Subgroups — #11926916

Order 1216.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×#64526	C₂	1	4	yes	maximal, complemented
3	#10597315	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₁₉	—	2	2	no	—
6	C₂×D₄×C₁₉	C₂²	1	2	yes	—
7	C₂×Dic₃₈	C₂²	1	2	yes	—
8	C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	#64526	—	2	8	no	—
10	C₄⋊Dic₁₉	—	2	2	no	—
11	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
12	C₂³×C₁₉	—	2	2	no	—
13	D₄×C₁₉	—	2	4	no	—
14	D₄×C₁₉	—	4	4	no	—
15	C₂×C₄×C₁₉	D₄	1	2	yes	—
16	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₉	—	2	2	no	—
18	Dic₃₈	—	2	4	no	—
19	C₁₉⋊C₈	D₄	1	4	yes	complemented
20	C₂²×C₁₉	—	4	2	no	—
21	C₂²×C₁₉	—	4	4	no	—
22	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
23	C₄×C₁₉	SD₁₆	1	4	yes	complemented
24	C₄×C₁₉	C₂×D₄	1	2	yes	—
25	Dic₁₉	—	4	2	no	—
26	#492	—	19	1	no	maximal, Sylow
27	C₂×C₁₉	—	8	2	no	—
28	C₂×C₁₉	#127	1	1	yes	characteristic
29	C₂×C₁₉	C₂×SD₁₆	1	2	yes	—
30	C₂×SD₁₆	—	19	4	no	—
31	C₄⋊Q₈	—	19	1	no	—
32	#127	D₁₉	1	1	yes	characteristic
33	C₄×C₈	—	19	1	no	—
34	C₁₉	#492	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	19	2	no	—
36	C₂×D₄	—	2	2	no	—
37	C₂×D₄	C₂×D₁₉	1	2	yes	—
38	SD₁₆	—	38	8	no	—
39	C₂×C₈	—	19	2	no	—
40	C₄⋊C₄	—	38	2	no	—
41	C₄²	C₂×D₁₉	1	1	yes	characteristic
42	C₂³	—	2	2	no	—
43	Q₈	—	38	4	no	—
44	D₄	—	2	4	no	—
45	D₄	—	4	4	no	—
46	C₂×C₄	—	38	2	no	—
47	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
48	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
49	C₈	—	19	4	no	—
50	C₂²	—	4	4	no	—
51	C₂²	—	4	2	no	—
52	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
53	C₄	—	76	2	no	—
54	C₄	#64526	1	4	yes	complemented
55	C₄	D₄×D₁₉	1	2	yes	—
56	C₂	—	8	2	no	—
57	C₂	C₂×#64526	1	2	yes	—
58	C₂	#10597386	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#127	C₂
socle	C₂²×C₁₉	C₂×D₄
hypercenter	#127	D₁₉
hypocenter	C₁₉	#492
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
2. C₂×#64526	C₂	semidirect
3. #10597315	C₂	semidirect
4. C₄×C₁₉⋊C₈	C₂	semidirect
19. C₁₉⋊C₈	D₄	semidirect
23. C₄×C₁₉	SD₁₆	semidirect
34. C₁₉	#492	semidirect
54. C₄	#64526	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#127	2
C₂×#64526	2
#10597315	2
C₄×C₁₉⋊C₈	2
#492	19