Subgroups — C₂×C₃₁×#3481 #21519473

Order 7936.

8722 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3481	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#553	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#551	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#546	C₂	1	4	yes	maximal, complemented
7	C₂×D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#529	C₂	1	4	yes	maximal, complemented
10	C₂×C₃₁×#525	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×#41×C₃₁	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×D₄×C₃₁	C₂	1	4	yes	maximal, complemented
13	C₂²×#41×C₃₁	C₂²	1	2	yes	—
14	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
15	C₂³×D₄×C₃₁	C₂²	1	4	yes	—
16	C₂⁴×C₄×C₃₁	C₂²	1	4	yes	complemented
17	C₃₁×#559	C₂²	1	16	yes	complemented
18	C₃₁×#554	C₂²	1	32	yes	complemented
19	C₃₁×#553	C₂²	1	64	yes	complemented
20	C₃₁×#551	C₂²	1	64	yes	complemented
21	C₃₁×#546	C₂²	1	64	yes	complemented
22	D₄²×C₃₁	C₂²	1	16	yes	complemented
23	C₃₁×#532	C₂²	1	16	yes	complemented
24	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
26	C₃₁×#529	C₂²	1	64	yes	complemented
27	C₂×C₃₁×#126	C₂²	1	8	yes	complemented
28	C₂×C₃₁×#125	C₂²	1	4	yes	complemented
29	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
30	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
31	C₃₁×#525	C₂²	1	64	yes	complemented
32	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
33	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
34	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
35	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	complemented
36	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
37	C₂×C₃₁×#121	C₂²	1	4	yes	—
38	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
39	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#120	C₂²	1	4	yes	—
41	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
42	C₄×#41×C₃₁	C₂²	1	32	yes	complemented
43	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
44	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
47	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
49	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
50	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
51	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
52	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
53	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
54	C₂×C₄×D₄×C₃₁	C₂²	1	64	yes	complemented
55	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
56	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
58	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
59	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
60	C₂²×C₄²×C₃₁	C₂²	1	4	yes	complemented
61	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₃₁	C₂³	1	4	yes	—
63	C₂×#41×C₃₁	—	2	16	no	—
64	C₂×#41×C₃₁	—	4	8	no	—
65	C₂×#41×C₃₁	C₂³	1	16	yes	—
66	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
67	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
68	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₃₁	—	2	32	no	—
70	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
71	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
72	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
73	C₂²×D₄×C₃₁	C₂³	1	32	yes	—
74	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
76	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
77	C₂³×C₄×C₃₁	—	4	16	no	—
78	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
79	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
82	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
84	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
85	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
86	C₂³×C₄×C₃₁	C₂³	1	32	yes	complemented
87	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
88	C₃₁×#127	C₂³	1	8	yes	—
89	C₃₁×#126	C₂³	1	64	yes	complemented
90	C₃₁×#125	C₂³	1	32	yes	complemented
91	C₃₁×#124	C₂³	1	32	yes	complemented
92	C₃₁×#124	C₂³	1	16	yes	complemented
93	C₃₁×#123	C₂³	1	32	yes	complemented
94	C₃₁×#123	C₂³	1	32	yes	complemented
95	C₃₁×#123	C₂³	1	64	yes	complemented
96	C₃₁×C₂²⋊Q₈	C₂³	1	64	yes	complemented
97	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
98	C₃₁×#121	C₂³	1	32	yes	—
99	C₃₁×#121	C₂³	1	64	yes	complemented
100	C₃₁×#121	C₂³	1	32	yes	complemented
101	C₃₁×#120	C₂³	1	32	yes	—
102	C₃₁×#120	C₂³	1	32	yes	complemented
103	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
104	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
105	C₄×D₄×C₃₁	C₂³	1	16	yes	—
106	C₄×D₄×C₃₁	C₂³	1	32	yes	—
107	C₄×D₄×C₃₁	C₂³	1	16	yes	—
108	C₄×D₄×C₃₁	C₂³	1	64	yes	complemented
109	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
110	C₄×D₄×C₃₁	C₂³	1	64	yes	complemented
111	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
112	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
113	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
114	C₃₁×#117	C₂³	1	32	yes	complemented
115	C₃₁×#117	C₂³	1	16	yes	complemented
116	C₃₁×#117	C₂³	1	32	yes	complemented
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	32	yes	complemented
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	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	64	yes	complemented
134	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	32	yes	complemented
141	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
142	C₂⁴×C₃₁	—	2	32	no	—
143	C₂⁴×C₃₁	—	4	8	no	—
144	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
145	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₃₁	C₂⁴	1	16	yes	—
147	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
148	#41×C₃₁	—	2	64	no	—
149	#41×C₃₁	—	4	32	no	—
150	C₂×Q₈×C₃₁	—	2	8	no	—
151	C₂×Q₈×C₃₁	—	4	4	no	—
152	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
153	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
154	C₂×D₄×C₃₁	—	2	32	no	—
155	C₂×D₄×C₃₁	—	2	16	no	—
156	C₂×D₄×C₃₁	—	2	128	no	—
157	C₂×D₄×C₃₁	—	2	16	no	—
158	C₂×D₄×C₃₁	—	4	8	no	—
159	C₂×D₄×C₃₁	—	4	4	no	—
160	C₂×D₄×C₃₁	#41	1	16	yes	complemented
161	C₂×D₄×C₃₁	C₂⁴	1	32	yes	—
162	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
163	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
164	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
165	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
166	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₃₁	—	2	16	no	—
168	C₂²×C₄×C₃₁	—	2	16	no	—
169	C₂²×C₄×C₃₁	—	2	8	no	—
170	C₂²×C₄×C₃₁	—	2	16	no	—
171	C₂²×C₄×C₃₁	—	2	16	no	—
172	C₂²×C₄×C₃₁	—	2	4	no	—
173	C₂²×C₄×C₃₁	—	4	64	no	—
174	C₂²×C₄×C₃₁	—	4	8	no	—
175	C₂²×C₄×C₃₁	—	4	16	no	—
176	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
182	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	—
189	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
190	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
192	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
193	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
194	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
195	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
196	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
197	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
198	C₄⋊C₄×C₃₁	C₂⁴	1	32	yes	—
199	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
200	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
201	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
202	C₂²⋊C₄×C₃₁	C₂⁴	1	32	yes	—
203	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
204	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
205	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
206	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
207	C₄²×C₃₁	C₂⁴	1	8	yes	—
208	C₄²×C₃₁	C₂⁴	1	4	yes	—
209	C₄²×C₃₁	C₂⁴	1	16	yes	—
210	C₄²×C₃₁	C₂⁴	1	16	yes	—
211	C₄²×C₃₁	C₂⁴	1	4	yes	—
212	C₄²×C₃₁	C₂⁴	1	16	yes	—
213	C₂×#3481	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₃₁	—	2	8	no	—
215	C₂³×C₃₁	—	2	8	no	—
216	C₂³×C₃₁	—	2	4	no	—
217	C₂³×C₃₁	—	2	64	no	—
218	C₂³×C₃₁	—	2	16	no	—
219	C₂³×C₃₁	—	2	8	no	—
220	C₂³×C₃₁	—	2	2	no	—
221	C₂³×C₃₁	—	4	16	no	—
222	C₂³×C₃₁	—	4	64	no	—
223	C₂³×C₃₁	C₂×#41	1	16	yes	—
224	C₂³×C₃₁	C₂⁵	1	8	yes	—
225	C₂³×C₃₁	C₂⁵	1	2	yes	—
226	C₂³×C₃₁	C₂⁵	1	8	yes	—
227	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
228	Q₈×C₃₁	—	2	16	no	—
229	Q₈×C₃₁	—	4	8	no	—
230	D₄×C₃₁	—	2	64	no	—
231	D₄×C₃₁	—	2	32	no	—
232	D₄×C₃₁	—	2	32	no	—
233	D₄×C₃₁	—	4	16	no	—
234	D₄×C₃₁	—	4	8	no	—
235	D₄×C₃₁	C₂×#41	1	32	yes	complemented
236	C₂×C₄×C₃₁	—	2	4	no	—
237	C₂×C₄×C₃₁	—	2	8	no	—
238	C₂×C₄×C₃₁	—	2	8	no	—
239	C₂×C₄×C₃₁	—	2	32	no	—
240	C₂×C₄×C₃₁	—	2	8	no	—
241	C₂×C₄×C₃₁	—	2	8	no	—
242	C₂×C₄×C₃₁	—	2	2	no	—
243	C₂×C₄×C₃₁	—	2	32	no	—
244	C₂×C₄×C₃₁	—	2	16	no	—
245	C₂×C₄×C₃₁	—	2	32	no	—
246	C₂×C₄×C₃₁	—	2	32	no	—
247	C₂×C₄×C₃₁	—	2	8	no	—
248	C₂×C₄×C₃₁	—	4	16	no	—
249	C₂×C₄×C₃₁	—	4	32	no	—
250	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
251	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
252	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
253	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
254	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
255	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
256	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
257	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
258	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
259	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
260	#3481	C₂×C₃₁	1	32	yes	direct product factor
261	C₂×#559	C₂×C₃₁	1	1	yes	characteristic, complemented
262	C₂×#554	C₂×C₃₁	1	2	yes	complemented
263	C₂×#553	C₂×C₃₁	1	4	yes	complemented
264	C₂×#551	C₂×C₃₁	1	4	yes	complemented
265	C₂×#546	C₂×C₃₁	1	4	yes	complemented
266	C₂×D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
267	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
268	C₂×#529	C₂×C₃₁	1	4	yes	complemented
269	C₂×#525	C₂×C₃₁	1	4	yes	complemented
270	C₂×C₄×#41	C₂×C₃₁	1	2	yes	complemented
271	C₂²×C₄×D₄	C₂×C₃₁	1	4	yes	complemented
272	C₂²×C₃₁	—	2	8	no	—
273	C₂²×C₃₁	—	2	8	no	—
274	C₂²×C₃₁	—	2	32	no	—
275	C₂²×C₃₁	—	2	4	no	—
276	C₂²×C₃₁	—	2	16	no	—
277	C₂²×C₃₁	—	2	8	no	—
278	C₂²×C₃₁	—	2	2	no	—
279	C₂²×C₃₁	—	4	64	no	—
280	C₂²×C₃₁	—	4	4	no	—
281	C₂²×C₃₁	—	4	16	no	—
282	C₂²×C₃₁	C₂²×#41	1	16	yes	—
283	C₂²×C₃₁	C₂²×#41	1	4	yes	—
284	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
286	C₄×C₃₁	—	2	4	no	—
287	C₄×C₃₁	—	2	8	no	—
288	C₄×C₃₁	—	2	8	no	—
289	C₄×C₃₁	—	2	8	no	—
290	C₄×C₃₁	—	2	8	no	—
291	C₄×C₃₁	—	2	2	no	—
292	C₄×C₃₁	C₂²×#41	1	8	yes	—
293	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
294	C₂²×#41	C₂²×C₃₁	1	2	yes	—
295	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
296	C₂³×D₄	C₂²×C₃₁	1	4	yes	—
297	C₂⁴×C₄	C₂²×C₃₁	1	4	yes	complemented
298	#559	C₂²×C₃₁	1	16	yes	complemented
299	#554	C₂²×C₃₁	1	32	yes	complemented
300	#553	C₂²×C₃₁	1	64	yes	complemented
301	#551	C₂²×C₃₁	1	64	yes	complemented
302	#546	C₂²×C₃₁	1	64	yes	complemented
303	D₄²	C₂²×C₃₁	1	16	yes	complemented
304	#532	C₂²×C₃₁	1	16	yes	complemented
305	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
306	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
307	#529	C₂²×C₃₁	1	64	yes	complemented
308	C₂×#126	C₂²×C₃₁	1	8	yes	complemented
309	C₂×#125	C₂²×C₃₁	1	4	yes	complemented
310	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
311	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
312	#525	C₂²×C₃₁	1	64	yes	complemented
313	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
314	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
315	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
316	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	complemented
317	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
318	C₂×#121	C₂²×C₃₁	1	4	yes	—
319	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
320	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
321	C₂×#120	C₂²×C₃₁	1	4	yes	—
322	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
323	C₄×#41	C₂²×C₃₁	1	32	yes	complemented
324	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
325	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
326	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
327	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
328	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
330	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
331	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
332	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
333	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
334	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
335	C₂×C₄×D₄	C₂²×C₃₁	1	64	yes	complemented
336	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
337	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
338	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
339	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
340	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
341	C₂²×C₄²	C₂²×C₃₁	1	4	yes	complemented
342	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
343	C₂×C₃₁	—	2	16	no	—
344	C₂×C₃₁	—	4	2	no	—
345	C₂×C₃₁	—	4	8	no	—
346	C₂×C₃₁	#3481	1	4	yes	direct product factor
347	C₂×C₃₁	C₂³×#41	1	2	yes	—
348	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂⁵	C₂³×C₃₁	1	4	yes	—
350	C₂×#41	—	2	16	no	—
351	C₂×#41	—	4	8	no	—
352	C₂×#41	C₂³×C₃₁	1	16	yes	—
353	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
354	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
355	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
356	C₂²×D₄	—	2	32	no	—
357	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
358	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
359	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
360	C₂²×D₄	C₂³×C₃₁	1	32	yes	—
361	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
362	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
363	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
364	C₂³×C₄	—	4	16	no	—
365	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
366	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
367	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
368	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
369	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
370	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
372	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
373	C₂³×C₄	C₂³×C₃₁	1	32	yes	complemented
374	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
375	#127	C₂³×C₃₁	1	8	yes	—
376	#126	C₂³×C₃₁	1	64	yes	complemented
377	#125	C₂³×C₃₁	1	32	yes	complemented
378	#124	C₂³×C₃₁	1	32	yes	complemented
379	#124	C₂³×C₃₁	1	16	yes	complemented
380	#123	C₂³×C₃₁	1	32	yes	complemented
381	#123	C₂³×C₃₁	1	32	yes	complemented
382	#123	C₂³×C₃₁	1	64	yes	complemented
383	C₂²⋊Q₈	C₂³×C₃₁	1	64	yes	complemented
384	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
385	#121	C₂³×C₃₁	1	32	yes	—
386	#121	C₂³×C₃₁	1	64	yes	complemented
387	#121	C₂³×C₃₁	1	32	yes	complemented
388	#120	C₂³×C₃₁	1	32	yes	—
389	#120	C₂³×C₃₁	1	32	yes	complemented
390	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
391	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
392	C₄×D₄	C₂³×C₃₁	1	16	yes	—
393	C₄×D₄	C₂³×C₃₁	1	32	yes	—
394	C₄×D₄	C₂³×C₃₁	1	16	yes	—
395	C₄×D₄	C₂³×C₃₁	1	64	yes	complemented
396	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
397	C₄×D₄	C₂³×C₃₁	1	64	yes	complemented
398	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
399	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
400	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
401	#117	C₂³×C₃₁	1	32	yes	complemented
402	#117	C₂³×C₃₁	1	16	yes	complemented
403	#117	C₂³×C₃₁	1	32	yes	complemented
404	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃₁	1	32	yes	complemented
412	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃₁	1	64	yes	complemented
421	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
423	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
424	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
426	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
427	C₂×C₄²	C₂³×C₃₁	1	32	yes	complemented
428	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
429	C₃₁	C₂×#3481	1	1	yes	characteristic, direct product factor, Sylow
430	C₂⁴	—	2	32	no	—
431	C₂⁴	—	4	8	no	—
432	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
433	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
434	C₂⁴	C₂⁴×C₃₁	1	16	yes	—
435	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
436	#41	—	2	64	no	—
437	#41	—	4	32	no	—
438	C₂×Q₈	—	2	8	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
441	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
442	C₂×D₄	—	2	32	no	—
443	C₂×D₄	—	2	16	no	—
444	C₂×D₄	—	2	128	no	—
445	C₂×D₄	—	2	16	no	—
446	C₂×D₄	—	4	8	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	#41×C₃₁	1	16	yes	complemented
449	C₂×D₄	C₂⁴×C₃₁	1	32	yes	—
450	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
451	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
452	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
453	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
454	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
455	C₂²×C₄	—	2	16	no	—
456	C₂²×C₄	—	2	16	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	2	16	no	—
459	C₂²×C₄	—	2	16	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	4	64	no	—
462	C₂²×C₄	—	4	8	no	—
463	C₂²×C₄	—	4	16	no	—
464	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
470	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
471	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
472	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
473	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
476	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	—
477	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
478	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
480	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
481	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
482	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
483	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
484	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
485	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
486	C₄⋊C₄	C₂⁴×C₃₁	1	32	yes	—
487	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
488	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
489	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
490	C₂²⋊C₄	C₂⁴×C₃₁	1	32	yes	—
491	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
492	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
493	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
494	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
495	C₄²	C₂⁴×C₃₁	1	8	yes	—
496	C₄²	C₂⁴×C₃₁	1	4	yes	—
497	C₄²	C₂⁴×C₃₁	1	16	yes	—
498	C₄²	C₂⁴×C₃₁	1	16	yes	—
499	C₄²	C₂⁴×C₃₁	1	4	yes	—
500	C₄²	C₂⁴×C₃₁	1	16	yes	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	64	no	—
505	C₂³	—	2	16	no	—
506	C₂³	—	2	8	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	16	no	—
509	C₂³	—	4	64	no	—
510	C₂³	C₂×#41×C₃₁	1	16	yes	—
511	C₂³	C₂⁵×C₃₁	1	8	yes	—
512	C₂³	C₂⁵×C₃₁	1	2	yes	—
513	C₂³	C₂⁵×C₃₁	1	8	yes	—
514	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
515	Q₈	—	2	16	no	—
516	Q₈	—	4	8	no	—
517	D₄	—	2	64	no	—
518	D₄	—	2	32	no	—
519	D₄	—	2	32	no	—
520	D₄	—	4	16	no	—
521	D₄	—	4	8	no	—
522	D₄	C₂×#41×C₃₁	1	32	yes	complemented
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	32	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	32	no	—
531	C₂×C₄	—	2	16	no	—
532	C₂×C₄	—	2	32	no	—
533	C₂×C₄	—	2	32	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	4	16	no	—
536	C₂×C₄	—	4	32	no	—
537	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
538	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
539	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
540	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
541	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
542	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
543	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
544	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
545	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
546	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	32	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	16	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	64	no	—
555	C₂²	—	4	16	no	—
556	C₂²	—	4	4	no	—
557	C₂²	C₂²×#41×C₃₁	1	16	yes	—
558	C₂²	C₂²×#41×C₃₁	1	4	yes	—
559	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
560	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
561	C₄	—	2	4	no	—
562	C₄	—	2	8	no	—
563	C₄	—	2	8	no	—
564	C₄	—	2	8	no	—
565	C₄	—	2	8	no	—
566	C₄	—	2	2	no	—
567	C₄	C₂²×#41×C₃₁	1	8	yes	—
568	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
569	C₂	—	2	16	no	—
570	C₂	—	4	8	no	—
571	C₂	—	4	2	no	—
572	C₂	C₃₁×#3481	1	4	yes	direct product factor
573	C₂	C₂³×#41×C₃₁	1	2	yes	—
574	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂³×C₃₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3481	C₂	direct (N × H)
2. C₂×C₃₁×#559	C₂	semidirect
3. C₂×C₃₁×#554	C₂	semidirect
4. C₂×C₃₁×#553	C₂	semidirect
5. C₂×C₃₁×#551	C₂	semidirect
6. C₂×C₃₁×#546	C₂	semidirect
7. C₂×D₄²×C₃₁	C₂	semidirect
8. C₂×C₃₁×#532	C₂	semidirect
9. C₂×C₃₁×#529	C₂	semidirect
10. C₂×C₃₁×#525	C₂	semidirect
11. C₂×C₄×#41×C₃₁	C₂	semidirect
12. C₂²×C₄×D₄×C₃₁	C₂	semidirect
14. C₂²×#41×C₃₁	C₂²	semidirect
16. C₂⁴×C₄×C₃₁	C₂²	semidirect
17. C₃₁×#559	C₂²	semidirect
18. C₃₁×#554	C₂²	semidirect
19. C₃₁×#553	C₂²	semidirect
20. C₃₁×#551	C₂²	semidirect
21. C₃₁×#546	C₂²	semidirect
22. D₄²×C₃₁	C₂²	semidirect
23. C₃₁×#532	C₂²	semidirect
24. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
26. C₃₁×#529	C₂²	semidirect
27. C₂×C₃₁×#126	C₂²	semidirect
28. C₂×C₃₁×#125	C₂²	semidirect
29. C₂×C₃₁×#124	C₂²	semidirect
30. C₂×C₃₁×#124	C₂²	semidirect
31. C₃₁×#525	C₂²	semidirect
32. C₂×C₃₁×#123	C₂²	semidirect
33. C₂×C₃₁×#123	C₂²	semidirect
34. C₂×C₃₁×#123	C₂²	semidirect
35. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₃₁×#121	C₂²	semidirect
39. C₂×C₃₁×#121	C₂²	semidirect
41. C₂×C₃₁×#120	C₂²	semidirect
42. C₄×#41×C₃₁	C₂²	semidirect
43. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
44. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
48. C₂×C₄×D₄×C₃₁	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₂×C₄×D₄×C₃₁	C₂²	semidirect
51. C₂×C₄×D₄×C₃₁	C₂²	semidirect
52. C₂×C₄×D₄×C₃₁	C₂²	semidirect
53. C₂×C₄×D₄×C₃₁	C₂²	semidirect
54. C₂×C₄×D₄×C₃₁	C₂²	semidirect
55. C₂×C₃₁×#117	C₂²	semidirect
56. C₂×C₃₁×#117	C₂²	semidirect
57. C₂×C₃₁×#117	C₂²	semidirect
58. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
59. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
60. C₂²×C₄²×C₃₁	C₂²	semidirect
61. C₂²×C₄²×C₃₁	C₂²	semidirect
66. C₂×#41×C₃₁	C₂³	semidirect
86. C₂³×C₄×C₃₁	C₂³	semidirect
87. C₃₁×C₄⋊Q₈	C₂³	semidirect
89. C₃₁×#126	C₂³	semidirect
90. C₃₁×#125	C₂³	semidirect
91. C₃₁×#124	C₂³	semidirect
92. C₃₁×#124	C₂³	semidirect
93. C₃₁×#123	C₂³	semidirect
94. C₃₁×#123	C₂³	semidirect
95. C₃₁×#123	C₂³	semidirect
96. C₃₁×C₂²⋊Q₈	C₂³	semidirect
97. C₃₁×C₂²⋊Q₈	C₂³	semidirect
99. C₃₁×#121	C₂³	semidirect
100. C₃₁×#121	C₂³	semidirect
102. C₃₁×#120	C₂³	semidirect
103. C₄×Q₈×C₃₁	C₂³	semidirect
104. C₄×Q₈×C₃₁	C₂³	semidirect
108. C₄×D₄×C₃₁	C₂³	semidirect
109. C₄×D₄×C₃₁	C₂³	semidirect
110. C₄×D₄×C₃₁	C₂³	semidirect
111. C₄×D₄×C₃₁	C₂³	semidirect
112. C₄×D₄×C₃₁	C₂³	semidirect
113. C₄×D₄×C₃₁	C₂³	semidirect
114. C₃₁×#117	C₂³	semidirect
115. C₃₁×#117	C₂³	semidirect
116. C₃₁×#117	C₂³	semidirect
124. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
133. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
140. C₂×C₄²×C₃₁	C₂³	semidirect
141. C₂×C₄²×C₃₁	C₂³	semidirect
160. C₂×D₄×C₃₁	#41	semidirect
213. C₂×#3481	C₃₁	direct (N × H)
235. D₄×C₃₁	C₂×#41	semidirect
260. #3481	C₂×C₃₁	direct (N × H)
261. C₂×#559	C₂×C₃₁	semidirect
262. C₂×#554	C₂×C₃₁	semidirect
263. C₂×#553	C₂×C₃₁	semidirect
264. C₂×#551	C₂×C₃₁	semidirect
265. C₂×#546	C₂×C₃₁	semidirect
266. C₂×D₄²	C₂×C₃₁	semidirect
267. C₂×#532	C₂×C₃₁	semidirect
268. C₂×#529	C₂×C₃₁	semidirect
269. C₂×#525	C₂×C₃₁	semidirect
270. C₂×C₄×#41	C₂×C₃₁	semidirect
271. C₂²×C₄×D₄	C₂×C₃₁	semidirect
295. C₂²×#41	C₂²×C₃₁	semidirect
297. C₂⁴×C₄	C₂²×C₃₁	semidirect
298. #559	C₂²×C₃₁	semidirect
299. #554	C₂²×C₃₁	semidirect
300. #553	C₂²×C₃₁	semidirect
301. #551	C₂²×C₃₁	semidirect
302. #546	C₂²×C₃₁	semidirect
303. D₄²	C₂²×C₃₁	semidirect
304. #532	C₂²×C₃₁	semidirect
305. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
307. #529	C₂²×C₃₁	semidirect
308. C₂×#126	C₂²×C₃₁	semidirect
309. C₂×#125	C₂²×C₃₁	semidirect
310. C₂×#124	C₂²×C₃₁	semidirect
311. C₂×#124	C₂²×C₃₁	semidirect
312. #525	C₂²×C₃₁	semidirect
313. C₂×#123	C₂²×C₃₁	semidirect
314. C₂×#123	C₂²×C₃₁	semidirect
315. C₂×#123	C₂²×C₃₁	semidirect
316. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
317. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
319. C₂×#121	C₂²×C₃₁	semidirect
320. C₂×#121	C₂²×C₃₁	semidirect
322. C₂×#120	C₂²×C₃₁	semidirect
323. C₄×#41	C₂²×C₃₁	semidirect
324. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
325. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
329. C₂×C₄×D₄	C₂²×C₃₁	semidirect
330. C₂×C₄×D₄	C₂²×C₃₁	semidirect
331. C₂×C₄×D₄	C₂²×C₃₁	semidirect
332. C₂×C₄×D₄	C₂²×C₃₁	semidirect
333. C₂×C₄×D₄	C₂²×C₃₁	semidirect
334. C₂×C₄×D₄	C₂²×C₃₁	semidirect
335. C₂×C₄×D₄	C₂²×C₃₁	semidirect
336. C₂×#117	C₂²×C₃₁	semidirect
337. C₂×#117	C₂²×C₃₁	semidirect
338. C₂×#117	C₂²×C₃₁	semidirect
339. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
340. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
341. C₂²×C₄²	C₂²×C₃₁	semidirect
342. C₂²×C₄²	C₂²×C₃₁	semidirect
346. C₂×C₃₁	#3481	direct (N × H)
353. C₂×#41	C₂³×C₃₁	semidirect
373. C₂³×C₄	C₂³×C₃₁	semidirect
374. C₄⋊Q₈	C₂³×C₃₁	semidirect
376. #126	C₂³×C₃₁	semidirect
377. #125	C₂³×C₃₁	semidirect
378. #124	C₂³×C₃₁	semidirect
379. #124	C₂³×C₃₁	semidirect
380. #123	C₂³×C₃₁	semidirect
381. #123	C₂³×C₃₁	semidirect
382. #123	C₂³×C₃₁	semidirect
383. C₂²⋊Q₈	C₂³×C₃₁	semidirect
384. C₂²⋊Q₈	C₂³×C₃₁	semidirect
386. #121	C₂³×C₃₁	semidirect
387. #121	C₂³×C₃₁	semidirect
389. #120	C₂³×C₃₁	semidirect
390. C₄×Q₈	C₂³×C₃₁	semidirect
391. C₄×Q₈	C₂³×C₃₁	semidirect
395. C₄×D₄	C₂³×C₃₁	semidirect
396. C₄×D₄	C₂³×C₃₁	semidirect
397. C₄×D₄	C₂³×C₃₁	semidirect
398. C₄×D₄	C₂³×C₃₁	semidirect
399. C₄×D₄	C₂³×C₃₁	semidirect
400. C₄×D₄	C₂³×C₃₁	semidirect
401. #117	C₂³×C₃₁	semidirect
402. #117	C₂³×C₃₁	semidirect
403. #117	C₂³×C₃₁	semidirect
411. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
420. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
427. C₂×C₄²	C₂³×C₃₁	semidirect
428. C₂×C₄²	C₂³×C₃₁	semidirect
429. C₃₁	C₂×#3481	direct (N × H)
448. C₂×D₄	#41×C₃₁	semidirect
522. D₄	C₂×#41×C₃₁	semidirect
572. C₂	C₃₁×#3481	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×#3481	2
C₂×C₃₁×#559	2
C₂×C₃₁×#554	2
C₂×C₃₁×#553	2
C₂×C₃₁×#551	2
C₂×C₃₁×#546	2
C₂×D₄²×C₃₁	2
C₂×C₃₁×#532	2
C₂×C₃₁×#529	2
C₂×C₃₁×#525	2
C₂×C₄×#41×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₂×#3481	31

Subgroups — C2×C31×#3481 #21519473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3481 #21519473