Finite Group Databasebeta

← #12109682

Subgroups — #12109682

Order 1280.

862 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊C8C211yesmaximal, characteristic
2#10606049C211yesmaximal, characteristic
3#10605483C211yesmaximal, characteristic
4C5×#1948C211yesmaximal, characteristic, complemented
5#10601370C212yesmaximal
6#10601357C212yesmaximal, complemented
7#10601247C211yesmaximal, characteristic, complemented
8#10600360C211yesmaximal, characteristic, complemented
9#10600259C211yesmaximal, characteristic, complemented
10#10599662C212yesmaximal
11#10599590C212yesmaximal, complemented
12C22×C8×D5C2212yes—
13C2×#4038—21no—
14C2×C42×D5C2211yescharacteristic
15C2×C5×#106C2212yes—
16C2×C5×C4⋊C8C2211yescharacteristic
17C5×#384C2211yescharacteristic
18C4×C5×C4⋊C4C2211yescharacteristic
19C2×#3949C2212yes—
20C2×#3946C2212yes—
21#65276—21no—
22#65276C2211yescharacteristic
23#65276C2212yes—
24#65276C2211yescharacteristic
25#65266—21no—
26#65266C2211yescharacteristic
27#65266C2211yescharacteristic
28C4⋊C4×Dic5—21no—
29C4⋊C4×Dic5C2212yes—
30C2×#3939C2212yes—
31C2×#3939C2212yes—
32C4×#685—21no—
33#65224C2211yescharacteristic
34C4×C4⋊Dic5C2211yescharacteristic
35#65221—21no—
36C2×C4⋊#168C2211yescharacteristic
37D5×C4⋊C8C418yescomplemented
38#64953—21no—
39#64940—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21962—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×C5—21no—
55C2×C42×C5C2311yescharacteristic
56C2×#685—22no—
57C2×#685—21no—
58C2×#685—21no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5C2311yescharacteristic
62C2×C4⋊Dic5C2312yes—
63C2×C4⋊Dic5C2311yescharacteristic
64C2×C4×Dic5—21no—
65C2×C4×Dic5—22no—
66C2×C4×Dic5D411yescharacteristic
67C2×C4×Dic5D411yescharacteristic
68C2×C4×Dic5C2311yescharacteristic
69C22×#168C2312yes—
70C2×C8×D5—42no—
71C2×C8×D5—42no—
72C2×C8×D5C2×C418yes—
73#4038—44no—
74C42×D5C2×C414yes—
75C42×D5Q814yes—
76C5×#106—42no—
77C5×C4⋊C8C2×C414yes—
78C5×#95—21no—
79#3963—21no—
80#3963—21no—
81#3963—21no—
82#3963—21no—
83#3963—21no—
84#3963—21no—
85#3963—21no—
86#3963—22no—
87#3963—22no—
88#3949—42no—
89#3946C2×C418yes—
90#3939—42no—
91#3939—42no—
92C4⋊#168C2×C414yes—
93C22×C4⋊C8—51no—
94#2285—51no—
95#2283—51no—
96#1949—52no—
97#1949—52no—
98#1948—51no—
99#1948D511yescharacteristic, complemented
100#1947—51no—
101#1947—51no—
102#1808—52no—
103#1807—52no—
104C23×D5C2×D411yescharacteristic
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2411yescharacteristic
111C22×Dic5—21no—
112C22×Dic5—21no—
113C22×Dic5—22no—
114C22×Dic5C2×D411yescharacteristic
115C22×Dic5C2×D411yescharacteristic
116C22×Dic5C2×D411yescharacteristic
117C2×C4×D5—22no—
118C2×C4×D5—22no—
119C2×C4×D5—22no—
120C2×C4×D5—22no—
121C2×C4×D5—21no—
122C2×C4×D5—21no—
123C2×C4×D5—21no—
124C2×C4×D5—21no—
125C2×C4×D5C4⋊C414yes—
126C2×C4×D5C4⋊C414yes—
127C2×C4×D5C22×C412yes—
128C2×C4×D5C2×Q812yes—
129C2×C5×C8—22no—
130C2×C5×C8—22no—
131C2×C5×C8C22×C414yes—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—22no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—42no—
139C5×C4⋊C4—42no—
140C42×C5—42no—
141C42×C5C22×C412yes—
142C42×C5C2×Q812yes—
143#685—44no—
144#685—42no—
145#685—42no—
146C4⋊Dic5—21no—
147C4⋊Dic5—22no—
148C4⋊Dic5—21no—
149C4⋊Dic5—22no—
150C4⋊Dic5—21no—
151C4⋊Dic5—21no—
152C4⋊Dic5—42no—
153C4⋊Dic5—42no—
154C4×Dic5—44no—
155C4×Dic5—42no—
156C4×Dic5C4⋊C414yes—
157C4×Dic5C4⋊C414yes—
158C4×Dic5C22×C412yes—
159C4×Dic5C2×Q812yes—
160C2×#168—22no—
161C2×#168—22no—
162C2×#168C22×C414yes—
163C8×D5—48no—
164C23×C8—52no—
165C2×#117—101no—
166C22×C42—51no—
167C2×#107—52no—
168C2×#107—52no—
169C2×#106—52no—
170C2×#106C2×D512yes—
171C2×C4⋊C8—52no—
172C2×C4⋊C8—51no—
173C2×C4⋊C8—58no—
174C2×C4⋊C8C2×D511yescharacteristic
175#384—51no—
176#384C2×D511yescharacteristic
177#383—101no—
178#382—51no—
179#382—51no—
180#382—101no—
181#381—101no—
182#380—51no—
183#380—52no—
184#380—51no—
185#380—101no—
186C4×C4⋊C4—52no—
187C4×C4⋊C4—51no—
188C4×C4⋊C4—101no—
189C4×C4⋊C4C2×D511yescharacteristic
190C4×C22⋊C4—101no—
191#376—101no—
192#340—52no—
193#340—52no—
194#340—52no—
195#340C2×D512yes—
196C23×C5C22×D411yescharacteristic
197C22×D5—21no—
198C22×D5—21no—
199C22×D5—21no—
200C22×D5—21no—
201C22×D5C2×C4⋊C412yes—
202C22×D5AGL(1,ℤ/8)12yes—
203C22×D5#13712yes—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—42no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5C2×C4⋊C412yes—
216C2×C4×C5C2×C4⋊C412yes—
217C2×C4×C5#13512yes—
218C2×C4×C5#13512yes—
219C2×C4×C5C23×C411yescharacteristic
220C2×C4×C5C22×Q811yescharacteristic
221C2×C4×C5H(5,𝔽2)11yescharacteristic
222C2×C4×C5H(5,𝔽2)11yescharacteristic
223C2×C4×C52−1+411yescharacteristic
224C2×C4×C52−1+411yescharacteristic
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—41no—
232C2×Dic5—42no—
233C2×Dic5—41no—
234C2×Dic5—41no—
235C2×Dic5—41no—
236C2×Dic5—42no—
237C2×Dic5—42no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5C2×C4⋊C412yes—
241C2×Dic5C2×C4⋊C412yes—
242C2×Dic5C2×C4⋊C412yes—
243C4×D5—28no—
244C4×D5—22no—
245C4×D5—22no—
246C4×D5—22no—
247C4×D5—22no—
248C4×D5—28no—
249C5×C8—24no—
250#168—24no—
251C23×C4—51no—
252C23×C4—51no—
253C23×C4—51no—
254C22×C8—52no—
255C22×C8—58no—
256C22×C8—202no—
257C22×C8—202no—
258C22×C8C22×D512yes—
259#117—204no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—51no—
264C2×C4⋊C4—52no—
265C2×C4⋊C4—101no—
266C2×C4⋊C4—101no—
267C2×C4⋊C4C22×D511yescharacteristic
268C2×C4⋊C4C22×D512yes—
269C2×C4⋊C4C22×D511yescharacteristic
270C2×C22⋊C4—102no—
271C2×C22⋊C4—101no—
272C2×C22⋊C4—101no—
273C2×C42—21no—
274C2×C42—51no—
275C2×C42—51no—
276C2×C42—51no—
277C2×C42—54no—
278C2×C42—54no—
279C2×C42—102no—
280C2×C42—101no—
281C2×C42C22×D511yescharacteristic
282#107—202no—
283#107—202no—
284#106—42no—
285#106—202no—
286C4⋊C8—58no—
287C4⋊C8—54no—
288C4⋊C8C4×D514yes—
289#95—21no—
290#95—101no—
291#95—101no—
292#95—101no—
293#95—101no—
294#95—101no—
295#95—101no—
296#95—102no—
297#95—102no—
298#95—101no—
299C22×C5C22×C4⋊C411yescharacteristic
300C22×C5#53711yescharacteristic
301C22×C5#53711yescharacteristic
302C22×C5C2×#13511yescharacteristic
303C22×C5C2×#13511yescharacteristic
304C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C5C2×#13711yescharacteristic
306C2×D5—22no—
307C2×D5—22no—
308C2×D5—22no—
309C2×D5—22no—
310C2×D5—22no—
311C2×D5—22no—
312C2×D5#42814yes—
313C4×C5—22no—
314C4×C5—81no—
315C4×C5—82no—
316C4×C5—81no—
317C4×C5#42714yes—
318C4×C5#51811yescharacteristic
319C4×C5#51911yescharacteristic
320C4×C5#54411yescharacteristic
321C4×C5#54411yescharacteristic
322Dic5—22no—
323Dic5—22no—
324Dic5—22no—
325Dic5—82no—
326Dic5—81no—
327Dic5—81no—
328C24—51no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—52no—
336C22×C4—52no—
337C22×C4—54no—
338C22×C4—54no—
339C22×C4—102no—
340C22×C4—102no—
341C22×C4—101no—
342C22×C4—101no—
343C22×C4—101no—
344C22×C4—101no—
345C22×C4—102no—
346C22×C4—102no—
347C22×C4—101no—
348C22×C4—101no—
349C22×C4—102no—
350C22×C4D4×D511yescharacteristic
351C22×C4D4×D511yescharacteristic
352C22×C4C23×D511yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—54no—
356C2×C8—102no—
357C2×C8—102no—
358C2×C8—208no—
359C2×C8C2×C4×D514yes—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4—102no—
371C4⋊C4—101no—
372C4⋊C4—102no—
373C4⋊C4—101no—
374C4⋊C4—202no—
375C4⋊C4—202no—
376C22⋊C4—204no—
377C22⋊C4—202no—
378C22⋊C4—202no—
379C42—42no—
380C42—52no—
381C42—52no—
382C42—54no—
383C42—54no—
384C42—204no—
385C42—202no—
386C42C2×C4×D512yes—
387C42Q8×D512yes—
388C2×C5#231611yescharacteristic
389C2×C5C2×#42711yescharacteristic
390C2×C5C2×#42811yescharacteristic
391C2×C5#324711yescharacteristic
392C2×C5#324711yescharacteristic
393C2×C5#324811yescharacteristic
394C2×C5#324811yescharacteristic
395D5—24no—
396C23—52no—
397C23—52no—
398C23—52no—
399C23—101no—
400C23—101no—
401C23—101no—
402C23—101no—
403C23C2×D4×D511yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—52no—
416C2×C4—52no—
417C2×C4—52no—
418C2×C4—108no—
419C2×C4—101no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—101no—
423C2×C4—101no—
424C2×C4—101no—
425C2×C4—102no—
426C2×C4—102no—
427C2×C4—102no—
428C2×C4—108no—
429C2×C4—102no—
430C2×C4—201no—
431C2×C4—201no—
432C2×C4—202no—
433C2×C4—202no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4—202no—
439C2×C4D5×C4⋊C412yes—
440C2×C4D5×C4⋊C412yes—
441C2×C4#406212yes—
442C2×C4#406212yes—
443C2×C4C22×C4×D511yescharacteristic
444C2×C4#414411yescharacteristic
445C2×C4C2×Q8×D511yescharacteristic
446C2×C4#414711yescharacteristic
447C2×C4#414911yescharacteristic
448C2×C4#415011yescharacteristic
449C8—24no—
450C8—104no—
451C5#2196211yescharacteristic, complemented, Sylow
452C22—54no—
453C22—102no—
454C22—102no—
455C22—102no—
456C22—102no—
457C22—102no—
458C22—102no—
459C22C2×D5×C4⋊C411yescharacteristic
460C22#6594211yescharacteristic
461C22#6596311yescharacteristic
462C22C2×#406211yescharacteristic
463C22C2×#406211yescharacteristic
464C22D5×AGL(1,ℤ/8)11yescharacteristic
465C22D5×#13711yescharacteristic
466C4—22no—
467C4—81no—
468C4—82no—
469C4—81no—
470C4—102no—
471C4—102no—
472C4—102no—
473C4—401no—
474C4—402no—
475C4—401no—
476C4#6514914yes—
477C4#6587911yescharacteristic
478C4#6590611yescharacteristic
479C4#6602311yescharacteristic
480C4#6606311yescharacteristic
481C2—104no—
482C2#1060792611yescharacteristic
483C2C2×#6514911yescharacteristic
484C2D5×#42811yescharacteristic
485C2#1061213211yescharacteristic
486C2#1061217011yescharacteristic
487C2#1061276511yescharacteristic
488C2#1061280211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1948C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1948D5
hypocenterC5#21962
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. C5×#1948C2semidirect
6. #10601357C2semidirect
7. #10601247C2semidirect
8. #10600360C2semidirect
9. #10600259C2semidirect
11. #10599590C2semidirect
37. D5×C4⋊C8C4semidirect
99. #1948D5semidirect
451. C5#21962semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊C82
#106060492
#106054832
C5×#19482
#106013702
#106013572
#106012472
#106003602
#106002592
#105996622
#105995902
#219625