Subgroups — C₂³×C₃×Dic₅ #92072

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₅	C₄	1	8	yes	complemented
5	C₂³×C₃×C₅	C₂²	1	7	yes	—
6	C₂×C₃×Dic₅	C₂²	1	28	yes	direct product factor
7	C₂³×C₃×C₄	—	5	1	no	maximal, Hall
8	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic
9	C₂²×Dic₅	C₂×C₃	1	14	yes	direct product factor
10	C₂²×C₃×C₅	C₂×C₄	1	28	yes	complemented
11	C₂²×C₃×C₅	C₂³	1	7	yes	—
12	C₃×Dic₅	C₂³	1	8	yes	direct product factor
13	C₂⁴×C₃	D₅	1	1	yes	characteristic
14	C₂²×C₃×C₄	—	5	14	no	—
15	C₂³×C₅	C₃×C₄	1	8	yes	complemented
16	C₂³×C₅	C₂²×C₃	1	7	yes	—
17	C₂×Dic₅	C₂²×C₃	1	28	yes	direct product factor
18	C₂³×C₄	—	5	1	no	Sylow
19	C₂×C₃×C₅	C₂²×C₄	1	14	yes	complemented
20	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
21	C₂³×C₃	Dic₅	1	8	yes	direct product factor
22	C₂³×C₃	C₂×D₅	1	7	yes	—
23	C₂×C₃×C₄	—	5	28	no	—
24	C₂²×C₅	C₂×C₃×C₄	1	28	yes	complemented
25	C₂²×C₅	C₂³×C₃	1	7	yes	—
26	Dic₅	C₂³×C₃	1	8	yes	direct product factor
27	C₂⁴	C₃×D₅	1	1	yes	characteristic
28	C₂²×C₄	—	5	14	no	—
29	C₃×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	C₂×Dic₅	1	28	yes	direct product factor
31	C₂²×C₃	C₂²×D₅	1	7	yes	—
32	C₃×C₄	—	5	8	no	—
33	C₂×C₅	C₂²×C₃×C₄	1	14	yes	complemented
34	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
35	C₂³	C₃×Dic₅	1	8	yes	direct product factor
36	C₂³	C₂×C₃×D₅	1	7	yes	—
37	C₂×C₄	—	5	28	no	—
38	C₂×C₃	C₂²×Dic₅	1	14	yes	direct product factor
39	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
40	C₅	C₂³×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
41	C₂²	C₂×C₃×Dic₅	1	28	yes	direct product factor
42	C₂²	C₂²×C₃×D₅	1	7	yes	—
43	C₄	—	5	8	no	—
44	C₃	C₂³×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₂²×C₃×Dic₅	1	14	yes	direct product factor
46	C₂	C₂³×C₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₃	D₅
commutator, hypocenter	C₅	C₂³×C₃×C₄
Frattini	C₂	C₂³×C₃×D₅
Fitting, socle, prime radical	C₂⁴×C₃×C₅	C₂
cosocle	C₂×C₅	C₂⁴×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Dic₅	C₂	direct (N × H)
3. C₂³×Dic₅	C₃	direct (N × H)
4. C₂³×C₃×C₅	C₄	semidirect
6. C₂×C₃×Dic₅	C₂²	direct (N × H)
9. C₂²×Dic₅	C₂×C₃	direct (N × H)
10. C₂²×C₃×C₅	C₂×C₄	semidirect
12. C₃×Dic₅	C₂³	direct (N × H)
15. C₂³×C₅	C₃×C₄	semidirect
17. C₂×Dic₅	C₂²×C₃	direct (N × H)
19. C₂×C₃×C₅	C₂²×C₄	semidirect
21. C₂³×C₃	Dic₅	direct (N × H)
24. C₂²×C₅	C₂×C₃×C₄	semidirect
26. Dic₅	C₂³×C₃	direct (N × H)
29. C₃×C₅	C₂³×C₄	semidirect
30. C₂²×C₃	C₂×Dic₅	direct (N × H)
33. C₂×C₅	C₂²×C₃×C₄	semidirect
35. C₂³	C₃×Dic₅	direct (N × H)
38. C₂×C₃	C₂²×Dic₅	direct (N × H)
40. C₅	C₂³×C₃×C₄	semidirect
41. C₂²	C₂×C₃×Dic₅	direct (N × H)
44. C₃	C₂³×Dic₅	direct (N × H)
45. C₂	C₂²×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
C₂⁴×C₃×C₅	2
C₂²×C₃×Dic₅	2
C₂³×Dic₅	3
C₂³×C₃×C₄	5

Subgroups — C23×C3×Dic5 #92072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×Dic₅ #92072