Subgroups — C₅×H(3,ℤ/4) #64804

Order 320.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#117	C₂	1	2	yes	maximal
3	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
4	C₅×M₁₆	—	2	2	no	—
5	C₂×C₅×C₈	C₄	1	2	yes	complemented
6	C₅×C₄⋊C₄	—	2	2	no	—
7	C₅×C₂²⋊C₄	—	2	2	no	—
8	C₄²×C₅	C₄	1	4	yes	complemented
9	H(3,ℤ/4)	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₅	D₄	1	1	yes	characteristic
11	C₂×C₄×C₅	—	2	4	no	—
12	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₅	D₄	1	2	yes	—
15	C₂×C₄×C₅	Q₈	1	1	yes	characteristic
16	C₅×C₈	—	2	2	no	—
17	C₂×M₁₆	C₂×C₅	1	1	yes	characteristic
18	#117	C₂×C₅	1	2	yes	—
19	C₂²×C₅	—	4	1	no	—
20	C₂²×C₅	C₂²⋊C₄	1	2	yes	—
21	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
22	C₄×C₅	—	4	4	no	—
23	C₄×C₅	C₄²	1	1	yes	characteristic
24	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₅	C₄⋊C₄	1	2	yes	—
26	C₂²×C₄	C₂²×C₅	1	1	yes	characteristic
27	M₁₆	—	2	2	no	—
28	C₂×C₈	C₄×C₅	1	2	yes	complemented
29	C₄⋊C₄	—	2	2	no	—
30	C₂²⋊C₄	—	2	2	no	—
31	C₄²	C₄×C₅	1	4	yes	complemented
32	C₂×C₅	—	2	2	no	—
33	C₂×C₅	—	2	1	no	—
34	C₂×C₅	#95	1	1	yes	characteristic
35	C₂³	C₅×D₄	1	1	yes	characteristic
36	C₂×C₄	—	2	4	no	—
37	C₂×C₄	C₂×C₄×C₅	1	1	yes	characteristic
38	C₂×C₄	C₂×C₄×C₅	1	2	yes	—
39	C₂×C₄	C₅×D₄	1	2	yes	—
40	C₂×C₄	C₅×Q₈	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₅	H(3,ℤ/4)	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	4	1	no	—
44	C₂²	C₅×C₂²⋊C₄	1	2	yes	—
45	C₂²	C₅×C₄⋊C₄	1	1	yes	characteristic
46	C₄	—	4	4	no	—
47	C₄	C₄²×C₅	1	1	yes	characteristic
48	C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
49	C₄	C₅×C₄⋊C₄	1	2	yes	—
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₅×#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₄²
commutator	C₄	C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂²×C₅
socle	C₂×C₅	#95
prime radical	C₂³×C₅	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂×C₅×C₈	C₄	semidirect
8. C₄²×C₅	C₄	semidirect
9. H(3,ℤ/4)	C₅	direct (N × H)
28. C₂×C₈	C₄×C₅	semidirect
31. C₄²	C₄×C₅	semidirect
42. C₅	H(3,ℤ/4)	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×M₁₆	2
C₅×#117	2
H(3,ℤ/4)	5

Subgroups — C5×H(3,ℤ/4) #64804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×H(3,ℤ/4) #64804