Group #39908038 — subgroups

Subgroups — D₃×D₂₉×C₅²⋊C₃ #39908038

Order 26100.

128 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 30 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	C₅²⋊C₃×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×D₃×D₂₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₉×C₅²⋊C₃	—	3	1	no	maximal
6	C₃×C₂₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₅²×D₈₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₃×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₅²×D₂₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₂₉×C₅²⋊C₃	—	3	1	no	—
11	D₂₉×C₅²⋊C₃	—	2	1	no	—
12	D₂₉×C₅²⋊C₃	—	3	1	no	—
13	D₂₉×C₅²⋊C₃	D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₅²×D₂₉	—	3	1	no	Hall
15	C₂₉×C₅²⋊C₃	—	2	1	no	—
16	C₂₉×C₅²⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅²×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₅×D₃×D₂₉	—	3	2	no	—
19	C₂×C₅²×C₂₉	—	3	1	no	—
20	C₅²×D₂₉	—	3	1	no	—
21	C₅²×D₂₉	C₃×D₃	1	1	yes	characteristic, complemented
22	C₃×D₃×D₂₉	—	25	1	no	maximal, Hall
23	C₂×D₃×C₅²⋊C₃	—	29	1	no	maximal, Hall
24	C₅×D₈₇	—	3	2	no	—
25	C₅×D₃×C₂₉	—	3	2	no	—
26	C₃×C₅×D₂₉	—	3	2	no	—
27	C₅²×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×D₂₉	—	9	2	no	—
29	C₃×D₈₇	—	25	1	no	—
30	C₃×D₃×C₂₉	—	25	1	no	—
31	C₃²×D₂₉	—	25	1	no	—
32	C₂×C₃×C₅²⋊C₃	—	29	1	no	—
33	D₃×C₅²⋊C₃	—	29	1	no	—
34	D₃×C₅²⋊C₃	D₂₉	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₂₉	—	3	2	no	—
36	C₂×C₃×D₂₉	—	75	1	no	—
37	D₃×D₂₉	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂×C₅²×D₃	—	29	1	no	—
39	C₂²×C₅²⋊C₃	—	87	1	no	—
40	C₂×C₅×C₂₉	—	9	2	no	—
41	C₅×D₂₉	—	3	2	no	—
42	C₅×D₂₉	—	9	2	no	—
43	C₃²×C₂₉	—	25	1	no	Hall
44	C₃×C₅²⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₂₉	—	75	1	no	—
46	D₈₇	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
47	C₃×D₂₉	—	25	1	no	—
48	C₃×D₂₉	—	50	1	no	—
49	C₃×D₂₉	—	75	1	no	—
50	C₃×D₂₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
51	D₃×C₂₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅²	—	29	1	no	—
53	C₅²×D₃	—	29	1	no	—
54	C₅²×D₃	C₃×D₂₉	1	1	yes	characteristic, complemented
55	C₂×C₅²⋊C₃	—	3	1	no	—
56	C₂×C₅²⋊C₃	—	29	1	no	—
57	C₂×C₅²⋊C₃	—	58	1	no	—
58	C₂×C₅²⋊C₃	—	87	1	no	—
59	C₅×C₂₉	—	3	2	no	—
60	C₂×D₂₉	—	3	1	no	Hall
61	C₂²×C₅²	—	87	1	no	Hall
62	C₃×C₂₉	—	25	1	no	—
63	C₃×C₂₉	—	50	1	no	—
64	C₃×C₂₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented
65	C₃×C₅²	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
66	C₅²⋊C₃	—	2	1	no	—
67	C₅²⋊C₃	D₃×D₂₉	1	1	yes	characteristic, direct product factor
68	C₂×C₅×D₃	—	87	2	no	—
69	C₂×C₂₉	—	3	1	no	—
70	D₂₉	—	3	1	no	—
71	D₂₉	D₃×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
72	C₂×C₅²	—	3	1	no	—
73	C₂×C₅²	—	29	1	no	—
74	C₂×C₅²	—	87	1	no	—
75	C₂×C₃×D₃	—	725	1	no	Hall
76	C₂×C₃×C₅	—	87	2	no	—
77	C₅×D₃	—	3	2	no	—
78	C₅×D₃	—	87	2	no	—
79	C₂₉	C₂×D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
80	C₅²	C₃×D₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₅	—	261	2	no	—
82	C₂×C₃²	—	725	1	no	—
83	C₃×D₃	—	25	1	no	—
84	C₃×D₃	—	725	1	no	—
85	C₃×C₅	—	3	2	no	—
86	C₂²×C₃	—	2175	1	no	—
87	C₂×D₃	—	29	1	no	—
88	C₂×C₅	—	261	2	no	—
89	C₂×C₅	—	9	2	no	—
90	C₂×C₅	—	87	2	no	—
91	C₃²	—	25	1	no	Sylow
92	C₂×C₃	—	29	1	no	—
93	C₂×C₃	—	75	1	no	—
94	C₂×C₃	—	2175	1	no	—
95	C₂×C₃	—	1450	1	no	—
96	C₂×C₃	—	725	1	no	—
97	D₃	—	29	1	no	—
98	D₃	D₂₉×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
99	C₅	—	3	2	no	—
100	C₂²	—	87	1	no	Sylow
101	C₃	—	25	1	no	—
102	C₃	—	50	1	no	—
103	C₃	C₂×D₂₉×C₅²⋊C₃	1	1	yes	characteristic, complemented
104	C₂	—	3	1	no	—
105	C₂	—	29	1	no	—
106	C₂	—	87	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅²⋊C₃×D₈₇

C₂

yes

maximal, characteristic, complemented

D₃×C₂₉×C₅²⋊C₃

C₂

yes

maximal, characteristic, complemented

C₃×D₂₉×C₅²⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅²×D₃×D₂₉

C₃

yes

maximal, characteristic, complemented

C₂×D₂₉×C₅²⋊C₃

—

maximal

C₃×C₂₉×C₅²⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₅²×D₈₇

C₂×C₃

yes

characteristic, complemented

C₅²×D₃×C₂₉

C₂×C₃

yes

characteristic, complemented

C₃×C₅²×D₂₉

C₂×C₃

yes

characteristic, complemented

C₂×C₂₉×C₅²⋊C₃

—

D₂₉×C₅²⋊C₃

—

D₂₉×C₅²⋊C₃

—

D₂₉×C₅²⋊C₃

D₃

yes

characteristic, direct product factor

C₂×C₅²×D₂₉

—

Hall

C₂₉×C₅²⋊C₃

—

C₂₉×C₅²⋊C₃

C₂×D₃

yes

characteristic, complemented

C₃×C₅²×C₂₉

C₂²×C₃

yes

characteristic, complemented

C₅×D₃×D₂₉

—

C₂×C₅²×C₂₉

—

C₅²×D₂₉

—

C₅²×D₂₉

C₃×D₃

yes

characteristic, complemented

C₃×D₃×D₂₉

—

maximal, Hall

C₂×D₃×C₅²⋊C₃

—

maximal, Hall

C₅×D₈₇

—

C₅×D₃×C₂₉

—

C₃×C₅×D₂₉

—

C₅²×C₂₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₅×D₂₉

—

C₃×D₈₇

—

C₃×D₃×C₂₉

—

C₃²×D₂₉

—

C₂×C₃×C₅²⋊C₃

—

D₃×C₅²⋊C₃

—

D₃×C₅²⋊C₃

D₂₉

yes

characteristic, direct product factor

C₃×C₅×C₂₉

—

C₂×C₃×D₂₉

—

D₃×D₂₉

C₅²⋊C₃

yes

characteristic, direct product factor

C₂×C₅²×D₃

—

C₂²×C₅²⋊C₃

—

C₂×C₅×C₂₉

—

C₅×D₂₉

—

C₅×D₂₉

—

C₃²×C₂₉

—

Hall

C₃×C₅²⋊C₃

C₂×D₂₉

yes

characteristic, complemented, Hall

C₂×C₃×C₂₉

—

D₈₇

C₂×C₅²⋊C₃

yes

characteristic, complemented

C₃×D₂₉

—

C₃×D₂₉

—

C₃×D₂₉

—

C₃×D₂₉

C₂×C₅²⋊C₃

yes

characteristic, complemented

D₃×C₂₉

C₂×C₅²⋊C₃

yes

characteristic, complemented

C₂×C₃×C₅²

—

C₅²×D₃

—

C₅²×D₃

C₃×D₂₉

yes

characteristic, complemented

C₂×C₅²⋊C₃

—

C₂×C₅²⋊C₃

—

C₂×C₅²⋊C₃

—

C₂×C₅²⋊C₃

—

C₅×C₂₉

—

C₂×D₂₉

—

Hall

C₂²×C₅²

—

Hall

C₃×C₂₉

—

C₃×C₂₉

—

C₃×C₂₉

C₂²×C₅²⋊C₃

yes

characteristic, complemented

C₃×C₅²

C₂×C₃×D₂₉

yes

characteristic, complemented

C₅²⋊C₃

—

C₅²⋊C₃

D₃×D₂₉

yes

characteristic, direct product factor

C₂×C₅×D₃

—

C₂×C₂₉

—

D₂₉

—

D₂₉

D₃×C₅²⋊C₃

yes

characteristic, direct product factor

C₂×C₅²

—

C₂×C₅²

—

C₂×C₅²

—

C₂×C₃×D₃

—

725

Hall

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

—

C₂₉

C₂×D₃×C₅²⋊C₃

yes

characteristic, complemented, Sylow

C₅²

C₃×D₃×D₂₉

yes

characteristic, complemented, Sylow

C₂²×C₅

—

261

—

C₂×C₃²

—

725

—

C₃×D₃

—

C₃×D₃

—

725

—

C₃×C₅

—

C₂²×C₃

—

2175

—

C₂×D₃

—

C₂×C₅

—

261

—

C₂×C₅

—

C₂×C₅

—

C₃²

—

Sylow

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

2175

—

C₂×C₃

—

1450

—

C₂×C₃

—

725

—

D₃

—

D₃

D₂₉×C₅²⋊C₃

yes

characteristic, direct product factor

C₅

—

100

C₂²

—

Sylow

101

C₃

—

102

C₃

—

103

C₃

C₂×D₂₉×C₅²⋊C₃

yes

characteristic, complemented

104

C₂

—

105

C₂

—

106

C₂

—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₂₉	C₂²×C₃
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁

subgroup

G/H

center, Frattini, hypercenter

C₁

commutator, Fitting, socle, cosocle, hypocenter

C₃×C₅²×C₂₉

C₂²×C₃

LCS

G ▷ C₃×C₅²×C₂₉

UCS

C₁

N	H ≅ G/N	type
1. C₅²⋊C₃×D₈₇	C₂	semidirect
2. D₃×C₂₉×C₅²⋊C₃	C₂	semidirect
3. C₃×D₂₉×C₅²⋊C₃	C₂	semidirect
4. C₅²×D₃×D₂₉	C₃	semidirect
6. C₃×C₂₉×C₅²⋊C₃	C₂²	semidirect
7. C₅²×D₈₇	C₂×C₃	semidirect
8. C₅²×D₃×C₂₉	C₂×C₃	semidirect
9. C₃×C₅²×D₂₉	C₂×C₃	semidirect
13. D₂₉×C₅²⋊C₃	D₃	direct (N × H)
16. C₂₉×C₅²⋊C₃	C₂×D₃	semidirect
17. C₃×C₅²×C₂₉	C₂²×C₃	semidirect
21. C₅²×D₂₉	C₃×D₃	semidirect
27. C₅²×C₂₉	C₂×C₃×D₃	semidirect
34. D₃×C₅²⋊C₃	D₂₉	direct (N × H)
37. D₃×D₂₉	C₅²⋊C₃	direct (N × H)
44. C₃×C₅²⋊C₃	C₂×D₂₉	semidirect
46. D₈₇	C₂×C₅²⋊C₃	semidirect
50. C₃×D₂₉	C₂×C₅²⋊C₃	semidirect
51. D₃×C₂₉	C₂×C₅²⋊C₃	semidirect
54. C₅²×D₃	C₃×D₂₉	semidirect
64. C₃×C₂₉	C₂²×C₅²⋊C₃	semidirect
65. C₃×C₅²	C₂×C₃×D₂₉	semidirect
67. C₅²⋊C₃	D₃×D₂₉	direct (N × H)
71. D₂₉	D₃×C₅²⋊C₃	direct (N × H)
79. C₂₉	C₂×D₃×C₅²⋊C₃	semidirect
80. C₅²	C₃×D₃×D₂₉	semidirect
98. D₃	D₂₉×C₅²⋊C₃	direct (N × H)
103. C₃	C₂×D₂₉×C₅²⋊C₃	semidirect

H ≅ G/N

type

1. C₅²⋊C₃×D₈₇

C₂

semidirect

2. D₃×C₂₉×C₅²⋊C₃

C₂

semidirect

3. C₃×D₂₉×C₅²⋊C₃

C₂

semidirect

4. C₅²×D₃×D₂₉

C₃

semidirect

6. C₃×C₂₉×C₅²⋊C₃

C₂²

semidirect

7. C₅²×D₈₇

C₂×C₃

semidirect

8. C₅²×D₃×C₂₉

C₂×C₃

semidirect

9. C₃×C₅²×D₂₉

C₂×C₃

semidirect

13. D₂₉×C₅²⋊C₃

D₃

direct (N × H)

16. C₂₉×C₅²⋊C₃

C₂×D₃

semidirect

17. C₃×C₅²×C₂₉

C₂²×C₃

semidirect

21. C₅²×D₂₉

C₃×D₃

semidirect

27. C₅²×C₂₉

C₂×C₃×D₃

semidirect

34. D₃×C₅²⋊C₃

D₂₉

direct (N × H)

37. D₃×D₂₉

C₅²⋊C₃

direct (N × H)

44. C₃×C₅²⋊C₃

C₂×D₂₉

semidirect

46. D₈₇

C₂×C₅²⋊C₃

semidirect

50. C₃×D₂₉

C₂×C₅²⋊C₃

semidirect

51. D₃×C₂₉

C₂×C₅²⋊C₃

semidirect

54. C₅²×D₃

C₃×D₂₉

semidirect

64. C₃×C₂₉

C₂²×C₅²⋊C₃

semidirect

65. C₃×C₅²

C₂×C₃×D₂₉

semidirect

67. C₅²⋊C₃

D₃×D₂₉

direct (N × H)

71. D₂₉

D₃×C₅²⋊C₃

direct (N × H)

79. C₂₉

C₂×D₃×C₅²⋊C₃

semidirect

80. C₅²

C₃×D₃×D₂₉

semidirect

98. D₃

D₂₉×C₅²⋊C₃

direct (N × H)

103. C₃

C₂×D₂₉×C₅²⋊C₃

semidirect

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

subgroup	index
C₅²⋊C₃×D₈₇	2
D₃×C₂₉×C₅²⋊C₃	2
C₃×D₂₉×C₅²⋊C₃	2
C₅²×D₃×D₂₉	3
C₂×D₂₉×C₅²⋊C₃	3
C₃×D₃×D₂₉	25
C₂×D₃×C₅²⋊C₃	29

subgroup

index

C₅²⋊C₃×D₈₇

D₃×C₂₉×C₅²⋊C₃

C₃×D₂₉×C₅²⋊C₃

C₅²×D₃×D₂₉

C₂×D₂₉×C₅²⋊C₃

C₃×D₃×D₂₉

C₂×D₃×C₅²⋊C₃

Subgroups — D₃×D₂₉×C₅²⋊C₃ #39908038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×D29×C52⋊C3 #39908038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₉×C₅²⋊C₃ #39908038