Subgroups — C₃²×C₅×C₃⋊C₈ #11761907

Order 1080.

144 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	—	3	1	no	maximal
3	C₃×C₅×C₃⋊C₈	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃³×C₅	C₄	1	1	yes	characteristic
5	C₃²×C₃⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₄×C₅	—	2	4	no	—
7	C₃²×C₄×C₅	D₃	1	1	yes	characteristic
8	C₃²×C₄×C₅	C₂×C₃	1	4	yes	—
9	C₃³×C₅	C₈	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₈	—	3	4	no	—
11	C₅×C₃⋊C₈	C₃²	1	1	yes	characteristic, direct product factor
12	C₃³×C₄	C₂×C₅	1	1	yes	characteristic
13	C₂×C₃²×C₅	—	2	4	no	—
14	C₂×C₃²×C₅	Dic₃	1	1	yes	characteristic
15	C₂×C₃²×C₅	C₃×C₄	1	4	yes	—
16	C₃²×C₈	—	3	1	no	—
17	C₃×C₃⋊C₈	C₃×C₅	1	4	yes	direct product factor
18	C₃×C₄×C₅	—	2	4	no	—
19	C₃×C₄×C₅	C₃×D₃	1	4	yes	—
20	C₃×C₄×C₅	C₂×C₃²	1	1	yes	characteristic
21	C₂×C₃³	C₄×C₅	1	1	yes	characteristic
22	C₃²×C₅	—	2	4	no	—
23	C₃²×C₅	C₃⋊C₈	1	1	yes	characteristic, direct product factor
24	C₃²×C₅	C₃×C₈	1	4	yes	complemented
25	C₅×C₈	—	3	1	no	Hall
26	C₃²×C₄	—	2	4	no	—
27	C₃²×C₄	C₅×D₃	1	1	yes	characteristic
28	C₃²×C₄	C₂×C₃×C₅	1	4	yes	—
29	C₂×C₃×C₅	—	2	4	no	—
30	C₂×C₃×C₅	C₃×Dic₃	1	4	yes	—
31	C₂×C₃×C₅	C₃²×C₄	1	1	yes	characteristic
32	C₃³	C₅×C₈	1	1	yes	characteristic, complemented, Sylow
33	C₃×C₈	—	3	4	no	—
34	C₃⋊C₈	C₃²×C₅	1	1	yes	characteristic, direct product factor
35	C₄×C₅	C₃²×D₃	1	1	yes	characteristic
36	C₂×C₃²	—	2	4	no	—
37	C₂×C₃²	C₅×Dic₃	1	1	yes	characteristic
38	C₂×C₃²	C₃×C₄×C₅	1	4	yes	—
39	C₃×C₅	—	2	4	no	—
40	C₃×C₅	C₃×C₃⋊C₈	1	4	yes	direct product factor
41	C₃×C₅	C₃²×C₈	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2	4	no	—
43	C₃×C₄	C₃×C₅×D₃	1	4	yes	—
44	C₃×C₄	C₂×C₃²×C₅	1	1	yes	characteristic
45	C₂×C₅	C₃²×Dic₃	1	1	yes	characteristic
46	C₃²	—	2	4	no	—
47	C₃²	C₅×C₃⋊C₈	1	1	yes	characteristic, direct product factor
48	C₃²	C₃×C₅×C₈	1	4	yes	complemented
49	C₈	—	3	1	no	Sylow
50	C₂×C₃	—	2	4	no	—
51	C₂×C₃	C₃×C₅×Dic₃	1	4	yes	—
52	C₂×C₃	C₃²×C₄×C₅	1	1	yes	characteristic
53	C₅	C₃²×C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
54	C₄	C₃²×C₅×D₃	1	1	yes	characteristic
55	C₃	—	2	4	no	—
56	C₃	C₃×C₅×C₃⋊C₈	1	4	yes	direct product factor
57	C₃	C₃²×C₅×C₈	1	1	yes	characteristic, complemented
58	C₂	C₃²×C₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄×C₅	D₃
commutator, hypocenter	C₃	C₃²×C₅×C₈
Frattini	C₄	C₃²×C₅×D₃
Fitting	C₃³×C₄×C₅	C₂
socle, prime radical	C₂×C₃³×C₅	C₄
cosocle	C₃×C₄	C₂×C₃²×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₃²×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₃⋊C₈	C₃	direct (N × H)
5. C₃²×C₃⋊C₈	C₅	direct (N × H)
9. C₃³×C₅	C₈	semidirect
11. C₅×C₃⋊C₈	C₃²	direct (N × H)
17. C₃×C₃⋊C₈	C₃×C₅	direct (N × H)
23. C₃²×C₅	C₃⋊C₈	direct (N × H)
24. C₃²×C₅	C₃×C₈	semidirect
32. C₃³	C₅×C₈	semidirect
34. C₃⋊C₈	C₃²×C₅	direct (N × H)
40. C₃×C₅	C₃×C₃⋊C₈	direct (N × H)
41. C₃×C₅	C₃²×C₈	semidirect
47. C₃²	C₅×C₃⋊C₈	direct (N × H)
48. C₃²	C₃×C₅×C₈	semidirect
53. C₅	C₃²×C₃⋊C₈	direct (N × H)
56. C₃	C₃×C₅×C₃⋊C₈	direct (N × H)
57. C₃	C₃²×C₅×C₈	semidirect

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
C₃×C₅×C₃⋊C₈	3
C₃²×C₃⋊C₈	5

Subgroups — C32×C5×C3⋊C8 #11761907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₃⋊C₈ #11761907