Finite Group Databasebeta

← C₃³×C₃₉₇ #24924301

Subgroups — C₃³×C₃₉₇ #24924301

Order 10719.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₉₇	C₃	1	13	yes	maximal, direct product factor
2	C₃×C₃₉₇	C₃²	1	13	yes	direct product factor
3	C₃₉₇	C₃³	1	1	yes	characteristic, direct product factor, Sylow
4	C₃³	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃²	C₃×C₃₉₇	1	13	yes	direct product factor
6	C₃	C₃²×C₃₉₇	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×C₃₉₇	C₃	direct (N × H)
2. C₃×C₃₉₇	C₃²	direct (N × H)
3. C₃₉₇	C₃³	direct (N × H)
4. C₃³	C₃₉₇	direct (N × H)
5. C₃²	C₃×C₃₉₇	direct (N × H)
6. C₃	C₃²×C₃₉₇	direct (N × H)