Subgroups — C₂×C₃₁×#3543 #21519503

Order 7936.

8814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3543	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#550	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#546	C₂	1	4	yes	maximal, complemented
6	C₂×D₄²×C₃₁	C₂	1	4	yes	maximal, complemented
7	C₂×D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#540	C₂	1	4	yes	maximal, complemented
9	C₂×C₃₁×#535	C₂	1	4	yes	maximal, complemented
10	C₂×C₃₁×#534	C₂	1	4	yes	maximal, complemented
11	C₂²×C₃₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#529	C₂	1	2	yes	maximal, complemented
13	C₂²×#41×C₃₁	C₂²	1	4	yes	complemented
14	C₂³×D₄×C₃₁	C₂²	1	2	yes	complemented
15	C₂³×D₄×C₃₁	C₂²	1	4	yes	complemented
16	C₂³×D₄×C₃₁	C₂²	1	4	yes	complemented
17	C₂³×D₄×C₃₁	C₂²	1	4	yes	complemented
18	C₃₁×#560	C₂²	1	64	yes	complemented
19	C₃₁×#559	C₂²	1	16	yes	complemented
20	C₃₁×#550	C₂²	1	32	yes	complemented
21	C₃₁×#546	C₂²	1	64	yes	complemented
22	D₄²×C₃₁	C₂²	1	64	yes	complemented
23	D₄²×C₃₁	C₂²	1	16	yes	complemented
24	C₃₁×#540	C₂²	1	64	yes	complemented
25	C₃₁×#535	C₂²	1	64	yes	complemented
26	C₃₁×#534	C₂²	1	64	yes	complemented
27	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#127	C₂²	1	4	yes	complemented
29	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
31	C₂×C₃₁×#127	C₂²	1	4	yes	complemented
32	C₂×C₃₁×#127	C₂²	1	16	yes	complemented
33	C₃₁×#529	C₂²	1	32	yes	complemented
34	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
35	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
36	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
37	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
38	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
39	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
41	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#121	C₂²	1	2	yes	—
44	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
45	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
46	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
47	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
48	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
49	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
50	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
51	C₂×C₃₁×#120	C₂²	1	8	yes	complemented
52	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
53	C₂×C₃₁×#120	C₂²	1	8	yes	complemented
54	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
56	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
58	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
59	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
60	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
61	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₃₁	C₂³	1	4	yes	—
63	C₂⁵×C₃₁	C₂³	1	4	yes	—
64	C₂×#41×C₃₁	—	4	16	no	—
65	C₂×#41×C₃₁	C₂³	1	32	yes	complemented
66	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
67	C₂²×D₄×C₃₁	—	4	16	no	—
68	C₂²×D₄×C₃₁	—	4	16	no	—
69	C₂²×D₄×C₃₁	—	4	8	no	—
70	C₂²×D₄×C₃₁	—	4	16	no	—
71	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
72	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
73	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
74	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
75	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
76	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
77	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
79	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
82	C₂²×D₄×C₃₁	C₂³	1	16	yes	complemented
83	C₂²×D₄×C₃₁	C₂³	1	32	yes	complemented
84	C₂²×D₄×C₃₁	C₂³	1	32	yes	complemented
85	C₂²×D₄×C₃₁	C₂³	1	32	yes	complemented
86	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
91	C₃₁×#127	C₂³	1	8	yes	—
92	C₃₁×#127	C₂³	1	32	yes	complemented
93	C₃₁×#127	C₂³	1	8	yes	complemented
94	C₃₁×#127	C₂³	1	16	yes	complemented
95	C₃₁×#127	C₂³	1	32	yes	complemented
96	C₃₁×#126	C₂³	1	32	yes	complemented
97	C₃₁×#125	C₂³	1	16	yes	complemented
98	C₃₁×#124	C₂³	1	16	yes	complemented
99	C₃₁×#124	C₂³	1	32	yes	complemented
100	C₃₁×#123	C₂³	1	32	yes	complemented
101	C₃₁×#123	C₂³	1	32	yes	complemented
102	C₃₁×#123	C₂³	1	32	yes	complemented
103	C₃₁×#123	C₂³	1	64	yes	complemented
104	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
105	C₃₁×#121	C₂³	1	16	yes	—
106	C₃₁×#121	C₂³	1	64	yes	complemented
107	C₃₁×#121	C₂³	1	64	yes	complemented
108	C₃₁×#121	C₂³	1	64	yes	complemented
109	C₃₁×#121	C₂³	1	32	yes	complemented
110	C₃₁×#121	C₂³	1	32	yes	complemented
111	C₃₁×#121	C₂³	1	64	yes	complemented
112	C₃₁×#120	C₂³	1	32	yes	complemented
113	C₃₁×#120	C₂³	1	64	yes	complemented
114	C₃₁×#120	C₂³	1	32	yes	complemented
115	C₃₁×#120	C₂³	1	64	yes	complemented
116	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
117	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
118	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
119	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
120	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
121	C₃₁×#117	C₂³	1	32	yes	complemented
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	complemented
138	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
143	C₂⁴×C₃₁	—	2	16	no	—
144	C₂⁴×C₃₁	—	4	16	no	—
145	C₂⁴×C₃₁	—	4	16	no	—
146	C₂⁴×C₃₁	—	4	8	no	—
147	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
148	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
149	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
150	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
151	C₂⁴×C₃₁	C₂⁴	1	16	yes	—
152	C₂⁴×C₃₁	C₂⁴	1	16	yes	—
153	#41×C₃₁	—	4	64	no	—
154	C₂×Q₈×C₃₁	—	2	8	no	—
155	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
156	C₂×D₄×C₃₁	—	2	16	no	—
157	C₂×D₄×C₃₁	—	2	8	no	—
158	C₂×D₄×C₃₁	—	2	16	no	—
159	C₂×D₄×C₃₁	—	2	16	no	—
160	C₂×D₄×C₃₁	—	4	64	no	—
161	C₂×D₄×C₃₁	—	4	64	no	—
162	C₂×D₄×C₃₁	—	4	16	no	—
163	C₂×D₄×C₃₁	—	4	16	no	—
164	C₂×D₄×C₃₁	—	4	4	no	—
165	C₂×D₄×C₃₁	—	4	8	no	—
166	C₂×D₄×C₃₁	—	4	4	no	—
167	C₂×D₄×C₃₁	—	4	16	no	—
168	C₂×D₄×C₃₁	—	4	32	no	—
169	C₂×D₄×C₃₁	—	4	16	no	—
170	C₂×D₄×C₃₁	—	4	64	no	—
171	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
172	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
173	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
174	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
175	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
176	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
177	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
178	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
179	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
180	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
181	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
182	C₂²×C₄×C₃₁	—	2	4	no	—
183	C₂²×C₄×C₃₁	—	2	8	no	—
184	C₂²×C₄×C₃₁	—	2	16	no	—
185	C₂²×C₄×C₃₁	—	4	8	no	—
186	C₂²×C₄×C₃₁	—	4	16	no	—
187	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
190	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
198	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
199	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
200	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
201	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
202	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
203	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
204	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
205	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
206	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
207	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
208	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
209	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
210	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
211	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
212	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
213	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
214	C₄²×C₃₁	C₂⁴	1	8	yes	—
215	C₄²×C₃₁	C₂⁴	1	4	yes	—
216	C₄²×C₃₁	C₂⁴	1	4	yes	—
217	C₄²×C₃₁	C₂⁴	1	16	yes	—
218	C₂×#3543	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₃₁	—	2	4	no	—
220	C₂³×C₃₁	—	2	8	no	—
221	C₂³×C₃₁	—	2	16	no	—
222	C₂³×C₃₁	—	2	8	no	—
223	C₂³×C₃₁	—	2	8	no	—
224	C₂³×C₃₁	—	2	8	no	—
225	C₂³×C₃₁	—	2	16	no	—
226	C₂³×C₃₁	—	2	8	no	—
227	C₂³×C₃₁	—	2	32	no	—
228	C₂³×C₃₁	—	4	32	no	—
229	C₂³×C₃₁	—	4	32	no	—
230	C₂³×C₃₁	—	4	16	no	—
231	C₂³×C₃₁	—	8	32	no	—
232	C₂³×C₃₁	—	8	32	no	—
233	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
234	C₂³×C₃₁	C₂⁵	1	8	yes	—
235	C₂³×C₃₁	C₂⁵	1	8	yes	—
236	C₂³×C₃₁	C₂⁵	1	8	yes	—
237	C₂³×C₃₁	C₂⁵	1	2	yes	—
238	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
239	Q₈×C₃₁	—	2	16	no	—
240	D₄×C₃₁	—	2	32	no	—
241	D₄×C₃₁	—	2	16	no	—
242	D₄×C₃₁	—	2	32	no	—
243	D₄×C₃₁	—	2	32	no	—
244	D₄×C₃₁	—	4	32	no	—
245	D₄×C₃₁	—	4	32	no	—
246	D₄×C₃₁	—	4	8	no	—
247	D₄×C₃₁	—	4	16	no	—
248	D₄×C₃₁	—	4	8	no	—
249	D₄×C₃₁	—	4	32	no	—
250	D₄×C₃₁	—	4	32	no	—
251	C₂×C₄×C₃₁	—	2	8	no	—
252	C₂×C₄×C₃₁	—	2	8	no	—
253	C₂×C₄×C₃₁	—	2	2	no	—
254	C₂×C₄×C₃₁	—	2	2	no	—
255	C₂×C₄×C₃₁	—	2	4	no	—
256	C₂×C₄×C₃₁	—	2	8	no	—
257	C₂×C₄×C₃₁	—	2	8	no	—
258	C₂×C₄×C₃₁	—	2	16	no	—
259	C₂×C₄×C₃₁	—	2	32	no	—
260	C₂×C₄×C₃₁	—	4	16	no	—
261	C₂×C₄×C₃₁	—	4	32	no	—
262	C₂×C₄×C₃₁	H(5,𝔽₂)	1	8	yes	—
263	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
264	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
265	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
266	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
267	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
268	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
269	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
270	#3543	C₂×C₃₁	1	32	yes	direct product factor
271	C₂×#560	C₂×C₃₁	1	4	yes	complemented
272	C₂×#559	C₂×C₃₁	1	1	yes	characteristic, complemented
273	C₂×#550	C₂×C₃₁	1	2	yes	complemented
274	C₂×#546	C₂×C₃₁	1	4	yes	complemented
275	C₂×D₄²	C₂×C₃₁	1	4	yes	complemented
276	C₂×D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
277	C₂×#540	C₂×C₃₁	1	4	yes	complemented
278	C₂×#535	C₂×C₃₁	1	4	yes	complemented
279	C₂×#534	C₂×C₃₁	1	4	yes	complemented
280	C₂²×#127	C₂×C₃₁	1	1	yes	characteristic, complemented
281	C₂×#529	C₂×C₃₁	1	2	yes	complemented
282	C₂²×C₃₁	—	2	4	no	—
283	C₂²×C₃₁	—	2	8	no	—
284	C₂²×C₃₁	—	2	8	no	—
285	C₂²×C₃₁	—	2	16	no	—
286	C₂²×C₃₁	—	2	8	no	—
287	C₂²×C₃₁	—	2	8	no	—
288	C₂²×C₃₁	—	2	8	no	—
289	C₂²×C₃₁	—	2	16	no	—
290	C₂²×C₃₁	—	2	8	no	—
291	C₂²×C₃₁	—	4	16	no	—
292	C₂²×C₃₁	—	4	16	no	—
293	C₂²×C₃₁	—	4	16	no	—
294	C₂²×C₃₁	—	8	32	no	—
295	C₂²×C₃₁	—	8	32	no	—
296	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
297	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
298	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
299	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
300	C₄×C₃₁	—	2	8	no	—
301	C₄×C₃₁	—	2	2	no	—
302	C₄×C₃₁	—	2	2	no	—
303	C₄×C₃₁	—	2	4	no	—
304	C₄×C₃₁	—	2	8	no	—
305	C₄×C₃₁	—	2	8	no	—
306	C₄×C₃₁	C₂×H(5,𝔽₂)	1	8	yes	—
307	C₂²×#41	C₂²×C₃₁	1	4	yes	complemented
308	C₂³×D₄	C₂²×C₃₁	1	2	yes	complemented
309	C₂³×D₄	C₂²×C₃₁	1	4	yes	complemented
310	C₂³×D₄	C₂²×C₃₁	1	4	yes	complemented
311	C₂³×D₄	C₂²×C₃₁	1	4	yes	complemented
312	#560	C₂²×C₃₁	1	64	yes	complemented
313	#559	C₂²×C₃₁	1	16	yes	complemented
314	#550	C₂²×C₃₁	1	32	yes	complemented
315	#546	C₂²×C₃₁	1	64	yes	complemented
316	D₄²	C₂²×C₃₁	1	64	yes	complemented
317	D₄²	C₂²×C₃₁	1	16	yes	complemented
318	#540	C₂²×C₃₁	1	64	yes	complemented
319	#535	C₂²×C₃₁	1	64	yes	complemented
320	#534	C₂²×C₃₁	1	64	yes	complemented
321	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
322	C₂×#127	C₂²×C₃₁	1	4	yes	complemented
323	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
324	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
325	C₂×#127	C₂²×C₃₁	1	4	yes	complemented
326	C₂×#127	C₂²×C₃₁	1	16	yes	complemented
327	#529	C₂²×C₃₁	1	32	yes	complemented
328	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
329	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
330	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
331	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
332	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
333	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
334	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
335	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
336	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
337	C₂×#121	C₂²×C₃₁	1	2	yes	—
338	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
339	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
340	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
341	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
342	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
343	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
344	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
345	C₂×#120	C₂²×C₃₁	1	8	yes	complemented
346	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
347	C₂×#120	C₂²×C₃₁	1	8	yes	complemented
348	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
349	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
350	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
351	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
352	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
353	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
354	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
355	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
356	C₂×C₃₁	—	2	4	no	—
357	C₂×C₃₁	—	4	8	no	—
358	C₂×C₃₁	—	4	8	no	—
359	C₂×C₃₁	—	4	8	no	—
360	C₂×C₃₁	#3543	1	4	yes	direct product factor
361	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	2	yes	—
363	C₂⁵	C₂³×C₃₁	1	4	yes	—
364	C₂⁵	C₂³×C₃₁	1	4	yes	—
365	C₂×#41	—	4	16	no	—
366	C₂×#41	C₂³×C₃₁	1	32	yes	complemented
367	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
368	C₂²×D₄	—	4	16	no	—
369	C₂²×D₄	—	4	16	no	—
370	C₂²×D₄	—	4	8	no	—
371	C₂²×D₄	—	4	16	no	—
372	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
373	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
374	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
375	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
376	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
377	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
378	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
379	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
380	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
381	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
382	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
383	C₂²×D₄	C₂³×C₃₁	1	16	yes	complemented
384	C₂²×D₄	C₂³×C₃₁	1	32	yes	complemented
385	C₂²×D₄	C₂³×C₃₁	1	32	yes	complemented
386	C₂²×D₄	C₂³×C₃₁	1	32	yes	complemented
387	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
388	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
389	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
391	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
392	#127	C₂³×C₃₁	1	8	yes	—
393	#127	C₂³×C₃₁	1	32	yes	complemented
394	#127	C₂³×C₃₁	1	8	yes	complemented
395	#127	C₂³×C₃₁	1	16	yes	complemented
396	#127	C₂³×C₃₁	1	32	yes	complemented
397	#126	C₂³×C₃₁	1	32	yes	complemented
398	#125	C₂³×C₃₁	1	16	yes	complemented
399	#124	C₂³×C₃₁	1	16	yes	complemented
400	#124	C₂³×C₃₁	1	32	yes	complemented
401	#123	C₂³×C₃₁	1	32	yes	complemented
402	#123	C₂³×C₃₁	1	32	yes	complemented
403	#123	C₂³×C₃₁	1	32	yes	complemented
404	#123	C₂³×C₃₁	1	64	yes	complemented
405	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
406	#121	C₂³×C₃₁	1	16	yes	—
407	#121	C₂³×C₃₁	1	64	yes	complemented
408	#121	C₂³×C₃₁	1	64	yes	complemented
409	#121	C₂³×C₃₁	1	64	yes	complemented
410	#121	C₂³×C₃₁	1	32	yes	complemented
411	#121	C₂³×C₃₁	1	32	yes	complemented
412	#121	C₂³×C₃₁	1	64	yes	complemented
413	#120	C₂³×C₃₁	1	32	yes	complemented
414	#120	C₂³×C₃₁	1	64	yes	complemented
415	#120	C₂³×C₃₁	1	32	yes	complemented
416	#120	C₂³×C₃₁	1	64	yes	complemented
417	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
418	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
419	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
420	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
421	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
422	#117	C₂³×C₃₁	1	32	yes	complemented
423	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	complemented
439	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
440	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
441	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
444	C₃₁	C₂×#3543	1	1	yes	characteristic, direct product factor, Sylow
445	C₂⁴	—	2	16	no	—
446	C₂⁴	—	4	16	no	—
447	C₂⁴	—	4	16	no	—
448	C₂⁴	—	4	8	no	—
449	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
450	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
451	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
452	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
453	C₂⁴	C₂⁴×C₃₁	1	16	yes	—
454	C₂⁴	C₂⁴×C₃₁	1	16	yes	—
455	#41	—	4	64	no	—
456	C₂×Q₈	—	2	8	no	—
457	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	2	16	no	—
462	C₂×D₄	—	4	64	no	—
463	C₂×D₄	—	4	64	no	—
464	C₂×D₄	—	4	16	no	—
465	C₂×D₄	—	4	16	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	8	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	4	16	no	—
470	C₂×D₄	—	4	32	no	—
471	C₂×D₄	—	4	16	no	—
472	C₂×D₄	—	4	64	no	—
473	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
474	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
475	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
476	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
477	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
478	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
479	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
480	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
481	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
482	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
483	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	16	no	—
487	C₂²×C₄	—	4	8	no	—
488	C₂²×C₄	—	4	16	no	—
489	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
495	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
498	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	—
499	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
500	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
501	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
502	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
503	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
504	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
505	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
506	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
507	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
508	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
509	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
510	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
511	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
512	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
513	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
514	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
515	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
516	C₄²	C₂⁴×C₃₁	1	8	yes	—
517	C₄²	C₂⁴×C₃₁	1	4	yes	—
518	C₄²	C₂⁴×C₃₁	1	4	yes	—
519	C₄²	C₂⁴×C₃₁	1	16	yes	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	16	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	16	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	32	no	—
529	C₂³	—	4	32	no	—
530	C₂³	—	4	32	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	8	32	no	—
533	C₂³	—	8	32	no	—
534	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
535	C₂³	C₂⁵×C₃₁	1	8	yes	—
536	C₂³	C₂⁵×C₃₁	1	8	yes	—
537	C₂³	C₂⁵×C₃₁	1	8	yes	—
538	C₂³	C₂⁵×C₃₁	1	2	yes	—
539	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
540	Q₈	—	2	16	no	—
541	D₄	—	2	32	no	—
542	D₄	—	2	16	no	—
543	D₄	—	2	32	no	—
544	D₄	—	2	32	no	—
545	D₄	—	4	32	no	—
546	D₄	—	4	32	no	—
547	D₄	—	4	8	no	—
548	D₄	—	4	16	no	—
549	D₄	—	4	8	no	—
550	D₄	—	4	32	no	—
551	D₄	—	4	32	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	2	32	no	—
561	C₂×C₄	—	4	16	no	—
562	C₂×C₄	—	4	32	no	—
563	C₂×C₄	C₃₁×H(5,𝔽₂)	1	8	yes	—
564	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
565	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
566	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
567	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
568	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
569	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
570	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	16	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	4	16	no	—
581	C₂²	—	4	16	no	—
582	C₂²	—	4	16	no	—
583	C₂²	—	8	32	no	—
584	C₂²	—	8	32	no	—
585	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
586	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
587	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
588	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
589	C₄	—	2	8	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	C₂×C₃₁×H(5,𝔽₂)	1	8	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	4	8	no	—
599	C₂	—	4	8	no	—
600	C₂	C₃₁×#3543	1	4	yes	direct product factor
601	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3543	C₂	direct (N × H)
2. C₂×C₃₁×#560	C₂	semidirect
3. C₂×C₃₁×#559	C₂	semidirect
4. C₂×C₃₁×#550	C₂	semidirect
5. C₂×C₃₁×#546	C₂	semidirect
6. C₂×D₄²×C₃₁	C₂	semidirect
7. C₂×D₄²×C₃₁	C₂	semidirect
8. C₂×C₃₁×#540	C₂	semidirect
9. C₂×C₃₁×#535	C₂	semidirect
10. C₂×C₃₁×#534	C₂	semidirect
11. C₂²×C₃₁×#127	C₂	semidirect
12. C₂×C₃₁×#529	C₂	semidirect
13. C₂²×#41×C₃₁	C₂²	semidirect
14. C₂³×D₄×C₃₁	C₂²	semidirect
15. C₂³×D₄×C₃₁	C₂²	semidirect
16. C₂³×D₄×C₃₁	C₂²	semidirect
17. C₂³×D₄×C₃₁	C₂²	semidirect
18. C₃₁×#560	C₂²	semidirect
19. C₃₁×#559	C₂²	semidirect
20. C₃₁×#550	C₂²	semidirect
21. C₃₁×#546	C₂²	semidirect
22. D₄²×C₃₁	C₂²	semidirect
23. D₄²×C₃₁	C₂²	semidirect
24. C₃₁×#540	C₂²	semidirect
25. C₃₁×#535	C₂²	semidirect
26. C₃₁×#534	C₂²	semidirect
28. C₂×C₃₁×#127	C₂²	semidirect
29. C₂×C₃₁×#127	C₂²	semidirect
30. C₂×C₃₁×#127	C₂²	semidirect
31. C₂×C₃₁×#127	C₂²	semidirect
32. C₂×C₃₁×#127	C₂²	semidirect
33. C₃₁×#529	C₂²	semidirect
34. C₂×C₃₁×#126	C₂²	semidirect
35. C₂×C₃₁×#125	C₂²	semidirect
36. C₂×C₃₁×#124	C₂²	semidirect
37. C₂×C₃₁×#124	C₂²	semidirect
38. C₂×C₃₁×#123	C₂²	semidirect
39. C₂×C₃₁×#123	C₂²	semidirect
40. C₂×C₃₁×#123	C₂²	semidirect
41. C₂×C₃₁×#123	C₂²	semidirect
42. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₃₁×#121	C₂²	semidirect
45. C₂×C₃₁×#121	C₂²	semidirect
46. C₂×C₃₁×#121	C₂²	semidirect
47. C₂×C₃₁×#121	C₂²	semidirect
48. C₂×C₃₁×#121	C₂²	semidirect
49. C₂×C₃₁×#121	C₂²	semidirect
50. C₂×C₃₁×#120	C₂²	semidirect
51. C₂×C₃₁×#120	C₂²	semidirect
52. C₂×C₃₁×#120	C₂²	semidirect
53. C₂×C₃₁×#120	C₂²	semidirect
54. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
55. C₂×C₄×D₄×C₃₁	C₂²	semidirect
56. C₂×C₄×D₄×C₃₁	C₂²	semidirect
57. C₂×C₄×D₄×C₃₁	C₂²	semidirect
58. C₂×C₄×D₄×C₃₁	C₂²	semidirect
59. C₂×C₃₁×#117	C₂²	semidirect
60. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
61. C₂²×C₄²×C₃₁	C₂²	semidirect
65. C₂×#41×C₃₁	C₂³	semidirect
82. C₂²×D₄×C₃₁	C₂³	semidirect
83. C₂²×D₄×C₃₁	C₂³	semidirect
84. C₂²×D₄×C₃₁	C₂³	semidirect
85. C₂²×D₄×C₃₁	C₂³	semidirect
92. C₃₁×#127	C₂³	semidirect
93. C₃₁×#127	C₂³	semidirect
94. C₃₁×#127	C₂³	semidirect
95. C₃₁×#127	C₂³	semidirect
96. C₃₁×#126	C₂³	semidirect
97. C₃₁×#125	C₂³	semidirect
98. C₃₁×#124	C₂³	semidirect
99. C₃₁×#124	C₂³	semidirect
100. C₃₁×#123	C₂³	semidirect
101. C₃₁×#123	C₂³	semidirect
102. C₃₁×#123	C₂³	semidirect
103. C₃₁×#123	C₂³	semidirect
104. C₃₁×C₂²⋊Q₈	C₂³	semidirect
106. C₃₁×#121	C₂³	semidirect
107. C₃₁×#121	C₂³	semidirect
108. C₃₁×#121	C₂³	semidirect
109. C₃₁×#121	C₂³	semidirect
110. C₃₁×#121	C₂³	semidirect
111. C₃₁×#121	C₂³	semidirect
112. C₃₁×#120	C₂³	semidirect
113. C₃₁×#120	C₂³	semidirect
114. C₃₁×#120	C₂³	semidirect
115. C₃₁×#120	C₂³	semidirect
116. C₄×Q₈×C₃₁	C₂³	semidirect
117. C₄×D₄×C₃₁	C₂³	semidirect
118. C₄×D₄×C₃₁	C₂³	semidirect
119. C₄×D₄×C₃₁	C₂³	semidirect
120. C₄×D₄×C₃₁	C₂³	semidirect
121. C₃₁×#117	C₂³	semidirect
137. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
142. C₂×C₄²×C₃₁	C₂³	semidirect
218. C₂×#3543	C₃₁	direct (N × H)
270. #3543	C₂×C₃₁	direct (N × H)
271. C₂×#560	C₂×C₃₁	semidirect
272. C₂×#559	C₂×C₃₁	semidirect
273. C₂×#550	C₂×C₃₁	semidirect
274. C₂×#546	C₂×C₃₁	semidirect
275. C₂×D₄²	C₂×C₃₁	semidirect
276. C₂×D₄²	C₂×C₃₁	semidirect
277. C₂×#540	C₂×C₃₁	semidirect
278. C₂×#535	C₂×C₃₁	semidirect
279. C₂×#534	C₂×C₃₁	semidirect
280. C₂²×#127	C₂×C₃₁	semidirect
281. C₂×#529	C₂×C₃₁	semidirect
307. C₂²×#41	C₂²×C₃₁	semidirect
308. C₂³×D₄	C₂²×C₃₁	semidirect
309. C₂³×D₄	C₂²×C₃₁	semidirect
310. C₂³×D₄	C₂²×C₃₁	semidirect
311. C₂³×D₄	C₂²×C₃₁	semidirect
312. #560	C₂²×C₃₁	semidirect
313. #559	C₂²×C₃₁	semidirect
314. #550	C₂²×C₃₁	semidirect
315. #546	C₂²×C₃₁	semidirect
316. D₄²	C₂²×C₃₁	semidirect
317. D₄²	C₂²×C₃₁	semidirect
318. #540	C₂²×C₃₁	semidirect
319. #535	C₂²×C₃₁	semidirect
320. #534	C₂²×C₃₁	semidirect
322. C₂×#127	C₂²×C₃₁	semidirect
323. C₂×#127	C₂²×C₃₁	semidirect
324. C₂×#127	C₂²×C₃₁	semidirect
325. C₂×#127	C₂²×C₃₁	semidirect
326. C₂×#127	C₂²×C₃₁	semidirect
327. #529	C₂²×C₃₁	semidirect
328. C₂×#126	C₂²×C₃₁	semidirect
329. C₂×#125	C₂²×C₃₁	semidirect
330. C₂×#124	C₂²×C₃₁	semidirect
331. C₂×#124	C₂²×C₃₁	semidirect
332. C₂×#123	C₂²×C₃₁	semidirect
333. C₂×#123	C₂²×C₃₁	semidirect
334. C₂×#123	C₂²×C₃₁	semidirect
335. C₂×#123	C₂²×C₃₁	semidirect
336. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
338. C₂×#121	C₂²×C₃₁	semidirect
339. C₂×#121	C₂²×C₃₁	semidirect
340. C₂×#121	C₂²×C₃₁	semidirect
341. C₂×#121	C₂²×C₃₁	semidirect
342. C₂×#121	C₂²×C₃₁	semidirect
343. C₂×#121	C₂²×C₃₁	semidirect
344. C₂×#120	C₂²×C₃₁	semidirect
345. C₂×#120	C₂²×C₃₁	semidirect
346. C₂×#120	C₂²×C₃₁	semidirect
347. C₂×#120	C₂²×C₃₁	semidirect
348. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
349. C₂×C₄×D₄	C₂²×C₃₁	semidirect
350. C₂×C₄×D₄	C₂²×C₃₁	semidirect
351. C₂×C₄×D₄	C₂²×C₃₁	semidirect
352. C₂×C₄×D₄	C₂²×C₃₁	semidirect
353. C₂×#117	C₂²×C₃₁	semidirect
354. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
355. C₂²×C₄²	C₂²×C₃₁	semidirect
360. C₂×C₃₁	#3543	direct (N × H)
366. C₂×#41	C₂³×C₃₁	semidirect
383. C₂²×D₄	C₂³×C₃₁	semidirect
384. C₂²×D₄	C₂³×C₃₁	semidirect
385. C₂²×D₄	C₂³×C₃₁	semidirect
386. C₂²×D₄	C₂³×C₃₁	semidirect
393. #127	C₂³×C₃₁	semidirect
394. #127	C₂³×C₃₁	semidirect
395. #127	C₂³×C₃₁	semidirect
396. #127	C₂³×C₃₁	semidirect
397. #126	C₂³×C₃₁	semidirect
398. #125	C₂³×C₃₁	semidirect
399. #124	C₂³×C₃₁	semidirect
400. #124	C₂³×C₃₁	semidirect
401. #123	C₂³×C₃₁	semidirect
402. #123	C₂³×C₃₁	semidirect
403. #123	C₂³×C₃₁	semidirect
404. #123	C₂³×C₃₁	semidirect
405. C₂²⋊Q₈	C₂³×C₃₁	semidirect
407. #121	C₂³×C₃₁	semidirect
408. #121	C₂³×C₃₁	semidirect
409. #121	C₂³×C₃₁	semidirect
410. #121	C₂³×C₃₁	semidirect
411. #121	C₂³×C₃₁	semidirect
412. #121	C₂³×C₃₁	semidirect
413. #120	C₂³×C₃₁	semidirect
414. #120	C₂³×C₃₁	semidirect
415. #120	C₂³×C₃₁	semidirect
416. #120	C₂³×C₃₁	semidirect
417. C₄×Q₈	C₂³×C₃₁	semidirect
418. C₄×D₄	C₂³×C₃₁	semidirect
419. C₄×D₄	C₂³×C₃₁	semidirect
420. C₄×D₄	C₂³×C₃₁	semidirect
421. C₄×D₄	C₂³×C₃₁	semidirect
422. #117	C₂³×C₃₁	semidirect
438. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
443. C₂×C₄²	C₂³×C₃₁	semidirect
444. C₃₁	C₂×#3543	direct (N × H)
600. C₂	C₃₁×#3543	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×#3543	2
C₂×C₃₁×#560	2
C₂×C₃₁×#559	2
C₂×C₃₁×#550	2
C₂×C₃₁×#546	2
C₂×D₄²×C₃₁	2
C₂×C₃₁×#540	2
C₂×C₃₁×#535	2
C₂×C₃₁×#534	2
C₂²×C₃₁×#127	2
C₂×C₃₁×#529	2
C₂×#3543	31

Subgroups — C2×C31×#3543 #21519503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3543 #21519503