Finite Group Databasebeta

← #11990205

Subgroups — #11990205

Order 1280.

724 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4076C211yesmaximal, characteristic
2C5×#1434C211yesmaximal, characteristic, complemented
3C4×C22⋊#168C211yesmaximal, characteristic, complemented
4C2×#64671C212yesmaximal
5#10598103C212yesmaximal, complemented
6C22×C42×C5C2211yescharacteristic
7C2×#4076C2211yescharacteristic
8C2×C4×C22⋊D5—21no—
9C2×C4×D20C411yescharacteristic, complemented
10C2×C5×#95—21no—
11C2×C5×#95—21no—
12C2×C5×#95C2212yes—
13#65502—21no—
14#65501C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65229—21no—
17#65228C411yescharacteristic, complemented
18C4×#685—21no—
19C4×C4⋊Dic5C411yescharacteristic, complemented
20#65217C411yescharacteristic, complemented
21C2×C4×#168—21no—
22#64744—21no—
23#64671C418yescomplemented
24#8220—51nomaximal, Sylow
25C23×C4×C5—22no—
26C23×C4×C5D411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C23×C4×C5C2311yescharacteristic
29C22×C22⋊D5—21no—
30C22×D20C2×C411yescharacteristic
31C22×C4×D5—21no—
32C2×C42×C5—42no—
33C2×C42×C5C2×C411yescharacteristic
34C2×C42×C5C2×C411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5D411yescharacteristic
37C2×C22⋊Dic5—21no—
38#4076—22no—
39#4076C2×C414yes—
40C4×C22⋊D5—42no—
41C4×C22⋊D5—42no—
42C2×#685—21no—
43C2×#685—21no—
44C2×#685—21no—
45C2×#685—21no—
46C2×C4⋊Dic5C2×C411yescharacteristic
47C2×C4⋊Dic5C2×C411yescharacteristic
48C2×C4⋊Dic5C2×C411yescharacteristic
49C2×#683—21no—
50C2×C4×Dic5—21no—
51C22×#168—22no—
52C4×D20—42no—
53C5×#95—22no—
54C5×#95—42no—
55C5×#95—42no—
56C5×#95C2×C414yescomplemented
57#3963—21no—
58#3963—21no—
59#3963—21no—
60C22⋊#168—22no—
61C22⋊#168C2×C414yescomplemented
62C4×#168—42no—
63C4×#121—51no—
64C4×C22⋊C8—51no—
65C2×#327—52no—
66#1434D511yescharacteristic, complemented
67#1294—52no—
68C24×C5C2×D411yescharacteristic
69C23×D5—21no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—24no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—42no—
79C22×C4×C5—42no—
80C22×C4×C5—42no—
81C22×C4×C5—42no—
82C22×C4×C5—42no—
83C22×C4×C5—42no—
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5C22⋊C411yescharacteristic
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22⋊C411yescharacteristic
88C22×C4×C5D812yes—
89C22×C4×C5SD1612yes—
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C22×C412yes—
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5#4112yes—
94C2×C22⋊D5—24no—
95C2×C22⋊D5—41no—
96C2×C22⋊D5—41no—
97C2×C22⋊D5—42no—
98C22×Dic5—21no—
99C22×Dic5—21no—
100C22×Dic5—21no—
101C2×D20—21no—
102C2×D20—41no—
103C2×D20—41no—
104C2×D20C4212yes—
105C2×C4×D5—42no—
106C2×C4×D5—42no—
107C2×C4×D5—42no—
108C42×C5—22no—
109C42×C5—22no—
110C42×C5—41no—
111C42×C5—41no—
112C22⋊Dic5—41no—
113C22⋊Dic5—41no—
114#685—24no—
115#685—42no—
116#685—42no—
117#685—42no—
118C4⋊Dic5—21no—
119C4⋊Dic5—41no—
120C4⋊Dic5—41no—
121C4⋊Dic5C4212yes—
122#683—42no—
123C4×Dic5—42no—
124C2×#168—24no—
125C2×#168—42no—
126C2×#168—42no—
127C2×#121—51no—
128C2×C4×D4—51no—
129C2×C4×D4—101no—
130C22×C42C2×D511yescharacteristic
131C2×C22⋊C8—52no—
132C2×C4×C8—101no—
133#390—51no—
134#389—51no—
135#388—101no—
136#386—101no—
137#380—51no—
138C4×C4⋊C4—51no—
139C4×C22⋊C4—101no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95C2×D512yes—
143#336—101no—
144#327—58no—
145C23×C5—21no—
146C23×C5—21no—
147C23×C5—21no—
148C23×C5—21no—
149C23×C5C2×C22⋊C411yescharacteristic
150C23×C5C4×D412yes—
151C23×C5C2×D811yescharacteristic
152C23×C5C2×SD1611yescharacteristic
153C23×C5#13512yes—
154C22×D5—22no—
155C22×D5—41no—
156C22×D5—41no—
157C22×D5—41no—
158C22×D5—41no—
159C22×D5—41no—
160C22×D5—41no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
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—42no—
175C2×C4×C5—42no—
176C2×C4×C5—42no—
177C2×C4×C5—42no—
178C2×C4×C5—44no—
179C2×C4×C5—44no—
180C2×C4×C5—44no—
181C2×C4×C5—44no—
182C2×C4×C5—82no—
183C2×C4×C5—82no—
184C2×C4×C5—82no—
185C2×C4×C5—82no—
186C2×C4×C5#9912yes—
187C2×C4×C5#10212yes—
188C2×C4×C5#10212yes—
189C2×C4×C5C2×C4211yescharacteristic
190C2×C4×C5#11711yescharacteristic
191C2×C4×C5C4×D412yes—
192C22⋊D5—44no—
193C22⋊D5—44no—
194C2×Dic5—22no—
195C2×Dic5—41no—
196C2×Dic5—41no—
197C2×Dic5—41no—
198C2×Dic5—41no—
199C2×Dic5—41no—
200C2×Dic5—41no—
201C2×Dic5—41no—
202C2×Dic5—41no—
203D20—42no—
204D20—42no—
205C4×D5—84no—
206#168—44no—
207C22×D4—51no—
208C22×D4—101no—
209C23×C4—22no—
210C23×C4—101no—
211C23×C4C22⋊D511yescharacteristic
212C23×C4C22⋊D511yescharacteristic
213C23×C4C22×D511yescharacteristic
214C22×C8—102no—
215#121—54no—
216#121—102no—
217C4×D4—202no—
218C4×D4—202no—
219C4×D4—202no—
220C2×C4⋊C4—51no—
221C2×C4⋊C4—51no—
222C2×C4⋊C4—51no—
223C2×C4⋊C4—101no—
224C2×C22⋊C4—101no—
225C2×C22⋊C4—101no—
226C2×C22⋊C4—101no—
227C2×C22⋊C4—101no—
228C2×C22⋊C4—101no—
229C2×C42—42no—
230C2×C42—101no—
231C2×C42C4×D511yescharacteristic
232C2×C42C4×D511yescharacteristic
233C2×C42D2011yescharacteristic
234C2×C42D2011yescharacteristic
235C22⋊C8—54no—
236C22⋊C8—102no—
237C4×C8—202no—
238#95—22no—
239#95—42no—
240#95—42no—
241#95—101no—
242#95—101no—
243#95—101no—
244#95C4×D514yescomplemented
245C22×C5—22no—
246C22×C5—22no—
247C22×C5—22no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—22no—
253C22×C5C4×C22⋊C411yescharacteristic
254C22×C5C2×#9911yescharacteristic
255C22×C5#41011yescharacteristic
256C22×C5C2×#10211yescharacteristic
257C22×C5#41611yescharacteristic
258C22×C5#42111yescharacteristic
259C22×C5#42111yescharacteristic
260C22×C5C4×D812yes—
261C22×C5C4×SD1612yes—
262C2×D5—42no—
263C2×D5—42no—
264C2×D5—42no—
265C2×D5—81no—
266C2×D5—81no—
267C2×D5—81no—
268C2×D5—81no—
269C4×C5—22no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5—22no—
273C4×C5—22no—
274C4×C5—22no—
275C4×C5—41no—
276C4×C5—84no—
277Dic5—42no—
278Dic5—81no—
279Dic5—81no—
280C24—101no—
281C24C2×C22⋊D511yescharacteristic
282C2×D4—52no—
283C2×D4—104no—
284C2×D4—101no—
285C2×D4—201no—
286C2×D4—201no—
287C2×D4—202no—
288C2×D4—201no—
289C2×D4—201no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—101no—
305C22×C4—101no—
306C22×C4—101no—
307C22×C4—202no—
308C22×C4—202no—
309C22×C4—202no—
310C22×C4#68511yescharacteristic
311C22×C4#68511yescharacteristic
312C22×C4#68511yescharacteristic
313C22×C4#68511yescharacteristic
314C22×C4#68612yes—
315C22×C4#68812yes—
316C22×C4C2×C4×D511yescharacteristic
317C22×C4C2×C4×D512yes—
318C22×C4C2×D2011yescharacteristic
319C22×C4#70912yes—
320C2×C8—104no—
321C2×C8—202no—
322C2×C8—202no—
323C4⋊C4—52no—
324C4⋊C4—101no—
325C4⋊C4—201no—
326C4⋊C4—201no—
327C4⋊C4—202no—
328C22⋊C4—104no—
329C22⋊C4—202no—
330C22⋊C4—201no—
331C22⋊C4—201no—
332C22⋊C4—202no—
333C22⋊C4—202no—
334C42—22no—
335C42—22no—
336C42—41no—
337C42—41no—
338C42—202no—
339C2×C5—22no—
340C2×C5—22no—
341C2×C5#151611yescharacteristic
342C2×C5#151711yescharacteristic
343C2×C5#151911yescharacteristic
344C2×C5#152111yescharacteristic
345C2×C5C4×#9911yescharacteristic
346C2×C5#175911yescharacteristic
347C2×C5C4×#10211yescharacteristic
348D5—82no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—102no—
354C23—201no—
355C23—201no—
356C23—201no—
357C23—201no—
358C23—201no—
359C23—201no—
360C23C2×#68511yescharacteristic
361C23C4×C22⋊D512yes—
362C23C2×#68611yescharacteristic
363C23C2×#68811yescharacteristic
364C23#409612yes—
365D4—202no—
366D4—202no—
367D4—204no—
368D4—204no—
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—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—102no—
395C2×C4—201no—
396C2×C4—201no—
397C2×C4—201no—
398C2×C4—201no—
399C2×C4—201no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4—404no—
404C2×C4#393812yes—
405C2×C4#394112yes—
406C2×C4#394112yes—
407C2×C4C42×D511yescharacteristic
408C2×C4#401811yescharacteristic
409C2×C4C4×D2012yes—
410C8—204no—
411C5#822011yescharacteristic, complemented, Sylow
412C22—22no—
413C22—22no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—202no—
421C22—202no—
422C22—202no—
423C22—401no—
424C22—401no—
425C22—401no—
426C22—401no—
427C22C4×#68511yescharacteristic
428C22C2×#393811yescharacteristic
429C22C2×#394111yescharacteristic
430C22#6529111yescharacteristic
431C22#6529411yescharacteristic
432C22#6529411yescharacteristic
433C22#6529511yescharacteristic
434C22C4×#68612yes—
435C22C4×#68812yes—
436C4—22no—
437C4—21no—
438C4—21no—
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—84no—
444C4—202no—
445C4—401no—
446C4—401no—
447C2—22no—
448C2—22no—
449C2—402no—
450C2#1060022311yescharacteristic
451C2C4×#393811yescharacteristic
452C2C4×#394111yescharacteristic
453C2#1060030211yescharacteristic
454C2#1060032511yescharacteristic
455C2#1060033811yescharacteristic
456C2#1060035811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC5×#1434C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#4076C22
cosocleC23×C4×C5C23
hypercenter#1434D5
hypocenterC5#8220
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C5×#1434C2semidirect
3. C4×C22⋊#168C2semidirect
5. #10598103C2semidirect
9. C2×C4×D20C4semidirect
17. #65228C4semidirect
19. C4×C4⋊Dic5C4semidirect
20. #65217C4semidirect
23. #64671C4semidirect
56. C5×#95C2×C4semidirect
61. C22⋊#168C2×C4semidirect
66. #1434D5semidirect
244. #95C4×D5semidirect
411. C5#8220semidirect

Maximal subgroups

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

subgroupindex
C4×#40762
C5×#14342
C4×C22⋊#1682
C2×#646712
#105981032
#82205