Subgroups — C₂²×C₃×Dic₅ #6802

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×C₃×Dic₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₄	1	4	yes	complemented
5	C₂²×C₃×C₅	C₂²	1	3	yes	—
6	C₃×Dic₅	C₂²	1	4	yes	direct product factor
7	C₂²×C₃×C₄	—	5	1	no	maximal, Hall
8	C₂³×C₅	C₂×C₃	1	1	yes	characteristic
9	C₂×Dic₅	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₅	C₂×C₄	1	6	yes	complemented
11	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
12	C₂³×C₃	D₅	1	1	yes	characteristic
13	C₂×C₃×C₄	—	5	6	no	—
14	C₂²×C₅	C₃×C₄	1	4	yes	complemented
15	C₂²×C₅	C₂²×C₃	1	3	yes	—
16	Dic₅	C₂²×C₃	1	4	yes	direct product factor
17	C₂²×C₄	—	5	1	no	Sylow
18	C₃×C₅	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	Dic₅	1	4	yes	direct product factor
20	C₂²×C₃	C₂×D₅	1	3	yes	—
21	C₃×C₄	—	5	4	no	—
22	C₂×C₅	C₂×C₃×C₄	1	6	yes	complemented
23	C₂×C₅	C₂³×C₃	1	1	yes	characteristic
24	C₂³	C₃×D₅	1	1	yes	characteristic
25	C₂×C₄	—	5	6	no	—
26	C₂×C₃	C₂×Dic₅	1	6	yes	direct product factor
27	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
28	C₅	C₂²×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₃×Dic₅	1	4	yes	direct product factor
30	C₂²	C₂×C₃×D₅	1	3	yes	—
31	C₄	—	5	4	no	—
32	C₃	C₂²×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₂×C₃×Dic₅	1	6	yes	direct product factor
34	C₂	C₂²×C₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₅
commutator, hypocenter	C₅	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×D₅
Fitting, socle, prime radical	C₂³×C₃×C₅	C₂
cosocle	C₂×C₅	C₂³×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂³×C₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Dic₅	C₂	direct (N × H)
3. C₂²×Dic₅	C₃	direct (N × H)
4. C₂²×C₃×C₅	C₄	semidirect
6. C₃×Dic₅	C₂²	direct (N × H)
9. C₂×Dic₅	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅	C₂×C₄	semidirect
14. C₂²×C₅	C₃×C₄	semidirect
16. Dic₅	C₂²×C₃	direct (N × H)
18. C₃×C₅	C₂²×C₄	semidirect
19. C₂²×C₃	Dic₅	direct (N × H)
22. C₂×C₅	C₂×C₃×C₄	semidirect
26. C₂×C₃	C₂×Dic₅	direct (N × H)
28. C₅	C₂²×C₃×C₄	semidirect
29. C₂²	C₃×Dic₅	direct (N × H)
32. C₃	C₂²×Dic₅	direct (N × H)
33. C₂	C₂×C₃×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
C₂³×C₃×C₅	2
C₂×C₃×Dic₅	2
C₂²×Dic₅	3
C₂²×C₃×C₄	5

Subgroups — C22×C3×Dic5 #6802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×Dic₅ #6802