Subgroups — C₃×#15691127 #22627445

Order 9375.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15691127	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₃×#10597837	C₅	1	5	yes	maximal, complemented
3	C₃×C₅×5₋¹⁺²	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃×#10597833	C₅	1	10	yes	maximal, complemented
5	C₃×#10597832	C₅	1	10	yes	maximal, complemented
6	C₃×#10597831	C₅	1	4	yes	maximal, complemented
7	C₃×H(3,𝔽₅)⋊C₅	C₅	1	1	yes	maximal, characteristic
8	#10597837	C₃×C₅	1	5	yes	complemented
9	C₅×5₋¹⁺²	C₃×C₅	1	1	yes	characteristic, complemented
10	#10597833	C₃×C₅	1	10	yes	complemented
11	#10597832	C₃×C₅	1	10	yes	complemented
12	#10597831	C₃×C₅	1	4	yes	complemented
13	H(3,𝔽₅)⋊C₅	C₃×C₅	1	1	yes	characteristic
14	C₃×C₅³	C₅²	1	1	yes	characteristic
15	C₃×5₋¹⁺²	—	5	5	no	—
16	C₃×5₋¹⁺²	—	5	20	no	—
17	C₃×5₋¹⁺²	C₅²	1	20	yes	—
18	C₃×H(3,𝔽₅)	C₅²	1	5	yes	—
19	C₃×C₅×C₂₅	—	5	5	no	—
20	C₃×C₅×C₂₅	C₅²	1	2	yes	—
21	C₃×C₅×C₂₅	C₅²	1	2	yes	—
22	C₃×C₅×C₂₅	C₅²	1	1	yes	characteristic
23	C₅³	C₃×C₅²	1	1	yes	characteristic
24	5₋¹⁺²	—	5	5	no	—
25	5₋¹⁺²	—	5	20	no	—
26	5₋¹⁺²	C₃×C₅²	1	20	yes	—
27	H(3,𝔽₅)	C₃×C₅²	1	5	yes	—
28	C₅×C₂₅	—	5	5	no	—
29	C₅×C₂₅	C₃×C₅²	1	2	yes	—
30	C₅×C₂₅	C₃×C₅²	1	2	yes	—
31	C₅×C₂₅	C₃×C₅²	1	1	yes	characteristic
32	C₃×C₅²	—	5	5	no	—
33	C₃×C₅²	—	5	1	no	—
34	C₃×C₅²	—	25	1	no	—
35	C₃×C₅²	C₅³	1	1	yes	characteristic
36	C₃×C₂₅	—	5	20	no	—
37	C₃×C₂₅	—	5	2	no	—
38	C₃×C₂₅	—	5	2	no	—
39	C₃×C₂₅	H(3,𝔽₅)	1	5	yes	—
40	C₅²	—	5	5	no	—
41	C₅²	—	5	1	no	—
42	C₅²	—	25	1	no	—
43	C₅²	C₃×C₅³	1	1	yes	characteristic
44	C₂₅	—	5	20	no	—
45	C₂₅	—	5	2	no	—
46	C₂₅	—	5	2	no	—
47	C₂₅	C₃×H(3,𝔽₅)	1	5	yes	—
48	C₃×C₅	—	5	1	no	—
49	C₃×C₅	—	25	5	no	—
50	C₃×C₅	—	25	1	no	—
51	C₃×C₅	C₅×H(3,𝔽₅)	1	1	yes	characteristic
52	C₅	—	5	1	no	—
53	C₅	—	25	5	no	—
54	C₅	—	25	1	no	—
55	C₅	C₃×C₅×H(3,𝔽₅)	1	1	yes	characteristic
56	C₃	#15691127	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₃×C₅	C₅×H(3,𝔽₅)
commutator, Frattini	C₅²	C₃×C₅³
LCS	G ▷ C₅² ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₃×C₅ ◁ C₃×C₅×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. #15691127	C₃	direct (N × H)
2. C₃×#10597837	C₅	semidirect
3. C₃×C₅×5₋¹⁺²	C₅	semidirect
4. C₃×#10597833	C₅	semidirect
5. C₃×#10597832	C₅	semidirect
6. C₃×#10597831	C₅	semidirect
8. #10597837	C₃×C₅	semidirect
9. C₅×5₋¹⁺²	C₃×C₅	semidirect
10. #10597833	C₃×C₅	semidirect
11. #10597832	C₃×C₅	semidirect
12. #10597831	C₃×C₅	semidirect
56. C₃	#15691127	direct (N × H)

Subgroups — C3×#15691127 #22627445

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#15691127 #22627445