Subgroups — C₂×C₃²×Dic₅ #67163

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×Dic₅	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₅	C₄	1	2	yes	complemented
5	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄	—	5	1	no	maximal, Hall
7	C₂²×C₃×C₅	C₂×C₃	1	4	yes	—
8	C₃×Dic₅	C₂×C₃	1	8	yes	direct product factor
9	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×Dic₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₃²	D₅	1	1	yes	characteristic
12	C₃²×C₄	—	5	2	no	—
13	C₂×C₃×C₅	C₃×C₄	1	8	yes	complemented
14	C₂×C₃×C₅	C₂²×C₃	1	4	yes	—
15	C₂×C₃×C₄	—	5	4	no	—
16	C₂²×C₅	C₂×C₃²	1	1	yes	characteristic
17	Dic₅	C₂×C₃²	1	2	yes	direct product factor
18	C₂×C₃²	Dic₅	1	2	yes	direct product factor
19	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
20	C₃×C₅	C₂×C₃×C₄	1	4	yes	complemented
21	C₂²×C₃	C₃×D₅	1	4	yes	—
22	C₃×C₄	—	5	8	no	—
23	C₂×C₅	C₃²×C₄	1	2	yes	complemented
24	C₂×C₅	C₂²×C₃²	1	1	yes	characteristic
25	C₃²	C₂×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₄	—	5	1	no	Sylow
27	C₂×C₃	C₃×Dic₅	1	8	yes	direct product factor
28	C₂×C₃	C₂×C₃×D₅	1	4	yes	—
29	C₅	C₂×C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂²	C₃²×D₅	1	1	yes	characteristic
31	C₄	—	5	2	no	—
32	C₃	C₂×C₃×Dic₅	1	4	yes	direct product factor
33	C₂	C₃²×Dic₅	1	2	yes	direct product factor
34	C₂	C₂×C₃²×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃²	D₅
commutator, hypocenter	C₅	C₂×C₃²×C₄
Frattini	C₂	C₂×C₃²×D₅
Fitting, socle, prime radical	C₂²×C₃²×C₅	C₂
cosocle	C₂×C₅	C₂²×C₃²
LCS	G ▷ C₅
UCS	C₁ ◁ C₂²×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃²×Dic₅	C₂	direct (N × H)
3. C₂×C₃×Dic₅	C₃	direct (N × H)
4. C₂×C₃²×C₅	C₄	semidirect
8. C₃×Dic₅	C₂×C₃	direct (N × H)
9. C₃²×C₅	C₂×C₄	semidirect
10. C₂×Dic₅	C₃²	direct (N × H)
13. C₂×C₃×C₅	C₃×C₄	semidirect
17. Dic₅	C₂×C₃²	direct (N × H)
18. C₂×C₃²	Dic₅	direct (N × H)
20. C₃×C₅	C₂×C₃×C₄	semidirect
23. C₂×C₅	C₃²×C₄	semidirect
25. C₃²	C₂×Dic₅	direct (N × H)
27. C₂×C₃	C₃×Dic₅	direct (N × H)
29. C₅	C₂×C₃²×C₄	semidirect
32. C₃	C₂×C₃×Dic₅	direct (N × H)
33. C₂	C₃²×Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₅	2
C₃²×Dic₅	2
C₂×C₃×Dic₅	3
C₂×C₃²×C₄	5

Subgroups — C2×C32×Dic5 #67163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×Dic₅ #67163