Subgroups — C₅×Dic₃⋊C₄ #6696

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	1	yes	maximal, characteristic
3	C₂×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₅×C₄⋊C₄	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₅	—	2	1	no	—
7	C₅×Dic₃	—	2	1	no	—
8	C₅×Dic₃	C₄	1	2	yes	complemented
9	Dic₃⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₄×C₅	—	3	1	no	—
11	C₂×C₄×C₅	—	3	1	no	—
12	C₂×C₄×C₅	D₃	1	1	yes	characteristic
13	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₅	D₄	1	1	yes	characteristic
15	C₂×C₃×C₅	Q₈	1	1	yes	characteristic
16	C₂×C₃×C₄	C₂×C₅	1	1	yes	characteristic
17	C₂×Dic₃	C₂×C₅	1	1	yes	characteristic
18	C₂×Dic₃	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
20	C₄×C₅	—	2	1	no	—
21	C₄×C₅	—	3	2	no	—
22	C₄×C₅	—	6	1	no	—
23	C₄⋊C₄	—	3	1	no	Sylow
24	C₃×C₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃	C₂²×C₅	1	1	yes	characteristic
26	C₃×C₄	—	2	1	no	—
27	Dic₃	—	2	1	no	—
28	Dic₃	C₄×C₅	1	2	yes	complemented
29	C₂×C₅	Dic₆	1	1	yes	characteristic
30	C₂×C₅	C₄×D₃	1	1	yes	characteristic
31	C₂×C₅	#67	1	1	yes	characteristic
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	C₅×D₃	1	1	yes	characteristic
35	C₂×C₃	C₂×C₄×C₅	1	1	yes	characteristic
36	C₂×C₃	C₅×D₄	1	1	yes	characteristic
37	C₂×C₃	C₅×Q₈	1	1	yes	characteristic
38	C₅	Dic₃⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	C₂×C₅×D₃	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	3	2	no	—
42	C₄	—	6	1	no	—
43	C₃	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₂	C₅×Dic₆	1	1	yes	characteristic
45	C₂	C₄×C₅×D₃	1	1	yes	characteristic
46	C₂	C₅×#67	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
8. C₅×Dic₃	C₄	semidirect
9. Dic₃⋊C₄	C₅	direct (N × H)
24. C₃×C₅	C₄⋊C₄	semidirect
28. Dic₃	C₄×C₅	semidirect
38. C₅	Dic₃⋊C₄	direct (N × H)
43. 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
Dic₃⋊C₄	5

Subgroups — C5×Dic3⋊C4 #6696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₃⋊C₄ #6696