Subgroups — #18070346

Order 4864.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561846	C₂	1	2	yes	maximal
2	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic
3	C₁₉⋊C₆₄	C₄	1	4	yes	complemented
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	C₈	1	2	yes	—
11	C₁₉×C₃₂	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₉	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₁₉	C₁₆	1	1	yes	characteristic
15	C₁₆×C₁₉	C₁₆	1	2	yes	—
16	C₁₆×C₁₉	C₄²	1	1	yes	characteristic
17	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
18	#7511	—	19	1	no	maximal, Sylow
19	C₂×C₄×C₁₉	—	2	1	no	—
20	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
21	C₈×C₁₉	—	2	1	no	—
22	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
23	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
24	M₁₂₈	—	19	2	no	—
25	#1397	D₁₉	1	1	yes	characteristic
26	C₂²×C₁₉	M₆₄	1	1	yes	characteristic
27	C₄×C₁₉	—	4	1	no	—
28	C₄×C₁₉	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₉	M₆₄	1	1	yes	characteristic
30	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
31	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
32	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
33	C₆₄	—	19	4	no	—
34	C₂×C₁₉	—	2	1	no	—
35	C₂×C₁₉	#1397	1	1	yes	characteristic
36	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
37	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
38	C₄×C₈	C₁₉⋊C₈	1	1	yes	characteristic
39	C₃₂	C₁₉⋊C₈	1	2	yes	—
40	C₃₂	C₄×D₁₉	1	2	yes	—
41	C₁₉	#7511	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
44	C₄²	C₁₉⋊C₁₆	1	1	yes	characteristic
45	C₁₆	C₁₉⋊C₁₆	1	2	yes	—
46	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
47	C₁₆	C₄×Dic₁₉	1	1	yes	characteristic
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
53	C₂²	#11926378	1	1	yes	characteristic
54	C₄	—	4	1	no	—
55	C₄	C₄×C₁₉⋊C₁₆	1	1	yes	characteristic
56	C₄	#11926378	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#14561769	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×Dic₁₉
commutator	C₄×C₁₉	C₄×C₁₆
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#1397	C₂
socle	C₂×C₁₉	#1397
prime radical	C₂²×C₁₉	M₆₄
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#1397	D₁₉
hypocenter	C₁₉	#7511
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₁₆ ◁ #1397

Complements

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

N	H ≅ G/N	type
3. C₁₉⋊C₆₄	C₄	semidirect
41. C₁₉	#7511	semidirect

Maximal subgroups

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

subgroup	index
#14561846	2
C₁₉×#1397	2
#7511	19