Finite Group Databasebeta

← #11999003

Subgroups — #11999003

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#465C211yesmaximal, characteristic
2#10602770C211yesmaximal, characteristic, complemented
3C8×C22⋊Dic5C211yesmaximal, characteristic, complemented
4#10602484C211yesmaximal, characteristic, complemented
5#10602481C211yesmaximal, characteristic, complemented
6#10602469C211yesmaximal, characteristic
7#10602466C211yesmaximal, characteristic
8C22×C5×SD16C411yescharacteristic, complemented
9C23×C5×C8C2211yescharacteristic
10C2×C5×C22⋊Q8C2211yescharacteristic
11C2×C5×#121C2211yescharacteristic
12C5×#465—21no—
13C5×#465—21no—
14C5×#465—21no—
15C5×#465—21no—
16C2×C5×#106C411yescharacteristic, complemented
17C2×C5×#103C411yescharacteristic, complemented
18C2×C5×#102C411yescharacteristic, complemented
19C4×C22⋊Dic5C2211yescharacteristic
20#65496C2211yescharacteristic
21#65496C2211yescharacteristic
22C2×C22⋊#168C2211yescharacteristic
23C2×#3951—21no—
24C2×C8×Dic5—21no—
25#64772—21no—
26#64770—21no—
27#64758—22no—
28#64757—22no—
29#64748—22no—
30#64745—22no—
31#9813—51nomaximal, Sylow
32C22×C5×Q8C2×C411yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4C2×C411yescharacteristic
35C23×C4×C5C2311yescharacteristic
36C2×C5×SD16—21no—
37C2×C5×SD16—21no—
38C2×C5×SD16—42no—
39C22×C5×C8—42no—
40C22×C5×C8C2×C411yescharacteristic
41C22×C5×C8C2×C411yescharacteristic
42C22×C5×C8D411yescharacteristic
43C22×C5×C8D411yescharacteristic
44C22×C5×C8D411yescharacteristic
45C22×C5×C8D411yescharacteristic
46C5×C22⋊Q8—21no—
47C5×C22⋊Q8—21no—
48C5×C22⋊Q8—21no—
49C5×C22⋊Q8—21no—
50C5×#121—21no—
51C5×#121—21no—
52C5×#121—21no—
53C5×#121—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4C2×C411yescharacteristic
56C2×C5×C4⋊C4C2×C411yescharacteristic
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—21no—
59C2×C22⋊Dic5—21no—
60C2×C4×Dic5—21no—
61C2×#681—21no—
62C2×#681—21no—
63C22×#168—21no—
64C5×#106—21no—
65C5×#106—21no—
66C5×#103—21no—
67C5×#103—21no—
68C5×#102—21no—
69C5×#102—21no—
70#3963D412yes—
71C22⋊#168—21no—
72C22⋊#168—21no—
73C22⋊#168—21no—
74C22⋊#168—21no—
75C22⋊#168—21no—
76C22⋊#168D412yes—
77#3951—42no—
78C8×Dic5—42no—
79C2×#465D511yescharacteristic
80#1810—51no—
81C8×C22⋊C4—51no—
82#1508—51no—
83#1507—51no—
84#1472—51no—
85#1471—51no—
86C24×C5—21no—
87C24×C5#4111yescharacteristic
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×Q8—41no—
91C2×C5×Q8—41no—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—82no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5C22×C411yescharacteristic
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C22×C4×C5C2×D411yescharacteristic
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5#4111yescharacteristic
110C22×Dic5—22no—
111C5×SD16—42no—
112C5×SD16—42no—
113C2×C5×C8—22no—
114C2×C5×C8—22no—
115C2×C5×C8—22no—
116C2×C5×C8—41no—
117C2×C5×C8—41no—
118C2×C5×C8—41no—
119C2×C5×C8C22⋊C411yescharacteristic
120C2×C5×C8C22⋊C411yescharacteristic
121C2×C5×C8C22⋊C411yescharacteristic
122C2×C5×C8C22⋊C411yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—41no—
128C5×C4⋊C4—41no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—41no—
132C5×C22⋊C4—41no—
133C22⋊Dic5—24no—
134C4×Dic5—41no—
135C4×Dic5—41no—
136#681—41no—
137#681—41no—
138#681—41no—
139#681—41no—
140C2×#168—22no—
141C2×#168—41no—
142C2×#168—41no—
143C2×#168—41no—
144C2×#168—41no—
145C22×SD16Dic511yescharacteristic, complemented
146C23×C8C2×D511yescharacteristic
147C2×C22⋊Q8C2×D511yescharacteristic
148C2×#121C2×D511yescharacteristic
149#465—21no—
150#465—21no—
151#465—21no—
152#465—21no—
153C2×#108—101no—
154C2×#106Dic511yescharacteristic, complemented
155C2×#103Dic511yescharacteristic, complemented
156C2×#102Dic511yescharacteristic, complemented
157#407—51no—
158#407—51no—
159C2×C22⋊C8—51no—
160C2×C4×C8—101no—
161C4×C22⋊C4—51no—
162#341—101no—
163#336—101no—
164#328—102no—
165#327—102no—
166#324—102no—
167#323—102no—
168C23×C5—22no—
169C23×C5—22no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—42no—
173C23×C5—81no—
174C23×C5—81no—
175C23×C5C4×D411yescharacteristic
176C23×C5#12111yescharacteristic
177C23×C5#12411yescharacteristic
178C5×Q8—41no—
179C5×Q8—41no—
180C5×Q8—81no—
181C5×D4—41no—
182C5×D4—41no—
183C5×D4—81no—
184C5×D4—82no—
185C5×D4—82no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—42no—
199C2×C4×C5—81no—
200C2×C4×C5—81no—
201C2×C4×C5C2×C22⋊C411yescharacteristic
202C2×C4×C5C4×D411yescharacteristic
203C2×C4×C5#12111yescharacteristic
204C2×C4×C5#12711yescharacteristic
205C2×Dic5—24no—
206C2×Dic5—42no—
207C2×Dic5—42no—
208C5×C8—21no—
209C5×C8—21no—
210C5×C8—21no—
211C5×C8#9912yes—
212#168—42no—
213#168—81no—
214#168—81no—
215C22×Q8C2×Dic511yescharacteristic
216C22×D4—21no—
217C22×D4C2×Dic511yescharacteristic
218C23×C4C22×D511yescharacteristic
219C2×SD16—21no—
220C2×SD16—21no—
221C2×SD16—42no—
222C2×M16—101no—
223C2×M16—101no—
224C22×C8—42no—
225C22×C8—101no—
226C22×C8C2×Dic511yescharacteristic
227C22×C8C2×Dic511yescharacteristic
228C22×C8C22⋊D511yescharacteristic
229C22×C8C22⋊D511yescharacteristic
230C22×C8C22⋊D511yescharacteristic
231C22×C8C22⋊D511yescharacteristic
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—21no—
237#121—21no—
238#121—21no—
239#121—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×Dic511yescharacteristic
242C2×C4⋊C4C2×Dic511yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—101no—
246C2×C42—101no—
247#108—202no—
248#106—21no—
249#106—21no—
250#103—21no—
251#103—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—52no—
255C22⋊C8—101no—
256C22⋊C8—101no—
257C22⋊C8—101no—
258C22⋊C8—101no—
259C22⋊C8—101no—
260C4×C8—202no—
261#95—52no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—44no—
270C22×C5—81no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—162no—
274C22×C5#39011yescharacteristic
275C22×C5#44312yes—
276C22×C5#47112yes—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—81no—
281C4×C5—81no—
282C4×C5—81no—
283C4×C5C2×#9911yescharacteristic
284C4×C5#41011yescharacteristic
285Dic5—44no—
286C24—21no—
287C24#71111yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—82no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—102no—
305C22×C4D4×D511yescharacteristic
306C22×C4D4×D511yescharacteristic
307C22×C4#71111yescharacteristic
308C22×C4C22×Dic511yescharacteristic
309C22×C4C2×C22⋊D511yescharacteristic
310C22×C4C2×C22⋊D511yescharacteristic
311SD16—42no—
312SD16—42no—
313M16—201no—
314M16—201no—
315M16—201no—
316M16—201no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—102no—
324C2×C8—201no—
325C2×C8—201no—
326C2×C8—201no—
327C2×C8—201no—
328C2×C8C22⋊Dic511yescharacteristic
329C2×C8C22⋊Dic511yescharacteristic
330C2×C8C22⋊Dic511yescharacteristic
331C2×C8C22⋊Dic511yescharacteristic
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—104no—
343C42—201no—
344C42—201no—
345C2×C5—22no—
346C2×C5—22no—
347C2×C5—41no—
348C2×C5—161no—
349C2×C5#196411yescharacteristic
350C2×C5#197411yescharacteristic
351C2×C5#197711yescharacteristic
352C23—22no—
353C23—22no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23D4×Dic511yescharacteristic
360C23#408211yescharacteristic
361C23#408411yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—81no—
365D4—41no—
366D4—41no—
367D4—81no—
368D4—82no—
369D4—82no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—104no—
386C2×C4—202no—
387C2×C4—202no—
388C2×C4D4×Dic511yescharacteristic
389C2×C4#408411yescharacteristic
390C2×C4#408611yescharacteristic
391C2×C4C2×C22⋊Dic511yescharacteristic
392C8—21no—
393C8—21no—
394C8—21no—
395C8—202no—
396C8—401no—
397C8—401no—
398C8#396612yes—
399C5#981311yescharacteristic, complemented, Sylow
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—162no—
412C22#6546612yes—
413C22#6548512yes—
414C22#6551011yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4—204no—
422C4C2×#396611yescharacteristic
423C4#6552911yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2#1060247911yescharacteristic
429C2#1060284511yescharacteristic
430C2#1060287711yescharacteristic
subgroupG/H
centerC22#65510
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#465C2
socleC22×C5#390
prime radicalC2×C5×#121C22
cosocleC23×C4×C5C23
hypercenterC2×#465D5
hypocenterC5#9813
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. #10602770C2semidirect
3. C8×C22⋊Dic5C2semidirect
4. #10602484C2semidirect
5. #10602481C2semidirect
8. C22×C5×SD16C4semidirect
16. C2×C5×#106C4semidirect
17. C2×C5×#103C4semidirect
18. C2×C5×#102C4semidirect
145. C22×SD16Dic5semidirect
154. C2×#106Dic5semidirect
155. C2×#103Dic5semidirect
156. C2×#102Dic5semidirect
399. C5#9813semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4652
#106027702
C8×C22⋊Dic52
#106024842
#106024812
#106024692
#106024662
#98135