Subgroups — C₅×C₃⋊(C₃⋊#157) #13108532

Order 1620.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#157	—	3	4	no	maximal
3	C₃⁴×C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊#157)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₃⋊D₃	D₃	1	4	yes	—
6	C₃²×C₅×D₃	—	6	2	no	—
7	C₅×#157	—	9	1	no	—
8	C₅×C₃⋊Dic₃	—	9	1	no	maximal
9	C₃²×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
10	C₃³×C₅	—	2	2	no	—
11	C₃³×C₅	—	4	8	no	—
12	C₃³×C₅	Dic₃	1	4	yes	complemented
13	C₃⋊#157	—	3	4	no	—
14	C₂×C₃²×C₅	—	9	1	no	—
15	C₅×C₃⋊D₃	C₃⋊D₃	1	1	yes	characteristic
16	C₃×C₅×D₃	—	6	8	no	—
17	C₃⁴	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₅×Dic₃	—	27	4	no	—
19	C₃×C₃⋊D₃	C₅×D₃	1	4	yes	—
20	C₃²×D₃	—	6	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	C₃⋊Dic₃	1	1	yes	characteristic, complemented
26	C₃²×C₅	#157	1	1	yes	characteristic, complemented
27	#157	—	9	1	no	—
28	C₃⋊Dic₃	—	9	1	no	—
29	C₂×C₃×C₅	—	9	4	no	—
30	C₅×D₃	—	6	2	no	—
31	C₃³	—	2	2	no	—
32	C₃³	—	4	8	no	—
33	C₃³	C₅×Dic₃	1	4	yes	complemented
34	C₄×C₅	—	81	1	no	Hall
35	C₂×C₃²	—	9	1	no	—
36	C₃⋊D₃	C₅×C₃⋊D₃	1	1	yes	characteristic
37	C₃×D₃	—	6	8	no	—
38	C₃×C₅	—	2	2	no	—
39	C₃×C₅	—	4	8	no	—
40	C₃×C₅	C₃⋊#157	1	4	yes	complemented
41	Dic₃	—	27	4	no	—
42	C₂×C₅	—	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	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented
48	C₃²	C₅×#157	1	1	yes	characteristic, complemented
49	C₂×C₃	—	9	4	no	—
50	D₃	—	6	2	no	—
51	C₅	C₃⋊(C₃⋊#157)	1	1	yes	characteristic, direct product factor, Sylow
52	C₄	—	81	1	no	Sylow
53	C₃	—	2	2	no	—
54	C₃	—	4	8	no	—
55	C₃	C₅×C₃⋊#157	1	4	yes	complemented
56	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₃⋊#157)
commutator, hypocenter	C₃⁴	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃⁴×C₅	C₄
prime radical	C₃²×C₅×C₃⋊D₃	C₂
cosocle	C₃²×C₃⋊D₃	C₂×C₅
LCS	G ▷ C₃⁴
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃⁴×C₅	C₄	semidirect
4. C₃⋊(C₃⋊#157)	C₅	direct (N × H)
12. C₃³×C₅	Dic₃	semidirect
17. C₃⁴	C₄×C₅	semidirect
25. C₃²×C₅	C₃⋊Dic₃	semidirect
26. C₃²×C₅	#157	semidirect
33. C₃³	C₅×Dic₃	semidirect
40. C₃×C₅	C₃⋊#157	semidirect
47. C₃²	C₅×C₃⋊Dic₃	semidirect
48. C₃²	C₅×#157	semidirect
51. C₅	C₃⋊(C₃⋊#157)	direct (N × H)
55. C₃	C₅×C₃⋊#157	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₃⋊D₃	2
C₅×C₃⋊#157	3
C₃⋊(C₃⋊#157)	5
C₅×C₃⋊Dic₃	9

Subgroups — C5×C3⋊(C3⋊#157) #13108532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(C₃⋊#157) #13108532