Subgroups — C₁₉×D₇₇₇ #44443294

Order 29526.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₂₅₉	—	3	1	no	maximal, Hall
3	C₇×C₁₉×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₉×D₁₁₁	—	7	1	no	maximal, Hall
5	C₃×C₁₉×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
6	D₇₇₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₉×D₃₇	—	21	1	no	Hall
8	C₁₉×D₂₁	—	37	1	no	maximal, Hall
9	C₃×C₇×C₃₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×C₃₇	D₂₁	1	1	yes	characteristic, complemented, Hall
11	D₂₅₉	—	3	1	no	Hall
12	C₃×C₇×C₁₉	D₃₇	1	1	yes	characteristic, complemented, Hall
13	D₇×C₁₉	—	111	1	no	Hall
14	C₇×C₃₇	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
15	D₁₁₁	—	7	1	no	Hall
16	C₇×C₁₉	D₁₁₁	1	1	yes	characteristic, complemented, Hall
17	D₃×C₁₉	—	259	1	no	Hall
18	C₃×C₃₇	D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
19	D₃₇	—	21	1	no	Hall
20	C₃×C₁₉	D₂₅₉	1	1	yes	characteristic, complemented, Hall
21	D₂₁	—	37	1	no	Hall
22	C₂×C₁₉	—	777	1	no	Hall
23	C₃₇	C₁₉×D₂₁	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	C₁₉×D₃₇	1	1	yes	characteristic, complemented, Hall
25	C₁₉	D₇₇₇	1	1	yes	characteristic, direct product factor, Sylow
26	D₇	—	111	1	no	Hall
27	C₇	C₁₉×D₁₁₁	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	259	1	no	Hall
29	C₃	C₁₉×D₂₅₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	777	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₇₇₇
commutator, cosocle, hypocenter	C₃×C₇×C₃₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉×C₃₇	C₂
LCS	G ▷ C₃×C₇×C₃₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₉×C₃₇	C₂	semidirect
3. C₇×C₁₉×C₃₇	D₃	semidirect
5. C₃×C₁₉×C₃₇	D₇	semidirect
6. D₇₇₇	C₁₉	direct (N × H)
9. C₃×C₇×C₃₇	C₂×C₁₉	semidirect
10. C₁₉×C₃₇	D₂₁	semidirect
12. C₃×C₇×C₁₉	D₃₇	semidirect
14. C₇×C₃₇	D₃×C₁₉	semidirect
16. C₇×C₁₉	D₁₁₁	semidirect
18. C₃×C₃₇	D₇×C₁₉	semidirect
20. C₃×C₁₉	D₂₅₉	semidirect
23. C₃₇	C₁₉×D₂₁	semidirect
24. C₃×C₇	C₁₉×D₃₇	semidirect
25. C₁₉	D₇₇₇	direct (N × H)
27. C₇	C₁₉×D₁₁₁	semidirect
29. C₃	C₁₉×D₂₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₉×C₃₇	2
C₁₉×D₂₅₉	3
C₁₉×D₁₁₁	7
D₇₇₇	19
C₁₉×D₂₁	37

Subgroups — C19×D777 #44443294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₇₇₇ #44443294