Subgroups — C₃₁×#61497 #21518256

Order 7936.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#554	C₂²	1	2	yes	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	—	2	2	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#551	—	2	2	no	—
37	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#548	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#547	C₂²	1	1	yes	characteristic
43	C₃₁×#546	C₂²	1	2	yes	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	C₂²	1	2	yes	complemented
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#533	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₃₁×#519	C₂²	1	2	yes	complemented
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#497	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#487	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	2	yes	complemented
70	C₃₁×#483	C₂²	1	2	yes	—
71	C₃₁×#483	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#475	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic
80	C₃₁×#474	C₂²	1	1	yes	characteristic
81	C₃₁×#470	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#467	C₂²	1	2	yes	—
85	C₃₁×#467	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#462	C₂²	1	2	yes	complemented
92	C₃₁×#461	C₂²	1	1	yes	characteristic
93	C₃₁×#461	C₂²	1	2	yes	—
94	C₃₁×#461	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#451	C₂²	1	2	yes	—
98	C₃₁×#451	C₂²	1	2	yes	complemented
99	C₃₁×#450	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#441	C₂²	1	2	yes	complemented
104	C₃₁×#441	C₂²	1	2	yes	complemented
105	C₃₁×#441	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	2	yes	—
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₃₁×#137	—	2	8	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	—	2	4	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	—	2	2	no	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	D₄	1	2	yes	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	1	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	D₄	1	1	yes	characteristic
184	C₃₁×#125	C₂³	1	2	yes	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	2	no	—
187	C₃₁×#124	D₄	1	1	yes	characteristic
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#120	—	2	2	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	1	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	4	no	—
325	C₂×Q₈×C₃₁	—	4	1	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	—	8	2	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	4	1	no	—
338	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	8	2	no	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
358	Q₁₆×C₃₁	—	2	4	no	—
359	Q₁₆×C₃₁	—	2	4	no	—
360	Q₁₆×C₃₁	—	4	2	no	—
361	Q₁₆×C₃₁	—	4	2	no	—
362	SD₁₆×C₃₁	—	2	2	no	—
363	SD₁₆×C₃₁	—	2	2	no	—
364	SD₁₆×C₃₁	—	2	4	no	—
365	SD₁₆×C₃₁	—	2	2	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	#41	1	4	yes	complemented
368	M₁₆×C₃₁	—	2	4	no	—
369	C₂×C₈×C₃₁	—	2	2	no	—
370	C₂×C₈×C₃₁	—	4	2	no	—
371	C₂×C₈×C₃₁	—	4	1	no	—
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	1	no	—
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	2	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	2	yes	—
452	#61497	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	1	no	—
455	C₂³×C₃₁	—	4	2	no	—
456	C₂³×C₃₁	—	4	2	no	—
457	C₂³×C₃₁	—	8	1	no	—
458	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
459	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	2	2	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	4	4	no	—
469	Q₈×C₃₁	—	4	2	no	—
470	Q₈×C₃₁	—	4	2	no	—
471	Q₈×C₃₁	—	4	2	no	—
472	Q₈×C₃₁	—	8	2	no	—
473	Q₈×C₃₁	C₂×#41	1	2	yes	—
474	D₄×C₃₁	—	2	4	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	1	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	4	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	C₂×#41	1	2	yes	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	4	no	—
501	C₂×C₄×C₃₁	—	4	4	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	—	8	1	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	1	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	—	2	1	no	—
522	C₈×C₃₁	—	2	2	no	—
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	C₂×#41	1	2	yes	—
525	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3520	C₂×C₃₁	1	1	yes	characteristic
527	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3359	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3344	C₂×C₃₁	1	2	yes	complemented
533	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3299	C₂×C₃₁	1	2	yes	complemented
535	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3296	C₂×C₃₁	1	2	yes	complemented
537	#3276	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3266	C₂×C₃₁	1	2	yes	complemented
539	#3178	C₂×C₃₁	1	2	yes	complemented
540	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3121	C₂×C₃₁	1	2	yes	complemented
542	#3120	C₂×C₃₁	1	2	yes	complemented
543	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#2947	C₂×C₃₁	1	2	yes	complemented
547	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	2	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	2	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	8	4	no	—
560	C₂²×C₃₁	#578	1	2	yes	—
561	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	1	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	2	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	—	4	2	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	#577	1	2	yes	—
580	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
581	C₄×C₃₁	#585	1	1	yes	characteristic
582	C₂×#137	C₂²×C₃₁	1	2	yes	—
583	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
584	#557	—	2	1	no	—
585	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#556	—	2	1	no	—
588	#556	C₂²×C₃₁	1	1	yes	characteristic
589	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#554	C₂²×C₃₁	1	2	yes	—
591	#552	—	2	1	no	—
592	#552	—	2	2	no	—
593	#552	C₂²×C₃₁	1	2	yes	—
594	#551	—	2	2	no	—
595	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
596	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
597	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#548	—	2	1	no	—
599	#547	C₂²×C₃₁	1	1	yes	characteristic
600	#547	C₂²×C₃₁	1	1	yes	characteristic
601	#546	C₂²×C₃₁	1	2	yes	—
602	#542	C₂²×C₃₁	1	2	yes	—
603	#541	—	2	2	no	—
604	#541	C₂²×C₃₁	1	2	yes	complemented
605	#539	—	2	2	no	—
606	#533	—	2	1	no	—
607	#533	C₂²×C₃₁	1	1	yes	characteristic
608	#533	C₂²×C₃₁	1	1	yes	characteristic
609	#529	—	2	1	no	—
610	#529	C₂²×C₃₁	1	1	yes	characteristic
611	#525	—	2	1	no	—
612	C₂×C₂²⋊Q₈	—	2	1	no	—
613	#520	C₂²×C₃₁	1	2	yes	—
614	#519	C₂²×C₃₁	1	2	yes	complemented
615	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
616	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
617	#501	C₂²×C₃₁	1	2	yes	complemented
618	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
619	#497	C₂²×C₃₁	1	2	yes	—
620	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#488	C₂²×C₃₁	1	2	yes	—
622	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#487	C₂²×C₃₁	1	2	yes	complemented
624	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#485	C₂²×C₃₁	1	2	yes	complemented
626	#484	C₂²×C₃₁	1	2	yes	—
627	#484	C₂²×C₃₁	1	2	yes	complemented
628	#483	C₂²×C₃₁	1	2	yes	—
629	#483	C₂²×C₃₁	1	2	yes	complemented
630	#482	C₂²×C₃₁	1	2	yes	—
631	#479	C₂²×C₃₁	1	2	yes	complemented
632	#478	C₂²×C₃₁	1	2	yes	—
633	#477	C₂²×C₃₁	1	2	yes	complemented
634	#475	C₂²×C₃₁	1	2	yes	complemented
635	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#474	C₂²×C₃₁	1	1	yes	characteristic
638	#474	C₂²×C₃₁	1	1	yes	characteristic
639	#470	C₂²×C₃₁	1	2	yes	complemented
640	#468	C₂²×C₃₁	1	2	yes	—
641	#467	C₂²×C₃₁	1	2	yes	—
642	#467	C₂²×C₃₁	1	2	yes	—
643	#467	C₂²×C₃₁	1	2	yes	complemented
644	#465	C₂²×C₃₁	1	2	yes	—
645	#464	C₂²×C₃₁	1	2	yes	—
646	#464	C₂²×C₃₁	1	2	yes	—
647	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#462	C₂²×C₃₁	1	2	yes	complemented
650	#461	C₂²×C₃₁	1	1	yes	characteristic
651	#461	C₂²×C₃₁	1	2	yes	—
652	#461	C₂²×C₃₁	1	1	yes	characteristic
653	#452	C₂²×C₃₁	1	2	yes	—
654	#452	C₂²×C₃₁	1	2	yes	—
655	#451	C₂²×C₃₁	1	2	yes	—
656	#451	C₂²×C₃₁	1	2	yes	complemented
657	#450	C₂²×C₃₁	1	2	yes	—
658	#448	C₂²×C₃₁	1	2	yes	—
659	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#441	C₂²×C₃₁	1	2	yes	complemented
662	#441	C₂²×C₃₁	1	2	yes	complemented
663	#441	C₂²×C₃₁	1	2	yes	complemented
664	#440	C₂²×C₃₁	1	2	yes	—
665	#440	C₂²×C₃₁	1	2	yes	—
666	#440	C₂²×C₃₁	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
668	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
669	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
670	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
673	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
679	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#435	C₂²×C₃₁	1	2	yes	—
681	C₈×D₄	C₂²×C₃₁	1	2	yes	—
682	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#433	C₂²×C₃₁	1	2	yes	complemented
684	#432	C₂²×C₃₁	1	1	yes	characteristic
685	#428	C₂²×C₃₁	1	2	yes	complemented
686	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
687	#416	C₂²×C₃₁	1	2	yes	—
688	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
689	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
690	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
691	#405	C₂²×C₃₁	1	2	yes	complemented
692	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
693	C₂×C₃₁	—	2	2	no	—
694	C₂×C₃₁	—	4	2	no	—
695	C₂×C₃₁	—	4	2	no	—
696	C₂×C₃₁	—	8	1	no	—
697	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
698	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
699	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
700	C₂×#41	—	2	1	no	—
701	C₂×#41	C₂³×C₃₁	1	2	yes	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
705	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
706	C₂³×C₄	—	2	1	no	—
707	#137	—	2	8	no	—
708	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂×SD₁₆	—	2	4	no	—
713	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	D₄×C₃₁	1	2	yes	—
739	#125	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	D₄×C₃₁	1	1	yes	characteristic
749	#125	C₂³×C₃₁	1	2	yes	—
750	#124	—	2	1	no	—
751	#124	—	2	2	no	—
752	#124	D₄×C₃₁	1	1	yes	characteristic
753	#124	C₂³×C₃₁	1	2	yes	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	D₄×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	D₄×C₃₁	1	1	yes	characteristic
781	#121	C₂³×C₃₁	1	2	yes	—
782	#120	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	2	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₃₁	1	2	yes	—
814	C₄×D₄	C₂³×C₃₁	1	2	yes	—
815	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	2	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	C₂³×C₃₁	1	2	yes	—
824	#117	C₂³×C₃₁	1	2	yes	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	—	2	2	no	—
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
835	#107	C₂³×C₃₁	1	2	yes	—
836	#107	C₂³×C₃₁	1	2	yes	—
837	#107	C₂³×C₃₁	1	2	yes	—
838	#107	C₂³×C₃₁	1	2	yes	—
839	#106	C₂³×C₃₁	1	1	yes	characteristic
840	#106	C₂³×C₃₁	1	1	yes	characteristic
841	#106	C₂³×C₃₁	1	1	yes	characteristic
842	#106	C₂³×C₃₁	1	1	yes	characteristic
843	#106	C₂³×C₃₁	1	2	yes	—
844	#106	C₂³×C₃₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
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	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	1	yes	characteristic
865	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	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	#97	C₂³×C₃₁	1	2	yes	—
873	#97	C₂³×C₃₁	1	2	yes	—
874	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₃₁	1	2	yes	—
879	C₃₁	#61497	1	1	yes	characteristic, direct product factor, Sylow
880	C₂⁴	—	2	1	no	—
881	#41	—	2	4	no	—
882	#41	—	4	2	no	—
883	#41	—	8	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	4	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	—	8	2	no	—
894	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
896	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	4	1	no	—
904	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
905	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	8	2	no	—
920	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
924	Q₁₆	—	2	4	no	—
925	Q₁₆	—	2	4	no	—
926	Q₁₆	—	4	2	no	—
927	Q₁₆	—	4	2	no	—
928	SD₁₆	—	2	2	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	#41×C₃₁	1	4	yes	complemented
934	M₁₆	—	2	4	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	4	2	no	—
937	C₂×C₈	—	4	1	no	—
938	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
942	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
943	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₃₁	1	2	yes	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	4	2	no	—
1022	C₂³	—	8	1	no	—
1023	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	4	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	4	2	no	—
1036	Q₈	—	4	2	no	—
1037	Q₈	—	8	2	no	—
1038	Q₈	C₂×#41×C₃₁	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	8	2	no	—
1047	D₄	C₂×#41×C₃₁	1	2	yes	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	1	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1083	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1084	C₈	—	2	1	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	2	no	—
1088	C₈	—	2	1	no	—
1089	C₈	C₂×#41×C₃₁	1	2	yes	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	8	4	no	—
1102	C₂²	C₃₁×#578	1	2	yes	—
1103	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	C₃₁×#577	1	2	yes	—
1122	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1123	C₄	C₃₁×#585	1	1	yes	characteristic
1124	C₂	—	2	2	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	1	no	—
1128	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1129	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1130	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3523	C₂	semidirect
3. C₃₁×#3398	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3364	C₂	semidirect
6. C₃₁×#3359	C₂	semidirect
7. C₃₁×#3353	C₂	semidirect
8. C₃₁×#3344	C₂	semidirect
9. C₃₁×#3302	C₂	semidirect
10. C₃₁×#3299	C₂	semidirect
11. C₃₁×#3298	C₂	semidirect
12. C₃₁×#3296	C₂	semidirect
13. C₃₁×#3276	C₂	semidirect
14. C₃₁×#3266	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3170	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₃₁×#3113	C₂	semidirect
20. C₃₁×#3110	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2947	C₂	semidirect
23. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
27. C₃₁×#557	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
39. D₄×Q₈×C₃₁	C₂²	semidirect
46. C₃₁×#541	C₂²	semidirect
56. C₃₁×#519	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
62. C₃₁×#494	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
69. C₃₁×#484	C₂²	semidirect
71. C₃₁×#483	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#475	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
85. C₃₁×#467	C₂²	semidirect
89. C₃₁×#462	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#462	C₂²	semidirect
98. C₃₁×#451	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
103. C₃₁×#441	C₂²	semidirect
104. C₃₁×#441	C₂²	semidirect
105. C₃₁×#441	C₂²	semidirect
109. C₄×Q₁₆×C₃₁	C₂²	semidirect
110. C₄×Q₁₆×C₃₁	C₂²	semidirect
111. C₄×Q₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
131. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
367. SD₁₆×C₃₁	#41	semidirect
452. #61497	C₃₁	direct (N × H)
525. #3523	C₂×C₃₁	semidirect
527. #3398	C₂×C₃₁	semidirect
528. #3386	C₂×C₃₁	semidirect
529. #3364	C₂×C₃₁	semidirect
530. #3359	C₂×C₃₁	semidirect
531. #3353	C₂×C₃₁	semidirect
532. #3344	C₂×C₃₁	semidirect
533. #3302	C₂×C₃₁	semidirect
534. #3299	C₂×C₃₁	semidirect
535. #3298	C₂×C₃₁	semidirect
536. #3296	C₂×C₃₁	semidirect
537. #3276	C₂×C₃₁	semidirect
538. #3266	C₂×C₃₁	semidirect
539. #3178	C₂×C₃₁	semidirect
540. #3170	C₂×C₃₁	semidirect
541. #3121	C₂×C₃₁	semidirect
542. #3120	C₂×C₃₁	semidirect
543. #3113	C₂×C₃₁	semidirect
544. #3110	C₂×C₃₁	semidirect
545. #2966	C₂×C₃₁	semidirect
546. #2947	C₂×C₃₁	semidirect
547. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
585. #557	C₂²×C₃₁	semidirect
586. #557	C₂²×C₃₁	semidirect
589. #556	C₂²×C₃₁	semidirect
597. D₄×Q₈	C₂²×C₃₁	semidirect
604. #541	C₂²×C₃₁	semidirect
614. #519	C₂²×C₃₁	semidirect
617. #501	C₂²×C₃₁	semidirect
618. #500	C₂²×C₃₁	semidirect
620. #494	C₂²×C₃₁	semidirect
622. #487	C₂²×C₃₁	semidirect
623. #487	C₂²×C₃₁	semidirect
624. #487	C₂²×C₃₁	semidirect
625. #485	C₂²×C₃₁	semidirect
627. #484	C₂²×C₃₁	semidirect
629. #483	C₂²×C₃₁	semidirect
631. #479	C₂²×C₃₁	semidirect
633. #477	C₂²×C₃₁	semidirect
634. #475	C₂²×C₃₁	semidirect
635. #475	C₂²×C₃₁	semidirect
636. #475	C₂²×C₃₁	semidirect
639. #470	C₂²×C₃₁	semidirect
643. #467	C₂²×C₃₁	semidirect
647. #462	C₂²×C₃₁	semidirect
648. #462	C₂²×C₃₁	semidirect
649. #462	C₂²×C₃₁	semidirect
656. #451	C₂²×C₃₁	semidirect
659. #446	C₂²×C₃₁	semidirect
660. C₈×Q₈	C₂²×C₃₁	semidirect
661. #441	C₂²×C₃₁	semidirect
662. #441	C₂²×C₃₁	semidirect
663. #441	C₂²×C₃₁	semidirect
667. C₄×Q₁₆	C₂²×C₃₁	semidirect
668. C₄×Q₁₆	C₂²×C₃₁	semidirect
669. C₄×Q₁₆	C₂²×C₃₁	semidirect
679. #436	C₂²×C₃₁	semidirect
682. C₈×D₄	C₂²×C₃₁	semidirect
683. #433	C₂²×C₃₁	semidirect
685. #428	C₂²×C₃₁	semidirect
689. C₂×#103	C₂²×C₃₁	semidirect
691. #405	C₂²×C₃₁	semidirect
879. C₃₁	#61497	direct (N × H)
933. SD₁₆	#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×#3523	2
C₃₁×#3520	2
C₃₁×#3398	2
C₃₁×#3386	2
C₃₁×#3364	2
C₃₁×#3359	2
C₃₁×#3353	2
C₃₁×#3344	2
C₃₁×#3302	2
C₃₁×#3299	2
C₃₁×#3298	2
C₃₁×#3296	2
C₃₁×#3276	2
C₃₁×#3266	2
C₃₁×#3178	2
C₃₁×#3170	2
C₃₁×#3121	2
C₃₁×#3120	2
C₃₁×#3113	2
C₃₁×#3110	2
C₃₁×#2966	2
C₃₁×#2947	2
C₂×C₄×SD₁₆×C₃₁	2
#61497	31

Subgroups — C31×#61497 #21518256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61497 #21518256