Subgroups — C₃×C₅×#672 #11924976

Order 1200.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#672	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄×C₅²	C₄	1	1	yes	characteristic
4	C₃×C₅×C₁₆	—	5	1	no	maximal
5	C₃×#672	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅²×C₈	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅²	C₈	1	1	yes	characteristic
8	C₃×C₅×C₈	—	2	2	no	—
9	C₃×C₅×C₈	D₅	1	1	yes	characteristic
10	C₃×C₅×C₈	C₂×C₅	1	1	yes	characteristic
11	C₄×C₅²	C₃×C₄	1	1	yes	characteristic
12	C₅×C₁₆	—	5	1	no	—
13	#672	C₃×C₅	1	1	yes	characteristic, direct product factor
14	C₃×C₅²	C₁₆	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄×C₅	—	2	2	no	—
16	C₃×C₄×C₅	Dic₅	1	1	yes	characteristic
17	C₃×C₄×C₅	C₄×C₅	1	1	yes	characteristic
18	C₂×C₅²	C₃×C₈	1	1	yes	characteristic
19	C₃×C₁₆	—	5	1	no	Hall
20	C₅×C₈	—	2	2	no	—
21	C₅×C₈	C₃×D₅	1	1	yes	characteristic
22	C₅×C₈	C₂×C₃×C₅	1	1	yes	characteristic
23	C₂×C₃×C₅	—	2	2	no	—
24	C₂×C₃×C₅	#168	1	1	yes	characteristic
25	C₂×C₃×C₅	C₅×C₈	1	1	yes	characteristic
26	C₅²	C₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₈	C₅×D₅	1	1	yes	characteristic
28	C₄×C₅	—	2	2	no	—
29	C₄×C₅	C₃×Dic₅	1	1	yes	characteristic
30	C₄×C₅	C₃×C₄×C₅	1	1	yes	characteristic
31	C₁₆	—	5	1	no	Sylow
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	#672	1	1	yes	characteristic, direct product factor
34	C₃×C₅	C₅×C₁₆	1	1	yes	characteristic, complemented
35	C₃×C₄	C₅×Dic₅	1	1	yes	characteristic
36	C₂×C₅	—	2	2	no	—
37	C₂×C₅	C₃×#168	1	1	yes	characteristic
38	C₂×C₅	C₃×C₅×C₈	1	1	yes	characteristic
39	C₈	C₃×C₅×D₅	1	1	yes	characteristic
40	C₂×C₃	C₅×#168	1	1	yes	characteristic
41	C₅	—	2	2	no	—
42	C₅	C₃×#672	1	1	yes	characteristic, direct product factor
43	C₅	C₃×C₅×C₁₆	1	1	yes	characteristic, complemented
44	C₄	C₃×C₅×Dic₅	1	1	yes	characteristic
45	C₃	C₅×#672	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₅×#168	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅×C₈	D₅
commutator, hypocenter	C₅	C₃×C₅×C₁₆
Frattini	C₈	C₃×C₅×D₅
Fitting	C₃×C₅²×C₈	C₂
socle, prime radical	C₂×C₃×C₅²	C₈
cosocle	C₅×C₈	C₂×C₃×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#672	C₃	direct (N × H)
5. C₃×#672	C₅	direct (N × H)
13. #672	C₃×C₅	direct (N × H)
14. C₃×C₅²	C₁₆	semidirect
26. C₅²	C₃×C₁₆	semidirect
33. C₃×C₅	#672	direct (N × H)
34. C₃×C₅	C₅×C₁₆	semidirect
42. C₅	C₃×#672	direct (N × H)
43. C₅	C₃×C₅×C₁₆	semidirect
45. C₃	C₅×#672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₈	2
C₅×#672	3
C₃×C₅×C₁₆	5
C₃×#672	5

Subgroups — C3×C5×#672 #11924976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#672 #11924976