Finite Group Databasebeta

← #13031144

Subgroups — #13031144

Order 1280.

1178 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4034C211yesmaximal, characteristic
2#10617473C211yesmaximal, characteristic
3#10617473C211yesmaximal, characteristic
4#10604279C214yesmaximal, complemented
5#10604278C214yesmaximal, complemented
6#10604277C214yesmaximal, complemented
7C23×Dic10—21no—
8C22×C5×C4⋊C4C411yescharacteristic
9C22×C4⋊Dic5C411yescharacteristic
10C22×#683—21no—
11C22×C4×Dic5C2211yescharacteristic
12C2×#4034—21no—
13C2×#4034—21no—
14C2×#4034—21no—
15C2×#4034—21no—
16C2×#4034—21no—
17C2×#4034—21no—
18C2×#4034C412yes—
19C2×#4034C412yes—
20C2×#4034C412yes—
21C2×#4034C2212yes—
22C2×#4034C2212yes—
23C2×#4034C2212yes—
24#65798—21no—
25#65798—21no—
26#65759—21no—
27#65759—21no—
28#65758C2212yes—
29#65758C2212yes—
30#65757C2212yes—
31#65757C2212yes—
32#65754C2212yes—
33#65754C2212yes—
34C4×#704—21no—
35C4×#704—21no—
36#65748—21no—
37#65748—21no—
38#64873C22116yescomplemented
39#17742—51nomaximal, Sylow
40C23×C4×C5—21no—
41C23×C4×C5C2×C411yescharacteristic
42C23×Dic5—21no—
43C23×Dic5D411yescharacteristic
44C23×Dic5D411yescharacteristic
45C22×Dic10—22no—
46C22×Dic10—22no—
47C22×Dic10—22no—
48C22×Dic10—22no—
49C22×Dic10—22no—
50C22×Dic10—22no—
51C22×Dic10—48no—
52C2×#704—22no—
53C2×#704—22no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4C2×C412yes—
58C2×C5×C4⋊C4C2×C412yes—
59C2×C5×C4⋊C4C2×C412yes—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5—21no—
62C2×C4⋊Dic5—21no—
63C2×C4⋊Dic5C2×C412yes—
64C2×C4⋊Dic5C2×C412yes—
65C2×C4⋊Dic5C2×C412yes—
66C2×#683—22no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683—22no—
70C2×#683—22no—
71C2×#683—22no—
72C2×C4×Dic5C2×C411yescharacteristic
73C2×C4×Dic5C2×C411yescharacteristic
74C2×C4×Dic5C2×C411yescharacteristic
75C2×C4×Dic5D411yescharacteristic
76C2×C4×Dic5D411yescharacteristic
77C2×C4×Dic5D411yescharacteristic
78C2×C4×Dic5D411yescharacteristic
79C2×C4×Dic5D411yescharacteristic
80C2×C4×Dic5D411yescharacteristic
81C2×C4×Dic5C2311yescharacteristic
82C2×C4×Dic5C2311yescharacteristic
83C2×C4×Dic5C2311yescharacteristic
84#4034—22no—
85#4034—22no—
86#4034—22no—
87#4034—22no—
88#4034—22no—
89#4034—22no—
90#4034—22no—
91#4034—22no—
92#4034—22no—
93#4034—22no—
94#4034—22no—
95#4034—22no—
96#4034C2×C414yes—
97#4034C2×C414yes—
98#4034C2×C414yes—
99#4034C2314yes—
100C22⋊#170—22no—
101C22⋊#170—22no—
102C22⋊#170—22no—
103C22⋊#170—22no—
104#4004C2314yes—
105#4004C2314yes—
106#4002—22no—
107#4002—22no—
108C4⋊#170—22no—
109C4⋊#170—22no—
110C4×#170—22no—
111C4×#170—22no—
112C22×C4⋊Q8—51no—
113#2920—51no—
114#2920—51no—
115#1556—54no—
116#1549—54no—
117#1546—54no—
118C24×C5C22⋊C411yescharacteristic
119C22×C4×C5—24no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—44no—
124C22×C4×C5C22⋊C411yescharacteristic
125C22×C4×C5C22⋊C411yescharacteristic
126C22×C4×C5C22⋊C411yescharacteristic
127C22×C4×C5C22×C411yescharacteristic
128C22×C4×C5C22×C411yescharacteristic
129C22×C4×C5C22×C411yescharacteristic
130C22×Dic5—24no—
131C22×Dic5—24no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—44no—
136C22×Dic5C22⋊C411yescharacteristic
137C22×Dic5C22⋊C411yescharacteristic
138C22×Dic5C22⋊C411yescharacteristic
139C22×Dic5C22⋊C411yescharacteristic
140C22×Dic5C22⋊C411yescharacteristic
141C22×Dic5C22⋊C411yescharacteristic
142C22×Dic5C2×D411yescharacteristic
143C22×Dic5C2×D411yescharacteristic
144C22×Dic5C2×D411yescharacteristic
145C22×Dic5C2×D411yescharacteristic
146C22×Dic5C2×D411yescharacteristic
147C22×Dic5C2×D411yescharacteristic
148C2×Dic10—24no—
149C2×Dic10—24no—
150C2×Dic10—24no—
151C2×Dic10—24no—
152C2×Dic10—48no—
153C2×Dic10—48no—
154C2×Dic10—48no—
155C2×Dic10—48no—
156C2×Dic10—48no—
157C2×Dic10—48no—
158#704—44no—
159#704—44no—
160C2×#170—24no—
161C2×#170—24no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4C22×C414yes—
166C4⋊Dic5—22no—
167C4⋊Dic5—22no—
168C4⋊Dic5—22no—
169C4⋊Dic5C22×C414yes—
170#683—24no—
171#683—24no—
172#683—24no—
173#683—24no—
174C4×Dic5C22⋊C411yescharacteristic
175C4×Dic5C22⋊C411yescharacteristic
176C4×Dic5C22⋊C411yescharacteristic
177C4×Dic5C22⋊C411yescharacteristic
178C4×Dic5C22⋊C411yescharacteristic
179C4×Dic5C22⋊C411yescharacteristic
180C4×Dic5C22×C411yescharacteristic
181C4×Dic5C22×C411yescharacteristic
182C4×Dic5C22×C411yescharacteristic
183C4×Dic5C2×D411yescharacteristic
184C4×Dic5C2×D411yescharacteristic
185C4×Dic5C2×D411yescharacteristic
186C4×Dic5C2×D411yescharacteristic
187C4×Dic5C2×D411yescharacteristic
188C4×Dic5C2×D411yescharacteristic
189C4×Dic5C2411yescharacteristic
190C23×Q8—101no—
191C2×C4⋊Q8—52no—
192C2×C4⋊Q8—52no—
193C2×C4⋊Q8—52no—
194C2×C4⋊Q8—52no—
195C2×C4⋊Q8—52no—
196C2×C4⋊Q8—52no—
197C2×C4⋊Q8—101no—
198C2×C4⋊Q8—101no—
199C2×C4⋊Q8—101no—
200C2×C4⋊Q8—101no—
201C2×C4⋊Q8—101no—
202C2×C4⋊Q8—101no—
203C22×C4⋊C4—51no—
204C22×C4⋊C4—101no—
205C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
206C22×C42—51no—
207#432—52no—
208#432—52no—
209#432—101no—
210#432—101no—
211#431—52no—
212#431—52no—
213#431—101no—
214#431—101no—
215#423—52no—
216#423—52no—
217#407—101no—
218#407—101no—
219C4×M16—101no—
220C4×M16—101no—
221#332—516no—
222C23×C5—22no—
223C23×C5—22no—
224C23×C5—22no—
225C23×C5C2×C22⋊C411yescharacteristic
226C23×C5C2×C22⋊C411yescharacteristic
227C23×C5C2×C22⋊C411yescharacteristic
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—44no—
235C2×C4×C5—44no—
236C2×C4×C5—44no—
237C2×C4×C5#10114yes—
238C2×C4×C5C2×C22⋊C411yescharacteristic
239C2×C4×C5C2×C22⋊C411yescharacteristic
240C2×C4×C5C2×C22⋊C411yescharacteristic
241C2×C4×C5C23×C411yescharacteristic
242C2×Dic5—22no—
243C2×Dic5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5—22no—
248C2×Dic5—22no—
249C2×Dic5—22no—
250C2×Dic5—22no—
251C2×Dic5—22no—
252C2×Dic5—24no—
253C2×Dic5—44no—
254C2×Dic5—44no—
255C2×Dic5—44no—
256C2×Dic5C2×C22⋊C411yescharacteristic
257C2×Dic5C2×C22⋊C411yescharacteristic
258C2×Dic5C2×C22⋊C411yescharacteristic
259C2×Dic5C2×C22⋊C411yescharacteristic
260C2×Dic5C2×C22⋊C411yescharacteristic
261C2×Dic5C2×C22⋊C411yescharacteristic
262C2×Dic5AGL(1,ℤ/8)14yes—
263C2×Dic5#13714yes—
264C2×Dic5C22×D411yescharacteristic
265C2×Dic5C22×D411yescharacteristic
266Dic10—48no—
267Dic10—48no—
268Dic10—48no—
269Dic10—48no—
270#170—44no—
271#170—44no—
272C22×Q8—102no—
273C22×Q8—102no—
274C22×Q8—102no—
275C22×Q8—102no—
276C22×Q8—102no—
277C22×Q8—102no—
278C22×Q8—208no—
279C23×C4—21no—
280C23×C4—51no—
281C23×C4—51no—
282C23×C4—101no—
283C23×C4C2×AGL(1,𝔽5)11yescharacteristic
284C2×M16—102no—
285C2×M16—102no—
286C4⋊Q8—54no—
287C4⋊Q8—54no—
288C4⋊Q8—54no—
289C4⋊Q8—54no—
290C4⋊Q8—102no—
291C4⋊Q8—102no—
292C4⋊Q8—102no—
293C4⋊Q8—102no—
294C4⋊Q8—102no—
295C4⋊Q8—102no—
296C4⋊Q8—102no—
297C4⋊Q8—102no—
298C4⋊Q8—102no—
299C4⋊Q8—102no—
300C4⋊Q8—102no—
301C4⋊Q8—102no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—52no—
306C2×C4⋊C4—52no—
307C2×C4⋊C4—52no—
308C2×C4⋊C4—102no—
309C2×C4⋊C4—102no—
310C2×C4⋊C4—102no—
311C2×C4⋊C4—102no—
312C2×C4⋊C4—102no—
313C2×C4⋊C4—102no—
314C2×C4⋊C4—101no—
315C2×C4⋊C4—101no—
316C2×C4⋊C4—101no—
317C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
318C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
319C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
320C2×C42—51no—
321C2×C42—51no—
322C2×C42—51no—
323C2×C42—51no—
324C2×C42—51no—
325C2×C42—51no—
326C2×C42—51no—
327C2×C42—51no—
328C2×C42—51no—
329C2×C42—51no—
330C2×C42—51no—
331C2×C42—51no—
332C4⋊C8—54no—
333C4⋊C8—54no—
334C4⋊C8—102no—
335C4⋊C8—102no—
336C22⋊C8—102no—
337C22⋊C8—102no—
338C22⋊C8—102no—
339C22⋊C8—102no—
340#97—102no—
341#97—102no—
342C4×C8—102no—
343C4×C8—102no—
344C22×C5—28no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—21no—
348C22×C5—21no—
349C22×C5—21no—
350C22×C5—21no—
351C22×C5C2×#10112yes—
352C22×C5#41812yes—
353C22×C5#41912yes—
354C22×C5C22×C22⋊C411yescharacteristic
355C4×C5—21no—
356C4×C5—21no—
357C4×C5—44no—
358C4×C5C2×#10112yes—
359C4×C5C2×#10112yes—
360Dic5—21no—
361Dic5—21no—
362Dic5—21no—
363Dic5—21no—
364Dic5—44no—
365Dic5#41812yes—
366Dic5#41912yes—
367Dic5C2×AGL(1,ℤ/8)12yes—
368Dic5C2×#13712yes—
369C24C22⋊AGL(1,𝔽5)11yescharacteristic
370C2×Q8—104no—
371C2×Q8—104no—
372C2×Q8—104no—
373C2×Q8—104no—
374C2×Q8—208no—
375C2×Q8—208no—
376C2×Q8—208no—
377C2×Q8—208no—
378C2×Q8—208no—
379C2×Q8—208no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—44no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—51no—
390C22×C4—51no—
391C22×C4—51no—
392C22×C4—51no—
393C22×C4—51no—
394C22×C4—51no—
395C22×C4—51no—
396C22×C4—51no—
397C22×C4—104no—
398C22×C4—104no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4—102no—
402C22×C4—204no—
403C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
404C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
405C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
406C22×C4C22×AGL(1,𝔽5)11yescharacteristic
407C22×C4C22×AGL(1,𝔽5)11yescharacteristic
408C22×C4C22×AGL(1,𝔽5)11yescharacteristic
409M16—204no—
410M16—204no—
411C2×C8—104no—
412C2×C8—104no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—54no—
417C4⋊C4—104no—
418C4⋊C4—104no—
419C4⋊C4—104no—
420C4⋊C4—104no—
421C4⋊C4—102no—
422C4⋊C4—102no—
423C4⋊C4—102no—
424C4⋊C4C22×AGL(1,𝔽5)14yes—
425C42—51no—
426C42—51no—
427C42—51no—
428C42—51no—
429C42—51no—
430C42—51no—
431C42—51no—
432C42—51no—
433C42—51no—
434C42—51no—
435C42—51no—
436C42—51no—
437C42—51no—
438C42—51no—
439C42—51no—
440C42—51no—
441C2×C5—22no—
442C2×C5—22no—
443C2×C5—22no—
444C2×C5C22×#10111yescharacteristic
445C2×C5C2×#41811yescharacteristic
446C2×C5C2×#41911yescharacteristic
447C23—22no—
448C23—22no—
449C23—22no—
450C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
451C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
452C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
453Q8—208no—
454Q8—208no—
455Q8—208no—
456Q8—208no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—51no—
467C2×C4—51no—
468C2×C4—51no—
469C2×C4—51no—
470C2×C4—54no—
471C2×C4—54no—
472C2×C4—51no—
473C2×C4—51no—
474C2×C4—51no—
475C2×C4—51no—
476C2×C4—102no—
477C2×C4—102no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—102no—
481C2×C4—102no—
482C2×C4—102no—
483C2×C4—102no—
484C2×C4—102no—
485C2×C4—102no—
486C2×C4—104no—
487C2×C4—204no—
488C2×C4—204no—
489C2×C4—204no—
490C2×C4#400514yes—
491C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
492C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
493C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
494C2×C4C23×AGL(1,𝔽5)11yescharacteristic
495C8—204no—
496C8—204no—
497C5#1774211yescharacteristic, complemented, Sylow
498C22—28no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22C2×#400512yes—
506C22#6576712yes—
507C22#6578212yes—
508C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
509C4—21no—
510C4—21no—
511C4—44no—
512C4—52no—
513C4—52no—
514C4—52no—
515C4—52no—
516C4—101no—
517C4—101no—
518C4—101no—
519C4—101no—
520C4—204no—
521C4C2×#400512yes—
522C4C2×#400512yes—
523C2—22no—
524C2—22no—
525C2—22no—
526C2C22×#400511yescharacteristic
527C2C2×#6576711yescharacteristic
528C2C2×#6578211yescharacteristic
subgroupG/H
centerC22C22×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC22×C5C22×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC4×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#17742
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10604279C2semidirect
5. #10604278C2semidirect
6. #10604277C2semidirect
38. #64873C22semidirect
497. C5#17742semidirect

Maximal subgroups

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

subgroupindex
C22×#40342
#106174732
#106042792
#106042782
#106042772
#177425