Finite Group Databasebeta

← #11997264

Subgroups — #11997264

Order 1280.

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

normal subgroups only

This group has 542 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×#2975C211yesmaximal, characteristic
2#10614104C211yesmaximal, characteristic
3#10602395C211yesmaximal, characteristic
4#10600766C212yesmaximal, complemented
5#10598175C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4081C412yes—
8C22×C4⋊Dic5C2211yescharacteristic
9C5×#436—24no—
10C5×#431—21no—
11C5×#407—21no—
12C5×#407C2212yes—
13#65501—21no—
14#65501C2211yescharacteristic
15#65496C2212yes—
16#65272—21no—
17#65242—21no—
18#65232C412yes—
19#65217—21no—
20#64774—24no—
21#64748—21no—
22#64745—21no—
23#9508—51nomaximal, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C23×Dic5C2×C412yes—
28C2×C5×M16—22no—
29C2×C5×M16D414yes—
30C4×C5×D4—22no—
31C4×C5×D4—22no—
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4C2×C411yescharacteristic
34C2×C5×C22⋊C4D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C22⋊Dic5—22no—
37C2×C22⋊Dic5C2×C412yes—
38#4081—44no—
39C2×C4⋊Dic5—22no—
40C2×C4⋊Dic5—21no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5—21no—
43C2×C4⋊Dic5—22no—
44C2×#683—22no—
45C2×#681—22no—
46C5×C4⋊C8—22no—
47C5×C22⋊C8—22no—
48C5×C22⋊C8—22no—
49C5×C22⋊C8—22no—
50C4×C5×C8—22no—
51#3963—22no—
52#3963—22no—
53#3963—21no—
54C22⋊#168—22no—
55C22⋊#168—22no—
56#2975D511yescharacteristic
57#2486—51no—
58#1821—52no—
59#1465—51no—
60#1305—52no—
61C24×C5C22⋊C411yescharacteristic
62C24×C5C22×C411yescharacteristic
63C2×C5×D4—22no—
64C2×C5×D4—22no—
65C2×C5×D4—41no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D412yes—
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5#4112yes—
77C22×Dic5—22no—
78C22×Dic5—22no—
79C22×Dic5—24no—
80C22×Dic5—42no—
81C22×Dic5—42no—
82C5×M16—44no—
83C5×M16—82no—
84C2×C5×C8—24no—
85C5×C4⋊C4—22no—
86C5×C22⋊C4—22no—
87C5×C22⋊C4—22no—
88C42×C5—21no—
89C42×C5—21no—
90C22⋊Dic5—44no—
91C22⋊Dic5—42no—
92C4⋊Dic5—42no—
93C4⋊Dic5—41no—
94C4⋊Dic5—42no—
95C4⋊Dic5—41no—
96#683—44no—
97#681—44no—
98C2×#168—42no—
99C2×#123—52no—
100C2×C4×D4C2×D511yescharacteristic
101C22×C4⋊C4—51no—
102#436—24no—
103#431—21no—
104#407—21no—
105#407—52no—
106#407C2×D512yes—
107#398—101no—
108#397—101no—
109#389—101no—
110#381—52no—
111#380—51no—
112#380—101no—
113#343—104no—
114#324—101no—
115#323—101no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5—41no—
125C23×C5C2×C22⋊C411yescharacteristic
126C23×C5C4×D412yes—
127C5×D4—44no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—24no—
131C2×C4×C5—22no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—41no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—81no—
140C2×C4×C5#10012yes—
141C2×C4×C5#12011yescharacteristic
142C2×C4×C5#12112yes—
143C2×C4×C5#12311yescharacteristic
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5—42no—
150C2×Dic5—84no—
151C5×C8—44no—
152#168—82no—
153C22×D4C4×D511yescharacteristic
154C23×C4—52no—
155C23×C4C22⋊D511yescharacteristic
156C23×C4C22×D511yescharacteristic
157C2×M16—22no—
158C2×M16—102no—
159C2×M16C22⋊D514yes—
160#123—204no—
161C4×D4—22no—
162C4×D4—22no—
163C2×C4⋊C4—102no—
164C2×C4⋊C4—101no—
165C2×C4⋊C4—102no—
166C2×C4⋊C4—102no—
167C2×C4⋊C4—101no—
168C2×C4⋊C4—101no—
169C2×C4⋊C4D2011yescharacteristic
170C2×C22⋊C4—52no—
171C2×C22⋊C4—102no—
172C2×C22⋊C4C4×D511yescharacteristic
173C2×C22⋊C4D2011yescharacteristic
174C2×C42C22⋊D511yescharacteristic
175C4⋊C8—22no—
176C22⋊C8—22no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—102no—
180C22⋊C8—102no—
181C4×C8—22no—
182#95—102no—
183#95—102no—
184#95—101no—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—22no—
190C22×C5—42no—
191C22×C5—42no—
192C22×C5—42no—
193C22×C5—41no—
194C22×C5—41no—
195C22×C5—41no—
196C22×C5—81no—
197C22×C5#38611yescharacteristic
198C22×C5C2×#10011yescharacteristic
199C22×C5#41311yescharacteristic
200C4×C5—22no—
201C4×C5—21no—
202C4×C5—22no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5#45812yes—
206Dic5—82no—
207Dic5—82no—
208C24#68511yescharacteristic
209C24C2×C4×D511yescharacteristic
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—102no—
218C22×C4—102no—
219C22×C4—104no—
220C22×C4—202no—
221C22×C4—202no—
222C22×C4#68511yescharacteristic
223C22×C4#68511yescharacteristic
224C22×C4#68511yescharacteristic
225C22×C4C2×D2011yescharacteristic
226C22×C4#70912yes—
227C22×C4C2×C22⋊D511yescharacteristic
228C22×C4C2×C22⋊D512yes—
229M16—44no—
230M16—82no—
231M16—204no—
232C2×C8—24no—
233C2×C8—202no—
234C4⋊C4—22no—
235C4⋊C4—202no—
236C4⋊C4—201no—
237C4⋊C4—204no—
238C4⋊C4—201no—
239C4⋊C4—202no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—204no—
243C22⋊C4—202no—
244C42—21no—
245C42—21no—
246C2×C5—21no—
247C2×C5—21no—
248C2×C5—42no—
249C2×C5—81no—
250C2×C5#189011yescharacteristic
251C2×C5#190011yescharacteristic
252C2×C5#191511yescharacteristic
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23C2×#68511yescharacteristic
263C23C4×C22⋊D512yes—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—202no—
278C2×C4—202no—
279C2×C4—202no—
280C2×C4—202no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—404no—
284C2×C4#395512yes—
285C2×C4#407511yescharacteristic
286C2×C4#407612yes—
287C2×C4#409911yescharacteristic
288C8—44no—
289C8—402no—
290C5#950811yescharacteristic, complemented, Sylow
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#395511yescharacteristic
304C22#6542111yescharacteristic
305C22#6550211yescharacteristic
306C4—22no—
307C4—22no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—402no—
312C4—402no—
313C4#6553212yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—81no—
318C2#1060244811yescharacteristic
319C2#1060279511yescharacteristic
320C2#1060282411yescharacteristic
subgroupG/H
centerC22#65502
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2975C2
socleC22×C5#386
prime radicalC22×C5×D4C2×C4
cosocleC23×C4×C5C23
hypercenter#2975D5
hypocenterC5#9508
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
4. #10600766C2semidirect
5. #10598175C2semidirect
290. C5#9508semidirect

Maximal subgroups

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

subgroupindex
C5×#29752
#106141042
#106023952
#106007662
#105981752
#95085