Subgroups — C₅×#137 #4123

Order 160.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Q₁₆	C₂	1	2	yes	maximal, complemented
4	C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
5	C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Q₈	—	2	1	no	—
7	C₅×Q₈	C₂²	1	2	yes	—
8	C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₅×D₄	—	2	1	no	—
10	C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅	—	2	1	no	—
12	C₂×C₄×C₅	—	2	1	no	—
13	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₅×C₈	C₂²	1	2	yes	—
15	#137	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂²×C₅	—	2	1	no	—
17	C₂²×C₅	D₄	1	1	yes	characteristic
18	C₄×C₅	—	2	1	no	—
19	C₄×C₅	—	2	2	no	—
20	C₄×C₅	D₄	1	1	yes	characteristic
21	C₄×C₅	C₂³	1	1	yes	characteristic
22	#41	C₂×C₅	1	1	yes	characteristic
23	C₂×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
24	Q₁₆	C₂×C₅	1	2	yes	complemented
25	SD₁₆	C₂×C₅	1	2	yes	complemented
26	M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
27	C₂×C₅	—	2	1	no	—
28	C₂×C₅	—	4	1	no	—
29	C₂×C₅	C₂×D₄	1	1	yes	characteristic
30	Q₈	—	2	1	no	—
31	Q₈	C₂²×C₅	1	2	yes	—
32	Q₈	C₂²×C₅	1	1	yes	characteristic
33	D₄	—	2	1	no	—
34	D₄	C₂²×C₅	1	1	yes	characteristic
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂²×C₅	1	1	yes	characteristic
38	C₈	C₂²×C₅	1	2	yes	—
39	C₅	#137	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	2	1	no	—
41	C₂²	C₅×D₄	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	2	2	no	—
44	C₄	C₅×D₄	1	1	yes	characteristic
45	C₄	C₂³×C₅	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂×C₅×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₅
prime radical	C₅×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈	C₂	semidirect
3. C₅×Q₁₆	C₂	semidirect
4. C₅×SD₁₆	C₂	semidirect
5. C₅×M₁₆	C₂	semidirect
15. #137	C₅	direct (N × H)
23. C₂×Q₈	C₂×C₅	semidirect
24. Q₁₆	C₂×C₅	semidirect
25. SD₁₆	C₂×C₅	semidirect
26. M₁₆	C₂×C₅	semidirect
39. C₅	#137	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#41	2
C₂×C₅×Q₈	2
C₅×Q₁₆	2
C₅×SD₁₆	2
C₅×M₁₆	2
#137	5

Subgroups — C5×#137 #4123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#137 #4123