Finite Group Databasebeta

← C3×#10602382 #14298404

Subgroups — C3×#10602382 #14298404

Order 1920.

544 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 186 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
1C2×C3×C5×#117C211yesmaximal, characteristic
2C3×#65496C212yesmaximal
3C3×#64750C214yesmaximal, complemented
4#10602382C311yesmaximal, characteristic, direct product factor, Hall
5C23×C3×C4×C5C2211yescharacteristic
6C3×C5×#117—24no—
7C2×C3×C5×C4⋊C4C2212yes—
8C2×C3×C5×C22⋊C4C412yes—
9C2×C3×C42×C5C412yes—
10C2×C3×#681C2214yes—
11C3×C22⋊#168—24no—
12C3×#1822—51nomaximal, Hall
13C2×C5×#117C2×C311yescharacteristic
14#65496C2×C312yes—
15#64750C2×C314yescomplemented
16C24×C3×C5C2×C411yescharacteristic
17C22×C3×C4×C5—24no—
18C22×C3×C4×C5C2×C411yescharacteristic
19C22×C3×C4×C5C2×C414yes—
20C22×C3×C4×C5D414yes—
21C22×C3×C4×C5C2311yescharacteristic
22C3×C5×C4⋊C4—24no—
23C3×C5×C22⋊C4—24no—
24C3×C42×C5—24no—
25C3×#681—28no—
26C2×C3×#168—24no—
27C2×C3×#117D511yescharacteristic
28C3×#407—52no—
29C3×#343—54no—
30C23×C4×C5C22×C311yescharacteristic
31C5×#117—24no—
32C2×C5×C4⋊C4C22×C312yes—
33C2×C5×C22⋊C4C3×C412yes—
34C2×C42×C5C3×C412yes—
35C2×#681C22×C314yes—
36C22⋊#168—24no—
37#1822—51noSylow
38C23×C3×C5—22no—
39C23×C3×C5—42no—
40C23×C3×C5C22⋊C412yes—
41C23×C3×C5C22×C411yescharacteristic
42C2×C3×C4×C5—22no—
43C2×C3×C4×C5—28no—
44C2×C3×C4×C5—24no—
45C2×C3×C4×C5—44no—
46C2×C3×C4×C5C22⋊C412yes—
47C2×C3×C4×C5C2×D412yes—
48C2×C3×C4×C5#4114yes—
49C3×#168—44no—
50C23×C3×C4C2×D511yescharacteristic
51C2×C3×M16—54no—
52C3×#117—24no—
53C2×C3×C4⋊C4C2×D512yes—
54C2×C3×C22⋊C4Dic512yes—
55C2×C3×C42Dic512yes—
56C3×C22⋊C8—104no—
57C24×C5C2×C3×C411yescharacteristic
58C22×C4×C5—24no—
59C22×C4×C5C2×C3×C411yescharacteristic
60C22×C4×C5C2×C3×C414yes—
61C22×C4×C5C3×D414yes—
62C22×C4×C5C23×C311yescharacteristic
63C5×C4⋊C4—24no—
64C5×C22⋊C4—24no—
65C42×C5—24no—
66#681—28no—
67C2×#168—24no—
68C2×#117C3×D511yescharacteristic
69#407—52no—
70#343—54no—
71C22×C3×C5—22no—
72C22×C3×C5—22no—
73C22×C3×C5—24no—
74C22×C3×C5—44no—
75C22×C3×C5C2×C22⋊C411yescharacteristic
76C22×C3×C5#11712yes—
77C3×C4×C5—22no—
78C3×C4×C5—44no—
79C3×C4×C5#12314yes—
80C24×C3C2×Dic511yescharacteristic
81C22×C3×C4—24no—
82C22×C3×C4C2×Dic511yescharacteristic
83C22×C3×C4C2×Dic514yes—
84C22×C3×C4C22⋊D514yes—
85C22×C3×C4C22×D511yescharacteristic
86C3×M16—108no—
87C2×C3×C8—104no—
88C3×C4⋊C4—24no—
89C3×C22⋊C4—24no—
90C3×C42—24no—
91C23×C5—22no—
92C23×C5—42no—
93C23×C5C3×C22⋊C412yes—
94C23×C5C22×C3×C411yescharacteristic
95C2×C4×C5—22no—
96C2×C4×C5—28no—
97C2×C4×C5—24no—
98C2×C4×C5—44no—
99C2×C4×C5C3×C22⋊C412yes—
100C2×C4×C5C2×C3×D412yes—
101C2×C4×C5C3×#4114yes—
102#168—44no—
103C23×C4C2×C3×D511yescharacteristic
104C2×M16—54no—
105#117—24no—
106C2×C4⋊C4C2×C3×D512yes—
107C2×C22⋊C4C3×Dic512yes—
108C2×C42C3×Dic512yes—
109C22⋊C8—104no—
110C2×C3×C5—22no—
111C2×C3×C5—42no—
112C2×C3×C5#38111yescharacteristic
113C2×C3×C5#41312yes—
114C23×C3—22no—
115C23×C3—42no—
116C23×C3C22⋊Dic512yes—
117C23×C3C22×Dic511yescharacteristic
118C2×C3×C4—22no—
119C2×C3×C4—28no—
120C2×C3×C4—24no—
121C2×C3×C4—44no—
122C2×C3×C4C22⋊Dic512yes—
123C2×C3×C4#70914yes—
124C2×C3×C4C2×C22⋊D512yes—
125C3×C8—204no—
126C22×C5—22no—
127C22×C5—22no—
128C22×C5—24no—
129C22×C5—44no—
130C22×C5C2×C3×C22⋊C411yescharacteristic
131C22×C5C3×#11712yes—
132C4×C5—22no—
133C4×C5—44no—
134C4×C5C3×#12314yes—
135C24C2×C3×Dic511yescharacteristic
136C22×C4—24no—
137C22×C4C2×C3×Dic511yescharacteristic
138C22×C4C2×C3×Dic514yes—
139C22×C4C3×C22⋊D514yes—
140C22×C4C22×C3×D511yescharacteristic
141M16—108no—
142C2×C8—104no—
143C4⋊C4—24no—
144C22⋊C4—24no—
145C42—24no—
146C3×C5#182211yescharacteristic, complemented, Hall
147C22×C3—22no—
148C22×C3—22no—
149C22×C3—24no—
150C22×C3—44no—
151C22×C3#407212yes—
152C22×C3C2×C22⋊Dic511yescharacteristic
153C3×C4—22no—
154C3×C4—44no—
155C3×C4#407514yes—
156C2×C5—22no—
157C2×C5—42no—
158C2×C5C3×#38111yescharacteristic
159C2×C5C3×#41312yes—
160C23—22no—
161C23—42no—
162C23C3×C22⋊Dic512yes—
163C23C22×C3×Dic511yescharacteristic
164C2×C4—22no—
165C2×C4—28no—
166C2×C4—24no—
167C2×C4—44no—
168C2×C4C3×C22⋊Dic512yes—
169C2×C4C3×#70914yes—
170C2×C4C2×C3×C22⋊D512yes—
171C8—204no—
172C2×C3—22no—
173C2×C3—42no—
174C2×C3#6550011yescharacteristic
175C2×C3#6552612yes—
176C5C3×#182211yescharacteristic, complemented, Sylow
177C22—22no—
178C22—22no—
179C22—24no—
180C22—44no—
181C22C3×#407212yes—
182C22C2×C3×C22⋊Dic511yescharacteristic
183C4—22no—
184C4—44no—
185C4C3×#407514yes—
186C3#1060238211yescharacteristic, direct product factor, Sylow
187C2—22no—
188C2—42no—
189C2C3×#6550011yescharacteristic
190C2C3×#6552612yes—
subgroupG/H
centerC22×C3C2×C22⋊Dic5
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#117C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#1822
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
3. C3×#64750C2semidirect
4. #10602382C3direct (N × H)
15. #64750C2×C3semidirect
146. C3×C5#1822semidirect
176. C5C3×#1822semidirect
186. C3#10602382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C3×#654962
C3×#647502
#106023823
C3×#18225