Subgroups — C₃²×#4380 #13108527

Order 1620.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#4380	C₃	1	4	yes	maximal, direct product factor
3	C₃⁴×C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×#157	—	5	1	no	maximal, Hall
5	C₃×C₃⋊D₁₅	C₂×C₃	1	4	yes	—
6	C₃²×D₁₅	—	6	2	no	—
7	#4380	C₃²	1	1	yes	characteristic, direct product factor
8	C₃²×AGL(1,𝔽₅)	—	9	1	no	maximal
9	C₃²×C₃⋊D₃	—	5	1	no	—
10	C₃³×C₅	—	2	2	no	—
11	C₃³×C₅	—	4	8	no	—
12	C₃³×C₅	C₃×C₄	1	4	yes	complemented
13	C₃×#157	—	5	4	no	—
14	C₃⋊D₁₅	C₂×C₃²	1	1	yes	characteristic
15	C₃×D₁₅	—	6	8	no	—
16	C₃²×D₅	—	9	1	no	—
17	C₃⁴	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	C₃×AGL(1,𝔽₅)	—	9	4	no	—
19	C₃×C₃⋊D₃	—	5	4	no	—
20	C₃²×D₃	—	30	2	no	—
21	C₃²×C₅	—	2	8	no	—
22	C₃²×C₅	—	4	8	no	—
23	C₃²×C₅	—	4	12	no	—
24	C₃²×C₅	—	4	8	no	—
25	C₃²×C₅	C₃²×C₄	1	1	yes	characteristic, complemented
26	C₃²×C₅	#157	1	1	yes	characteristic, complemented
27	#157	—	5	1	no	—
28	C₃²×C₄	—	45	1	no	—
29	D₁₅	—	6	2	no	—
30	C₃×D₅	—	9	4	no	—
31	C₃³	—	2	2	no	—
32	C₃³	—	4	8	no	—
33	C₃³	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
34	AGL(1,𝔽₅)	—	9	1	no	Hall
35	C₂×C₃²	—	45	1	no	—
36	C₃⋊D₃	—	5	1	no	—
37	C₃×D₃	—	30	8	no	—
38	C₃×C₅	—	2	2	no	—
39	C₃×C₅	—	4	8	no	—
40	C₃×C₅	C₃×#157	1	4	yes	complemented
41	C₃×C₄	—	45	4	no	—
42	D₅	—	9	1	no	—
43	C₃²	—	2	8	no	—
44	C₃²	—	4	8	no	—
45	C₃²	—	4	12	no	—
46	C₃²	—	4	8	no	—
47	C₃²	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
48	C₃²	#4380	1	1	yes	characteristic, direct product factor
49	C₂×C₃	—	45	4	no	—
50	D₃	—	30	2	no	—
51	C₅	C₃²×#157	1	1	yes	characteristic, complemented, Sylow
52	C₄	—	45	1	no	Sylow
53	C₃	—	2	2	no	—
54	C₃	—	4	8	no	—
55	C₃	C₃×#4380	1	4	yes	direct product factor
56	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	#4380
commutator, hypocenter	C₃²×C₅	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃⁴×C₅	C₄
prime radical	C₃²×C₃⋊D₁₅	C₂
cosocle	C₃⋊D₁₅	C₂×C₃²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×#4380	C₃	direct (N × H)
3. C₃⁴×C₅	C₄	semidirect
7. #4380	C₃²	direct (N × H)
12. C₃³×C₅	C₃×C₄	semidirect
17. C₃⁴	AGL(1,𝔽₅)	semidirect
25. C₃²×C₅	C₃²×C₄	semidirect
26. C₃²×C₅	#157	semidirect
33. C₃³	C₃×AGL(1,𝔽₅)	semidirect
40. C₃×C₅	C₃×#157	semidirect
47. C₃²	C₃²×AGL(1,𝔽₅)	semidirect
48. C₃²	#4380	direct (N × H)
51. C₅	C₃²×#157	semidirect
55. C₃	C₃×#4380	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃⋊D₁₅	2
C₃×#4380	3
C₃²×#157	5
C₃²×AGL(1,𝔽₅)	9

Subgroups — C32×#4380 #13108527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4380 #13108527