Subgroups — C₅×C₄⋊Dic₃ #6697

Order 240.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₃	C₂	1	2	yes	maximal
3	C₅×C₄⋊C₄	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	2	yes	complemented
6	C₅×Dic₃	—	2	2	no	—
7	C₄⋊Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₄×C₅	—	3	2	no	—
9	C₂×C₄×C₅	D₃	1	1	yes	characteristic
10	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₅	D₄	1	1	yes	characteristic
12	C₂×C₃×C₅	Q₈	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂×C₅	1	1	yes	characteristic
14	C₂×Dic₃	C₂×C₅	1	2	yes	—
15	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
16	C₄×C₅	—	6	2	no	—
17	C₄×C₅	Dic₃	1	2	yes	complemented
18	C₄⋊C₄	—	3	1	no	Sylow
19	C₃×C₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃	C₂²×C₅	1	1	yes	characteristic
21	C₃×C₄	C₄×C₅	1	2	yes	complemented
22	Dic₃	—	2	2	no	—
23	C₂×C₅	Dic₆	1	1	yes	characteristic
24	C₂×C₅	D₁₂	1	1	yes	characteristic
25	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
26	C₂×C₄	—	3	2	no	—
27	C₂×C₄	C₅×D₃	1	1	yes	characteristic
28	C₂×C₃	C₂×C₄×C₅	1	1	yes	characteristic
29	C₂×C₃	C₅×D₄	1	1	yes	characteristic
30	C₂×C₃	C₅×Q₈	1	1	yes	characteristic
31	C₅	C₄⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²	C₂×C₅×D₃	1	1	yes	characteristic
33	C₄	—	6	2	no	—
34	C₄	C₅×Dic₃	1	2	yes	complemented
35	C₃	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
36	C₂	C₅×Dic₆	1	1	yes	characteristic
37	C₂	C₅×D₁₂	1	1	yes	characteristic
38	C₂	C₂×C₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃
commutator	C₂×C₃	C₂×C₄×C₅
Frattini	C₂²	C₂×C₅×D₃
Fitting	C₂×C₃×C₄×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂²
cosocle	C₂²×C₃	C₂²×C₅
hypercenter	C₂×C₄×C₅	D₃
hypocenter	C₃	C₅×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
5. C₃×C₄×C₅	C₄	semidirect
7. C₄⋊Dic₃	C₅	direct (N × H)
17. C₄×C₅	Dic₃	semidirect
19. C₃×C₅	C₄⋊C₄	semidirect
21. C₃×C₄	C₄×C₅	semidirect
31. C₅	C₄⋊Dic₃	direct (N × H)
34. C₄	C₅×Dic₃	semidirect
35. C₃	C₅×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅	2
C₂×C₅×Dic₃	2
C₅×C₄⋊C₄	3
C₄⋊Dic₃	5

Subgroups — C5×C4⋊Dic3 #6697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊Dic₃ #6697