Subgroups — C₂₅×#13093364 #49150201

Order 37050.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#10625202	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₂₅×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#13093364	C₅	1	1	yes	maximal, characteristic
4	C₁₃×C₁₉×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×#10625202	C₂×C₅	1	1	yes	characteristic
6	C₂×C₂₅×C₁₉⋊C₃	—	13	1	no	maximal, Hall
7	C₅×C₁₉×D₁₃	C₃×C₅	1	1	yes	characteristic
8	C₂₅×D₁₃⋊C₃	—	19	1	no	maximal, Hall
9	#13093364	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂₅×C₁₉⋊C₃	—	13	1	no	Hall
11	C₅×C₁₃×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂₅×C₁₃⋊C₃	—	19	1	no	Hall
13	C₂×C₁₉×C₂₅	—	13	1	no	Hall
14	#10625202	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₂₅×D₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₁₉⋊C₃	—	13	1	no	—
17	C₁₉×D₁₃	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
18	C₁₉×C₂₅	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₅×D₁₃⋊C₃	—	19	1	no	—
20	C₁₃×C₂₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₉⋊C₃	—	13	1	no	—
22	C₁₃×C₁₉	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₃⋊C₃	—	19	1	no	—
24	C₂×C₅×C₁₉	—	13	1	no	—
25	C₂×C₃×C₂₅	—	247	1	no	Hall
26	C₅×D₁₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic
27	C₂×C₁₉⋊C₃	—	13	1	no	Hall
28	C₅×C₁₉	C₅×D₁₃⋊C₃	1	1	yes	characteristic
29	D₁₃⋊C₃	—	19	1	no	Hall
30	C₃×C₂₅	—	247	1	no	Hall
31	C₅×C₁₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
32	C₁₉⋊C₃	—	13	1	no	Hall
33	C₂×C₂₅	—	13	1	no	Hall
34	C₁₃⋊C₃	—	19	1	no	Hall
35	C₂×C₁₉	—	13	1	no	Hall
36	C₂×C₃×C₅	—	247	1	no	—
37	D₁₃	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
38	C₂₅	#13093364	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₉	C₂₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	—	247	1	no	—
41	C₁₃	C₂×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	13	1	no	—
43	C₂×C₃	—	247	1	no	Hall
44	C₅	C₅×#13093364	1	1	yes	characteristic
45	C₃	—	247	1	no	Sylow
46	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₅	#13093364
commutator, hypocenter	C₁₃×C₁₉	C₂×C₃×C₂₅
Frattini	C₅	C₅×#13093364
Fitting	C₁₃×C₁₉×C₂₅	C₂×C₃
socle, cosocle	C₅×C₁₃×C₁₉	C₂×C₃×C₅
prime radical	C₅×#13093364	C₅
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×#10625202	C₂	semidirect
2. C₁₉×C₂₅×D₁₃	C₃	semidirect
4. C₁₃×C₁₉×C₂₅	C₂×C₃	semidirect
9. #13093364	C₂₅	direct (N × H)
14. #10625202	C₂×C₂₅	semidirect
15. C₂₅×D₁₃	C₁₉⋊C₃	semidirect
17. C₁₉×D₁₃	C₃×C₂₅	semidirect
18. C₁₉×C₂₅	D₁₃⋊C₃	semidirect
20. C₁₃×C₂₅	C₂×C₁₉⋊C₃	semidirect
22. C₁₃×C₁₉	C₂×C₃×C₂₅	semidirect
37. D₁₃	C₂₅×C₁₉⋊C₃	semidirect
38. C₂₅	#13093364	direct (N × H)
39. C₁₉	C₂₅×D₁₃⋊C₃	semidirect
41. C₁₃	C₂×C₂₅×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×#10625202	2
C₁₉×C₂₅×D₁₃	3
C₅×#13093364	5
C₂×C₂₅×C₁₉⋊C₃	13
C₂₅×D₁₃⋊C₃	19

Subgroups — C25×#13093364 #49150201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#13093364 #49150201