Subgroups — C₅×#213 #6699

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₈	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅	—	2	1	no	—
6	C₂×C₅×D₃	—	2	1	no	—
7	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	#213	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×D₄	—	3	1	no	—
10	C₅×D₄	D₃	1	1	yes	characteristic, complemented
11	C₅×C₈	—	3	1	no	—
12	C₂×C₃×C₅	—	4	1	no	—
13	C₂×C₃×C₅	D₄	1	1	yes	characteristic
14	C₅×D₃	—	4	1	no	—
15	C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
16	D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
18	C₂²×C₅	—	2	1	no	—
19	C₂²×C₅	—	6	1	no	—
20	C₄×C₅	C₂×D₃	1	1	yes	characteristic
21	D₈	—	3	1	no	Sylow
22	C₃×C₅	D₈	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃	—	2	1	no	—
24	C₂×D₃	—	2	1	no	—
25	C₃×C₄	C₂²×C₅	1	1	yes	characteristic
26	C₂×C₅	—	4	1	no	—
27	C₂×C₅	—	12	1	no	—
28	C₂×C₅	#67	1	1	yes	characteristic
29	D₄	—	3	1	no	—
30	D₄	C₅×D₃	1	1	yes	characteristic, complemented
31	C₈	—	3	1	no	—
32	C₂×C₃	—	4	1	no	—
33	C₂×C₃	C₅×D₄	1	1	yes	characteristic
34	D₃	—	4	1	no	—
35	C₅	#213	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	—	2	1	no	—
37	C₂²	—	6	1	no	—
38	C₄	C₂×C₅×D₃	1	1	yes	characteristic
39	C₃	C₅×D₈	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	4	1	no	—
41	C₂	—	12	1	no	—
42	C₂	C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#67
commutator, cosocle	C₃×C₄	C₂²×C₅
Frattini	C₄	C₂×C₅×D₃
Fitting	C₃×C₅×D₄	C₂
socle	C₂×C₃×C₅	D₄
hypercenter	C₅×D₄	D₃
hypocenter	C₃	C₅×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₄	C₂	semidirect
2. C₅×D₁₂	C₂	semidirect
3. C₅×C₃⋊C₈	C₂	semidirect
8. #213	C₅	direct (N × H)
10. C₅×D₄	D₃	semidirect
15. C₃×D₄	C₂×C₅	semidirect
16. D₁₂	C₂×C₅	semidirect
17. C₃⋊C₈	C₂×C₅	semidirect
22. C₃×C₅	D₈	semidirect
30. D₄	C₅×D₃	semidirect
35. C₅	#213	direct (N × H)
39. C₃	C₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₄	2
C₅×D₁₂	2
C₅×C₃⋊C₈	2
C₅×D₈	3
#213	5

Subgroups — C5×#213 #6699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#213 #6699