Finite Group Databasebeta

← #11998293

Subgroups — #11998293

Order 1280.

700 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
1C5×#2850C211yesmaximal, characteristic
2C2×#64758C212yesmaximal, complemented
3C2×#64757C212yesmaximal
4#10602328C211yesmaximal, characteristic, complemented
5#10602322C211yesmaximal, characteristic, complemented
6C2×C5×#124C411yescharacteristic, complemented
7C2×C5×C22⋊Q8C2211yescharacteristic
8C2×C5×#121C2211yescharacteristic
9C22×C42×C5C2211yescharacteristic
10C22×C4⋊Dic5—21no—
11C5×#391C411yescharacteristic, complemented
12C5×#390C411yescharacteristic, complemented
13C5×#388—21no—
14C5×#388—21no—
15C5×#386—21no—
16C5×#386—21no—
17C5×#382C411yescharacteristic, complemented
18C2×#3963—21no—
19C2×#3963C2212yes—
20C2×C22⋊#168C2212yes—
21C2×#3935—21no—
22#64758—24no—
23#64757—24no—
24#64744—21no—
25#9682—51nomaximal, Sylow
26C22×C5×Q8C2×C411yescharacteristic
27C22×C5×D4—21no—
28C22×C5×D4C2×C411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C23×C4×C5C2311yescharacteristic
32C23×Dic5—22no—
33C5×#124—42no—
34C5×C22⋊Q8—22no—
35C5×C22⋊Q8—22no—
36C5×#121—22no—
37C5×#121—22no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—21no—
46C2×C5×C22⋊C4—21no—
47C2×C42×C5—42no—
48C2×C42×C5C2×C411yescharacteristic
49C2×C42×C5C2×C411yescharacteristic
50C2×C42×C5D411yescharacteristic
51C2×C42×C5D411yescharacteristic
52C2×C4⋊Dic5—24no—
53C2×C4⋊Dic5—42no—
54C2×C4⋊Dic5—42no—
55C22×#168—22no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95—21no—
60#3963—22no—
61#3963—22no—
62#3963—42no—
63C22⋊#168—22no—
64C22⋊#168D414yes—
65#3935—42no—
66#2850D511yescharacteristic
67#1749—51no—
68C2×#328—52no—
69C2×#327—52no—
70C4⋊#95—51no—
71C24×C5—21no—
72C24×C5C2×D411yescharacteristic
73C2×C5×Q8—22no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×D4—22no—
77C2×C5×D4—41no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—22no—
88C22×C4×C5—22no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5C22⋊C411yescharacteristic
99C22×C4×C5C22⋊C411yescharacteristic
100C22×C4×C5C22⋊C411yescharacteristic
101C22×C4×C5C22⋊C411yescharacteristic
102C22×C4×C5C22×C411yescharacteristic
103C22×C4×C5C2×D412yes—
104C22×C4×C5C2×D411yescharacteristic
105C22×C4×C5#4112yes—
106C22×Dic5—24no—
107C22×Dic5—42no—
108C22×Dic5—42no—
109C22×Dic5—42no—
110C22×Dic5—42no—
111C22×Dic5—42no—
112C22×Dic5—42no—
113C5×C4⋊C4—22no—
114C5×C4⋊C4—22no—
115C5×C4⋊C4—42no—
116C5×C22⋊C4—42no—
117C5×C22⋊C4—42no—
118C5×C22⋊C4—41no—
119C5×C22⋊C4—41no—
120C5×C22⋊C4—42no—
121C5×C22⋊C4—42no—
122C5×C22⋊C4—42no—
123C42×C5—22no—
124C42×C5—22no—
125C42×C5—41no—
126C42×C5—41no—
127C4⋊Dic5—48no—
128C2×#168—24no—
129C2×#168—42no—
130C2×#168—42no—
131C2×#124Dic511yescharacteristic, complemented
132C2×C22⋊Q8C2×D511yescharacteristic
133C2×#121C2×D511yescharacteristic
134C22×C4⋊C4—101no—
135C22×C42C2×D511yescharacteristic
136C2×C22⋊C8—52no—
137C2×#97—101no—
138#391Dic511yescharacteristic, complemented
139#390Dic511yescharacteristic, complemented
140#388—21no—
141#388—21no—
142#386—21no—
143#386—21no—
144#382Dic511yescharacteristic, complemented
145C2×#95—52no—
146C2×#95—101no—
147#336—101no—
148#328—104no—
149#327—104no—
150C23×C5—21no—
151C23×C5—21no—
152C23×C5—21no—
153C23×C5—21no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5—41no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5C2×C22⋊C411yescharacteristic
162C23×C5#12411yescharacteristic
163C23×C5#12711yescharacteristic
164C23×C5AGL(1,ℤ/8)11yescharacteristic
165C23×C5AGL(1,ℤ/8)11yescharacteristic
166C23×C5#13711yescharacteristic
167C23×C5#13711yescharacteristic
168C5×Q8—82no—
169C5×D4—82no—
170C5×D4—81no—
171C5×D4—81no—
172C5×D4—81no—
173C5×D4—81no—
174C2×C4×C5—24no—
175C2×C4×C5—24no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—42no—
191C2×C4×C5—42no—
192C2×C4×C5—42no—
193C2×C4×C5—42no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5#9912yes—
204C2×C4×C5#10412yes—
205C2×C4×C5C4×D412yes—
206C2×C4×C5#12112yes—
207C2×Dic5—44no—
208C2×Dic5—44no—
209C2×Dic5—44no—
210C2×Dic5—82no—
211C2×Dic5—82no—
212C2×Dic5—82no—
213C2×Dic5—82no—
214#168—44no—
215C22×Q8C2×Dic511yescharacteristic
216C22×D4—21no—
217C22×D4C2×Dic511yescharacteristic
218C23×C4—102no—
219C23×C4C22⋊D511yescharacteristic
220C23×C4C22⋊D511yescharacteristic
221C23×C4C22×D511yescharacteristic
222C22×C8—102no—
223#124—42no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226#121—22no—
227#121—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—104no—
230C2×C4⋊C4—202no—
231C2×C4⋊C4—202no—
232C2×C4⋊C4C2×Dic511yescharacteristic
233C2×C4⋊C4C2×Dic511yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—42no—
241C2×C42C2×Dic511yescharacteristic
242C2×C42C2×Dic511yescharacteristic
243C2×C42C22⋊D511yescharacteristic
244C2×C42C22⋊D511yescharacteristic
245C22⋊C8—54no—
246C22⋊C8—102no—
247#97—202no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—102no—
253#95—102no—
254#95—202no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—81no—
268C22×C5—81no—
269C22×C5—81no—
270C22×C5—81no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—81no—
274C22×C5#39011yescharacteristic
275C22×C5C2×#9911yescharacteristic
276C22×C5#41011yescharacteristic
277C22×C5#41711yescharacteristic
278C22×C5#41711yescharacteristic
279C22×C5C2×#10411yescharacteristic
280C22×C5#42111yescharacteristic
281C22×C5#48911yescharacteristic
282C22×C5#48911yescharacteristic
283C22×C5#49611yescharacteristic
284C22×C5#49711yescharacteristic
285C4×C5—22no—
286C4×C5—22no—
287C4×C5—22no—
288C4×C5—22no—
289C4×C5—41no—
290C4×C5—41no—
291C4×C5—81no—
292C4×C5—81no—
293C4×C5—81no—
294Dic5—84no—
295C24—21no—
296C24C2×C22⋊D511yescharacteristic
297C2×Q8—22no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—22no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—104no—
323C22×C4—202no—
324C22×C4—202no—
325C22×C4—202no—
326C22×C4—202no—
327C22×C4—202no—
328C22×C4—202no—
329C22×C4C22⋊Dic511yescharacteristic
330C22×C4C22⋊Dic511yescharacteristic
331C22×C4C22⋊Dic511yescharacteristic
332C22×C4C22⋊Dic511yescharacteristic
333C22×C4D4×D512yes—
334C22×C4#71112yes—
335C22×C4C22×Dic511yescharacteristic
336C22×C4C2×C22⋊D511yescharacteristic
337C2×C8—104no—
338C2×C8—202no—
339C2×C8—202no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—208no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C42—22no—
352C42—22no—
353C42—41no—
354C42—41no—
355C2×C5—21no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5—21no—
359C2×C5—161no—
360C2×C5#150411yescharacteristic
361C2×C5#150911yescharacteristic
362C2×C5#151211yescharacteristic
363C2×C5#151311yescharacteristic
364C2×C5#195911yescharacteristic
365C2×C5#196411yescharacteristic
366C2×C5#198011yescharacteristic
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23#408211yescharacteristic
379C23#408611yescharacteristic
380C23#409511yescharacteristic
381C23#409511yescharacteristic
382C23#409711yescharacteristic
383C23#409711yescharacteristic
384C23C2×C22⋊Dic511yescharacteristic
385Q8—82no—
386D4—82no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4—81no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—204no—
421C2×C4—204no—
422C2×C4—204no—
423C2×C4—402no—
424C2×C4—402no—
425C2×C4—402no—
426C2×C4—402no—
427C2×C4#396612yes—
428C2×C4#396912yes—
429C2×C4D4×Dic512yes—
430C2×C4#408412yes—
431C8—204no—
432C5#968211yescharacteristic, complemented, Sylow
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#6534411yescharacteristic
453C22#6534411yescharacteristic
454C22#6534711yescharacteristic
455C22#6534911yescharacteristic
456C22C2×#396611yescharacteristic
457C22#6551011yescharacteristic
458C22#6552111yescharacteristic
459C22#6552111yescharacteristic
460C22C2×#396911yescharacteristic
461C22#6552511yescharacteristic
462C22#6552911yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—404no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—161no—
478C2#1060247911yescharacteristic
479C2#1060250111yescharacteristic
480C2#1060250211yescharacteristic
481C2#1060251911yescharacteristic
482C2#1060254811yescharacteristic
483C2#1060254911yescharacteristic
484C2#1060261111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2850C2
socleC23×C5C2×C22⋊C4
prime radicalC2×C5×#121C22
cosocleC23×C4×C5C23
hypercenter#2850D5
hypocenterC5#9682
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
2. C2×#64758C2semidirect
4. #10602328C2semidirect
5. #10602322C2semidirect
6. C2×C5×#124C4semidirect
11. C5×#391C4semidirect
12. C5×#390C4semidirect
17. C5×#382C4semidirect
131. C2×#124Dic5semidirect
138. #391Dic5semidirect
139. #390Dic5semidirect
144. #382Dic5semidirect
432. C5#9682semidirect

Maximal subgroups

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

subgroupindex
C5×#28502
C2×#647582
C2×#647572
#106023282
#106023222
#96825