Subgroups — C₃₁×#60934 #21517693

Order 7936.

1892 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×#3494	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3259	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3257	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3247	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3245	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3045	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#555	—	2	2	no	—
22	C₃₁×#553	—	2	2	no	—
23	C₃₁×#553	—	2	2	no	—
24	C₃₁×#551	—	2	4	no	—
25	C₃₁×#547	—	2	2	no	—
26	C₃₁×#546	—	2	4	no	—
27	C₃₁×#544	C₂²	1	2	yes	—
28	C₃₁×#542	C₂²	1	4	yes	complemented
29	C₃₁×#540	C₂²	1	4	yes	complemented
30	C₃₁×#535	C₂²	1	2	yes	—
31	C₃₁×#532	C₂²	1	4	yes	complemented
32	C₃₁×#529	C₂²	1	4	yes	complemented
33	C₃₁×#525	C₂²	1	2	yes	—
34	C₂×C₃₁×#121	C₂²	1	2	yes	—
35	C₃₁×#520	C₂²	1	2	yes	—
36	C₃₁×#518	C₂²	1	2	yes	—
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₃₁×#479	C₂²	1	4	yes	complemented
39	C₃₁×#478	C₂²	1	4	yes	complemented
40	C₃₁×#478	C₂²	1	4	yes	complemented
41	C₃₁×#478	C₂²	1	4	yes	complemented
42	C₃₁×#477	C₂²	1	4	yes	complemented
43	C₃₁×#476	C₂²	1	4	yes	complemented
44	C₃₁×#474	C₂²	1	4	yes	complemented
45	C₃₁×#474	C₂²	1	4	yes	complemented
46	C₃₁×#469	C₂²	1	4	yes	complemented
47	C₃₁×#468	C₂²	1	4	yes	complemented
48	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#466	C₂²	1	2	yes	—
51	C₃₁×#466	C₂²	1	2	yes	—
52	C₃₁×#466	C₂²	1	2	yes	—
53	C₃₁×#466	C₂²	1	2	yes	—
54	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#466	C₂²	1	4	yes	complemented
56	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#465	C₂²	1	2	yes	complemented
58	C₃₁×#465	C₂²	1	4	yes	complemented
59	C₃₁×#465	C₂²	1	2	yes	complemented
60	C₃₁×#464	C₂²	1	4	yes	complemented
61	C₃₁×#463	C₂²	1	4	yes	complemented
62	C₃₁×#463	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#460	C₂²	1	4	yes	complemented
65	C₃₁×#459	C₂²	1	4	yes	complemented
66	C₃₁×#459	C₂²	1	4	yes	complemented
67	C₃₁×#459	C₂²	1	4	yes	complemented
68	C₃₁×#428	C₂²	1	2	yes	—
69	C₃₁×#427	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
71	C₃₁×#424	C₂²	1	2	yes	—
72	C₃₁×#424	C₂²	1	2	yes	—
73	C₃₁×#424	C₂²	1	2	yes	complemented
74	C₃₁×#424	C₂²	1	2	yes	complemented
75	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
76	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
77	C₃₁×#418	C₂²	1	2	yes	—
78	C₃₁×#417	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	2	yes	—
80	C₂×C₃₁×#102	C₂²	1	2	yes	—
81	C₂×#41×C₃₁	—	2	4	no	—
82	C₂×#41×C₃₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₃₁	—	2	2	no	—
84	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
87	C₃₁×#135	—	4	2	no	—
88	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
89	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×D₈×C₃₁	—	4	2	no	—
92	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₂×D₈×C₃₁	C₂³	1	4	yes	—
94	C₂×D₈×C₃₁	C₂³	1	2	yes	—
95	C₂×D₈×C₃₁	C₂³	1	2	yes	—
96	C₂×M₁₆×C₃₁	—	4	2	no	—
97	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
98	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
99	C₂²×C₈×C₃₁	—	4	2	no	—
100	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₃₁×#127	C₂³	1	4	yes	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#125	—	2	2	no	—
113	C₃₁×#125	C₂³	1	4	yes	—
114	C₃₁×#124	—	2	4	no	—
115	C₃₁×#124	—	2	4	no	—
116	C₃₁×#124	C₂³	1	4	yes	—
117	C₃₁×#123	—	2	2	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×C₂²⋊Q₈	—	2	4	no	—
123	C₃₁×C₂²⋊Q₈	—	2	4	no	—
124	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
125	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	2	no	—
128	C₃₁×#121	—	2	4	no	—
129	C₃₁×#121	—	2	2	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	C₂³	1	4	yes	—
134	C₃₁×#121	C₂³	1	2	yes	—
135	C₃₁×#121	C₂³	1	2	yes	—
136	C₃₁×#121	C₂³	1	4	yes	—
137	C₃₁×#120	—	2	2	no	—
138	C₃₁×#120	—	2	4	no	—
139	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
140	C₄×D₄×C₃₁	—	2	2	no	—
141	C₄×D₄×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	4	no	—
143	C₄×D₄×C₃₁	—	2	2	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	4	no	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	C₂³	1	4	yes	—
148	C₄×D₄×C₃₁	C₂³	1	4	yes	—
149	C₄×D₄×C₃₁	C₂³	1	4	yes	—
150	C₃₁×#117	—	2	2	no	—
151	C₃₁×#117	—	2	4	no	—
152	C₃₁×#117	D₄	1	2	yes	—
153	C₃₁×#117	D₄	1	2	yes	—
154	C₃₁×#117	C₂³	1	2	yes	—
155	C₃₁×#117	C₂³	1	2	yes	—
156	C₃₁×#117	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
158	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
162	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
164	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
165	C₃₁×#107	C₂³	1	2	yes	—
166	C₃₁×#107	C₂³	1	2	yes	—
167	C₃₁×#107	C₂³	1	1	yes	characteristic
168	C₃₁×#107	C₂³	1	1	yes	characteristic
169	C₃₁×#107	C₂³	1	4	yes	—
170	C₃₁×#106	C₂³	1	2	yes	—
171	C₃₁×#106	C₂³	1	4	yes	—
172	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
173	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
174	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
175	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
176	C₃₁×#103	C₂³	1	2	yes	—
177	C₃₁×#103	C₂³	1	2	yes	—
178	C₃₁×#103	C₂³	1	4	yes	—
179	C₃₁×#102	C₂³	1	4	yes	—
180	C₃₁×#102	C₂³	1	4	yes	—
181	C₃₁×#102	C₂³	1	2	yes	—
182	C₃₁×#102	C₂³	1	2	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₂⁴×C₃₁	—	2	2	no	—
187	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
188	#41×C₃₁	—	2	4	no	—
189	#41×C₃₁	—	2	4	no	—
190	#41×C₃₁	—	8	8	no	—
191	C₂×Q₈×C₃₁	—	2	4	no	—
192	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
193	C₂×D₄×C₃₁	—	2	2	no	—
194	C₂×D₄×C₃₁	—	2	2	no	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	2	no	—
197	C₂×D₄×C₃₁	—	2	4	no	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	4	no	—
203	C₂×D₄×C₃₁	—	8	4	no	—
204	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
205	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₃₁	—	2	2	no	—
207	C₂²×C₄×C₃₁	—	2	2	no	—
208	C₂²×C₄×C₃₁	—	2	2	no	—
209	C₂²×C₄×C₃₁	—	2	2	no	—
210	C₂²×C₄×C₃₁	—	2	4	no	—
211	C₂²×C₄×C₃₁	—	2	4	no	—
212	C₂²×C₄×C₃₁	—	2	4	no	—
213	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
221	Q₁₆×C₃₁	—	4	1	no	—
222	SD₁₆×C₃₁	—	4	2	no	—
223	SD₁₆×C₃₁	—	4	4	no	—
224	D₈×C₃₁	—	4	2	no	—
225	D₈×C₃₁	—	4	2	no	—
226	D₈×C₃₁	—	4	1	no	—
227	D₈×C₃₁	—	4	4	no	—
228	M₁₆×C₃₁	—	2	4	no	—
229	M₁₆×C₃₁	—	4	2	no	—
230	C₂×C₈×C₃₁	—	2	2	no	—
231	C₂×C₈×C₃₁	—	2	2	no	—
232	C₂×C₈×C₃₁	—	4	1	no	—
233	C₂×C₈×C₃₁	—	4	1	no	—
234	C₂×C₈×C₃₁	—	4	1	no	—
235	C₂×C₈×C₃₁	—	4	1	no	—
236	C₂×C₈×C₃₁	—	4	2	no	—
237	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
240	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₃₁	—	2	2	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	2	no	—
249	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₃₁	—	2	2	no	—
257	C₂²⋊C₄×C₃₁	—	2	2	no	—
258	C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	4	no	—
261	C₂²⋊C₄×C₃₁	—	2	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
269	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
270	C₄²×C₃₁	—	2	4	no	—
271	C₄²×C₃₁	—	2	2	no	—
272	C₄²×C₃₁	C₂×D₄	1	4	yes	—
273	C₄²×C₃₁	C₂⁴	1	4	yes	—
274	#60934	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	2	2	no	—
277	C₂³×C₃₁	—	2	4	no	—
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	4	1	no	—
280	C₂³×C₃₁	—	4	4	no	—
281	C₂³×C₃₁	—	8	2	no	—
282	C₂³×C₃₁	—	8	2	no	—
283	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
285	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₃₁	—	2	2	no	—
287	Q₈×C₃₁	—	2	2	no	—
288	Q₈×C₃₁	—	8	4	no	—
289	D₄×C₃₁	—	2	4	no	—
290	D₄×C₃₁	—	2	2	no	—
291	D₄×C₃₁	—	2	4	no	—
292	D₄×C₃₁	—	2	2	no	—
293	D₄×C₃₁	—	4	4	no	—
294	D₄×C₃₁	—	4	8	no	—
295	D₄×C₃₁	—	4	4	no	—
296	D₄×C₃₁	—	4	4	no	—
297	D₄×C₃₁	—	8	4	no	—
298	D₄×C₃₁	—	8	4	no	—
299	D₄×C₃₁	—	8	2	no	—
300	D₄×C₃₁	—	8	4	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	4	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	1	no	—
306	C₂×C₄×C₃₁	—	2	1	no	—
307	C₂×C₄×C₃₁	—	2	1	no	—
308	C₂×C₄×C₃₁	—	2	1	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	4	no	—
313	C₂×C₄×C₃₁	—	4	2	no	—
314	C₂×C₄×C₃₁	—	4	4	no	—
315	C₂×C₄×C₃₁	—	8	4	no	—
316	C₂×C₄×C₃₁	—	8	4	no	—
317	C₂×C₄×C₃₁	—	8	4	no	—
318	C₂×C₄×C₃₁	—	8	2	no	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
325	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
326	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
327	C₈×C₃₁	—	2	1	no	—
328	C₈×C₃₁	—	2	1	no	—
329	C₈×C₃₁	—	2	1	no	—
330	C₈×C₃₁	—	2	1	no	—
331	C₈×C₃₁	—	2	4	no	—
332	#3494	C₂×C₃₁	1	2	yes	complemented
333	#3262	C₂×C₃₁	1	2	yes	complemented
334	#3259	C₂×C₃₁	1	2	yes	complemented
335	#3257	C₂×C₃₁	1	4	yes	complemented
336	#3250	C₂×C₃₁	1	2	yes	complemented
337	#3247	C₂×C₃₁	1	4	yes	complemented
338	#3245	C₂×C₃₁	1	2	yes	complemented
339	#3083	C₂×C₃₁	1	2	yes	complemented
340	#3081	C₂×C₃₁	1	2	yes	complemented
341	#3055	C₂×C₃₁	1	2	yes	complemented
342	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
343	C₂×#466	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3045	C₂×C₃₁	1	2	yes	complemented
345	#3041	C₂×C₃₁	1	2	yes	complemented
346	C₂×#424	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	—	4	4	no	—
355	C₂²×C₃₁	—	4	4	no	—
356	C₂²×C₃₁	—	4	2	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	—	4	4	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	4	no	—
361	C₂²×C₃₁	—	16	4	no	—
362	C₂²×C₃₁	#537	1	2	yes	—
363	C₂²×C₃₁	#576	1	2	yes	—
364	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₃₁	—	2	4	no	—
366	C₄×C₃₁	—	2	1	no	—
367	C₄×C₃₁	—	2	1	no	—
368	C₄×C₃₁	—	2	4	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	4	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	#537	1	2	yes	—
374	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
377	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
378	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
379	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
380	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
381	#555	—	2	2	no	—
382	#553	—	2	2	no	—
383	#553	—	2	2	no	—
384	#551	—	2	4	no	—
385	#547	—	2	2	no	—
386	#546	—	2	4	no	—
387	#544	C₂²×C₃₁	1	2	yes	—
388	#542	C₂²×C₃₁	1	4	yes	complemented
389	#540	C₂²×C₃₁	1	4	yes	complemented
390	#535	C₂²×C₃₁	1	2	yes	—
391	#532	C₂²×C₃₁	1	4	yes	complemented
392	#529	C₂²×C₃₁	1	4	yes	complemented
393	#525	C₂²×C₃₁	1	2	yes	—
394	C₂×#121	C₂²×C₃₁	1	2	yes	—
395	#520	C₂²×C₃₁	1	2	yes	—
396	#518	C₂²×C₃₁	1	2	yes	—
397	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
398	#479	C₂²×C₃₁	1	4	yes	complemented
399	#478	C₂²×C₃₁	1	4	yes	complemented
400	#478	C₂²×C₃₁	1	4	yes	complemented
401	#478	C₂²×C₃₁	1	4	yes	complemented
402	#477	C₂²×C₃₁	1	4	yes	complemented
403	#476	C₂²×C₃₁	1	4	yes	complemented
404	#474	C₂²×C₃₁	1	4	yes	complemented
405	#474	C₂²×C₃₁	1	4	yes	complemented
406	#469	C₂²×C₃₁	1	4	yes	complemented
407	#468	C₂²×C₃₁	1	4	yes	complemented
408	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
409	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	#466	C₂²×C₃₁	1	2	yes	—
411	#466	C₂²×C₃₁	1	2	yes	—
412	#466	C₂²×C₃₁	1	2	yes	—
413	#466	C₂²×C₃₁	1	2	yes	—
414	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
415	#466	C₂²×C₃₁	1	4	yes	complemented
416	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
417	#465	C₂²×C₃₁	1	2	yes	complemented
418	#465	C₂²×C₃₁	1	4	yes	complemented
419	#465	C₂²×C₃₁	1	2	yes	complemented
420	#464	C₂²×C₃₁	1	4	yes	complemented
421	#463	C₂²×C₃₁	1	4	yes	complemented
422	#463	C₂²×C₃₁	1	4	yes	complemented
423	#463	C₂²×C₃₁	1	4	yes	complemented
424	#460	C₂²×C₃₁	1	4	yes	complemented
425	#459	C₂²×C₃₁	1	4	yes	complemented
426	#459	C₂²×C₃₁	1	4	yes	complemented
427	#459	C₂²×C₃₁	1	4	yes	complemented
428	#428	C₂²×C₃₁	1	2	yes	—
429	#427	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
431	#424	C₂²×C₃₁	1	2	yes	—
432	#424	C₂²×C₃₁	1	2	yes	—
433	#424	C₂²×C₃₁	1	2	yes	complemented
434	#424	C₂²×C₃₁	1	2	yes	complemented
435	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
436	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
437	#418	C₂²×C₃₁	1	2	yes	—
438	#417	C₂²×C₃₁	1	2	yes	—
439	#416	C₂²×C₃₁	1	2	yes	—
440	C₂×#102	C₂²×C₃₁	1	2	yes	—
441	C₂×C₃₁	—	2	2	no	—
442	C₂×C₃₁	—	2	2	no	—
443	C₂×C₃₁	—	4	1	no	—
444	C₂×C₃₁	—	8	2	no	—
445	C₂×C₃₁	—	8	4	no	—
446	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
447	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
448	C₂×C₃₁	#3584	1	1	yes	characteristic
449	C₂×#41	—	2	4	no	—
450	C₂×#41	C₂³×C₃₁	1	2	yes	—
451	C₂²×D₄	—	2	2	no	—
452	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
453	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
454	AGL(1,ℤ/8)	—	4	4	no	—
455	#135	—	4	2	no	—
456	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
457	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
458	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
459	C₂×D₈	—	4	2	no	—
460	C₂×D₈	C₂³×C₃₁	1	2	yes	—
461	C₂×D₈	C₂³×C₃₁	1	2	yes	—
462	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
463	C₂×D₈	C₂³×C₃₁	1	4	yes	—
464	C₂×M₁₆	—	4	2	no	—
465	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
466	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
467	C₂²×C₈	—	4	2	no	—
468	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
477	#127	C₂³×C₃₁	1	4	yes	—
478	#126	—	2	4	no	—
479	#126	—	2	4	no	—
480	#125	—	2	2	no	—
481	#125	C₂³×C₃₁	1	4	yes	—
482	#124	—	2	4	no	—
483	#124	—	2	4	no	—
484	#124	C₂³×C₃₁	1	4	yes	—
485	#123	—	2	2	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
493	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	4	no	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	4	no	—
500	#121	—	2	4	no	—
501	#121	C₂³×C₃₁	1	4	yes	—
502	#121	C₂³×C₃₁	1	4	yes	—
503	#121	C₂³×C₃₁	1	2	yes	—
504	#121	C₂³×C₃₁	1	2	yes	—
505	#120	—	2	2	no	—
506	#120	—	2	4	no	—
507	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	C₂³×C₃₁	1	4	yes	—
516	C₄×D₄	C₂³×C₃₁	1	4	yes	—
517	C₄×D₄	C₂³×C₃₁	1	4	yes	—
518	#117	—	2	2	no	—
519	#117	—	2	4	no	—
520	#117	D₄×C₃₁	1	2	yes	—
521	#117	D₄×C₃₁	1	2	yes	—
522	#117	C₂³×C₃₁	1	2	yes	—
523	#117	C₂³×C₃₁	1	2	yes	—
524	#117	C₂³×C₃₁	1	2	yes	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
532	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
533	#107	C₂³×C₃₁	1	2	yes	—
534	#107	C₂³×C₃₁	1	2	yes	—
535	#107	C₂³×C₃₁	1	1	yes	characteristic
536	#107	C₂³×C₃₁	1	1	yes	characteristic
537	#107	C₂³×C₃₁	1	4	yes	—
538	#106	C₂³×C₃₁	1	2	yes	—
539	#106	C₂³×C₃₁	1	4	yes	—
540	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
541	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
542	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
543	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
544	#103	C₂³×C₃₁	1	2	yes	—
545	#103	C₂³×C₃₁	1	2	yes	—
546	#103	C₂³×C₃₁	1	4	yes	—
547	#102	C₂³×C₃₁	1	4	yes	—
548	#102	C₂³×C₃₁	1	4	yes	—
549	#102	C₂³×C₃₁	1	2	yes	—
550	#102	C₂³×C₃₁	1	2	yes	—
551	#102	C₂³×C₃₁	1	4	yes	—
552	#102	C₂³×C₃₁	1	4	yes	—
553	#102	C₂³×C₃₁	1	4	yes	—
554	C₃₁	#60934	1	1	yes	characteristic, direct product factor, Sylow
555	C₂⁴	—	2	2	no	—
556	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
557	#41	—	2	4	no	—
558	#41	—	2	4	no	—
559	#41	—	8	8	no	—
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	8	4	no	—
573	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
574	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
583	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
590	Q₁₆	—	4	1	no	—
591	SD₁₆	—	4	2	no	—
592	SD₁₆	—	4	4	no	—
593	D₈	—	4	2	no	—
594	D₈	—	4	2	no	—
595	D₈	—	4	1	no	—
596	D₈	—	4	4	no	—
597	M₁₆	—	2	4	no	—
598	M₁₆	—	4	2	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	4	1	no	—
602	C₂×C₈	—	4	1	no	—
603	C₂×C₈	—	4	1	no	—
604	C₂×C₈	—	4	1	no	—
605	C₂×C₈	—	4	2	no	—
606	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
607	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
609	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
624	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
638	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	C₂×D₄×C₃₁	1	4	yes	—
642	C₄²	C₂⁴×C₃₁	1	4	yes	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	8	2	no	—
650	C₂³	—	8	2	no	—
651	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
652	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
653	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	8	4	no	—
657	D₄	—	2	4	no	—
658	D₄	—	2	2	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	4	no	—
665	D₄	—	8	4	no	—
666	D₄	—	8	4	no	—
667	D₄	—	8	2	no	—
668	D₄	—	8	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
692	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
693	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
694	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
695	C₈	—	2	1	no	—
696	C₈	—	2	1	no	—
697	C₈	—	2	1	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	4	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	—	4	4	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	16	4	no	—
715	C₂²	C₃₁×#537	1	2	yes	—
716	C₂²	C₃₁×#576	1	2	yes	—
717	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	C₃₁×#537	1	2	yes	—
727	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
728	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
729	C₂	—	2	2	no	—
730	C₂	—	2	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	8	4	no	—
733	C₂	—	8	2	no	—
734	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
735	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
736	C₂	C₃₁×#3584	1	1	yes	characteristic

	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3494	C₂	semidirect
2. C₃₁×#3262	C₂	semidirect
3. C₃₁×#3259	C₂	semidirect
4. C₃₁×#3257	C₂	semidirect
5. C₃₁×#3250	C₂	semidirect
6. C₃₁×#3247	C₂	semidirect
7. C₃₁×#3245	C₂	semidirect
8. C₃₁×#3083	C₂	semidirect
9. C₃₁×#3081	C₂	semidirect
10. C₃₁×#3055	C₂	semidirect
11. C₃₁×#3050	C₂	semidirect
12. C₂×C₃₁×#466	C₂	semidirect
13. C₃₁×#3045	C₂	semidirect
14. C₃₁×#3041	C₂	semidirect
15. C₂×C₃₁×#424	C₂	semidirect
28. C₃₁×#542	C₂²	semidirect
29. C₃₁×#540	C₂²	semidirect
31. C₃₁×#532	C₂²	semidirect
32. C₃₁×#529	C₂²	semidirect
38. C₃₁×#479	C₂²	semidirect
39. C₃₁×#478	C₂²	semidirect
40. C₃₁×#478	C₂²	semidirect
41. C₃₁×#478	C₂²	semidirect
42. C₃₁×#477	C₂²	semidirect
43. C₃₁×#476	C₂²	semidirect
44. C₃₁×#474	C₂²	semidirect
45. C₃₁×#474	C₂²	semidirect
46. C₃₁×#469	C₂²	semidirect
47. C₃₁×#468	C₂²	semidirect
48. C₃₁×#467	C₂²	semidirect
49. C₃₁×#467	C₂²	semidirect
54. C₃₁×#466	C₂²	semidirect
55. C₃₁×#466	C₂²	semidirect
56. C₃₁×#466	C₂²	semidirect
57. C₃₁×#465	C₂²	semidirect
58. C₃₁×#465	C₂²	semidirect
59. C₃₁×#465	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
61. C₃₁×#463	C₂²	semidirect
62. C₃₁×#463	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#460	C₂²	semidirect
65. C₃₁×#459	C₂²	semidirect
66. C₃₁×#459	C₂²	semidirect
67. C₃₁×#459	C₂²	semidirect
73. C₃₁×#424	C₂²	semidirect
74. C₃₁×#424	C₂²	semidirect
75. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
76. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
274. #60934	C₃₁	direct (N × H)
332. #3494	C₂×C₃₁	semidirect
333. #3262	C₂×C₃₁	semidirect
334. #3259	C₂×C₃₁	semidirect
335. #3257	C₂×C₃₁	semidirect
336. #3250	C₂×C₃₁	semidirect
337. #3247	C₂×C₃₁	semidirect
338. #3245	C₂×C₃₁	semidirect
339. #3083	C₂×C₃₁	semidirect
340. #3081	C₂×C₃₁	semidirect
341. #3055	C₂×C₃₁	semidirect
342. #3050	C₂×C₃₁	semidirect
343. C₂×#466	C₂×C₃₁	semidirect
344. #3045	C₂×C₃₁	semidirect
345. #3041	C₂×C₃₁	semidirect
346. C₂×#424	C₂×C₃₁	semidirect
388. #542	C₂²×C₃₁	semidirect
389. #540	C₂²×C₃₁	semidirect
391. #532	C₂²×C₃₁	semidirect
392. #529	C₂²×C₃₁	semidirect
398. #479	C₂²×C₃₁	semidirect
399. #478	C₂²×C₃₁	semidirect
400. #478	C₂²×C₃₁	semidirect
401. #478	C₂²×C₃₁	semidirect
402. #477	C₂²×C₃₁	semidirect
403. #476	C₂²×C₃₁	semidirect
404. #474	C₂²×C₃₁	semidirect
405. #474	C₂²×C₃₁	semidirect
406. #469	C₂²×C₃₁	semidirect
407. #468	C₂²×C₃₁	semidirect
408. #467	C₂²×C₃₁	semidirect
409. #467	C₂²×C₃₁	semidirect
414. #466	C₂²×C₃₁	semidirect
415. #466	C₂²×C₃₁	semidirect
416. #466	C₂²×C₃₁	semidirect
417. #465	C₂²×C₃₁	semidirect
418. #465	C₂²×C₃₁	semidirect
419. #465	C₂²×C₃₁	semidirect
420. #464	C₂²×C₃₁	semidirect
421. #463	C₂²×C₃₁	semidirect
422. #463	C₂²×C₃₁	semidirect
423. #463	C₂²×C₃₁	semidirect
424. #460	C₂²×C₃₁	semidirect
425. #459	C₂²×C₃₁	semidirect
426. #459	C₂²×C₃₁	semidirect
427. #459	C₂²×C₃₁	semidirect
433. #424	C₂²×C₃₁	semidirect
434. #424	C₂²×C₃₁	semidirect
435. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
436. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
554. C₃₁	#60934	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×#3494	2
C₃₁×#3262	2
C₃₁×#3259	2
C₃₁×#3257	2
C₃₁×#3250	2
C₃₁×#3247	2
C₃₁×#3245	2
C₃₁×#3083	2
C₃₁×#3081	2
C₃₁×#3055	2
C₃₁×#3050	2
C₂×C₃₁×#466	2
C₃₁×#3045	2
C₃₁×#3041	2
C₂×C₃₁×#424	2
#60934	31

Subgroups — C31×#60934 #21517693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60934 #21517693