Subgroups — C₃₁×#61872 #21518631

Order 7936.

1722 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#562	—	2	2	no	—
21	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#559	C₂²	1	2	yes	complemented
23	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#554	—	2	1	no	—
25	C₃₁×#554	—	2	2	no	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#554	C₂²	1	2	yes	—
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
31	D₄×Q₈×C₃₁	—	2	1	no	—
32	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
33	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#547	—	2	1	no	—
36	C₃₁×#544	C₂²	1	2	yes	—
37	C₃₁×#543	—	2	1	no	—
38	C₃₁×#543	—	2	1	no	—
39	C₃₁×#542	—	2	1	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#540	C₂²	1	2	yes	—
42	C₃₁×#539	—	2	2	no	—
43	C₃₁×#536	—	2	1	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#529	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
49	C₃₁×#518	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#501	C₂²	1	2	yes	complemented
53	C₃₁×#501	C₂²	1	2	yes	complemented
54	C₃₁×#501	C₂²	1	2	yes	complemented
55	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#499	C₂²	1	2	yes	complemented
57	C₃₁×#498	C₂²	1	2	yes	complemented
58	C₃₁×#490	C₂²	1	2	yes	complemented
59	C₃₁×#490	C₂²	1	2	yes	complemented
60	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#483	C₂²	1	1	yes	characteristic
67	C₃₁×#482	C₂²	1	2	yes	—
68	C₃₁×#482	C₂²	1	2	yes	—
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#481	C₂²	1	2	yes	—
71	C₃₁×#480	C₂²	1	1	yes	characteristic
72	C₃₁×#479	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#476	C₂²	1	2	yes	—
82	C₃₁×#476	C₂²	1	2	yes	—
83	C₃₁×#476	C₂²	1	2	yes	complemented
84	C₃₁×#476	C₂²	1	2	yes	complemented
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#475	C₂²	1	2	yes	complemented
87	C₃₁×#474	C₂²	1	2	yes	—
88	C₃₁×#474	C₂²	1	2	yes	complemented
89	C₃₁×#474	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#459	C₂²	1	2	yes	—
94	C₃₁×#459	C₂²	1	2	yes	—
95	C₃₁×#459	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	1	yes	characteristic
97	C₃₁×#447	C₂²	1	2	yes	—
98	C₃₁×#447	C₂²	1	1	yes	characteristic
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#446	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#446	C₂²	1	2	yes	complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#442	C₂²	1	2	yes	—
106	C₃₁×#442	C₂²	1	2	yes	—
107	C₃₁×#442	C₂²	1	2	yes	—
108	C₃₁×#442	C₂²	1	2	yes	—
109	C₃₁×#440	C₂²	1	2	yes	—
110	C₃₁×#440	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×D₈×C₃₁	C₂²	1	2	yes	—
113	C₄×D₈×C₃₁	C₂²	1	2	yes	—
114	C₄×D₈×C₃₁	C₂²	1	2	yes	—
115	C₃₁×#433	C₂²	1	2	yes	—
116	C₃₁×#433	C₂²	1	2	yes	—
117	C₃₁×#432	C₂²	1	1	yes	characteristic
118	C₃₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂²×Q₈×C₃₁	—	2	2	no	—
122	C₂²×Q₈×C₃₁	—	2	1	no	—
123	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	—	2	1	no	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×D₈×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₃₁×C₄⋊Q₈	—	2	1	no	—
130	C₃₁×C₄⋊Q₈	—	2	2	no	—
131	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
132	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
133	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×#127	C₂³	1	2	yes	—
140	C₃₁×#127	C₂³	1	1	yes	characteristic
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	1	no	—
143	C₃₁×#125	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	D₄	1	2	yes	—
146	C₃₁×#125	C₂³	1	2	yes	—
147	C₃₁×#125	C₂³	1	1	yes	characteristic
148	C₃₁×#125	C₂³	1	2	yes	—
149	C₃₁×#125	C₂³	1	2	yes	—
150	C₃₁×#125	C₂³	1	2	yes	—
151	C₃₁×#124	—	2	1	no	—
152	C₃₁×#124	—	2	2	no	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	—	2	1	no	—
155	C₃₁×#124	C₂³	1	2	yes	—
156	C₃₁×#124	C₂³	1	1	yes	characteristic
157	C₃₁×#123	—	2	1	no	—
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×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	1	no	—
169	C₃₁×C₂²⋊Q₈	—	2	1	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	1	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	1	no	—
193	C₃₁×#121	—	2	2	no	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	C₂³	1	1	yes	characteristic
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₄×Q₈×C₃₁	—	2	1	no	—
198	C₄×Q₈×C₃₁	—	2	1	no	—
199	C₄×Q₈×C₃₁	—	2	1	no	—
200	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
201	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₄×D₄×C₃₁	—	2	1	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	2	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	1	no	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₄×D₄×C₃₁	C₂³	1	2	yes	—
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
224	C₃₁×#117	—	2	1	no	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
234	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#107	C₂³	1	2	yes	—
237	C₃₁×#107	C₂³	1	2	yes	—
238	C₃₁×#107	C₂³	1	2	yes	—
239	C₃₁×#107	C₂³	1	2	yes	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#106	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
251	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#102	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×#97	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	1	yes	characteristic
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	8	2	no	—
282	#41×C₃₁	—	8	2	no	—
283	C₂×Q₈×C₃₁	—	2	1	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	8	4	no	—
290	C₂×Q₈×C₃₁	—	8	2	no	—
291	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₃₁	—	2	4	no	—
296	C₂×D₄×C₃₁	—	2	1	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₃₁	—	2	1	no	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	1	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	2	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	2	no	—
313	C₂²×C₄×C₃₁	—	2	2	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
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	—	8	2	no	—
319	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	SD₁₆×C₃₁	—	2	4	no	—
323	D₈×C₃₁	—	2	4	no	—
324	D₈×C₃₁	—	2	4	no	—
325	D₈×C₃₁	—	2	4	no	—
326	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	1	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	1	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
353	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	—	2	1	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	1	no	—
374	C₂²⋊C₄×C₃₁	—	2	1	no	—
375	C₂²⋊C₄×C₃₁	—	2	1	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₄²×C₃₁	—	2	1	no	—
387	C₄²×C₃₁	—	2	2	no	—
388	C₄²×C₃₁	—	2	2	no	—
389	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₃₁	C₂⁴	1	2	yes	—
392	C₄²×C₃₁	C₂⁴	1	2	yes	—
393	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
395	#61872	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂³×C₃₁	—	2	4	no	—
397	C₂³×C₃₁	—	2	2	no	—
398	C₂³×C₃₁	—	2	1	no	—
399	C₂³×C₃₁	—	2	2	no	—
400	C₂³×C₃₁	—	8	1	no	—
401	C₂³×C₃₁	—	8	1	no	—
402	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₃₁	—	2	2	no	—
404	Q₈×C₃₁	—	4	2	no	—
405	Q₈×C₃₁	—	4	1	no	—
406	Q₈×C₃₁	—	4	1	no	—
407	Q₈×C₃₁	—	4	2	no	—
408	Q₈×C₃₁	—	4	2	no	—
409	Q₈×C₃₁	—	8	1	no	—
410	Q₈×C₃₁	—	8	2	no	—
411	Q₈×C₃₁	—	8	2	no	—
412	Q₈×C₃₁	—	8	2	no	—
413	D₄×C₃₁	—	2	4	no	—
414	D₄×C₃₁	—	2	2	no	—
415	D₄×C₃₁	—	2	2	no	—
416	D₄×C₃₁	—	2	2	no	—
417	D₄×C₃₁	—	2	2	no	—
418	D₄×C₃₁	—	4	2	no	—
419	D₄×C₃₁	—	8	1	no	—
420	D₄×C₃₁	—	8	2	no	—
421	D₄×C₃₁	—	8	2	no	—
422	D₄×C₃₁	—	8	1	no	—
423	D₄×C₃₁	—	8	2	no	—
424	D₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	1	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	4	1	no	—
434	C₂×C₄×C₃₁	—	4	1	no	—
435	C₂×C₄×C₃₁	—	4	4	no	—
436	C₂×C₄×C₃₁	—	4	2	no	—
437	C₂×C₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	—	8	2	no	—
439	C₂×C₄×C₃₁	—	8	2	no	—
440	C₂×C₄×C₃₁	—	8	2	no	—
441	C₂×C₄×C₃₁	—	8	2	no	—
442	C₂×C₄×C₃₁	—	8	2	no	—
443	C₂×C₄×C₃₁	—	8	2	no	—
444	C₂×C₄×C₃₁	—	8	2	no	—
445	C₂×C₄×C₃₁	—	8	2	no	—
446	C₂×C₄×C₃₁	—	8	1	no	—
447	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
457	C₈×C₃₁	—	2	2	no	—
458	C₈×C₃₁	—	2	2	no	—
459	C₈×C₃₁	—	2	2	no	—
460	C₈×C₃₁	—	2	2	no	—
461	#3554	C₂×C₃₁	1	1	yes	characteristic, complemented
462	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#3389	C₂×C₃₁	1	2	yes	complemented
464	#3388	C₂×C₃₁	1	2	yes	complemented
465	#3384	C₂×C₃₁	1	2	yes	complemented
466	#3384	C₂×C₃₁	1	2	yes	complemented
467	#3373	C₂×C₃₁	1	2	yes	complemented
468	#3370	C₂×C₃₁	1	2	yes	complemented
469	#3370	C₂×C₃₁	1	2	yes	complemented
470	#3366	C₂×C₃₁	1	2	yes	complemented
471	#3244	C₂×C₃₁	1	2	yes	complemented
472	#3241	C₂×C₃₁	1	2	yes	complemented
473	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3122	C₂×C₃₁	1	2	yes	complemented
476	#3118	C₂×C₃₁	1	2	yes	complemented
477	#3114	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
480	C₂²×C₃₁	—	2	1	no	—
481	C₂²×C₃₁	—	2	1	no	—
482	C₂²×C₃₁	—	2	1	no	—
483	C₂²×C₃₁	—	2	4	no	—
484	C₂²×C₃₁	—	4	2	no	—
485	C₂²×C₃₁	—	4	2	no	—
486	C₂²×C₃₁	—	4	1	no	—
487	C₂²×C₃₁	—	4	2	no	—
488	C₂²×C₃₁	—	4	2	no	—
489	C₂²×C₃₁	—	4	1	no	—
490	C₂²×C₃₁	—	4	1	no	—
491	C₂²×C₃₁	—	4	2	no	—
492	C₂²×C₃₁	—	8	4	no	—
493	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
494	C₄×C₃₁	—	2	1	no	—
495	C₄×C₃₁	—	2	1	no	—
496	C₄×C₃₁	—	2	1	no	—
497	C₄×C₃₁	—	2	1	no	—
498	C₄×C₃₁	—	2	2	no	—
499	C₄×C₃₁	—	2	2	no	—
500	C₄×C₃₁	—	2	2	no	—
501	C₄×C₃₁	—	2	2	no	—
502	C₄×C₃₁	—	2	1	no	—
503	C₄×C₃₁	—	4	1	no	—
504	C₄×C₃₁	—	4	2	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	2	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	2	no	—
509	C₄×C₃₁	—	4	1	no	—
510	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
511	#562	—	2	2	no	—
512	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
513	#559	C₂²×C₃₁	1	2	yes	complemented
514	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	#554	—	2	1	no	—
516	#554	—	2	2	no	—
517	#554	C₂²×C₃₁	1	2	yes	—
518	#554	C₂²×C₃₁	1	2	yes	—
519	#554	C₂²×C₃₁	1	2	yes	—
520	#554	C₂²×C₃₁	1	2	yes	complemented
521	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
522	D₄×Q₈	—	2	1	no	—
523	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
524	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
525	#548	—	2	1	no	—
526	#547	—	2	1	no	—
527	#544	C₂²×C₃₁	1	2	yes	—
528	#543	—	2	1	no	—
529	#543	—	2	1	no	—
530	#542	—	2	1	no	—
531	#542	C₂²×C₃₁	1	2	yes	—
532	#540	C₂²×C₃₁	1	2	yes	—
533	#539	—	2	2	no	—
534	#536	—	2	1	no	—
535	#533	C₂²×C₃₁	1	1	yes	characteristic
536	#533	C₂²×C₃₁	1	1	yes	characteristic
537	#532	C₂²×C₃₁	1	1	yes	characteristic
538	#529	C₂²×C₃₁	1	1	yes	characteristic
539	C₂×C₂²⋊Q₈	—	2	2	no	—
540	#518	C₂²×C₃₁	1	2	yes	—
541	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
542	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	#501	C₂²×C₃₁	1	2	yes	complemented
544	#501	C₂²×C₃₁	1	2	yes	complemented
545	#501	C₂²×C₃₁	1	2	yes	complemented
546	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	#499	C₂²×C₃₁	1	2	yes	complemented
548	#498	C₂²×C₃₁	1	2	yes	complemented
549	#490	C₂²×C₃₁	1	2	yes	complemented
550	#490	C₂²×C₃₁	1	2	yes	complemented
551	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
552	#489	C₂²×C₃₁	1	2	yes	complemented
553	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#488	C₂²×C₃₁	1	2	yes	complemented
555	#486	C₂²×C₃₁	1	2	yes	complemented
556	#485	C₂²×C₃₁	1	2	yes	—
557	#483	C₂²×C₃₁	1	1	yes	characteristic
558	#482	C₂²×C₃₁	1	2	yes	—
559	#482	C₂²×C₃₁	1	2	yes	—
560	#482	C₂²×C₃₁	1	2	yes	—
561	#481	C₂²×C₃₁	1	2	yes	—
562	#480	C₂²×C₃₁	1	1	yes	characteristic
563	#479	C₂²×C₃₁	1	2	yes	complemented
564	#479	C₂²×C₃₁	1	2	yes	complemented
565	#478	C₂²×C₃₁	1	2	yes	—
566	#478	C₂²×C₃₁	1	2	yes	—
567	#478	C₂²×C₃₁	1	2	yes	—
568	#478	C₂²×C₃₁	1	2	yes	complemented
569	#478	C₂²×C₃₁	1	2	yes	complemented
570	#478	C₂²×C₃₁	1	2	yes	complemented
571	#478	C₂²×C₃₁	1	2	yes	complemented
572	#476	C₂²×C₃₁	1	2	yes	—
573	#476	C₂²×C₃₁	1	2	yes	—
574	#476	C₂²×C₃₁	1	2	yes	complemented
575	#476	C₂²×C₃₁	1	2	yes	complemented
576	#476	C₂²×C₃₁	1	2	yes	complemented
577	#475	C₂²×C₃₁	1	2	yes	complemented
578	#474	C₂²×C₃₁	1	2	yes	—
579	#474	C₂²×C₃₁	1	2	yes	complemented
580	#474	C₂²×C₃₁	1	2	yes	complemented
581	#463	C₂²×C₃₁	1	2	yes	—
582	#463	C₂²×C₃₁	1	2	yes	—
583	#463	C₂²×C₃₁	1	2	yes	—
584	#459	C₂²×C₃₁	1	2	yes	—
585	#459	C₂²×C₃₁	1	2	yes	—
586	#459	C₂²×C₃₁	1	2	yes	—
587	#450	C₂²×C₃₁	1	1	yes	characteristic
588	#447	C₂²×C₃₁	1	2	yes	—
589	#447	C₂²×C₃₁	1	1	yes	characteristic
590	#446	C₂²×C₃₁	1	2	yes	complemented
591	#446	C₂²×C₃₁	1	2	yes	complemented
592	#446	C₂²×C₃₁	1	2	yes	complemented
593	#446	C₂²×C₃₁	1	2	yes	complemented
594	#442	C₂²×C₃₁	1	2	yes	—
595	#442	C₂²×C₃₁	1	2	yes	—
596	#442	C₂²×C₃₁	1	2	yes	—
597	#442	C₂²×C₃₁	1	2	yes	—
598	#442	C₂²×C₃₁	1	2	yes	—
599	#442	C₂²×C₃₁	1	2	yes	—
600	#440	C₂²×C₃₁	1	2	yes	—
601	#440	C₂²×C₃₁	1	2	yes	—
602	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
603	C₄×D₈	C₂²×C₃₁	1	2	yes	—
604	C₄×D₈	C₂²×C₃₁	1	2	yes	—
605	C₄×D₈	C₂²×C₃₁	1	2	yes	—
606	#433	C₂²×C₃₁	1	2	yes	—
607	#433	C₂²×C₃₁	1	2	yes	—
608	#432	C₂²×C₃₁	1	1	yes	characteristic
609	#432	C₂²×C₃₁	1	1	yes	characteristic
610	C₂×C₃₁	—	4	1	no	—
611	C₂×C₃₁	—	4	4	no	—
612	C₂×C₃₁	—	8	1	no	—
613	C₂×C₃₁	—	8	2	no	—
614	C₂×C₃₁	#3486	1	1	yes	characteristic
615	C₂×C₃₁	#3585	1	1	yes	characteristic
616	C₂×C₃₁	#3585	1	1	yes	characteristic
617	C₂×#41	—	2	1	no	—
618	C₂×#41	—	2	1	no	—
619	C₂²×Q₈	—	2	2	no	—
620	C₂²×Q₈	—	2	1	no	—
621	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
622	C₂³×C₄	—	2	1	no	—
623	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
624	C₂×D₈	C₂³×C₃₁	1	2	yes	—
625	C₂×D₈	C₂³×C₃₁	1	2	yes	—
626	C₂×D₈	C₂³×C₃₁	1	2	yes	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	2	no	—
629	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
630	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
635	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
636	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
637	#127	C₂³×C₃₁	1	1	yes	characteristic
638	#127	C₂³×C₃₁	1	2	yes	—
639	#126	—	2	2	no	—
640	#126	—	2	1	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	D₄×C₃₁	1	2	yes	—
644	#125	C₂³×C₃₁	1	1	yes	characteristic
645	#125	C₂³×C₃₁	1	2	yes	—
646	#125	C₂³×C₃₁	1	2	yes	—
647	#125	C₂³×C₃₁	1	2	yes	—
648	#125	C₂³×C₃₁	1	2	yes	—
649	#124	—	2	1	no	—
650	#124	—	2	2	no	—
651	#124	—	2	2	no	—
652	#124	—	2	1	no	—
653	#124	C₂³×C₃₁	1	1	yes	characteristic
654	#124	C₂³×C₃₁	1	2	yes	—
655	#123	—	2	1	no	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	1	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	1	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
685	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
686	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
687	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
688	#121	—	2	1	no	—
689	#121	—	2	2	no	—
690	#121	—	2	1	no	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	C₂³×C₃₁	1	1	yes	characteristic
694	#121	C₂³×C₃₁	1	2	yes	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
700	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
701	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	C₂³×C₃₁	1	2	yes	—
712	C₄×D₄	C₂³×C₃₁	1	2	yes	—
713	C₄×D₄	C₂³×C₃₁	1	2	yes	—
714	C₄×D₄	C₂³×C₃₁	1	2	yes	—
715	C₄×D₄	C₂³×C₃₁	1	2	yes	—
716	C₄×D₄	C₂³×C₃₁	1	2	yes	—
717	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
718	C₄×D₄	C₂³×C₃₁	1	2	yes	—
719	C₄×D₄	C₂³×C₃₁	1	2	yes	—
720	C₄×D₄	C₂³×C₃₁	1	2	yes	—
721	C₄×D₄	C₂³×C₃₁	1	2	yes	—
722	#117	—	2	1	no	—
723	#117	C₂³×C₃₁	1	2	yes	—
724	#117	C₂³×C₃₁	1	2	yes	—
725	C₂×C₄⋊C₄	—	2	2	no	—
726	C₂×C₄⋊C₄	—	2	2	no	—
727	C₂×C₄⋊C₄	—	2	2	no	—
728	C₂×C₄⋊C₄	—	2	2	no	—
729	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	—	2	1	no	—
731	C₂×C₂²⋊C₄	—	2	2	no	—
732	C₂×C₂²⋊C₄	—	2	2	no	—
733	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
734	#107	C₂³×C₃₁	1	2	yes	—
735	#107	C₂³×C₃₁	1	2	yes	—
736	#107	C₂³×C₃₁	1	2	yes	—
737	#107	C₂³×C₃₁	1	2	yes	—
738	#107	C₂³×C₃₁	1	2	yes	—
739	#106	C₂³×C₃₁	1	2	yes	—
740	#106	C₂³×C₃₁	1	2	yes	—
741	#106	C₂³×C₃₁	1	2	yes	—
742	#106	C₂³×C₃₁	1	2	yes	—
743	#106	C₂³×C₃₁	1	2	yes	—
744	#106	C₂³×C₃₁	1	2	yes	—
745	#106	C₂³×C₃₁	1	2	yes	—
746	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
747	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
748	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
749	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
750	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
751	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
752	#103	C₂³×C₃₁	1	2	yes	—
753	#103	C₂³×C₃₁	1	2	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#102	C₂³×C₃₁	1	2	yes	—
756	#102	C₂³×C₃₁	1	2	yes	—
757	#102	C₂³×C₃₁	1	2	yes	—
758	#102	C₂³×C₃₁	1	2	yes	—
759	#102	C₂³×C₃₁	1	2	yes	—
760	#102	C₂³×C₃₁	1	2	yes	—
761	#102	C₂³×C₃₁	1	2	yes	—
762	#102	C₂³×C₃₁	1	2	yes	—
763	#102	C₂³×C₃₁	1	2	yes	—
764	#102	C₂³×C₃₁	1	2	yes	—
765	#102	C₂³×C₃₁	1	2	yes	—
766	#102	C₂³×C₃₁	1	2	yes	—
767	#102	C₂³×C₃₁	1	2	yes	—
768	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
771	#97	C₂³×C₃₁	1	2	yes	—
772	#97	C₂³×C₃₁	1	1	yes	characteristic
773	#97	C₂³×C₃₁	1	1	yes	characteristic
774	#97	C₂³×C₃₁	1	2	yes	—
775	#97	C₂³×C₃₁	1	2	yes	—
776	C₄×C₈	C₂³×C₃₁	1	2	yes	—
777	C₄×C₈	C₂³×C₃₁	1	2	yes	—
778	C₃₁	#61872	1	1	yes	characteristic, direct product factor, Sylow
779	C₂⁴	—	2	1	no	—
780	#41	—	8	2	no	—
781	#41	—	8	2	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	8	4	no	—
789	C₂×Q₈	—	8	2	no	—
790	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
791	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
792	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
793	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
803	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	8	2	no	—
818	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
821	SD₁₆	—	2	4	no	—
822	D₈	—	2	4	no	—
823	D₈	—	2	4	no	—
824	D₈	—	2	4	no	—
825	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
826	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
827	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
828	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
850	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
854	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
855	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
856	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
857	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
858	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
861	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
862	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	1	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
884	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
885	C₄²	—	2	1	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
890	C₄²	C₂⁴×C₃₁	1	2	yes	—
891	C₄²	C₂⁴×C₃₁	1	2	yes	—
892	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂³	—	2	4	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	8	1	no	—
899	C₂³	—	8	1	no	—
900	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
901	Q₈	—	2	2	no	—
902	Q₈	—	4	2	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	1	no	—
905	Q₈	—	4	2	no	—
906	Q₈	—	4	2	no	—
907	Q₈	—	8	1	no	—
908	Q₈	—	8	2	no	—
909	Q₈	—	8	2	no	—
910	Q₈	—	8	2	no	—
911	D₄	—	2	4	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	4	2	no	—
917	D₄	—	8	1	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	2	no	—
920	D₄	—	8	1	no	—
921	D₄	—	8	2	no	—
922	D₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	2	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	1	no	—
945	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
952	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
954	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₈	—	2	2	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	4	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	8	4	no	—
972	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	2	1	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	1	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
990	C₂	—	4	1	no	—
991	C₂	—	4	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₃₁×#3486	1	1	yes	characteristic
995	C₂	C₃₁×#3585	1	1	yes	characteristic
996	C₂	C₃₁×#3585	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3554	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3384	C₂	semidirect
6. C₃₁×#3384	C₂	semidirect
7. C₃₁×#3373	C₂	semidirect
8. C₃₁×#3370	C₂	semidirect
9. C₃₁×#3370	C₂	semidirect
10. C₃₁×#3366	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3241	C₂	semidirect
13. C₃₁×#3240	C₂	semidirect
14. C₃₁×#3235	C₂	semidirect
15. C₃₁×#3122	C₂	semidirect
16. C₃₁×#3118	C₂	semidirect
17. C₃₁×#3114	C₂	semidirect
18. C₃₁×#3109	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
21. C₃₁×#559	C₂²	semidirect
22. C₃₁×#559	C₂²	semidirect
23. C₃₁×#557	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#550	C₂²	semidirect
33. D₄×Q₈×C₃₁	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#501	C₂²	semidirect
53. C₃₁×#501	C₂²	semidirect
54. C₃₁×#501	C₂²	semidirect
55. C₃₁×#501	C₂²	semidirect
56. C₃₁×#499	C₂²	semidirect
57. C₃₁×#498	C₂²	semidirect
58. C₃₁×#490	C₂²	semidirect
59. C₃₁×#490	C₂²	semidirect
60. C₃₁×#489	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
83. C₃₁×#476	C₂²	semidirect
84. C₃₁×#476	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
88. C₃₁×#474	C₂²	semidirect
89. C₃₁×#474	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#446	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
395. #61872	C₃₁	direct (N × H)
461. #3554	C₂×C₃₁	semidirect
462. #3501	C₂×C₃₁	semidirect
463. #3389	C₂×C₃₁	semidirect
464. #3388	C₂×C₃₁	semidirect
465. #3384	C₂×C₃₁	semidirect
466. #3384	C₂×C₃₁	semidirect
467. #3373	C₂×C₃₁	semidirect
468. #3370	C₂×C₃₁	semidirect
469. #3370	C₂×C₃₁	semidirect
470. #3366	C₂×C₃₁	semidirect
471. #3244	C₂×C₃₁	semidirect
472. #3241	C₂×C₃₁	semidirect
473. #3240	C₂×C₃₁	semidirect
474. #3235	C₂×C₃₁	semidirect
475. #3122	C₂×C₃₁	semidirect
476. #3118	C₂×C₃₁	semidirect
477. #3114	C₂×C₃₁	semidirect
478. #3109	C₂×C₃₁	semidirect
479. #2987	C₂×C₃₁	semidirect
512. #559	C₂²×C₃₁	semidirect
513. #559	C₂²×C₃₁	semidirect
514. #557	C₂²×C₃₁	semidirect
520. #554	C₂²×C₃₁	semidirect
521. #550	C₂²×C₃₁	semidirect
524. D₄×Q₈	C₂²×C₃₁	semidirect
542. #501	C₂²×C₃₁	semidirect
543. #501	C₂²×C₃₁	semidirect
544. #501	C₂²×C₃₁	semidirect
545. #501	C₂²×C₃₁	semidirect
546. #501	C₂²×C₃₁	semidirect
547. #499	C₂²×C₃₁	semidirect
548. #498	C₂²×C₃₁	semidirect
549. #490	C₂²×C₃₁	semidirect
550. #490	C₂²×C₃₁	semidirect
551. #489	C₂²×C₃₁	semidirect
552. #489	C₂²×C₃₁	semidirect
553. #489	C₂²×C₃₁	semidirect
554. #488	C₂²×C₃₁	semidirect
555. #486	C₂²×C₃₁	semidirect
563. #479	C₂²×C₃₁	semidirect
564. #479	C₂²×C₃₁	semidirect
568. #478	C₂²×C₃₁	semidirect
569. #478	C₂²×C₃₁	semidirect
570. #478	C₂²×C₃₁	semidirect
571. #478	C₂²×C₃₁	semidirect
574. #476	C₂²×C₃₁	semidirect
575. #476	C₂²×C₃₁	semidirect
576. #476	C₂²×C₃₁	semidirect
577. #475	C₂²×C₃₁	semidirect
579. #474	C₂²×C₃₁	semidirect
580. #474	C₂²×C₃₁	semidirect
590. #446	C₂²×C₃₁	semidirect
591. #446	C₂²×C₃₁	semidirect
592. #446	C₂²×C₃₁	semidirect
593. #446	C₂²×C₃₁	semidirect
778. C₃₁	#61872	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×#3554	2
C₃₁×#3501	2
C₃₁×#3389	2
C₃₁×#3388	2
C₃₁×#3384	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3244	2
C₃₁×#3241	2
C₃₁×#3240	2
C₃₁×#3235	2
C₃₁×#3122	2
C₃₁×#3118	2
C₃₁×#3114	2
C₃₁×#3109	2
C₃₁×#2987	2
#61872	31

Subgroups — C31×#61872 #21518631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61872 #21518631