Subgroups — C₃₁×#17769 #21474528

Order 7936.

918 conjugacy classes of subgroups.

The subgroup lattice has 742 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×#1561	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1557	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1557	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1553	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#1544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#556	—	2	1	no	—
17	C₃₁×#555	C₄	1	2	yes	—
18	C₃₁×#554	C₄	1	2	yes	—
19	C₃₁×#553	C₄	1	2	yes	—
20	C₃₁×#553	C₄	1	2	yes	—
21	C₃₁×#548	—	2	1	no	—
22	C₃₁×#548	—	2	1	no	—
23	C₃₁×#547	—	2	1	no	—
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×#332	C₂²	1	1	yes	characteristic
56	C₃₁×#332	C₂²	1	1	yes	characteristic
57	C₃₁×#332	C₂²	1	1	yes	characteristic
58	C₃₁×#332	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	—	2	1	no	—
74	C₂×#41×C₃₁	D₄	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	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	C₂×C₄	1	2	yes	—
91	C₃₁×#125	C₂×C₄	1	2	yes	—
92	C₃₁×#124	—	2	2	no	—
93	C₃₁×#124	—	2	2	no	—
94	C₃₁×#124	—	2	1	no	—
95	C₃₁×#124	—	2	1	no	—
96	C₃₁×#124	—	2	1	no	—
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	1	no	—
103	C₃₁×C₂²⋊Q₈	—	2	1	no	—
104	C₃₁×C₂²⋊Q₈	—	2	2	no	—
105	C₃₁×C₂²⋊Q₈	—	2	2	no	—
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	C₂×C₄	1	2	yes	—
113	C₃₁×#121	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
118	C₄×Q₈×C₃₁	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
127	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
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	2	no	—
136	C₃₁×#117	C₂×C₄	1	2	yes	—
137	C₃₁×#117	C₂×C₄	1	2	yes	—
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	2	no	—
143	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
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	1	no	—
179	#41×C₃₁	—	8	1	no	—
180	#41×C₃₁	—	8	1	no	—
181	#41×C₃₁	—	8	1	no	—
182	C₂×Q₈×C₃₁	—	2	2	no	—
183	C₂×Q₈×C₃₁	—	2	1	no	—
184	C₂×Q₈×C₃₁	—	2	1	no	—
185	C₂×Q₈×C₃₁	—	2	1	no	—
186	C₂×Q₈×C₃₁	—	8	1	no	—
187	C₂×Q₈×C₃₁	—	8	1	no	—
188	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
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	1	no	—
193	C₂×D₄×C₃₁	—	2	1	no	—
194	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
196	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₃₁	—	2	2	no	—
199	C₂²×C₄×C₃₁	—	2	2	no	—
200	C₂²×C₄×C₃₁	—	2	2	no	—
201	C₂²×C₄×C₃₁	—	2	2	no	—
202	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₃₁	C₂²×C₄	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	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
211	M₁₆×C₃₁	—	4	2	no	—
212	M₁₆×C₃₁	—	8	1	no	—
213	M₁₆×C₃₁	—	8	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	—	2	1	no	—
220	C₂×C₈×C₃₁	—	2	1	no	—
221	C₂×C₈×C₃₁	—	2	1	no	—
222	C₂×C₈×C₃₁	—	4	2	no	—
223	C₂×C₈×C₃₁	—	8	1	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	2	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	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
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	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
256	C₄²×C₃₁	—	2	2	no	—
257	C₄²×C₃₁	—	2	2	no	—
258	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
259	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
260	C₄²×C₃₁	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
268	#17769	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂³×C₃₁	—	2	2	no	—
270	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	Q₈×C₃₁	—	4	1	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	—	4	1	no	—
279	Q₈×C₃₁	—	4	1	no	—
280	Q₈×C₃₁	—	8	2	no	—
281	D₄×C₃₁	—	4	1	no	—
282	D₄×C₃₁	—	4	1	no	—
283	D₄×C₃₁	—	4	1	no	—
284	D₄×C₃₁	—	4	2	no	—
285	D₄×C₃₁	—	4	4	no	—
286	D₄×C₃₁	—	4	1	no	—
287	D₄×C₃₁	—	4	1	no	—
288	D₄×C₃₁	—	4	1	no	—
289	D₄×C₃₁	—	4	1	no	—
290	D₄×C₃₁	—	8	2	no	—
291	D₄×C₃₁	—	8	2	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	1	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	4	1	no	—
308	C₂×C₄×C₃₁	—	4	1	no	—
309	C₂×C₄×C₃₁	—	4	1	no	—
310	C₂×C₄×C₃₁	—	4	4	no	—
311	C₂×C₄×C₃₁	—	8	2	no	—
312	C₂×C₄×C₃₁	—	8	2	no	—
313	C₂×C₄×C₃₁	—	8	2	no	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
324	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₈×C₃₁	—	4	1	no	—
333	C₈×C₃₁	—	4	1	no	—
334	#3511	C₂×C₃₁	1	1	yes	characteristic
335	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#1561	C₂×C₃₁	1	1	yes	characteristic, complemented
338	#1557	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#1557	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#1556	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#1553	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#1553	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#1552	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#1552	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#1547	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#1546	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#1544	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#1540	C₂×C₃₁	1	1	yes	characteristic, complemented
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	—	2	1	no	—
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	1	no	—
358	C₂²×C₃₁	—	4	2	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	2	no	—
361	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	—	4	2	no	—
375	C₄×C₃₁	#575	1	1	yes	characteristic
376	C₄×C₃₁	#575	1	1	yes	characteristic
377	C₄×C₃₁	#576	1	1	yes	characteristic
378	C₄×C₃₁	#577	1	1	yes	characteristic
379	#556	—	2	1	no	—
380	#555	C₄×C₃₁	1	2	yes	—
381	#554	C₄×C₃₁	1	2	yes	—
382	#553	C₄×C₃₁	1	2	yes	—
383	#553	C₄×C₃₁	1	2	yes	—
384	#548	—	2	1	no	—
385	#548	—	2	1	no	—
386	#547	—	2	1	no	—
387	#542	—	2	1	no	—
388	#542	—	2	1	no	—
389	#537	—	2	1	no	—
390	#533	C₂²×C₃₁	1	1	yes	characteristic
391	#533	C₂²×C₃₁	1	1	yes	characteristic
392	#532	C₂²×C₃₁	1	1	yes	characteristic
393	#532	C₂²×C₃₁	1	1	yes	characteristic
394	#532	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
396	#520	—	2	1	no	—
397	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
398	#446	—	2	1	no	—
399	#436	—	2	1	no	—
400	#435	—	2	1	no	—
401	#435	—	2	1	no	—
402	#433	—	2	1	no	—
403	#433	—	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	#431	C₂²×C₃₁	1	1	yes	characteristic
411	#423	C₂²×C₃₁	1	1	yes	characteristic
412	#423	C₂²×C₃₁	1	1	yes	characteristic
413	#423	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	#408	—	2	1	no	—
417	#405	—	2	1	no	—
418	#332	C₂²×C₃₁	1	1	yes	characteristic
419	#332	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	#332	C₂²×C₃₁	1	1	yes	characteristic
429	#332	C₂²×C₃₁	1	1	yes	characteristic
430	#331	C₂²×C₃₁	1	1	yes	characteristic
431	#331	C₂²×C₃₁	1	1	yes	characteristic
432	#331	C₂²×C₃₁	1	1	yes	characteristic
433	#331	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×C₃₁	—	4	1	no	—
435	C₂×C₃₁	—	4	1	no	—
436	C₂×C₃₁	—	4	1	no	—
437	C₂×C₃₁	—	8	2	no	—
438	C₂×C₃₁	#2889	1	1	yes	characteristic
439	C₂×C₃₁	#2896	1	1	yes	characteristic
440	C₂×C₃₁	#2897	1	1	yes	characteristic
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
445	C₂²×Q₈	—	2	1	no	—
446	C₂×M₁₆	—	2	1	no	—
447	C₂×M₁₆	—	2	1	no	—
448	C₂×M₁₆	—	2	1	no	—
449	C₂²×C₈	—	2	1	no	—
450	C₂²×C₈	—	2	1	no	—
451	C₄⋊Q₈	—	2	1	no	—
452	C₄⋊Q₈	—	2	1	no	—
453	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
454	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
456	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
457	#127	C₂³×C₃₁	1	1	yes	characteristic
458	#126	—	2	2	no	—
459	#126	—	2	2	no	—
460	#125	C₂×C₄×C₃₁	1	2	yes	—
461	#125	C₂×C₄×C₃₁	1	2	yes	—
462	#124	—	2	2	no	—
463	#124	—	2	2	no	—
464	#124	—	2	1	no	—
465	#124	—	2	1	no	—
466	#124	—	2	1	no	—
467	#123	—	2	2	no	—
468	#123	—	2	2	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	2	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	#121	C₂×C₄×C₃₁	1	2	yes	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
490	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	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	C₂×C₄×C₃₁	1	2	yes	—
499	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
500	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
501	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
502	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
503	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
504	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
505	#117	—	2	2	no	—
506	#117	C₂×C₄×C₃₁	1	2	yes	—
507	#117	C₂×C₄×C₃₁	1	2	yes	—
508	#117	D₄×C₃₁	1	1	yes	characteristic
509	#117	D₄×C₃₁	1	1	yes	characteristic
510	#117	D₄×C₃₁	1	1	yes	characteristic
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
514	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
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	C₂²⋊C₈	—	2	1	no	—
537	#97	—	2	1	no	—
538	#97	—	2	1	no	—
539	#97	—	2	1	no	—
540	#97	—	2	1	no	—
541	C₄×C₈	—	2	1	no	—
542	C₄×C₈	—	2	1	no	—
543	C₄×C₈	—	2	1	no	—
544	C₃₁	#17769	1	1	yes	characteristic, direct product factor, Sylow
545	#41	—	4	1	no	—
546	#41	—	4	1	no	—
547	#41	—	4	2	no	—
548	#41	—	4	2	no	—
549	#41	—	8	1	no	—
550	#41	—	8	1	no	—
551	#41	—	8	1	no	—
552	#41	—	8	1	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	8	1	no	—
558	C₂×Q₈	—	8	1	no	—
559	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
566	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
567	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
568	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
574	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
575	C₂²×C₄	C₂²×C₄×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	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
582	M₁₆	—	4	2	no	—
583	M₁₆	—	8	1	no	—
584	M₁₆	—	8	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	4	2	no	—
594	C₂×C₈	—	8	1	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
609	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
610	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
611	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
612	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
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	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
625	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
626	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
627	C₄²	—	2	2	no	—
628	C₄²	—	2	2	no	—
629	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
630	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
631	C₄²	C₂²×C₄×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	C₂×D₄×C₃₁	1	1	yes	characteristic
636	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
639	C₂³	—	2	2	no	—
640	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
641	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
642	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	8	2	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	2	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	8	2	no	—
661	D₄	—	8	2	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	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	2	no	—
682	C₂×C₄	—	8	2	no	—
683	C₂×C₄	—	8	2	no	—
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	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
690	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
691	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
692	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
693	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
696	C₈	—	4	1	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
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	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	C₃₁×#575	1	1	yes	characteristic
731	C₄	C₃₁×#575	1	1	yes	characteristic
732	C₄	C₃₁×#576	1	1	yes	characteristic
733	C₄	C₃₁×#577	1	1	yes	characteristic
734	C₂	—	4	1	no	—
735	C₂	—	4	1	no	—
736	C₂	—	4	1	no	—
737	C₂	—	8	2	no	—
738	C₂	C₃₁×#2889	1	1	yes	characteristic
739	C₂	C₃₁×#2896	1	1	yes	characteristic
740	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×#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×#1561	C₂	semidirect
5. C₃₁×#1557	C₂	semidirect
6. C₃₁×#1557	C₂	semidirect
7. C₃₁×#1556	C₂	semidirect
8. C₃₁×#1553	C₂	semidirect
9. C₃₁×#1553	C₂	semidirect
10. C₃₁×#1552	C₂	semidirect
11. C₃₁×#1552	C₂	semidirect
12. C₃₁×#1547	C₂	semidirect
13. C₃₁×#1546	C₂	semidirect
14. C₃₁×#1544	C₂	semidirect
15. C₃₁×#1540	C₂	semidirect
268. #17769	C₃₁	direct (N × H)
335. #2989	C₂×C₃₁	semidirect
336. #2925	C₂×C₃₁	semidirect
337. #1561	C₂×C₃₁	semidirect
338. #1557	C₂×C₃₁	semidirect
339. #1557	C₂×C₃₁	semidirect
340. #1556	C₂×C₃₁	semidirect
341. #1553	C₂×C₃₁	semidirect
342. #1553	C₂×C₃₁	semidirect
343. #1552	C₂×C₃₁	semidirect
344. #1552	C₂×C₃₁	semidirect
345. #1547	C₂×C₃₁	semidirect
346. #1546	C₂×C₃₁	semidirect
347. #1544	C₂×C₃₁	semidirect
348. #1540	C₂×C₃₁	semidirect
544. C₃₁	#17769	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×#1561	2
C₃₁×#1557	2
C₃₁×#1556	2
C₃₁×#1553	2
C₃₁×#1552	2
C₃₁×#1547	2
C₃₁×#1546	2
C₃₁×#1544	2
C₃₁×#1540	2
#17769	31

Subgroups — C31×#17769 #21474528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17769 #21474528