Subgroups — C₄×#11926265 #18071887

Order 4864.

654 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₁₉⋊C₈	C₂	1	2	yes	maximal
2	C₂×#11926265	C₂	1	4	yes	maximal
3	C₄²×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₉⋊C₈	C₄	1	8	yes	—
5	C₂×C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
6	#11926265	C₄	1	16	yes	direct product factor
7	C₂×C₄×C₈×C₁₉	C₄	1	4	yes	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
9	C₄³×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
15	C₄×C₈×C₁₉	C₈	1	16	yes	complemented
16	C₄×C₈×C₁₉	C₂×C₄	1	8	yes	—
17	C₄×C₁₉⋊C₈	—	2	16	no	—
18	C₄×C₁₉⋊C₈	C₂×C₄	1	16	yes	—
19	C₂²×C₄×C₁₉	C₄²	1	4	yes	—
20	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₄²	1	8	yes	—
23	C₂×C₈×C₁₉	C₂×C₈	1	16	yes	—
24	C₄²×C₁₉	C₂×C₈	1	8	yes	—
25	C₄²×C₁₉	M₁₆	1	16	yes	—
26	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
27	C₂×C₁₉⋊C₈	—	2	16	no	—
28	C₂×C₁₉⋊C₈	C₄²	1	16	yes	—
29	C₄×#322	—	19	1	no	maximal, Sylow
30	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₄×C₈	1	8	yes	—
32	C₂×C₄×C₁₉	#97	1	16	yes	—
33	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
34	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
35	C₂×C₄×C₁₉	C₂²×C₈	1	4	yes	—
36	C₂×C₄×C₁₉	C₂×M₁₆	1	8	yes	—
37	C₈×C₁₉	C₄×C₈	1	16	yes	complemented
38	C₁₉⋊C₈	—	2	16	no	—
39	C₄²×C₈	—	19	2	no	—
40	C₄²×C₈	D₁₉	1	1	yes	characteristic
41	C₂×#322	—	19	4	no	—
42	C₂²×C₁₉	C₄³	1	1	yes	characteristic
43	C₂²×C₁₉	C₂×C₄×C₈	1	2	yes	—
44	C₂²×C₁₉	C₂×#97	1	4	yes	—
45	C₄×C₁₉	#322	1	16	yes	complemented
46	C₄×C₁₉	C₂×C₄×C₈	1	4	yes	—
47	C₄×C₁₉	C₄×M₁₆	1	8	yes	—
48	C₂×C₄×C₈	—	19	4	no	—
49	C₂×C₄×C₈	—	19	8	no	—
50	C₂×C₄×C₈	Dic₁₉	1	4	yes	—
51	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
52	C₄³	C₂×D₁₉	1	1	yes	characteristic
53	#322	—	19	16	no	—
54	C₂×C₁₉	C₂×#322	1	4	yes	—
55	C₂×C₁₉	C₄²×C₈	1	1	yes	characteristic
56	C₂×C₁₉	C₄×#97	1	2	yes	—
57	C₂²×C₈	—	19	8	no	—
58	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
59	C₂×C₄²	C₄×D₁₉	1	4	yes	—
60	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
61	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
62	C₄×C₈	—	19	16	no	—
63	C₄×C₈	—	38	16	no	—
64	C₄×C₈	C₁₉⋊C₈	1	16	yes	complemented
65	C₄×C₈	C₄×D₁₉	1	8	yes	—
66	C₁₉	C₄×#322	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	C₄×Dic₁₉	1	4	yes	—
68	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
69	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
70	C₂×C₈	—	19	16	no	—
71	C₂×C₈	—	38	16	no	—
72	C₂×C₈	C₂×C₁₉⋊C₈	1	16	yes	—
73	C₂×C₈	C₄×Dic₁₉	1	8	yes	—
74	C₄²	#64515	1	16	yes	—
75	C₄²	C₂×C₁₉⋊C₈	1	8	yes	—
76	C₄²	C₂×C₄×D₁₉	1	4	yes	—
77	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
78	C₂×C₄	C₄×C₁₉⋊C₈	1	8	yes	—
79	C₂×C₄	#10597272	1	16	yes	—
80	C₂×C₄	C₄²×D₁₉	1	4	yes	—
81	C₂×C₄	C₂×#64515	1	8	yes	—
82	C₂×C₄	C₂²×C₁₉⋊C₈	1	4	yes	—
83	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
84	C₈	—	38	16	no	—
85	C₈	C₄×C₁₉⋊C₈	1	16	yes	complemented
86	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
87	C₂²	C₂×C₄×C₁₉⋊C₈	1	2	yes	—
88	C₂²	C₂×#10597272	1	4	yes	—
89	C₄	#11926265	1	16	yes	direct product factor
90	C₄	C₂×C₄×C₁₉⋊C₈	1	4	yes	—
91	C₄	C₄×#64515	1	8	yes	—
92	C₂	C₂×#11926265	1	4	yes	—
93	C₂	C₄²×C₁₉⋊C₈	1	1	yes	characteristic
94	C₂	C₄×#10597272	1	2	yes	—

	subgroup	G/H
center	C₄³	C₂×D₁₉
commutator	C₂×C₁₉	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×C₈	D₁₉
hypocenter	C₁₉	C₄×#322
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
6. #11926265	C₄	direct (N × H)
15. C₄×C₈×C₁₉	C₈	semidirect
37. C₈×C₁₉	C₄×C₈	semidirect
45. C₄×C₁₉	#322	semidirect
64. C₄×C₈	C₁₉⋊C₈	semidirect
66. C₁₉	C₄×#322	semidirect
85. C₈	C₄×C₁₉⋊C₈	semidirect
89. C₄	#11926265	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₁₉⋊C₈	2
C₂×#11926265	2
C₄²×C₈×C₁₉	2
C₄×#322	19

Subgroups — C4×#11926265 #18071887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926265 #18071887