₁₆×C₃₁	—	2	4	no	—
303	SD₁₆×C₃₁	—	2	4	no	—
304	SD₁₆×C₃₁	—	2	4	no	—
305	SD₁₆×C₃₁	—	4	2	no	—
306	D₈×C₃₁	—	2	4	no	—
307	D₈×C₃₁	—	4	1	no	—
308	D₈×C₃₁	#41	1	4	yes	—
309	M₁₆×C₃₁	—	2	4	no	—
310	C₂×C₈×C₃₁	—	2	2	no	—
311	C₂×C₈×C₃₁	—	4	1	no	—
312	C₂×C₈×C₃₁	—	4	2	no	—
313	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
317	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
318	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	2	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	2	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	2	no	—
349	C₂²⋊C₄×C₃₁	—	2	2	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	2	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₄²×C₃₁	—	2	2	no	—
369	C₄²×C₃₁	—	2	2	no	—
370	C₄²×C₃₁	—	2	2	no	—
371	C₄²×C₃₁	—	2	2	no	—
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄²×C₃₁	C₂⁴	1	2	yes	—
379	#61501	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂³×C₃₁	—	2	2	no	—
381	C₂³×C₃₁	—	2	2	no	—
382	C₂³×C₃₁	—	4	4	no	—
383	C₂³×C₃₁	—	8	2	no	—
384	C₂³×C₃₁	—	8	2	no	—
385	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
386	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₃₁	—	2	2	no	—
388	Q₈×C₃₁	—	2	2	no	—
389	Q₈×C₃₁	—	2	2	no	—
390	Q₈×C₃₁	—	2	2	no	—
391	Q₈×C₃₁	—	4	1	no	—
392	Q₈×C₃₁	—	8	2	no	—
393	D₄×C₃₁	—	2	2	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	2	2	no	—
396	D₄×C₃₁	—	4	1	no	—
397	D₄×C₃₁	—	4	2	no	—
398	D₄×C₃₁	—	4	4	no	—
399	D₄×C₃₁	—	4	4	no	—
400	D₄×C₃₁	—	4	4	no	—
401	D₄×C₃₁	—	8	2	no	—
402	D₄×C₃₁	—	8	2	no	—
403	D₄×C₃₁	C₂×#41	1	4	yes	—
404	C₂×C₄×C₃₁	—	2	1	no	—
405	C₂×C₄×C₃₁	—	2	2	no	—
406	C₂×C₄×C₃₁	—	2	2	no	—
407	C₂×C₄×C₃₁	—	2	1	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	4	1	no	—
415	C₂×C₄×C₃₁	—	4	1	no	—
416	C₂×C₄×C₃₁	—	4	4	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	—	8	2	no	—
420	C₂×C₄×C₃₁	—	8	2	no	—
421	C₂×C₄×C₃₁	—	8	2	no	—
422	C₂×C₄×C₃₁	—	8	2	no	—
423	C₂×C₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	—	8	2	no	—
425	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
434	C₈×C₃₁	—	2	1	no	—
435	C₈×C₃₁	—	2	2	no	—
436	C₈×C₃₁	—	2	1	no	—
437	C₈×C₃₁	—	2	1	no	—
438	C₈×C₃₁	—	2	2	no	—
439	C₈×C₃₁	C₂×#41	1	2	yes	—
440	#3521	C₂×C₃₁	1	2	yes	complemented
441	#3402	C₂×C₃₁	1	1	yes	characteristic, complemented
442	#3389	C₂×C₃₁	1	1	yes	characteristic, complemented
443	#3360	C₂×C₃₁	1	2	yes	complemented
444	#3352	C₂×C₃₁	1	1	yes	characteristic, complemented
445	#3350	C₂×C₃₁	1	2	yes	complemented
446	#3302	C₂×C₃₁	1	2	yes	complemented
447	#3297	C₂×C₃₁	1	2	yes	complemented
448	#3296	C₂×C₃₁	1	2	yes	complemented
449	#3273	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#3267	C₂×C₃₁	1	2	yes	complemented
451	#3178	C₂×C₃₁	1	2	yes	complemented
452	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
453	#3120	C₂×C₃₁	1	2	yes	complemented
454	#3118	C₂×C₃₁	1	2	yes	complemented
455	#3111	C₂×C₃₁	1	2	yes	complemented
456	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#2946	C₂×C₃₁	1	2	yes	complemented
458	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
459	C₂²×C₃₁	—	2	1	no	—
460	C₂²×C₃₁	—	2	1	no	—
461	C₂²×C₃₁	—	2	2	no	—
462	C₂²×C₃₁	—	2	2	no	—
463	C₂²×C₃₁	—	2	1	no	—
464	C₂²×C₃₁	—	2	2	no	—
465	C₂²×C₃₁	—	2	4	no	—
466	C₂²×C₃₁	—	4	2	no	—
467	C₂²×C₃₁	—	4	2	no	—
468	C₂²×C₃₁	—	4	2	no	—
469	C₂²×C₃₁	—	4	2	no	—
470	C₂²×C₃₁	—	4	2	no	—
471	C₂²×C₃₁	—	16	4	no	—
472	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
473	C₄×C₃₁	—	2	1	no	—
474	C₄×C₃₁	—	2	1	no	—
475	C₄×C₃₁	—	2	1	no	—
476	C₄×C₃₁	—	2	1	no	—
477	C₄×C₃₁	—	2	2	no	—
478	C₄×C₃₁	—	2	2	no	—
479	C₄×C₃₁	—	2	1	no	—
480	C₄×C₃₁	—	2	2	no	—
481	C₄×C₃₁	—	4	2	no	—
482	C₄×C₃₁	—	4	2	no	—
483	C₄×C₃₁	—	4	2	no	—
484	C₄×C₃₁	—	4	2	no	—
485	C₄×C₃₁	—	4	2	no	—
486	C₄×C₃₁	—	4	2	no	—
487	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
488	C₄×C₃₁	#585	1	1	yes	characteristic
489	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
490	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
491	#556	C₂²×C₃₁	1	2	yes	complemented
492	#556	C₂²×C₃₁	1	2	yes	complemented
493	#554	C₂²×C₃₁	1	2	yes	complemented
494	#553	—	2	2	no	—
495	#553	C₂²×C₃₁	1	2	yes	—
496	#552	—	2	2	no	—
497	#552	C₂²×C₃₁	1	2	yes	—
498	#551	—	2	2	no	—
499	#551	—	2	2	no	—
500	#547	C₂²×C₃₁	1	2	yes	—
501	#546	C₂²×C₃₁	1	2	yes	—
502	#546	C₂²×C₃₁	1	2	yes	complemented
503	#542	C₂²×C₃₁	1	2	yes	—
504	#541	C₂²×C₃₁	1	2	yes	complemented
505	#539	—	2	2	no	—
506	#538	—	2	2	no	—
507	#529	—	2	2	no	—
508	#529	C₂²×C₃₁	1	1	yes	characteristic
509	#529	C₂²×C₃₁	1	2	yes	complemented
510	C₂×#126	—	2	2	no	—
511	#520	C₂²×C₃₁	1	2	yes	—
512	#518	C₂²×C₃₁	1	2	yes	complemented
513	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
514	#501	C₂²×C₃₁	1	2	yes	complemented
515	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	#497	C₂²×C₃₁	1	2	yes	complemented
517	#495	C₂²×C₃₁	1	1	yes	characteristic
518	#488	C₂²×C₃₁	1	2	yes	complemented
519	#488	C₂²×C₃₁	1	2	yes	complemented
520	#487	C₂²×C₃₁	1	2	yes	complemented
521	#485	C₂²×C₃₁	1	2	yes	complemented
522	#485	C₂²×C₃₁	1	2	yes	complemented
523	#484	C₂²×C₃₁	1	2	yes	complemented
524	#483	C₂²×C₃₁	1	2	yes	complemented
525	#482	C₂²×C₃₁	1	2	yes	—
526	#482	C₂²×C₃₁	1	2	yes	complemented
527	#479	C₂²×C₃₁	1	2	yes	complemented
528	#479	C₂²×C₃₁	1	2	yes	complemented
529	#478	C₂²×C₃₁	1	2	yes	complemented
530	#478	C₂²×C₃₁	1	2	yes	complemented
531	#476	C₂²×C₃₁	1	2	yes	complemented
532	#474	C₂²×C₃₁	1	2	yes	complemented
533	#470	C₂²×C₃₁	1	2	yes	complemented
534	#468	C₂²×C₃₁	1	2	yes	—
535	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
536	#467	C₂²×C₃₁	1	2	yes	complemented
537	#466	C₂²×C₃₁	1	1	yes	characteristic
538	#465	C₂²×C₃₁	1	2	yes	—
539	#465	C₂²×C₃₁	1	2	yes	complemented
540	#464	C₂²×C₃₁	1	2	yes	complemented
541	#463	C₂²×C₃₁	1	2	yes	—
542	#463	C₂²×C₃₁	1	2	yes	—
543	#463	C₂²×C₃₁	1	2	yes	—
544	#462	C₂²×C₃₁	1	2	yes	complemented
545	#461	C₂²×C₃₁	1	2	yes	complemented
546	#452	C₂²×C₃₁	1	2	yes	—
547	#452	C₂²×C₃₁	1	2	yes	—
548	#452	C₂²×C₃₁	1	2	yes	complemented
549	#450	C₂²×C₃₁	1	2	yes	complemented
550	#449	C₂²×C₃₁	1	2	yes	—
551	#447	C₂²×C₃₁	1	2	yes	—
552	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
553	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#442	C₂²×C₃₁	1	2	yes	—
555	#442	C₂²×C₃₁	1	2	yes	—
556	#441	C₂²×C₃₁	1	2	yes	complemented
557	#440	C₂²×C₃₁	1	2	yes	complemented
558	#440	C₂²×C₃₁	1	2	yes	complemented
559	#440	C₂²×C₃₁	1	2	yes	complemented
560	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
563	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
564	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
565	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
566	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
567	C₄×D₈	C₂²×C₃₁	1	2	yes	—
568	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
569	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
570	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
571	#436	C₂²×C₃₁	1	1	yes	characteristic
572	#435	C₂²×C₃₁	1	2	yes	complemented
573	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
574	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
575	#433	C₂²×C₃₁	1	2	yes	complemented
576	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
577	#428	C₂²×C₃₁	1	2	yes	complemented
578	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
579	#416	C₂²×C₃₁	1	2	yes	—
580	#416	C₂²×C₃₁	1	2	yes	complemented
581	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
582	#405	C₂²×C₃₁	1	2	yes	complemented
583	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	C₂×C₃₁	—	4	1	no	—
585	C₂×C₃₁	—	4	2	no	—
586	C₂×C₃₁	—	4	4	no	—
587	C₂×C₃₁	—	8	2	no	—
588	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
589	C₂×C₃₁	#3584	1	1	yes	characteristic
590	C₂×C₃₁	#3584	1	1	yes	characteristic
591	C₂×#41	C₂³×C₃₁	1	2	yes	—
592	C₂×#41	C₂³×C₃₁	1	2	yes	—
593	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
594	AGL(1,ℤ/8)	—	2	8	no	—
595	#135	—	2	4	no	—
596	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
597	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
603	C₂×D₈	C₂³×C₃₁	1	2	yes	—
604	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
605	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
607	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
610	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
611	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	D₄×C₃₁	1	2	yes	—
623	#125	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	D₄×C₃₁	1	1	yes	characteristic
627	#125	C₂³×C₃₁	1	2	yes	—
628	#125	C₂³×C₃₁	1	2	yes	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	D₄×C₃₁	1	1	yes	characteristic
632	#124	C₂³×C₃₁	1	2	yes	—
633	#124	C₂³×C₃₁	1	2	yes	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	D₄×C₃₁	1	2	yes	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
649	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
650	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	D₄×C₃₁	1	1	yes	characteristic
658	#121	C₂³×C₃₁	1	2	yes	—
659	#121	C₂³×C₃₁	1	2	yes	—
660	#120	—	2	2	no	—
661	#120	—	2	2	no	—
662	C₄×Q₈	—	2	2	no	—
663	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
664	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
665	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
666	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
667	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	C₂³×C₃₁	1	2	yes	—
677	C₄×D₄	C₂³×C₃₁	1	2	yes	—
678	C₄×D₄	C₂³×C₃₁	1	2	yes	—
679	C₄×D₄	C₂³×C₃₁	1	2	yes	—
680	C₄×D₄	C₂³×C₃₁	1	2	yes	—
681	C₄×D₄	C₂³×C₃₁	1	2	yes	—
682	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₄×D₄	C₂³×C₃₁	1	2	yes	—
684	#117	—	2	2	no	—
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	C₂³×C₃₁	1	2	yes	—
690	#117	C₂³×C₃₁	1	2	yes	—
691	#117	C₂³×C₃₁	1	2	yes	—
692	C₂×C₄⋊C₄	—	2	2	no	—
693	C₂×C₄⋊C₄	—	2	2	no	—
694	C₂×C₄⋊C₄	—	2	2	no	—
695	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
696	C₂×C₂²⋊C₄	—	2	2	no	—
697	C₂×C₂²⋊C₄	—	2	2	no	—
698	C₂×C₂²⋊C₄	—	2	2	no	—
699	C₂×C₂²⋊C₄	—	2	2	no	—
700	C₂×C₄²	—	2	2	no	—
701	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
702	#107	C₂³×C₃₁	1	1	yes	characteristic
703	#107	C₂³×C₃₁	1	1	yes	characteristic
704	#107	C₂³×C₃₁	1	2	yes	—
705	#107	C₂³×C₃₁	1	1	yes	characteristic
706	#107	C₂³×C₃₁	1	1	yes	characteristic
707	#107	C₂³×C₃₁	1	2	yes	—
708	#106	C₂³×C₃₁	1	2	yes	—
709	#106	C₂³×C₃₁	1	2	yes	—
710	#106	C₂³×C₃₁	1	2	yes	—
711	#106	C₂³×C₃₁	1	2	yes	—
712	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
715	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
716	#103	C₂³×C₃₁	1	2	yes	—
717	#103	C₂³×C₃₁	1	2	yes	—
718	#103	C₂³×C₃₁	1	2	yes	—
719	#103	C₂³×C₃₁	1	2	yes	—
720	#103	C₂³×C₃₁	1	2	yes	—
721	#103	C₂³×C₃₁	1	2	yes	—
722	#103	C₂³×C₃₁	1	2	yes	—
723	#103	C₂³×C₃₁	1	2	yes	—
724	#102	C₂³×C₃₁	1	2	yes	—
725	#102	C₂³×C₃₁	1	2	yes	—
726	#102	C₂³×C₃₁	1	2	yes	—
727	#102	C₂³×C₃₁	1	2	yes	—
728	#102	C₂³×C₃₁	1	2	yes	—
729	#102	C₂³×C₃₁	1	2	yes	—
730	#102	C₂³×C₃₁	1	2	yes	—
731	#102	C₂³×C₃₁	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
735	#97	C₂³×C₃₁	1	2	yes	—
736	#97	C₂³×C₃₁	1	2	yes	—
737	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₄×C₈	C₂³×C₃₁	1	2	yes	—
742	C₃₁	#61501	1	1	yes	characteristic, direct product factor, Sylow
743	C₂⁴	—	2	2	no	—
744	#41	—	2	4	no	—
745	#41	—	2	4	no	—
746	#41	—	4	2	no	—
747	#41	—	4	2	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
750	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
751	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
760	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
761	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
762	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
773	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
776	Q₁₆	—	2	2	no	—
777	Q₁₆	—	4	1	no	—
778	Q₁₆	—	4	2	no	—
779	SD₁₆	—	2	4	no	—
780	SD₁₆	—	2	4	no	—
781	SD₁₆	—	2	4	no	—
782	SD₁₆	—	4	2	no	—
783	D₈	—	2	4	no	—
784	D₈	—	4	1	no	—
785	D₈	#41×C₃₁	1	4	yes	—
786	M₁₆	—	2	4	no	—
787	C₂×C₈	—	2	2	no	—
788	C₂×C₈	—	4	1	no	—
789	C₂×C₈	—	4	2	no	—
790	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
794	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
813	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
816	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
818	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
852	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
853	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
854	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
855	C₄²	C₂⁴×C₃₁	1	2	yes	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	8	2	no	—
860	C₂³	—	8	2	no	—
861	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
862	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
863	Q₈	—	2	2	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	4	1	no	—
868	Q₈	—	8	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	4	1	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	2	no	—
879	D₄	C₂×#41×C₃₁	1	4	yes	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	—	8	2	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	—	8	2	no	—
901	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
905	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
909	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
910	C₈	—	2	1	no	—
911	C₈	—	2	2	no	—
912	C₈	—	2	1	no	—
913	C₈	—	2	1	no	—
914	C₈	—	2	2	no	—
915	C₈	C₂×#41×C₃₁	1	2	yes	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	4	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	16	4	no	—
929	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
930	C₄	—	2	1	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
945	C₄	C₃₁×#585	1	1	yes	characteristic
946	C₂	—	4	2	no	—
947	C₂	—	4	1	no	—
948	C₂	—	4	4	no	—
949	C₂	—	8	2	no	—
950	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
951	C₂	C₃₁×#3584	1	1	yes	characteristic
952	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3521	C₂	semidirect
2. C₃₁×#3402	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3360	C₂	semidirect
5. C₃₁×#3352	C₂	semidirect
6. C₃₁×#3350	C₂	semidirect
7. C₃₁×#3302	C₂	semidirect
8. C₃₁×#3297	C₂	semidirect
9. C₃₁×#3296	C₂	semidirect
10. C₃₁×#3273	C₂	semidirect
11. C₃₁×#3267	C₂	semidirect
12. C₃₁×#3178	C₂	semidirect
13. C₃₁×#3168	C₂	semidirect
14. C₃₁×#3120	C₂	semidirect
15. C₃₁×#3118	C₂	semidirect
16. C₃₁×#3111	C₂	semidirect
17. C₃₁×#2966	C₂	semidirect
18. C₃₁×#2946	C₂	semidirect
19. C₄×C₃₁×#135	C₂	semidirect
22. C₃₁×#556	C₂²	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
33. C₃₁×#546	C₂²	semidirect
35. C₃₁×#541	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
43. C₃₁×#518	C₂²	semidirect
44. C₄×#41×C₃₁	C₂²	semidirect
45. C₃₁×#501	C₂²	semidirect
46. C₃₁×#499	C₂²	semidirect
47. C₃₁×#497	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#488	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#484	C₂²	semidirect
55. C₃₁×#483	C₂²	semidirect
57. C₃₁×#482	C₂²	semidirect
58. C₃₁×#479	C₂²	semidirect
59. C₃₁×#479	C₂²	semidirect
60. C₃₁×#478	C₂²	semidirect
61. C₃₁×#478	C₂²	semidirect
62. C₃₁×#476	C₂²	semidirect
63. C₃₁×#474	C₂²	semidirect
64. C₃₁×#470	C₂²	semidirect
66. C₃₁×#467	C₂²	semidirect
67. C₃₁×#467	C₂²	semidirect
70. C₃₁×#465	C₂²	semidirect
71. C₃₁×#464	C₂²	semidirect
75. C₃₁×#462	C₂²	semidirect
76. C₃₁×#461	C₂²	semidirect
79. C₃₁×#452	C₂²	semidirect
80. C₃₁×#450	C₂²	semidirect
83. C₃₁×#446	C₂²	semidirect
84. C₈×Q₈×C₃₁	C₂²	semidirect
87. C₃₁×#441	C₂²	semidirect
88. C₃₁×#440	C₂²	semidirect
89. C₃₁×#440	C₂²	semidirect
90. C₃₁×#440	C₂²	semidirect
91. C₄×Q₁₆×C₃₁	C₂²	semidirect
92. C₄×Q₁₆×C₃₁	C₂²	semidirect
93. C₄×Q₁₆×C₃₁	C₂²	semidirect
94. C₄×SD₁₆×C₃₁	C₂²	semidirect
95. C₄×SD₁₆×C₃₁	C₂²	semidirect
96. C₄×SD₁₆×C₃₁	C₂²	semidirect
97. C₄×SD₁₆×C₃₁	C₂²	semidirect
103. C₃₁×#435	C₂²	semidirect
105. C₈×D₄×C₃₁	C₂²	semidirect
106. C₃₁×#433	C₂²	semidirect
107. C₃₁×#432	C₂²	semidirect
108. C₃₁×#428	C₂²	semidirect
109. C₃₁×#427	C₂²	semidirect
111. C₃₁×#416	C₂²	semidirect
112. C₂×C₃₁×#102	C₂²	semidirect
113. C₃₁×#405	C₂²	semidirect
114. C₂×C₄×C₈×C₃₁	C₂²	semidirect
379. #61501	C₃₁	direct (N × H)
440. #3521	C₂×C₃₁	semidirect
441. #3402	C₂×C₃₁	semidirect
442. #3389	C₂×C₃₁	semidirect
443. #3360	C₂×C₃₁	semidirect
444. #3352	C₂×C₃₁	semidirect
445. #3350	C₂×C₃₁	semidirect
446. #3302	C₂×C₃₁	semidirect
447. #3297	C₂×C₃₁	semidirect
448. #3296	C₂×C₃₁	semidirect
449. #3273	C₂×C₃₁	semidirect
450. #3267	C₂×C₃₁	semidirect
451. #3178	C₂×C₃₁	semidirect
452. #3168	C₂×C₃₁	semidirect
453. #3120	C₂×C₃₁	semidirect
454. #3118	C₂×C₃₁	semidirect
455. #3111	C₂×C₃₁	semidirect
456. #2966	C₂×C₃₁	semidirect
457. #2946	C₂×C₃₁	semidirect
458. C₄×#135	C₂×C₃₁	semidirect
491. #556	C₂²×C₃₁	semidirect
492. #556	C₂²×C₃₁	semidirect
493. #554	C₂²×C₃₁	semidirect
502. #546	C₂²×C₃₁	semidirect
504. #541	C₂²×C₃₁	semidirect
509. #529	C₂²×C₃₁	semidirect
512. #518	C₂²×C₃₁	semidirect
513. C₄×#41	C₂²×C₃₁	semidirect
514. #501	C₂²×C₃₁	semidirect
515. #499	C₂²×C₃₁	semidirect
516. #497	C₂²×C₃₁	semidirect
518. #488	C₂²×C₃₁	semidirect
519. #488	C₂²×C₃₁	semidirect
520. #487	C₂²×C₃₁	semidirect
521. #485	C₂²×C₃₁	semidirect
522. #485	C₂²×C₃₁	semidirect
523. #484	C₂²×C₃₁	semidirect
524. #483	C₂²×C₃₁	semidirect
526. #482	C₂²×C₃₁	semidirect
527. #479	C₂²×C₃₁	semidirect
528. #479	C₂²×C₃₁	semidirect
529. #478	C₂²×C₃₁	semidirect
530. #478	C₂²×C₃₁	semidirect
531. #476	C₂²×C₃₁	semidirect
532. #474	C₂²×C₃₁	semidirect
533. #470	C₂²×C₃₁	semidirect
535. #467	C₂²×C₃₁	semidirect
536. #467	C₂²×C₃₁	semidirect
539. #465	C₂²×C₃₁	semidirect
540. #464	C₂²×C₃₁	semidirect
544. #462	C₂²×C₃₁	semidirect
545. #461	C₂²×C₃₁	semidirect
548. #452	C₂²×C₃₁	semidirect
549. #450	C₂²×C₃₁	semidirect
552. #446	C₂²×C₃₁	semidirect
553. C₈×Q₈	C₂²×C₃₁	semidirect
556. #441	C₂²×C₃₁	semidirect
557. #440	C₂²×C₃₁	semidirect
558. #440	C₂²×C₃₁	semidirect
559. #440	C₂²×C₃₁	semidirect
560. C₄×Q₁₆	C₂²×C₃₁	semidirect
561. C₄×Q₁₆	C₂²×C₃₁	semidirect
562. C₄×Q₁₆	C₂²×C₃₁	semidirect
563. C₄×SD₁₆	C₂²×C₃₁	semidirect
564. C₄×SD₁₆	C₂²×C₃₁	semidirect
565. C₄×SD₁₆	C₂²×C₃₁	semidirect
566. C₄×SD₁₆	C₂²×C₃₁	semidirect
572. #435	C₂²×C₃₁	semidirect
574. C₈×D₄	C₂²×C₃₁	semidirect
575. #433	C₂²×C₃₁	semidirect
576. #432	C₂²×C₃₁	semidirect
577. #428	C₂²×C₃₁	semidirect
578. #427	C₂²×C₃₁	semidirect
580. #416	C₂²×C₃₁	semidirect
581. C₂×#102	C₂²×C₃₁	semidirect
582. #405	C₂²×C₃₁	semidirect
583. C₂×C₄×C₈	C₂²×C₃₁	semidirect
742. C₃₁	#61501	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×#3521	2
C₃₁×#3402	2
C₃₁×#3389	2
C₃₁×#3360	2
C₃₁×#3352	2
C₃₁×#3350	2
C₃₁×#3302	2
C₃₁×#3297	2
C₃₁×#3296	2
C₃₁×#3273	2
C₃₁×#3267	2
C₃₁×#3178	2
C₃₁×#3168	2
C₃₁×#3120	2
C₃₁×#3118	2
C₃₁×#3111	2
C₃₁×#2966	2
C₃₁×#2946	2
C₄×C₃₁×#135	2
#61501	31

Subgroups — C31×#61501 #21518260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61501 #21518260