Finite Group Databasebeta

← C₃²×C₇²×C₁₉ #22552713

Subgroups — C₃²×C₇²×C₁₉ #22552713

Order 8379.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₁₉	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₇×C₁₉	C₇	1	8	yes	maximal, direct product factor
3	C₇²×C₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃²×C₇²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇×C₁₉	C₃×C₇	1	32	yes	direct product factor
6	C₃²×C₁₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇²	C₃×C₁₉	1	4	yes	direct product factor
8	C₇×C₁₉	C₃²×C₇	1	8	yes	direct product factor
9	C₃²×C₇	C₇×C₁₉	1	8	yes	direct product factor
10	C₃×C₁₉	C₃×C₇²	1	4	yes	direct product factor
11	C₇²	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₇	C₃×C₇×C₁₉	1	32	yes	direct product factor
13	C₁₉	C₃²×C₇²	1	1	yes	characteristic, direct product factor, Sylow
14	C₃²	C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₇	C₃²×C₇×C₁₉	1	8	yes	direct product factor
16	C₃	C₃×C₇²×C₁₉	1	4	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. C₃×C₇²×C₁₉	C₃	direct (N × H)
2. C₃²×C₇×C₁₉	C₇	direct (N × H)
3. C₇²×C₁₉	C₃²	direct (N × H)
4. C₃²×C₇²	C₁₉	direct (N × H)
5. C₃×C₇×C₁₉	C₃×C₇	direct (N × H)
6. C₃²×C₁₉	C₇²	direct (N × H)
7. C₃×C₇²	C₃×C₁₉	direct (N × H)
8. C₇×C₁₉	C₃²×C₇	direct (N × H)
9. C₃²×C₇	C₇×C₁₉	direct (N × H)
10. C₃×C₁₉	C₃×C₇²	direct (N × H)
11. C₇²	C₃²×C₁₉	direct (N × H)
12. C₃×C₇	C₃×C₇×C₁₉	direct (N × H)
13. C₁₉	C₃²×C₇²	direct (N × H)
14. C₃²	C₇²×C₁₉	direct (N × H)
15. C₇	C₃²×C₇×C₁₉	direct (N × H)
16. C₃	C₃×C₇²×C₁₉	direct (N × H)