Finite Group Databasebeta

← #11996994

Subgroups — #11996994

Order 1280.

448 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C5×#2983C211yesmaximal, characteristic
2#10614209C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10601615C212yesmaximal
5#10598241C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4015C2211yescharacteristic
8C5×#446—24no—
9C5×#432—21no—
10C5×#432C2212yes—
11C5×#431—21no—
12#65519C412yes—
13#65268—21no—
14#65268—21no—
15#65265C412yes—
16C4×C4⋊Dic5C2211yescharacteristic
17#65217—21no—
18#65217—21no—
19#65215C2212yes—
20#64748—21no—
21#64748—21no—
22#64706—24no—
23#9454—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×Dic10—21no—
26C4×C5×Q8—22no—
27C4×C5×Q8—22no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5C2×C412yes—
37C2×#683—22no—
38C2×#683—22no—
39C2×C4×Dic5C2×C412yes—
40#4015—22no—
41#4015—22no—
42C5×C4⋊C8—22no—
43C5×C4⋊C8—22no—
44C5×C4⋊C8D414yes—
45C5×C22⋊C8—22no—
46C5×#97—22no—
47C5×#97—22no—
48C4×C5×C8—22no—
49#3963—22no—
50#3963—22no—
51#3963—21no—
52C22⋊#168—22no—
53C4⋊#168—22no—
54#3935—22no—
55#2983D511yescharacteristic
56#2567—51no—
57#1556—52no—
58#1467—51no—
59#1285—52no—
60C2×C5×Q8—22no—
61C2×C5×Q8—22no—
62C2×C5×Q8—41no—
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—22no—
71C22×Dic5—22no—
72C2×Dic10—42no—
73C2×Dic10—82no—
74C2×C5×C8—24no—
75C5×C4⋊C4—22no—
76C5×C4⋊C4—22no—
77C5×C4⋊C4—22no—
78C42×C5—21no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5C2×D412yes—
83C42×C5#4112yes—
84C4⋊Dic5—24no—
85C4⋊Dic5—24no—
86C4⋊Dic5—41no—
87C4⋊Dic5—41no—
88#683—82no—
89#683—82no—
90C4×Dic5—42no—
91C2×#168—42no—
92C2×C4⋊Q8—51no—
93C2×C4×Q8C2×D511yescharacteristic
94#446—24no—
95#432—21no—
96#432—52no—
97#432C2×D512yes—
98#431—21no—
99#395—101no—
100#395—101no—
101#391—52no—
102#389—101no—
103#389—101no—
104#384—52no—
105C4×C4⋊C4—51no—
106#332—104no—
107#324—101no—
108#324—101no—
109C23×C5C2×C22⋊C411yescharacteristic
110C5×Q8—44no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—22no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5#10112yes—
125C2×C4×C5C4×D412yes—
126C2×C4×C5#12011yescharacteristic
127C2×C4×C5#12112yes—
128C2×C4×C5#12311yescharacteristic
129C2×Dic5—24no—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135Dic10—84no—
136C5×C8—44no—
137#168—82no—
138C22×Q8—101no—
139C22×Q8C4×D511yescharacteristic
140C4⋊Q8—102no—
141C4⋊Q8—102no—
142C4×Q8—22no—
143C4×Q8—22no—
144C2×C4⋊C4—52no—
145C2×C4⋊C4—101no—
146C2×C4⋊C4—101no—
147C2×C4⋊C4—102no—
148C2×C4⋊C4—102no—
149C2×C4⋊C4C4×D511yescharacteristic
150C2×C4⋊C4D2011yescharacteristic
151C2×C4⋊C4D2011yescharacteristic
152C2×C42—52no—
153C2×C42C22⋊D511yescharacteristic
154C2×C42C22⋊D511yescharacteristic
155C2×C42C22×D511yescharacteristic
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—102no—
159C4⋊C8C22⋊D514yes—
160C22⋊C8—22no—
161C22⋊C8—102no—
162#97—22no—
163#97—22no—
164#97—102no—
165C4×C8—22no—
166#95—102no—
167#95—102no—
168#95—101no—
169C22×C5—21no—
170C22×C5—21no—
171C22×C5#38611yescharacteristic
172C22×C5C2×#10111yescharacteristic
173C22×C5#41311yescharacteristic
174C4×C5—21no—
175C4×C5—22no—
176C4×C5—22no—
177C4×C5—22no—
178C4×C5—41no—
179C4×C5—41no—
180C4×C5—41no—
181C4×C5#45612yes—
182Dic5—44no—
183Dic5—82no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8—202no—
188C2×Q8—402no—
189C22×C4—102no—
190C22×C4—102no—
191C22×C4#68511yescharacteristic
192C22×C4#68511yescharacteristic
193C22×C4#68511yescharacteristic
194C22×C4#68511yescharacteristic
195C22×C4C2×C4×D511yescharacteristic
196C22×C4C2×D2011yescharacteristic
197C22×C4C2×C22⋊D511yescharacteristic
198C2×C8—24no—
199C2×C8—202no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—104no—
204C4⋊C4—104no—
205C4⋊C4—201no—
206C4⋊C4—201no—
207C4⋊C4—402no—
208C4⋊C4—402no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—202no—
214C42#70912yes—
215C42C2×C22⋊D512yes—
216C2×C5—21no—
217C2×C5—21no—
218C2×C5#188611yescharacteristic
219C2×C5#190111yescharacteristic
220C2×C5#191011yescharacteristic
221C23C2×#68511yescharacteristic
222Q8—44no—
223Q8—404no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—104no—
238C2×C4—202no—
239C2×C4—202no—
240C2×C4—202no—
241C2×C4—202no—
242C2×C4—202no—
243C2×C4#395612yes—
244C2×C4C4×C22⋊D512yes—
245C2×C4#407511yescharacteristic
246C2×C4#407612yes—
247C2×C4#409911yescharacteristic
248C8—44no—
249C8—402no—
250C5#945411yescharacteristic, complemented, Sylow
251C22—21no—
252C22—21no—
253C22#6542111yescharacteristic
254C22C2×#395611yescharacteristic
255C22#6550211yescharacteristic
256C4—22no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—204no—
264C4—402no—
265C4#6553512yes—
266C2—21no—
267C2—21no—
268C2#1060245311yescharacteristic
269C2#1060279611yescharacteristic
270C2#1060281811yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2983C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2983D5
hypocenterC5#9454
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
250. C5#9454semidirect

Maximal subgroups

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

subgroupindex
C5×#29832
#106142092
#106024182
#106016152
#105982412
#94545