Subgroups — #18071911

Order 4864.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563380	C₂	1	3	yes	maximal
2	C₂×#11926266	C₂	1	3	yes	maximal
3	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
5	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
6	#11926298	C₄	1	12	yes	—
7	#11926266	C₄	1	12	yes	complemented
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₈²×C₁₉	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₉	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉	C₂×C₄	1	6	yes	—
13	C₂²×C₁₉⋊C₈	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₉	C₂×C₄	1	6	yes	—
15	C₄×C₈×C₁₉	C₂×C₄	1	6	yes	—
16	C₄×C₁₉⋊C₈	C₂×C₄	1	12	yes	—
17	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
18	C₂²×Dic₁₉	C₄²	1	4	yes	—
19	C₂×C₈×C₁₉	—	2	12	no	—
20	C₂×C₈×C₁₉	C₄²	1	12	yes	—
21	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
22	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
23	C₄×Dic₁₉	—	2	12	no	—
24	C₂×C₁₉⋊C₈	—	2	12	no	—
25	C₂×C₁₉⋊C₈	C₄²	1	12	yes	—
26	#7845	—	19	1	no	maximal, Sylow
27	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
28	C₂×C₄×C₁₉	C₂×C₄²	1	3	yes	—
29	C₂×C₄×C₁₉	C₂×C₄²	1	3	yes	—
30	C₂×C₄×C₁₉	#131	1	12	yes	—
31	C₂×Dic₁₉	—	2	12	no	—
32	C₈×C₁₉	—	2	12	no	—
33	C₁₉⋊C₈	—	2	12	no	—
34	#1744	—	19	3	no	—
35	C₂×#322	—	19	3	no	—
36	C₂×C₈²	D₁₉	1	1	yes	characteristic
37	C₂²×C₁₉	C₄³	1	1	yes	characteristic
38	C₂²×C₁₉	#405	1	6	yes	—
39	C₄×C₁₉	#405	1	6	yes	—
40	C₄×C₁₉	#405	1	6	yes	—
41	Dic₁₉	—	4	4	no	—
42	C₂×C₄×C₈	—	19	3	no	—
43	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
44	C₄³	—	19	1	no	—
45	#336	—	19	12	no	—
46	#322	—	19	12	no	—
47	C₈²	Dic₁₉	1	4	yes	complemented
48	C₂×C₁₉	#1454	1	4	yes	—
49	C₂×C₁₉	#1726	1	3	yes	—
50	C₂²×C₈	—	19	6	no	—
51	C₂²×C₈	C₄×D₁₉	1	6	yes	—
52	C₂×C₄²	—	19	6	no	—
53	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
54	C₄×C₈	—	19	12	no	—
55	C₄×C₈	C₄×D₁₉	1	6	yes	—
56	C₄×C₈	C₂×Dic₁₉	1	6	yes	—
57	C₁₉	#7845	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	19	4	no	—
59	C₂²×C₄	C₂×C₄×D₁₉	1	3	yes	—
60	C₂×C₈	—	2	12	no	—
61	C₂×C₈	—	19	12	no	—
62	C₂×C₈	—	38	12	no	—
63	C₂×C₈	C₄×Dic₁₉	1	12	yes	—
64	C₄²	—	38	12	no	—
65	C₄²	C₂×C₄×D₁₉	1	3	yes	—
66	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
67	C₂³	C₄²×D₁₉	1	1	yes	characteristic
68	C₂×C₄	—	38	12	no	—
69	C₂×C₄	C₄²×D₁₉	1	3	yes	—
70	C₂×C₄	#10597347	1	12	yes	—
71	C₂×C₄	C₂×C₄×Dic₁₉	1	3	yes	—
72	C₈	—	2	12	no	—
73	C₈	—	38	12	no	—
74	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
75	C₂²	#11926498	1	6	yes	—
76	C₄	—	76	4	no	—
77	C₄	#11926498	1	6	yes	—
78	C₄	#11926499	1	6	yes	—
79	C₂	#14561934	1	4	yes	—
80	C₂	#14563321	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₂×C₈²×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#7845
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
7. #11926266	C₄	semidirect
9. C₈²×C₁₉	C₄	semidirect
47. C₈²	Dic₁₉	semidirect
57. C₁₉	#7845	semidirect

Maximal subgroups

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

subgroup	index
#14563380	2
C₂×#11926266	2
C₂×C₈²×C₁₉	2
#7845	19