Group #15699228 — subgroups

Subgroups — C₁₃×#12889 #15699228

Order 3328.

310 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 174 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×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1846	C₂	1	2	yes	maximal
3	C₁₃×#1380	C₂	1	4	yes	maximal
4	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
5	C₂×C₁₃×#107	C₂²	1	4	yes	—
6	C₂×C₁₃×#106	—	2	2	no	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#382	—	2	2	no	—
9	C₄×C₁₃×C₁₆	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
13	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	—	2	4	no	—
15	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
16	C₁₃×#107	—	2	8	no	—
17	C₁₃×#106	—	4	4	no	—
18	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₃	Q₈	1	2	yes	—
20	C₁₃×#95	—	4	4	no	—
21	#12889	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₄×C₁₃	—	4	4	no	—
23	C₂²×C₄×C₁₃	D₈	1	2	yes	—
24	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
27	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₈×C₁₃	#41	1	4	yes	—
30	C₁₃×C₄⋊C₄	—	4	4	no	—
31	C₁₃×C₄⋊C₄	—	4	4	no	—
32	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
33	C₄²×C₁₃	Q₁₆	1	2	yes	—
34	C₁₃×C₁₆	—	2	4	no	—
35	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
36	#1846	C₂×C₁₃	1	2	yes	—
37	#1380	C₂×C₁₃	1	4	yes	—
38	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
39	C₂×C₄×C₁₃	—	2	4	no	—
40	C₂×C₄×C₁₃	—	8	4	no	—
41	C₂×C₄×C₁₃	—	8	8	no	—
42	C₂×C₄×C₁₃	#107	1	4	yes	—
43	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₃	#124	1	2	yes	—
45	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
46	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
47	C₈×C₁₃	#106	1	4	yes	—
48	C₈×C₁₃	#117	1	2	yes	—
49	C₈×C₁₃	#125	1	2	yes	—
50	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
51	C₂×#107	C₂²×C₁₃	1	4	yes	—
52	C₂×#106	—	2	2	no	—
53	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
54	#382	—	2	2	no	—
55	C₄×C₁₆	C₄×C₁₃	1	4	yes	complemented
56	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
57	C₂²×C₁₃	#486	1	2	yes	—
58	C₂²×C₁₃	#508	1	4	yes	—
59	C₄×C₁₃	—	2	4	no	—
60	C₄×C₁₃	—	16	4	no	—
61	C₄×C₁₃	#382	1	1	yes	characteristic
62	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
63	C₄×C₁₃	#487	1	2	yes	—
64	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
65	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
66	C₂×C₄⋊C₄	—	2	4	no	—
67	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
68	C₂×C₁₆	—	2	4	no	—
69	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
70	#107	—	2	8	no	—
71	#106	—	4	4	no	—
72	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
73	C₄×C₈	Q₈×C₁₃	1	2	yes	—
74	#95	—	4	4	no	—
75	C₂×C₁₃	#1834	1	1	yes	characteristic
76	C₂×C₁₃	#2158	1	2	yes	—
77	C₂×C₁₃	#2242	1	4	yes	—
78	C₂²×C₄	—	4	4	no	—
79	C₂²×C₄	C₁₃×D₈	1	2	yes	—
80	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
81	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
82	C₂×C₈	C₁₃×SD₁₆	1	4	yes	—
83	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
84	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
85	C₂×C₈	C₁₃×#41	1	4	yes	—
86	C₄⋊C₄	—	4	4	no	—
87	C₄⋊C₄	—	4	4	no	—
88	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
89	C₄²	C₁₃×Q₁₆	1	2	yes	—
90	C₁₆	—	2	4	no	—
91	C₁₃	#12889	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	8	4	no	—
95	C₂×C₄	—	8	8	no	—
96	C₂×C₄	C₁₃×#107	1	4	yes	—
97	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄	C₁₃×#124	1	2	yes	—
99	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
100	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
101	C₈	C₁₃×#106	1	4	yes	—
102	C₈	C₁₃×#117	1	2	yes	—
103	C₈	C₁₃×#125	1	2	yes	—
104	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
105	C₂²	C₁₃×#486	1	2	yes	—
106	C₂²	C₁₃×#508	1	4	yes	—
107	C₄	—	2	4	no	—
108	C₄	—	16	4	no	—
109	C₄	C₁₃×#382	1	1	yes	characteristic
110	C₄	C₂×C₁₃×#106	1	1	yes	characteristic
111	C₄	C₁₃×#487	1	2	yes	—
112	C₂	C₁₃×#1834	1	1	yes	characteristic
113	C₂	C₁₃×#2158	1	2	yes	—
114	C₂	C₁₃×#2242	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₁₃×C₁₆

C₂

yes

maximal, characteristic

C₁₃×#1846

C₂

yes

maximal

C₁₃×#1380

C₂

yes

maximal

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₁₃×#107

C₂²

yes

—

C₂×C₁₃×#106

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#382

—

C₄×C₁₃×C₁₆

C₄

yes

complemented

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₁₃×#107

—

C₁₃×#106

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₁₃×#95

—

#12889

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

D₈

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

Q₁₆

yes

—

C₁₃×C₁₆

—

C₂×C₄×C₁₆

C₂×C₁₃

yes

characteristic

#1846

C₂×C₁₃

yes

—

#1380

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#117

yes

—

C₈×C₁₃

#125

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

—

C₂×#107

C₂²×C₁₃

yes

—

C₂×#106

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#382

—

C₄×C₁₆

C₄×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

#508

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂²×C₈

D₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

D₄×C₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

#107

—

#106

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

#95

—

C₂×C₁₃

#1834

yes

characteristic

C₂×C₁₃

#2158

yes

—

C₂×C₁₃

#2242

yes

—

C₂²×C₄

—

C₂²×C₄

C₁₃×D₈

yes

—

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×SD₁₆

yes

—

C₂×C₈

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

C₂×Q₈×C₁₃

yes

characteristic

C₂×C₈

C₁₃×#41

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₁₃×C₄⋊C₄

yes

—

C₄²

C₁₃×Q₁₆

yes

—

C₁₆

—

C₁₃

#12889

yes

characteristic, direct product factor, Sylow

C₂³

C₂×C₁₃×D₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₃×#107

yes

—

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

C₂×C₄

C₁₃×#124

yes

—

C₂×C₄

C₂×C₁₃×SD₁₆

yes

—

100

C₂×C₄

C₂×C₁₃×Q₁₆

yes

characteristic

101

C₈

C₁₃×#106

yes

—

102

C₈

C₁₃×#117

yes

—

103

C₈

C₁₃×#125

yes

—

104

C₂²

C₂×C₁₃×#107

yes

characteristic

105

C₂²

C₁₃×#486

yes

—

106

C₂²

C₁₃×#508

yes

—

107

C₄

—

108

C₄

—

109

C₄

C₁₃×#382

yes

characteristic

110

C₄

C₂×C₁₃×#106

yes

characteristic

111

C₄

C₁₃×#487

yes

—

112

C₂

C₁₃×#1834

yes

characteristic

113

C₂

C₁₃×#2158

yes

—

114

C₂

C₁₃×#2242

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

C₂×D₈

commutator

C₂×C₈

C₂²×C₄×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
9. C₄×C₁₃×C₁₆	C₄	semidirect
21. #12889	C₁₃	direct (N × H)
55. C₄×C₁₆	C₄×C₁₃	semidirect
91. C₁₃	#12889	direct (N × H)

H ≅ G/N

type

9. C₄×C₁₃×C₁₆

C₄

semidirect

21. #12889

C₁₃

direct (N × H)

55. C₄×C₁₆

C₄×C₁₃

semidirect

91. C₁₃

#12889

direct (N × H)

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

subgroup	index
C₂×C₄×C₁₃×C₁₆	2
C₁₃×#1846	2
C₁₃×#1380	2
#12889	13

subgroup

index

C₂×C₄×C₁₃×C₁₆

C₁₃×#1846

C₁₃×#1380

#12889

Subgroups — C₁₃×#12889 #15699228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12889 #15699228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12889 #15699228