Subgroups — #14563746

Order 2432.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597290	C₂	1	2	yes	maximal
2	#11926314	C₂	1	4	yes	maximal, complemented
3	C₁₉×#518	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₄×D₄×C₁₉	—	2	4	no	—
6	C₁₉×#117	C₂²	1	2	yes	—
7	C₂×C₂²⋊C₄×C₁₉	C₄	1	4	yes	—
8	C₂×#64520	C₂²	1	4	yes	—
9	#10597290	—	2	4	no	—
10	C₂⁴×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×D₄×C₁₉	—	2	4	no	—
12	C₂×D₄×C₁₉	D₄	1	4	yes	—
13	C₂²×C₄×C₁₉	—	2	4	no	—
14	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂²⋊C₄×C₁₉	—	2	4	no	—
17	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
18	C₄²×C₁₉	—	2	2	no	—
19	#64520	—	2	4	no	—
20	#64520	—	2	4	no	—
21	C₂×C₁₉⋊C₈	—	2	4	no	—
22	C₂³×C₁₉	—	2	4	no	—
23	C₂³×C₁₉	—	8	2	no	—
24	C₂³×C₁₉	C₂²⋊C₄	1	4	yes	—
25	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
26	D₄×C₁₉	—	2	8	no	—
27	C₂×C₄×C₁₉	—	2	4	no	—
28	C₂×C₄×C₁₉	—	8	4	no	—
29	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₁₉	#41	1	4	yes	—
31	C₁₉⋊C₈	—	4	4	no	—
32	#1829	—	19	1	no	maximal, Sylow
33	C₂²×C₁₉	—	2	4	no	—
34	C₂²×C₁₉	—	4	1	no	—
35	C₂²×C₁₉	—	4	4	no	—
36	C₂²×C₁₉	—	8	4	no	—
37	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₁₉	#117	1	2	yes	—
39	C₄×C₁₉	—	4	4	no	—
40	C₄×C₁₉	#123	1	4	yes	—
41	#518	D₁₉	1	1	yes	characteristic
42	C₂×#100	—	19	2	no	—
43	#344	—	19	4	no	—
44	C₂×C₁₉	—	2	1	no	—
45	C₂×C₁₉	—	2	2	no	—
46	C₂×C₁₉	—	4	4	no	—
47	C₂×C₁₉	#381	1	1	yes	characteristic
48	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
49	C₂×M₁₆	—	19	4	no	—
50	C₄×D₄	—	2	4	no	—
51	#117	C₂×D₁₉	1	2	yes	—
52	C₂×C₂²⋊C₄	Dic₁₉	1	4	yes	—
53	#100	—	38	4	no	—
54	C₁₉	#1829	1	1	yes	characteristic, complemented, Sylow
55	C₂⁴	C₂×Dic₁₉	1	2	yes	—
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	C₂²⋊D₁₉	1	4	yes	—
58	C₂²×C₄	—	2	4	no	—
59	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
60	M₁₆	—	38	4	no	—
61	M₁₆	—	38	4	no	—
62	C₂×C₈	—	38	4	no	—
63	C₄⋊C₄	—	2	2	no	—
64	C₂²⋊C₄	—	2	4	no	—
65	C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
66	C₄²	—	2	2	no	—
67	C₂³	—	2	4	no	—
68	C₂³	—	8	2	no	—
69	C₂³	C₂²⋊Dic₁₉	1	4	yes	—
70	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
71	D₄	—	2	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	#64541	1	4	yes	—
75	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
76	C₈	—	76	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	4	no	—
81	C₂²	#10597372	1	2	yes	—
82	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
83	C₄	—	4	4	no	—
84	C₄	#10597375	1	4	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	C₂	#11926407	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926407
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#518	C₂
socle	C₂×C₁₉	#381
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#518	D₁₉
hypocenter	C₁₉	#1829
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #518

Complements

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

N	H ≅ G/N	type
2. #11926314	C₂	semidirect
54. C₁₉	#1829	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597290	2
#11926314	2
C₁₉×#518	2
#1829	19