Finite Group Databasebeta

← #12003900

Subgroups — #12003900

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×#1939C211yesmaximal, characteristic, complemented
2C2×#64705C211yesmaximal, characteristic
3#10600565C211yesmaximal, characteristic
4C2×#64678C211yesmaximal, characteristic, complemented
5#10600280C211yesmaximal, characteristic
6#10600260C211yesmaximal, characteristic, complemented
7#10598193C211yesmaximal, characteristic, complemented
8C2×#4020C2211yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×#3953—21no—
14C2×#3953—21no—
15C2×#3941—21no—
16C2×#3941—21no—
17C2×#3940—21no—
18#65224C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C5×#336—21no—
22#64749—21no—
23#64705—22no—
24#64678—22no—
25#10599—51nomaximal, Sylow
26C22×D20—21no—
27C22×D20—21no—
28C22×D20—21no—
29C22×C5×C8—21no—
30C22×C5×C8D411yescharacteristic
31C22×C5×C8D411yescharacteristic
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C42×C5—21no—
35C2×C42×C5C2311yescharacteristic
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—21no—
39C22×#168—21no—
40C22×#168—21no—
41#4020—21no—
42#4020—21no—
43#4020—21no—
44#4020Q812yes—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—42no—
48C4×C5×C8—21no—
49C4×C5×C8—21no—
50C5×#95—21no—
51#3953—42no—
52#3953—42no—
53#3941—42no—
54#3941—42no—
55#3940—42no—
56C4⋊#168—21no—
57C4⋊#168—21no—
58C4⋊#168—21no—
59C4⋊#168D412yes—
60#1982—51no—
61#1957—51no—
62#1948—51no—
63#1939D511yescharacteristic, complemented
64C2×#335—51no—
65C2×#331—51no—
66#1296—51no—
67C23×D5—41no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×C4×C5#4111yescharacteristic
73C22×Dic5—41no—
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—21no—
91C2×C5×C8—21no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—41no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8SD1612yes—
99C5×C4⋊C4—21no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4D812yes—
103C42×C5—41no—
104C42×C5—41no—
105C42×C5C2×D411yescharacteristic
106C42×C5C2×Q811yescharacteristic
107C42×C5#4111yescharacteristic
108C42×C5#4111yescharacteristic
109C4⋊Dic5—41no—
110C4⋊Dic5—41no—
111C4⋊Dic5—41no—
112C4⋊Dic5—41no—
113C4⋊Dic5—81no—
114C2×#168—22no—
115C2×#168—41no—
116C2×#168—41no—
117C2×#168—41no—
118C2×#168—41no—
119C2×#168—41no—
120C2×#127—51no—
121C2×#106—101no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—51no—
124C2×C4⋊C8—51no—
125C2×C4⋊C8C2×D511yescharacteristic
126C2×#102—101no—
127C2×#102—101no—
128C2×#102—101no—
129C2×#102—101no—
130C2×C4×C8C2×D511yescharacteristic
131#384—51no—
132C4×C4⋊C4C2×D511yescharacteristic
133#340—101no—
134#336—21no—
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#12111yescharacteristic
154C2×C4×C5#12111yescharacteristic
155C2×C4×C5C22⋊Q811yescharacteristic
156C2×C4×C5C22⋊Q811yescharacteristic
157C2×C4×C5C22⋊Q811yescharacteristic
158C2×C4×C5#12611yescharacteristic
159C2×C4×C5C2×D811yescharacteristic
160C2×C4×C5C2×SD1611yescharacteristic
161C2×C4×C5#13511yescharacteristic
162C2×C4×C5#13511yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C5#13711yescharacteristic
167C2×Dic5—81no—
168C2×Dic5—81no—
169C2×Dic5—81no—
170D20—42no—
171D20—42no—
172D20—42no—
173D20—42no—
174D20—82no—
175D20—82no—
176D20—81no—
177D20—81no—
178D20—81no—
179D20—81no—
180C5×C8—22no—
181C5×C8—41no—
182C5×C8—81no—
183#168—42no—
184#168—81no—
185C22×D4—101no—
186C22×D4—101no—
187C22×D4—101no—
188C22×C8—21no—
189C22×C8—101no—
190C22×C8—101no—
191C22×C8C22⋊D511yescharacteristic
192C22×C8C22⋊D511yescharacteristic
193#127—52no—
194#127—101no—
195#127—101no—
196#127—101no—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—101no—
199C2×C4⋊C4—101no—
200C2×C4⋊C4D2011yescharacteristic
201C2×C4⋊C4D2011yescharacteristic
202C2×C42—21no—
203C2×C42C22×D511yescharacteristic
204#106—202no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8—52no—
209C4⋊C8—101no—
210C4⋊C8—101no—
211C4⋊C8—101no—
212#102—202no—
213#102—202no—
214#102—202no—
215#102—202no—
216C4×C8—21no—
217C4×C8—21no—
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#45911yescharacteristic
238C4×C5#46411yescharacteristic
239C4×C5#46511yescharacteristic
240C4×C5#46911yescharacteristic
241C4×C5#47411yescharacteristic
242C4×C5#47611yescharacteristic
243C4×C5#47811yescharacteristic
244C4×C5#47811yescharacteristic
245Dic5—161no—
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—201no—
266C22×C4C2×D2011yescharacteristic
267C22×C4#70911yescharacteristic
268C22×C4C2×C22⋊D511yescharacteristic
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—102no—
278C2×C8—201no—
279C2×C8—201no—
280C2×C8—201no—
281C2×C8—201no—
282C2×C8—201no—
283C2×C8#68812yes—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—201no—
288C4⋊C4—201no—
289C4⋊C4—201no—
290C4⋊C4—201no—
291C4⋊C4—401no—
292C4⋊C4D4012yes—
293C42—41no—
294C42—41no—
295C42D4×D511yescharacteristic
296C42#71111yescharacteristic
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#407611yescharacteristic
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—401no—
334C2×C4—401no—
335C2×C4—401no—
336C2×C4#404111yescharacteristic
337C2×C4#404211yescharacteristic
338C2×C4#404311yescharacteristic
339C2×C4#404411yescharacteristic
340C2×C4C2×D4011yescharacteristic
341C2×C4#405011yescharacteristic
342C2×C4#405411yescharacteristic
343C2×C4#405511yescharacteristic
344C2×C4#407811yescharacteristic
345C2×C4#408511yescharacteristic
346C2×C4C2×#68811yescharacteristic
347C2×C4#409211yescharacteristic
348C2×C4#409511yescharacteristic
349C2×C4#409611yescharacteristic
350C8—22no—
351C8—41no—
352C8—81no—
353C8—202no—
354C8—401no—
355C5#1059911yescharacteristic, complemented, Sylow
356C22—402no—
357C22—402no—
358C22—402no—
359C22—801no—
360C22—801no—
361C22—801no—
362C22—801no—
363C22#6528311yescharacteristic
364C22#6530511yescharacteristic
365C22#6531611yescharacteristic
366C22#6540411yescharacteristic
367C22#6542311yescharacteristic
368C22#6543011yescharacteristic
369C22#6543111yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—801no—
375C4#6513211yescharacteristic
376C4#6513411yescharacteristic
377C4#6513511yescharacteristic
378C4#6513611yescharacteristic
379C4#6532811yescharacteristic
380C4#6533711yescharacteristic
381C4#6535511yescharacteristic
382C4#6537311yescharacteristic
383C2—802no—
384C2#1060042211yescharacteristic
385C2#1060127711yescharacteristic
386C2#1060133511yescharacteristic
387C2#1060164211yescharacteristic
388C2#1060166211yescharacteristic
389C2#1060173211yescharacteristic
390C2#1060175111yescharacteristic
subgroupG/H
centerC23#4076
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1939C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenter#1939D5
hypocenterC5#10599
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C5×#1939C2semidirect
4. C2×#64678C2semidirect
6. #10600260C2semidirect
7. #10598193C2semidirect
63. #1939D5semidirect
355. C5#10599semidirect

Maximal subgroups

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

subgroupindex
C5×#19392
C2×#647052
#106005652
C2×#646782
#106002802
#106002602
#105981932
#105995