Subgroups — C₃₁×#61051 #21517810

Order 7936.

2734 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3485	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3283	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3280	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3267	C₂	1	8	yes	maximal, complemented
7	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3042	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3005	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
17	C₃₁×#576	—	2	8	no	—
18	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
19	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₃₁×#135	—	2	8	no	—
22	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
28	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
30	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#547	—	2	4	no	—
33	C₃₁×#547	C₂²	1	8	yes	complemented
34	C₃₁×#546	—	2	4	no	—
35	C₃₁×#546	C₂²	1	8	yes	complemented
36	C₃₁×#536	C₂²	1	2	yes	—
37	C₃₁×#536	C₂²	1	2	yes	complemented
38	C₃₁×#534	—	2	4	no	—
39	C₃₁×#525	C₂²	1	1	yes	characteristic
40	C₃₁×#525	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#123	—	2	4	no	—
42	C₃₁×#518	C₂²	1	2	yes	complemented
43	C₃₁×#497	C₂²	1	4	yes	complemented
44	C₃₁×#495	C₂²	1	2	yes	complemented
45	C₃₁×#494	C₂²	1	2	yes	complemented
46	C₃₁×#470	C₂²	1	4	yes	complemented
47	C₃₁×#467	C₂²	1	4	yes	complemented
48	C₃₁×#467	C₂²	1	2	yes	complemented
49	C₃₁×#466	C₂²	1	2	yes	complemented
50	C₃₁×#465	C₂²	1	4	yes	complemented
51	C₃₁×#463	C₂²	1	8	yes	complemented
52	C₃₁×#461	C₂²	1	8	yes	complemented
53	C₃₁×#452	C₂²	1	8	yes	complemented
54	C₃₁×#452	C₂²	1	8	yes	complemented
55	C₃₁×#450	C₂²	1	8	yes	complemented
56	C₃₁×#449	C₂²	1	8	yes	complemented
57	C₃₁×#442	C₂²	1	4	yes	complemented
58	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
59	C₃₁×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
61	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#419	C₂²	1	2	yes	complemented
64	C₃₁×#418	C₂²	1	2	yes	complemented
65	C₃₁×#416	C₂²	1	2	yes	complemented
66	C₃₁×#408	C₂²	1	1	yes	characteristic
67	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×H(5,𝔽₂)	—	2	8	no	—
70	C₃₁×H(5,𝔽₂)	—	4	4	no	—
71	C₂×#41×C₃₁	—	2	2	no	—
72	C₂×#41×C₃₁	—	2	4	no	—
73	C₂×#41×C₃₁	—	2	8	no	—
74	C₂×#41×C₃₁	—	4	4	no	—
75	C₂×#41×C₃₁	C₂³	1	2	yes	—
76	C₂×#41×C₃₁	C₂³	1	8	yes	—
77	C₂×#41×C₃₁	C₂³	1	4	yes	—
78	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
80	C₂²×D₄×C₃₁	—	2	2	no	—
81	C₂²×D₄×C₃₁	—	2	4	no	—
82	C₂²×D₄×C₃₁	—	2	2	no	—
83	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
84	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂³×C₄×C₃₁	—	2	2	no	—
86	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₃₁×#137	—	4	4	no	—
88	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
89	C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
90	C₃₁×#135	—	2	16	no	—
91	C₃₁×#135	—	2	16	no	—
92	C₃₁×#135	—	2	8	no	—
93	C₃₁×#135	—	2	4	no	—
94	C₂×Q₁₆×C₃₁	—	2	4	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	—	2	8	no	—
100	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂×D₈×C₃₁	—	2	8	no	—
105	C₂×D₈×C₃₁	D₄	1	8	yes	complemented
106	C₂×D₈×C₃₁	C₂³	1	4	yes	—
107	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂×D₈×C₃₁	C₂³	1	2	yes	—
109	C₂×D₈×C₃₁	C₂³	1	2	yes	—
110	C₃₁×#131	—	2	4	no	—
111	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
114	C₂²×C₈×C₃₁	—	2	4	no	—
115	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
117	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
118	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
119	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	—	2	2	no	—
121	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	C₂³	1	4	yes	—
124	C₃₁×#123	—	2	4	no	—
125	C₃₁×#123	—	2	2	no	—
126	C₃₁×#123	—	2	8	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×#123	—	2	8	no	—
129	C₃₁×#123	—	2	8	no	—
130	C₃₁×#123	D₄	1	2	yes	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₃₁×#121	—	2	8	no	—
136	C₃₁×#121	—	2	8	no	—
137	C₃₁×#121	D₄	1	2	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#120	—	2	2	no	—
140	C₃₁×#120	—	2	8	no	—
141	C₃₁×#120	D₄	1	2	yes	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	C₂³	1	8	yes	—
145	C₄×D₄×C₃₁	C₂³	1	4	yes	—
146	C₃₁×#117	C₂³	1	2	yes	—
147	C₃₁×#117	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
149	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
151	C₃₁×#107	C₂³	1	2	yes	—
152	C₃₁×#106	C₂³	1	2	yes	—
153	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
154	C₃₁×#103	C₂³	1	4	yes	—
155	C₃₁×#103	C₂³	1	8	yes	—
156	C₃₁×#102	C₂³	1	4	yes	—
157	C₃₁×#102	C₂³	1	8	yes	—
158	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₃₁×#97	C₂³	1	2	yes	—
161	C₄×C₈×C₃₁	C₂³	1	2	yes	—
162	C₂⁴×C₃₁	—	2	2	no	—
163	C₂⁴×C₃₁	—	2	4	no	—
164	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
165	#41×C₃₁	—	2	2	no	—
166	#41×C₃₁	—	2	2	no	—
167	#41×C₃₁	—	2	16	no	—
168	#41×C₃₁	—	2	8	no	—
169	#41×C₃₁	—	2	4	no	—
170	#41×C₃₁	—	2	4	no	—
171	#41×C₃₁	—	4	8	no	—
172	#41×C₃₁	—	4	4	no	—
173	#41×C₃₁	—	4	16	no	—
174	#41×C₃₁	—	4	8	no	—
175	C₂×Q₈×C₃₁	—	2	2	no	—
176	C₂×Q₈×C₃₁	—	2	4	no	—
177	C₂×Q₈×C₃₁	—	2	4	no	—
178	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
180	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
181	C₂×D₄×C₃₁	—	2	8	no	—
182	C₂×D₄×C₃₁	—	2	8	no	—
183	C₂×D₄×C₃₁	—	2	2	no	—
184	C₂×D₄×C₃₁	—	2	4	no	—
185	C₂×D₄×C₃₁	—	2	4	no	—
186	C₂×D₄×C₃₁	—	2	2	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	4	4	no	—
190	C₂×D₄×C₃₁	—	4	8	no	—
191	C₂×D₄×C₃₁	—	4	16	no	—
192	C₂×D₄×C₃₁	—	4	8	no	—
193	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
196	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
197	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
198	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
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	—	2	8	no	—
203	C₂²×C₄×C₃₁	—	2	4	no	—
204	C₂²×C₄×C₃₁	—	2	2	no	—
205	C₂²×C₄×C₃₁	—	2	8	no	—
206	C₂²×C₄×C₃₁	—	4	8	no	—
207	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
212	Q₁₆×C₃₁	—	2	4	no	—
213	Q₁₆×C₃₁	—	2	4	no	—
214	Q₁₆×C₃₁	—	2	2	no	—
215	Q₁₆×C₃₁	—	4	4	no	—
216	SD₁₆×C₃₁	—	2	16	no	—
217	SD₁₆×C₃₁	—	2	8	no	—
218	SD₁₆×C₃₁	—	2	4	no	—
219	SD₁₆×C₃₁	—	4	4	no	—
220	D₈×C₃₁	—	2	8	no	—
221	D₈×C₃₁	—	2	2	no	—
222	D₈×C₃₁	C₂×D₄	1	8	yes	—
223	D₈×C₃₁	C₂×D₄	1	8	yes	—
224	M₁₆×C₃₁	—	2	2	no	—
225	M₁₆×C₃₁	—	2	2	no	—
226	M₁₆×C₃₁	—	2	4	no	—
227	C₂×C₈×C₃₁	—	2	2	no	—
228	C₂×C₈×C₃₁	—	2	4	no	—
229	C₂×C₈×C₃₁	—	2	4	no	—
230	C₂×C₈×C₃₁	—	2	4	no	—
231	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
232	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
233	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
234	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
235	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₃₁	—	2	4	no	—
238	C₄⋊C₄×C₃₁	—	2	8	no	—
239	C₄⋊C₄×C₃₁	—	2	8	no	—
240	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
241	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₃₁	—	2	2	no	—
244	C₂²⋊C₄×C₃₁	—	2	8	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	8	no	—
248	C₂²⋊C₄×C₃₁	—	2	8	no	—
249	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
250	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
251	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
252	C₄²×C₃₁	—	2	2	no	—
253	C₄²×C₃₁	C₂⁴	1	2	yes	—
254	#61051	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₃₁	—	2	2	no	—
256	C₂³×C₃₁	—	2	4	no	—
257	C₂³×C₃₁	—	2	8	no	—
258	C₂³×C₃₁	—	2	2	no	—
259	C₂³×C₃₁	—	4	2	no	—
260	C₂³×C₃₁	—	4	8	no	—
261	C₂³×C₃₁	—	8	4	no	—
262	C₂³×C₃₁	—	8	8	no	—
263	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
264	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
265	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
266	Q₈×C₃₁	—	2	2	no	—
267	Q₈×C₃₁	—	2	2	no	—
268	Q₈×C₃₁	—	2	4	no	—
269	Q₈×C₃₁	—	2	4	no	—
270	Q₈×C₃₁	—	2	2	no	—
271	Q₈×C₃₁	—	4	4	no	—
272	D₄×C₃₁	—	2	4	no	—
273	D₄×C₃₁	—	2	8	no	—
274	D₄×C₃₁	—	2	2	no	—
275	D₄×C₃₁	—	2	2	no	—
276	D₄×C₃₁	—	2	4	no	—
277	D₄×C₃₁	—	2	2	no	—
278	D₄×C₃₁	—	4	4	no	—
279	D₄×C₃₁	—	4	8	no	—
280	D₄×C₃₁	—	4	8	no	—
281	D₄×C₃₁	—	4	16	no	—
282	D₄×C₃₁	—	4	4	no	—
283	D₄×C₃₁	—	8	4	no	—
284	D₄×C₃₁	C₂²×D₄	1	8	yes	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	4	no	—
287	C₂×C₄×C₃₁	—	2	2	no	—
288	C₂×C₄×C₃₁	—	2	2	no	—
289	C₂×C₄×C₃₁	—	2	2	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	4	no	—
292	C₂×C₄×C₃₁	—	2	4	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	4	16	no	—
295	C₂×C₄×C₃₁	—	4	8	no	—
296	C₂×C₄×C₃₁	—	4	4	no	—
297	C₂×C₄×C₃₁	—	4	4	no	—
298	C₂×C₄×C₃₁	—	8	8	no	—
299	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
305	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
306	C₈×C₃₁	—	2	2	no	—
307	C₈×C₃₁	—	2	2	no	—
308	C₈×C₃₁	—	2	2	no	—
309	C₈×C₃₁	C₂²×D₄	1	2	yes	—
310	C₈×C₃₁	C₂²×D₄	1	2	yes	—
311	C₂×#576	C₂×C₃₁	1	1	yes	characteristic, complemented
312	C₂²×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
313	#3485	C₂×C₃₁	1	2	yes	complemented
314	#3283	C₂×C₃₁	1	4	yes	complemented
315	#3280	C₂×C₃₁	1	4	yes	complemented
316	#3267	C₂×C₃₁	1	8	yes	complemented
317	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#3059	C₂×C₃₁	1	1	yes	characteristic, complemented
319	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
320	#3042	C₂×C₃₁	1	2	yes	complemented
321	#3009	C₂×C₃₁	1	2	yes	complemented
322	#3005	C₂×C₃₁	1	2	yes	complemented
323	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
325	C₂²×C₃₁	—	2	2	no	—
326	C₂²×C₃₁	—	2	2	no	—
327	C₂²×C₃₁	—	2	4	no	—
328	C₂²×C₃₁	—	2	2	no	—
329	C₂²×C₃₁	—	2	2	no	—
330	C₂²×C₃₁	—	2	2	no	—
331	C₂²×C₃₁	—	2	8	no	—
332	C₂²×C₃₁	—	4	4	no	—
333	C₂²×C₃₁	—	4	8	no	—
334	C₂²×C₃₁	—	4	4	no	—
335	C₂²×C₃₁	—	4	2	no	—
336	C₂²×C₃₁	—	8	8	no	—
337	C₂²×C₃₁	—	16	8	no	—
338	C₂²×C₃₁	D₄²	1	2	yes	—
339	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
340	C₄×C₃₁	—	2	4	no	—
341	C₄×C₃₁	—	2	2	no	—
342	C₄×C₃₁	—	2	2	no	—
343	C₄×C₃₁	—	4	4	no	—
344	C₄×C₃₁	—	4	2	no	—
345	C₄×C₃₁	—	4	4	no	—
346	C₄×C₃₁	D₄²	1	2	yes	—
347	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
348	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
350	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
351	#576	—	2	8	no	—
352	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
353	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
354	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
355	C₂×#135	—	2	8	no	—
356	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
357	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
358	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
359	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
360	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
361	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
362	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
363	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
364	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
365	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
366	#547	—	2	4	no	—
367	#547	C₂²×C₃₁	1	8	yes	complemented
368	#546	—	2	4	no	—
369	#546	C₂²×C₃₁	1	8	yes	complemented
370	#536	C₂²×C₃₁	1	2	yes	—
371	#536	C₂²×C₃₁	1	2	yes	complemented
372	#534	—	2	4	no	—
373	#525	C₂²×C₃₁	1	1	yes	characteristic
374	#525	C₂²×C₃₁	1	2	yes	complemented
375	C₂×#123	—	2	4	no	—
376	#518	C₂²×C₃₁	1	2	yes	complemented
377	#497	C₂²×C₃₁	1	4	yes	complemented
378	#495	C₂²×C₃₁	1	2	yes	complemented
379	#494	C₂²×C₃₁	1	2	yes	complemented
380	#470	C₂²×C₃₁	1	4	yes	complemented
381	#467	C₂²×C₃₁	1	4	yes	complemented
382	#467	C₂²×C₃₁	1	2	yes	complemented
383	#466	C₂²×C₃₁	1	2	yes	complemented
384	#465	C₂²×C₃₁	1	4	yes	complemented
385	#463	C₂²×C₃₁	1	8	yes	complemented
386	#461	C₂²×C₃₁	1	8	yes	complemented
387	#452	C₂²×C₃₁	1	8	yes	complemented
388	#452	C₂²×C₃₁	1	8	yes	complemented
389	#450	C₂²×C₃₁	1	8	yes	complemented
390	#449	C₂²×C₃₁	1	8	yes	complemented
391	#442	C₂²×C₃₁	1	4	yes	complemented
392	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
393	#435	C₂²×C₃₁	1	4	yes	complemented
394	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
395	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
396	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
397	#419	C₂²×C₃₁	1	2	yes	complemented
398	#418	C₂²×C₃₁	1	2	yes	complemented
399	#416	C₂²×C₃₁	1	2	yes	complemented
400	#408	C₂²×C₃₁	1	1	yes	characteristic
401	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
403	C₂×C₃₁	—	2	2	no	—
404	C₂×C₃₁	—	4	2	no	—
405	C₂×C₃₁	—	4	2	no	—
406	C₂×C₃₁	—	4	8	no	—
407	C₂×C₃₁	—	8	2	no	—
408	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
409	C₂×C₃₁	#3584	1	2	yes	—
410	H(5,𝔽₂)	—	2	8	no	—
411	H(5,𝔽₂)	—	4	4	no	—
412	C₂×#41	—	2	2	no	—
413	C₂×#41	—	2	4	no	—
414	C₂×#41	—	2	8	no	—
415	C₂×#41	—	4	4	no	—
416	C₂×#41	C₂³×C₃₁	1	2	yes	—
417	C₂×#41	C₂³×C₃₁	1	8	yes	—
418	C₂×#41	C₂³×C₃₁	1	4	yes	—
419	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
420	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
421	C₂²×D₄	—	2	2	no	—
422	C₂²×D₄	—	2	4	no	—
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
425	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
426	C₂³×C₄	—	2	2	no	—
427	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
428	#137	—	4	4	no	—
429	AGL(1,ℤ/8)	—	2	8	no	—
430	AGL(1,ℤ/8)	—	2	16	no	—
431	#135	—	2	16	no	—
432	#135	—	2	16	no	—
433	#135	—	2	8	no	—
434	#135	—	2	4	no	—
435	C₂×Q₁₆	—	2	4	no	—
436	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
437	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
438	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
439	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
440	C₂×SD₁₆	—	2	8	no	—
441	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
442	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
443	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
444	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
445	C₂×D₈	—	2	8	no	—
446	C₂×D₈	D₄×C₃₁	1	8	yes	complemented
447	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
448	C₂×D₈	C₂³×C₃₁	1	4	yes	—
449	C₂×D₈	C₂³×C₃₁	1	2	yes	—
450	C₂×D₈	C₂³×C₃₁	1	2	yes	—
451	#131	—	2	4	no	—
452	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
453	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
454	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
455	C₂²×C₈	—	2	4	no	—
456	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
458	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
459	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
460	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
463	#124	—	2	2	no	—
464	#124	C₂³×C₃₁	1	4	yes	—
465	#123	—	2	4	no	—
466	#123	—	2	2	no	—
467	#123	—	2	8	no	—
468	#123	—	2	4	no	—
469	#123	—	2	8	no	—
470	#123	—	2	8	no	—
471	#123	D₄×C₃₁	1	2	yes	—
472	C₂²⋊Q₈	—	2	4	no	—
473	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
474	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
475	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
476	#121	—	2	8	no	—
477	#121	—	2	8	no	—
478	#121	D₄×C₃₁	1	2	yes	—
479	#121	C₂³×C₃₁	1	4	yes	—
480	#120	—	2	2	no	—
481	#120	—	2	8	no	—
482	#120	D₄×C₃₁	1	2	yes	—
483	C₄×D₄	—	2	4	no	—
484	C₄×D₄	—	2	4	no	—
485	C₄×D₄	C₂³×C₃₁	1	8	yes	—
486	C₄×D₄	C₂³×C₃₁	1	4	yes	—
487	#117	C₂³×C₃₁	1	2	yes	—
488	#117	C₂³×C₃₁	1	1	yes	characteristic
489	C₂×C₄⋊C₄	—	2	8	no	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₂²⋊C₄	—	2	8	no	—
492	#107	C₂³×C₃₁	1	2	yes	—
493	#106	C₂³×C₃₁	1	2	yes	—
494	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
495	#103	C₂³×C₃₁	1	4	yes	—
496	#103	C₂³×C₃₁	1	8	yes	—
497	#102	C₂³×C₃₁	1	4	yes	—
498	#102	C₂³×C₃₁	1	8	yes	—
499	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
500	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
501	#97	C₂³×C₃₁	1	2	yes	—
502	C₄×C₈	C₂³×C₃₁	1	2	yes	—
503	C₃₁	#61051	1	1	yes	characteristic, direct product factor, Sylow
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
507	#41	—	2	2	no	—
508	#41	—	2	2	no	—
509	#41	—	2	16	no	—
510	#41	—	2	8	no	—
511	#41	—	2	4	no	—
512	#41	—	2	4	no	—
513	#41	—	4	8	no	—
514	#41	—	4	4	no	—
515	#41	—	4	16	no	—
516	#41	—	4	8	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
522	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
523	C₂×D₄	—	2	8	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	8	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	8	no	—
535	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
536	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
537	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
538	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
539	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
540	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	8	no	—
548	C₂²×C₄	—	4	8	no	—
549	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
554	Q₁₆	—	2	4	no	—
555	Q₁₆	—	2	4	no	—
556	Q₁₆	—	2	2	no	—
557	Q₁₆	—	4	4	no	—
558	SD₁₆	—	2	16	no	—
559	SD₁₆	—	2	8	no	—
560	SD₁₆	—	2	4	no	—
561	SD₁₆	—	4	4	no	—
562	D₈	—	2	8	no	—
563	D₈	—	2	2	no	—
564	D₈	C₂×D₄×C₃₁	1	8	yes	—
565	D₈	C₂×D₄×C₃₁	1	8	yes	—
566	M₁₆	—	2	2	no	—
567	M₁₆	—	2	2	no	—
568	M₁₆	—	2	4	no	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	4	no	—
571	C₂×C₈	—	2	4	no	—
572	C₂×C₈	—	2	4	no	—
573	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
574	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
575	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
576	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
577	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
578	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
583	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
592	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
593	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
594	C₄²	—	2	2	no	—
595	C₄²	C₂⁴×C₃₁	1	2	yes	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	8	4	no	—
603	C₂³	—	8	8	no	—
604	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
605	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
606	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	2	4	no	—
610	Q₈	—	2	4	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	4	4	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	8	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	4	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	8	no	—
621	D₄	—	4	8	no	—
622	D₄	—	4	16	no	—
623	D₄	—	4	4	no	—
624	D₄	—	8	4	no	—
625	D₄	C₂²×D₄×C₃₁	1	8	yes	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	4	16	no	—
636	C₂×C₄	—	4	8	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	8	8	no	—
640	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
641	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
642	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
644	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
645	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
646	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
647	C₈	—	2	2	no	—
648	C₈	—	2	2	no	—
649	C₈	—	2	2	no	—
650	C₈	C₂²×D₄×C₃₁	1	2	yes	—
651	C₈	C₂²×D₄×C₃₁	1	2	yes	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	8	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	8	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	8	8	no	—
664	C₂²	—	16	8	no	—
665	C₂²	D₄²×C₃₁	1	2	yes	—
666	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	4	no	—
673	C₄	D₄²×C₃₁	1	2	yes	—
674	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
675	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	—	2	2	no	—
677	C₂	—	4	2	no	—
678	C₂	—	4	2	no	—
679	C₂	—	4	8	no	—
680	C₂	—	8	2	no	—
681	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
682	C₂	C₃₁×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#576	C₂	semidirect
2. C₂²×C₃₁×#135	C₂	semidirect
3. C₃₁×#3485	C₂	semidirect
4. C₃₁×#3283	C₂	semidirect
5. C₃₁×#3280	C₂	semidirect
6. C₃₁×#3267	C₂	semidirect
7. C₃₁×#3156	C₂	semidirect
8. C₃₁×#3059	C₂	semidirect
9. C₃₁×#3050	C₂	semidirect
10. C₃₁×#3042	C₂	semidirect
11. C₃₁×#3009	C₂	semidirect
12. C₃₁×#3005	C₂	semidirect
13. C₃₁×#2948	C₂	semidirect
14. C₃₁×#2929	C₂	semidirect
16. C₂²×#41×C₃₁	C₂²	semidirect
18. C₂×C₃₁×#137	C₂²	semidirect
20. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃₁×#135	C₂²	semidirect
24. C₂×C₃₁×#135	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
26. C₂²×Q₁₆×C₃₁	C₂²	semidirect
27. C₂²×SD₁₆×C₃₁	C₂²	semidirect
29. C₂²×D₈×C₃₁	C₂²	semidirect
31. C₂³×C₈×C₃₁	C₂²	semidirect
33. C₃₁×#547	C₂²	semidirect
35. C₃₁×#546	C₂²	semidirect
37. C₃₁×#536	C₂²	semidirect
40. C₃₁×#525	C₂²	semidirect
42. C₃₁×#518	C₂²	semidirect
43. C₃₁×#497	C₂²	semidirect
44. C₃₁×#495	C₂²	semidirect
45. C₃₁×#494	C₂²	semidirect
46. C₃₁×#470	C₂²	semidirect
47. C₃₁×#467	C₂²	semidirect
48. C₃₁×#467	C₂²	semidirect
49. C₃₁×#466	C₂²	semidirect
50. C₃₁×#465	C₂²	semidirect
51. C₃₁×#463	C₂²	semidirect
52. C₃₁×#461	C₂²	semidirect
53. C₃₁×#452	C₂²	semidirect
54. C₃₁×#452	C₂²	semidirect
55. C₃₁×#450	C₂²	semidirect
56. C₃₁×#449	C₂²	semidirect
57. C₃₁×#442	C₂²	semidirect
58. C₄×D₈×C₃₁	C₂²	semidirect
59. C₃₁×#435	C₂²	semidirect
60. C₈×D₄×C₃₁	C₂²	semidirect
61. C₃₁×#427	C₂²	semidirect
62. C₃₁×#424	C₂²	semidirect
63. C₃₁×#419	C₂²	semidirect
64. C₃₁×#418	C₂²	semidirect
65. C₃₁×#416	C₂²	semidirect
67. C₃₁×#407	C₂²	semidirect
68. C₃₁×#405	C₂²	semidirect
105. C₂×D₈×C₃₁	D₄	semidirect
254. #61051	C₃₁	direct (N × H)
311. C₂×#576	C₂×C₃₁	semidirect
312. C₂²×#135	C₂×C₃₁	semidirect
313. #3485	C₂×C₃₁	semidirect
314. #3283	C₂×C₃₁	semidirect
315. #3280	C₂×C₃₁	semidirect
316. #3267	C₂×C₃₁	semidirect
317. #3156	C₂×C₃₁	semidirect
318. #3059	C₂×C₃₁	semidirect
319. #3050	C₂×C₃₁	semidirect
320. #3042	C₂×C₃₁	semidirect
321. #3009	C₂×C₃₁	semidirect
322. #3005	C₂×C₃₁	semidirect
323. #2948	C₂×C₃₁	semidirect
324. #2929	C₂×C₃₁	semidirect
350. C₂²×#41	C₂²×C₃₁	semidirect
352. C₂×#137	C₂²×C₃₁	semidirect
354. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
357. C₂×#135	C₂²×C₃₁	semidirect
358. C₂×#135	C₂²×C₃₁	semidirect
359. C₂×#135	C₂²×C₃₁	semidirect
360. C₂²×Q₁₆	C₂²×C₃₁	semidirect
361. C₂²×SD₁₆	C₂²×C₃₁	semidirect
363. C₂²×D₈	C₂²×C₃₁	semidirect
365. C₂³×C₈	C₂²×C₃₁	semidirect
367. #547	C₂²×C₃₁	semidirect
369. #546	C₂²×C₃₁	semidirect
371. #536	C₂²×C₃₁	semidirect
374. #525	C₂²×C₃₁	semidirect
376. #518	C₂²×C₃₁	semidirect
377. #497	C₂²×C₃₁	semidirect
378. #495	C₂²×C₃₁	semidirect
379. #494	C₂²×C₃₁	semidirect
380. #470	C₂²×C₃₁	semidirect
381. #467	C₂²×C₃₁	semidirect
382. #467	C₂²×C₃₁	semidirect
383. #466	C₂²×C₃₁	semidirect
384. #465	C₂²×C₃₁	semidirect
385. #463	C₂²×C₃₁	semidirect
386. #461	C₂²×C₃₁	semidirect
387. #452	C₂²×C₃₁	semidirect
388. #452	C₂²×C₃₁	semidirect
389. #450	C₂²×C₃₁	semidirect
390. #449	C₂²×C₃₁	semidirect
391. #442	C₂²×C₃₁	semidirect
392. C₄×D₈	C₂²×C₃₁	semidirect
393. #435	C₂²×C₃₁	semidirect
394. C₈×D₄	C₂²×C₃₁	semidirect
395. #427	C₂²×C₃₁	semidirect
396. #424	C₂²×C₃₁	semidirect
397. #419	C₂²×C₃₁	semidirect
398. #418	C₂²×C₃₁	semidirect
399. #416	C₂²×C₃₁	semidirect
401. #407	C₂²×C₃₁	semidirect
402. #405	C₂²×C₃₁	semidirect
446. C₂×D₈	D₄×C₃₁	semidirect
503. C₃₁	#61051	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#576	2
C₂²×C₃₁×#135	2
C₃₁×#3485	2
C₃₁×#3283	2
C₃₁×#3280	2
C₃₁×#3267	2
C₃₁×#3156	2
C₃₁×#3059	2
C₃₁×#3050	2
C₃₁×#3042	2
C₃₁×#3009	2
C₃₁×#3005	2
C₃₁×#2948	2
C₃₁×#2929	2
#61051	31

Subgroups — C31×#61051 #21517810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61051 #21517810