Subgroups — C₁₉×#237 #11744977

Order 912.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#67	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₃×C₁₉	C₂	1	2	yes	maximal, complemented
4	C₄×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₁₉	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₁₉	C₂²	1	2	yes	—
8	C₂×D₃×C₁₉	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	Dic₃×C₁₉	C₂²	1	2	yes	—
11	Dic₃×C₁₉	C₂²	1	1	yes	characteristic
12	Q₈×C₁₉	—	3	1	no	—
13	D₄×C₁₉	—	3	2	no	—
14	D₄×C₁₉	D₃	1	1	yes	characteristic, complemented
15	C₂×C₄×C₁₉	—	3	2	no	—
16	C₂×C₄×C₁₉	—	3	1	no	—
17	C₂×C₃×C₁₉	—	2	2	no	—
18	C₂×C₃×C₁₉	C₂³	1	1	yes	characteristic
19	D₃×C₁₉	—	2	1	no	—
20	C₂²×C₁₉	—	3	1	no	—
21	C₂²×C₁₉	C₂×D₃	1	2	yes	—
22	C₄×C₁₉	—	3	1	no	—
23	C₄×C₁₉	—	3	2	no	—
24	C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
25	C₃×C₁₉	#41	1	1	yes	characteristic, complemented, Hall
26	#237	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₁₉	—	2	2	no	—
28	C₂×C₁₉	—	6	1	no	—
29	C₂×C₁₉	C₂²×D₃	1	1	yes	characteristic
30	C₃×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
31	#67	C₂×C₁₉	1	2	yes	complemented
32	C₂×Dic₃	C₂×C₁₉	1	2	yes	complemented
33	C₄×D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
34	Dic₆	C₂×C₁₉	1	1	yes	characteristic, complemented
35	C₁₉	#237	1	1	yes	characteristic, direct product factor, Sylow
36	#41	—	3	1	no	Sylow
37	C₂²×C₃	C₂²×C₁₉	1	2	yes	—
38	C₂×D₃	C₂²×C₁₉	1	1	yes	characteristic
39	C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
40	Dic₃	C₂²×C₁₉	1	2	yes	—
41	Dic₃	C₂²×C₁₉	1	1	yes	characteristic
42	Q₈	—	3	1	no	—
43	D₄	—	3	2	no	—
44	D₄	D₃×C₁₉	1	1	yes	characteristic, complemented
45	C₂×C₄	—	3	2	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	C₂³×C₁₉	1	1	yes	characteristic
49	D₃	—	2	1	no	—
50	C₂²	—	3	1	no	—
51	C₂²	C₂×D₃×C₁₉	1	2	yes	—
52	C₄	—	3	1	no	—
53	C₄	—	3	2	no	—
54	C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
55	C₃	#41×C₁₉	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	2	no	—
57	C₂	—	6	1	no	—
58	C₂	C₂²×D₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₉	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₁₉
Frattini	C₂	C₂²×D₃×C₁₉
Fitting	C₃×D₄×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂³
hypercenter	D₄×C₁₉	D₃
hypocenter	C₃	#41×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ D₄×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₁₉	C₂	semidirect
2. C₁₉×#67	C₂	semidirect
3. C₂×Dic₃×C₁₉	C₂	semidirect
4. C₄×D₃×C₁₉	C₂	semidirect
5. C₁₉×Dic₆	C₂	semidirect
14. D₄×C₁₉	D₃	semidirect
25. C₃×C₁₉	#41	semidirect
26. #237	C₁₉	direct (N × H)
30. C₃×D₄	C₂×C₁₉	semidirect
31. #67	C₂×C₁₉	semidirect
32. C₂×Dic₃	C₂×C₁₉	semidirect
33. C₄×D₃	C₂×C₁₉	semidirect
34. Dic₆	C₂×C₁₉	semidirect
35. C₁₉	#237	direct (N × H)
44. D₄	D₃×C₁₉	semidirect
55. C₃	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₄×C₁₉	2
C₁₉×#67	2
C₂×Dic₃×C₁₉	2
C₄×D₃×C₁₉	2
C₁₉×Dic₆	2
#41×C₁₉	3
#237	19

Subgroups — C19×#237 #11744977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#237 #11744977