Subgroups — C₃₁×#62094 #21518853

Order 7936.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1078 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×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3254	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×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3046	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#135	C₂²	1	2	yes	—
24	C₃₁×#563	—	2	1	no	—
25	C₃₁×#562	—	2	1	no	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#553	—	2	2	no	—
29	C₃₁×#553	C₂²	1	2	yes	—
30	C₃₁×#551	—	2	2	no	—
31	C₃₁×#550	—	2	1	no	—
32	C₃₁×#550	C₂²	1	2	yes	—
33	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
36	C₃₁×#548	C₂²	1	2	yes	—
37	C₃₁×#547	—	2	1	no	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	—	2	2	no	—
42	C₃₁×#542	C₂²	1	2	yes	—
43	C₃₁×#540	—	2	2	no	—
44	C₃₁×#540	C₂²	1	2	yes	complemented
45	C₃₁×#538	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	—
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#532	—	2	1	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₃₁×#520	C₂²	1	2	yes	complemented
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#496	C₂²	1	2	yes	—
56	C₃₁×#496	C₂²	1	2	yes	—
57	C₃₁×#492	C₂²	1	2	yes	complemented
58	C₃₁×#491	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#488	C₂²	1	2	yes	—
61	C₃₁×#485	C₂²	1	2	yes	—
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#480	C₂²	1	2	yes	—
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#478	C₂²	1	2	yes	—
66	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#474	C₂²	1	2	yes	complemented
70	C₃₁×#469	C₂²	1	2	yes	—
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	2	yes	—
73	C₃₁×#468	C₂²	1	2	yes	complemented
74	C₃₁×#466	C₂²	1	2	yes	—
75	C₃₁×#465	C₂²	1	2	yes	complemented
76	C₃₁×#464	C₂²	1	2	yes	—
77	C₃₁×#464	C₂²	1	2	yes	—
78	C₃₁×#464	C₂²	1	2	yes	—
79	C₃₁×#463	C₂²	1	2	yes	—
80	C₃₁×#463	C₂²	1	2	yes	—
81	C₃₁×#463	C₂²	1	2	yes	—
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#461	C₂²	1	2	yes	complemented
88	C₃₁×#461	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	2	yes	complemented
90	C₃₁×#460	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	—
92	C₃₁×#452	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	2	yes	—
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#448	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#441	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	—
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	2	yes	—
108	C₃₁×#436	C₂²	1	2	yes	—
109	C₃₁×#435	C₂²	1	2	yes	—
110	C₃₁×#435	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₃₁×#423	C₂²	1	1	yes	characteristic
115	C₃₁×#419	C₂²	1	1	yes	characteristic
116	C₃₁×#418	C₂²	1	1	yes	characteristic
117	C₃₁×#417	C₂²	1	2	yes	—
118	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×#41×C₃₁	C₂³	1	2	yes	—
125	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₃₁×#137	—	4	2	no	—
129	C₃₁×#137	—	4	4	no	—
130	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
131	C₃₁×#135	—	4	4	no	—
132	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×D₈×C₃₁	C₂³	1	2	yes	—
142	C₂×D₈×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	2	yes	—
144	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₃₁×C₄⋊Q₈	—	2	1	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×#127	—	2	1	no	—
155	C₃₁×#127	—	2	2	no	—
156	C₃₁×#127	C₂³	1	2	yes	—
157	C₃₁×#127	C₂³	1	1	yes	characteristic
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	D₄	1	2	yes	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	1	no	—
165	C₃₁×#125	D₄	1	1	yes	characteristic
166	C₃₁×#125	C₂³	1	2	yes	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	—	2	1	no	—
172	C₃₁×#124	D₄	1	1	yes	characteristic
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	D₄	1	2	yes	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	D₄	1	1	yes	characteristic
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#120	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	2	yes	—
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	1	no	—
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₃₁×#117	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₄²×C₃₁	—	2	1	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#107	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	#41×C₃₁	—	2	4	no	—
286	#41×C₃₁	—	2	2	no	—
287	#41×C₃₁	—	4	1	no	—
288	#41×C₃₁	—	4	2	no	—
289	#41×C₃₁	—	4	2	no	—
290	#41×C₃₁	—	4	2	no	—
291	#41×C₃₁	—	8	2	no	—
292	#41×C₃₁	—	8	2	no	—
293	#41×C₃₁	—	8	2	no	—
294	C₂×Q₈×C₃₁	—	2	1	no	—
295	C₂×Q₈×C₃₁	—	2	1	no	—
296	C₂×Q₈×C₃₁	—	2	2	no	—
297	C₂×Q₈×C₃₁	—	2	1	no	—
298	C₂×Q₈×C₃₁	—	4	2	no	—
299	C₂×Q₈×C₃₁	—	4	1	no	—
300	C₂×Q₈×C₃₁	—	4	1	no	—
301	C₂×Q₈×C₃₁	—	4	2	no	—
302	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₃₁	—	2	1	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	2	2	no	—
312	C₂×D₄×C₃₁	—	2	2	no	—
313	C₂×D₄×C₃₁	—	2	1	no	—
314	C₂×D₄×C₃₁	—	2	1	no	—
315	C₂×D₄×C₃₁	—	2	2	no	—
316	C₂×D₄×C₃₁	—	2	2	no	—
317	C₂×D₄×C₃₁	—	2	1	no	—
318	C₂×D₄×C₃₁	—	4	1	no	—
319	C₂×D₄×C₃₁	—	4	1	no	—
320	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
321	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	1	no	—
329	C₂²×C₄×C₃₁	—	2	1	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	2	2	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	2	2	no	—
336	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
340	Q₁₆×C₃₁	—	2	4	no	—
341	Q₁₆×C₃₁	—	2	4	no	—
342	SD₁₆×C₃₁	—	2	4	no	—
343	SD₁₆×C₃₁	—	4	2	no	—
344	SD₁₆×C₃₁	—	4	2	no	—
345	SD₁₆×C₃₁	—	4	2	no	—
346	SD₁₆×C₃₁	—	4	2	no	—
347	SD₁₆×C₃₁	—	4	2	no	—
348	SD₁₆×C₃₁	—	4	2	no	—
349	D₈×C₃₁	—	4	2	no	—
350	D₈×C₃₁	—	4	2	no	—
351	D₈×C₃₁	—	4	2	no	—
352	M₁₆×C₃₁	—	4	1	no	—
353	M₁₆×C₃₁	—	4	2	no	—
354	M₁₆×C₃₁	—	4	1	no	—
355	C₂×C₈×C₃₁	—	4	2	no	—
356	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
357	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
358	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	1	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	1	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	1	no	—
397	C₂²⋊C₄×C₃₁	—	2	1	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
400	C₂²⋊C₄×C₃₁	—	2	2	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄²×C₃₁	—	2	1	no	—
410	C₄²×C₃₁	—	2	1	no	—
411	C₄²×C₃₁	—	2	1	no	—
412	C₄²×C₃₁	—	2	2	no	—
413	C₄²×C₃₁	—	2	2	no	—
414	C₄²×C₃₁	—	2	2	no	—
415	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₃₁	C₂⁴	1	2	yes	—
418	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
420	#62094	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
421	C₂³×C₃₁	—	2	2	no	—
422	C₂³×C₃₁	—	2	1	no	—
423	C₂³×C₃₁	—	2	2	no	—
424	C₂³×C₃₁	—	4	2	no	—
425	C₂³×C₃₁	—	8	1	no	—
426	C₂³×C₃₁	—	8	1	no	—
427	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
429	Q₈×C₃₁	—	2	1	no	—
430	Q₈×C₃₁	—	2	2	no	—
431	Q₈×C₃₁	—	2	2	no	—
432	Q₈×C₃₁	—	2	2	no	—
433	Q₈×C₃₁	—	2	2	no	—
434	Q₈×C₃₁	—	4	1	no	—
435	Q₈×C₃₁	—	4	2	no	—
436	Q₈×C₃₁	—	8	1	no	—
437	Q₈×C₃₁	—	8	2	no	—
438	Q₈×C₃₁	—	8	1	no	—
439	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
440	D₄×C₃₁	—	2	2	no	—
441	D₄×C₃₁	—	2	1	no	—
442	D₄×C₃₁	—	2	2	no	—
443	D₄×C₃₁	—	2	2	no	—
444	D₄×C₃₁	—	2	2	no	—
445	D₄×C₃₁	—	2	1	no	—
446	D₄×C₃₁	—	4	2	no	—
447	D₄×C₃₁	—	4	1	no	—
448	D₄×C₃₁	—	4	4	no	—
449	D₄×C₃₁	—	4	2	no	—
450	D₄×C₃₁	—	4	2	no	—
451	D₄×C₃₁	—	8	1	no	—
452	D₄×C₃₁	—	8	2	no	—
453	D₄×C₃₁	—	8	1	no	—
454	D₄×C₃₁	—	8	2	no	—
455	D₄×C₃₁	—	8	2	no	—
456	D₄×C₃₁	—	8	2	no	—
457	D₄×C₃₁	—	8	2	no	—
458	D₄×C₃₁	—	8	2	no	—
459	D₄×C₃₁	—	8	2	no	—
460	C₂×C₄×C₃₁	—	2	1	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	4	1	no	—
472	C₂×C₄×C₃₁	—	4	1	no	—
473	C₂×C₄×C₃₁	—	4	4	no	—
474	C₂×C₄×C₃₁	—	4	2	no	—
475	C₂×C₄×C₃₁	—	4	2	no	—
476	C₂×C₄×C₃₁	—	8	2	no	—
477	C₂×C₄×C₃₁	—	8	1	no	—
478	C₂×C₄×C₃₁	—	8	2	no	—
479	C₂×C₄×C₃₁	—	8	2	no	—
480	C₂×C₄×C₃₁	—	8	2	no	—
481	C₂×C₄×C₃₁	—	8	2	no	—
482	C₂×C₄×C₃₁	—	8	1	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
493	C₈×C₃₁	—	2	2	no	—
494	C₈×C₃₁	—	2	2	no	—
495	C₈×C₃₁	—	2	2	no	—
496	C₈×C₃₁	—	2	2	no	—
497	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3517	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3397	C₂×C₃₁	1	2	yes	complemented
500	#3377	C₂×C₃₁	1	2	yes	complemented
501	#3322	C₂×C₃₁	1	2	yes	complemented
502	#3320	C₂×C₃₁	1	2	yes	complemented
503	#3308	C₂×C₃₁	1	2	yes	complemented
504	#3278	C₂×C₃₁	1	2	yes	complemented
505	#3271	C₂×C₃₁	1	2	yes	complemented
506	#3268	C₂×C₃₁	1	2	yes	complemented
507	#3257	C₂×C₃₁	1	2	yes	complemented
508	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3221	C₂×C₃₁	1	2	yes	complemented
510	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3124	C₂×C₃₁	1	2	yes	complemented
512	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3046	C₂×C₃₁	1	2	yes	complemented
514	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#2995	C₂×C₃₁	1	1	yes	characteristic, complemented
516	C₂²×C₃₁	—	2	1	no	—
517	C₂²×C₃₁	—	2	2	no	—
518	C₂²×C₃₁	—	2	1	no	—
519	C₂²×C₃₁	—	2	2	no	—
520	C₂²×C₃₁	—	2	2	no	—
521	C₂²×C₃₁	—	2	1	no	—
522	C₂²×C₃₁	—	4	1	no	—
523	C₂²×C₃₁	—	4	2	no	—
524	C₂²×C₃₁	—	4	2	no	—
525	C₂²×C₃₁	—	4	1	no	—
526	C₂²×C₃₁	—	4	2	no	—
527	C₂²×C₃₁	—	4	2	no	—
528	C₂²×C₃₁	—	4	1	no	—
529	C₂²×C₃₁	—	4	2	no	—
530	C₂²×C₃₁	—	4	2	no	—
531	C₂²×C₃₁	—	16	2	no	—
532	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₃₁	—	2	1	no	—
534	C₄×C₃₁	—	2	1	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	2	1	no	—
537	C₄×C₃₁	—	2	1	no	—
538	C₄×C₃₁	—	2	2	no	—
539	C₄×C₃₁	—	2	2	no	—
540	C₄×C₃₁	—	2	1	no	—
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	2	no	—
544	C₄×C₃₁	—	4	2	no	—
545	C₄×C₃₁	—	4	1	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₄×C₃₁	#585	1	1	yes	characteristic
550	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
551	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
552	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
553	C₂×#135	C₂²×C₃₁	1	2	yes	—
554	#563	—	2	1	no	—
555	#562	—	2	1	no	—
556	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
557	#556	C₂²×C₃₁	1	2	yes	—
558	#553	—	2	2	no	—
559	#553	C₂²×C₃₁	1	2	yes	—
560	#551	—	2	2	no	—
561	#550	—	2	1	no	—
562	#550	C₂²×C₃₁	1	2	yes	—
563	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
566	#548	C₂²×C₃₁	1	2	yes	—
567	#547	—	2	1	no	—
568	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#546	C₂²×C₃₁	1	2	yes	—
570	#543	—	2	1	no	—
571	#542	—	2	2	no	—
572	#542	C₂²×C₃₁	1	2	yes	—
573	#540	—	2	2	no	—
574	#540	C₂²×C₃₁	1	2	yes	complemented
575	#538	—	2	1	no	—
576	#536	C₂²×C₃₁	1	2	yes	—
577	#533	C₂²×C₃₁	1	1	yes	characteristic
578	#532	—	2	1	no	—
579	#532	C₂²×C₃₁	1	1	yes	characteristic
580	#529	—	2	1	no	—
581	#529	C₂²×C₃₁	1	1	yes	characteristic
582	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
583	#520	C₂²×C₃₁	1	2	yes	complemented
584	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
585	#496	C₂²×C₃₁	1	2	yes	—
586	#496	C₂²×C₃₁	1	2	yes	—
587	#492	C₂²×C₃₁	1	2	yes	complemented
588	#491	C₂²×C₃₁	1	2	yes	complemented
589	#489	C₂²×C₃₁	1	2	yes	—
590	#488	C₂²×C₃₁	1	2	yes	—
591	#485	C₂²×C₃₁	1	2	yes	—
592	#484	C₂²×C₃₁	1	2	yes	complemented
593	#480	C₂²×C₃₁	1	2	yes	—
594	#479	C₂²×C₃₁	1	2	yes	complemented
595	#478	C₂²×C₃₁	1	2	yes	—
596	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#477	C₂²×C₃₁	1	2	yes	complemented
598	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#474	C₂²×C₃₁	1	2	yes	complemented
600	#469	C₂²×C₃₁	1	2	yes	—
601	#468	C₂²×C₃₁	1	2	yes	—
602	#468	C₂²×C₃₁	1	2	yes	—
603	#468	C₂²×C₃₁	1	2	yes	complemented
604	#466	C₂²×C₃₁	1	2	yes	—
605	#465	C₂²×C₃₁	1	2	yes	complemented
606	#464	C₂²×C₃₁	1	2	yes	—
607	#464	C₂²×C₃₁	1	2	yes	—
608	#464	C₂²×C₃₁	1	2	yes	—
609	#463	C₂²×C₃₁	1	2	yes	—
610	#463	C₂²×C₃₁	1	2	yes	—
611	#463	C₂²×C₃₁	1	2	yes	—
612	#463	C₂²×C₃₁	1	2	yes	—
613	#463	C₂²×C₃₁	1	2	yes	—
614	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
615	#462	C₂²×C₃₁	1	2	yes	complemented
616	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#461	C₂²×C₃₁	1	2	yes	complemented
618	#461	C₂²×C₃₁	1	2	yes	complemented
619	#460	C₂²×C₃₁	1	2	yes	complemented
620	#460	C₂²×C₃₁	1	2	yes	complemented
621	#459	C₂²×C₃₁	1	2	yes	—
622	#452	C₂²×C₃₁	1	2	yes	—
623	#452	C₂²×C₃₁	1	2	yes	complemented
624	#449	C₂²×C₃₁	1	2	yes	—
625	#449	C₂²×C₃₁	1	2	yes	—
626	#449	C₂²×C₃₁	1	2	yes	—
627	#448	C₂²×C₃₁	1	2	yes	—
628	#448	C₂²×C₃₁	1	2	yes	complemented
629	#448	C₂²×C₃₁	1	2	yes	complemented
630	#447	C₂²×C₃₁	1	2	yes	—
631	#446	C₂²×C₃₁	1	2	yes	complemented
632	#441	C₂²×C₃₁	1	2	yes	complemented
633	#440	C₂²×C₃₁	1	2	yes	—
634	#440	C₂²×C₃₁	1	2	yes	complemented
635	#440	C₂²×C₃₁	1	2	yes	complemented
636	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
637	C₄×D₈	C₂²×C₃₁	1	2	yes	—
638	#436	C₂²×C₃₁	1	2	yes	—
639	#435	C₂²×C₃₁	1	2	yes	—
640	#435	C₂²×C₃₁	1	2	yes	complemented
641	#433	C₂²×C₃₁	1	2	yes	complemented
642	#432	C₂²×C₃₁	1	1	yes	characteristic
643	#424	C₂²×C₃₁	1	2	yes	complemented
644	#423	C₂²×C₃₁	1	1	yes	characteristic
645	#419	C₂²×C₃₁	1	1	yes	characteristic
646	#418	C₂²×C₃₁	1	1	yes	characteristic
647	#417	C₂²×C₃₁	1	2	yes	—
648	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
649	C₂×C₃₁	—	4	2	no	—
650	C₂×C₃₁	—	4	1	no	—
651	C₂×C₃₁	—	8	1	no	—
652	C₂×C₃₁	—	8	2	no	—
653	C₂×C₃₁	—	8	2	no	—
654	C₂×C₃₁	#3488	1	1	yes	characteristic
655	C₂×C₃₁	#3585	1	1	yes	characteristic
656	C₂×C₃₁	#3586	1	1	yes	characteristic
657	C₂×#41	—	2	1	no	—
658	C₂×#41	—	2	1	no	—
659	C₂×#41	—	2	1	no	—
660	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
661	C₂×#41	C₂³×C₃₁	1	2	yes	—
662	C₂×#41	C₂³×C₃₁	1	2	yes	—
663	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
664	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
665	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
666	#137	—	4	2	no	—
667	#137	—	4	4	no	—
668	AGL(1,ℤ/8)	—	4	2	no	—
669	#135	—	4	4	no	—
670	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
672	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
673	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
679	C₂×D₈	C₂³×C₃₁	1	2	yes	—
680	C₂×D₈	C₂³×C₃₁	1	2	yes	—
681	C₂×D₈	C₂³×C₃₁	1	2	yes	—
682	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
685	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
690	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
692	#127	—	2	1	no	—
693	#127	—	2	2	no	—
694	#127	C₂³×C₃₁	1	1	yes	characteristic
695	#127	C₂³×C₃₁	1	2	yes	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	D₄×C₃₁	1	2	yes	—
701	#125	—	2	2	no	—
702	#125	—	2	1	no	—
703	#125	D₄×C₃₁	1	1	yes	characteristic
704	#125	C₂³×C₃₁	1	2	yes	—
705	#124	—	2	2	no	—
706	#124	—	2	2	no	—
707	#124	—	2	1	no	—
708	#124	—	2	1	no	—
709	#124	—	2	1	no	—
710	#124	D₄×C₃₁	1	1	yes	characteristic
711	#124	C₂³×C₃₁	1	2	yes	—
712	#124	C₂³×C₃₁	1	2	yes	—
713	#124	C₂³×C₃₁	1	2	yes	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	D₄×C₃₁	1	2	yes	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	1	no	—
738	#121	—	2	1	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	2	no	—
744	#121	—	2	2	no	—
745	#121	—	2	2	no	—
746	#121	D₄×C₃₁	1	1	yes	characteristic
747	#121	C₂³×C₃₁	1	2	yes	—
748	#121	C₂³×C₃₁	1	2	yes	—
749	#121	C₂³×C₃₁	1	2	yes	—
750	#121	C₂³×C₃₁	1	2	yes	—
751	#120	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	1	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₃₁	1	2	yes	—
773	C₄×D₄	C₂³×C₃₁	1	2	yes	—
774	C₄×D₄	C₂³×C₃₁	1	2	yes	—
775	C₄×D₄	C₂³×C₃₁	1	2	yes	—
776	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
777	#117	—	2	1	no	—
778	#117	—	2	2	no	—
779	#117	—	2	2	no	—
780	#117	—	2	1	no	—
781	#117	C₂³×C₃₁	1	1	yes	characteristic
782	#117	C₂³×C₃₁	1	2	yes	—
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
785	C₂×C₂²⋊C₄	—	2	1	no	—
786	C₂×C₂²⋊C₄	—	2	1	no	—
787	C₂×C₂²⋊C₄	—	2	2	no	—
788	C₂×C₄²	—	2	1	no	—
789	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
790	#107	C₂³×C₃₁	1	2	yes	—
791	#107	C₂³×C₃₁	1	2	yes	—
792	#107	C₂³×C₃₁	1	2	yes	—
793	#106	C₂³×C₃₁	1	2	yes	—
794	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
795	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
796	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
798	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
799	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
800	#103	C₂³×C₃₁	1	2	yes	—
801	#103	C₂³×C₃₁	1	2	yes	—
802	#103	C₂³×C₃₁	1	2	yes	—
803	#103	C₂³×C₃₁	1	2	yes	—
804	#103	C₂³×C₃₁	1	2	yes	—
805	#103	C₂³×C₃₁	1	2	yes	—
806	#103	C₂³×C₃₁	1	2	yes	—
807	#103	C₂³×C₃₁	1	2	yes	—
808	#103	C₂³×C₃₁	1	2	yes	—
809	#102	C₂³×C₃₁	1	2	yes	—
810	#102	C₂³×C₃₁	1	2	yes	—
811	#102	C₂³×C₃₁	1	2	yes	—
812	#102	C₂³×C₃₁	1	2	yes	—
813	#102	C₂³×C₃₁	1	2	yes	—
814	#102	C₂³×C₃₁	1	2	yes	—
815	#102	C₂³×C₃₁	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
819	#97	C₂³×C₃₁	1	2	yes	—
820	#97	C₂³×C₃₁	1	2	yes	—
821	C₄×C₈	C₂³×C₃₁	1	2	yes	—
822	C₃₁	#62094	1	1	yes	characteristic, direct product factor, Sylow
823	C₂⁴	—	2	1	no	—
824	#41	—	2	4	no	—
825	#41	—	2	2	no	—
826	#41	—	4	1	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	#41	—	4	2	no	—
830	#41	—	8	2	no	—
831	#41	—	8	2	no	—
832	#41	—	8	2	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	2	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	—	4	1	no	—
840	C₂×Q₈	—	4	2	no	—
841	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
842	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
843	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
844	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	4	1	no	—
859	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
860	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
862	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
863	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	1	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	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
879	Q₁₆	—	2	4	no	—
880	Q₁₆	—	2	4	no	—
881	SD₁₆	—	2	4	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	SD₁₆	—	4	2	no	—
885	SD₁₆	—	4	2	no	—
886	SD₁₆	—	4	2	no	—
887	SD₁₆	—	4	2	no	—
888	D₈	—	4	2	no	—
889	D₈	—	4	2	no	—
890	D₈	—	4	2	no	—
891	M₁₆	—	4	1	no	—
892	M₁₆	—	4	2	no	—
893	M₁₆	—	4	1	no	—
894	C₂×C₈	—	4	2	no	—
895	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
896	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
897	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
898	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
920	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
921	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
922	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	1	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	1	no	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
944	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
956	C₄²	C₂⁴×C₃₁	1	2	yes	—
957	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	4	2	no	—
963	C₂³	—	8	1	no	—
964	C₂³	—	8	1	no	—
965	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
966	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
967	Q₈	—	2	1	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	2	no	—
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	4	1	no	—
973	Q₈	—	4	2	no	—
974	Q₈	—	8	1	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	1	no	—
977	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
978	D₄	—	2	2	no	—
979	D₄	—	2	1	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	1	no	—
984	D₄	—	4	2	no	—
985	D₄	—	4	1	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	2	no	—
988	D₄	—	4	2	no	—
989	D₄	—	8	1	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	1	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	2	no	—
994	D₄	—	8	2	no	—
995	D₄	—	8	2	no	—
996	D₄	—	8	2	no	—
997	D₄	—	8	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1026	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₈	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	16	2	no	—
1051	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1068	C₄	C₃₁×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	8	2	no	—
1072	C₂	—	8	1	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₃₁×#3488	1	1	yes	characteristic
1075	C₂	C₃₁×#3585	1	1	yes	characteristic
1076	C₂	C₃₁×#3586	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×#3517	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3322	C₂	semidirect
6. C₃₁×#3320	C₂	semidirect
7. C₃₁×#3308	C₂	semidirect
8. C₃₁×#3278	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3268	C₂	semidirect
11. C₃₁×#3257	C₂	semidirect
12. C₃₁×#3254	C₂	semidirect
13. C₃₁×#3221	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3116	C₂	semidirect
17. C₃₁×#3046	C₂	semidirect
18. C₃₁×#3040	C₂	semidirect
19. C₃₁×#2995	C₂	semidirect
21. C₂×C₃₁×#137	C₂²	semidirect
26. C₃₁×#557	C₂²	semidirect
33. C₃₁×#550	C₂²	semidirect
34. C₃₁×#550	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
44. C₃₁×#540	C₂²	semidirect
53. C₃₁×#520	C₂²	semidirect
57. C₃₁×#492	C₂²	semidirect
58. C₃₁×#491	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#476	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
73. C₃₁×#468	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
84. C₃₁×#462	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#461	C₂²	semidirect
87. C₃₁×#461	C₂²	semidirect
88. C₃₁×#461	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
93. C₃₁×#452	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
99. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#441	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
110. C₃₁×#435	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
118. C₂×C₃₁×#103	C₂²	semidirect
420. #62094	C₃₁	direct (N × H)
497. #3561	C₂×C₃₁	semidirect
498. #3517	C₂×C₃₁	semidirect
499. #3397	C₂×C₃₁	semidirect
500. #3377	C₂×C₃₁	semidirect
501. #3322	C₂×C₃₁	semidirect
502. #3320	C₂×C₃₁	semidirect
503. #3308	C₂×C₃₁	semidirect
504. #3278	C₂×C₃₁	semidirect
505. #3271	C₂×C₃₁	semidirect
506. #3268	C₂×C₃₁	semidirect
507. #3257	C₂×C₃₁	semidirect
508. #3254	C₂×C₃₁	semidirect
509. #3221	C₂×C₃₁	semidirect
510. #3213	C₂×C₃₁	semidirect
511. #3124	C₂×C₃₁	semidirect
512. #3116	C₂×C₃₁	semidirect
513. #3046	C₂×C₃₁	semidirect
514. #3040	C₂×C₃₁	semidirect
515. #2995	C₂×C₃₁	semidirect
551. C₂×#137	C₂²×C₃₁	semidirect
556. #557	C₂²×C₃₁	semidirect
563. #550	C₂²×C₃₁	semidirect
564. #550	C₂²×C₃₁	semidirect
568. #547	C₂²×C₃₁	semidirect
574. #540	C₂²×C₃₁	semidirect
583. #520	C₂²×C₃₁	semidirect
587. #492	C₂²×C₃₁	semidirect
588. #491	C₂²×C₃₁	semidirect
592. #484	C₂²×C₃₁	semidirect
594. #479	C₂²×C₃₁	semidirect
596. #477	C₂²×C₃₁	semidirect
597. #477	C₂²×C₃₁	semidirect
598. #476	C₂²×C₃₁	semidirect
599. #474	C₂²×C₃₁	semidirect
603. #468	C₂²×C₃₁	semidirect
605. #465	C₂²×C₃₁	semidirect
614. #462	C₂²×C₃₁	semidirect
615. #462	C₂²×C₃₁	semidirect
616. #461	C₂²×C₃₁	semidirect
617. #461	C₂²×C₃₁	semidirect
618. #461	C₂²×C₃₁	semidirect
619. #460	C₂²×C₃₁	semidirect
620. #460	C₂²×C₃₁	semidirect
623. #452	C₂²×C₃₁	semidirect
628. #448	C₂²×C₃₁	semidirect
629. #448	C₂²×C₃₁	semidirect
631. #446	C₂²×C₃₁	semidirect
632. #441	C₂²×C₃₁	semidirect
634. #440	C₂²×C₃₁	semidirect
635. #440	C₂²×C₃₁	semidirect
636. C₄×Q₁₆	C₂²×C₃₁	semidirect
640. #435	C₂²×C₃₁	semidirect
641. #433	C₂²×C₃₁	semidirect
643. #424	C₂²×C₃₁	semidirect
648. C₂×#103	C₂²×C₃₁	semidirect
822. C₃₁	#62094	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×#3517	2
C₃₁×#3397	2
C₃₁×#3377	2
C₃₁×#3322	2
C₃₁×#3320	2
C₃₁×#3308	2
C₃₁×#3278	2
C₃₁×#3271	2
C₃₁×#3268	2
C₃₁×#3257	2
C₃₁×#3254	2
C₃₁×#3221	2
C₃₁×#3213	2
C₃₁×#3124	2
C₃₁×#3116	2
C₃₁×#3046	2
C₃₁×#3040	2
C₃₁×#2995	2
#62094	31

Subgroups — C31×#62094 #21518853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62094 #21518853