Subgroups — C₁₉⋊#13183544 #45691597

Order 33516.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#11725078	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊#5997)	—	3	1	no	maximal
3	C₁₉×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
5	C₁₉⋊#5997	—	9	1	no	Hall
6	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic
7	C₁₉×D₇⋊C₉	—	14	1	no	—
8	C₁₉×C₇⋊D₇	D₉	1	1	yes	characteristic
9	#13183544	—	19	1	no	maximal, Hall
10	C₁₉×C₇⋊C₉	—	14	1	no	—
11	C₇²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
12	#11725078	D₁₉	1	1	yes	characteristic
13	C₃×D₇×C₁₉	—	14	1	no	—
14	C₃×D₇×C₁₉	—	42	1	no	—
15	Dic₁₇₁	—	49	1	no	maximal, Hall
16	C₃⋊#5997	—	57	1	no	—
17	#89205	Dic₁₉	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇×C₁₉	—	2	1	no	—
19	C₃×C₇×C₁₉	—	6	1	no	—
20	C₂×C₉×C₁₉	—	49	1	no	—
21	C₃×C₇⋊D₇	D₅₇	1	1	yes	characteristic
22	D₇×C₁₉	—	14	1	no	—
23	D₇×C₁₉	—	42	1	no	—
24	Dic₅₇	—	147	1	no	—
25	#5997	—	171	1	no	Hall
26	C₉×C₁₉	—	49	1	no	Hall
27	C₃×C₇²	Dic₅₇	1	1	yes	characteristic
28	C₇×C₁₉	—	2	1	no	—
29	C₇×C₁₉	—	6	1	no	—
30	D₇⋊C₉	—	14	1	no	—
31	C₂×C₃×C₁₉	—	49	1	no	—
32	C₇⋊D₇	D₁₇₁	1	1	yes	characteristic
33	Dic₁₉	—	441	1	no	Hall
34	C₇⋊C₉	—	14	1	no	—
35	C₃×C₁₉	#10596885	1	1	yes	characteristic
36	C₇²	Dic₁₇₁	1	1	yes	characteristic, complemented, Sylow
37	C₃×D₇	—	14	1	no	—
38	C₃×D₇	—	42	1	no	—
39	C₂×C₁₉	—	49	1	no	—
40	Dic₉	—	931	1	no	Hall
41	C₃×C₇	—	2	1	no	—
42	C₃×C₇	—	6	1	no	—
43	C₁₉	#13183544	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	—	49	1	no	—
45	D₇	—	14	1	no	—
46	D₇	—	42	1	no	—
47	Dic₃	—	2793	1	no	—
48	C₉	—	49	1	no	Sylow
49	C₇	—	2	1	no	—
50	C₇	—	6	1	no	—
51	C₂×C₃	—	49	1	no	—
52	C₄	—	8379	1	no	Sylow
53	C₃	C₁₉⋊#10596885	1	1	yes	characteristic
54	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₁₉×#89205	C₄
Frattini	C₃	C₁₉⋊#10596885
Fitting, socle	C₃×C₇²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₇⋊D₇	D₃
cosocle	C₁₉×#11725078	C₂
LCS	G ▷ C₁₉×#89205
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₁₉×#89205	C₄	semidirect
11. C₇²×C₁₉	Dic₉	semidirect
17. #89205	Dic₁₉	semidirect
36. C₇²	Dic₁₇₁	semidirect
43. C₁₉	#13183544	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#11725078	2
C₃⋊(C₁₉⋊#5997)	3
#13183544	19
Dic₁₇₁	49

Subgroups — C19⋊#13183544 #45691597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#13183544 #45691597