Subgroups — C₂³×Dic₁₅ #92102

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×Dic₁₅	C₂	1	14	yes	maximal, direct product factor
3	C₂³×Dic₅	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₅	C₄	1	8	yes	complemented
5	C₂³×C₃×C₅	C₂²	1	7	yes	—
6	C₂×Dic₁₅	C₂²	1	28	yes	direct product factor
7	C₂³×Dic₃	—	5	1	no	maximal, Hall
8	C₂⁴×C₅	D₃	1	1	yes	characteristic
9	C₂²×Dic₅	—	3	14	no	—
10	C₂²×C₃×C₅	C₂×C₄	1	28	yes	complemented
11	C₂²×C₃×C₅	C₂³	1	7	yes	—
12	Dic₁₅	C₂³	1	8	yes	direct product factor
13	C₂⁴×C₃	D₅	1	1	yes	characteristic
14	C₂²×Dic₃	—	5	14	no	—
15	C₂³×C₅	Dic₃	1	8	yes	complemented
16	C₂³×C₅	C₂×D₃	1	7	yes	—
17	C₂×Dic₅	—	3	28	no	—
18	C₂³×C₄	—	15	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	complemented
22	C₂³×C₃	C₂×D₅	1	7	yes	—
23	C₂×Dic₃	—	5	28	no	—
24	C₂²×C₅	C₂×Dic₃	1	28	yes	complemented
25	C₂²×C₅	C₂²×D₃	1	7	yes	—
26	Dic₅	—	3	8	no	—
27	C₂⁴	D₁₅	1	1	yes	characteristic
28	C₂²×C₄	—	15	14	no	—
29	C₃×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	C₂×Dic₅	1	28	yes	complemented
31	C₂²×C₃	C₂²×D₅	1	7	yes	—
32	Dic₃	—	5	8	no	—
33	C₂×C₅	C₂²×Dic₃	1	14	yes	complemented
34	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
35	C₂³	Dic₁₅	1	8	yes	direct product factor
36	C₂³	C₂×D₁₅	1	7	yes	—
37	C₂×C₄	—	15	28	no	—
38	C₂×C₃	C₂²×Dic₅	1	14	yes	complemented
39	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
40	C₅	C₂³×Dic₃	1	1	yes	characteristic, complemented, Sylow
41	C₂²	C₂×Dic₁₅	1	28	yes	direct product factor
42	C₂²	C₂²×D₁₅	1	7	yes	—
43	C₄	—	15	8	no	—
44	C₃	C₂³×Dic₅	1	1	yes	characteristic, complemented, Sylow
45	C₂	C₂²×Dic₁₅	1	14	yes	direct product factor
46	C₂	C₂³×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	D₁₅
commutator, hypocenter	C₃×C₅	C₂³×C₄
Frattini	C₂	C₂³×D₁₅
Fitting, socle, prime radical	C₂⁴×C₃×C₅	C₂
cosocle	C₂×C₃×C₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₅	C₂	direct (N × H)
4. C₂³×C₃×C₅	C₄	semidirect
6. C₂×Dic₁₅	C₂²	direct (N × H)
10. C₂²×C₃×C₅	C₂×C₄	semidirect
12. Dic₁₅	C₂³	direct (N × H)
15. C₂³×C₅	Dic₃	semidirect
19. C₂×C₃×C₅	C₂²×C₄	semidirect
21. C₂³×C₃	Dic₅	semidirect
24. C₂²×C₅	C₂×Dic₃	semidirect
29. C₃×C₅	C₂³×C₄	semidirect
30. C₂²×C₃	C₂×Dic₅	semidirect
33. C₂×C₅	C₂²×Dic₃	semidirect
35. C₂³	Dic₁₅	direct (N × H)
38. C₂×C₃	C₂²×Dic₅	semidirect
40. C₅	C₂³×Dic₃	semidirect
41. C₂²	C₂×Dic₁₅	direct (N × H)
44. C₃	C₂³×Dic₅	semidirect
45. C₂	C₂²×Dic₁₅	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×Dic₁₅	2
C₂³×Dic₅	3
C₂³×Dic₃	5

Subgroups — C23×Dic15 #92102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₁₅ #92102