Finite Group Databasebeta

← #12003510

Subgroups — #12003510

Order 1280.

554 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65374C211yesmaximal, characteristic
2C5×#1988C211yesmaximal, characteristic, complemented
3C2×#64767C211yesmaximal, characteristic, complemented
4C2×#64705C211yesmaximal, characteristic
5#10600280C211yesmaximal, characteristic
6#10600277C211yesmaximal, characteristic, complemented
7#10598194C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C22×#688—21no—
10C22×#688—21no—
11C2×#4020C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C4×C5×C4⋊C4C2211yescharacteristic
14#65374—22no—
15#65374—22no—
16C2×#3941—21no—
17C2×#3941—21no—
18C2×C4⋊#168—21no—
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22C5×#340—21no—
23C5×#340—21no—
24#64767—22no—
25#64744—21no—
26#64705—22no—
27#10537—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×D20—21no—
30C22×D20—21no—
31C22×D20—21no—
32C22×C5×C8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8D412yes—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C42×C5—21no—
42C2×C42×C5C2311yescharacteristic
43C2×#688—24no—
44C2×#688—24no—
45C2×#688—42no—
46C2×#688—42no—
47C2×#688—42no—
48C2×#688—42no—
49C22×#168—21no—
50C22×#168—21no—
51C22×#168D411yescharacteristic
52C22×#168D411yescharacteristic
53#4020—21no—
54#4020—21no—
55#4020—21no—
56#4020D412yes—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×#95—21no—
60#3941—42no—
61#3941—42no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168—21no—
66C4⋊#168—42no—
67C4×#168—21no—
68C4×#168—21no—
69C2×#492—51no—
70#1988D511yescharacteristic, complemented
71#1982—51no—
72#1939—51no—
73C2×#332—51no—
74C2×#331—51no—
75#1277—51no—
76C23×D5—41no—
77C2×C5×Q8—22no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C2×C5×Q8—41no—
82C2×C5×Q8—41no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—41no—
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4111yescharacteristic
89C2×D20—22no—
90C2×D20—22no—
91C2×D20—22no—
92C2×D20—41no—
93C2×D20—41no—
94C2×D20—41no—
95C2×D20—41no—
96C2×D20—41no—
97C2×D20—41no—
98C2×D20—41no—
99C2×D20—41no—
100C2×D20—41no—
101C2×D20—41no—
102C2×D20—41no—
103C2×D20—81no—
104C2×D20—81no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C4⋊C4SD1612yescomplemented
116C42×C5—41no—
117C42×C5—41no—
118C42×C5C2×D411yescharacteristic
119C42×C5C2×D411yescharacteristic
120C42×C5#4111yescharacteristic
121C42×C5#4111yescharacteristic
122#688—48no—
123#688—48no—
124C2×#168—21no—
125C2×#168—21no—
126C2×#168—21no—
127C2×#168—21no—
128C2×#168—41no—
129C2×#168—41no—
130C2×#168—41no—
131C2×#168—41no—
132C2×#168—41no—
133C2×#168—41no—
134C2×#168D812yes—
135C2×#168SD1612yes—
136C22×SD16—101no—
137C22×SD16—101no—
138C2×C4⋊Q8C2×D511yescharacteristic
139C2×#127—51no—
140#492—102no—
141#492—102no—
142C2×C4⋊C8—51no—
143C2×C4⋊C8—51no—
144C2×C4⋊C8—101no—
145C2×C4⋊C8C2×D511yescharacteristic
146C2×#102—101no—
147C2×#102—101no—
148C2×C4×C8—51no—
149C4×C4⋊C4C2×D511yescharacteristic
150#340—21no—
151#340—21no—
152#336—101no—
153#332—102no—
154#331—102no—
155C23×C5#12111yescharacteristic
156C22×D5—42no—
157C22×D5—81no—
158C22×D5—81no—
159C22×D5—81no—
160C22×D5—81no—
161C22×D5—81no—
162C22×D5—81no—
163C5×Q8—42no—
164C5×Q8—42no—
165C5×Q8—81no—
166C5×Q8—81no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—22no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—42no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—81no—
177C2×C4×C5—81no—
178C2×C4×C5#12011yescharacteristic
179C2×C4×C5#12111yescharacteristic
180C2×C4×C5#12111yescharacteristic
181C2×C4×C5#12311yescharacteristic
182C2×C4×C5#12311yescharacteristic
183C2×C4×C5#12411yescharacteristic
184C2×C4×C5C2×D811yescharacteristic
185C2×C4×C5C2×SD1611yescharacteristic
186C2×C4×C5C2×SD1611yescharacteristic
187C2×C4×C5#13511yescharacteristic
188C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C5#13711yescharacteristic
192D20—42no—
193D20—42no—
194D20—42no—
195D20—42no—
196D20—82no—
197D20—82no—
198D20—81no—
199D20—81no—
200D20—81no—
201D20—81no—
202C5×C8—81no—
203#168—22no—
204#168—22no—
205#168—81no—
206#168—81no—
207C22×Q8—21no—
208C22×D4—101no—
209C22×D4—101no—
210C22×D4—101no—
211C2×SD16—104no—
212C2×SD16—104no—
213C2×SD16—202no—
214C2×SD16—202no—
215C2×SD16—202no—
216C2×SD16—202no—
217C22×C8—21no—
218C22×C8—51no—
219C22×C8—51no—
220C22×C8—101no—
221C22×C8—101no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8D2012yes—
226#127—52no—
227#127—101no—
228#127—101no—
229#127—101no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4C22⋊D511yescharacteristic
233C2×C4⋊C4C22⋊D511yescharacteristic
234C2×C42—21no—
235C2×C42C22×D511yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—101no—
239C4⋊C8—101no—
240C4⋊C8—101no—
241C4⋊C8—101no—
242C4⋊C8—202no—
243#102—202no—
244#102—202no—
245C4×C8—101no—
246C4×C8—101no—
247#95—21no—
248C22×C5#39411yescharacteristic
249C22×C5#45911yescharacteristic
250C22×C5#46011yescharacteristic
251C22×C5#46511yescharacteristic
252C22×C5#46811yescharacteristic
253C22×C5#47111yescharacteristic
254C22×C5#47111yescharacteristic
255C2×D5—82no—
256C2×D5—82no—
257C2×D5—82no—
258C2×D5—161no—
259C2×D5—161no—
260C2×D5—161no—
261C2×D5—161no—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5—81no—
266C4×C5—82no—
267C4×C5#44711yescharacteristic
268C4×C5#45011yescharacteristic
269C4×C5#46011yescharacteristic
270C4×C5#46111yescharacteristic
271C4×C5#46311yescharacteristic
272C4×C5#46411yescharacteristic
273C4×C5#48611yescharacteristic
274C4×C5#49011yescharacteristic
275C24—201no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—102no—
283C2×D4—102no—
284C2×D4—102no—
285C2×D4—201no—
286C2×D4—201no—
287C2×D4—201no—
288C2×D4—201no—
289C2×D4—201no—
290C2×D4—201no—
291C2×D4—201no—
292C2×D4—201no—
293C2×D4—201no—
294C2×D4—201no—
295C2×D4—201no—
296C2×D4—401no—
297C2×D4—401no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4D4×D511yescharacteristic
302C22×C4#71111yescharacteristic
303C22×C4C2×C22⋊D511yescharacteristic
304SD16—208no—
305SD16—208no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—52no—
310C2×C8—52no—
311C2×C8—101no—
312C2×C8—101no—
313C2×C8—101no—
314C2×C8—101no—
315C2×C8—201no—
316C2×C8—201no—
317C2×C8—201no—
318C2×C8—201no—
319C2×C8—201no—
320C2×C8—201no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4#68812yescomplemented
329C42—41no—
330C42—41no—
331C42C2×D2011yescharacteristic
332C42#70911yescharacteristic
333C42D4×D511yescharacteristic
334C42#71111yescharacteristic
335C2×C5#166511yescharacteristic
336C2×C5#166611yescharacteristic
337C2×C5#168511yescharacteristic
338C2×C5#168611yescharacteristic
339C2×C5#204111yescharacteristic
340C2×C5#204611yescharacteristic
341C2×C5#205511yescharacteristic
342D5—162no—
343C23—202no—
344C23—401no—
345C23—401no—
346C23—401no—
347C23—401no—
348C23—401no—
349C23—401no—
350C23#408511yescharacteristic
351Q8—42no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355D4—202no—
356D4—202no—
357D4—202no—
358D4—202no—
359D4—402no—
360D4—402no—
361D4—401no—
362D4—401no—
363D4—401no—
364D4—401no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4#402811yescharacteristic
377C2×C4#402911yescharacteristic
378C2×C4#403111yescharacteristic
379C2×C4#403211yescharacteristic
380C2×C4D5×D811yescharacteristic
381C2×C4#405711yescharacteristic
382C2×C4D5×SD1611yescharacteristic
383C2×C4#406011yescharacteristic
384C2×C4#407611yescharacteristic
385C2×C4#408411yescharacteristic
386C2×C4C2×#68811yescharacteristic
387C2×C4#408811yescharacteristic
388C2×C4#409511yescharacteristic
389C2×C4#409611yescharacteristic
390C8—81no—
391C8—102no—
392C8—102no—
393C8—401no—
394C8—401no—
395C5#1053711yescharacteristic, complemented, Sylow
396C22—402no—
397C22—402no—
398C22—402no—
399C22—801no—
400C22—801no—
401C22—801no—
402C22—801no—
403C22#6525011yescharacteristic
404C22#6533711yescharacteristic
405C22#6533811yescharacteristic
406C22#6543911yescharacteristic
407C22#6545211yescharacteristic
408C22#6549211yescharacteristic
409C22#6549211yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—82no—
414C4—81no—
415C4#6504911yescharacteristic
416C4#6505311yescharacteristic
417C4#6506211yescharacteristic
418C4#6506511yescharacteristic
419C4#6531611yescharacteristic
420C4#6531711yescharacteristic
421C4#6534611yescharacteristic
422C4#6537211yescharacteristic
423C2—802no—
424C2#1060047311yescharacteristic
425C2#1060097011yescharacteristic
426C2#1060113211yescharacteristic
427C2#1060189311yescharacteristic
428C2#1060189711yescharacteristic
429C2#1060190911yescharacteristic
430C2#1060191311yescharacteristic
subgroupG/H
centerC23#4085
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1988C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenter#1988D5
hypocenterC5#10537
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
2. C5×#1988C2semidirect
3. C2×#64767C2semidirect
6. #10600277C2semidirect
7. #10598194C2semidirect
70. #1988D5semidirect
115. C5×C4⋊C4SD16semidirect
328. C4⋊C4#688semidirect
395. C5#10537semidirect

Maximal subgroups

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

subgroupindex
C2×#653742
C5×#19882
C2×#647672
C2×#647052
#106002802
#106002772
#105981942
#105375