Subgroups — C₂²×C₅×Dic₃ #6812

Order 240.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₄	1	4	yes	complemented
5	C₂²×C₃×C₅	C₂²	1	3	yes	—
6	C₅×Dic₃	C₂²	1	4	yes	direct product factor
7	C₂²×Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₅	D₃	1	1	yes	characteristic
9	C₂×C₄×C₅	—	3	6	no	—
10	C₂×C₃×C₅	C₂×C₄	1	6	yes	complemented
11	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
12	C₂³×C₃	C₂×C₅	1	1	yes	characteristic
13	C₂×Dic₃	C₂×C₅	1	6	yes	direct product factor
14	C₂²×C₅	Dic₃	1	4	yes	direct product factor
15	C₂²×C₅	C₂×D₃	1	3	yes	—
16	C₄×C₅	—	3	4	no	—
17	C₂²×C₄	—	3	1	no	Sylow
18	C₃×C₅	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	C₄×C₅	1	4	yes	complemented
20	C₂²×C₃	C₂²×C₅	1	3	yes	—
21	Dic₃	C₂²×C₅	1	4	yes	direct product factor
22	C₂×C₅	C₂×Dic₃	1	6	yes	direct product factor
23	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
24	C₂³	C₅×D₃	1	1	yes	characteristic
25	C₂×C₄	—	3	6	no	—
26	C₂×C₃	C₂×C₄×C₅	1	6	yes	complemented
27	C₂×C₃	C₂³×C₅	1	1	yes	characteristic
28	C₅	C₂²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₅×Dic₃	1	4	yes	direct product factor
30	C₂²	C₂×C₅×D₃	1	3	yes	—
31	C₄	—	3	4	no	—
32	C₃	C₂²×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₂×C₅×Dic₃	1	6	yes	direct product factor
34	C₂	C₂²×C₅×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₅	D₃
commutator, hypocenter	C₃	C₂²×C₄×C₅
Frattini	C₂	C₂²×C₅×D₃
Fitting, socle, prime radical	C₂³×C₃×C₅	C₂
cosocle	C₂×C₃	C₂³×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₃	C₂	direct (N × H)
4. C₂²×C₃×C₅	C₄	semidirect
6. C₅×Dic₃	C₂²	direct (N × H)
7. C₂²×Dic₃	C₅	direct (N × H)
10. C₂×C₃×C₅	C₂×C₄	semidirect
13. C₂×Dic₃	C₂×C₅	direct (N × H)
14. C₂²×C₅	Dic₃	direct (N × H)
18. C₃×C₅	C₂²×C₄	semidirect
19. C₂²×C₃	C₄×C₅	semidirect
21. Dic₃	C₂²×C₅	direct (N × H)
22. C₂×C₅	C₂×Dic₃	direct (N × H)
26. C₂×C₃	C₂×C₄×C₅	semidirect
28. C₅	C₂²×Dic₃	direct (N × H)
29. C₂²	C₅×Dic₃	direct (N × H)
32. C₃	C₂²×C₄×C₅	semidirect
33. C₂	C₂×C₅×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅	2
C₂×C₅×Dic₃	2
C₂²×C₄×C₅	3
C₂²×Dic₃	5

Subgroups — C22×C5×Dic3 #6812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×Dic₃ #6812