Finite Group Databasebeta

← D45×D155 #42124570

Subgroups — D45×D155 #42124570

Order 27900.

144 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊D1395C211yesmaximal, characteristic, complemented
2C5×C31×D45C211yesmaximal, characteristic, complemented
3C5×C9×D155C211yesmaximal, characteristic, complemented
4D15×D155—31nomaximal
5C52×C9×C31C2211yescharacteristic, complemented, Hall
6D9×D155—51nomaximal
7D31×D45—51nomaximal
8C3⋊(C5⋊D155)—31no—
9C5×D15×C31—31no—
10C3×C5×D155D311yescharacteristic
11D5×D155—91noHall
12D1395—51no—
13D1395—51no—
14D1395—102no—
15C31×D45D511yescharacteristic, complemented
16C5×D9×C31—51no—
17C9×D155D511yescharacteristic, complemented
18C5×C9×D31—51no—
19C3×C52×C31C2×D311yescharacteristic
20D3×D155—151no—
21D15×D31—151no—
22C5⋊D155—91no—
23C5×D155D911yescharacteristic, complemented
24C5×D5×C31—91no—
25C5×C9×C31—22no—
26C5×C9×C31C2×D511yescharacteristic, complemented
27C5×C9×C31C2×D511yescharacteristic, complemented
28D9×D31—251noHall
29D465—151no—
30D465—151no—
31D465—302no—
32D15×C31—31no—
33C5×D3×C31—151no—
34C3×D155D1511yescharacteristic
35C3×C5×D31—51no—
36D5×D45—311nomaximal, Hall
37C52×C31C2×D911yescharacteristic, complemented, Hall
38C2×D155—451no—
39D5×D31—451no—
40D279—251no—
41C9×D31—51no—
42D9×C31—51no—
43C3×C5×C31—22no—
44C3×C5×C31D3×D511yescharacteristic
45C3×C5×C31C2×D1511yescharacteristic
46C5⋊D45—311no—
47C5×D45D3111yescharacteristic, complemented
48C5×C9×D5—311no—
49D3×D31—751no—
50C2×C5×C31—451no—
51D155—451no—
52D155—451no—
53D155—902no—
54D155D4511yescharacteristic, direct product factor
55C5×D31—51no—
56D5×C31—91no—
57D5×D15—931no—
58C9×C31D5211yescharacteristic, complemented, Hall
59C52×C9C2×D3111yescharacteristic, complemented, Hall
60D93—751no—
61C3×D31—51no—
62D3×C31—151no—
63C2×D45—1551no—
64D5×D9—1551no—
65C5×C31—22no—
66C5×C31D5×D911yescharacteristic, complemented
67C5×C31C2×D4511yescharacteristic, complemented
68C3⋊(C5⋊D5)—931no—
69C5×D15—31no—
70C3×C5×D5—311no—
71C2×D31—2251noHall
72D52—2791noHall
73C3×C31D5×D1511yescharacteristic
74C2×C5×C9—1551no—
75D45—3102no—
76D45—1551no—
77D45—1551no—
78D45D15511yescharacteristic, direct product factor
79C9×D5—311no—
80C5×D9—51no—
81C3×C52D3×D3111yescharacteristic
82C2×C31—451no—
83D31—51no—
84D31—2251no—
85C2×D15—4651no—
86D3×D5—4651no—
87C5⋊D5—2791no—
88C5×D5—91no—
89C5×D5—311no—
90C5×C9—22no—
91C5×C9D5×D3111yescharacteristic, complemented
92C5×C9C2×D15511yescharacteristic, complemented
93C2×D9—7751noHall
94C31D5×D4511yescharacteristic, complemented, Sylow
95C2×C3×C5—1551no—
96D15—31no—
97D15—9302no—
98D15—4651no—
99D15—4651no—
100C3×D5—311no—
101C5×D3—151no—
102C52D9×D3111yescharacteristic, complemented, Sylow
103C2×D5—13951no—
104C2×D5—13951no—
105C2×C9—1551no—
106D9—51no—
107D9—7751no—
108C3×C5—22no—
109C3×C5D15×D3111yescharacteristic
110C3×C5D3×D15511yescharacteristic
111C2×D3—23251no—
112C2×C5—451no—
113C2×C5—1551no—
114D5—91no—
115D5—311no—
116D5—13951no—
117D5—13951no—
118D5—27902no—
119C9D5×D15511yescharacteristic, complemented, Sylow
120C2×C3—1551no—
121D3—151no—
122D3—23251no—
123C5—22no—
124C5D31×D4511yescharacteristic, complemented
125C5D9×D15511yescharacteristic, complemented
126C22—69751noSylow
127C3D15×D15511yescharacteristic
128C2—451no—
129C2—69751no—
130C2—1551no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC52×C9×C31C22
FrattiniC3D15×D155
socleC3×C52×C31C2×D3
LCSG ▷ C52×C9×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5⋊D1395C2semidirect
2. C5×C31×D45C2semidirect
3. C5×C9×D155C2semidirect
5. C52×C9×C31C22semidirect
15. C31×D45D5semidirect
17. C9×D155D5semidirect
23. C5×D155D9semidirect
26. C5×C9×C31C2×D5semidirect
27. C5×C9×C31C2×D5semidirect
37. C52×C31C2×D9semidirect
47. C5×D45D31semidirect
54. D155D45direct (N × H)
58. C9×C31D52semidirect
59. C52×C9C2×D31semidirect
66. C5×C31D5×D9semidirect
67. C5×C31C2×D45semidirect
78. D45D155direct (N × H)
91. C5×C9D5×D31semidirect
92. C5×C9C2×D155semidirect
94. C31D5×D45semidirect
102. C52D9×D31semidirect
119. C9D5×D155semidirect
124. C5D31×D45semidirect
125. C5D9×D155semidirect

Maximal subgroups

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

subgroupindex
C5⋊D13952
C5×C31×D452
C5×C9×D1552
D15×D1553
D9×D1555
D31×D455
D5×D4531