Finite Group Databasebeta

← #12008909

Subgroups — #12008909

Order 1280.

534 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2534C211yesmaximal, characteristic
2#10602396C211yesmaximal, characteristic, complemented
3#10602393C211yesmaximal, characteristic, complemented
4#10598118C212yesmaximal, complemented
5#10598113C212yesmaximal, complemented
6C2×C5×#123C411yescharacteristic
7C2×C5×#120C411yescharacteristic
8C2×C4×C5×D4C2211yescharacteristic
9C22×C5×C22⋊C4C411yescharacteristic
10C5×#396—21no—
11C5×#394—21no—
12C5×#388—21no—
13C5×#386—21no—
14C5×#381C2211yescharacteristic
15C5×#380C411yescharacteristic
16C5×#379C2211yescharacteristic
17C2×C22⋊#168—21no—
18#65215—21no—
19#64748—21no—
20#64745—21no—
21#64745C2212yes—
22#64745C2212yes—
23#11560—51nomaximal, Sylow
24C25×C5C2×C411yescharacteristic
25C22×C5×D4—21no—
26C22×C5×D4C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C5×#123—42no—
31C5×#120—42no—
32C4×C5×D4—41no—
33C4×C5×D4—41no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—41no—
44C2×C5×C22⋊C4—41no—
45C2×C5×C22⋊C4C2×C411yescharacteristic
46C2×C5×C22⋊C4C2×C411yescharacteristic
47C2×C5×C22⋊C4D411yescharacteristic
48C2×C5×C22⋊C4C2311yescharacteristic
49C2×C42×C5D411yescharacteristic
50C22×#168—41no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C22⋊#168—22no—
55C22⋊#168—22no—
56C22⋊#168—41no—
57C4⋊#168—41no—
58#3935—41no—
59#2534D511yescharacteristic
60#1466—51no—
61#1459—51no—
62#1317—52no—
63#1316—52no—
64C24×C5—21no—
65C24×C5—22no—
66C24×C5—41no—
67C24×C5—42no—
68C24×C5—41no—
69C24×C5—81no—
70C24×C5C22⋊C411yescharacteristic
71C24×C5C22×C411yescharacteristic
72C2×C5×D4—22no—
73C2×C5×D4—22no—
74C2×C5×D4—41no—
75C2×C5×D4—42no—
76C2×C5×D4—42no—
77C2×C5×D4—81no—
78C22×C4×C5—21no—
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—22no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—81no—
89C22×C4×C5—81no—
90C22×C4×C5C22⋊C411yescharacteristic
91C22×C4×C5C22⋊C411yescharacteristic
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5C2×D411yescharacteristic
95C5×C4⋊C4—41no—
96C5×C4⋊C4—42no—
97C5×C4⋊C4—81no—
98C5×C22⋊C4—41no—
99C5×C22⋊C4—41no—
100C5×C22⋊C4—42no—
101C5×C22⋊C4—42no—
102C5×C22⋊C4—42no—
103C5×C22⋊C4—42no—
104C5×C22⋊C4—41no—
105C5×C22⋊C4—41no—
106C5×C22⋊C4—41no—
107C5×C22⋊C4—41no—
108C5×C22⋊C4—81no—
109C42×C5—21no—
110C42×C5—21no—
111C2×#168—42no—
112C2×#168—42no—
113C2×#168—82no—
114C2×#123Dic511yescharacteristic
115C2×#120Dic511yescharacteristic
116C2×C4×D4C2×D511yescharacteristic
117C22×C22⋊C4Dic511yescharacteristic
118#432—101no—
119C2×C22⋊C8—101no—
120#396—21no—
121#394—21no—
122#388—21no—
123#386—21no—
124#381C2×D511yescharacteristic
125#380Dic511yescharacteristic
126#379C2×D511yescharacteristic
127#324—101no—
128#323—52no—
129#323—52no—
130#323—101no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—22no—
136C23×C5—41no—
137C23×C5—41no—
138C23×C5—41no—
139C23×C5—41no—
140C23×C5—41no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—42no—
144C23×C5—42no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5—82no—
149C23×C5—84no—
150C23×C5—84no—
151C23×C5—82no—
152C23×C5#10012yes—
153C23×C5C2×C22⋊C411yescharacteristic
154C23×C5#13112yes—
155C5×D4—44no—
156C5×D4—84no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—41no—
164C2×C4×C5—42no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—81no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5—82no—
181C2×C4×C5#9911yescharacteristic
182C2×C4×C5#9911yescharacteristic
183#168—82no—
184#168—82no—
185C25C2×Dic511yescharacteristic
186C22×D4—21no—
187C22×D4C2×Dic511yescharacteristic
188C23×C4C2×Dic511yescharacteristic
189C23×C4C2×Dic511yescharacteristic
190C23×C4C22⋊D511yescharacteristic
191C22×C8—201no—
192#123—42no—
193#120—42no—
194C4×D4—41no—
195C4×D4—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C22⋊D511yescharacteristic
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4C2×Dic511yescharacteristic
208C2×C22⋊C4C2×Dic511yescharacteristic
209C2×C22⋊C4C22⋊D511yescharacteristic
210C2×C22⋊C4C22×D511yescharacteristic
211C2×C42C22⋊D511yescharacteristic
212C4⋊C8—201no—
213C22⋊C8—102no—
214C22⋊C8—102no—
215C22⋊C8—201no—
216#97—201no—
217#95—21no—
218#95—21no—
219#95—21no—
220C22×C5—21no—
221C22×C5—21no—
222C22×C5—22no—
223C22×C5—22no—
224C22×C5—42no—
225C22×C5—42no—
226C22×C5—42no—
227C22×C5—42no—
228C22×C5—42no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—42no—
234C22×C5—81no—
235C22×C5—81no—
236C22×C5—81no—
237C22×C5—84no—
238C22×C5—84no—
239C22×C5—81no—
240C22×C5—81no—
241C22×C5#40811yescharacteristic
242C22×C5C2×#9911yescharacteristic
243C22×C5C2×#10011yescharacteristic
244C4×C5—21no—
245C4×C5—21no—
246C4×C5—41no—
247C4×C5—41no—
248C4×C5—41no—
249C4×C5—41no—
250C4×C5—81no—
251C4×C5—81no—
252C4×C5—81no—
253C24—21no—
254C24—22no—
255C24—41no—
256C24—42no—
257C24—41no—
258C24—81no—
259C24C22⋊Dic511yescharacteristic
260C24C22×Dic511yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—81no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—81no—
278C22×C4—81no—
279C22×C4C22⋊Dic511yescharacteristic
280C22×C4C22⋊Dic511yescharacteristic
281C22×C4C22⋊Dic511yescharacteristic
282C22×C4C2×C22⋊D511yescharacteristic
283C22×C4C2×C22⋊D511yescharacteristic
284C2×C8—202no—
285C2×C8—202no—
286C2×C8—402no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—81no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—81no—
301C42—21no—
302C42—21no—
303C2×C5—21no—
304C2×C5—21no—
305C2×C5—42no—
306C2×C5—42no—
307C2×C5—82no—
308C2×C5#147111yescharacteristic
309C2×C5#212011yescharacteristic
310C2×C5#212111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—42no—
324C23—42no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—82no—
329C23—84no—
330C23—84no—
331C23—82no—
332C23#396512yes—
333C23#409412yes—
334C23C2×C22⋊Dic511yescharacteristic
335D4—44no—
336D4—84no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4#396611yescharacteristic
362C2×C4#396611yescharacteristic
363C8—402no—
364C8—402no—
365C5#1156011yescharacteristic, complemented, Sylow
366C22—21no—
367C22—21no—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—84no—
384C22—84no—
385C22—81no—
386C22—81no—
387C22C2×#396511yescharacteristic
388C22C2×#396611yescharacteristic
389C22#6552311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—81no—
398C4—81no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—82no—
404C2#1060246911yescharacteristic
405C2#1060250911yescharacteristic
406C2#1060264011yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC24×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#2534C2
socleC22×C5C2×#99
prime radicalC2×C5×#120C4
cosocleC2×C5×C22⋊C4C23
hypercenter#2534D5
hypocenterC5#11560
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2534

Complements

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

NH ≅ G/Ntype
2. #10602396C2semidirect
3. #10602393C2semidirect
4. #10598118C2semidirect
5. #10598113C2semidirect
365. C5#11560semidirect

Maximal subgroups

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

subgroupindex
C5×#25342
#106023962
#106023932
#105981182
#105981132
#115605