Finite Group Databasebeta

← #11997049

Subgroups — #11997049

Order 1280.

554 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 103 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×#2313C211yesmaximal, characteristic, complemented
2#10613911C211yesmaximal, characteristic
3#10602355C211yesmaximal, characteristic, complemented
4#10600324C212yesmaximal
5#10598119C212yesmaximal, complemented
6C22×C5×C4⋊C4C2211yescharacteristic
7C2×#4076C2211yescharacteristic
8C5×#387—24no—
9C5×#381C2212yes—
10C5×#380—21no—
11C4×C5×C22⋊C4—21no—
12#65502—21no—
13#65502—21no—
14C4×C22⋊Dic5C2211yescharacteristic
15#65496C2212yes—
16#65282—22no—
17#65277C412yescomplemented
18#65266C412yescomplemented
19#64750—22no—
20#64671—24no—
21#9465—51nomaximal, Sylow
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C22×C22⋊D5—21no—
26C22×D20C2×C411yescharacteristic
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4C2×C412yes—
31C2×C5×C4⋊C4D412yes—
32C2×C5×C22⋊C4—22no—
33C2×C42×C5—22no—
34C2×C22⋊Dic5—21no—
35#4076—22no—
36#4076—22no—
37C2×#685—21no—
38C2×#685—22no—
39C2×#685—22no—
40C2×C4⋊Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C412yes—
42C2×#681—22no—
43C5×#95—22no—
44C5×#95—22no—
45C5×#95—22no—
46C5×#95D414yes—
47#3963—22no—
48#3963—22no—
49#3963—21no—
50C22⋊#168—22no—
51C22⋊#168—22no—
52#2504—51no—
53#2313D511yescharacteristic, complemented
54#1821—51no—
55#1510—52no—
56#1284—52no—
57C24×C5C2×D411yescharacteristic
58C23×D5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—24no—
64C22×C4×C5—42no—
65C22×C4×C5—81no—
66C22×C4×C5—81no—
67C22×C4×C5C22⋊C412yes—
68C22×C4×C5C22⋊C412yes—
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D412yes—
72C22×C4×C5#4112yes—
73C2×C22⋊D5—44no—
74C2×C22⋊D5—41no—
75C2×C22⋊D5—41no—
76C22×Dic5—22no—
77C22×Dic5—21no—
78C2×D20—22no—
79C2×D20—42no—
80C5×C4⋊C4—24no—
81C5×C4⋊C4—24no—
82C5×C4⋊C4—82no—
83C5×C22⋊C4—44no—
84C42×C5—82no—
85C22⋊Dic5—42no—
86#685—42no—
87#685—82no—
88#685—82no—
89C4⋊Dic5—22no—
90C4×Dic5—42no—
91#681—44no—
92C2×#168—42no—
93C2×#121—51no—
94C22×C4⋊C4C2×D511yescharacteristic
95#407—52no—
96#397—102no—
97#390—52no—
98#387—24no—
99#386—101no—
100#386—101no—
101#382—52no—
102#381C2×D512yes—
103#380—21no—
104C4×C22⋊C4—21no—
105C4×C22⋊C4—51no—
106#343—102no—
107#327—104no—
108C23×C5—22no—
109C23×C5—22no—
110C23×C5—41no—
111C23×C5C2×C22⋊C411yescharacteristic
112C23×C5#12011yescharacteristic
113C23×C5#12311yescharacteristic
114C22×D5—42no—
115C22×D5—42no—
116C22×D5—41no—
117C22×D5—42no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—22no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—44no—
129C2×C4×C5—44no—
130C2×C4×C5—44no—
131C2×C4×C5—81no—
132C2×C4×C5—81no—
133C2×C4×C5C4×D412yes—
134C2×C4×C5#12112yes—
135C22⋊D5—82no—
136C22⋊D5—82no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—41no—
141C2×Dic5—42no—
142D20—82no—
143#168—82no—
144C22×D4—51no—
145C22×D4—101no—
146C23×C4C22⋊D511yescharacteristic
147C23×C4C22⋊D511yescharacteristic
148C23×C4C22×D511yescharacteristic
149C2×M16—102no—
150#121—102no—
151#121—102no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—51no—
156C2×C4⋊C4C4×D512yes—
157C2×C4⋊C4D2012yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—101no—
160C2×C22⋊C4—101no—
161C2×C22⋊C4—102no—
162C2×C22⋊C4—102no—
163C2×C42—22no—
164C2×C42—52no—
165C22⋊C8—102no—
166C22⋊C8—102no—
167#95—22no—
168#95—22no—
169#95—22no—
170#95—102no—
171#95—102no—
172#95—101no—
173#95C22⋊D514yes—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—21no—
181C22×C5—44no—
182C22×C5#38611yescharacteristic
183C22×C5#41012yes—
184C22×C5#45412yes—
185C2×D5—84no—
186C2×D5—81no—
187C2×D5—81no—
188C2×D5—81no—
189C4×C5—22no—
190C4×C5—22no—
191C4×C5—42no—
192C4×C5—42no—
193C4×C5—84no—
194Dic5—82no—
195Dic5—81no—
196C24—101no—
197C24C2×C22⋊D511yescharacteristic
198C2×D4—102no—
199C2×D4—202no—
200C2×D4—204no—
201C2×D4—201no—
202C2×D4—201no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—24no—
208C22×C4—42no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4—101no—
212C22×C4—102no—
213C22×C4#68512yes—
214C22×C4#68512yes—
215C22×C4C2×C4×D511yescharacteristic
216C22×C4C2×D2011yescharacteristic
217C22×C4#70912yes—
218C22×C4C2×C22⋊D512yes—
219M16—204no—
220C2×C8—202no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—82no—
224C4⋊C4—102no—
225C22⋊C4—44no—
226C22⋊C4—202no—
227C22⋊C4—202no—
228C22⋊C4—402no—
229C22⋊C4—402no—
230C42—82no—
231C42—202no—
232C2×C5—22no—
233C2×C5—22no—
234C2×C5—41no—
235C2×C5#188811yescharacteristic
236C2×C5#189911yescharacteristic
237C2×C5#191111yescharacteristic
238D5—161no—
239C23—22no—
240C23—22no—
241C23—41no—
242C23—202no—
243C23—202no—
244C23—202no—
245C23—201no—
246C23C2×#68511yescharacteristic
247C23#407511yescharacteristic
248C23#409911yescharacteristic
249D4—402no—
250D4—402no—
251D4—402no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—202no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4—201no—
272C2×C4C4×C22⋊D512yes—
273C2×C4#407612yes—
274C8—402no—
275C5#946511yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—404no—
285C22—401no—
286C22—401no—
287C22—401no—
288C22#6529512yes—
289C22#6550211yescharacteristic
290C22#6553412yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—84no—
296C4—402no—
297C4—401no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—801no—
302C2#1060238811yescharacteristic
303C2#1060244511yescharacteristic
304C2#1060245411yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2313C2
socleC22×C5#386
prime radicalC2×#4076C22
cosocleC23×C4×C5C23
hypercenter#2313D5
hypocenterC5#9465
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
1. C5×#2313C2semidirect
3. #10602355C2semidirect
5. #10598119C2semidirect
17. #65277C4semidirect
18. #65266C4semidirect
53. #2313D5semidirect
275. C5#9465semidirect

Maximal subgroups

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

subgroupindex
C5×#23132
#106139112
#106023552
#106003242
#105981192
#94655