Finite Group Databasebeta

← C₃×C₇³×C₂₉ #72206708

Subgroups — C₃×C₇³×C₂₉ #72206708

Order 29841.

464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇³×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇²×C₂₉	C₇	1	57	yes	maximal, direct product factor
3	C₇²×C₂₉	C₃×C₇	1	57	yes	direct product factor
4	C₃×C₇³	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₂₉	C₇²	1	57	yes	direct product factor
6	C₇³	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₇×C₂₉	C₃×C₇²	1	57	yes	direct product factor
8	C₃×C₇²	C₇×C₂₉	1	57	yes	direct product factor
9	C₃×C₂₉	C₇³	1	1	yes	characteristic, direct product factor, Hall
10	C₇²	C₃×C₇×C₂₉	1	57	yes	direct product factor
11	C₂₉	C₃×C₇³	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₇	C₇²×C₂₉	1	57	yes	direct product factor
13	C₇	C₃×C₇²×C₂₉	1	57	yes	direct product factor
14	C₃	C₇³×C₂₉	1	1	yes	characteristic, direct product factor, Sylow

	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. C₇³×C₂₉	C₃	direct (N × H)
2. C₃×C₇²×C₂₉	C₇	direct (N × H)
3. C₇²×C₂₉	C₃×C₇	direct (N × H)
4. C₃×C₇³	C₂₉	direct (N × H)
5. C₃×C₇×C₂₉	C₇²	direct (N × H)
6. C₇³	C₃×C₂₉	direct (N × H)
7. C₇×C₂₉	C₃×C₇²	direct (N × H)
8. C₃×C₇²	C₇×C₂₉	direct (N × H)
9. C₃×C₂₉	C₇³	direct (N × H)
10. C₇²	C₃×C₇×C₂₉	direct (N × H)
11. C₂₉	C₃×C₇³	direct (N × H)
12. C₃×C₇	C₇²×C₂₉	direct (N × H)
13. C₇	C₃×C₇²×C₂₉	direct (N × H)
14. C₃	C₇³×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇³×C₂₉	3
C₃×C₇²×C₂₉	7
C₃×C₇³	29