Finite Group Databasebeta

← #13031162

Subgroups — #13031162

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
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2#10617039C211yesmaximal, characteristic
3#10617037C211yesmaximal, characteristic
4#10604971C214yesmaximal, complemented
5#10604662C214yesmaximal, complemented
6#10604659C214yesmaximal, complemented
7C22×Q8×D5C412yes—
8C2×C5×C4⋊Q8C411yescharacteristic
9C2×#4090C2212yes—
10D5×C4⋊Q8—21no—
11D5×C4⋊Q8—21no—
12D5×C4⋊Q8—21no—
13D5×C4⋊Q8—21no—
14D5×C4⋊Q8C412yes—
15D5×C4⋊Q8C412yes—
16D5×C4⋊Q8C2212yes—
17D5×C4⋊Q8C2212yes—
18C2×D5×C4⋊C4—21no—
19C2×D5×C4⋊C4—21no—
20C2×#4034—21no—
21C2×#4034—21no—
22C2×C42×D5C2211yescharacteristic
23C2×#4015C411yescharacteristic
24#65758C2212yes—
25#65757—21no—
26#65756—21no—
27#65755—21no—
28#65754C2212yes—
29C4×#704—21no—
30#65684C2212yes—
31#65684C2212yes—
32#65683—21no—
33#65682C2212yes—
34#65680—21no—
35#65678—21no—
36#65678C2212yes—
37C4×#700—21no—
38#64931C22116yescomplemented
39#17746—51nomaximal, Sylow
40C22×C5×Q8C2×C412yes—
41C2×Q8×D5—22no—
42C2×Q8×D5—22no—
43C2×Q8×D5—48no—
44C2×Q8×D5C2×C414yes—
45C2×Q8×D5C2×C414yes—
46C22×C4×D5—22no—
47C22×C4×D5C2×C411yescharacteristic
48C22×C4×D5D411yescharacteristic
49C22×C4×D5D411yescharacteristic
50C22×Dic10—22no—
51C22×Dic10C2×C412yes—
52C2×#704—22no—
53C2×#700—22no—
54C5×C4⋊Q8—21no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8C2×C412yes—
57C5×C4⋊Q8C2×C412yes—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C42×C5C2×C411yescharacteristic
61#4090—22no—
62#4090—22no—
63#4090C2×C414yes—
64#4090C2314yes—
65C2×C4⋊Dic5—21no—
66C2×C4⋊Dic5—21no—
67C2×#683—22no—
68C2×#683—22no—
69C2×C4×Dic5D411yescharacteristic
70C2×C4×Dic5D411yescharacteristic
71C2×C4×Dic5C2311yescharacteristic
72D5×C4⋊C4—22no—
73D5×C4⋊C4—22no—
74D5×C4⋊C4—22no—
75D5×C4⋊C4—22no—
76D5×C4⋊C4—22no—
77D5×C4⋊C4—22no—
78D5×C4⋊C4—22no—
79D5×C4⋊C4—22no—
80#4034—22no—
81#4034—22no—
82#4034—22no—
83#4034—22no—
84#4034—22no—
85#4034—22no—
86#4034—22no—
87#4034—22no—
88C42×D5C2×C411yescharacteristic
89C42×D5C2×C411yescharacteristic
90C42×D5D411yescharacteristic
91C42×D5D411yescharacteristic
92C42×D5D411yescharacteristic
93C42×D5D411yescharacteristic
94C42×D5C2311yescharacteristic
95C42×D5C2311yescharacteristic
96#4015—21no—
97#4015—21no—
98#4015C2×C412yes—
99#4015C2×C412yes—
100C22⋊#170—22no—
101#4004—22no—
102#4004C2314yes—
103#4004C2314yes—
104#4003—22no—
105#4003—22no—
106#4003—22no—
107#4002—22no—
108#4002—22no—
109C4⋊#170—22no—
110C4×#170—22no—
111C4×#170—22no—
112C22×C4⋊Q8—51no—
113#2920—51no—
114#2920—51no—
115#1558—54no—
116#1548—54no—
117#1548—54no—
118C23×D5C22⋊C411yescharacteristic
119C2×C5×Q8—22no—
120C2×C5×Q8—44no—
121C2×C5×Q8C22×C414yes—
122C22×C4×C5—22no—
123C22×C4×C5C22⋊C411yescharacteristic
124C22×C4×C5C22⋊C411yescharacteristic
125C22×C4×C5C22×C411yescharacteristic
126C22×Dic5—22no—
127C22×Dic5C22⋊C411yescharacteristic
128C22×Dic5C2×D411yescharacteristic
129C22×Dic5C2×D411yescharacteristic
130Q8×D5—48no—
131Q8×D5—48no—
132Q8×D5—48no—
133Q8×D5—48no—
134C2×C4×D5—24no—
135C2×C4×D5—24no—
136C2×C4×D5—24no—
137C2×C4×D5—24no—
138C2×C4×D5—24no—
139C2×C4×D5—48no—
140C2×C4×D5C22⋊C411yescharacteristic
141C2×C4×D5C22⋊C411yescharacteristic
142C2×C4×D5C22⋊C411yescharacteristic
143C2×C4×D5C22⋊C411yescharacteristic
144C2×C4×D5C22⋊C411yescharacteristic
145C2×C4×D5C22⋊C411yescharacteristic
146C2×C4×D5C22×C411yescharacteristic
147C2×C4×D5C22×C411yescharacteristic
148C2×C4×D5C2×D411yescharacteristic
149C2×C4×D5C2×D411yescharacteristic
150C2×C4×D5C2×D411yescharacteristic
151C2×C4×D5C2×D411yescharacteristic
152C2×Dic10—22no—
153C2×Dic10—24no—
154C2×Dic10—24no—
155C2×Dic10—48no—
156C2×Dic10—44no—
157C2×Dic10C22×C414yes—
158#704—44no—
159C2×#170—24no—
160C2×#170—24no—
161#700—44no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—22no—
166C42×C5C22⋊C411yescharacteristic
167C42×C5C22⋊C411yescharacteristic
168C42×C5C22×C411yescharacteristic
169C42×C5C22×C411yescharacteristic
170C4⋊Dic5—22no—
171C4⋊Dic5—22no—
172C4⋊Dic5—22no—
173C4⋊Dic5—22no—
174#683—24no—
175#683—24no—
176#683—24no—
177#683—24no—
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—52no—
191C2×C4⋊Q8—52no—
192C2×C4⋊Q8—52no—
193C2×C4⋊Q8—52no—
194C2×C4⋊Q8—52no—
195C2×C4⋊Q8—52no—
196C2×C4⋊Q8—51no—
197C2×C4⋊Q8—101no—
198C2×C4⋊Q8—101no—
199C2×C4⋊Q8—101no—
200C2×C4⋊Q8—101no—
201C2×C4⋊Q8—101no—
202C2×C4⋊Q8—101no—
203C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
204C22×C4⋊C4—101no—
205C22×C4⋊C4—101no—
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#333—516no—
222C23×C5C2×C22⋊C411yescharacteristic
223C22×D5—22no—
224C22×D5—22no—
225C22×D5—22no—
226C22×D5C2×C22⋊C411yescharacteristic
227C22×D5C2×C22⋊C411yescharacteristic
228C5×Q8—44no—
229C5×Q8—44no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—44no—
235C2×C4×C5C2×C22⋊C411yescharacteristic
236C2×C4×C5C2×C22⋊C411yescharacteristic
237C2×C4×C5C2×C22⋊C411yescharacteristic
238C2×C4×C5C2×C22⋊C411yescharacteristic
239C2×C4×C5C2×C22⋊C411yescharacteristic
240C2×C4×C5C23×C411yescharacteristic
241C2×Dic5—22no—
242C2×Dic5—22no—
243C2×Dic5—24no—
244C2×Dic5—44no—
245C2×Dic5C2×C22⋊C411yescharacteristic
246C2×Dic5C2×C22⋊C411yescharacteristic
247C2×Dic5C2×C22⋊C411yescharacteristic
248C2×Dic5C2×C22⋊C411yescharacteristic
249C2×Dic5#13714yes—
250C2×Dic5C22×D411yescharacteristic
251C2×Dic5C22×D411yescharacteristic
252C4×D5—22no—
253C4×D5—22no—
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—22no—
257C4×D5—22no—
258C4×D5—22no—
259C4×D5—22no—
260C4×D5—22no—
261C4×D5—22no—
262C4×D5—48no—
263C4×D5—48no—
264C4×D5#10014yes—
265C4×D5#13714yes—
266Dic10—48no—
267Dic10—44no—
268Dic10—48no—
269Dic10—44no—
270#170—44no—
271#170—44no—
272C22×Q8—54no—
273C22×Q8—54no—
274C22×Q8—52no—
275C22×Q8—102no—
276C22×Q8—102no—
277C22×Q8—102no—
278C22×Q8—208no—
279C22×Q8C2×AGL(1,𝔽5)12yes—
280C23×C4—51no—
281C23×C4—51no—
282C23×C4—51no—
283C23×C4—102no—
284C2×M16—102no—
285C2×M16—102no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—54no—
289C4⋊Q8—54no—
290C4⋊Q8—52no—
291C4⋊Q8—52no—
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—
302C4⋊Q8—101no—
303C4⋊Q8—101no—
304C4⋊Q8C2×AGL(1,𝔽5)12yes—
305C4⋊Q8C2×AGL(1,𝔽5)12yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
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—102no—
315C2×C4⋊C4—102no—
316C2×C4⋊C4—102no—
317C2×C4⋊C4—102no—
318C2×C4⋊C4—101no—
319C2×C4⋊C4—101no—
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×C42C2×AGL(1,𝔽5)11yescharacteristic
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—21no—
345C22×C5—21no—
346C22×C5#41912yes—
347C22×C5C22×C22⋊C411yescharacteristic
348C2×D5—28no—
349C2×D5—21no—
350C2×D5—21no—
351C2×D5—21no—
352C2×D5—21no—
353C2×D5C2×#10012yes—
354C2×D5#41912yes—
355C4×C5—21no—
356C4×C5—21no—
357C4×C5—21no—
358C4×C5—21no—
359C4×C5—44no—
360C4×C5C2×#10012yes—
361C4×C5#41912yes—
362Dic5—21no—
363Dic5—21no—
364Dic5—44no—
365Dic5C2×#10012yes—
366Dic5#41912yes—
367Dic5C2×#13712yes—
368Dic5C2×#13712yes—
369C24—51no—
370C2×Q8—22no—
371C2×Q8—44no—
372C2×Q8—54no—
373C2×Q8—104no—
374C2×Q8—104no—
375C2×Q8—102no—
376C2×Q8—204no—
377C2×Q8—208no—
378C2×Q8—208no—
379C2×Q8—208no—
380C2×Q8—208no—
381C2×Q8—208no—
382C2×Q8C22×AGL(1,𝔽5)14yes—
383C22×C4—22no—
384C22×C4—51no—
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—51no—
398C22×C4—51no—
399C22×C4—104no—
400C22×C4—104no—
401C22×C4—104no—
402C22×C4—104no—
403C22×C4—104no—
404C22×C4—102no—
405C22×C4—208no—
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—22no—
417C4⋊C4—104no—
418C4⋊C4—104no—
419C4⋊C4—104no—
420C4⋊C4—104no—
421C4⋊C4—102no—
422C4⋊C4—102no—
423C4⋊C4—102no—
424C4⋊C4—102no—
425C42—51no—
426C42—51no—
427C42—51no—
428C42—51no—
429C42—51no—
430C42—51no—
431C42—51no—
432C42—51no—
433C42—51no—
434C42—51no—
435C42—51no—
436C42—51no—
437C42C22⋊AGL(1,𝔽5)11yescharacteristic
438C42C22⋊AGL(1,𝔽5)11yescharacteristic
439C42C22×AGL(1,𝔽5)11yescharacteristic
440C42C22×AGL(1,𝔽5)11yescharacteristic
441C2×C5—22no—
442C2×C5C22×#10011yescharacteristic
443C2×C5C2×#41911yescharacteristic
444C2×C5C2×#41911yescharacteristic
445D5—22no—
446D5—22no—
447C23—51no—
448C23—51no—
449C23—102no—
450C23—102no—
451C23—102no—
452C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
453Q8—44no—
454Q8—44no—
455Q8—204no—
456Q8—208no—
457Q8—208no—
458Q8—204no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—44no—
464C2×C4—51no—
465C2×C4—51no—
466C2×C4—51no—
467C2×C4—51no—
468C2×C4—54no—
469C2×C4—54no—
470C2×C4—54no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—102no—
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—104no—
486C2×C4—208no—
487C2×C4—208no—
488C2×C4—204no—
489C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
490C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
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#1774611yescharacteristic, complemented, Sylow
498C22—21no—
499C22—21no—
500C22—52no—
501C22—52no—
502C22—108no—
503C22—101no—
504C22—101no—
505C22—101no—
506C22—101no—
507C22#6578212yes—
508C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—44no—
514C4—52no—
515C4—52no—
516C4—52no—
517C4—52no—
518C4—101no—
519C4—101no—
520C4—204no—
521C4D5⋊#10012yes—
522C4#6578212yes—
523C2—22no—
524C2—102no—
525C2—102no—
526C2C2×D5⋊#10011yescharacteristic
527C2C2×#6578211yescharacteristic
528C2C2×#6578211yescharacteristic
subgroupG/H
centerC22C22×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC4×Dic5C24
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#17746
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10604971C2semidirect
5. #10604662C2semidirect
6. #10604659C2semidirect
38. #64931C22semidirect
497. C5#17746semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
#106170392
#106170372
#106049712
#106046622
#106046592
#177465