Subgroups — C₂×C₃₁×#3337 #21517987

Order 7936.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#553	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3337	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₃₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#553	—	2	4	no	—
21	C₃₁×#553	C₂²	1	8	yes	—
22	C₃₁×#552	—	2	4	no	—
23	C₃₁×#552	C₂²	1	8	yes	complemented
24	C₂×C₃₁×#126	—	2	1	no	—
25	C₂×C₃₁×#126	—	2	1	no	—
26	C₂×C₃₁×#125	—	2	1	no	—
27	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#123	—	2	1	no	—
30	C₂×C₃₁×#123	—	2	1	no	—
31	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#121	—	2	1	no	—
34	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₃₁	—	2	1	no	—
38	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	—	2	1	no	—
41	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#499	C₂²	1	8	yes	complemented
46	C₃₁×#485	C₂²	1	8	yes	complemented
47	C₃₁×#484	C₂²	1	8	yes	complemented
48	C₃₁×#482	C₂²	1	8	yes	complemented
49	C₃₁×#480	C₂²	1	8	yes	complemented
50	C₃₁×#479	C₂²	1	8	yes	complemented
51	C₃₁×#478	C₂²	1	8	yes	complemented
52	C₃₁×#465	C₂²	1	8	yes	complemented
53	C₃₁×#465	C₂²	1	8	yes	complemented
54	C₄×SD₁₆×C₃₁	C₂²	1	8	yes	complemented
55	C₈×D₄×C₃₁	C₂²	1	8	yes	complemented
56	C₃₁×#427	C₂²	1	8	yes	complemented
57	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
59	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
61	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
63	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
64	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
66	C₂×C₃₁×#106	C₂²	1	8	yes	complemented
67	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₃₁	—	2	1	no	—
79	C₂²×D₄×C₃₁	—	2	1	no	—
80	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	—	2	1	no	—
83	C₂³×C₄×C₃₁	—	2	1	no	—
84	C₂³×C₄×C₃₁	—	2	1	no	—
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×SD₁₆×C₃₁	—	2	4	no	—
88	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
89	C₂²×C₈×C₃₁	—	2	4	no	—
90	C₂²×C₈×C₃₁	—	2	4	no	—
91	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
95	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
96	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₃₁×#126	—	2	8	no	—
98	C₃₁×#126	—	2	8	no	—
99	C₃₁×#125	—	2	8	no	—
100	C₃₁×#125	—	2	2	no	—
101	C₃₁×#125	—	2	2	no	—
102	C₃₁×#125	C₂³	1	4	yes	—
103	C₃₁×#125	C₂³	1	4	yes	—
104	C₃₁×#123	—	2	8	no	—
105	C₃₁×#123	—	2	8	no	—
106	C₃₁×C₂²⋊Q₈	—	2	2	no	—
107	C₃₁×C₂²⋊Q₈	—	2	2	no	—
108	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₃₁×#121	—	2	8	no	—
111	C₃₁×#121	—	2	2	no	—
112	C₃₁×#121	—	2	2	no	—
113	C₃₁×#121	C₂³	1	4	yes	—
114	C₃₁×#121	C₂³	1	4	yes	—
115	C₄×Q₈×C₃₁	—	2	2	no	—
116	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
117	C₄×D₄×C₃₁	—	2	8	no	—
118	C₄×D₄×C₃₁	—	2	2	no	—
119	C₄×D₄×C₃₁	D₄	1	4	yes	—
120	C₄×D₄×C₃₁	C₂³	1	4	yes	—
121	C₄×D₄×C₃₁	C₂³	1	4	yes	—
122	C₃₁×#117	—	2	2	no	—
123	C₃₁×#117	—	2	2	no	—
124	C₃₁×#117	—	2	8	no	—
125	C₃₁×#117	C₂³	1	4	yes	—
126	C₃₁×#117	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
132	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
133	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
134	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
135	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
136	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
137	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
138	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₃₁	—	2	1	no	—
157	C₂×C₄²×C₃₁	—	2	1	no	—
158	C₂×C₄²×C₃₁	—	2	1	no	—
159	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
160	C₃₁×#107	C₂³	1	4	yes	—
161	C₃₁×#107	C₂³	1	4	yes	—
162	C₃₁×#107	C₂³	1	4	yes	—
163	C₃₁×#107	C₂³	1	4	yes	—
164	C₃₁×#106	C₂³	1	4	yes	—
165	C₃₁×#106	C₂³	1	4	yes	—
166	C₃₁×#106	C₂³	1	4	yes	—
167	C₃₁×#106	C₂³	1	4	yes	—
168	C₃₁×#106	C₂³	1	4	yes	—
169	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
170	C₃₁×#103	C₂³	1	4	yes	—
171	C₃₁×#103	C₂³	1	4	yes	—
172	C₃₁×#103	C₂³	1	4	yes	—
173	C₃₁×#102	C₂³	1	4	yes	—
174	C₃₁×#102	C₂³	1	4	yes	—
175	C₃₁×#102	C₂³	1	4	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₄×C₈×C₃₁	C₂³	1	4	yes	—
179	C₂⁴×C₃₁	—	2	1	no	—
180	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₃₁	—	2	1	no	—
183	C₂×Q₈×C₃₁	—	2	2	no	—
184	C₂×Q₈×C₃₁	—	2	2	no	—
185	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
186	C₂×D₄×C₃₁	—	2	4	no	—
187	C₂×D₄×C₃₁	—	2	4	no	—
188	C₂×D₄×C₃₁	—	2	4	no	—
189	C₂×D₄×C₃₁	—	2	1	no	—
190	C₂×D₄×C₃₁	—	2	2	no	—
191	C₂×D₄×C₃₁	—	2	2	no	—
192	C₂×D₄×C₃₁	—	4	4	no	—
193	C₂×D₄×C₃₁	—	8	2	no	—
194	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
195	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₃₁	—	2	2	no	—
197	C₂²×C₄×C₃₁	—	2	2	no	—
198	C₂²×C₄×C₃₁	—	2	2	no	—
199	C₂²×C₄×C₃₁	—	2	2	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	2	1	no	—
202	C₂²×C₄×C₃₁	—	2	1	no	—
203	C₂²×C₄×C₃₁	—	2	1	no	—
204	C₂²×C₄×C₃₁	—	2	1	no	—
205	C₂²×C₄×C₃₁	—	2	1	no	—
206	C₂²×C₄×C₃₁	—	2	1	no	—
207	C₂²×C₄×C₃₁	—	2	1	no	—
208	C₂²×C₄×C₃₁	—	2	4	no	—
209	C₂²×C₄×C₃₁	—	2	4	no	—
210	C₂²×C₄×C₃₁	—	4	4	no	—
211	C₂²×C₄×C₃₁	—	8	2	no	—
212	C₂²×C₄×C₃₁	—	8	2	no	—
213	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
218	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	SD₁₆×C₃₁	—	2	8	no	—
223	C₂×C₈×C₃₁	—	2	2	no	—
224	C₂×C₈×C₃₁	—	2	2	no	—
225	C₂×C₈×C₃₁	—	2	2	no	—
226	C₂×C₈×C₃₁	—	2	8	no	—
227	C₂×C₈×C₃₁	—	2	8	no	—
228	C₂×C₈×C₃₁	#41	1	4	yes	—
229	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
230	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
231	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
232	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
233	C₄⋊C₄×C₃₁	—	2	1	no	—
234	C₄⋊C₄×C₃₁	—	2	1	no	—
235	C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₄⋊C₄×C₃₁	—	2	1	no	—
237	C₄⋊C₄×C₃₁	—	2	4	no	—
238	C₄⋊C₄×C₃₁	—	2	4	no	—
239	C₄⋊C₄×C₃₁	—	2	4	no	—
240	C₄⋊C₄×C₃₁	—	2	4	no	—
241	C₄⋊C₄×C₃₁	—	2	4	no	—
242	C₄⋊C₄×C₃₁	—	2	4	no	—
243	C₄⋊C₄×C₃₁	—	2	4	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	1	no	—
247	C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
249	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂²⋊C₄×C₃₁	—	2	4	no	—
256	C₂²⋊C₄×C₃₁	—	2	4	no	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	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	C₂×D₄	1	4	yes	—
263	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
264	C₄²×C₃₁	—	2	4	no	—
265	C₄²×C₃₁	—	2	4	no	—
266	C₄²×C₃₁	—	2	4	no	—
267	C₄²×C₃₁	C₂×D₄	1	2	yes	—
268	C₄²×C₃₁	C₂⁴	1	2	yes	—
269	C₂×#3337	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	—	2	2	no	—
274	C₂³×C₃₁	—	2	2	no	—
275	C₂³×C₃₁	—	2	2	no	—
276	C₂³×C₃₁	—	4	2	no	—
277	C₂³×C₃₁	—	4	2	no	—
278	C₂³×C₃₁	—	4	2	no	—
279	C₂³×C₃₁	#135	1	4	yes	—
280	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
281	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
282	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₃₁	—	2	2	no	—
284	Q₈×C₃₁	—	2	2	no	—
285	Q₈×C₃₁	—	4	2	no	—
286	D₄×C₃₁	—	2	8	no	—
287	D₄×C₃₁	—	2	2	no	—
288	D₄×C₃₁	—	2	2	no	—
289	D₄×C₃₁	—	4	8	no	—
290	D₄×C₃₁	—	4	2	no	—
291	D₄×C₃₁	—	8	4	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	2	2	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	2	4	no	—
297	C₂×C₄×C₃₁	—	2	4	no	—
298	C₂×C₄×C₃₁	—	2	2	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	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	2	2	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	4	2	no	—
310	C₂×C₄×C₃₁	—	4	8	no	—
311	C₂×C₄×C₃₁	—	4	2	no	—
312	C₂×C₄×C₃₁	—	4	2	no	—
313	C₂×C₄×C₃₁	—	4	2	no	—
314	C₂×C₄×C₃₁	—	4	2	no	—
315	C₂×C₄×C₃₁	—	4	2	no	—
316	C₂×C₄×C₃₁	—	4	2	no	—
317	C₂×C₄×C₃₁	—	8	4	no	—
318	C₂×C₄×C₃₁	—	8	4	no	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₃₁	C₂×#41	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	2	no	—
328	C₈×C₃₁	—	2	2	no	—
329	C₈×C₃₁	—	2	2	no	—
330	C₈×C₃₁	C₂×#41	1	4	yes	—
331	C₂×#553	C₂×C₃₁	1	1	yes	characteristic
332	C₂×#552	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#3337	C₂×C₃₁	1	16	yes	direct product factor
334	C₂×#499	C₂×C₃₁	1	1	yes	characteristic, complemented
335	C₂×#484	C₂×C₃₁	1	1	yes	characteristic, complemented
336	C₂×#485	C₂×C₃₁	1	1	yes	characteristic, complemented
337	C₂×#482	C₂×C₃₁	1	1	yes	characteristic, complemented
338	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
339	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
340	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
341	C₂×#465	C₂×C₃₁	1	1	yes	characteristic, complemented
342	C₂×#465	C₂×C₃₁	1	1	yes	characteristic, complemented
343	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
344	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
345	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₂²×#106	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂²×C₃₁	—	2	8	no	—
348	C₂²×C₃₁	—	2	2	no	—
349	C₂²×C₃₁	—	2	2	no	—
350	C₂²×C₃₁	—	2	2	no	—
351	C₂²×C₃₁	—	2	2	no	—
352	C₂²×C₃₁	—	2	2	no	—
353	C₂²×C₃₁	—	4	4	no	—
354	C₂²×C₃₁	—	4	2	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	4	2	no	—
357	C₂²×C₃₁	—	8	4	no	—
358	C₂²×C₃₁	#547	1	2	yes	—
359	C₂²×C₃₁	C₂×#135	1	4	yes	—
360	C₂²×C₃₁	C₂×#135	1	2	yes	—
361	C₂²×C₃₁	#577	1	2	yes	—
362	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	2	2	no	—
365	C₄×C₃₁	—	2	2	no	—
366	C₄×C₃₁	—	2	2	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	2	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	#547	1	2	yes	—
375	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
376	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
378	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
379	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
380	#553	—	2	4	no	—
381	#553	C₂²×C₃₁	1	8	yes	—
382	#552	—	2	4	no	—
383	#552	C₂²×C₃₁	1	8	yes	complemented
384	C₂×#126	—	2	1	no	—
385	C₂×#126	—	2	1	no	—
386	C₂×#125	—	2	1	no	—
387	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
388	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
389	C₂×#123	—	2	1	no	—
390	C₂×#123	—	2	1	no	—
391	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
392	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
393	C₂×#121	—	2	1	no	—
394	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
397	C₂×C₄×D₄	—	2	1	no	—
398	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
400	C₂×#117	—	2	1	no	—
401	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
405	#499	C₂²×C₃₁	1	8	yes	complemented
406	#485	C₂²×C₃₁	1	8	yes	complemented
407	#484	C₂²×C₃₁	1	8	yes	complemented
408	#482	C₂²×C₃₁	1	8	yes	complemented
409	#480	C₂²×C₃₁	1	8	yes	complemented
410	#479	C₂²×C₃₁	1	8	yes	complemented
411	#478	C₂²×C₃₁	1	8	yes	complemented
412	#465	C₂²×C₃₁	1	8	yes	complemented
413	#465	C₂²×C₃₁	1	8	yes	complemented
414	C₄×SD₁₆	C₂²×C₃₁	1	8	yes	complemented
415	C₈×D₄	C₂²×C₃₁	1	8	yes	complemented
416	#427	C₂²×C₃₁	1	8	yes	complemented
417	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
418	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
419	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
420	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
421	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
423	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
424	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
425	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×#106	C₂²×C₃₁	1	8	yes	complemented
427	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
428	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
429	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
431	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
432	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
433	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
436	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
437	C₂×C₃₁	—	2	4	no	—
438	C₂×C₃₁	—	4	2	no	—
439	C₂×C₃₁	—	8	2	no	—
440	C₂×C₃₁	#3337	1	4	yes	direct product factor
441	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
442	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
443	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	—	2	1	no	—
452	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
454	C₂×SD₁₆	—	2	4	no	—
455	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
456	C₂²×C₈	—	2	4	no	—
457	C₂²×C₈	—	2	4	no	—
458	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
461	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
462	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
464	#126	—	2	8	no	—
465	#126	—	2	8	no	—
466	#125	—	2	8	no	—
467	#125	—	2	2	no	—
468	#125	—	2	2	no	—
469	#125	C₂³×C₃₁	1	4	yes	—
470	#125	C₂³×C₃₁	1	4	yes	—
471	#123	—	2	8	no	—
472	#123	—	2	8	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
476	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
477	#121	—	2	8	no	—
478	#121	—	2	2	no	—
479	#121	—	2	2	no	—
480	#121	C₂³×C₃₁	1	4	yes	—
481	#121	C₂³×C₃₁	1	4	yes	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	D₄×C₃₁	1	4	yes	—
487	C₄×D₄	C₂³×C₃₁	1	4	yes	—
488	C₄×D₄	C₂³×C₃₁	1	4	yes	—
489	#117	—	2	2	no	—
490	#117	—	2	2	no	—
491	#117	—	2	8	no	—
492	#117	C₂³×C₃₁	1	4	yes	—
493	#117	C₂³×C₃₁	1	4	yes	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	2	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
527	#107	C₂³×C₃₁	1	4	yes	—
528	#107	C₂³×C₃₁	1	4	yes	—
529	#107	C₂³×C₃₁	1	4	yes	—
530	#107	C₂³×C₃₁	1	4	yes	—
531	#106	C₂³×C₃₁	1	4	yes	—
532	#106	C₂³×C₃₁	1	4	yes	—
533	#106	C₂³×C₃₁	1	4	yes	—
534	#106	C₂³×C₃₁	1	4	yes	—
535	#106	C₂³×C₃₁	1	4	yes	—
536	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
537	#103	C₂³×C₃₁	1	4	yes	—
538	#103	C₂³×C₃₁	1	4	yes	—
539	#103	C₂³×C₃₁	1	4	yes	—
540	#102	C₂³×C₃₁	1	4	yes	—
541	#102	C₂³×C₃₁	1	4	yes	—
542	#102	C₂³×C₃₁	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
545	C₄×C₈	C₂³×C₃₁	1	4	yes	—
546	C₃₁	C₂×#3337	1	1	yes	characteristic, direct product factor, Sylow
547	C₂⁴	—	2	1	no	—
548	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
549	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	8	2	no	—
562	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
563	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	4	4	no	—
579	C₂²×C₄	—	8	2	no	—
580	C₂²×C₄	—	8	2	no	—
581	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	2	yes	—
586	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
590	SD₁₆	—	2	8	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	2	no	—
594	C₂×C₈	—	2	8	no	—
595	C₂×C₈	—	2	8	no	—
596	C₂×C₈	#41×C₃₁	1	4	yes	—
597	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
598	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
599	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
600	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
617	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
618	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
619	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
631	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	C₂×D₄×C₃₁	1	2	yes	—
636	C₄²	C₂⁴×C₃₁	1	2	yes	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	C₃₁×#135	1	4	yes	—
647	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
648	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
649	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	4	2	no	—
653	D₄	—	2	8	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	4	8	no	—
657	D₄	—	4	2	no	—
658	D₄	—	8	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	—	8	4	no	—
686	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
691	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
692	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
693	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
694	C₈	—	2	2	no	—
695	C₈	—	2	2	no	—
696	C₈	—	2	2	no	—
697	C₈	C₂×#41×C₃₁	1	4	yes	—
698	C₂²	—	2	8	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	8	4	no	—
709	C₂²	C₃₁×#547	1	2	yes	—
710	C₂²	C₂×C₃₁×#135	1	4	yes	—
711	C₂²	C₂×C₃₁×#135	1	2	yes	—
712	C₂²	C₃₁×#577	1	2	yes	—
713	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	C₃₁×#547	1	2	yes	—
726	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
727	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
728	C₂	—	2	4	no	—
729	C₂	—	4	2	no	—
730	C₂	—	8	2	no	—
731	C₂	C₃₁×#3337	1	4	yes	direct product factor
732	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
733	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
734	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#553	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#552	C₂	semidirect
3. C₃₁×#3337	C₂	direct (N × H)
4. C₂×C₃₁×#499	C₂	semidirect
5. C₂×C₃₁×#484	C₂	semidirect
6. C₂×C₃₁×#485	C₂	semidirect
7. C₂×C₃₁×#482	C₂	semidirect
8. C₂×C₃₁×#480	C₂	semidirect
9. C₂×C₃₁×#479	C₂	semidirect
10. C₂×C₃₁×#478	C₂	semidirect
11. C₂×C₃₁×#465	C₂	semidirect
12. C₂×C₃₁×#465	C₂	semidirect
13. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
14. C₂×C₈×D₄×C₃₁	C₂	semidirect
15. C₂×C₃₁×#427	C₂	semidirect
16. C₂²×C₃₁×#106	C₂	semidirect
23. C₃₁×#552	C₂²	semidirect
45. C₃₁×#499	C₂²	semidirect
46. C₃₁×#485	C₂²	semidirect
47. C₃₁×#484	C₂²	semidirect
48. C₃₁×#482	C₂²	semidirect
49. C₃₁×#480	C₂²	semidirect
50. C₃₁×#479	C₂²	semidirect
51. C₃₁×#478	C₂²	semidirect
52. C₃₁×#465	C₂²	semidirect
53. C₃₁×#465	C₂²	semidirect
54. C₄×SD₁₆×C₃₁	C₂²	semidirect
55. C₈×D₄×C₃₁	C₂²	semidirect
56. C₃₁×#427	C₂²	semidirect
66. C₂×C₃₁×#106	C₂²	semidirect
269. C₂×#3337	C₃₁	direct (N × H)
332. C₂×#552	C₂×C₃₁	semidirect
333. #3337	C₂×C₃₁	direct (N × H)
334. C₂×#499	C₂×C₃₁	semidirect
335. C₂×#484	C₂×C₃₁	semidirect
336. C₂×#485	C₂×C₃₁	semidirect
337. C₂×#482	C₂×C₃₁	semidirect
338. C₂×#480	C₂×C₃₁	semidirect
339. C₂×#479	C₂×C₃₁	semidirect
340. C₂×#478	C₂×C₃₁	semidirect
341. C₂×#465	C₂×C₃₁	semidirect
342. C₂×#465	C₂×C₃₁	semidirect
343. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
344. C₂×C₈×D₄	C₂×C₃₁	semidirect
345. C₂×#427	C₂×C₃₁	semidirect
346. C₂²×#106	C₂×C₃₁	semidirect
383. #552	C₂²×C₃₁	semidirect
405. #499	C₂²×C₃₁	semidirect
406. #485	C₂²×C₃₁	semidirect
407. #484	C₂²×C₃₁	semidirect
408. #482	C₂²×C₃₁	semidirect
409. #480	C₂²×C₃₁	semidirect
410. #479	C₂²×C₃₁	semidirect
411. #478	C₂²×C₃₁	semidirect
412. #465	C₂²×C₃₁	semidirect
413. #465	C₂²×C₃₁	semidirect
414. C₄×SD₁₆	C₂²×C₃₁	semidirect
415. C₈×D₄	C₂²×C₃₁	semidirect
416. #427	C₂²×C₃₁	semidirect
426. C₂×#106	C₂²×C₃₁	semidirect
440. C₂×C₃₁	#3337	direct (N × H)
546. C₃₁	C₂×#3337	direct (N × H)
731. C₂	C₃₁×#3337	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×#553	2
C₂×C₃₁×#552	2
C₃₁×#3337	2
C₂×C₃₁×#499	2
C₂×C₃₁×#484	2
C₂×C₃₁×#485	2
C₂×C₃₁×#482	2
C₂×C₃₁×#480	2
C₂×C₃₁×#479	2
C₂×C₃₁×#478	2
C₂×C₃₁×#465	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₈×D₄×C₃₁	2
C₂×C₃₁×#427	2
C₂²×C₃₁×#106	2
C₂×#3337	31

Subgroups — C2×C31×#3337 #21517987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3337 #21517987