Finite Group Databasebeta

← #12109846

Subgroups — #12109846

Order 1280.

806 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65122C211yesmaximal, characteristic
2#10606049C211yesmaximal, characteristic
3#10605483C211yesmaximal, characteristic
4C5×#1947C211yesmaximal, characteristic, complemented
5#10601426C212yesmaximal
6#10601400C212yesmaximal, complemented
7#10601246C211yesmaximal, characteristic, complemented
8#10600361C211yesmaximal, characteristic, complemented
9#10600260C211yesmaximal, characteristic, complemented
10#10599670C212yesmaximal
11#10599641C212yesmaximal, complemented
12C2×#4038C2212yes—
13C2×C42×D5C2211yescharacteristic
14C2×C5×#107C2212yes—
15C2×C5×C4⋊C8C2211yescharacteristic
16C5×#384C2211yescharacteristic
17C4×C5×C4⋊C4C2211yescharacteristic
18C2×#3952C2212yes—
19C2×#3950C2212yes—
20C2×C8×Dic5C2212yes—
21#65276—21no—
22#65276—21no—
23#65276C2211yescharacteristic
24#65276C2211yescharacteristic
25#65266C2211yescharacteristic
26#65266C2211yescharacteristic
27#65266C2212yes—
28C4⋊C4×Dic5—21no—
29C4⋊C4×Dic5—21no—
30C2×#3940C2212yes—
31C2×#3940C2212yes—
32C4×#685—21no—
33#65224C2211yescharacteristic
34C4×C4⋊Dic5C2211yescharacteristic
35#65221—21no—
36C2×C4⋊#168C2211yescharacteristic
37#65122C418yescomplemented
38#64953—21no—
39#64940—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21985—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—
70#4038—42no—
71#4038—42no—
72C42×D5C2×C414yes—
73C42×D5Q814yes—
74C5×#107—42no—
75C5×C4⋊C8C2×C414yes—
76C5×#95—21no—
77#3963—21no—
78#3963—21no—
79#3963—21no—
80#3963—21no—
81#3963—21no—
82#3963—21no—
83#3963—21no—
84#3963—22no—
85#3963—22no—
86#3952C2×C418yes—
87#3950—42no—
88C8×Dic5C2×C418yes—
89#3940—42no—
90#3940—42no—
91C4⋊#168C2×C414yes—
92C2×#431—51no—
93#2285—51no—
94#2283—51no—
95#1948—51no—
96#1948—51no—
97#1947—51no—
98#1947D511yescharacteristic, complemented
99#1854—52no—
100#1854—52no—
101#1846—52no—
102#1835—52no—
103C23×D5C2×D411yescharacteristic
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—22no—
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—21no—
119C2×C4×D5—21no—
120C2×C4×D5—21no—
121C2×C4×D5—21no—
122C2×C4×D5—41no—
123C2×C4×D5—41no—
124C2×C4×D5C4⋊C414yes—
125C2×C4×D5C4⋊C414yes—
126C2×C4×D5C22×C412yes—
127C2×C4×D5C2×Q812yes—
128C2×C5×C8—22no—
129C2×C5×C8—22no—
130C2×C5×C8C22×C414yes—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—42no—
138C5×C4⋊C4—42no—
139C42×C5—42no—
140C42×C5C22×C412yes—
141C42×C5C2×Q812yes—
142#685—44no—
143#685—42no—
144#685—42no—
145C4⋊Dic5—21no—
146C4⋊Dic5—22no—
147C4⋊Dic5—21no—
148C4⋊Dic5—22no—
149C4⋊Dic5—21no—
150C4⋊Dic5—21no—
151C4⋊Dic5—42no—
152C4⋊Dic5—42no—
153C4×Dic5—44no—
154C4×Dic5—42no—
155C4×Dic5C4⋊C414yes—
156C4×Dic5C4⋊C414yes—
157C4×Dic5C22×C412yes—
158C4×Dic5C2×Q812yes—
159C2×#168—22no—
160C2×#168—22no—
161C2×#168C22×C414yes—
162C2×#117—52no—
163C22×C42—51no—
164#431—58no—
165C2×#107—52no—
166C2×#107C2×D512yes—
167C2×#106—52no—
168C2×#106—52no—
169C2×C4⋊C8—51no—
170C2×C4⋊C8C2×D511yescharacteristic
171C2×C22⋊C8—52no—
172C2×C4×C8—52no—
173#384—51no—
174#384C2×D511yescharacteristic
175#383—101no—
176#382—51no—
177#382—52no—
178#382—51no—
179#381—101no—
180#380—51no—
181#380—51no—
182#380—101no—
183#380—101no—
184C4×C4⋊C4—51no—
185C4×C4⋊C4—101no—
186C4×C4⋊C4—101no—
187C4×C4⋊C4C2×D511yescharacteristic
188C4×C22⋊C4—101no—
189#376—101no—
190#340—52no—
191#340—52no—
192#340—52no—
193#340C2×D512yes—
194C23×C5C22×D411yescharacteristic
195C22×D5—21no—
196C22×D5—21no—
197C22×D5—21no—
198C22×D5—21no—
199C22×D5—21no—
200C22×D5—21no—
201C22×D5C2×C4⋊C412yes—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—42no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—42no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—42no—
213C2×C4×C5C2×C4⋊C412yes—
214C2×C4×C5C2×C4⋊C412yes—
215C2×C4×C5#13512yes—
216C2×C4×C5#13512yes—
217C2×C4×C5C23×C411yescharacteristic
218C2×C4×C5C22×Q811yescharacteristic
219C2×C4×C5H(5,𝔽2)11yescharacteristic
220C2×C4×C5H(5,𝔽2)11yescharacteristic
221C2×C4×C52−1+411yescharacteristic
222C2×C4×C52−1+411yescharacteristic
223C2×Dic5—21no—
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—42no—
230C2×Dic5—41no—
231C2×Dic5—41no—
232C2×Dic5—41no—
233C2×Dic5—41no—
234C2×Dic5—42no—
235C2×Dic5—42no—
236C2×Dic5—41no—
237C2×Dic5—41no—
238C2×Dic5C2×C4⋊C412yes—
239C2×Dic5C2×C4⋊C412yes—
240C2×Dic5C2×C4⋊C412yes—
241C4×D5—22no—
242C4×D5—22no—
243C4×D5—22no—
244C4×D5—22no—
245C4×D5—28no—
246C4×D5—44no—
247C5×C8—24no—
248#168—24no—
249C23×C4—51no—
250C23×C4—51no—
251C23×C4—51no—
252C22×C8—52no—
253C22×C8C22×D512yes—
254#117—202no—
255#117—202no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—52no—
259C2×C4⋊C4—51no—
260C2×C4⋊C4—51no—
261C2×C4⋊C4—101no—
262C2×C4⋊C4—101no—
263C2×C4⋊C4C22×D512yes—
264C2×C4⋊C4C22×D511yescharacteristic
265C2×C4⋊C4C22×D511yescharacteristic
266C2×C22⋊C4—102no—
267C2×C22⋊C4—101no—
268C2×C22⋊C4—101no—
269C2×C42—21no—
270C2×C42—51no—
271C2×C42—51no—
272C2×C42—51no—
273C2×C42—54no—
274C2×C42—54no—
275C2×C42—102no—
276C2×C42—101no—
277C2×C42C22×D511yescharacteristic
278#107—42no—
279#107—202no—
280#106—202no—
281#106—202no—
282C4⋊C8—54no—
283C4⋊C8C4×D514yes—
284C22⋊C8—58no—
285C4×C8—58no—
286#95—21no—
287#95—101no—
288#95—101no—
289#95—101no—
290#95—101no—
291#95—101no—
292#95—101no—
293#95—102no—
294#95—102no—
295#95—101no—
296C22×C5C22×C4⋊C411yescharacteristic
297C22×C5#53511yescharacteristic
298C22×C5#53611yescharacteristic
299C22×C5C2×#13511yescharacteristic
300C22×C5C2×#13511yescharacteristic
301C22×C5#57511yescharacteristic
302C22×C5#57511yescharacteristic
303C2×D5—22no—
304C2×D5—22no—
305C2×D5—22no—
306C2×D5—41no—
307C2×D5—41no—
308C2×D5—41no—
309C2×D5—41no—
310C4×C5—22no—
311C4×C5—82no—
312C4×C5—81no—
313C4×C5—81no—
314C4×C5#42714yes—
315C4×C5#52011yescharacteristic
316C4×C5#52011yescharacteristic
317C4×C5#54411yescharacteristic
318C4×C5#54411yescharacteristic
319Dic5—22no—
320Dic5—22no—
321Dic5—22no—
322Dic5—82no—
323Dic5—81no—
324Dic5—81no—
325C24—51no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—51no—
330C22×C4—51no—
331C22×C4—51no—
332C22×C4—52no—
333C22×C4—52no—
334C22×C4—54no—
335C22×C4—54no—
336C22×C4—101no—
337C22×C4—101no—
338C22×C4—101no—
339C22×C4—101no—
340C22×C4—102no—
341C22×C4—102no—
342C22×C4—101no—
343C22×C4—101no—
344C22×C4—102no—
345C22×C4—201no—
346C22×C4—201no—
347C22×C4D4×D511yescharacteristic
348C22×C4D4×D511yescharacteristic
349C22×C4C23×D511yescharacteristic
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—54no—
353C2×C8—102no—
354C2×C8—102no—
355C2×C8C2×C4×D514yes—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—101no—
365C4⋊C4—102no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—102no—
369C4⋊C4—101no—
370C4⋊C4—202no—
371C4⋊C4—202no—
372C22⋊C4—204no—
373C22⋊C4—202no—
374C22⋊C4—202no—
375C42—42no—
376C42—52no—
377C42—52no—
378C42—54no—
379C42—54no—
380C42—204no—
381C42—202no—
382C42C2×C4×D512yes—
383C42Q8×D512yes—
384C2×C5#231711yescharacteristic
385C2×C5C2×#42711yescharacteristic
386C2×C5#291111yescharacteristic
387C2×C5#321211yescharacteristic
388C2×C5#321211yescharacteristic
389C2×C5#323311yescharacteristic
390C2×C5#323311yescharacteristic
391D5—42no—
392C23—52no—
393C23—101no—
394C23—101no—
395C23—101no—
396C23—101no—
397C23—101no—
398C23—101no—
399C23C2×D4×D511yescharacteristic
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—52no—
412C2×C4—52no—
413C2×C4—52no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—101no—
417C2×C4—101no—
418C2×C4—101no—
419C2×C4—101no—
420C2×C4—102no—
421C2×C4—102no—
422C2×C4—102no—
423C2×C4—108no—
424C2×C4—102no—
425C2×C4—204no—
426C2×C4—201no—
427C2×C4—201no—
428C2×C4—202no—
429C2×C4—201no—
430C2×C4—201no—
431C2×C4—202no—
432C2×C4—202no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4D5×C4⋊C412yes—
436C2×C4D5×C4⋊C412yes—
437C2×C4#405812yes—
438C2×C4#406512yes—
439C2×C4C22×C4×D511yescharacteristic
440C2×C4#414411yescharacteristic
441C2×C4C2×Q8×D511yescharacteristic
442C2×C4#414711yescharacteristic
443C2×C4#414911yescharacteristic
444C2×C4#415011yescharacteristic
445C8—24no—
446C8—104no—
447C5#2198511yescharacteristic, complemented, Sylow
448C22—102no—
449C22—102no—
450C22—102no—
451C22—201no—
452C22—201no—
453C22—201no—
454C22—201no—
455C22C2×D5×C4⋊C411yescharacteristic
456C22#6594111yescharacteristic
457C22#6596211yescharacteristic
458C22C2×#405811yescharacteristic
459C22C2×#406511yescharacteristic
460C22#6610711yescharacteristic
461C22#6611111yescharacteristic
462C4—22no—
463C4—81no—
464C4—82no—
465C4—81no—
466C4—102no—
467C4—102no—
468C4—102no—
469C4—401no—
470C4—401no—
471C4—402no—
472C4#6516914yes—
473C4#6588011yescharacteristic
474C4#6590811yescharacteristic
475C4#6602311yescharacteristic
476C4#6606311yescharacteristic
477C2—202no—
478C2#1060769911yescharacteristic
479C2C2×#6516911yescharacteristic
480C2#1061093911yescharacteristic
481C2#1061206811yescharacteristic
482C2#1061221211yescharacteristic
483C2#1061270111yescharacteristic
484C2#1061284411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1947C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1947D5
hypocenterC5#21985
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
4. C5×#1947C2semidirect
6. #10601400C2semidirect
7. #10601246C2semidirect
8. #10600361C2semidirect
9. #10600260C2semidirect
11. #10599641C2semidirect
37. #65122C4semidirect
98. #1947D5semidirect
447. C5#21985semidirect

Maximal subgroups

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

subgroupindex
C2×#651222
#106060492
#106054832
C5×#19472
#106014262
#106014002
#106012462
#106003612
#106002602
#105996702
#105996412
#219855