Subgroups — #18070445

Order 4864.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561839	C₂	1	1	yes	maximal, characteristic
2	#14561837	C₂	1	1	yes	maximal, characteristic
3	C₁₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	#11926374	—	2	1	no	—
5	#11926370	—	2	1	no	—
6	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₉×C₆₄	C₄	1	2	yes	complemented
8	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
9	#10597276	—	4	1	no	—
10	#10597275	—	4	1	no	—
11	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₉×C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
14	C₄⋊Dic₁₉	—	8	1	no	—
15	#64520	—	8	1	no	—
16	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
18	#7548	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
20	C₂×Dic₁₉	—	16	1	no	—
21	C₈×C₁₉	#107	1	1	yes	characteristic
22	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
23	C₁₉⋊C₈	—	16	1	no	—
24	M₁₂₈	D₁₉	1	1	yes	characteristic
25	#1425	—	19	1	no	—
26	#1424	—	19	1	no	—
27	C₂²×C₁₉	SD₆₄	1	1	yes	characteristic
28	C₄×C₁₉	#366	1	1	yes	characteristic
29	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
30	Dic₁₉	—	32	1	no	—
31	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
32	#368	—	38	1	no	—
33	#366	—	38	1	no	—
34	C₆₄	Dic₁₉	1	2	yes	complemented
35	C₂×C₁₉	—	2	1	no	—
36	C₂×C₁₉	#1424	1	1	yes	characteristic
37	C₂×C₁₆	D₇₆	1	1	yes	characteristic
38	#108	—	76	1	no	—
39	#107	—	76	1	no	—
40	C₃₂	Dic₃₈	1	1	yes	characteristic
41	C₃₂	C₂×Dic₁₉	1	1	yes	characteristic
42	C₁₉	#7548	1	1	yes	characteristic, complemented, Sylow
43	M₁₆	—	152	1	no	—
44	C₂×C₈	D₁₅₂	1	1	yes	characteristic
45	C₄⋊C₄	—	152	1	no	—
46	C₁₆	Dic₇₆	1	1	yes	characteristic
47	C₁₆	C₄⋊Dic₁₉	1	1	yes	characteristic
48	C₂×C₄	—	304	1	no	—
49	C₂×C₄	D₃₀₄	1	1	yes	characteristic
50	C₈	—	304	1	no	—
51	C₈	Dic₁₅₂	1	1	yes	characteristic
52	C₈	#10597275	1	1	yes	characteristic
53	C₂²	#11926383	1	1	yes	characteristic
54	C₄	—	608	1	no	—
55	C₄	#11926370	1	1	yes	characteristic
56	C₄	#11926383	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#14561837	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561837
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×M₁₂₈	C₂
socle	C₂×C₁₉	#1424
prime radical	C₂²×C₁₉	SD₆₄
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₉
hypocenter	C₁₉	#7548
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
7. C₁₉×C₆₄	C₄	semidirect
34. C₆₄	Dic₁₉	semidirect
42. C₁₉	#7548	semidirect

Maximal subgroups

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

subgroup	index
#14561839	2
#14561837	2
C₁₉×M₁₂₈	2
#7548	19