Finite Group Databasebeta

← #12017597

Subgroups — #12017597

Order 1280.

540 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 111 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×#2486C211yesmaximal, characteristic
2C2×#64759C214yesmaximal
3C4×#3966C211yesmaximal, characteristic
4#10602410C211yesmaximal, characteristic
5C2×C5×#123C2212yes—
6C2×C4×C5×D4C2211yescharacteristic
7C22×C5×C4⋊C4C411yescharacteristic, complemented
8C5×#398—21no—
9C5×#397—21no—
10C5×#389—21no—
11C5×#381C412yescomplemented
12C5×#380—21no—
13C5×#380C411yescharacteristic, complemented
14C2×#3966C2212yes—
15C2×#3965C2212yes—
16C4×C22⋊Dic5—21no—
17#65213—21no—
18#64759—28no—
19#64750—21no—
20#64746—21no—
21#13220—51nomaximal, Sylow
22C22×C5×D4C2311yescharacteristic
23C23×C4×C5C2×C412yes—
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C5×#123—24no—
27C5×#123—24no—
28C4×C5×D4—41no—
29C4×C5×D4—41no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4—41no—
35C2×C5×C4⋊C4—41no—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C22⋊C4—22no—
38C2×C5×C22⋊C4C2×C412yes—
39C2×C5×C22⋊C4C2×C411yescharacteristic
40C2×C5×C22⋊C4D411yescharacteristic
41C2×C42×C5D411yescharacteristic
42C2×C22⋊Dic5—22no—
43C2×C4×Dic5—41no—
44C2×#681—22no—
45C5×#95—22no—
46C5×#95—21no—
47C5×#95—22no—
48#3966—22no—
49#3966D414yes—
50#3965—24no—
51#3963—41no—
52C4⋊#168—41no—
53C4⋊#168—41no—
54#2486D511yescharacteristic
55C2×#352—54no—
56#1800—51no—
57C4×#99—51no—
58C24×C5C22×C411yescharacteristic
59C24×C5C2×D411yescharacteristic
60C2×C5×D4—41no—
61C2×C5×D4—41no—
62C2×C5×D4C2×D412yes—
63C2×C5×D4#4112yes—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—24no—
71C22×C4×C5—42no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×Dic5—42no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—42no—
83C5×C4⋊C4—42no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4—42no—
88C5×C22⋊C4—24no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—41no—
91C5×C22⋊C4—44no—
92C42×C5—21no—
93C42×C5—21no—
94C22⋊Dic5—24no—
95C22⋊Dic5—42no—
96C4×Dic5—82no—
97#681—42no—
98#681—42no—
99C2×#168—42no—
100C2×#123C2×D512yes—
101C2×C4×D4C2×D511yescharacteristic
102C22×C4⋊C4Dic511yescharacteristic, complemented
103#423—101no—
104C2×#100—52no—
105C2×#99—52no—
106#398—21no—
107#397—21no—
108#389—21no—
109#381Dic512yescomplemented
110#380—21no—
111#380Dic511yescharacteristic, complemented
112C4×C22⋊C4—101no—
113#352—108no—
114#343—101no—
115#342—101no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5C2×C22⋊C411yescharacteristic
125C23×C5C4×D412yes—
126C23×C5#12112yes—
127C5×D4—42no—
128C5×D4—42no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—22no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—42no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×C4×C5—81no—
148C2×C4×C5—84no—
149C2×C4×C5#9911yescharacteristic
150C2×C4×C5#9911yescharacteristic
151C2×C4×C5#12411yescharacteristic
152C2×C4×C5#12711yescharacteristic
153C2×Dic5—44no—
154C2×Dic5—82no—
155C2×Dic5—82no—
156#168—82no—
157C22×D4C22×D511yescharacteristic
158C23×C4C2×Dic512yes—
159C23×C4C2×Dic511yescharacteristic
160C23×C4C22⋊D511yescharacteristic
161C2×M16—102no—
162#123—24no—
163#123—24no—
164C4×D4—41no—
165C4×D4—41no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4C22⋊D511yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—102no—
175C2×C22⋊C4C2×Dic512yes—
176C2×C22⋊C4C2×Dic511yescharacteristic
177C2×C22⋊C4C22⋊D511yescharacteristic
178C2×C42—201no—
179C2×C42C22⋊D511yescharacteristic
180C4⋊C8—201no—
181C4⋊C8—201no—
182#100—104no—
183#99—54no—
184#99—102no—
185#95—22no—
186#95—21no—
187#95—22no—
188#95—201no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5—22no—
192C22×C5—22no—
193C22×C5—42no—
194C22×C5—42no—
195C22×C5—42no—
196C22×C5—41no—
197C22×C5—41no—
198C22×C5—41no—
199C22×C5—41no—
200C22×C5—81no—
201C22×C5#39011yescharacteristic
202C22×C5C2×#9911yescharacteristic
203C22×C5#41011yescharacteristic
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5—82no—
211C4×C5—82no—
212C4×C5#35212yescomplemented
213Dic5—84no—
214C24C22×Dic511yescharacteristic
215C24C2×C22⋊D511yescharacteristic
216C2×D4—41no—
217C2×D4—41no—
218C2×D4D4×D512yes—
219C2×D4#71112yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—202no—
232C22×C4C22⋊Dic511yescharacteristic
233C22×C4C22⋊Dic511yescharacteristic
234C22×C4C22⋊Dic511yescharacteristic
235C22×C4C22⋊Dic511yescharacteristic
236C22×C4C2×C22⋊D511yescharacteristic
237M16—202no—
238M16—202no—
239C2×C8—202no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C22⋊C4—24no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—44no—
251C22⋊C4—104no—
252C22⋊C4—202no—
253C42—21no—
254C42—21no—
255C42—402no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5—42no—
259C2×C5—42no—
260C2×C5#196411yescharacteristic
261C2×C5C2×#35211yescharacteristic
262C2×C5#212311yescharacteristic
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23D4×Dic512yes—
272C23#408412yes—
273C23C2×C22⋊Dic511yescharacteristic
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—84no—
296C2×C4—204no—
297C2×C4—402no—
298C2×C4—402no—
299C2×C4#396611yescharacteristic
300C2×C4#396611yescharacteristic
301C2×C4#408211yescharacteristic
302C2×C4#408611yescharacteristic
303C8—402no—
304C5#1322011yescharacteristic, complemented, Sylow
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22C2×#396611yescharacteristic
318C22#6551011yescharacteristic
319C22#6552911yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—82no—
327C4—82no—
328C4—404no—
329C4#6475912yescomplemented
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2#1060247911yescharacteristic
335C2C2×#6475911yescharacteristic
336C2#1060266311yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC24×C5C22×C4
FrattiniC22×D4C22×D5
FittingC5×#2486C2
socleC22×C5C2×#99
prime radical, cosocleC22×C5×D4C23
hypercenter#2486D5
hypocenterC5#13220
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
7. C22×C5×C4⋊C4C4semidirect
11. C5×#381C4semidirect
13. C5×#380C4semidirect
102. C22×C4⋊C4Dic5semidirect
109. #381Dic5semidirect
111. #380Dic5semidirect
212. C4×C5#352semidirect
304. C5#13220semidirect
329. C4#64759semidirect

Maximal subgroups

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

subgroupindex
C5×#24862
C2×#647592
C4×#39662
#106024102
#132205