Group #18019698 — subgroups

Subgroups — C₂×C₁₉×SD₁₂₈ #18019698

Order 4864.

134 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×D₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×SD₁₂₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₉×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×Q₃₂	—	2	1	no	—
6	C₂×C₁₉×D₁₆	—	2	1	no	—
7	C₁₉×Q₆₄	—	2	1	no	—
8	C₁₉×Q₆₄	C₂²	1	2	yes	complemented
9	C₁₉×D₃₂	—	2	1	no	—
10	C₁₉×D₃₂	C₂²	1	2	yes	—
11	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₉×C₆₄	C₂²	1	2	yes	complemented
13	C₂×Q₁₆×C₁₉	—	4	1	no	—
14	C₂×D₈×C₁₉	—	4	1	no	—
15	C₁₉×Q₃₂	—	2	2	no	—
16	C₁₉×Q₃₂	—	4	1	no	—
17	C₁₉×D₁₆	—	2	2	no	—
18	C₁₉×D₁₆	—	4	1	no	—
19	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
20	C₁₉×C₃₂	D₄	1	1	yes	characteristic
21	C₁₉×C₃₂	C₂³	1	1	yes	characteristic
22	C₂×Q₈×C₁₉	—	8	1	no	—
23	C₂×D₄×C₁₉	—	8	1	no	—
24	Q₁₆×C₁₉	—	4	2	no	—
25	Q₁₆×C₁₉	—	8	1	no	—
26	D₈×C₁₉	—	4	2	no	—
27	D₈×C₁₉	—	8	1	no	—
28	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
29	C₁₆×C₁₉	D₈	1	1	yes	characteristic
30	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×SD₁₂₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂³×C₁₉	—	16	1	no	—
33	Q₈×C₁₉	—	8	2	no	—
34	Q₈×C₁₉	—	16	1	no	—
35	D₄×C₁₉	—	8	2	no	—
36	D₄×C₁₉	—	16	1	no	—
37	C₂×C₄×C₁₉	—	16	1	no	—
38	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
39	C₈×C₁₉	D₁₆	1	1	yes	characteristic
40	C₈×C₁₉	C₂×D₈	1	1	yes	characteristic
41	C₂×Q₆₄	C₂×C₁₉	1	1	yes	characteristic, complemented
42	C₂×D₃₂	C₂×C₁₉	1	1	yes	characteristic
43	SD₁₂₈	C₂×C₁₉	1	4	yes	direct product factor
44	C₂×C₆₄	C₂×C₁₉	1	1	yes	characteristic, complemented
45	C₂²×C₁₉	—	16	2	no	—
46	C₂²×C₁₉	—	32	2	no	—
47	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
48	C₄×C₁₉	—	16	2	no	—
49	C₄×C₁₉	D₃₂	1	1	yes	characteristic
50	C₄×C₁₉	C₂×D₁₆	1	1	yes	characteristic
51	C₂×Q₃₂	—	2	1	no	—
52	C₂×D₁₆	—	2	1	no	—
53	Q₆₄	—	2	1	no	—
54	Q₆₄	C₂²×C₁₉	1	2	yes	complemented
55	D₃₂	—	2	1	no	—
56	D₃₂	C₂²×C₁₉	1	2	yes	—
57	C₂×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
58	C₆₄	C₂²×C₁₉	1	2	yes	complemented
59	C₂×C₁₉	—	32	2	no	—
60	C₂×C₁₉	SD₁₂₈	1	2	yes	direct product factor
61	C₂×C₁₉	C₂×D₃₂	1	1	yes	characteristic
62	C₂×Q₁₆	—	4	1	no	—
63	C₂×D₈	—	4	1	no	—
64	Q₃₂	—	2	2	no	—
65	Q₃₂	—	4	1	no	—
66	D₁₆	—	2	2	no	—
67	D₁₆	—	4	1	no	—
68	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
69	C₃₂	D₄×C₁₉	1	1	yes	characteristic
70	C₃₂	C₂³×C₁₉	1	1	yes	characteristic
71	C₁₉	C₂×SD₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×Q₈	—	8	1	no	—
73	C₂×D₄	—	8	1	no	—
74	Q₁₆	—	4	2	no	—
75	Q₁₆	—	8	1	no	—
76	D₈	—	4	2	no	—
77	D₈	—	8	1	no	—
78	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
79	C₁₆	D₈×C₁₉	1	1	yes	characteristic
80	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
81	C₂³	—	16	1	no	—
82	Q₈	—	8	2	no	—
83	Q₈	—	16	1	no	—
84	D₄	—	8	2	no	—
85	D₄	—	16	1	no	—
86	C₂×C₄	—	16	1	no	—
87	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
88	C₈	C₁₉×D₁₆	1	1	yes	characteristic
89	C₈	C₂×D₈×C₁₉	1	1	yes	characteristic
90	C₂²	—	16	2	no	—
91	C₂²	—	32	2	no	—
92	C₂²	C₁₉×D₃₂	1	1	yes	characteristic
93	C₄	—	16	2	no	—
94	C₄	C₁₉×D₃₂	1	1	yes	characteristic
95	C₄	C₂×C₁₉×D₁₆	1	1	yes	characteristic
96	C₂	—	32	2	no	—
97	C₂	C₁₉×SD₁₂₈	1	2	yes	direct product factor
98	C₂	C₂×C₁₉×D₃₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×Q₆₄

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₃₂

C₂

yes

maximal, characteristic

C₁₉×SD₁₂₈

C₂

yes

maximal, direct product factor

C₂×C₁₉×C₆₄

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×D₁₆

—

C₁₉×Q₆₄

—

C₁₉×Q₆₄

C₂²

yes

complemented

C₁₉×D₃₂

—

C₁₉×D₃₂

C₂²

yes

—

C₂×C₁₉×C₃₂

C₂²

yes

characteristic

C₁₉×C₆₄

C₂²

yes

complemented

C₂×Q₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

D₄

yes

characteristic

C₁₉×C₃₂

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

C₂×D₄

yes

characteristic

C₂×SD₁₂₈

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

C₂×D₈

yes

characteristic

C₂×Q₆₄

C₂×C₁₉

yes

characteristic, complemented

C₂×D₃₂

C₂×C₁₉

yes

characteristic

SD₁₂₈

C₂×C₁₉

yes

direct product factor

C₂×C₆₄

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

D₃₂

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

D₃₂

yes

characteristic

C₄×C₁₉

C₂×D₁₆

yes

characteristic

C₂×Q₃₂

—

C₂×D₁₆

—

Q₆₄

—

Q₆₄

C₂²×C₁₉

yes

complemented

D₃₂

—

D₃₂

C₂²×C₁₉

yes

—

C₂×C₃₂

C₂²×C₁₉

yes

characteristic

C₆₄

C₂²×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

SD₁₂₈

yes

direct product factor

C₂×C₁₉

C₂×D₃₂

yes

characteristic

C₂×Q₁₆

—

C₂×D₈

—

Q₃₂

—

Q₃₂

—

D₁₆

—

D₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₃₂

D₄×C₁₉

yes

characteristic

C₃₂

C₂³×C₁₉

yes

characteristic

C₁₉

C₂×SD₁₂₈

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

D₈

—

D₈

—

C₂×C₈

D₈×C₁₉

yes

characteristic

C₁₆

D₈×C₁₉

yes

characteristic

C₁₆

C₂×D₄×C₁₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

C₁₉×D₁₆

yes

characteristic

C₈

C₁₉×D₁₆

yes

characteristic

C₈

C₂×D₈×C₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

C₁₉×D₃₂

yes

characteristic

C₄

—

C₄

C₁₉×D₃₂

yes

characteristic

C₄

C₂×C₁₉×D₁₆

yes

characteristic

C₂

—

C₂

C₁₉×SD₁₂₈

yes

direct product factor

C₂

C₂×C₁₉×D₃₂

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂³×C₁₉
prime radical	C₂×C₁₉×D₃₂	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₂×C₁₉×C₃₂ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

D₃₂

commutator, Frattini, cosocle

C₃₂

C₂³×C₁₉

prime radical

C₂×C₁₉×D₃₂

C₂

LCS

G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₂×C₁₉×C₃₂ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×Q₆₄	C₂	semidirect
3. C₁₉×SD₁₂₈	C₂	direct (N × H)
4. C₂×C₁₉×C₆₄	C₂	semidirect
8. C₁₉×Q₆₄	C₂²	semidirect
12. C₁₉×C₆₄	C₂²	semidirect
31. C₂×SD₁₂₈	C₁₉	direct (N × H)
41. C₂×Q₆₄	C₂×C₁₉	semidirect
43. SD₁₂₈	C₂×C₁₉	direct (N × H)
44. C₂×C₆₄	C₂×C₁₉	semidirect
54. Q₆₄	C₂²×C₁₉	semidirect
58. C₆₄	C₂²×C₁₉	semidirect
60. C₂×C₁₉	SD₁₂₈	direct (N × H)
71. C₁₉	C₂×SD₁₂₈	direct (N × H)
97. C₂	C₁₉×SD₁₂₈	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×Q₆₄

C₂

semidirect

3. C₁₉×SD₁₂₈

C₂

direct (N × H)

4. C₂×C₁₉×C₆₄

C₂

semidirect

8. C₁₉×Q₆₄

C₂²

semidirect

12. C₁₉×C₆₄

C₂²

semidirect

31. C₂×SD₁₂₈

C₁₉

direct (N × H)

41. C₂×Q₆₄

C₂×C₁₉

semidirect

43. SD₁₂₈

C₂×C₁₉

direct (N × H)

44. C₂×C₆₄

C₂×C₁₉

semidirect

54. Q₆₄

C₂²×C₁₉

semidirect

58. C₆₄

C₂²×C₁₉

semidirect

60. C₂×C₁₉

SD₁₂₈

direct (N × H)

71. C₁₉

C₂×SD₁₂₈

direct (N × H)

97. C₂

C₁₉×SD₁₂₈

direct (N × H)

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

subgroup	index
C₂×C₁₉×Q₆₄	2
C₂×C₁₉×D₃₂	2
C₁₉×SD₁₂₈	2
C₂×C₁₉×C₆₄	2
C₂×SD₁₂₈	19

subgroup

index

C₂×C₁₉×Q₆₄

C₂×C₁₉×D₃₂

C₁₉×SD₁₂₈

C₂×C₁₉×C₆₄

C₂×SD₁₂₈

Subgroups — C₂×C₁₉×SD₁₂₈ #18019698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C19×SD128 #18019698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×SD₁₂₈ #18019698