Subgroups — C₄×C₅×#10625202 #28414718

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#10625202	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#10625202	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×#10625202	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×#10625202	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₅×C₁₉⋊C₃	—	13	1	no	maximal, Hall
9	C₄×C₁₃×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₄×C₅×C₁₃⋊C₃	—	19	1	no	maximal, Hall
11	#10625202	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₁₉⋊C₃	—	13	1	no	—
13	C₂×C₁₃×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
14	C₂×C₅×C₁₃⋊C₃	—	19	1	no	—
15	C₄×C₅×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₅×C₁₉⋊C₃	—	13	1	no	Hall
17	C₄×C₅×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₁₃×C₁₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
19	C₄×C₁₉⋊C₃	—	13	1	no	Hall
20	C₅×C₁₃⋊C₃	—	19	1	no	Hall
21	C₂×C₅×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
22	C₄×C₁₃⋊C₃	—	19	1	no	Hall
23	C₂×C₅×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
24	C₂×C₁₉⋊C₃	—	13	1	no	—
25	C₅×C₁₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃⋊C₃	—	19	1	no	—
27	C₄×C₁₉	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₅×C₁₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄×C₅	—	247	1	no	Hall
30	C₁₉⋊C₃	—	13	1	no	Hall
31	C₄×C₁₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₁₃⋊C₃	—	19	1	no	Hall
33	C₂×C₁₉	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic
34	C₂×C₃×C₅	—	247	1	no	—
35	C₂×C₁₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
36	C₄×C₅	#10625202	1	1	yes	characteristic, direct product factor, Hall
37	C₁₉	C₄×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	—	247	1	no	Hall
39	C₁₃	C₄×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	247	1	no	Hall
41	C₂×C₅	C₂×#10625202	1	1	yes	characteristic
42	C₂×C₃	—	247	1	no	—
43	C₅	C₄×#10625202	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₅×#10625202	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	247	1	no	Sylow
46	C₂	C₂×C₅×#10625202	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	#10625202
commutator, hypocenter	C₁₃×C₁₉	C₃×C₄×C₅
Frattini	C₂	C₂×C₅×#10625202
Fitting	C₄×C₅×C₁₃×C₁₉	C₃
socle	C₂×C₅×C₁₃×C₁₉	C₂×C₃
prime radical	C₂×C₅×#10625202	C₂
cosocle	C₂×C₁₃×C₁₉	C₂×C₃×C₅
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₁₃×C₁₉	C₃	semidirect
3. C₅×#10625202	C₄	direct (N × H)
4. C₄×#10625202	C₅	direct (N × H)
7. C₅×C₁₃×C₁₉	C₃×C₄	semidirect
9. C₄×C₁₃×C₁₉	C₃×C₅	semidirect
11. #10625202	C₄×C₅	direct (N × H)
15. C₄×C₅×C₁₉	C₁₃⋊C₃	semidirect
17. C₄×C₅×C₁₃	C₁₉⋊C₃	semidirect
18. C₁₃×C₁₉	C₃×C₄×C₅	semidirect
25. C₅×C₁₉	C₄×C₁₃⋊C₃	semidirect
27. C₄×C₁₉	C₅×C₁₃⋊C₃	semidirect
28. C₅×C₁₃	C₄×C₁₉⋊C₃	semidirect
31. C₄×C₁₃	C₅×C₁₉⋊C₃	semidirect
36. C₄×C₅	#10625202	direct (N × H)
37. C₁₉	C₄×C₅×C₁₃⋊C₃	semidirect
39. C₁₃	C₄×C₅×C₁₉⋊C₃	semidirect
43. C₅	C₄×#10625202	direct (N × H)
44. C₄	C₅×#10625202	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#10625202	2
C₄×C₅×C₁₃×C₁₉	3
C₄×#10625202	5
C₄×C₅×C₁₉⋊C₃	13
C₄×C₅×C₁₃⋊C₃	19

Subgroups — C4×C5×#10625202 #28414718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#10625202 #28414718