Subgroups — C₂×C₅×#14555735 #36372575

Order 22230.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14555735	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₂×#14555735	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅×C₁₃×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	#14555735	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×#4294	—	13	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₁₉	C₃×C₅	1	1	yes	characteristic
9	C₅×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₁₃⋊C₉	—	19	1	no	maximal, Hall
11	C₅×#4294	—	13	1	no	Hall
12	C₃×C₁₃×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×C₁₃⋊C₉	—	19	1	no	Hall
14	C₂×C₃×C₅×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic
15	C₂×C₁₃×C₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic
17	C₂×#4294	—	13	1	no	Hall
18	C₃×C₅×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₁₃×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₃⋊C₉	—	19	1	no	Hall
21	C₃×C₅×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
22	C₂×C₅×C₁₉	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
23	#4294	—	13	1	no	Hall
24	C₂×C₅×C₁₃	#4294	1	1	yes	characteristic, complemented, Hall
25	C₁₃⋊C₉	—	19	1	no	Hall
26	C₂×C₃×C₁₉	C₅×C₁₃⋊C₃	1	1	yes	characteristic
27	C₅×C₁₉	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₉	—	247	1	no	Hall
29	C₂×C₃×C₁₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic
30	C₅×C₁₃	C₂×#4294	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₉	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic
32	C₅×C₉	—	247	1	no	Hall
33	C₃×C₁₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
34	C₂×C₁₉	C₅×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	#10625202	1	1	yes	characteristic
36	C₂×C₁₃	C₅×#4294	1	1	yes	characteristic, complemented, Hall
37	C₁₉	C₂×C₅×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	247	1	no	Hall
39	C₃×C₅	C₂×#10625202	1	1	yes	characteristic
40	C₁₃	C₂×C₅×#4294	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	#14555735	1	1	yes	characteristic, direct product factor, Hall
42	C₉	—	247	1	no	Sylow
43	C₂×C₃	C₅×#10625202	1	1	yes	characteristic
44	C₅	C₂×#14555735	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂×C₅×#10625202	1	1	yes	characteristic
46	C₂	C₅×#14555735	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	#10625202
commutator, hypocenter	C₁₃×C₁₉	C₂×C₅×C₉
Frattini	C₃	C₂×C₅×#10625202
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₃×C₁₉	C₃
cosocle	C₃×C₁₃×C₁₉	C₂×C₃×C₅
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14555735	C₂	direct (N × H)
3. C₂×#14555735	C₅	direct (N × H)
5. C₂×C₅×C₁₃×C₁₉	C₉	semidirect
6. #14555735	C₂×C₅	direct (N × H)
9. C₅×C₁₃×C₁₉	C₂×C₉	semidirect
15. C₂×C₁₃×C₁₉	C₅×C₉	semidirect
19. C₁₃×C₁₉	C₂×C₅×C₉	semidirect
22. C₂×C₅×C₁₉	C₁₃⋊C₉	semidirect
24. C₂×C₅×C₁₃	#4294	semidirect
27. C₅×C₁₉	C₂×C₁₃⋊C₉	semidirect
30. C₅×C₁₃	C₂×#4294	semidirect
34. C₂×C₁₉	C₅×C₁₃⋊C₉	semidirect
36. C₂×C₁₃	C₅×#4294	semidirect
37. C₁₉	C₂×C₅×C₁₃⋊C₉	semidirect
40. C₁₃	C₂×C₅×#4294	semidirect
41. C₂×C₅	#14555735	direct (N × H)
44. C₅	C₂×#14555735	direct (N × H)
46. C₂	C₅×#14555735	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#14555735	2
C₂×C₃×C₅×C₁₃×C₁₉	3
C₂×#14555735	5
C₂×C₅×#4294	13
C₂×C₅×C₁₃⋊C₉	19

Subgroups — C2×C5×#14555735 #36372575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#14555735 #36372575