Subgroups — C₃×C₂₅×C₂²⋊(C₁₉⋊C₃) #30685519

Order 17100.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₂²⋊(C₁₉⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₉×C₂₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₅×C₁₉⋊C₃	—	4	1	no	maximal, Hall
4	C₃×C₅×C₂²⋊(C₁₉⋊C₃)	C₅	1	1	yes	maximal, characteristic
5	C₂×C₃×C₁₉×C₂₅	—	3	1	no	—
6	C₂²×C₁₉×C₂₅	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉×C₂₅	A₄	1	1	yes	characteristic, complemented
8	C₂₅×C₁₉⋊C₃	—	4	3	no	—
9	C₂²×C₃×C₅×C₁₉	C₃×C₅	1	1	yes	characteristic
10	C₅×C₂²⋊(C₁₉⋊C₃)	C₃×C₅	1	3	yes	—
11	C₂×C₁₉×C₂₅	—	3	1	no	—
12	C₃×A₄×C₂₅	—	19	1	no	maximal, Hall
13	C₃×C₅×C₁₉⋊C₃	—	4	1	no	—
14	C₃×C₂²⋊(C₁₉⋊C₃)	C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₅×C₁₉	—	3	1	no	—
16	C₁₉×C₂₅	C₃×A₄	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅×C₁₉	C₃²×C₅	1	1	yes	characteristic
18	C₂²×C₃×C₂₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented
19	A₄×C₂₅	—	19	3	no	—
20	C₃×C₅×C₁₉	C₅×A₄	1	1	yes	characteristic
21	C₅×C₁₉⋊C₃	—	4	3	no	—
22	C₂²×C₃×C₁₉	C₃×C₂₅	1	1	yes	characteristic, complemented
23	C₂²⋊(C₁₉⋊C₃)	C₃×C₂₅	1	3	yes	direct product factor
24	C₃²×C₂₅	—	76	1	no	Hall
25	C₂×C₅×C₁₉	—	3	1	no	—
26	C₃×C₅×A₄	—	19	1	no	—
27	C₃×C₁₉⋊C₃	—	4	1	no	Hall
28	C₂×C₃×C₂₅	—	3	1	no	—
29	C₂×C₃×C₁₉	—	3	1	no	—
30	C₂²×C₂₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₉	C₃×C₅×A₄	1	1	yes	characteristic
32	C₂²×C₁₉	C₃²×C₂₅	1	1	yes	characteristic, complemented, Hall
33	C₃×C₂₅	—	76	3	no	—
34	C₃×C₂₅	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
35	C₂²×C₃×C₅	C₅×C₁₉⋊C₃	1	1	yes	characteristic
36	C₅×A₄	—	19	3	no	—
37	C₃×C₁₉	A₄×C₂₅	1	1	yes	characteristic, complemented
38	C₁₉⋊C₃	—	4	3	no	—
39	C₂×C₂₅	—	3	1	no	—
40	C₃²×C₅	—	76	1	no	—
41	C₂×C₁₉	—	3	1	no	—
42	C₃×A₄	—	19	1	no	Hall
43	C₂×C₃×C₅	—	3	1	no	—
44	C₂₅	C₃×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²×C₅	C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic
46	C₁₉	C₃×A₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₅	—	76	3	no	—
48	C₃×C₅	C₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
49	C₂²×C₃	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
50	A₄	—	19	3	no	—
51	C₂×C₅	—	3	1	no	—
52	C₃²	—	76	1	no	Sylow
53	C₂×C₃	—	3	1	no	—
54	C₅	C₃×C₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
55	C₂²	C₃×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	76	3	no	—
57	C₃	C₂₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₅	C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₉	C₃²×C₂₅
Frattini	C₅	C₃×C₅×C₂²⋊(C₁₉⋊C₃)
Fitting	C₂²×C₃×C₁₉×C₂₅	C₃
socle	C₂²×C₃×C₅×C₁₉	C₃×C₅
prime radical	C₃×C₅×C₂²⋊(C₁₉⋊C₃)	C₅
cosocle	C₂²×C₅×C₁₉	C₃²×C₅
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×C₂²⋊(C₁₉⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₁₉×C₂₅	C₃	semidirect
6. C₂²×C₁₉×C₂₅	C₃²	semidirect
7. C₃×C₁₉×C₂₅	A₄	semidirect
14. C₃×C₂²⋊(C₁₉⋊C₃)	C₂₅	direct (N × H)
16. C₁₉×C₂₅	C₃×A₄	semidirect
18. C₂²×C₃×C₂₅	C₁₉⋊C₃	semidirect
22. C₂²×C₃×C₁₉	C₃×C₂₅	semidirect
23. C₂²⋊(C₁₉⋊C₃)	C₃×C₂₅	direct (N × H)
30. C₂²×C₂₅	C₃×C₁₉⋊C₃	semidirect
32. C₂²×C₁₉	C₃²×C₂₅	semidirect
34. C₃×C₂₅	C₂²⋊(C₁₉⋊C₃)	direct (N × H)
37. C₃×C₁₉	A₄×C₂₅	semidirect
44. C₂₅	C₃×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
46. C₁₉	C₃×A₄×C₂₅	semidirect
49. C₂²×C₃	C₂₅×C₁₉⋊C₃	semidirect
55. C₂²	C₃×C₂₅×C₁₉⋊C₃	semidirect
57. C₃	C₂₅×C₂²⋊(C₁₉⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×C₂²⋊(C₁₉⋊C₃)	3
C₂²×C₃×C₁₉×C₂₅	3
C₃×C₂₅×C₁₉⋊C₃	4
C₃×C₅×C₂²⋊(C₁₉⋊C₃)	5
C₃×A₄×C₂₅	19

Subgroups — C3×C25×C22⋊(C19⋊C3) #30685519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₅×C₂²⋊(C₁₉⋊C₃) #30685519