Subgroups — C₂×#4015 #65802

Order 320.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀	C₂	1	2	yes	maximal
2	C₂×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₅	C₂	1	4	yes	maximal
4	#4015	C₂	1	8	yes	maximal, direct product factor
5	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₅	C₂²	1	2	yes	—
7	C₂²×Dic₅	C₂²	1	4	yes	—
8	C₂×Dic₁₀	—	2	8	no	—
9	C₂×Dic₁₀	C₂²	1	8	yes	—
10	C₄²×C₅	C₂²	1	4	yes	—
11	C₄⋊Dic₅	C₂²	1	16	yes	—
12	C₂×C₄⋊Q₈	—	5	1	no	maximal, Sylow
13	C₂³×C₅	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₅	D₄	1	4	yes	—
15	C₂×C₄×C₅	Q₈	1	8	yes	complemented
16	C₂×C₄×C₅	C₂³	1	2	yes	—
17	C₂×C₄×C₅	C₂³	1	4	yes	—
18	C₂×Dic₅	—	2	8	no	—
19	C₂×Dic₅	C₂³	1	8	yes	—
20	Dic₁₀	—	2	16	no	—
21	C₂²×Q₈	—	5	2	no	—
22	C₄⋊Q₈	—	5	8	no	—
23	C₂×C₄⋊C₄	—	5	4	no	—
24	C₂×C₄²	D₅	1	1	yes	characteristic
25	C₂²×C₅	C₂×D₄	1	2	yes	—
26	C₂²×C₅	C₂×Q₈	1	4	yes	—
27	C₂²×C₅	C₂⁴	1	1	yes	characteristic
28	C₄×C₅	C₂×D₄	1	4	yes	—
29	C₄×C₅	C₂×Q₈	1	8	yes	complemented
30	Dic₅	—	2	8	no	—
31	C₂×Q₈	—	5	8	no	—
32	C₂×Q₈	—	10	8	no	—
33	C₂²×C₄	—	5	4	no	—
34	C₂²×C₄	C₂×D₅	1	2	yes	—
35	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
36	C₄⋊C₄	—	5	16	no	—
37	C₄²	C₂×D₅	1	4	yes	—
38	C₂×C₅	C₄⋊Q₈	1	4	yes	complemented
39	C₂×C₅	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₅	C₂²×Q₈	1	2	yes	—
41	C₂³	C₂²×D₅	1	1	yes	characteristic
42	Q₈	—	10	16	no	—
43	C₂×C₄	—	5	8	no	—
44	C₂×C₄	—	10	8	no	—
45	C₂×C₄	Dic₁₀	1	8	yes	complemented
46	C₂×C₄	D₂₀	1	4	yes	—
47	C₂×C₄	C₂²×D₅	1	4	yes	—
48	C₂×C₄	C₂²×D₅	1	2	yes	—
49	C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
50	C₂²	C₂×Dic₁₀	1	4	yes	—
51	C₂²	C₂×D₂₀	1	2	yes	—
52	C₂²	C₂³×D₅	1	1	yes	characteristic
53	C₄	—	10	8	no	—
54	C₄	C₂×Dic₁₀	1	8	yes	complemented
55	C₄	C₂×D₂₀	1	4	yes	—
56	C₂	#4015	1	4	yes	direct product factor
57	C₂	C₂²×Dic₁₀	1	2	yes	—
58	C₂	C₂²×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴
Frattini	C₂²	C₂³×D₅
Fitting	C₂×C₄²×C₅	C₂
socle, prime radical	C₂³×C₅	C₂³
hypercenter	C₂×C₄²	D₅
hypocenter	C₅	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #4015	C₂	direct (N × H)
15. C₂×C₄×C₅	Q₈	semidirect
29. C₄×C₅	C₂×Q₈	semidirect
38. C₂×C₅	C₄⋊Q₈	semidirect
45. C₂×C₄	Dic₁₀	semidirect
49. C₅	C₂×C₄⋊Q₈	semidirect
54. C₄	C₂×Dic₁₀	semidirect
56. C₂	#4015	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₀	2
C₂×C₄²×C₅	2
C₂×C₄⋊Dic₅	2
#4015	2
C₂×C₄⋊Q₈	5

Subgroups — C2×#4015 #65802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4015 #65802