Finite Group Databasebeta

← #12003898

Subgroups — #12003898

Order 1280.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1948C211yesmaximal, characteristic, complemented
2C2×#64705C211yesmaximal, characteristic
3C2×#64699C211yesmaximal, characteristic, complemented
4#10600373C211yesmaximal, characteristic
5#10600280C211yesmaximal, characteristic
6#10600277C211yesmaximal, characteristic, complemented
7#10598125C211yesmaximal, characteristic, complemented
8C2×#4020C2211yescharacteristic
9C2×C5×#106—21no—
10C2×C5×C4⋊C8C2211yescharacteristic
11C5×#384C2211yescharacteristic
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×#3941—21no—
14C2×#3941—21no—
15C2×#3941—21no—
16C2×#3941—21no—
17C2×C4⋊#168—21no—
18C2×C4⋊#168C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21C5×#340—21no—
22#64744—21no—
23#64705—22no—
24#64699—22no—
25#10599—51nomaximal, Sylow
26C22×D20—21no—
27C22×D20—21no—
28C22×D20—21no—
29C22×C5×C8—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C42×C5—21no—
36C2×C42×C5C2311yescharacteristic
37C22×#168—21no—
38C22×#168—21no—
39C22×#168D411yescharacteristic
40C22×#168D411yescharacteristic
41#4020—21no—
42#4020—21no—
43#4020—21no—
44#4020Q812yes—
45C5×#106—42no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8D412yes—
48C5×#95—21no—
49#3941—42no—
50#3941—42no—
51#3941—42no—
52#3941—42no—
53C4⋊#168—21no—
54C4⋊#168—21no—
55C4⋊#168—21no—
56C4⋊#168—21no—
57C4⋊#168—42no—
58C4×#168—21no—
59C4×#168—21no—
60#1982—51no—
61#1957—51no—
62#1948D511yescharacteristic, complemented
63#1939—51no—
64C2×#335—51no—
65C2×#331—51no—
66#1296—51no—
67C23×D5—41no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—41no—
71C22×C4×C5C2×D411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5#4111yescharacteristic
74C2×D20—22no—
75C2×D20—22no—
76C2×D20—22no—
77C2×D20—41no—
78C2×D20—41no—
79C2×D20—41no—
80C2×D20—41no—
81C2×D20—41no—
82C2×D20—41no—
83C2×D20—41no—
84C2×D20—41no—
85C2×D20—41no—
86C2×D20—41no—
87C2×D20—41no—
88C2×D20—81no—
89C2×D20—81no—
90C2×C5×C8—22no—
91C2×C5×C8—41no—
92C2×C5×C8—41no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—81no—
101C5×C4⋊C4D812yes—
102C42×C5—41no—
103C42×C5—41no—
104C42×C5C2×D411yescharacteristic
105C42×C5C2×Q811yescharacteristic
106C42×C5#4111yescharacteristic
107C42×C5#4111yescharacteristic
108C2×#168—21no—
109C2×#168—21no—
110C2×#168—21no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—41no—
114C2×#168—41no—
115C2×#168—41no—
116C2×#168—41no—
117C2×#168—41no—
118C2×#168—41no—
119C2×#168SD1612yes—
120C2×#127—51no—
121C2×#106—21no—
122C2×C4⋊C8—51no—
123C2×C4⋊C8—51no—
124C2×C4⋊C8—101no—
125C2×C4⋊C8C2×D511yescharacteristic
126C2×#102—101no—
127C2×#102—101no—
128C2×#102—101no—
129C2×#102—101no—
130C2×C4×C8—51no—
131#384C2×D511yescharacteristic
132C4×C4⋊C4C2×D511yescharacteristic
133#340—21no—
134#336—101no—
135#335—102no—
136#331—102no—
137C23×C5#12111yescharacteristic
138C22×D5—42no—
139C22×D5—81no—
140C22×D5—81no—
141C22×D5—81no—
142C22×D5—81no—
143C22×D5—81no—
144C22×D5—81no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—22no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—81no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5#12111yescharacteristic
157C2×C4×C5#12111yescharacteristic
158C2×C4×C5C22⋊Q811yescharacteristic
159C2×C4×C5C22⋊Q811yescharacteristic
160C2×C4×C5C22⋊Q811yescharacteristic
161C2×C4×C5#12611yescharacteristic
162C2×C4×C5C2×D811yescharacteristic
163C2×C4×C5C2×SD1611yescharacteristic
164C2×C4×C5#13511yescharacteristic
165C2×C4×C5#13511yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C5#13711yescharacteristic
170D20—42no—
171D20—42no—
172D20—42no—
173D20—42no—
174D20—82no—
175D20—82no—
176D20—81no—
177D20—81no—
178D20—81no—
179D20—81no—
180C5×C8—42no—
181#168—22no—
182#168—41no—
183#168—81no—
184#168—81no—
185C22×D4—101no—
186C22×D4—101no—
187C22×D4—101no—
188C22×C8—21no—
189C22×C8—51no—
190C22×C8—51no—
191C22×C8—101no—
192C22×C8—101no—
193#127—52no—
194#127—101no—
195#127—101no—
196#127—101no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C22⋊D511yescharacteristic
201C2×C4⋊C4C22⋊D511yescharacteristic
202C2×C42—21no—
203C2×C42C22×D511yescharacteristic
204#106—42no—
205C4⋊C8—21no—
206C4⋊C8—101no—
207C4⋊C8—101no—
208C4⋊C8—101no—
209C4⋊C8—101no—
210C4⋊C8—202no—
211C4⋊C8D2012yes—
212#102—202no—
213#102—202no—
214#102—202no—
215#102—202no—
216C4×C8—101no—
217C4×C8—101no—
218#95—21no—
219C22×C5#39611yescharacteristic
220C22×C5#46011yescharacteristic
221C22×C5#46311yescharacteristic
222C22×C5#46611yescharacteristic
223C22×C5#46811yescharacteristic
224C22×C5#47111yescharacteristic
225C22×C5#47211yescharacteristic
226C2×D5—82no—
227C2×D5—82no—
228C2×D5—82no—
229C2×D5—161no—
230C2×D5—161no—
231C2×D5—161no—
232C2×D5—161no—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—42no—
236C4×C5—81no—
237C4×C5—161no—
238C4×C5#45911yescharacteristic
239C4×C5#46411yescharacteristic
240C4×C5#46511yescharacteristic
241C4×C5#46911yescharacteristic
242C4×C5#47411yescharacteristic
243C4×C5#47611yescharacteristic
244C4×C5#47811yescharacteristic
245C4×C5#47811yescharacteristic
246C24—201no—
247C2×D4—102no—
248C2×D4—102no—
249C2×D4—102no—
250C2×D4—201no—
251C2×D4—201no—
252C2×D4—201no—
253C2×D4—201no—
254C2×D4—201no—
255C2×D4—201no—
256C2×D4—201no—
257C2×D4—201no—
258C2×D4—201no—
259C2×D4—201no—
260C2×D4—201no—
261C2×D4—401no—
262C2×D4—401no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4D4×D511yescharacteristic
267C22×C4#71111yescharacteristic
268C22×C4C2×C22⋊D511yescharacteristic
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—52no—
273C2×C8—101no—
274C2×C8—101no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8—101no—
278C2×C8—201no—
279C2×C8—201no—
280C2×C8—201no—
281C2×C8—201no—
282C2×C8—201no—
283C2×C8—201no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C4⋊C4#68612yes—
293C42—41no—
294C42—41no—
295C42C2×D2011yescharacteristic
296C42#70911yescharacteristic
297C42Q8×D511yescharacteristic
298C42#71311yescharacteristic
299C2×C5#166811yescharacteristic
300C2×C5#168111yescharacteristic
301C2×C5#168611yescharacteristic
302C2×C5#169711yescharacteristic
303C2×C5#206311yescharacteristic
304C2×C5#206511yescharacteristic
305C2×C5#206711yescharacteristic
306D5—162no—
307C23—202no—
308C23—401no—
309C23—401no—
310C23—401no—
311C23—401no—
312C23—401no—
313C23—401no—
314C23#408511yescharacteristic
315D4—202no—
316D4—202no—
317D4—202no—
318D4—202no—
319D4—402no—
320D4—402no—
321D4—401no—
322D4—401no—
323D4—401no—
324D4—401no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4#404111yescharacteristic
337C2×C4#404211yescharacteristic
338C2×C4#404311yescharacteristic
339C2×C4#404411yescharacteristic
340C2×C4D5×SD1611yescharacteristic
341C2×C4#406011yescharacteristic
342C2×C4#406011yescharacteristic
343C2×C4#406211yescharacteristic
344C2×C4#407611yescharacteristic
345C2×C4C2×#68611yescharacteristic
346C2×C4#408811yescharacteristic
347C2×C4#409211yescharacteristic
348C2×C4#409511yescharacteristic
349C2×C4#409611yescharacteristic
350C8—42no—
351C8—102no—
352C8—201no—
353C8—401no—
354C8—401no—
355C5#1059911yescharacteristic, complemented, Sylow
356C22—402no—
357C22—402no—
358C22—402no—
359C22—801no—
360C22—801no—
361C22—801no—
362C22—801no—
363C22#6528311yescharacteristic
364C22#6532711yescharacteristic
365C22#6533811yescharacteristic
366C22#6545211yescharacteristic
367C22#6545411yescharacteristic
368C22#6548811yescharacteristic
369C22#6549211yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#6515311yescharacteristic
376C4#6515411yescharacteristic
377C4#6515911yescharacteristic
378C4#6516011yescharacteristic
379C4#6530411yescharacteristic
380C4#6531711yescharacteristic
381C4#6535511yescharacteristic
382C4#6537611yescharacteristic
383C2—802no—
384C2#1060042311yescharacteristic
385C2#1060137811yescharacteristic
386C2#1060146911yescharacteristic
387C2#1060181411yescharacteristic
388C2#1060183211yescharacteristic
389C2#1060191311yescharacteristic
390C2#1060193111yescharacteristic
subgroupG/H
centerC23#4085
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1948C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenter#1948D5
hypocenterC5#10599
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C5×#1948C2semidirect
3. C2×#64699C2semidirect
6. #10600277C2semidirect
7. #10598125C2semidirect
62. #1948D5semidirect
355. C5#10599semidirect

Maximal subgroups

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

subgroupindex
C5×#19482
C2×#647052
C2×#646992
#106003732
#106002802
#106002772
#105981252
#105995