Subgroups — #14563772

Order 2432.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#11926308	C₂	1	4	yes	maximal
4	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64520	C₂²	1	2	yes	—
8	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
9	C₁₉×C₄⋊C₈	—	2	2	no	—
10	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
11	C₄×C₁₉⋊C₈	C₄	1	2	yes	—
12	C₄×C₁₉⋊C₈	C₄	1	2	yes	—
13	C₂²×C₄×C₁₉	Q₈	1	2	yes	—
14	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	M₁₆×C₁₉	—	2	4	no	—
16	C₂×C₈×C₁₉	—	2	2	no	—
17	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₁₉	D₄	1	2	yes	—
20	#64520	—	2	4	no	—
21	C₂×C₁₉⋊C₈	—	2	2	no	—
22	C₂×C₁₉⋊C₈	—	2	2	no	—
23	C₂×C₁₉⋊C₈	—	2	2	no	—
24	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
25	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₁₉	—	2	4	no	—
27	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	#41	1	2	yes	—
32	C₂×C₄×C₁₉	#41	1	2	yes	—
33	C₈×C₁₉	—	4	2	no	—
34	C₁₉⋊C₈	—	2	4	no	—
35	C₁₉⋊C₈	—	4	2	no	—
36	#1837	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	—	2	2	no	—
38	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₁₉	#125	1	2	yes	—
40	C₄×C₁₉	—	2	2	no	—
41	C₄×C₁₉	#108	1	4	yes	—
42	C₄×C₁₉	#117	1	2	yes	—
43	C₄×C₁₉	#124	1	1	yes	characteristic
44	C₄×C₁₉	#124	1	1	yes	characteristic
45	#423	—	19	1	no	—
46	#423	D₁₉	1	1	yes	characteristic
47	C₂×C₄×C₈	—	19	1	no	—
48	#341	—	19	4	no	—
49	C₂×C₁₉	—	2	2	no	—
50	C₂×C₁₉	#382	1	1	yes	characteristic
51	C₂×C₁₉	C₂×#108	1	2	yes	—
52	C₂×M₁₆	—	19	2	no	—
53	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
54	C₂²×C₈	—	19	2	no	—
55	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
56	C₄⋊C₈	—	2	2	no	—
57	C₄⋊C₈	—	38	2	no	—
58	C₄×C₈	—	19	2	no	—
59	C₄×C₈	—	19	2	no	—
60	C₁₉	#1837	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	Dic₃₈	1	2	yes	—
62	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
63	M₁₆	—	2	4	no	—
64	M₁₆	—	38	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	19	4	no	—
67	C₂×C₈	—	38	2	no	—
68	C₂×C₈	—	38	2	no	—
69	C₂×C₈	—	38	2	no	—
70	C₄²	C₄×D₁₉	1	1	yes	characteristic
71	C₄²	C₄×D₁₉	1	1	yes	characteristic
72	C₄²	C₂²⋊D₁₉	1	2	yes	—
73	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
76	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
78	C₂×C₄	#64543	1	2	yes	—
79	C₂×C₄	#64545	1	2	yes	—
80	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
81	C₈	—	4	2	no	—
82	C₈	—	38	4	no	—
83	C₈	—	76	2	no	—
84	C₂²	—	2	2	no	—
85	C₂²	#10597336	1	2	yes	—
86	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	#10597279	1	4	yes	—
89	C₄	#10597338	1	2	yes	—
90	C₄	#10597382	1	1	yes	characteristic
91	C₄	#10597393	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	#11926409	1	1	yes	characteristic
94	C₂	C₂×#10597279	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#423	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#423	D₁₉
hypocenter	C₁₉	#1837
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
60. C₁₉	#1837	semidirect

Maximal subgroups

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

subgroup	index
#11926568	2
C₂×C₄×C₁₉⋊C₈	2
#11926308	2
C₁₉×#423	2
#1837	19