Finite Group Databasebeta

← #12104183

Subgroups — #12104183

Order 1280.

894 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65124C211yesmaximal, characteristic
2#10606049C211yesmaximal, characteristic
3C4×#4038C211yesmaximal, characteristic
4C5×#1948C211yesmaximal, characteristic, complemented
5#10601373C212yesmaximal
6#10601346C212yesmaximal, complemented
7#10601246C211yesmaximal, characteristic, complemented
8#10600360C211yesmaximal, characteristic, complemented
9#10600260C211yesmaximal, characteristic, complemented
10#10599670C212yesmaximal
11#10599579C212yesmaximal, complemented
12C2×#4038—21no—
13C2×#4038C2211yescharacteristic
14C2×#4038C2211yescharacteristic
15C2×C42×D5C2211yescharacteristic
16C2×C5×#106C2212yes—
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#384C2211yescharacteristic
19C4×C5×C4⋊C4C2211yescharacteristic
20C2×#3952C2212yes—
21C2×#3950C2212yes—
22C2×#3947C2212yes—
23#65276—21no—
24#65276C2212yes—
25#65266—21no—
26C4⋊C4×Dic5—21no—
27C4⋊C4×Dic5C2211yescharacteristic
28C4⋊C4×Dic5C2211yescharacteristic
29C4⋊C4×Dic5C2212yes—
30C2×#3940C2212yes—
31C2×#3939C2212yes—
32C4×#685—21no—
33#65224C2211yescharacteristic
34C4×C4⋊Dic5C2211yescharacteristic
35C42×Dic5—21no—
36C2×C4⋊#168C2211yescharacteristic
37#65124C418yescomplemented
38#64955—21no—
39#64937—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21364—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⋊C4C2312yes—
52C2×C5×C4⋊C4C2311yescharacteristic
53C2×C5×C4⋊C4C2311yescharacteristic
54C2×C42×C5—21no—
55C2×C42×C5C2311yescharacteristic
56C2×#685—21no—
57C2×#685—21no—
58C2×#685—22no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5C2312yes—
62C2×C4⋊Dic5C2311yescharacteristic
63C2×C4⋊Dic5C2311yescharacteristic
64C2×C4×Dic5—21no—
65C2×C4×Dic5—21no—
66C2×C4×Dic5—21no—
67C2×C4×Dic5—22no—
68C2×C4×Dic5—21no—
69C2×C4×Dic5—21no—
70C2×C4×Dic5D411yescharacteristic
71C2×C4×Dic5D411yescharacteristic
72C2×C4×Dic5C2311yescharacteristic
73C22×#168C2312yes—
74#4038—22no—
75#4038—22no—
76#4038—22no—
77#4038—22no—
78#4038—44no—
79C42×D5C2×C414yes—
80C42×D5Q814yes—
81C5×#106—24no—
82C5×C4⋊C8C2×C414yes—
83C5×#95—21no—
84#3963—21no—
85#3963—21no—
86#3963—21no—
87#3963—22no—
88#3963—22no—
89#3952C2×C418yes—
90#3950—24no—
91#3947C2×C418yes—
92#3940—24no—
93#3939—24no—
94C4⋊#168C2×C414yes—
95C2×#432—51no—
96#2285—51no—
97C4×#117—51no—
98#1948—51no—
99#1948D511yescharacteristic, complemented
100#1947—51no—
101#1947—51no—
102#1854—52no—
103#1854—52no—
104#1776—52no—
105#1776—52no—
106C23×D5C2×D411yescharacteristic
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—22no—
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2411yescharacteristic
113C22×Dic5—21no—
114C22×Dic5—21no—
115C22×Dic5—22no—
116C22×Dic5C2×D411yescharacteristic
117C22×Dic5C2×D411yescharacteristic
118C22×Dic5C2×D411yescharacteristic
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×D5—41no—
126C2×C4×D5—41no—
127C2×C4×D5C4⋊C414yes—
128C2×C4×D5C4⋊C414yes—
129C2×C4×D5C22×C412yes—
130C2×C4×D5C2×Q812yes—
131C2×C5×C8—22no—
132C2×C5×C8—22no—
133C2×C5×C8C22×C414yes—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—22no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—42no—
139C5×C4⋊C4—42no—
140C5×C4⋊C4#4112yes—
141C5×C4⋊C4#4112yes—
142C42×C5—42no—
143C42×C5C22×C412yes—
144C42×C5C2×Q812yes—
145#685—24no—
146#685—24no—
147#685—44no—
148C4⋊Dic5—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5—22no—
151C4⋊Dic5—22no—
152C4⋊Dic5—42no—
153C4⋊Dic5—42no—
154C4⋊Dic5#4112yes—
155C4⋊Dic5#4112yes—
156C4×Dic5—24no—
157C4×Dic5—24no—
158C4×Dic5—44no—
159C4×Dic5—42no—
160C4×Dic5—42no—
161C4×Dic5—42no—
162C4×Dic5C4⋊C414yes—
163C4×Dic5C4⋊C414yes—
164C4×Dic5C22×C412yes—
165C4×Dic5C2×Q812yes—
166C2×#168—22no—
167C2×#168—22no—
168C2×#168C22×C414yes—
169C2×#117—51no—
170C2×#117—51no—
171C2×#117—101no—
172C22×C42—51no—
173#432—58no—
174C2×#107—52no—
175C2×#107—52no—
176C2×#106—52no—
177C2×#106C2×D512yes—
178C2×C4⋊C8—51no—
179C2×C4⋊C8C2×D511yescharacteristic
180C2×C22⋊C8—52no—
181C2×#97—52no—
182#384—51no—
183#384C2×D511yescharacteristic
184#382—101no—
185#380—52no—
186#380—101no—
187C4×C4⋊C4—51no—
188C4×C4⋊C4—51no—
189C4×C4⋊C4—52no—
190C4×C4⋊C4—51no—
191C4×C4⋊C4—101no—
192C4×C4⋊C4C2×D511yescharacteristic
193C4×C22⋊C4—101no—
194C4×C22⋊C4—101no—
195#376—101no—
196C43—101no—
197#340—52no—
198#340—52no—
199#340—52no—
200#340C2×D512yes—
201C23×C5C22×D411yescharacteristic
202C22×D5—21no—
203C22×D5—21no—
204C22×D5—21no—
205C22×D5—21no—
206C22×D5—21no—
207C22×D5—21no—
208C22×D5C2×C4⋊C412yes—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—22no—
212C2×C4×C5—22no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—42no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5C2×C4⋊C412yes—
221C2×C4×C5C2×C4⋊C412yes—
222C2×C4×C5AGL(1,ℤ/8)12yes—
223C2×C4×C5#13712yes—
224C2×C4×C5C23×C411yescharacteristic
225C2×C4×C5C22×Q811yescharacteristic
226C2×C4×C5C2×#4111yescharacteristic
227C2×C4×C5C2×#4111yescharacteristic
228C2×C4×C5C2×#4111yescharacteristic
229C2×C4×C5C2×#4111yescharacteristic
230C2×Dic5—21no—
231C2×Dic5—21no—
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—22no—
237C2×Dic5—22no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5—42no—
243C2×Dic5—42no—
244C2×Dic5—42no—
245C2×Dic5C2×C4⋊C412yes—
246C2×Dic5C2×C4⋊C412yes—
247C2×Dic5C2×C4⋊C412yes—
248C4×D5—22no—
249C4×D5—22no—
250C4×D5—22no—
251C4×D5—22no—
252C4×D5—28no—
253C4×D5—44no—
254C5×C8—24no—
255#168—24no—
256C23×C4—51no—
257C23×C4—51no—
258C23×C4—51no—
259C22×C8—52no—
260C22×C8C22×D512yes—
261#117—102no—
262#117—102no—
263#117—102no—
264#117—102no—
265#117—204no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—51no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—52no—
271C2×C4⋊C4—101no—
272C2×C4⋊C4—101no—
273C2×C4⋊C4C22×D512yes—
274C2×C4⋊C4C22×D511yescharacteristic
275C2×C4⋊C4C22×D511yescharacteristic
276C2×C22⋊C4—101no—
277C2×C22⋊C4—101no—
278C2×C22⋊C4—102no—
279C2×C42—21no—
280C2×C42—51no—
281C2×C42—51no—
282C2×C42—51no—
283C2×C42—54no—
284C2×C42—54no—
285C2×C42—101no—
286C2×C42—101no—
287C2×C42—102no—
288C2×C42—101no—
289C2×C42—101no—
290C2×C42—101no—
291C2×C42C22×D511yescharacteristic
292#107—104no—
293#107—104no—
294#106—24no—
295#106—104no—
296C4⋊C8—54no—
297C4⋊C8C4×D514yes—
298C22⋊C8—58no—
299#97—58no—
300#95—21no—
301#95—101no—
302#95—101no—
303#95—102no—
304#95—102no—
305#95—101no—
306C22×C5C22×C4⋊C411yescharacteristic
307C22×C5#52511yescharacteristic
308C22×C5#52511yescharacteristic
309C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C5C2×#13711yescharacteristic
311C22×C5#57511yescharacteristic
312C22×C5#57511yescharacteristic
313C2×D5—22no—
314C2×D5—22no—
315C2×D5—22no—
316C2×D5—41no—
317C2×D5—41no—
318C2×D5—41no—
319C2×D5—41no—
320C4×C5—22no—
321C4×C5—42no—
322C4×C5—42no—
323C4×C5—82no—
324C4×C5#42814yes—
325C4×C5C4×#4111yescharacteristic
326C4×C5C4×#4111yescharacteristic
327C4×C5#53311yescharacteristic
328C4×C5#53311yescharacteristic
329Dic5—22no—
330Dic5—22no—
331Dic5—22no—
332Dic5—42no—
333Dic5—42no—
334Dic5—82no—
335C24—51no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—51no—
340C22×C4—51no—
341C22×C4—51no—
342C22×C4—52no—
343C22×C4—52no—
344C22×C4—54no—
345C22×C4—54no—
346C22×C4—101no—
347C22×C4—101no—
348C22×C4—101no—
349C22×C4—101no—
350C22×C4—102no—
351C22×C4—102no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4—102no—
355C22×C4—201no—
356C22×C4—201no—
357C22×C4D4×D511yescharacteristic
358C22×C4D4×D511yescharacteristic
359C22×C4C23×D511yescharacteristic
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—54no—
363C2×C8—102no—
364C2×C8—102no—
365C2×C8C2×C4×D514yes—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—52no—
373C4⋊C4—52no—
374C4⋊C4—101no—
375C4⋊C4—101no—
376C4⋊C4—102no—
377C4⋊C4—102no—
378C4⋊C4—202no—
379C4⋊C4—202no—
380C4⋊C4#71112yes—
381C4⋊C4#71312yes—
382C22⋊C4—104no—
383C22⋊C4—104no—
384C22⋊C4—204no—
385C42—42no—
386C42—52no—
387C42—52no—
388C42—54no—
389C42—54no—
390C42—104no—
391C42—104no—
392C42—204no—
393C42—202no—
394C42—202no—
395C42—202no—
396C42C2×C4×D512yes—
397C42Q8×D512yes—
398C2×C5#229611yescharacteristic
399C2×C5C2×#42811yescharacteristic
400C2×C5#291111yescharacteristic
401C2×C5#311511yescharacteristic
402C2×C5#311511yescharacteristic
403C2×C5#311611yescharacteristic
404C2×C5#311611yescharacteristic
405D5—42no—
406C23—52no—
407C23—101no—
408C23—101no—
409C23—101no—
410C23—101no—
411C23—101no—
412C23—101no—
413C23C2×D4×D511yescharacteristic
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—52no—
426C2×C4—52no—
427C2×C4—52no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—102no—
435C2×C4—102no—
436C2×C4—102no—
437C2×C4—108no—
438C2×C4—102no—
439C2×C4—102no—
440C2×C4—102no—
441C2×C4—204no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—201no—
446C2×C4—202no—
447C2×C4—202no—
448C2×C4—202no—
449C2×C4D5×C4⋊C412yes—
450C2×C4D5×C4⋊C412yes—
451C2×C4#406012yes—
452C2×C4#406112yes—
453C2×C4C22×C4×D511yescharacteristic
454C2×C4C2×#71111yescharacteristic
455C2×C4C2×Q8×D511yescharacteristic
456C2×C4C2×#71311yescharacteristic
457C2×C4D5×#4111yescharacteristic
458C2×C4D5×#4111yescharacteristic
459C8—24no—
460C8—104no—
461C5#2136411yescharacteristic, complemented, Sylow
462C22—102no—
463C22—102no—
464C22—102no—
465C22—201no—
466C22—201no—
467C22—201no—
468C22—201no—
469C22C2×D5×C4⋊C411yescharacteristic
470C22#6594011yescharacteristic
471C22#6596111yescharacteristic
472C22C2×#406011yescharacteristic
473C22C2×#406111yescharacteristic
474C22#6610711yescharacteristic
475C22#6611111yescharacteristic
476C4—22no—
477C4—42no—
478C4—42no—
479C4—82no—
480C4—102no—
481C4—102no—
482C4—102no—
483C4—202no—
484C4—202no—
485C4—402no—
486C4#6515014yes—
487C4C4×#71111yescharacteristic
488C4C4×#71311yescharacteristic
489C4#6602211yescharacteristic
490C4#6606211yescharacteristic
491C2—202no—
492C2#1060769411yescharacteristic
493C2C2×#6515011yescharacteristic
494C2#1061093911yescharacteristic
495C2#1061209411yescharacteristic
496C2#1061214211yescharacteristic
497C2#1061273011yescharacteristic
498C2#1061277811yescharacteristic
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#21364
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. #10601346C2semidirect
7. #10601246C2semidirect
8. #10600360C2semidirect
9. #10600260C2semidirect
11. #10599579C2semidirect
37. #65124C4semidirect
99. #1948D5semidirect
461. C5#21364semidirect

Maximal subgroups

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

subgroupindex
C2×#651242
#106060492
C4×#40382
C5×#19482
#106013732
#106013462
#106012462
#106003602
#106002602
#105996702
#105995792
#213645