Subgroups — C₅×#20301658 #49147063

Order 36900.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#20301658	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#13093288	—	5	1	no	maximal
5	C₅²×D₃×C₄₁	—	6	2	no	—
6	C₅×Dic₂₀₅	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₃×C₄₁	—	2	2	no	—
8	C₅×C₃⋊D₃×C₄₁	D₅	1	1	yes	characteristic
9	C₅×C₃⋊D₃×C₄₁	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₄₁	—	2	2	no	—
11	C₂×C₅²×C₄₁	—	9	1	no	—
12	C₃²×C₅×C₄₁	—	2	2	no	—
13	C₃²×C₅×C₄₁	Dic₅	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented
15	#13093288	—	5	1	no	Hall
16	C₅×D₃×C₄₁	—	6	2	no	—
17	C₅×D₃×C₄₁	—	6	2	no	—
18	C₅×D₃×C₄₁	—	6	8	no	—
19	C₅²×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
20	C₅×#4379	—	41	1	no	maximal, Hall
21	Dic₂₀₅	—	9	1	no	—
22	C₅×Dic₄₁	—	45	1	no	—
23	C₃⋊D₃×C₄₁	C₅×D₅	1	1	yes	characteristic
24	C₃×C₅×C₄₁	—	2	8	no	—
25	C₃×C₅×C₄₁	—	2	2	no	—
26	C₃×C₅×C₄₁	—	2	2	no	—
27	C₅²×C₃⋊D₃	D₄₁	1	1	yes	characteristic
28	C₂×C₅×C₄₁	—	9	1	no	—
29	C₂×C₅×C₄₁	—	9	1	no	—
30	C₂×C₅×C₄₁	—	18	2	no	—
31	C₃²×C₄₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
32	D₃×C₄₁	—	6	2	no	—
33	C₃²×C₅²	Dic₄₁	1	1	yes	characteristic, complemented, Hall
34	C₅×C₄₁	—	2	2	no	—
35	C₅×C₄₁	C₅×#157	1	1	yes	characteristic, complemented
36	C₅×C₄₁	#4379	1	1	yes	characteristic, complemented
37	#4379	—	41	1	no	—
38	C₅×#157	—	205	1	no	—
39	Dic₄₁	—	45	1	no	Hall
40	C₅²×D₃	—	6	2	no	—
41	C₃×C₄₁	—	2	2	no	—
42	C₅×Dic₅	—	369	1	no	Hall
43	C₅×C₃⋊D₃	—	2	2	no	—
44	C₅×C₃⋊D₃	C₅×D₄₁	1	1	yes	characteristic
45	C₅×C₃⋊D₃	D₂₀₅	1	1	yes	characteristic
46	C₂×C₄₁	—	9	1	no	—
47	C₃×C₅²	—	2	2	no	—
48	C₂×C₅²	—	9	1	no	—
49	C₃²×C₅	—	2	2	no	—
50	C₃²×C₅	C₅×Dic₄₁	1	1	yes	characteristic, complemented
51	C₃²×C₅	Dic₂₀₅	1	1	yes	characteristic, complemented
52	C₄₁	C₅×#4379	1	1	yes	characteristic, complemented, Sylow
53	#157	—	205	1	no	Hall
54	C₅×D₃	—	6	2	no	—
55	C₅×D₃	—	6	2	no	—
56	C₅×D₃	—	6	8	no	—
57	C₅²	#13093288	1	1	yes	characteristic, complemented, Sylow
58	C₄×C₅	—	1845	1	no	—
59	Dic₅	—	369	1	no	—
60	C₃⋊D₃	C₅×D₂₀₅	1	1	yes	characteristic
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₂×C₅	—	9	1	no	—
65	C₂×C₅	—	9	1	no	—
66	C₂×C₅	—	18	2	no	—
67	C₃²	C₅×Dic₂₀₅	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	6	2	no	—
69	C₅	—	2	2	no	—
70	C₅	C₅×#13093288	1	1	yes	characteristic, complemented
71	C₅	#20301658	1	1	yes	characteristic, direct product factor
72	C₄	—	1845	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#20301658
commutator, hypocenter	C₃²×C₅×C₄₁	C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₄₁	C₄
prime radical	C₅²×C₃⋊D₃×C₄₁	C₂
cosocle	C₅×C₃⋊D₃×C₄₁	C₂×C₅
LCS	G ▷ C₃²×C₅×C₄₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₄₁	C₄	semidirect
3. #20301658	C₅	direct (N × H)
13. C₃²×C₅×C₄₁	Dic₅	semidirect
14. C₃²×C₅×C₄₁	C₄×C₅	semidirect
19. C₅²×C₄₁	#157	semidirect
31. C₃²×C₄₁	C₅×Dic₅	semidirect
33. C₃²×C₅²	Dic₄₁	semidirect
35. C₅×C₄₁	C₅×#157	semidirect
36. C₅×C₄₁	#4379	semidirect
50. C₃²×C₅	C₅×Dic₄₁	semidirect
51. C₃²×C₅	Dic₂₀₅	semidirect
52. C₄₁	C₅×#4379	semidirect
57. C₅²	#13093288	semidirect
67. C₃²	C₅×Dic₂₀₅	semidirect
70. C₅	C₅×#13093288	semidirect
71. C₅	#20301658	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₃⋊D₃×C₄₁	2
#20301658	5
C₅×#13093288	5
C₅×Dic₂₀₅	9
C₅×#4379	41

Subgroups — C5×#20301658 #49147063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20301658 #49147063