Group #15699237 — subgroups

Subgroups — C₁₃×#12898 #15699237

Order 3328.

414 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 286 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	C₂×C₁₃×C₄⋊C₁₆	C₂	1	6	yes	maximal
2	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
4	C₂×C₄×C₈×C₁₃	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
6	C₄³×C₁₃	C₄	1	1	yes	characteristic
7	C₁₃×C₄⋊C₁₆	—	2	12	no	—
8	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₁₃	C₈	1	3	yes	—
11	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
12	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
13	C₂×C₁₃×C₁₆	—	2	12	no	—
14	C₄×C₈×C₁₃	—	2	6	no	—
15	C₄×C₈×C₁₃	D₄	1	6	yes	—
16	C₄×C₈×C₁₃	Q₈	1	6	yes	—
17	#12898	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
19	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
20	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₃	—	2	6	no	—
22	C₂×C₈×C₁₃	C₄⋊C₄	1	6	yes	—
23	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
24	C₂×C₈×C₁₃	C₂×Q₈	1	3	yes	—
25	C₄²×C₁₃	—	2	6	no	—
26	C₄²×C₁₃	C₁₆	1	4	yes	complemented
27	C₄²×C₁₃	C₄⋊C₄	1	6	yes	—
28	C₄²×C₁₃	M₁₆	1	6	yes	—
29	C₁₃×C₁₆	—	4	4	no	—
30	C₂×C₄⋊C₁₆	C₂×C₁₃	1	6	yes	—
31	C₄²×C₈	C₂×C₁₃	1	1	yes	characteristic
32	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₃	—	2	6	no	—
34	C₂×C₄×C₁₃	C₄⋊C₈	1	6	yes	—
35	C₂×C₄×C₁₃	C₄⋊C₈	1	6	yes	—
36	C₂×C₄×C₁₃	C₂×C₁₆	1	6	yes	—
37	C₂×C₄×C₁₃	M₃₂	1	6	yes	—
38	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
39	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
40	C₈×C₁₃	—	2	6	no	—
41	C₈×C₁₃	#127	1	1	yes	characteristic
42	C₈×C₁₃	C₄⋊Q₈	1	3	yes	—
43	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	—
44	C₂×C₄×C₈	C₄×C₁₃	1	3	yes	—
45	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
46	C₄³	C₄×C₁₃	1	1	yes	characteristic
47	C₄⋊C₁₆	—	2	12	no	—
48	C₂²×C₁₃	C₂×C₄⋊C₈	1	3	yes	—
49	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
50	C₂²×C₁₃	C₂×M₃₂	1	3	yes	—
51	C₄×C₁₃	—	2	6	no	—
52	C₄×C₁₃	C₄⋊C₁₆	1	12	yes	complemented
53	C₄×C₁₃	#384	1	1	yes	characteristic
54	C₄×C₁₃	#423	1	3	yes	—
55	C₂²×C₈	C₂×C₄×C₁₃	1	3	yes	—
56	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
57	C₂×C₄²	C₈×C₁₃	1	3	yes	—
58	C₂×C₄²	C₈×C₁₃	1	1	yes	characteristic
59	C₂×C₄²	C₂×C₄×C₁₃	1	3	yes	—
60	C₂×C₁₆	—	2	12	no	—
61	C₄×C₈	—	2	6	no	—
62	C₄×C₈	D₄×C₁₃	1	6	yes	—
63	C₄×C₈	Q₈×C₁₃	1	6	yes	—
64	C₂×C₁₃	#1842	1	1	yes	characteristic
65	C₂×C₁₃	C₂×C₄⋊C₁₆	1	3	yes	—
66	C₂×C₁₃	#2150	1	3	yes	—
67	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
68	C₂²×C₄	C₂×C₈×C₁₃	1	3	yes	—
69	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
70	C₂×C₈	—	2	6	no	—
71	C₂×C₈	C₁₃×C₄⋊C₄	1	6	yes	—
72	C₂×C₈	C₂×D₄×C₁₃	1	3	yes	—
73	C₂×C₈	C₂×Q₈×C₁₃	1	3	yes	—
74	C₄²	—	2	6	no	—
75	C₄²	C₁₃×C₁₆	1	4	yes	complemented
76	C₄²	C₁₃×C₄⋊C₄	1	6	yes	—
77	C₄²	C₁₃×M₁₆	1	6	yes	—
78	C₁₆	—	4	4	no	—
79	C₁₃	#12898	1	1	yes	characteristic, direct product factor, Sylow
80	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	C₁₃×C₄⋊C₈	1	6	yes	—
83	C₂×C₄	C₁₃×C₄⋊C₈	1	6	yes	—
84	C₂×C₄	C₂×C₁₃×C₁₆	1	6	yes	—
85	C₂×C₄	C₁₃×M₃₂	1	6	yes	—
86	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	3	yes	—
87	C₂×C₄	C₂×C₁₃×M₁₆	1	3	yes	—
88	C₈	—	2	6	no	—
89	C₈	C₁₃×#127	1	1	yes	characteristic
90	C₈	C₁₃×C₄⋊Q₈	1	3	yes	—
91	C₂²	C₂×C₁₃×C₄⋊C₈	1	3	yes	—
92	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
93	C₂²	C₂×C₁₃×M₃₂	1	3	yes	—
94	C₄	—	2	6	no	—
95	C₄	C₁₃×C₄⋊C₁₆	1	12	yes	complemented
96	C₄	C₁₃×#384	1	1	yes	characteristic
97	C₄	C₁₃×#423	1	3	yes	—
98	C₂	C₁₃×#1842	1	1	yes	characteristic
99	C₂	C₂×C₁₃×C₄⋊C₁₆	1	3	yes	—
100	C₂	C₁₃×#2150	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₁₆

C₂

yes

maximal

C₄²×C₈×C₁₃

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₄

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₄³×C₁₃

C₄

yes

characteristic

C₁₃×C₄⋊C₁₆

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₈

yes

—

C₂×C₄²×C₁₃

C₈

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#12898

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

C₁₆

yes

complemented

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

M₁₆

yes

—

C₁₃×C₁₆

—

C₂×C₄⋊C₁₆

C₂×C₁₃

yes

—

C₄²×C₈

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

—

C₂×C₄×C₁₃

M₃₂

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₈×C₁₃

—

C₈×C₁₃

#127

yes

characteristic

C₈×C₁₃

C₄⋊Q₈

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

—

C₂×C₄×C₈

C₄×C₁₃

yes

—

C₂×C₄×C₈

C₂²×C₁₃

yes

—

C₄³

C₄×C₁₃

yes

characteristic

C₄⋊C₁₆

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₂²×C₁₃

C₂×M₃₂

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₄⋊C₁₆

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂²×C₈

C₂×C₄×C₁₃

yes

—

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄²

C₈×C₁₃

yes

—

C₂×C₄²

C₈×C₁₃

yes

characteristic

C₂×C₄²

C₂×C₄×C₁₃

yes

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

D₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₂×C₁₃

#1842

yes

characteristic

C₂×C₁₃

C₂×C₄⋊C₁₆

yes

—

C₂×C₁₃

#2150

yes

—

C₂²×C₄

C₂×C₈×C₁₃

yes

—

C₂²×C₄

C₂×C₈×C₁₃

yes

—

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₂×D₄×C₁₃

yes

—

C₂×C₈

C₂×Q₈×C₁₃

yes

—

C₄²

—

C₄²

C₁₃×C₁₆

yes

complemented

C₄²

C₁₃×C₄⋊C₄

yes

—

C₄²

C₁₃×M₁₆

yes

—

C₁₆

—

C₁₃

#12898

yes

characteristic, direct product factor, Sylow

C₂³

C₂²×C₈×C₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

C₁₃×C₄⋊C₈

yes

—

C₂×C₄

C₁₃×C₄⋊C₈

yes

—

C₂×C₄

C₂×C₁₃×C₁₆

yes

—

C₂×C₄

C₁₃×M₃₂

yes

—

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

—

C₂×C₄

C₂×C₁₃×M₁₆

yes

—

C₈

—

C₈

C₁₃×#127

yes

characteristic

C₈

C₁₃×C₄⋊Q₈

yes

—

C₂²

C₂×C₁₃×C₄⋊C₈

yes

—

C₂²

C₂²×C₁₃×C₁₆

yes

characteristic

C₂²

C₂×C₁₃×M₃₂

yes

—

C₄

—

C₄

C₁₃×C₄⋊C₁₆

yes

complemented

C₄

C₁₃×#384

yes

characteristic

C₄

C₁₃×#423

yes

—

C₂

C₁₃×#1842

yes

characteristic

C₂

C₂×C₁₃×C₄⋊C₁₆

yes

—

100

C₂

C₁₃×#2150

yes

—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂²	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

subgroup

G/H

center

C₂²×C₈×C₁₃

C₂³

commutator

C₂²

C₂²×C₁₃×C₁₆

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle, prime radical

C₂³×C₁₃

C₂²×C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
17. #12898	C₁₃	direct (N × H)
26. C₄²×C₁₃	C₁₆	semidirect
52. C₄×C₁₃	C₄⋊C₁₆	semidirect
75. C₄²	C₁₃×C₁₆	semidirect
79. C₁₃	#12898	direct (N × H)
95. C₄	C₁₃×C₄⋊C₁₆	semidirect

H ≅ G/N

type

17. #12898

C₁₃

direct (N × H)

26. C₄²×C₁₃

C₁₆

semidirect

52. C₄×C₁₃

C₄⋊C₁₆

semidirect

75. C₄²

C₁₃×C₁₆

semidirect

79. C₁₃

#12898

direct (N × H)

95. C₄

C₁₃×C₄⋊C₁₆

semidirect

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

subgroup	index
C₂×C₁₃×C₄⋊C₁₆	2
C₄²×C₈×C₁₃	2
#12898	13

subgroup

index

C₂×C₁₃×C₄⋊C₁₆

C₄²×C₈×C₁₃

#12898

Subgroups — C₁₃×#12898 #15699237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12898 #15699237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12898 #15699237