Subgroups — C₃×C₇²×C₁₁×C₁₉ #44502172

Order 30723.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇×C₁₁×C₁₉	C₇	1	8	yes	maximal, direct product factor
3	C₃×C₇²×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇²×C₁₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₁×C₁₉	C₃×C₇	1	8	yes	direct product factor
6	C₇²×C₁₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₁₁×C₁₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₇²×C₁₁	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₁₉	C₇×C₁₁	1	8	yes	direct product factor
10	C₃×C₇×C₁₁	C₇×C₁₉	1	8	yes	direct product factor
11	C₁₁×C₁₉	C₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₇²	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₁₉	C₃×C₇×C₁₁	1	8	yes	direct product factor
14	C₇×C₁₁	C₃×C₇×C₁₉	1	8	yes	direct product factor
15	C₃×C₁₉	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₇²	C₃×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₁₁	C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₇	C₇×C₁₁×C₁₉	1	8	yes	direct product factor
19	C₁₉	C₃×C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₃×C₇²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₃×C₇×C₁₁×C₁₉	1	8	yes	direct product factor
22	C₃	C₇²×C₁₁×C₁₉	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. C₇²×C₁₁×C₁₉	C₃	direct (N × H)
2. C₃×C₇×C₁₁×C₁₉	C₇	direct (N × H)
3. C₃×C₇²×C₁₉	C₁₁	direct (N × H)
4. C₃×C₇²×C₁₁	C₁₉	direct (N × H)
5. C₇×C₁₁×C₁₉	C₃×C₇	direct (N × H)
6. C₇²×C₁₉	C₃×C₁₁	direct (N × H)
7. C₃×C₁₁×C₁₉	C₇²	direct (N × H)
8. C₇²×C₁₁	C₃×C₁₉	direct (N × H)
9. C₃×C₇×C₁₉	C₇×C₁₁	direct (N × H)
10. C₃×C₇×C₁₁	C₇×C₁₉	direct (N × H)
11. C₁₁×C₁₉	C₃×C₇²	direct (N × H)
12. C₃×C₇²	C₁₁×C₁₉	direct (N × H)
13. C₇×C₁₉	C₃×C₇×C₁₁	direct (N × H)
14. C₇×C₁₁	C₃×C₇×C₁₉	direct (N × H)
15. C₃×C₁₉	C₇²×C₁₁	direct (N × H)
16. C₇²	C₃×C₁₁×C₁₉	direct (N × H)
17. C₃×C₁₁	C₇²×C₁₉	direct (N × H)
18. C₃×C₇	C₇×C₁₁×C₁₉	direct (N × H)
19. C₁₉	C₃×C₇²×C₁₁	direct (N × H)
20. C₁₁	C₃×C₇²×C₁₉	direct (N × H)
21. C₇	C₃×C₇×C₁₁×C₁₉	direct (N × H)
22. C₃	C₇²×C₁₁×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₁×C₁₉	3
C₃×C₇×C₁₁×C₁₉	7
C₃×C₇²×C₁₉	11
C₃×C₇²×C₁₁	19

Subgroups — C3×C72×C11×C19 #44502172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×C₁₁×C₁₉ #44502172