Subgroups — #18070437

Order 4864.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561846	C₂	1	2	yes	maximal
2	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊C₆₄	—	2	2	no	—
4	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₉	C₈	1	1	yes	characteristic
10	C₁₉×C₃₂	—	2	1	no	—
11	C₁₉×C₃₂	D₄	1	1	yes	characteristic
12	C₁₉×C₃₂	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₁₉	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₉	C₁₆	1	1	yes	characteristic
16	C₁₆×C₁₉	—	2	1	no	—
17	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
19	#7544	—	19	1	no	maximal, Sylow
20	C₂×C₄×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
22	C₈×C₁₉	C₃₂	1	2	yes	—
23	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₁₉	M₃₂	1	1	yes	characteristic
25	M₁₂₈	—	19	2	no	—
26	C₄×C₃₂	D₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	M₆₄	1	1	yes	characteristic
28	C₄×C₁₉	—	2	2	no	—
29	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
30	C₄×C₁₉	C₂×C₃₂	1	1	yes	characteristic
31	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
32	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
33	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
34	C₆₄	—	38	2	no	—
35	C₂×C₁₉	—	2	1	no	—
36	C₂×C₁₉	C₄⋊C₃₂	1	1	yes	characteristic
37	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
39	C₄×C₈	C₁₉⋊C₈	1	1	yes	characteristic
40	C₃₂	—	2	1	no	—
41	C₃₂	Dic₃₈	1	1	yes	characteristic
42	C₃₂	D₇₆	1	1	yes	characteristic
43	C₁₉	#7544	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
45	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
46	C₄²	C₁₉⋊C₁₆	1	1	yes	characteristic
47	C₁₆	—	2	1	no	—
48	C₁₆	#64520	1	1	yes	characteristic
49	C₁₆	C₄⋊Dic₁₉	1	1	yes	characteristic
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
52	C₈	C₁₉⋊C₃₂	1	2	yes	—
53	C₈	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
54	C₈	#10597269	1	1	yes	characteristic
55	C₂²	#11926378	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
58	C₄	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₄⋊(C₁₉⋊C₃₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	D₇₆
commutator	C₄×C₁₉	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₄×C₁₉×C₃₂	C₂
socle	C₂×C₁₉	C₄⋊C₃₂
prime radical	C₂²×C₁₉	M₆₄
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	C₄×C₃₂	D₁₉
hypocenter	C₁₉	#7544
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
43. C₁₉	#7544	semidirect

Maximal subgroups

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

subgroup	index
#14561846	2
C₄×C₁₉×C₃₂	2
#7544	19