Subgroups — C₅×#19153497 #43274151

Order 28860.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15668363	C₂	1	1	yes	maximal, characteristic
2	C₅×#14515322	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#13089650	C₄	1	1	yes	characteristic, complemented, Hall
4	#19153497	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×D₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic
6	#15668363	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₅×Dic₃₇⋊C₃	—	13	1	no	maximal, Hall
9	#14515322	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	#13089650	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₃₇⋊C₃	—	13	1	no	—
12	D₁₃×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×AGL(1,𝔽₁₃)	—	37	1	no	maximal, Hall
14	C₅×Dic₃₇	—	13	1	no	Hall
15	C₅×C₃₇⋊C₃	—	13	1	no	Hall
16	C₁₃×C₃₇	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	Dic₃₇⋊C₃	—	13	1	no	Hall
18	C₅×D₁₃⋊C₃	—	37	1	no	—
19	C₂×C₅×C₃₇	—	13	1	no	—
20	C₅×#261	—	37	1	no	Hall
21	C₂×C₃₇⋊C₃	—	13	1	no	—
22	C₅×C₁₃⋊C₃	—	37	1	no	Hall
23	C₅×C₃₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
24	AGL(1,𝔽₁₃)	—	37	1	no	Hall
25	Dic₃₇	—	13	1	no	Hall
26	C₅×D₁₃	D₃₇⋊C₃	1	1	yes	characteristic
27	C₃₇⋊C₃	—	13	1	no	Hall
28	D₁₃⋊C₃	—	37	1	no	—
29	C₂×C₃₇	—	13	1	no	—
30	C₅×C₁₃	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄×C₅	—	481	1	no	Hall
32	#261	—	37	1	no	Hall
33	C₁₃⋊C₃	—	37	1	no	Hall
34	C₃₇	C₅×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₅	—	481	1	no	—
36	D₁₃	C₅×D₃₇⋊C₃	1	1	yes	characteristic
37	C₄×C₅	—	481	1	no	Hall
38	C₃×C₅	—	481	1	no	Hall
39	C₁₃	C₅×Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	481	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	481	1	no	—
43	C₅	#19153497	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	481	1	no	Sylow
45	C₃	—	481	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#19153497
commutator, hypocenter	C₁₃×C₃₇	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₃₇	C₃×C₄
prime radical	C₅×#15668363	C₂
cosocle	D₁₃×C₃₇	C₂×C₃×C₅
LCS	G ▷ C₁₃×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#14515322	C₃	semidirect
3. C₅×#13089650	C₄	semidirect
4. #19153497	C₅	direct (N × H)
7. C₅×C₁₃×C₃₇	C₃×C₄	semidirect
9. #14515322	C₃×C₅	semidirect
10. #13089650	C₄×C₅	semidirect
16. C₁₃×C₃₇	C₃×C₄×C₅	semidirect
23. C₅×C₃₇	AGL(1,𝔽₁₃)	semidirect
30. C₅×C₁₃	Dic₃₇⋊C₃	semidirect
34. C₃₇	C₅×AGL(1,𝔽₁₃)	semidirect
39. C₁₃	C₅×Dic₃₇⋊C₃	semidirect
43. C₅	#19153497	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×#15668363	2
C₅×#14515322	3
#19153497	5
C₅×Dic₃₇⋊C₃	13
C₅×AGL(1,𝔽₁₃)	37

Subgroups — C5×#19153497 #43274151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19153497 #43274151