Subgroups — C₃₁×#61638 #21518397

Order 7936.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3304	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3200	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3199	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3002	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×H(3,𝔽₄)	—	2	1	no	—
29	C₃₁×#560	—	2	1	no	—
30	C₃₁×#559	—	2	1	no	—
31	C₃₁×#556	C₂²	1	2	yes	complemented
32	C₃₁×#555	C₂²	1	2	yes	complemented
33	C₃₁×#551	—	2	1	no	—
34	C₃₁×#550	—	2	2	no	—
35	C₃₁×#550	C₂²	1	2	yes	—
36	C₃₁×#550	C₂²	1	2	yes	complemented
37	C₃₁×#548	—	2	2	no	—
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#548	C₂²	1	2	yes	complemented
40	C₃₁×#548	C₂²	1	2	yes	complemented
41	C₃₁×#546	C₂²	1	2	yes	complemented
42	C₃₁×#542	—	2	2	no	—
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#538	—	2	2	no	—
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#535	—	2	1	no	—
47	C₃₁×#535	—	2	1	no	—
48	C₃₁×#535	C₂²	1	1	yes	characteristic
49	C₃₁×#535	C₂²	1	1	yes	characteristic
50	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#525	—	2	1	no	—
52	C₃₁×#525	—	2	1	no	—
53	C₃₁×#525	C₂²	1	2	yes	—
54	C₃₁×#525	C₂²	1	1	yes	characteristic
55	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#496	C₂²	1	2	yes	complemented
58	C₃₁×#495	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#486	C₂²	1	2	yes	complemented
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#485	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	complemented
65	C₃₁×#482	C₂²	1	2	yes	complemented
66	C₃₁×#482	C₂²	1	2	yes	complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#475	C₂²	1	2	yes	complemented
69	C₃₁×#469	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	complemented
71	C₃₁×#467	C₂²	1	2	yes	complemented
72	C₃₁×#466	C₂²	1	2	yes	complemented
73	C₃₁×#466	C₂²	1	2	yes	complemented
74	C₃₁×#465	C₂²	1	2	yes	complemented
75	C₃₁×#465	C₂²	1	2	yes	complemented
76	C₃₁×#465	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×#463	C₂²	1	2	yes	complemented
81	C₃₁×#460	C₂²	1	2	yes	complemented
82	C₃₁×#459	C₂²	1	2	yes	complemented
83	C₃₁×#452	C₂²	1	2	yes	complemented
84	C₃₁×#452	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#452	C₂²	1	2	yes	complemented
87	C₃₁×#452	C₂²	1	2	yes	complemented
88	C₃₁×#451	C₂²	1	2	yes	complemented
89	C₃₁×#451	C₂²	1	2	yes	complemented
90	C₃₁×#450	C₂²	1	2	yes	complemented
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	2	yes	—
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×#441	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#416	C₂²	1	2	yes	complemented
113	C₃₁×#416	C₂²	1	2	yes	complemented
114	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#408	C₂²	1	1	yes	characteristic
117	C₃₁×#408	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
119	C₃₁×2₋¹⁺⁴	—	4	2	no	—
120	C₃₁×2₋¹⁺⁴	—	4	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	1	no	—
123	C₂×#41×C₃₁	—	2	1	no	—
124	C₂×#41×C₃₁	—	2	2	no	—
125	C₂×#41×C₃₁	—	4	2	no	—
126	C₂×#41×C₃₁	—	4	2	no	—
127	C₂×#41×C₃₁	C₂³	1	2	yes	—
128	C₂×#41×C₃₁	C₂³	1	2	yes	—
129	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×#41×C₃₁	C₂³	1	2	yes	—
133	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₃₁	—	2	1	no	—
135	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	—	2	1	no	—
143	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×#137	—	4	2	no	—
145	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
146	C₃₁×#135	—	4	4	no	—
147	C₃₁×#135	—	4	4	no	—
148	C₂×Q₁₆×C₃₁	—	4	2	no	—
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	—	4	2	no	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
165	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
166	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₃₁×C₄⋊Q₈	—	2	1	no	—
169	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₃₁×#127	—	2	2	no	—
171	C₃₁×#127	—	2	2	no	—
172	C₃₁×#127	—	2	1	no	—
173	C₃₁×#127	—	2	1	no	—
174	C₃₁×#127	C₂³	1	2	yes	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	D₄	1	1	yes	characteristic
197	C₃₁×#123	D₄	1	1	yes	characteristic
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	D₄	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#120	—	2	2	no	—
225	C₃₁×#120	—	2	1	no	—
226	C₃₁×#120	—	2	1	no	—
227	C₃₁×#120	—	2	1	no	—
228	C₃₁×#120	—	2	1	no	—
229	C₃₁×#120	—	2	1	no	—
230	C₃₁×#120	—	2	2	no	—
231	C₃₁×#120	—	2	1	no	—
232	C₃₁×#120	—	2	1	no	—
233	C₃₁×#120	D₄	1	1	yes	characteristic
234	C₃₁×#120	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₃₁	—	2	2	no	—
236	C₄×Q₈×C₃₁	—	2	2	no	—
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₃₁×#117	C₂³	1	1	yes	characteristic
258	C₃₁×#117	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₃₁×#107	C₂³	1	2	yes	—
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#106	C₂³	1	2	yes	—
263	C₃₁×#106	C₂³	1	2	yes	—
264	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
265	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#103	C₂³	1	2	yes	—
273	C₃₁×#103	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×#102	C₂³	1	2	yes	—
279	C₃₁×#102	C₂³	1	2	yes	—
280	C₃₁×#102	C₂³	1	2	yes	—
281	C₃₁×#102	C₂³	1	2	yes	—
282	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₃₁	C₂³	1	2	yes	—
290	C₂⁴×C₃₁	—	2	1	no	—
291	C₂⁴×C₃₁	—	2	1	no	—
292	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
293	#41×C₃₁	—	2	4	no	—
294	#41×C₃₁	—	2	4	no	—
295	#41×C₃₁	—	2	2	no	—
296	#41×C₃₁	—	2	2	no	—
297	#41×C₃₁	—	4	1	no	—
298	#41×C₃₁	—	4	1	no	—
299	#41×C₃₁	—	4	2	no	—
300	#41×C₃₁	—	4	2	no	—
301	#41×C₃₁	—	4	1	no	—
302	#41×C₃₁	—	4	1	no	—
303	#41×C₃₁	—	4	1	no	—
304	#41×C₃₁	—	4	1	no	—
305	#41×C₃₁	—	4	4	no	—
306	#41×C₃₁	—	4	4	no	—
307	#41×C₃₁	—	4	2	no	—
308	#41×C₃₁	—	4	2	no	—
309	#41×C₃₁	—	4	8	no	—
310	#41×C₃₁	—	4	4	no	—
311	C₂×Q₈×C₃₁	—	2	2	no	—
312	C₂×Q₈×C₃₁	—	2	2	no	—
313	C₂×Q₈×C₃₁	—	2	1	no	—
314	C₂×Q₈×C₃₁	—	2	1	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	4	1	no	—
321	C₂×Q₈×C₃₁	—	4	1	no	—
322	C₂×Q₈×C₃₁	—	4	1	no	—
323	C₂×Q₈×C₃₁	—	4	1	no	—
324	C₂×Q₈×C₃₁	—	4	4	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	1	no	—
346	C₂×D₄×C₃₁	—	4	1	no	—
347	C₂×D₄×C₃₁	—	4	1	no	—
348	C₂×D₄×C₃₁	—	4	1	no	—
349	C₂×D₄×C₃₁	—	4	1	no	—
350	C₂×D₄×C₃₁	—	4	4	no	—
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	1	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	4	1	no	—
371	C₂²×C₄×C₃₁	—	4	1	no	—
372	C₂²×C₄×C₃₁	—	4	4	no	—
373	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
379	Q₁₆×C₃₁	—	2	4	no	—
380	Q₁₆×C₃₁	—	2	4	no	—
381	Q₁₆×C₃₁	—	4	2	no	—
382	SD₁₆×C₃₁	—	2	4	no	—
383	SD₁₆×C₃₁	—	2	4	no	—
384	SD₁₆×C₃₁	—	4	2	no	—
385	SD₁₆×C₃₁	—	4	2	no	—
386	SD₁₆×C₃₁	—	4	2	no	—
387	SD₁₆×C₃₁	—	4	2	no	—
388	D₈×C₃₁	—	4	2	no	—
389	D₈×C₃₁	—	4	2	no	—
390	D₈×C₃₁	—	4	2	no	—
391	M₁₆×C₃₁	—	4	1	no	—
392	M₁₆×C₃₁	—	4	1	no	—
393	C₂×C₈×C₃₁	—	4	1	no	—
394	C₂×C₈×C₃₁	—	4	1	no	—
395	C₂×C₈×C₃₁	—	4	2	no	—
396	C₂×C₈×C₃₁	—	4	2	no	—
397	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
398	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
399	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
400	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	C₂⁴	1	2	yes	—
448	#61638	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₃₁	—	2	2	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	4	1	no	—
453	C₂³×C₃₁	—	4	2	no	—
454	C₂³×C₃₁	—	4	2	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	—	8	1	no	—
457	C₂³×C₃₁	—	8	2	no	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₃₁	—	2	4	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	2	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	4	1	no	—
470	Q₈×C₃₁	—	4	2	no	—
471	Q₈×C₃₁	—	4	2	no	—
472	Q₈×C₃₁	—	8	2	no	—
473	Q₈×C₃₁	—	8	1	no	—
474	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
475	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	1	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	1	no	—
485	D₄×C₃₁	—	4	1	no	—
486	D₄×C₃₁	—	4	1	no	—
487	D₄×C₃₁	—	4	4	no	—
488	D₄×C₃₁	—	4	4	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	4	2	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	4	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	1	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	D₄×C₃₁	—	8	2	no	—
499	D₄×C₃₁	—	8	2	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	—	8	2	no	—
502	D₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	2	4	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	1	no	—
514	C₂×C₄×C₃₁	—	2	2	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	4	1	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	4	no	—
522	C₂×C₄×C₃₁	—	4	4	no	—
523	C₂×C₄×C₃₁	—	4	2	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	4	2	no	—
526	C₂×C₄×C₃₁	—	4	2	no	—
527	C₂×C₄×C₃₁	—	4	2	no	—
528	C₂×C₄×C₃₁	—	8	2	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	—	8	1	no	—
531	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
538	C₈×C₃₁	—	2	2	no	—
539	C₈×C₃₁	—	2	2	no	—
540	C₈×C₃₁	—	2	2	no	—
541	C₈×C₃₁	—	2	2	no	—
542	#3540	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3487	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3321	C₂×C₃₁	1	2	yes	complemented
545	#3313	C₂×C₃₁	1	2	yes	complemented
546	#3305	C₂×C₃₁	1	2	yes	complemented
547	#3304	C₂×C₃₁	1	2	yes	complemented
548	#3285	C₂×C₃₁	1	2	yes	complemented
549	#3282	C₂×C₃₁	1	2	yes	complemented
550	#3271	C₂×C₃₁	1	2	yes	complemented
551	#3268	C₂×C₃₁	1	2	yes	complemented
552	#3224	C₂×C₃₁	1	2	yes	complemented
553	#3200	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3199	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3191	C₂×C₃₁	1	2	yes	complemented
556	#3121	C₂×C₃₁	1	2	yes	complemented
557	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3002	C₂×C₃₁	1	2	yes	complemented
560	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	1	no	—
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	8	2	no	—
579	C₂²×C₃₁	—	8	4	no	—
580	C₂²×C₃₁	—	16	2	no	—
581	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	2	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	2	2	no	—
587	C₄×C₃₁	—	2	1	no	—
588	C₄×C₃₁	—	2	1	no	—
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	—	4	2	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	2	no	—
595	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
598	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	C₂×#135	C₂²×C₃₁	1	2	yes	—
602	C₂×#135	C₂²×C₃₁	1	2	yes	—
603	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	H(3,𝔽₄)	—	2	1	no	—
606	#560	—	2	1	no	—
607	#559	—	2	1	no	—
608	#556	C₂²×C₃₁	1	2	yes	complemented
609	#555	C₂²×C₃₁	1	2	yes	complemented
610	#551	—	2	1	no	—
611	#550	—	2	2	no	—
612	#550	C₂²×C₃₁	1	2	yes	—
613	#550	C₂²×C₃₁	1	2	yes	complemented
614	#548	—	2	2	no	—
615	#548	C₂²×C₃₁	1	2	yes	—
616	#548	C₂²×C₃₁	1	2	yes	complemented
617	#548	C₂²×C₃₁	1	2	yes	complemented
618	#546	C₂²×C₃₁	1	2	yes	complemented
619	#542	—	2	2	no	—
620	#542	C₂²×C₃₁	1	2	yes	—
621	#538	—	2	2	no	—
622	#536	C₂²×C₃₁	1	1	yes	characteristic
623	#535	—	2	1	no	—
624	#535	—	2	1	no	—
625	#535	C₂²×C₃₁	1	1	yes	characteristic
626	#535	C₂²×C₃₁	1	1	yes	characteristic
627	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#525	—	2	1	no	—
629	#525	—	2	1	no	—
630	#525	C₂²×C₃₁	1	2	yes	—
631	#525	C₂²×C₃₁	1	1	yes	characteristic
632	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#496	C₂²×C₃₁	1	2	yes	complemented
635	#495	C₂²×C₃₁	1	2	yes	complemented
636	#489	C₂²×C₃₁	1	2	yes	complemented
637	#486	C₂²×C₃₁	1	2	yes	complemented
638	#485	C₂²×C₃₁	1	2	yes	complemented
639	#485	C₂²×C₃₁	1	2	yes	complemented
640	#482	C₂²×C₃₁	1	2	yes	—
641	#482	C₂²×C₃₁	1	2	yes	complemented
642	#482	C₂²×C₃₁	1	2	yes	complemented
643	#482	C₂²×C₃₁	1	2	yes	complemented
644	#477	C₂²×C₃₁	1	2	yes	complemented
645	#475	C₂²×C₃₁	1	2	yes	complemented
646	#469	C₂²×C₃₁	1	2	yes	complemented
647	#468	C₂²×C₃₁	1	2	yes	complemented
648	#467	C₂²×C₃₁	1	2	yes	complemented
649	#466	C₂²×C₃₁	1	2	yes	complemented
650	#466	C₂²×C₃₁	1	2	yes	complemented
651	#465	C₂²×C₃₁	1	2	yes	complemented
652	#465	C₂²×C₃₁	1	2	yes	complemented
653	#465	C₂²×C₃₁	1	2	yes	complemented
654	#464	C₂²×C₃₁	1	2	yes	complemented
655	#464	C₂²×C₃₁	1	2	yes	complemented
656	#464	C₂²×C₃₁	1	2	yes	complemented
657	#463	C₂²×C₃₁	1	2	yes	complemented
658	#460	C₂²×C₃₁	1	2	yes	complemented
659	#459	C₂²×C₃₁	1	2	yes	complemented
660	#452	C₂²×C₃₁	1	2	yes	complemented
661	#452	C₂²×C₃₁	1	2	yes	complemented
662	#452	C₂²×C₃₁	1	2	yes	complemented
663	#452	C₂²×C₃₁	1	2	yes	complemented
664	#452	C₂²×C₃₁	1	2	yes	complemented
665	#451	C₂²×C₃₁	1	2	yes	complemented
666	#451	C₂²×C₃₁	1	2	yes	complemented
667	#450	C₂²×C₃₁	1	2	yes	complemented
668	#449	C₂²×C₃₁	1	2	yes	—
669	#449	C₂²×C₃₁	1	2	yes	—
670	#449	C₂²×C₃₁	1	2	yes	—
671	#449	C₂²×C₃₁	1	2	yes	complemented
672	#449	C₂²×C₃₁	1	2	yes	complemented
673	#448	C₂²×C₃₁	1	2	yes	—
674	#448	C₂²×C₃₁	1	2	yes	complemented
675	#448	C₂²×C₃₁	1	2	yes	complemented
676	#447	C₂²×C₃₁	1	2	yes	—
677	#447	C₂²×C₃₁	1	2	yes	complemented
678	#441	C₂²×C₃₁	1	2	yes	complemented
679	#440	C₂²×C₃₁	1	2	yes	complemented
680	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
681	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
682	#435	C₂²×C₃₁	1	2	yes	complemented
683	#435	C₂²×C₃₁	1	2	yes	complemented
684	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
685	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
686	#433	C₂²×C₃₁	1	2	yes	complemented
687	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#416	C₂²×C₃₁	1	2	yes	complemented
690	#416	C₂²×C₃₁	1	2	yes	complemented
691	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#408	C₂²×C₃₁	1	1	yes	characteristic
694	#408	C₂²×C₃₁	1	1	yes	characteristic
695	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
696	C₂×C₃₁	—	4	1	no	—
697	C₂×C₃₁	—	4	2	no	—
698	C₂×C₃₁	—	4	1	no	—
699	C₂×C₃₁	—	4	1	no	—
700	C₂×C₃₁	—	8	1	no	—
701	C₂×C₃₁	—	8	2	no	—
702	C₂×C₃₁	—	8	2	no	—
703	C₂×C₃₁	#3484	1	1	yes	characteristic
704	C₂×C₃₁	#3584	1	2	yes	—
705	2₋¹⁺⁴	—	4	2	no	—
706	2₋¹⁺⁴	—	4	2	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	—	2	2	no	—
711	C₂×#41	—	4	2	no	—
712	C₂×#41	—	4	2	no	—
713	C₂×#41	C₂³×C₃₁	1	2	yes	—
714	C₂×#41	C₂³×C₃₁	1	2	yes	—
715	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×#41	C₂³×C₃₁	1	2	yes	—
718	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
728	C₂³×C₄	—	2	1	no	—
729	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
730	#137	—	4	2	no	—
731	AGL(1,ℤ/8)	—	4	2	no	—
732	#135	—	4	4	no	—
733	#135	—	4	4	no	—
734	C₂×Q₁₆	—	4	2	no	—
735	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
738	C₂×SD₁₆	—	4	2	no	—
739	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×D₈	C₂³×C₃₁	1	2	yes	—
746	C₂×D₈	C₂³×C₃₁	1	2	yes	—
747	C₂×D₈	C₂³×C₃₁	1	2	yes	—
748	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
749	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
753	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
756	#127	—	2	2	no	—
757	#127	—	2	2	no	—
758	#127	—	2	1	no	—
759	#127	—	2	1	no	—
760	#127	C₂³×C₃₁	1	2	yes	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#124	—	2	1	no	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₃₁	1	2	yes	—
775	#124	C₂³×C₃₁	1	2	yes	—
776	#123	—	2	1	no	—
777	#123	—	2	1	no	—
778	#123	—	2	1	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	D₄×C₃₁	1	1	yes	characteristic
783	#123	D₄×C₃₁	1	1	yes	characteristic
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	D₄×C₃₁	1	2	yes	—
804	#121	C₂³×C₃₁	1	2	yes	—
805	#121	C₂³×C₃₁	1	2	yes	—
806	#121	C₂³×C₃₁	1	2	yes	—
807	#121	C₂³×C₃₁	1	2	yes	—
808	#121	C₂³×C₃₁	1	2	yes	—
809	#121	C₂³×C₃₁	1	2	yes	—
810	#120	—	2	2	no	—
811	#120	—	2	1	no	—
812	#120	—	2	1	no	—
813	#120	—	2	1	no	—
814	#120	—	2	1	no	—
815	#120	—	2	1	no	—
816	#120	—	2	2	no	—
817	#120	—	2	1	no	—
818	#120	—	2	1	no	—
819	#120	D₄×C₃₁	1	1	yes	characteristic
820	#120	D₄×C₃₁	1	1	yes	characteristic
821	C₄×Q₈	—	2	2	no	—
822	C₄×Q₈	—	2	2	no	—
823	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
825	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	C₂³×C₃₁	1	1	yes	characteristic
841	#117	C₂³×C₃₁	1	2	yes	—
842	#117	C₂³×C₃₁	1	1	yes	characteristic
843	#117	C₂³×C₃₁	1	1	yes	characteristic
844	#117	C₂³×C₃₁	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	#107	C₂³×C₃₁	1	2	yes	—
847	#107	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
874	#97	C₂³×C₃₁	1	2	yes	—
875	C₄×C₈	C₂³×C₃₁	1	2	yes	—
876	C₃₁	#61638	1	1	yes	characteristic, direct product factor, Sylow
877	C₂⁴	—	2	1	no	—
878	C₂⁴	—	2	1	no	—
879	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
880	#41	—	2	4	no	—
881	#41	—	2	4	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	—	4	1	no	—
885	#41	—	4	1	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	1	no	—
889	#41	—	4	1	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	4	4	no	—
893	#41	—	4	4	no	—
894	#41	—	4	2	no	—
895	#41	—	4	2	no	—
896	#41	—	4	8	no	—
897	#41	—	4	4	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	4	1	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	1	no	—
911	C₂×Q₈	—	4	4	no	—
912	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	4	1	no	—
934	C₂×D₄	—	4	1	no	—
935	C₂×D₄	—	4	1	no	—
936	C₂×D₄	—	4	1	no	—
937	C₂×D₄	—	4	4	no	—
938	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
941	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
944	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	4	1	no	—
958	C₂²×C₄	—	4	1	no	—
959	C₂²×C₄	—	4	4	no	—
960	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	Q₁₆	—	2	4	no	—
967	Q₁₆	—	2	4	no	—
968	Q₁₆	—	4	2	no	—
969	SD₁₆	—	2	4	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	D₈	—	4	2	no	—
976	D₈	—	4	2	no	—
977	D₈	—	4	2	no	—
978	M₁₆	—	4	1	no	—
979	M₁₆	—	4	1	no	—
980	C₂×C₈	—	4	1	no	—
981	C₂×C₈	—	4	1	no	—
982	C₂×C₈	—	4	2	no	—
983	C₂×C₈	—	4	2	no	—
984	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
985	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
986	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
987	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂⁴×C₃₁	1	2	yes	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	1	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1046	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1047	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1048	Q₈	—	2	4	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	1	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	8	2	no	—
1059	Q₈	—	8	1	no	—
1060	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1061	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	C₂×C₄	—	2	4	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	4	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1123	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	2	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	8	2	no	—
1146	C₂²	—	8	4	no	—
1147	C₂²	—	16	2	no	—
1148	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1149	C₄	—	2	2	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1163	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1164	C₂	—	4	1	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	4	1	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	8	2	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	C₃₁×#3484	1	1	yes	characteristic
1172	C₂	C₃₁×#3584	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3540	C₂	semidirect
2. C₃₁×#3487	C₂	semidirect
3. C₃₁×#3321	C₂	semidirect
4. C₃₁×#3313	C₂	semidirect
5. C₃₁×#3305	C₂	semidirect
6. C₃₁×#3304	C₂	semidirect
7. C₃₁×#3285	C₂	semidirect
8. C₃₁×#3282	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3268	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3200	C₂	semidirect
13. C₃₁×#3199	C₂	semidirect
14. C₃₁×#3191	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3011	C₂	semidirect
17. C₃₁×#3010	C₂	semidirect
18. C₃₁×#3002	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×Q₁₆×C₃₁	C₂²	semidirect
27. C₂²×SD₁₆×C₃₁	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
32. C₃₁×#555	C₂²	semidirect
36. C₃₁×#550	C₂²	semidirect
39. C₃₁×#548	C₂²	semidirect
40. C₃₁×#548	C₂²	semidirect
41. C₃₁×#546	C₂²	semidirect
50. C₃₁×#535	C₂²	semidirect
55. C₃₁×#525	C₂²	semidirect
56. C₃₁×#519	C₂²	semidirect
57. C₃₁×#496	C₂²	semidirect
58. C₃₁×#495	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#486	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
64. C₃₁×#482	C₂²	semidirect
65. C₃₁×#482	C₂²	semidirect
66. C₃₁×#482	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#475	C₂²	semidirect
69. C₃₁×#469	C₂²	semidirect
70. C₃₁×#468	C₂²	semidirect
71. C₃₁×#467	C₂²	semidirect
72. C₃₁×#466	C₂²	semidirect
73. C₃₁×#466	C₂²	semidirect
74. C₃₁×#465	C₂²	semidirect
75. C₃₁×#465	C₂²	semidirect
76. C₃₁×#465	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#460	C₂²	semidirect
82. C₃₁×#459	C₂²	semidirect
83. C₃₁×#452	C₂²	semidirect
84. C₃₁×#452	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
87. C₃₁×#452	C₂²	semidirect
88. C₃₁×#451	C₂²	semidirect
89. C₃₁×#451	C₂²	semidirect
90. C₃₁×#450	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
97. C₃₁×#448	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#441	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₄×Q₁₆×C₃₁	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₈×D₄×C₃₁	C₂²	semidirect
108. C₈×D₄×C₃₁	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#419	C₂²	semidirect
111. C₃₁×#419	C₂²	semidirect
112. C₃₁×#416	C₂²	semidirect
113. C₃₁×#416	C₂²	semidirect
114. C₃₁×#416	C₂²	semidirect
115. C₃₁×#416	C₂²	semidirect
118. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
448. #61638	C₃₁	direct (N × H)
542. #3540	C₂×C₃₁	semidirect
543. #3487	C₂×C₃₁	semidirect
544. #3321	C₂×C₃₁	semidirect
545. #3313	C₂×C₃₁	semidirect
546. #3305	C₂×C₃₁	semidirect
547. #3304	C₂×C₃₁	semidirect
548. #3285	C₂×C₃₁	semidirect
549. #3282	C₂×C₃₁	semidirect
550. #3271	C₂×C₃₁	semidirect
551. #3268	C₂×C₃₁	semidirect
552. #3224	C₂×C₃₁	semidirect
553. #3200	C₂×C₃₁	semidirect
554. #3199	C₂×C₃₁	semidirect
555. #3191	C₂×C₃₁	semidirect
556. #3121	C₂×C₃₁	semidirect
557. #3011	C₂×C₃₁	semidirect
558. #3010	C₂×C₃₁	semidirect
559. #3002	C₂×C₃₁	semidirect
560. #2977	C₂×C₃₁	semidirect
598. C₂²×#41	C₂²×C₃₁	semidirect
599. C₂×#137	C₂²×C₃₁	semidirect
600. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
603. C₂²×Q₁₆	C₂²×C₃₁	semidirect
604. C₂²×SD₁₆	C₂²×C₃₁	semidirect
608. #556	C₂²×C₃₁	semidirect
609. #555	C₂²×C₃₁	semidirect
613. #550	C₂²×C₃₁	semidirect
616. #548	C₂²×C₃₁	semidirect
617. #548	C₂²×C₃₁	semidirect
618. #546	C₂²×C₃₁	semidirect
627. #535	C₂²×C₃₁	semidirect
632. #525	C₂²×C₃₁	semidirect
633. #519	C₂²×C₃₁	semidirect
634. #496	C₂²×C₃₁	semidirect
635. #495	C₂²×C₃₁	semidirect
636. #489	C₂²×C₃₁	semidirect
637. #486	C₂²×C₃₁	semidirect
638. #485	C₂²×C₃₁	semidirect
639. #485	C₂²×C₃₁	semidirect
641. #482	C₂²×C₃₁	semidirect
642. #482	C₂²×C₃₁	semidirect
643. #482	C₂²×C₃₁	semidirect
644. #477	C₂²×C₃₁	semidirect
645. #475	C₂²×C₃₁	semidirect
646. #469	C₂²×C₃₁	semidirect
647. #468	C₂²×C₃₁	semidirect
648. #467	C₂²×C₃₁	semidirect
649. #466	C₂²×C₃₁	semidirect
650. #466	C₂²×C₃₁	semidirect
651. #465	C₂²×C₃₁	semidirect
652. #465	C₂²×C₃₁	semidirect
653. #465	C₂²×C₃₁	semidirect
654. #464	C₂²×C₃₁	semidirect
655. #464	C₂²×C₃₁	semidirect
656. #464	C₂²×C₃₁	semidirect
657. #463	C₂²×C₃₁	semidirect
658. #460	C₂²×C₃₁	semidirect
659. #459	C₂²×C₃₁	semidirect
660. #452	C₂²×C₃₁	semidirect
661. #452	C₂²×C₃₁	semidirect
662. #452	C₂²×C₃₁	semidirect
663. #452	C₂²×C₃₁	semidirect
664. #452	C₂²×C₃₁	semidirect
665. #451	C₂²×C₃₁	semidirect
666. #451	C₂²×C₃₁	semidirect
667. #450	C₂²×C₃₁	semidirect
671. #449	C₂²×C₃₁	semidirect
672. #449	C₂²×C₃₁	semidirect
674. #448	C₂²×C₃₁	semidirect
675. #448	C₂²×C₃₁	semidirect
677. #447	C₂²×C₃₁	semidirect
678. #441	C₂²×C₃₁	semidirect
679. #440	C₂²×C₃₁	semidirect
680. C₄×Q₁₆	C₂²×C₃₁	semidirect
681. C₄×SD₁₆	C₂²×C₃₁	semidirect
682. #435	C₂²×C₃₁	semidirect
683. #435	C₂²×C₃₁	semidirect
684. C₈×D₄	C₂²×C₃₁	semidirect
685. C₈×D₄	C₂²×C₃₁	semidirect
686. #433	C₂²×C₃₁	semidirect
687. #419	C₂²×C₃₁	semidirect
688. #419	C₂²×C₃₁	semidirect
689. #416	C₂²×C₃₁	semidirect
690. #416	C₂²×C₃₁	semidirect
691. #416	C₂²×C₃₁	semidirect
692. #416	C₂²×C₃₁	semidirect
695. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
876. C₃₁	#61638	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×#3540	2
C₃₁×#3487	2
C₃₁×#3321	2
C₃₁×#3313	2
C₃₁×#3305	2
C₃₁×#3304	2
C₃₁×#3285	2
C₃₁×#3282	2
C₃₁×#3271	2
C₃₁×#3268	2
C₃₁×#3224	2
C₃₁×#3200	2
C₃₁×#3199	2
C₃₁×#3191	2
C₃₁×#3121	2
C₃₁×#3011	2
C₃₁×#3010	2
C₃₁×#3002	2
C₃₁×#2977	2
#61638	31

Subgroups — C31×#61638 #21518397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61638 #21518397