Subgroups — C₃₁×#62022 #21518781

Order 7936.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3045	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
22	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#562	—	2	1	no	—
25	C₃₁×H(3,𝔽₄)	—	2	1	no	—
26	C₃₁×#559	—	2	1	no	—
27	C₃₁×#559	C₂²	1	2	yes	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
29	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#548	C₂²	1	2	yes	—
34	C₃₁×#548	C₂²	1	2	yes	complemented
35	C₃₁×#547	—	2	2	no	—
36	C₃₁×#547	C₂²	1	2	yes	complemented
37	C₃₁×#546	—	2	2	no	—
38	C₃₁×#546	C₂²	1	2	yes	—
39	D₄²×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#542	—	2	2	no	—
41	C₃₁×#542	C₂²	1	2	yes	—
42	C₃₁×#542	C₂²	1	2	yes	complemented
43	C₃₁×#538	—	2	2	no	—
44	C₃₁×#538	—	2	1	no	—
45	C₃₁×#535	C₂²	1	2	yes	—
46	C₃₁×#534	—	2	1	no	—
47	C₃₁×#532	—	2	1	no	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₃₁×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#496	C₂²	1	2	yes	—
56	C₃₁×#496	C₂²	1	2	yes	complemented
57	C₃₁×#495	C₂²	1	2	yes	complemented
58	C₃₁×#489	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#486	C₂²	1	2	yes	—
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#480	C₂²	1	2	yes	—
63	C₃₁×#480	C₂²	1	2	yes	complemented
64	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#477	C₂²	1	2	yes	complemented
67	C₃₁×#474	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#474	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	—
71	C₃₁×#468	C₂²	1	2	yes	complemented
72	C₃₁×#467	C₂²	1	2	yes	complemented
73	C₃₁×#466	C₂²	1	2	yes	—
74	C₃₁×#466	C₂²	1	2	yes	complemented
75	C₃₁×#466	C₂²	1	2	yes	complemented
76	C₃₁×#464	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#464	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	complemented
84	C₃₁×#463	C₂²	1	2	yes	complemented
85	C₃₁×#463	C₂²	1	2	yes	complemented
86	C₃₁×#460	C₂²	1	2	yes	—
87	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#459	C₂²	1	2	yes	—
90	C₃₁×#459	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	complemented
92	C₃₁×#452	C₂²	1	2	yes	complemented
93	C₃₁×#452	C₂²	1	2	yes	complemented
94	C₃₁×#450	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	complemented
97	C₃₁×#448	C₂²	1	2	yes	complemented
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#417	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂×#41×C₃₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₃₁	—	2	2	no	—
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
130	C₃₁×#135	—	4	4	no	—
131	C₂×Q₁₆×C₃₁	—	4	2	no	—
132	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₃₁	—	4	2	no	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×D₈×C₃₁	C₂³	1	2	yes	—
142	C₂×D₈×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	2	yes	—
145	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×#127	—	2	1	no	—
155	C₃₁×#127	C₂³	1	2	yes	—
156	C₃₁×#127	C₂³	1	1	yes	characteristic
157	C₃₁×#127	C₂³	1	1	yes	characteristic
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	D₄	1	2	yes	—
161	C₃₁×#125	—	2	1	no	—
162	C₃₁×#125	D₄	1	1	yes	characteristic
163	C₃₁×#124	—	2	1	no	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	2	no	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	—	2	1	no	—
172	C₃₁×#124	—	2	1	no	—
173	C₃₁×#124	D₄	1	1	yes	characteristic
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#124	C₂³	1	2	yes	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	D₄	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	1	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	D₄	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₃₁×#120	—	2	2	no	—
211	C₃₁×#120	—	2	2	no	—
212	C₃₁×#120	—	2	2	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₃₁×#120	—	2	2	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₄²×C₃₁	—	2	1	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#107	C₂³	1	2	yes	—
255	C₃₁×#107	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	C₂⁴×C₃₁	—	2	2	no	—
286	#41×C₃₁	—	2	4	no	—
287	#41×C₃₁	—	4	2	no	—
288	#41×C₃₁	—	4	2	no	—
289	#41×C₃₁	—	4	2	no	—
290	#41×C₃₁	—	8	2	no	—
291	#41×C₃₁	—	8	2	no	—
292	#41×C₃₁	—	8	4	no	—
293	C₂×Q₈×C₃₁	—	2	1	no	—
294	C₂×Q₈×C₃₁	—	2	1	no	—
295	C₂×Q₈×C₃₁	—	2	1	no	—
296	C₂×Q₈×C₃₁	—	2	2	no	—
297	C₂×Q₈×C₃₁	—	2	1	no	—
298	C₂×Q₈×C₃₁	—	2	2	no	—
299	C₂×Q₈×C₃₁	—	4	1	no	—
300	C₂×Q₈×C₃₁	—	4	1	no	—
301	C₂×Q₈×C₃₁	—	4	1	no	—
302	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	2	2	no	—
312	C₂×D₄×C₃₁	—	2	1	no	—
313	C₂×D₄×C₃₁	—	2	2	no	—
314	C₂×D₄×C₃₁	—	2	1	no	—
315	C₂×D₄×C₃₁	—	2	1	no	—
316	C₂×D₄×C₃₁	—	2	1	no	—
317	C₂×D₄×C₃₁	—	2	2	no	—
318	C₂×D₄×C₃₁	—	2	2	no	—
319	C₂×D₄×C₃₁	—	2	1	no	—
320	C₂×D₄×C₃₁	—	4	1	no	—
321	C₂×D₄×C₃₁	—	4	2	no	—
322	C₂×D₄×C₃₁	—	4	1	no	—
323	C₂×D₄×C₃₁	—	4	2	no	—
324	C₂×D₄×C₃₁	—	8	4	no	—
325	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
328	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
329	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₃₁	—	2	1	no	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	2	1	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	2	2	no	—
336	C₂²×C₄×C₃₁	—	2	2	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	2	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
344	Q₁₆×C₃₁	—	2	4	no	—
345	Q₁₆×C₃₁	—	4	2	no	—
346	SD₁₆×C₃₁	—	2	4	no	—
347	SD₁₆×C₃₁	—	2	4	no	—
348	SD₁₆×C₃₁	—	4	2	no	—
349	SD₁₆×C₃₁	—	4	2	no	—
350	SD₁₆×C₃₁	—	4	2	no	—
351	SD₁₆×C₃₁	—	4	2	no	—
352	D₈×C₃₁	—	4	2	no	—
353	D₈×C₃₁	—	4	2	no	—
354	D₈×C₃₁	—	4	2	no	—
355	D₈×C₃₁	—	4	2	no	—
356	M₁₆×C₃₁	—	4	2	no	—
357	C₂×C₈×C₃₁	—	4	1	no	—
358	C₂×C₈×C₃₁	—	4	1	no	—
359	C₂×C₈×C₃₁	—	4	2	no	—
360	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
363	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
400	C₂²⋊C₄×C₃₁	—	2	2	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄²×C₃₁	—	2	1	no	—
411	C₄²×C₃₁	—	2	1	no	—
412	C₄²×C₃₁	—	2	1	no	—
413	C₄²×C₃₁	—	2	1	no	—
414	C₄²×C₃₁	—	2	2	no	—
415	C₄²×C₃₁	—	2	2	no	—
416	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₃₁	C₂⁴	1	2	yes	—
419	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
421	#62022	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂³×C₃₁	—	2	2	no	—
423	C₂³×C₃₁	—	2	2	no	—
424	C₂³×C₃₁	—	2	2	no	—
425	C₂³×C₃₁	—	4	2	no	—
426	C₂³×C₃₁	—	8	1	no	—
427	C₂³×C₃₁	—	8	2	no	—
428	C₂³×C₃₁	—	8	2	no	—
429	C₂³×C₃₁	—	8	1	no	—
430	C₂³×C₃₁	—	8	2	no	—
431	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
432	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	Q₈×C₃₁	—	2	1	no	—
434	Q₈×C₃₁	—	2	1	no	—
435	Q₈×C₃₁	—	2	2	no	—
436	Q₈×C₃₁	—	2	1	no	—
437	Q₈×C₃₁	—	2	2	no	—
438	Q₈×C₃₁	—	4	1	no	—
439	Q₈×C₃₁	—	4	2	no	—
440	Q₈×C₃₁	—	8	1	no	—
441	Q₈×C₃₁	—	8	1	no	—
442	Q₈×C₃₁	—	8	1	no	—
443	Q₈×C₃₁	—	8	2	no	—
444	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
445	D₄×C₃₁	—	2	4	no	—
446	D₄×C₃₁	—	2	2	no	—
447	D₄×C₃₁	—	2	2	no	—
448	D₄×C₃₁	—	2	2	no	—
449	D₄×C₃₁	—	2	2	no	—
450	D₄×C₃₁	—	2	2	no	—
451	D₄×C₃₁	—	2	2	no	—
452	D₄×C₃₁	—	4	1	no	—
453	D₄×C₃₁	—	4	4	no	—
454	D₄×C₃₁	—	4	2	no	—
455	D₄×C₃₁	—	4	4	no	—
456	D₄×C₃₁	—	4	4	no	—
457	D₄×C₃₁	—	8	1	no	—
458	D₄×C₃₁	—	8	2	no	—
459	D₄×C₃₁	—	8	2	no	—
460	D₄×C₃₁	—	8	1	no	—
461	D₄×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	8	1	no	—
463	D₄×C₃₁	—	8	1	no	—
464	D₄×C₃₁	—	8	2	no	—
465	D₄×C₃₁	—	8	2	no	—
466	D₄×C₃₁	—	8	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	4	1	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	4	2	no	—
482	C₂×C₄×C₃₁	—	4	2	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	—	8	2	no	—
485	C₂×C₄×C₃₁	—	8	2	no	—
486	C₂×C₄×C₃₁	—	8	2	no	—
487	C₂×C₄×C₃₁	—	8	2	no	—
488	C₂×C₄×C₃₁	—	8	1	no	—
489	C₂×C₄×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
499	C₈×C₃₁	—	2	2	no	—
500	C₈×C₃₁	—	2	2	no	—
501	C₈×C₃₁	—	2	2	no	—
502	C₈×C₃₁	—	2	2	no	—
503	#3558	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
505	#3403	C₂×C₃₁	1	2	yes	complemented
506	#3375	C₂×C₃₁	1	2	yes	complemented
507	#3314	C₂×C₃₁	1	2	yes	complemented
508	#3308	C₂×C₃₁	1	2	yes	complemented
509	#3294	C₂×C₃₁	1	2	yes	complemented
510	#3285	C₂×C₃₁	1	2	yes	complemented
511	#3268	C₂×C₃₁	1	2	yes	complemented
512	#3265	C₂×C₃₁	1	2	yes	complemented
513	#3262	C₂×C₃₁	1	2	yes	complemented
514	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3224	C₂×C₃₁	1	2	yes	complemented
516	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3124	C₂×C₃₁	1	2	yes	complemented
518	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3045	C₂×C₃₁	1	2	yes	complemented
520	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
522	C₂²×C₃₁	—	2	1	no	—
523	C₂²×C₃₁	—	2	1	no	—
524	C₂²×C₃₁	—	2	2	no	—
525	C₂²×C₃₁	—	2	2	no	—
526	C₂²×C₃₁	—	2	2	no	—
527	C₂²×C₃₁	—	4	2	no	—
528	C₂²×C₃₁	—	4	2	no	—
529	C₂²×C₃₁	—	4	2	no	—
530	C₂²×C₃₁	—	4	2	no	—
531	C₂²×C₃₁	—	4	2	no	—
532	C₂²×C₃₁	—	4	2	no	—
533	C₂²×C₃₁	—	4	2	no	—
534	C₂²×C₃₁	—	4	2	no	—
535	C₂²×C₃₁	—	4	2	no	—
536	C₂²×C₃₁	—	16	2	no	—
537	C₂²×C₃₁	—	16	4	no	—
538	C₂²×C₃₁	#576	1	2	yes	—
539	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
540	C₄×C₃₁	—	2	1	no	—
541	C₄×C₃₁	—	2	1	no	—
542	C₄×C₃₁	—	2	2	no	—
543	C₄×C₃₁	—	2	2	no	—
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	2	2	no	—
546	C₄×C₃₁	—	2	1	no	—
547	C₄×C₃₁	—	2	1	no	—
548	C₄×C₃₁	—	2	2	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	2	no	—
551	C₄×C₃₁	—	4	1	no	—
552	C₄×C₃₁	—	4	1	no	—
553	C₄×C₃₁	—	4	2	no	—
554	C₄×C₃₁	—	4	2	no	—
555	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₄×C₃₁	#585	1	1	yes	characteristic
557	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
558	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
559	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
561	#562	—	2	1	no	—
562	H(3,𝔽₄)	—	2	1	no	—
563	#559	—	2	1	no	—
564	#559	C₂²×C₃₁	1	2	yes	—
565	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
566	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#554	—	2	1	no	—
568	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#548	C₂²×C₃₁	1	2	yes	—
571	#548	C₂²×C₃₁	1	2	yes	complemented
572	#547	—	2	2	no	—
573	#547	C₂²×C₃₁	1	2	yes	complemented
574	#546	—	2	2	no	—
575	#546	C₂²×C₃₁	1	2	yes	—
576	D₄²	C₂²×C₃₁	1	2	yes	—
577	#542	—	2	2	no	—
578	#542	C₂²×C₃₁	1	2	yes	—
579	#542	C₂²×C₃₁	1	2	yes	complemented
580	#538	—	2	2	no	—
581	#538	—	2	1	no	—
582	#535	C₂²×C₃₁	1	2	yes	—
583	#534	—	2	1	no	—
584	#532	—	2	1	no	—
585	#532	C₂²×C₃₁	1	1	yes	characteristic
586	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#529	—	2	1	no	—
588	#529	C₂²×C₃₁	1	1	yes	characteristic
589	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
590	#520	C₂²×C₃₁	1	2	yes	complemented
591	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
592	#496	C₂²×C₃₁	1	2	yes	—
593	#496	C₂²×C₃₁	1	2	yes	complemented
594	#495	C₂²×C₃₁	1	2	yes	complemented
595	#489	C₂²×C₃₁	1	2	yes	complemented
596	#489	C₂²×C₃₁	1	2	yes	complemented
597	#486	C₂²×C₃₁	1	2	yes	—
598	#484	C₂²×C₃₁	1	2	yes	complemented
599	#480	C₂²×C₃₁	1	2	yes	—
600	#480	C₂²×C₃₁	1	2	yes	complemented
601	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#477	C₂²×C₃₁	1	2	yes	complemented
604	#474	C₂²×C₃₁	1	2	yes	complemented
605	#474	C₂²×C₃₁	1	2	yes	complemented
606	#474	C₂²×C₃₁	1	2	yes	complemented
607	#468	C₂²×C₃₁	1	2	yes	—
608	#468	C₂²×C₃₁	1	2	yes	complemented
609	#467	C₂²×C₃₁	1	2	yes	complemented
610	#466	C₂²×C₃₁	1	2	yes	—
611	#466	C₂²×C₃₁	1	2	yes	complemented
612	#466	C₂²×C₃₁	1	2	yes	complemented
613	#464	C₂²×C₃₁	1	2	yes	complemented
614	#464	C₂²×C₃₁	1	2	yes	complemented
615	#464	C₂²×C₃₁	1	2	yes	complemented
616	#464	C₂²×C₃₁	1	2	yes	complemented
617	#464	C₂²×C₃₁	1	2	yes	complemented
618	#464	C₂²×C₃₁	1	2	yes	complemented
619	#463	C₂²×C₃₁	1	2	yes	complemented
620	#463	C₂²×C₃₁	1	2	yes	complemented
621	#463	C₂²×C₃₁	1	2	yes	complemented
622	#463	C₂²×C₃₁	1	2	yes	complemented
623	#460	C₂²×C₃₁	1	2	yes	—
624	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#459	C₂²×C₃₁	1	2	yes	—
627	#459	C₂²×C₃₁	1	2	yes	complemented
628	#459	C₂²×C₃₁	1	2	yes	complemented
629	#452	C₂²×C₃₁	1	2	yes	complemented
630	#452	C₂²×C₃₁	1	2	yes	complemented
631	#450	C₂²×C₃₁	1	2	yes	complemented
632	#449	C₂²×C₃₁	1	2	yes	—
633	#449	C₂²×C₃₁	1	2	yes	complemented
634	#448	C₂²×C₃₁	1	2	yes	complemented
635	#448	C₂²×C₃₁	1	2	yes	complemented
636	#447	C₂²×C₃₁	1	2	yes	—
637	#447	C₂²×C₃₁	1	2	yes	complemented
638	#446	C₂²×C₃₁	1	2	yes	complemented
639	#440	C₂²×C₃₁	1	2	yes	complemented
640	#440	C₂²×C₃₁	1	2	yes	complemented
641	#440	C₂²×C₃₁	1	2	yes	complemented
642	#440	C₂²×C₃₁	1	2	yes	complemented
643	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
644	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
645	#435	C₂²×C₃₁	1	2	yes	complemented
646	#435	C₂²×C₃₁	1	2	yes	complemented
647	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
648	#433	C₂²×C₃₁	1	2	yes	complemented
649	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#424	C₂²×C₃₁	1	2	yes	complemented
651	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#417	C₂²×C₃₁	1	2	yes	complemented
653	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
655	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
656	C₂×C₃₁	—	2	2	no	—
657	C₂×C₃₁	—	4	2	no	—
658	C₂×C₃₁	—	8	2	no	—
659	C₂×C₃₁	—	8	2	no	—
660	C₂×C₃₁	—	8	2	no	—
661	C₂×C₃₁	#3488	1	1	yes	characteristic
662	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
663	C₂×C₃₁	#3586	1	1	yes	characteristic
664	C₂×#41	—	2	2	no	—
665	C₂×#41	—	2	1	no	—
666	C₂×#41	—	2	1	no	—
667	C₂×#41	C₂³×C₃₁	1	2	yes	—
668	C₂×#41	C₂³×C₃₁	1	2	yes	—
669	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
670	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
671	C₂²×D₄	—	2	2	no	—
672	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
673	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
674	AGL(1,ℤ/8)	—	4	4	no	—
675	#135	—	4	4	no	—
676	C₂×Q₁₆	—	4	2	no	—
677	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
679	C₂×SD₁₆	—	4	2	no	—
680	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
683	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
686	C₂×D₈	C₂³×C₃₁	1	2	yes	—
687	C₂×D₈	C₂³×C₃₁	1	2	yes	—
688	C₂×D₈	C₂³×C₃₁	1	2	yes	—
689	C₂×D₈	C₂³×C₃₁	1	2	yes	—
690	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
691	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
693	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
699	#127	—	2	1	no	—
700	#127	C₂³×C₃₁	1	1	yes	characteristic
701	#127	C₂³×C₃₁	1	1	yes	characteristic
702	#127	C₂³×C₃₁	1	2	yes	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	D₄×C₃₁	1	2	yes	—
706	#125	—	2	1	no	—
707	#125	D₄×C₃₁	1	1	yes	characteristic
708	#124	—	2	1	no	—
709	#124	—	2	2	no	—
710	#124	—	2	2	no	—
711	#124	—	2	2	no	—
712	#124	—	2	2	no	—
713	#124	—	2	2	no	—
714	#124	—	2	1	no	—
715	#124	—	2	1	no	—
716	#124	—	2	1	no	—
717	#124	—	2	1	no	—
718	#124	D₄×C₃₁	1	1	yes	characteristic
719	#124	C₂³×C₃₁	1	2	yes	—
720	#124	C₂³×C₃₁	1	2	yes	—
721	#124	C₂³×C₃₁	1	2	yes	—
722	#124	C₂³×C₃₁	1	2	yes	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	D₄×C₃₁	1	2	yes	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
739	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
740	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	1	no	—
744	#121	—	2	1	no	—
745	#121	—	2	2	no	—
746	#121	—	2	2	no	—
747	#121	—	2	2	no	—
748	#121	—	2	2	no	—
749	#121	—	2	2	no	—
750	#121	D₄×C₃₁	1	1	yes	characteristic
751	#121	C₂³×C₃₁	1	2	yes	—
752	#121	C₂³×C₃₁	1	2	yes	—
753	#121	C₂³×C₃₁	1	2	yes	—
754	#121	C₂³×C₃₁	1	2	yes	—
755	#120	—	2	2	no	—
756	#120	—	2	2	no	—
757	#120	—	2	2	no	—
758	#120	—	2	2	no	—
759	#120	—	2	2	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
768	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
769	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	C₂³×C₃₁	1	2	yes	—
781	C₄×D₄	C₂³×C₃₁	1	2	yes	—
782	C₄×D₄	C₂³×C₃₁	1	2	yes	—
783	C₄×D₄	C₂³×C₃₁	1	2	yes	—
784	C₄×D₄	C₂³×C₃₁	1	2	yes	—
785	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
786	#117	—	2	2	no	—
787	#117	C₂³×C₃₁	1	2	yes	—
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	2	2	no	—
790	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
792	C₂×C₂²⋊C₄	—	2	1	no	—
793	C₂×C₂²⋊C₄	—	2	1	no	—
794	C₂×C₂²⋊C₄	—	2	2	no	—
795	C₂×C₄²	—	2	1	no	—
796	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
797	#107	C₂³×C₃₁	1	2	yes	—
798	#107	C₂³×C₃₁	1	2	yes	—
799	#107	C₂³×C₃₁	1	2	yes	—
800	#107	C₂³×C₃₁	1	2	yes	—
801	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
802	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
803	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
804	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
805	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
806	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
807	#103	C₂³×C₃₁	1	2	yes	—
808	#103	C₂³×C₃₁	1	2	yes	—
809	#103	C₂³×C₃₁	1	2	yes	—
810	#103	C₂³×C₃₁	1	2	yes	—
811	#103	C₂³×C₃₁	1	2	yes	—
812	#103	C₂³×C₃₁	1	2	yes	—
813	#102	C₂³×C₃₁	1	2	yes	—
814	#102	C₂³×C₃₁	1	2	yes	—
815	#102	C₂³×C₃₁	1	2	yes	—
816	#102	C₂³×C₃₁	1	2	yes	—
817	#102	C₂³×C₃₁	1	2	yes	—
818	#102	C₂³×C₃₁	1	2	yes	—
819	#102	C₂³×C₃₁	1	2	yes	—
820	#102	C₂³×C₃₁	1	2	yes	—
821	#102	C₂³×C₃₁	1	2	yes	—
822	#102	C₂³×C₃₁	1	2	yes	—
823	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
826	#97	C₂³×C₃₁	1	2	yes	—
827	#97	C₂³×C₃₁	1	2	yes	—
828	C₄×C₈	C₂³×C₃₁	1	2	yes	—
829	C₃₁	#62022	1	1	yes	characteristic, direct product factor, Sylow
830	C₂⁴	—	2	1	no	—
831	C₂⁴	—	2	2	no	—
832	#41	—	2	4	no	—
833	#41	—	4	2	no	—
834	#41	—	4	2	no	—
835	#41	—	4	2	no	—
836	#41	—	8	2	no	—
837	#41	—	8	2	no	—
838	#41	—	8	4	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	4	1	no	—
846	C₂×Q₈	—	4	1	no	—
847	C₂×Q₈	—	4	1	no	—
848	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
849	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
851	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	1	no	—
861	C₂×D₄	—	2	1	no	—
862	C₂×D₄	—	2	1	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	4	1	no	—
867	C₂×D₄	—	4	2	no	—
868	C₂×D₄	—	4	1	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	—	8	4	no	—
871	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
872	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
874	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
875	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
887	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
890	Q₁₆	—	2	4	no	—
891	Q₁₆	—	4	2	no	—
892	SD₁₆	—	2	4	no	—
893	SD₁₆	—	2	4	no	—
894	SD₁₆	—	4	2	no	—
895	SD₁₆	—	4	2	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	D₈	—	4	2	no	—
899	D₈	—	4	2	no	—
900	D₈	—	4	2	no	—
901	D₈	—	4	2	no	—
902	M₁₆	—	4	2	no	—
903	C₂×C₈	—	4	1	no	—
904	C₂×C₈	—	4	1	no	—
905	C₂×C₈	—	4	2	no	—
906	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
907	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
908	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
909	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
952	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
955	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
963	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₄²	C₂⁴×C₃₁	1	2	yes	—
965	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	4	2	no	—
971	C₂³	—	8	1	no	—
972	C₂³	—	8	2	no	—
973	C₂³	—	8	2	no	—
974	C₂³	—	8	1	no	—
975	C₂³	—	8	2	no	—
976	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
977	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	4	1	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	8	1	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	1	no	—
988	Q₈	—	8	2	no	—
989	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
990	D₄	—	2	4	no	—
991	D₄	—	2	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	2	no	—
995	D₄	—	2	2	no	—
996	D₄	—	2	2	no	—
997	D₄	—	4	1	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	4	4	no	—
1002	D₄	—	8	1	no	—
1003	D₄	—	8	2	no	—
1004	D₄	—	8	2	no	—
1005	D₄	—	8	1	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	1	no	—
1008	D₄	—	8	1	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1043	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1044	C₈	—	2	2	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	2	no	—
1047	C₈	—	2	2	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	16	2	no	—
1063	C₂²	—	16	4	no	—
1064	C₂²	C₃₁×#576	1	2	yes	—
1065	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1066	C₄	—	2	2	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	2	no	—
1081	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1082	C₄	C₃₁×#585	1	1	yes	characteristic
1083	C₂	—	2	2	no	—
1084	C₂	—	4	2	no	—
1085	C₂	—	8	2	no	—
1086	C₂	—	8	2	no	—
1087	C₂	—	8	2	no	—
1088	C₂	C₃₁×#3488	1	1	yes	characteristic
1089	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1090	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3558	C₂	semidirect
2. C₃₁×#3522	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3375	C₂	semidirect
5. C₃₁×#3314	C₂	semidirect
6. C₃₁×#3308	C₂	semidirect
7. C₃₁×#3294	C₂	semidirect
8. C₃₁×#3285	C₂	semidirect
9. C₃₁×#3268	C₂	semidirect
10. C₃₁×#3265	C₂	semidirect
11. C₃₁×#3262	C₂	semidirect
12. C₃₁×#3245	C₂	semidirect
13. C₃₁×#3224	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3112	C₂	semidirect
17. C₃₁×#3045	C₂	semidirect
18. C₂×C₃₁×#464	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
20. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₃₁×#135	C₂²	semidirect
22. C₂²×Q₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#559	C₂²	semidirect
29. Q₈²×C₃₁	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
32. C₃₁×#550	C₂²	semidirect
34. C₃₁×#548	C₂²	semidirect
36. C₃₁×#547	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
49. C₃₁×#532	C₂²	semidirect
53. C₃₁×#520	C₂²	semidirect
54. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
56. C₃₁×#496	C₂²	semidirect
57. C₃₁×#495	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
63. C₃₁×#480	C₂²	semidirect
64. C₃₁×#477	C₂²	semidirect
65. C₃₁×#477	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#467	C₂²	semidirect
74. C₃₁×#466	C₂²	semidirect
75. C₃₁×#466	C₂²	semidirect
76. C₃₁×#464	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#464	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#463	C₂²	semidirect
84. C₃₁×#463	C₂²	semidirect
85. C₃₁×#463	C₂²	semidirect
87. C₃₁×#460	C₂²	semidirect
88. C₃₁×#460	C₂²	semidirect
90. C₃₁×#459	C₂²	semidirect
91. C₃₁×#459	C₂²	semidirect
92. C₃₁×#452	C₂²	semidirect
93. C₃₁×#452	C₂²	semidirect
94. C₃₁×#450	C₂²	semidirect
96. C₃₁×#449	C₂²	semidirect
97. C₃₁×#448	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
107. C₄×D₈×C₃₁	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
110. C₈×D₄×C₃₁	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
112. C₃₁×#432	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
114. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
115. C₃₁×#417	C₂²	semidirect
116. C₂×C₃₁×#103	C₂²	semidirect
118. C₂×C₃₁×#102	C₂²	semidirect
421. #62022	C₃₁	direct (N × H)
503. #3558	C₂×C₃₁	semidirect
504. #3522	C₂×C₃₁	semidirect
505. #3403	C₂×C₃₁	semidirect
506. #3375	C₂×C₃₁	semidirect
507. #3314	C₂×C₃₁	semidirect
508. #3308	C₂×C₃₁	semidirect
509. #3294	C₂×C₃₁	semidirect
510. #3285	C₂×C₃₁	semidirect
511. #3268	C₂×C₃₁	semidirect
512. #3265	C₂×C₃₁	semidirect
513. #3262	C₂×C₃₁	semidirect
514. #3245	C₂×C₃₁	semidirect
515. #3224	C₂×C₃₁	semidirect
516. #3213	C₂×C₃₁	semidirect
517. #3124	C₂×C₃₁	semidirect
518. #3112	C₂×C₃₁	semidirect
519. #3045	C₂×C₃₁	semidirect
520. C₂×#464	C₂×C₃₁	semidirect
521. #2992	C₂×C₃₁	semidirect
557. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
558. C₂×#135	C₂²×C₃₁	semidirect
559. C₂²×Q₁₆	C₂²×C₃₁	semidirect
565. #559	C₂²×C₃₁	semidirect
566. Q₈²	C₂²×C₃₁	semidirect
568. #554	C₂²×C₃₁	semidirect
569. #550	C₂²×C₃₁	semidirect
571. #548	C₂²×C₃₁	semidirect
573. #547	C₂²×C₃₁	semidirect
579. #542	C₂²×C₃₁	semidirect
586. #532	C₂²×C₃₁	semidirect
590. #520	C₂²×C₃₁	semidirect
591. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
593. #496	C₂²×C₃₁	semidirect
594. #495	C₂²×C₃₁	semidirect
595. #489	C₂²×C₃₁	semidirect
596. #489	C₂²×C₃₁	semidirect
598. #484	C₂²×C₃₁	semidirect
600. #480	C₂²×C₃₁	semidirect
601. #477	C₂²×C₃₁	semidirect
602. #477	C₂²×C₃₁	semidirect
603. #477	C₂²×C₃₁	semidirect
604. #474	C₂²×C₃₁	semidirect
605. #474	C₂²×C₃₁	semidirect
606. #474	C₂²×C₃₁	semidirect
608. #468	C₂²×C₃₁	semidirect
609. #467	C₂²×C₃₁	semidirect
611. #466	C₂²×C₃₁	semidirect
612. #466	C₂²×C₃₁	semidirect
613. #464	C₂²×C₃₁	semidirect
614. #464	C₂²×C₃₁	semidirect
615. #464	C₂²×C₃₁	semidirect
616. #464	C₂²×C₃₁	semidirect
617. #464	C₂²×C₃₁	semidirect
618. #464	C₂²×C₃₁	semidirect
619. #463	C₂²×C₃₁	semidirect
620. #463	C₂²×C₃₁	semidirect
621. #463	C₂²×C₃₁	semidirect
622. #463	C₂²×C₃₁	semidirect
624. #460	C₂²×C₃₁	semidirect
625. #460	C₂²×C₃₁	semidirect
627. #459	C₂²×C₃₁	semidirect
628. #459	C₂²×C₃₁	semidirect
629. #452	C₂²×C₃₁	semidirect
630. #452	C₂²×C₃₁	semidirect
631. #450	C₂²×C₃₁	semidirect
633. #449	C₂²×C₃₁	semidirect
634. #448	C₂²×C₃₁	semidirect
635. #448	C₂²×C₃₁	semidirect
637. #447	C₂²×C₃₁	semidirect
638. #446	C₂²×C₃₁	semidirect
639. #440	C₂²×C₃₁	semidirect
640. #440	C₂²×C₃₁	semidirect
641. #440	C₂²×C₃₁	semidirect
642. #440	C₂²×C₃₁	semidirect
643. C₄×Q₁₆	C₂²×C₃₁	semidirect
644. C₄×D₈	C₂²×C₃₁	semidirect
645. #435	C₂²×C₃₁	semidirect
646. #435	C₂²×C₃₁	semidirect
647. C₈×D₄	C₂²×C₃₁	semidirect
648. #433	C₂²×C₃₁	semidirect
649. #432	C₂²×C₃₁	semidirect
650. #424	C₂²×C₃₁	semidirect
651. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
652. #417	C₂²×C₃₁	semidirect
653. C₂×#103	C₂²×C₃₁	semidirect
655. C₂×#102	C₂²×C₃₁	semidirect
829. C₃₁	#62022	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×#3558	2
C₃₁×#3522	2
C₃₁×#3403	2
C₃₁×#3375	2
C₃₁×#3314	2
C₃₁×#3308	2
C₃₁×#3294	2
C₃₁×#3285	2
C₃₁×#3268	2
C₃₁×#3265	2
C₃₁×#3262	2
C₃₁×#3245	2
C₃₁×#3224	2
C₃₁×#3213	2
C₃₁×#3124	2
C₃₁×#3112	2
C₃₁×#3045	2
C₂×C₃₁×#464	2
C₃₁×#2992	2
#62022	31

Subgroups — C31×#62022 #21518781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62022 #21518781