Subgroups — C₃×C₅×C₃⋊C₃₂ #13083901

Order 1440.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₃₂	—	3	1	no	maximal
3	C₅×C₃⋊C₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
5	C₃×C₃⋊C₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₆	—	2	1	no	—
7	C₃×C₅×C₁₆	D₃	1	1	yes	characteristic
8	C₃×C₅×C₁₆	C₂×C₃	1	1	yes	characteristic
9	C₃²×C₄×C₅	C₈	1	1	yes	characteristic
10	C₅×C₃₂	—	3	1	no	Hall
11	C₃²×C₁₆	C₂×C₅	1	1	yes	characteristic
12	C₃×C₅×C₈	—	2	1	no	—
13	C₃×C₅×C₈	Dic₃	1	1	yes	characteristic
14	C₃×C₅×C₈	C₃×C₄	1	1	yes	characteristic
15	C₃×C₃₂	—	3	1	no	—
16	C₃⋊C₃₂	C₃×C₅	1	1	yes	characteristic, direct product factor
17	C₂×C₃²×C₅	C₁₆	1	1	yes	characteristic
18	C₅×C₁₆	C₃×D₃	1	1	yes	characteristic
19	C₃²×C₈	C₄×C₅	1	1	yes	characteristic
20	C₃×C₄×C₅	—	2	1	no	—
21	C₃×C₄×C₅	C₃⋊C₈	1	1	yes	characteristic
22	C₃×C₄×C₅	C₃×C₈	1	1	yes	characteristic
23	C₃×C₁₆	—	2	1	no	—
24	C₃×C₁₆	C₅×D₃	1	1	yes	characteristic
25	C₃×C₁₆	C₂×C₃×C₅	1	1	yes	characteristic
26	C₃²×C₅	C₃₂	1	1	yes	characteristic, complemented, Hall
27	C₅×C₈	C₃×Dic₃	1	1	yes	characteristic
28	C₃²×C₄	C₅×C₈	1	1	yes	characteristic
29	C₃₂	—	3	1	no	Sylow
30	C₂×C₃×C₅	—	2	1	no	—
31	C₂×C₃×C₅	C₃⋊C₁₆	1	1	yes	characteristic
32	C₂×C₃×C₅	C₃×C₁₆	1	1	yes	characteristic
33	C₃×C₈	—	2	1	no	—
34	C₃×C₈	C₅×Dic₃	1	1	yes	characteristic
35	C₃×C₈	C₃×C₄×C₅	1	1	yes	characteristic
36	C₄×C₅	C₃×C₃⋊C₈	1	1	yes	characteristic
37	C₂×C₃²	C₅×C₁₆	1	1	yes	characteristic
38	C₁₆	C₃×C₅×D₃	1	1	yes	characteristic
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃⋊C₃₂	1	1	yes	characteristic, direct product factor
41	C₃×C₅	C₃×C₃₂	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	C₅×C₃⋊C₈	1	1	yes	characteristic
44	C₃×C₄	C₃×C₅×C₈	1	1	yes	characteristic
45	C₂×C₅	C₃×C₃⋊C₁₆	1	1	yes	characteristic
46	C₃²	C₅×C₃₂	1	1	yes	characteristic, complemented, Sylow
47	C₈	C₃×C₅×Dic₃	1	1	yes	characteristic
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	C₅×C₃⋊C₁₆	1	1	yes	characteristic
50	C₂×C₃	C₃×C₅×C₁₆	1	1	yes	characteristic
51	C₅	C₃×C₃⋊C₃₂	1	1	yes	characteristic, direct product factor, Sylow
52	C₄	C₃×C₅×C₃⋊C₈	1	1	yes	characteristic
53	C₃	—	2	1	no	—
54	C₃	C₅×C₃⋊C₃₂	1	1	yes	characteristic, direct product factor
55	C₃	C₃×C₅×C₃₂	1	1	yes	characteristic, complemented
56	C₂	C₃×C₅×C₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₆	D₃
commutator, hypocenter	C₃	C₃×C₅×C₃₂
Frattini	C₁₆	C₃×C₅×D₃
Fitting	C₃²×C₅×C₁₆	C₂
socle, prime radical	C₂×C₃²×C₅	C₁₆
cosocle	C₃×C₁₆	C₂×C₃×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₅×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₅×C₃⋊C₃₂	C₃	direct (N × H)
5. C₃×C₃⋊C₃₂	C₅	direct (N × H)
16. C₃⋊C₃₂	C₃×C₅	direct (N × H)
26. C₃²×C₅	C₃₂	semidirect
40. C₃×C₅	C₃⋊C₃₂	direct (N × H)
41. C₃×C₅	C₃×C₃₂	semidirect
46. C₃²	C₅×C₃₂	semidirect
51. C₅	C₃×C₃⋊C₃₂	direct (N × H)
54. C₃	C₅×C₃⋊C₃₂	direct (N × H)
55. C₃	C₃×C₅×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₆	2
C₃×C₅×C₃₂	3
C₅×C₃⋊C₃₂	3
C₃×C₃⋊C₃₂	5

Subgroups — C3×C5×C3⋊C32 #13083901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₃⋊C₃₂ #13083901