Subgroups — C₃₁×#17775 #21474534

Order 7936.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1559	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1557	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1556	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1554	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1553	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1551	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#556	—	2	1	no	—
17	C₃₁×#555	—	2	1	no	—
18	C₃₁×#554	—	2	1	no	—
19	C₃₁×#553	—	2	1	no	—
20	C₃₁×#553	—	2	1	no	—
21	C₃₁×#548	—	2	1	no	—
22	C₃₁×#548	—	2	1	no	—
23	C₃₁×#547	—	2	1	no	—
24	C₃₁×#542	C₄	1	2	yes	—
25	C₃₁×#542	C₄	1	2	yes	—
26	C₃₁×#537	C₄	1	2	yes	—
27	C₃₁×#533	C₂²	1	1	yes	characteristic
28	C₃₁×#533	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃₁×#520	C₄	1	2	yes	—
34	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#446	—	2	1	no	—
36	C₃₁×#446	—	2	1	no	—
37	C₃₁×#435	—	2	1	no	—
38	C₃₁×#435	—	2	1	no	—
39	C₃₁×#435	—	2	1	no	—
40	C₃₁×#435	—	2	1	no	—
41	C₈×D₄×C₃₁	—	2	1	no	—
42	C₈×D₄×C₃₁	—	2	1	no	—
43	C₃₁×#432	C₂²	1	1	yes	characteristic
44	C₃₁×#432	C₂²	1	1	yes	characteristic
45	C₃₁×#432	C₂²	1	1	yes	characteristic
46	C₃₁×#432	C₂²	1	1	yes	characteristic
47	C₃₁×#431	C₂²	1	1	yes	characteristic
48	C₃₁×#431	C₂²	1	1	yes	characteristic
49	C₃₁×#423	C₂²	1	1	yes	characteristic
50	C₃₁×#423	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₃₁×#333	C₂²	1	1	yes	characteristic
56	C₃₁×#333	C₂²	1	1	yes	characteristic
57	C₃₁×#333	C₂²	1	1	yes	characteristic
58	C₃₁×#333	C₂²	1	1	yes	characteristic
59	C₃₁×#332	C₂²	1	1	yes	characteristic
60	C₃₁×#332	C₂²	1	1	yes	characteristic
61	C₃₁×#332	C₂²	1	1	yes	characteristic
62	C₃₁×#332	C₂²	1	1	yes	characteristic
63	C₃₁×#332	C₂²	1	1	yes	characteristic
64	C₃₁×#332	C₂²	1	1	yes	characteristic
65	C₃₁×#332	C₂²	1	1	yes	characteristic
66	C₃₁×#332	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	1	yes	characteristic
75	C₂²×Q₈×C₃₁	—	2	1	no	—
76	C₂×M₁₆×C₃₁	—	2	1	no	—
77	C₂×M₁₆×C₃₁	—	2	1	no	—
78	C₂²×C₈×C₃₁	—	2	1	no	—
79	C₂²×C₈×C₃₁	—	2	1	no	—
80	C₂²×C₈×C₃₁	—	2	1	no	—
81	C₂²×C₈×C₃₁	—	2	1	no	—
82	C₃₁×C₄⋊Q₈	—	2	1	no	—
83	C₃₁×C₄⋊Q₈	—	2	1	no	—
84	C₃₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
85	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₃₁×#127	C₂³	1	1	yes	characteristic
89	C₃₁×#126	—	2	2	no	—
90	C₃₁×#126	—	2	2	no	—
91	C₃₁×#125	—	2	1	no	—
92	C₃₁×#125	—	2	1	no	—
93	C₃₁×#124	—	2	2	no	—
94	C₃₁×#124	—	2	2	no	—
95	C₃₁×#124	—	2	1	no	—
96	C₃₁×#124	—	2	1	no	—
97	C₃₁×#124	C₂×C₄	1	2	yes	—
98	C₃₁×#123	—	2	2	no	—
99	C₃₁×#123	—	2	2	no	—
100	C₃₁×C₂²⋊Q₈	—	2	2	no	—
101	C₃₁×C₂²⋊Q₈	—	2	1	no	—
102	C₃₁×C₂²⋊Q₈	—	2	1	no	—
103	C₃₁×C₂²⋊Q₈	—	2	2	no	—
104	C₃₁×C₂²⋊Q₈	—	2	2	no	—
105	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
106	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
107	C₃₁×#121	—	2	2	no	—
108	C₃₁×#121	—	2	2	no	—
109	C₃₁×#121	—	2	2	no	—
110	C₃₁×#121	—	2	1	no	—
111	C₃₁×#121	—	2	1	no	—
112	C₃₁×#121	—	2	1	no	—
113	C₃₁×#121	—	2	1	no	—
114	C₃₁×#121	C₂×C₄	1	2	yes	—
115	C₃₁×#121	C₂×C₄	1	2	yes	—
116	C₄×Q₈×C₃₁	—	2	1	no	—
117	C₄×Q₈×C₃₁	—	2	1	no	—
118	C₄×Q₈×C₃₁	C₂×C₄	1	2	yes	—
119	C₄×Q₈×C₃₁	C₂×C₄	1	2	yes	—
120	C₄×Q₈×C₃₁	D₄	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	C₂×C₄	1	2	yes	—
129	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
130	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
131	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
132	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
133	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
134	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
135	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
136	C₃₁×#117	—	2	1	no	—
137	C₃₁×#117	—	2	1	no	—
138	C₃₁×#117	—	2	2	no	—
139	C₃₁×#117	C₂×C₄	1	1	yes	characteristic
140	C₃₁×#117	C₂×C₄	1	1	yes	characteristic
141	C₃₁×#117	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
143	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
144	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
153	C₃₁×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	—	2	1	no	—
168	C₃₁×#97	—	2	1	no	—
169	C₃₁×#97	—	2	1	no	—
170	C₃₁×#97	—	2	1	no	—
171	C₃₁×#97	—	2	1	no	—
172	C₄×C₈×C₃₁	—	2	1	no	—
173	C₄×C₈×C₃₁	—	2	1	no	—
174	#41×C₃₁	—	4	2	no	—
175	#41×C₃₁	—	4	4	no	—
176	#41×C₃₁	—	8	1	no	—
177	#41×C₃₁	—	8	1	no	—
178	#41×C₃₁	—	8	1	no	—
179	#41×C₃₁	—	8	1	no	—
180	C₂×Q₈×C₃₁	—	2	2	no	—
181	C₂×Q₈×C₃₁	—	2	1	no	—
182	C₂×Q₈×C₃₁	—	2	1	no	—
183	C₂×Q₈×C₃₁	—	8	1	no	—
184	C₂×Q₈×C₃₁	—	8	1	no	—
185	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
186	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
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	1	no	—
191	C₂×D₄×C₃₁	—	2	1	no	—
192	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
193	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
196	C₂²×C₄×C₃₁	—	2	2	no	—
197	C₂²×C₄×C₃₁	—	2	2	no	—
198	C₂²×C₄×C₃₁	—	2	2	no	—
199	C₂²×C₄×C₃₁	—	2	2	no	—
200	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
209	M₁₆×C₃₁	—	8	1	no	—
210	M₁₆×C₃₁	—	8	1	no	—
211	C₂×C₈×C₃₁	—	2	1	no	—
212	C₂×C₈×C₃₁	—	2	1	no	—
213	C₂×C₈×C₃₁	—	2	1	no	—
214	C₂×C₈×C₃₁	—	2	1	no	—
215	C₂×C₈×C₃₁	—	2	1	no	—
216	C₂×C₈×C₃₁	—	2	1	no	—
217	C₂×C₈×C₃₁	—	2	1	no	—
218	C₂×C₈×C₃₁	—	2	1	no	—
219	C₂×C₈×C₃₁	—	8	1	no	—
220	C₂×C₈×C₃₁	—	8	1	no	—
221	C₂×C₈×C₃₁	—	8	1	no	—
222	C₂×C₈×C₃₁	—	8	1	no	—
223	C₄⋊C₄×C₃₁	—	2	2	no	—
224	C₄⋊C₄×C₃₁	—	2	2	no	—
225	C₄⋊C₄×C₃₁	—	2	2	no	—
226	C₄⋊C₄×C₃₁	—	2	2	no	—
227	C₄⋊C₄×C₃₁	—	2	2	no	—
228	C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₄⋊C₄×C₃₁	—	2	1	no	—
230	C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₄⋊C₄×C₃₁	—	2	1	no	—
232	C₄⋊C₄×C₃₁	—	2	1	no	—
233	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
234	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
235	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
236	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
237	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
238	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
239	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
240	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
241	C₂²⋊C₄×C₃₁	—	2	2	no	—
242	C₂²⋊C₄×C₃₁	—	2	2	no	—
243	C₂²⋊C₄×C₃₁	—	2	2	no	—
244	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
251	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
252	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
253	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
254	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
255	C₄²×C₃₁	—	2	2	no	—
256	C₄²×C₃₁	—	2	2	no	—
257	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
258	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
259	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
260	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₃₁	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
267	#17775	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	Q₈×C₃₁	—	4	1	no	—
273	Q₈×C₃₁	—	4	2	no	—
274	Q₈×C₃₁	—	4	1	no	—
275	Q₈×C₃₁	—	4	1	no	—
276	Q₈×C₃₁	—	4	1	no	—
277	Q₈×C₃₁	—	4	1	no	—
278	Q₈×C₃₁	—	8	2	no	—
279	D₄×C₃₁	—	2	2	no	—
280	D₄×C₃₁	—	2	2	no	—
281	D₄×C₃₁	—	4	1	no	—
282	D₄×C₃₁	—	4	2	no	—
283	D₄×C₃₁	—	4	4	no	—
284	D₄×C₃₁	—	4	1	no	—
285	D₄×C₃₁	—	4	1	no	—
286	D₄×C₃₁	—	4	1	no	—
287	D₄×C₃₁	—	4	1	no	—
288	D₄×C₃₁	—	8	2	no	—
289	D₄×C₃₁	—	8	2	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	1	no	—
292	C₂×C₄×C₃₁	—	2	1	no	—
293	C₂×C₄×C₃₁	—	2	1	no	—
294	C₂×C₄×C₃₁	—	2	1	no	—
295	C₂×C₄×C₃₁	—	2	1	no	—
296	C₂×C₄×C₃₁	—	2	1	no	—
297	C₂×C₄×C₃₁	—	2	1	no	—
298	C₂×C₄×C₃₁	—	2	1	no	—
299	C₂×C₄×C₃₁	—	2	1	no	—
300	C₂×C₄×C₃₁	—	2	1	no	—
301	C₂×C₄×C₃₁	—	2	1	no	—
302	C₂×C₄×C₃₁	—	2	1	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	4	1	no	—
307	C₂×C₄×C₃₁	—	4	1	no	—
308	C₂×C₄×C₃₁	—	4	4	no	—
309	C₂×C₄×C₃₁	—	8	2	no	—
310	C₂×C₄×C₃₁	—	8	2	no	—
311	C₂×C₄×C₃₁	—	8	2	no	—
312	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
324	C₈×C₃₁	—	4	1	no	—
325	C₈×C₃₁	—	4	1	no	—
326	C₈×C₃₁	—	4	1	no	—
327	C₈×C₃₁	—	4	1	no	—
328	C₈×C₃₁	—	4	1	no	—
329	C₈×C₃₁	—	4	1	no	—
330	C₈×C₃₁	—	4	1	no	—
331	C₈×C₃₁	—	4	1	no	—
332	#3511	C₂×C₃₁	1	1	yes	characteristic
333	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
335	#1559	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#1557	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#1556	C₂×C₃₁	1	1	yes	characteristic, complemented
338	#1554	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#1553	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#1551	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#1551	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#1550	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#1547	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#1542	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#1540	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂²×C₃₁	—	2	1	no	—
348	C₂²×C₃₁	—	2	1	no	—
349	C₂²×C₃₁	—	2	1	no	—
350	C₂²×C₃₁	—	2	1	no	—
351	C₂²×C₃₁	—	2	1	no	—
352	C₂²×C₃₁	—	2	1	no	—
353	C₂²×C₃₁	—	2	1	no	—
354	C₂²×C₃₁	—	2	1	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	4	2	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	#413	1	2	yes	—
359	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
360	C₄×C₃₁	—	2	1	no	—
361	C₄×C₃₁	—	2	1	no	—
362	C₄×C₃₁	—	2	1	no	—
363	C₄×C₃₁	—	2	1	no	—
364	C₄×C₃₁	—	2	1	no	—
365	C₄×C₃₁	—	2	1	no	—
366	C₄×C₃₁	—	2	1	no	—
367	C₄×C₃₁	—	2	1	no	—
368	C₄×C₃₁	—	2	1	no	—
369	C₄×C₃₁	—	2	1	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	2	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	#576	1	1	yes	characteristic
374	C₄×C₃₁	#577	1	1	yes	characteristic
375	C₄×C₃₁	#577	1	1	yes	characteristic
376	C₄×C₃₁	#578	1	1	yes	characteristic
377	#556	—	2	1	no	—
378	#555	—	2	1	no	—
379	#554	—	2	1	no	—
380	#553	—	2	1	no	—
381	#553	—	2	1	no	—
382	#548	—	2	1	no	—
383	#548	—	2	1	no	—
384	#547	—	2	1	no	—
385	#542	C₄×C₃₁	1	2	yes	—
386	#542	C₄×C₃₁	1	2	yes	—
387	#537	C₄×C₃₁	1	2	yes	—
388	#533	C₂²×C₃₁	1	1	yes	characteristic
389	#533	C₂²×C₃₁	1	1	yes	characteristic
390	#532	C₂²×C₃₁	1	1	yes	characteristic
391	#532	C₂²×C₃₁	1	1	yes	characteristic
392	#532	C₂²×C₃₁	1	1	yes	characteristic
393	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
394	#520	C₄×C₃₁	1	2	yes	—
395	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
396	#446	—	2	1	no	—
397	#446	—	2	1	no	—
398	#435	—	2	1	no	—
399	#435	—	2	1	no	—
400	#435	—	2	1	no	—
401	#435	—	2	1	no	—
402	C₈×D₄	—	2	1	no	—
403	C₈×D₄	—	2	1	no	—
404	#432	C₂²×C₃₁	1	1	yes	characteristic
405	#432	C₂²×C₃₁	1	1	yes	characteristic
406	#432	C₂²×C₃₁	1	1	yes	characteristic
407	#432	C₂²×C₃₁	1	1	yes	characteristic
408	#431	C₂²×C₃₁	1	1	yes	characteristic
409	#431	C₂²×C₃₁	1	1	yes	characteristic
410	#423	C₂²×C₃₁	1	1	yes	characteristic
411	#423	C₂²×C₃₁	1	1	yes	characteristic
412	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
413	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
414	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
415	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
416	#333	C₂²×C₃₁	1	1	yes	characteristic
417	#333	C₂²×C₃₁	1	1	yes	characteristic
418	#333	C₂²×C₃₁	1	1	yes	characteristic
419	#333	C₂²×C₃₁	1	1	yes	characteristic
420	#332	C₂²×C₃₁	1	1	yes	characteristic
421	#332	C₂²×C₃₁	1	1	yes	characteristic
422	#332	C₂²×C₃₁	1	1	yes	characteristic
423	#332	C₂²×C₃₁	1	1	yes	characteristic
424	#332	C₂²×C₃₁	1	1	yes	characteristic
425	#332	C₂²×C₃₁	1	1	yes	characteristic
426	#332	C₂²×C₃₁	1	1	yes	characteristic
427	#332	C₂²×C₃₁	1	1	yes	characteristic
428	#331	C₂²×C₃₁	1	1	yes	characteristic
429	#331	C₂²×C₃₁	1	1	yes	characteristic
430	#331	C₂²×C₃₁	1	1	yes	characteristic
431	#331	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×C₃₁	—	2	2	no	—
433	C₂×C₃₁	—	4	1	no	—
434	C₂×C₃₁	—	4	1	no	—
435	C₂×C₃₁	—	8	2	no	—
436	C₂×C₃₁	C₂×#413	1	1	yes	characteristic
437	C₂×C₃₁	#2897	1	1	yes	characteristic
438	C₂×C₃₁	#2898	1	1	yes	characteristic
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
442	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
443	C₂²×Q₈	—	2	1	no	—
444	C₂×M₁₆	—	2	1	no	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂²×C₈	—	2	1	no	—
447	C₂²×C₈	—	2	1	no	—
448	C₂²×C₈	—	2	1	no	—
449	C₂²×C₈	—	2	1	no	—
450	C₄⋊Q₈	—	2	1	no	—
451	C₄⋊Q₈	—	2	1	no	—
452	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
453	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
454	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
456	#127	C₂³×C₃₁	1	1	yes	characteristic
457	#126	—	2	2	no	—
458	#126	—	2	2	no	—
459	#125	—	2	1	no	—
460	#125	—	2	1	no	—
461	#124	—	2	2	no	—
462	#124	—	2	2	no	—
463	#124	—	2	1	no	—
464	#124	—	2	1	no	—
465	#124	C₂×C₄×C₃₁	1	2	yes	—
466	#123	—	2	2	no	—
467	#123	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
474	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	C₂×C₄×C₃₁	1	2	yes	—
483	#121	C₂×C₄×C₃₁	1	2	yes	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	C₂×C₄×C₃₁	1	2	yes	—
487	C₄×Q₈	C₂×C₄×C₃₁	1	2	yes	—
488	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
489	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
497	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
498	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
499	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
500	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
501	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
502	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
503	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
504	#117	—	2	1	no	—
505	#117	—	2	1	no	—
506	#117	—	2	2	no	—
507	#117	C₂×C₄×C₃₁	1	1	yes	characteristic
508	#117	C₂×C₄×C₃₁	1	1	yes	characteristic
509	#117	C₂×C₄×C₃₁	1	1	yes	characteristic
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	2	no	—
512	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
513	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
516	C₄⋊C₈	—	2	1	no	—
517	C₄⋊C₈	—	2	1	no	—
518	C₄⋊C₈	—	2	1	no	—
519	C₄⋊C₈	—	2	1	no	—
520	C₄⋊C₈	—	2	1	no	—
521	C₄⋊C₈	—	2	1	no	—
522	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
523	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
524	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
525	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
526	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
527	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
529	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₂²⋊C₈	—	2	1	no	—
531	C₂²⋊C₈	—	2	1	no	—
532	C₂²⋊C₈	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	C₂²⋊C₈	—	2	1	no	—
535	C₂²⋊C₈	—	2	1	no	—
536	#97	—	2	1	no	—
537	#97	—	2	1	no	—
538	#97	—	2	1	no	—
539	#97	—	2	1	no	—
540	C₄×C₈	—	2	1	no	—
541	C₄×C₈	—	2	1	no	—
542	C₃₁	#17775	1	1	yes	characteristic, direct product factor, Sylow
543	#41	—	4	2	no	—
544	#41	—	4	4	no	—
545	#41	—	8	1	no	—
546	#41	—	8	1	no	—
547	#41	—	8	1	no	—
548	#41	—	8	1	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	8	1	no	—
553	C₂×Q₈	—	8	1	no	—
554	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
555	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
562	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
563	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
564	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
570	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
571	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
578	M₁₆	—	8	1	no	—
579	M₁₆	—	8	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	8	1	no	—
589	C₂×C₈	—	8	1	no	—
590	C₂×C₈	—	8	1	no	—
591	C₂×C₈	—	8	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
603	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
604	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
605	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
606	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
607	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
608	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
609	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
619	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
620	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
621	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
622	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
623	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
624	C₄²	—	2	2	no	—
625	C₄²	—	2	2	no	—
626	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
627	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
628	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
629	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
631	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
632	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
633	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
634	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
636	C₂³	—	2	2	no	—
637	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
638	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
639	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
640	Q₈	—	4	1	no	—
641	Q₈	—	4	2	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	8	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	8	2	no	—
657	D₄	—	8	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
681	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
682	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
683	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
684	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
685	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
686	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
687	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
688	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
689	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₈	—	4	1	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	C₃₁×#413	1	2	yes	—
712	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	C₃₁×#576	1	1	yes	characteristic
727	C₄	C₃₁×#577	1	1	yes	characteristic
728	C₄	C₃₁×#577	1	1	yes	characteristic
729	C₄	C₃₁×#578	1	1	yes	characteristic
730	C₂	—	2	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	8	2	no	—
734	C₂	C₂×C₃₁×#413	1	1	yes	characteristic
735	C₂	C₃₁×#2897	1	1	yes	characteristic
736	C₂	C₃₁×#2898	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×#3511	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×#2990	C₂	semidirect
3. C₃₁×#2990	C₂	semidirect
4. C₃₁×#1559	C₂	semidirect
5. C₃₁×#1557	C₂	semidirect
6. C₃₁×#1556	C₂	semidirect
7. C₃₁×#1554	C₂	semidirect
8. C₃₁×#1553	C₂	semidirect
9. C₃₁×#1551	C₂	semidirect
10. C₃₁×#1551	C₂	semidirect
11. C₃₁×#1550	C₂	semidirect
12. C₃₁×#1547	C₂	semidirect
13. C₃₁×#1542	C₂	semidirect
14. C₃₁×#1540	C₂	semidirect
15. C₂×C₃₁×#332	C₂	semidirect
267. #17775	C₃₁	direct (N × H)
333. #2990	C₂×C₃₁	semidirect
334. #2990	C₂×C₃₁	semidirect
335. #1559	C₂×C₃₁	semidirect
336. #1557	C₂×C₃₁	semidirect
337. #1556	C₂×C₃₁	semidirect
338. #1554	C₂×C₃₁	semidirect
339. #1553	C₂×C₃₁	semidirect
340. #1551	C₂×C₃₁	semidirect
341. #1551	C₂×C₃₁	semidirect
342. #1550	C₂×C₃₁	semidirect
343. #1547	C₂×C₃₁	semidirect
344. #1542	C₂×C₃₁	semidirect
345. #1540	C₂×C₃₁	semidirect
346. C₂×#332	C₂×C₃₁	semidirect
542. C₃₁	#17775	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×#3511	2
C₃₁×#2990	2
C₃₁×#1559	2
C₃₁×#1557	2
C₃₁×#1556	2
C₃₁×#1554	2
C₃₁×#1553	2
C₃₁×#1551	2
C₃₁×#1550	2
C₃₁×#1547	2
C₃₁×#1542	2
C₃₁×#1540	2
C₂×C₃₁×#332	2
#17775	31

Subgroups — C31×#17775 #21474534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17775 #21474534