Subgroups — #14561920

Order 2432.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926595	C₂	1	2	yes	maximal
2	C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926265	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₁₉⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₁₉	C₄	1	2	yes	—
7	C₄²×D₁₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₉	C₂²	1	2	yes	—
9	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	(C₂×D₁₉)⋊C₈	C₄	1	4	yes	—
11	Dic₁₉⋊C₈	C₄	1	4	yes	—
12	C₈×Dic₁₉	C₄	1	2	yes	—
13	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
23	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
24	C₈×D₁₉	C₈	1	8	yes	complemented
25	C₂²×D₁₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
28	C₂×Dic₁₉	C₄²	1	2	yes	—
29	C₂×Dic₁₉	C₄²	1	1	yes	characteristic
30	C₄×D₁₉	—	2	4	no	—
31	C₄×D₁₉	C₂×C₈	1	4	yes	—
32	C₈×C₁₉	—	2	4	no	—
33	C₈×C₁₉	C₂×C₈	1	4	yes	—
34	C₁₉⋊C₈	—	2	4	no	—
35	C₁₉⋊C₈	C₂×C₈	1	4	yes	—
36	#1450	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
38	C₂×D₁₉	—	2	2	no	—
39	C₂×D₁₉	C₄×C₈	1	2	yes	—
40	C₄×C₁₉	C₂²×C₈	1	2	yes	—
41	C₄×C₁₉	#131	1	4	yes	—
42	Dic₁₉	—	2	2	no	—
43	Dic₁₉	C₄×C₈	1	2	yes	—
44	#431	—	19	2	no	—
45	C₂×C₄×C₈	—	19	1	no	—
46	#322	—	19	1	no	—
47	#322	D₁₉	1	1	yes	characteristic, complemented
48	C₈²	—	19	2	no	—
49	C₂×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
50	C₂×C₁₉	#405	1	2	yes	—
51	D₁₉	—	2	2	no	—
52	C₂²×C₈	—	19	2	no	—
53	C₂×C₄²	—	19	1	no	—
54	C₄⋊C₈	—	19	4	no	—
55	C₂²⋊C₈	—	19	4	no	—
56	C₄×C₈	—	19	2	no	—
57	C₄×C₈	—	19	1	no	—
58	C₄×C₈	—	19	2	no	—
59	C₄×C₈	C₂×D₁₉	1	2	yes	—
60	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₁₉	#1450	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	19	1	no	—
63	C₂²×C₄	—	19	2	no	—
64	C₂×C₈	—	19	2	no	—
65	C₂×C₈	—	19	8	no	—
66	C₂×C₈	—	19	4	no	—
67	C₂×C₈	C₄×D₁₉	1	4	yes	—
68	C₂×C₈	C₄×D₁₉	1	2	yes	—
69	C₄²	—	19	1	no	—
70	C₄²	—	19	2	no	—
71	C₄²	C₂²×D₁₉	1	1	yes	characteristic
72	C₂³	—	19	1	no	—
73	C₂×C₄	—	19	1	no	—
74	C₂×C₄	—	19	4	no	—
75	C₂×C₄	—	19	2	no	—
76	C₂×C₄	—	38	4	no	—
77	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
78	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
79	C₈	—	2	4	no	—
80	C₈	—	19	4	no	—
81	C₈	—	38	4	no	—
82	C₈	C₈×D₁₉	1	4	yes	—
83	C₂²	—	19	2	no	—
84	C₂²	—	38	2	no	—
85	C₂²	C₄²×D₁₉	1	1	yes	characteristic
86	C₄	—	19	2	no	—
87	C₄	—	38	2	no	—
88	C₄	C₂×C₈×D₁₉	1	2	yes	—
89	C₄	#10597353	1	4	yes	—
90	C₂	—	38	2	no	—
91	C₂	C₄×C₈×D₁₉	1	1	yes	characteristic
92	C₂	#11926501	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₉
commutator	C₂×C₁₉	C₂×C₄×C₈
Fitting	C₁₉×#322	C₂
socle	C₂²×C₁₉	C₂×C₄²
prime radical	C₂²×D₁₉	C₄²
cosocle	C₄²×C₁₉	C₂³
hypercenter	#322	D₁₉
hypocenter	C₁₉	#1450
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. #11926265	C₂	semidirect
4. C₈×C₁₉⋊C₈	C₂	semidirect
5. C₁₉×#322	C₂	semidirect
24. C₈×D₁₉	C₈	semidirect
47. #322	D₁₉	semidirect
61. C₁₉	#1450	semidirect

Maximal subgroups

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

subgroup	index
#11926595	2
C₄×C₈×D₁₉	2
#11926265	2
C₈×C₁₉⋊C₈	2
C₁₉×#322	2
#1450	19