Group #13118141 — subgroups

Subgroups — #13118141

Order 1664.

400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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×#376	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
3	C₄×#6101	C₂	1	4	yes	maximal
4	#11718321	C₂	1	4	yes	maximal
5	#11718318	C₂	1	4	yes	maximal
6	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
9	C₂×#6101	C₂²	1	4	yes	—
10	C₂×#6101	C₂²	1	4	yes	—
11	C₂×C₄×Dic₁₃	C₂²	1	4	yes	—
12	C₁₃×#95	C₂²	1	4	yes	—
13	#88071	C₂²	1	2	yes	—
14	#88071	C₂²	1	4	yes	—
15	#88071	C₂²	1	4	yes	—
16	#88071	C₂²	1	2	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
19	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₃	C₂³	1	4	yes	—
21	C₂²×Dic₁₃	C₂³	1	4	yes	—
22	C₄²×C₁₃	—	2	4	no	—
23	C₄²×C₁₃	Q₈	1	4	yes	—
24	C₄⋊Dic₁₃	—	2	8	no	—
25	#6101	—	2	8	no	—
26	#6101	—	2	8	no	—
27	C₄×Dic₁₃	—	2	8	no	—
28	#2402	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₁₃	—	2	4	no	—
31	C₂×C₄×C₁₃	—	2	4	no	—
32	C₂×C₄×C₁₃	—	2	4	no	—
33	C₂×C₄×C₁₃	—	2	4	no	—
34	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
35	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₁₃	#41	1	4	yes	—
37	C₂×Dic₁₃	—	2	4	no	—
38	C₂×Dic₁₃	—	2	4	no	—
39	C₂×Dic₁₃	—	2	4	no	—
40	C₂×Dic₁₃	—	2	4	no	—
41	C₂×Dic₁₃	—	2	4	no	—
42	C₂×Dic₁₃	#41	1	8	yes	—
43	#400	—	13	4	no	—
44	#398	—	13	4	no	—
45	C₄×C₄⋊C₄	—	13	4	no	—
46	C₄×C₄⋊C₄	—	13	2	no	—
47	#376	D₁₃	1	1	yes	characteristic
48	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
49	C₂²×C₁₃	C₂×#41	1	2	yes	—
50	C₂²×C₁₃	C₂×#41	1	4	yes	—
51	C₄×C₁₃	—	2	4	no	—
52	C₄×C₁₃	—	4	4	no	—
53	C₄×C₁₃	#125	1	4	yes	—
54	Dic₁₃	—	2	8	no	—
55	Dic₁₃	—	4	4	no	—
56	C₂×C₄⋊C₄	—	13	4	no	—
57	C₂×C₄⋊C₄	—	13	4	no	—
58	C₂×C₄⋊C₄	—	13	4	no	—
59	C₂×C₄²	—	13	4	no	—
60	C₂×C₄²	C₂×D₁₃	1	2	yes	—
61	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
62	#95	—	13	2	no	—
63	#95	—	13	4	no	—
64	#95	—	13	4	no	—
65	#95	—	13	2	no	—
66	#95	C₂×D₁₃	1	4	yes	—
67	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
68	C₂×C₁₃	#529	1	4	yes	—
69	C₂×C₁₃	#533	1	2	yes	—
70	C₂²×C₄	—	13	4	no	—
71	C₂²×C₄	—	13	4	no	—
72	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
73	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
75	C₄⋊C₄	—	26	8	no	—
76	C₄⋊C₄	—	26	8	no	—
77	C₄⋊C₄	—	26	8	no	—
78	C₄²	—	2	4	no	—
79	C₄²	—	26	8	no	—
80	C₄²	Dic₂₆	1	4	yes	—
81	C₁₃	#2402	1	1	yes	characteristic, complemented, Sylow
82	C₂³	C₂³×D₁₃	1	1	yes	characteristic
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	13	8	no	—
88	C₂×C₄	—	26	4	no	—
89	C₂×C₄	—	26	4	no	—
90	C₂×C₄	—	26	4	no	—
91	C₂×C₄	—	26	4	no	—
92	C₂×C₄	—	26	4	no	—
93	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
94	C₂×C₄	C₂×Dic₂₆	1	2	yes	—
95	C₂×C₄	#6127	1	4	yes	—
96	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
97	C₂²	C₂×#6127	1	2	yes	—
98	C₂²	#41×D₁₃	1	4	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	4	4	no	—
101	C₄	—	26	8	no	—
102	C₄	—	52	4	no	—
103	C₄	#88124	1	4	yes	—
104	C₂	C₂×#88124	1	1	yes	characteristic
105	C₂	#11719222	1	2	yes	—
106	C₂	#11719233	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#376

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₁₃

C₂

yes

maximal

C₄×#6101

C₂

yes

maximal

#11718321

C₂

yes

maximal

#11718318

C₂

yes

maximal

C₂×C₄²×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

Q₈

yes

—

C₄⋊Dic₁₃

—

#6101

—

#6101

—

C₄×Dic₁₃

—

#2402

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#41

yes

—

#400

—

#398

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

#376

D₁₃

yes

characteristic

C₂²×C₁₃

C₂²×Q₈

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

C₂×#41

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#125

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

—

C₂×D₁₃

yes

—

C₂×C₁₃

C₂×#125

yes

characteristic

C₂×C₁₃

#529

yes

—

C₂×C₁₃

#533

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

Dic₂₆

yes

—

C₁₃

#2402

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₂₆

yes

—

C₂×C₄

C₂×Dic₂₆

yes

—

C₂×C₄

#6127

yes

—

C₂²

C₂²×Dic₂₆

yes

characteristic

C₂²

C₂×#6127

yes

—

C₂²

#41×D₁₃

yes

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#88124

yes

—

104

C₂

C₂×#88124

yes

characteristic

105

C₂

#11719222

yes

—

106

C₂

#11719233

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Frattini	C₂³	C₂³×D₁₃
Fitting	C₁₃×#376	C₂
hypercenter	#376	D₁₃
hypocenter	C₁₃	#2402
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₁₃

commutator, socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

Frattini

C₂³

C₂³×D₁₃

Fitting

C₁₃×#376

C₂

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
81. C₁₃	#2402	semidirect

H ≅ G/N

type

81. C₁₃

#2402

semidirect

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

subgroup	index
C₁₃×#376	2
C₄×C₄⋊Dic₁₃	2
C₄×#6101	2
#11718321	2
#11718318	2
#2402	13

subgroup

index

C₁₃×#376

C₄×C₄⋊Dic₁₃

Subgroups — #13118141

Conjugacy classes of subgroups

Complements

Maximal subgroups