Subgroups — C₃₁×#17766 #21474525

Order 7936.

982 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1560	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1559	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1557	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1551	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#559	—	2	1	no	—
17	C₃₁×#559	C₄	1	2	yes	—
18	C₃₁×#550	—	2	1	no	—
19	C₃₁×#550	C₄	1	2	yes	—
20	C₃₁×#546	—	2	1	no	—
21	C₃₁×#546	—	2	1	no	—
22	C₃₁×#546	C₄	1	2	yes	—
23	C₃₁×#546	C₄	1	2	yes	—
24	C₃₁×#540	—	2	1	no	—
25	C₃₁×#540	—	2	1	no	—
26	C₃₁×#535	—	2	1	no	—
27	C₃₁×#533	C₂²	1	1	yes	characteristic
28	C₃₁×#532	C₂²	1	1	yes	characteristic
29	C₃₁×#532	C₂²	1	1	yes	characteristic
30	C₃₁×#532	C₂²	1	1	yes	characteristic
31	C₃₁×#532	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
33	C₃₁×#518	—	2	1	no	—
34	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#446	—	2	1	no	—
36	C₃₁×#436	—	2	1	no	—
37	C₃₁×#435	—	2	1	no	—
38	C₃₁×#435	—	2	1	no	—
39	C₃₁×#433	—	2	1	no	—
40	C₃₁×#433	—	2	1	no	—
41	C₃₁×#432	C₂²	1	1	yes	characteristic
42	C₃₁×#432	C₂²	1	1	yes	characteristic
43	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#431	C₂²	1	1	yes	characteristic
46	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#423	C₂²	1	1	yes	characteristic
49	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#408	—	2	1	no	—
54	C₃₁×#405	—	2	1	no	—
55	C₃₁×#333	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#333	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#333	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#333	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#332	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#332	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#332	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#332	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#331	C₂²	1	1	yes	characteristic
64	C₃₁×#331	C₂²	1	1	yes	characteristic
65	C₃₁×#331	C₂²	1	1	yes	characteristic
66	C₃₁×#331	C₂²	1	1	yes	characteristic
67	C₃₁×#331	C₂²	1	1	yes	characteristic
68	C₃₁×#331	C₂²	1	1	yes	characteristic
69	C₃₁×#331	C₂²	1	1	yes	characteristic
70	C₃₁×#331	C₂²	1	1	yes	characteristic
71	C₂×#41×C₃₁	—	2	1	no	—
72	C₂×#41×C₃₁	—	2	1	no	—
73	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
74	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
75	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
76	C₂²×D₄×C₃₁	—	2	1	no	—
77	C₂²×D₄×C₃₁	—	2	1	no	—
78	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
79	C₂×M₁₆×C₃₁	—	2	1	no	—
80	C₂×M₁₆×C₃₁	—	2	1	no	—
81	C₂×M₁₆×C₃₁	—	2	1	no	—
82	C₂²×C₈×C₃₁	—	2	1	no	—
83	C₂²×C₈×C₃₁	—	2	1	no	—
84	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₃₁×#127	—	2	2	no	—
87	C₃₁×#127	—	2	1	no	—
88	C₃₁×#127	—	2	1	no	—
89	C₃₁×#127	C₂×C₄	1	2	yes	—
90	C₃₁×#127	C₂³	1	1	yes	characteristic
91	C₃₁×#127	C₂³	1	1	yes	characteristic
92	C₃₁×#125	—	2	1	no	—
93	C₃₁×#124	—	2	2	no	—
94	C₃₁×#124	—	2	1	no	—
95	C₃₁×#124	—	2	1	no	—
96	C₃₁×#124	C₂×C₄	1	2	yes	—
97	C₃₁×#124	C₂×C₄	1	2	yes	—
98	C₃₁×#123	—	2	2	no	—
99	C₃₁×#123	—	2	2	no	—
100	C₃₁×#123	—	2	2	no	—
101	C₃₁×#123	—	2	2	no	—
102	C₃₁×C₂²⋊Q₈	—	2	1	no	—
103	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
104	C₃₁×#121	—	2	1	no	—
105	C₃₁×#121	—	2	1	no	—
106	C₃₁×#121	—	2	1	no	—
107	C₃₁×#121	—	2	1	no	—
108	C₃₁×#121	—	2	1	no	—
109	C₃₁×#121	—	2	1	no	—
110	C₃₁×#121	—	2	2	no	—
111	C₃₁×#121	—	2	2	no	—
112	C₃₁×#121	—	2	2	no	—
113	C₃₁×#121	—	2	2	no	—
114	C₃₁×#121	C₂×C₄	1	2	yes	—
115	C₃₁×#121	C₂×C₄	1	2	yes	—
116	C₃₁×#120	—	2	2	no	—
117	C₃₁×#120	—	2	2	no	—
118	C₄×Q₈×C₃₁	—	2	1	no	—
119	C₄×Q₈×C₃₁	C₂×C₄	1	2	yes	—
120	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
121	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
122	C₄×D₄×C₃₁	—	2	2	no	—
123	C₄×D₄×C₃₁	—	2	2	no	—
124	C₄×D₄×C₃₁	—	2	1	no	—
125	C₄×D₄×C₃₁	—	2	1	no	—
126	C₄×D₄×C₃₁	—	2	1	no	—
127	C₄×D₄×C₃₁	—	2	1	no	—
128	C₄×D₄×C₃₁	—	2	1	no	—
129	C₄×D₄×C₃₁	—	2	1	no	—
130	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
131	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
132	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
133	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
134	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
135	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
136	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
137	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
138	C₃₁×#117	—	2	1	no	—
139	C₃₁×#117	D₄	1	1	yes	characteristic
140	C₃₁×#117	D₄	1	1	yes	characteristic
141	C₃₁×#117	D₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
144	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
147	C₃₁×C₄⋊C₈	—	2	1	no	—
148	C₃₁×C₄⋊C₈	—	2	1	no	—
149	C₃₁×C₄⋊C₈	—	2	1	no	—
150	C₃₁×C₄⋊C₈	—	2	1	no	—
151	C₃₁×C₄⋊C₈	—	2	1	no	—
152	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₂²⋊C₈	—	2	1	no	—
161	C₃₁×C₂²⋊C₈	—	2	1	no	—
162	C₃₁×C₂²⋊C₈	—	2	1	no	—
163	C₃₁×C₂²⋊C₈	—	2	1	no	—
164	C₃₁×C₂²⋊C₈	—	2	1	no	—
165	C₃₁×C₂²⋊C₈	—	2	1	no	—
166	C₃₁×C₂²⋊C₈	—	2	1	no	—
167	C₃₁×#97	—	2	1	no	—
168	C₃₁×#97	—	2	1	no	—
169	C₃₁×#97	—	2	1	no	—
170	C₃₁×#97	—	2	1	no	—
171	C₄×C₈×C₃₁	—	2	1	no	—
172	C₄×C₈×C₃₁	—	2	1	no	—
173	C₄×C₈×C₃₁	—	2	1	no	—
174	C₂⁴×C₃₁	—	2	2	no	—
175	#41×C₃₁	—	4	1	no	—
176	#41×C₃₁	—	4	1	no	—
177	#41×C₃₁	—	8	1	no	—
178	#41×C₃₁	—	8	1	no	—
179	#41×C₃₁	—	8	1	no	—
180	#41×C₃₁	—	8	1	no	—
181	#41×C₃₁	—	8	2	no	—
182	#41×C₃₁	—	8	2	no	—
183	C₂×Q₈×C₃₁	—	2	1	no	—
184	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
185	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
186	C₂×D₄×C₃₁	—	2	2	no	—
187	C₂×D₄×C₃₁	—	2	2	no	—
188	C₂×D₄×C₃₁	—	2	2	no	—
189	C₂×D₄×C₃₁	—	2	2	no	—
190	C₂×D₄×C₃₁	—	2	2	no	—
191	C₂×D₄×C₃₁	—	2	2	no	—
192	C₂×D₄×C₃₁	—	2	2	no	—
193	C₂×D₄×C₃₁	—	2	1	no	—
194	C₂×D₄×C₃₁	—	2	1	no	—
195	C₂×D₄×C₃₁	—	2	1	no	—
196	C₂×D₄×C₃₁	—	2	1	no	—
197	C₂×D₄×C₃₁	—	4	2	no	—
198	C₂×D₄×C₃₁	—	4	2	no	—
199	C₂×D₄×C₃₁	—	8	1	no	—
200	C₂×D₄×C₃₁	—	8	1	no	—
201	C₂×D₄×C₃₁	—	8	2	no	—
202	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
203	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
204	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
205	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
206	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
207	C₂²×C₄×C₃₁	—	2	2	no	—
208	C₂²×C₄×C₃₁	—	2	2	no	—
209	C₂²×C₄×C₃₁	—	2	2	no	—
210	C₂²×C₄×C₃₁	—	2	2	no	—
211	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
220	M₁₆×C₃₁	—	4	2	no	—
221	M₁₆×C₃₁	—	8	1	no	—
222	M₁₆×C₃₁	—	8	1	no	—
223	C₂×C₈×C₃₁	—	2	1	no	—
224	C₂×C₈×C₃₁	—	2	1	no	—
225	C₂×C₈×C₃₁	—	2	1	no	—
226	C₂×C₈×C₃₁	—	2	1	no	—
227	C₂×C₈×C₃₁	—	2	1	no	—
228	C₂×C₈×C₃₁	—	2	1	no	—
229	C₂×C₈×C₃₁	—	2	1	no	—
230	C₂×C₈×C₃₁	—	2	1	no	—
231	C₂×C₈×C₃₁	—	4	2	no	—
232	C₂×C₈×C₃₁	—	8	1	no	—
233	C₄⋊C₄×C₃₁	—	2	2	no	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₄⋊C₄×C₃₁	—	2	1	no	—
237	C₄⋊C₄×C₃₁	—	2	1	no	—
238	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
239	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
240	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
241	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
242	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
243	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
244	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
245	C₂²⋊C₄×C₃₁	—	2	2	no	—
246	C₂²⋊C₄×C₃₁	—	2	2	no	—
247	C₂²⋊C₄×C₃₁	—	2	2	no	—
248	C₂²⋊C₄×C₃₁	—	2	2	no	—
249	C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂²⋊C₄×C₃₁	—	2	2	no	—
251	C₂²⋊C₄×C₃₁	—	2	2	no	—
252	C₂²⋊C₄×C₃₁	—	2	2	no	—
253	C₂²⋊C₄×C₃₁	—	2	2	no	—
254	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
255	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
256	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
257	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
258	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
259	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
260	C₄²×C₃₁	—	2	2	no	—
261	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
262	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
263	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
264	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
271	#17766	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	4	4	no	—
275	C₂³×C₃₁	—	8	2	no	—
276	C₂³×C₃₁	—	8	2	no	—
277	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	Q₈×C₃₁	—	4	1	no	—
281	Q₈×C₃₁	—	4	2	no	—
282	Q₈×C₃₁	—	4	1	no	—
283	Q₈×C₃₁	—	4	1	no	—
284	D₄×C₃₁	—	4	1	no	—
285	D₄×C₃₁	—	4	1	no	—
286	D₄×C₃₁	—	4	1	no	—
287	D₄×C₃₁	—	4	2	no	—
288	D₄×C₃₁	—	4	2	no	—
289	D₄×C₃₁	—	4	4	no	—
290	D₄×C₃₁	—	4	1	no	—
291	D₄×C₃₁	—	4	1	no	—
292	D₄×C₃₁	—	4	1	no	—
293	D₄×C₃₁	—	4	1	no	—
294	D₄×C₃₁	—	4	1	no	—
295	D₄×C₃₁	—	4	1	no	—
296	D₄×C₃₁	—	4	1	no	—
297	D₄×C₃₁	—	4	1	no	—
298	D₄×C₃₁	—	8	2	no	—
299	D₄×C₃₁	—	8	2	no	—
300	D₄×C₃₁	—	8	2	no	—
301	D₄×C₃₁	—	8	2	no	—
302	D₄×C₃₁	—	8	2	no	—
303	D₄×C₃₁	—	8	2	no	—
304	C₂×C₄×C₃₁	—	2	1	no	—
305	C₂×C₄×C₃₁	—	2	1	no	—
306	C₂×C₄×C₃₁	—	2	1	no	—
307	C₂×C₄×C₃₁	—	2	1	no	—
308	C₂×C₄×C₃₁	—	2	1	no	—
309	C₂×C₄×C₃₁	—	2	1	no	—
310	C₂×C₄×C₃₁	—	2	1	no	—
311	C₂×C₄×C₃₁	—	2	1	no	—
312	C₂×C₄×C₃₁	—	2	1	no	—
313	C₂×C₄×C₃₁	—	2	1	no	—
314	C₂×C₄×C₃₁	—	2	1	no	—
315	C₂×C₄×C₃₁	—	2	1	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	4	1	no	—
319	C₂×C₄×C₃₁	—	4	1	no	—
320	C₂×C₄×C₃₁	—	4	1	no	—
321	C₂×C₄×C₃₁	—	8	2	no	—
322	C₂×C₄×C₃₁	—	8	2	no	—
323	C₂×C₄×C₃₁	—	8	2	no	—
324	C₂×C₄×C₃₁	—	8	2	no	—
325	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₈×C₃₁	—	4	1	no	—
338	C₈×C₃₁	—	4	1	no	—
339	C₈×C₃₁	—	4	1	no	—
340	C₈×C₃₁	—	4	1	no	—
341	C₈×C₃₁	—	4	1	no	—
342	C₈×C₃₁	—	4	1	no	—
343	C₈×C₃₁	—	4	1	no	—
344	C₈×C₃₁	—	4	1	no	—
345	#3508	C₂×C₃₁	1	1	yes	characteristic
346	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#1560	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#1559	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#1557	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#1555	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#1554	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#1553	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#1551	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#1551	C₂×C₃₁	1	1	yes	characteristic, complemented
356	#1547	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#1545	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#1543	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#1540	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	1	no	—
362	C₂²×C₃₁	—	2	1	no	—
363	C₂²×C₃₁	—	2	1	no	—
364	C₂²×C₃₁	—	2	1	no	—
365	C₂²×C₃₁	—	2	1	no	—
366	C₂²×C₃₁	—	2	1	no	—
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	2	1	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	16	4	no	—
376	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
377	C₄×C₃₁	—	2	1	no	—
378	C₄×C₃₁	—	2	1	no	—
379	C₄×C₃₁	—	2	1	no	—
380	C₄×C₃₁	—	2	1	no	—
381	C₄×C₃₁	—	2	1	no	—
382	C₄×C₃₁	—	2	1	no	—
383	C₄×C₃₁	—	2	1	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	4	2	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	#575	1	1	yes	characteristic
390	C₄×C₃₁	#575	1	1	yes	characteristic
391	C₄×C₃₁	#576	1	1	yes	characteristic
392	C₄×C₃₁	#577	1	1	yes	characteristic
393	#559	—	2	1	no	—
394	#559	C₄×C₃₁	1	2	yes	—
395	#550	—	2	1	no	—
396	#550	C₄×C₃₁	1	2	yes	—
397	#546	—	2	1	no	—
398	#546	—	2	1	no	—
399	#546	C₄×C₃₁	1	2	yes	—
400	#546	C₄×C₃₁	1	2	yes	—
401	#540	—	2	1	no	—
402	#540	—	2	1	no	—
403	#535	—	2	1	no	—
404	#533	C₂²×C₃₁	1	1	yes	characteristic
405	#532	C₂²×C₃₁	1	1	yes	characteristic
406	#532	C₂²×C₃₁	1	1	yes	characteristic
407	#532	C₂²×C₃₁	1	1	yes	characteristic
408	#532	C₂²×C₃₁	1	1	yes	characteristic
409	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
410	#518	—	2	1	no	—
411	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
412	#446	—	2	1	no	—
413	#436	—	2	1	no	—
414	#435	—	2	1	no	—
415	#435	—	2	1	no	—
416	#433	—	2	1	no	—
417	#433	—	2	1	no	—
418	#432	C₂²×C₃₁	1	1	yes	characteristic
419	#432	C₂²×C₃₁	1	1	yes	characteristic
420	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
421	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	#431	C₂²×C₃₁	1	1	yes	characteristic
423	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
425	#423	C₂²×C₃₁	1	1	yes	characteristic
426	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
428	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
429	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	#408	—	2	1	no	—
431	#405	—	2	1	no	—
432	#333	C₂²×C₃₁	1	1	yes	characteristic, complemented
433	#333	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	#333	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	#333	C₂²×C₃₁	1	1	yes	characteristic, complemented
436	#332	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	#332	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	#332	C₂²×C₃₁	1	1	yes	characteristic, complemented
439	#332	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	#331	C₂²×C₃₁	1	1	yes	characteristic
441	#331	C₂²×C₃₁	1	1	yes	characteristic
442	#331	C₂²×C₃₁	1	1	yes	characteristic
443	#331	C₂²×C₃₁	1	1	yes	characteristic
444	#331	C₂²×C₃₁	1	1	yes	characteristic
445	#331	C₂²×C₃₁	1	1	yes	characteristic
446	#331	C₂²×C₃₁	1	1	yes	characteristic
447	#331	C₂²×C₃₁	1	1	yes	characteristic
448	C₂×C₃₁	—	4	1	no	—
449	C₂×C₃₁	—	4	1	no	—
450	C₂×C₃₁	—	4	1	no	—
451	C₂×C₃₁	—	8	2	no	—
452	C₂×C₃₁	—	8	2	no	—
453	C₂×C₃₁	#2888	1	1	yes	characteristic
454	C₂×C₃₁	#2896	1	1	yes	characteristic
455	C₂×C₃₁	#2897	1	1	yes	characteristic
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
459	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
460	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
464	C₂×M₁₆	—	2	1	no	—
465	C₂×M₁₆	—	2	1	no	—
466	C₂×M₁₆	—	2	1	no	—
467	C₂²×C₈	—	2	1	no	—
468	C₂²×C₈	—	2	1	no	—
469	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
471	#127	—	2	2	no	—
472	#127	—	2	1	no	—
473	#127	—	2	1	no	—
474	#127	C₂×C₄×C₃₁	1	2	yes	—
475	#127	C₂³×C₃₁	1	1	yes	characteristic
476	#127	C₂³×C₃₁	1	1	yes	characteristic
477	#125	—	2	1	no	—
478	#124	—	2	2	no	—
479	#124	—	2	1	no	—
480	#124	—	2	1	no	—
481	#124	C₂×C₄×C₃₁	1	2	yes	—
482	#124	C₂×C₄×C₃₁	1	2	yes	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	2	no	—
486	#123	—	2	2	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
489	#121	—	2	1	no	—
490	#121	—	2	1	no	—
491	#121	—	2	1	no	—
492	#121	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	C₂×C₄×C₃₁	1	2	yes	—
500	#121	C₂×C₄×C₃₁	1	2	yes	—
501	#120	—	2	2	no	—
502	#120	—	2	2	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	C₂×C₄×C₃₁	1	2	yes	—
505	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
506	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
516	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
517	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
518	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
519	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
520	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
521	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
522	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
523	#117	—	2	1	no	—
524	#117	D₄×C₃₁	1	1	yes	characteristic
525	#117	D₄×C₃₁	1	1	yes	characteristic
526	#117	D₄×C₃₁	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
532	C₄⋊C₈	—	2	1	no	—
533	C₄⋊C₈	—	2	1	no	—
534	C₄⋊C₈	—	2	1	no	—
535	C₄⋊C₈	—	2	1	no	—
536	C₄⋊C₈	—	2	1	no	—
537	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
540	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
545	C₂²⋊C₈	—	2	1	no	—
546	C₂²⋊C₈	—	2	1	no	—
547	C₂²⋊C₈	—	2	1	no	—
548	C₂²⋊C₈	—	2	1	no	—
549	C₂²⋊C₈	—	2	1	no	—
550	C₂²⋊C₈	—	2	1	no	—
551	C₂²⋊C₈	—	2	1	no	—
552	#97	—	2	1	no	—
553	#97	—	2	1	no	—
554	#97	—	2	1	no	—
555	#97	—	2	1	no	—
556	C₄×C₈	—	2	1	no	—
557	C₄×C₈	—	2	1	no	—
558	C₄×C₈	—	2	1	no	—
559	C₃₁	#17766	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	—	2	2	no	—
561	#41	—	4	1	no	—
562	#41	—	4	1	no	—
563	#41	—	8	1	no	—
564	#41	—	8	1	no	—
565	#41	—	8	1	no	—
566	#41	—	8	1	no	—
567	#41	—	8	2	no	—
568	#41	—	8	2	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
571	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	8	1	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	—	8	2	no	—
588	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
589	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
590	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
591	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
592	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
606	M₁₆	—	4	2	no	—
607	M₁₆	—	8	1	no	—
608	M₁₆	—	8	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	4	2	no	—
618	C₂×C₈	—	8	1	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
625	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
626	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
627	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
628	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
629	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
630	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
641	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
642	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
643	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
644	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
645	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
646	C₄²	—	2	2	no	—
647	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
648	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
649	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
650	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
652	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
653	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
654	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
655	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
656	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	8	2	no	—
661	C₂³	—	8	2	no	—
662	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
663	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
664	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
665	Q₈	—	4	1	no	—
666	Q₈	—	4	2	no	—
667	Q₈	—	4	1	no	—
668	Q₈	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	2	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	1	no	—
683	D₄	—	8	2	no	—
684	D₄	—	8	2	no	—
685	D₄	—	8	2	no	—
686	D₄	—	8	2	no	—
687	D₄	—	8	2	no	—
688	D₄	—	8	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	—	8	2	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	—	8	2	no	—
710	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
711	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
714	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
716	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
717	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
718	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
719	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
722	C₈	—	4	1	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₈	—	4	1	no	—
727	C₈	—	4	1	no	—
728	C₈	—	4	1	no	—
729	C₈	—	4	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	16	4	no	—
746	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	C₃₁×#575	1	1	yes	characteristic
760	C₄	C₃₁×#575	1	1	yes	characteristic
761	C₄	C₃₁×#576	1	1	yes	characteristic
762	C₄	C₃₁×#577	1	1	yes	characteristic
763	C₂	—	4	1	no	—
764	C₂	—	4	1	no	—
765	C₂	—	4	1	no	—
766	C₂	—	8	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₃₁×#2888	1	1	yes	characteristic
769	C₂	C₃₁×#2896	1	1	yes	characteristic
770	C₂	C₃₁×#2897	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₃₁×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
2. C₃₁×#2989	C₂	semidirect
3. C₃₁×#2925	C₂	semidirect
4. C₃₁×#1560	C₂	semidirect
5. C₃₁×#1559	C₂	semidirect
6. C₃₁×#1557	C₂	semidirect
7. C₃₁×#1555	C₂	semidirect
8. C₃₁×#1554	C₂	semidirect
9. C₃₁×#1553	C₂	semidirect
10. C₃₁×#1551	C₂	semidirect
11. C₃₁×#1551	C₂	semidirect
12. C₃₁×#1547	C₂	semidirect
13. C₃₁×#1545	C₂	semidirect
14. C₃₁×#1543	C₂	semidirect
15. C₃₁×#1540	C₂	semidirect
43. C₃₁×#432	C₂²	semidirect
44. C₃₁×#432	C₂²	semidirect
46. C₃₁×#431	C₂²	semidirect
47. C₃₁×#431	C₂²	semidirect
49. C₃₁×#423	C₂²	semidirect
50. C₃₁×#423	C₂²	semidirect
51. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
52. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
55. C₃₁×#333	C₂²	semidirect
56. C₃₁×#333	C₂²	semidirect
57. C₃₁×#333	C₂²	semidirect
58. C₃₁×#333	C₂²	semidirect
59. C₃₁×#332	C₂²	semidirect
60. C₃₁×#332	C₂²	semidirect
61. C₃₁×#332	C₂²	semidirect
62. C₃₁×#332	C₂²	semidirect
271. #17766	C₃₁	direct (N × H)
346. #2989	C₂×C₃₁	semidirect
347. #2925	C₂×C₃₁	semidirect
348. #1560	C₂×C₃₁	semidirect
349. #1559	C₂×C₃₁	semidirect
350. #1557	C₂×C₃₁	semidirect
351. #1555	C₂×C₃₁	semidirect
352. #1554	C₂×C₃₁	semidirect
353. #1553	C₂×C₃₁	semidirect
354. #1551	C₂×C₃₁	semidirect
355. #1551	C₂×C₃₁	semidirect
356. #1547	C₂×C₃₁	semidirect
357. #1545	C₂×C₃₁	semidirect
358. #1543	C₂×C₃₁	semidirect
359. #1540	C₂×C₃₁	semidirect
420. #432	C₂²×C₃₁	semidirect
421. #432	C₂²×C₃₁	semidirect
423. #431	C₂²×C₃₁	semidirect
424. #431	C₂²×C₃₁	semidirect
426. #423	C₂²×C₃₁	semidirect
427. #423	C₂²×C₃₁	semidirect
428. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
429. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
432. #333	C₂²×C₃₁	semidirect
433. #333	C₂²×C₃₁	semidirect
434. #333	C₂²×C₃₁	semidirect
435. #333	C₂²×C₃₁	semidirect
436. #332	C₂²×C₃₁	semidirect
437. #332	C₂²×C₃₁	semidirect
438. #332	C₂²×C₃₁	semidirect
439. #332	C₂²×C₃₁	semidirect
559. C₃₁	#17766	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×#3508	2
C₃₁×#2989	2
C₃₁×#2925	2
C₃₁×#1560	2
C₃₁×#1559	2
C₃₁×#1557	2
C₃₁×#1555	2
C₃₁×#1554	2
C₃₁×#1553	2
C₃₁×#1551	2
C₃₁×#1547	2
C₃₁×#1545	2
C₃₁×#1543	2
C₃₁×#1540	2
#17766	31

Subgroups — C31×#17766 #21474525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17766 #21474525