Finite Group Databasebeta

← #12109877

Subgroups — #12109877

Order 1280.

786 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64994C211yesmaximal, characteristic
2#10606049C211yesmaximal, characteristic
3#10605878C211yesmaximal, characteristic
4C5×#1847C211yesmaximal, characteristic, complemented
5#10601426C212yesmaximal
6#10601409C212yesmaximal, complemented
7#10601373C212yesmaximal
8#10601357C212yesmaximal, complemented
9#10600608C211yesmaximal, characteristic, complemented
10#10600368C211yesmaximal, characteristic, complemented
11#10600343C211yesmaximal, characteristic, complemented
12C2×#4038C2212yes—
13C2×C42×D5C2211yescharacteristic
14C2×C5×#107C2212yes—
15C2×C5×#106C2212yes—
16C2×C5×#97C2211yescharacteristic
17C5×#384C2211yescharacteristic
18C5×#382C2211yescharacteristic
19C2×#3952C2212yes—
20C2×#3946C2212yes—
21#65276—21no—
22#65276—21no—
23#65276C2211yescharacteristic
24#65276C2211yescharacteristic
25#65266C2212yes—
26C4⋊C4×Dic5—21no—
27C4⋊C4×Dic5—21no—
28C4⋊C4×Dic5C2211yescharacteristic
29C4⋊C4×Dic5C2211yescharacteristic
30C2×#3940C2212yes—
31C2×#3939C2212yes—
32#65225C2211yescharacteristic
33#65224C2211yescharacteristic
34C2×#3935C2211yescharacteristic
35#64994C418yescomplemented
36#64955—21no—
37#64953—21no—
38#64940—21no—
39#64937—21no—
40#64771C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21989—51nomaximal, Sylow
45C22×C4×D5D411yescharacteristic
46C22×C4×D5D411yescharacteristic
47C22×C4×D5C2311yescharacteristic
48C22×C5×C8C2312yes—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4C2311yescharacteristic
52C2×C5×C4⋊C4C2311yescharacteristic
53C2×C5×C4⋊C4C2312yes—
54C2×C42×C5C2311yescharacteristic
55C2×#685—22no—
56C2×#685—21no—
57C2×#685—21no—
58C2×C4⋊Dic5—21no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5C2312yes—
61C2×C4⋊Dic5C2311yescharacteristic
62C2×C4⋊Dic5C2311yescharacteristic
63C2×C4×Dic5—22no—
64C2×C4×Dic5—21no—
65C2×C4×Dic5—21no—
66C2×C4×Dic5D411yescharacteristic
67C2×C4×Dic5D411yescharacteristic
68C2×C4×Dic5C2311yescharacteristic
69C22×#168C2312yes—
70#4038—42no—
71#4038—42no—
72C42×D5C2×C414yes—
73C42×D5Q814yes—
74C5×#107—42no—
75C5×#106—42no—
76C5×#97C2×C414yes—
77C5×#95—21no—
78C5×#95—21no—
79#3963—21no—
80#3963—21no—
81#3963—21no—
82#3963—21no—
83#3963—21no—
84#3963—21no—
85#3963—22no—
86#3963—22no—
87#3952C2×C418yes—
88#3946C2×C418yes—
89#3940—42no—
90#3939—42no—
91#3935C2×C414yes—
92C2×#432—51no—
93#2285—51no—
94#2283—51no—
95#1949—52no—
96#1949—52no—
97#1854—52no—
98#1854—52no—
99#1847—51no—
100#1847D511yescharacteristic, complemented
101#1836—51no—
102#1836—51no—
103C23×D5C2×D411yescharacteristic
104C22×C4×C5—22no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5C2×D411yescharacteristic
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2411yescharacteristic
110C22×Dic5—21no—
111C22×Dic5—21no—
112C22×Dic5—22no—
113C22×Dic5C2×D411yescharacteristic
114C22×Dic5C2×D411yescharacteristic
115C22×Dic5C2×D411yescharacteristic
116C2×C4×D5—22no—
117C2×C4×D5—22no—
118C2×C4×D5—41no—
119C2×C4×D5—41no—
120C2×C4×D5—41no—
121C2×C4×D5—41no—
122C2×C4×D5C4⋊C414yes—
123C2×C4×D5C4⋊C414yes—
124C2×C4×D5C22×C412yes—
125C2×C4×D5C2×Q812yes—
126C2×C5×C8—22no—
127C2×C5×C8—22no—
128C2×C5×C8C22×C414yes—
129C5×C4⋊C4—22no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—22no—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—42no—
134C5×C4⋊C4—42no—
135C42×C5C22×C412yes—
136C42×C5C2×Q812yes—
137#685—44no—
138#685—42no—
139#685—42no—
140C4⋊Dic5—22no—
141C4⋊Dic5—22no—
142C4⋊Dic5—22no—
143C4⋊Dic5—22no—
144C4⋊Dic5—42no—
145C4⋊Dic5—42no—
146C4×Dic5—44no—
147C4×Dic5—42no—
148C4×Dic5—42no—
149C4×Dic5C4⋊C414yes—
150C4×Dic5C4⋊C414yes—
151C4×Dic5C22×C412yes—
152C4×Dic5C2×Q812yes—
153C2×#168—22no—
154C2×#168—22no—
155C2×#168C22×C414yes—
156C2×#117—52no—
157C22×C42—51no—
158#432—58no—
159C2×#107—52no—
160C2×#107C2×D512yes—
161C2×#106—52no—
162C2×#106C2×D512yes—
163C2×C4⋊C8—52no—
164C2×C22⋊C8—52no—
165C2×#97—51no—
166C2×#97C2×D511yescharacteristic
167#384—51no—
168#384C2×D511yescharacteristic
169#383—101no—
170#382—52no—
171#382—51no—
172#382C2×D511yescharacteristic
173#381—101no—
174#380—51no—
175#380—51no—
176#380—101no—
177#380—101no—
178C4×C4⋊C4—51no—
179C4×C4⋊C4—51no—
180C4×C4⋊C4—101no—
181C4×C4⋊C4—101no—
182C4×C22⋊C4—101no—
183#376—101no—
184#340—52no—
185#340—52no—
186#340—52no—
187#340—52no—
188C23×C5C22×D411yescharacteristic
189C22×D5—21no—
190C22×D5—21no—
191C22×D5—21no—
192C22×D5—21no—
193C22×D5—21no—
194C22×D5—21no—
195C22×D5C2×C4⋊C412yes—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—42no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—42no—
208C2×C4×C5—42no—
209C2×C4×C5C2×C4⋊C412yes—
210C2×C4×C5C2×C4⋊C412yes—
211C2×C4×C5C23×C411yescharacteristic
212C2×C4×C5C22×Q811yescharacteristic
213C2×C4×C5H(5,𝔽2)12yes—
214C2×C4×C52−1+412yes—
215C2×Dic5—21no—
216C2×Dic5—21no—
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—21no—
220C2×Dic5—21no—
221C2×Dic5—42no—
222C2×Dic5—41no—
223C2×Dic5—41no—
224C2×Dic5—41no—
225C2×Dic5—41no—
226C2×Dic5—42no—
227C2×Dic5—42no—
228C2×Dic5—41no—
229C2×Dic5—41no—
230C2×Dic5C2×C4⋊C412yes—
231C2×Dic5C2×C4⋊C412yes—
232C2×Dic5C2×C4⋊C412yes—
233C4×D5—24no—
234C4×D5—24no—
235C4×D5—44no—
236C4×D5—44no—
237C5×C8—24no—
238#168—24no—
239C23×C4—51no—
240C23×C4—51no—
241C23×C4—51no—
242C22×C8—52no—
243C22×C8C22×D512yes—
244#117—202no—
245#117—202no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—52no—
249C2×C4⋊C4—51no—
250C2×C4⋊C4—51no—
251C2×C4⋊C4—101no—
252C2×C4⋊C4—101no—
253C2×C4⋊C4C22×D512yes—
254C2×C4⋊C4C22×D511yescharacteristic
255C2×C4⋊C4C22×D511yescharacteristic
256C2×C22⋊C4—102no—
257C2×C22⋊C4—101no—
258C2×C22⋊C4—101no—
259C2×C42—51no—
260C2×C42—51no—
261C2×C42—51no—
262C2×C42—54no—
263C2×C42—54no—
264C2×C42—102no—
265C2×C42—101no—
266C2×C42—101no—
267C2×C42C22×D511yescharacteristic
268#107—42no—
269#107—202no—
270#106—42no—
271#106—202no—
272C4⋊C8—58no—
273C22⋊C8—58no—
274#97—54no—
275#97C4×D514yes—
276#95—21no—
277#95—21no—
278#95—101no—
279#95—101no—
280#95—101no—
281#95—101no—
282#95—102no—
283#95—102no—
284#95—101no—
285#95—101no—
286C22×C5C22×C4⋊C411yescharacteristic
287C22×C5#53511yescharacteristic
288C22×C5#53611yescharacteristic
289C22×C5#57511yescharacteristic
290C22×C5#57511yescharacteristic
291C22×C5#57511yescharacteristic
292C22×C5#57511yescharacteristic
293C2×D5—22no—
294C2×D5—22no—
295C2×D5—22no—
296C2×D5—41no—
297C2×D5—41no—
298C2×D5—41no—
299C2×D5—41no—
300C4×C5—22no—
301C4×C5—22no—
302C4×C5—82no—
303C4×C5—81no—
304C4×C5—81no—
305C4×C5#52012yes—
306C4×C5#54412yes—
307Dic5—22no—
308Dic5—22no—
309Dic5—22no—
310Dic5—82no—
311Dic5—81no—
312Dic5—81no—
313C24—51no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—52no—
321C22×C4—52no—
322C22×C4—54no—
323C22×C4—54no—
324C22×C4—102no—
325C22×C4—102no—
326C22×C4—101no—
327C22×C4—101no—
328C22×C4—102no—
329C22×C4—201no—
330C22×C4—201no—
331C22×C4—201no—
332C22×C4—201no—
333C22×C4D4×D511yescharacteristic
334C22×C4D4×D511yescharacteristic
335C22×C4C23×D511yescharacteristic
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—54no—
339C2×C8—102no—
340C2×C8—102no—
341C2×C8C2×C4×D514yes—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—102no—
349C4⋊C4—102no—
350C4⋊C4—102no—
351C4⋊C4—102no—
352C4⋊C4—202no—
353C4⋊C4—202no—
354C22⋊C4—204no—
355C22⋊C4—202no—
356C22⋊C4—202no—
357C42—52no—
358C42—52no—
359C42—54no—
360C42—54no—
361C42—204no—
362C42—202no—
363C42—202no—
364C42C2×C4×D512yes—
365C42Q8×D512yes—
366C2×C5#231711yescharacteristic
367C2×C5#291111yescharacteristic
368C2×C5#291111yescharacteristic
369C2×C5#321911yescharacteristic
370C2×C5#321911yescharacteristic
371C2×C5#324011yescharacteristic
372C2×C5#324011yescharacteristic
373D5—42no—
374C23—52no—
375C23—101no—
376C23—101no—
377C23—101no—
378C23—101no—
379C23—101no—
380C23—101no—
381C23C2×D4×D511yescharacteristic
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—52no—
396C2×C4—52no—
397C2×C4—52no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—104no—
405C2×C4—104no—
406C2×C4—204no—
407C2×C4—204no—
408C2×C4—202no—
409C2×C4—201no—
410C2×C4—201no—
411C2×C4—201no—
412C2×C4—201no—
413C2×C4—201no—
414C2×C4—201no—
415C2×C4—202no—
416C2×C4—202no—
417C2×C4D5×C4⋊C412yes—
418C2×C4D5×C4⋊C412yes—
419C2×C4C22×C4×D511yescharacteristic
420C2×C4#414412yes—
421C2×C4C2×Q8×D511yescharacteristic
422C2×C4#414712yes—
423C8—24no—
424C8—104no—
425C5#2198911yescharacteristic, complemented, Sylow
426C22—102no—
427C22—102no—
428C22—102no—
429C22—201no—
430C22—201no—
431C22—201no—
432C22—201no—
433C22C2×D5×C4⋊C411yescharacteristic
434C22#6604911yescharacteristic
435C22#6605811yescharacteristic
436C22#6610711yescharacteristic
437C22#6610711yescharacteristic
438C22#6611111yescharacteristic
439C22#6611111yescharacteristic
440C4—22no—
441C4—22no—
442C4—82no—
443C4—81no—
444C4—81no—
445C4—102no—
446C4—102no—
447C4—102no—
448C4—402no—
449C4—401no—
450C4—401no—
451C4#6583812yes—
452C4#6606312yes—
453C2—202no—
454C2#1060609011yescharacteristic
455C2#1061093911yescharacteristic
456C2#1061093911yescharacteristic
457C2#1061358311yescharacteristic
458C2#1061360811yescharacteristic
459C2#1061371511yescharacteristic
460C2#1061371611yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1847C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1847D5
hypocenterC5#21989
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. C5×#1847C2semidirect
6. #10601409C2semidirect
8. #10601357C2semidirect
9. #10600608C2semidirect
10. #10600368C2semidirect
11. #10600343C2semidirect
35. #64994C4semidirect
100. #1847D5semidirect
425. C5#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#649942
#106060492
#106058782
C5×#18472
#106014262
#106014092
#106013732
#106013572
#106006082
#106003682
#106003432
#219895