Finite Group Databasebeta

← #12021835

Subgroups — #12021835

Order 1280.

1862 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C211yesmaximal, characteristic
2C2×#65276C211yesmaximal, characteristic
3C2×C4×#685C211yesmaximal, characteristic
4C5×C4⋊#95C211yesmaximal, characteristic, complemented
5#10602356C211yesmaximal, characteristic, complemented
6#10602356C211yesmaximal, characteristic, complemented
7#10602328C211yesmaximal, characteristic, complemented
8#10600222C214yesmaximal
9#10600196C214yesmaximal, complemented
10C23×C4×D5C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×#685C2212yes—
15C22×#685C2212yes—
16C22×#685C2212yes—
17C22×C4⋊Dic5C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×C4×Dic5C2211yescharacteristic
20C22×C4×Dic5C2212yes—
21C2×#4038—24no—
22C2×#4038—24no—
23C2×#4038C418yescomplemented
24C2×C5×#95C2214yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2214yes—
28C2×#3963C2214yes—
29C2×#3963C2214yes—
30#65276—24no—
31C4×#685—24no—
32#13939—51nomaximal, Sylow
33C24×D5C2311yescharacteristic
34C23×C4×C5C2312yes—
35C23×C4×C5C2312yes—
36C23×C4×C5C2312yes—
37C23×C4×C5C2311yescharacteristic
38C23×Dic5C2312yes—
39C23×Dic5C2312yes—
40C23×Dic5C2312yes—
41C23×Dic5C2311yescharacteristic
42C22×C4×D5—22no—
43C22×C4×D5—22no—
44C22×C4×D5—22no—
45C22×C4×D5—22no—
46C22×C4×D5C2×C414yes—
47C22×C4×D5D414yes—
48C22×C4×D5D414yes—
49C2×C5×C4⋊C4—22no—
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—22no—
52C2×C5×C4⋊C4—22no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4C2×C414yes—
55C2×C42×C5—22no—
56C2×C42×C5—22no—
57C2×C42×C5—22no—
58C2×#685—24no—
59C2×#685—24no—
60C2×#685—24no—
61C2×#685—24no—
62C2×#685—24no—
63C2×#685—24no—
64C2×#685—44no—
65C2×#685C2×C418yes—
66C2×C4⋊Dic5—22no—
67C2×C4⋊Dic5—22no—
68C2×C4⋊Dic5—22no—
69C2×C4⋊Dic5—22no—
70C2×C4⋊Dic5—22no—
71C2×C4⋊Dic5C2×C414yes—
72C2×C4×Dic5—24no—
73C2×C4×Dic5—24no—
74C2×C4×Dic5—22no—
75C2×C4×Dic5—22no—
76C2×C4×Dic5—22no—
77C2×C4×Dic5C2×C418yes—
78#4038—232no—
79C5×#95—44no—
80#3963—28no—
81#3963—24no—
82#3963—24no—
83#3963—28no—
84#3963—44no—
85C22×#117—51no—
86C2×#380—51no—
87C2×C4×C22⋊C4—51no—
88#1440—54no—
89C4⋊#95—51no—
90C4⋊#95—51no—
91C4⋊#95—51no—
92C4⋊#95D511yescharacteristic, complemented
93#1434—54no—
94C24×C5C2411yescharacteristic
95C23×D5—21no—
96C23×D5—21no—
97C23×D5—21no—
98C23×D5—21no—
99C23×D5—22no—
100C23×D5—22no—
101C23×D5—22no—
102C23×D5—22no—
103C23×D5C22×C412yes—
104C23×D5C2×D412yes—
105C23×D5C2×D412yes—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—24no—
113C22×C4×C5—22no—
114C22×C4×C5—24no—
115C22×C4×C5—22no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—24no—
120C22×C4×C5—24no—
121C22×C4×C5C22×C414yes—
122C22×C4×C5C22×C412yes—
123C22×C4×C5C2×D412yes—
124C22×C4×C5C2×D412yes—
125C22×C4×C5#4112yes—
126C22×C4×C5#4112yes—
127C22×C4×C5#4112yes—
128C22×C4×C5#4114yes—
129C22×C4×C5#4112yes—
130C22×Dic5—21no—
131C22×Dic5—21no—
132C22×Dic5—21no—
133C22×Dic5—21no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—24no—
138C22×Dic5—24no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—24no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—24no—
149C22×Dic5C22×C414yes—
150C22×Dic5C22×C412yes—
151C22×Dic5C2×D412yes—
152C22×Dic5C2×D412yes—
153C22×Dic5#4114yes—
154C2×C4×D5—28no—
155C2×C4×D5—28no—
156C2×C4×D5—28no—
157C2×C4×D5—28no—
158C2×C4×D5—28no—
159C2×C4×D5—28no—
160C2×C4×D5C22⋊C4116yes—
161C5×C4⋊C4—28no—
162C5×C4⋊C4—44no—
163C42×C5—44no—
164#685—216no—
165#685—216no—
166#685—48no—
167C4⋊Dic5—28no—
168C4⋊Dic5—44no—
169C4×Dic5—216no—
170C4×Dic5—44no—
171C24×C4—51no—
172C2×#117—58no—
173C2×#117—104no—
174C2×#117—104no—
175C22×C4⋊C4—51no—
176C22×C4⋊C4—51no—
177C22×C4⋊C4C2×D511yescharacteristic
178C22×C4⋊C4C2×D511yescharacteristic
179C22×C22⋊C4—52no—
180C22×C22⋊C4—52no—
181C22×C22⋊C4—52no—
182C22×C42—52no—
183C22×C42—51no—
184C22×C42C2×D511yescharacteristic
185#380—104no—
186C4×C22⋊C4—104no—
187C2×#95—52no—
188C2×#95—52no—
189C2×#95—54no—
190C2×#95—54no—
191C2×#95—54no—
192C2×#95C2×D514yes—
193C23×C5C23×C411yescharacteristic
194C23×C5C22×D411yescharacteristic
195C23×C5C22×D411yescharacteristic
196C23×C5C2×#4111yescharacteristic
197C23×C5C2×#4111yescharacteristic
198C23×C5C2×#4111yescharacteristic
199C23×C5C2×#4111yescharacteristic
200C23×C5C2×#4112yes—
201C23×C5C2×#4112yes—
202C23×C5H(5,𝔽2)12yes—
203C23×C52−1+412yes—
204C22×D5—22no—
205C22×D5—22no—
206C22×D5—24no—
207C22×D5—24no—
208C22×D5—22no—
209C22×D5—22no—
210C22×D5—22no—
211C22×D5—22no—
212C22×D5—24no—
213C22×D5—22no—
214C22×D5—22no—
215C22×D5—22no—
216C22×D5—22no—
217C22×D5—24no—
218C22×D5—42no—
219C22×D5—42no—
220C22×D5—42no—
221C22×D5—42no—
222C22×D5—42no—
223C22×D5—42no—
224C22×D5—42no—
225C22×D5—42no—
226C22×D5C2×C22⋊C414yes—
227C2×C4×C5—24no—
228C2×C4×C5—28no—
229C2×C4×C5—24no—
230C2×C4×C5—24no—
231C2×C4×C5—24no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—44no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—44no—
243C2×C4×C5—44no—
244C2×C4×C5C2×C22⋊C414yes—
245C2×C4×C5#11714yes—
246C2×C4×C5#11714yes—
247C2×C4×C5#12314yes—
248C2×C4×C5#12314yes—
249C2×C4×C5#12314yes—
250C2×C4×C5#12314yes—
251C2×Dic5—22no—
252C2×Dic5—22no—
253C2×Dic5—22no—
254C2×Dic5—22no—
255C2×Dic5—22no—
256C2×Dic5—22no—
257C2×Dic5—24no—
258C2×Dic5—28no—
259C2×Dic5—24no—
260C2×Dic5—24no—
261C2×Dic5—24no—
262C2×Dic5—42no—
263C2×Dic5—44no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—44no—
273C2×Dic5—44no—
274C2×Dic5C2×C22⋊C414yes—
275C4×D5—232no—
276C25—51no—
277C23×C4—51no—
278C23×C4—54no—
279C23×C4—54no—
280C23×C4—54no—
281C23×C4—52no—
282C23×C4—52no—
283C23×C4—52no—
284C23×C4—102no—
285C23×C4—102no—
286C23×C4—102no—
287C23×C4—102no—
288C23×C4C22×D512yes—
289C23×C4C22×D512yes—
290C23×C4C22×D512yes—
291C23×C4C22×D511yescharacteristic
292#117—1032no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—54no—
299C2×C4⋊C4—102no—
300C2×C4⋊C4—102no—
301C2×C4⋊C4—102no—
302C2×C4⋊C4—102no—
303C2×C4⋊C4—102no—
304C2×C4⋊C4C4×D514yes—
305C2×C22⋊C4—58no—
306C2×C22⋊C4—104no—
307C2×C22⋊C4—104no—
308C2×C22⋊C4—104no—
309C2×C22⋊C4—104no—
310C2×C22⋊C4—104no—
311C2×C22⋊C4—104no—
312C2×C22⋊C4—204no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—58no—
317C2×C42—104no—
318C2×C42—104no—
319C2×C42—102no—
320C2×C42—102no—
321C2×C42—102no—
322#95—44no—
323#95—104no—
324#95—108no—
325#95—104no—
326#95—108no—
327#95—204no—
328C22×C5C22×C22⋊C411yescharacteristic
329C22×C5C2×#11711yescharacteristic
330C22×C5C2×#11711yescharacteristic
331C22×C5C4×#4112yes—
332C22×C5#52012yes—
333C22×C5C2×#12311yescharacteristic
334C22×C5C2×#12311yescharacteristic
335C22×C5C2×#12311yescharacteristic
336C22×C5C2×#12311yescharacteristic
337C22×C5#52512yes—
338C22×C5#53211yescharacteristic
339C22×C5#53211yescharacteristic
340C22×C5#53511yescharacteristic
341C22×C5#53611yescharacteristic
342C22×C5#53712yes—
343C22×C5#55212yes—
344C22×C5#55212yes—
345C22×C5#55312yes—
346C22×C5#55312yes—
347C22×C5#55512yes—
348C22×C5#55512yes—
349C22×C5#55612yes—
350C22×C5#55612yes—
351C2×D5—24no—
352C2×D5—24no—
353C2×D5—24no—
354C2×D5—44no—
355C2×D5—44no—
356C2×D5—44no—
357C2×D5—44no—
358C2×D5—42no—
359C2×D5—42no—
360C2×D5—42no—
361C2×D5—42no—
362C4×C5—44no—
363C4×C5—44no—
364C4×C5—82no—
365C4×C5#38118yes—
366Dic5—24no—
367Dic5—44no—
368Dic5—44no—
369Dic5—82no—
370C24—52no—
371C24—52no—
372C24—52no—
373C24—101no—
374C24—101no—
375C24—101no—
376C24—102no—
377C24—102no—
378C24—101no—
379C24—102no—
380C24—102no—
381C24C23×D511yescharacteristic
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—52no—
398C22×C4—52no—
399C22×C4—52no—
400C22×C4—516no—
401C22×C4—54no—
402C22×C4—54no—
403C22×C4—101no—
404C22×C4—101no—
405C22×C4—101no—
406C22×C4—101no—
407C22×C4—108no—
408C22×C4—108no—
409C22×C4—108no—
410C22×C4—108no—
411C22×C4—108no—
412C22×C4—108no—
413C22×C4—102no—
414C22×C4—102no—
415C22×C4—102no—
416C22×C4—102no—
417C22×C4—102no—
418C22×C4—104no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—104no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—104no—
426C22×C4—104no—
427C22×C4—102no—
428C22×C4C2×C4×D514yes—
429C22×C4C2×C4×D512yes—
430C22×C4#70912yes—
431C22×C4#70912yes—
432C22×C4D4×D512yes—
433C22×C4D4×D512yes—
434C22×C4#71112yes—
435C22×C4#71314yes—
436C22×C4#71312yes—
437C4⋊C4—28no—
438C4⋊C4—44no—
439C4⋊C4—108no—
440C4⋊C4—204no—
441C22⋊C4—1016no—
442C22⋊C4—1016no—
443C22⋊C4—208no—
444C42—44no—
445C42—1016no—
446C42—204no—
447C2×C5C2×#38111yescharacteristic
448C2×C5#229711yescharacteristic
449C2×C5#231111yescharacteristic
450C2×C5#234612yes—
451C2×C5#234712yes—
452C2×C5#248512yes—
453C2×C5#248512yes—
454C2×C5#249911yescharacteristic
455C2×C5#249911yescharacteristic
456C2×C5#250011yescharacteristic
457C2×C5#250011yescharacteristic
458D5—44no—
459C23—54no—
460C23—102no—
461C23—102no—
462C23—102no—
463C23—102no—
464C23—102no—
465C23—102no—
466C23—102no—
467C23—102no—
468C23—104no—
469C23—104no—
470C23—104no—
471C23—104no—
472C23—102no—
473C23—102no—
474C23—202no—
475C23—202no—
476C23—202no—
477C23—202no—
478C23—202no—
479C23—202no—
480C23—202no—
481C23—202no—
482C23C22×C4×D511yescharacteristic
483C23C2×#70911yescharacteristic
484C23C2×#70911yescharacteristic
485C23C2×D4×D511yescharacteristic
486C23C2×D4×D511yescharacteristic
487C23C2×#71111yescharacteristic
488C23#414412yes—
489C23C2×#71312yes—
490C23C2×#71311yescharacteristic
491C23D5×#4112yes—
492C23#415012yes—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—28no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—42no—
510C2×C4—54no—
511C2×C4—102no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—102no—
517C2×C4—1032no—
518C2×C4—104no—
519C2×C4—104no—
520C2×C4—108no—
521C2×C4—104no—
522C2×C4—104no—
523C2×C4—202no—
524C2×C4—202no—
525C2×C4—202no—
526C2×C4—202no—
527C2×C4—202no—
528C2×C4—204no—
529C2×C4—202no—
530C2×C4—202no—
531C2×C4—202no—
532C2×C4—204no—
533C2×C4—202no—
534C2×C4—204no—
535C2×C4#401814yes—
536C2×C4D5×C22⋊C414yes—
537C2×C4#402914yes—
538C2×C4#402914yes—
539C2×C4#403814yes—
540C2×C4#404014yes—
541C2×C4#404014yes—
542C5#1393911yescharacteristic, complemented, Sylow
543C22—104no—
544C22—104no—
545C22—104no—
546C22—202no—
547C22—204no—
548C22—202no—
549C22—204no—
550C22—204no—
551C22—204no—
552C22—202no—
553C22—202no—
554C22C2×#401811yescharacteristic
555C22C2×D5×C22⋊C411yescharacteristic
556C22C2×#402911yescharacteristic
557C22C2×#402911yescharacteristic
558C22C2×#403811yescharacteristic
559C22C2×#404011yescharacteristic
560C22C2×#404011yescharacteristic
561C22#6584812yes—
562C22#6586712yes—
563C22#6588012yes—
564C22#6589212yes—
565C22C4×#71312yes—
566C22#6591812yes—
567C22#6594212yes—
568C22#6595012yes—
569C22#6596112yes—
570C22#6597612yes—
571C22#6600211yescharacteristic
572C22#6600911yescharacteristic
573C22#6602812yes—
574C22#6604911yescharacteristic
575C22#6605911yescharacteristic
576C22#6606812yes—
577C4—44no—
578C4—44no—
579C4—82no—
580C4—104no—
581C4—204no—
582C4—204no—
583C4—402no—
584C4#6495318yes—
585C2—204no—
586C2C2×#6495311yescharacteristic
587C2#1060536512yes—
588C2#1060575612yes—
589C2#1060589611yescharacteristic
590C2#1060609811yescharacteristic
591C2#1060771012yes—
592C2#1060796112yes—
593C2#1060802511yescharacteristic
594C2#1060806511yescharacteristic
595C2#1060820911yescharacteristic
596C2#1060836511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13939
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C5×C4⋊#95C2semidirect
5. #10602356C2semidirect
6. #10602356C2semidirect
7. #10602328C2semidirect
9. #10600196C2semidirect
23. C2×#4038C4semidirect
92. C4⋊#95D5semidirect
542. C5#13939semidirect

Maximal subgroups

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

subgroupindex
C22×#40382
C2×#652762
C2×C4×#6852
C5×C4⋊#952
#106023562
#106023282
#106002222
#106001962
#139395