Subgroups — C₂×C₅×D₁₆ #65668

Order 320.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₈	C₂	1	2	yes	maximal, complemented
2	C₅×D₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₄	—	2	2	no	—
5	C₅×D₈	—	2	2	no	—
6	C₅×D₈	C₂²	1	4	yes	complemented
7	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₅×C₁₆	C₂²	1	2	yes	complemented
9	C₂×D₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₅	—	4	2	no	—
11	C₅×D₄	—	2	4	no	—
12	C₅×D₄	—	4	2	no	—
13	C₂×C₄×C₅	D₄	1	1	yes	characteristic
14	C₅×C₈	D₄	1	1	yes	characteristic
15	C₅×C₈	C₂³	1	1	yes	characteristic
16	C₂×D₈	C₂×C₅	1	2	yes	complemented
17	D₁₆	C₂×C₅	1	4	yes	direct product factor
18	C₂×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
19	C₂²×C₅	—	4	4	no	—
20	C₂²×C₅	—	8	4	no	—
21	C₂²×C₅	D₈	1	1	yes	characteristic
22	C₄×C₅	D₈	1	1	yes	characteristic
23	C₄×C₅	C₂×D₄	1	1	yes	characteristic
24	C₂×D₄	—	2	2	no	—
25	D₈	—	2	2	no	—
26	D₈	C₂²×C₅	1	4	yes	complemented
27	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
28	C₁₆	C₂²×C₅	1	2	yes	complemented
29	C₂×C₅	—	8	4	no	—
30	C₂×C₅	D₁₆	1	2	yes	direct product factor
31	C₂×C₅	C₂×D₈	1	1	yes	characteristic
32	C₂³	—	4	2	no	—
33	D₄	—	2	4	no	—
34	D₄	—	4	2	no	—
35	C₂×C₄	C₅×D₄	1	1	yes	characteristic
36	C₈	C₅×D₄	1	1	yes	characteristic
37	C₈	C₂³×C₅	1	1	yes	characteristic
38	C₅	C₂×D₁₆	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	—	4	4	no	—
40	C₂²	—	8	4	no	—
41	C₂²	C₅×D₈	1	1	yes	characteristic
42	C₄	C₅×D₈	1	1	yes	characteristic
43	C₄	C₂×C₅×D₄	1	1	yes	characteristic
44	C₂	—	8	4	no	—
45	C₂	C₅×D₁₆	1	2	yes	direct product factor
46	C₂	C₂×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₈	C₂	semidirect
2. C₅×D₁₆	C₂	direct (N × H)
3. C₂×C₅×C₁₆	C₂	semidirect
6. C₅×D₈	C₂²	semidirect
8. C₅×C₁₆	C₂²	semidirect
9. C₂×D₁₆	C₅	direct (N × H)
16. C₂×D₈	C₂×C₅	semidirect
17. D₁₆	C₂×C₅	direct (N × H)
18. C₂×C₁₆	C₂×C₅	semidirect
26. D₈	C₂²×C₅	semidirect
28. C₁₆	C₂²×C₅	semidirect
30. C₂×C₅	D₁₆	direct (N × H)
38. C₅	C₂×D₁₆	direct (N × H)
45. C₂	C₅×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
C₂×C₅×D₈	2
C₅×D₁₆	2
C₂×C₅×C₁₆	2
C₂×D₁₆	5

Subgroups — C2×C5×D16 #65668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₆ #65668