Subgroups — C₂×D₅×C₁₆ #65188

Order 320.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#672	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₆	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₅	C₄	1	1	yes	characteristic
6	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂×#168	C₄	1	1	yes	characteristic
8	C₈×D₅	C₄	1	2	yes	—
9	C₈×D₅	C₂²	1	2	yes	—
10	C₅×C₁₆	C₂²	1	2	yes	complemented
11	#672	C₂²	1	2	yes	complemented
12	C₂²×C₁₆	—	5	1	no	maximal, Sylow
13	C₂²×D₅	C₈	1	1	yes	characteristic
14	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₅	C₈	1	1	yes	characteristic
16	C₄×D₅	C₈	1	2	yes	—
17	C₄×D₅	C₂×C₄	1	2	yes	—
18	C₅×C₈	C₂×C₄	1	1	yes	characteristic
19	C₅×C₈	C₂³	1	1	yes	characteristic
20	#168	C₂×C₄	1	2	yes	—
21	C₂²×C₈	—	5	1	no	—
22	C₂×C₁₆	—	5	1	no	—
23	C₂×C₁₆	—	5	4	no	—
24	C₂×C₁₆	D₅	1	1	yes	characteristic, direct product factor
25	C₂²×C₅	C₂×C₈	1	1	yes	characteristic
26	C₂×D₅	C₁₆	1	4	yes	direct product factor
27	C₂×D₅	C₂×C₈	1	2	yes	—
28	C₄×C₅	C₂×C₈	1	1	yes	characteristic
29	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
30	Dic₅	C₂×C₈	1	2	yes	—
31	C₂²×C₄	—	5	1	no	—
32	C₂×C₈	—	5	1	no	—
33	C₂×C₈	—	5	2	no	—
34	C₂×C₈	—	5	2	no	—
35	C₂×C₈	C₂×D₅	1	1	yes	characteristic
36	C₁₆	—	5	2	no	—
37	C₁₆	C₂×D₅	1	2	yes	direct product factor
38	C₂×C₅	C₂×C₁₆	1	2	yes	complemented
39	C₂×C₅	C₂²×C₈	1	1	yes	characteristic
40	D₅	C₂×C₁₆	1	4	yes	direct product factor
41	C₂³	—	5	1	no	—
42	C₂×C₄	—	5	1	no	—
43	C₂×C₄	—	5	2	no	—
44	C₂×C₄	—	5	2	no	—
45	C₂×C₄	C₄×D₅	1	1	yes	characteristic
46	C₈	—	5	2	no	—
47	C₈	C₄×D₅	1	1	yes	characteristic
48	C₈	C₂²×D₅	1	1	yes	characteristic
49	C₅	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
50	C₂²	—	5	4	no	—
51	C₂²	—	5	2	no	—
52	C₂²	C₈×D₅	1	1	yes	characteristic
53	C₄	—	5	2	no	—
54	C₄	C₈×D₅	1	1	yes	characteristic
55	C₄	C₂×C₄×D₅	1	1	yes	characteristic
56	C₂	—	5	4	no	—
57	C₂	D₅×C₁₆	1	2	yes	direct product factor
58	C₂	C₂×C₈×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	D₅
commutator, hypocenter	C₅	C₂²×C₁₆
Frattini	C₈	C₂²×D₅
Fitting	C₂×C₅×C₁₆	C₂
socle	C₂²×C₅	C₂×C₈
prime radical	C₂²×D₅	C₈
cosocle	C₅×C₈	C₂³
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₁₆	C₂	semidirect
3. C₂×#672	C₂	semidirect
4. D₅×C₁₆	C₂	direct (N × H)
10. C₅×C₁₆	C₂²	semidirect
11. #672	C₂²	semidirect
24. C₂×C₁₆	D₅	direct (N × H)
26. C₂×D₅	C₁₆	direct (N × H)
37. C₁₆	C₂×D₅	direct (N × H)
38. C₂×C₅	C₂×C₁₆	semidirect
40. D₅	C₂×C₁₆	direct (N × H)
49. C₅	C₂²×C₁₆	semidirect
57. C₂	D₅×C₁₆	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×C₈×D₅	2
C₂×C₅×C₁₆	2
C₂×#672	2
D₅×C₁₆	2
C₂²×C₁₆	5

Subgroups — C2×D5×C16 #65188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₁₆ #65188