Finite Group Databasebeta

← C₃×C₉×C₃₉₇ #24924298

Subgroups — C₃×C₉×C₃₉₇ #24924298

Order 10719.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₉₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₃₉₇	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₃₉₇	C₉	1	3	yes	direct product factor
4	C₃×C₃₉₇	C₃²	1	1	yes	characteristic
5	C₃₉₇	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₃×C₉	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃²	C₃×C₃₉₇	1	1	yes	characteristic
8	C₉	C₃×C₃₉₇	1	3	yes	direct product factor
9	C₃	C₉×C₃₉₇	1	3	yes	direct product factor
10	C₃	C₃²×C₃₉₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃²×C₃₉₇
socle, prime radical	C₃²×C₃₉₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₃₉₇	C₃	direct (N × H)
3. C₃×C₃₉₇	C₉	direct (N × H)
5. C₃₉₇	C₃×C₉	direct (N × H)
6. C₃×C₉	C₃₉₇	direct (N × H)
8. C₉	C₃×C₃₉₇	direct (N × H)
9. C₃	C₉×C₃₉₇	direct (N × H)