Subgroups — C₃³×C₅×C₈ #11761913

Order 1080.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₈	C₃	1	13	yes	maximal, direct product factor
3	C₂×C₃³×C₅	C₄	1	1	yes	characteristic
4	C₃³×C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃²×C₄×C₅	C₂×C₃	1	13	yes	—
6	C₃³×C₅	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₈	C₃²	1	13	yes	direct product factor
8	C₃³×C₄	C₂×C₅	1	1	yes	characteristic
9	C₂×C₃²×C₅	C₃×C₄	1	13	yes	—
10	C₃²×C₈	C₃×C₅	1	13	yes	direct product factor
11	C₃×C₄×C₅	C₂×C₃²	1	13	yes	—
12	C₂×C₃³	C₄×C₅	1	1	yes	characteristic
13	C₃²×C₅	C₃×C₈	1	13	yes	direct product factor
14	C₅×C₈	C₃³	1	1	yes	characteristic, direct product factor, Hall
15	C₃²×C₄	C₂×C₃×C₅	1	13	yes	—
16	C₂×C₃×C₅	C₃²×C₄	1	13	yes	—
17	C₃³	C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₈	C₃²×C₅	1	13	yes	direct product factor
19	C₄×C₅	C₂×C₃³	1	1	yes	characteristic
20	C₂×C₃²	C₃×C₄×C₅	1	13	yes	—
21	C₃×C₅	C₃²×C₈	1	13	yes	direct product factor
22	C₃×C₄	C₂×C₃²×C₅	1	13	yes	—
23	C₂×C₅	C₃³×C₄	1	1	yes	characteristic
24	C₃²	C₃×C₅×C₈	1	13	yes	direct product factor
25	C₈	C₃³×C₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃	C₃²×C₄×C₅	1	13	yes	—
27	C₅	C₃³×C₈	1	1	yes	characteristic, direct product factor, Sylow
28	C₄	C₂×C₃³×C₅	1	1	yes	characteristic
29	C₃	C₃²×C₅×C₈	1	13	yes	direct product factor
30	C₂	C₃³×C₄×C₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃³×C₅
socle, prime radical	C₂×C₃³×C₅	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₈	C₃	direct (N × H)
4. C₃³×C₈	C₅	direct (N × H)
6. C₃³×C₅	C₈	direct (N × H)
7. C₃×C₅×C₈	C₃²	direct (N × H)
10. C₃²×C₈	C₃×C₅	direct (N × H)
13. C₃²×C₅	C₃×C₈	direct (N × H)
14. C₅×C₈	C₃³	direct (N × H)
17. C₃³	C₅×C₈	direct (N × H)
18. C₃×C₈	C₃²×C₅	direct (N × H)
21. C₃×C₅	C₃²×C₈	direct (N × H)
24. C₃²	C₃×C₅×C₈	direct (N × H)
25. C₈	C₃³×C₅	direct (N × H)
27. C₅	C₃³×C₈	direct (N × H)
29. C₃	C₃²×C₅×C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×C₅	2
C₃²×C₅×C₈	3
C₃³×C₈	5

Subgroups — C33×C5×C8 #11761913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₅×C₈ #11761913