Finite Group Databasebeta

← C₃³×C₅×C₇₉ #72189227

Subgroups — C₃³×C₅×C₇₉ #72189227

Order 10665.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇₉	C₃	1	13	yes	maximal, direct product factor
2	C₃³×C₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇₉	C₃²	1	13	yes	direct product factor
4	C₃²×C₇₉	C₃×C₅	1	13	yes	direct product factor
5	C₅×C₇₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₇₉	C₃²×C₅	1	13	yes	direct product factor
7	C₃³×C₅	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇₉	C₃³×C₅	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²×C₅	C₃×C₇₉	1	13	yes	direct product factor
10	C₃³	C₅×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×C₅	C₃²×C₇₉	1	13	yes	direct product factor
12	C₃²	C₃×C₅×C₇₉	1	13	yes	direct product factor
13	C₅	C₃³×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₃²×C₅×C₇₉	1	13	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇₉	C₃	direct (N × H)
2. C₃³×C₇₉	C₅	direct (N × H)
3. C₃×C₅×C₇₉	C₃²	direct (N × H)
4. C₃²×C₇₉	C₃×C₅	direct (N × H)
5. C₅×C₇₉	C₃³	direct (N × H)
6. C₃×C₇₉	C₃²×C₅	direct (N × H)
7. C₃³×C₅	C₇₉	direct (N × H)
8. C₇₉	C₃³×C₅	direct (N × H)
9. C₃²×C₅	C₃×C₇₉	direct (N × H)
10. C₃³	C₅×C₇₉	direct (N × H)
11. C₃×C₅	C₃²×C₇₉	direct (N × H)
12. C₃²	C₃×C₅×C₇₉	direct (N × H)
13. C₅	C₃³×C₇₉	direct (N × H)
14. C₃	C₃²×C₅×C₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇₉	3
C₃³×C₇₉	5
C₃³×C₅	79