Finite Group Databasebeta

← #11989254

Subgroups — #11989254

Order 1280.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#423C211yesmaximal, characteristic
2#10610769C211yesmaximal, characteristic
3C2×#65124C211yesmaximal, characteristic
4C5×#1292C211yesmaximal, characteristic, complemented
5#10598202C211yesmaximal, characteristic, complemented
6#10598202C211yesmaximal, characteristic, complemented
7#10598196C211yesmaximal, characteristic, complemented
8C2×D5×M16—21no—
9C2×C42×D5C2211yescharacteristic
10C5×#423C2211yescharacteristic
11C5×#423C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13#65415—21no—
14#65407—21no—
15M16×Dic5—21no—
16C2×#3952C412yes—
17C2×#3947C412yes—
18#65213C2211yescharacteristic
19#65213C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21#65126—21no—
22#65126C412yes—
23#65124—21no—
24#65124—21no—
25#65124—21no—
26#65124—21no—
27#65124—21no—
28#65124C412yes—
29#65122—21no—
30#65122C412yes—
31D5×C4⋊C8—21no—
32D5×C4⋊C8C412yes—
33#8003—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5D411yescharacteristic
36C22×C4×D5Q811yescharacteristic
37C2×C5×M16—21no—
38C2×C5×M16—21no—
39C22×C5×C8C2×C412yes—
40C2×C42×C5C2311yescharacteristic
41C2×C4×Dic5C2×C411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5Q811yescharacteristic
44C2×#681—21no—
45C2×#681—21no—
46C22×#168C2×C412yes—
47D5×M16—42no—
48D5×M16—42no—
49C2×#676—22no—
50C2×C8×D5—22no—
51C42×D5C2×C411yescharacteristic
52C42×D5C2×C411yescharacteristic
53C42×D5C2×C411yescharacteristic
54C42×D5C2×C411yescharacteristic
55C42×D5D411yescharacteristic
56C42×D5D411yescharacteristic
57C42×D5D411yescharacteristic
58C42×D5D411yescharacteristic
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8C2×C412yes—
64C5×C4⋊C8C2×C412yes—
65#3952—22no—
66#3952—22no—
67#3952—22no—
68#3952—22no—
69#3947—22no—
70#3947—22no—
71#3947—22no—
72#3946—22no—
73#3946—22no—
74C8×Dic5—22no—
75C4⋊#168—21no—
76C4⋊#168—21no—
77C4⋊#168—21no—
78C4⋊#168—21no—
79C4⋊#168C2×C412yes—
80C4⋊#168C2×C412yes—
81#2920—51no—
82C2×#432—51no—
83C2×#423—51no—
84#1292—51no—
85#1292—51no—
86#1292—51no—
87#1292D511yescharacteristic, complemented
88C23×D5C4⋊C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×Q811yescharacteristic
92C22×Dic5C4⋊C411yescharacteristic
93C22×Dic5C4⋊C411yescharacteristic
94C22×Dic5C4⋊C411yescharacteristic
95C2×C4×D5—21no—
96C2×C4×D5—21no—
97C2×C4×D5—21no—
98C2×C4×D5—21no—
99C2×C4×D5—41no—
100C2×C4×D5—41no—
101C2×C4×D5—42no—
102C2×C4×D5C4211yescharacteristic
103C2×C4×D5C4211yescharacteristic
104C2×C4×D5C22⋊C411yescharacteristic
105C2×C4×D5C22⋊C411yescharacteristic
106C2×C4×D5C22⋊C411yescharacteristic
107C2×C4×D5C22⋊C411yescharacteristic
108C2×C4×D5C22⋊C411yescharacteristic
109C2×C4×D5C22⋊C411yescharacteristic
110C2×C4×D5C4⋊C411yescharacteristic
111C2×C4×D5C4⋊C411yescharacteristic
112C2×C4×D5C4⋊C411yescharacteristic
113C2×C4×D5C4⋊C411yescharacteristic
114C5×M16—41no—
115C5×M16—41no—
116C5×M16—41no—
117C5×M16—41no—
118C2×C5×C8—22no—
119C2×C5×C8—22no—
120C2×C5×C8—22no—
121C2×C5×C8—42no—
122C42×C5C22×C411yescharacteristic
123C42×C5C22×C411yescharacteristic
124C42×C5C2×D411yescharacteristic
125C42×C5C2×D411yescharacteristic
126C4×Dic5C4211yescharacteristic
127C4×Dic5C4211yescharacteristic
128C4×Dic5C22⋊C411yescharacteristic
129C4×Dic5C22⋊C411yescharacteristic
130C4×Dic5C22⋊C411yescharacteristic
131C4×Dic5C22⋊C411yescharacteristic
132C4×Dic5C22⋊C411yescharacteristic
133C4×Dic5C22⋊C411yescharacteristic
134C4×Dic5C4⋊C411yescharacteristic
135C4×Dic5C4⋊C411yescharacteristic
136C4×Dic5C4⋊C411yescharacteristic
137C4×Dic5C4⋊C411yescharacteristic
138#681—41no—
139#681—41no—
140#681—41no—
141#681—41no—
142C2×#168—22no—
143C2×#168—22no—
144C2×#168—22no—
145C2×#168—42no—
146#676—44no—
147C8×D5—44no—
148C22×M16—101no—
149C22×C42—51no—
150#432—52no—
151#432—101no—
152#432—101no—
153#432—101no—
154#432—101no—
155#432—101no—
156#431—52no—
157#431—101no—
158#423—51no—
159#423—51no—
160#423—52no—
161#423—101no—
162#423—101no—
163#423C2×D511yescharacteristic
164#423C2×D511yescharacteristic
165C2×C4⋊C8—52no—
166C2×C4⋊C8—51no—
167C2×C4⋊C8—101no—
168C2×C4⋊C8C2×D511yescharacteristic
169#407—101no—
170C2×C22⋊C8—52no—
171C4×M16—101no—
172C2×#97—52no—
173C23×C5C2×C4⋊C411yescharacteristic
174C22×D5—21no—
175C22×D5—21no—
176C22×D5—22no—
177C22×D5—41no—
178C22×D5#9511yescharacteristic
179C22×D5#9511yescharacteristic
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—41no—
183C2×C4×C5C2×C4211yescharacteristic
184C2×C4×C5C2×C22⋊C411yescharacteristic
185C2×C4×C5C2×C22⋊C411yescharacteristic
186C2×C4×C5C2×C22⋊C411yescharacteristic
187C2×C4×C5C2×C4⋊C411yescharacteristic
188C2×C4×C5C2×C4⋊C411yescharacteristic
189C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C5#13711yescharacteristic
192C2×C4×C5#13711yescharacteristic
193C2×Dic5—21no—
194C2×Dic5—21no—
195C2×Dic5—41no—
196C2×Dic5—41no—
197C2×Dic5#9511yescharacteristic
198C2×Dic5#9511yescharacteristic
199C2×Dic5#9511yescharacteristic
200C2×Dic5#9511yescharacteristic
201C2×Dic5#9511yescharacteristic
202C2×Dic5#9511yescharacteristic
203C4×D5—22no—
204C4×D5—22no—
205C4×D5—21no—
206C4×D5—21no—
207C4×D5—21no—
208C4×D5—21no—
209C4×D5—21no—
210C4×D5—21no—
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—41no—
218C4×D5—41no—
219C4×D5—41no—
220C4×D5—41no—
221C5×C8—42no—
222C5×C8—42no—
223C5×C8—42no—
224#168—42no—
225#168—42no—
226#168—42no—
227C23×C4—51no—
228C23×C4—51no—
229C23×C4—51no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—102no—
233C2×M16—101no—
234C2×M16—101no—
235C2×M16—202no—
236C2×M16—202no—
237C22×C8—52no—
238C22×C8—102no—
239C22×C8C4×D512yes—
240C2×C42—51no—
241C2×C42—51no—
242C2×C42—51no—
243C2×C42—51no—
244C2×C42—51no—
245C2×C42—51no—
246C2×C42—51no—
247C2×C42—51no—
248C2×C42—51no—
249C2×C42—51no—
250C2×C42—51no—
251C2×C42C22×D511yescharacteristic
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—52no—
257C4⋊C8—52no—
258C4⋊C8—102no—
259C4⋊C8—102no—
260C4⋊C8—101no—
261C4⋊C8—101no—
262C4⋊C8—101no—
263C4⋊C8—101no—
264C4⋊C8C4×D512yes—
265C4⋊C8C4×D512yes—
266C22⋊C8—102no—
267C22⋊C8—102no—
268C22⋊C8—102no—
269C22⋊C8—102no—
270#97—102no—
271#97—102no—
272#97—102no—
273C4×C8—102no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5C2×#9511yescharacteristic
277C22×C5#42811yescharacteristic
278C22×C5#42811yescharacteristic
279C2×D5—21no—
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—21no—
283C2×D5—21no—
284C2×D5—42no—
285C2×D5—42no—
286C2×D5#33812yes—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5#41311yescharacteristic
291C4×C5#41311yescharacteristic
292C4×C5#41711yescharacteristic
293C4×C5#41711yescharacteristic
294C4×C5#41811yescharacteristic
295C4×C5#41911yescharacteristic
296Dic5—21no—
297Dic5—21no—
298Dic5—21no—
299Dic5—21no—
300Dic5—21no—
301Dic5—21no—
302C24—51no—
303C22×C4—51no—
304C22×C4—51no—
305C22×C4—51no—
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—51no—
311C22×C4—51no—
312C22×C4—51no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—51no—
318C22×C4—101no—
319C22×C4—101no—
320C22×C4—101no—
321C22×C4—101no—
322C22×C4—201no—
323C22×C4—201no—
324C22×C4—202no—
325C22×C4C2×C4×D511yescharacteristic
326C22×C4D4×D511yescharacteristic
327C22×C4Q8×D511yescharacteristic
328M16—41no—
329M16—41no—
330M16—41no—
331M16—41no—
332M16—204no—
333M16—201no—
334M16—201no—
335M16—201no—
336M16—201no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—42no—
341C2×C8—102no—
342C2×C8—102no—
343C2×C8—102no—
344C2×C8—204no—
345C2×C8—202no—
346C42—51no—
347C42—51no—
348C42—51no—
349C42—51no—
350C42—51no—
351C42—51no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42—51no—
356C42—51no—
357C42—51no—
358C42C2×C4×D511yescharacteristic
359C42C2×C4×D511yescharacteristic
360C42D4×D511yescharacteristic
361C42D4×D511yescharacteristic
362C2×C5—21no—
363C2×C5—21no—
364C2×C5C2×#33811yescharacteristic
365C2×C5#173611yescharacteristic
366C2×C5#174211yescharacteristic
367D5—22no—
368D5—41no—
369C23—51no—
370C23—51no—
371C23—102no—
372C23—101no—
373C23—101no—
374C23—201no—
375C23D5×C4⋊C411yescharacteristic
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—102no—
386C2×C4—102no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—101no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—101no—
396C2×C4—101no—
397C2×C4—101no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4—201no—
404C2×C4—201no—
405C2×C4—201no—
406C2×C4—201no—
407C2×C4C42×D511yescharacteristic
408C2×C4D5×C22⋊C411yescharacteristic
409C2×C4D5×C22⋊C411yescharacteristic
410C2×C4D5×C22⋊C411yescharacteristic
411C2×C4D5×C4⋊C411yescharacteristic
412C2×C4D5×C4⋊C411yescharacteristic
413C2×C4#405711yescharacteristic
414C2×C4#406011yescharacteristic
415C2×C4#406111yescharacteristic
416C2×C4#406411yescharacteristic
417C8—42no—
418C8—42no—
419C8—42no—
420C8—202no—
421C8—202no—
422C8—202no—
423C5#800311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—52no—
427C22—101no—
428C22—101no—
429C22—101no—
430C22—101no—
431C22—101no—
432C22—202no—
433C22—202no—
434C22D5×#9511yescharacteristic
435C22#6515011yescharacteristic
436C22#6517011yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—101no—
441C4—101no—
442C4—101no—
443C4—101no—
444C4—101no—
445C4—101no—
446C4#6503411yescharacteristic
447C4#6504011yescharacteristic
448C4#6505911yescharacteristic
449C4#6506011yescharacteristic
450C4#6509111yescharacteristic
451C4#6509211yescharacteristic
452C2—21no—
453C2—21no—
454C2—102no—
455C2—201no—
456C2D5×#33811yescharacteristic
457C2#1059966011yescharacteristic
458C2#1059978211yescharacteristic
subgroupG/H
centerC22D5×#95
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1292C2
socleC22×C5C2×#95
prime radicalC23×D5C4⋊C4
cosocleC2×C42×C5C23
hypercenter#1292D5
hypocenterC5#8003
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
4. C5×#1292C2semidirect
5. #10598202C2semidirect
6. #10598202C2semidirect
7. #10598196C2semidirect
87. #1292D5semidirect
423. C5#8003semidirect

Maximal subgroups

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

subgroupindex
D5×#4232
#106107692
C2×#651242
C5×#12922
#105982022
#105981962
#80035