Group #14319317 — subgroups

Subgroups — C₄³×C₅×D₃ #14319317

Order 1920.

2544 conjugacy classes of subgroups; only the 1530 normal subgroups are shown.

normal subgroups only

This group has 2544 conjugacy classes of subgroups — too many to draw. Only its 1530 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×C₄²×C₅×D₃	C₂	1	7	yes	maximal
2	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₅×Dic₃	C₂	1	7	yes	maximal, complemented
4	C₂×C₄³×C₅	—	3	1	no	maximal, Hall
5	C₂²×C₄×C₅×D₃	C₂²	1	7	yes	—
6	C₂×C₃×C₄²×C₅	C₂²	1	7	yes	—
7	C₂×C₄×C₅×Dic₃	C₂²	1	21	yes	—
8	C₄²×C₅×D₃	C₄	1	56	yes	direct product factor
9	C₄³×D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₄²×C₅	—	3	7	no	—
11	C₄³×C₅	—	3	7	no	—
12	C₄³×C₅	D₃	1	1	yes	characteristic, direct product factor
13	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₅	C₂³	1	7	yes	—
15	C₂²×C₅×Dic₃	C₂³	1	7	yes	—
16	C₂×C₄×C₅×D₃	C₂×C₄	1	84	yes	—
17	C₃×C₄²×C₅	C₂×C₄	1	28	yes	complemented
18	C₄×C₅×Dic₃	C₂×C₄	1	84	yes	complemented
19	C₂×C₄²×D₃	C₂×C₅	1	7	yes	—
20	C₃×C₄³	C₂×C₅	1	1	yes	characteristic, complemented
21	C₄²×Dic₃	C₂×C₅	1	7	yes	complemented
22	C₂³×C₄×C₅	—	3	7	no	—
23	C₂×C₄²×C₅	—	3	21	no	—
24	C₂×C₄²×C₅	—	3	56	no	—
25	C₂×C₄²×C₅	C₂×D₃	1	7	yes	—
26	C₂×C₄³	—	3	1	no	Sylow
27	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
28	C₂²×C₅×D₃	C₂²×C₄	1	14	yes	—
29	C₂×C₃×C₄×C₅	C₂²×C₄	1	42	yes	—
30	C₂×C₅×Dic₃	C₂²×C₄	1	42	yes	—
31	C₄×C₅×D₃	C₄²	1	112	yes	direct product factor
32	C₂²×C₄×D₃	C₂²×C₅	1	7	yes	—
33	C₂×C₃×C₄²	C₂²×C₅	1	7	yes	—
34	C₂×C₄×Dic₃	C₂²×C₅	1	21	yes	—
35	C₄²×D₃	C₄×C₅	1	56	yes	direct product factor
36	C₂⁴×C₅	—	3	1	no	—
37	C₂²×C₄×C₅	—	3	7	no	—
38	C₂²×C₄×C₅	—	3	84	no	—
39	C₂²×C₄×C₅	C₂²×D₃	1	7	yes	—
40	C₄²×C₅	—	3	84	no	—
41	C₄²×C₅	C₄×D₃	1	28	yes	direct product factor
42	C₂²×C₄²	—	3	7	no	—
43	C₄³	—	3	7	no	—
44	C₄³	C₅×D₃	1	1	yes	characteristic, direct product factor
45	C₂²×C₃×C₅	C₂³×C₄	1	7	yes	—
46	C₂×C₅×D₃	C₂×C₄²	1	28	yes	—
47	C₃×C₄×C₅	C₂×C₄²	1	28	yes	complemented
48	C₅×Dic₃	C₂×C₄²	1	28	yes	complemented
49	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
50	C₂²×C₃×C₄	C₂³×C₅	1	7	yes	—
51	C₂²×Dic₃	C₂³×C₅	1	7	yes	—
52	C₂×C₄×D₃	C₂×C₄×C₅	1	84	yes	—
53	C₃×C₄²	C₂×C₄×C₅	1	28	yes	complemented
54	C₄×Dic₃	C₂×C₄×C₅	1	84	yes	complemented
55	C₂³×C₅	—	3	14	no	—
56	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
57	C₂×C₄×C₅	—	3	42	no	—
58	C₂×C₄×C₅	—	3	112	no	—
59	C₂×C₄×C₅	C₂×C₄×D₃	1	42	yes	—
60	C₂³×C₄	—	3	7	no	—
61	C₂×C₄²	—	3	21	no	—
62	C₂×C₄²	—	3	56	no	—
63	C₂×C₄²	C₂×C₅×D₃	1	7	yes	—
64	C₂×C₃×C₅	C₂²×C₄²	1	7	yes	—
65	C₅×D₃	C₄³	1	8	yes	direct product factor
66	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
67	C₂²×D₃	C₂²×C₄×C₅	1	14	yes	—
68	C₂×C₃×C₄	C₂²×C₄×C₅	1	42	yes	—
69	C₂×Dic₃	C₂²×C₄×C₅	1	42	yes	—
70	C₄×D₃	C₄²×C₅	1	112	yes	direct product factor
71	C₂²×C₅	—	3	28	no	—
72	C₂²×C₅	C₂²×C₄×D₃	1	7	yes	—
73	C₄×C₅	—	3	28	no	—
74	C₄×C₅	C₄²×D₃	1	28	yes	direct product factor
75	C₂⁴	—	3	1	no	—
76	C₂²×C₄	—	3	7	no	—
77	C₂²×C₄	—	3	84	no	—
78	C₂²×C₄	C₂²×C₅×D₃	1	7	yes	—
79	C₄²	—	3	84	no	—
80	C₄²	C₄×C₅×D₃	1	28	yes	direct product factor
81	C₃×C₅	C₂×C₄³	1	1	yes	characteristic, complemented, Hall
82	C₂²×C₃	C₂³×C₄×C₅	1	7	yes	—
83	C₂×D₃	C₂×C₄²×C₅	1	28	yes	—
84	C₃×C₄	C₂×C₄²×C₅	1	28	yes	complemented
85	Dic₃	C₂×C₄²×C₅	1	28	yes	complemented
86	C₂×C₅	—	3	8	no	—
87	C₂×C₅	C₂×C₄²×D₃	1	7	yes	—
88	C₂³	—	3	14	no	—
89	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
90	C₂×C₄	—	3	42	no	—
91	C₂×C₄	—	3	112	no	—
92	C₂×C₄	C₂×C₄×C₅×D₃	1	42	yes	—
93	C₂×C₃	C₂²×C₄²×C₅	1	7	yes	—
94	D₃	C₄³×C₅	1	8	yes	direct product factor
95	C₅	C₄³×D₃	1	1	yes	characteristic, direct product factor, Sylow
96	C₂²	—	3	28	no	—
97	C₂²	C₂²×C₄×C₅×D₃	1	7	yes	—
98	C₄	—	3	28	no	—
99	C₄	C₄²×C₅×D₃	1	28	yes	direct product factor
100	C₃	C₂×C₄³×C₅	1	1	yes	characteristic, complemented, Sylow
101	C₂	—	3	8	no	—
102	C₂	C₂×C₄²×C₅×D₃	1	7	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×C₅×D₃

C₂

yes

maximal

C₃×C₄³×C₅

C₂

yes

maximal, characteristic, complemented

C₄²×C₅×Dic₃

C₂

yes

maximal, complemented

C₂×C₄³×C₅

—

maximal, Hall

C₂²×C₄×C₅×D₃

C₂²

yes

—

C₂×C₃×C₄²×C₅

C₂²

yes

—

C₂×C₄×C₅×Dic₃

C₂²

yes

—

C₄²×C₅×D₃

C₄

yes

direct product factor

C₄³×D₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₄²×C₅

—

C₄³×C₅

—

C₄³×C₅

D₃

yes

characteristic, direct product factor

C₂³×C₅×D₃

C₂³

yes

characteristic

C₂²×C₃×C₄×C₅

C₂³

yes

—

C₂²×C₅×Dic₃

C₂³

yes

—

C₂×C₄×C₅×D₃

C₂×C₄

yes

—

C₃×C₄²×C₅

C₂×C₄

yes

complemented

C₄×C₅×Dic₃

C₂×C₄

yes

complemented

C₂×C₄²×D₃

C₂×C₅

yes

—

C₃×C₄³

C₂×C₅

yes

characteristic, complemented

C₄²×Dic₃

C₂×C₅

yes

complemented

C₂³×C₄×C₅

—

C₂×C₄²×C₅

—

C₂×C₄²×C₅

—

C₂×C₄²×C₅

C₂×D₃

yes

—

C₂×C₄³

—

Sylow

C₂³×C₃×C₅

C₂⁴

yes

characteristic

C₂²×C₅×D₃

C₂²×C₄

yes

—

C₂×C₃×C₄×C₅

C₂²×C₄

yes

—

C₂×C₅×Dic₃

C₂²×C₄

yes

—

C₄×C₅×D₃

C₄²

112

yes

direct product factor

C₂²×C₄×D₃

C₂²×C₅

yes

—

C₂×C₃×C₄²

C₂²×C₅

yes

—

C₂×C₄×Dic₃

C₂²×C₅

yes

—

C₄²×D₃

C₄×C₅

yes

direct product factor

C₂⁴×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²×D₃

yes

—

C₄²×C₅

—

C₄²×C₅

C₄×D₃

yes

direct product factor

C₂²×C₄²

—

C₄³

—

C₄³

C₅×D₃

yes

characteristic, direct product factor

C₂²×C₃×C₅

C₂³×C₄

yes

—

C₂×C₅×D₃

C₂×C₄²

yes

—

C₃×C₄×C₅

C₂×C₄²

yes

complemented

C₅×Dic₃

C₂×C₄²

yes

complemented

C₂³×D₃

C₂³×C₅

yes

characteristic

C₂²×C₃×C₄

C₂³×C₅

yes

—

C₂²×Dic₃

C₂³×C₅

yes

—

C₂×C₄×D₃

C₂×C₄×C₅

yes

—

C₃×C₄²

C₂×C₄×C₅

yes

complemented

C₄×Dic₃

C₂×C₄×C₅

yes

complemented

C₂³×C₅

—

C₂³×C₅

C₂³×D₃

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

112

—

C₂×C₄×C₅

C₂×C₄×D₃

yes

—

C₂³×C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×C₅×D₃

yes

—

C₂×C₃×C₅

C₂²×C₄²

yes

—

C₅×D₃

C₄³

yes

direct product factor

C₂³×C₃

C₂⁴×C₅

yes

characteristic

C₂²×D₃

C₂²×C₄×C₅

yes

—

C₂×C₃×C₄

C₂²×C₄×C₅

yes

—

C₂×Dic₃

C₂²×C₄×C₅

yes

—

C₄×D₃

C₄²×C₅

112

yes

direct product factor

C₂²×C₅

—

C₂²×C₅

C₂²×C₄×D₃

yes

—

C₄×C₅

—

C₄×C₅

C₄²×D₃

yes

direct product factor

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×C₅×D₃

yes

—

C₄²

—

C₄²

C₄×C₅×D₃

yes

direct product factor

C₃×C₅

C₂×C₄³

yes

characteristic, complemented, Hall

C₂²×C₃

C₂³×C₄×C₅

yes

—

C₂×D₃

C₂×C₄²×C₅

yes

—

C₃×C₄

C₂×C₄²×C₅

yes

complemented

Dic₃

C₂×C₄²×C₅

yes

complemented

C₂×C₅

—

C₂×C₅

C₂×C₄²×D₃

yes

—

C₂³

—

C₂³

C₂³×C₅×D₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

112

—

C₂×C₄

C₂×C₄×C₅×D₃

yes

—

C₂×C₃

C₂²×C₄²×C₅

yes

—

D₃

C₄³×C₅

yes

direct product factor

C₅

C₄³×D₃

yes

characteristic, direct product factor, Sylow

C₂²

—

C₂²

C₂²×C₄×C₅×D₃

yes

—

C₄

—

C₄

C₄²×C₅×D₃

yes

direct product factor

100

C₃

C₂×C₄³×C₅

yes

characteristic, complemented, Sylow

101

C₂

—

102

C₂

C₂×C₄²×C₅×D₃

yes

—

	subgroup	G/H
center, hypercenter	C₄³×C₅	D₃
commutator, hypocenter	C₃	C₂×C₄³×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄³×C₅	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₄³×C₅

subgroup

G/H

center, hypercenter

C₄³×C₅

D₃

commutator, hypocenter

C₃

C₂×C₄³×C₅

Frattini

C₂³

C₂³×C₅×D₃

Fitting

C₃×C₄³×C₅

C₂

socle

C₂³×C₃×C₅

C₂⁴

prime radical

C₂³×C₅×D₃

C₂³

cosocle

C₂³×C₃

C₂⁴×C₅

LCS

G ▷ C₃

UCS

C₁ ◁ C₄³×C₅

N	H ≅ G/N	type
2. C₃×C₄³×C₅	C₂	semidirect
3. C₄²×C₅×Dic₃	C₂	semidirect
8. C₄²×C₅×D₃	C₄	direct (N × H)
9. C₄³×D₃	C₅	direct (N × H)
12. C₄³×C₅	D₃	direct (N × H)
17. C₃×C₄²×C₅	C₂×C₄	semidirect
18. C₄×C₅×Dic₃	C₂×C₄	semidirect
20. C₃×C₄³	C₂×C₅	semidirect
21. C₄²×Dic₃	C₂×C₅	semidirect
31. C₄×C₅×D₃	C₄²	direct (N × H)
35. C₄²×D₃	C₄×C₅	direct (N × H)
41. C₄²×C₅	C₄×D₃	direct (N × H)
44. C₄³	C₅×D₃	direct (N × H)
47. C₃×C₄×C₅	C₂×C₄²	semidirect
48. C₅×Dic₃	C₂×C₄²	semidirect
53. C₃×C₄²	C₂×C₄×C₅	semidirect
54. C₄×Dic₃	C₂×C₄×C₅	semidirect
65. C₅×D₃	C₄³	direct (N × H)
70. C₄×D₃	C₄²×C₅	direct (N × H)
74. C₄×C₅	C₄²×D₃	direct (N × H)
80. C₄²	C₄×C₅×D₃	direct (N × H)
81. C₃×C₅	C₂×C₄³	semidirect
84. C₃×C₄	C₂×C₄²×C₅	semidirect
85. Dic₃	C₂×C₄²×C₅	semidirect
94. D₃	C₄³×C₅	direct (N × H)
95. C₅	C₄³×D₃	direct (N × H)
99. C₄	C₄²×C₅×D₃	direct (N × H)
100. C₃	C₂×C₄³×C₅	semidirect

H ≅ G/N

type

2. C₃×C₄³×C₅

C₂

semidirect

3. C₄²×C₅×Dic₃

C₂

semidirect

8. C₄²×C₅×D₃

C₄

direct (N × H)

9. C₄³×D₃

C₅

direct (N × H)

12. C₄³×C₅

D₃

direct (N × H)

17. C₃×C₄²×C₅

C₂×C₄

semidirect

18. C₄×C₅×Dic₃

C₂×C₄

semidirect

20. C₃×C₄³

C₂×C₅

semidirect

21. C₄²×Dic₃

C₂×C₅

semidirect

31. C₄×C₅×D₃

C₄²

direct (N × H)

35. C₄²×D₃

C₄×C₅

direct (N × H)

41. C₄²×C₅

C₄×D₃

direct (N × H)

44. C₄³

C₅×D₃

direct (N × H)

47. C₃×C₄×C₅

C₂×C₄²

semidirect

48. C₅×Dic₃

C₂×C₄²

semidirect

53. C₃×C₄²

C₂×C₄×C₅

semidirect

54. C₄×Dic₃

C₂×C₄×C₅

semidirect

65. C₅×D₃

C₄³

direct (N × H)

70. C₄×D₃

C₄²×C₅

direct (N × H)

74. C₄×C₅

C₄²×D₃

direct (N × H)

80. C₄²

C₄×C₅×D₃

direct (N × H)

81. C₃×C₅

C₂×C₄³

semidirect

84. C₃×C₄

C₂×C₄²×C₅

semidirect

85. Dic₃

C₂×C₄²×C₅

semidirect

94. D₃

C₄³×C₅

direct (N × H)

95. C₅

C₄³×D₃

direct (N × H)

99. C₄

C₄²×C₅×D₃

direct (N × H)

100. C₃

C₂×C₄³×C₅

semidirect

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₃×C₄³×C₅	2
C₄²×C₅×Dic₃	2
C₂×C₄³×C₅	3
C₄³×D₃	5

subgroup

index

C₂×C₄²×C₅×D₃

C₃×C₄³×C₅

C₄²×C₅×Dic₃

C₂×C₄³×C₅

C₄³×D₃

Subgroups — C₄³×C₅×D₃ #14319317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43×C5×D3 #14319317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₅×D₃ #14319317