Subgroups — C₃₁×#17768 #21474527

Order 7936.

918 conjugacy classes of subgroups.

The subgroup lattice has 732 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×#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×#1558	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1557	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×#1550	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#556	C₄	1	2	yes	—
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	C₄	1	2	yes	—
22	C₃₁×#548	C₄	1	2	yes	—
23	C₃₁×#547	C₄	1	2	yes	—
24	C₃₁×#542	—	2	1	no	—
25	C₃₁×#542	—	2	1	no	—
26	C₃₁×#537	—	2	1	no	—
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	—	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
44	C₃₁×#432	C₂²	1	1	yes	characteristic
45	C₃₁×#431	C₂²	1	1	yes	characteristic
46	C₃₁×#431	C₂²	1	1	yes	characteristic
47	C₃₁×#431	C₂²	1	1	yes	characteristic
48	C₃₁×#423	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	C₃₁×#408	—	2	1	no	—
54	C₃₁×#405	—	2	1	no	—
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×#333	C₂²	1	1	yes	characteristic
60	C₃₁×#333	C₂²	1	1	yes	characteristic
61	C₃₁×#333	C₂²	1	1	yes	characteristic
62	C₃₁×#333	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	C₂×C₄	1	2	yes	—
73	C₂×#41×C₃₁	C₂×C₄	1	2	yes	—
74	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
75	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
76	C₂×M₁₆×C₃₁	—	2	1	no	—
77	C₂×M₁₆×C₃₁	—	2	1	no	—
78	C₂×M₁₆×C₃₁	—	2	1	no	—
79	C₂²×C₈×C₃₁	—	2	1	no	—
80	C₂²×C₈×C₃₁	—	2	1	no	—
81	C₃₁×C₄⋊Q₈	—	2	1	no	—
82	C₃₁×C₄⋊Q₈	—	2	1	no	—
83	C₃₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
84	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₃₁×#127	C₂³	1	1	yes	characteristic
88	C₃₁×#126	—	2	2	no	—
89	C₃₁×#126	—	2	2	no	—
90	C₃₁×#125	—	2	1	no	—
91	C₃₁×#125	—	2	1	no	—
92	C₃₁×#124	—	2	2	no	—
93	C₃₁×#124	—	2	2	no	—
94	C₃₁×#124	—	2	1	no	—
95	C₃₁×#124	C₂×C₄	1	2	yes	—
96	C₃₁×#124	C₂×C₄	1	2	yes	—
97	C₃₁×#123	—	2	2	no	—
98	C₃₁×#123	—	2	2	no	—
99	C₃₁×C₂²⋊Q₈	—	2	2	no	—
100	C₃₁×C₂²⋊Q₈	—	2	1	no	—
101	C₃₁×C₂²⋊Q₈	—	2	1	no	—
102	C₃₁×C₂²⋊Q₈	—	2	2	no	—
103	C₃₁×C₂²⋊Q₈	—	2	2	no	—
104	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
105	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
106	C₃₁×#121	—	2	2	no	—
107	C₃₁×#121	—	2	2	no	—
108	C₃₁×#121	—	2	2	no	—
109	C₃₁×#121	—	2	1	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	C₄×Q₈×C₃₁	—	2	1	no	—
116	C₄×Q₈×C₃₁	—	2	1	no	—
117	C₄×Q₈×C₃₁	C₂×C₄	1	2	yes	—
118	C₄×Q₈×C₃₁	C₂×C₄	1	2	yes	—
119	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
120	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
121	C₄×D₄×C₃₁	—	2	2	no	—
122	C₄×D₄×C₃₁	—	2	2	no	—
123	C₄×D₄×C₃₁	—	2	1	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	1	yes	characteristic
130	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
131	C₄×D₄×C₃₁	C₂×C₄	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	C₃₁×#117	—	2	1	no	—
136	C₃₁×#117	—	2	1	no	—
137	C₃₁×#117	—	2	2	no	—
138	C₃₁×#117	D₄	1	1	yes	characteristic
139	C₃₁×#117	D₄	1	1	yes	characteristic
140	C₃₁×#117	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
142	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
143	C₂×C₄⋊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	#41×C₃₁	—	4	1	no	—
175	#41×C₃₁	—	4	1	no	—
176	#41×C₃₁	—	4	2	no	—
177	#41×C₃₁	—	4	2	no	—
178	#41×C₃₁	—	8	2	no	—
179	#41×C₃₁	—	8	2	no	—
180	C₂×Q₈×C₃₁	—	2	2	no	—
181	C₂×Q₈×C₃₁	—	2	1	no	—
182	C₂×Q₈×C₃₁	—	8	2	no	—
183	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
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	1	no	—
190	C₂×D₄×C₃₁	—	2	1	no	—
191	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
195	C₂²×C₄×C₃₁	—	2	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	C₂×D₄	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	M₁₆×C₃₁	—	4	2	no	—
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	—	4	2	no	—
220	C₂×C₈×C₃₁	—	8	1	no	—
221	C₄⋊C₄×C₃₁	—	2	2	no	—
222	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
228	C₄⋊C₄×C₃₁	—	2	1	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	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
239	C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
248	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₃₁	—	2	2	no	—
254	C₄²×C₃₁	—	2	2	no	—
255	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
257	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
258	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₃₁	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
265	#17768	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	Q₈×C₃₁	—	4	1	no	—
271	Q₈×C₃₁	—	4	2	no	—
272	Q₈×C₃₁	—	4	2	no	—
273	Q₈×C₃₁	—	4	1	no	—
274	Q₈×C₃₁	—	4	1	no	—
275	Q₈×C₃₁	—	8	2	no	—
276	D₄×C₃₁	—	4	1	no	—
277	D₄×C₃₁	—	4	1	no	—
278	D₄×C₃₁	—	4	1	no	—
279	D₄×C₃₁	—	4	2	no	—
280	D₄×C₃₁	—	4	4	no	—
281	D₄×C₃₁	—	4	1	no	—
282	D₄×C₃₁	—	4	1	no	—
283	D₄×C₃₁	—	4	1	no	—
284	D₄×C₃₁	—	4	1	no	—
285	D₄×C₃₁	—	8	2	no	—
286	D₄×C₃₁	—	8	2	no	—
287	C₂×C₄×C₃₁	—	2	1	no	—
288	C₂×C₄×C₃₁	—	2	1	no	—
289	C₂×C₄×C₃₁	—	2	1	no	—
290	C₂×C₄×C₃₁	—	2	1	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	2	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	4	1	no	—
303	C₂×C₄×C₃₁	—	4	1	no	—
304	C₂×C₄×C₃₁	—	4	1	no	—
305	C₂×C₄×C₃₁	—	4	4	no	—
306	C₂×C₄×C₃₁	—	8	2	no	—
307	C₂×C₄×C₃₁	—	8	2	no	—
308	C₂×C₄×C₃₁	—	8	2	no	—
309	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
321	C₈×C₃₁	—	4	1	no	—
322	C₈×C₃₁	—	4	1	no	—
323	C₈×C₃₁	—	4	1	no	—
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	#3511	C₂×C₃₁	1	1	yes	characteristic
330	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#1560	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#1559	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#1558	C₂×C₃₁	1	1	yes	characteristic, complemented
335	#1557	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#1554	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#1553	C₂×C₃₁	1	1	yes	characteristic, complemented
338	#1551	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#1551	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#1550	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#1548	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#1543	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#1542	C₂×C₃₁	1	1	yes	characteristic, complemented
344	C₂²×C₃₁	—	2	1	no	—
345	C₂²×C₃₁	—	2	1	no	—
346	C₂²×C₃₁	—	2	1	no	—
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	—	4	2	no	—
354	C₂²×C₃₁	—	4	2	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
357	C₄×C₃₁	—	2	1	no	—
358	C₄×C₃₁	—	2	1	no	—
359	C₄×C₃₁	—	2	1	no	—
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	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	#575	1	1	yes	characteristic
371	C₄×C₃₁	#575	1	1	yes	characteristic
372	C₄×C₃₁	#577	1	1	yes	characteristic
373	C₄×C₃₁	#578	1	1	yes	characteristic
374	#556	C₄×C₃₁	1	2	yes	—
375	#555	—	2	1	no	—
376	#554	—	2	1	no	—
377	#553	—	2	1	no	—
378	#553	—	2	1	no	—
379	#548	C₄×C₃₁	1	2	yes	—
380	#548	C₄×C₃₁	1	2	yes	—
381	#547	C₄×C₃₁	1	2	yes	—
382	#542	—	2	1	no	—
383	#542	—	2	1	no	—
384	#537	—	2	1	no	—
385	#533	C₂²×C₃₁	1	1	yes	characteristic
386	#533	C₂²×C₃₁	1	1	yes	characteristic
387	#532	C₂²×C₃₁	1	1	yes	characteristic
388	#532	C₂²×C₃₁	1	1	yes	characteristic
389	#532	C₂²×C₃₁	1	1	yes	characteristic
390	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
391	#520	—	2	1	no	—
392	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
393	#446	—	2	1	no	—
394	#436	—	2	1	no	—
395	#435	—	2	1	no	—
396	#435	—	2	1	no	—
397	#433	—	2	1	no	—
398	#433	—	2	1	no	—
399	#432	C₂²×C₃₁	1	1	yes	characteristic
400	#432	C₂²×C₃₁	1	1	yes	characteristic
401	#432	C₂²×C₃₁	1	1	yes	characteristic
402	#432	C₂²×C₃₁	1	1	yes	characteristic
403	#431	C₂²×C₃₁	1	1	yes	characteristic
404	#431	C₂²×C₃₁	1	1	yes	characteristic
405	#431	C₂²×C₃₁	1	1	yes	characteristic
406	#423	C₂²×C₃₁	1	1	yes	characteristic
407	#423	C₂²×C₃₁	1	1	yes	characteristic
408	#423	C₂²×C₃₁	1	1	yes	characteristic
409	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
410	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
411	#408	—	2	1	no	—
412	#405	—	2	1	no	—
413	#333	C₂²×C₃₁	1	1	yes	characteristic
414	#333	C₂²×C₃₁	1	1	yes	characteristic
415	#333	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	#333	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	#331	C₂²×C₃₁	1	1	yes	characteristic
426	#331	C₂²×C₃₁	1	1	yes	characteristic
427	#331	C₂²×C₃₁	1	1	yes	characteristic
428	#331	C₂²×C₃₁	1	1	yes	characteristic
429	C₂×C₃₁	—	4	1	no	—
430	C₂×C₃₁	—	4	1	no	—
431	C₂×C₃₁	—	4	1	no	—
432	C₂×C₃₁	—	8	2	no	—
433	C₂×C₃₁	#2888	1	1	yes	characteristic
434	C₂×C₃₁	#2896	1	1	yes	characteristic
435	C₂×C₃₁	#2898	1	1	yes	characteristic
436	C₂×#41	—	2	1	no	—
437	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
438	C₂×#41	C₂×C₄×C₃₁	1	2	yes	—
439	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
440	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
441	C₂×M₁₆	—	2	1	no	—
442	C₂×M₁₆	—	2	1	no	—
443	C₂×M₁₆	—	2	1	no	—
444	C₂²×C₈	—	2	1	no	—
445	C₂²×C₈	—	2	1	no	—
446	C₄⋊Q₈	—	2	1	no	—
447	C₄⋊Q₈	—	2	1	no	—
448	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
449	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
451	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
452	#127	C₂³×C₃₁	1	1	yes	characteristic
453	#126	—	2	2	no	—
454	#126	—	2	2	no	—
455	#125	—	2	1	no	—
456	#125	—	2	1	no	—
457	#124	—	2	2	no	—
458	#124	—	2	2	no	—
459	#124	—	2	1	no	—
460	#124	C₂×C₄×C₃₁	1	2	yes	—
461	#124	C₂×C₄×C₃₁	1	2	yes	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
470	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	1	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	—	2	1	no	—
479	#121	C₂×C₄×C₃₁	1	2	yes	—
480	C₄×Q₈	—	2	1	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	C₂×C₄×C₃₁	1	2	yes	—
483	C₄×Q₈	C₂×C₄×C₃₁	1	2	yes	—
484	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
485	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	—	2	1	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
494	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
495	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
496	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
497	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
498	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
499	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
500	#117	—	2	1	no	—
501	#117	—	2	1	no	—
502	#117	—	2	2	no	—
503	#117	D₄×C₃₁	1	1	yes	characteristic
504	#117	D₄×C₃₁	1	1	yes	characteristic
505	#117	D₄×C₃₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
512	C₄⋊C₈	—	2	1	no	—
513	C₄⋊C₈	—	2	1	no	—
514	C₄⋊C₈	—	2	1	no	—
515	C₄⋊C₈	—	2	1	no	—
516	C₄⋊C₈	—	2	1	no	—
517	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
518	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	C₂²⋊C₈	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	C₂²⋊C₈	—	2	1	no	—
528	C₂²⋊C₈	—	2	1	no	—
529	C₂²⋊C₈	—	2	1	no	—
530	C₂²⋊C₈	—	2	1	no	—
531	C₂²⋊C₈	—	2	1	no	—
532	#97	—	2	1	no	—
533	#97	—	2	1	no	—
534	#97	—	2	1	no	—
535	#97	—	2	1	no	—
536	C₄×C₈	—	2	1	no	—
537	C₄×C₈	—	2	1	no	—
538	C₄×C₈	—	2	1	no	—
539	C₃₁	#17768	1	1	yes	characteristic, direct product factor, Sylow
540	#41	—	4	1	no	—
541	#41	—	4	1	no	—
542	#41	—	4	2	no	—
543	#41	—	4	2	no	—
544	#41	—	8	2	no	—
545	#41	—	8	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	8	2	no	—
549	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
550	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
551	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
558	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
559	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
560	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
566	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
567	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×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	M₁₆	—	4	2	no	—
575	M₁₆	—	8	1	no	—
576	M₁₆	—	8	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	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	—	4	2	no	—
586	C₂×C₈	—	8	1	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
599	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
600	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
601	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
614	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
615	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
616	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
617	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
618	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
619	C₄²	—	2	2	no	—
620	C₄²	—	2	2	no	—
621	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
622	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
623	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
624	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
625	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
626	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
628	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
629	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
631	C₂³	—	2	2	no	—
632	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
633	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
634	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
635	Q₈	—	4	1	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	8	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	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	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	8	2	no	—
672	C₂×C₄	—	8	2	no	—
673	C₂×C₄	—	8	2	no	—
674	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
675	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
676	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
677	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
678	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
679	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
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	C₂³×C₄×C₃₁	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	C₃₁×#575	1	1	yes	characteristic
721	C₄	C₃₁×#575	1	1	yes	characteristic
722	C₄	C₃₁×#577	1	1	yes	characteristic
723	C₄	C₃₁×#578	1	1	yes	characteristic
724	C₂	—	4	1	no	—
725	C₂	—	4	1	no	—
726	C₂	—	4	1	no	—
727	C₂	—	8	2	no	—
728	C₂	C₃₁×#2888	1	1	yes	characteristic
729	C₂	C₃₁×#2896	1	1	yes	characteristic
730	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×#2989	C₂	semidirect
3. C₃₁×#2925	C₂	semidirect
4. C₃₁×#1560	C₂	semidirect
5. C₃₁×#1559	C₂	semidirect
6. C₃₁×#1558	C₂	semidirect
7. C₃₁×#1557	C₂	semidirect
8. C₃₁×#1554	C₂	semidirect
9. C₃₁×#1553	C₂	semidirect
10. C₃₁×#1551	C₂	semidirect
11. C₃₁×#1551	C₂	semidirect
12. C₃₁×#1550	C₂	semidirect
13. C₃₁×#1548	C₂	semidirect
14. C₃₁×#1543	C₂	semidirect
15. C₃₁×#1542	C₂	semidirect
265. #17768	C₃₁	direct (N × H)
330. #2989	C₂×C₃₁	semidirect
331. #2925	C₂×C₃₁	semidirect
332. #1560	C₂×C₃₁	semidirect
333. #1559	C₂×C₃₁	semidirect
334. #1558	C₂×C₃₁	semidirect
335. #1557	C₂×C₃₁	semidirect
336. #1554	C₂×C₃₁	semidirect
337. #1553	C₂×C₃₁	semidirect
338. #1551	C₂×C₃₁	semidirect
339. #1551	C₂×C₃₁	semidirect
340. #1550	C₂×C₃₁	semidirect
341. #1548	C₂×C₃₁	semidirect
342. #1543	C₂×C₃₁	semidirect
343. #1542	C₂×C₃₁	semidirect
539. C₃₁	#17768	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×#2989	2
C₃₁×#2925	2
C₃₁×#1560	2
C₃₁×#1559	2
C₃₁×#1558	2
C₃₁×#1557	2
C₃₁×#1554	2
C₃₁×#1553	2
C₃₁×#1551	2
C₃₁×#1550	2
C₃₁×#1548	2
C₃₁×#1543	2
C₃₁×#1542	2
#17768	31

Subgroups — C31×#17768 #21474527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17768 #21474527