Finite Group Databasebeta

← #11998445

Subgroups — #11998445

Order 1280.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 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#10602327C211yesmaximal, characteristic, complemented
5#10602323C211yesmaximal, characteristic, complemented
6C2×C5×#124C411yescharacteristic, complemented
7C2×C5×C22⋊Q8C2211yescharacteristic
8C2×C5×#121C2211yescharacteristic
9C22×C42×C5C2211yescharacteristic
10C5×#391C411yescharacteristic, complemented
11C5×#390C411yescharacteristic, complemented
12C5×#388—21no—
13C5×#388—21no—
14C5×#386—21no—
15C5×#386—21no—
16C5×#382C411yescharacteristic, complemented
17C2×#3963—21no—
18C2×#3963—21no—
19C2×#3963C2212yes—
20C2×C22⋊#168C2212yes—
21C2×C4⋊#168—21no—
22#64758—24no—
23#64757—24no—
24#64744—21no—
25#9716—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
52C22×#168—22no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57#3963—22no—
58#3963—42no—
59#3963—42no—
60#3963D414yes—
61C22⋊#168—22no—
62C22⋊#168—22no—
63C4⋊#168—42no—
64#2850D511yescharacteristic
65#1797—51no—
66C2×#328—52no—
67C2×#327—52no—
68#1434—51no—
69C24×C5—21no—
70C24×C5C2×D411yescharacteristic
71C2×C5×Q8—22no—
72C2×C5×Q8—41no—
73C2×C5×Q8—41no—
74C2×C5×D4—22no—
75C2×C5×D4—41no—
76C2×C5×D4—41no—
77C2×C5×D4—42no—
78C2×C5×D4—42no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C22×C4×C5—22no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—22no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5C22⋊C411yescharacteristic
94C22×C4×C5C22⋊C411yescharacteristic
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C22⋊C411yescharacteristic
97C22×C4×C5C22×C411yescharacteristic
98C22×C4×C5C2×D412yes—
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5#4112yes—
101C22×Dic5—24no—
102C22×Dic5—42no—
103C22×Dic5—42no—
104C22×Dic5—42no—
105C22×Dic5—42no—
106C22×Dic5—42no—
107C22×Dic5—42no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C22⋊C4—42no—
113C5×C22⋊C4—42no—
114C5×C22⋊C4—42no—
115C5×C22⋊C4—42no—
116C5×C22⋊C4—42no—
117C5×C22⋊C4—41no—
118C5×C22⋊C4—41no—
119C42×C5—22no—
120C42×C5—22no—
121C42×C5—41no—
122C42×C5—41no—
123C2×#168—42no—
124C2×#168—42no—
125C2×#168—42no—
126C2×#124Dic511yescharacteristic, complemented
127C2×C22⋊Q8C2×D511yescharacteristic
128C2×#121C2×D511yescharacteristic
129C22×C42C2×D511yescharacteristic
130C2×C4⋊C8—101no—
131C2×C22⋊C8—52no—
132#391Dic511yescharacteristic, complemented
133#390Dic511yescharacteristic, complemented
134#388—21no—
135#388—21no—
136#386—21no—
137#386—21no—
138#382Dic511yescharacteristic, complemented
139C2×#95—52no—
140C2×#95—101no—
141C2×#95—101no—
142#336—101no—
143#328—104no—
144#327—104no—
145C23×C5—21no—
146C23×C5—21no—
147C23×C5—21no—
148C23×C5—21no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5—41no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5C2×C22⋊C411yescharacteristic
157C23×C5#12112yes—
158C23×C5#13512yes—
159C23×C5AGL(1,ℤ/8)11yescharacteristic
160C23×C5#13711yescharacteristic
161C5×Q8—82no—
162C5×D4—82no—
163C5×D4—82no—
164C5×D4—82no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—42no—
181C2×C4×C5—42no—
182C2×C4×C5—44no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5#9912yes—
195C2×C4×C5C4×D412yes—
196C2×C4×C5#12411yescharacteristic
197C2×C4×C5#12711yescharacteristic
198C2×Dic5—44no—
199C2×Dic5—44no—
200C2×Dic5—44no—
201C2×Dic5—82no—
202C2×Dic5—82no—
203C2×Dic5—82no—
204C2×Dic5—82no—
205#168—82no—
206C22×Q8C2×Dic511yescharacteristic
207C22×D4—21no—
208C22×D4C2×Dic511yescharacteristic
209C23×C4—102no—
210C23×C4C22⋊D511yescharacteristic
211C23×C4C22⋊D511yescharacteristic
212C23×C4C22×D511yescharacteristic
213C22×C8—102no—
214#124—42no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217#121—22no—
218#121—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic511yescharacteristic
221C2×C4⋊C4C2×Dic511yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C42—42no—
229C2×C42C2×Dic511yescharacteristic
230C2×C42C2×Dic511yescharacteristic
231C2×C42C22⋊D511yescharacteristic
232C2×C42C22⋊D511yescharacteristic
233C4⋊C8—202no—
234C22⋊C8—102no—
235C22⋊C8—102no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—54no—
241#95—102no—
242#95—202no—
243#95—202no—
244C22×C5—22no—
245C22×C5—22no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—22no—
251C22×C5—22no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5—81no—
259C22×C5#39011yescharacteristic
260C22×C5C2×#9911yescharacteristic
261C22×C5#41011yescharacteristic
262C22×C5#41611yescharacteristic
263C22×C5#41711yescharacteristic
264C22×C5#42111yescharacteristic
265C22×C5#42111yescharacteristic
266C22×C5#46312yes—
267C22×C5#46412yes—
268C4×C5—21no—
269C4×C5—22no—
270C4×C5—21no—
271C4×C5—22no—
272C4×C5—41no—
273C4×C5—41no—
274C4×C5—41no—
275C4×C5—81no—
276C4×C5—81no—
277C4×C5—81no—
278Dic5—84no—
279C24—21no—
280C24C2×C22⋊D511yescharacteristic
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×D4—22no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—41no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—104no—
304C22×C4—202no—
305C22×C4—202no—
306C22×C4—202no—
307C22×C4—202no—
308C22×C4—202no—
309C22×C4—202no—
310C22×C4C22⋊Dic511yescharacteristic
311C22×C4C22⋊Dic511yescharacteristic
312C22×C4C22⋊Dic511yescharacteristic
313C22×C4C22⋊Dic511yescharacteristic
314C22×C4D4×D512yes—
315C22×C4#71112yes—
316C22×C4C22×Dic511yescharacteristic
317C22×C4C2×C22⋊D511yescharacteristic
318C2×C8—202no—
319C2×C8—202no—
320C2×C8—202no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C42—22no—
333C42—22no—
334C42—41no—
335C42—41no—
336C2×C5—22no—
337C2×C5—22no—
338C2×C5—161no—
339C2×C5#151211yescharacteristic
340C2×C5#151311yescharacteristic
341C2×C5#151611yescharacteristic
342C2×C5#152111yescharacteristic
343C2×C5#196311yescharacteristic
344C2×C5#196411yescharacteristic
345C2×C5#198311yescharacteristic
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23#408412yes—
358C23#409511yescharacteristic
359C23#409612yes—
360C23#409711yescharacteristic
361C23C2×C22⋊Dic511yescharacteristic
362Q8—82no—
363D4—82no—
364D4—82no—
365D4—82no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—204no—
396C2×C4—204no—
397C2×C4—204no—
398C2×C4—402no—
399C2×C4—402no—
400C2×C4—402no—
401C2×C4—402no—
402C2×C4#396612yes—
403C2×C4D4×Dic512yes—
404C2×C4#408211yescharacteristic
405C2×C4#408611yescharacteristic
406C8—402no—
407C5#971611yescharacteristic, complemented, Sylow
408C22—21no—
409C22—21no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22#6534312yes—
424C22#6534612yes—
425C22C2×#396611yescharacteristic
426C22#6551011yescharacteristic
427C22#6552111yescharacteristic
428C22#6552211yescharacteristic
429C22#6552511yescharacteristic
430C22#6552511yescharacteristic
431C22#6552911yescharacteristic
432C4—22no—
433C4—21no—
434C4—22no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—404no—
443C2—22no—
444C2—22no—
445C2—161no—
446C2#1060247911yescharacteristic
447C2#1060250211yescharacteristic
448C2#1060250311yescharacteristic
449C2#1060251411yescharacteristic
450C2#1060254911yescharacteristic
451C2#1060255011yescharacteristic
452C2#1060260911yescharacteristic
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#9716
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. #10602327C2semidirect
5. #10602323C2semidirect
6. C2×C5×#124C4semidirect
10. C5×#391C4semidirect
11. C5×#390C4semidirect
16. C5×#382C4semidirect
126. C2×#124Dic5semidirect
132. #391Dic5semidirect
133. #390Dic5semidirect
138. #382Dic5semidirect
407. C5#9716semidirect

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
#106023272
#106023232
#97165