Subgroups — C₂⁵×D₁₆ #72287461

Order 1024.

108373 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₈	C₂	1	2	yes	maximal, complemented
2	C₂⁴×D₁₆	C₂	1	124	yes	maximal, direct product factor
3	C₂⁵×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁵×D₄	—	2	2	no	—
5	C₂⁴×D₈	—	2	62	no	—
6	C₂⁴×D₈	C₂²	1	124	yes	complemented
7	C₂⁵×C₈	C₂²	1	1	yes	characteristic
8	C₂³×D₁₆	C₂²	1	2480	yes	direct product factor
9	C₂⁴×C₁₆	C₂²	1	62	yes	complemented
10	C₂⁷	—	4	2	no	—
11	C₂⁴×D₄	—	2	124	no	—
12	C₂⁴×D₄	—	4	62	no	—
13	C₂⁵×C₄	D₄	1	1	yes	characteristic
14	C₂³×D₈	—	2	1860	no	—
15	C₂³×D₈	C₂³	1	1240	yes	complemented
16	C₂⁴×C₈	D₄	1	31	yes	—
17	C₂⁴×C₈	C₂³	1	31	yes	—
18	C₂²×D₁₆	C₂³	1	9920	yes	direct product factor
19	C₂³×C₁₆	C₂³	1	620	yes	complemented
20	C₂⁶	—	4	124	no	—
21	C₂⁶	—	8	64	no	—
22	C₂⁶	D₈	1	1	yes	characteristic
23	C₂³×D₄	—	2	1240	no	—
24	C₂³×D₄	—	4	1860	no	—
25	C₂⁴×C₄	D₈	1	31	yes	—
26	C₂⁴×C₄	C₂×D₄	1	31	yes	—
27	C₂²×D₈	—	2	8680	no	—
28	C₂²×D₈	C₂⁴	1	2480	yes	complemented
29	C₂³×C₈	C₂×D₄	1	465	yes	—
30	C₂³×C₈	C₂⁴	1	155	yes	—
31	C₂×D₁₆	C₂⁴	1	7936	yes	direct product factor
32	C₂²×C₁₆	C₂⁴	1	1240	yes	complemented
33	C₂⁵	—	4	1240	no	—
34	C₂⁵	—	8	1984	no	—
35	C₂⁵	D₁₆	1	32	yes	direct product factor
36	C₂⁵	C₂×D₈	1	31	yes	—
37	C₂²×D₄	—	2	2480	no	—
38	C₂²×D₄	—	4	8680	no	—
39	C₂³×C₄	C₂×D₈	1	465	yes	—
40	C₂³×C₄	C₂²×D₄	1	155	yes	—
41	C₂×D₈	—	2	7440	no	—
42	C₂×D₈	C₂⁵	1	992	yes	complemented
43	C₂²×C₈	C₂²×D₄	1	1085	yes	—
44	C₂²×C₈	C₂⁵	1	155	yes	—
45	D₁₆	C₂⁵	1	1024	yes	direct product factor
46	C₂×C₁₆	C₂⁵	1	496	yes	complemented
47	C₂⁴	—	4	2480	no	—
48	C₂⁴	—	8	9920	no	—
49	C₂⁴	C₂×D₁₆	1	496	yes	direct product factor
50	C₂⁴	C₂²×D₈	1	155	yes	—
51	C₂×D₄	—	2	992	no	—
52	C₂×D₄	—	4	7440	no	—
53	C₂²×C₄	C₂²×D₈	1	1085	yes	—
54	C₂²×C₄	C₂³×D₄	1	155	yes	—
55	D₈	—	2	992	no	—
56	D₈	C₂⁶	1	64	yes	complemented
57	C₂×C₈	C₂³×D₄	1	465	yes	—
58	C₂×C₈	C₂⁶	1	31	yes	—
59	C₁₆	C₂⁶	1	32	yes	complemented
60	C₂³	—	4	992	no	—
61	C₂³	—	8	9920	no	—
62	C₂³	C₂²×D₁₆	1	1240	yes	direct product factor
63	C₂³	C₂³×D₈	1	155	yes	—
64	D₄	—	2	64	no	—
65	D₄	—	4	992	no	—
66	C₂×C₄	C₂³×D₈	1	465	yes	—
67	C₂×C₄	C₂⁴×D₄	1	31	yes	—
68	C₈	C₂⁴×D₄	1	31	yes	—
69	C₈	C₂⁷	1	1	yes	characteristic
70	C₂²	—	4	64	no	—
71	C₂²	—	8	1984	no	—
72	C₂²	C₂³×D₁₆	1	620	yes	direct product factor
73	C₂²	C₂⁴×D₈	1	31	yes	—
74	C₄	C₂⁴×D₈	1	31	yes	—
75	C₄	C₂⁵×D₄	1	1	yes	characteristic
76	C₂	—	8	64	no	—
77	C₂	C₂⁴×D₁₆	1	62	yes	direct product factor
78	C₂	C₂⁵×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁶	D₈
commutator, Frattini, cosocle	C₈	C₂⁷
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ C₂⁵×C₄ ◁ C₂⁵×C₈ ◁ G
LECS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₈	C₂	semidirect
2. C₂⁴×D₁₆	C₂	direct (N × H)
3. C₂⁵×C₁₆	C₂	semidirect
6. C₂⁴×D₈	C₂²	semidirect
8. C₂³×D₁₆	C₂²	direct (N × H)
9. C₂⁴×C₁₆	C₂²	semidirect
15. C₂³×D₈	C₂³	semidirect
18. C₂²×D₁₆	C₂³	direct (N × H)
19. C₂³×C₁₆	C₂³	semidirect
28. C₂²×D₈	C₂⁴	semidirect
31. C₂×D₁₆	C₂⁴	direct (N × H)
32. C₂²×C₁₆	C₂⁴	semidirect
35. C₂⁵	D₁₆	direct (N × H)
42. C₂×D₈	C₂⁵	semidirect
45. D₁₆	C₂⁵	direct (N × H)
46. C₂×C₁₆	C₂⁵	semidirect
49. C₂⁴	C₂×D₁₆	direct (N × H)
56. D₈	C₂⁶	semidirect
59. C₁₆	C₂⁶	semidirect
62. C₂³	C₂²×D₁₆	direct (N × H)
72. C₂²	C₂³×D₁₆	direct (N × H)
77. C₂	C₂⁴×D₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×D₈	2
C₂⁴×D₁₆	2
C₂⁵×C₁₆	2

Subgroups — C25×D16 #72287461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×D₁₆ #72287461