Subgroups — C₃×C₁₉×#87705 #36384501

Order 22743.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#87705	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₇×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×C₁₉⋊C₃	—	7	1	no	maximal, Hall
4	C₇×C₁₉²	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×#87705	C₁₉	1	1	yes	maximal, characteristic, direct product factor
6	C₃×C₁₉×ΓL(1,𝔽₈)	—	19	1	no	maximal
7	C₃×C₁₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
8	C₁₉×C₁₉⋊C₃	—	7	3	no	—
9	C₃×C₇×C₁₉	—	3	6	no	—
10	C₃×C₇×C₁₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
11	C₃×C₇×C₁₉	C₃×C₁₉	1	1	yes	characteristic, complemented
12	#87705	C₃×C₁₉	1	3	yes	direct product factor
13	C₁₉×ΓL(1,𝔽₈)	—	19	3	no	—
14	C₁₉²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
15	C₃²×C₁₉	—	133	1	no	—
16	C₃×C₁₉⋊C₃	—	7	1	no	—
17	C₇×C₁₉	—	3	6	no	—
18	C₇×C₁₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
19	C₇×C₁₉	C₃²×C₁₉	1	1	yes	characteristic, complemented
20	C₃×ΓL(1,𝔽₈)	—	19	1	no	Hall
21	C₃×C₁₉	—	3	6	no	—
22	C₃×C₁₉	—	133	3	no	—
23	C₃×C₁₉	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₃×C₁₉	#87705	1	1	yes	characteristic, direct product factor
25	C₁₉⋊C₃	—	7	3	no	—
26	C₃×C₇	C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented
27	ΓL(1,𝔽₈)	—	19	3	no	—
28	C₁₉	—	3	6	no	—
29	C₁₉	C₃×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
30	C₁₉	C₃×#87705	1	1	yes	characteristic, direct product factor
31	C₃²	—	133	1	no	Sylow
32	C₇	C₃×C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	133	3	no	—
34	C₃	C₁₉×#87705	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#87705
commutator, cosocle, hypocenter	C₇×C₁₉	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉²	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×#87705	C₃	direct (N × H)
2. C₃×C₇×C₁₉²	C₃	semidirect
4. C₇×C₁₉²	C₃²	semidirect
5. C₃×#87705	C₁₉	direct (N × H)
7. C₃×C₁₉²	ΓL(1,𝔽₈)	semidirect
10. C₃×C₇×C₁₉	C₁₉⋊C₃	semidirect
11. C₃×C₇×C₁₉	C₃×C₁₉	semidirect
12. #87705	C₃×C₁₉	direct (N × H)
14. C₁₉²	C₃×ΓL(1,𝔽₈)	semidirect
18. C₇×C₁₉	C₃×C₁₉⋊C₃	semidirect
19. C₇×C₁₉	C₃²×C₁₉	semidirect
23. C₃×C₁₉	C₁₉×ΓL(1,𝔽₈)	semidirect
24. C₃×C₁₉	#87705	direct (N × H)
26. C₃×C₇	C₁₉×C₁₉⋊C₃	semidirect
29. C₁₉	C₃×C₁₉×ΓL(1,𝔽₈)	semidirect
30. C₁₉	C₃×#87705	direct (N × H)
32. C₇	C₃×C₁₉×C₁₉⋊C₃	semidirect
34. C₃	C₁₉×#87705	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#87705	3
C₃×C₇×C₁₉²	3
C₃×C₁₉×C₁₉⋊C₃	7
C₃×#87705	19
C₃×C₁₉×ΓL(1,𝔽₈)	19

Subgroups — C3×C19×#87705 #36384501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#87705 #36384501