Subgroups — C₃₁×#61254 #21518013

Order 7936.

1872 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3346	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3344	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3338	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3095	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3092	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#428	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#556	C₂²	1	1	yes	characteristic
21	C₃₁×#555	C₂²	1	1	yes	characteristic
22	C₃₁×#554	—	2	1	no	—
23	C₃₁×#554	—	2	2	no	—
24	C₃₁×#554	—	2	1	no	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#554	C₂²	1	1	yes	characteristic
27	C₃₁×#554	C₂²	1	4	yes	—
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#553	C₂²	1	2	yes	—
30	C₃₁×#552	—	2	1	no	—
31	C₃₁×#552	C₂²	1	2	yes	—
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#547	C₂²	1	1	yes	characteristic
34	C₃₁×#546	—	2	1	no	—
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₃₁×#529	—	2	2	no	—
38	C₃₁×#529	—	2	1	no	—
39	C₂×C₃₁×#125	—	2	1	no	—
40	C₃₁×#525	C₂²	1	2	yes	—
41	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	—	2	1	no	—
47	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#117	C₂²	1	2	yes	—
49	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
50	C₃₁×#501	C₂²	1	4	yes	complemented
51	C₃₁×#500	C₂²	1	2	yes	complemented
52	C₃₁×#498	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	4	yes	complemented
54	C₃₁×#485	C₂²	1	4	yes	complemented
55	C₃₁×#484	C₂²	1	4	yes	complemented
56	C₃₁×#484	C₂²	1	4	yes	complemented
57	C₃₁×#483	C₂²	1	4	yes	complemented
58	C₃₁×#483	C₂²	1	4	yes	complemented
59	C₃₁×#481	C₂²	1	4	yes	complemented
60	C₃₁×#480	C₂²	1	4	yes	complemented
61	C₃₁×#479	C₂²	1	4	yes	complemented
62	C₃₁×#477	C₂²	1	2	yes	complemented
63	C₃₁×#477	C₂²	1	2	yes	complemented
64	C₃₁×#476	C₂²	1	2	yes	complemented
65	C₃₁×#475	C₂²	1	2	yes	complemented
66	C₃₁×#475	C₂²	1	2	yes	complemented
67	C₃₁×#474	C₂²	1	2	yes	complemented
68	C₃₁×#470	C₂²	1	4	yes	complemented
69	C₃₁×#468	C₂²	1	4	yes	complemented
70	C₃₁×#467	C₂²	1	4	yes	complemented
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#441	C₂²	1	2	yes	complemented
73	C₃₁×#440	C₂²	1	2	yes	complemented
74	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
76	C₃₁×#436	C₂²	1	2	yes	—
77	C₃₁×#435	C₂²	1	4	yes	—
78	C₈×D₄×C₃₁	C₂²	1	2	yes	—
79	C₃₁×#428	C₂²	1	2	yes	—
80	C₃₁×#428	C₂²	1	2	yes	—
81	C₃₁×#428	C₂²	1	2	yes	—
82	C₃₁×#428	C₂²	1	2	yes	—
83	C₃₁×#428	C₂²	1	1	yes	characteristic
84	C₃₁×#428	C₂²	1	4	yes	complemented
85	C₃₁×#428	C₂²	1	4	yes	complemented
86	C₂×C₃₁×#107	C₂²	1	4	yes	complemented
87	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
88	C₃₁×#423	C₂²	1	1	yes	characteristic
89	C₃₁×#419	C₂²	1	2	yes	—
90	C₃₁×#419	C₂²	1	1	yes	characteristic
91	C₃₁×#417	C₂²	1	2	yes	—
92	C₃₁×#417	C₂²	1	1	yes	characteristic
93	C₃₁×#407	C₂²	1	2	yes	—
94	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	—	2	1	no	—
98	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₃₁	—	2	2	no	—
101	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
102	C₃₁×#137	—	2	4	no	—
103	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×M₁₆×C₃₁	—	2	8	no	—
106	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
111	C₃₁×C₄⋊Q₈	—	2	1	no	—
112	C₃₁×C₄⋊Q₈	—	2	1	no	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	—	2	2	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	2	no	—
124	C₃₁×#125	—	2	1	no	—
125	C₃₁×#125	C₂³	1	2	yes	—
126	C₃₁×#124	—	2	1	no	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	1	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	4	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	C₂³	1	2	yes	—
149	C₃₁×#121	C₂³	1	2	yes	—
150	C₃₁×#120	—	2	2	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₃₁	—	2	4	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
170	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
171	C₄×D₄×C₃₁	D₄	1	2	yes	—
172	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₃₁×#117	—	2	2	no	—
178	C₃₁×#117	—	2	2	no	—
179	C₃₁×#117	—	2	1	no	—
180	C₃₁×#117	—	2	2	no	—
181	C₃₁×#117	—	2	1	no	—
182	C₃₁×#117	C₂³	1	1	yes	characteristic
183	C₃₁×#117	C₂³	1	2	yes	—
184	C₃₁×#117	C₂³	1	2	yes	—
185	C₃₁×#117	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
187	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
188	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
189	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
190	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
202	C₂×C₄²×C₃₁	—	2	2	no	—
203	C₂×C₄²×C₃₁	—	2	1	no	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₃₁×#107	C₂³	1	2	yes	—
207	C₃₁×#107	C₂³	1	4	yes	—
208	C₃₁×#107	C₂³	1	4	yes	—
209	C₃₁×#107	C₂³	1	4	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×#106	C₂³	1	2	yes	—
212	C₃₁×#106	C₂³	1	4	yes	—
213	C₃₁×#106	C₂³	1	4	yes	—
214	C₃₁×#106	C₂³	1	4	yes	—
215	C₃₁×#106	C₂³	1	4	yes	—
216	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	4	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#103	C₂³	1	2	yes	—
222	C₃₁×#103	C₂³	1	4	yes	—
223	C₃₁×#103	C₂³	1	4	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	4	yes	—
228	C₃₁×#97	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	2	yes	—
230	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
231	#41×C₃₁	—	2	2	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	4	4	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	2	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	8	2	no	—
242	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₃₁	—	2	4	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	2	no	—
248	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₃₁	—	2	4	no	—
253	C₂²×C₄×C₃₁	—	2	4	no	—
254	C₂²×C₄×C₃₁	—	2	1	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	1	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	8	4	no	—
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
273	Q₁₆×C₃₁	—	2	4	no	—
274	SD₁₆×C₃₁	—	2	4	no	—
275	M₁₆×C₃₁	—	2	4	no	—
276	M₁₆×C₃₁	—	2	2	no	—
277	M₁₆×C₃₁	—	2	8	no	—
278	M₁₆×C₃₁	#41	1	4	yes	complemented
279	C₂×C₈×C₃₁	—	2	8	no	—
280	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
281	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
282	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	4	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	4	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
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	1	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	2	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₂²⋊C₄×C₃₁	—	2	1	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	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	4	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	1	no	—
322	C₂²⋊C₄×C₃₁	—	2	1	no	—
323	C₂²⋊C₄×C₃₁	—	2	2	no	—
324	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
328	C₄²×C₃₁	—	2	1	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	1	no	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	2	no	—
336	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
340	#61254	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂³×C₃₁	—	2	4	no	—
342	C₂³×C₃₁	—	2	4	no	—
343	C₂³×C₃₁	—	2	1	no	—
344	C₂³×C₃₁	—	4	2	no	—
345	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
346	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
348	Q₈×C₃₁	—	2	2	no	—
349	Q₈×C₃₁	—	2	1	no	—
350	Q₈×C₃₁	—	2	2	no	—
351	Q₈×C₃₁	—	2	1	no	—
352	Q₈×C₃₁	—	4	2	no	—
353	Q₈×C₃₁	—	4	2	no	—
354	Q₈×C₃₁	—	8	1	no	—
355	Q₈×C₃₁	—	8	2	no	—
356	Q₈×C₃₁	—	8	2	no	—
357	D₄×C₃₁	—	2	4	no	—
358	D₄×C₃₁	—	2	2	no	—
359	D₄×C₃₁	—	2	1	no	—
360	D₄×C₃₁	—	2	1	no	—
361	D₄×C₃₁	—	4	2	no	—
362	D₄×C₃₁	—	4	4	no	—
363	D₄×C₃₁	—	8	2	no	—
364	D₄×C₃₁	#137	1	4	yes	complemented
365	C₂×C₄×C₃₁	—	2	4	no	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	2	4	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	4	no	—
381	C₂×C₄×C₃₁	—	4	1	no	—
382	C₂×C₄×C₃₁	—	4	2	no	—
383	C₂×C₄×C₃₁	—	4	4	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	4	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	—	4	2	no	—
388	C₂×C₄×C₃₁	—	8	1	no	—
389	C₂×C₄×C₃₁	—	8	2	no	—
390	C₂×C₄×C₃₁	—	8	4	no	—
391	C₂×C₄×C₃₁	—	8	4	no	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
400	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
401	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
402	C₈×C₃₁	—	2	4	no	—
403	C₈×C₃₁	—	2	2	no	—
404	C₈×C₃₁	C₂×#41	1	4	yes	—
405	#3475	C₂×C₃₁	1	1	yes	characteristic
406	C₂×#554	C₂×C₃₁	1	1	yes	characteristic, complemented
407	#3357	C₂×C₃₁	1	2	yes	complemented
408	#3356	C₂×C₃₁	1	2	yes	complemented
409	#3346	C₂×C₃₁	1	4	yes	complemented
410	#3344	C₂×C₃₁	1	4	yes	complemented
411	#3338	C₂×C₃₁	1	2	yes	complemented
412	#3335	C₂×C₃₁	1	2	yes	complemented
413	#3165	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3095	C₂×C₃₁	1	2	yes	complemented
415	#3092	C₂×C₃₁	1	2	yes	complemented
416	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
417	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#3056	C₂×C₃₁	1	2	yes	complemented
419	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
420	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₂×#428	C₂×C₃₁	1	2	yes	complemented
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	2	1	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	2	2	no	—
428	C₂²×C₃₁	—	2	2	no	—
429	C₂²×C₃₁	—	4	8	no	—
430	C₂²×C₃₁	—	4	1	no	—
431	C₂²×C₃₁	—	4	1	no	—
432	C₂²×C₃₁	—	4	1	no	—
433	C₂²×C₃₁	#547	1	2	yes	—
434	C₂²×C₃₁	C₂×#137	1	4	yes	—
435	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
436	C₄×C₃₁	—	2	1	no	—
437	C₄×C₃₁	—	2	1	no	—
438	C₄×C₃₁	—	2	2	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	—	4	4	no	—
443	C₄×C₃₁	—	4	1	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	—	4	1	no	—
448	C₄×C₃₁	—	4	2	no	—
449	C₄×C₃₁	#547	1	2	yes	—
450	C₄×C₃₁	C₂×#137	1	2	yes	—
451	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
452	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
454	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
455	#556	C₂²×C₃₁	1	1	yes	characteristic
456	#555	C₂²×C₃₁	1	1	yes	characteristic
457	#554	—	2	1	no	—
458	#554	—	2	2	no	—
459	#554	—	2	1	no	—
460	#554	C₂²×C₃₁	1	2	yes	—
461	#554	C₂²×C₃₁	1	1	yes	characteristic
462	#554	C₂²×C₃₁	1	4	yes	—
463	#554	C₂²×C₃₁	1	2	yes	—
464	#553	C₂²×C₃₁	1	2	yes	—
465	#552	—	2	1	no	—
466	#552	C₂²×C₃₁	1	2	yes	—
467	#551	—	2	2	no	—
468	#547	C₂²×C₃₁	1	1	yes	characteristic
469	#546	—	2	1	no	—
470	#533	C₂²×C₃₁	1	1	yes	characteristic
471	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
472	#529	—	2	2	no	—
473	#529	—	2	1	no	—
474	C₂×#125	—	2	1	no	—
475	#525	C₂²×C₃₁	1	2	yes	—
476	C₂×C₂²⋊Q₈	—	2	2	no	—
477	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
478	C₄×#41	—	2	1	no	—
479	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×C₄×D₄	—	2	1	no	—
482	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×#117	C₂²×C₃₁	1	2	yes	—
484	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
485	#501	C₂²×C₃₁	1	4	yes	complemented
486	#500	C₂²×C₃₁	1	2	yes	complemented
487	#498	C₂²×C₃₁	1	2	yes	complemented
488	#485	C₂²×C₃₁	1	4	yes	complemented
489	#485	C₂²×C₃₁	1	4	yes	complemented
490	#484	C₂²×C₃₁	1	4	yes	complemented
491	#484	C₂²×C₃₁	1	4	yes	complemented
492	#483	C₂²×C₃₁	1	4	yes	complemented
493	#483	C₂²×C₃₁	1	4	yes	complemented
494	#481	C₂²×C₃₁	1	4	yes	complemented
495	#480	C₂²×C₃₁	1	4	yes	complemented
496	#479	C₂²×C₃₁	1	4	yes	complemented
497	#477	C₂²×C₃₁	1	2	yes	complemented
498	#477	C₂²×C₃₁	1	2	yes	complemented
499	#476	C₂²×C₃₁	1	2	yes	complemented
500	#475	C₂²×C₃₁	1	2	yes	complemented
501	#475	C₂²×C₃₁	1	2	yes	complemented
502	#474	C₂²×C₃₁	1	2	yes	complemented
503	#470	C₂²×C₃₁	1	4	yes	complemented
504	#468	C₂²×C₃₁	1	4	yes	complemented
505	#467	C₂²×C₃₁	1	4	yes	complemented
506	#465	C₂²×C₃₁	1	4	yes	complemented
507	#441	C₂²×C₃₁	1	2	yes	complemented
508	#440	C₂²×C₃₁	1	2	yes	complemented
509	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
510	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
511	#436	C₂²×C₃₁	1	2	yes	—
512	#435	C₂²×C₃₁	1	4	yes	—
513	C₈×D₄	C₂²×C₃₁	1	2	yes	—
514	#428	C₂²×C₃₁	1	2	yes	—
515	#428	C₂²×C₃₁	1	2	yes	—
516	#428	C₂²×C₃₁	1	2	yes	—
517	#428	C₂²×C₃₁	1	2	yes	—
518	#428	C₂²×C₃₁	1	1	yes	characteristic
519	#428	C₂²×C₃₁	1	4	yes	complemented
520	#428	C₂²×C₃₁	1	4	yes	complemented
521	C₂×#107	C₂²×C₃₁	1	4	yes	complemented
522	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
523	#423	C₂²×C₃₁	1	1	yes	characteristic
524	#419	C₂²×C₃₁	1	2	yes	—
525	#419	C₂²×C₃₁	1	1	yes	characteristic
526	#417	C₂²×C₃₁	1	2	yes	—
527	#417	C₂²×C₃₁	1	1	yes	characteristic
528	#407	C₂²×C₃₁	1	2	yes	—
529	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×C₃₁	—	2	2	no	—
531	C₂×C₃₁	—	2	4	no	—
532	C₂×C₃₁	—	4	2	no	—
533	C₂×C₃₁	—	8	1	no	—
534	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
535	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
536	C₂×C₃₁	#3585	1	1	yes	characteristic
537	C₂×#41	—	2	1	no	—
538	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
541	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
542	C₂³×C₄	—	2	2	no	—
543	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
544	#137	—	2	4	no	—
545	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
546	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
547	C₂×M₁₆	—	2	8	no	—
548	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
549	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
550	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
551	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
552	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
559	#126	—	2	2	no	—
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	4	no	—
565	#125	—	2	2	no	—
566	#125	—	2	1	no	—
567	#125	C₂³×C₃₁	1	2	yes	—
568	#124	—	2	1	no	—
569	#124	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
585	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
586	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
587	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	C₂³×C₃₁	1	2	yes	—
591	#121	C₂³×C₃₁	1	2	yes	—
592	#120	—	2	2	no	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
599	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
600	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
612	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
613	C₄×D₄	D₄×C₃₁	1	2	yes	—
614	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₃₁	1	2	yes	—
618	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
619	#117	—	2	2	no	—
620	#117	—	2	2	no	—
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	#117	—	2	1	no	—
624	#117	C₂³×C₃₁	1	1	yes	characteristic
625	#117	C₂³×C₃₁	1	2	yes	—
626	#117	C₂³×C₃₁	1	2	yes	—
627	#117	C₂³×C₃₁	1	2	yes	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₂²⋊C₄	—	2	2	no	—
642	C₂×C₂²⋊C₄	—	2	2	no	—
643	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
644	C₂×C₄²	—	2	2	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
648	#107	C₂³×C₃₁	1	2	yes	—
649	#107	C₂³×C₃₁	1	4	yes	—
650	#107	C₂³×C₃₁	1	4	yes	—
651	#107	C₂³×C₃₁	1	4	yes	—
652	#107	C₂³×C₃₁	1	4	yes	—
653	#106	C₂³×C₃₁	1	2	yes	—
654	#106	C₂³×C₃₁	1	4	yes	—
655	#106	C₂³×C₃₁	1	4	yes	—
656	#106	C₂³×C₃₁	1	4	yes	—
657	#106	C₂³×C₃₁	1	4	yes	—
658	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
660	#103	C₂³×C₃₁	1	2	yes	—
661	#103	C₂³×C₃₁	1	4	yes	—
662	#103	C₂³×C₃₁	1	2	yes	—
663	#103	C₂³×C₃₁	1	2	yes	—
664	#103	C₂³×C₃₁	1	4	yes	—
665	#103	C₂³×C₃₁	1	4	yes	—
666	#102	C₂³×C₃₁	1	2	yes	—
667	#102	C₂³×C₃₁	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
670	#97	C₂³×C₃₁	1	2	yes	—
671	C₄×C₈	C₂³×C₃₁	1	2	yes	—
672	C₃₁	#61254	1	1	yes	characteristic, direct product factor, Sylow
673	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
674	#41	—	2	2	no	—
675	#41	—	2	2	no	—
676	#41	—	4	4	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	8	2	no	—
685	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
686	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
693	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
694	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	8	4	no	—
708	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
711	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
716	Q₁₆	—	2	4	no	—
717	SD₁₆	—	2	4	no	—
718	M₁₆	—	2	4	no	—
719	M₁₆	—	2	2	no	—
720	M₁₆	—	2	8	no	—
721	M₁₆	#41×C₃₁	1	4	yes	complemented
722	C₂×C₈	—	2	8	no	—
723	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
724	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
725	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
751	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
768	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
783	C₂³	—	2	4	no	—
784	C₂³	—	2	4	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
788	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
789	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	1	no	—
794	Q₈	—	4	2	no	—
795	Q₈	—	4	2	no	—
796	Q₈	—	8	1	no	—
797	Q₈	—	8	2	no	—
798	Q₈	—	8	2	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	1	no	—
802	D₄	—	2	1	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	4	no	—
805	D₄	—	8	2	no	—
806	D₄	C₃₁×#137	1	4	yes	complemented
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	8	1	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	—	8	4	no	—
833	C₂×C₄	—	8	4	no	—
834	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
841	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
842	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
843	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
844	C₈	—	2	4	no	—
845	C₈	—	2	2	no	—
846	C₈	C₂×#41×C₃₁	1	4	yes	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	8	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	C₃₁×#547	1	2	yes	—
859	C₂²	C₂×C₃₁×#137	1	4	yes	—
860	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	4	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	C₃₁×#547	1	2	yes	—
875	C₄	C₂×C₃₁×#137	1	2	yes	—
876	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
877	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂	—	2	2	no	—
879	C₂	—	2	4	no	—
880	C₂	—	4	2	no	—
881	C₂	—	8	1	no	—
882	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
883	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
884	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#554	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3356	C₂	semidirect
5. C₃₁×#3346	C₂	semidirect
6. C₃₁×#3344	C₂	semidirect
7. C₃₁×#3338	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3165	C₂	semidirect
10. C₃₁×#3095	C₂	semidirect
11. C₃₁×#3092	C₂	semidirect
12. C₃₁×#3079	C₂	semidirect
13. C₃₁×#3078	C₂	semidirect
14. C₃₁×#3056	C₂	semidirect
15. C₄×C₃₁×#137	C₂	semidirect
16. D₄×M₁₆×C₃₁	C₂	semidirect
17. C₂×C₃₁×#428	C₂	semidirect
50. C₃₁×#501	C₂²	semidirect
51. C₃₁×#500	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#485	C₂²	semidirect
55. C₃₁×#484	C₂²	semidirect
56. C₃₁×#484	C₂²	semidirect
57. C₃₁×#483	C₂²	semidirect
58. C₃₁×#483	C₂²	semidirect
59. C₃₁×#481	C₂²	semidirect
60. C₃₁×#480	C₂²	semidirect
61. C₃₁×#479	C₂²	semidirect
62. C₃₁×#477	C₂²	semidirect
63. C₃₁×#477	C₂²	semidirect
64. C₃₁×#476	C₂²	semidirect
65. C₃₁×#475	C₂²	semidirect
66. C₃₁×#475	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#470	C₂²	semidirect
69. C₃₁×#468	C₂²	semidirect
70. C₃₁×#467	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#441	C₂²	semidirect
73. C₃₁×#440	C₂²	semidirect
74. C₄×Q₁₆×C₃₁	C₂²	semidirect
75. C₄×SD₁₆×C₃₁	C₂²	semidirect
84. C₃₁×#428	C₂²	semidirect
85. C₃₁×#428	C₂²	semidirect
86. C₂×C₃₁×#107	C₂²	semidirect
87. C₂×C₃₁×#106	C₂²	semidirect
278. M₁₆×C₃₁	#41	semidirect
340. #61254	C₃₁	direct (N × H)
364. D₄×C₃₁	#137	semidirect
406. C₂×#554	C₂×C₃₁	semidirect
407. #3357	C₂×C₃₁	semidirect
408. #3356	C₂×C₃₁	semidirect
409. #3346	C₂×C₃₁	semidirect
410. #3344	C₂×C₃₁	semidirect
411. #3338	C₂×C₃₁	semidirect
412. #3335	C₂×C₃₁	semidirect
413. #3165	C₂×C₃₁	semidirect
414. #3095	C₂×C₃₁	semidirect
415. #3092	C₂×C₃₁	semidirect
416. #3079	C₂×C₃₁	semidirect
417. #3078	C₂×C₃₁	semidirect
418. #3056	C₂×C₃₁	semidirect
419. C₄×#137	C₂×C₃₁	semidirect
420. D₄×M₁₆	C₂×C₃₁	semidirect
421. C₂×#428	C₂×C₃₁	semidirect
485. #501	C₂²×C₃₁	semidirect
486. #500	C₂²×C₃₁	semidirect
487. #498	C₂²×C₃₁	semidirect
488. #485	C₂²×C₃₁	semidirect
489. #485	C₂²×C₃₁	semidirect
490. #484	C₂²×C₃₁	semidirect
491. #484	C₂²×C₃₁	semidirect
492. #483	C₂²×C₃₁	semidirect
493. #483	C₂²×C₃₁	semidirect
494. #481	C₂²×C₃₁	semidirect
495. #480	C₂²×C₃₁	semidirect
496. #479	C₂²×C₃₁	semidirect
497. #477	C₂²×C₃₁	semidirect
498. #477	C₂²×C₃₁	semidirect
499. #476	C₂²×C₃₁	semidirect
500. #475	C₂²×C₃₁	semidirect
501. #475	C₂²×C₃₁	semidirect
502. #474	C₂²×C₃₁	semidirect
503. #470	C₂²×C₃₁	semidirect
504. #468	C₂²×C₃₁	semidirect
505. #467	C₂²×C₃₁	semidirect
506. #465	C₂²×C₃₁	semidirect
507. #441	C₂²×C₃₁	semidirect
508. #440	C₂²×C₃₁	semidirect
509. C₄×Q₁₆	C₂²×C₃₁	semidirect
510. C₄×SD₁₆	C₂²×C₃₁	semidirect
519. #428	C₂²×C₃₁	semidirect
520. #428	C₂²×C₃₁	semidirect
521. C₂×#107	C₂²×C₃₁	semidirect
522. C₂×#106	C₂²×C₃₁	semidirect
672. C₃₁	#61254	direct (N × H)
721. M₁₆	#41×C₃₁	semidirect
806. D₄	C₃₁×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3475	2
C₂×C₃₁×#554	2
C₃₁×#3357	2
C₃₁×#3356	2
C₃₁×#3346	2
C₃₁×#3344	2
C₃₁×#3338	2
C₃₁×#3335	2
C₃₁×#3165	2
C₃₁×#3095	2
C₃₁×#3092	2
C₃₁×#3079	2
C₃₁×#3078	2
C₃₁×#3056	2
C₄×C₃₁×#137	2
D₄×M₁₆×C₃₁	2
C₂×C₃₁×#428	2
#61254	31

Subgroups — C31×#61254 #21518013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61254 #21518013