Finite Group Databasebeta

← #11995368

Subgroups — #11995368

Order 1280.

622 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 131 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×#2316C211yesmaximal, characteristic, complemented
2#10613930C211yesmaximal, characteristic
3C2×#64748C211yesmaximal, characteristic, complemented
4#10600302C212yesmaximal
5#10598116C212yesmaximal, complemented
6C2×C5×#117—21no—
7C22×C5×C4⋊C4C2211yescharacteristic
8C2×#4076C2211yescharacteristic
9C2×#4075—21no—
10C5×#389—24no—
11C5×#380—21no—
12C5×#380C2212yes—
13#65502—21no—
14#65501C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65283—22no—
17#65280C412yescomplemented
18#65272C412yescomplemented
19#64748—22no—
20#64671—24no—
21#9204—51nomaximal, Sylow
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C22×C22⋊D5—21no—
26C22×D20C2×C411yescharacteristic
27C5×#117—42no—
28C5×#117—42no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4—22no—
34C2×C5×C4⋊C4C2×C412yes—
35C2×C5×C4⋊C4D412yes—
36C2×C5×C22⋊C4—22no—
37C2×C42×C5—22no—
38C2×C22⋊Dic5—21no—
39#4076—22no—
40#4076—22no—
41#4075—42no—
42#4075—42no—
43C2×#685—22no—
44C2×#685—21no—
45C2×#685—22no—
46C2×C4⋊Dic5—21no—
47C2×C4⋊Dic5C2×C411yescharacteristic
48C2×#683—22no—
49C22×#168—22no—
50C5×#95—22no—
51C5×#95D414yes—
52#3963—22no—
53#3963C2×C412yes—
54C22⋊#168—22no—
55C22⋊#168—22no—
56#2618—51no—
57#2316D511yescharacteristic, complemented
58#1519—52no—
59C2×#324—51no—
60#1289—52no—
61C24×C5C2×D411yescharacteristic
62C23×D5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—24no—
70C22×C4×C5—81no—
71C22×C4×C5—81no—
72C22×C4×C5C22⋊C412yes—
73C22×C4×C5C22⋊C412yes—
74C22×C4×C5D812yes—
75C22×C4×C5SD1612yes—
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D412yes—
79C22×C4×C5#4112yes—
80C2×C22⋊D5—41no—
81C2×C22⋊D5—41no—
82C2×C22⋊D5—41no—
83C2×C22⋊D5—41no—
84C2×C22⋊D5—41no—
85C2×C22⋊D5—41no—
86C22×Dic5—22no—
87C22×Dic5—21no—
88C2×D20—22no—
89C2×D20—81no—
90C5×C4⋊C4—24no—
91C5×C4⋊C4—24no—
92C5×C4⋊C4—44no—
93C5×C4⋊C4—82no—
94C5×C4⋊C4—82no—
95C5×C22⋊C4—42no—
96C5×C22⋊C4—42no—
97C42×C5—44no—
98C22⋊Dic5—41no—
99C22⋊Dic5—41no—
100#685—44no—
101#685—42no—
102#685—82no—
103C4⋊Dic5—22no—
104C4⋊Dic5—81no—
105#683—44no—
106C2×#168—42no—
107C2×#168—82no—
108C2×#123—101no—
109C2×#121—51no—
110C2×#117—21no—
111C22×C4⋊C4C2×D511yescharacteristic
112C2×C22⋊C8—52no—
113#398—52no—
114#396—102no—
115#394—52no—
116#389—24no—
117#386—101no—
118#380—21no—
119#380—51no—
120#380C2×D512yes—
121#327—104no—
122#324—102no—
123C23×C5—41no—
124C23×C5—41no—
125C23×C5C2×C22⋊C411yescharacteristic
126C23×C5#12011yescharacteristic
127C23×C5#12311yescharacteristic
128C23×C5C2×D811yescharacteristic
129C23×C5C2×SD1611yescharacteristic
130C23×C5AGL(1,ℤ/8)11yescharacteristic
131C23×C5#13711yescharacteristic
132C22×D5—42no—
133C22×D5—42no—
134C22×D5—41no—
135C22×D5—41no—
136C22×D5—41no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—42no—
145C2×C4×C5—41no—
146C2×C4×C5—42no—
147C2×C4×C5—41no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—44no—
151C2×C4×C5—44no—
152C2×C4×C5—44no—
153C2×C4×C5—81no—
154C2×C4×C5#10214yes—
155C2×C4×C5C4×D412yes—
156C2×C4×C5#12112yes—
157C22⋊D5—81no—
158C22⋊D5—81no—
159C22⋊D5—81no—
160C22⋊D5—81no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—42no—
166C2×Dic5—41no—
167D20—82no—
168#168—82no—
169C22×D4—51no—
170C22×D4—101no—
171C23×C4C22⋊D511yescharacteristic
172C23×C4C22⋊D511yescharacteristic
173C23×C4C22×D511yescharacteristic
174C22×C8—102no—
175#123—202no—
176#123—202no—
177#121—102no—
178#121—102no—
179#117—42no—
180#117—42no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—51no—
187C2×C4⋊C4—102no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4C4×D512yes—
190C2×C4⋊C4D2012yes—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—101no—
193C2×C22⋊C4—102no—
194C2×C22⋊C4—101no—
195C2×C22⋊C4—102no—
196C2×C42—22no—
197C22⋊C8—102no—
198C22⋊C8—102no—
199#95—22no—
200#95—52no—
201#95—102no—
202#95C22⋊D514yes—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5#38611yescharacteristic
214C22×C5C2×#10211yescharacteristic
215C22×C5#41711yescharacteristic
216C22×C5#44711yescharacteristic
217C22×C5#44811yescharacteristic
218C22×C5#48011yescharacteristic
219C22×C5#48111yescharacteristic
220C2×D5—82no—
221C2×D5—82no—
222C2×D5—81no—
223C2×D5—81no—
224C2×D5—81no—
225C4×C5—24no—
226C4×C5—22no—
227C4×C5—22no—
228C4×C5—42no—
229C4×C5—84no—
230Dic5—82no—
231Dic5—81no—
232C24—101no—
233C24C2×C22⋊D511yescharacteristic
234C2×D4—102no—
235C2×D4—201no—
236C2×D4—201no—
237C2×D4—201no—
238C2×D4—201no—
239C2×D4—201no—
240C2×D4—201no—
241C2×D4—401no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—24no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—102no—
252C22×C4—101no—
253C22×C4#68512yes—
254C22×C4#68512yes—
255C22×C4#68612yes—
256C22×C4#68812yes—
257C22×C4C2×C4×D511yescharacteristic
258C22×C4C2×D2011yescharacteristic
259C22×C4#70912yes—
260C22×C4C2×C22⋊D512yes—
261C2×C8—202no—
262C2×C8—402no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—44no—
266C4⋊C4—82no—
267C4⋊C4—82no—
268C4⋊C4—102no—
269C4⋊C4—204no—
270C4⋊C4—401no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—201no—
274C22⋊C4—201no—
275C22⋊C4—204no—
276C22⋊C4—202no—
277C22⋊C4—402no—
278C42—44no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5—21no—
284C2×C5—21no—
285C2×C5#187411yescharacteristic
286C2×C5#191211yescharacteristic
287C2×C5#191311yescharacteristic
288D5—161no—
289C23—41no—
290C23—41no—
291C23—202no—
292C23—202no—
293C23—201no—
294C23—201no—
295C23—201no—
296C23C2×#68511yescharacteristic
297C23#407511yescharacteristic
298C23C2×#68611yescharacteristic
299C23#407811yescharacteristic
300C23C2×#68811yescharacteristic
301C23#408811yescharacteristic
302C23#409911yescharacteristic
303D4—402no—
304D4—401no—
305D4—401no—
306D4—401no—
307D4—401no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—81no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—201no—
328C2×C4—202no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4#394114yes—
332C2×C4C4×C22⋊D512yes—
333C2×C4#407612yes—
334C8—402no—
335C5#920411yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—402no—
347C22—402no—
348C22—401no—
349C22—401no—
350C22—401no—
351C22C2×#394111yescharacteristic
352C22#6525511yescharacteristic
353C22#6525611yescharacteristic
354C22#6525711yescharacteristic
355C22#6550211yescharacteristic
356C22#6550611yescharacteristic
357C22#6551611yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—402no—
364C4—401no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—801no—
372C2#1060235311yescharacteristic
373C2#1060244911yescharacteristic
374C2#1060245611yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2316C2
socleC22×C5#386
prime radicalC2×#4076C22
cosocleC23×C4×C5C23
hypercenter#2316D5
hypocenterC5#9204
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
1. C5×#2316C2semidirect
3. C2×#64748C2semidirect
5. #10598116C2semidirect
17. #65280C4semidirect
18. #65272C4semidirect
57. #2316D5semidirect
335. C5#9204semidirect

Maximal subgroups

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

subgroupindex
C5×#23162
#106139302
C2×#647482
#106003022
#105981162
#92045