Group #13111148 — subgroups

Subgroups — C₁₃×#2090 #13111148

Order 1664.

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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×#428	C₂	1	2	yes	maximal
2	C₂×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#424	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#343	C₂	1	2	yes	maximal
5	C₁₃×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#117	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₁₃×#107	—	2	2	no	—
12	C₁₃×#106	—	2	2	no	—
13	C₁₃×#106	—	2	2	no	—
14	C₁₃×C₄⋊C₈	—	2	2	no	—
15	C₂²×C₄×C₁₃	—	2	2	no	—
16	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₁₃×M₁₆	—	2	2	no	—
18	C₁₃×M₁₆	—	2	2	no	—
19	C₁₃×M₁₆	Q₈	1	4	yes	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	—	2	2	no	—
22	C₂×C₈×C₁₃	—	2	1	no	—
23	C₂×C₈×C₁₃	D₄	1	2	yes	—
24	C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₁₃×C₄⋊C₄	D₄	1	2	yes	—
27	C₁₃×C₂²⋊C₄	—	2	1	no	—
28	C₄²×C₁₃	—	2	1	no	—
29	#2090	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂³×C₁₃	#41	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	—	4	2	no	—
33	C₂×C₄×C₁₃	—	8	2	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
37	C₂×C₄×C₁₃	#41	1	2	yes	—
38	C₈×C₁₃	—	2	4	no	—
39	C₈×C₁₃	—	2	2	no	—
40	C₈×C₁₃	—	4	1	no	—
41	#428	C₂×C₁₃	1	2	yes	—
42	C₂×#106	C₂×C₁₃	1	1	yes	characteristic
43	#424	C₂×C₁₃	1	1	yes	characteristic
44	#343	C₂×C₁₃	1	2	yes	—
45	#341	C₂×C₁₃	1	1	yes	characteristic
46	C₂²×C₁₃	—	2	2	no	—
47	C₂²×C₁₃	#121	1	1	yes	characteristic
48	C₂²×C₁₃	#125	1	2	yes	—
49	C₄×C₁₃	—	4	2	no	—
50	C₄×C₁₃	—	8	2	no	—
51	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
52	C₄×C₁₃	#123	1	1	yes	characteristic
53	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
54	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
55	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
56	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
57	#117	C₂²×C₁₃	1	1	yes	characteristic
58	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
59	#107	—	2	2	no	—
60	#106	—	2	2	no	—
61	#106	—	2	2	no	—
62	C₄⋊C₈	—	2	2	no	—
63	C₂×C₁₃	—	2	2	no	—
64	C₂×C₁₃	#398	1	1	yes	characteristic
65	C₂×C₁₃	#471	1	2	yes	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	Q₈×C₁₃	1	4	yes	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	D₄×C₁₃	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	D₄×C₁₃	1	2	yes	—
78	C₂²⋊C₄	—	2	1	no	—
79	C₄²	—	2	1	no	—
80	C₁₃	#2090	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³	C₁₃×#41	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	8	2	no	—
85	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
86	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
87	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
88	C₂×C₄	C₁₃×#41	1	2	yes	—
89	C₈	—	2	4	no	—
90	C₈	—	2	2	no	—
91	C₈	—	4	1	no	—
92	C₂²	—	2	2	no	—
93	C₂²	C₁₃×#121	1	1	yes	characteristic
94	C₂²	C₁₃×#125	1	2	yes	—
95	C₄	—	4	2	no	—
96	C₄	—	8	2	no	—
97	C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
98	C₄	C₁₃×#123	1	1	yes	characteristic
99	C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	C₁₃×#398	1	1	yes	characteristic
102	C₂	C₁₃×#471	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#428

C₂

yes

maximal

C₂×C₁₃×#106

C₂

yes

maximal, characteristic

C₁₃×#424

C₂

yes

maximal, characteristic

C₁₃×#343

C₂

yes

maximal

C₁₃×#341

C₂

yes

maximal, characteristic

C₂×C₁₃×M₁₆

C₂²

yes

characteristic

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#117

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₁₃×#107

—

C₁₃×#106

—

C₁₃×#106

—

C₁₃×C₄⋊C₈

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

Q₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

D₄

yes

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

#2090

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₃

#41

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#428

C₂×C₁₃

yes

—

C₂×#106

C₂×C₁₃

yes

characteristic

#424

C₂×C₁₃

yes

characteristic

#343

C₂×C₁₃

yes

—

#341

C₂×C₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

#121

yes

characteristic

C₂²×C₁₃

#125

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

C₄×C₁₃

#123

yes

characteristic

C₄×C₁₃

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

C₂²×C₁₃

yes

characteristic

C₂×M₁₆

C₂²×C₁₃

yes

—

C₂²×C₈

C₂²×C₁₃

yes

characteristic

#117

C₂²×C₁₃

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₃

yes

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

#398

yes

characteristic

C₂×C₁₃

#471

yes

—

C₂²×C₄

—

C₂²×C₄

C₂³×C₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Q₈×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₁₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₁₃

#2090

yes

characteristic, direct product factor, Sylow

C₂³

C₁₃×#41

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₃

yes

characteristic

C₂×C₄

C₂×D₄×C₁₃

yes

characteristic

C₂×C₄

C₂×Q₈×C₁₃

yes

—

C₂×C₄

C₁₃×#41

yes

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₁₃×#121

yes

characteristic

C₂²

C₁₃×#125

yes

—

C₄

—

C₄

—

C₄

C₁₃×C₂²⋊Q₈

yes

—

C₄

C₁₃×#123

yes

characteristic

C₄

C₁₃×C₄⋊Q₈

yes

characteristic

100

C₂

—

101

C₂

C₁₃×#398

yes

characteristic

102

C₂

C₁₃×#471

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂³×C₁₃	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#121

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₃

C₂³×C₁₃

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

N	H ≅ G/N	type
29. #2090	C₁₃	direct (N × H)
80. C₁₃	#2090	direct (N × H)

H ≅ G/N

type

29. #2090

C₁₃

direct (N × H)

80. C₁₃

#2090

direct (N × H)

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

subgroup	index
C₁₃×#428	2
C₂×C₁₃×#106	2
C₁₃×#424	2
C₁₃×#343	2
C₁₃×#341	2
#2090	13

subgroup

index

C₁₃×#428

C₂×C₁₃×#106

C₁₃×#424

C₁₃×#343

C₁₃×#341

#2090

Subgroups — C₁₃×#2090 #13111148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#2090 #13111148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2090 #13111148