Subgroups — C₂×D₁₉×C₆₇⋊C₃ #29504155

Order 15276.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₉×C₆₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₉×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₉×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×C₆₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₉×C₆₇	C₂×C₃	1	2	yes	complemented
7	C₁₉×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₆₇⋊C₃	—	19	1	no	maximal, Hall
9	C₂×C₆₇⋊C₃	—	19	2	no	—
10	C₂×C₆₇⋊C₃	D₁₉	1	1	yes	characteristic, direct product factor
11	C₂²×C₆₇	—	19	1	no	Hall
12	C₂×C₃×D₁₉	—	67	1	no	maximal, Hall
13	C₆₇⋊C₃	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₆₇	—	19	2	no	—
15	C₂×C₆₇	C₃×D₁₉	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₉	—	67	1	no	—
17	C₃×D₁₉	—	67	2	no	—
18	C₂×D₁₉	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₆₇	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₉	—	67	1	no	Hall
21	C₂×C₁₉	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
22	D₁₉	C₂×C₆₇⋊C₃	1	2	yes	direct product factor
23	C₁₉	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1273	1	no	Hall
25	C₂×C₃	—	67	1	no	—
26	C₂×C₃	—	1273	2	no	—
27	C₂²	—	19	1	no	Sylow
28	C₃	—	67	1	no	Sylow
29	C₂	—	19	2	no	—
30	C₂	D₁₉×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₉×C₆₇⋊C₃
commutator, cosocle, hypocenter	C₁₉×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₆₇	C₂×C₃
LCS	G ▷ C₁₉×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₉×C₆₇⋊C₃	C₂	direct (N × H)
2. C₂×C₁₉×C₆₇⋊C₃	C₂	semidirect
3. C₂×D₁₉×C₆₇	C₃	semidirect
4. C₁₉×C₆₇⋊C₃	C₂²	semidirect
5. C₂×C₁₉×C₆₇	C₂×C₃	semidirect
6. D₁₉×C₆₇	C₂×C₃	semidirect
7. C₁₉×C₆₇	C₂²×C₃	semidirect
10. C₂×C₆₇⋊C₃	D₁₉	direct (N × H)
13. C₆₇⋊C₃	C₂×D₁₉	direct (N × H)
15. C₂×C₆₇	C₃×D₁₉	semidirect
18. C₂×D₁₉	C₆₇⋊C₃	direct (N × H)
19. C₆₇	C₂×C₃×D₁₉	semidirect
21. C₂×C₁₉	C₂×C₆₇⋊C₃	semidirect
22. D₁₉	C₂×C₆₇⋊C₃	direct (N × H)
23. C₁₉	C₂²×C₆₇⋊C₃	semidirect
30. C₂	D₁₉×C₆₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₉×C₆₇⋊C₃	2
C₂×C₁₉×C₆₇⋊C₃	2
C₂×D₁₉×C₆₇	3
C₂²×C₆₇⋊C₃	19
C₂×C₃×D₁₉	67

Subgroups — C2×D19×C67⋊C3 #29504155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₉×C₆₇⋊C₃ #29504155