Finite Group Databasebeta

← #11997014

Subgroups — #11997014

Order 1280.

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

normal subgroups only

This group has 536 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, complemented
2#10614207C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic, complemented
4#10601611C212yesmaximal
5#10598241C212yesmaximal, complemented
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4093C412yes—
8C2×#4020C2211yescharacteristic
9C5×#446—24no—
10C5×#432—21no—
11C5×#432C2212yes—
12C5×#431—21no—
13#65280—21no—
14#65280—21no—
15#65277C412yes—
16#65228—21no—
17#65228—21no—
18C4×C4⋊Dic5C2211yescharacteristic
19#65215C2212yes—
20#64748—21no—
21#64748—21no—
22#64705—24no—
23#9458—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×D20—21no—
26C22×D20—21no—
27C22×D20C2×C412yes—
28C4×C5×Q8—22no—
29C4×C5×Q8—22no—
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C42×C5D411yescharacteristic
35C2×C42×C5C2311yescharacteristic
36#4093—44no—
37C2×#685—22no—
38C2×#685—22no—
39C2×#685—22no—
40C2×#685—22no—
41C2×C4⋊Dic5—21no—
42C2×C4×Dic5C2×C412yes—
43#4020—22no—
44#4020—22no—
45C5×C4⋊C8—22no—
46C5×C4⋊C8—22no—
47C5×C4⋊C8D414yes—
48C5×C22⋊C8—22no—
49C5×#97—22no—
50C5×#97—22no—
51C4×C5×C8—22no—
52#3963—21no—
53C22⋊#168—22no—
54C4⋊#168—22no—
55#3935—22no—
56#2983D511yescharacteristic, complemented
57#2548—51no—
58#1555—52no—
59#1467—51no—
60#1285—52no—
61C23×D5—22no—
62C2×C5×Q8—22no—
63C2×C5×Q8—22no—
64C2×C5×Q8—41no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×Dic5—22no—
73C2×D20—24no—
74C2×D20—42no—
75C2×D20—42no—
76C2×D20—42no—
77C2×D20—42no—
78C2×D20—41no—
79C2×D20—42no—
80C2×D20—41no—
81C2×D20—82no—
82C2×C5×C8—24no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C42×C5—21no—
87C42×C5—21no—
88C42×C5—21no—
89C42×C5—21no—
90C42×C5C2×D412yes—
91C42×C5#4112yes—
92#685—44no—
93#685—44no—
94#685—82no—
95#685—82no—
96C4⋊Dic5—42no—
97C4×Dic5—42no—
98C2×#168—42no—
99C2×#127—51no—
100C2×#124—52no—
101C2×C4×Q8C2×D511yescharacteristic
102#446—24no—
103#432—21no—
104#432—52no—
105#432C2×D512yes—
106#431—21no—
107#394—101no—
108#394—101no—
109#390—52no—
110#390—101no—
111#390—101no—
112C4×C4⋊C4—51no—
113#331—104no—
114#324—101no—
115#324—101no—
116C23×C5C2×C22⋊C411yescharacteristic
117C22×D5—42no—
118C22×D5—42no—
119C22×D5—42no—
120C22×D5—42no—
121C22×D5—42no—
122C22×D5—42no—
123C22×D5—42no—
124C5×Q8—44no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—22no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5#10012yes—
139C2×C4×C5C4×D412yes—
140C2×C4×C5#12011yescharacteristic
141C2×C4×C5#12112yes—
142C2×C4×C5#12311yescharacteristic
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146D20—84no—
147D20—82no—
148D20—84no—
149D20—82no—
150C5×C8—44no—
151#168—82no—
152C22×Q8C4×D511yescharacteristic
153C22×D4—52no—
154C22×D4—101no—
155C22×D4—101no—
156#127—102no—
157#127—102no—
158#124—204no—
159C4×Q8—22no—
160C4×Q8—22no—
161C2×C4⋊C4—101no—
162C2×C4⋊C4C4×D511yescharacteristic
163C2×C4⋊C4D2011yescharacteristic
164C2×C4⋊C4D2011yescharacteristic
165C2×C22⋊C4—102no—
166C2×C22⋊C4—102no—
167C2×C22⋊C4—102no—
168C2×C22⋊C4—102no—
169C2×C42—52no—
170C2×C42C22⋊D511yescharacteristic
171C2×C42C22⋊D511yescharacteristic
172C2×C42C22×D511yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—102no—
176C4⋊C8C22⋊D514yes—
177C22⋊C8—22no—
178C22⋊C8—102no—
179#97—22no—
180#97—22no—
181#97—102no—
182C4×C8—22no—
183#95—101no—
184C22×C5—21no—
185C22×C5—21no—
186C22×C5#38611yescharacteristic
187C22×C5C2×#10011yescharacteristic
188C22×C5#41311yescharacteristic
189C2×D5—82no—
190C2×D5—82no—
191C2×D5—82no—
192C2×D5—82no—
193C2×D5—82no—
194C2×D5—82no—
195C2×D5—82no—
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—22no—
199C4×C5—22no—
200C4×C5—41no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C5#45412yes—
204Dic5—82no—
205C24—102no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—41no—
209C2×D4—104no—
210C2×D4—202no—
211C2×D4—202no—
212C2×D4—202no—
213C2×D4—202no—
214C2×D4—201no—
215C2×D4—201no—
216C2×D4—202no—
217C2×D4—402no—
218C22×C4—102no—
219C22×C4#68511yescharacteristic
220C22×C4#68511yescharacteristic
221C22×C4#68511yescharacteristic
222C22×C4#68511yescharacteristic
223C22×C4C2×C4×D511yescharacteristic
224C22×C4C2×D2011yescharacteristic
225C22×C4C2×C22⋊D511yescharacteristic
226C2×C8—24no—
227C2×C8—202no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—202no—
232C22⋊C4—204no—
233C22⋊C4—204no—
234C22⋊C4—402no—
235C22⋊C4—402no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—202no—
241C42#70912yes—
242C42C2×C22⋊D512yes—
243C2×C5—21no—
244C2×C5—21no—
245C2×C5#188811yescharacteristic
246C2×C5#190011yescharacteristic
247C2×C5#191011yescharacteristic
248D5—162no—
249C23—202no—
250C23—202no—
251C23—202no—
252C23—202no—
253C23—202no—
254C23—202no—
255C23—202no—
256C23C2×#68511yescharacteristic
257Q8—44no—
258D4—404no—
259D4—402no—
260D4—404no—
261D4—402no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—202no—
276C2×C4—202no—
277C2×C4—202no—
278C2×C4#395512yes—
279C2×C4C4×C22⋊D512yes—
280C2×C4#407511yescharacteristic
281C2×C4#407612yes—
282C2×C4#409911yescharacteristic
283C8—44no—
284C8—402no—
285C5#945811yescharacteristic, complemented, Sylow
286C22—21no—
287C22—21no—
288C22—402no—
289C22—402no—
290C22—402no—
291C22—402no—
292C22—402no—
293C22—402no—
294C22—402no—
295C22C2×#395511yescharacteristic
296C22#6542111yescharacteristic
297C22#6550211yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—402no—
306C4#6553412yes—
307C2—21no—
308C2—21no—
309C2—802no—
310C2#1060245411yescharacteristic
311C2#1060279511yescharacteristic
312C2#1060281811yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2983C2
socleC22×C5#386
prime radicalC2×#4020C22
cosocleC2×C42×C5C23
hypercenter#2983D5
hypocenterC5#9458
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
1. C5×#2983C2semidirect
3. #10602418C2semidirect
5. #10598241C2semidirect
56. #2983D5semidirect
285. C5#9458semidirect

Maximal subgroups

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

subgroupindex
C5×#29832
#106142072
#106024182
#106016112
#105982412
#94585