Subgroups — C₃×C₁₉²×Dic₇ #44476555

Order 30324.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₉²	C₂	1	1	yes	maximal, characteristic
2	C₁₉²×Dic₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₉²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₉²	—	7	1	no	maximal, Hall
6	C₇×C₁₉²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₉²	D₇	1	1	yes	characteristic
8	C₃×C₁₉×Dic₇	C₁₉	1	20	yes	maximal, direct product factor
9	C₄×C₁₉²	—	7	1	no	Hall
10	C₃×C₁₉²	Dic₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₉	C₂×C₁₉	1	20	yes	—
12	C₂×C₁₉²	C₃×D₇	1	1	yes	characteristic
13	C₁₉×Dic₇	C₃×C₁₉	1	20	yes	direct product factor
14	C₃×C₇×C₁₉	C₄×C₁₉	1	20	yes	complemented
15	C₁₉²	C₃×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₇×C₁₉	C₂×C₃×C₁₉	1	20	yes	—
17	C₃×C₄×C₁₉	—	7	20	no	—
18	C₇×C₁₉	C₃×C₄×C₁₉	1	20	yes	complemented
19	C₂×C₃×C₁₉	D₇×C₁₉	1	20	yes	—
20	C₃×Dic₇	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₁₉	—	7	20	no	—
22	C₃×C₁₉	C₁₉×Dic₇	1	20	yes	direct product factor
23	C₂×C₃×C₇	C₂×C₁₉²	1	1	yes	characteristic
24	C₂×C₁₉	C₃×D₇×C₁₉	1	20	yes	—
25	Dic₇	C₃×C₁₉²	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₇	C₄×C₁₉²	1	1	yes	characteristic, complemented, Hall
27	C₁₉	C₃×C₁₉×Dic₇	1	20	yes	direct product factor
28	C₂×C₇	C₂×C₃×C₁₉²	1	1	yes	characteristic
29	C₃×C₄	—	7	1	no	Hall
30	C₇	C₃×C₄×C₁₉²	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₇×C₁₉²	1	1	yes	characteristic
32	C₄	—	7	1	no	Sylow
33	C₃	C₁₉²×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×D₇×C₁₉²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉²	D₇
commutator, hypocenter	C₇	C₃×C₄×C₁₉²
Frattini	C₂	C₃×D₇×C₁₉²
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₉²	C₂
cosocle	C₂×C₇	C₂×C₃×C₁₉²
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₉²

Complements

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

N	H ≅ G/N	type
2. C₁₉²×Dic₇	C₃	direct (N × H)
3. C₃×C₇×C₁₉²	C₄	semidirect
6. C₇×C₁₉²	C₃×C₄	semidirect
8. C₃×C₁₉×Dic₇	C₁₉	direct (N × H)
10. C₃×C₁₉²	Dic₇	direct (N × H)
13. C₁₉×Dic₇	C₃×C₁₉	direct (N × H)
14. C₃×C₇×C₁₉	C₄×C₁₉	semidirect
15. C₁₉²	C₃×Dic₇	direct (N × H)
18. C₇×C₁₉	C₃×C₄×C₁₉	semidirect
20. C₃×Dic₇	C₁₉²	direct (N × H)
22. C₃×C₁₉	C₁₉×Dic₇	direct (N × H)
25. Dic₇	C₃×C₁₉²	direct (N × H)
26. C₃×C₇	C₄×C₁₉²	semidirect
27. C₁₉	C₃×C₁₉×Dic₇	direct (N × H)
30. C₇	C₃×C₄×C₁₉²	semidirect
33. C₃	C₁₉²×Dic₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₉²	2
C₁₉²×Dic₇	3
C₃×C₄×C₁₉²	7
C₃×C₁₉×Dic₇	19

Subgroups — C3×C192×Dic7 #44476555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉²×Dic₇ #44476555