Subgroups — C₃×C₄×C₁₉×C₄₇ #24924258

Order 10716.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×C₄₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₄₇	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₄×C₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄₇	C₂×C₁₉	1	1	yes	characteristic
8	C₃×C₄×C₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₄₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₄₇	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₉	C₂×C₄₇	1	1	yes	characteristic
12	C₂×C₄₇	C₂×C₃×C₁₉	1	1	yes	characteristic
13	C₄×C₁₉	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₉	C₄×C₄₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄₇	C₃×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	C₂×C₃×C₄₇	1	1	yes	characteristic
17	C₁₉	C₃×C₄×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₉×C₄₇	1	1	yes	characteristic
20	C₄	C₃×C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₄×C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₁₉×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₁₉×C₄₇
socle, prime radical	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×C₄₇	C₃	direct (N × H)
3. C₃×C₁₉×C₄₇	C₄	direct (N × H)
5. C₁₉×C₄₇	C₃×C₄	direct (N × H)
6. C₃×C₄×C₄₇	C₁₉	direct (N × H)
8. C₃×C₄×C₁₉	C₄₇	direct (N × H)
9. C₄×C₄₇	C₃×C₁₉	direct (N × H)
10. C₃×C₄₇	C₄×C₁₉	direct (N × H)
13. C₄×C₁₉	C₃×C₄₇	direct (N × H)
14. C₃×C₁₉	C₄×C₄₇	direct (N × H)
15. C₄₇	C₃×C₄×C₁₉	direct (N × H)
17. C₁₉	C₃×C₄×C₄₇	direct (N × H)
18. C₃×C₄	C₁₉×C₄₇	direct (N × H)
20. C₄	C₃×C₁₉×C₄₇	direct (N × H)
21. C₃	C₄×C₁₉×C₄₇	direct (N × H)

Subgroups — C3×C4×C19×C47 #24924258

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₄×C₁₉×C₄₇ #24924258