Group #23744879 — subgroups

Subgroups — C₁₃×#10624728 #23744879

Order 9477.

192 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 128 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	C₃×C₁₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₁₃×C₉⋊C₂₇	C₃	1	2	yes	maximal, complemented
4	C₁₃×C₉⋊C₂₇	C₃	1	4	yes	maximal, complemented
5	C₁₃×C₃²⋊C₂₇	C₃	1	2	yes	maximal
6	C₁₃×#6864	C₃	1	2	yes	maximal, complemented
7	C₉×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃×C₁₃×3₋¹⁺²	C₉	1	1	yes	characteristic
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₁₃×C₂₇⋊C₃	—	3	3	no	—
11	C₃×C₁₃×C₂₇	C₃²	1	2	yes	—
12	C₃×C₁₃×C₂₇	C₃²	1	4	yes	—
13	C₃×C₁₃×C₂₇	C₃²	1	2	yes	—
14	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
15	C₁₃×C₉⋊C₉	C₉	1	4	yes	—
16	C₁₃×C₉⋊C₉	C₉	1	2	yes	—
17	C₁₃×C₃²⋊C₉	C₉	1	2	yes	—
18	C₉²×C₁₃	C₃²	1	1	yes	characteristic
19	C₉²×C₁₃	C₃²	1	2	yes	—
20	#10624728	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	3	3	no	—
23	C₃×C₉×C₁₃	—	3	1	no	—
24	C₃×C₉×C₁₃	—	3	2	no	—
25	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
26	C₃×C₉×C₁₃	C₃×C₉	1	4	yes	—
27	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
28	C₃×C₉×C₁₃	C₃×C₉	1	2	yes	—
29	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
30	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
31	C₁₃×C₂₇	—	3	2	no	—
32	C₁₃×C₂₇	—	3	2	no	—
33	C₁₃×C₂₇	—	3	4	no	—
34	C₁₃×C₂₇	3₋¹⁺²	1	3	yes	complemented
35	C₃×C₂₇⋊C₃	C₃×C₁₃	1	1	yes	characteristic
36	C₉×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
37	C₉⋊C₂₇	C₃×C₁₃	1	2	yes	complemented
38	C₉⋊C₂₇	C₃×C₁₃	1	4	yes	complemented
39	C₃²⋊C₂₇	C₃×C₁₃	1	2	yes	—
40	#6864	C₃×C₁₃	1	2	yes	complemented
41	C₉×C₂₇	C₃×C₁₃	1	1	yes	characteristic, complemented
42	C₃²×C₁₃	—	3	1	no	—
43	C₃²×C₁₃	—	3	1	no	—
44	C₃²×C₁₃	—	3	2	no	—
45	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
46	C₉×C₁₃	—	3	2	no	—
47	C₉×C₁₃	—	3	2	no	—
48	C₉×C₁₃	—	3	2	no	—
49	C₉×C₁₃	—	3	4	no	—
50	C₉×C₁₃	C₂₇⋊C₃	1	3	yes	complemented
51	C₉×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
52	C₉×C₁₃	#737	1	2	yes	—
53	C₃×3₋¹⁺²	C₉×C₁₃	1	1	yes	characteristic
54	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
55	C₂₇⋊C₃	—	3	3	no	—
56	C₃×C₂₇	C₃²×C₁₃	1	2	yes	—
57	C₃×C₂₇	C₃²×C₁₃	1	4	yes	—
58	C₃×C₂₇	C₃²×C₁₃	1	2	yes	—
59	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
60	C₉⋊C₉	C₉×C₁₃	1	4	yes	—
61	C₉⋊C₉	C₉×C₁₃	1	2	yes	—
62	C₃²⋊C₉	C₉×C₁₃	1	2	yes	—
63	C₉²	C₃²×C₁₃	1	1	yes	characteristic
64	C₉²	C₃²×C₁₃	1	2	yes	—
65	C₃×C₁₃	—	9	1	no	—
66	C₃×C₁₃	C₉×3₋¹⁺²	1	1	yes	characteristic
67	C₃×C₁₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic
68	C₃×C₁₃	#6903	1	2	yes	—
69	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
70	3₋¹⁺²	—	3	3	no	—
71	C₃×C₉	—	3	1	no	—
72	C₃×C₉	—	3	2	no	—
73	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
74	C₃×C₉	C₃×C₉×C₁₃	1	4	yes	—
75	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
76	C₃×C₉	C₃×C₉×C₁₃	1	2	yes	—
77	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
78	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
79	C₂₇	—	3	2	no	—
80	C₂₇	—	3	2	no	—
81	C₂₇	—	3	4	no	—
82	C₂₇	C₁₃×3₋¹⁺²	1	3	yes	complemented
83	C₁₃	#10624728	1	1	yes	characteristic, direct product factor, Sylow
84	C₃²	—	3	1	no	—
85	C₃²	—	3	1	no	—
86	C₃²	—	3	2	no	—
87	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
88	C₉	—	3	2	no	—
89	C₉	—	3	2	no	—
90	C₉	—	3	2	no	—
91	C₉	—	3	4	no	—
92	C₉	C₁₃×C₂₇⋊C₃	1	3	yes	complemented
93	C₉	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
94	C₉	C₁₃×#737	1	2	yes	—
95	C₃	—	9	1	no	—
96	C₃	C₉×C₁₃×3₋¹⁺²	1	1	yes	characteristic
97	C₃	C₃×C₁₃×C₂₇⋊C₃	1	1	yes	characteristic
98	C₃	C₁₃×#6903	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₁₃×C₂₇⋊C₃

C₃

yes

maximal, characteristic

C₉×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₁₃×C₉⋊C₂₇

C₃

yes

maximal, complemented

C₁₃×C₉⋊C₂₇

C₃

yes

maximal, complemented

C₁₃×C₃²⋊C₂₇

C₃

yes

maximal

C₁₃×#6864

C₃

yes

maximal, complemented

C₉×C₁₃×C₂₇

C₃

yes

maximal, characteristic, complemented

C₃×C₁₃×3₋¹⁺²

C₉

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₂₇⋊C₃

—

C₃×C₁₃×C₂₇

C₃²

yes

—

C₃×C₁₃×C₂₇

C₃²

yes

—

C₃×C₁₃×C₂₇

C₃²

yes

—

C₃×C₁₃×C₂₇

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

C₉

yes

—

C₁₃×C₉⋊C₉

C₉

yes

—

C₁₃×C₃²⋊C₉

C₉

yes

—

C₉²×C₁₃

C₃²

yes

characteristic

C₉²×C₁₃

C₃²

yes

—

#10624728

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

C₃×C₉

yes

characteristic

C₁₃×3₋¹⁺²

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

characteristic

C₃×C₉×C₁₃

C₃³

yes

characteristic

C₁₃×C₂₇

—

C₁₃×C₂₇

—

C₁₃×C₂₇

—

C₁₃×C₂₇

3₋¹⁺²

yes

complemented

C₃×C₂₇⋊C₃

C₃×C₁₃

yes

characteristic

C₉×3₋¹⁺²

C₃×C₁₃

yes

characteristic

C₉⋊C₂₇

C₃×C₁₃

yes

complemented

C₉⋊C₂₇

C₃×C₁₃

yes

complemented

C₃²⋊C₂₇

C₃×C₁₃

yes

—

#6864

C₃×C₁₃

yes

complemented

C₉×C₂₇

C₃×C₁₃

yes

characteristic, complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃²×C₉

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₂₇⋊C₃

yes

complemented

C₉×C₁₃

C₃×3₋¹⁺²

yes

characteristic

C₉×C₁₃

#737

yes

—

C₃×3₋¹⁺²

C₉×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₂₇⋊C₃

—

C₃×C₂₇

C₃²×C₁₃

yes

—

C₃×C₂₇

C₃²×C₁₃

yes

—

C₃×C₂₇

C₃²×C₁₃

yes

—

C₃×C₂₇

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

C₉×C₁₃

yes

—

C₉⋊C₉

C₉×C₁₃

yes

—

C₃²⋊C₉

C₉×C₁₃

yes

—

C₉²

C₃²×C₁₃

yes

characteristic

C₉²

C₃²×C₁₃

yes

—

C₃×C₁₃

—

C₃×C₁₃

C₉×3₋¹⁺²

yes

characteristic

C₃×C₁₃

C₃×C₂₇⋊C₃

yes

characteristic

C₃×C₁₃

#6903

yes

—

C₃³

C₃×C₉×C₁₃

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

characteristic

C₃×C₉

C₃³×C₁₃

yes

characteristic

C₂₇

—

C₂₇

—

C₂₇

—

C₂₇

C₁₃×3₋¹⁺²

yes

complemented

C₁₃

#10624728

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₉×C₁₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₉

C₁₃×C₂₇⋊C₃

yes

complemented

C₉

C₃×C₁₃×3₋¹⁺²

yes

characteristic

C₉

C₁₃×#737

yes

—

C₃

—

C₃

C₉×C₁₃×3₋¹⁺²

yes

characteristic

C₃

C₃×C₁₃×C₂₇⋊C₃

yes

characteristic

C₃

C₁₃×#6903

yes

—

	subgroup	G/H
center	C₃×C₉×C₁₃	C₃³
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃²×C₁₃	C₃²×C₉
prime radical	C₃³×C₁₃	C₃×C₉
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₃ ◁ G

subgroup

G/H

center

C₃×C₉×C₁₃

C₃³

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃×C₉

C₃³×C₁₃

socle

C₃²×C₁₃

C₃²×C₉

prime radical

C₃³×C₁₃

C₃×C₉

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
3. C₁₃×C₉⋊C₂₇	C₃	semidirect
4. C₁₃×C₉⋊C₂₇	C₃	semidirect
6. C₁₃×#6864	C₃	semidirect
7. C₉×C₁₃×C₂₇	C₃	semidirect
20. #10624728	C₁₃	direct (N × H)
34. C₁₃×C₂₇	3₋¹⁺²	semidirect
37. C₉⋊C₂₇	C₃×C₁₃	semidirect
38. C₉⋊C₂₇	C₃×C₁₃	semidirect
40. #6864	C₃×C₁₃	semidirect
41. C₉×C₂₇	C₃×C₁₃	semidirect
50. C₉×C₁₃	C₂₇⋊C₃	semidirect
82. C₂₇	C₁₃×3₋¹⁺²	semidirect
83. C₁₃	#10624728	direct (N × H)
92. C₉	C₁₃×C₂₇⋊C₃	semidirect

H ≅ G/N

type

3. C₁₃×C₉⋊C₂₇

C₃

semidirect

4. C₁₃×C₉⋊C₂₇

C₃

semidirect

6. C₁₃×#6864

C₃

semidirect

7. C₉×C₁₃×C₂₇

C₃

semidirect

20. #10624728

C₁₃

direct (N × H)

34. C₁₃×C₂₇

3₋¹⁺²

semidirect

37. C₉⋊C₂₇

C₃×C₁₃

semidirect

38. C₉⋊C₂₇

C₃×C₁₃

semidirect

40. #6864

C₃×C₁₃

semidirect

41. C₉×C₂₇

C₃×C₁₃

semidirect

50. C₉×C₁₃

C₂₇⋊C₃

semidirect

82. C₂₇

C₁₃×3₋¹⁺²

semidirect

83. C₁₃

#10624728

direct (N × H)

92. C₉

C₁₃×C₂₇⋊C₃

semidirect

Subgroups — C₁₃×#10624728 #23744879

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624728 #23744879

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624728 #23744879