Subgroups — C₃×C₈×C₁₉×C₆₇ #72207331

Order 30552.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₉×C₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₄×C₁₉×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₁₉×C₆₇	C₄	1	1	yes	characteristic
4	C₄×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₉×C₆₇	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₉×C₆₇	C₃×C₄	1	1	yes	characteristic
7	C₃×C₈×C₆₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₆₇	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄×C₆₇	C₂×C₁₉	1	1	yes	characteristic
10	C₈×C₆₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₈×C₁₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₆₇	C₄×C₁₉	1	1	yes	characteristic
13	C₄×C₆₇	C₂×C₃×C₁₉	1	1	yes	characteristic
14	C₃×C₄×C₁₉	C₂×C₆₇	1	1	yes	characteristic
15	C₃×C₆₇	C₈×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₈×C₁₉	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₇	C₃×C₄×C₁₉	1	1	yes	characteristic
18	C₂×C₃×C₁₉	C₄×C₆₇	1	1	yes	characteristic
19	C₄×C₁₉	C₂×C₃×C₆₇	1	1	yes	characteristic
20	C₆₇	C₃×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₉	C₈×C₆₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₉	C₃×C₄×C₆₇	1	1	yes	characteristic
23	C₃×C₈	C₁₉×C₆₇	1	1	yes	characteristic, direct product factor, Hall
24	C₁₉	C₃×C₈×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₄	C₂×C₁₉×C₆₇	1	1	yes	characteristic
26	C₈	C₃×C₁₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₄×C₁₉×C₆₇	1	1	yes	characteristic
28	C₄	C₂×C₃×C₁₉×C₆₇	1	1	yes	characteristic
29	C₃	C₈×C₁₉×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₄×C₁₉×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₉×C₆₇
socle, prime radical	C₂×C₃×C₁₉×C₆₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×C₁₉×C₆₇	C₃	direct (N × H)
5. C₃×C₁₉×C₆₇	C₈	direct (N × H)
7. C₃×C₈×C₆₇	C₁₉	direct (N × H)
8. C₁₉×C₆₇	C₃×C₈	direct (N × H)
10. C₈×C₆₇	C₃×C₁₉	direct (N × H)
11. C₃×C₈×C₁₉	C₆₇	direct (N × H)
15. C₃×C₆₇	C₈×C₁₉	direct (N × H)
16. C₈×C₁₉	C₃×C₆₇	direct (N × H)
20. C₆₇	C₃×C₈×C₁₉	direct (N × H)
21. C₃×C₁₉	C₈×C₆₇	direct (N × H)
23. C₃×C₈	C₁₉×C₆₇	direct (N × H)
24. C₁₉	C₃×C₈×C₆₇	direct (N × H)
26. C₈	C₃×C₁₉×C₆₇	direct (N × H)
29. C₃	C₈×C₁₉×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₉×C₆₇	3
C₃×C₄×C₁₉×C₆₇	2
C₃×C₈×C₆₇	19
C₃×C₈×C₁₉	67

Subgroups — C3×C8×C19×C67 #72207331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₁₉×C₆₇ #72207331