Subgroups — C₃₁×#62557 #21519316

Order 7936.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3221	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#562	—	2	1	no	—
23	C₃₁×#562	—	2	1	no	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	complemented
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#553	C₂²	1	2	yes	complemented
28	C₃₁×#551	—	2	2	no	—
29	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#548	C₂²	1	2	yes	—
31	C₃₁×#547	—	2	2	no	—
32	C₃₁×#547	C₂²	1	2	yes	—
33	C₃₁×#546	C₂²	1	2	yes	—
34	C₃₁×#544	C₂²	1	2	yes	complemented
35	C₃₁×#543	—	2	1	no	—
36	C₃₁×#542	—	2	2	no	—
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#540	C₂²	1	2	yes	complemented
39	C₃₁×#539	—	2	2	no	—
40	C₃₁×#539	—	2	1	no	—
41	C₃₁×#538	—	2	1	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#536	C₂²	1	2	yes	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₃₁×#529	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#496	C₂²	1	2	yes	—
52	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#491	C₂²	1	2	yes	complemented
54	C₃₁×#491	C₂²	1	2	yes	complemented
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#489	C₂²	1	2	yes	—
57	C₃₁×#488	C₂²	1	2	yes	—
58	C₃₁×#488	C₂²	1	2	yes	—
59	C₃₁×#488	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	2	yes	—
61	C₃₁×#488	C₂²	1	2	yes	—
62	C₃₁×#487	C₂²	1	2	yes	complemented
63	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	2	yes	—
67	C₃₁×#483	C₂²	1	2	yes	—
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#481	C₂²	1	2	yes	—
71	C₃₁×#479	C₂²	1	2	yes	complemented
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×#476	C₂²	1	2	yes	—
76	C₃₁×#475	C₂²	1	2	yes	complemented
77	C₃₁×#469	C₂²	1	2	yes	—
78	C₃₁×#468	C₂²	1	2	yes	complemented
79	C₃₁×#466	C₂²	1	2	yes	—
80	C₃₁×#465	C₂²	1	2	yes	—
81	C₃₁×#465	C₂²	1	2	yes	—
82	C₃₁×#465	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#463	C₂²	1	2	yes	—
85	C₃₁×#463	C₂²	1	2	yes	—
86	C₃₁×#463	C₂²	1	2	yes	—
87	C₃₁×#461	C₂²	1	2	yes	complemented
88	C₃₁×#461	C₂²	1	2	yes	complemented
89	C₃₁×#449	C₂²	1	2	yes	—
90	C₃₁×#449	C₂²	1	2	yes	—
91	C₃₁×#448	C₂²	1	2	yes	—
92	C₃₁×#448	C₂²	1	2	yes	complemented
93	C₃₁×#448	C₂²	1	2	yes	complemented
94	C₃₁×#447	C₂²	1	2	yes	—
95	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
96	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#442	C₂²	1	2	yes	—
98	C₃₁×#440	C₂²	1	2	yes	complemented
99	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₈×C₃₁	C₂²	1	2	yes	—
103	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₈×D₄×C₃₁	C₂²	1	2	yes	—
106	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#419	C₂²	1	2	yes	complemented
110	C₃₁×#417	C₂²	1	2	yes	—
111	C₃₁×#416	C₂²	1	2	yes	—
112	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
113	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
114	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
116	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	D₄	1	2	yes	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	1	no	—
151	C₃₁×#125	—	2	1	no	—
152	C₃₁×#125	—	2	1	no	—
153	C₃₁×#125	D₄	1	1	yes	characteristic
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#125	C₂³	1	2	yes	—
156	C₃₁×#125	C₂³	1	2	yes	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	2	no	—
159	C₃₁×#124	—	2	1	no	—
160	C₃₁×#124	—	2	1	no	—
161	C₃₁×#124	—	2	1	no	—
162	C₃₁×#124	D₄	1	1	yes	characteristic
163	C₃₁×#124	C₂³	1	2	yes	—
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	2	yes	—
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	D₄	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	D₄	1	1	yes	characteristic
202	C₃₁×#121	C₂³	1	2	yes	—
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#120	—	2	2	no	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×D₄×C₃₁	—	2	2	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	1	no	—
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	1	yes	characteristic
222	C₃₁×#117	—	2	1	no	—
223	C₃₁×#117	—	2	2	no	—
224	C₃₁×#117	C₂³	1	2	yes	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₃₁	—	2	1	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×#106	C₂³	1	2	yes	—
239	C₃₁×#106	C₂³	1	2	yes	—
240	C₃₁×#106	C₂³	1	2	yes	—
241	C₃₁×#106	C₂³	1	2	yes	—
242	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
243	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
244	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	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×#103	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×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
269	C₃₁×#97	C₂³	1	2	yes	—
270	C₃₁×#97	C₂³	1	2	yes	—
271	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
273	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
274	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
275	C₄×C₈×C₃₁	C₂³	1	2	yes	—
276	C₂⁴×C₃₁	—	2	1	no	—
277	#41×C₃₁	—	4	2	no	—
278	#41×C₃₁	—	4	2	no	—
279	#41×C₃₁	—	8	2	no	—
280	#41×C₃₁	—	8	4	no	—
281	C₂×Q₈×C₃₁	—	2	1	no	—
282	C₂×Q₈×C₃₁	—	2	2	no	—
283	C₂×Q₈×C₃₁	—	2	2	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	4	1	no	—
287	C₂×Q₈×C₃₁	—	4	1	no	—
288	C₂×Q₈×C₃₁	—	4	2	no	—
289	C₂×Q₈×C₃₁	—	4	2	no	—
290	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	2	no	—
295	C₂×D₄×C₃₁	—	2	2	no	—
296	C₂×D₄×C₃₁	—	2	2	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	—	4	1	no	—
302	C₂×D₄×C₃₁	—	4	1	no	—
303	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	—	2	1	no	—
308	C₂²×C₄×C₃₁	—	2	1	no	—
309	C₂²×C₄×C₃₁	—	2	1	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	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
321	SD₁₆×C₃₁	—	4	2	no	—
322	SD₁₆×C₃₁	—	4	2	no	—
323	SD₁₆×C₃₁	—	4	2	no	—
324	SD₁₆×C₃₁	—	4	2	no	—
325	D₈×C₃₁	—	4	2	no	—
326	D₈×C₃₁	—	4	2	no	—
327	M₁₆×C₃₁	—	4	2	no	—
328	C₂×C₈×C₃₁	—	4	2	no	—
329	C₂×C₈×C₃₁	—	4	1	no	—
330	C₂×C₈×C₃₁	—	4	1	no	—
331	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	1	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	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	2	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	2	no	—
392	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄²×C₃₁	C₂⁴	1	2	yes	—
397	#62557	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂³×C₃₁	—	2	2	no	—
399	C₂³×C₃₁	—	2	2	no	—
400	C₂³×C₃₁	—	4	2	no	—
401	C₂³×C₃₁	—	8	1	no	—
402	C₂³×C₃₁	—	8	1	no	—
403	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
404	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
405	Q₈×C₃₁	—	2	2	no	—
406	Q₈×C₃₁	—	2	2	no	—
407	Q₈×C₃₁	—	2	2	no	—
408	Q₈×C₃₁	—	2	2	no	—
409	Q₈×C₃₁	—	4	1	no	—
410	Q₈×C₃₁	—	8	1	no	—
411	Q₈×C₃₁	—	8	2	no	—
412	Q₈×C₃₁	—	8	1	no	—
413	Q₈×C₃₁	—	8	1	no	—
414	Q₈×C₃₁	—	8	2	no	—
415	D₄×C₃₁	—	2	4	no	—
416	D₄×C₃₁	—	2	2	no	—
417	D₄×C₃₁	—	2	2	no	—
418	D₄×C₃₁	—	2	2	no	—
419	D₄×C₃₁	—	2	2	no	—
420	D₄×C₃₁	—	4	1	no	—
421	D₄×C₃₁	—	4	4	no	—
422	D₄×C₃₁	—	8	1	no	—
423	D₄×C₃₁	—	8	1	no	—
424	D₄×C₃₁	—	8	1	no	—
425	D₄×C₃₁	—	8	2	no	—
426	D₄×C₃₁	—	8	2	no	—
427	D₄×C₃₁	—	8	2	no	—
428	D₄×C₃₁	—	8	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	1	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	4	1	no	—
441	C₂×C₄×C₃₁	—	4	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	2	no	—
447	C₂×C₄×C₃₁	—	8	1	no	—
448	C₂×C₄×C₃₁	—	8	2	no	—
449	C₂×C₄×C₃₁	—	8	1	no	—
450	C₂×C₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
460	C₈×C₃₁	—	2	1	no	—
461	C₈×C₃₁	—	2	1	no	—
462	C₈×C₃₁	—	2	2	no	—
463	C₈×C₃₁	—	2	1	no	—
464	C₈×C₃₁	—	2	1	no	—
465	C₈×C₃₁	—	2	2	no	—
466	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#3559	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3376	C₂×C₃₁	1	2	yes	complemented
469	#3360	C₂×C₃₁	1	2	yes	complemented
470	#3326	C₂×C₃₁	1	2	yes	complemented
471	#3320	C₂×C₃₁	1	2	yes	complemented
472	#3306	C₂×C₃₁	1	2	yes	complemented
473	#3301	C₂×C₃₁	1	2	yes	complemented
474	#3298	C₂×C₃₁	1	2	yes	complemented
475	#3297	C₂×C₃₁	1	2	yes	complemented
476	#3244	C₂×C₃₁	1	2	yes	complemented
477	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#3221	C₂×C₃₁	1	2	yes	complemented
479	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#3179	C₂×C₃₁	1	2	yes	complemented
481	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#3137	C₂×C₃₁	1	2	yes	complemented
483	C₂×#488	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
485	C₂²×C₃₁	—	2	1	no	—
486	C₂²×C₃₁	—	2	1	no	—
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	2	2	no	—
490	C₂²×C₃₁	—	4	2	no	—
491	C₂²×C₃₁	—	4	2	no	—
492	C₂²×C₃₁	—	4	2	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	16	2	no	—
497	C₂²×C₃₁	#577	1	2	yes	—
498	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
499	C₄×C₃₁	—	2	1	no	—
500	C₄×C₃₁	—	2	1	no	—
501	C₄×C₃₁	—	2	2	no	—
502	C₄×C₃₁	—	2	2	no	—
503	C₄×C₃₁	—	2	1	no	—
504	C₄×C₃₁	—	2	1	no	—
505	C₄×C₃₁	—	2	1	no	—
506	C₄×C₃₁	—	2	2	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	2	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	2	no	—
511	C₄×C₃₁	—	4	2	no	—
512	C₄×C₃₁	—	4	2	no	—
513	C₄×C₃₁	#585	1	1	yes	characteristic
514	C₄×C₃₁	#585	1	1	yes	characteristic
515	#563	—	2	1	no	—
516	#563	—	2	1	no	—
517	#562	—	2	1	no	—
518	#562	—	2	1	no	—
519	#556	C₂²×C₃₁	1	2	yes	—
520	#554	C₂²×C₃₁	1	2	yes	complemented
521	#553	C₂²×C₃₁	1	2	yes	—
522	#553	C₂²×C₃₁	1	2	yes	complemented
523	#551	—	2	2	no	—
524	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
525	#548	C₂²×C₃₁	1	2	yes	—
526	#547	—	2	2	no	—
527	#547	C₂²×C₃₁	1	2	yes	—
528	#546	C₂²×C₃₁	1	2	yes	—
529	#544	C₂²×C₃₁	1	2	yes	complemented
530	#543	—	2	1	no	—
531	#542	—	2	2	no	—
532	#542	C₂²×C₃₁	1	2	yes	—
533	#540	C₂²×C₃₁	1	2	yes	complemented
534	#539	—	2	2	no	—
535	#539	—	2	1	no	—
536	#538	—	2	1	no	—
537	#537	—	2	1	no	—
538	#536	C₂²×C₃₁	1	2	yes	—
539	#533	C₂²×C₃₁	1	1	yes	characteristic
540	#532	C₂²×C₃₁	1	1	yes	characteristic
541	#529	C₂²×C₃₁	1	1	yes	characteristic
542	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
543	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
544	#501	C₂²×C₃₁	1	2	yes	complemented
545	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
546	#496	C₂²×C₃₁	1	2	yes	—
547	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#491	C₂²×C₃₁	1	2	yes	complemented
549	#491	C₂²×C₃₁	1	2	yes	complemented
550	#489	C₂²×C₃₁	1	2	yes	—
551	#489	C₂²×C₃₁	1	2	yes	—
552	#488	C₂²×C₃₁	1	2	yes	—
553	#488	C₂²×C₃₁	1	2	yes	—
554	#488	C₂²×C₃₁	1	2	yes	—
555	#488	C₂²×C₃₁	1	2	yes	—
556	#488	C₂²×C₃₁	1	2	yes	—
557	#487	C₂²×C₃₁	1	2	yes	complemented
558	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#485	C₂²×C₃₁	1	2	yes	complemented
561	#484	C₂²×C₃₁	1	2	yes	—
562	#483	C₂²×C₃₁	1	2	yes	—
563	#483	C₂²×C₃₁	1	2	yes	complemented
564	#482	C₂²×C₃₁	1	2	yes	—
565	#481	C₂²×C₃₁	1	2	yes	—
566	#479	C₂²×C₃₁	1	2	yes	complemented
567	#479	C₂²×C₃₁	1	2	yes	complemented
568	#479	C₂²×C₃₁	1	2	yes	complemented
569	#478	C₂²×C₃₁	1	2	yes	—
570	#476	C₂²×C₃₁	1	2	yes	—
571	#475	C₂²×C₃₁	1	2	yes	complemented
572	#469	C₂²×C₃₁	1	2	yes	—
573	#468	C₂²×C₃₁	1	2	yes	complemented
574	#466	C₂²×C₃₁	1	2	yes	—
575	#465	C₂²×C₃₁	1	2	yes	—
576	#465	C₂²×C₃₁	1	2	yes	—
577	#465	C₂²×C₃₁	1	2	yes	complemented
578	#463	C₂²×C₃₁	1	2	yes	—
579	#463	C₂²×C₃₁	1	2	yes	—
580	#463	C₂²×C₃₁	1	2	yes	—
581	#463	C₂²×C₃₁	1	2	yes	—
582	#461	C₂²×C₃₁	1	2	yes	complemented
583	#461	C₂²×C₃₁	1	2	yes	complemented
584	#449	C₂²×C₃₁	1	2	yes	—
585	#449	C₂²×C₃₁	1	2	yes	—
586	#448	C₂²×C₃₁	1	2	yes	—
587	#448	C₂²×C₃₁	1	2	yes	complemented
588	#448	C₂²×C₃₁	1	2	yes	complemented
589	#447	C₂²×C₃₁	1	2	yes	—
590	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#442	C₂²×C₃₁	1	2	yes	—
593	#440	C₂²×C₃₁	1	2	yes	complemented
594	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
595	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
596	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
597	C₄×D₈	C₂²×C₃₁	1	2	yes	—
598	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#435	C₂²×C₃₁	1	2	yes	—
600	C₈×D₄	C₂²×C₃₁	1	2	yes	—
601	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#433	C₂²×C₃₁	1	2	yes	complemented
603	#432	C₂²×C₃₁	1	1	yes	characteristic
604	#419	C₂²×C₃₁	1	2	yes	complemented
605	#417	C₂²×C₃₁	1	2	yes	—
606	#416	C₂²×C₃₁	1	2	yes	—
607	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
608	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
609	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
610	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
611	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
612	#405	C₂²×C₃₁	1	2	yes	complemented
613	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
614	C₂×C₃₁	—	2	2	no	—
615	C₂×C₃₁	—	4	2	no	—
616	C₂×C₃₁	—	8	2	no	—
617	C₂×C₃₁	—	8	2	no	—
618	C₂×C₃₁	#3500	1	1	yes	characteristic
619	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
620	C₂×C₃₁	#3584	1	1	yes	characteristic
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	C₂³×C₃₁	1	2	yes	—
624	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
626	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
627	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
631	C₂×D₈	C₂³×C₃₁	1	2	yes	—
632	C₂×D₈	C₂³×C₃₁	1	2	yes	—
633	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
634	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
635	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
636	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
637	C₄⋊Q₈	—	2	2	no	—
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
640	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
641	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
644	#127	C₂³×C₃₁	1	1	yes	characteristic
645	#126	—	2	2	no	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	D₄×C₃₁	1	2	yes	—
651	#125	—	2	2	no	—
652	#125	—	2	1	no	—
653	#125	—	2	1	no	—
654	#125	—	2	1	no	—
655	#125	D₄×C₃₁	1	1	yes	characteristic
656	#125	C₂³×C₃₁	1	2	yes	—
657	#125	C₂³×C₃₁	1	2	yes	—
658	#125	C₂³×C₃₁	1	2	yes	—
659	#124	—	2	2	no	—
660	#124	—	2	2	no	—
661	#124	—	2	1	no	—
662	#124	—	2	1	no	—
663	#124	—	2	1	no	—
664	#124	D₄×C₃₁	1	1	yes	characteristic
665	#124	C₂³×C₃₁	1	2	yes	—
666	#124	C₂³×C₃₁	1	2	yes	—
667	#124	C₂³×C₃₁	1	2	yes	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	D₄×C₃₁	1	2	yes	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	—	2	2	no	—
699	#121	—	2	1	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	D₄×C₃₁	1	1	yes	characteristic
704	#121	C₂³×C₃₁	1	2	yes	—
705	#121	C₂³×C₃₁	1	2	yes	—
706	#121	C₂³×C₃₁	1	2	yes	—
707	#121	C₂³×C₃₁	1	2	yes	—
708	#120	—	2	2	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
711	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
712	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	2	no	—
717	C₄×D₄	—	2	1	no	—
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	C₄×D₄	C₂³×C₃₁	1	2	yes	—
723	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
724	#117	—	2	1	no	—
725	#117	—	2	2	no	—
726	#117	C₂³×C₃₁	1	2	yes	—
727	#117	C₂³×C₃₁	1	2	yes	—
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	1	no	—
730	C₂×C₄⋊C₄	—	2	2	no	—
731	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
734	C₂×C₂²⋊C₄	—	2	1	no	—
735	C₂×C₂²⋊C₄	—	2	1	no	—
736	C₂×C₂²⋊C₄	—	2	2	no	—
737	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
738	#107	C₂³×C₃₁	1	2	yes	—
739	#107	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
747	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
748	#103	C₂³×C₃₁	1	2	yes	—
749	#103	C₂³×C₃₁	1	2	yes	—
750	#103	C₂³×C₃₁	1	2	yes	—
751	#103	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	#103	C₂³×C₃₁	1	2	yes	—
756	#103	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#103	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	2	yes	—
770	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
771	#97	C₂³×C₃₁	1	2	yes	—
772	#97	C₂³×C₃₁	1	2	yes	—
773	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄×C₈	C₂³×C₃₁	1	2	yes	—
778	C₃₁	#62557	1	1	yes	characteristic, direct product factor, Sylow
779	C₂⁴	—	2	1	no	—
780	#41	—	4	2	no	—
781	#41	—	4	2	no	—
782	#41	—	8	2	no	—
783	#41	—	8	4	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	4	1	no	—
790	C₂×Q₈	—	4	1	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
794	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
795	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	4	1	no	—
805	C₂×D₄	—	4	1	no	—
806	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
807	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
808	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
809	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	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	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	D₈	—	4	2	no	—
829	D₈	—	4	2	no	—
830	M₁₆	—	4	2	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	—	4	1	no	—
833	C₂×C₈	—	4	1	no	—
834	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
835	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
836	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
839	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	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	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
861	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
864	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
866	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
891	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
897	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
898	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₄²	C₂⁴×C₃₁	1	2	yes	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	8	1	no	—
904	C₂³	—	8	1	no	—
905	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
906	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
907	Q₈	—	2	2	no	—
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	4	1	no	—
912	Q₈	—	8	1	no	—
913	Q₈	—	8	2	no	—
914	Q₈	—	8	1	no	—
915	Q₈	—	8	1	no	—
916	Q₈	—	8	2	no	—
917	D₄	—	2	4	no	—
918	D₄	—	2	2	no	—
919	D₄	—	2	2	no	—
920	D₄	—	2	2	no	—
921	D₄	—	2	2	no	—
922	D₄	—	4	1	no	—
923	D₄	—	4	4	no	—
924	D₄	—	8	1	no	—
925	D₄	—	8	1	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	2	no	—
929	D₄	—	8	2	no	—
930	D₄	—	8	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	1	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	1	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
955	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
957	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
958	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
961	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
962	C₈	—	2	1	no	—
963	C₈	—	2	1	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	1	no	—
966	C₈	—	2	1	no	—
967	C₈	—	2	2	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	16	2	no	—
980	C₂²	C₃₁×#577	1	2	yes	—
981	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
982	C₄	—	2	2	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	C₃₁×#585	1	1	yes	characteristic
997	C₄	C₃₁×#585	1	1	yes	characteristic
998	C₂	—	2	2	no	—
999	C₂	—	4	2	no	—
1000	C₂	—	8	2	no	—
1001	C₂	—	8	2	no	—
1002	C₂	C₃₁×#3500	1	1	yes	characteristic
1003	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1004	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×#3561	C₂	semidirect
2. C₃₁×#3559	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3360	C₂	semidirect
5. C₃₁×#3326	C₂	semidirect
6. C₃₁×#3320	C₂	semidirect
7. C₃₁×#3306	C₂	semidirect
8. C₃₁×#3301	C₂	semidirect
9. C₃₁×#3298	C₂	semidirect
10. C₃₁×#3297	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3236	C₂	semidirect
13. C₃₁×#3221	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3179	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3137	C₂	semidirect
18. C₂×C₃₁×#488	C₂	semidirect
19. C₃₁×#2966	C₂	semidirect
25. C₃₁×#554	C₂²	semidirect
27. C₃₁×#553	C₂²	semidirect
34. C₃₁×#544	C₂²	semidirect
38. C₃₁×#540	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#498	C₂²	semidirect
52. C₃₁×#492	C₂²	semidirect
53. C₃₁×#491	C₂²	semidirect
54. C₃₁×#491	C₂²	semidirect
62. C₃₁×#487	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
71. C₃₁×#479	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
78. C₃₁×#468	C₂²	semidirect
82. C₃₁×#465	C₂²	semidirect
87. C₃₁×#461	C₂²	semidirect
88. C₃₁×#461	C₂²	semidirect
92. C₃₁×#448	C₂²	semidirect
93. C₃₁×#448	C₂²	semidirect
95. C₃₁×#446	C₂²	semidirect
96. C₈×Q₈×C₃₁	C₂²	semidirect
98. C₃₁×#440	C₂²	semidirect
99. C₄×SD₁₆×C₃₁	C₂²	semidirect
100. C₄×SD₁₆×C₃₁	C₂²	semidirect
101. C₄×SD₁₆×C₃₁	C₂²	semidirect
103. C₃₁×#436	C₂²	semidirect
106. C₈×D₄×C₃₁	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
109. C₃₁×#419	C₂²	semidirect
114. C₂×C₃₁×#103	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
397. #62557	C₃₁	direct (N × H)
466. #3561	C₂×C₃₁	semidirect
467. #3559	C₂×C₃₁	semidirect
468. #3376	C₂×C₃₁	semidirect
469. #3360	C₂×C₃₁	semidirect
470. #3326	C₂×C₃₁	semidirect
471. #3320	C₂×C₃₁	semidirect
472. #3306	C₂×C₃₁	semidirect
473. #3301	C₂×C₃₁	semidirect
474. #3298	C₂×C₃₁	semidirect
475. #3297	C₂×C₃₁	semidirect
476. #3244	C₂×C₃₁	semidirect
477. #3236	C₂×C₃₁	semidirect
478. #3221	C₂×C₃₁	semidirect
479. #3213	C₂×C₃₁	semidirect
480. #3179	C₂×C₃₁	semidirect
481. #3167	C₂×C₃₁	semidirect
482. #3137	C₂×C₃₁	semidirect
483. C₂×#488	C₂×C₃₁	semidirect
484. #2966	C₂×C₃₁	semidirect
520. #554	C₂²×C₃₁	semidirect
522. #553	C₂²×C₃₁	semidirect
529. #544	C₂²×C₃₁	semidirect
533. #540	C₂²×C₃₁	semidirect
544. #501	C₂²×C₃₁	semidirect
545. #498	C₂²×C₃₁	semidirect
547. #492	C₂²×C₃₁	semidirect
548. #491	C₂²×C₃₁	semidirect
549. #491	C₂²×C₃₁	semidirect
557. #487	C₂²×C₃₁	semidirect
558. #487	C₂²×C₃₁	semidirect
559. #486	C₂²×C₃₁	semidirect
560. #485	C₂²×C₃₁	semidirect
563. #483	C₂²×C₃₁	semidirect
566. #479	C₂²×C₃₁	semidirect
567. #479	C₂²×C₃₁	semidirect
568. #479	C₂²×C₃₁	semidirect
571. #475	C₂²×C₃₁	semidirect
573. #468	C₂²×C₃₁	semidirect
577. #465	C₂²×C₃₁	semidirect
582. #461	C₂²×C₃₁	semidirect
583. #461	C₂²×C₃₁	semidirect
587. #448	C₂²×C₃₁	semidirect
588. #448	C₂²×C₃₁	semidirect
590. #446	C₂²×C₃₁	semidirect
591. C₈×Q₈	C₂²×C₃₁	semidirect
593. #440	C₂²×C₃₁	semidirect
594. C₄×SD₁₆	C₂²×C₃₁	semidirect
595. C₄×SD₁₆	C₂²×C₃₁	semidirect
596. C₄×SD₁₆	C₂²×C₃₁	semidirect
598. #436	C₂²×C₃₁	semidirect
601. C₈×D₄	C₂²×C₃₁	semidirect
602. #433	C₂²×C₃₁	semidirect
604. #419	C₂²×C₃₁	semidirect
609. C₂×#103	C₂²×C₃₁	semidirect
612. #405	C₂²×C₃₁	semidirect
778. C₃₁	#62557	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×#3561	2
C₃₁×#3559	2
C₃₁×#3376	2
C₃₁×#3360	2
C₃₁×#3326	2
C₃₁×#3320	2
C₃₁×#3306	2
C₃₁×#3301	2
C₃₁×#3298	2
C₃₁×#3297	2
C₃₁×#3244	2
C₃₁×#3236	2
C₃₁×#3221	2
C₃₁×#3213	2
C₃₁×#3179	2
C₃₁×#3167	2
C₃₁×#3137	2
C₂×C₃₁×#488	2
C₃₁×#2966	2
#62557	31

Subgroups — C31×#62557 #21519316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62557 #21519316