Finite Group Databasebeta

← C5×D5×D153 #29505798

Subgroups — C5×D5×D153 #29505798

Order 15300.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D765C211yesmaximal, characteristic, complemented
2C52×D153C211yesmaximal, characteristic, complemented
3C5×C9×D5×C17C211yesmaximal, characteristic, complemented
4C5×D5×D51—31nomaximal
5C52×C9×C17C2211yescharacteristic, complemented, Hall
6C2×C5×D153—51nomaximal
7D5×D153C511yesmaximal, characteristic, direct product factor
8C5×D255—31no—
9C52×D51—31no—
10C3×C5×D5×C17D311yescharacteristic
11C5×D5×D17—91noHall
12C2×C5×C9×C17—51no—
13D765C2×C511yescharacteristic, complemented
14C5×D153—22no—
15C5×D153—51no—
16C5×D153D511yescharacteristic, direct product factor
17C5×D153C2×C511yescharacteristic, complemented
18C9×D5×C17C2×C511yescharacteristic, complemented
19C3×C52×C17C2×D311yescharacteristic
20C2×C5×D51—151no—
21D5×D51—31no—
22C5×D5×D9—171nomaximal, Hall
23C5×D85—91no—
24C5×D5×C17D911yescharacteristic, complemented
25C52×D17—91no—
26C5×C9×C17—22no—
27C5×C9×C17C2×D511yescharacteristic, complemented
28C5×C9×C17C22×C511yescharacteristic, complemented
29C2×D153—51noHall
30C2×C3×C5×C17—51no—
31D255—31no—
32C5×D51—31no—
33C5×D51—31no—
34C5×D51—62no—
35C5×D51—151no—
36C3×D5×C17C5×D311yescharacteristic
37C5×D45—171no—
38C52×D9—171no—
39C5×C9×D5D1711yescharacteristic, complemented
40C52×C17C2×D911yescharacteristic, complemented, Hall
41C2×C5×D17—451no—
42D5×D17—91no—
43C2×C9×C17—51no—
44D153—51no—
45D153C5×D511yescharacteristic, direct product factor
46C5×D3×D5—511no—
47C3×C5×C17—22no—
48C3×C5×C17D3×D511yescharacteristic
49C3×C5×C17C2×C5×D311yescharacteristic
50C52×C9C2×D1711yescharacteristic, complemented, Hall
51C2×D51—151no—
52C2×C5×D9—851no—
53D5×D9—171no—
54C2×C5×C17—51no—
55D85—91no—
56C5×D17—91no—
57C5×D17—91no—
58C5×D17—182no—
59C5×D17—451no—
60D5×C17C5×D911yescharacteristic, complemented
61C9×C17C2×C5×D511yescharacteristic, complemented, Hall
62C5×D15—511no—
63C52×D3—511no—
64C3×C5×D5D5111yescharacteristic
65C2×C3×C17—51no—
66D51—31no—
67D51—151no—
68C2×C5×D5—1531noHall
69C2×C5×C9—51no—
70D45—171no—
71C9×D5C5×D1711yescharacteristic, complemented
72C5×D9—171no—
73C5×D9—171no—
74C5×D9—342no—
75C5×D9—851no—
76C5×C17—22no—
77C5×C17D5×D911yescharacteristic, complemented
78C5×C17C2×C5×D911yescharacteristic, complemented
79C3×C52C2×D5111yescharacteristic
80C2×D17—451noHall
81C2×C5×D3—2551no—
82D3×D5—511no—
83C3×C17C5×D3×D511yescharacteristic
84C2×C52—1531no—
85C5×D5—1531no—
86C5×D5D15311yescharacteristic, direct product factor
87C5×C9—22no—
88C5×C9D5×D1711yescharacteristic, complemented
89C5×C9C2×C5×D1711yescharacteristic, complemented
90C2×D9—851noHall
91C2×C17—51no—
92D17—91no—
93D17—451no—
94C2×C3×C5—51no—
95D15—511no—
96C3×D5C5×D5111yescharacteristic
97C5×D3—511no—
98C5×D3—511no—
99C5×D3—1022no—
100C5×D3—2551no—
101C52C2×D15311yescharacteristic, complemented, Sylow
102C22×C5—7651no—
103C2×D5—1531no—
104C2×C9—51no—
105D9—171no—
106D9—851no—
107C17C5×D5×D911yescharacteristic, complemented, Sylow
108C3×C5—22no—
109C3×C5D5×D5111yescharacteristic
110C3×C5C2×C5×D5111yescharacteristic
111C2×D3—2551no—
112C2×C5—51no—
113C2×C5—3062no—
114C2×C5—1531no—
115C2×C5—1531no—
116C2×C5—7651no—
117D5—1531no—
118D5C5×D15311yescharacteristic, direct product factor
119C9C5×D5×D1711yescharacteristic, complemented, Sylow
120C2×C3—51no—
121D3—511no—
122D3—2551no—
123C5—22no—
124C5D5×D15311yescharacteristic, direct product factor
125C5C2×C5×D15311yescharacteristic, complemented
126C22—7651noSylow
127C3C5×D5×D5111yescharacteristic
128C2—51no—
129C2—1531no—
130C2—7651no—
subgroupG/H
center, hypercenterC5D5×D153
commutator, cosocle, hypocenterC5×C9×C17C22×C5
FrattiniC3C5×D5×D51
FittingC52×C9×C17C22
socleC3×C52×C17C2×D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×D765C2semidirect
2. C52×D153C2semidirect
3. C5×C9×D5×C17C2semidirect
5. C52×C9×C17C22semidirect
7. D5×D153C5direct (N × H)
13. D765C2×C5semidirect
16. C5×D153D5direct (N × H)
17. C5×D153C2×C5semidirect
18. C9×D5×C17C2×C5semidirect
24. C5×D5×C17D9semidirect
27. C5×C9×C17C2×D5semidirect
28. C5×C9×C17C22×C5semidirect
39. C5×C9×D5D17semidirect
40. C52×C17C2×D9semidirect
45. D153C5×D5direct (N × H)
50. C52×C9C2×D17semidirect
60. D5×C17C5×D9semidirect
61. C9×C17C2×C5×D5semidirect
71. C9×D5C5×D17semidirect
77. C5×C17D5×D9semidirect
78. C5×C17C2×C5×D9semidirect
86. C5×D5D153direct (N × H)
88. C5×C9D5×D17semidirect
89. C5×C9C2×C5×D17semidirect
101. C52C2×D153semidirect
107. C17C5×D5×D9semidirect
118. D5C5×D153direct (N × H)
119. C9C5×D5×D17semidirect
124. C5D5×D153direct (N × H)
125. C5C2×C5×D153semidirect

Maximal subgroups

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

subgroupindex
C5×D7652
C52×D1532
C5×C9×D5×C172
C5×D5×D513
C2×C5×D1535
D5×D1535
C5×D5×D917