Subgroups — C₃⋊#19150292 #30660827

Order 16758.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₇⋊D₁₃₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150292	—	3	1	no	maximal
4	C₁₉×#3862	—	2	1	no	—
5	C₁₉×#3862	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	—	7	2	no	maximal
8	C₇⋊D₁₃₃	—	3	1	no	Hall
9	C₃×C₁₉×ΓL(1,𝔽₈)	—	14	2	no	—
10	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#64425	—	19	1	no	maximal, Hall
12	D₃₉₉	—	7	2	no	—
13	D₃₉₉	—	21	2	no	—
14	ΓL(1,𝔽₈)⋊D₁₉	—	21	2	no	—
15	C₃×#3862	D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₁₉	—	3	2	no	—
17	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	complemented
18	C₁₉×ΓL(1,𝔽₈)	—	14	2	no	—
19	C₁₉×ΓL(1,𝔽₈)	—	14	2	no	—
20	C₃×D₅₇	—	49	1	no	Hall
21	C₃⋊(C₇⋊D₇)	—	19	1	no	—
22	#64425	—	57	1	no	—
23	D₁₃₃	—	21	2	no	—
24	D₁₃₃	—	63	2	no	—
25	C₃²×C₁₉	—	98	1	no	Hall
26	C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented
27	#3862	—	2	1	no	—
28	#3862	D₅₇	1	1	yes	characteristic, complemented
29	C₇×C₁₉	—	3	2	no	—
30	C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
31	C₃⋊AGL(1,𝔽₇)	—	133	2	no	—
32	D₅₇	—	49	1	no	—
33	C₃×D₁₉	—	147	1	no	—
34	C₇⋊D₇	—	57	1	no	Hall
35	C₃×ΓL(1,𝔽₈)	—	14	2	no	—
36	C₃×C₁₉	—	98	1	no	—
37	C₃×C₁₉	—	98	1	no	—
38	C₃×C₁₉	#64425	1	1	yes	characteristic, complemented
39	C₇²	C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
40	D₂₁	—	133	2	no	—
41	D₂₁	—	399	2	no	—
42	AGL(1,𝔽₇)	—	399	2	no	—
43	D₁₉	—	147	1	no	Hall
44	C₃×C₇	—	3	2	no	—
45	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	2	yes	complemented
46	ΓL(1,𝔽₈)	—	14	2	no	—
47	ΓL(1,𝔽₈)	—	14	2	no	—
48	C₁₉	C₃⋊#64425	1	1	yes	characteristic, complemented, Sylow
49	C₃×D₃	—	931	1	no	Hall
50	D₇	—	399	2	no	—
51	D₇	—	1197	2	no	—
52	C₃²	—	98	1	no	Sylow
53	C₇	—	3	2	no	—
54	C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	1	2	yes	complemented
55	C₂×C₃	—	2793	1	no	—
56	D₃	—	931	1	no	—
57	C₃	—	98	1	no	—
58	C₃	—	98	1	no	—
59	C₃	#19150292	1	1	yes	characteristic, complemented
60	C₂	—	2793	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3862	C₂	semidirect
2. C₃⋊(C₇⋊D₁₃₃)	C₃	semidirect
5. C₁₉×#3862	D₃	semidirect
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
10. C₇²×C₁₉	C₃×D₃	semidirect
15. C₃×#3862	D₁₉	semidirect
17. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
26. C₃×C₇²	C₃×D₁₉	semidirect
28. #3862	D₅₇	semidirect
30. C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
38. C₃×C₁₉	#64425	semidirect
39. C₇²	C₃×D₅₇	semidirect
45. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	semidirect
48. C₁₉	C₃⋊#64425	semidirect
54. C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	semidirect
59. C₃	#19150292	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#3862	2
C₃⋊(C₇⋊D₁₃₃)	3
#19150292	3
C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	7
C₃⋊#64425	19

Subgroups — C3⋊#19150292 #30660827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#19150292 #30660827