Subgroups — (C₁₉⋊C₃)⋊#64418 #30660730

Order 16758.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊#64418	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×(C₁₉⋊C₃)⋊D₇	—	3	1	no	maximal
4	C₁₉⋊#3862	—	2	1	no	—
5	C₁₉×#3862	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇²×C₁₉⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₇×D₁₃₃	—	3	1	no	Hall
8	ΓL(1,𝔽₈)×C₁₉⋊C₃	—	14	1	no	—
9	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃×#64418	—	19	1	no	maximal, Hall
11	(C₁₉⋊C₃)⋊D₇	—	3	1	no	—
12	C₇×D₁₉⋊C₃	—	21	1	no	—
13	C₃×#3862	—	19	1	no	Hall
14	#87705	—	14	1	no	—
15	#87704	—	14	1	no	—
16	C₇×C₁₉⋊C₃	—	2	1	no	—
17	C₇×C₁₉⋊C₃	—	3	1	no	—
18	C₇×C₁₉⋊C₃	—	3	1	no	—
19	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
20	C₃⋊(D₁₉⋊C₃)	—	49	1	no	maximal, Hall
21	C₃×C₇×D₇	—	57	1	no	—
22	#64418	—	19	1	no	—
23	D₁₃₃	—	3	1	no	—
24	C₇×D₁₉	—	21	1	no	—
25	C₃×C₁₉⋊C₃	—	49	1	no	Hall
26	C₃×C₇²	—	19	1	no	—
27	#3862	—	38	1	no	—
28	#3862	D₁₉⋊C₃	1	1	yes	characteristic, complemented
29	C₇×C₁₉	—	2	1	no	—
30	C₇×C₁₉	—	3	1	no	—
31	C₇×C₁₉	—	3	1	no	—
32	D₅₇	—	49	1	no	—
33	D₁₉⋊C₃	—	21	1	no	—
34	C₇×D₇	—	57	1	no	Hall
35	C₃×ΓL(1,𝔽₈)	—	266	1	no	—
36	C₃×C₁₉	—	49	1	no	—
37	C₁₉⋊C₃	—	98	1	no	—
38	C₁₉⋊C₃	#64418	1	1	yes	characteristic, complemented
39	C₇²	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₇	—	399	1	no	—
41	C₃×D₇	—	57	1	no	—
42	D₁₉	—	21	1	no	Hall
43	C₃×C₇	—	38	1	no	—
44	C₃×C₇	—	57	1	no	—
45	C₃×C₇	—	57	1	no	—
46	ΓL(1,𝔽₈)	—	266	1	no	—
47	ΓL(1,𝔽₈)	—	266	1	no	—
48	ΓL(1,𝔽₈)	—	14	1	no	—
49	C₁₉	C₃×#64418	1	1	yes	characteristic, complemented, Sylow
50	C₃×D₃	—	931	1	no	Hall
51	C₂×C₇	—	399	1	no	—
52	D₇	—	57	1	no	—
53	C₃²	—	931	1	no	Sylow
54	C₇	—	2	1	no	—
55	C₇	—	3	1	no	—
56	C₇	—	3	1	no	—
57	C₂×C₃	—	399	1	no	—
58	D₃	—	931	1	no	—
59	C₃	—	19	1	no	—
60	C₃	—	49	1	no	—
61	C₃	—	1862	1	no	—
62	C₂	—	399	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₉×#3862	C₂×C₃
Fitting, socle	C₇²×C₁₉	C₃×D₃
LCS	G ▷ C₁₉×#3862
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₃×#3862	C₂	semidirect
2. C₁₉⋊#64418	C₃	semidirect
5. C₁₉×#3862	C₂×C₃	semidirect
6. C₇²×C₁₉⋊C₃	D₃	semidirect
9. C₇²×C₁₉	C₃×D₃	semidirect
28. #3862	D₁₉⋊C₃	semidirect
38. C₁₉⋊C₃	#64418	semidirect
39. C₇²	C₃⋊(D₁₉⋊C₃)	semidirect
49. C₁₉	C₃×#64418	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊C₃×#3862	2
C₁₉⋊#64418	3
C₇×(C₁₉⋊C₃)⋊D₇	3
C₃×#64418	19
C₃⋊(D₁₉⋊C₃)	49

Subgroups — (C19⋊C3)⋊#64418 #30660730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₁₉⋊C₃)⋊#64418 #30660730