Finite Group Databasebeta

← #12104186

Subgroups — #12104186

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic5C211yesmaximal, characteristic
2C2×#65008C211yesmaximal, characteristic
3#10605595C211yesmaximal, characteristic
4C5×#1852C211yesmaximal, characteristic
5#10602348C211yesmaximal, characteristic
6#10601408C212yesmaximal, complemented
7#10601398C212yesmaximal, complemented
8#10600721C211yesmaximal, characteristic
9#10600298C211yesmaximal, characteristic
10#10599589C212yesmaximal, complemented
11#10599579C212yesmaximal, complemented
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic5C2211yescharacteristic
14C22×C4×Dic5—21no—
15C22×C4×Dic5C2211yescharacteristic
16C2×#4023—21no—
17C2×C5×#107C2212yes—
18C2×C5×C22⋊C8C2211yescharacteristic
19C5×#380C2211yescharacteristic
20#65501C2211yescharacteristic
21C2×#3963—21no—
22C2×C22⋊#168C2211yescharacteristic
23C2×#3949C2212yes—
24C2×#3947C2212yes—
25C2×#3946C2212yes—
26#65265C2211yescharacteristic
27#65265C2211yescharacteristic
28C4⋊C4×Dic5—21no—
29C4⋊C4×Dic5—21no—
30C4⋊C4×Dic5C2211yescharacteristic
31C4⋊C4×Dic5C2211yescharacteristic
32C4⋊C4×Dic5C2212yes—
33C4⋊C4×Dic5C2212yes—
34C2×#3940C2212yes—
35C2×#3939C2212yes—
36#65231—21no—
37#65008C418yescomplemented
38#64939—21no—
39#64938—21no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#21365—51nomaximal, Sylow
45C23×C4×C5—21no—
46C23×C4×C5C2311yescharacteristic
47C23×Dic5—21no—
48C23×Dic5D411yescharacteristic
49C23×Dic5D411yescharacteristic
50C22×C5×C8C2312yes—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4C2311yescharacteristic
54C2×C5×C4⋊C4C2311yescharacteristic
55C2×C5×C4⋊C4C2312yes—
56C2×C5×C22⋊C4—21no—
57C2×C22⋊Dic5—21no—
58C2×C4⋊Dic5—21no—
59C2×C4⋊Dic5—24no—
60C2×C4⋊Dic5C2311yescharacteristic
61C2×C4⋊Dic5C2311yescharacteristic
62C2×C4⋊Dic5C2312yes—
63C2×#683—21no—
64C2×#683—21no—
65C2×#683—21no—
66C2×#683—21no—
67C2×C4×Dic5—21no—
68C2×C4×Dic5—21no—
69C2×C4×Dic5—22no—
70C2×C4×Dic5—22no—
71C2×C4×Dic5—44no—
72C2×C4×Dic5C2×C414yes—
73C2×C4×Dic5D411yescharacteristic
74C2×C4×Dic5D411yescharacteristic
75C2×C4×Dic5Q814yes—
76C2×C4×Dic5C2311yescharacteristic
77C2×C4×Dic5C2311yescharacteristic
78C22×#168C2312yes—
79#4023—44no—
80C5×#107—24no—
81C5×C22⋊C8C2×C414yes—
82C5×#95—21no—
83#3963—21no—
84#3963—21no—
85#3963—21no—
86#3963—22no—
87#3963—22no—
88C22⋊#168C2×C414yes—
89#3949—24no—
90#3947C2×C418yescomplemented
91#3946C2×C418yescomplemented
92#3940—24no—
93#3939—24no—
94C2×#432—51no—
95#2285—51no—
96C2×C4×C4⋊C4—51no—
97#1948—52no—
98#1947—52no—
99#1853—51no—
100#1853—51no—
101#1852—51no—
102#1852D511yescharacteristic
103#1776—52no—
104#1776—52no—
105C24×C5C2×D411yescharacteristic
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—24no—
109C22×C4×C5—22no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—42no—
113C22×C4×C5—42no—
114C22×C4×C5C22×C412yes—
115C22×C4×C5C2×D411yescharacteristic
116C22×C4×C5C2×Q812yes—
117C22×C4×C5C2411yescharacteristic
118C22×Dic5—22no—
119C22×Dic5—22no—
120C22×Dic5—22no—
121C22×Dic5—22no—
122C22×Dic5—24no—
123C22×Dic5—22no—
124C22×Dic5—21no—
125C22×Dic5—21no—
126C22×Dic5—42no—
127C22×Dic5—42no—
128C22×Dic5C4⋊C414yes—
129C22×Dic5C4⋊C414yes—
130C22×Dic5C2×D411yescharacteristic
131C22×Dic5C2×D411yescharacteristic
132C22×Dic5C2×D411yescharacteristic
133C22×Dic5C2×D411yescharacteristic
134C2×C5×C8—22no—
135C2×C5×C8—22no—
136C2×C5×C8C22×C414yes—
137C5×C4⋊C4—24no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—22no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4#4114yes—
142C5×C22⋊C4—42no—
143C22⋊Dic5—42no—
144C4⋊Dic5—24no—
145C4⋊Dic5—22no—
146C4⋊Dic5—22no—
147C4⋊Dic5—22no—
148C4⋊Dic5#4114yes—
149#683—42no—
150#683—42no—
151#683—42no—
152#683—42no—
153C4×Dic5—42no—
154C4×Dic5—42no—
155C4×Dic5—44no—
156C4×Dic5—44no—
157C4×Dic5C4⋊C414yes—
158C4×Dic5C4⋊C414yes—
159C4×Dic5C22×C412yes—
160C4×Dic5C22×C412yes—
161C4×Dic5C2×Q812yes—
162C4×Dic5C2×Q812yes—
163C2×#168—22no—
164C2×#168—22no—
165C2×#168C22×C414yes—
166C2×#117—101no—
167C22×C4⋊C4—51no—
168C22×C4⋊C4C2×D511yescharacteristic
169C22×C42—51no—
170C22×C42—101no—
171#432—58no—
172C2×#107—52no—
173C2×#107C2×D512yes—
174C2×#106—52no—
175C2×#106—52no—
176C2×C4⋊C8—52no—
177C2×C22⋊C8—51no—
178C2×C22⋊C8C2×D511yescharacteristic
179C2×#97—52no—
180#384—51no—
181#384—51no—
182#382—101no—
183#380—51no—
184#380—101no—
185#380C2×D511yescharacteristic
186C4×C4⋊C4—52no—
187C4×C4⋊C4—52no—
188C4×C4⋊C4—51no—
189C4×C4⋊C4—51no—
190C4×C4⋊C4—101no—
191C4×C4⋊C4—101no—
192C4×C4⋊C4—101no—
193C2×#95—101no—
194#340—52no—
195#340—52no—
196#340—52no—
197#340C2×D512yes—
198C23×C5—21no—
199C23×C5—21no—
200C23×C5—21no—
201C23×C5—21no—
202C23×C5C2×C4⋊C412yes—
203C23×C5AGL(1,ℤ/8)12yes—
204C23×C5#13712yes—
205C23×C5C22×D411yescharacteristic
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—24no—
209C2×C4×C5—24no—
210C2×C4×C5—24no—
211C2×C4×C5—48no—
212C2×C4×C5—42no—
213C2×C4×C5—42no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5C2×C4⋊C412yes—
221C2×C4×C5C23×C411yescharacteristic
222C2×C4×C5C22×Q811yescharacteristic
223C2×C4×C5C2×#4112yes—
224C2×C4×C5C2×#4112yes—
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—28no—
232C2×Dic5—28no—
233C2×Dic5—24no—
234C2×Dic5—48no—
235C2×Dic5—42no—
236C2×Dic5—42no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5—41no—
243C2×Dic5C2×C4⋊C412yes—
244C2×Dic5C2×C4⋊C412yes—
245C2×Dic5C2×C4⋊C412yes—
246C2×Dic5C2×C4⋊C412yes—
247C2×Dic5AGL(1,ℤ/8)12yes—
248C2×Dic5#13712yes—
249C5×C8—24no—
250#168—24no—
251C23×C4—21no—
252C23×C4—51no—
253C23×C4—51no—
254C23×C4—101no—
255C23×C4C22×D511yescharacteristic
256C22×C8—52no—
257C22×C8C22×D512yes—
258#117—204no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—52no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—51no—
264C2×C4⋊C4—104no—
265C2×C4⋊C4—101no—
266C2×C4⋊C4—101no—
267C2×C4⋊C4—101no—
268C2×C4⋊C4—101no—
269C2×C4⋊C4—101no—
270C2×C4⋊C4C22×D511yescharacteristic
271C2×C4⋊C4C22×D511yescharacteristic
272C2×C4⋊C4C22×D512yes—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—101no—
275C2×C42—54no—
276C2×C42—51no—
277C2×C42—51no—
278C2×C42—54no—
279C2×C42—51no—
280C2×C42—51no—
281C2×C42—101no—
282C2×C42—101no—
283C2×C42—102no—
284C2×C42—102no—
285C2×C42—204no—
286#107—24no—
287#107—104no—
288#106—104no—
289#106—104no—
290C4⋊C8—58no—
291C22⋊C8—54no—
292C22⋊C8C4×D514yes—
293#97—58no—
294#95—21no—
295#95—102no—
296#95—102no—
297#95—101no—
298#95—101no—
299#95—101no—
300C22×C5—22no—
301C22×C5—22no—
302C22×C5—22no—
303C22×C5—22no—
304C22×C5—22no—
305C22×C5—22no—
306C22×C5#42814yes—
307C22×C5C22×C4⋊C411yescharacteristic
308C22×C5#52511yescharacteristic
309C22×C5#52511yescharacteristic
310C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C5C2×#13711yescharacteristic
313C22×C5C2×#13711yescharacteristic
314C4×C5—22no—
315C4×C5—44no—
316C4×C5—81no—
317C4×C5—81no—
318C4×C5C4×#4112yes—
319C4×C5#53312yes—
320Dic5—22no—
321Dic5—22no—
322Dic5—22no—
323Dic5—44no—
324Dic5—81no—
325Dic5—81no—
326Dic5#42814yes—
327C24D4×D511yescharacteristic
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—51no—
339C22×C4—51no—
340C22×C4—54no—
341C22×C4—54no—
342C22×C4—102no—
343C22×C4—102no—
344C22×C4—102no—
345C22×C4—102no—
346C22×C4—104no—
347C22×C4—102no—
348C22×C4—101no—
349C22×C4—101no—
350C22×C4—202no—
351C22×C4—202no—
352C22×C4C2×C4×D512yes—
353C22×C4D4×D511yescharacteristic
354C22×C4Q8×D512yes—
355C22×C4C23×D511yescharacteristic
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—54no—
359C2×C8—102no—
360C2×C8—102no—
361C2×C8C2×C4×D514yes—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—54no—
367C4⋊C4—104no—
368C4⋊C4—102no—
369C4⋊C4—102no—
370C4⋊C4—102no—
371C4⋊C4—202no—
372C4⋊C4—202no—
373C4⋊C4—202no—
374C4⋊C4—202no—
375C4⋊C4#71114yes—
376C22⋊C4—42no—
377C22⋊C4—202no—
378C42—52no—
379C42—52no—
380C42—52no—
381C42—52no—
382C42—54no—
383C42—54no—
384C42—204no—
385C42—204no—
386C42—202no—
387C42—202no—
388C2×C5—24no—
389C2×C5#229611yescharacteristic
390C2×C5C2×#42811yescharacteristic
391C2×C5C2×#42811yescharacteristic
392C2×C5#310911yescharacteristic
393C2×C5#311011yescharacteristic
394C2×C5#311211yescharacteristic
395C2×C5#311311yescharacteristic
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23D5×C4⋊C412yes—
401C23#405712yes—
402C23#406412yes—
403C23C2×D4×D511yescharacteristic
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—48no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—52no—
419C2×C4—52no—
420C2×C4—52no—
421C2×C4—52no—
422C2×C4—52no—
423C2×C4—52no—
424C2×C4—108no—
425C2×C4—101no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—108no—
432C2×C4—104no—
433C2×C4—208no—
434C2×C4—202no—
435C2×C4—202no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4—201no—
439C2×C4—201no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4D5×C4⋊C412yes—
443C2×C4C22×C4×D511yescharacteristic
444C2×C4C2×#71112yes—
445C2×C4C2×Q8×D511yescharacteristic
446C2×C4D5×#4112yes—
447C8—24no—
448C8—104no—
449C5#2136511yescharacteristic, complemented, Sylow
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22#6517014yes—
457C22C2×D5×C4⋊C411yescharacteristic
458C22#6592011yescharacteristic
459C22#6599011yescharacteristic
460C22C2×#405711yescharacteristic
461C22C2×#406411yescharacteristic
462C22D5×AGL(1,ℤ/8)11yescharacteristic
463C22D5×#13711yescharacteristic
464C4—22no—
465C4—44no—
466C4—54no—
467C4—81no—
468C4—81no—
469C4—102no—
470C4—102no—
471C4—102no—
472C4—204no—
473C4—401no—
474C4—401no—
475C4C4×#71112yes—
476C4#6595612yes—
477C2—24no—
478C2#1060610911yescharacteristic
479C2C2×#6517011yescharacteristic
480C2D5×#42811yescharacteristic
481C2#1061172111yescharacteristic
482C2#1061190511yescharacteristic
483C2#1061300111yescharacteristic
484C2#1061318511yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1852C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenter#1852D5
hypocenterC5#21365
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
6. #10601408C2semidirect
7. #10601398C2semidirect
10. #10599589C2semidirect
11. #10599579C2semidirect
37. #65008C4semidirect
90. #3947C2×C4semidirect
91. #3946C2×C4semidirect
449. C5#21365semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic52
C2×#650082
#106055952
C5×#18522
#106023482
#106014082
#106013982
#106007212
#106002982
#105995892
#105995792
#213655