Subgroups — C₂³×#64515 #14578336

Order 2432.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#64515	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₁₉	C₄	1	1	yes	characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₁₉	C₄	1	14	yes	—
9	C₂²×C₄×D₁₉	C₂²	1	14	yes	—
10	C₂²×C₈×C₁₉	C₂²	1	14	yes	complemented
11	C₂²×C₁₉⋊C₈	C₂²	1	14	yes	complemented
12	C₂×#64515	C₂²	1	112	yes	direct product factor
13	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂³×D₁₉	—	2	8	no	—
15	C₂³×D₁₉	C₂×C₄	1	14	yes	—
16	C₂²×C₄×C₁₉	C₂×C₄	1	7	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	7	yes	—
18	C₂²×Dic₁₉	C₂×C₄	1	14	yes	—
19	C₂×C₄×D₁₉	C₂×C₄	1	84	yes	—
20	C₂×C₄×D₁₉	C₂³	1	28	yes	—
21	C₂×C₈×C₁₉	C₂³	1	28	yes	complemented
22	C₂×C₁₉⋊C₈	C₂³	1	28	yes	complemented
23	#64515	C₂³	1	64	yes	direct product factor
24	C₂³×C₁₉	M₁₆	1	8	yes	complemented
25	C₂³×C₁₉	C₂²×C₄	1	7	yes	—
26	C₂²×D₁₉	—	2	56	no	—
27	C₂²×D₁₉	C₂²×C₄	1	28	yes	—
28	C₂×C₄×C₁₉	C₂²×C₄	1	21	yes	—
29	C₂×C₄×C₁₉	C₂⁴	1	7	yes	—
30	C₂×Dic₁₉	C₂²×C₄	1	28	yes	—
31	C₄×D₁₉	C₂²×C₄	1	56	yes	—
32	C₄×D₁₉	C₂⁴	1	8	yes	—
33	C₈×C₁₉	C₂⁴	1	8	yes	complemented
34	C₁₉⋊C₈	C₂⁴	1	8	yes	complemented
35	C₂³×M₁₆	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂×M₁₆	1	28	yes	complemented
37	C₂²×C₁₉	C₂³×C₄	1	7	yes	—
38	C₂×D₁₉	—	2	56	no	—
39	C₂×D₁₉	C₂³×C₄	1	8	yes	—
40	C₄×C₁₉	C₂³×C₄	1	7	yes	—
41	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
42	Dic₁₉	C₂³×C₄	1	8	yes	—
43	C₂⁴×C₄	—	19	1	no	—
44	C₂²×M₁₆	—	19	28	no	—
45	C₂³×C₈	—	19	1	no	—
46	C₂³×C₈	D₁₉	1	1	yes	characteristic, complemented
47	C₂×C₁₉	C₂²×M₁₆	1	14	yes	complemented
48	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
49	D₁₉	—	2	8	no	—
50	C₂⁵	—	19	1	no	—
51	C₂³×C₄	—	19	1	no	—
52	C₂³×C₄	—	19	14	no	—
53	C₂³×C₄	—	19	14	no	—
54	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
55	C₂×M₁₆	—	19	112	no	—
56	C₂²×C₈	—	19	14	no	—
57	C₂²×C₈	C₂×D₁₉	1	14	yes	complemented
58	C₁₉	C₂³×M₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	—	19	14	no	—
60	C₂⁴	—	38	8	no	—
61	C₂⁴	C₄×D₁₉	1	1	yes	characteristic
62	C₂²×C₄	—	19	14	no	—
63	C₂²×C₄	—	19	84	no	—
64	C₂²×C₄	—	19	28	no	—
65	C₂²×C₄	C₄×D₁₉	1	7	yes	—
66	C₂²×C₄	C₂²×D₁₉	1	7	yes	—
67	M₁₆	—	19	64	no	—
68	C₂×C₈	—	19	28	no	—
69	C₂×C₈	C₂²×D₁₉	1	28	yes	complemented
70	C₂³	—	19	28	no	—
71	C₂³	—	38	56	no	—
72	C₂³	#64515	1	8	yes	direct product factor
73	C₂³	C₂×C₄×D₁₉	1	7	yes	—
74	C₂×C₄	—	19	28	no	—
75	C₂×C₄	—	19	56	no	—
76	C₂×C₄	—	19	8	no	—
77	C₂×C₄	C₂×C₄×D₁₉	1	21	yes	—
78	C₂×C₄	C₂³×D₁₉	1	7	yes	—
79	C₈	—	19	8	no	—
80	C₈	C₂³×D₁₉	1	8	yes	complemented
81	C₂²	—	19	8	no	—
82	C₂²	—	38	56	no	—
83	C₂²	C₂×#64515	1	28	yes	direct product factor
84	C₂²	C₂²×C₄×D₁₉	1	7	yes	—
85	C₄	—	19	8	no	—
86	C₄	C₂²×C₄×D₁₉	1	7	yes	—
87	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
88	C₂	—	38	8	no	—
89	C₂	C₂²×#64515	1	14	yes	direct product factor
90	C₂	C₂³×C₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle	C₂⁴×C₁₉	C₂×C₄
prime radical	C₂⁴×D₁₉	C₄
cosocle	C₄×C₁₉	C₂⁵
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	C₂³×M₁₆
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#64515	C₂	direct (N × H)
3. C₂³×C₁₉⋊C₈	C₂	semidirect
4. C₂³×C₈×C₁₉	C₂	semidirect
10. C₂²×C₈×C₁₉	C₂²	semidirect
11. C₂²×C₁₉⋊C₈	C₂²	semidirect
12. C₂×#64515	C₂²	direct (N × H)
21. C₂×C₈×C₁₉	C₂³	semidirect
22. C₂×C₁₉⋊C₈	C₂³	semidirect
23. #64515	C₂³	direct (N × H)
24. C₂³×C₁₉	M₁₆	semidirect
33. C₈×C₁₉	C₂⁴	semidirect
34. C₁₉⋊C₈	C₂⁴	semidirect
36. C₂²×C₁₉	C₂×M₁₆	semidirect
46. C₂³×C₈	D₁₉	semidirect
47. C₂×C₁₉	C₂²×M₁₆	semidirect
57. C₂²×C₈	C₂×D₁₉	semidirect
58. C₁₉	C₂³×M₁₆	semidirect
69. C₂×C₈	C₂²×D₁₉	semidirect
72. C₂³	#64515	direct (N × H)
80. C₈	C₂³×D₁₉	semidirect
83. C₂²	C₂×#64515	direct (N × H)
89. C₂	C₂²×#64515	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×D₁₉	2
C₂²×#64515	2
C₂³×C₁₉⋊C₈	2
C₂³×C₈×C₁₉	2
C₂³×M₁₆	19

Subgroups — C23×#64515 #14578336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#64515 #14578336