Subgroups — C₇×C₂₅×C₁₃⋊C₉ #35205997

Order 20475.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₂₅	C₃	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃⋊C₉	C₅	1	1	yes	maximal, characteristic
3	C₂₅×C₁₃⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₂₅	C₉	1	1	yes	characteristic, complemented, Hall
5	C₇×C₉×C₂₅	—	13	1	no	maximal, Hall
6	C₃×C₅×C₇×C₁₃	C₃×C₅	1	1	yes	characteristic
7	C₃×C₁₃×C₂₅	C₃×C₇	1	1	yes	characteristic
8	C₇×C₁₃⋊C₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₃⋊C₉	C₅×C₇	1	1	yes	characteristic
10	C₃×C₇×C₂₅	C₁₃⋊C₃	1	1	yes	characteristic
11	C₅×C₇×C₁₃	C₅×C₉	1	1	yes	characteristic
12	C₁₃×C₂₅	C₇×C₉	1	1	yes	characteristic, complemented, Hall
13	C₅×C₇×C₉	—	13	1	no	—
14	C₃×C₇×C₁₃	C₃×C₂₅	1	1	yes	characteristic
15	C₉×C₂₅	—	13	1	no	Hall
16	C₃×C₅×C₁₃	C₃×C₅×C₇	1	1	yes	characteristic
17	C₇×C₂₅	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃⋊C₉	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅×C₇	C₅×C₁₃⋊C₃	1	1	yes	characteristic
20	C₇×C₁₃	C₉×C₂₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₂₅	C₇×C₁₃⋊C₃	1	1	yes	characteristic
22	C₅×C₁₃	C₅×C₇×C₉	1	1	yes	characteristic
23	C₇×C₉	—	13	1	no	Hall
24	C₅×C₉	—	13	1	no	—
25	C₃×C₁₃	C₃×C₇×C₂₅	1	1	yes	characteristic
26	C₅×C₇	C₅×C₁₃⋊C₉	1	1	yes	characteristic
27	C₂₅	C₇×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₃×C₇	C₂₅×C₁₃⋊C₃	1	1	yes	characteristic
29	C₃×C₅	C₅×C₇×C₁₃⋊C₃	1	1	yes	characteristic
30	C₁₃	C₇×C₉×C₂₅	1	1	yes	characteristic, complemented, Sylow
31	C₉	—	13	1	no	Sylow
32	C₇	C₂₅×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₅	C₅×C₇×C₁₃⋊C₉	1	1	yes	characteristic
34	C₃	C₇×C₂₅×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₇×C₂₅	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₇×C₉×C₂₅
Frattini	C₃×C₅	C₅×C₇×C₁₃⋊C₃
Fitting	C₃×C₇×C₁₃×C₂₅	C₃
socle, prime radical	C₃×C₅×C₇×C₁₃	C₃×C₅
cosocle	C₃×C₅×C₁₃	C₃×C₅×C₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇×C₂₅

Complements

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

N	H ≅ G/N	type
3. C₂₅×C₁₃⋊C₉	C₇	direct (N × H)
4. C₇×C₁₃×C₂₅	C₉	semidirect
8. C₇×C₁₃⋊C₉	C₂₅	direct (N × H)
12. C₁₃×C₂₅	C₇×C₉	semidirect
17. C₇×C₂₅	C₁₃⋊C₉	direct (N × H)
18. C₁₃⋊C₉	C₇×C₂₅	direct (N × H)
20. C₇×C₁₃	C₉×C₂₅	semidirect
27. C₂₅	C₇×C₁₃⋊C₉	direct (N × H)
30. C₁₃	C₇×C₉×C₂₅	semidirect
32. C₇	C₂₅×C₁₃⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₂₅	3
C₅×C₇×C₁₃⋊C₉	5
C₂₅×C₁₃⋊C₉	7
C₇×C₉×C₂₅	13

Subgroups — C7×C25×C13⋊C9 #35205997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₂₅×C₁₃⋊C₉ #35205997