Finite Group Databasebeta

← C₂×C₁₉×C₆₂₅ #72201068

Subgroups — C₂×C₁₉×C₆₂₅ #72201068

Order 23750.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₂₅	C₅	1	1	yes	maximal, characteristic
2	C₁₉×C₆₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₂₅	C₂×C₅	1	1	yes	characteristic
4	C₂×C₆₂₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₉×C₂₅	C₂₅	1	1	yes	characteristic
6	C₆₂₅	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₁₉×C₂₅	C₂×C₂₅	1	1	yes	characteristic
8	C₂×C₁₂₅	C₅×C₁₉	1	1	yes	characteristic
9	C₂×C₅×C₁₉	C₁₂₅	1	1	yes	characteristic
10	C₁₂₅	C₂×C₅×C₁₉	1	1	yes	characteristic
11	C₅×C₁₉	C₂×C₁₂₅	1	1	yes	characteristic
12	C₂×C₂₅	C₁₉×C₂₅	1	1	yes	characteristic
13	C₂×C₁₉	C₆₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂₅	C₂×C₁₉×C₂₅	1	1	yes	characteristic
15	C₁₉	C₂×C₆₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₅	C₁₉×C₁₂₅	1	1	yes	characteristic
17	C₅	C₂×C₁₉×C₁₂₅	1	1	yes	characteristic
18	C₂	C₁₉×C₆₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₂₅	C₂×C₅×C₁₉
socle, prime radical	C₂×C₅×C₁₉	C₁₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×C₆₂₅	C₂	direct (N × H)
4. C₂×C₆₂₅	C₁₉	direct (N × H)
6. C₆₂₅	C₂×C₁₉	direct (N × H)
13. C₂×C₁₉	C₆₂₅	direct (N × H)
15. C₁₉	C₂×C₆₂₅	direct (N × H)
18. C₂	C₁₉×C₆₂₅	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×C₁₉×C₁₂₅	5
C₁₉×C₆₂₅	2
C₂×C₆₂₅	19