Group #23744875 — subgroups

Subgroups — C₁₃×#10624724 #23744875

Order 9477.

224 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 116 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×#6908	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6903	C₃	1	3	yes	maximal, complemented
3	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6873	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6872	C₃	1	3	yes	maximal, complemented
6	C₁₃×#6869	C₃	1	2	yes	maximal, complemented
7	C₁₃×#737	C₃²	1	3	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×#733	C₉	1	2	yes	—
10	C₁₃×#732	C₉	1	1	yes	characteristic
11	C₁₃×#731	C₉	1	3	yes	—
12	C₁₃×AΣL(1,𝔽₂₇)	C₉	1	3	yes	—
13	C₁₃×C₂₇⋊C₃	—	3	6	no	—
14	C₁₃×C₂₇⋊C₃	C₃²	1	6	yes	—
15	C₃×C₁₃×C₂₇	—	3	2	no	—
16	C₃×C₁₃×C₂₇	—	3	1	no	—
17	C₃×C₁₃×C₂₇	—	3	3	no	—
18	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
19	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
20	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
21	#10624724	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
23	C₁₃×3₋¹⁺²	—	3	6	no	—
24	C₁₃×3₋¹⁺²	C₃×C₉	1	6	yes	—
25	C₁₃×H(3,𝔽₃)	C₃×C₉	1	3	yes	—
26	C₃×C₉×C₁₃	—	3	1	no	—
27	C₃×C₉×C₁₃	—	3	3	no	—
28	C₃×C₉×C₁₃	—	3	2	no	—
29	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
30	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
31	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
32	C₁₃×C₂₇	—	3	1	no	—
33	C₁₃×C₂₇	—	3	1	no	—
34	C₁₃×C₂₇	—	3	6	no	—
35	C₁₃×C₂₇	H(3,𝔽₃)	1	2	yes	—
36	C₁₃×C₂₇	H(3,𝔽₃)	1	1	yes	characteristic
37	#6908	C₃×C₁₃	1	1	yes	characteristic
38	#6903	C₃×C₁₃	1	3	yes	complemented
39	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic, complemented
40	#6873	C₃×C₁₃	1	3	yes	complemented
41	#6872	C₃×C₁₃	1	3	yes	complemented
42	#6869	C₃×C₁₃	1	2	yes	complemented
43	C₃²×C₁₃	—	3	3	no	—
44	C₃²×C₁₃	—	3	1	no	—
45	C₃²×C₁₃	—	3	3	no	—
46	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
47	C₉×C₁₃	—	3	1	no	—
48	C₉×C₁₃	—	3	1	no	—
49	C₉×C₁₃	—	3	6	no	—
50	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₉×C₁₃	#737	1	2	yes	—
52	#737	C₃²×C₁₃	1	3	yes	—
53	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
54	#733	C₉×C₁₃	1	2	yes	—
55	#732	C₉×C₁₃	1	1	yes	characteristic
56	#731	C₉×C₁₃	1	3	yes	—
57	AΣL(1,𝔽₂₇)	C₉×C₁₃	1	3	yes	—
58	C₂₇⋊C₃	—	3	6	no	—
59	C₂₇⋊C₃	C₃²×C₁₃	1	6	yes	—
60	C₃×C₂₇	—	3	2	no	—
61	C₃×C₂₇	—	3	1	no	—
62	C₃×C₂₇	—	3	3	no	—
63	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
64	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
65	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
66	C₃×C₁₃	—	3	3	no	—
67	C₃×C₁₃	—	3	1	no	—
68	C₃×C₁₃	—	9	3	no	—
69	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
70	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
71	3₋¹⁺²	—	3	6	no	—
72	3₋¹⁺²	C₃×C₉×C₁₃	1	6	yes	—
73	H(3,𝔽₃)	C₃×C₉×C₁₃	1	3	yes	—
74	C₃×C₉	—	3	1	no	—
75	C₃×C₉	—	3	3	no	—
76	C₃×C₉	—	3	2	no	—
77	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
78	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
79	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
80	C₂₇	—	3	1	no	—
81	C₂₇	—	3	1	no	—
82	C₂₇	—	3	6	no	—
83	C₂₇	C₁₃×H(3,𝔽₃)	1	2	yes	—
84	C₂₇	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
85	C₁₃	#10624724	1	1	yes	characteristic, direct product factor, Sylow
86	C₃²	—	3	3	no	—
87	C₃²	—	3	1	no	—
88	C₃²	—	3	3	no	—
89	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
90	C₉	—	3	1	no	—
91	C₉	—	3	1	no	—
92	C₉	—	3	6	no	—
93	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
94	C₉	C₁₃×#737	1	2	yes	—
95	C₃	—	3	1	no	—
96	C₃	—	3	3	no	—
97	C₃	—	9	3	no	—
98	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6908

C₃

yes

maximal, characteristic

C₁₃×#6903

C₃

yes

maximal, complemented

C₃²×C₁₃×C₂₇

C₃

yes

maximal, characteristic, complemented

C₁₃×#6873

C₃

yes

maximal, complemented

C₁₃×#6872

C₃

yes

maximal, complemented

C₁₃×#6869

C₃

yes

maximal, complemented

C₁₃×#737

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×#733

C₉

yes

—

C₁₃×#732

C₉

yes

characteristic

C₁₃×#731

C₉

yes

—

C₁₃×AΣL(1,𝔽₂₇)

C₉

yes

—

C₁₃×C₂₇⋊C₃

—

C₁₃×C₂₇⋊C₃

C₃²

yes

—

C₃×C₁₃×C₂₇

—

C₃×C₁₃×C₂₇

—

C₃×C₁₃×C₂₇

—

C₃×C₁₃×C₂₇

C₃²

yes

characteristic

C₃×C₁₃×C₂₇

C₃²

yes

characteristic

C₃×C₁₃×C₂₇

C₃²

yes

characteristic

#10624724

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

C₃×C₉

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

C₃×C₉

yes

—

C₁₃×H(3,𝔽₃)

C₃×C₉

yes

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

C₃×C₉

yes

characteristic

C₃×C₉×C₁₃

C₃×C₉

yes

characteristic

C₃×C₉×C₁₃

C₃³

yes

characteristic

C₁₃×C₂₇

—

C₁₃×C₂₇

—

C₁₃×C₂₇

—

C₁₃×C₂₇

H(3,𝔽₃)

yes

—

C₁₃×C₂₇

H(3,𝔽₃)

yes

characteristic

#6908

C₃×C₁₃

yes

characteristic

#6903

C₃×C₁₃

yes

complemented

C₃²×C₂₇

C₃×C₁₃

yes

characteristic, complemented

#6873

C₃×C₁₃

yes

complemented

#6872

C₃×C₁₃

yes

complemented

#6869

C₃×C₁₃

yes

complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃²×C₉

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₁₃

#737

yes

—

#737

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

#733

C₉×C₁₃

yes

—

#732

C₉×C₁₃

yes

characteristic

#731

C₉×C₁₃

yes

—

AΣL(1,𝔽₂₇)

C₉×C₁₃

yes

—

C₂₇⋊C₃

—

C₂₇⋊C₃

C₃²×C₁₃

yes

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

C₃²×C₁₃

yes

characteristic

C₃×C₂₇

C₃²×C₁₃

yes

characteristic

C₃×C₂₇

C₃²×C₁₃

yes

characteristic

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

C₉×H(3,𝔽₃)

yes

characteristic

C₃³

C₃×C₉×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

C₃×C₉×C₁₃

yes

—

H(3,𝔽₃)

C₃×C₉×C₁₃

yes

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₉×C₁₃

yes

characteristic

C₃×C₉

C₃×C₉×C₁₃

yes

characteristic

C₃×C₉

C₃³×C₁₃

yes

characteristic

C₂₇

—

C₂₇

—

C₂₇

—

C₂₇

C₁₃×H(3,𝔽₃)

yes

—

C₂₇

C₁₃×H(3,𝔽₃)

yes

characteristic

C₁₃

#10624724

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₉×C₁₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

C₉

C₁₃×#737

yes

—

C₃

—

C₃

—

C₃

—

C₃

C₉×C₁₃×H(3,𝔽₃)

yes

characteristic

	subgroup	G/H
center	C₁₃×C₂₇	H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃×C₁₃	C₉×H(3,𝔽₃)
prime radical	C₁₃×#6908	C₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₁₃×C₂₇ ◁ C₃×C₁₃×C₂₇ ◁ G

subgroup

G/H

center

C₁₃×C₂₇

H(3,𝔽₃)

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃×C₉

C₃³×C₁₃

socle

C₃×C₁₃

C₉×H(3,𝔽₃)

prime radical

C₁₃×#6908

C₃

LCS

G ▷ C₃² ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₁₃×C₂₇ ◁ C₃×C₁₃×C₂₇ ◁ G

N	H ≅ G/N	type
2. C₁₃×#6903	C₃	semidirect
3. C₃²×C₁₃×C₂₇	C₃	semidirect
4. C₁₃×#6873	C₃	semidirect
5. C₁₃×#6872	C₃	semidirect
6. C₁₃×#6869	C₃	semidirect
21. #10624724	C₁₃	direct (N × H)
38. #6903	C₃×C₁₃	semidirect
39. C₃²×C₂₇	C₃×C₁₃	semidirect
40. #6873	C₃×C₁₃	semidirect
41. #6872	C₃×C₁₃	semidirect
42. #6869	C₃×C₁₃	semidirect
85. C₁₃	#10624724	direct (N × H)

H ≅ G/N

type

2. C₁₃×#6903

C₃

semidirect

3. C₃²×C₁₃×C₂₇

C₃

semidirect

4. C₁₃×#6873

C₃

semidirect

5. C₁₃×#6872

C₃

semidirect

6. C₁₃×#6869

C₃

semidirect

21. #10624724

C₁₃

direct (N × H)

38. #6903

C₃×C₁₃

semidirect

39. C₃²×C₂₇

C₃×C₁₃

semidirect

40. #6873

C₃×C₁₃

semidirect

41. #6872

C₃×C₁₃

semidirect

42. #6869

C₃×C₁₃

semidirect

85. C₁₃

#10624724

direct (N × H)

Subgroups — C₁₃×#10624724 #23744875

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624724 #23744875

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624724 #23744875