Subgroups — C₁₉×C₂₅×#157 #30685513

Order 17100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₉×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₉×#157	C₅	1	1	yes	maximal, characteristic
4	D₃×C₁₉×C₂₅	—	6	2	no	—
5	C₄×C₁₉×C₂₅	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₃×C₁₉	C₂×C₅	1	1	yes	characteristic
7	C₃×C₁₉×C₂₅	—	2	2	no	—
8	C₂×C₁₉×C₂₅	—	9	1	no	—
9	C₂₅×#157	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₅×C₁₉	C₄×C₅	1	1	yes	characteristic
11	C₁₉×#157	C₂₅	1	1	yes	characteristic, direct product factor, Hall
12	C₅×D₃×C₁₉	—	6	2	no	—
13	C₁₉×C₂₅	#157	1	1	yes	characteristic, direct product factor, Hall
14	C₃⋊D₃×C₂₅	C₂×C₁₉	1	1	yes	characteristic
15	C₄×C₅×C₁₉	—	9	1	no	—
16	C₃⋊D₃×C₁₉	C₂×C₂₅	1	1	yes	characteristic
17	C₃×C₅×C₁₉	—	2	2	no	—
18	C₃²×C₂₅	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₁₉	—	9	1	no	—
20	C₅×#157	C₅×C₁₉	1	1	yes	characteristic
21	C₃²×C₁₉	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
22	D₃×C₂₅	—	6	2	no	—
23	D₃×C₁₉	—	6	2	no	—
24	C₄×C₂₅	—	9	1	no	Hall
25	C₅×C₁₉	C₅×#157	1	1	yes	characteristic
26	C₅×C₃⋊D₃	C₂×C₅×C₁₉	1	1	yes	characteristic
27	C₄×C₁₉	—	9	1	no	Hall
28	C₃×C₂₅	—	2	2	no	—
29	C₃×C₁₉	—	2	2	no	—
30	C₂×C₂₅	—	9	1	no	—
31	C₃²×C₅	C₄×C₅×C₁₉	1	1	yes	characteristic
32	C₂×C₁₉	—	9	1	no	—
33	#157	C₁₉×C₂₅	1	1	yes	characteristic, direct product factor, Hall
34	C₅×D₃	—	6	2	no	—
35	C₂₅	C₁₉×#157	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₅	—	9	1	no	—
37	C₁₉	C₂₅×#157	1	1	yes	characteristic, direct product factor, Sylow
38	C₃⋊D₃	C₂×C₁₉×C₂₅	1	1	yes	characteristic
39	C₃×C₅	—	2	2	no	—
40	C₂×C₅	—	9	1	no	—
41	C₃²	C₄×C₁₉×C₂₅	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	C₅×C₁₉×#157	1	1	yes	characteristic
44	C₄	—	9	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉×C₂₅	#157
commutator, hypocenter	C₃²	C₄×C₁₉×C₂₅
Frattini	C₅	C₅×C₁₉×#157
Fitting	C₃²×C₁₉×C₂₅	C₄
socle	C₃²×C₅×C₁₉	C₄×C₅
prime radical	C₅×C₃⋊D₃×C₁₉	C₂×C₅
cosocle	C₅×C₃⋊D₃	C₂×C₅×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₉×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₉×C₂₅	C₄	semidirect
9. C₂₅×#157	C₁₉	direct (N × H)
11. C₁₉×#157	C₂₅	direct (N × H)
13. C₁₉×C₂₅	#157	direct (N × H)
18. C₃²×C₂₅	C₄×C₁₉	semidirect
21. C₃²×C₁₉	C₄×C₂₅	semidirect
33. #157	C₁₉×C₂₅	direct (N × H)
35. C₂₅	C₁₉×#157	direct (N × H)
37. C₁₉	C₂₅×#157	direct (N × H)
41. C₃²	C₄×C₁₉×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₁₉×C₂₅	2
C₅×C₁₉×#157	5
C₄×C₁₉×C₂₅	9
C₂₅×#157	19

Subgroups — C19×C25×#157 #30685513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₂₅×#157 #30685513