Subgroups — C₃₁×#60759 #21517518

Order 7936.

2118 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3202	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3201	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3195	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3189	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3091	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3059	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3011	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3004	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
22	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#131	C₂²	1	2	yes	—
24	D₄×Q₈×C₃₁	—	2	1	no	—
25	C₃₁×#548	—	2	1	no	—
26	C₃₁×#547	—	2	2	no	—
27	C₃₁×#547	—	2	1	no	—
28	C₃₁×#546	—	2	2	no	—
29	C₃₁×#546	—	2	1	no	—
30	C₃₁×#537	C₂²	1	2	yes	—
31	C₃₁×#537	C₂²	1	1	yes	characteristic
32	C₃₁×#536	—	2	2	no	—
33	C₃₁×#536	—	2	1	no	—
34	C₃₁×#536	—	2	1	no	—
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#536	C₂²	1	4	yes	—
37	C₃₁×#536	C₂²	1	2	yes	—
38	C₃₁×#536	C₂²	1	2	yes	—
39	C₃₁×#536	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₃₁×#124	—	2	1	no	—
42	C₃₁×#525	C₂²	1	1	yes	characteristic
43	C₃₁×#525	C₂²	1	2	yes	—
44	C₂×C₃₁×#123	—	2	2	no	—
45	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₃₁×#520	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
51	C₃₁×#485	C₂²	1	2	yes	complemented
52	C₃₁×#485	C₂²	1	4	yes	complemented
53	C₃₁×#485	C₂²	1	4	yes	complemented
54	C₃₁×#485	C₂²	1	4	yes	complemented
55	C₃₁×#484	C₂²	1	1	yes	characteristic
56	C₃₁×#484	C₂²	1	2	yes	—
57	C₃₁×#484	C₂²	1	4	yes	complemented
58	C₃₁×#483	C₂²	1	1	yes	characteristic
59	C₃₁×#483	C₂²	1	2	yes	—
60	C₃₁×#483	C₂²	1	4	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	complemented
62	C₃₁×#481	C₂²	1	1	yes	characteristic
63	C₃₁×#480	C₂²	1	1	yes	characteristic
64	C₃₁×#470	C₂²	1	4	yes	complemented
65	C₃₁×#470	C₂²	1	4	yes	complemented
66	C₃₁×#470	C₂²	1	4	yes	complemented
67	C₃₁×#468	C₂²	1	4	yes	complemented
68	C₃₁×#467	C₂²	1	4	yes	complemented
69	C₃₁×#467	C₂²	1	4	yes	complemented
70	C₃₁×#467	C₂²	1	4	yes	complemented
71	C₃₁×#465	C₂²	1	4	yes	complemented
72	C₃₁×#452	C₂²	1	4	yes	complemented
73	C₃₁×#452	C₂²	1	4	yes	complemented
74	C₃₁×#451	C₂²	1	2	yes	—
75	C₃₁×#451	C₂²	1	2	yes	—
76	C₃₁×#451	C₂²	1	2	yes	—
77	C₃₁×#451	C₂²	1	4	yes	complemented
78	C₃₁×#451	C₂²	1	4	yes	complemented
79	C₃₁×#451	C₂²	1	4	yes	complemented
80	C₃₁×#451	C₂²	1	2	yes	complemented
81	C₃₁×#448	C₂²	1	2	yes	—
82	C₃₁×#448	C₂²	1	2	yes	complemented
83	C₃₁×#428	C₂²	1	2	yes	complemented
84	C₃₁×#427	C₂²	1	2	yes	complemented
85	C₃₁×#419	C₂²	1	2	yes	complemented
86	C₃₁×#419	C₂²	1	2	yes	complemented
87	C₃₁×#416	C₂²	1	2	yes	complemented
88	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
89	C₃₁×#408	C₂²	1	2	yes	—
90	C₃₁×#408	C₂²	1	4	yes	—
91	C₃₁×#407	C₂²	1	1	yes	characteristic
92	C₃₁×#407	C₂²	1	2	yes	—
93	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₃₁×2₋¹⁺⁴	—	4	4	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	1	no	—
98	C₂×#41×C₃₁	—	4	4	no	—
99	C₂×#41×C₃₁	D₄	1	2	yes	—
100	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
101	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
102	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×#41×C₃₁	C₂³	1	2	yes	—
104	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
106	C₂×#41×C₃₁	C₂³	1	2	yes	—
107	C₂²×Q₈×C₃₁	—	2	1	no	—
108	C₂²×Q₈×C₃₁	—	2	1	no	—
109	C₂²×Q₈×C₃₁	—	2	1	no	—
110	C₂²×Q₈×C₃₁	—	2	1	no	—
111	C₂²×Q₈×C₃₁	—	4	4	no	—
112	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
113	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
114	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
116	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
117	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	D₄	1	2	yes	—
119	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	—	2	1	no	—
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₃₁×#137	—	4	4	no	—
124	C₂×Q₁₆×C₃₁	—	4	4	no	—
125	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
126	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
127	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
129	C₃₁×#131	—	4	4	no	—
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	4	no	—
137	C₃₁×C₄⋊Q₈	—	2	1	no	—
138	C₃₁×C₄⋊Q₈	—	2	2	no	—
139	C₃₁×#124	—	2	2	no	—
140	C₃₁×#124	—	2	2	no	—
141	C₃₁×#124	—	2	4	no	—
142	C₃₁×#124	—	2	1	no	—
143	C₃₁×#124	—	2	2	no	—
144	C₃₁×#123	—	2	4	no	—
145	C₃₁×#123	—	2	4	no	—
146	C₃₁×#123	—	2	4	no	—
147	C₃₁×#123	—	2	4	no	—
148	C₃₁×#123	—	2	2	no	—
149	C₃₁×#123	—	2	2	no	—
150	C₃₁×#123	—	2	2	no	—
151	C₃₁×#123	—	2	1	no	—
152	C₃₁×#123	—	2	2	no	—
153	C₃₁×C₂²⋊Q₈	—	2	1	no	—
154	C₃₁×C₂²⋊Q₈	—	2	2	no	—
155	C₃₁×C₂²⋊Q₈	—	2	2	no	—
156	C₃₁×C₂²⋊Q₈	—	2	2	no	—
157	C₃₁×C₂²⋊Q₈	—	2	2	no	—
158	C₃₁×C₂²⋊Q₈	—	2	2	no	—
159	C₃₁×C₂²⋊Q₈	—	2	1	no	—
160	C₃₁×C₂²⋊Q₈	—	2	2	no	—
161	C₃₁×C₂²⋊Q₈	—	2	1	no	—
162	C₃₁×C₂²⋊Q₈	—	2	2	no	—
163	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
168	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
169	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
170	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
171	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	2	no	—
177	C₃₁×#121	—	2	1	no	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	C₂³	1	1	yes	characteristic
180	C₃₁×#121	C₂³	1	1	yes	characteristic
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#120	—	2	1	no	—
183	C₃₁×#120	—	2	2	no	—
184	C₄×Q₈×C₃₁	—	2	1	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	1	no	—
187	C₄×D₄×C₃₁	—	2	1	no	—
188	C₄×D₄×C₃₁	—	2	2	no	—
189	C₄×D₄×C₃₁	—	2	1	no	—
190	C₄×D₄×C₃₁	—	2	2	no	—
191	C₃₁×#117	—	2	1	no	—
192	C₃₁×#117	—	2	1	no	—
193	C₃₁×#117	C₂³	1	2	yes	—
194	C₃₁×#117	C₂³	1	1	yes	characteristic
195	C₃₁×#117	C₂³	1	2	yes	—
196	C₃₁×#117	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
209	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
210	C₂×C₄²×C₃₁	—	2	1	no	—
211	C₃₁×#107	C₂³	1	2	yes	—
212	C₃₁×#107	C₂³	1	2	yes	—
213	C₃₁×#107	C₂³	1	4	yes	—
214	C₃₁×#106	C₂³	1	2	yes	—
215	C₃₁×#106	C₂³	1	2	yes	—
216	C₃₁×#106	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#103	C₂³	1	4	yes	—
222	C₃₁×#103	C₂³	1	4	yes	—
223	C₃₁×#103	C₂³	1	4	yes	—
224	C₃₁×#103	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	2	yes	—
226	C₃₁×#102	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
230	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
233	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
234	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
236	#41×C₃₁	—	2	4	no	—
237	#41×C₃₁	—	2	4	no	—
238	#41×C₃₁	—	2	4	no	—
239	#41×C₃₁	—	4	4	no	—
240	#41×C₃₁	—	4	4	no	—
241	#41×C₃₁	—	4	2	no	—
242	#41×C₃₁	—	4	2	no	—
243	#41×C₃₁	—	4	4	no	—
244	#41×C₃₁	—	4	8	no	—
245	#41×C₃₁	—	4	4	no	—
246	C₂×Q₈×C₃₁	—	2	2	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	—	2	1	no	—
249	C₂×Q₈×C₃₁	—	2	2	no	—
250	C₂×Q₈×C₃₁	—	2	2	no	—
251	C₂×Q₈×C₃₁	—	2	4	no	—
252	C₂×Q₈×C₃₁	—	2	4	no	—
253	C₂×Q₈×C₃₁	—	2	4	no	—
254	C₂×Q₈×C₃₁	—	4	4	no	—
255	C₂×Q₈×C₃₁	—	4	4	no	—
256	C₂×Q₈×C₃₁	—	4	2	no	—
257	C₂×Q₈×C₃₁	—	4	4	no	—
258	C₂×Q₈×C₃₁	—	4	4	no	—
259	C₂×Q₈×C₃₁	—	4	4	no	—
260	C₂×Q₈×C₃₁	—	4	4	no	—
261	C₂×Q₈×C₃₁	—	4	4	no	—
262	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
265	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
266	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
267	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂×D₄×C₃₁	—	2	1	no	—
269	C₂×D₄×C₃₁	—	2	2	no	—
270	C₂×D₄×C₃₁	—	2	1	no	—
271	C₂×D₄×C₃₁	—	2	2	no	—
272	C₂×D₄×C₃₁	—	2	1	no	—
273	C₂×D₄×C₃₁	—	4	2	no	—
274	C₂×D₄×C₃₁	—	4	4	no	—
275	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	—	2	4	no	—
284	C₂²×C₄×C₃₁	—	2	1	no	—
285	C₂²×C₄×C₃₁	—	2	1	no	—
286	C₂²×C₄×C₃₁	—	2	2	no	—
287	C₂²×C₄×C₃₁	—	2	2	no	—
288	C₂²×C₄×C₃₁	—	2	1	no	—
289	C₂²×C₄×C₃₁	—	2	2	no	—
290	C₂²×C₄×C₃₁	—	2	2	no	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	1	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	1	no	—
295	C₂²×C₄×C₃₁	—	4	4	no	—
296	C₂²×C₄×C₃₁	—	4	4	no	—
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	Q₁₆×C₃₁	—	4	4	no	—
309	Q₁₆×C₃₁	—	4	4	no	—
310	Q₁₆×C₃₁	—	4	4	no	—
311	SD₁₆×C₃₁	—	4	4	no	—
312	M₁₆×C₃₁	—	2	4	no	—
313	M₁₆×C₃₁	—	4	4	no	—
314	C₂×C₈×C₃₁	—	2	4	no	—
315	C₂×C₈×C₃₁	—	4	4	no	—
316	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
317	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
318	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	1	no	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	4	no	—
325	C₄⋊C₄×C₃₁	—	2	4	no	—
326	C₄⋊C₄×C₃₁	—	2	4	no	—
327	C₄⋊C₄×C₃₁	—	2	4	no	—
328	C₄⋊C₄×C₃₁	—	2	1	no	—
329	C₄⋊C₄×C₃₁	—	2	1	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	1	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
336	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂²⋊C₄×C₃₁	—	2	2	no	—
340	C₂²⋊C₄×C₃₁	—	2	1	no	—
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	2	no	—
344	C₂²⋊C₄×C₃₁	—	2	2	no	—
345	C₂²⋊C₄×C₃₁	—	2	2	no	—
346	C₂²⋊C₄×C₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₃₁	—	2	4	no	—
348	C₂²⋊C₄×C₃₁	—	2	4	no	—
349	C₂²⋊C₄×C₃₁	—	2	4	no	—
350	C₂²⋊C₄×C₃₁	—	2	2	no	—
351	C₂²⋊C₄×C₃₁	—	2	1	no	—
352	C₂²⋊C₄×C₃₁	—	2	2	no	—
353	C₂²⋊C₄×C₃₁	—	2	1	no	—
354	C₂²⋊C₄×C₃₁	—	2	1	no	—
355	C₂²⋊C₄×C₃₁	—	2	1	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₄²×C₃₁	—	2	2	no	—
358	C₄²×C₃₁	—	2	2	no	—
359	C₄²×C₃₁	—	2	2	no	—
360	C₄²×C₃₁	—	2	1	no	—
361	#60759	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂³×C₃₁	—	2	2	no	—
363	C₂³×C₃₁	—	2	2	no	—
364	C₂³×C₃₁	—	2	4	no	—
365	C₂³×C₃₁	—	2	1	no	—
366	C₂³×C₃₁	—	4	1	no	—
367	C₂³×C₃₁	—	4	2	no	—
368	C₂³×C₃₁	—	4	2	no	—
369	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
370	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
371	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
374	Q₈×C₃₁	—	2	2	no	—
375	Q₈×C₃₁	—	2	2	no	—
376	Q₈×C₃₁	—	2	4	no	—
377	Q₈×C₃₁	—	2	4	no	—
378	Q₈×C₃₁	—	2	4	no	—
379	Q₈×C₃₁	—	2	2	no	—
380	Q₈×C₃₁	—	4	2	no	—
381	Q₈×C₃₁	—	4	4	no	—
382	Q₈×C₃₁	—	4	4	no	—
383	Q₈×C₃₁	—	4	4	no	—
384	Q₈×C₃₁	—	4	4	no	—
385	Q₈×C₃₁	—	4	2	no	—
386	D₄×C₃₁	—	2	4	no	—
387	D₄×C₃₁	—	2	4	no	—
388	D₄×C₃₁	—	2	2	no	—
389	D₄×C₃₁	—	2	2	no	—
390	D₄×C₃₁	—	2	2	no	—
391	D₄×C₃₁	—	4	2	no	—
392	D₄×C₃₁	—	4	2	no	—
393	D₄×C₃₁	—	4	2	no	—
394	D₄×C₃₁	—	4	4	no	—
395	D₄×C₃₁	—	4	2	no	—
396	D₄×C₃₁	—	4	2	no	—
397	D₄×C₃₁	—	8	1	no	—
398	D₄×C₃₁	—	8	2	no	—
399	C₂×C₄×C₃₁	—	2	2	no	—
400	C₂×C₄×C₃₁	—	2	2	no	—
401	C₂×C₄×C₃₁	—	2	2	no	—
402	C₂×C₄×C₃₁	—	2	4	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	2	no	—
405	C₂×C₄×C₃₁	—	2	4	no	—
406	C₂×C₄×C₃₁	—	2	1	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	2	no	—
409	C₂×C₄×C₃₁	—	2	2	no	—
410	C₂×C₄×C₃₁	—	2	1	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	1	no	—
413	C₂×C₄×C₃₁	—	2	4	no	—
414	C₂×C₄×C₃₁	—	4	2	no	—
415	C₂×C₄×C₃₁	—	4	2	no	—
416	C₂×C₄×C₃₁	—	4	2	no	—
417	C₂×C₄×C₃₁	—	4	4	no	—
418	C₂×C₄×C₃₁	—	4	2	no	—
419	C₂×C₄×C₃₁	—	4	4	no	—
420	C₂×C₄×C₃₁	—	4	4	no	—
421	C₂×C₄×C₃₁	—	4	4	no	—
422	C₂×C₄×C₃₁	—	4	4	no	—
423	C₂×C₄×C₃₁	—	4	2	no	—
424	C₂×C₄×C₃₁	—	4	2	no	—
425	C₂×C₄×C₃₁	—	4	2	no	—
426	C₂×C₄×C₃₁	—	8	1	no	—
427	C₂×C₄×C₃₁	—	8	2	no	—
428	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
434	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
435	C₈×C₃₁	—	2	2	no	—
436	C₈×C₃₁	—	2	2	no	—
437	C₈×C₃₁	—	2	4	no	—
438	#3489	C₂×C₃₁	1	1	yes	characteristic
439	C₂×#536	C₂×C₃₁	1	1	yes	characteristic, complemented
440	#3202	C₂×C₃₁	1	4	yes	complemented
441	#3201	C₂×C₃₁	1	4	yes	complemented
442	#3196	C₂×C₃₁	1	2	yes	complemented
443	#3195	C₂×C₃₁	1	2	yes	complemented
444	#3190	C₂×C₃₁	1	2	yes	complemented
445	#3189	C₂×C₃₁	1	2	yes	complemented
446	#3097	C₂×C₃₁	1	2	yes	complemented
447	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
448	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
449	#3063	C₂×C₃₁	1	2	yes	complemented
450	#3059	C₂×C₃₁	1	2	yes	complemented
451	#3011	C₂×C₃₁	1	2	yes	complemented
452	#3004	C₂×C₃₁	1	1	yes	characteristic, complemented
453	C₂×#451	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#2880	C₂×C₃₁	1	1	yes	characteristic, complemented
455	C₂²×C₃₁	—	2	1	no	—
456	C₂²×C₃₁	—	2	1	no	—
457	C₂²×C₃₁	—	2	1	no	—
458	C₂²×C₃₁	—	2	1	no	—
459	C₂²×C₃₁	—	2	2	no	—
460	C₂²×C₃₁	—	2	1	no	—
461	C₂²×C₃₁	—	2	2	no	—
462	C₂²×C₃₁	—	2	1	no	—
463	C₂²×C₃₁	—	2	2	no	—
464	C₂²×C₃₁	—	2	2	no	—
465	C₂²×C₃₁	—	2	1	no	—
466	C₂²×C₃₁	—	2	2	no	—
467	C₂²×C₃₁	—	2	2	no	—
468	C₂²×C₃₁	—	4	4	no	—
469	C₂²×C₃₁	—	4	1	no	—
470	C₂²×C₃₁	—	4	1	no	—
471	C₂²×C₃₁	—	4	1	no	—
472	C₂²×C₃₁	—	8	4	no	—
473	C₂²×C₃₁	#534	1	2	yes	—
474	C₂²×C₃₁	#578	1	2	yes	—
475	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
476	C₄×C₃₁	—	2	1	no	—
477	C₄×C₃₁	—	2	1	no	—
478	C₄×C₃₁	—	2	2	no	—
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	4	2	no	—
481	C₄×C₃₁	—	4	2	no	—
482	C₄×C₃₁	—	4	1	no	—
483	C₄×C₃₁	—	4	2	no	—
484	C₄×C₃₁	—	4	1	no	—
485	C₄×C₃₁	—	4	4	no	—
486	C₄×C₃₁	—	4	2	no	—
487	C₄×C₃₁	—	4	1	no	—
488	C₄×C₃₁	#534	1	2	yes	—
489	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
490	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
491	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
492	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
493	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
494	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
495	C₂×#131	C₂²×C₃₁	1	2	yes	—
496	D₄×Q₈	—	2	1	no	—
497	#548	—	2	1	no	—
498	#547	—	2	2	no	—
499	#547	—	2	1	no	—
500	#546	—	2	2	no	—
501	#546	—	2	1	no	—
502	#537	C₂²×C₃₁	1	2	yes	—
503	#537	C₂²×C₃₁	1	1	yes	characteristic
504	#536	—	2	2	no	—
505	#536	—	2	1	no	—
506	#536	—	2	1	no	—
507	#536	C₂²×C₃₁	1	2	yes	—
508	#536	C₂²×C₃₁	1	4	yes	—
509	#536	C₂²×C₃₁	1	2	yes	—
510	#536	C₂²×C₃₁	1	2	yes	—
511	#536	C₂²×C₃₁	1	1	yes	characteristic
512	C₂×C₄⋊Q₈	—	2	1	no	—
513	C₂×#124	—	2	1	no	—
514	#525	C₂²×C₃₁	1	1	yes	characteristic
515	#525	C₂²×C₃₁	1	2	yes	—
516	C₂×#123	—	2	2	no	—
517	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
520	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
521	#520	C₂²×C₃₁	1	1	yes	characteristic
522	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
523	#485	C₂²×C₃₁	1	2	yes	complemented
524	#485	C₂²×C₃₁	1	4	yes	complemented
525	#485	C₂²×C₃₁	1	4	yes	complemented
526	#485	C₂²×C₃₁	1	4	yes	complemented
527	#484	C₂²×C₃₁	1	1	yes	characteristic
528	#484	C₂²×C₃₁	1	2	yes	—
529	#484	C₂²×C₃₁	1	4	yes	complemented
530	#483	C₂²×C₃₁	1	1	yes	characteristic
531	#483	C₂²×C₃₁	1	2	yes	—
532	#483	C₂²×C₃₁	1	4	yes	complemented
533	#482	C₂²×C₃₁	1	2	yes	complemented
534	#481	C₂²×C₃₁	1	1	yes	characteristic
535	#480	C₂²×C₃₁	1	1	yes	characteristic
536	#470	C₂²×C₃₁	1	4	yes	complemented
537	#470	C₂²×C₃₁	1	4	yes	complemented
538	#470	C₂²×C₃₁	1	4	yes	complemented
539	#468	C₂²×C₃₁	1	4	yes	complemented
540	#467	C₂²×C₃₁	1	4	yes	complemented
541	#467	C₂²×C₃₁	1	4	yes	complemented
542	#467	C₂²×C₃₁	1	4	yes	complemented
543	#465	C₂²×C₃₁	1	4	yes	complemented
544	#452	C₂²×C₃₁	1	4	yes	complemented
545	#452	C₂²×C₃₁	1	4	yes	complemented
546	#451	C₂²×C₃₁	1	2	yes	—
547	#451	C₂²×C₃₁	1	2	yes	—
548	#451	C₂²×C₃₁	1	2	yes	—
549	#451	C₂²×C₃₁	1	4	yes	complemented
550	#451	C₂²×C₃₁	1	4	yes	complemented
551	#451	C₂²×C₃₁	1	4	yes	complemented
552	#451	C₂²×C₃₁	1	2	yes	complemented
553	#448	C₂²×C₃₁	1	2	yes	—
554	#448	C₂²×C₃₁	1	2	yes	complemented
555	#428	C₂²×C₃₁	1	2	yes	complemented
556	#427	C₂²×C₃₁	1	2	yes	complemented
557	#419	C₂²×C₃₁	1	2	yes	complemented
558	#419	C₂²×C₃₁	1	2	yes	complemented
559	#416	C₂²×C₃₁	1	2	yes	complemented
560	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
561	#408	C₂²×C₃₁	1	2	yes	—
562	#408	C₂²×C₃₁	1	4	yes	—
563	#407	C₂²×C₃₁	1	1	yes	characteristic
564	#407	C₂²×C₃₁	1	2	yes	—
565	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
566	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
567	C₂×C₃₁	—	2	2	no	—
568	C₂×C₃₁	—	2	2	no	—
569	C₂×C₃₁	—	4	1	no	—
570	C₂×C₃₁	—	4	2	no	—
571	C₂×C₃₁	—	4	2	no	—
572	C₂×C₃₁	—	8	1	no	—
573	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
574	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
575	C₂×C₃₁	#3586	1	1	yes	characteristic
576	2₋¹⁺⁴	—	4	4	no	—
577	C₂×#41	—	2	2	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	4	4	no	—
580	C₂×#41	D₄×C₃₁	1	2	yes	—
581	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
582	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
583	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
584	C₂×#41	C₂³×C₃₁	1	2	yes	—
585	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
586	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
587	C₂×#41	C₂³×C₃₁	1	2	yes	—
588	C₂²×Q₈	—	2	1	no	—
589	C₂²×Q₈	—	2	1	no	—
590	C₂²×Q₈	—	2	1	no	—
591	C₂²×Q₈	—	2	1	no	—
592	C₂²×Q₈	—	4	4	no	—
593	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
595	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
596	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
597	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
598	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
599	C₂²×D₄	D₄×C₃₁	1	2	yes	—
600	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
601	C₂³×C₄	—	2	1	no	—
602	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
604	#137	—	4	4	no	—
605	C₂×Q₁₆	—	4	4	no	—
606	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
607	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
608	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
609	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
610	#131	—	4	4	no	—
611	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
612	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
613	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
614	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	—	2	4	no	—
618	C₄⋊Q₈	—	2	1	no	—
619	C₄⋊Q₈	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	—	2	4	no	—
623	#124	—	2	1	no	—
624	#124	—	2	2	no	—
625	#123	—	2	4	no	—
626	#123	—	2	4	no	—
627	#123	—	2	4	no	—
628	#123	—	2	4	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	1	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	1	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
646	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
647	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
648	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
649	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
650	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
653	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
654	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	—	2	1	no	—
659	#121	—	2	2	no	—
660	#121	C₂³×C₃₁	1	1	yes	characteristic
661	#121	C₂³×C₃₁	1	1	yes	characteristic
662	#121	C₂³×C₃₁	1	2	yes	—
663	#120	—	2	1	no	—
664	#120	—	2	2	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	2	no	—
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	C₂³×C₃₁	1	2	yes	—
675	#117	C₂³×C₃₁	1	2	yes	—
676	#117	C₂³×C₃₁	1	1	yes	characteristic
677	#117	C₂³×C₃₁	1	2	yes	—
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	2	no	—
680	C₂×C₄⋊C₄	—	2	1	no	—
681	C₂×C₄⋊C₄	—	2	2	no	—
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	2	no	—
688	C₂×C₂²⋊C₄	—	2	2	no	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₄²	—	2	1	no	—
692	#107	C₂³×C₃₁	1	2	yes	—
693	#107	C₂³×C₃₁	1	2	yes	—
694	#107	C₂³×C₃₁	1	4	yes	—
695	#106	C₂³×C₃₁	1	2	yes	—
696	#106	C₂³×C₃₁	1	2	yes	—
697	#106	C₂³×C₃₁	1	4	yes	—
698	#103	C₂³×C₃₁	1	4	yes	—
699	#103	C₂³×C₃₁	1	4	yes	—
700	#103	C₂³×C₃₁	1	2	yes	—
701	#103	C₂³×C₃₁	1	2	yes	—
702	#103	C₂³×C₃₁	1	4	yes	—
703	#103	C₂³×C₃₁	1	4	yes	—
704	#103	C₂³×C₃₁	1	4	yes	—
705	#103	C₂³×C₃₁	1	4	yes	—
706	#102	C₂³×C₃₁	1	2	yes	—
707	#102	C₂³×C₃₁	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
713	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
715	C₃₁	#60759	1	1	yes	characteristic, direct product factor, Sylow
716	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
718	#41	—	2	4	no	—
719	#41	—	2	4	no	—
720	#41	—	2	4	no	—
721	#41	—	4	4	no	—
722	#41	—	4	4	no	—
723	#41	—	4	2	no	—
724	#41	—	4	2	no	—
725	#41	—	4	4	no	—
726	#41	—	4	8	no	—
727	#41	—	4	4	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	1	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	2	4	no	—
735	C₂×Q₈	—	2	4	no	—
736	C₂×Q₈	—	4	4	no	—
737	C₂×Q₈	—	4	4	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	4	4	no	—
740	C₂×Q₈	—	4	4	no	—
741	C₂×Q₈	—	4	4	no	—
742	C₂×Q₈	—	4	4	no	—
743	C₂×Q₈	—	4	4	no	—
744	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
746	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
747	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
748	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
749	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	4	no	—
757	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
758	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
759	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
760	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
761	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
762	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
763	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
764	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	4	4	no	—
778	C₂²×C₄	—	4	4	no	—
779	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
782	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
783	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
790	Q₁₆	—	4	4	no	—
791	Q₁₆	—	4	4	no	—
792	Q₁₆	—	4	4	no	—
793	SD₁₆	—	4	4	no	—
794	M₁₆	—	2	4	no	—
795	M₁₆	—	4	4	no	—
796	C₂×C₈	—	2	4	no	—
797	C₂×C₈	—	4	4	no	—
798	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
799	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
800	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
820	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	1	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	1	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	4	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	4	1	no	—
848	C₂³	—	4	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
851	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
852	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
853	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
854	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	4	no	—
858	Q₈	—	2	4	no	—
859	Q₈	—	2	4	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	4	2	no	—
862	Q₈	—	4	4	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	Q₈	—	4	4	no	—
866	Q₈	—	4	2	no	—
867	D₄	—	2	4	no	—
868	D₄	—	2	4	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	4	2	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	2	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	2	no	—
877	D₄	—	4	2	no	—
878	D₄	—	8	1	no	—
879	D₄	—	8	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	8	1	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
913	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
915	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
916	C₈	—	2	2	no	—
917	C₈	—	2	2	no	—
918	C₈	—	2	4	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	4	4	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	8	4	no	—
937	C₂²	C₃₁×#534	1	2	yes	—
938	C₂²	C₃₁×#578	1	2	yes	—
939	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	4	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	C₃₁×#534	1	2	yes	—
953	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
954	C₂	—	2	2	no	—
955	C₂	—	2	2	no	—
956	C₂	—	4	1	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	8	1	no	—
960	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
961	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
962	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#536	C₂	semidirect
3. C₃₁×#3202	C₂	semidirect
4. C₃₁×#3201	C₂	semidirect
5. C₃₁×#3196	C₂	semidirect
6. C₃₁×#3195	C₂	semidirect
7. C₃₁×#3190	C₂	semidirect
8. C₃₁×#3189	C₂	semidirect
9. C₃₁×#3097	C₂	semidirect
10. C₃₁×#3095	C₂	semidirect
11. C₃₁×#3091	C₂	semidirect
12. C₃₁×#3063	C₂	semidirect
13. C₃₁×#3059	C₂	semidirect
14. C₃₁×#3011	C₂	semidirect
15. C₃₁×#3004	C₂	semidirect
16. C₂×C₃₁×#451	C₂	semidirect
17. C₃₁×#2880	C₂	semidirect
21. C₂×C₃₁×#137	C₂²	semidirect
22. C₂²×Q₁₆×C₃₁	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#485	C₂²	semidirect
57. C₃₁×#484	C₂²	semidirect
60. C₃₁×#483	C₂²	semidirect
61. C₃₁×#482	C₂²	semidirect
64. C₃₁×#470	C₂²	semidirect
65. C₃₁×#470	C₂²	semidirect
66. C₃₁×#470	C₂²	semidirect
67. C₃₁×#468	C₂²	semidirect
68. C₃₁×#467	C₂²	semidirect
69. C₃₁×#467	C₂²	semidirect
70. C₃₁×#467	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#452	C₂²	semidirect
73. C₃₁×#452	C₂²	semidirect
77. C₃₁×#451	C₂²	semidirect
78. C₃₁×#451	C₂²	semidirect
79. C₃₁×#451	C₂²	semidirect
80. C₃₁×#451	C₂²	semidirect
82. C₃₁×#448	C₂²	semidirect
83. C₃₁×#428	C₂²	semidirect
84. C₃₁×#427	C₂²	semidirect
85. C₃₁×#419	C₂²	semidirect
86. C₃₁×#419	C₂²	semidirect
87. C₃₁×#416	C₂²	semidirect
88. C₂×C₃₁×#103	C₂²	semidirect
361. #60759	C₃₁	direct (N × H)
439. C₂×#536	C₂×C₃₁	semidirect
440. #3202	C₂×C₃₁	semidirect
441. #3201	C₂×C₃₁	semidirect
442. #3196	C₂×C₃₁	semidirect
443. #3195	C₂×C₃₁	semidirect
444. #3190	C₂×C₃₁	semidirect
445. #3189	C₂×C₃₁	semidirect
446. #3097	C₂×C₃₁	semidirect
447. #3095	C₂×C₃₁	semidirect
448. #3091	C₂×C₃₁	semidirect
449. #3063	C₂×C₃₁	semidirect
450. #3059	C₂×C₃₁	semidirect
451. #3011	C₂×C₃₁	semidirect
452. #3004	C₂×C₃₁	semidirect
453. C₂×#451	C₂×C₃₁	semidirect
454. #2880	C₂×C₃₁	semidirect
493. C₂×#137	C₂²×C₃₁	semidirect
494. C₂²×Q₁₆	C₂²×C₃₁	semidirect
523. #485	C₂²×C₃₁	semidirect
524. #485	C₂²×C₃₁	semidirect
525. #485	C₂²×C₃₁	semidirect
526. #485	C₂²×C₃₁	semidirect
529. #484	C₂²×C₃₁	semidirect
532. #483	C₂²×C₃₁	semidirect
533. #482	C₂²×C₃₁	semidirect
536. #470	C₂²×C₃₁	semidirect
537. #470	C₂²×C₃₁	semidirect
538. #470	C₂²×C₃₁	semidirect
539. #468	C₂²×C₃₁	semidirect
540. #467	C₂²×C₃₁	semidirect
541. #467	C₂²×C₃₁	semidirect
542. #467	C₂²×C₃₁	semidirect
543. #465	C₂²×C₃₁	semidirect
544. #452	C₂²×C₃₁	semidirect
545. #452	C₂²×C₃₁	semidirect
549. #451	C₂²×C₃₁	semidirect
550. #451	C₂²×C₃₁	semidirect
551. #451	C₂²×C₃₁	semidirect
552. #451	C₂²×C₃₁	semidirect
554. #448	C₂²×C₃₁	semidirect
555. #428	C₂²×C₃₁	semidirect
556. #427	C₂²×C₃₁	semidirect
557. #419	C₂²×C₃₁	semidirect
558. #419	C₂²×C₃₁	semidirect
559. #416	C₂²×C₃₁	semidirect
560. C₂×#103	C₂²×C₃₁	semidirect
715. C₃₁	#60759	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×#3489	2
C₂×C₃₁×#536	2
C₃₁×#3202	2
C₃₁×#3201	2
C₃₁×#3196	2
C₃₁×#3195	2
C₃₁×#3190	2
C₃₁×#3189	2
C₃₁×#3097	2
C₃₁×#3095	2
C₃₁×#3091	2
C₃₁×#3063	2
C₃₁×#3059	2
C₃₁×#3011	2
C₃₁×#3004	2
C₂×C₃₁×#451	2
C₃₁×#2880	2
#60759	31

Subgroups — C31×#60759 #21517518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60759 #21517518