Subgroups — C₃₁×#61212 #21517971

Order 7936.

2110 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3496	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3331	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3323	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3302	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3296	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3099	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#131	C₂²	1	2	yes	complemented
22	C₃₁×#559	—	2	1	no	—
23	C₃₁×#557	—	2	1	no	—
24	C₃₁×#556	—	2	2	no	—
25	C₃₁×#556	C₂²	1	2	yes	complemented
26	C₃₁×#554	C₂²	1	2	yes	complemented
27	C₃₁×#552	C₂²	1	4	yes	complemented
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#547	C₂²	1	2	yes	—
30	C₃₁×#546	—	2	2	no	—
31	C₃₁×#546	C₂²	1	4	yes	—
32	D₄²×C₃₁	—	2	1	no	—
33	D₄²×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#539	—	2	2	no	—
35	C₃₁×#537	C₂²	1	2	yes	—
36	C₃₁×#536	C₂²	1	2	yes	complemented
37	C₃₁×#534	—	2	2	no	—
38	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₃₁×#529	—	2	2	no	—
42	C₂×C₃₁×#121	—	2	2	no	—
43	C₃₁×#520	C₂²	1	2	yes	complemented
44	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#488	C₂²	1	2	yes	complemented
47	C₃₁×#488	C₂²	1	2	yes	complemented
48	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#485	C₂²	1	4	yes	complemented
53	C₃₁×#483	C₂²	1	4	yes	complemented
54	C₃₁×#482	C₂²	1	4	yes	complemented
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#476	C₂²	1	2	yes	complemented
58	C₃₁×#474	C₂²	1	2	yes	complemented
59	C₃₁×#470	C₂²	1	4	yes	complemented
60	C₃₁×#468	C₂²	1	4	yes	complemented
61	C₃₁×#467	C₂²	1	4	yes	complemented
62	C₃₁×#465	C₂²	1	4	yes	complemented
63	C₃₁×#464	C₂²	1	4	yes	complemented
64	C₃₁×#462	C₂²	1	2	yes	complemented
65	C₃₁×#460	C₂²	1	2	yes	complemented
66	C₃₁×#452	C₂²	1	4	yes	complemented
67	C₃₁×#452	C₂²	1	4	yes	complemented
68	C₃₁×#450	C₂²	1	4	yes	complemented
69	C₃₁×#450	C₂²	1	4	yes	complemented
70	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
71	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
72	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
74	C₃₁×#436	C₂²	1	2	yes	complemented
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
77	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
78	C₃₁×#428	C₂²	1	2	yes	complemented
79	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#418	C₂²	1	2	yes	—
82	C₃₁×#418	C₂²	1	4	yes	complemented
83	C₃₁×#417	C₂²	1	4	yes	complemented
84	C₃₁×#417	C₂²	1	2	yes	complemented
85	C₃₁×#416	C₂²	1	2	yes	complemented
86	C₃₁×#416	C₂²	1	2	yes	complemented
87	C₃₁×#416	C₂²	1	4	yes	complemented
88	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
90	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
91	C₃₁×#408	C₂²	1	2	yes	complemented
92	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×H(5,𝔽₂)	—	2	8	no	—
94	C₃₁×H(5,𝔽₂)	—	4	4	no	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	C₂³	1	2	yes	—
97	C₂×#41×C₃₁	C₂³	1	4	yes	—
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₃₁	—	2	4	no	—
101	C₂²×D₄×C₃₁	—	2	2	no	—
102	C₂²×D₄×C₃₁	—	2	2	no	—
103	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
104	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₃₁	—	2	1	no	—
106	C₃₁×#137	—	4	4	no	—
107	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₃₁	—	2	4	no	—
109	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₃₁×#131	—	4	4	no	—
113	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
114	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
115	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
118	C₃₁×C₄⋊Q₈	—	2	2	no	—
119	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×#127	D₄	1	1	yes	characteristic
124	C₃₁×#127	C₂³	1	1	yes	characteristic
125	C₃₁×#126	—	2	4	no	—
126	C₃₁×#126	—	2	4	no	—
127	C₃₁×#125	—	2	2	no	—
128	C₃₁×#125	—	2	4	no	—
129	C₃₁×#125	C₂³	1	2	yes	—
130	C₃₁×#124	—	2	2	no	—
131	C₃₁×#124	—	2	2	no	—
132	C₃₁×#124	D₄	1	2	yes	—
133	C₃₁×#124	C₂³	1	2	yes	—
134	C₃₁×#123	—	2	4	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×#123	—	2	4	no	—
137	C₃₁×#123	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	1	no	—
140	C₃₁×C₂²⋊Q₈	—	2	1	no	—
141	C₃₁×C₂²⋊Q₈	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₃₁×#121	—	2	4	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	1	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	—	2	4	no	—
152	C₃₁×#121	D₄	1	2	yes	—
153	C₃₁×#121	D₄	1	2	yes	—
154	C₃₁×#121	C₂³	1	4	yes	—
155	C₃₁×#120	—	2	4	no	—
156	C₃₁×#120	—	2	4	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	2	no	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	—	2	1	no	—
161	C₄×Q₈×C₃₁	—	2	1	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
165	C₄×D₄×C₃₁	—	2	4	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	1	no	—
172	C₄×D₄×C₃₁	C₂³	1	2	yes	—
173	C₄×D₄×C₃₁	C₂³	1	2	yes	—
174	C₄×D₄×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₃₁×#117	—	2	4	no	—
177	C₃₁×#117	C₂³	1	2	yes	—
178	C₃₁×#117	C₂³	1	4	yes	—
179	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
180	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
186	C₂×C₄²×C₃₁	—	2	1	no	—
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₃₁×#107	C₂³	1	4	yes	—
189	C₃₁×#106	C₂³	1	2	yes	—
190	C₃₁×#106	C₂³	1	2	yes	—
191	C₃₁×#106	C₂³	1	4	yes	—
192	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
193	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
194	C₃₁×#103	C₂³	1	2	yes	—
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	yes	—
197	C₃₁×#103	C₂³	1	4	yes	—
198	C₃₁×#103	C₂³	1	2	yes	—
199	C₃₁×#103	C₂³	1	2	yes	—
200	C₃₁×#103	C₂³	1	2	yes	—
201	C₃₁×#102	C₂³	1	2	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	2	yes	—
204	C₃₁×#102	C₂³	1	4	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×#102	C₂³	1	2	yes	—
208	C₃₁×#102	C₂³	1	2	yes	—
209	C₃₁×#102	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
211	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₂⁴×C₃₁	—	2	1	no	—
217	C₂⁴×C₃₁	—	2	4	no	—
218	#41×C₃₁	—	2	4	no	—
219	#41×C₃₁	—	2	4	no	—
220	#41×C₃₁	—	2	8	no	—
221	#41×C₃₁	—	2	4	no	—
222	#41×C₃₁	—	2	4	no	—
223	#41×C₃₁	—	4	4	no	—
224	#41×C₃₁	—	4	8	no	—
225	C₂×Q₈×C₃₁	—	2	1	no	—
226	C₂×Q₈×C₃₁	—	2	1	no	—
227	C₂×Q₈×C₃₁	—	2	1	no	—
228	C₂×Q₈×C₃₁	—	2	2	no	—
229	C₂×Q₈×C₃₁	—	2	2	no	—
230	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
231	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
233	C₂×D₄×C₃₁	—	2	8	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	2	no	—
236	C₂×D₄×C₃₁	—	2	4	no	—
237	C₂×D₄×C₃₁	—	2	1	no	—
238	C₂×D₄×C₃₁	—	2	1	no	—
239	C₂×D₄×C₃₁	—	2	4	no	—
240	C₂×D₄×C₃₁	—	2	1	no	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	4	4	no	—
243	C₂×D₄×C₃₁	—	4	8	no	—
244	C₂×D₄×C₃₁	—	4	16	no	—
245	C₂×D₄×C₃₁	—	8	4	no	—
246	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
248	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₃₁	#41	1	4	yes	—
251	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	1	no	—
255	C₂²×C₄×C₃₁	—	2	1	no	—
256	C₂²×C₄×C₃₁	—	2	4	no	—
257	C₂²×C₄×C₃₁	—	2	4	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	8	2	no	—
262	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
266	Q₁₆×C₃₁	—	4	4	no	—
267	SD₁₆×C₃₁	—	2	4	no	—
268	SD₁₆×C₃₁	—	2	4	no	—
269	SD₁₆×C₃₁	—	4	4	no	—
270	M₁₆×C₃₁	—	2	4	no	—
271	M₁₆×C₃₁	—	4	4	no	—
272	C₂×C₈×C₃₁	—	2	2	no	—
273	C₂×C₈×C₃₁	—	2	2	no	—
274	C₂×C₈×C₃₁	—	4	4	no	—
275	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	4	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	4	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
300	C₂²⋊C₄×C₃₁	—	2	4	no	—
301	C₂²⋊C₄×C₃₁	—	2	4	no	—
302	C₂²⋊C₄×C₃₁	—	2	2	no	—
303	C₂²⋊C₄×C₃₁	—	2	4	no	—
304	C₂²⋊C₄×C₃₁	—	2	4	no	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	4	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
311	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
312	C₄²×C₃₁	—	2	2	no	—
313	C₄²×C₃₁	—	2	2	no	—
314	C₄²×C₃₁	—	2	4	no	—
315	C₄²×C₃₁	—	2	2	no	—
316	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
320	#61212	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₃₁	—	2	2	no	—
322	C₂³×C₃₁	—	2	4	no	—
323	C₂³×C₃₁	—	2	2	no	—
324	C₂³×C₃₁	—	4	8	no	—
325	C₂³×C₃₁	—	8	1	no	—
326	C₂³×C₃₁	—	8	1	no	—
327	C₂³×C₃₁	—	8	4	no	—
328	C₂³×C₃₁	—	8	4	no	—
329	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
330	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₃₁	—	2	4	no	—
332	Q₈×C₃₁	—	2	2	no	—
333	Q₈×C₃₁	—	2	2	no	—
334	Q₈×C₃₁	—	2	2	no	—
335	Q₈×C₃₁	—	2	2	no	—
336	Q₈×C₃₁	—	4	2	no	—
337	Q₈×C₃₁	—	4	2	no	—
338	Q₈×C₃₁	—	8	1	no	—
339	D₄×C₃₁	—	2	8	no	—
340	D₄×C₃₁	—	2	4	no	—
341	D₄×C₃₁	—	2	4	no	—
342	D₄×C₃₁	—	2	4	no	—
343	D₄×C₃₁	—	2	2	no	—
344	D₄×C₃₁	—	2	2	no	—
345	D₄×C₃₁	—	2	2	no	—
346	D₄×C₃₁	—	4	2	no	—
347	D₄×C₃₁	—	4	8	no	—
348	D₄×C₃₁	—	4	8	no	—
349	D₄×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	4	2	no	—
351	D₄×C₃₁	—	8	1	no	—
352	D₄×C₃₁	—	8	4	no	—
353	D₄×C₃₁	C₂×#41	1	4	yes	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	2	4	no	—
356	C₂×C₄×C₃₁	—	2	4	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	4	1	no	—
364	C₂×C₄×C₃₁	—	4	8	no	—
365	C₂×C₄×C₃₁	—	4	2	no	—
366	C₂×C₄×C₃₁	—	4	4	no	—
367	C₂×C₄×C₃₁	—	4	4	no	—
368	C₂×C₄×C₃₁	—	8	2	no	—
369	C₂×C₄×C₃₁	—	8	1	no	—
370	C₂×C₄×C₃₁	—	8	4	no	—
371	C₂×C₄×C₃₁	—	8	1	no	—
372	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
379	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
381	C₈×C₃₁	—	2	1	no	—
382	C₈×C₃₁	—	2	1	no	—
383	C₈×C₃₁	—	2	1	no	—
384	C₈×C₃₁	—	2	1	no	—
385	C₈×C₃₁	—	2	4	no	—
386	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
387	#3496	C₂×C₃₁	1	1	yes	characteristic
388	#3331	C₂×C₃₁	1	2	yes	complemented
389	#3324	C₂×C₃₁	1	2	yes	complemented
390	#3323	C₂×C₃₁	1	4	yes	complemented
391	#3302	C₂×C₃₁	1	2	yes	complemented
392	#3296	C₂×C₃₁	1	4	yes	complemented
393	#3295	C₂×C₃₁	1	2	yes	complemented
394	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
395	#3099	C₂×C₃₁	1	2	yes	complemented
396	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
397	#3063	C₂×C₃₁	1	2	yes	complemented
398	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
399	#3009	C₂×C₃₁	1	2	yes	complemented
400	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#2931	C₂×C₃₁	1	1	yes	characteristic, complemented
402	#2897	C₂×C₃₁	1	2	yes	complemented
403	C₂²×C₃₁	—	2	1	no	—
404	C₂²×C₃₁	—	2	1	no	—
405	C₂²×C₃₁	—	2	4	no	—
406	C₂²×C₃₁	—	2	4	no	—
407	C₂²×C₃₁	—	2	4	no	—
408	C₂²×C₃₁	—	2	4	no	—
409	C₂²×C₃₁	—	4	2	no	—
410	C₂²×C₃₁	—	4	2	no	—
411	C₂²×C₃₁	—	4	2	no	—
412	C₂²×C₃₁	—	4	2	no	—
413	C₂²×C₃₁	—	4	2	no	—
414	C₂²×C₃₁	—	8	4	no	—
415	C₂²×C₃₁	—	16	8	no	—
416	C₂²×C₃₁	#546	1	2	yes	—
417	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₃₁	—	2	1	no	—
419	C₄×C₃₁	—	2	1	no	—
420	C₄×C₃₁	—	2	4	no	—
421	C₄×C₃₁	—	2	1	no	—
422	C₄×C₃₁	—	4	2	no	—
423	C₄×C₃₁	—	4	2	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	2	no	—
427	C₄×C₃₁	—	4	2	no	—
428	C₄×C₃₁	#546	1	2	yes	—
429	C₄×C₃₁	#577	1	2	yes	—
430	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
431	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
433	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
434	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×#131	C₂²×C₃₁	1	2	yes	complemented
436	#559	—	2	1	no	—
437	#557	—	2	1	no	—
438	#556	—	2	2	no	—
439	#556	C₂²×C₃₁	1	2	yes	complemented
440	#554	C₂²×C₃₁	1	2	yes	complemented
441	#552	C₂²×C₃₁	1	4	yes	complemented
442	#547	—	2	1	no	—
443	#547	C₂²×C₃₁	1	2	yes	—
444	#546	—	2	2	no	—
445	#546	C₂²×C₃₁	1	4	yes	—
446	D₄²	—	2	1	no	—
447	D₄²	C₂²×C₃₁	1	2	yes	—
448	#539	—	2	2	no	—
449	#537	C₂²×C₃₁	1	2	yes	—
450	#536	C₂²×C₃₁	1	2	yes	complemented
451	#534	—	2	2	no	—
452	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	#532	C₂²×C₃₁	1	1	yes	characteristic
454	#532	C₂²×C₃₁	1	1	yes	characteristic
455	#529	—	2	2	no	—
456	C₂×#121	—	2	2	no	—
457	#520	C₂²×C₃₁	1	2	yes	complemented
458	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
460	#488	C₂²×C₃₁	1	2	yes	complemented
461	#488	C₂²×C₃₁	1	2	yes	complemented
462	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
463	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
464	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
465	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	#485	C₂²×C₃₁	1	4	yes	complemented
467	#483	C₂²×C₃₁	1	4	yes	complemented
468	#482	C₂²×C₃₁	1	4	yes	complemented
469	#481	C₂²×C₃₁	1	4	yes	complemented
470	#478	C₂²×C₃₁	1	4	yes	complemented
471	#476	C₂²×C₃₁	1	2	yes	complemented
472	#474	C₂²×C₃₁	1	2	yes	complemented
473	#470	C₂²×C₃₁	1	4	yes	complemented
474	#468	C₂²×C₃₁	1	4	yes	complemented
475	#467	C₂²×C₃₁	1	4	yes	complemented
476	#465	C₂²×C₃₁	1	4	yes	complemented
477	#464	C₂²×C₃₁	1	4	yes	complemented
478	#462	C₂²×C₃₁	1	2	yes	complemented
479	#460	C₂²×C₃₁	1	2	yes	complemented
480	#452	C₂²×C₃₁	1	4	yes	complemented
481	#452	C₂²×C₃₁	1	4	yes	complemented
482	#450	C₂²×C₃₁	1	4	yes	complemented
483	#450	C₂²×C₃₁	1	4	yes	complemented
484	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
485	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
486	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
487	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
488	#436	C₂²×C₃₁	1	2	yes	complemented
489	#436	C₂²×C₃₁	1	2	yes	complemented
490	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
491	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
492	#428	C₂²×C₃₁	1	2	yes	complemented
493	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
494	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
495	#418	C₂²×C₃₁	1	2	yes	—
496	#418	C₂²×C₃₁	1	4	yes	complemented
497	#417	C₂²×C₃₁	1	4	yes	complemented
498	#417	C₂²×C₃₁	1	2	yes	complemented
499	#416	C₂²×C₃₁	1	2	yes	complemented
500	#416	C₂²×C₃₁	1	2	yes	complemented
501	#416	C₂²×C₃₁	1	4	yes	complemented
502	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
503	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
504	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
505	#408	C₂²×C₃₁	1	2	yes	complemented
506	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	C₂×C₃₁	—	2	2	no	—
508	C₂×C₃₁	—	4	4	no	—
509	C₂×C₃₁	—	4	4	no	—
510	C₂×C₃₁	—	8	2	no	—
511	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
512	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
513	C₂×C₃₁	#3584	1	1	yes	characteristic
514	H(5,𝔽₂)	—	2	8	no	—
515	H(5,𝔽₂)	—	4	4	no	—
516	C₂×#41	—	2	2	no	—
517	C₂×#41	C₂³×C₃₁	1	2	yes	—
518	C₂×#41	C₂³×C₃₁	1	4	yes	—
519	C₂×#41	C₂³×C₃₁	1	2	yes	—
520	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	2	no	—
523	C₂²×D₄	—	2	2	no	—
524	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
525	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	#137	—	4	4	no	—
528	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
529	C₂×SD₁₆	—	2	4	no	—
530	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
533	#131	—	4	4	no	—
534	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
535	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
536	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
539	C₄⋊Q₈	—	2	2	no	—
540	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
544	#127	D₄×C₃₁	1	1	yes	characteristic
545	#127	C₂³×C₃₁	1	1	yes	characteristic
546	#126	—	2	4	no	—
547	#126	—	2	4	no	—
548	#125	—	2	2	no	—
549	#125	—	2	4	no	—
550	#125	C₂³×C₃₁	1	2	yes	—
551	#124	—	2	2	no	—
552	#124	—	2	2	no	—
553	#124	D₄×C₃₁	1	2	yes	—
554	#124	C₂³×C₃₁	1	2	yes	—
555	#123	—	2	4	no	—
556	#123	—	2	4	no	—
557	#123	—	2	4	no	—
558	#123	—	2	4	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
564	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
565	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
566	#121	—	2	4	no	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	2	no	—
572	#121	—	2	4	no	—
573	#121	D₄×C₃₁	1	2	yes	—
574	#121	D₄×C₃₁	1	2	yes	—
575	#121	C₂³×C₃₁	1	4	yes	—
576	#120	—	2	4	no	—
577	#120	—	2	4	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
585	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
586	C₄×D₄	—	2	4	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	C₂³×C₃₁	1	2	yes	—
594	C₄×D₄	C₂³×C₃₁	1	2	yes	—
595	C₄×D₄	C₂³×C₃₁	1	2	yes	—
596	C₄×D₄	C₂³×C₃₁	1	2	yes	—
597	#117	—	2	4	no	—
598	#117	C₂³×C₃₁	1	2	yes	—
599	#117	C₂³×C₃₁	1	4	yes	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	4	no	—
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
609	#107	C₂³×C₃₁	1	4	yes	—
610	#106	C₂³×C₃₁	1	2	yes	—
611	#106	C₂³×C₃₁	1	2	yes	—
612	#106	C₂³×C₃₁	1	4	yes	—
613	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
614	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
615	#103	C₂³×C₃₁	1	2	yes	—
616	#103	C₂³×C₃₁	1	2	yes	—
617	#103	C₂³×C₃₁	1	2	yes	—
618	#103	C₂³×C₃₁	1	4	yes	—
619	#103	C₂³×C₃₁	1	2	yes	—
620	#103	C₂³×C₃₁	1	2	yes	—
621	#103	C₂³×C₃₁	1	2	yes	—
622	#102	C₂³×C₃₁	1	2	yes	—
623	#102	C₂³×C₃₁	1	2	yes	—
624	#102	C₂³×C₃₁	1	2	yes	—
625	#102	C₂³×C₃₁	1	4	yes	—
626	#102	C₂³×C₃₁	1	4	yes	—
627	#102	C₂³×C₃₁	1	4	yes	—
628	#102	C₂³×C₃₁	1	2	yes	—
629	#102	C₂³×C₃₁	1	2	yes	—
630	#102	C₂³×C₃₁	1	2	yes	—
631	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
633	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
635	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
636	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
637	C₃₁	#61212	1	1	yes	characteristic, direct product factor, Sylow
638	C₂⁴	—	2	1	no	—
639	C₂⁴	—	2	4	no	—
640	#41	—	2	4	no	—
641	#41	—	2	4	no	—
642	#41	—	2	8	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	4	4	no	—
646	#41	—	4	8	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
653	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
654	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
655	C₂×D₄	—	2	8	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	16	no	—
667	C₂×D₄	—	8	4	no	—
668	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
669	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
670	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₂×D₄	#41×C₃₁	1	4	yes	—
673	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
674	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	8	2	no	—
684	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
687	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
688	Q₁₆	—	4	4	no	—
689	SD₁₆	—	2	4	no	—
690	SD₁₆	—	2	4	no	—
691	SD₁₆	—	4	4	no	—
692	M₁₆	—	2	4	no	—
693	M₁₆	—	4	4	no	—
694	C₂×C₈	—	2	2	no	—
695	C₂×C₈	—	2	2	no	—
696	C₂×C₈	—	4	4	no	—
697	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
699	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
701	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
733	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
740	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
741	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
742	C₂³	—	2	2	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	4	8	no	—
746	C₂³	—	8	1	no	—
747	C₂³	—	8	1	no	—
748	C₂³	—	8	4	no	—
749	C₂³	—	8	4	no	—
750	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
751	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	8	1	no	—
760	D₄	—	2	8	no	—
761	D₄	—	2	4	no	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	4	2	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	4	no	—
771	D₄	—	4	2	no	—
772	D₄	—	8	1	no	—
773	D₄	—	8	4	no	—
774	D₄	C₂×#41×C₃₁	1	4	yes	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	—	8	1	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	1	no	—
793	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
799	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
800	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
801	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	1	no	—
806	C₈	—	2	4	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	8	4	no	—
819	C₂²	—	16	8	no	—
820	C₂²	C₃₁×#546	1	2	yes	—
821	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
822	C₄	—	2	4	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	C₃₁×#546	1	2	yes	—
833	C₄	C₃₁×#577	1	2	yes	—
834	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
835	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂	—	2	2	no	—
837	C₂	—	4	4	no	—
838	C₂	—	4	4	no	—
839	C₂	—	8	2	no	—
840	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
841	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
842	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3331	C₂	semidirect
4. C₃₁×#3324	C₂	semidirect
5. C₃₁×#3323	C₂	semidirect
6. C₃₁×#3302	C₂	semidirect
7. C₃₁×#3296	C₂	semidirect
8. C₃₁×#3295	C₂	semidirect
9. C₃₁×#3131	C₂	semidirect
10. C₃₁×#3099	C₂	semidirect
11. C₃₁×#3077	C₂	semidirect
12. C₃₁×#3063	C₂	semidirect
13. C₃₁×#3037	C₂	semidirect
14. C₃₁×#3009	C₂	semidirect
15. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
16. C₃₁×#2931	C₂	semidirect
17. C₃₁×#2897	C₂	semidirect
19. C₂×C₃₁×#137	C₂²	semidirect
21. C₂×C₃₁×#131	C₂²	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
27. C₃₁×#552	C₂²	semidirect
36. C₃₁×#536	C₂²	semidirect
38. C₃₁×#533	C₂²	semidirect
43. C₃₁×#520	C₂²	semidirect
44. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#488	C₂²	semidirect
47. C₃₁×#488	C₂²	semidirect
48. C₃₁×#487	C₂²	semidirect
49. C₃₁×#487	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#483	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#474	C₂²	semidirect
59. C₃₁×#470	C₂²	semidirect
60. C₃₁×#468	C₂²	semidirect
61. C₃₁×#467	C₂²	semidirect
62. C₃₁×#465	C₂²	semidirect
63. C₃₁×#464	C₂²	semidirect
64. C₃₁×#462	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
66. C₃₁×#452	C₂²	semidirect
67. C₃₁×#452	C₂²	semidirect
68. C₃₁×#450	C₂²	semidirect
69. C₃₁×#450	C₂²	semidirect
70. C₄×SD₁₆×C₃₁	C₂²	semidirect
71. C₄×SD₁₆×C₃₁	C₂²	semidirect
72. C₄×SD₁₆×C₃₁	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₃₁×#436	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₈×D₄×C₃₁	C₂²	semidirect
77. C₈×D₄×C₃₁	C₂²	semidirect
78. C₃₁×#428	C₂²	semidirect
79. C₂×C₃₁×#106	C₂²	semidirect
80. C₃₁×#423	C₂²	semidirect
82. C₃₁×#418	C₂²	semidirect
83. C₃₁×#417	C₂²	semidirect
84. C₃₁×#417	C₂²	semidirect
85. C₃₁×#416	C₂²	semidirect
86. C₃₁×#416	C₂²	semidirect
87. C₃₁×#416	C₂²	semidirect
88. C₂×C₃₁×#103	C₂²	semidirect
90. C₂×C₃₁×#102	C₂²	semidirect
91. C₃₁×#408	C₂²	semidirect
92. C₂×C₄×C₈×C₃₁	C₂²	semidirect
320. #61212	C₃₁	direct (N × H)
386. #3507	C₂×C₃₁	semidirect
388. #3331	C₂×C₃₁	semidirect
389. #3324	C₂×C₃₁	semidirect
390. #3323	C₂×C₃₁	semidirect
391. #3302	C₂×C₃₁	semidirect
392. #3296	C₂×C₃₁	semidirect
393. #3295	C₂×C₃₁	semidirect
394. #3131	C₂×C₃₁	semidirect
395. #3099	C₂×C₃₁	semidirect
396. #3077	C₂×C₃₁	semidirect
397. #3063	C₂×C₃₁	semidirect
398. #3037	C₂×C₃₁	semidirect
399. #3009	C₂×C₃₁	semidirect
400. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
401. #2931	C₂×C₃₁	semidirect
402. #2897	C₂×C₃₁	semidirect
433. C₂×#137	C₂²×C₃₁	semidirect
435. C₂×#131	C₂²×C₃₁	semidirect
439. #556	C₂²×C₃₁	semidirect
440. #554	C₂²×C₃₁	semidirect
441. #552	C₂²×C₃₁	semidirect
450. #536	C₂²×C₃₁	semidirect
452. #533	C₂²×C₃₁	semidirect
457. #520	C₂²×C₃₁	semidirect
458. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
460. #488	C₂²×C₃₁	semidirect
461. #488	C₂²×C₃₁	semidirect
462. #487	C₂²×C₃₁	semidirect
463. #487	C₂²×C₃₁	semidirect
464. #486	C₂²×C₃₁	semidirect
465. #486	C₂²×C₃₁	semidirect
466. #485	C₂²×C₃₁	semidirect
467. #483	C₂²×C₃₁	semidirect
468. #482	C₂²×C₃₁	semidirect
469. #481	C₂²×C₃₁	semidirect
470. #478	C₂²×C₃₁	semidirect
471. #476	C₂²×C₃₁	semidirect
472. #474	C₂²×C₃₁	semidirect
473. #470	C₂²×C₃₁	semidirect
474. #468	C₂²×C₃₁	semidirect
475. #467	C₂²×C₃₁	semidirect
476. #465	C₂²×C₃₁	semidirect
477. #464	C₂²×C₃₁	semidirect
478. #462	C₂²×C₃₁	semidirect
479. #460	C₂²×C₃₁	semidirect
480. #452	C₂²×C₃₁	semidirect
481. #452	C₂²×C₃₁	semidirect
482. #450	C₂²×C₃₁	semidirect
483. #450	C₂²×C₃₁	semidirect
484. C₄×SD₁₆	C₂²×C₃₁	semidirect
485. C₄×SD₁₆	C₂²×C₃₁	semidirect
486. C₄×SD₁₆	C₂²×C₃₁	semidirect
487. C₄×SD₁₆	C₂²×C₃₁	semidirect
488. #436	C₂²×C₃₁	semidirect
489. #436	C₂²×C₃₁	semidirect
490. C₈×D₄	C₂²×C₃₁	semidirect
491. C₈×D₄	C₂²×C₃₁	semidirect
492. #428	C₂²×C₃₁	semidirect
493. C₂×#106	C₂²×C₃₁	semidirect
494. #423	C₂²×C₃₁	semidirect
496. #418	C₂²×C₃₁	semidirect
497. #417	C₂²×C₃₁	semidirect
498. #417	C₂²×C₃₁	semidirect
499. #416	C₂²×C₃₁	semidirect
500. #416	C₂²×C₃₁	semidirect
501. #416	C₂²×C₃₁	semidirect
502. C₂×#103	C₂²×C₃₁	semidirect
504. C₂×#102	C₂²×C₃₁	semidirect
505. #408	C₂²×C₃₁	semidirect
506. C₂×C₄×C₈	C₂²×C₃₁	semidirect
637. C₃₁	#61212	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×#3507	2
C₃₁×#3496	2
C₃₁×#3331	2
C₃₁×#3324	2
C₃₁×#3323	2
C₃₁×#3302	2
C₃₁×#3296	2
C₃₁×#3295	2
C₃₁×#3131	2
C₃₁×#3099	2
C₃₁×#3077	2
C₃₁×#3063	2
C₃₁×#3037	2
C₃₁×#3009	2
C₂×C₄×SD₁₆×C₃₁	2
C₃₁×#2931	2
C₃₁×#2897	2
#61212	31

Subgroups — C31×#61212 #21517971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61212 #21517971