Finite Group Databasebeta

← #13016160

Subgroups — #13016160

Order 1280.

638 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 160 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×#65683C212yesmaximal
2D5×#382C211yesmaximal, characteristic
3#10598722C214yesmaximal, complemented
4C2×D5×C4⋊C4C412yes—
5C2×C42×D5C2211yescharacteristic
6C2×#4003—22no—
7C2×#4002C2214yes—
8C2×C4⋊#170—22no—
9#65683—24no—
10#65683C418yescomplemented
11C5×#382C411yescharacteristic
12#65266C2212yes—
13#65225C411yescharacteristic
14D5×#95—22no—
15#64939—22no—
16#8030—51nomaximal, Sylow
17C22×C4×D5—22no—
18C22×C4×D5C2×C411yescharacteristic
19C22×C4×D5D412yes—
20C22×#170—24no—
21C2×C5×C4⋊C4C2×C412yes—
22C2×C42×C5C2×C411yescharacteristic
23C2×C4⋊Dic5C2×C412yes—
24C2×#683—22no—
25C2×C4×Dic5D412yes—
26C2×C4×Dic5C2311yescharacteristic
27D5×C4⋊C4—44no—
28C42×D5C2×C414yes—
29C42×D5D412yes—
30C42×D5Q812yes—
31#4003—28no—
32#4002—24no—
33#4002C2×C418yescomplemented
34C4⋊#170—28no—
35C5×#95—22no—
36#3963—22no—
37#3963—24no—
38C2×#432—52no—
39C2×#382—51no—
40#1295—54no—
41C23×D5C22⋊C411yescharacteristic
42C22×C4×C5—22no—
43C22×C4×C5C22⋊C412yes—
44C22×C4×C5C22×C411yescharacteristic
45C22×Dic5—22no—
46C22×Dic5C22⋊C411yescharacteristic
47C22×Dic5C2×D412yes—
48C2×C4×D5—22no—
49C2×C4×D5—22no—
50C2×C4×D5—44no—
51C2×C4×D5—48no—
52C2×C4×D5—44no—
53C2×C4×D5C4212yes—
54C2×C4×D5C22⋊C414yes—
55C2×C4×D5C4⋊C412yes—
56C2×C4×D5C4⋊C414yes—
57C2×#170—28no—
58C2×#170—48no—
59C5×C4⋊C4—42no—
60C42×C5C4212yes—
61C42×C5C4⋊C412yes—
62C4⋊Dic5—42no—
63#683—44no—
64C4×Dic5C22⋊C414yes—
65C4×Dic5C4⋊C414yes—
66C4×Dic5C22×C412yes—
67C4×Dic5C2×D411yescharacteristic
68C4×Dic5C2×Q811yescharacteristic
69C22×C4⋊C4—52no—
70C22×C42—51no—
71#432—58no—
72#432—104no—
73C2×C4⋊C8—102no—
74C2×C22⋊C8—102no—
75C2×#97—54no—
76#382—52no—
77#382—51no—
78#382—102no—
79#382AGL(1,𝔽5)11yescharacteristic
80C2×#95—102no—
81C23×C5C2×C22⋊C411yescharacteristic
82C22×D5—24no—
83C22×D5#9512yes—
84C22×D5#10012yes—
85C22×D5#10112yes—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—24no—
89C2×C4×C5—42no—
90C2×C4×C5—44no—
91C2×C4×C5#9514yes—
92C2×C4×C5C2×C4211yescharacteristic
93C2×C4×C5C2×C4⋊C411yescharacteristic
94C2×Dic5—21no—
95C2×Dic5—21no—
96C2×Dic5—24no—
97C2×Dic5—42no—
98C2×Dic5—44no—
99C2×Dic5#9512yes—
100C2×Dic5C2×C22⋊C412yes—
101C2×Dic5C2×C4⋊C412yes—
102C4×D5—24no—
103C4×D5—24no—
104C4×D5—44no—
105C4×D5—44no—
106C4×D5—88no—
107#170—48no—
108C23×C4—51no—
109C23×C4—52no—
110C23×C4—102no—
111C22×C8—104no—
112C2×C4⋊C4—52no—
113C2×C4⋊C4—102no—
114C2×C4⋊C4—204no—
115C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
116C2×C42—52no—
117C2×C42—51no—
118C2×C42—54no—
119C2×C42—52no—
120C2×C42—52no—
121C2×C42C2×AGL(1,𝔽5)11yescharacteristic
122C4⋊C8—108no—
123C22⋊C8—108no—
124#97—58no—
125#97—104no—
126#95—22no—
127#95—104no—
128#95—102no—
129C22×C5C2×#9511yescharacteristic
130C22×C5C2×#10011yescharacteristic
131C22×C5C2×#10111yescharacteristic
132C22×C5#42114yes—
133C2×D5—24no—
134C2×D5—24no—
135C2×D5—24no—
136C2×D5#34314yes—
137C4×C5—24no—
138C4×C5—21no—
139C4×C5—21no—
140C4×C5—82no—
141Dic5—22no—
142Dic5—22no—
143Dic5—22no—
144Dic5—82no—
145C24—51no—
146C22×C4—22no—
147C22×C4—52no—
148C22×C4—51no—
149C22×C4—52no—
150C22×C4—52no—
151C22×C4—54no—
152C22×C4—54no—
153C22×C4—102no—
154C22×C4—102no—
155C22×C4—102no—
156C22×C4—204no—
157C22×C4—204no—
158C22×C4—208no—
159C22×C4C22⋊AGL(1,𝔽5)12yes—
160C22×C4C22×AGL(1,𝔽5)11yescharacteristic
161C2×C8—108no—
162C2×C8—208no—
163C4⋊C4—42no—
164C4⋊C4—202no—
165C4⋊C4—204no—
166C42—52no—
167C42—51no—
168C42—51no—
169C42—54no—
170C42—54no—
171C42C4×AGL(1,𝔽5)12yes—
172C42C4⋊AGL(1,𝔽5)12yes—
173C2×C5#153312yes—
174C2×C5#153412yes—
175C2×C5#173312yes—
176C2×C5C2×#34311yescharacteristic
177D5—24no—
178C23—52no—
179C23—52no—
180C23—52no—
181C23—104no—
182C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
183C2×C4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—44no—
187C2×C4—42no—
188C2×C4—52no—
189C2×C4—52no—
190C2×C4—52no—
191C2×C4—104no—
192C2×C4—104no—
193C2×C4—104no—
194C2×C4—101no—
195C2×C4—101no—
196C2×C4—204no—
197C2×C4—204no—
198C2×C4—204no—
199C2×C4—202no—
200C2×C4—408no—
201C2×C4(C2×AGL(1,𝔽5))⋊C414yes—
202C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
203C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
204C8—208no—
205C5#803011yescharacteristic, complemented, Sylow
206C22—54no—
207C22—104no—
208C22—104no—
209C22—104no—
210C22C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
211C22D5⋊#10011yescharacteristic
212C22D5⋊#10111yescharacteristic
213C22#6579514yes—
214C4—21no—
215C4—21no—
216C4—24no—
217C4—82no—
218C4—102no—
219C4—102no—
220C4—102no—
221C4—402no—
222C2—104no—
223C2#1060433411yescharacteristic
224C2#1060437312yes—
225C2#1060454312yes—
226C2#1060457912yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#382C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#382AGL(1,𝔽5)
hypocenterC5#8030
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #10598722C2semidirect
10. #65683C4semidirect
33. #4002C2×C4semidirect
205. C5#8030semidirect

Maximal subgroups

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

subgroupindex
C2×#656832
D5×#3822
#105987222
#80305