Subgroups — C₃₁×#60758 #21517517

Order 7936.

2186 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3488	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3201	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3200	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3193	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3187	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3094	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×#3057	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3004	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#131	C₂²	1	2	yes	complemented
24	C₃₁×#550	—	2	1	no	—
25	C₃₁×#548	—	2	1	no	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#546	—	2	1	no	—
28	D₄²×C₃₁	—	2	2	no	—
29	D₄²×C₃₁	—	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	complemented
37	C₃₁×#536	C₂²	1	2	yes	complemented
38	C₃₁×#535	C₂²	1	2	yes	—
39	C₃₁×#535	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	2	yes	complemented
46	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#121	C₂²	1	2	yes	—
49	C₃₁×#520	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
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×#484	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#484	C₂²	1	4	yes	complemented
56	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#483	C₂²	1	4	yes	complemented
58	C₃₁×#482	C₂²	1	2	yes	complemented
59	C₃₁×#482	C₂²	1	4	yes	complemented
60	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#481	C₂²	1	2	yes	complemented
62	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#480	C₂²	1	2	yes	complemented
64	C₃₁×#470	C₂²	1	4	yes	complemented
65	C₃₁×#468	C₂²	1	4	yes	complemented
66	C₃₁×#468	C₂²	1	4	yes	complemented
67	C₃₁×#468	C₂²	1	4	yes	complemented
68	C₃₁×#467	C₂²	1	4	yes	complemented
69	C₃₁×#465	C₂²	1	4	yes	complemented
70	C₃₁×#465	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	complemented
75	C₃₁×#451	C₂²	1	2	yes	complemented
76	C₃₁×#450	C₂²	1	4	yes	complemented
77	C₃₁×#450	C₂²	1	4	yes	complemented
78	C₃₁×#448	C₂²	1	2	yes	complemented
79	C₃₁×#448	C₂²	1	2	yes	complemented
80	C₃₁×#448	C₂²	1	2	yes	complemented
81	C₃₁×#448	C₂²	1	2	yes	complemented
82	C₃₁×#448	C₂²	1	4	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×#418	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	complemented
91	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#407	C₂²	1	2	yes	complemented
93	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₃₁×H(5,𝔽₂)	—	4	4	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	4	4	no	—
98	C₂×#41×C₃₁	D₄	1	2	yes	—
99	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
100	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
101	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×#41×C₃₁	C₂³	1	2	yes	—
103	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
104	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×#41×C₃₁	C₂³	1	2	yes	—
106	C₂²×Q₈×C₃₁	—	2	1	no	—
107	C₂²×Q₈×C₃₁	—	2	1	no	—
108	C₂²×Q₈×C₃₁	—	2	1	no	—
109	C₂²×Q₈×C₃₁	—	4	4	no	—
110	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
111	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
112	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
114	C₂²×D₄×C₃₁	—	2	1	no	—
115	C₂²×D₄×C₃₁	—	2	2	no	—
116	C₂²×D₄×C₃₁	—	2	2	no	—
117	C₂²×D₄×C₃₁	—	2	1	no	—
118	C₂²×D₄×C₃₁	D₄	1	2	yes	—
119	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
122	C₂³×C₄×C₃₁	—	2	1	no	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₃₁×#137	—	4	4	no	—
126	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₃₁	—	4	4	no	—
128	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
131	C₃₁×#131	—	4	4	no	—
132	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
134	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
135	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	—	2	2	no	—
138	C₃₁×C₄⋊Q₈	—	2	4	no	—
139	C₃₁×#127	—	2	1	no	—
140	C₃₁×#127	—	2	2	no	—
141	C₃₁×#124	—	2	1	no	—
142	C₃₁×#124	—	2	2	no	—
143	C₃₁×#124	—	2	2	no	—
144	C₃₁×#124	—	2	2	no	—
145	C₃₁×#124	—	2	4	no	—
146	C₃₁×#123	—	2	4	no	—
147	C₃₁×#123	—	2	4	no	—
148	C₃₁×#123	—	2	4	no	—
149	C₃₁×#123	—	2	4	no	—
150	C₃₁×#123	—	2	1	no	—
151	C₃₁×#123	—	2	2	no	—
152	C₃₁×C₂²⋊Q₈	—	2	1	no	—
153	C₃₁×C₂²⋊Q₈	—	2	2	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	C₂³	1	4	yes	—
159	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
160	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
163	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
164	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×#121	—	2	2	no	—
166	C₃₁×#121	—	2	2	no	—
167	C₃₁×#121	—	2	2	no	—
168	C₃₁×#121	—	2	1	no	—
169	C₃₁×#121	—	2	2	no	—
170	C₃₁×#121	—	2	1	no	—
171	C₃₁×#121	—	2	2	no	—
172	C₃₁×#121	—	2	1	no	—
173	C₃₁×#121	—	2	2	no	—
174	C₃₁×#121	C₂³	1	2	yes	—
175	C₃₁×#121	C₂³	1	1	yes	characteristic
176	C₃₁×#121	C₂³	1	2	yes	—
177	C₃₁×#121	C₂³	1	1	yes	characteristic
178	C₃₁×#121	C₂³	1	2	yes	—
179	C₃₁×#121	C₂³	1	2	yes	—
180	C₃₁×#121	C₂³	1	2	yes	—
181	C₃₁×#120	—	2	1	no	—
182	C₃₁×#120	—	2	2	no	—
183	C₃₁×#120	—	2	2	no	—
184	C₃₁×#120	—	2	2	no	—
185	C₃₁×#120	—	2	2	no	—
186	C₄×Q₈×C₃₁	—	2	1	no	—
187	C₄×D₄×C₃₁	—	2	2	no	—
188	C₄×D₄×C₃₁	—	2	1	no	—
189	C₄×D₄×C₃₁	—	2	1	no	—
190	C₄×D₄×C₃₁	—	2	2	no	—
191	C₄×D₄×C₃₁	—	2	1	no	—
192	C₄×D₄×C₃₁	—	2	2	no	—
193	C₃₁×#117	—	2	1	no	—
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	C₂³	1	2	yes	—
196	C₃₁×#117	C₂³	1	1	yes	characteristic
197	C₃₁×#117	C₂³	1	2	yes	—
198	C₃₁×#117	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	—	2	2	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×#102	C₂³	1	2	yes	—
224	C₃₁×#102	C₂³	1	2	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#102	C₂³	1	4	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
233	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
234	C₂⁴×C₃₁	—	2	2	no	—
235	C₂⁴×C₃₁	—	2	1	no	—
236	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
238	#41×C₃₁	—	2	4	no	—
239	#41×C₃₁	—	2	4	no	—
240	#41×C₃₁	—	2	4	no	—
241	#41×C₃₁	—	4	4	no	—
242	#41×C₃₁	—	4	4	no	—
243	#41×C₃₁	—	4	2	no	—
244	#41×C₃₁	—	4	2	no	—
245	#41×C₃₁	—	4	4	no	—
246	#41×C₃₁	—	4	4	no	—
247	C₂×Q₈×C₃₁	—	2	2	no	—
248	C₂×Q₈×C₃₁	—	2	2	no	—
249	C₂×Q₈×C₃₁	—	2	2	no	—
250	C₂×Q₈×C₃₁	—	2	4	no	—
251	C₂×Q₈×C₃₁	—	2	4	no	—
252	C₂×Q₈×C₃₁	—	4	4	no	—
253	C₂×Q₈×C₃₁	—	4	4	no	—
254	C₂×Q₈×C₃₁	—	4	2	no	—
255	C₂×Q₈×C₃₁	—	4	4	no	—
256	C₂×Q₈×C₃₁	—	4	4	no	—
257	C₂×Q₈×C₃₁	—	4	4	no	—
258	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
261	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
262	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₃₁	—	2	1	no	—
264	C₂×D₄×C₃₁	—	2	2	no	—
265	C₂×D₄×C₃₁	—	2	2	no	—
266	C₂×D₄×C₃₁	—	2	1	no	—
267	C₂×D₄×C₃₁	—	2	2	no	—
268	C₂×D₄×C₃₁	—	2	1	no	—
269	C₂×D₄×C₃₁	—	2	2	no	—
270	C₂×D₄×C₃₁	—	2	2	no	—
271	C₂×D₄×C₃₁	—	2	2	no	—
272	C₂×D₄×C₃₁	—	2	2	no	—
273	C₂×D₄×C₃₁	—	2	1	no	—
274	C₂×D₄×C₃₁	—	2	4	no	—
275	C₂×D₄×C₃₁	—	4	2	no	—
276	C₂×D₄×C₃₁	—	4	4	no	—
277	C₂×D₄×C₃₁	—	4	4	no	—
278	C₂×D₄×C₃₁	—	4	8	no	—
279	C₂×D₄×C₃₁	—	4	4	no	—
280	C₂×D₄×C₃₁	—	8	2	no	—
281	C₂×D₄×C₃₁	—	8	4	no	—
282	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
287	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
290	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	—	2	4	no	—
292	C₂²×C₄×C₃₁	—	2	1	no	—
293	C₂²×C₄×C₃₁	—	2	1	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	—	2	2	no	—
297	C₂²×C₄×C₃₁	—	2	2	no	—
298	C₂²×C₄×C₃₁	—	2	1	no	—
299	C₂²×C₄×C₃₁	—	2	2	no	—
300	C₂²×C₄×C₃₁	—	2	1	no	—
301	C₂²×C₄×C₃₁	—	4	4	no	—
302	C₂²×C₄×C₃₁	—	4	4	no	—
303	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
308	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	Q₁₆×C₃₁	—	4	4	no	—
315	SD₁₆×C₃₁	—	4	4	no	—
316	SD₁₆×C₃₁	—	4	4	no	—
317	SD₁₆×C₃₁	—	4	4	no	—
318	M₁₆×C₃₁	—	2	4	no	—
319	M₁₆×C₃₁	—	4	4	no	—
320	C₂×C₈×C₃₁	—	2	4	no	—
321	C₂×C₈×C₃₁	—	4	4	no	—
322	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
323	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
324	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
329	C₄⋊C₄×C₃₁	—	2	1	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂²⋊C₄×C₃₁	—	2	2	no	—
342	C₂²⋊C₄×C₃₁	—	2	2	no	—
343	C₂²⋊C₄×C₃₁	—	2	4	no	—
344	C₂²⋊C₄×C₃₁	—	2	4	no	—
345	C₂²⋊C₄×C₃₁	—	2	4	no	—
346	C₂²⋊C₄×C₃₁	—	2	4	no	—
347	C₂²⋊C₄×C₃₁	—	2	2	no	—
348	C₂²⋊C₄×C₃₁	—	2	1	no	—
349	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	1	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₄²×C₃₁	—	2	2	no	—
360	C₄²×C₃₁	—	2	2	no	—
361	C₄²×C₃₁	—	2	2	no	—
362	C₄²×C₃₁	—	2	1	no	—
363	#60758	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₂³×C₃₁	—	2	2	no	—
365	C₂³×C₃₁	—	2	2	no	—
366	C₂³×C₃₁	—	2	4	no	—
367	C₂³×C₃₁	—	2	2	no	—
368	C₂³×C₃₁	—	2	1	no	—
369	C₂³×C₃₁	—	4	1	no	—
370	C₂³×C₃₁	—	4	2	no	—
371	C₂³×C₃₁	—	4	2	no	—
372	C₂³×C₃₁	—	4	4	no	—
373	C₂³×C₃₁	—	4	2	no	—
374	C₂³×C₃₁	—	8	1	no	—
375	C₂³×C₃₁	—	8	2	no	—
376	C₂³×C₃₁	—	8	1	no	—
377	C₂³×C₃₁	—	8	2	no	—
378	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
379	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
380	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	Q₈×C₃₁	—	2	2	no	—
384	Q₈×C₃₁	—	2	2	no	—
385	Q₈×C₃₁	—	2	4	no	—
386	Q₈×C₃₁	—	2	4	no	—
387	Q₈×C₃₁	—	2	2	no	—
388	Q₈×C₃₁	—	4	2	no	—
389	Q₈×C₃₁	—	4	4	no	—
390	Q₈×C₃₁	—	4	4	no	—
391	Q₈×C₃₁	—	4	4	no	—
392	D₄×C₃₁	—	2	4	no	—
393	D₄×C₃₁	—	2	4	no	—
394	D₄×C₃₁	—	2	2	no	—
395	D₄×C₃₁	—	2	2	no	—
396	D₄×C₃₁	—	2	4	no	—
397	D₄×C₃₁	—	2	2	no	—
398	D₄×C₃₁	—	4	2	no	—
399	D₄×C₃₁	—	4	2	no	—
400	D₄×C₃₁	—	4	2	no	—
401	D₄×C₃₁	—	4	4	no	—
402	D₄×C₃₁	—	4	4	no	—
403	D₄×C₃₁	—	4	2	no	—
404	D₄×C₃₁	—	4	4	no	—
405	D₄×C₃₁	—	4	2	no	—
406	D₄×C₃₁	—	4	2	no	—
407	D₄×C₃₁	—	8	1	no	—
408	D₄×C₃₁	—	8	2	no	—
409	D₄×C₃₁	—	8	2	no	—
410	D₄×C₃₁	—	8	2	no	—
411	D₄×C₃₁	—	8	2	no	—
412	C₂×C₄×C₃₁	—	2	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	4	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	4	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	4	no	—
426	C₂×C₄×C₃₁	—	4	2	no	—
427	C₂×C₄×C₃₁	—	4	2	no	—
428	C₂×C₄×C₃₁	—	4	2	no	—
429	C₂×C₄×C₃₁	—	4	4	no	—
430	C₂×C₄×C₃₁	—	4	2	no	—
431	C₂×C₄×C₃₁	—	4	4	no	—
432	C₂×C₄×C₃₁	—	4	4	no	—
433	C₂×C₄×C₃₁	—	4	4	no	—
434	C₂×C₄×C₃₁	—	4	2	no	—
435	C₂×C₄×C₃₁	—	4	2	no	—
436	C₂×C₄×C₃₁	—	8	1	no	—
437	C₂×C₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
444	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
445	C₈×C₃₁	—	2	2	no	—
446	C₈×C₃₁	—	2	2	no	—
447	C₈×C₃₁	—	2	4	no	—
448	#3488	C₂×C₃₁	1	1	yes	characteristic
449	C₂×#536	C₂×C₃₁	1	1	yes	characteristic, complemented
450	#3201	C₂×C₃₁	1	4	yes	complemented
451	#3200	C₂×C₃₁	1	4	yes	complemented
452	#3196	C₂×C₃₁	1	2	yes	complemented
453	#3193	C₂×C₃₁	1	2	yes	complemented
454	#3190	C₂×C₃₁	1	2	yes	complemented
455	#3187	C₂×C₃₁	1	2	yes	complemented
456	#3097	C₂×C₃₁	1	2	yes	complemented
457	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#3091	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#3063	C₂×C₃₁	1	2	yes	complemented
460	#3057	C₂×C₃₁	1	2	yes	complemented
461	#3009	C₂×C₃₁	1	2	yes	complemented
462	#3004	C₂×C₃₁	1	1	yes	characteristic, complemented
463	C₂×#448	C₂×C₃₁	1	1	yes	characteristic, complemented
464	#2880	C₂×C₃₁	1	1	yes	characteristic, complemented
465	C₂²×C₃₁	—	2	1	no	—
466	C₂²×C₃₁	—	2	1	no	—
467	C₂²×C₃₁	—	2	1	no	—
468	C₂²×C₃₁	—	2	1	no	—
469	C₂²×C₃₁	—	2	1	no	—
470	C₂²×C₃₁	—	2	2	no	—
471	C₂²×C₃₁	—	2	2	no	—
472	C₂²×C₃₁	—	2	1	no	—
473	C₂²×C₃₁	—	2	2	no	—
474	C₂²×C₃₁	—	2	2	no	—
475	C₂²×C₃₁	—	2	2	no	—
476	C₂²×C₃₁	—	2	1	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	4	4	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	1	no	—
481	C₂²×C₃₁	—	4	2	no	—
482	C₂²×C₃₁	—	4	1	no	—
483	C₂²×C₃₁	—	4	2	no	—
484	C₂²×C₃₁	—	4	1	no	—
485	C₂²×C₃₁	—	8	4	no	—
486	C₂²×C₃₁	—	16	2	no	—
487	C₂²×C₃₁	—	16	4	no	—
488	C₂²×C₃₁	#534	1	2	yes	—
489	C₂²×C₃₁	#577	1	2	yes	—
490	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
491	C₄×C₃₁	—	2	1	no	—
492	C₄×C₃₁	—	2	1	no	—
493	C₄×C₃₁	—	2	2	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	1	no	—
497	C₄×C₃₁	—	4	1	no	—
498	C₄×C₃₁	—	4	4	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	1	no	—
502	C₄×C₃₁	#534	1	2	yes	—
503	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
504	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
505	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
506	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
508	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
509	C₂×#131	C₂²×C₃₁	1	2	yes	complemented
510	#550	—	2	1	no	—
511	#548	—	2	1	no	—
512	#546	—	2	2	no	—
513	#546	—	2	1	no	—
514	D₄²	—	2	2	no	—
515	D₄²	—	2	1	no	—
516	#537	C₂²×C₃₁	1	2	yes	—
517	#537	C₂²×C₃₁	1	1	yes	characteristic
518	#536	—	2	2	no	—
519	#536	—	2	1	no	—
520	#536	—	2	1	no	—
521	#536	C₂²×C₃₁	1	2	yes	—
522	#536	C₂²×C₃₁	1	4	yes	complemented
523	#536	C₂²×C₃₁	1	2	yes	complemented
524	#535	C₂²×C₃₁	1	2	yes	—
525	#535	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×C₄⋊Q₈	—	2	1	no	—
527	C₂×#124	—	2	1	no	—
528	#525	C₂²×C₃₁	1	1	yes	characteristic
529	#525	C₂²×C₃₁	1	2	yes	—
530	C₂×#123	—	2	2	no	—
531	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
532	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
533	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
534	C₂×#121	C₂²×C₃₁	1	2	yes	—
535	#520	C₂²×C₃₁	1	1	yes	characteristic
536	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
537	#485	C₂²×C₃₁	1	2	yes	complemented
538	#485	C₂²×C₃₁	1	4	yes	complemented
539	#485	C₂²×C₃₁	1	4	yes	complemented
540	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
541	#484	C₂²×C₃₁	1	4	yes	complemented
542	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	#483	C₂²×C₃₁	1	4	yes	complemented
544	#482	C₂²×C₃₁	1	2	yes	complemented
545	#482	C₂²×C₃₁	1	4	yes	complemented
546	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
547	#481	C₂²×C₃₁	1	2	yes	complemented
548	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	#480	C₂²×C₃₁	1	2	yes	complemented
550	#470	C₂²×C₃₁	1	4	yes	complemented
551	#468	C₂²×C₃₁	1	4	yes	complemented
552	#468	C₂²×C₃₁	1	4	yes	complemented
553	#468	C₂²×C₃₁	1	4	yes	complemented
554	#467	C₂²×C₃₁	1	4	yes	complemented
555	#465	C₂²×C₃₁	1	4	yes	complemented
556	#465	C₂²×C₃₁	1	4	yes	complemented
557	#465	C₂²×C₃₁	1	4	yes	complemented
558	#452	C₂²×C₃₁	1	4	yes	complemented
559	#452	C₂²×C₃₁	1	4	yes	complemented
560	#451	C₂²×C₃₁	1	2	yes	complemented
561	#451	C₂²×C₃₁	1	2	yes	complemented
562	#450	C₂²×C₃₁	1	4	yes	complemented
563	#450	C₂²×C₃₁	1	4	yes	complemented
564	#448	C₂²×C₃₁	1	2	yes	complemented
565	#448	C₂²×C₃₁	1	2	yes	complemented
566	#448	C₂²×C₃₁	1	2	yes	complemented
567	#448	C₂²×C₃₁	1	2	yes	complemented
568	#448	C₂²×C₃₁	1	4	yes	complemented
569	#428	C₂²×C₃₁	1	2	yes	complemented
570	#427	C₂²×C₃₁	1	2	yes	complemented
571	#419	C₂²×C₃₁	1	2	yes	complemented
572	#418	C₂²×C₃₁	1	2	yes	complemented
573	#416	C₂²×C₃₁	1	2	yes	complemented
574	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
575	#408	C₂²×C₃₁	1	2	yes	—
576	#408	C₂²×C₃₁	1	4	yes	complemented
577	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	#407	C₂²×C₃₁	1	2	yes	complemented
579	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
580	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
581	C₂×C₃₁	—	2	2	no	—
582	C₂×C₃₁	—	2	2	no	—
583	C₂×C₃₁	—	4	1	no	—
584	C₂×C₃₁	—	4	2	no	—
585	C₂×C₃₁	—	4	2	no	—
586	C₂×C₃₁	—	8	2	no	—
587	C₂×C₃₁	—	8	1	no	—
588	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
589	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
590	C₂×C₃₁	#3586	1	1	yes	characteristic
591	H(5,𝔽₂)	—	4	4	no	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	—	4	4	no	—
594	C₂×#41	D₄×C₃₁	1	2	yes	—
595	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
596	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
597	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
598	C₂×#41	C₂³×C₃₁	1	2	yes	—
599	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
600	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
601	C₂×#41	C₂³×C₃₁	1	2	yes	—
602	C₂²×Q₈	—	2	1	no	—
603	C₂²×Q₈	—	2	1	no	—
604	C₂²×Q₈	—	2	1	no	—
605	C₂²×Q₈	—	4	4	no	—
606	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
607	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
608	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
609	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
610	C₂²×D₄	—	2	1	no	—
611	C₂²×D₄	—	2	2	no	—
612	C₂²×D₄	—	2	2	no	—
613	C₂²×D₄	—	2	1	no	—
614	C₂²×D₄	D₄×C₃₁	1	2	yes	—
615	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
618	C₂³×C₄	—	2	1	no	—
619	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
621	#137	—	4	4	no	—
622	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
623	C₂×SD₁₆	—	4	4	no	—
624	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
625	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
626	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
627	#131	—	4	4	no	—
628	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
629	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
630	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
631	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
632	C₄⋊Q₈	—	2	2	no	—
633	C₄⋊Q₈	—	2	2	no	—
634	C₄⋊Q₈	—	2	4	no	—
635	#127	—	2	1	no	—
636	#127	—	2	2	no	—
637	#124	—	2	1	no	—
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	4	no	—
642	#123	—	2	4	no	—
643	#123	—	2	4	no	—
644	#123	—	2	4	no	—
645	#123	—	2	4	no	—
646	#123	—	2	1	no	—
647	#123	—	2	2	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
655	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
656	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
657	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
658	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
659	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
660	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	1	no	—
665	#121	—	2	2	no	—
666	#121	—	2	1	no	—
667	#121	—	2	2	no	—
668	#121	—	2	1	no	—
669	#121	—	2	2	no	—
670	#121	C₂³×C₃₁	1	2	yes	—
671	#121	C₂³×C₃₁	1	1	yes	characteristic
672	#121	C₂³×C₃₁	1	2	yes	—
673	#121	C₂³×C₃₁	1	2	yes	—
674	#121	C₂³×C₃₁	1	2	yes	—
675	#121	C₂³×C₃₁	1	1	yes	characteristic
676	#121	C₂³×C₃₁	1	2	yes	—
677	#120	—	2	1	no	—
678	#120	—	2	2	no	—
679	#120	—	2	2	no	—
680	#120	—	2	2	no	—
681	#120	—	2	2	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	2	no	—
689	#117	—	2	1	no	—
690	#117	—	2	1	no	—
691	#117	C₂³×C₃₁	1	2	yes	—
692	#117	C₂³×C₃₁	1	2	yes	—
693	#117	C₂³×C₃₁	1	1	yes	characteristic
694	#117	C₂³×C₃₁	1	2	yes	—
695	C₂×C₄⋊C₄	—	2	2	no	—
696	C₂×C₄⋊C₄	—	2	2	no	—
697	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
701	C₂×C₂²⋊C₄	—	2	1	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	—	2	1	no	—
705	C₂×C₂²⋊C₄	—	2	2	no	—
706	C₂×C₄²	—	2	1	no	—
707	#107	C₂³×C₃₁	1	2	yes	—
708	#107	C₂³×C₃₁	1	2	yes	—
709	#107	C₂³×C₃₁	1	4	yes	—
710	#106	C₂³×C₃₁	1	2	yes	—
711	#106	C₂³×C₃₁	1	2	yes	—
712	#106	C₂³×C₃₁	1	4	yes	—
713	#103	C₂³×C₃₁	1	4	yes	—
714	#103	C₂³×C₃₁	1	4	yes	—
715	#103	C₂³×C₃₁	1	2	yes	—
716	#103	C₂³×C₃₁	1	2	yes	—
717	#103	C₂³×C₃₁	1	4	yes	—
718	#103	C₂³×C₃₁	1	4	yes	—
719	#102	C₂³×C₃₁	1	2	yes	—
720	#102	C₂³×C₃₁	1	2	yes	—
721	#102	C₂³×C₃₁	1	4	yes	—
722	#102	C₂³×C₃₁	1	4	yes	—
723	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
727	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
729	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
730	C₃₁	#60758	1	1	yes	characteristic, direct product factor, Sylow
731	C₂⁴	—	2	2	no	—
732	C₂⁴	—	2	1	no	—
733	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
734	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	2	4	no	—
738	#41	—	4	4	no	—
739	#41	—	4	4	no	—
740	#41	—	4	2	no	—
741	#41	—	4	2	no	—
742	#41	—	4	4	no	—
743	#41	—	4	4	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	4	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	4	4	no	—
750	C₂×Q₈	—	4	4	no	—
751	C₂×Q₈	—	4	2	no	—
752	C₂×Q₈	—	4	4	no	—
753	C₂×Q₈	—	4	4	no	—
754	C₂×Q₈	—	4	4	no	—
755	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
758	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
759	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	1	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	4	no	—
774	C₂×D₄	—	4	4	no	—
775	C₂×D₄	—	4	8	no	—
776	C₂×D₄	—	4	4	no	—
777	C₂×D₄	—	8	2	no	—
778	C₂×D₄	—	8	4	no	—
779	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
780	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
781	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
782	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
783	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
784	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
785	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
786	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
787	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	4	4	no	—
799	C₂²×C₄	—	4	4	no	—
800	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
801	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
804	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
805	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
811	Q₁₆	—	4	4	no	—
812	SD₁₆	—	4	4	no	—
813	SD₁₆	—	4	4	no	—
814	SD₁₆	—	4	4	no	—
815	M₁₆	—	2	4	no	—
816	M₁₆	—	4	4	no	—
817	C₂×C₈	—	2	4	no	—
818	C₂×C₈	—	4	4	no	—
819	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
820	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
821	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	4	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
837	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	1	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	1	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	8	1	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	1	no	—
873	C₂³	—	8	2	no	—
874	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
875	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
876	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
877	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	2	4	no	—
882	Q₈	—	2	4	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	4	2	no	—
885	Q₈	—	4	4	no	—
886	Q₈	—	4	4	no	—
887	Q₈	—	4	4	no	—
888	D₄	—	2	4	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	2	no	—
896	D₄	—	4	2	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	2	no	—
900	D₄	—	4	4	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	2	no	—
903	D₄	—	8	1	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	D₄	—	8	2	no	—
907	D₄	—	8	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	8	1	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
939	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
940	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
941	C₈	—	2	2	no	—
942	C₈	—	2	2	no	—
943	C₈	—	2	4	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	4	4	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	8	4	no	—
965	C₂²	—	16	2	no	—
966	C₂²	—	16	4	no	—
967	C₂²	C₃₁×#534	1	2	yes	—
968	C₂²	C₃₁×#577	1	2	yes	—
969	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	4	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	1	no	—
981	C₄	C₃₁×#534	1	2	yes	—
982	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
983	C₂	—	2	2	no	—
984	C₂	—	2	2	no	—
985	C₂	—	4	1	no	—
986	C₂	—	4	2	no	—
987	C₂	—	4	2	no	—
988	C₂	—	8	2	no	—
989	C₂	—	8	1	no	—
990	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
991	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
992	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×#3488	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×#3201	C₂	semidirect
4. C₃₁×#3200	C₂	semidirect
5. C₃₁×#3196	C₂	semidirect
6. C₃₁×#3193	C₂	semidirect
7. C₃₁×#3190	C₂	semidirect
8. C₃₁×#3187	C₂	semidirect
9. C₃₁×#3097	C₂	semidirect
10. C₃₁×#3094	C₂	semidirect
11. C₃₁×#3091	C₂	semidirect
12. C₃₁×#3063	C₂	semidirect
13. C₃₁×#3057	C₂	semidirect
14. C₃₁×#3009	C₂	semidirect
15. C₃₁×#3004	C₂	semidirect
16. C₂×C₃₁×#448	C₂	semidirect
17. C₃₁×#2880	C₂	semidirect
20. C₂³×Q₈×C₃₁	C₂²	semidirect
21. C₂×C₃₁×#137	C₂²	semidirect
22. C₂²×SD₁₆×C₃₁	C₂²	semidirect
23. C₂×C₃₁×#131	C₂²	semidirect
36. C₃₁×#536	C₂²	semidirect
37. C₃₁×#536	C₂²	semidirect
45. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
50. C₂×C₃₁×#117	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#484	C₂²	semidirect
55. C₃₁×#484	C₂²	semidirect
56. C₃₁×#483	C₂²	semidirect
57. C₃₁×#483	C₂²	semidirect
58. C₃₁×#482	C₂²	semidirect
59. C₃₁×#482	C₂²	semidirect
60. C₃₁×#481	C₂²	semidirect
61. C₃₁×#481	C₂²	semidirect
62. C₃₁×#480	C₂²	semidirect
63. C₃₁×#480	C₂²	semidirect
64. C₃₁×#470	C₂²	semidirect
65. C₃₁×#468	C₂²	semidirect
66. C₃₁×#468	C₂²	semidirect
67. C₃₁×#468	C₂²	semidirect
68. C₃₁×#467	C₂²	semidirect
69. C₃₁×#465	C₂²	semidirect
70. C₃₁×#465	C₂²	semidirect
71. C₃₁×#465	C₂²	semidirect
72. C₃₁×#452	C₂²	semidirect
73. C₃₁×#452	C₂²	semidirect
74. C₃₁×#451	C₂²	semidirect
75. C₃₁×#451	C₂²	semidirect
76. C₃₁×#450	C₂²	semidirect
77. C₃₁×#450	C₂²	semidirect
78. C₃₁×#448	C₂²	semidirect
79. C₃₁×#448	C₂²	semidirect
80. C₃₁×#448	C₂²	semidirect
81. C₃₁×#448	C₂²	semidirect
82. C₃₁×#448	C₂²	semidirect
83. C₃₁×#428	C₂²	semidirect
84. C₃₁×#427	C₂²	semidirect
85. C₃₁×#419	C₂²	semidirect
86. C₃₁×#418	C₂²	semidirect
87. C₃₁×#416	C₂²	semidirect
88. C₂×C₃₁×#103	C₂²	semidirect
90. C₃₁×#408	C₂²	semidirect
91. C₃₁×#407	C₂²	semidirect
92. C₃₁×#407	C₂²	semidirect
93. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
94. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
363. #60758	C₃₁	direct (N × H)
449. C₂×#536	C₂×C₃₁	semidirect
450. #3201	C₂×C₃₁	semidirect
451. #3200	C₂×C₃₁	semidirect
452. #3196	C₂×C₃₁	semidirect
453. #3193	C₂×C₃₁	semidirect
454. #3190	C₂×C₃₁	semidirect
455. #3187	C₂×C₃₁	semidirect
456. #3097	C₂×C₃₁	semidirect
457. #3094	C₂×C₃₁	semidirect
458. #3091	C₂×C₃₁	semidirect
459. #3063	C₂×C₃₁	semidirect
460. #3057	C₂×C₃₁	semidirect
461. #3009	C₂×C₃₁	semidirect
462. #3004	C₂×C₃₁	semidirect
463. C₂×#448	C₂×C₃₁	semidirect
464. #2880	C₂×C₃₁	semidirect
506. C₂³×Q₈	C₂²×C₃₁	semidirect
507. C₂×#137	C₂²×C₃₁	semidirect
508. C₂²×SD₁₆	C₂²×C₃₁	semidirect
509. C₂×#131	C₂²×C₃₁	semidirect
522. #536	C₂²×C₃₁	semidirect
523. #536	C₂²×C₃₁	semidirect
531. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
532. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
536. C₂×#117	C₂²×C₃₁	semidirect
537. #485	C₂²×C₃₁	semidirect
538. #485	C₂²×C₃₁	semidirect
539. #485	C₂²×C₃₁	semidirect
540. #484	C₂²×C₃₁	semidirect
541. #484	C₂²×C₃₁	semidirect
542. #483	C₂²×C₃₁	semidirect
543. #483	C₂²×C₃₁	semidirect
544. #482	C₂²×C₃₁	semidirect
545. #482	C₂²×C₃₁	semidirect
546. #481	C₂²×C₃₁	semidirect
547. #481	C₂²×C₃₁	semidirect
548. #480	C₂²×C₃₁	semidirect
549. #480	C₂²×C₃₁	semidirect
550. #470	C₂²×C₃₁	semidirect
551. #468	C₂²×C₃₁	semidirect
552. #468	C₂²×C₃₁	semidirect
553. #468	C₂²×C₃₁	semidirect
554. #467	C₂²×C₃₁	semidirect
555. #465	C₂²×C₃₁	semidirect
556. #465	C₂²×C₃₁	semidirect
557. #465	C₂²×C₃₁	semidirect
558. #452	C₂²×C₃₁	semidirect
559. #452	C₂²×C₃₁	semidirect
560. #451	C₂²×C₃₁	semidirect
561. #451	C₂²×C₃₁	semidirect
562. #450	C₂²×C₃₁	semidirect
563. #450	C₂²×C₃₁	semidirect
564. #448	C₂²×C₃₁	semidirect
565. #448	C₂²×C₃₁	semidirect
566. #448	C₂²×C₃₁	semidirect
567. #448	C₂²×C₃₁	semidirect
568. #448	C₂²×C₃₁	semidirect
569. #428	C₂²×C₃₁	semidirect
570. #427	C₂²×C₃₁	semidirect
571. #419	C₂²×C₃₁	semidirect
572. #418	C₂²×C₃₁	semidirect
573. #416	C₂²×C₃₁	semidirect
574. C₂×#103	C₂²×C₃₁	semidirect
576. #408	C₂²×C₃₁	semidirect
577. #407	C₂²×C₃₁	semidirect
578. #407	C₂²×C₃₁	semidirect
579. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
580. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
730. C₃₁	#60758	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×#3488	2
C₂×C₃₁×#536	2
C₃₁×#3201	2
C₃₁×#3200	2
C₃₁×#3196	2
C₃₁×#3193	2
C₃₁×#3190	2
C₃₁×#3187	2
C₃₁×#3097	2
C₃₁×#3094	2
C₃₁×#3091	2
C₃₁×#3063	2
C₃₁×#3057	2
C₃₁×#3009	2
C₃₁×#3004	2
C₂×C₃₁×#448	2
C₃₁×#2880	2
#60758	31

Subgroups — C31×#60758 #21517517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60758 #21517517