Finite Group Databasebeta

← #12014447

Subgroups — #12014447

Order 1280.

636 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2321C211yesmaximal, characteristic
2C2×#64756C212yesmaximal
3C4×#3966C211yesmaximal, characteristic, complemented
4C4×#3965C211yesmaximal, characteristic, complemented
5#10598128C212yesmaximal, complemented
6C2×C5×#120C2211yescharacteristic
7C2×C4×C5×D4C2211yescharacteristic
8C22×C5×C22⋊C4C411yescharacteristic, complemented
9C5×#390—21no—
10C5×#388—21no—
11C5×#388—21no—
12C5×#386—21no—
13C5×#386C2211yescharacteristic
14C5×#385C411yescharacteristic, complemented
15C5×#379C411yescharacteristic, complemented
16C4×C5×C22⋊C4C411yescharacteristic, complemented
17C2×#3966C2212yes—
18C2×#3965C2212yes—
19C4×C22⋊Dic5—21no—
20C4×#681—21no—
21#64756C418yescomplemented
22#64750—21no—
23#64746—21no—
24#12622—51nomaximal, Sylow
25C25×C5C2×C411yescharacteristic
26C22×C5×D4—21no—
27C22×C5×D4C2311yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C5×#120—22no—
32C5×#120C2×C414yes—
33C4×C5×D4—41no—
34C4×C5×D4—41no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—41no—
44C2×C5×C22⋊C4—41no—
45C2×C5×C22⋊C4C2×C411yescharacteristic
46C2×C5×C22⋊C4C2×C411yescharacteristic
47C2×C5×C22⋊C4C2×C411yescharacteristic
48C2×C5×C22⋊C4D411yescharacteristic
49C2×C42×C5—21no—
50C2×C42×C5D411yescharacteristic
51C2×C22⋊Dic5—22no—
52C2×C4×Dic5—41no—
53C2×#681—22no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57#3966—22no—
58#3966C2×C414yes—
59#3965—22no—
60#3965C2×C414yes—
61#3963—41no—
62#3935—41no—
63C4×#168—41no—
64#2321D511yescharacteristic
65C2×AΣL(1,𝔽16)—52no—
66C4×#100—51no—
67C4×#99—51no—
68#1390—52no—
69C24×C5—21no—
70C24×C5—21no—
71C24×C5—41no—
72C24×C5—41no—
73C24×C5—81no—
74C24×C5—81no—
75C24×C5C4212yescomplemented
76C24×C5C22×C411yescharacteristic
77C24×C5C2×D411yescharacteristic
78C2×C5×D4—24no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—81no—
82C2×C5×D4—81no—
83C2×C5×D4C22×C412yes—
84C2×C5×D4#4112yes—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—41no—
93C22×C4×C5—81no—
94C22×C4×C5—81no—
95C22×C4×C5—81no—
96C22×C4×C5C22⋊C411yescharacteristic
97C22×C4×C5C22⋊C411yescharacteristic
98C22×C4×C5C22⋊C411yescharacteristic
99C22×C4×C5C22⋊C411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C22×Dic5—42no—
102C5×C4⋊C4—41no—
103C5×C4⋊C4—81no—
104C5×C22⋊C4—21no—
105C5×C22⋊C4—24no—
106C5×C22⋊C4—41no—
107C5×C22⋊C4—41no—
108C5×C22⋊C4—42no—
109C5×C22⋊C4—41no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—41no—
112C5×C22⋊C4—81no—
113C5×C22⋊C4—81no—
114C5×C22⋊C4—81no—
115C5×C22⋊C4C4212yescomplemented
116C42×C5—21no—
117C42×C5—21no—
118C42×C5—81no—
119C22⋊Dic5—24no—
120C22⋊Dic5—42no—
121C4×Dic5—82no—
122#681—24no—
123#681—42no—
124C2×#168—42no—
125C2×#120C2×D511yescharacteristic
126C2×C4×D4C2×D511yescharacteristic
127C22×C22⋊C4Dic511yescharacteristic, complemented
128C2×#100—52no—
129C2×#99—52no—
130C4×M16—101no—
131#390—21no—
132#388—21no—
133#388—21no—
134#386—21no—
135#386C2×D511yescharacteristic
136#385Dic511yescharacteristic, complemented
137#379Dic511yescharacteristic, complemented
138C4×C22⋊C4—101no—
139C4×C22⋊C4Dic511yescharacteristic, complemented
140AΣL(1,𝔽16)—58no—
141#343—101no—
142#342—101no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5—21no—
146C23×C5—21no—
147C23×C5—22no—
148C23×C5—41no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5—41no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—42no—
157C23×C5—42no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—82no—
161C23×C5—82no—
162C23×C5—82no—
163C23×C5—82no—
164C23×C5—84no—
165C23×C5C2×C4211yescharacteristic
166C23×C5C2×C22⋊C411yescharacteristic
167C23×C5#11711yescharacteristic
168C23×C5C4×D412yes—
169C5×D4—42no—
170C5×D4—42no—
171C5×D4—84no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
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—81no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5—82no—
195C2×C4×C5#9911yescharacteristic
196C2×C4×C5#9911yescharacteristic
197C2×C4×C5C4×D412yes—
198C2×Dic5—44no—
199C2×Dic5—82no—
200C2×Dic5—82no—
201#168—44no—
202C25C2×Dic511yescharacteristic
203C22×D4—21no—
204C22×D4C22×D511yescharacteristic
205C23×C4C2×Dic511yescharacteristic
206C23×C4C2×Dic511yescharacteristic
207C23×C4C22⋊D511yescharacteristic
208C2×M16—102no—
209#120—22no—
210#120C4×D514yes—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22⋊D511yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—102no—
224C2×C22⋊C4C2×Dic511yescharacteristic
225C2×C22⋊C4C2×Dic511yescharacteristic
226C2×C22⋊C4C2×Dic511yescharacteristic
227C2×C22⋊C4C22⋊D511yescharacteristic
228C2×C42—21no—
229C2×C42—201no—
230C2×C42C22⋊D511yescharacteristic
231#100—54no—
232#100—102no—
233#99—54no—
234#99—102no—
235#97—201no—
236C4×C8—201no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—201no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—22no—
244C22×C5—21no—
245C22×C5—21no—
246C22×C5—42no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—42no—
250C22×C5—42no—
251C22×C5—42no—
252C22×C5—41no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5—42no—
257C22×C5—81no—
258C22×C5—81no—
259C22×C5—81no—
260C22×C5—84no—
261C22×C5—84no—
262C22×C5—81no—
263C22×C5—81no—
264C22×C5C4×C22⋊C411yescharacteristic
265C22×C5C2×#9911yescharacteristic
266C22×C5#41011yescharacteristic
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—22no—
270C4×C5—42no—
271C4×C5—41no—
272C4×C5—41no—
273C4×C5—41no—
274C4×C5—81no—
275C4×C5—81no—
276Dic5—84no—
277C24—21no—
278C24—21no—
279C24—41no—
280C24—41no—
281C24—81no—
282C24—81no—
283C24C4×Dic512yescomplemented
284C24C22×Dic511yescharacteristic
285C24C2×C22⋊D511yescharacteristic
286C2×D4—24no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—81no—
290C2×D4—81no—
291C2×D4C2×C4×D512yes—
292C2×D4#70912yes—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—81no—
302C22×C4—81no—
303C22×C4—81no—
304C22×C4—202no—
305C22×C4C22⋊Dic511yescharacteristic
306C22×C4C22⋊Dic511yescharacteristic
307C22×C4C22⋊Dic511yescharacteristic
308C22×C4C22⋊Dic511yescharacteristic
309C22×C4C2×C22⋊D511yescharacteristic
310M16—104no—
311M16—202no—
312C2×C8—202no—
313C4⋊C4—41no—
314C4⋊C4—81no—
315C22⋊C4—21no—
316C22⋊C4—24no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C22⋊C4—104no—
327C22⋊C4—202no—
328C22⋊C4C4×Dic512yescomplemented
329C42—21no—
330C42—21no—
331C42—81no—
332C42—402no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5—42no—
336C2×C5—41no—
337C2×C5—41no—
338C2×C5—82no—
339C2×C5C4×#9911yescharacteristic
340C2×C5#212111yescharacteristic
341C2×C5#212211yescharacteristic
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—22no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—82no—
360C23—82no—
361C23—82no—
362C23—82no—
363C23—84no—
364C23C2×C4×Dic511yescharacteristic
365C23#407211yescharacteristic
366C23C4×C22⋊D512yes—
367C23C2×C22⋊Dic511yescharacteristic
368D4—42no—
369D4—42no—
370D4—84no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—204no—
395C2×C4—402no—
396C2×C4—402no—
397C2×C4#396611yescharacteristic
398C2×C4#396611yescharacteristic
399C2×C4C4×C22⋊D512yes—
400C8—204no—
401C5#1262211yescharacteristic, complemented, Sylow
402C22—21no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—42no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—84no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22C4×C22⋊Dic511yescharacteristic
426C22C2×#396611yescharacteristic
427C22#6552911yescharacteristic
428C4—21no—
429C4—21no—
430C4—22no—
431C4—42no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—81no—
436C4—81no—
437C4—404no—
438C2—21no—
439C2—21no—
440C2—42no—
441C2—41no—
442C2—41no—
443C2—82no—
444C2C4×#396611yescharacteristic
445C2#1060264011yescharacteristic
446C2#1060265211yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC23×C5C2×C42
FrattiniC22×D4C22×D5
FittingC5×#2321C2
socleC22×C5C2×#99
prime radicalC2×C5×#120C22
cosocleC22×C5×D4C23
hypercenter#2321D5
hypocenterC5#12622
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2321

Complements

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

NH ≅ G/Ntype
3. C4×#3966C2semidirect
4. C4×#3965C2semidirect
5. #10598128C2semidirect
8. C22×C5×C22⋊C4C4semidirect
14. C5×#385C4semidirect
15. C5×#379C4semidirect
16. C4×C5×C22⋊C4C4semidirect
21. #64756C4semidirect
75. C24×C5C42semidirect
115. C5×C22⋊C4C42semidirect
127. C22×C22⋊C4Dic5semidirect
136. #385Dic5semidirect
137. #379Dic5semidirect
139. C4×C22⋊C4Dic5semidirect
283. C24C4×Dic5semidirect
328. C22⋊C4C4×Dic5semidirect
401. C5#12622semidirect

Maximal subgroups

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

subgroupindex
C5×#23212
C2×#647562
C4×#39662
C4×#39652
#105981282
#126225