Subgroups — #18076270

Order 4864.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561507	C₂	1	3	yes	maximal
2	#14561500	C₂	1	3	yes	maximal
3	C₁₉×#1455	C₂	1	1	yes	maximal, characteristic
4	#11926601	C₂²	1	3	yes	—
5	#11926412	C₂²	1	1	yes	characteristic
6	C₄×M₁₆×C₁₉	C₂²	1	3	yes	—
7	C₁₉×#322	C₄	1	3	yes	complemented
8	C₈²×C₁₉	C₄	1	1	yes	characteristic, complemented
9	C₂×M₁₆×C₁₉	—	2	3	no	—
10	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
11	C₁₉×#97	—	2	3	no	—
12	C₄×C₈×C₁₉	C₂×C₄	1	3	yes	—
13	C₄×C₈×C₁₉	C₂×C₄	1	3	yes	—
14	C₁₉⋊#95	—	2	3	no	—
15	C₂²⋊(C₁₉⋊C₈)	—	2	3	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	3	no	—
17	#10597260	—	2	3	no	—
18	C₂²×C₄×C₁₉	#41	1	3	yes	—
19	C₂²×Dic₁₉	—	4	1	no	—
20	M₁₆×C₁₉	—	4	6	no	—
21	C₂×C₈×C₁₉	—	2	3	no	—
22	C₂×C₈×C₁₉	—	2	3	no	—
23	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
24	C₄²×C₁₉	#41	1	3	yes	—
25	C₂×C₁₉⋊C₈	—	4	3	no	—
26	#8803	—	19	1	no	maximal, Sylow
27	C₂³×C₁₉	#126	1	1	yes	characteristic
28	C₂×C₄×C₁₉	—	4	3	no	—
29	C₂×C₄×C₁₉	#117	1	3	yes	—
30	C₂×C₄×C₁₉	#126	1	3	yes	—
31	C₂×Dic₁₉	—	8	3	no	—
32	C₈×C₁₉	—	2	6	no	—
33	C₈×C₁₉	—	4	3	no	—
34	C₁₉⋊C₈	—	8	3	no	—
35	#1455	D₁₉	1	1	yes	characteristic
36	#1291	—	19	3	no	—
37	#1288	—	19	3	no	—
38	C₂²×C₁₉	—	2	3	no	—
39	C₂²×C₁₉	#383	1	1	yes	characteristic
40	C₄×C₁₉	—	2	3	no	—
41	C₄×C₁₉	—	2	3	no	—
42	Dic₁₉	—	16	1	no	—
43	#432	—	19	3	no	—
44	C₄×M₁₆	C₂×D₁₉	1	3	yes	—
45	#383	—	19	1	no	—
46	#322	Dic₁₉	1	3	yes	complemented
47	C₈²	Dic₁₉	1	1	yes	characteristic, complemented
48	C₂×C₁₉	—	4	1	no	—
49	C₂×C₁₉	#1841	1	3	yes	—
50	C₂×M₁₆	—	2	3	no	—
51	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
52	C₄⋊C₈	—	38	3	no	—
53	C₂²⋊C₈	—	38	3	no	—
54	#97	—	2	3	no	—
55	#97	—	38	3	no	—
56	C₄×C₈	C₂×Dic₁₉	1	3	yes	—
57	C₄×C₈	C₂×Dic₁₉	1	3	yes	—
58	#95	—	38	3	no	—
59	C₁₉	#8803	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₄	—	76	1	no	—
61	C₂²×C₄	#64541	1	3	yes	—
62	M₁₆	—	4	6	no	—
63	C₂×C₈	—	2	3	no	—
64	C₂×C₈	—	2	3	no	—
65	C₂×C₈	—	76	3	no	—
66	C₄²	#64541	1	3	yes	—
67	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
68	C₂³	#10597322	1	1	yes	characteristic
69	C₂×C₄	—	4	3	no	—
70	C₂×C₄	—	152	3	no	—
71	C₂×C₄	#10597322	1	3	yes	—
72	C₂×C₄	#10597372	1	3	yes	—
73	C₈	—	2	6	no	—
74	C₈	—	4	3	no	—
75	C₈	—	152	3	no	—
76	C₂²	—	2	3	no	—
77	C₂²	#11926412	1	1	yes	characteristic
78	C₄	—	2	3	no	—
79	C₄	—	2	3	no	—
80	C₄	—	304	1	no	—
81	C₂	—	4	1	no	—
82	C₂	#14563784	1	3	yes	—

	subgroup	G/H
center	C₂²	#11926412
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1455	C₂
socle	C₂²×C₁₉	#383
prime radical	C₂³×C₁₉	#126
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1455	D₁₉
hypocenter	C₁₉	#8803
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1455

Complements

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

N	H ≅ G/N	type
7. C₁₉×#322	C₄	semidirect
8. C₈²×C₁₉	C₄	semidirect
46. #322	Dic₁₉	semidirect
47. C₈²	Dic₁₉	semidirect
59. C₁₉	#8803	semidirect

Maximal subgroups

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

subgroup	index
#14561507	2
#14561500	2
C₁₉×#1455	2
#8803	19