Finite Group Databasebeta

← #12108654

Subgroups — #12108654

Order 1280.

1302 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×#64994C211yesmaximal, characteristic
3#10605878C211yesmaximal, characteristic
4C5×#1960C211yesmaximal, characteristic, complemented
5#10602579C211yesmaximal, characteristic, complemented
6#10601059C214yesmaximal
7#10601022C214yesmaximal, complemented
8#10600615C211yesmaximal, characteristic, complemented
9#10600345C211yesmaximal, characteristic, complemented
10C22×Q8×D5C2212yes—
11C2×C5×C4⋊Q8C2211yescharacteristic
12C2×#4090C2212yes—
13D5×C4⋊Q8—24no—
14D5×C4⋊Q8C418yescomplemented
15C2×D5×C4⋊C4—21no—
16C2×D5×C4⋊C4—21no—
17C2×#4034—21no—
18C2×#4034—21no—
19C2×C42×D5C2211yescharacteristic
20C2×#4015C2211yescharacteristic
21C2×C5×#103C2214yes—
22C2×C5×#97C2211yescharacteristic
23C5×#382C2211yescharacteristic
24C2×#3967C2214yes—
25C2×#3952C2212yes—
26C2×#3948C2214yes—
27C2×#3946C2212yes—
28#65276C2212yes—
29C4⋊C4×Dic5C2212yes—
30C2×#3942C2214yes—
31#65225C2211yescharacteristic
32C2×#3935C2211yescharacteristic
33#64994—24no—
34#64955—21no—
35#64953—21no—
36#64940—21no—
37#64937—21no—
38#21811—51nomaximal, Sylow
39C22×C5×Q8C2312yes—
40C2×Q8×D5—24no—
41C2×Q8×D5—44no—
42C2×Q8×D5—44no—
43C2×Q8×D5C2×C418yes—
44C22×C4×D5—22no—
45C22×C4×D5D411yescharacteristic
46C22×C4×D5D411yescharacteristic
47C22×C4×D5C2311yescharacteristic
48C22×Dic10—22no—
49C22×Dic10C2312yes—
50C22×C5×C8C2312yes—
51C5×C4⋊Q8—22no—
52C5×C4⋊Q8C2×C414yes—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4C2312yes—
56C2×C42×C5C2311yescharacteristic
57#4090—24no—
58#4090C2×C418yes—
59C2×#685—22no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5—21no—
62C2×C4⋊Dic5C2312yes—
63C2×#683—22no—
64C2×#683—22no—
65C2×C4×Dic5—22no—
66C2×C4×Dic5D411yescharacteristic
67C2×C4×Dic5D411yescharacteristic
68C2×C4×Dic5C2311yescharacteristic
69C22×#168C2312yes—
70D5×C4⋊C4—28no—
71D5×C4⋊C4—28no—
72#4034—28no—
73#4034—28no—
74C42×D5C2×C414yes—
75C42×D5D414yes—
76#4015—22no—
77#4015C2×C414yes—
78C5×#103—44no—
79C5×#97—22no—
80C5×#95—21no—
81C5×#95—21no—
82#3967—44no—
83#3963—21no—
84#3963—21no—
85#3963—22no—
86#3963—22no—
87#3952—24no—
88#3948—44no—
89#3946—24no—
90#3942—44no—
91#3935—22no—
92C22×C4⋊Q8—51no—
93C2×#432—51no—
94#2283—51no—
95#1981—54no—
96#1960—51no—
97#1960—51no—
98#1960—51no—
99#1960D511yescharacteristic, complemented
100#1787—54no—
101C23×D5C2×D411yescharacteristic
102C2×C5×Q8—22no—
103C2×C5×Q8—24no—
104C2×C5×Q8—24no—
105C2×C5×Q8C22×C414yes—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5C2411yescharacteristic
111C22×Dic5—22no—
112C22×Dic5—22no—
113C22×Dic5C2×D411yescharacteristic
114C22×Dic5C2×D411yescharacteristic
115C22×Dic5C2×D411yescharacteristic
116Q8×D5—416no—
117Q8×D5—416no—
118C2×C4×D5—24no—
119C2×C4×D5—22no—
120C2×C4×D5—22no—
121C2×C4×D5—24no—
122C2×C4×D5—28no—
123C2×C4×D5—44no—
124C2×C4×D5—44no—
125C2×C4×D5C22⋊C414yes—
126C2×C4×D5C22⋊C414yes—
127C2×C4×D5C22×C412yes—
128C2×C4×D5C2×D412yes—
129C2×Dic10—24no—
130C2×Dic10—24no—
131C2×Dic10—22no—
132C2×Dic10—28no—
133C2×Dic10—44no—
134C2×Dic10—44no—
135C2×Dic10C22×C414yes—
136C2×C5×C8—22no—
137C2×C5×C8—22no—
138C2×C5×C8—22no—
139C5×C4⋊C4—24no—
140C5×C4⋊C4—24no—
141C5×C4⋊C4—24no—
142C42×C5C22×C412yes—
143C42×C5C2×D412yes—
144#685—44no—
145C4⋊Dic5—24no—
146C4⋊Dic5—24no—
147C4⋊Dic5—24no—
148#683—28no—
149#683—28no—
150C4×Dic5—44no—
151C4×Dic5C22⋊C414yes—
152C4×Dic5C22⋊C414yes—
153C4×Dic5C22×C412yes—
154C4×Dic5C2×D412yes—
155C2×#168—22no—
156C2×#168—22no—
157C2×#168—22no—
158C23×Q8—52no—
159C2×C4⋊Q8—52no—
160C2×C4⋊Q8—58no—
161C2×C4⋊Q8—51no—
162C2×C4⋊Q8—101no—
163C2×C4⋊Q8—101no—
164C2×C4⋊Q8—104no—
165C2×C4⋊Q8C2×D511yescharacteristic
166C22×C4⋊C4—101no—
167C22×C4⋊C4—101no—
168C22×C42—51no—
169#432—104no—
170C2×C4⋊C8—52no—
171C2×#103—54no—
172C2×#103—54no—
173C2×#103—54no—
174C2×#103C2×D514yes—
175C2×C22⋊C8—52no—
176C2×#97—51no—
177C2×#97C2×D511yescharacteristic
178#383—101no—
179#382—51no—
180#382C2×D511yescharacteristic
181#381—101no—
182#380—52no—
183C4×C4⋊C4—52no—
184C4×C22⋊C4—101no—
185#376—101no—
186C23×C5C22×D411yescharacteristic
187C22×D5—21no—
188C22×D5—21no—
189C22×D5—22no—
190C22×D5C2×C22⋊C412yes—
191C22×D5#13714yes—
192C5×Q8—28no—
193C5×Q8—44no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5—24no—
197C2×C4×C5—42no—
198C2×C4×C5—42no—
199C2×C4×C5—42no—
200C2×C4×C5—42no—
201C2×C4×C5—42no—
202C2×C4×C5C2×C22⋊C412yes—
203C2×C4×C5C2×C22⋊C412yes—
204C2×C4×C5C23×C411yescharacteristic
205C2×C4×C5C22×D411yescharacteristic
206C2×C4×C5H(5,𝔽2)12yes—
207C2×C4×C5H(5,𝔽2)12yes—
208C2×Dic5—21no—
209C2×Dic5—21no—
210C2×Dic5—22no—
211C2×Dic5—24no—
212C2×Dic5—42no—
213C2×Dic5—42no—
214C2×Dic5—42no—
215C2×Dic5—42no—
216C2×Dic5—42no—
217C2×Dic5C2×C22⋊C412yes—
218C2×Dic5C2×C22⋊C412yes—
219C2×Dic5C2×C22⋊C412yes—
220C2×Dic5#13714yes—
221C4×D5—28no—
222C4×D5—24no—
223C4×D5—24no—
224C4×D5—28no—
225C4×D5—416no—
226Dic10—28no—
227Dic10—416no—
228Dic10—44no—
229C5×C8—42no—
230#168—42no—
231C22×Q8—58no—
232C22×Q8—52no—
233C22×Q8—102no—
234C22×Q8—104no—
235C22×Q8—204no—
236C22×Q8—204no—
237C22×Q8C22×D512yes—
238C23×C4—51no—
239C23×C4—51no—
240C23×C4—51no—
241C23×C4—102no—
242C22×C8—52no—
243C22×C8C22×D512yes—
244C4⋊Q8—22no—
245C4⋊Q8—58no—
246C4⋊Q8—54no—
247C4⋊Q8—108no—
248C4⋊Q8—108no—
249C4⋊Q8—104no—
250C4⋊Q8—102no—
251C4⋊Q8C4×D514yes—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—52no—
255C2×C4⋊C4—108no—
256C2×C4⋊C4—108no—
257C2×C4⋊C4—102no—
258C2×C4⋊C4—102no—
259C2×C4⋊C4—101no—
260C2×C4⋊C4—101no—
261C2×C4⋊C4C22×D512yes—
262C2×C22⋊C4—102no—
263C2×C42—51no—
264C2×C42—51no—
265C2×C42—51no—
266C2×C42—54no—
267C2×C42—54no—
268C2×C42—102no—
269C2×C42C22×D511yescharacteristic
270C4⋊C8—104no—
271#103—44no—
272#103—204no—
273#103—204no—
274#103—204no—
275C22⋊C8—104no—
276#97—22no—
277#97—102no—
278#95—21no—
279#95—21no—
280#95—102no—
281#95—102no—
282#95—101no—
283#95—101no—
284C22×C5C22×C22⋊C411yescharacteristic
285C22×C5#53511yescharacteristic
286C22×C5#53511yescharacteristic
287C22×C5C2×#13712yes—
288C22×C5C2×#13712yes—
289C2×D5—22no—
290C2×D5—22no—
291C2×D5—24no—
292C2×D5—24no—
293C2×D5#41914yes—
294C4×C5—22no—
295C4×C5—22no—
296C4×C5—44no—
297C4×C5—82no—
298C4×C5#51812yes—
299C4×C5#53512yes—
300Dic5—22no—
301Dic5—22no—
302Dic5—44no—
303Dic5—82no—
304Dic5#41914yes—
305C24—51no—
306C2×Q8—22no—
307C2×Q8—24no—
308C2×Q8—24no—
309C2×Q8—54no—
310C2×Q8—108no—
311C2×Q8—102no—
312C2×Q8—104no—
313C2×Q8—104no—
314C2×Q8—204no—
315C2×Q8—204no—
316C2×Q8—2016no—
317C2×Q8—2016no—
318C2×Q8C2×C4×D514yes—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—51no—
322C22×C4—51no—
323C22×C4—51no—
324C22×C4—52no—
325C22×C4—52no—
326C22×C4—54no—
327C22×C4—54no—
328C22×C4—104no—
329C22×C4—104no—
330C22×C4—108no—
331C22×C4—102no—
332C22×C4—102no—
333C22×C4—102no—
334C22×C4—102no—
335C22×C4—204no—
336C22×C4—204no—
337C22×C4D4×D511yescharacteristic
338C22×C4D4×D511yescharacteristic
339C22×C4C23×D511yescharacteristic
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—102no—
344C2×C8—102no—
345C2×C8—102no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—108no—
350C4⋊C4—108no—
351C4⋊C4—104no—
352C4⋊C4—104no—
353C4⋊C4—104no—
354C22⋊C4—204no—
355C42—52no—
356C42—52no—
357C42—54no—
358C42—54no—
359C42—204no—
360C42C2×C4×D512yes—
361C42D4×D512yes—
362C2×C5#230911yescharacteristic
363C2×C5C2×#41911yescharacteristic
364C2×C5C2×#41911yescharacteristic
365C2×C5#321812yes—
366C2×C5#321812yes—
367D5—24no—
368C23—52no—
369C23—54no—
370C23—101no—
371C23—102no—
372C23—101no—
373C23C2×D4×D511yescharacteristic
374Q8—28no—
375Q8—44no—
376Q8—108no—
377Q8—2016no—
378Q8—204no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—52no—
388C2×C4—54no—
389C2×C4—52no—
390C2×C4—52no—
391C2×C4—108no—
392C2×C4—108no—
393C2×C4—101no—
394C2×C4—102no—
395C2×C4—101no—
396C2×C4—104no—
397C2×C4—104no—
398C2×C4—104no—
399C2×C4—2016no—
400C2×C4—202no—
401C2×C4—202no—
402C2×C4—202no—
403C2×C4—202no—
404C2×C4—202no—
405C2×C4D5×C22⋊C412yes—
406C2×C4D5×C22⋊C412yes—
407C2×C4C22×C4×D511yescharacteristic
408C2×C4C2×D4×D511yescharacteristic
409C2×C4#414412yes—
410C2×C4#414912yes—
411C8—42no—
412C8—202no—
413C5#2181111yescharacteristic, complemented, Sylow
414C22—54no—
415C22—102no—
416C22—104no—
417C22—104no—
418C22—102no—
419C22C2×D5×C22⋊C411yescharacteristic
420C22#6600811yescharacteristic
421C22#6604911yescharacteristic
422C22D5×#13712yes—
423C22D5×#13712yes—
424C4—22no—
425C4—22no—
426C4—44no—
427C4—54no—
428C4—82no—
429C4—102no—
430C4—102no—
431C4—204no—
432C4—402no—
433C4#6587912yes—
434C4#6594112yes—
435C2—104no—
436C2#1060815911yescharacteristic
437C2D5×#41911yescharacteristic
438C2D5×#41911yescharacteristic
439C2#1061347212yes—
440C2#1061360712yes—
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1960C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1960D5
hypocenterC5#21811
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
4. C5×#1960C2semidirect
5. #10602579C2semidirect
7. #10601022C2semidirect
8. #10600615C2semidirect
9. #10600345C2semidirect
14. D5×C4⋊Q8C4semidirect
99. #1960D5semidirect
413. C5#21811semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×#649942
#106058782
C5×#19602
#106025792
#106010592
#106010222
#106006152
#106003452
#218115