Finite Group Databasebeta

← #10617730⋊C3 #14514029

Subgroups — #10617730⋊C3 #14514029

Order 1920.

486 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic
2#66161⋊C3C212yesmaximal
3#65903⋊C3C214yesmaximal, complemented
4#10617730C311yesmaximal, characteristic, complemented, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6C3×#4016—41nomaximal
7C4×C5×SL(2,𝔽3)C2212yes—
8Dic5×SL(2,𝔽3)C2214yes—
9#3504⋊C3—51nomaximal, Hall
10C4×C5×#41C2×C311yescharacteristic
11#66161C2×C312yes—
12#65903C2×C314yes—
13#65873—34no—
14#65853—32no—
15#65804—31no—
16C2×#4016—31no—
17C5×#41⋊C3Q812yescomplemented
18C2×C5×SL(2,𝔽3)C2311yescharacteristic
19C3×C42×C5—41no—
20C3×C4⋊Dic5—42no—
21C3×#683—44no—
22#557⋊C3—54no—
23#520⋊C3—52no—
24C4×#41⋊C3D511yescharacteristic
25C2×C5×#41C22×C311yescharacteristic
26C4×C5×Q8C22×C312yes—
27C4×C5×D4—32no—
28C5×#117—31no—
29C2×C42×C5—31no—
30Q8×Dic5C22×C314yes—
31D4×Dic5—34no—
32#4072—32no—
33C2×C4⋊Dic5—32no—
34#4070—34no—
35C2×#683—34no—
36#4036—34no—
37#4034—34no—
38#4024—38no—
39#4016—32no—
40#4016—31no—
41#4016—34no—
42#4016A411yescharacteristic
43#4015—32no—
44C4×Dic10—34no—
45#3504—51noSylow
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5—42no—
48C2×C3×Dic5—44no—
49C5×SL(2,𝔽3)C2×Q811yescharacteristic
50C2×#41⋊C3C2×D511yescharacteristic
51C3×#125—201no—
52C4×SL(2,𝔽3)—54no—
53C4×SL(2,𝔽3)C2×D512yes—
54C5×#41—32no—
55C5×#41C3×Q812yes—
56C2×C5×Q8C23×C311yescharacteristic
57C2×C5×D4—31no—
58C22×C4×C5—31no—
59C22×C4×C5—32no—
60C22×Dic5—34no—
61C2×Dic10—34no—
62C5×C4⋊C4—32no—
63C5×C22⋊C4—32no—
64C42×C5—31no—
65C42×C5—32no—
66C42×C5C2×A411yescharacteristic
67C22⋊Dic5—34no—
68C4⋊Dic5—32no—
69C4⋊Dic5—34no—
70C4⋊Dic5—34no—
71C4⋊Dic5C2×A412yes—
72#683—38no—
73#683—34no—
74#683C2×A414yes—
75C4×Dic5—34no—
76#557—54no—
77#554—154no—
78#544—152no—
79#533—151no—
80C2×#125—151no—
81#520—52no—
82C4×#41C3×D511yescharacteristic
83C22×C3×C5—41no—
84C3×C4×C5—42no—
85C3×C4×C5—82no—
86C3×Dic5—84no—
87#41⋊C3Dic1012yescomplemented
88C2×SL(2,𝔽3)C22×D511yescharacteristic
89C3×C4⋊C4—204no—
90C3×C4⋊C4—202no—
91C3×C42—41no—
92C23×C5—31no—
93C5×Q8—31no—
94C5×Q8C2×C3×Q811yescharacteristic
95C5×D4—32no—
96C5×D4—32no—
97C2×C4×C5—31no—
98C2×C4×C5—32no—
99C2×C4×C5—32no—
100C2×C4×C5—32no—
101C2×C4×C5—122no—
102C2×C4×C5C22×A412yes—
103C2×C4×C5C22×A411yescharacteristic
104C2×Dic5—34no—
105C2×Dic5—124no—
106C2×Dic5C22×A414yes—
107Dic10—124no—
108C2×#41C2×C3×D511yescharacteristic
109C4⋊Q8—152no—
110C4⋊Q8—154no—
111#125—51no—
112#125—154no—
113#125—152no—
114#125—154no—
115#125—151no—
116C22⋊Q8—158no—
117C22⋊Q8—154no—
118C4×Q8—54no—
119C4×Q8—154no—
120C4×Q8C2×C3×D512yes—
121C4×D4—32no—
122C4×D4—154no—
123#117—31no—
124#117—152no—
125C2×C4⋊C4—154no—
126C2×C4⋊C4—152no—
127C2×C42—31no—
128C2×C3×C5—41no—
129C2×C3×C5—42no—
130C2×C3×C4—41no—
131C2×C3×C4—42no—
132C2×C3×C4—204no—
133SL(2,𝔽3)C2×Dic1011yescharacteristic
134C22×C5—32no—
135C22×C5—62no—
136C22×C5C23×A411yescharacteristic
137C4×C5—22no—
138C4×C5—31no—
139C4×C5—31no—
140C4×C5—62no—
141C4×C5Q8×A412yes—
142Dic5—24no—
143Dic5—64no—
144#41—32no—
145#41C3×Dic1012yes—
146C2×Q8—154no—
147C2×Q8C22×C3×D511yescharacteristic
148C2×D4—31no—
149C22×C4—31no—
150C22×C4—32no—
151C22×C4—154no—
152C4⋊C4—32no—
153C4⋊C4—52no—
154C4⋊C4—54no—
155C4⋊C4—154no—
156C4⋊C4—154no—
157C4⋊C4—158no—
158C4⋊C4—154no—
159C4⋊C4—152no—
160C22⋊C4—32no—
161C22⋊C4—154no—
162C42—31no—
163C42—32no—
164C42—154no—
165C42D5×A411yescharacteristic
166C3×C5—41noHall
167C22×C3—41no—
168C3×C4—42no—
169C3×C4—82no—
170C3×C4—404no—
171C2×C5—62no—
172C2×C5C2×Q8×A411yescharacteristic
173C2×C5#594512yes—
174C23—31no—
175Q8—31no—
176Q8—604no—
177Q8C2×C3×Dic1011yescharacteristic
178D4—32no—
179D4—32no—
180C2×C4—31no—
181C2×C4—32no—
182C2×C4—32no—
183C2×C4—32no—
184C2×C4—54no—
185C2×C4—122no—
186C2×C4—154no—
187C2×C4—604no—
188C2×C4C2×D5×A412yes—
189C2×C4C2×D5×A411yescharacteristic
190C2×C3—41no—
191C2×C3—42no—
192C5#3504⋊C311yescharacteristic, complemented, Sylow
193C22—32no—
194C22—62no—
195C22C22×D5×A411yescharacteristic
196C4—22no—
197C4—31no—
198C4—31no—
199C4—62no—
200C4—104no—
201C4—304no—
202C4A4×Dic1012yes—
203C3—41noSylow
204C2—62no—
205C2C2×A4×Dic1011yescharacteristic
206C2#66283⋊C312yes—
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
prime radicalC2×C5×#41⋊C3C22
hypercenterC42D5×A4
hypocenterC5×Q8C2×C3×Q8
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #65903⋊C3C2semidirect
4. #10617730C3semidirect
17. C5×#41⋊C3Q8semidirect
87. #41⋊C3Dic10semidirect
192. C5#3504⋊C3semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#66161⋊C32
#65903⋊C32
#106177303
C3×#40164
#3504⋊C35