Subgroups — #11926549

Order 1216.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#10597372	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#64520	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597289	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₁₉	—	2	1	no	—
6	C₂×D₄×C₁₉	—	2	1	no	—
7	C₂×D₄×C₁₉	—	2	2	no	—
8	C₂×D₄×C₁₉	C₄	1	4	yes	complemented
9	C₂×D₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₁₉	—	2	1	no	—
12	C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
13	C₄×Dic₁₉	—	2	1	no	—
14	#64520	—	2	2	no	—
15	C₂×C₁₉⋊C₈	C₂²	1	2	yes	complemented
16	C₂³×C₁₉	—	2	4	no	—
17	C₂³×C₁₉	—	2	2	no	—
18	C₂³×C₁₉	—	4	4	no	—
19	C₂³×C₁₉	D₄	1	1	yes	characteristic
20	D₄×C₁₉	—	2	4	no	—
21	D₄×C₁₉	—	2	2	no	—
22	D₄×C₁₉	C₂×C₄	1	4	yes	—
23	C₂×C₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄×C₁₉	D₄	1	2	yes	—
26	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×Dic₁₉	—	2	2	no	—
28	C₁₉⋊C₈	—	2	2	no	—
29	C₂²×C₁₉	—	2	2	no	—
30	C₂²×C₁₉	—	2	4	no	—
31	C₂²×C₁₉	—	4	8	no	—
32	C₂²×C₁₉	—	4	4	no	—
33	C₂²×C₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
36	C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	Dic₁₉	—	4	2	no	—
39	#418	—	19	1	no	maximal, Sylow
40	C₂×C₁₉	—	2	2	no	—
41	C₂×C₁₉	—	4	4	no	—
42	C₂×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
44	C₂²×D₄	D₁₉	1	1	yes	characteristic
45	C₂×M₁₆	—	19	1	no	—
46	#117	—	19	1	no	—
47	#102	—	19	4	no	—
48	C₁₉	#418	1	1	yes	characteristic, complemented, Sylow
49	C₂⁴	—	2	1	no	—
50	C₂×D₄	—	2	1	no	—
51	C₂×D₄	—	2	2	no	—
52	C₂×D₄	Dic₁₉	1	4	yes	complemented
53	C₂×D₄	C₂×D₁₉	1	2	yes	—
54	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
55	M₁₆	—	38	2	no	—
56	C₂×C₈	—	19	2	no	—
57	C₄⋊C₄	—	19	2	no	—
58	C₂²⋊C₄	—	38	1	no	—
59	C₄²	—	38	1	no	—
60	C₂³	—	2	4	no	—
61	C₂³	—	2	2	no	—
62	C₂³	—	4	4	no	—
63	C₂³	C₂²⋊D₁₉	1	1	yes	characteristic
64	D₄	—	2	4	no	—
65	D₄	—	2	2	no	—
66	D₄	C₂×Dic₁₉	1	4	yes	—
67	C₂×C₄	—	38	2	no	—
68	C₂×C₄	C₂×Dic₁₉	1	2	yes	—
69	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₁₉	1	2	yes	—
71	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
72	C₈	—	38	2	no	—
73	C₂²	—	2	2	no	—
74	C₂²	—	2	4	no	—
75	C₂²	—	4	8	no	—
76	C₂²	—	4	4	no	—
77	C₂²	C₂²⋊Dic₁₉	1	2	yes	—
78	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
79	C₄	—	76	2	no	—
80	C₄	C₂²⋊Dic₁₉	1	2	yes	—
81	C₄	C₂²×Dic₁₉	1	1	yes	characteristic
82	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	4	4	no	—
85	C₂	#10597378	1	2	yes	—
86	C₂	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₉
Fitting, prime radical	C₂²×D₄×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₄
cosocle	C₂×C₄×C₁₉	C₂³
hypercenter	C₂²×D₄	D₁₉
hypocenter	C₁₉	#418
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
2. #10597372	C₂	semidirect
3. C₂×#64520	C₂	semidirect
4. #10597289	C₂	semidirect
8. C₂×D₄×C₁₉	C₄	semidirect
12. C₄⋊Dic₁₉	C₂²	semidirect
15. C₂×C₁₉⋊C₈	C₂²	semidirect
48. C₁₉	#418	semidirect
52. C₂×D₄	Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×C₁₉	2
#10597372	2
C₂×#64520	2
#10597289	2
#418	19