Subgroups — #11926943

Order 1216.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#125	C₂	1	1	yes	maximal, characteristic
2	#10597316	C₂	1	1	yes	maximal, characteristic
3	#10597265	C₂	1	2	yes	maximal
4	#10597264	C₂	1	2	yes	maximal
5	C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₁₉	—	2	2	no	—
7	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	Dic₁₉⋊C₄	—	2	2	no	—
11	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₉	—	2	2	no	—
14	C₂×C₄×C₁₉	D₄	1	2	yes	—
15	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₂×Dic₁₉	—	2	2	no	—
17	C₁₉⋊C₈	Q₈	1	2	yes	—
18	C₁₉⋊C₈	Q₈	1	2	yes	—
19	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
20	C₄×C₁₉	—	2	2	no	—
21	C₄×C₁₉	—	4	2	no	—
22	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₉	—	4	2	no	—
25	#499	—	19	1	no	maximal, Sylow
26	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₁₉	#135	1	2	yes	—
28	#125	—	19	1	no	—
29	#125	D₁₉	1	1	yes	characteristic
30	#107	—	19	2	no	—
31	#106	—	19	2	no	—
32	C₄×C₈	—	19	1	no	—
33	C₁₉	#499	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₈	—	19	1	no	—
35	C₂×C₈	—	19	1	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	19	2	no	—
38	C₄⋊C₄	—	38	2	no	—
39	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
40	C₄²	C₂×D₁₉	1	1	yes	characteristic
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	38	2	no	—
43	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
44	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
45	C₈	—	19	2	no	—
46	C₈	—	19	2	no	—
47	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	4	2	no	—
50	C₄	—	76	2	no	—
51	C₄	Q₈×D₁₉	1	1	yes	characteristic
52	C₄	Q₈×D₁₉	1	1	yes	characteristic
53	C₂	#10597390	1	1	yes	characteristic
54	C₂	#10597396	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#125	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	#125	D₁₉
hypocenter	C₁₉	#499
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
33. C₁₉	#499	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#125	2
#10597316	2
#10597265	2
#10597264	2
C₄×C₁₉⋊C₈	2
#499	19