Group #15696925 — subgroups

Subgroups — C₁₃×#10586 #15696925

Order 3328.

350 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2845	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1836	C₂	1	3	yes	maximal
3	C₁₃×#1295	C₂	1	3	yes	maximal
4	C₂×C₁₃×#97	C₂²	1	3	yes	—
5	C₁₃×#398	—	2	6	no	—
6	C₁₃×#384	C₂²	1	1	yes	characteristic
7	C₁₃×#382	C₂²	1	3	yes	—
8	C₁₃×#340	—	2	6	no	—
9	C₂²×C₈×C₁₃	—	2	3	no	—
10	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
11	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
12	C₂×C₁₃×C₄⋊C₄	D₄	1	6	yes	—
13	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
14	C₁₃×#97	—	2	3	no	—
15	C₁₃×#97	Q₈	1	6	yes	—
16	C₁₃×#95	—	2	2	no	—
17	C₁₃×#95	—	2	6	no	—
18	#10586	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₄×C₁₃	—	2	6	no	—
20	C₂²×C₄×C₁₃	—	4	1	no	—
21	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
22	C₂×C₈×C₁₃	—	2	6	no	—
23	C₂×C₈×C₁₃	—	4	3	no	—
24	C₂×C₈×C₁₃	—	4	3	no	—
25	C₁₃×C₄⋊C₄	—	4	6	no	—
26	C₁₃×C₄⋊C₄	—	4	6	no	—
27	C₁₃×C₄⋊C₄	—	8	6	no	—
28	C₄²×C₁₃	C₂×Q₈	1	3	yes	—
29	C₄²×C₁₃	#41	1	1	yes	characteristic
30	#2845	C₂×C₁₃	1	1	yes	characteristic
31	#1836	C₂×C₁₃	1	3	yes	—
32	#1295	C₂×C₁₃	1	3	yes	—
33	C₂³×C₁₃	#120	1	1	yes	characteristic
34	C₂×C₄×C₁₃	—	2	3	no	—
35	C₂×C₄×C₁₃	—	2	3	no	—
36	C₂×C₄×C₁₃	—	4	6	no	—
37	C₂×C₄×C₁₃	—	4	6	no	—
38	C₂×C₄×C₁₃	—	4	6	no	—
39	C₂×C₄×C₁₃	—	8	3	no	—
40	C₂×C₄×C₁₃	C₂²⋊Q₈	1	3	yes	—
41	C₂×C₄×C₁₃	C₄⋊Q₈	1	3	yes	—
42	C₈×C₁₃	—	4	6	no	—
43	C₂×#97	C₂²×C₁₃	1	3	yes	—
44	#398	—	2	6	no	—
45	#384	C₂²×C₁₃	1	1	yes	characteristic
46	#382	C₂²×C₁₃	1	3	yes	—
47	#340	—	2	6	no	—
48	C₂²×C₁₃	#395	1	1	yes	characteristic
49	C₂²×C₁₃	#454	1	3	yes	—
50	C₂²×C₁₃	#455	1	3	yes	—
51	C₄×C₁₃	—	2	3	no	—
52	C₄×C₁₃	—	2	3	no	—
53	C₄×C₁₃	—	8	6	no	—
54	C₄×C₁₃	—	16	1	no	—
55	C₂²×C₈	—	2	3	no	—
56	C₂×C₄⋊C₄	—	2	3	no	—
57	C₂×C₄⋊C₄	—	2	6	no	—
58	C₂×C₄⋊C₄	D₄×C₁₃	1	6	yes	—
59	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
60	#97	—	2	3	no	—
61	#97	Q₈×C₁₃	1	6	yes	—
62	#95	—	2	2	no	—
63	#95	—	2	6	no	—
64	C₂×C₁₃	#1658	1	1	yes	characteristic
65	C₂×C₁₃	#1662	1	3	yes	—
66	C₂×C₁₃	#2061	1	3	yes	—
67	C₂²×C₄	—	2	6	no	—
68	C₂²×C₄	—	4	1	no	—
69	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
70	C₂×C₈	—	2	6	no	—
71	C₂×C₈	—	4	3	no	—
72	C₂×C₈	—	4	3	no	—
73	C₄⋊C₄	—	4	6	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄²	C₂×Q₈×C₁₃	1	3	yes	—
77	C₄²	C₁₃×#41	1	1	yes	characteristic
78	C₁₃	#10586	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³	C₁₃×#120	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	8	3	no	—
86	C₂×C₄	C₁₃×C₂²⋊Q₈	1	3	yes	—
87	C₂×C₄	C₁₃×C₄⋊Q₈	1	3	yes	—
88	C₈	—	4	6	no	—
89	C₂²	C₁₃×#395	1	1	yes	characteristic
90	C₂²	C₁₃×#454	1	3	yes	—
91	C₂²	C₁₃×#455	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	16	1	no	—
96	C₂	C₁₃×#1658	1	1	yes	characteristic
97	C₂	C₁₃×#1662	1	3	yes	—
98	C₂	C₁₃×#2061	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2845

C₂

yes

maximal, characteristic

C₁₃×#1836

C₂

yes

maximal

C₁₃×#1295

C₂

yes

maximal

C₂×C₁₃×#97

C₂²

yes

—

C₁₃×#398

—

C₁₃×#384

C₂²

yes

characteristic

C₁₃×#382

C₂²

yes

—

C₁₃×#340

—

C₂²×C₈×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#97

—

C₁₃×#97

Q₈

yes

—

C₁₃×#95

—

C₁₃×#95

—

#10586

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

#41

yes

characteristic

#2845

C₂×C₁₃

yes

characteristic

#1836

C₂×C₁₃

yes

—

#1295

C₂×C₁₃

yes

—

C₂³×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

—

C₈×C₁₃

—

C₂×#97

C₂²×C₁₃

yes

—

#398

—

#384

C₂²×C₁₃

yes

characteristic

#382

C₂²×C₁₃

yes

—

#340

—

C₂²×C₁₃

#395

yes

characteristic

C₂²×C₁₃

#454

yes

—

C₂²×C₁₃

#455

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

#97

—

#97

Q₈×C₁₃

yes

—

#95

—

#95

—

C₂×C₁₃

#1658

yes

characteristic

C₂×C₁₃

#1662

yes

—

C₂×C₁₃

#2061

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Q₈×C₁₃

yes

—

C₄²

C₁₃×#41

yes

characteristic

C₁₃

#10586

yes

characteristic, direct product factor, Sylow

C₂³

C₁₃×#120

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

C₂×C₄

C₁₃×C₄⋊Q₈

yes

—

C₈

—

C₂²

C₁₃×#395

yes

characteristic

C₂²

C₁₃×#454

yes

—

C₂²

C₁₃×#455

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

C₁₃×#1658

yes

characteristic

C₂

C₁₃×#1662

yes

—

C₂

C₁₃×#2061

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
18. #10586	C₁₃	direct (N × H)
78. C₁₃	#10586	direct (N × H)

H ≅ G/N

type

18. #10586

C₁₃

direct (N × H)

78. C₁₃

#10586

direct (N × H)

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

subgroup	index
C₁₃×#2845	2
C₁₃×#1836	2
C₁₃×#1295	2
#10586	13

subgroup

index

C₁₃×#2845

C₁₃×#1836

C₁₃×#1295

#10586

Subgroups — C₁₃×#10586 #15696925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10586 #15696925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10586 #15696925