Group #15695155 — subgroups

Subgroups — C₁₃×#8816 #15695155

Order 3328.

422 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 238 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	C₁₃×#1845	C₂	1	2	yes	maximal
2	C₁₃×#1834	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#107	—	2	4	no	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#384	C₂²	1	4	yes	—
8	C₁₃×#340	—	2	8	no	—
9	C₈²×C₁₃	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₃	D₄	1	4	yes	—
11	C₂²×C₈×C₁₃	D₄	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
13	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
14	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×#107	—	4	8	no	—
16	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₃	Q₈	1	4	yes	—
19	C₄×C₈×C₁₃	Q₈	1	2	yes	—
20	#8816	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₄×C₁₃	—	4	4	no	—
22	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
24	C₂×C₈×C₁₃	—	2	8	no	—
25	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
26	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
27	C₂×C₈×C₁₃	D₈	1	4	yes	—
28	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
29	C₁₃×C₄⋊C₄	—	4	8	no	—
30	C₁₃×C₄⋊C₄	—	4	16	no	—
31	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
34	#1845	C₂×C₁₃	1	2	yes	—
35	#1834	C₂×C₁₃	1	4	yes	—
36	C₂×C₈²	C₂×C₁₃	1	1	yes	characteristic
37	C₂³×C₁₃	#127	1	1	yes	characteristic
38	C₂×C₄×C₁₃	—	8	4	no	—
39	C₂×C₄×C₁₃	—	8	8	no	—
40	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
43	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
44	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
45	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
46	C₂×C₄×C₁₃	#135	1	8	yes	—
47	C₈×C₁₃	—	2	8	no	—
48	C₈×C₁₃	#107	1	8	yes	—
49	C₂×#107	—	2	4	no	—
50	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
51	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
52	#384	C₂²×C₁₃	1	4	yes	—
53	#340	—	2	8	no	—
54	C₈²	C₄×C₁₃	1	4	yes	complemented
55	C₂²×C₁₃	#384	1	1	yes	characteristic
56	C₂²×C₁₃	#493	1	1	yes	characteristic
57	C₂²×C₁₃	#494	1	1	yes	characteristic
58	C₂²×C₁₃	#495	1	4	yes	—
59	C₄×C₁₃	—	16	4	no	—
60	C₄×C₁₃	C₂×#107	1	2	yes	—
61	C₄×C₁₃	#427	1	4	yes	—
62	C₄×C₁₃	#499	1	4	yes	—
63	C₄×C₁₃	#500	1	2	yes	—
64	C₂²×C₈	D₄×C₁₃	1	4	yes	—
65	C₂²×C₈	D₄×C₁₃	1	2	yes	—
66	C₂×C₄⋊C₄	—	2	8	no	—
67	C₂×C₄⋊C₄	—	2	4	no	—
68	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
69	#107	—	4	8	no	—
70	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
71	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
72	C₄×C₈	Q₈×C₁₃	1	4	yes	—
73	C₄×C₈	Q₈×C₁₃	1	2	yes	—
74	C₂×C₁₃	#1709	1	2	yes	—
75	C₂×C₁₃	#1710	1	2	yes	—
76	C₂×C₁₃	#1845	1	1	yes	characteristic
77	C₂×C₁₃	#1846	1	2	yes	—
78	C₂²×C₄	—	4	4	no	—
79	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
80	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
81	C₂×C₈	—	2	8	no	—
82	C₂×C₈	C₁₃×C₄⋊C₄	1	8	yes	—
83	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
84	C₂×C₈	C₁₃×D₈	1	4	yes	—
85	C₂×C₈	C₁₃×Q₁₆	1	4	yes	—
86	C₄⋊C₄	—	4	8	no	—
87	C₄⋊C₄	—	4	16	no	—
88	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
89	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
90	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
91	C₁₃	#8816	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³	C₁₃×#127	1	1	yes	characteristic
93	C₂×C₄	—	8	4	no	—
94	C₂×C₄	—	8	8	no	—
95	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
97	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
98	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
99	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
100	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
101	C₂×C₄	C₁₃×#135	1	8	yes	—
102	C₈	—	2	8	no	—
103	C₈	C₁₃×#107	1	8	yes	—
104	C₂²	C₁₃×#384	1	1	yes	characteristic
105	C₂²	C₁₃×#493	1	1	yes	characteristic
106	C₂²	C₁₃×#494	1	1	yes	characteristic
107	C₂²	C₁₃×#495	1	4	yes	—
108	C₄	—	16	4	no	—
109	C₄	C₂×C₁₃×#107	1	2	yes	—
110	C₄	C₁₃×#427	1	4	yes	—
111	C₄	C₁₃×#499	1	4	yes	—
112	C₄	C₁₃×#500	1	2	yes	—
113	C₂	C₁₃×#1709	1	2	yes	—
114	C₂	C₁₃×#1710	1	2	yes	—
115	C₂	C₁₃×#1845	1	1	yes	characteristic
116	C₂	C₁₃×#1846	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#1845

C₂

yes

maximal

C₁₃×#1834

C₂

yes

maximal

C₂×C₈²×C₁₃

C₂

yes

maximal, characteristic

C₂×C₁₃×#107

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

C₁₃×#340

—

C₈²×C₁₃

C₄

yes

complemented

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#107

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#8816

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

D₈

yes

—

C₂×C₈×C₁₃

Q₁₆

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

—

#1845

C₂×C₁₃

yes

—

#1834

C₂×C₁₃

yes

—

C₂×C₈²

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#127

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₈×C₁₃

—

C₈×C₁₃

#107

yes

—

C₂×#107

—

C₂×C₄×C₈

C₂²×C₁₃

yes

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#384

C₂²×C₁₃

yes

—

#340

—

C₈²

C₄×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×#107

yes

—

C₄×C₁₃

#427

yes

—

C₄×C₁₃

#499

yes

—

C₄×C₁₃

#500

yes

—

C₂²×C₈

D₄×C₁₃

yes

—

C₂²×C₈

D₄×C₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

#107

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₂×C₁₃

#1709

yes

—

C₂×C₁₃

#1710

yes

—

C₂×C₁₃

#1845

yes

characteristic

C₂×C₁₃

#1846

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

C₂²×C₄

C₂×D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×D₈

yes

—

C₂×C₈

C₁₃×Q₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×C₄×C₁₃

yes

characteristic

C₄²

C₂×Q₈×C₁₃

yes

characteristic

C₄²

C₂×Q₈×C₁₃

yes

—

C₁₃

#8816

yes

characteristic, direct product factor, Sylow

C₂³

C₁₃×#127

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

—

C₂×C₄

C₁₃×C₄⋊Q₈

yes

—

C₂×C₄

C₁₃×C₄⋊Q₈

yes

characteristic

C₂×C₄

C₂×C₁₃×D₈

yes

—

100

C₂×C₄

C₂×C₁₃×Q₁₆

yes

—

101

C₂×C₄

C₁₃×#135

yes

—

102

C₈

—

103

C₈

C₁₃×#107

yes

—

104

C₂²

C₁₃×#384

yes

characteristic

105

C₂²

C₁₃×#493

yes

characteristic

106

C₂²

C₁₃×#494

yes

characteristic

107

C₂²

C₁₃×#495

yes

—

108

C₄

—

109

C₄

C₂×C₁₃×#107

yes

—

110

C₄

C₁₃×#427

yes

—

111

C₄

C₁₃×#499

yes

—

112

C₄

C₁₃×#500

yes

—

113

C₂

C₁₃×#1709

yes

—

114

C₂

C₁₃×#1710

yes

—

115

C₂

C₁₃×#1845

yes

characteristic

116

C₂

C₁₃×#1846

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

#127

commutator

C₄²

C₂²×C₄×C₁₃

Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
9. C₈²×C₁₃	C₄	semidirect
20. #8816	C₁₃	direct (N × H)
54. C₈²	C₄×C₁₃	semidirect
91. C₁₃	#8816	direct (N × H)

H ≅ G/N

type

9. C₈²×C₁₃

C₄

semidirect

20. #8816

C₁₃

direct (N × H)

54. C₈²

C₄×C₁₃

semidirect

91. C₁₃

#8816

direct (N × H)

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

subgroup	index
C₁₃×#1845	2
C₁₃×#1834	2
C₂×C₈²×C₁₃	2
#8816	13

subgroup

index

C₁₃×#1845

C₁₃×#1834

C₂×C₈²×C₁₃

#8816

Subgroups — C₁₃×#8816 #15695155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#8816 #15695155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8816 #15695155