Subgroups — C₃₁×#61996 #21518755

Order 7936.

1914 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3331	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3326	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3275	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3272	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3101	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3036	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	—
20	C₃₁×#559	C₂²	1	1	yes	characteristic
21	C₃₁×#556	C₂²	1	2	yes	complemented
22	C₃₁×#555	—	2	1	no	—
23	C₃₁×#554	—	2	1	no	—
24	C₃₁×#554	C₂²	1	1	yes	characteristic
25	C₃₁×#554	C₂²	1	1	yes	characteristic
26	C₃₁×#553	—	2	2	no	—
27	C₃₁×#553	—	2	1	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#551	—	2	2	no	—
30	C₃₁×#548	C₂²	1	4	yes	complemented
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#546	—	2	1	no	—
33	C₃₁×#546	C₂²	1	2	yes	—
34	D₄²×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#542	—	2	2	no	—
36	C₃₁×#537	—	2	1	no	—
37	C₃₁×#533	C₂²	1	2	yes	complemented
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	2	yes	complemented
40	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#529	—	2	1	no	—
43	C₃₁×#529	C₂²	1	2	yes	—
44	C₃₁×#525	—	2	2	no	—
45	C₃₁×#520	—	2	1	no	—
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	—	2	1	no	—
49	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
50	C₃₁×#495	C₂²	1	4	yes	complemented
51	C₃₁×#492	C₂²	1	2	yes	—
52	C₃₁×#488	C₂²	1	4	yes	complemented
53	C₃₁×#487	C₂²	1	2	yes	complemented
54	C₃₁×#483	C₂²	1	4	yes	complemented
55	C₃₁×#482	C₂²	1	2	yes	complemented
56	C₃₁×#479	C₂²	1	4	yes	complemented
57	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#476	C₂²	1	1	yes	characteristic
59	C₃₁×#476	C₂²	1	2	yes	complemented
60	C₃₁×#476	C₂²	1	2	yes	complemented
61	C₃₁×#470	C₂²	1	4	yes	complemented
62	C₃₁×#469	C₂²	1	4	yes	complemented
63	C₃₁×#468	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#463	C₂²	1	4	yes	—
66	C₃₁×#463	C₂²	1	4	yes	complemented
67	C₃₁×#462	C₂²	1	2	yes	complemented
68	C₃₁×#462	C₂²	1	2	yes	complemented
69	C₃₁×#461	C₂²	1	2	yes	—
70	C₃₁×#461	C₂²	1	2	yes	—
71	C₃₁×#461	C₂²	1	2	yes	complemented
72	C₃₁×#461	C₂²	1	2	yes	complemented
73	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#459	C₂²	1	1	yes	characteristic
75	C₃₁×#459	C₂²	1	2	yes	—
76	C₃₁×#459	C₂²	1	2	yes	complemented
77	C₃₁×#452	C₂²	1	4	yes	complemented
78	C₃₁×#450	C₂²	1	4	yes	—
79	C₃₁×#449	C₂²	1	2	yes	—
80	C₃₁×#449	C₂²	1	4	yes	—
81	C₃₁×#448	C₂²	1	4	yes	complemented
82	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
86	C₄×D₈×C₃₁	C₂²	1	2	yes	—
87	C₃₁×#436	C₂²	1	2	yes	—
88	C₃₁×#436	C₂²	1	4	yes	complemented
89	C₃₁×#431	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#419	C₂²	1	2	yes	complemented
94	C₃₁×#417	C₂²	1	4	yes	complemented
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₁	—	2	2	no	—
104	C₃₁×#137	—	4	4	no	—
105	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
106	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×D₈×C₃₁	C₂³	1	2	yes	—
112	C₂×D₈×C₃₁	C₂³	1	4	yes	—
113	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×#127	C₂³	1	1	yes	characteristic
122	C₃₁×#127	C₂³	1	1	yes	characteristic
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#125	—	2	1	no	—
127	C₃₁×#125	—	2	2	no	—
128	C₃₁×#125	C₂³	1	2	yes	—
129	C₃₁×#124	—	2	1	no	—
130	C₃₁×#124	—	2	4	no	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	—	2	1	no	—
133	C₃₁×#124	C₂³	1	4	yes	—
134	C₃₁×#124	C₂³	1	2	yes	—
135	C₃₁×#123	—	2	2	no	—
136	C₃₁×#123	—	2	2	no	—
137	C₃₁×#123	—	2	2	no	—
138	C₃₁×#123	—	2	2	no	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	1	no	—
141	C₃₁×C₂²⋊Q₈	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	4	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	4	no	—
151	C₃₁×#121	—	2	1	no	—
152	C₃₁×#121	—	2	2	no	—
153	C₃₁×#121	—	2	1	no	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	1	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	C₂³	1	2	yes	—
158	C₃₁×#121	C₂³	1	2	yes	—
159	C₃₁×#121	C₂³	1	2	yes	—
160	C₃₁×#120	—	2	2	no	—
161	C₃₁×#120	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	2	no	—
163	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
165	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	4	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	2	no	—
180	C₄×D₄×C₃₁	—	2	1	no	—
181	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
182	C₄×D₄×C₃₁	D₄	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₄×D₄×C₃₁	C₂³	1	2	yes	—
186	C₄×D₄×C₃₁	C₂³	1	2	yes	—
187	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₃₁	C₂³	1	2	yes	—
189	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₃₁	C₂³	1	2	yes	—
191	C₃₁×#117	—	2	2	no	—
192	C₃₁×#117	—	2	2	no	—
193	C₃₁×#117	—	2	1	no	—
194	C₃₁×#117	—	2	2	no	—
195	C₃₁×#117	D₄	1	1	yes	characteristic
196	C₃₁×#117	D₄	1	2	yes	—
197	C₃₁×#117	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
199	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
201	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
205	C₂×C₄²×C₃₁	—	2	1	no	—
206	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#106	C₂³	1	4	yes	—
210	C₃₁×#106	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	4	yes	—
230	C₂⁴×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	2	no	—
232	#41×C₃₁	—	4	2	no	—
233	#41×C₃₁	—	4	1	no	—
234	#41×C₃₁	—	4	4	no	—
235	#41×C₃₁	—	4	4	no	—
236	#41×C₃₁	—	4	4	no	—
237	#41×C₃₁	—	8	2	no	—
238	C₂×Q₈×C₃₁	—	2	1	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	4	2	no	—
242	C₂×Q₈×C₃₁	—	4	2	no	—
243	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₃₁	—	2	4	no	—
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	4	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	1	no	—
255	C₂×D₄×C₃₁	—	2	1	no	—
256	C₂×D₄×C₃₁	—	2	1	no	—
257	C₂×D₄×C₃₁	—	4	2	no	—
258	C₂×D₄×C₃₁	—	4	4	no	—
259	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
262	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
263	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	—	2	2	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	2	1	no	—
268	C₂²×C₄×C₃₁	—	2	1	no	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	2	2	no	—
271	C₂²×C₄×C₃₁	—	2	2	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	—	2	2	no	—
274	C₂²×C₄×C₃₁	—	8	4	no	—
275	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	Q₁₆×C₃₁	—	4	4	no	—
282	SD₁₆×C₃₁	—	2	8	no	—
283	SD₁₆×C₃₁	—	4	4	no	—
284	SD₁₆×C₃₁	—	4	2	no	—
285	SD₁₆×C₃₁	—	4	4	no	—
286	D₈×C₃₁	—	2	4	no	—
287	D₈×C₃₁	—	4	4	no	—
288	M₁₆×C₃₁	—	4	4	no	—
289	M₁₆×C₃₁	—	4	2	no	—
290	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
291	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
292	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	2	no	—
298	C₄⋊C₄×C₃₁	—	2	4	no	—
299	C₄⋊C₄×C₃₁	—	2	2	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	1	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	2	no	—
306	C₄⋊C₄×C₃₁	—	2	4	no	—
307	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	1	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	4	no	—
329	C₂²⋊C₄×C₃₁	—	2	2	no	—
330	C₂²⋊C₄×C₃₁	—	2	2	no	—
331	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₄²×C₃₁	—	2	1	no	—
335	C₄²×C₃₁	—	2	1	no	—
336	C₄²×C₃₁	—	2	1	no	—
337	C₄²×C₃₁	—	2	4	no	—
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₃₁	C₂×D₄	1	2	yes	—
341	C₄²×C₃₁	C₂×D₄	1	2	yes	—
342	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₄²×C₃₁	C₂⁴	1	2	yes	—
344	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
345	#61996	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂³×C₃₁	—	2	1	no	—
347	C₂³×C₃₁	—	2	2	no	—
348	C₂³×C₃₁	—	2	2	no	—
349	C₂³×C₃₁	—	4	4	no	—
350	C₂³×C₃₁	—	4	4	no	—
351	C₂³×C₃₁	—	8	2	no	—
352	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
353	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₃₁	—	2	2	no	—
355	Q₈×C₃₁	—	2	4	no	—
356	Q₈×C₃₁	—	2	1	no	—
357	Q₈×C₃₁	—	2	1	no	—
358	Q₈×C₃₁	—	2	4	no	—
359	Q₈×C₃₁	—	4	2	no	—
360	Q₈×C₃₁	—	8	2	no	—
361	Q₈×C₃₁	—	8	1	no	—
362	D₄×C₃₁	—	2	2	no	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	2	2	no	—
365	D₄×C₃₁	—	2	1	no	—
366	D₄×C₃₁	—	2	2	no	—
367	D₄×C₃₁	—	2	2	no	—
368	D₄×C₃₁	—	4	2	no	—
369	D₄×C₃₁	—	4	4	no	—
370	D₄×C₃₁	—	4	2	no	—
371	D₄×C₃₁	—	4	2	no	—
372	D₄×C₃₁	—	4	4	no	—
373	D₄×C₃₁	—	4	4	no	—
374	D₄×C₃₁	—	4	2	no	—
375	D₄×C₃₁	—	4	2	no	—
376	D₄×C₃₁	—	8	1	no	—
377	D₄×C₃₁	—	8	4	no	—
378	D₄×C₃₁	—	8	2	no	—
379	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	2	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	1	no	—
385	C₂×C₄×C₃₁	—	2	2	no	—
386	C₂×C₄×C₃₁	—	2	1	no	—
387	C₂×C₄×C₃₁	—	2	1	no	—
388	C₂×C₄×C₃₁	—	2	1	no	—
389	C₂×C₄×C₃₁	—	2	2	no	—
390	C₂×C₄×C₃₁	—	2	1	no	—
391	C₂×C₄×C₃₁	—	2	4	no	—
392	C₂×C₄×C₃₁	—	2	2	no	—
393	C₂×C₄×C₃₁	—	4	2	no	—
394	C₂×C₄×C₃₁	—	4	2	no	—
395	C₂×C₄×C₃₁	—	4	2	no	—
396	C₂×C₄×C₃₁	—	4	4	no	—
397	C₂×C₄×C₃₁	—	4	2	no	—
398	C₂×C₄×C₃₁	—	4	4	no	—
399	C₂×C₄×C₃₁	—	8	2	no	—
400	C₂×C₄×C₃₁	—	8	2	no	—
401	C₂×C₄×C₃₁	—	8	4	no	—
402	C₂×C₄×C₃₁	—	8	2	no	—
403	C₂×C₄×C₃₁	—	8	2	no	—
404	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
413	C₈×C₃₁	—	2	2	no	—
414	C₈×C₃₁	—	2	4	no	—
415	C₈×C₃₁	—	2	2	no	—
416	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#3394	C₂×C₃₁	1	2	yes	complemented
419	#3360	C₂×C₃₁	1	2	yes	complemented
420	#3331	C₂×C₃₁	1	2	yes	complemented
421	#3326	C₂×C₃₁	1	4	yes	complemented
422	#3275	C₂×C₃₁	1	4	yes	complemented
423	#3272	C₂×C₃₁	1	2	yes	complemented
424	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
425	#3252	C₂×C₃₁	1	2	yes	complemented
426	#3212	C₂×C₃₁	1	2	yes	complemented
427	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
428	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
429	#3101	C₂×C₃₁	1	2	yes	complemented
430	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
431	#3036	C₂×C₃₁	1	2	yes	complemented
432	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
433	C₂²×C₃₁	—	2	1	no	—
434	C₂²×C₃₁	—	2	2	no	—
435	C₂²×C₃₁	—	2	2	no	—
436	C₂²×C₃₁	—	2	1	no	—
437	C₂²×C₃₁	—	2	2	no	—
438	C₂²×C₃₁	—	2	2	no	—
439	C₂²×C₃₁	—	2	1	no	—
440	C₂²×C₃₁	—	4	1	no	—
441	C₂²×C₃₁	—	4	1	no	—
442	C₂²×C₃₁	—	4	2	no	—
443	C₂²×C₃₁	—	4	2	no	—
444	C₂²×C₃₁	—	4	2	no	—
445	C₂²×C₃₁	—	4	2	no	—
446	C₂²×C₃₁	—	4	2	no	—
447	C₂²×C₃₁	—	4	2	no	—
448	C₂²×C₃₁	—	8	8	no	—
449	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
450	C₄×C₃₁	—	2	1	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	1	no	—
453	C₄×C₃₁	—	2	2	no	—
454	C₄×C₃₁	—	2	2	no	—
455	C₄×C₃₁	—	2	1	no	—
456	C₄×C₃₁	—	4	1	no	—
457	C₄×C₃₁	—	4	4	no	—
458	C₄×C₃₁	—	4	1	no	—
459	C₄×C₃₁	—	4	2	no	—
460	C₄×C₃₁	—	4	1	no	—
461	C₄×C₃₁	—	4	2	no	—
462	C₄×C₃₁	#575	1	2	yes	—
463	C₄×C₃₁	#577	1	2	yes	—
464	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	C₄×C₃₁	#585	1	1	yes	characteristic
466	C₂×#137	C₂²×C₃₁	1	2	yes	—
467	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	—
468	#559	C₂²×C₃₁	1	1	yes	characteristic
469	#556	C₂²×C₃₁	1	2	yes	complemented
470	#555	—	2	1	no	—
471	#554	—	2	1	no	—
472	#554	C₂²×C₃₁	1	1	yes	characteristic
473	#554	C₂²×C₃₁	1	1	yes	characteristic
474	#553	—	2	2	no	—
475	#553	—	2	1	no	—
476	#553	C₂²×C₃₁	1	2	yes	—
477	#551	—	2	2	no	—
478	#548	C₂²×C₃₁	1	4	yes	complemented
479	#547	C₂²×C₃₁	1	2	yes	—
480	#546	—	2	1	no	—
481	#546	C₂²×C₃₁	1	2	yes	—
482	D₄²	C₂²×C₃₁	1	1	yes	characteristic
483	#542	—	2	2	no	—
484	#537	—	2	1	no	—
485	#533	C₂²×C₃₁	1	2	yes	complemented
486	#532	C₂²×C₃₁	1	1	yes	characteristic
487	#532	C₂²×C₃₁	1	2	yes	complemented
488	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
489	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
490	#529	—	2	1	no	—
491	#529	C₂²×C₃₁	1	2	yes	—
492	#525	—	2	2	no	—
493	#520	—	2	1	no	—
494	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
495	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
496	C₂×C₄×D₄	—	2	1	no	—
497	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
498	#495	C₂²×C₃₁	1	4	yes	complemented
499	#492	C₂²×C₃₁	1	2	yes	—
500	#488	C₂²×C₃₁	1	4	yes	complemented
501	#487	C₂²×C₃₁	1	2	yes	complemented
502	#483	C₂²×C₃₁	1	4	yes	complemented
503	#482	C₂²×C₃₁	1	2	yes	complemented
504	#479	C₂²×C₃₁	1	4	yes	complemented
505	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
506	#476	C₂²×C₃₁	1	1	yes	characteristic
507	#476	C₂²×C₃₁	1	2	yes	complemented
508	#476	C₂²×C₃₁	1	2	yes	complemented
509	#470	C₂²×C₃₁	1	4	yes	complemented
510	#469	C₂²×C₃₁	1	4	yes	complemented
511	#468	C₂²×C₃₁	1	4	yes	—
512	#464	C₂²×C₃₁	1	4	yes	complemented
513	#463	C₂²×C₃₁	1	4	yes	—
514	#463	C₂²×C₃₁	1	4	yes	complemented
515	#462	C₂²×C₃₁	1	2	yes	complemented
516	#462	C₂²×C₃₁	1	2	yes	complemented
517	#461	C₂²×C₃₁	1	2	yes	—
518	#461	C₂²×C₃₁	1	2	yes	—
519	#461	C₂²×C₃₁	1	2	yes	complemented
520	#461	C₂²×C₃₁	1	2	yes	complemented
521	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
522	#459	C₂²×C₃₁	1	1	yes	characteristic
523	#459	C₂²×C₃₁	1	2	yes	—
524	#459	C₂²×C₃₁	1	2	yes	complemented
525	#452	C₂²×C₃₁	1	4	yes	complemented
526	#450	C₂²×C₃₁	1	4	yes	—
527	#449	C₂²×C₃₁	1	2	yes	—
528	#449	C₂²×C₃₁	1	4	yes	—
529	#448	C₂²×C₃₁	1	4	yes	complemented
530	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
531	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
532	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
533	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
534	C₄×D₈	C₂²×C₃₁	1	2	yes	—
535	#436	C₂²×C₃₁	1	2	yes	—
536	#436	C₂²×C₃₁	1	4	yes	complemented
537	#431	C₂²×C₃₁	1	2	yes	complemented
538	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
539	#423	C₂²×C₃₁	1	2	yes	complemented
540	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
541	#419	C₂²×C₃₁	1	2	yes	complemented
542	#417	C₂²×C₃₁	1	4	yes	complemented
543	C₂×C₃₁	—	4	1	no	—
544	C₂×C₃₁	—	4	2	no	—
545	C₂×C₃₁	—	4	2	no	—
546	C₂×C₃₁	—	8	2	no	—
547	C₂×C₃₁	—	8	2	no	—
548	C₂×C₃₁	#3488	1	1	yes	characteristic
549	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
550	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
554	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
555	C₂×#41	C₂³×C₃₁	1	4	yes	—
556	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
559	C₂³×C₄	—	2	2	no	—
560	#137	—	4	4	no	—
561	AGL(1,ℤ/8)	—	4	8	no	—
562	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
563	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
567	C₂×D₈	C₂³×C₃₁	1	2	yes	—
568	C₂×D₈	C₂³×C₃₁	1	4	yes	—
569	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
570	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
576	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
577	#127	C₂³×C₃₁	1	1	yes	characteristic
578	#127	C₂³×C₃₁	1	1	yes	characteristic
579	#126	—	2	2	no	—
580	#126	—	2	4	no	—
581	#126	—	2	2	no	—
582	#125	—	2	1	no	—
583	#125	—	2	2	no	—
584	#125	C₂³×C₃₁	1	2	yes	—
585	#124	—	2	1	no	—
586	#124	—	2	4	no	—
587	#124	—	2	1	no	—
588	#124	—	2	1	no	—
589	#124	C₂³×C₃₁	1	2	yes	—
590	#124	C₂³×C₃₁	1	4	yes	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	4	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
604	#121	—	2	2	no	—
605	#121	—	2	2	no	—
606	#121	—	2	4	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	—	2	1	no	—
612	#121	—	2	2	no	—
613	#121	C₂³×C₃₁	1	2	yes	—
614	#121	C₂³×C₃₁	1	2	yes	—
615	#121	C₂³×C₃₁	1	2	yes	—
616	#120	—	2	2	no	—
617	#120	—	2	2	no	—
618	C₄×Q₈	—	2	2	no	—
619	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
623	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
638	C₄×D₄	D₄×C₃₁	1	2	yes	—
639	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₄×D₄	C₂³×C₃₁	1	2	yes	—
641	C₄×D₄	C₂³×C₃₁	1	2	yes	—
642	C₄×D₄	C₂³×C₃₁	1	2	yes	—
643	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₃₁	1	2	yes	—
645	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₄×D₄	C₂³×C₃₁	1	2	yes	—
647	#117	—	2	2	no	—
648	#117	—	2	2	no	—
649	#117	—	2	1	no	—
650	#117	—	2	2	no	—
651	#117	D₄×C₃₁	1	1	yes	characteristic
652	#117	D₄×C₃₁	1	2	yes	—
653	#117	C₂³×C₃₁	1	1	yes	characteristic
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	2	no	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₂²⋊C₄	—	2	2	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
664	#107	C₂³×C₃₁	1	2	yes	—
665	#106	C₂³×C₃₁	1	4	yes	—
666	#106	C₂³×C₃₁	1	2	yes	—
667	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
669	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
670	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
671	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
672	#103	C₂³×C₃₁	1	4	yes	—
673	#103	C₂³×C₃₁	1	4	yes	—
674	#103	C₂³×C₃₁	1	4	yes	—
675	#103	C₂³×C₃₁	1	4	yes	—
676	#103	C₂³×C₃₁	1	2	yes	—
677	#102	C₂³×C₃₁	1	2	yes	—
678	#102	C₂³×C₃₁	1	4	yes	—
679	#102	C₂³×C₃₁	1	2	yes	—
680	#102	C₂³×C₃₁	1	2	yes	—
681	#102	C₂³×C₃₁	1	4	yes	—
682	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
683	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
684	C₄×C₈	C₂³×C₃₁	1	2	yes	—
685	C₄×C₈	C₂³×C₃₁	1	4	yes	—
686	C₃₁	#61996	1	1	yes	characteristic, direct product factor, Sylow
687	C₂⁴	—	2	2	no	—
688	#41	—	2	2	no	—
689	#41	—	4	2	no	—
690	#41	—	4	1	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	8	2	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
701	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
702	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
718	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
719	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
720	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	8	4	no	—
732	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
738	Q₁₆	—	4	4	no	—
739	SD₁₆	—	2	8	no	—
740	SD₁₆	—	4	4	no	—
741	SD₁₆	—	4	2	no	—
742	SD₁₆	—	4	4	no	—
743	D₈	—	2	4	no	—
744	D₈	—	4	4	no	—
745	M₁₆	—	4	4	no	—
746	M₁₆	—	4	2	no	—
747	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
748	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
749	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
765	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
767	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
771	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
791	C₄²	—	2	1	no	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	1	no	—
794	C₄²	—	2	4	no	—
795	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
796	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
797	C₄²	C₂×D₄×C₃₁	1	2	yes	—
798	C₄²	C₂×D₄×C₃₁	1	2	yes	—
799	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
800	C₄²	C₂⁴×C₃₁	1	2	yes	—
801	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	4	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	8	2	no	—
808	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
809	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
810	Q₈	—	2	2	no	—
811	Q₈	—	2	4	no	—
812	Q₈	—	2	1	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	8	2	no	—
817	Q₈	—	8	1	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	2	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	4	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	4	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	1	no	—
833	D₄	—	8	4	no	—
834	D₄	—	8	2	no	—
835	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	—	8	2	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
866	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
868	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
869	C₈	—	2	2	no	—
870	C₈	—	2	4	no	—
871	C₈	—	2	2	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	8	8	no	—
888	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
889	C₄	—	2	1	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	4	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	C₃₁×#575	1	2	yes	—
902	C₄	C₃₁×#577	1	2	yes	—
903	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
904	C₄	C₃₁×#585	1	1	yes	characteristic
905	C₂	—	4	2	no	—
906	C₂	—	4	1	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	2	no	—
909	C₂	—	8	2	no	—
910	C₂	C₃₁×#3488	1	1	yes	characteristic
911	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
912	C₂	C₂×C₃₁×#577	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3481	C₂	semidirect
3. C₃₁×#3394	C₂	semidirect
4. C₃₁×#3360	C₂	semidirect
5. C₃₁×#3331	C₂	semidirect
6. C₃₁×#3326	C₂	semidirect
7. C₃₁×#3275	C₂	semidirect
8. C₃₁×#3272	C₂	semidirect
9. C₃₁×#3253	C₂	semidirect
10. C₃₁×#3252	C₂	semidirect
11. C₃₁×#3212	C₂	semidirect
12. C₃₁×#3206	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3101	C₂	semidirect
15. C₃₁×#3039	C₂	semidirect
16. C₃₁×#3036	C₂	semidirect
17. C₃₁×#2991	C₂	semidirect
21. C₃₁×#556	C₂²	semidirect
30. C₃₁×#548	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
50. C₃₁×#495	C₂²	semidirect
52. C₃₁×#488	C₂²	semidirect
53. C₃₁×#487	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
56. C₃₁×#479	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#476	C₂²	semidirect
61. C₃₁×#470	C₂²	semidirect
62. C₃₁×#469	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
66. C₃₁×#463	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#462	C₂²	semidirect
71. C₃₁×#461	C₂²	semidirect
72. C₃₁×#461	C₂²	semidirect
73. C₃₁×#460	C₂²	semidirect
76. C₃₁×#459	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
81. C₃₁×#448	C₂²	semidirect
82. C₈×Q₈×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
88. C₃₁×#436	C₂²	semidirect
89. C₃₁×#431	C₂²	semidirect
90. C₃₁×#431	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₃₁×#423	C₂²	semidirect
93. C₃₁×#419	C₂²	semidirect
94. C₃₁×#417	C₂²	semidirect
345. #61996	C₃₁	direct (N × H)
416. #3511	C₂×C₃₁	semidirect
417. #3481	C₂×C₃₁	semidirect
418. #3394	C₂×C₃₁	semidirect
419. #3360	C₂×C₃₁	semidirect
420. #3331	C₂×C₃₁	semidirect
421. #3326	C₂×C₃₁	semidirect
422. #3275	C₂×C₃₁	semidirect
423. #3272	C₂×C₃₁	semidirect
424. #3253	C₂×C₃₁	semidirect
425. #3252	C₂×C₃₁	semidirect
426. #3212	C₂×C₃₁	semidirect
427. #3206	C₂×C₃₁	semidirect
428. #3106	C₂×C₃₁	semidirect
429. #3101	C₂×C₃₁	semidirect
430. #3039	C₂×C₃₁	semidirect
431. #3036	C₂×C₃₁	semidirect
432. #2991	C₂×C₃₁	semidirect
469. #556	C₂²×C₃₁	semidirect
478. #548	C₂²×C₃₁	semidirect
485. #533	C₂²×C₃₁	semidirect
487. #532	C₂²×C₃₁	semidirect
488. #532	C₂²×C₃₁	semidirect
489. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
498. #495	C₂²×C₃₁	semidirect
500. #488	C₂²×C₃₁	semidirect
501. #487	C₂²×C₃₁	semidirect
502. #483	C₂²×C₃₁	semidirect
503. #482	C₂²×C₃₁	semidirect
504. #479	C₂²×C₃₁	semidirect
505. #477	C₂²×C₃₁	semidirect
507. #476	C₂²×C₃₁	semidirect
508. #476	C₂²×C₃₁	semidirect
509. #470	C₂²×C₃₁	semidirect
510. #469	C₂²×C₃₁	semidirect
512. #464	C₂²×C₃₁	semidirect
514. #463	C₂²×C₃₁	semidirect
515. #462	C₂²×C₃₁	semidirect
516. #462	C₂²×C₃₁	semidirect
519. #461	C₂²×C₃₁	semidirect
520. #461	C₂²×C₃₁	semidirect
521. #460	C₂²×C₃₁	semidirect
524. #459	C₂²×C₃₁	semidirect
525. #452	C₂²×C₃₁	semidirect
529. #448	C₂²×C₃₁	semidirect
530. C₈×Q₈	C₂²×C₃₁	semidirect
532. C₄×SD₁₆	C₂²×C₃₁	semidirect
533. C₄×SD₁₆	C₂²×C₃₁	semidirect
536. #436	C₂²×C₃₁	semidirect
537. #431	C₂²×C₃₁	semidirect
538. #431	C₂²×C₃₁	semidirect
539. #423	C₂²×C₃₁	semidirect
540. #423	C₂²×C₃₁	semidirect
541. #419	C₂²×C₃₁	semidirect
542. #417	C₂²×C₃₁	semidirect
686. C₃₁	#61996	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×#3511	2
C₃₁×#3481	2
C₃₁×#3394	2
C₃₁×#3360	2
C₃₁×#3331	2
C₃₁×#3326	2
C₃₁×#3275	2
C₃₁×#3272	2
C₃₁×#3253	2
C₃₁×#3252	2
C₃₁×#3212	2
C₃₁×#3206	2
C₃₁×#3106	2
C₃₁×#3101	2
C₃₁×#3039	2
C₃₁×#3036	2
C₃₁×#2991	2
#61996	31

Subgroups — C31×#61996 #21518755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61996 #21518755