Finite Group Databasebeta

← #13029323

Subgroups — #13029323

Order 1280.

1174 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65838C211yesmaximal, characteristic
2#10617094C212yesmaximal, complemented
3#10604885C212yesmaximal, complemented
4#10604883C212yesmaximal, complemented
5#10604879C212yesmaximal, complemented
6#10604294C212yesmaximal, complemented
7#10604293C212yesmaximal, complemented
8#10604289C212yesmaximal, complemented
9C22×#709C411yescharacteristic
10C22×C5×C4⋊C4C411yescharacteristic
11C2×C4×C22⋊D5C411yescharacteristic
12C2×C4×C22⋊D5C411yescharacteristic
13C2×C4×C22⋊D5C2211yescharacteristic
14C2×C4×C22⋊D5C2211yescharacteristic
15C2×#4072C2211yescharacteristic
16#65838—28no—
17C2×#4039C411yescharacteristic
18C2×#4039C2211yescharacteristic
19C2×#4038C2211yescharacteristic
20C2×#4038C2211yescharacteristic
21C2×D5×C4⋊C4C411yescharacteristic
22C2×D5×C4⋊C4C411yescharacteristic
23C2×#4033C411yescharacteristic
24C2×#4033C2211yescharacteristic
25#65759C2214yes—
26#65757C2214yes—
27#65754C2214yes—
28#65707—28no—
29#64933C2214yes—
30#64915C2214yes—
31#64915C2214yes—
32#64913C2214yes—
33#17372—51nomaximal, Sylow
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5C2×C411yescharacteristic
36C23×C4×C5C2×C411yescharacteristic
37C22×C22⋊D5C2×C411yescharacteristic
38C22×C22⋊D5C2×C411yescharacteristic
39C2×#709—24no—
40C2×#709—24no—
41C2×#709—24no—
42C22×D20C2×C411yescharacteristic
43C22×C4×D5C2×C411yescharacteristic
44C22×C4×D5C2×C411yescharacteristic
45C22×C4×D5C2×C411yescharacteristic
46C22×C4×D5C2×C411yescharacteristic
47C22×C4×D5C2×C411yescharacteristic
48C22×C4×D5C2×C411yescharacteristic
49C22×Dic10C2×C411yescharacteristic
50C2×C5×C4⋊C4—24no—
51C2×C5×C4⋊C4C2×C411yescharacteristic
52C2×C5×C4⋊C4C2×C411yescharacteristic
53C2×C5×C4⋊C4C2×C411yescharacteristic
54C2×C5×C4⋊C4C2×C411yescharacteristic
55C2×C22⋊Dic5C2×C411yescharacteristic
56C2×C22⋊Dic5C2311yescharacteristic
57C4×C22⋊D5—24no—
58C4×C22⋊D5—24no—
59C4×C22⋊D5—24no—
60C4×C22⋊D5—24no—
61C2×#685C2×C411yescharacteristic
62C2×#685C2×C411yescharacteristic
63C2×#685C2311yescharacteristic
64C2×#685C2311yescharacteristic
65#4072—24no—
66C2×C4⋊Dic5C2×C411yescharacteristic
67C2×C4⋊Dic5C2311yescharacteristic
68C2×#683C2×C411yescharacteristic
69C2×#683C2×C411yescharacteristic
70C2×#683C2×C411yescharacteristic
71C2×#683C2×C411yescharacteristic
72C2×C4×Dic5C2×C411yescharacteristic
73C2×C4×Dic5C2×C411yescharacteristic
74C2×C4×Dic5C2×C411yescharacteristic
75C2×C4×Dic5C2311yescharacteristic
76C2×C4×Dic5C2311yescharacteristic
77C2×C4×Dic5C2311yescharacteristic
78#4039—24no—
79#4039—24no—
80#4038—24no—
81#4038—24no—
82D5×C4⋊C4—24no—
83D5×C4⋊C4—24no—
84#4033—24no—
85#4033D418yes—
86C22⋊#170C2318yes—
87#4004—24no—
88#4004—24no—
89#4002—24no—
90#4002—24no—
91C4⋊#170—24no—
92C4×#170—24no—
93C2×#520—51no—
94#2983—52no—
95#1466—52no—
96#1466—52no—
97#1464—52no—
98#1464—52no—
99#1460—52no—
100#1458—52no—
101C24×C5C22×C411yescharacteristic
102C23×D5C22×C411yescharacteristic
103C23×D5C22×C411yescharacteristic
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—81no—
110C22×C4×C5—81no—
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C22×C411yescharacteristic
113C22×C4×C5C22×C411yescharacteristic
114C22×C4×C5C22×C411yescharacteristic
115C22×C4×C5C22×C411yescharacteristic
116C22×C4×C5C22×C411yescharacteristic
117C2×C22⋊D5—22no—
118C2×C22⋊D5—22no—
119C2×C22⋊D5—22no—
120C2×C22⋊D5—22no—
121C2×C22⋊D5—22no—
122C2×C22⋊D5M1614yes—
123C22×Dic5C22×C411yescharacteristic
124C22×Dic5C22×C411yescharacteristic
125C22×Dic5C22×C411yescharacteristic
126C22×Dic5C22×C411yescharacteristic
127C22×Dic5C22×C411yescharacteristic
128C22×Dic5C2411yescharacteristic
129#709—232no—
130C2×D20—22no—
131C2×D20—22no—
132C2×D20—22no—
133C2×C4×D5—22no—
134C2×C4×D5—22no—
135C2×C4×D5—22no—
136C2×C4×D5—22no—
137C2×C4×D5—22no—
138C2×C4×D5—22no—
139C2×C4×D5—22no—
140C2×C4×D5—22no—
141C2×C4×D5—22no—
142C2×C4×D5—81no—
143C2×C4×D5—81no—
144C2×C4×D5—81no—
145C2×C4×D5—81no—
146C2×C4×D5M1614yes—
147C2×Dic10—22no—
148C2×Dic10—22no—
149C2×Dic10C22⋊C414yes—
150C2×#170—28no—
151C5×C4⋊C4—22no—
152C5×C4⋊C4—22no—
153C5×C4⋊C4—22no—
154C5×C4⋊C4C22⋊C414yes—
155C22⋊Dic5—22no—
156C22⋊Dic5—22no—
157#685—22no—
158#685—22no—
159#685—22no—
160#685—22no—
161C4⋊Dic5—22no—
162C4⋊Dic5—22no—
163#683—22no—
164#683—22no—
165#683C22⋊C414yes—
166#683C22⋊C414yes—
167C4×Dic5—22no—
168C4×Dic5—22no—
169C4×Dic5—22no—
170C4×Dic5C2×D414yes—
171C4×Dic5C2×D414yes—
172C4×Dic5C2×D414yes—
173C22×#41—51no—
174#520—108no—
175C2×C4×Q8—51no—
176C2×C4×Q8—51no—
177C2×C4×D4—51no—
178C2×C4×D4—51no—
179C2×C4×D4—51no—
180C2×C4×D4—51no—
181C2×C4×D4—51no—
182C2×C4×D4—51no—
183C2×#117—51no—
184C2×#117—51no—
185C2×#117—51no—
186C22×C4⋊C4—51no—
187C22×C4⋊C4—51no—
188C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
189#446—108no—
190#432—54no—
191#432—54no—
192#431—54no—
193#324—54no—
194#323—54no—
195#323—54no—
196#323—54no—
197C23×C5—21no—
198C23×C5—21no—
199C23×C5—41no—
200C23×C5—41no—
201C23×C5C2×M1612yes—
202C23×C5C23×C411yescharacteristic
203C22×D5—21no—
204C22×D5—21no—
205C22×D5—21no—
206C22×D5—21no—
207C22×D5—41no—
208C22×D5—41no—
209C22×D5—41no—
210C22×D5—41no—
211C22×D5C2×M1612yes—
212C22×D5C2×M1612yes—
213C2×C4×C5—28no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—82no—
225C2×C4×C5—82no—
226C2×C4×C5C2×C22⋊C412yes—
227C2×C4×C5C2×C22⋊C412yes—
228C2×C4×C5C2×C22⋊C412yes—
229C2×C4×C5C2×M1612yes—
230C22⋊D5—28no—
231C22⋊D5—28no—
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—41no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5C2×C22⋊C412yes—
241C2×Dic5C2×C22⋊C412yes—
242C2×Dic5C2×C22⋊C412yes—
243C2×Dic5C2×M1612yes—
244C2×Dic5C2×M1612yes—
245C2×Dic5C22×D412yes—
246D20—28no—
247C4×D5—28no—
248C4×D5—28no—
249C4×D5—82no—
250C4×D5—82no—
251C4×D5—82no—
252C4×D5—82no—
253Dic10—28no—
254#170—48no—
255C2×#41—104no—
256C2×#41—104no—
257C2×#41—104no—
258C22×Q8—51no—
259C22×D4—51no—
260C22×D4—51no—
261C22×D4—51no—
262C23×C4—51no—
263C23×C4—51no—
264C23×C4—51no—
265C23×C4—51no—
266C23×C4—51no—
267C23×C4—51no—
268C23×C4C2×AGL(1,𝔽5)11yescharacteristic
269C23×C4C2×AGL(1,𝔽5)11yescharacteristic
270C23×C4C2×AGL(1,𝔽5)11yescharacteristic
271C4×Q8—58no—
272C4×Q8—104no—
273C4×D4—104no—
274C4×D4—104no—
275C4×D4—104no—
276C4×D4—104no—
277C4×D4—104no—
278C4×D4—104no—
279#117—104no—
280#117—104no—
281#117—104no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—51no—
284C2×C4⋊C4—51no—
285C2×C4⋊C4—51no—
286C2×C4⋊C4—51no—
287C2×C4⋊C4—51no—
288C2×C4⋊C4—51no—
289C2×C4⋊C4—104no—
290C2×C4⋊C4—104no—
291C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
292C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
293C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
294C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
295C2×C22⋊C4—51no—
296C2×C22⋊C4—51no—
297C2×C22⋊C4—51no—
298C2×C22⋊C4—51no—
299C2×C22⋊C4—51no—
300C2×C22⋊C4—51no—
301C2×C42—51no—
302C2×C42—51no—
303C2×C42—51no—
304C2×C42—51no—
305C2×C42—51no—
306C2×C42—51no—
307C4⋊C8—104no—
308C4⋊C8—104no—
309C4⋊C8—104no—
310C22⋊C8—58no—
311#97—104no—
312#97—104no—
313C4×C8—104no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—22no—
317C22×C5—42no—
318C22×C5—42no—
319C22×C5—41no—
320C22×C5—41no—
321C22×C5C22×C22⋊C411yescharacteristic
322C22×C5C22×M1611yescharacteristic
323C22×C5C22×M1611yescharacteristic
324C2×D5—22no—
325C2×D5—22no—
326C2×D5—42no—
327C2×D5—42no—
328C2×D5—41no—
329C2×D5—41no—
330C2×D5—41no—
331C2×D5—41no—
332C2×D5—42no—
333C2×D5—42no—
334C4×C5—22no—
335C4×C5—22no—
336C4×C5—22no—
337C4×C5—22no—
338C4×C5—41no—
339C4×C5—41no—
340Dic5—22no—
341Dic5—22no—
342Dic5—22no—
343Dic5—41no—
344Dic5—41no—
345Dic5#40714yes—
346C24—51no—
347C24—51no—
348C24C22×AGL(1,𝔽5)11yescharacteristic
349#41—1032no—
350C2×Q8—54no—
351C2×Q8—102no—
352C2×Q8—102no—
353C2×D4—54no—
354C2×D4—102no—
355C2×D4—102no—
356C2×D4—102no—
357C2×D4—102no—
358C2×D4—102no—
359C2×D4—102no—
360C2×D4—102no—
361C2×D4—102no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—51no—
370C22×C4—51no—
371C22×C4—54no—
372C22×C4—51no—
373C22×C4—51no—
374C22×C4—81no—
375C22×C4—81no—
376C22×C4—102no—
377C22×C4—102no—
378C22×C4—102no—
379C22×C4—102no—
380C22×C4—102no—
381C22×C4—102no—
382C22×C4—102no—
383C22×C4—102no—
384C22×C4—102no—
385C22×C4—401no—
386C22×C4—401no—
387C22×C4—401no—
388C22×C4—401no—
389C22×C4C22×AGL(1,𝔽5)11yescharacteristic
390C22×C4C22×AGL(1,𝔽5)11yescharacteristic
391C22×C4C22×AGL(1,𝔽5)11yescharacteristic
392C22×C4C22×AGL(1,𝔽5)11yescharacteristic
393C22×C4C22×AGL(1,𝔽5)11yescharacteristic
394C22×C4C22×AGL(1,𝔽5)11yescharacteristic
395C2×C8—108no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—54no—
400C4⋊C4—54no—
401C4⋊C4—102no—
402C4⋊C4—102no—
403C4⋊C4—102no—
404C4⋊C4—102no—
405C4⋊C4C22⋊AGL(1,𝔽5)14yes—
406C22⋊C4—102no—
407C22⋊C4—102no—
408C22⋊C4—102no—
409C22⋊C4—102no—
410C22⋊C4—102no—
411C22⋊C4—102no—
412C42—54no—
413C42—54no—
414C42—54no—
415C42—102no—
416C42—102no—
417C42—102no—
418C2×C5—21no—
419C2×C5—21no—
420C2×C5—42no—
421C2×C5C2×#40711yescharacteristic
422C2×C5#288411yescharacteristic
423C2×C5#288811yescharacteristic
424D5—42no—
425D5—42no—
426C23—21no—
427C23—21no—
428C23—41no—
429C23—41no—
430C23—52no—
431C23—52no—
432C23—101no—
433C23—101no—
434C23—101no—
435C23—101no—
436C23—201no—
437C23—201no—
438C23—201no—
439C23—201no—
440C23D5⋊M1612yes—
441C23C23×AGL(1,𝔽5)11yescharacteristic
442Q8—108no—
443D4—108no—
444D4—108no—
445D4—108no—
446C2×C4—28no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—52no—
458C2×C4—52no—
459C2×C4—52no—
460C2×C4—52no—
461C2×C4—52no—
462C2×C4—52no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—108no—
466C2×C4—108no—
467C2×C4—101no—
468C2×C4—101no—
469C2×C4—101no—
470C2×C4—101no—
471C2×C4—201no—
472C2×C4—201no—
473C2×C4—201no—
474C2×C4—201no—
475C2×C4—402no—
476C2×C4—402no—
477C2×C4—402no—
478C2×C4—402no—
479C2×C4D5⋊M1612yes—
480C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
481C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
482C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
483C8—208no—
484C5#1737211yescharacteristic, complemented, Sylow
485C22—21no—
486C22—21no—
487C22—22no—
488C22—42no—
489C22—42no—
490C22—41no—
491C22—41no—
492C22—102no—
493C22—102no—
494C22—202no—
495C22—202no—
496C22—202no—
497C22—202no—
498C22—201no—
499C22—201no—
500C22—201no—
501C22—201no—
502C22C2×D5⋊M1611yescharacteristic
503C22C2×D5⋊M1611yescharacteristic
504C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
505C4—22no—
506C4—22no—
507C4—22no—
508C4—22no—
509C4—41no—
510C4—41no—
511C4—54no—
512C4—102no—
513C4—102no—
514C4—102no—
515C4—201no—
516C4—201no—
517C2—21no—
518C2—21no—
519C2—42no—
520C2—202no—
521C2—202no—
522C2D5⋊#40711yescharacteristic
523C2#1061750311yescharacteristic
524C2#1061751411yescharacteristic
subgroupG/H
centerC22C22×C22⋊AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC22×C5C22×C22⋊C4
prime radicalC22×#709C4
cosocleC22×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#17372
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10617094C2semidirect
3. #10604885C2semidirect
4. #10604883C2semidirect
5. #10604879C2semidirect
6. #10604294C2semidirect
7. #10604293C2semidirect
8. #10604289C2semidirect
484. C5#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#658382
#106170942
#106048852
#106048832
#106048792
#106042942
#106042932
#106042892
#173725