Subgroups — #18069155

Order 4864.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561553	C₂	1	2	yes	maximal
2	C₁₉×#1311	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
6	C₈²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₈	1	2	yes	—
8	C₂×C₁₆×C₁₉	C₈	1	2	yes	—
9	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₁₉⋊C₁₆	—	2	4	no	—
12	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₉	M₁₆	1	4	yes	—
15	C₄²×C₁₉	C₄²	1	1	yes	characteristic
16	C₁₆×C₁₉	—	2	2	no	—
17	C₁₆×C₁₉	C₁₆	1	4	yes	complemented
18	C₁₉⋊C₁₆	—	4	4	no	—
19	#7053	—	19	1	no	maximal, Sylow
20	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
21	C₂×C₄×C₁₉	#97	1	2	yes	—
22	C₈×C₁₉	—	2	4	no	—
23	C₈×C₁₉	C₂×C₁₆	1	2	yes	—
24	C₈×C₁₉	M₃₂	1	2	yes	—
25	#1312	—	19	2	no	—
26	#1311	D₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	#322	1	1	yes	characteristic
28	C₄×C₁₉	C₄×C₁₆	1	1	yes	characteristic
29	C₄×C₁₉	#346	1	1	yes	characteristic
30	C₄×C₁₉	#347	1	4	yes	—
31	C₄×C₁₆	—	19	4	no	—
32	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
33	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
34	C₈²	C₂×D₁₉	1	1	yes	characteristic
35	C₂×C₁₉	#1312	1	1	yes	characteristic
36	C₂×C₁₉	#1313	1	2	yes	—
37	C₂×C₁₆	—	38	4	no	—
38	C₂×C₁₆	C₁₉⋊C₈	1	2	yes	—
39	C₂×C₁₆	C₁₉⋊C₈	1	2	yes	—
40	C₄×C₈	C₄×D₁₉	1	2	yes	—
41	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
42	C₁₉	#7053	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₈	#64515	1	4	yes	—
44	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
45	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
46	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
47	C₁₆	—	2	2	no	—
48	C₁₆	—	76	4	no	—
49	C₁₆	C₁₉⋊C₁₆	1	4	yes	complemented
50	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
51	C₂×C₄	#10597272	1	2	yes	—
52	C₈	—	2	4	no	—
53	C₈	C₂×C₁₉⋊C₁₆	1	2	yes	—
54	C₈	#10597269	1	2	yes	—
55	C₂²	#11926265	1	1	yes	characteristic
56	C₄	C₄×C₁₉⋊C₁₆	1	1	yes	characteristic
57	C₄	#11926320	1	1	yes	characteristic
58	C₄	#11926321	1	4	yes	—
59	C₂	#14561553	1	1	yes	characteristic
60	C₂	#14561555	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₁₉
commutator	C₄×C₁₉	C₄×C₁₆
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1311	C₂
socle, prime radical	C₂²×C₁₉	#322
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1311	D₁₉
hypocenter	C₁₉	#7053
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ #1311

Complements

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

N	H ≅ G/N	type
17. C₁₆×C₁₉	C₁₆	semidirect
42. C₁₉	#7053	semidirect
49. C₁₆	C₁₉⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
#14561553	2
C₁₉×#1311	2
#7053	19