Finite Group Databasebeta

← D75⋊D93 #42124447

Subgroups — D75⋊D93 #42124447

Order 27900.

132 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 34 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
1C25×C3⋊D93C211yesmaximal, characteristic, complemented
2C3×D2325C211yesmaximal, characteristic, complemented
3C3×C31×D75C211yesmaximal, characteristic, complemented
4D75⋊D31—31nomaximal
5D25×D93—31nomaximal
6C32×C25×C31C2211yescharacteristic, complemented, Hall
7D15⋊D93—51nomaximal
8D2325D311yescharacteristic, complemented
9C31×D75D311yescharacteristic, complemented
10C25×D93—31no—
11C25×D93—31no—
12C25×D93—61no—
13C3×D775—31no—
14C3×C31×D25—31no—
15D25×D31—91noHall
16C5×C3⋊D93D511yescharacteristic
17C3×D465—51no—
18C3×D15×C31—51no—
19C3×C25×C31—21no—
20C3×C25×C31C2×D311yescharacteristic, complemented
21C3×C25×C31C2×D311yescharacteristic, complemented
22D15⋊D31—151no—
23D5×D93—151no—
24D775—31no—
25C25×D31—91no—
26C31×D25—31no—
27C32×C5×C31C2×D511yescharacteristic
28D3×D93—251noHall
29D465—51no—
30D15×C31—51no—
31C5×D93—31no—
32C5×D93—31no—
33C5×D93—61no—
34C3×D155—151no—
35C3×D5×C31—151no—
36(C3⋊D3)⋊D25—311nomaximal, Hall
37C25×C31D3211yescharacteristic, complemented, Hall
38D5×D31—451no—
39C3⋊D93D2511yescharacteristic, complemented
40C3×D93—251no—
41C3×D3×C31—251no—
42C3×C5×C31—21no—
43C3×C5×C31D3×D511yescharacteristic
44C3×C5×C31D3×D511yescharacteristic
45C3⋊D3×C25—311no—
46C3×D75—311no—
47C3×D75D3111yescharacteristic, complemented
48C2×D93—751no—
49D3×D31—751no—
50D155—151no—
51C5×D31—91no—
52D5×C31—151no—
53D3×D25—931no—
54D3×D25—931no—
55C32×C31C2×D2511yescharacteristic, complemented, Hall
56C32×C25C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—751no—
58D93—31no—
59D93—31no—
60D93—61no—
61D93—251no—
62C3×D31—751no—
63D3×C31—251no—
64(C3⋊D3)⋊D5—1551no—
65C5×C31(C3⋊D3)⋊D511yescharacteristic
66D75—311no—
67D75D9311yescharacteristic, complemented
68C3×D25—31no—
69C3×D25—931no—
70D3×C25—931no—
71D3×C25—931no—
72D3×C25—1861no—
73C2×D31—2251noHall
74C2×D25—2791noHall
75C3×C31—21no—
76C3×C31D3×D2511yescharacteristic, complemented
77C3×C31D3×D2511yescharacteristic, complemented
78C5×C3⋊D3—311no—
79C3×D15—51no—
80C3×D15—1551no—
81C3×C25—21no—
82C3×C25D3×D3111yescharacteristic, complemented
83C3×C25C2×D9311yescharacteristic, complemented
84C2×C31—751no—
85D31—91no—
86D31—751no—
87D3×D5—4651no—
88D3×D5—4651no—
89C2×C25—2791no—
90D25—31no—
91D25—931no—
92C32×C5D5×D3111yescharacteristic
93D32—7751noHall
94C31(C3⋊D3)⋊D2511yescharacteristic, complemented, Sylow
95D15—51no—
96D15—1551no—
97C3×D5—151no—
98C3×D5—4651no—
99C5×D3—931no—
100C5×D3—931no—
101C5×D3—1861no—
102C25D3×D9311yescharacteristic, complemented, Sylow
103C2×D5—13951no—
104C3⋊D3—311no—
105C3×D3—7751no—
106C3×D3—251no—
107C3×C5—21no—
108C3×C5D5×D9311yescharacteristic
109C3×C5D15⋊D3111yescharacteristic
110C2×D3—23251no—
111C2×D3—23251no—
112C2×C5—2791no—
113D5—151no—
114D5—4651no—
115C32D25×D3111yescharacteristic, complemented, Sylow
116C2×C3—23251no—
117C2×C3—751no—
118D3—7751no—
119D3—251no—
120D3—931no—
121D3—931no—
122D3—1861no—
123C5D15⋊D9311yescharacteristic
124C22—69751noSylow
125C3—21no—
126C3D25×D9311yescharacteristic, complemented
127C3D75⋊D3111yescharacteristic, complemented
128C2—23251no—
129C2—2791no—
130C2—751no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C25×C31C22
FrattiniC5D15⋊D93
socleC32×C5×C31C2×D5
LCSG ▷ C32×C25×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C25×C3⋊D93C2semidirect
2. C3×D2325C2semidirect
3. C3×C31×D75C2semidirect
6. C32×C25×C31C22semidirect
8. D2325D3semidirect
9. C31×D75D3semidirect
20. C3×C25×C31C2×D3semidirect
21. C3×C25×C31C2×D3semidirect
37. C25×C31D32semidirect
39. C3⋊D93D25semidirect
47. C3×D75D31semidirect
55. C32×C31C2×D25semidirect
56. C32×C25C2×D31semidirect
67. D75D93semidirect
76. C3×C31D3×D25semidirect
77. C3×C31D3×D25semidirect
82. C3×C25D3×D31semidirect
83. C3×C25C2×D93semidirect
94. C31(C3⋊D3)⋊D25semidirect
102. C25D3×D93semidirect
115. C32D25×D31semidirect
126. C3D25×D93semidirect
127. C3D75⋊D31semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D932
C3×D23252
C3×C31×D752
D75⋊D313
D25×D933
D15⋊D935
(C3⋊D3)⋊D2531