Finite Group Databasebeta

← #72230610

Subgroups — #72230610

Order 3600.

432 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#14268305C212yesmaximal, complemented
2C5×#67158C212yesmaximal, complemented
3C3⋊Dic3×C5⋊D5C211yesmaximal, characteristic
4C3×#10597126C212yesmaximal
5#11925431—32nomaximal
6C2×C32×C5⋊D5C2211yescharacteristic
7C3⋊(C3⋊#1039)C2211yescharacteristic
8C52×C3⋊Dic3C2211yescharacteristic
9C3×C5×Dic15C2214yes—
10D5×#627—52nomaximal
11#10597126D312yes—
12#10597124—34no—
13Dic3×C5⋊D5—32no—
14Dic3×C5⋊D5—61no—
15C5×#1204—34no—
16C3×#6036—32no—
17C2×C32×C52C2311yescharacteristic
18C32×C5⋊D5Q812yescomplemented
19#87872—91noHall
20#67158D512yescomplemented
21#67153—54no—
22C5×#627—52no—
23D5×C3⋊Dic3—52no—
24D5×C3⋊Dic3—102no—
25C3×D5×Dic3—54no—
26C2×C3×C5⋊D5—21no—
27C2×C3×C5⋊D5C2×D312yes—
28C3⋊#1039—32no—
29C3⋊#1039—61no—
30C5×Dic15C2×D314yes—
31C52×Dic3—32no—
32C52×Dic3—61no—
33C3×C5×Dic5—34no—
34D5×Dic6—154no—
35C32×C52C2×Q811yescharacteristic, complemented, Hall
36C4×C5⋊D5—91no—
37C5×Dic10—92no—
38#6039—92no—
39#6036—32no—
40C2×C32×D5—52no—
41C2×C32×D5—102no—
42C3⋊Dic15—52no—
43C3⋊Dic15—102no—
44C5×C3⋊Dic3—22no—
45C5×C3⋊Dic3C2×D512yes—
46C3×Dic15C2×D514yes—
47C3×C5×Dic3—54no—
48C2×C3×C52—21no—
49C2×C3×C52C22×D312yes—
50C3×C5⋊D5—22no—
51C3×C5⋊D5Dic614yescomplemented
52C2×#627—251noHall
53Dic30—154no—
54C5×Dic6—154no—
55C3×C4×D5—154no—
56#1204—34no—
57#1204—154no—
58D5×Dic3—54no—
59D5×Dic3—154no—
60D5×Dic3—304no—
61D5×Dic3—302no—
62D5×Dic3—304no—
63C2×C5⋊D5D3211yescharacteristic
64C4×C52—91no—
65#1039—91no—
66C5×Dic5—34no—
67C2×C32×C5—22no—
68C2×C32×C5C22×D512yes—
69C32×D5—54no—
70C32×D5—104no—
71Q8×D5—452no—
72C3×C52—21no—
73C3×C52C2×Dic612yescomplemented
74C2×C3⋊Dic3—251no—
75C2×C3×Dic3—252no—
76#627—52no—
77#627—252no—
78C2×C3×D5—54no—
79C2×C3×D5—104no—
80C2×C3×D5—102no—
81C2×C3×D5—104no—
82C3×C4×C5—154no—
83Dic15—154no—
84Dic15—304no—
85Dic15—302no—
86Dic15—304no—
87Dic15D3×D514yes—
88C3×Dic5—34no—
89C5×Dic3—34no—
90C5×Dic3—54no—
91C5×Dic3—64no—
92C5×Dic3—62no—
93C5×Dic3—64no—
94C2×C52C2×D3211yescharacteristic
95C5⋊D5#62712yescomplemented
96C2×Dic6—752no—
97C32×C5—22no—
98C32×C5Q8×D512yescomplemented
99C5×Q8—452no—
100C4×D5—154no—
101C4×D5—452no—
102C4×D5—902no—
103Dic10—92no—
104Dic10—454no—
105C22×C32—251no—
106C3⋊Dic3—251no—
107C3⋊Dic3D5211yescharacteristic
108C3×Dic3—54no—
109C2×C3×C5—24no—
110C2×C3×C5—22no—
111C2×C3×C5—24no—
112C2×C3×C5C2×D3×D514yes—
113C3×D5—58no—
114C3×D5—108no—
115C3×D5—104no—
116C3×D5—108no—
117C52C2×#62711yescharacteristic, complemented, Sylow
118C2×C3×C4—752no—
119C2×Dic3—252no—
120C2×Dic3—752no—
121C2×Dic3—1501no—
122Dic6—154no—
123Dic6—754no—
124C2×D5—52no—
125C2×D5—102no—
126C4×C5—92no—
127C4×C5—154no—
128C4×C5—182no—
129Dic5—34no—
130Dic5—452no—
131Dic5—902no—
132C2×C32—252no—
133C2×C32C2×D5211yescharacteristic
134C2×Q8—2251noSylow
135C3×C5—24no—
136C3×C5—22no—
137C3×C5—24no—
138C3×C5D5×Dic614yescomplemented
139C22×C3—252no—
140C22×C3—501no—
141C3×C4—154no—
142Dic3—32no—
143Dic3—54no—
144Dic3—61no—
145Dic3—752no—
146Dic3—1501no—
147C2×C5—22no—
148C2×C5D32×D512yes—
149D5—54no—
150D5—104no—
151C32#8787211yescharacteristic, complemented, Sylow
152Q8—452no—
153Q8—2252no—
154C2×C4—752no—
155C2×C4—2251no—
156C2×C3—21no—
157C2×C3—254no—
158C2×C3—502no—
159C2×C3D3×D5212yes—
160C5—22no—
161C5D5×#62712yescomplemented
162C22—251no—
163C4—91no—
164C4—154no—
165C4—2251no—
166C3—21no—
167C3#1192543112yescomplemented
168C2—252no—
169C2#1426848711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#14268487
commutator, Fitting, socle, cosocleC2×C32×C52C23
prime radicalC2×C32×C5⋊D5C22
hypocenterC32×C52C2×Q8
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #14268305C2semidirect
2. C5×#67158C2semidirect
18. C32×C5⋊D5Q8semidirect
20. #67158D5semidirect
35. C32×C52C2×Q8semidirect
51. C3×C5⋊D5Dic6semidirect
73. C3×C52C2×Dic6semidirect
95. C5⋊D5#627semidirect
98. C32×C5Q8×D5semidirect
117. C52C2×#627semidirect
138. C3×C5D5×Dic6semidirect
151. C32#87872semidirect
161. C5D5×#627semidirect
167. C3#11925431semidirect

Maximal subgroups

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

subgroupindex
#142683052
C5×#671582
C3⋊Dic3×C5⋊D52
C3×#105971262
#119254313
D5×#6275