Finite Group Databasebeta

← #12015263

Subgroups — #12015263

Order 1280.

808 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#120C211yesmaximal, characteristic
2C2×#64756C212yesmaximal
3#10602412C211yesmaximal, characteristic, complemented
4#10602410C211yesmaximal, characteristic, complemented
5#10598128C212yesmaximal, complemented
6C24×C4×C5C411yescharacteristic, complemented
7C2×C5×#120C2211yescharacteristic
8C2×C4×C5×D4—21no—
9C2×C4×C5×D4C2211yescharacteristic
10C5×#386—21no—
11C5×#386C2211yescharacteristic
12C5×#385—21no—
13C5×#385C411yescharacteristic, complemented
14C5×#379C411yescharacteristic, complemented
15C4×C5×C22⋊C4—21no—
16C4×C5×C22⋊C4C411yescharacteristic, complemented
17C2×#3966C2212yes—
18C2×#3965C2212yes—
19#65501—21no—
20#65213—21no—
21#64756—24no—
22#64750—21no—
23#64746—21no—
24#12793—51nomaximal, Sylow
25C25×C5C2×C411yescharacteristic
26C22×C5×D4—21no—
27C22×C5×D4C2311yescharacteristic
28C23×C4×C5—21no—
29C23×C4×C5—21no—
30C23×C4×C5—44no—
31C23×C4×C5—41no—
32C23×C4×C5—41no—
33C23×C4×C5C2×C411yescharacteristic
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C5×#120—21no—
37C5×#120—21no—
38C5×#120D412yes—
39C5×#120Q812yes—
40C4×C5×D4—41no—
41C4×C5×D4—41no—
42C4×C5×D4—44no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4D411yescharacteristic
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4C2×C411yescharacteristic
50C2×C5×C22⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4C2×C411yescharacteristic
52C2×C5×C22⋊C4D411yescharacteristic
53C2×C42×C5—21no—
54C2×C42×C5D411yescharacteristic
55C2×C22⋊Dic5—22no—
56C2×C4⋊Dic5—41no—
57C2×#681—22no—
58C5×#95—21no—
59C5×#95—21no—
60C5×#95—21no—
61#3966—22no—
62#3966—22no—
63#3965—22no—
64#3965—22no—
65#3963—41no—
66C4⋊#168—41no—
67C4⋊#168—41no—
68C4×#120D511yescharacteristic
69C2×AΣL(1,𝔽16)—52no—
70#1800—51no—
71#1799—51no—
72#1390—52no—
73C24×C5—21no—
74C24×C5—21no—
75C24×C5—42no—
76C24×C5—41no—
77C24×C5—42no—
78C24×C5—41no—
79C24×C5C4⋊C412yescomplemented
80C24×C5C22×C411yescharacteristic
81C24×C5C2×D411yescharacteristic
82C2×C5×D4—22no—
83C2×C5×D4—22no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—42no—
87C2×C5×D4—42no—
88C2×C5×D4C2×D411yescharacteristic
89C2×C5×D4C2×Q811yescharacteristic
90C2×C5×D4#4111yescharacteristic
91C2×C5×D4#4111yescharacteristic
92C22×C4×C5—24no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—42no—
101C22×C4×C5—42no—
102C22×C4×C5—42no—
103C22×C4×C5—42no—
104C22×C4×C5—42no—
105C22×C4×C5—42no—
106C22×C4×C5—42no—
107C22×C4×C5—44no—
108C22×C4×C5—44no—
109C22×C4×C5—44no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5—41no—
113C22×C4×C5—44no—
114C22×C4×C5C22⋊C411yescharacteristic
115C22×C4×C5C22⋊C411yescharacteristic
116C22×C4×C5C22⋊C411yescharacteristic
117C22×C4×C5C22⋊C411yescharacteristic
118C22×C4×C5C2×D411yescharacteristic
119C22×Dic5—42no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—42no—
122C5×C22⋊C4—21no—
123C5×C22⋊C4—22no—
124C5×C22⋊C4—22no—
125C5×C22⋊C4—41no—
126C5×C22⋊C4—41no—
127C5×C22⋊C4—42no—
128C5×C22⋊C4—42no—
129C5×C22⋊C4—42no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4C4⋊C412yescomplemented
132C42×C5—21no—
133C42×C5—21no—
134C42×C5—42no—
135C22⋊Dic5—42no—
136C22⋊Dic5—42no—
137C4⋊Dic5—82no—
138#681—42no—
139#681—42no—
140C2×#168—42no—
141C24×C4Dic511yescharacteristic, complemented
142C2×#120C2×D511yescharacteristic
143C2×C4×D4—21no—
144C2×C4×D4C2×D511yescharacteristic
145#423—101no—
146C2×#100—52no—
147C2×#99—52no—
148#386—21no—
149#386C2×D511yescharacteristic
150#385—21no—
151#385Dic511yescharacteristic, complemented
152#380—101no—
153#379Dic511yescharacteristic, complemented
154C4×C22⋊C4—21no—
155C4×C22⋊C4Dic511yescharacteristic, complemented
156AΣL(1,𝔽16)—104no—
157#343—101no—
158#342—101no—
159C23×C5—22no—
160C23×C5—22no—
161C23×C5—22no—
162C23×C5—21no—
163C23×C5—21no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—41no—
167C23×C5—44no—
168C23×C5—42no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—44no—
173C23×C5—42no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—42no—
177C23×C5—42no—
178C23×C5—42no—
179C23×C5—48no—
180C23×C5—42no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5C2×C22⋊C411yescharacteristic
184C23×C5C2×C4⋊C411yescharacteristic
185C23×C5#11711yescharacteristic
186C23×C5#12111yescharacteristic
187C23×C5C22⋊Q811yescharacteristic
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—41no—
191C5×D4—41no—
192C5×D4—44no—
193C5×D4—44no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—44no—
203C2×C4×C5—42no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—48no—
208C2×C4×C5—42no—
209C2×C4×C5—41no—
210C2×C4×C5—42no—
211C2×C4×C5—44no—
212C2×C4×C5—42no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—42no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—81no—
221C2×C4×C5#9911yescharacteristic
222C2×C4×C5#9911yescharacteristic
223C2×C4×C5#12111yescharacteristic
224C2×C4×C5C22⋊Q811yescharacteristic
225C2×Dic5—82no—
226C2×Dic5—82no—
227C2×Dic5—82no—
228#168—82no—
229C25C2×Dic511yescharacteristic
230C22×D4—21no—
231C22×D4C22×D511yescharacteristic
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—44no—
235C23×C4—41no—
236C23×C4—41no—
237C23×C4C2×Dic511yescharacteristic
238C23×C4C2×Dic511yescharacteristic
239C23×C4C22⋊D511yescharacteristic
240C2×M16—102no—
241#120—21no—
242#120—21no—
243#120Dic1012yes—
244#120D2012yes—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—44no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—201no—
250C2×C4⋊C4C22⋊D511yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—102no—
256C2×C22⋊C4C2×Dic511yescharacteristic
257C2×C22⋊C4C2×Dic511yescharacteristic
258C2×C22⋊C4C2×Dic511yescharacteristic
259C2×C22⋊C4C22⋊D511yescharacteristic
260C2×C42—21no—
261C2×C42C22⋊D511yescharacteristic
262C4⋊C8—201no—
263C4⋊C8—201no—
264#100—102no—
265#100—102no—
266#99—102no—
267#99—102no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—201no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—24no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—42no—
284C22×C5—42no—
285C22×C5—42no—
286C22×C5—42no—
287C22×C5—44no—
288C22×C5—44no—
289C22×C5—44no—
290C22×C5—44no—
291C22×C5—42no—
292C22×C5—41no—
293C22×C5—42no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5—42no—
297C22×C5—41no—
298C22×C5—81no—
299C22×C5#38011yescharacteristic
300C22×C5C2×#9911yescharacteristic
301C22×C5#41011yescharacteristic
302C4×C5—21no—
303C4×C5—21no—
304C4×C5—21no—
305C4×C5—42no—
306C4×C5—42no—
307C4×C5—41no—
308C4×C5—41no—
309C4×C5—41no—
310C4×C5—81no—
311C4×C5AΣL(1,𝔽16)12yescomplemented
312Dic5—162no—
313C24—21no—
314C24—21no—
315C24—42no—
316C24—41no—
317C24—42no—
318C24—41no—
319C24C4⋊Dic512yescomplemented
320C24C22×Dic511yescharacteristic
321C24C2×C22⋊D511yescharacteristic
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4C2×Dic1011yescharacteristic
329C2×D4C2×D2011yescharacteristic
330C2×D4#70911yescharacteristic
331C2×D4#70911yescharacteristic
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—44no—
354C22×C4—202no—
355C22×C4C22⋊Dic511yescharacteristic
356C22×C4C22⋊Dic511yescharacteristic
357C22×C4C22⋊Dic511yescharacteristic
358C22×C4C22⋊Dic511yescharacteristic
359C22×C4C2×C22⋊D511yescharacteristic
360M16—202no—
361M16—202no—
362C2×C8—202no—
363C4⋊C4—41no—
364C4⋊C4—42no—
365C4⋊C4—402no—
366C22⋊C4—21no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—41no—
375C22⋊C4—202no—
376C22⋊C4—202no—
377C22⋊C4C4⋊Dic512yescomplemented
378C42—21no—
379C42—21no—
380C42—42no—
381C2×C5—21no—
382C2×C5—21no—
383C2×C5—41no—
384C2×C5—44no—
385C2×C5—41no—
386C2×C5—41no—
387C2×C5—41no—
388C2×C5#179911yescharacteristic
389C2×C5C2×AΣL(1,𝔽16)11yescharacteristic
390C2×C5#212011yescharacteristic
391C23—22no—
392C23—22no—
393C23—22no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—41no—
399C23—44no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—44no—
405C23—42no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—48no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23#407011yescharacteristic
416C23C2×C4⋊Dic511yescharacteristic
417C23#407211yescharacteristic
418C23#407611yescharacteristic
419C23C2×C22⋊Dic511yescharacteristic
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—44no—
425D4—44no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—48no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—402no—
454C2×C4—402no—
455C2×C4—402no—
456C2×C4#396611yescharacteristic
457C2×C4#396611yescharacteristic
458C2×C4#407011yescharacteristic
459C2×C4#407611yescharacteristic
460C8—402no—
461C5#1279311yescharacteristic, complemented, Sylow
462C22—21no—
463C22—21no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—41no—
482C22—42no—
483C22—41no—
484C22—42no—
485C22—42no—
486C22—41no—
487C22—41no—
488C22—81no—
489C22#6550111yescharacteristic
490C22C2×#396611yescharacteristic
491C22#6552911yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—41no—
497C4—42no—
498C4—41no—
499C4—41no—
500C4—81no—
501C4—802no—
502C4#6475612yescomplemented
503C2—21no—
504C2—21no—
505C2—41no—
506C2—44no—
507C2—41no—
508C2—41no—
509C2—41no—
510C2#1060241211yescharacteristic
511C2C2×#6475611yescharacteristic
512C2#1060250911yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC24×C5C22×C4
FrattiniC22×D4C22×D5
FittingC4×C5×#120C2
socleC22×C5C2×#99
prime radicalC2×C5×#120C22
cosocleC22×C5×D4C23
hypercenterC4×#120D5
hypocenterC5#12793
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
3. #10602412C2semidirect
4. #10602410C2semidirect
5. #10598128C2semidirect
6. C24×C4×C5C4semidirect
13. C5×#385C4semidirect
14. C5×#379C4semidirect
16. C4×C5×C22⋊C4C4semidirect
79. C24×C5C4⋊C4semidirect
131. C5×C22⋊C4C4⋊C4semidirect
141. C24×C4Dic5semidirect
151. #385Dic5semidirect
153. #379Dic5semidirect
155. C4×C22⋊C4Dic5semidirect
311. C4×C5AΣL(1,𝔽16)semidirect
319. C24C4⋊Dic5semidirect
377. C22⋊C4C4⋊Dic5semidirect
461. C5#12793semidirect
502. C4#64756semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1202
C2×#647562
#106024122
#106024102
#105981282
#127935