Subgroups — C₃₁×#61629 #21518388

Order 7936.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3188	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3012	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#447	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
24	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
25	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
26	C₃₁×#562	—	2	2	no	—
27	C₃₁×#554	C₂²	1	2	yes	complemented
28	C₃₁×#548	C₂²	1	2	yes	complemented
29	C₃₁×#547	C₂²	1	2	yes	complemented
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	—	2	1	no	—
32	C₃₁×#546	—	2	2	no	—
33	C₃₁×#546	C₂²	1	2	yes	—
34	C₃₁×#546	C₂²	1	2	yes	complemented
35	C₃₁×#546	C₂²	1	2	yes	complemented
36	D₄²×C₃₁	—	2	1	no	—
37	D₄²×C₃₁	—	2	1	no	—
38	D₄²×C₃₁	C₂²	1	2	yes	—
39	D₄²×C₃₁	C₂²	1	2	yes	complemented
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	C₂²	1	2	yes	complemented
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#538	—	2	1	no	—
44	C₃₁×#537	—	2	1	no	—
45	C₃₁×#537	C₂²	1	2	yes	complemented
46	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#534	—	2	2	no	—
49	C₃₁×#525	C₂²	1	1	yes	characteristic
50	C₃₁×#525	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃₁×#120	—	2	2	no	—
54	C₃₁×#518	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#496	C₂²	1	2	yes	complemented
56	C₃₁×#495	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#486	C₂²	1	2	yes	complemented
59	C₃₁×#485	C₂²	1	2	yes	complemented
60	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#481	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#480	C₂²	1	2	yes	complemented
67	C₃₁×#476	C₂²	1	2	yes	complemented
68	C₃₁×#474	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×#463	C₂²	1	2	yes	complemented
79	C₃₁×#463	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×#451	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#450	C₂²	1	2	yes	complemented
87	C₃₁×#450	C₂²	1	2	yes	complemented
88	C₃₁×#450	C₂²	1	2	yes	complemented
89	C₃₁×#450	C₂²	1	2	yes	complemented
90	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#450	C₂²	1	2	yes	complemented
92	C₃₁×#449	C₂²	1	2	yes	complemented
93	C₃₁×#449	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#447	C₂²	1	2	yes	—
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	complemented
100	C₃₁×#447	C₂²	1	2	yes	complemented
101	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#447	C₂²	1	2	yes	complemented
103	C₃₁×#442	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#417	C₂²	1	2	yes	complemented
113	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
114	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂⁵×C₃₁	—	2	1	no	—
120	C₃₁×H(5,𝔽₂)	—	4	4	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	2	no	—
123	C₂×#41×C₃₁	C₂³	1	2	yes	—
124	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×#41×C₃₁	C₂³	1	2	yes	complemented
127	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₃₁	—	2	1	no	—
129	C₂²×D₄×C₃₁	—	2	2	no	—
130	C₂²×D₄×C₃₁	—	2	1	no	—
131	C₂²×D₄×C₃₁	—	2	2	no	—
132	C₂²×D₄×C₃₁	—	2	2	no	—
133	C₂²×D₄×C₃₁	—	2	1	no	—
134	C₂²×D₄×C₃₁	—	2	1	no	—
135	C₂²×D₄×C₃₁	—	2	1	no	—
136	C₂²×D₄×C₃₁	—	4	4	no	—
137	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
145	C₃₁×#135	—	4	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	complemented
147	C₂×SD₁₆×C₃₁	—	4	4	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	complemented
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	complemented
154	C₂×D₈×C₃₁	—	4	4	no	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	complemented
160	C₂×M₁₆×C₃₁	C₂³	1	2	yes	complemented
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₂²×C₈×C₃₁	C₂³	1	2	yes	complemented
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	complemented
165	C₃₁×#127	—	2	1	no	—
166	C₃₁×#127	C₂³	1	2	yes	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	complemented
174	C₃₁×#123	—	2	1	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
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	D₄	1	1	yes	characteristic
191	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	complemented
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	D₄	1	1	yes	characteristic
211	C₃₁×#121	D₄	1	1	yes	characteristic
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#121	C₂³	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	complemented
219	C₃₁×#120	—	2	1	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₃₁×#120	—	2	2	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₃₁×#120	—	2	2	no	—
224	C₃₁×#120	—	2	2	no	—
225	C₃₁×#120	—	2	2	no	—
226	C₃₁×#120	—	2	2	no	—
227	C₃₁×#120	—	2	2	no	—
228	C₃₁×#120	—	2	2	no	—
229	C₃₁×#120	D₄	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	complemented
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
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	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	complemented
242	C₃₁×#117	C₂³	1	1	yes	characteristic
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	complemented
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
250	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
251	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
253	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
254	C₃₁×#107	C₂³	1	2	yes	complemented
255	C₃₁×#107	C₂³	1	2	yes	complemented
256	C₃₁×#106	C₂³	1	2	yes	complemented
257	C₃₁×#106	C₂³	1	2	yes	complemented
258	C₃₁×C₄⋊C₈	C₂³	1	2	yes	complemented
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	complemented
260	C₃₁×#103	C₂³	1	2	yes	complemented
261	C₃₁×#103	C₂³	1	2	yes	complemented
262	C₃₁×#103	C₂³	1	2	yes	complemented
263	C₃₁×#103	C₂³	1	2	yes	complemented
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	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	complemented
273	C₃₁×#102	C₂³	1	2	yes	complemented
274	C₃₁×#102	C₂³	1	2	yes	complemented
275	C₃₁×#102	C₂³	1	2	yes	complemented
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	complemented
283	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	complemented
284	C₃₁×#97	C₂³	1	2	yes	complemented
285	C₄×C₈×C₃₁	C₂³	1	2	yes	complemented
286	C₂⁴×C₃₁	—	2	1	no	—
287	C₂⁴×C₃₁	—	2	2	no	—
288	C₂⁴×C₃₁	—	2	2	no	—
289	C₂⁴×C₃₁	—	2	1	no	—
290	C₂⁴×C₃₁	—	2	1	no	—
291	C₂⁴×C₃₁	—	2	2	no	—
292	C₂⁴×C₃₁	—	4	4	no	—
293	C₂⁴×C₃₁	—	8	2	no	—
294	C₂⁴×C₃₁	—	8	2	no	—
295	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
296	#41×C₃₁	—	2	4	no	—
297	#41×C₃₁	—	4	2	no	—
298	#41×C₃₁	—	4	2	no	—
299	#41×C₃₁	—	4	2	no	—
300	#41×C₃₁	—	4	2	no	—
301	#41×C₃₁	—	4	2	no	—
302	#41×C₃₁	—	4	4	no	—
303	#41×C₃₁	—	8	4	no	—
304	C₂×Q₈×C₃₁	—	2	1	no	—
305	C₂×Q₈×C₃₁	—	2	2	no	—
306	C₂×Q₈×C₃₁	—	4	2	no	—
307	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
310	C₂×D₄×C₃₁	—	2	4	no	—
311	C₂×D₄×C₃₁	—	2	4	no	—
312	C₂×D₄×C₃₁	—	2	4	no	—
313	C₂×D₄×C₃₁	—	2	4	no	—
314	C₂×D₄×C₃₁	—	2	1	no	—
315	C₂×D₄×C₃₁	—	2	1	no	—
316	C₂×D₄×C₃₁	—	2	2	no	—
317	C₂×D₄×C₃₁	—	2	1	no	—
318	C₂×D₄×C₃₁	—	2	2	no	—
319	C₂×D₄×C₃₁	—	2	2	no	—
320	C₂×D₄×C₃₁	—	2	2	no	—
321	C₂×D₄×C₃₁	—	2	2	no	—
322	C₂×D₄×C₃₁	—	2	2	no	—
323	C₂×D₄×C₃₁	—	2	2	no	—
324	C₂×D₄×C₃₁	—	2	1	no	—
325	C₂×D₄×C₃₁	—	2	2	no	—
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	4	2	no	—
333	C₂×D₄×C₃₁	—	4	2	no	—
334	C₂×D₄×C₃₁	—	4	2	no	—
335	C₂×D₄×C₃₁	—	4	2	no	—
336	C₂×D₄×C₃₁	—	4	2	no	—
337	C₂×D₄×C₃₁	—	4	4	no	—
338	C₂×D₄×C₃₁	—	4	4	no	—
339	C₂×D₄×C₃₁	—	4	4	no	—
340	C₂×D₄×C₃₁	—	4	4	no	—
341	C₂×D₄×C₃₁	—	4	8	no	—
342	C₂×D₄×C₃₁	—	8	4	no	—
343	C₂×D₄×C₃₁	—	8	4	no	—
344	C₂×D₄×C₃₁	—	8	2	no	—
345	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	4	2	no	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
371	Q₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	2	4	no	—
373	SD₁₆×C₃₁	—	2	4	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	SD₁₆×C₃₁	—	4	2	no	—
377	SD₁₆×C₃₁	—	4	2	no	—
378	D₈×C₃₁	—	2	4	no	—
379	D₈×C₃₁	—	2	4	no	—
380	D₈×C₃₁	—	4	2	no	—
381	D₈×C₃₁	—	4	2	no	—
382	D₈×C₃₁	—	4	2	no	—
383	M₁₆×C₃₁	—	4	2	no	—
384	C₂×C₈×C₃₁	—	4	2	no	—
385	C₂×C₈×C₃₁	—	4	2	no	—
386	C₂×C₈×C₃₁	—	4	2	no	—
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
390	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	C₂⁴	1	2	yes	—
437	#61629	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂³×C₃₁	—	2	4	no	—
439	C₂³×C₃₁	—	2	2	no	—
440	C₂³×C₃₁	—	2	2	no	—
441	C₂³×C₃₁	—	2	2	no	—
442	C₂³×C₃₁	—	2	2	no	—
443	C₂³×C₃₁	—	2	2	no	—
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	4	1	no	—
446	C₂³×C₃₁	—	4	4	no	—
447	C₂³×C₃₁	—	4	4	no	—
448	C₂³×C₃₁	—	4	4	no	—
449	C₂³×C₃₁	—	4	2	no	—
450	C₂³×C₃₁	—	4	4	no	—
451	C₂³×C₃₁	—	4	4	no	—
452	C₂³×C₃₁	—	4	2	no	—
453	C₂³×C₃₁	—	8	2	no	—
454	C₂³×C₃₁	—	8	2	no	—
455	C₂³×C₃₁	—	8	1	no	—
456	C₂³×C₃₁	—	8	1	no	—
457	C₂³×C₃₁	—	8	1	no	—
458	C₂³×C₃₁	—	8	1	no	—
459	C₂³×C₃₁	—	8	1	no	—
460	C₂³×C₃₁	—	8	1	no	—
461	C₂³×C₃₁	—	8	2	no	—
462	C₂³×C₃₁	—	8	2	no	—
463	C₂³×C₃₁	—	8	16	no	—
464	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
468	Q₈×C₃₁	—	2	2	no	—
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	4	1	no	—
472	Q₈×C₃₁	—	8	1	no	—
473	Q₈×C₃₁	—	8	2	no	—
474	D₄×C₃₁	—	2	4	no	—
475	D₄×C₃₁	—	2	4	no	—
476	D₄×C₃₁	—	2	4	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	2	no	—
483	D₄×C₃₁	—	4	1	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	4	4	no	—
486	D₄×C₃₁	—	4	4	no	—
487	D₄×C₃₁	—	4	4	no	—
488	D₄×C₃₁	—	4	2	no	—
489	D₄×C₃₁	—	4	4	no	—
490	D₄×C₃₁	—	4	2	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	4	4	no	—
493	D₄×C₃₁	—	4	2	no	—
494	D₄×C₃₁	—	8	1	no	—
495	D₄×C₃₁	—	8	2	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	H(5,𝔽₂)	1	4	yes	—
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	2	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	2	no	—
511	C₂×C₄×C₃₁	—	2	2	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	2	no	—
514	C₂×C₄×C₃₁	—	4	1	no	—
515	C₂×C₄×C₃₁	—	4	1	no	—
516	C₂×C₄×C₃₁	—	4	1	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	—	8	1	no	—
525	C₂×C₄×C₃₁	—	8	1	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
534	C₈×C₃₁	—	2	2	no	—
535	C₈×C₃₁	—	2	2	no	—
536	C₈×C₃₁	—	2	2	no	—
537	C₈×C₃₁	—	2	2	no	—
538	#3536	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3484	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3314	C₂×C₃₁	1	2	yes	complemented
541	#3306	C₂×C₃₁	1	2	yes	complemented
542	#3295	C₂×C₃₁	1	2	yes	complemented
543	#3294	C₂×C₃₁	1	2	yes	complemented
544	#3282	C₂×C₃₁	1	2	yes	complemented
545	#3280	C₂×C₃₁	1	2	yes	complemented
546	#3265	C₂×C₃₁	1	2	yes	complemented
547	#3264	C₂×C₃₁	1	2	yes	complemented
548	#3224	C₂×C₃₁	1	2	yes	complemented
549	#3198	C₂×C₃₁	1	2	yes	complemented
550	#3190	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3188	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3118	C₂×C₃₁	1	2	yes	complemented
553	#3012	C₂×C₃₁	1	2	yes	complemented
554	C₂×#450	C₂×C₃₁	1	1	yes	characteristic, complemented
555	C₂×#447	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
557	C₂²×C₃₁	—	2	1	no	—
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	1	no	—
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	4	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	2	1	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	4	4	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	1	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	1	no	—
578	C₂²×C₃₁	—	4	2	no	—
579	C₂²×C₃₁	—	4	2	no	—
580	C₂²×C₃₁	—	8	8	no	—
581	C₂²×C₃₁	—	8	8	no	—
582	C₂²×C₃₁	—	8	4	no	—
583	C₂²×C₃₁	—	8	4	no	—
584	C₂²×C₃₁	—	16	2	no	—
585	C₂²×C₃₁	—	16	4	no	—
586	C₂²×C₃₁	#576	1	2	yes	—
587	C₂²×C₃₁	#577	1	2	yes	—
588	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	2	1	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	2	no	—
594	C₄×C₃₁	—	2	2	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	2	no	—
597	C₄×C₃₁	—	4	2	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	—	4	2	no	—
600	C₄×C₃₁	—	4	1	no	—
601	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
602	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
604	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
605	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
606	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
607	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
608	#562	—	2	2	no	—
609	#554	C₂²×C₃₁	1	2	yes	complemented
610	#548	C₂²×C₃₁	1	2	yes	complemented
611	#547	C₂²×C₃₁	1	2	yes	complemented
612	#546	—	2	1	no	—
613	#546	—	2	1	no	—
614	#546	—	2	2	no	—
615	#546	C₂²×C₃₁	1	2	yes	—
616	#546	C₂²×C₃₁	1	2	yes	complemented
617	#546	C₂²×C₃₁	1	2	yes	complemented
618	D₄²	—	2	1	no	—
619	D₄²	—	2	1	no	—
620	D₄²	C₂²×C₃₁	1	2	yes	—
621	D₄²	C₂²×C₃₁	1	2	yes	complemented
622	#543	—	2	1	no	—
623	#542	C₂²×C₃₁	1	2	yes	complemented
624	#539	—	2	1	no	—
625	#538	—	2	1	no	—
626	#537	—	2	1	no	—
627	#537	C₂²×C₃₁	1	2	yes	complemented
628	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#534	—	2	2	no	—
631	#525	C₂²×C₃₁	1	1	yes	characteristic
632	#525	C₂²×C₃₁	1	1	yes	characteristic
633	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	C₂×#120	—	2	2	no	—
636	#518	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#496	C₂²×C₃₁	1	2	yes	complemented
638	#495	C₂²×C₃₁	1	2	yes	complemented
639	#489	C₂²×C₃₁	1	2	yes	complemented
640	#486	C₂²×C₃₁	1	2	yes	complemented
641	#485	C₂²×C₃₁	1	2	yes	complemented
642	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#482	C₂²×C₃₁	1	2	yes	complemented
645	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#481	C₂²×C₃₁	1	2	yes	complemented
647	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#480	C₂²×C₃₁	1	2	yes	complemented
649	#476	C₂²×C₃₁	1	2	yes	complemented
650	#474	C₂²×C₃₁	1	2	yes	complemented
651	#469	C₂²×C₃₁	1	2	yes	complemented
652	#468	C₂²×C₃₁	1	2	yes	complemented
653	#467	C₂²×C₃₁	1	2	yes	complemented
654	#466	C₂²×C₃₁	1	2	yes	complemented
655	#466	C₂²×C₃₁	1	2	yes	complemented
656	#465	C₂²×C₃₁	1	2	yes	complemented
657	#465	C₂²×C₃₁	1	2	yes	complemented
658	#465	C₂²×C₃₁	1	2	yes	complemented
659	#464	C₂²×C₃₁	1	2	yes	complemented
660	#463	C₂²×C₃₁	1	2	yes	complemented
661	#463	C₂²×C₃₁	1	2	yes	complemented
662	#463	C₂²×C₃₁	1	2	yes	complemented
663	#460	C₂²×C₃₁	1	2	yes	complemented
664	#459	C₂²×C₃₁	1	2	yes	complemented
665	#452	C₂²×C₃₁	1	2	yes	complemented
666	#452	C₂²×C₃₁	1	2	yes	complemented
667	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#450	C₂²×C₃₁	1	2	yes	complemented
669	#450	C₂²×C₃₁	1	2	yes	complemented
670	#450	C₂²×C₃₁	1	2	yes	complemented
671	#450	C₂²×C₃₁	1	2	yes	complemented
672	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#450	C₂²×C₃₁	1	2	yes	complemented
674	#449	C₂²×C₃₁	1	2	yes	complemented
675	#449	C₂²×C₃₁	1	2	yes	complemented
676	#449	C₂²×C₃₁	1	2	yes	complemented
677	#449	C₂²×C₃₁	1	2	yes	complemented
678	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#447	C₂²×C₃₁	1	2	yes	—
680	#447	C₂²×C₃₁	1	2	yes	complemented
681	#447	C₂²×C₃₁	1	2	yes	complemented
682	#447	C₂²×C₃₁	1	2	yes	complemented
683	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#447	C₂²×C₃₁	1	2	yes	complemented
685	#442	C₂²×C₃₁	1	2	yes	complemented
686	#440	C₂²×C₃₁	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
688	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
689	#435	C₂²×C₃₁	1	2	yes	complemented
690	#435	C₂²×C₃₁	1	2	yes	complemented
691	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
692	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
693	#433	C₂²×C₃₁	1	2	yes	complemented
694	#417	C₂²×C₃₁	1	2	yes	complemented
695	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
697	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
698	#408	C₂²×C₃₁	1	2	yes	complemented
699	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	C₂×C₃₁	—	2	2	no	—
702	C₂×C₃₁	—	2	2	no	—
703	C₂×C₃₁	—	4	1	no	—
704	C₂×C₃₁	—	4	2	no	—
705	C₂×C₃₁	—	4	4	no	—
706	C₂×C₃₁	—	8	2	no	—
707	C₂×C₃₁	—	8	2	no	—
708	C₂×C₃₁	—	8	1	no	—
709	C₂×C₃₁	#3484	1	1	yes	characteristic
710	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
711	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
712	C₂⁵	—	2	1	no	—
713	H(5,𝔽₂)	—	4	4	no	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	2	no	—
716	C₂×#41	C₂³×C₃₁	1	2	yes	—
717	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×#41	C₂³×C₃₁	1	2	yes	complemented
720	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	—	2	2	no	—
723	C₂²×D₄	—	2	1	no	—
724	C₂²×D₄	—	2	2	no	—
725	C₂²×D₄	—	2	2	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	—	4	4	no	—
730	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
732	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
733	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
734	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
737	AGL(1,ℤ/8)	—	4	4	no	—
738	#135	—	4	4	no	—
739	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	complemented
740	C₂×SD₁₆	—	4	4	no	—
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×SD₁₆	C₂³×C₃₁	1	2	yes	complemented
746	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	complemented
747	C₂×D₈	—	4	4	no	—
748	C₂×D₈	C₂³×C₃₁	1	2	yes	—
749	C₂×D₈	C₂³×C₃₁	1	2	yes	—
750	C₂×D₈	C₂³×C₃₁	1	2	yes	—
751	C₂×D₈	C₂³×C₃₁	1	2	yes	—
752	C₂×D₈	C₂³×C₃₁	1	2	yes	complemented
753	C₂×M₁₆	C₂³×C₃₁	1	2	yes	complemented
754	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
755	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
756	C₂²×C₈	C₂³×C₃₁	1	2	yes	complemented
757	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
758	#127	—	2	1	no	—
759	#127	C₂³×C₃₁	1	2	yes	—
760	#126	—	2	2	no	—
761	#125	—	2	2	no	—
762	#124	—	2	1	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	C₂³×C₃₁	1	2	yes	—
766	#124	C₂³×C₃₁	1	2	yes	complemented
767	#123	—	2	1	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	D₄×C₃₁	1	2	yes	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
784	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	complemented
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	D₄×C₃₁	1	1	yes	characteristic
804	#121	D₄×C₃₁	1	1	yes	characteristic
805	#121	C₂³×C₃₁	1	2	yes	—
806	#121	C₂³×C₃₁	1	2	yes	—
807	#121	C₂³×C₃₁	1	1	yes	characteristic
808	#121	C₂³×C₃₁	1	1	yes	characteristic
809	#121	C₂³×C₃₁	1	2	yes	—
810	#121	C₂³×C₃₁	1	2	yes	—
811	#121	C₂³×C₃₁	1	2	yes	complemented
812	#120	—	2	1	no	—
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	D₄×C₃₁	1	2	yes	—
823	C₄×Q₈	C₂³×C₃₁	1	2	yes	complemented
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	C₂³×C₃₁	1	2	yes	—
832	C₄×D₄	C₂³×C₃₁	1	2	yes	—
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	complemented
835	#117	C₂³×C₃₁	1	1	yes	characteristic
836	#117	C₂³×C₃₁	1	1	yes	characteristic
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	complemented
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	1	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	#107	C₂³×C₃₁	1	2	yes	complemented
848	#107	C₂³×C₃₁	1	2	yes	complemented
849	#106	C₂³×C₃₁	1	2	yes	complemented
850	#106	C₂³×C₃₁	1	2	yes	complemented
851	C₄⋊C₈	C₂³×C₃₁	1	2	yes	complemented
852	C₄⋊C₈	C₂³×C₃₁	1	2	yes	complemented
853	#103	C₂³×C₃₁	1	2	yes	complemented
854	#103	C₂³×C₃₁	1	2	yes	complemented
855	#103	C₂³×C₃₁	1	2	yes	complemented
856	#103	C₂³×C₃₁	1	2	yes	complemented
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	2	yes	—
859	#102	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	complemented
866	#102	C₂³×C₃₁	1	2	yes	complemented
867	#102	C₂³×C₃₁	1	2	yes	complemented
868	#102	C₂³×C₃₁	1	2	yes	complemented
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	complemented
876	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	complemented
877	#97	C₂³×C₃₁	1	2	yes	complemented
878	C₄×C₈	C₂³×C₃₁	1	2	yes	complemented
879	C₃₁	#61629	1	1	yes	characteristic, direct product factor, Sylow
880	C₂⁴	—	2	1	no	—
881	C₂⁴	—	2	2	no	—
882	C₂⁴	—	2	2	no	—
883	C₂⁴	—	2	1	no	—
884	C₂⁴	—	2	1	no	—
885	C₂⁴	—	2	2	no	—
886	C₂⁴	—	4	4	no	—
887	C₂⁴	—	8	2	no	—
888	C₂⁴	—	8	2	no	—
889	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
890	#41	—	2	4	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	2	no	—
896	#41	—	4	4	no	—
897	#41	—	8	4	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	4	2	no	—
901	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	4	no	—
906	C₂×D₄	—	2	4	no	—
907	C₂×D₄	—	2	4	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	4	no	—
932	C₂×D₄	—	4	4	no	—
933	C₂×D₄	—	4	4	no	—
934	C₂×D₄	—	4	4	no	—
935	C₂×D₄	—	4	8	no	—
936	C₂×D₄	—	8	4	no	—
937	C₂×D₄	—	8	4	no	—
938	C₂×D₄	—	8	2	no	—
939	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	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	2	no	—
958	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×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	Q₁₆	—	4	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	2	4	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	D₈	—	2	4	no	—
973	D₈	—	2	4	no	—
974	D₈	—	4	2	no	—
975	D₈	—	4	2	no	—
976	D₈	—	4	2	no	—
977	M₁₆	—	4	2	no	—
978	C₂×C₈	—	4	2	no	—
979	C₂×C₈	—	4	2	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
982	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
983	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
984	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	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	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	C₂⁴×C₃₁	1	2	yes	—
1031	C₂³	—	2	4	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	4	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	4	4	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	4	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	1	no	—
1051	C₂³	—	8	1	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	8	1	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	16	no	—
1057	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1058	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1059	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1060	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	2	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	8	1	no	—
1066	Q₈	—	8	2	no	—
1067	D₄	—	2	4	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	4	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
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	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1126	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₈	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	4	4	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	8	8	no	—
1155	C₂²	—	8	8	no	—
1156	C₂²	—	8	4	no	—
1157	C₂²	—	8	4	no	—
1158	C₂²	—	16	2	no	—
1159	C₂²	—	16	4	no	—
1160	C₂²	C₃₁×#576	1	2	yes	—
1161	C₂²	C₃₁×#577	1	2	yes	—
1162	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1176	C₂	—	2	2	no	—
1177	C₂	—	2	2	no	—
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	4	4	no	—
1181	C₂	—	8	2	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	2	no	—
1184	C₂	C₃₁×#3484	1	1	yes	characteristic
1185	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1186	C₂	C₂×C₃₁×#577	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3536	C₂	semidirect
2. C₃₁×#3484	C₂	semidirect
3. C₃₁×#3314	C₂	semidirect
4. C₃₁×#3306	C₂	semidirect
5. C₃₁×#3295	C₂	semidirect
6. C₃₁×#3294	C₂	semidirect
7. C₃₁×#3282	C₂	semidirect
8. C₃₁×#3280	C₂	semidirect
9. C₃₁×#3265	C₂	semidirect
10. C₃₁×#3264	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3198	C₂	semidirect
13. C₃₁×#3190	C₂	semidirect
14. C₃₁×#3188	C₂	semidirect
15. C₃₁×#3118	C₂	semidirect
16. C₃₁×#3012	C₂	semidirect
17. C₂×C₃₁×#450	C₂	semidirect
18. C₂×C₃₁×#447	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
20. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
22. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃₁×#135	C₂²	semidirect
24. C₂²×SD₁₆×C₃₁	C₂²	semidirect
25. C₂²×D₈×C₃₁	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
28. C₃₁×#548	C₂²	semidirect
29. C₃₁×#547	C₂²	semidirect
34. C₃₁×#546	C₂²	semidirect
35. C₃₁×#546	C₂²	semidirect
39. D₄²×C₃₁	C₂²	semidirect
41. C₃₁×#542	C₂²	semidirect
45. C₃₁×#537	C₂²	semidirect
46. C₃₁×#535	C₂²	semidirect
47. C₃₁×#535	C₂²	semidirect
51. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₃₁×#121	C₂²	semidirect
54. C₃₁×#518	C₂²	semidirect
55. C₃₁×#496	C₂²	semidirect
56. C₃₁×#495	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#486	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
60. C₃₁×#484	C₂²	semidirect
61. C₃₁×#483	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
66. C₃₁×#480	C₂²	semidirect
67. C₃₁×#476	C₂²	semidirect
68. C₃₁×#474	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×#463	C₂²	semidirect
79. C₃₁×#463	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×#451	C₂²	semidirect
86. C₃₁×#450	C₂²	semidirect
87. C₃₁×#450	C₂²	semidirect
88. C₃₁×#450	C₂²	semidirect
89. C₃₁×#450	C₂²	semidirect
90. C₃₁×#450	C₂²	semidirect
91. C₃₁×#450	C₂²	semidirect
92. C₃₁×#449	C₂²	semidirect
93. C₃₁×#449	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#448	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#447	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#447	C₂²	semidirect
102. C₃₁×#447	C₂²	semidirect
103. C₃₁×#442	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₄×SD₁₆×C₃₁	C₂²	semidirect
106. C₄×D₈×C₃₁	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₈×D₄×C₃₁	C₂²	semidirect
110. C₈×D₄×C₃₁	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
112. C₃₁×#417	C₂²	semidirect
113. C₂×C₃₁×#102	C₂²	semidirect
114. C₂×C₃₁×#102	C₂²	semidirect
115. C₂×C₃₁×#102	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
117. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
118. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
126. C₂×#41×C₃₁	C₂³	semidirect
146. C₂×Q₁₆×C₃₁	C₂³	semidirect
152. C₂×SD₁₆×C₃₁	C₂³	semidirect
153. C₂×SD₁₆×C₃₁	C₂³	semidirect
159. C₂×D₈×C₃₁	C₂³	semidirect
160. C₂×M₁₆×C₃₁	C₂³	semidirect
163. C₂²×C₈×C₃₁	C₂³	semidirect
164. C₃₁×C₄⋊Q₈	C₂³	semidirect
173. C₃₁×#124	C₂³	semidirect
196. C₃₁×C₂²⋊Q₈	C₂³	semidirect
218. C₃₁×#121	C₂³	semidirect
230. C₄×Q₈×C₃₁	C₂³	semidirect
241. C₄×D₄×C₃₁	C₂³	semidirect
247. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
254. C₃₁×#107	C₂³	semidirect
255. C₃₁×#107	C₂³	semidirect
256. C₃₁×#106	C₂³	semidirect
257. C₃₁×#106	C₂³	semidirect
258. C₃₁×C₄⋊C₈	C₂³	semidirect
259. C₃₁×C₄⋊C₈	C₂³	semidirect
260. C₃₁×#103	C₂³	semidirect
261. C₃₁×#103	C₂³	semidirect
262. C₃₁×#103	C₂³	semidirect
263. C₃₁×#103	C₂³	semidirect
272. C₃₁×#102	C₂³	semidirect
273. C₃₁×#102	C₂³	semidirect
274. C₃₁×#102	C₂³	semidirect
275. C₃₁×#102	C₂³	semidirect
282. C₃₁×C₂²⋊C₈	C₂³	semidirect
283. C₃₁×C₂²⋊C₈	C₂³	semidirect
284. C₃₁×#97	C₂³	semidirect
285. C₄×C₈×C₃₁	C₂³	semidirect
437. #61629	C₃₁	direct (N × H)
538. #3536	C₂×C₃₁	semidirect
539. #3484	C₂×C₃₁	semidirect
540. #3314	C₂×C₃₁	semidirect
541. #3306	C₂×C₃₁	semidirect
542. #3295	C₂×C₃₁	semidirect
543. #3294	C₂×C₃₁	semidirect
544. #3282	C₂×C₃₁	semidirect
545. #3280	C₂×C₃₁	semidirect
546. #3265	C₂×C₃₁	semidirect
547. #3264	C₂×C₃₁	semidirect
548. #3224	C₂×C₃₁	semidirect
549. #3198	C₂×C₃₁	semidirect
550. #3190	C₂×C₃₁	semidirect
551. #3188	C₂×C₃₁	semidirect
552. #3118	C₂×C₃₁	semidirect
553. #3012	C₂×C₃₁	semidirect
554. C₂×#450	C₂×C₃₁	semidirect
555. C₂×#447	C₂×C₃₁	semidirect
556. #2977	C₂×C₃₁	semidirect
602. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
604. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
605. C₂×#135	C₂²×C₃₁	semidirect
606. C₂²×SD₁₆	C₂²×C₃₁	semidirect
607. C₂²×D₈	C₂²×C₃₁	semidirect
609. #554	C₂²×C₃₁	semidirect
610. #548	C₂²×C₃₁	semidirect
611. #547	C₂²×C₃₁	semidirect
616. #546	C₂²×C₃₁	semidirect
617. #546	C₂²×C₃₁	semidirect
621. D₄²	C₂²×C₃₁	semidirect
623. #542	C₂²×C₃₁	semidirect
627. #537	C₂²×C₃₁	semidirect
628. #535	C₂²×C₃₁	semidirect
629. #535	C₂²×C₃₁	semidirect
633. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
634. C₂×#121	C₂²×C₃₁	semidirect
636. #518	C₂²×C₃₁	semidirect
637. #496	C₂²×C₃₁	semidirect
638. #495	C₂²×C₃₁	semidirect
639. #489	C₂²×C₃₁	semidirect
640. #486	C₂²×C₃₁	semidirect
641. #485	C₂²×C₃₁	semidirect
642. #484	C₂²×C₃₁	semidirect
643. #483	C₂²×C₃₁	semidirect
644. #482	C₂²×C₃₁	semidirect
645. #481	C₂²×C₃₁	semidirect
646. #481	C₂²×C₃₁	semidirect
647. #480	C₂²×C₃₁	semidirect
648. #480	C₂²×C₃₁	semidirect
649. #476	C₂²×C₃₁	semidirect
650. #474	C₂²×C₃₁	semidirect
651. #469	C₂²×C₃₁	semidirect
652. #468	C₂²×C₃₁	semidirect
653. #467	C₂²×C₃₁	semidirect
654. #466	C₂²×C₃₁	semidirect
655. #466	C₂²×C₃₁	semidirect
656. #465	C₂²×C₃₁	semidirect
657. #465	C₂²×C₃₁	semidirect
658. #465	C₂²×C₃₁	semidirect
659. #464	C₂²×C₃₁	semidirect
660. #463	C₂²×C₃₁	semidirect
661. #463	C₂²×C₃₁	semidirect
662. #463	C₂²×C₃₁	semidirect
663. #460	C₂²×C₃₁	semidirect
664. #459	C₂²×C₃₁	semidirect
665. #452	C₂²×C₃₁	semidirect
666. #452	C₂²×C₃₁	semidirect
667. #451	C₂²×C₃₁	semidirect
668. #450	C₂²×C₃₁	semidirect
669. #450	C₂²×C₃₁	semidirect
670. #450	C₂²×C₃₁	semidirect
671. #450	C₂²×C₃₁	semidirect
672. #450	C₂²×C₃₁	semidirect
673. #450	C₂²×C₃₁	semidirect
674. #449	C₂²×C₃₁	semidirect
675. #449	C₂²×C₃₁	semidirect
676. #449	C₂²×C₃₁	semidirect
677. #449	C₂²×C₃₁	semidirect
678. #448	C₂²×C₃₁	semidirect
680. #447	C₂²×C₃₁	semidirect
681. #447	C₂²×C₃₁	semidirect
682. #447	C₂²×C₃₁	semidirect
683. #447	C₂²×C₃₁	semidirect
684. #447	C₂²×C₃₁	semidirect
685. #442	C₂²×C₃₁	semidirect
686. #440	C₂²×C₃₁	semidirect
687. C₄×SD₁₆	C₂²×C₃₁	semidirect
688. C₄×D₈	C₂²×C₃₁	semidirect
689. #435	C₂²×C₃₁	semidirect
690. #435	C₂²×C₃₁	semidirect
691. C₈×D₄	C₂²×C₃₁	semidirect
692. C₈×D₄	C₂²×C₃₁	semidirect
693. #433	C₂²×C₃₁	semidirect
694. #417	C₂²×C₃₁	semidirect
695. C₂×#102	C₂²×C₃₁	semidirect
696. C₂×#102	C₂²×C₃₁	semidirect
697. C₂×#102	C₂²×C₃₁	semidirect
698. #408	C₂²×C₃₁	semidirect
699. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
700. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
719. C₂×#41	C₂³×C₃₁	semidirect
739. C₂×Q₁₆	C₂³×C₃₁	semidirect
745. C₂×SD₁₆	C₂³×C₃₁	semidirect
746. C₂×SD₁₆	C₂³×C₃₁	semidirect
752. C₂×D₈	C₂³×C₃₁	semidirect
753. C₂×M₁₆	C₂³×C₃₁	semidirect
756. C₂²×C₈	C₂³×C₃₁	semidirect
757. C₄⋊Q₈	C₂³×C₃₁	semidirect
766. #124	C₂³×C₃₁	semidirect
789. C₂²⋊Q₈	C₂³×C₃₁	semidirect
811. #121	C₂³×C₃₁	semidirect
823. C₄×Q₈	C₂³×C₃₁	semidirect
834. C₄×D₄	C₂³×C₃₁	semidirect
840. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
847. #107	C₂³×C₃₁	semidirect
848. #107	C₂³×C₃₁	semidirect
849. #106	C₂³×C₃₁	semidirect
850. #106	C₂³×C₃₁	semidirect
851. C₄⋊C₈	C₂³×C₃₁	semidirect
852. C₄⋊C₈	C₂³×C₃₁	semidirect
853. #103	C₂³×C₃₁	semidirect
854. #103	C₂³×C₃₁	semidirect
855. #103	C₂³×C₃₁	semidirect
856. #103	C₂³×C₃₁	semidirect
865. #102	C₂³×C₃₁	semidirect
866. #102	C₂³×C₃₁	semidirect
867. #102	C₂³×C₃₁	semidirect
868. #102	C₂³×C₃₁	semidirect
875. C₂²⋊C₈	C₂³×C₃₁	semidirect
876. C₂²⋊C₈	C₂³×C₃₁	semidirect
877. #97	C₂³×C₃₁	semidirect
878. C₄×C₈	C₂³×C₃₁	semidirect
879. C₃₁	#61629	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×#3536	2
C₃₁×#3484	2
C₃₁×#3314	2
C₃₁×#3306	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3282	2
C₃₁×#3280	2
C₃₁×#3265	2
C₃₁×#3264	2
C₃₁×#3224	2
C₃₁×#3198	2
C₃₁×#3190	2
C₃₁×#3188	2
C₃₁×#3118	2
C₃₁×#3012	2
C₂×C₃₁×#450	2
C₂×C₃₁×#447	2
C₃₁×#2977	2
#61629	31

Subgroups — C31×#61629 #21518388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61629 #21518388