Subgroups — C₂⁵×SD₁₆ #10587002

Order 512.

70018 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁵×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×SD₁₆	C₂	1	124	yes	maximal, direct product factor
4	C₂⁵×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁷	—	2	1	no	—
6	C₂⁴×Q₈	—	2	31	no	—
7	C₂⁴×Q₈	C₂²	1	62	yes	complemented
8	C₂⁴×D₄	—	2	31	no	—
9	C₂⁴×D₄	C₂²	1	62	yes	—
10	C₂⁵×C₄	—	2	1	no	—
11	C₂⁵×C₄	C₂²	1	1	yes	characteristic
12	C₂³×SD₁₆	C₂²	1	2480	yes	direct product factor
13	C₂⁴×C₈	C₂²	1	62	yes	complemented
14	C₂⁶	—	2	62	no	—
15	C₂⁶	—	4	32	no	—
16	C₂⁶	D₄	1	1	yes	characteristic
17	C₂³×Q₈	—	2	930	no	—
18	C₂³×Q₈	C₂³	1	620	yes	complemented
19	C₂³×D₄	—	2	930	no	—
20	C₂³×D₄	C₂³	1	620	yes	—
21	C₂⁴×C₄	—	2	62	no	—
22	C₂⁴×C₄	D₄	1	31	yes	—
23	C₂⁴×C₄	C₂³	1	31	yes	—
24	C₂²×SD₁₆	C₂³	1	9920	yes	direct product factor
25	C₂³×C₈	C₂³	1	620	yes	complemented
26	C₂⁵	—	2	620	no	—
27	C₂⁵	—	4	992	no	—
28	C₂⁵	SD₁₆	1	32	yes	direct product factor
29	C₂⁵	C₂×D₄	1	31	yes	—
30	C₂²×Q₈	—	2	4340	no	—
31	C₂²×Q₈	C₂⁴	1	1240	yes	complemented
32	C₂²×D₄	—	2	4340	no	—
33	C₂²×D₄	C₂⁴	1	1240	yes	—
34	C₂³×C₄	—	2	620	no	—
35	C₂³×C₄	C₂×D₄	1	465	yes	—
36	C₂³×C₄	C₂⁴	1	155	yes	—
37	C₂×SD₁₆	C₂⁴	1	7936	yes	direct product factor
38	C₂²×C₈	C₂⁴	1	1240	yes	complemented
39	C₂⁴	—	2	1240	no	—
40	C₂⁴	—	4	4960	no	—
41	C₂⁴	C₂×SD₁₆	1	496	yes	direct product factor
42	C₂⁴	C₂²×D₄	1	155	yes	—
43	C₂×Q₈	—	2	3720	no	—
44	C₂×Q₈	C₂⁵	1	496	yes	complemented
45	C₂×D₄	—	2	3720	no	—
46	C₂×D₄	C₂⁵	1	496	yes	—
47	C₂²×C₄	—	2	1240	no	—
48	C₂²×C₄	C₂²×D₄	1	1085	yes	—
49	C₂²×C₄	C₂⁵	1	155	yes	—
50	SD₁₆	C₂⁵	1	1024	yes	direct product factor
51	C₂×C₈	C₂⁵	1	496	yes	complemented
52	C₂³	—	2	496	no	—
53	C₂³	—	4	4960	no	—
54	C₂³	C₂²×SD₁₆	1	1240	yes	direct product factor
55	C₂³	C₂³×D₄	1	155	yes	—
56	Q₈	—	2	496	no	—
57	Q₈	C₂⁶	1	32	yes	complemented
58	D₄	—	2	496	no	—
59	D₄	C₂⁶	1	32	yes	—
60	C₂×C₄	—	2	496	no	—
61	C₂×C₄	C₂³×D₄	1	465	yes	—
62	C₂×C₄	C₂⁶	1	31	yes	—
63	C₈	C₂⁶	1	32	yes	complemented
64	C₂²	—	2	32	no	—
65	C₂²	—	4	992	no	—
66	C₂²	C₂³×SD₁₆	1	620	yes	direct product factor
67	C₂²	C₂⁴×D₄	1	31	yes	—
68	C₄	—	2	32	no	—
69	C₄	C₂⁴×D₄	1	31	yes	—
70	C₄	C₂⁷	1	1	yes	characteristic
71	C₂	—	4	32	no	—
72	C₂	C₂⁴×SD₁₆	1	62	yes	direct product factor
73	C₂	C₂⁵×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁶	D₄
commutator, Frattini, cosocle	C₄	C₂⁷
prime radical	C₂⁵×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Q₈	C₂	semidirect
3. C₂⁴×SD₁₆	C₂	direct (N × H)
4. C₂⁵×C₈	C₂	semidirect
7. C₂⁴×Q₈	C₂²	semidirect
12. C₂³×SD₁₆	C₂²	direct (N × H)
13. C₂⁴×C₈	C₂²	semidirect
18. C₂³×Q₈	C₂³	semidirect
24. C₂²×SD₁₆	C₂³	direct (N × H)
25. C₂³×C₈	C₂³	semidirect
28. C₂⁵	SD₁₆	direct (N × H)
31. C₂²×Q₈	C₂⁴	semidirect
37. C₂×SD₁₆	C₂⁴	direct (N × H)
38. C₂²×C₈	C₂⁴	semidirect
41. C₂⁴	C₂×SD₁₆	direct (N × H)
44. C₂×Q₈	C₂⁵	semidirect
50. SD₁₆	C₂⁵	direct (N × H)
51. C₂×C₈	C₂⁵	semidirect
54. C₂³	C₂²×SD₁₆	direct (N × H)
57. Q₈	C₂⁶	semidirect
63. C₈	C₂⁶	semidirect
66. C₂²	C₂³×SD₁₆	direct (N × H)
72. C₂	C₂⁴×SD₁₆	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×Q₈	2
C₂⁵×D₄	2
C₂⁴×SD₁₆	2
C₂⁵×C₈	2

Subgroups — C25×SD16 #10587002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×SD₁₆ #10587002