Group #15748964 — subgroups

Subgroups — C₂³×C₁₃×D₁₆ #15748964

Order 3328.

2590 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

normal subgroups only

This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1054 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	C₂³×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×D₁₆	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄×C₁₃	—	2	2	no	—
5	C₂²×C₁₃×D₈	—	2	14	no	—
6	C₂²×C₁₃×D₈	C₂²	1	28	yes	complemented
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×D₁₆	C₂²	1	112	yes	direct product factor
9	C₂²×C₁₃×C₁₆	C₂²	1	14	yes	complemented
10	C₂⁵×C₁₃	—	4	2	no	—
11	C₂²×D₄×C₁₃	—	2	28	no	—
12	C₂²×D₄×C₁₃	—	4	14	no	—
13	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₁₃×D₈	—	2	84	no	—
15	C₂×C₁₃×D₈	C₂³	1	56	yes	complemented
16	C₂²×C₈×C₁₃	D₄	1	7	yes	—
17	C₂²×C₈×C₁₃	C₂³	1	7	yes	—
18	C₁₃×D₁₆	C₂³	1	64	yes	direct product factor
19	C₂×C₁₃×C₁₆	C₂³	1	28	yes	complemented
20	C₂³×D₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂⁴×C₁₃	—	4	28	no	—
22	C₂⁴×C₁₃	—	8	16	no	—
23	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
24	C₂×D₄×C₁₃	—	2	56	no	—
25	C₂×D₄×C₁₃	—	4	84	no	—
26	C₂²×C₄×C₁₃	D₈	1	7	yes	—
27	C₂²×C₄×C₁₃	C₂×D₄	1	7	yes	—
28	C₁₃×D₈	—	2	56	no	—
29	C₁₃×D₈	C₂⁴	1	16	yes	complemented
30	C₂×C₈×C₁₃	C₂×D₄	1	21	yes	—
31	C₂×C₈×C₁₃	C₂⁴	1	7	yes	—
32	C₁₃×C₁₆	C₂⁴	1	8	yes	complemented
33	C₂³×D₈	C₂×C₁₃	1	2	yes	complemented
34	C₂²×D₁₆	C₂×C₁₃	1	28	yes	direct product factor
35	C₂³×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
36	C₂³×C₁₃	—	4	56	no	—
37	C₂³×C₁₃	—	8	112	no	—
38	C₂³×C₁₃	D₁₆	1	8	yes	direct product factor
39	C₂³×C₁₃	C₂×D₈	1	7	yes	—
40	D₄×C₁₃	—	2	16	no	—
41	D₄×C₁₃	—	4	56	no	—
42	C₂×C₄×C₁₃	C₂×D₈	1	21	yes	—
43	C₂×C₄×C₁₃	C₂²×D₄	1	7	yes	—
44	C₈×C₁₃	C₂²×D₄	1	7	yes	—
45	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
46	C₂³×D₄	—	2	2	no	—
47	C₂²×D₈	—	2	14	no	—
48	C₂²×D₈	C₂²×C₁₃	1	28	yes	complemented
49	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
50	C₂×D₁₆	C₂²×C₁₃	1	112	yes	direct product factor
51	C₂²×C₁₆	C₂²×C₁₃	1	14	yes	complemented
52	C₂²×C₁₃	—	4	16	no	—
53	C₂²×C₁₃	—	8	112	no	—
54	C₂²×C₁₃	C₂×D₁₆	1	28	yes	direct product factor
55	C₂²×C₁₃	C₂²×D₈	1	7	yes	—
56	C₄×C₁₃	C₂²×D₈	1	7	yes	—
57	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
58	C₂⁵	—	4	2	no	—
59	C₂²×D₄	—	2	28	no	—
60	C₂²×D₄	—	4	14	no	—
61	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
62	C₂×D₈	—	2	84	no	—
63	C₂×D₈	C₂³×C₁₃	1	56	yes	complemented
64	C₂²×C₈	D₄×C₁₃	1	7	yes	—
65	C₂²×C₈	C₂³×C₁₃	1	7	yes	—
66	D₁₆	C₂³×C₁₃	1	64	yes	direct product factor
67	C₂×C₁₆	C₂³×C₁₃	1	28	yes	complemented
68	C₂×C₁₃	—	8	16	no	—
69	C₂×C₁₃	C₂²×D₁₆	1	14	yes	direct product factor
70	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
71	C₂⁴	—	4	28	no	—
72	C₂⁴	—	8	16	no	—
73	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
74	C₂×D₄	—	2	56	no	—
75	C₂×D₄	—	4	84	no	—
76	C₂²×C₄	C₁₃×D₈	1	7	yes	—
77	C₂²×C₄	C₂×D₄×C₁₃	1	7	yes	—
78	D₈	—	2	56	no	—
79	D₈	C₂⁴×C₁₃	1	16	yes	complemented
80	C₂×C₈	C₂×D₄×C₁₃	1	21	yes	—
81	C₂×C₈	C₂⁴×C₁₃	1	7	yes	—
82	C₁₆	C₂⁴×C₁₃	1	8	yes	complemented
83	C₁₃	C₂³×D₁₆	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³	—	4	56	no	—
85	C₂³	—	8	112	no	—
86	C₂³	C₁₃×D₁₆	1	8	yes	direct product factor
87	C₂³	C₂×C₁₃×D₈	1	7	yes	—
88	D₄	—	2	16	no	—
89	D₄	—	4	56	no	—
90	C₂×C₄	C₂×C₁₃×D₈	1	21	yes	—
91	C₂×C₄	C₂²×D₄×C₁₃	1	7	yes	—
92	C₈	C₂²×D₄×C₁₃	1	7	yes	—
93	C₈	C₂⁵×C₁₃	1	1	yes	characteristic
94	C₂²	—	4	16	no	—
95	C₂²	—	8	112	no	—
96	C₂²	C₂×C₁₃×D₁₆	1	28	yes	direct product factor
97	C₂²	C₂²×C₁₃×D₈	1	7	yes	—
98	C₄	C₂²×C₁₃×D₈	1	7	yes	—
99	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
100	C₂	—	8	16	no	—
101	C₂	C₂²×C₁₃×D₁₆	1	14	yes	direct product factor
102	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₁₃×D₈

C₂

yes

maximal, complemented

C₂²×C₁₃×D₁₆

C₂

yes

maximal, direct product factor

C₂³×C₁₃×C₁₆

C₂

yes

maximal, characteristic, complemented

C₂³×D₄×C₁₃

—

C₂²×C₁₃×D₈

—

C₂²×C₁₃×D₈

C₂²

yes

complemented

C₂³×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×D₁₆

C₂²

112

yes

direct product factor

C₂²×C₁₃×C₁₆

C₂²

yes

complemented

C₂⁵×C₁₃

—

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

—

C₂³×C₄×C₁₃

D₄

yes

characteristic

C₂×C₁₃×D₈

—

C₂×C₁₃×D₈

C₂³

yes

complemented

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

—

C₁₃×D₁₆

C₂³

yes

direct product factor

C₂×C₁₃×C₁₆

C₂³

yes

complemented

C₂³×D₁₆

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂⁴×C₁₃

—

C₂⁴×C₁₃

D₈

yes

characteristic

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

D₈

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₁₃×D₈

—

C₁₃×D₈

C₂⁴

yes

complemented

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂⁴

yes

—

C₁₃×C₁₆

C₂⁴

yes

complemented

C₂³×D₈

C₂×C₁₃

yes

complemented

C₂²×D₁₆

C₂×C₁₃

yes

direct product factor

C₂³×C₁₆

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

112

—

C₂³×C₁₃

D₁₆

yes

direct product factor

C₂³×C₁₃

C₂×D₈

yes

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

C₂²×D₄

yes

—

C₈×C₁₃

C₂²×D₄

yes

—

C₈×C₁₃

C₂⁵

yes

characteristic

C₂³×D₄

—

C₂²×D₈

—

C₂²×D₈

C₂²×C₁₃

yes

complemented

C₂³×C₈

C₂²×C₁₃

yes

characteristic

C₂×D₁₆

C₂²×C₁₃

112

yes

direct product factor

C₂²×C₁₆

C₂²×C₁₃

yes

complemented

C₂²×C₁₃

—

C₂²×C₁₃

—

112

—

C₂²×C₁₃

C₂×D₁₆

yes

direct product factor

C₂²×C₁₃

C₂²×D₈

yes

—

C₄×C₁₃

C₂²×D₈

yes

—

C₄×C₁₃

C₂³×D₄

yes

characteristic

C₂⁵

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

D₄×C₁₃

yes

characteristic

C₂×D₈

—

C₂×D₈

C₂³×C₁₃

yes

complemented

C₂²×C₈

D₄×C₁₃

yes

—

C₂²×C₈

C₂³×C₁₃

yes

—

D₁₆

C₂³×C₁₃

yes

direct product factor

C₂×C₁₆

C₂³×C₁₃

yes

complemented

C₂×C₁₃

—

C₂×C₁₃

C₂²×D₁₆

yes

direct product factor

C₂×C₁₃

C₂³×D₈

yes

characteristic

C₂⁴

—

C₂⁴

—

C₂⁴

C₁₃×D₈

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₁₃×D₈

yes

—

C₂²×C₄

C₂×D₄×C₁₃

yes

—

D₈

—

D₈

C₂⁴×C₁₃

yes

complemented

C₂×C₈

C₂×D₄×C₁₃

yes

—

C₂×C₈

C₂⁴×C₁₃

yes

—

C₁₆

C₂⁴×C₁₃

yes

complemented

C₁₃

C₂³×D₁₆

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

112

—

C₂³

C₁₃×D₁₆

yes

direct product factor

C₂³

C₂×C₁₃×D₈

yes

—

D₄

—

D₄

—

C₂×C₄

C₂×C₁₃×D₈

yes

—

C₂×C₄

C₂²×D₄×C₁₃

yes

—

C₈

C₂²×D₄×C₁₃

yes

—

C₈

C₂⁵×C₁₃

yes

characteristic

C₂²

—

C₂²

—

112

—

C₂²

C₂×C₁₃×D₁₆

yes

direct product factor

C₂²

C₂²×C₁₃×D₈

yes

—

C₄

C₂²×C₁₃×D₈

yes

—

C₄

C₂³×D₄×C₁₃

yes

characteristic

100

C₂

—

101

C₂

C₂²×C₁₃×D₁₆

yes

direct product factor

102

C₂

C₂³×C₁₃×D₈

yes

characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₁₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂⁴×C₁₃

D₈

commutator, Frattini, cosocle

C₈

C₂⁵×C₁₃

LCS

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂⁴×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₂³×C₁₃×D₈	C₂	semidirect
2. C₂²×C₁₃×D₁₆	C₂	direct (N × H)
3. C₂³×C₁₃×C₁₆	C₂	semidirect
6. C₂²×C₁₃×D₈	C₂²	semidirect
8. C₂×C₁₃×D₁₆	C₂²	direct (N × H)
9. C₂²×C₁₃×C₁₆	C₂²	semidirect
15. C₂×C₁₃×D₈	C₂³	semidirect
18. C₁₃×D₁₆	C₂³	direct (N × H)
19. C₂×C₁₃×C₁₆	C₂³	semidirect
20. C₂³×D₁₆	C₁₃	direct (N × H)
29. C₁₃×D₈	C₂⁴	semidirect
32. C₁₃×C₁₆	C₂⁴	semidirect
33. C₂³×D₈	C₂×C₁₃	semidirect
34. C₂²×D₁₆	C₂×C₁₃	direct (N × H)
35. C₂³×C₁₆	C₂×C₁₃	semidirect
38. C₂³×C₁₃	D₁₆	direct (N × H)
48. C₂²×D₈	C₂²×C₁₃	semidirect
50. C₂×D₁₆	C₂²×C₁₃	direct (N × H)
51. C₂²×C₁₆	C₂²×C₁₃	semidirect
54. C₂²×C₁₃	C₂×D₁₆	direct (N × H)
63. C₂×D₈	C₂³×C₁₃	semidirect
66. D₁₆	C₂³×C₁₃	direct (N × H)
67. C₂×C₁₆	C₂³×C₁₃	semidirect
69. C₂×C₁₃	C₂²×D₁₆	direct (N × H)
79. D₈	C₂⁴×C₁₃	semidirect
82. C₁₆	C₂⁴×C₁₃	semidirect
83. C₁₃	C₂³×D₁₆	direct (N × H)
86. C₂³	C₁₃×D₁₆	direct (N × H)
96. C₂²	C₂×C₁₃×D₁₆	direct (N × H)
101. C₂	C₂²×C₁₃×D₁₆	direct (N × H)

H ≅ G/N

type

1. C₂³×C₁₃×D₈

C₂

semidirect

2. C₂²×C₁₃×D₁₆

C₂

direct (N × H)

3. C₂³×C₁₃×C₁₆

C₂

semidirect

6. C₂²×C₁₃×D₈

C₂²

semidirect

8. C₂×C₁₃×D₁₆

C₂²

direct (N × H)

9. C₂²×C₁₃×C₁₆

C₂²

semidirect

15. C₂×C₁₃×D₈

C₂³

semidirect

18. C₁₃×D₁₆

C₂³

direct (N × H)

19. C₂×C₁₃×C₁₆

C₂³

semidirect

20. C₂³×D₁₆

C₁₃

direct (N × H)

29. C₁₃×D₈

C₂⁴

semidirect

32. C₁₃×C₁₆

C₂⁴

semidirect

33. C₂³×D₈

C₂×C₁₃

semidirect

34. C₂²×D₁₆

C₂×C₁₃

direct (N × H)

35. C₂³×C₁₆

C₂×C₁₃

semidirect

38. C₂³×C₁₃

D₁₆

direct (N × H)

48. C₂²×D₈

C₂²×C₁₃

semidirect

50. C₂×D₁₆

C₂²×C₁₃

direct (N × H)

51. C₂²×C₁₆

C₂²×C₁₃

semidirect

54. C₂²×C₁₃

C₂×D₁₆

direct (N × H)

63. C₂×D₈

C₂³×C₁₃

semidirect

66. D₁₆

C₂³×C₁₃

direct (N × H)

67. C₂×C₁₆

C₂³×C₁₃

semidirect

69. C₂×C₁₃

C₂²×D₁₆

direct (N × H)

79. D₈

C₂⁴×C₁₃

semidirect

82. C₁₆

C₂⁴×C₁₃

semidirect

83. C₁₃

C₂³×D₁₆

direct (N × H)

86. C₂³

C₁₃×D₁₆

direct (N × H)

96. C₂²

C₂×C₁₃×D₁₆

direct (N × H)

101. C₂

C₂²×C₁₃×D₁₆

direct (N × H)

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

subgroup	index
C₂³×C₁₃×D₈	2
C₂²×C₁₃×D₁₆	2
C₂³×C₁₃×C₁₆	2
C₂³×D₁₆	13

subgroup

index

C₂³×C₁₃×D₈

C₂²×C₁₃×D₁₆

C₂³×C₁₃×C₁₆

C₂³×D₁₆

Subgroups — C₂³×C₁₃×D₁₆ #15748964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×C13×D16 #15748964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₃×D₁₆ #15748964