Subgroups — C₃₁×#61451 #21518210

Order 7936.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3109	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#442	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₃₁	—	2	1	no	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#547	C₂²	1	1	yes	characteristic
37	C₃₁×#547	C₂²	1	2	yes	complemented
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	2	no	—
41	C₃₁×#546	C₂²	1	2	yes	complemented
42	D₄²×C₃₁	C₂²	1	1	yes	characteristic
43	D₄²×C₃₁	C₂²	1	2	yes	complemented
44	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#532	C₂²	1	2	yes	complemented
46	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#529	—	2	1	no	—
49	C₃₁×#529	C₂²	1	2	yes	complemented
50	C₃₁×#525	—	2	2	no	—
51	C₃₁×#525	—	2	2	no	—
52	C₃₁×#525	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₃₁	—	2	1	no	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#490	C₂²	1	2	yes	complemented
64	C₃₁×#489	C₂²	1	2	yes	complemented
65	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#483	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#481	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#478	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#469	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	complemented
84	C₃₁×#466	C₂²	1	2	yes	complemented
85	C₃₁×#465	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#459	C₂²	1	1	yes	characteristic
91	C₃₁×#459	C₂²	1	2	yes	complemented
92	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#459	C₂²	1	2	yes	complemented
94	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#450	C₂²	1	2	yes	complemented
96	C₃₁×#449	C₂²	1	2	yes	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×#446	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	1	yes	characteristic
105	C₃₁×#442	C₂²	1	2	yes	complemented
106	C₃₁×#442	C₂²	1	2	yes	complemented
107	C₃₁×#442	C₂²	1	1	yes	characteristic, complemented
108	C₃₁×#442	C₂²	1	2	yes	complemented
109	C₃₁×#442	C₂²	1	2	yes	complemented
110	C₃₁×#442	C₂²	1	2	yes	complemented
111	C₃₁×#442	C₂²	1	2	yes	complemented
112	C₃₁×#442	C₂²	1	2	yes	complemented
113	C₃₁×#442	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#440	C₂²	1	2	yes	complemented
116	C₃₁×#440	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#435	C₂²	1	2	yes	complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#432	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
129	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	2	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	4	8	no	—
142	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	—	2	1	no	—
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	—	2	2	no	—
148	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
149	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₃₁	—	2	2	no	—
152	C₂³×C₄×C₃₁	—	2	1	no	—
153	C₂³×C₄×C₃₁	—	2	2	no	—
154	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
155	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	—	2	8	no	—
159	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
169	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
170	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×#127	C₂³	1	1	yes	characteristic
174	C₃₁×#127	C₂³	1	2	yes	—
175	C₃₁×#127	C₂³	1	1	yes	characteristic
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	—	2	2	no	—
217	C₃₁×#120	—	2	2	no	—
218	C₃₁×#120	—	2	2	no	—
219	C₃₁×#120	—	2	2	no	—
220	C₄×Q₈×C₃₁	D₄	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×D₄×C₃₁	—	2	1	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
240	C₄×D₄×C₃₁	D₄	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	D₄	1	2	yes	—
258	C₃₁×#117	D₄	1	1	yes	characteristic
259	C₃₁×#117	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
270	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	1	yes	characteristic
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₃₁×#97	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₃₁	—	2	2	no	—
316	C₂⁴×C₃₁	—	2	1	no	—
317	C₂⁴×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	2	4	no	—
319	#41×C₃₁	—	2	2	no	—
320	#41×C₃₁	—	4	1	no	—
321	#41×C₃₁	—	4	8	no	—
322	#41×C₃₁	—	4	4	no	—
323	#41×C₃₁	—	4	8	no	—
324	#41×C₃₁	—	4	4	no	—
325	#41×C₃₁	—	4	4	no	—
326	#41×C₃₁	—	8	2	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	2	1	no	—
329	C₂×Q₈×C₃₁	—	2	1	no	—
330	C₂×Q₈×C₃₁	—	4	4	no	—
331	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₃₁	—	2	4	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	4	no	—
336	C₂×D₄×C₃₁	—	2	1	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	—	2	2	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	2	2	no	—
349	C₂×D₄×C₃₁	—	2	1	no	—
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	4	2	no	—
352	C₂×D₄×C₃₁	—	4	2	no	—
353	C₂×D₄×C₃₁	—	4	1	no	—
354	C₂×D₄×C₃₁	—	4	8	no	—
355	C₂×D₄×C₃₁	—	4	4	no	—
356	C₂×D₄×C₃₁	—	4	4	no	—
357	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
360	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
361	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	1	no	—
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	2	no	—
371	C₂²×C₄×C₃₁	—	2	1	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	1	no	—
378	C₂²×C₄×C₃₁	—	2	2	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	4	8	no	—
381	C₂²×C₄×C₃₁	—	4	4	no	—
382	C₂²×C₄×C₃₁	—	8	4	no	—
383	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
389	SD₁₆×C₃₁	—	2	2	no	—
390	SD₁₆×C₃₁	—	2	2	no	—
391	SD₁₆×C₃₁	—	4	2	no	—
392	D₈×C₃₁	—	2	4	no	—
393	D₈×C₃₁	—	2	4	no	—
394	D₈×C₃₁	—	2	2	no	—
395	D₈×C₃₁	—	2	4	no	—
396	D₈×C₃₁	—	4	2	no	—
397	D₈×C₃₁	—	4	2	no	—
398	D₈×C₃₁	#41	1	4	yes	complemented
399	M₁₆×C₃₁	—	2	2	no	—
400	M₁₆×C₃₁	—	4	1	no	—
401	C₂×C₈×C₃₁	—	2	4	no	—
402	C₂×C₈×C₃₁	—	4	2	no	—
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
407	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	—	2	1	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	1	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	1	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	1	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	2	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	—	2	1	no	—
456	C₄²×C₃₁	—	2	1	no	—
457	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₃₁	C₂×D₄	1	2	yes	—
460	C₄²×C₃₁	C₂×D₄	1	2	yes	—
461	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
462	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
463	C₄²×C₃₁	C₂⁴	1	2	yes	—
464	#61451	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂³×C₃₁	—	2	1	no	—
466	C₂³×C₃₁	—	2	1	no	—
467	C₂³×C₃₁	—	2	2	no	—
468	C₂³×C₃₁	—	2	2	no	—
469	C₂³×C₃₁	—	2	1	no	—
470	C₂³×C₃₁	—	4	4	no	—
471	C₂³×C₃₁	—	4	4	no	—
472	C₂³×C₃₁	—	4	2	no	—
473	C₂³×C₃₁	—	4	2	no	—
474	C₂³×C₃₁	—	4	4	no	—
475	C₂³×C₃₁	—	4	4	no	—
476	C₂³×C₃₁	—	8	2	no	—
477	C₂³×C₃₁	—	8	2	no	—
478	C₂³×C₃₁	—	8	1	no	—
479	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
480	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
481	Q₈×C₃₁	—	2	2	no	—
482	Q₈×C₃₁	—	2	1	no	—
483	Q₈×C₃₁	—	2	1	no	—
484	Q₈×C₃₁	—	4	4	no	—
485	Q₈×C₃₁	—	4	2	no	—
486	Q₈×C₃₁	—	8	1	no	—
487	D₄×C₃₁	—	2	4	no	—
488	D₄×C₃₁	—	2	2	no	—
489	D₄×C₃₁	—	2	2	no	—
490	D₄×C₃₁	—	2	1	no	—
491	D₄×C₃₁	—	2	1	no	—
492	D₄×C₃₁	—	2	1	no	—
493	D₄×C₃₁	—	2	2	no	—
494	D₄×C₃₁	—	2	1	no	—
495	D₄×C₃₁	—	2	2	no	—
496	D₄×C₃₁	—	4	2	no	—
497	D₄×C₃₁	—	4	4	no	—
498	D₄×C₃₁	—	4	4	no	—
499	D₄×C₃₁	—	4	4	no	—
500	D₄×C₃₁	—	4	2	no	—
501	D₄×C₃₁	—	4	4	no	—
502	D₄×C₃₁	—	4	4	no	—
503	D₄×C₃₁	—	4	4	no	—
504	D₄×C₃₁	—	4	4	no	—
505	D₄×C₃₁	—	4	2	no	—
506	D₄×C₃₁	—	4	2	no	—
507	D₄×C₃₁	—	8	2	no	—
508	D₄×C₃₁	—	8	1	no	—
509	D₄×C₃₁	—	8	1	no	—
510	D₄×C₃₁	—	8	2	no	—
511	D₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	complemented
512	D₄×C₃₁	C₂×#41	1	2	yes	—
513	D₄×C₃₁	C₂×#41	1	2	yes	complemented
514	C₂×C₄×C₃₁	—	2	4	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	1	no	—
518	C₂×C₄×C₃₁	—	2	2	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	2	1	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	1	no	—
523	C₂×C₄×C₃₁	—	2	2	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	2	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	4	2	no	—
528	C₂×C₄×C₃₁	—	4	1	no	—
529	C₂×C₄×C₃₁	—	4	2	no	—
530	C₂×C₄×C₃₁	—	4	2	no	—
531	C₂×C₄×C₃₁	—	4	4	no	—
532	C₂×C₄×C₃₁	—	4	4	no	—
533	C₂×C₄×C₃₁	—	4	2	no	—
534	C₂×C₄×C₃₁	—	4	4	no	—
535	C₂×C₄×C₃₁	—	4	2	no	—
536	C₂×C₄×C₃₁	—	4	4	no	—
537	C₂×C₄×C₃₁	—	4	2	no	—
538	C₂×C₄×C₃₁	—	4	4	no	—
539	C₂×C₄×C₃₁	—	4	2	no	—
540	C₂×C₄×C₃₁	—	4	2	no	—
541	C₂×C₄×C₃₁	—	4	2	no	—
542	C₂×C₄×C₃₁	—	8	2	no	—
543	C₂×C₄×C₃₁	—	8	2	no	—
544	C₂×C₄×C₃₁	—	8	2	no	—
545	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
554	C₈×C₃₁	—	2	2	no	—
555	C₈×C₃₁	—	2	1	no	—
556	C₈×C₃₁	—	2	1	no	—
557	C₈×C₃₁	—	2	2	no	—
558	C₈×C₃₁	—	2	1	no	—
559	C₈×C₃₁	C₂×#41	1	2	yes	complemented
560	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
561	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
563	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#3345	C₂×C₃₁	1	2	yes	complemented
567	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3318	C₂×C₃₁	1	2	yes	complemented
569	#3306	C₂×C₃₁	1	2	yes	complemented
570	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
571	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
572	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
573	#3264	C₂×C₃₁	1	2	yes	complemented
574	#3184	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#3180	C₂×C₃₁	1	2	yes	complemented
576	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
577	#3114	C₂×C₃₁	1	2	yes	complemented
578	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#3109	C₂×C₃₁	1	2	yes	complemented
580	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
581	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
582	C₂×#442	C₂×C₃₁	1	2	yes	complemented
583	C₂²×C₃₁	—	2	2	no	—
584	C₂²×C₃₁	—	2	2	no	—
585	C₂²×C₃₁	—	2	1	no	—
586	C₂²×C₃₁	—	2	1	no	—
587	C₂²×C₃₁	—	2	2	no	—
588	C₂²×C₃₁	—	2	2	no	—
589	C₂²×C₃₁	—	2	1	no	—
590	C₂²×C₃₁	—	4	1	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	1	no	—
593	C₂²×C₃₁	—	4	1	no	—
594	C₂²×C₃₁	—	4	2	no	—
595	C₂²×C₃₁	—	4	2	no	—
596	C₂²×C₃₁	—	4	1	no	—
597	C₂²×C₃₁	—	4	2	no	—
598	C₂²×C₃₁	—	4	2	no	—
599	C₂²×C₃₁	—	4	1	no	—
600	C₂²×C₃₁	—	4	2	no	—
601	C₂²×C₃₁	—	4	1	no	—
602	C₂²×C₃₁	—	4	2	no	—
603	C₂²×C₃₁	—	8	8	no	—
604	C₂²×C₃₁	—	8	8	no	—
605	C₂²×C₃₁	—	8	4	no	—
606	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
607	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₃₁	—	2	1	no	—
609	C₄×C₃₁	—	2	2	no	—
610	C₄×C₃₁	—	2	1	no	—
611	C₄×C₃₁	—	2	1	no	—
612	C₄×C₃₁	—	2	2	no	—
613	C₄×C₃₁	—	2	1	no	—
614	C₄×C₃₁	—	2	2	no	—
615	C₄×C₃₁	—	4	1	no	—
616	C₄×C₃₁	—	4	2	no	—
617	C₄×C₃₁	—	4	1	no	—
618	C₄×C₃₁	—	4	1	no	—
619	C₄×C₃₁	—	4	2	no	—
620	C₄×C₃₁	—	4	1	no	—
621	C₄×C₃₁	—	4	1	no	—
622	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
623	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
624	C₄×C₃₁	#585	1	1	yes	characteristic
625	C₂²×#41	—	2	1	no	—
626	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
627	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
628	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	#553	—	2	1	no	—
632	#553	C₂²×C₃₁	1	2	yes	complemented
633	#551	—	2	2	no	—
634	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#548	—	2	1	no	—
637	#547	C₂²×C₃₁	1	1	yes	characteristic
638	#547	C₂²×C₃₁	1	2	yes	complemented
639	#546	—	2	1	no	—
640	#546	—	2	1	no	—
641	#546	—	2	2	no	—
642	#546	C₂²×C₃₁	1	2	yes	complemented
643	D₄²	C₂²×C₃₁	1	1	yes	characteristic
644	D₄²	C₂²×C₃₁	1	2	yes	complemented
645	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#532	C₂²×C₃₁	1	2	yes	complemented
647	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#529	—	2	1	no	—
650	#529	C₂²×C₃₁	1	2	yes	complemented
651	#525	—	2	2	no	—
652	#525	—	2	2	no	—
653	#525	—	2	1	no	—
654	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
655	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	C₂×C₄×D₄	—	2	1	no	—
657	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
658	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
660	#501	C₂²×C₃₁	1	2	yes	complemented
661	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#496	C₂²×C₃₁	1	2	yes	complemented
663	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#490	C₂²×C₃₁	1	2	yes	complemented
665	#489	C₂²×C₃₁	1	2	yes	complemented
666	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#483	C₂²×C₃₁	1	2	yes	complemented
669	#482	C₂²×C₃₁	1	2	yes	complemented
670	#481	C₂²×C₃₁	1	2	yes	complemented
671	#481	C₂²×C₃₁	1	2	yes	complemented
672	#481	C₂²×C₃₁	1	2	yes	complemented
673	#480	C₂²×C₃₁	1	2	yes	complemented
674	#478	C₂²×C₃₁	1	2	yes	complemented
675	#478	C₂²×C₃₁	1	2	yes	complemented
676	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#476	C₂²×C₃₁	1	2	yes	complemented
678	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#476	C₂²×C₃₁	1	2	yes	complemented
680	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#469	C₂²×C₃₁	1	2	yes	complemented
683	#469	C₂²×C₃₁	1	2	yes	complemented
684	#466	C₂²×C₃₁	1	2	yes	complemented
685	#466	C₂²×C₃₁	1	2	yes	complemented
686	#465	C₂²×C₃₁	1	2	yes	complemented
687	#465	C₂²×C₃₁	1	2	yes	complemented
688	#463	C₂²×C₃₁	1	2	yes	complemented
689	#463	C₂²×C₃₁	1	2	yes	complemented
690	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#459	C₂²×C₃₁	1	1	yes	characteristic
692	#459	C₂²×C₃₁	1	2	yes	complemented
693	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#459	C₂²×C₃₁	1	2	yes	complemented
695	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#450	C₂²×C₃₁	1	2	yes	complemented
697	#449	C₂²×C₃₁	1	2	yes	complemented
698	#447	C₂²×C₃₁	1	2	yes	—
699	#447	C₂²×C₃₁	1	2	yes	complemented
700	#447	C₂²×C₃₁	1	2	yes	complemented
701	#447	C₂²×C₃₁	1	2	yes	complemented
702	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	#442	C₂²×C₃₁	1	2	yes	—
705	#442	C₂²×C₃₁	1	1	yes	characteristic
706	#442	C₂²×C₃₁	1	2	yes	complemented
707	#442	C₂²×C₃₁	1	2	yes	complemented
708	#442	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#442	C₂²×C₃₁	1	2	yes	complemented
710	#442	C₂²×C₃₁	1	2	yes	complemented
711	#442	C₂²×C₃₁	1	2	yes	complemented
712	#442	C₂²×C₃₁	1	2	yes	complemented
713	#442	C₂²×C₃₁	1	2	yes	complemented
714	#442	C₂²×C₃₁	1	2	yes	complemented
715	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#440	C₂²×C₃₁	1	2	yes	complemented
717	#440	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
721	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
722	#435	C₂²×C₃₁	1	2	yes	complemented
723	#435	C₂²×C₃₁	1	2	yes	complemented
724	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	#432	C₂²×C₃₁	1	2	yes	complemented
727	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
729	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
730	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
733	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
734	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
735	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
736	C₂×C₃₁	—	2	4	no	—
737	C₂×C₃₁	—	4	1	no	—
738	C₂×C₃₁	—	4	2	no	—
739	C₂×C₃₁	—	4	2	no	—
740	C₂×C₃₁	—	8	2	no	—
741	C₂×C₃₁	—	8	2	no	—
742	C₂×C₃₁	—	8	1	no	—
743	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
744	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
745	C₂×C₃₁	#3585	1	1	yes	characteristic
746	C₂×#41	—	2	1	no	—
747	C₂×#41	—	2	1	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	4	8	no	—
753	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
754	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
755	C₂²×Q₈	—	2	1	no	—
756	C₂²×D₄	—	2	1	no	—
757	C₂²×D₄	—	2	1	no	—
758	C₂²×D₄	—	2	2	no	—
759	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
760	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
761	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
762	C₂³×C₄	—	2	2	no	—
763	C₂³×C₄	—	2	1	no	—
764	C₂³×C₄	—	2	2	no	—
765	AGL(1,ℤ/8)	—	2	4	no	—
766	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
767	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
769	C₂×D₈	—	2	8	no	—
770	C₂×D₈	C₂³×C₃₁	1	2	yes	—
771	C₂×D₈	C₂³×C₃₁	1	2	yes	—
772	C₂×D₈	C₂³×C₃₁	1	2	yes	—
773	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₂×D₈	C₂³×C₃₁	1	2	yes	—
775	C₂×D₈	C₂³×C₃₁	1	2	yes	—
776	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
779	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
780	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
781	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
783	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	#127	C₂³×C₃₁	1	1	yes	characteristic
785	#127	C₂³×C₃₁	1	2	yes	—
786	#127	C₂³×C₃₁	1	1	yes	characteristic
787	#126	—	2	2	no	—
788	#126	—	2	2	no	—
789	#125	—	2	1	no	—
790	#125	C₂³×C₃₁	1	2	yes	—
791	#124	—	2	1	no	—
792	#124	—	2	1	no	—
793	#124	—	2	2	no	—
794	#124	—	2	1	no	—
795	#124	C₂³×C₃₁	1	2	yes	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	C₂²⋊Q₈	—	2	1	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	2	no	—
817	#121	—	2	1	no	—
818	#121	—	2	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	C₂³×C₃₁	1	2	yes	—
822	#121	C₂³×C₃₁	1	2	yes	—
823	#121	C₂³×C₃₁	1	2	yes	—
824	#121	C₂³×C₃₁	1	2	yes	—
825	#121	C₂³×C₃₁	1	2	yes	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
851	C₄×D₄	D₄×C₃₁	1	2	yes	—
852	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₃₁	1	2	yes	—
855	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₃₁	1	2	yes	—
857	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₃₁	1	2	yes	—
859	C₄×D₄	C₂³×C₃₁	1	2	yes	—
860	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₃₁	1	2	yes	—
862	C₄×D₄	C₂³×C₃₁	1	2	yes	—
863	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
864	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₃₁	1	2	yes	—
866	#117	—	2	1	no	—
867	#117	—	2	2	no	—
868	#117	D₄×C₃₁	1	2	yes	—
869	#117	D₄×C₃₁	1	1	yes	characteristic
870	#117	C₂³×C₃₁	1	1	yes	characteristic
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
873	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
875	C₂×C₂²⋊C₄	—	2	2	no	—
876	C₂×C₂²⋊C₄	—	2	1	no	—
877	C₂×C₂²⋊C₄	—	2	2	no	—
878	C₂×C₂²⋊C₄	—	2	2	no	—
879	C₂×C₄²	—	2	1	no	—
880	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
881	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
882	#107	C₂³×C₃₁	1	1	yes	characteristic
883	#107	C₂³×C₃₁	1	1	yes	characteristic
884	#107	C₂³×C₃₁	1	2	yes	—
885	#106	C₂³×C₃₁	1	1	yes	characteristic
886	#106	C₂³×C₃₁	1	2	yes	—
887	#106	C₂³×C₃₁	1	2	yes	—
888	#106	C₂³×C₃₁	1	2	yes	—
889	#106	C₂³×C₃₁	1	1	yes	characteristic
890	#106	C₂³×C₃₁	1	2	yes	—
891	#106	C₂³×C₃₁	1	2	yes	—
892	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
894	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
895	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
896	#103	C₂³×C₃₁	1	1	yes	characteristic
897	#103	C₂³×C₃₁	1	1	yes	characteristic
898	#103	C₂³×C₃₁	1	2	yes	—
899	#102	C₂³×C₃₁	1	1	yes	characteristic
900	#102	C₂³×C₃₁	1	1	yes	characteristic
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	2	yes	—
903	#102	C₂³×C₃₁	1	2	yes	—
904	#102	C₂³×C₃₁	1	2	yes	—
905	#102	C₂³×C₃₁	1	2	yes	—
906	#102	C₂³×C₃₁	1	2	yes	—
907	#102	C₂³×C₃₁	1	1	yes	characteristic
908	#102	C₂³×C₃₁	1	1	yes	characteristic
909	#102	C₂³×C₃₁	1	1	yes	characteristic
910	#102	C₂³×C₃₁	1	1	yes	characteristic
911	#102	C₂³×C₃₁	1	2	yes	—
912	#102	C₂³×C₃₁	1	2	yes	—
913	#102	C₂³×C₃₁	1	2	yes	—
914	#102	C₂³×C₃₁	1	2	yes	—
915	#102	C₂³×C₃₁	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
919	#97	C₂³×C₃₁	1	1	yes	characteristic
920	#97	C₂³×C₃₁	1	2	yes	—
921	#97	C₂³×C₃₁	1	2	yes	—
922	#97	C₂³×C₃₁	1	2	yes	—
923	#97	C₂³×C₃₁	1	1	yes	characteristic
924	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
925	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
926	C₃₁	#61451	1	1	yes	characteristic, direct product factor, Sylow
927	C₂⁴	—	2	2	no	—
928	C₂⁴	—	2	1	no	—
929	C₂⁴	—	2	2	no	—
930	#41	—	2	4	no	—
931	#41	—	2	2	no	—
932	#41	—	4	1	no	—
933	#41	—	4	8	no	—
934	#41	—	4	4	no	—
935	#41	—	4	8	no	—
936	#41	—	4	4	no	—
937	#41	—	4	4	no	—
938	#41	—	8	2	no	—
939	C₂×Q₈	—	2	2	no	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	4	4	no	—
943	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	4	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	1	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	1	no	—
966	C₂×D₄	—	4	8	no	—
967	C₂×D₄	—	4	4	no	—
968	C₂×D₄	—	4	4	no	—
969	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
972	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
973	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	4	8	no	—
993	C₂²×C₄	—	4	4	no	—
994	C₂²×C₄	—	8	4	no	—
995	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1000	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	2	2	no	—
1003	SD₁₆	—	4	2	no	—
1004	D₈	—	2	4	no	—
1005	D₈	—	2	4	no	—
1006	D₈	—	2	2	no	—
1007	D₈	—	2	4	no	—
1008	D₈	—	4	2	no	—
1009	D₈	—	4	2	no	—
1010	D₈	#41×C₃₁	1	4	yes	complemented
1011	M₁₆	—	2	2	no	—
1012	M₁₆	—	4	1	no	—
1013	C₂×C₈	—	2	4	no	—
1014	C₂×C₈	—	4	2	no	—
1015	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1020	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1041	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1065	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1070	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1071	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1072	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1073	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1074	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1075	C₄²	C₂⁴×C₃₁	1	2	yes	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	4	4	no	—
1082	C₂³	—	4	4	no	—
1083	C₂³	—	4	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	4	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	8	2	no	—
1088	C₂³	—	8	2	no	—
1089	C₂³	—	8	1	no	—
1090	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1091	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	1	no	—
1094	Q₈	—	2	1	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	8	1	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	2	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	2	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	4	no	—
1109	D₄	—	4	4	no	—
1110	D₄	—	4	4	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	1	no	—
1121	D₄	—	8	2	no	—
1122	D₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	complemented
1123	D₄	C₂×#41×C₃₁	1	2	yes	—
1124	D₄	C₂×#41×C₃₁	1	2	yes	complemented
1125	C₂×C₄	—	2	4	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	4	no	—
1143	C₂×C₄	—	4	4	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1159	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1164	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1165	C₈	—	2	2	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₈	—	2	2	no	—
1169	C₈	—	2	1	no	—
1170	C₈	C₂×#41×C₃₁	1	2	yes	complemented
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	2	no	—
1173	C₂²	—	2	1	no	—
1174	C₂²	—	2	2	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	1	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	8	8	no	—
1192	C₂²	—	8	8	no	—
1193	C₂²	—	8	4	no	—
1194	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
1195	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
1211	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1212	C₄	C₃₁×#585	1	1	yes	characteristic
1213	C₂	—	2	4	no	—
1214	C₂	—	4	1	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	8	2	no	—
1218	C₂	—	8	1	no	—
1219	C₂	—	8	2	no	—
1220	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1221	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
1222	C₂	C₃₁×#3585	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3481	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3373	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3345	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3318	C₂	semidirect
10. C₃₁×#3306	C₂	semidirect
11. C₃₁×#3295	C₂	semidirect
12. C₃₁×#3294	C₂	semidirect
13. D₄×D₈×C₃₁	C₂	semidirect
14. C₃₁×#3264	C₂	semidirect
15. C₃₁×#3184	C₂	semidirect
16. C₃₁×#3180	C₂	semidirect
17. C₃₁×#3115	C₂	semidirect
18. C₃₁×#3114	C₂	semidirect
19. C₃₁×#3109	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#2970	C₂	semidirect
22. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₃₁×#442	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
33. C₃₁×#550	C₂²	semidirect
34. D₄×Q₈×C₃₁	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
41. C₃₁×#546	C₂²	semidirect
43. D₄²×C₃₁	C₂²	semidirect
44. D₄²×C₃₁	C₂²	semidirect
45. C₃₁×#532	C₂²	semidirect
46. C₃₁×#532	C₂²	semidirect
47. C₃₁×#532	C₂²	semidirect
49. C₃₁×#529	C₂²	semidirect
54. C₄×#41×C₃₁	C₂²	semidirect
56. C₂×C₄×D₄×C₃₁	C₂²	semidirect
57. C₂×C₄×D₄×C₃₁	C₂²	semidirect
58. C₂×C₄×D₄×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
62. C₃₁×#493	C₂²	semidirect
63. C₃₁×#490	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#483	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#481	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#478	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#476	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#469	C₂²	semidirect
82. C₃₁×#469	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
91. C₃₁×#459	C₂²	semidirect
92. C₃₁×#459	C₂²	semidirect
93. C₃₁×#459	C₂²	semidirect
94. C₃₁×#459	C₂²	semidirect
95. C₃₁×#450	C₂²	semidirect
96. C₃₁×#449	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#447	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
106. C₃₁×#442	C₂²	semidirect
107. C₃₁×#442	C₂²	semidirect
108. C₃₁×#442	C₂²	semidirect
109. C₃₁×#442	C₂²	semidirect
110. C₃₁×#442	C₂²	semidirect
111. C₃₁×#442	C₂²	semidirect
112. C₃₁×#442	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₃₁×#440	C₂²	semidirect
116. C₃₁×#440	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#435	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#432	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₂×C₃₁×#106	C₂²	semidirect
129. C₃₁×#418	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₂×C₃₁×#102	C₂²	semidirect
132. C₂×C₃₁×#102	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₂×C₃₁×#97	C₂²	semidirect
398. D₈×C₃₁	#41	semidirect
464. #61451	C₃₁	direct (N × H)
511. D₄×C₃₁	AGL(1,ℤ/8)	semidirect
513. D₄×C₃₁	C₂×#41	semidirect
559. C₈×C₃₁	C₂×#41	semidirect
560. #3481	C₂×C₃₁	semidirect
561. D₄×#41	C₂×C₃₁	semidirect
562. #3399	C₂×C₃₁	semidirect
563. #3384	C₂×C₃₁	semidirect
564. #3373	C₂×C₃₁	semidirect
565. #3366	C₂×C₃₁	semidirect
566. #3345	C₂×C₃₁	semidirect
567. #3335	C₂×C₃₁	semidirect
568. #3318	C₂×C₃₁	semidirect
569. #3306	C₂×C₃₁	semidirect
570. #3295	C₂×C₃₁	semidirect
571. #3294	C₂×C₃₁	semidirect
572. D₄×D₈	C₂×C₃₁	semidirect
573. #3264	C₂×C₃₁	semidirect
574. #3184	C₂×C₃₁	semidirect
575. #3180	C₂×C₃₁	semidirect
576. #3115	C₂×C₃₁	semidirect
577. #3114	C₂×C₃₁	semidirect
578. #3109	C₂×C₃₁	semidirect
579. #3109	C₂×C₃₁	semidirect
580. #2970	C₂×C₃₁	semidirect
581. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
582. C₂×#442	C₂×C₃₁	semidirect
628. #559	C₂²×C₃₁	semidirect
629. #554	C₂²×C₃₁	semidirect
630. #554	C₂²×C₃₁	semidirect
632. #553	C₂²×C₃₁	semidirect
634. #550	C₂²×C₃₁	semidirect
635. D₄×Q₈	C₂²×C₃₁	semidirect
638. #547	C₂²×C₃₁	semidirect
642. #546	C₂²×C₃₁	semidirect
644. D₄²	C₂²×C₃₁	semidirect
645. D₄²	C₂²×C₃₁	semidirect
646. #532	C₂²×C₃₁	semidirect
647. #532	C₂²×C₃₁	semidirect
648. #532	C₂²×C₃₁	semidirect
650. #529	C₂²×C₃₁	semidirect
655. C₄×#41	C₂²×C₃₁	semidirect
657. C₂×C₄×D₄	C₂²×C₃₁	semidirect
658. C₂×C₄×D₄	C₂²×C₃₁	semidirect
659. C₂×C₄×D₄	C₂²×C₃₁	semidirect
660. #501	C₂²×C₃₁	semidirect
661. #498	C₂²×C₃₁	semidirect
662. #496	C₂²×C₃₁	semidirect
663. #493	C₂²×C₃₁	semidirect
664. #490	C₂²×C₃₁	semidirect
665. #489	C₂²×C₃₁	semidirect
666. #486	C₂²×C₃₁	semidirect
667. #486	C₂²×C₃₁	semidirect
668. #483	C₂²×C₃₁	semidirect
669. #482	C₂²×C₃₁	semidirect
670. #481	C₂²×C₃₁	semidirect
671. #481	C₂²×C₃₁	semidirect
672. #481	C₂²×C₃₁	semidirect
673. #480	C₂²×C₃₁	semidirect
674. #478	C₂²×C₃₁	semidirect
675. #478	C₂²×C₃₁	semidirect
676. #476	C₂²×C₃₁	semidirect
677. #476	C₂²×C₃₁	semidirect
678. #476	C₂²×C₃₁	semidirect
679. #476	C₂²×C₃₁	semidirect
680. #475	C₂²×C₃₁	semidirect
681. #474	C₂²×C₃₁	semidirect
682. #469	C₂²×C₃₁	semidirect
683. #469	C₂²×C₃₁	semidirect
684. #466	C₂²×C₃₁	semidirect
685. #466	C₂²×C₃₁	semidirect
686. #465	C₂²×C₃₁	semidirect
687. #465	C₂²×C₃₁	semidirect
688. #463	C₂²×C₃₁	semidirect
689. #463	C₂²×C₃₁	semidirect
690. #460	C₂²×C₃₁	semidirect
692. #459	C₂²×C₃₁	semidirect
693. #459	C₂²×C₃₁	semidirect
694. #459	C₂²×C₃₁	semidirect
695. #459	C₂²×C₃₁	semidirect
696. #450	C₂²×C₃₁	semidirect
697. #449	C₂²×C₃₁	semidirect
699. #447	C₂²×C₃₁	semidirect
700. #447	C₂²×C₃₁	semidirect
701. #447	C₂²×C₃₁	semidirect
702. #446	C₂²×C₃₁	semidirect
703. #446	C₂²×C₃₁	semidirect
706. #442	C₂²×C₃₁	semidirect
707. #442	C₂²×C₃₁	semidirect
708. #442	C₂²×C₃₁	semidirect
709. #442	C₂²×C₃₁	semidirect
710. #442	C₂²×C₃₁	semidirect
711. #442	C₂²×C₃₁	semidirect
712. #442	C₂²×C₃₁	semidirect
713. #442	C₂²×C₃₁	semidirect
714. #442	C₂²×C₃₁	semidirect
715. #440	C₂²×C₃₁	semidirect
716. #440	C₂²×C₃₁	semidirect
717. #440	C₂²×C₃₁	semidirect
718. C₄×SD₁₆	C₂²×C₃₁	semidirect
719. C₄×SD₁₆	C₂²×C₃₁	semidirect
721. C₄×D₈	C₂²×C₃₁	semidirect
722. #435	C₂²×C₃₁	semidirect
723. #435	C₂²×C₃₁	semidirect
724. C₈×D₄	C₂²×C₃₁	semidirect
725. C₈×D₄	C₂²×C₃₁	semidirect
726. #432	C₂²×C₃₁	semidirect
727. #432	C₂²×C₃₁	semidirect
728. #428	C₂²×C₃₁	semidirect
729. C₂×#106	C₂²×C₃₁	semidirect
730. #418	C₂²×C₃₁	semidirect
731. #417	C₂²×C₃₁	semidirect
732. C₂×#102	C₂²×C₃₁	semidirect
733. C₂×#102	C₂²×C₃₁	semidirect
734. C₄×M₁₆	C₂²×C₃₁	semidirect
735. C₂×#97	C₂²×C₃₁	semidirect
926. C₃₁	#61451	direct (N × H)
1010. D₈	#41×C₃₁	semidirect
1122. D₄	C₃₁×AGL(1,ℤ/8)	semidirect
1124. D₄	C₂×#41×C₃₁	semidirect
1170. C₈	C₂×#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3481	2
D₄×#41×C₃₁	2
C₃₁×#3399	2
C₃₁×#3384	2
C₃₁×#3373	2
C₃₁×#3366	2
C₃₁×#3345	2
C₃₁×#3335	2
C₃₁×#3318	2
C₃₁×#3306	2
C₃₁×#3295	2
C₃₁×#3294	2
D₄×D₈×C₃₁	2
C₃₁×#3264	2
C₃₁×#3184	2
C₃₁×#3180	2
C₃₁×#3115	2
C₃₁×#3114	2
C₃₁×#3109	2
C₃₁×#2970	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₂×C₃₁×#442	2
#61451	31

Subgroups — C31×#61451 #21518210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61451 #21518210