Group #30685481 — subgroups

Subgroups — C₂×D₃×C₂₅×C₁₉⋊C₃ #30685481

Order 17100.

132 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 63 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×C₃×C₂₅×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₅×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₉×C₂₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂₅×C₁₉⋊C₃	—	3	1	no	maximal
5	C₃×C₂₅×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×D₃×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic
7	D₃×C₁₉×C₂₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₂₅×C₁₉⋊C₃	—	2	1	no	—
9	C₂×C₂₅×C₁₉⋊C₃	—	3	2	no	—
10	C₂×C₂₅×C₁₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₁₉×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²×C₁₉×C₂₅	—	3	1	no	Hall
13	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic
14	C₅×D₃×C₁₉⋊C₃	C₂×C₅	1	2	yes	—
15	C₃×C₁₉×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂₅×C₁₉⋊C₃	—	2	1	no	—
17	C₂₅×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₅×D₃×C₁₉	C₃×C₅	1	1	yes	characteristic
19	C₂²×C₅×C₁₉⋊C₃	—	3	1	no	—
20	C₂×C₁₉×C₂₅	—	3	2	no	—
21	C₂×C₁₉×C₂₅	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₃×C₂₅	—	19	1	no	maximal, Hall
23	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic
24	C₂×D₃×C₁₉⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
26	C₅×D₃×C₁₉	C₂×C₃×C₅	1	2	yes	—
27	C₂×C₅×C₁₉⋊C₃	—	2	1	no	—
28	C₂×C₅×C₁₉⋊C₃	—	3	2	no	—
29	C₂×C₅×C₁₉⋊C₃	C₅×D₃	1	1	yes	characteristic
30	C₁₉×C₂₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃²×C₂₅	—	19	1	no	—
32	C₃×D₃×C₂₅	—	19	2	no	—
33	C₂²×C₅×C₁₉	—	3	1	no	—
34	C₂×C₃×C₁₉⋊C₃	C₂×C₂₅	1	1	yes	characteristic, complemented
35	D₃×C₁₉⋊C₃	C₂×C₂₅	1	2	yes	direct product factor
36	C₂²×C₃×C₂₅	—	57	1	no	—
37	C₂×D₃×C₂₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
38	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
39	C₅×C₁₉⋊C₃	—	2	1	no	—
40	C₅×C₁₉⋊C₃	C₂×C₅×D₃	1	1	yes	characteristic
41	C₂×D₃×C₁₉	C₃×C₂₅	1	1	yes	characteristic, complemented
42	C₂²×C₁₉⋊C₃	—	3	1	no	—
43	C₃²×C₂₅	—	19	1	no	Hall
44	C₂×C₅×C₁₉	—	3	2	no	—
45	C₂×C₅×C₁₉	C₃×C₅×D₃	1	1	yes	characteristic
46	C₂×C₃×C₅×D₃	—	19	1	no	—
47	C₃×C₁₉⋊C₃	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₂₅	—	19	1	no	—
49	C₂×C₃×C₂₅	—	38	1	no	—
50	C₂×C₃×C₂₅	—	57	2	no	—
51	C₂×C₃×C₂₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
52	D₃×C₂₅	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
53	C₂×C₃×C₁₉	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
54	D₃×C₁₉	C₂×C₃×C₂₅	1	2	yes	complemented
55	C₂×C₁₉⋊C₃	—	2	1	no	—
56	C₂×C₁₉⋊C₃	—	3	2	no	—
57	C₂×C₁₉⋊C₃	D₃×C₂₅	1	1	yes	characteristic, direct product factor
58	C₂²×C₂₅	—	3	1	no	Hall
59	C₅×C₁₉	C₂×C₃×C₅×D₃	1	1	yes	characteristic
60	C₂×C₃²×C₅	—	19	1	no	—
61	C₃×C₅×D₃	—	19	2	no	—
62	C₂²×C₁₉	—	3	1	no	Hall
63	C₃×C₂₅	—	19	1	no	—
64	C₃×C₂₅	—	38	1	no	—
65	C₃×C₂₅	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₅	—	57	1	no	—
67	C₂×C₅×D₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic
68	C₃×C₁₉	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented
69	C₁₉⋊C₃	—	2	1	no	—
70	C₁₉⋊C₃	C₂×D₃×C₂₅	1	1	yes	characteristic, direct product factor
71	C₂×C₂₅	—	3	2	no	—
72	C₂×C₂₅	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
73	C₃²×C₅	—	19	1	no	—
74	C₂×C₁₉	—	3	2	no	—
75	C₂×C₁₉	C₃×D₃×C₂₅	1	1	yes	characteristic, complemented
76	C₂×C₃×D₃	—	19	1	no	Hall
77	C₂×C₃×C₅	—	19	1	no	—
78	C₂×C₃×C₅	—	38	1	no	—
79	C₂×C₃×C₅	—	57	2	no	—
80	C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
81	C₅×D₃	C₂×C₅×C₁₉⋊C₃	1	2	yes	—
82	C₂₅	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²×C₅	—	3	1	no	—
84	C₁₉	C₂×C₃×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₃²	—	19	1	no	—
86	C₃×D₃	—	19	2	no	—
87	C₃×C₅	—	19	1	no	—
88	C₃×C₅	—	38	1	no	—
89	C₃×C₅	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic
90	C₂²×C₃	—	57	1	no	—
91	C₂×D₃	C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
92	C₂×C₅	—	3	2	no	—
93	C₂×C₅	C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic
94	C₃²	—	19	1	no	Sylow
95	C₂×C₃	—	19	1	no	—
96	C₂×C₃	—	38	1	no	—
97	C₂×C₃	—	57	2	no	—
98	C₂×C₃	C₂×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
99	D₃	C₂×C₂₅×C₁₉⋊C₃	1	2	yes	direct product factor
100	C₅	C₂×C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic
101	C₂²	—	3	1	no	Sylow
102	C₃	—	19	1	no	—
103	C₃	—	38	1	no	—
104	C₃	C₂²×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
105	C₂	—	3	2	no	—
106	C₂	D₃×C₂₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₂₅×C₁₉⋊C₃

C₂

yes

maximal, characteristic, complemented

D₃×C₂₅×C₁₉⋊C₃

C₂

yes

maximal, direct product factor

C₂×D₃×C₁₉×C₂₅

C₃

yes

maximal, characteristic, complemented

C₂²×C₂₅×C₁₉⋊C₃

—

maximal

C₃×C₂₅×C₁₉⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₉⋊C₃

C₅

yes

maximal, characteristic

D₃×C₁₉×C₂₅

C₂×C₃

yes

complemented

C₂×C₂₅×C₁₉⋊C₃

—

C₂×C₂₅×C₁₉⋊C₃

—

C₂×C₂₅×C₁₉⋊C₃

D₃

yes

characteristic, direct product factor

C₂×C₃×C₁₉×C₂₅

C₂×C₃

yes

characteristic, complemented

C₂²×C₁₉×C₂₅

—

Hall

C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

yes

characteristic

C₅×D₃×C₁₉⋊C₃

C₂×C₅

yes

—

C₃×C₁₉×C₂₅

C₂²×C₃

yes

characteristic, complemented

C₂₅×C₁₉⋊C₃

—

C₂₅×C₁₉⋊C₃

C₂×D₃

yes

characteristic, direct product factor

C₂×C₅×D₃×C₁₉

C₃×C₅

yes

characteristic

C₂²×C₅×C₁₉⋊C₃

—

C₂×C₁₉×C₂₅

—

C₂×C₁₉×C₂₅

C₃×D₃

yes

characteristic, complemented

C₂×C₃×D₃×C₂₅

—

maximal, Hall

C₃×C₅×C₁₉⋊C₃

C₂²×C₅

yes

characteristic

C₂×D₃×C₁₉⋊C₃

C₂₅

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

characteristic

C₅×D₃×C₁₉

C₂×C₃×C₅

yes

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

C₅×D₃

yes

characteristic

C₁₉×C₂₅

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₂₅

—

C₃×D₃×C₂₅

—

C₂²×C₅×C₁₉

—

C₂×C₃×C₁₉⋊C₃

C₂×C₂₅

yes

characteristic, complemented

D₃×C₁₉⋊C₃

C₂×C₂₅

yes

direct product factor

C₂²×C₃×C₂₅

—

C₂×D₃×C₂₅

C₁₉⋊C₃

yes

characteristic, direct product factor

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

characteristic

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

C₂×C₅×D₃

yes

characteristic

C₂×D₃×C₁₉

C₃×C₂₅

yes

characteristic, complemented

C₂²×C₁₉⋊C₃

—

C₃²×C₂₅

—

Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×C₅×D₃

yes

characteristic

C₂×C₃×C₅×D₃

—

C₃×C₁₉⋊C₃

C₂²×C₂₅

yes

characteristic, complemented, Hall

C₂×C₃×C₂₅

—

C₂×C₃×C₂₅

—

C₂×C₃×C₂₅

—

C₂×C₃×C₂₅

C₂×C₁₉⋊C₃

yes

characteristic, complemented

D₃×C₂₅

C₂×C₁₉⋊C₃

yes

direct product factor

C₂×C₃×C₁₉

C₂×C₃×C₂₅

yes

characteristic, complemented

D₃×C₁₉

C₂×C₃×C₂₅

yes

complemented

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

D₃×C₂₅

yes

characteristic, direct product factor

C₂²×C₂₅

—

Hall

C₅×C₁₉

C₂×C₃×C₅×D₃

yes

characteristic

C₂×C₃²×C₅

—

C₃×C₅×D₃

—

C₂²×C₁₉

—

Hall

C₃×C₂₅

—

C₃×C₂₅

—

C₃×C₂₅

C₂²×C₁₉⋊C₃

yes

characteristic, complemented

C₂²×C₃×C₅

—

C₂×C₅×D₃

C₅×C₁₉⋊C₃

yes

characteristic

C₃×C₁₉

C₂²×C₃×C₂₅

yes

characteristic, complemented

C₁₉⋊C₃

—

C₁₉⋊C₃

C₂×D₃×C₂₅

yes

characteristic, direct product factor

C₂×C₂₅

—

C₂×C₂₅

D₃×C₁₉⋊C₃

yes

characteristic, direct product factor

C₃²×C₅

—

C₂×C₁₉

—

C₂×C₁₉

C₃×D₃×C₂₅

yes

characteristic, complemented

C₂×C₃×D₃

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

yes

characteristic

C₅×D₃

C₂×C₅×C₁₉⋊C₃

yes

—

C₂₅

C₂×D₃×C₁₉⋊C₃

yes

characteristic, direct product factor, Sylow

C₂²×C₅

—

C₁₉

C₂×C₃×D₃×C₂₅

yes

characteristic, complemented, Sylow

C₂×C₃²

—

C₃×D₃

—

C₃×C₅

—

C₃×C₅

—

C₃×C₅

C₂²×C₅×C₁₉⋊C₃

yes

characteristic

C₂²×C₃

—

C₂×D₃

C₂₅×C₁₉⋊C₃

yes

characteristic, direct product factor

C₂×C₅

—

C₂×C₅

C₅×D₃×C₁₉⋊C₃

yes

characteristic

C₃²

—

Sylow

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

C₂×C₂₅×C₁₉⋊C₃

yes

characteristic, complemented

D₃

C₂×C₂₅×C₁₉⋊C₃

yes

direct product factor

100

C₅

C₂×C₅×D₃×C₁₉⋊C₃

yes

characteristic

101

C₂²

—

Sylow

102

C₃

—

103

C₃

—

104

C₃

C₂²×C₂₅×C₁₉⋊C₃

yes

characteristic, complemented

105

C₂

—

106

C₂

D₃×C₂₅×C₁₉⋊C₃

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₃×C₁₉⋊C₃
commutator, hypocenter	C₃×C₁₉	C₂²×C₃×C₂₅
Frattini	C₅	C₂×C₅×D₃×C₁₉⋊C₃
Fitting	C₂×C₃×C₁₉×C₂₅	C₂×C₃
socle	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅
prime radical	C₂×C₅×D₃×C₁₉⋊C₃	C₅
cosocle	C₃×C₅×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₂₅

subgroup

G/H

center, hypercenter

C₂×C₂₅

D₃×C₁₉⋊C₃

commutator, hypocenter

C₃×C₁₉

C₂²×C₃×C₂₅

Frattini

C₅

C₂×C₅×D₃×C₁₉⋊C₃

Fitting

C₂×C₃×C₁₉×C₂₅

C₂×C₃

socle

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

prime radical

C₂×C₅×D₃×C₁₉⋊C₃

C₅

cosocle

C₃×C₅×C₁₉

C₂²×C₃×C₅

LCS

G ▷ C₃×C₁₉

UCS

C₁ ◁ C₂×C₂₅

N	H ≅ G/N	type
1. C₂×C₃×C₂₅×C₁₉⋊C₃	C₂	semidirect
2. D₃×C₂₅×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₁₉×C₂₅	C₃	semidirect
5. C₃×C₂₅×C₁₉⋊C₃	C₂²	semidirect
7. D₃×C₁₉×C₂₅	C₂×C₃	semidirect
10. C₂×C₂₅×C₁₉⋊C₃	D₃	direct (N × H)
11. C₂×C₃×C₁₉×C₂₅	C₂×C₃	semidirect
15. C₃×C₁₉×C₂₅	C₂²×C₃	semidirect
17. C₂₅×C₁₉⋊C₃	C₂×D₃	direct (N × H)
21. C₂×C₁₉×C₂₅	C₃×D₃	semidirect
24. C₂×D₃×C₁₉⋊C₃	C₂₅	direct (N × H)
30. C₁₉×C₂₅	C₂×C₃×D₃	semidirect
34. C₂×C₃×C₁₉⋊C₃	C₂×C₂₅	semidirect
35. D₃×C₁₉⋊C₃	C₂×C₂₅	direct (N × H)
37. C₂×D₃×C₂₅	C₁₉⋊C₃	direct (N × H)
41. C₂×D₃×C₁₉	C₃×C₂₅	semidirect
47. C₃×C₁₉⋊C₃	C₂²×C₂₅	semidirect
51. C₂×C₃×C₂₅	C₂×C₁₉⋊C₃	semidirect
52. D₃×C₂₅	C₂×C₁₉⋊C₃	direct (N × H)
53. C₂×C₃×C₁₉	C₂×C₃×C₂₅	semidirect
54. D₃×C₁₉	C₂×C₃×C₂₅	semidirect
57. C₂×C₁₉⋊C₃	D₃×C₂₅	direct (N × H)
65. C₃×C₂₅	C₂²×C₁₉⋊C₃	semidirect
68. C₃×C₁₉	C₂²×C₃×C₂₅	semidirect
70. C₁₉⋊C₃	C₂×D₃×C₂₅	direct (N × H)
72. C₂×C₂₅	D₃×C₁₉⋊C₃	direct (N × H)
75. C₂×C₁₉	C₃×D₃×C₂₅	semidirect
82. C₂₅	C₂×D₃×C₁₉⋊C₃	direct (N × H)
84. C₁₉	C₂×C₃×D₃×C₂₅	semidirect
91. C₂×D₃	C₂₅×C₁₉⋊C₃	direct (N × H)
98. C₂×C₃	C₂×C₂₅×C₁₉⋊C₃	semidirect
99. D₃	C₂×C₂₅×C₁₉⋊C₃	direct (N × H)
104. C₃	C₂²×C₂₅×C₁₉⋊C₃	semidirect
106. C₂	D₃×C₂₅×C₁₉⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₂×C₃×C₂₅×C₁₉⋊C₃

C₂

semidirect

2. D₃×C₂₅×C₁₉⋊C₃

C₂

direct (N × H)

3. C₂×D₃×C₁₉×C₂₅

C₃

semidirect

5. C₃×C₂₅×C₁₉⋊C₃

C₂²

semidirect

7. D₃×C₁₉×C₂₅

C₂×C₃

semidirect

10. C₂×C₂₅×C₁₉⋊C₃

D₃

direct (N × H)

11. C₂×C₃×C₁₉×C₂₅

C₂×C₃

semidirect

15. C₃×C₁₉×C₂₅

C₂²×C₃

semidirect

17. C₂₅×C₁₉⋊C₃

C₂×D₃

direct (N × H)

21. C₂×C₁₉×C₂₅

C₃×D₃

semidirect

24. C₂×D₃×C₁₉⋊C₃

C₂₅

direct (N × H)

30. C₁₉×C₂₅

C₂×C₃×D₃

semidirect

34. C₂×C₃×C₁₉⋊C₃

C₂×C₂₅

semidirect

35. D₃×C₁₉⋊C₃

C₂×C₂₅

direct (N × H)

37. C₂×D₃×C₂₅

C₁₉⋊C₃

direct (N × H)

41. C₂×D₃×C₁₉

C₃×C₂₅

semidirect

47. C₃×C₁₉⋊C₃

C₂²×C₂₅

semidirect

51. C₂×C₃×C₂₅

C₂×C₁₉⋊C₃

semidirect

52. D₃×C₂₅

C₂×C₁₉⋊C₃

direct (N × H)

53. C₂×C₃×C₁₉

C₂×C₃×C₂₅

semidirect

54. D₃×C₁₉

C₂×C₃×C₂₅

semidirect

57. C₂×C₁₉⋊C₃

D₃×C₂₅

direct (N × H)

65. C₃×C₂₅

C₂²×C₁₉⋊C₃

semidirect

68. C₃×C₁₉

C₂²×C₃×C₂₅

semidirect

70. C₁₉⋊C₃

C₂×D₃×C₂₅

direct (N × H)

72. C₂×C₂₅

D₃×C₁₉⋊C₃

direct (N × H)

75. C₂×C₁₉

C₃×D₃×C₂₅

semidirect

82. C₂₅

C₂×D₃×C₁₉⋊C₃

direct (N × H)

84. C₁₉

C₂×C₃×D₃×C₂₅

semidirect

91. C₂×D₃

C₂₅×C₁₉⋊C₃

direct (N × H)

98. C₂×C₃

C₂×C₂₅×C₁₉⋊C₃

semidirect

99. D₃

C₂×C₂₅×C₁₉⋊C₃

direct (N × H)

104. C₃

C₂²×C₂₅×C₁₉⋊C₃

semidirect

106. C₂

D₃×C₂₅×C₁₉⋊C₃

direct (N × H)

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

subgroup	index
C₂×C₃×C₂₅×C₁₉⋊C₃	2
D₃×C₂₅×C₁₉⋊C₃	2
C₂×D₃×C₁₉×C₂₅	3
C₂²×C₂₅×C₁₉⋊C₃	3
C₂×C₅×D₃×C₁₉⋊C₃	5
C₂×C₃×D₃×C₂₅	19

subgroup

index

C₂×C₃×C₂₅×C₁₉⋊C₃

D₃×C₂₅×C₁₉⋊C₃

C₂×D₃×C₁₉×C₂₅

C₂²×C₂₅×C₁₉⋊C₃

C₂×C₅×D₃×C₁₉⋊C₃

C₂×C₃×D₃×C₂₅

Subgroups — C₂×D₃×C₂₅×C₁₉⋊C₃ #30685481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×D3×C25×C19⋊C3 #30685481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₂₅×C₁₉⋊C₃ #30685481