Group #15695154 — subgroups

Subgroups — C₁₃×#8815 #15695154

Order 3328.

422 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 238 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×#1844	C₂	1	2	yes	maximal
2	C₁₃×#1834	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#106	—	2	4	no	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#384	C₂²	1	4	yes	—
8	C₁₃×#340	—	2	8	no	—
9	C₈²×C₁₃	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₃	D₄	1	4	yes	—
11	C₂²×C₈×C₁₃	D₄	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
13	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
14	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×#106	—	4	8	no	—
16	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
17	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₃	Q₈	1	4	yes	—
19	C₄×C₈×C₁₃	Q₈	1	2	yes	—
20	#8815	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₄×C₁₃	—	4	4	no	—
22	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
24	C₂×C₈×C₁₃	—	2	8	no	—
25	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
26	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
27	C₂×C₈×C₁₃	SD₁₆	1	8	yes	—
28	C₁₃×C₄⋊C₄	—	4	8	no	—
29	C₁₃×C₄⋊C₄	—	4	16	no	—
30	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
32	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
33	#1844	C₂×C₁₃	1	2	yes	—
34	#1834	C₂×C₁₃	1	4	yes	—
35	C₂×C₈²	C₂×C₁₃	1	1	yes	characteristic
36	C₂³×C₁₃	#127	1	1	yes	characteristic
37	C₂×C₄×C₁₃	—	8	4	no	—
38	C₂×C₄×C₁₃	—	8	8	no	—
39	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
43	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
44	C₂×C₄×C₁₃	#135	1	8	yes	—
45	C₈×C₁₃	—	2	8	no	—
46	C₈×C₁₃	#106	1	8	yes	—
47	C₂×#106	—	2	4	no	—
48	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
49	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
50	#384	C₂²×C₁₃	1	4	yes	—
51	#340	—	2	8	no	—
52	C₈²	C₄×C₁₃	1	4	yes	complemented
53	C₂²×C₁₃	#384	1	1	yes	characteristic
54	C₂²×C₁₃	#492	1	2	yes	—
55	C₂²×C₁₃	#495	1	4	yes	—
56	C₄×C₁₃	—	16	4	no	—
57	C₄×C₁₃	C₂×#106	1	2	yes	—
58	C₄×C₁₃	#427	1	4	yes	—
59	C₄×C₁₃	#498	1	2	yes	—
60	C₄×C₁₃	#499	1	4	yes	—
61	C₂²×C₈	D₄×C₁₃	1	4	yes	—
62	C₂²×C₈	D₄×C₁₃	1	2	yes	—
63	C₂×C₄⋊C₄	—	2	8	no	—
64	C₂×C₄⋊C₄	—	2	4	no	—
65	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
66	#106	—	4	8	no	—
67	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
68	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
69	C₄×C₈	Q₈×C₁₃	1	4	yes	—
70	C₄×C₈	Q₈×C₁₃	1	2	yes	—
71	C₂×C₁₃	#1708	1	4	yes	—
72	C₂×C₁₃	#1844	1	1	yes	characteristic
73	C₂×C₁₃	#1846	1	2	yes	—
74	C₂²×C₄	—	4	4	no	—
75	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
76	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
77	C₂×C₈	—	2	8	no	—
78	C₂×C₈	C₁₃×C₄⋊C₄	1	8	yes	—
79	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
80	C₂×C₈	C₁₃×SD₁₆	1	8	yes	—
81	C₄⋊C₄	—	4	8	no	—
82	C₄⋊C₄	—	4	16	no	—
83	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
84	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
85	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
86	C₁₃	#8815	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³	C₁₃×#127	1	1	yes	characteristic
88	C₂×C₄	—	8	4	no	—
89	C₂×C₄	—	8	8	no	—
90	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
92	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
93	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
94	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
95	C₂×C₄	C₁₃×#135	1	8	yes	—
96	C₈	—	2	8	no	—
97	C₈	C₁₃×#106	1	8	yes	—
98	C₂²	C₁₃×#384	1	1	yes	characteristic
99	C₂²	C₁₃×#492	1	2	yes	—
100	C₂²	C₁₃×#495	1	4	yes	—
101	C₄	—	16	4	no	—
102	C₄	C₂×C₁₃×#106	1	2	yes	—
103	C₄	C₁₃×#427	1	4	yes	—
104	C₄	C₁₃×#498	1	2	yes	—
105	C₄	C₁₃×#499	1	4	yes	—
106	C₂	C₁₃×#1708	1	4	yes	—
107	C₂	C₁₃×#1844	1	1	yes	characteristic
108	C₂	C₁₃×#1846	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#1844

C₂

yes

maximal

C₁₃×#1834

C₂

yes

maximal

C₂×C₈²×C₁₃

C₂

yes

maximal, characteristic

C₂×C₁₃×#106

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

C₁₃×#340

—

C₈²×C₁₃

C₄

yes

complemented

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#106

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#8815

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

—

#1844

C₂×C₁₃

yes

—

#1834

C₂×C₁₃

yes

—

C₂×C₈²

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#127

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₄⋊Q₈

yes

—

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₈×C₁₃

—

C₈×C₁₃

#106

yes

—

C₂×#106

—

C₂×C₄×C₈

C₂²×C₁₃

yes

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#384

C₂²×C₁₃

yes

—

#340

—

C₈²

C₄×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

#495

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×#106

yes

—

C₄×C₁₃

#427

yes

—

C₄×C₁₃

#498

yes

—

C₄×C₁₃

#499

yes

—

C₂²×C₈

D₄×C₁₃

yes

—

C₂²×C₈

D₄×C₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

#106

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₂×C₁₃

#1708

yes

—

C₂×C₁₃

#1844

yes

characteristic

C₂×C₁₃

#1846

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

C₂²×C₄

C₂×D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×SD₁₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×C₄×C₁₃

yes

characteristic

C₄²

C₂×Q₈×C₁₃

yes

characteristic

C₄²

C₂×Q₈×C₁₃

yes

—

C₁₃

#8815

yes

characteristic, direct product factor, Sylow

C₂³

C₁₃×#127

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

—

C₂×C₄

C₁₃×C₄⋊Q₈

yes

characteristic

C₂×C₄

C₁₃×C₄⋊Q₈

yes

—

C₂×C₄

C₂×C₁₃×SD₁₆

yes

—

C₂×C₄

C₁₃×#135

yes

—

C₈

—

C₈

C₁₃×#106

yes

—

C₂²

C₁₃×#384

yes

characteristic

C₂²

C₁₃×#492

yes

—

100

C₂²

C₁₃×#495

yes

—

101

C₄

—

102

C₄

C₂×C₁₃×#106

yes

—

103

C₄

C₁₃×#427

yes

—

104

C₄

C₁₃×#498

yes

—

105

C₄

C₁₃×#499

yes

—

106

C₂

C₁₃×#1708

yes

—

107

C₂

C₁₃×#1844

yes

characteristic

108

C₂

C₁₃×#1846

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

#127

commutator

C₄²

C₂²×C₄×C₁₃

Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
9. C₈²×C₁₃	C₄	semidirect
20. #8815	C₁₃	direct (N × H)
52. C₈²	C₄×C₁₃	semidirect
86. C₁₃	#8815	direct (N × H)

H ≅ G/N

type

9. C₈²×C₁₃

C₄

semidirect

20. #8815

C₁₃

direct (N × H)

52. C₈²

C₄×C₁₃

semidirect

86. C₁₃

#8815

direct (N × H)

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

subgroup	index
C₁₃×#1844	2
C₁₃×#1834	2
C₂×C₈²×C₁₃	2
#8815	13

subgroup

index

C₁₃×#1844

C₁₃×#1834

C₂×C₈²×C₁₃

#8815

Subgroups — C₁₃×#8815 #15695154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#8815 #15695154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8815 #15695154