Subgroups — C₂²×C₃₁×#546 #21519456

Order 7936.

14462 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₃₁	C₂	semidirect
2. C₂⁴×D₄×C₃₁	C₂	semidirect
3. C₂×C₃₁×#546	C₂	direct (N × H)
4. C₂²×C₃₁×#124	C₂	semidirect
5. C₂²×C₃₁×#123	C₂	semidirect
6. C₂²×C₃₁×C₂²⋊Q₈	C₂	semidirect
7. C₂²×C₃₁×#121	C₂	semidirect
8. C₂²×C₃₁×#121	C₂	semidirect
9. C₂²×C₃₁×#120	C₂	semidirect
10. C₂²×C₄×D₄×C₃₁	C₂	semidirect
11. C₂²×C₄×D₄×C₃₁	C₂	semidirect
12. C₂³×C₂²⋊C₄×C₃₁	C₂	semidirect
15. C₂²×#41×C₃₁	C₂²	semidirect
16. C₂³×Q₈×C₃₁	C₂²	semidirect
22. C₂³×D₄×C₃₁	C₂²	semidirect
23. C₂³×D₄×C₃₁	C₂²	semidirect
24. C₂³×D₄×C₃₁	C₂²	semidirect
26. C₂⁴×C₄×C₃₁	C₂²	semidirect
27. C₂⁴×C₄×C₃₁	C₂²	semidirect
28. C₂⁴×C₄×C₃₁	C₂²	semidirect
29. C₃₁×#546	C₂²	direct (N × H)
30. C₂×C₃₁×#124	C₂²	semidirect
31. C₂×C₃₁×#123	C₂²	semidirect
32. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₃₁×#121	C₂²	semidirect
34. C₂×C₃₁×#121	C₂²	semidirect
35. C₂×C₃₁×#120	C₂²	semidirect
36. C₂×C₄×D₄×C₃₁	C₂²	semidirect
37. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
45. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
46. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
47. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
49. C₂²×C₄²×C₃₁	C₂²	semidirect
59. C₂×#41×C₃₁	C₂³	semidirect
61. C₂²×Q₈×C₃₁	C₂³	semidirect
68. C₂²×D₄×C₃₁	D₄	semidirect
73. C₂²×D₄×C₃₁	C₂³	semidirect
74. C₂²×D₄×C₃₁	C₂³	semidirect
75. C₂²×D₄×C₃₁	C₂³	semidirect
88. C₂³×C₄×C₃₁	C₂³	semidirect
89. C₂³×C₄×C₃₁	C₂³	semidirect
90. C₂³×C₄×C₃₁	C₂³	semidirect
91. C₃₁×#124	C₂³	semidirect
92. C₃₁×#123	C₂³	semidirect
93. C₃₁×C₂²⋊Q₈	C₂³	semidirect
94. C₃₁×#121	C₂³	semidirect
95. C₃₁×#121	C₂³	semidirect
96. C₃₁×#120	C₂³	semidirect
97. C₄×D₄×C₃₁	C₂³	semidirect
98. C₄×D₄×C₃₁	C₂³	semidirect
99. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
100. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
101. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
104. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
105. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
106. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
107. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
108. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
109. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
110. C₂×C₄²×C₃₁	C₂³	semidirect
126. C₂⁴×C₃₁	#41	semidirect
135. C₂×Q₈×C₃₁	C₂⁴	semidirect
142. C₂×D₄×C₃₁	C₂×D₄	semidirect
147. C₂×D₄×C₃₁	C₂⁴	semidirect
148. C₂×D₄×C₃₁	C₂⁴	semidirect
168. C₂²×C₄×C₃₁	C₂⁴	semidirect
169. C₂²×C₄×C₃₁	C₂⁴	semidirect
170. C₂²×C₄×C₃₁	C₂⁴	semidirect
171. C₄⋊C₄×C₃₁	C₂⁴	semidirect
172. C₄⋊C₄×C₃₁	C₂⁴	semidirect
173. C₄⋊C₄×C₃₁	C₂⁴	semidirect
176. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
177. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
178. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
179. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
180. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
181. C₄²×C₃₁	C₂⁴	semidirect
182. C₂²×#546	C₃₁	direct (N × H)
204. C₂³×C₃₁	C₂×#41	semidirect
217. D₄×C₃₁	C₂²×D₄	semidirect
236. C₂³×#41	C₂×C₃₁	semidirect
237. C₂⁴×D₄	C₂×C₃₁	semidirect
238. C₂×#546	C₂×C₃₁	direct (N × H)
239. C₂²×#124	C₂×C₃₁	semidirect
240. C₂²×#123	C₂×C₃₁	semidirect
241. C₂²×C₂²⋊Q₈	C₂×C₃₁	semidirect
242. C₂²×#121	C₂×C₃₁	semidirect
243. C₂²×#121	C₂×C₃₁	semidirect
244. C₂²×#120	C₂×C₃₁	semidirect
245. C₂²×C₄×D₄	C₂×C₃₁	semidirect
246. C₂²×C₄×D₄	C₂×C₃₁	semidirect
247. C₂³×C₂²⋊C₄	C₂×C₃₁	semidirect
263. C₂²×C₃₁	#546	direct (N × H)
267. C₂²×C₃₁	C₂²×#41	semidirect
279. C₂²×#41	C₂²×C₃₁	semidirect
280. C₂³×Q₈	C₂²×C₃₁	semidirect
286. C₂³×D₄	C₂²×C₃₁	semidirect
287. C₂³×D₄	C₂²×C₃₁	semidirect
288. C₂³×D₄	C₂²×C₃₁	semidirect
290. C₂⁴×C₄	C₂²×C₃₁	semidirect
291. C₂⁴×C₄	C₂²×C₃₁	semidirect
292. C₂⁴×C₄	C₂²×C₃₁	semidirect
293. #546	C₂²×C₃₁	direct (N × H)
294. C₂×#124	C₂²×C₃₁	semidirect
295. C₂×#123	C₂²×C₃₁	semidirect
296. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
297. C₂×#121	C₂²×C₃₁	semidirect
298. C₂×#121	C₂²×C₃₁	semidirect
299. C₂×#120	C₂²×C₃₁	semidirect
300. C₂×C₄×D₄	C₂²×C₃₁	semidirect
301. C₂×C₄×D₄	C₂²×C₃₁	semidirect
302. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
303. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
304. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
307. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
308. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
309. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
310. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
311. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
312. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
313. C₂²×C₄²	C₂²×C₃₁	semidirect
318. C₂×C₃₁	C₂×#546	direct (N × H)
331. C₂×#41	C₂³×C₃₁	semidirect
333. C₂²×Q₈	C₂³×C₃₁	semidirect
340. C₂²×D₄	D₄×C₃₁	semidirect
345. C₂²×D₄	C₂³×C₃₁	semidirect
346. C₂²×D₄	C₂³×C₃₁	semidirect
347. C₂²×D₄	C₂³×C₃₁	semidirect
360. C₂³×C₄	C₂³×C₃₁	semidirect
361. C₂³×C₄	C₂³×C₃₁	semidirect
362. C₂³×C₄	C₂³×C₃₁	semidirect
363. #124	C₂³×C₃₁	semidirect
364. #123	C₂³×C₃₁	semidirect
365. C₂²⋊Q₈	C₂³×C₃₁	semidirect
366. #121	C₂³×C₃₁	semidirect
367. #121	C₂³×C₃₁	semidirect
368. #120	C₂³×C₃₁	semidirect
369. C₄×D₄	C₂³×C₃₁	semidirect
370. C₄×D₄	C₂³×C₃₁	semidirect
371. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
372. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
373. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
376. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
377. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
378. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
379. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
380. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
381. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
382. C₂×C₄²	C₂³×C₃₁	semidirect
383. C₃₁	C₂²×#546	direct (N × H)
399. C₂⁴	#41×C₃₁	semidirect
408. C₂×Q₈	C₂⁴×C₃₁	semidirect
415. C₂×D₄	C₂×D₄×C₃₁	semidirect
420. C₂×D₄	C₂⁴×C₃₁	semidirect
421. C₂×D₄	C₂⁴×C₃₁	semidirect
441. C₂²×C₄	C₂⁴×C₃₁	semidirect
442. C₂²×C₄	C₂⁴×C₃₁	semidirect
443. C₂²×C₄	C₂⁴×C₃₁	semidirect
444. C₄⋊C₄	C₂⁴×C₃₁	semidirect
445. C₄⋊C₄	C₂⁴×C₃₁	semidirect
446. C₄⋊C₄	C₂⁴×C₃₁	semidirect
449. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
450. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
451. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
452. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
453. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
454. C₄²	C₂⁴×C₃₁	semidirect
476. C₂³	C₂×#41×C₃₁	semidirect
489. D₄	C₂²×D₄×C₃₁	semidirect
523. C₂²	C₃₁×#546	direct (N × H)
527. C₂²	C₂²×#41×C₃₁	semidirect
541. C₂	C₂×C₃₁×#546	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₃₁	2
C₂⁴×D₄×C₃₁	2
C₂×C₃₁×#546	2
C₂²×C₃₁×#124	2
C₂²×C₃₁×#123	2
C₂²×C₃₁×C₂²⋊Q₈	2
C₂²×C₃₁×#121	2
C₂²×C₃₁×#120	2
C₂²×C₄×D₄×C₃₁	2
C₂³×C₂²⋊C₄×C₃₁	2
C₂²×#546	31

Subgroups — C22×C31×#546 #21519456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#546 #21519456