Subgroups — #18072976

Order 4864.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597260	C₂	1	2	yes	maximal
2	C₁₉⋊#1273	C₂	1	4	yes	maximal
3	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	C₄	1	8	yes	—
5	C₂×C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
6	C₂×C₁₉×#97	C₄	1	4	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
8	C₄³×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
14	C₁₉×#97	—	2	8	no	—
15	C₄×C₈×C₁₉	—	2	4	no	—
16	#10597260	—	2	16	no	—
17	C₄×C₁₉⋊C₈	—	2	8	no	—
18	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
19	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	—	2	4	no	—
22	C₂×C₈×C₁₉	—	2	4	no	—
23	C₂×C₈×C₁₉	M₁₆	1	8	yes	—
24	C₄²×C₁₉	—	2	8	no	—
25	C₄²×C₁₉	—	2	4	no	—
26	C₄²×C₁₉	#41	1	4	yes	—
27	C₂×C₁₉⋊C₈	—	2	8	no	—
28	C₂×C₁₉⋊C₈	—	2	8	no	—
29	C₂×C₁₉⋊C₈	M₁₆	1	16	yes	—
30	#8136	—	19	1	no	maximal, Sylow
31	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	8	no	—
33	C₂×C₄×C₁₉	—	2	4	no	—
34	C₂×C₄×C₁₉	#117	1	4	yes	—
35	C₂×C₄×C₁₉	#117	1	2	yes	—
36	C₂×C₄×C₁₉	C₂×M₁₆	1	8	yes	—
37	C₂×C₄×C₁₉	C₂×M₁₆	1	4	yes	—
38	C₈×C₁₉	—	2	8	no	—
39	C₁₉⋊C₈	—	2	16	no	—
40	C₄×#97	—	19	2	no	—
41	C₄×#97	D₁₉	1	1	yes	characteristic
42	#1273	—	19	4	no	—
43	C₂²×C₁₉	#376	1	1	yes	characteristic
44	C₂²×C₁₉	C₄×M₁₆	1	4	yes	—
45	C₂²×C₁₉	C₄×M₁₆	1	2	yes	—
46	C₄×C₁₉	—	4	4	no	—
47	C₄×C₁₉	#432	1	8	yes	—
48	C₄×C₁₉	#432	1	4	yes	—
49	C₂×#97	—	19	8	no	—
50	C₂×#97	Dic₁₉	1	4	yes	—
51	C₂×C₄×C₈	—	19	4	no	—
52	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
53	C₄³	C₂×D₁₉	1	1	yes	characteristic
54	C₂×C₁₉	#1455	1	4	yes	—
55	C₂×C₁₉	#1745	1	2	yes	—
56	C₂×C₁₉	#1745	1	1	yes	characteristic
57	C₂²×C₈	—	19	8	no	—
58	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
59	C₂×C₄²	C₄×D₁₉	1	4	yes	—
60	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
61	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
62	#97	—	2	8	no	—
63	#97	—	38	16	no	—
64	C₄×C₈	—	2	4	no	—
65	C₄×C₈	—	38	8	no	—
66	C₁₉	#8136	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
68	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
69	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
70	C₂×C₈	—	2	4	no	—
71	C₂×C₈	—	2	4	no	—
72	C₂×C₈	—	19	16	no	—
73	C₂×C₈	—	38	8	no	—
74	C₂×C₈	—	38	8	no	—
75	C₂×C₈	#64520	1	8	yes	—
76	C₄²	—	2	8	no	—
77	C₄²	—	2	4	no	—
78	C₄²	#64541	1	4	yes	—
79	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
80	C₂×C₄	—	2	8	no	—
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	#10597318	1	4	yes	—
83	C₂×C₄	M₁₆×D₁₉	1	8	yes	—
84	C₂×C₄	C₂×#64520	1	4	yes	—
85	C₂×C₄	#10597372	1	2	yes	—
86	C₈	—	2	8	no	—
87	C₈	—	38	16	no	—
88	C₂²	#11926390	1	1	yes	characteristic
89	C₂²	M₁₆×Dic₁₉	1	4	yes	—
90	C₂²	C₄×#64520	1	2	yes	—
91	C₄	—	4	4	no	—
92	C₄	#11926599	1	8	yes	—
93	C₄	#11926601	1	4	yes	—
94	C₂	#14561938	1	4	yes	—
95	C₂	#14563383	1	2	yes	—
96	C₂	#14563384	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂×C₄²
Fitting	C₄×C₁₉×#97	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	#8136
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
66. C₁₉	#8136	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597260	2
C₁₉⋊#1273	2
C₄×C₁₉×#97	2
#8136	19