Group #15696951 — subgroups

Subgroups — C₁₃×#10612 #15696951

Order 3328.

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1574	C₂	1	3	yes	maximal, complemented
2	C₁₃×#1545	C₂	1	3	yes	maximal
3	C₁₃×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
5	C₁₃×#431	C₂²	1	3	yes	—
6	C₁₃×#423	C₂²	1	3	yes	—
7	C₁₃×#335	—	2	3	no	—
8	C₁₃×#334	—	2	3	no	—
9	C₁₃×#331	—	2	3	no	—
10	C₁₃×#331	—	2	3	no	—
11	C₂²×D₄×C₁₃	—	2	3	no	—
12	C₂×C₁₃×M₁₆	—	2	3	no	—
13	C₁₃×#127	—	2	3	no	—
14	C₁₃×#127	Q₈	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
16	C₁₃×C₄⋊C₈	—	2	3	no	—
17	C₁₃×C₄⋊C₈	—	2	3	no	—
18	C₁₃×C₄⋊C₈	D₄	1	3	yes	—
19	C₁₃×C₄⋊C₈	D₄	1	3	yes	—
20	C₁₃×C₂²⋊C₈	—	2	3	no	—
21	C₄×C₈×C₁₃	—	2	3	no	—
22	#10612	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂⁴×C₁₃	—	4	1	no	—
24	C₂×D₄×C₁₃	—	2	6	no	—
25	C₂×D₄×C₁₃	—	4	3	no	—
26	C₂×D₄×C₁₃	—	8	3	no	—
27	C₂×D₄×C₁₃	—	8	3	no	—
28	C₂²×C₄×C₁₃	#41	1	3	yes	—
29	C₁₃×M₁₆	—	8	3	no	—
30	C₂×C₈×C₁₃	—	2	3	no	—
31	C₂×C₈×C₁₃	—	2	3	no	—
32	C₂×C₈×C₁₃	—	4	3	no	—
33	C₄²×C₁₃	C₂×D₄	1	3	yes	—
34	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	#1574	C₂×C₁₃	1	3	yes	complemented
36	#1545	C₂×C₁₃	1	3	yes	—
37	#1309	C₂×C₁₃	1	1	yes	characteristic, complemented
38	C₂³×C₁₃	—	4	2	no	—
39	C₂³×C₁₃	—	8	6	no	—
40	C₂³×C₁₃	#126	1	1	yes	characteristic
41	D₄×C₁₃	—	8	6	no	—
42	D₄×C₁₃	—	8	3	no	—
43	D₄×C₁₃	—	8	3	no	—
44	C₂×C₄×C₁₃	—	2	3	no	—
45	C₂×C₄×C₁₃	—	2	3	no	—
46	C₂×C₄×C₁₃	#121	1	3	yes	—
47	C₂×C₄×C₁₃	C₂²⋊Q₈	1	3	yes	—
48	C₈×C₁₃	—	4	3	no	—
49	C₈×C₁₃	—	4	3	no	—
50	C₈×C₁₃	—	8	3	no	—
51	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
52	#431	C₂²×C₁₃	1	3	yes	—
53	#423	C₂²×C₁₃	1	3	yes	—
54	#335	—	2	3	no	—
55	#334	—	2	3	no	—
56	#331	—	2	3	no	—
57	#331	—	2	3	no	—
58	C₂²×C₁₃	—	2	3	no	—
59	C₂²×C₁₃	—	8	6	no	—
60	C₂²×C₁₃	—	16	4	no	—
61	C₂²×C₁₃	#396	1	1	yes	characteristic
62	C₄×C₁₃	—	2	3	no	—
63	C₄×C₁₃	#471	1	3	yes	—
64	C₄×C₁₃	#472	1	3	yes	—
65	C₂²×D₄	—	2	3	no	—
66	C₂×M₁₆	—	2	3	no	—
67	#127	—	2	3	no	—
68	#127	Q₈×C₁₃	1	2	yes	—
69	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
70	C₄⋊C₈	—	2	3	no	—
71	C₄⋊C₈	—	2	3	no	—
72	C₄⋊C₈	D₄×C₁₃	1	3	yes	—
73	C₄⋊C₈	D₄×C₁₃	1	3	yes	—
74	C₂²⋊C₈	—	2	3	no	—
75	C₄×C₈	—	2	3	no	—
76	C₂×C₁₃	—	4	1	no	—
77	C₂×C₁₃	—	16	2	no	—
78	C₂×C₁₃	#2063	1	3	yes	—
79	C₂⁴	—	4	1	no	—
80	C₂×D₄	—	2	6	no	—
81	C₂×D₄	—	4	3	no	—
82	C₂×D₄	—	8	3	no	—
83	C₂×D₄	—	8	3	no	—
84	C₂²×C₄	C₁₃×#41	1	3	yes	—
85	M₁₆	—	8	3	no	—
86	C₂×C₈	—	2	3	no	—
87	C₂×C₈	—	2	3	no	—
88	C₂×C₈	—	4	3	no	—
89	C₄²	C₂×D₄×C₁₃	1	3	yes	—
90	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
91	C₁₃	#10612	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³	—	4	2	no	—
93	C₂³	—	8	6	no	—
94	C₂³	C₁₃×#126	1	1	yes	characteristic
95	D₄	—	8	6	no	—
96	D₄	—	8	3	no	—
97	D₄	—	8	3	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	C₁₃×#121	1	3	yes	—
101	C₂×C₄	C₁₃×C₂²⋊Q₈	1	3	yes	—
102	C₈	—	4	3	no	—
103	C₈	—	4	3	no	—
104	C₈	—	8	3	no	—
105	C₂²	—	2	3	no	—
106	C₂²	—	8	6	no	—
107	C₂²	—	16	4	no	—
108	C₂²	C₁₃×#396	1	1	yes	characteristic
109	C₄	—	2	3	no	—
110	C₄	C₁₃×#471	1	3	yes	—
111	C₄	C₁₃×#472	1	3	yes	—
112	C₂	—	4	1	no	—
113	C₂	—	16	2	no	—
114	C₂	C₁₃×#2063	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#1574

C₂

yes

maximal, complemented

C₁₃×#1545

C₂

yes

maximal

C₁₃×#1309

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×#127

C₂²

yes

characteristic

C₁₃×#431

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₁₃×#335

—

C₁₃×#334

—

C₁₃×#331

—

C₁₃×#331

—

C₂²×D₄×C₁₃

—

C₂×C₁₃×M₁₆

—

C₁₃×#127

—

C₁₃×#127

Q₈

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

D₄

yes

—

C₁₃×C₄⋊C₈

D₄

yes

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

#10612

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

#41

yes

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

#1574

C₂×C₁₃

yes

complemented

#1545

C₂×C₁₃

yes

—

#1309

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#126

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

C₂×#127

C₂²×C₁₃

yes

characteristic

#431

C₂²×C₁₃

yes

—

#423

C₂²×C₁₃

yes

—

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#396

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

#471

yes

—

C₄×C₁₃

#472

yes

—

C₂²×D₄

—

C₂×M₁₆

—

#127

—

#127

Q₈×C₁₃

yes

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

D₄×C₁₃

yes

—

C₄⋊C₈

D₄×C₁₃

yes

—

C₂²⋊C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#2063

yes

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₁₃×#41

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₂×D₄×C₁₃

yes

—

C₄²

C₂×Q₈×C₁₃

yes

characteristic

C₁₃

#10612

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

C₂³

C₁₃×#126

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₁₃×#121

yes

—

101

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₁₃×#396

yes

characteristic

109

C₄

—

110

C₄

C₁₃×#471

yes

—

111

C₄

C₁₃×#472

yes

—

112

C₂

—

113

C₂

—

114

C₂

C₁₃×#2063

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#396

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂×C₁₃×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#1574	C₂	semidirect
3. C₁₃×#1309	C₂	semidirect
22. #10612	C₁₃	direct (N × H)
35. #1574	C₂×C₁₃	semidirect
37. #1309	C₂×C₁₃	semidirect
91. C₁₃	#10612	direct (N × H)

H ≅ G/N

type

1. C₁₃×#1574

C₂

semidirect

3. C₁₃×#1309

C₂

semidirect

22. #10612

C₁₃

direct (N × H)

35. #1574

C₂×C₁₃

semidirect

37. #1309

C₂×C₁₃

semidirect

91. C₁₃

#10612

direct (N × H)

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

subgroup	index
C₁₃×#1574	2
C₁₃×#1545	2
C₁₃×#1309	2
#10612	13

subgroup

index

C₁₃×#1574

C₁₃×#1545

C₁₃×#1309

#10612

Subgroups — C₁₃×#10612 #15696951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10612 #15696951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10612 #15696951