Finite Group Databasebeta

← #14280968

Subgroups — #14280968

Order 1920.

880 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91473C211yesmaximal, characteristic
2#11750827C211yesmaximal, characteristic, complemented
3#11748509C211yesmaximal, characteristic, complemented
4C5×#4468C211yesmaximal, characteristic, complemented
5C3×#64688C211yesmaximal, characteristic, complemented
6#11745949C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic, complemented
8#10598913—31nomaximal, Hall
9C23×D3×D5C411yescharacteristic
10C22×C4×D15C2211yescharacteristic
11C22×#1200C411yescharacteristic
12C2×#6705—21no—
13C2×C5×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×#685C2211yescharacteristic
15C2×(C2×D3)⋊Dic5C411yescharacteristic
16C2×#6665C411yescharacteristic
17#91473—21no—
18#91473—21no—
19#91473—21no—
20#91473—21no—
21C2×#6651—21no—
22C3×C5×C22⋊C8C2211yescharacteristic, complemented
23#91114C2211yescharacteristic, complemented
24#91104—21no—
25C5×#830C2211yescharacteristic, complemented
26C3×C22⋊#168C2211yescharacteristic, complemented
27#90957—21no—
28#68120—51nomaximal, Hall
29C2×D5×C22⋊C4—31no—
30#65015—31no—
31#65015—31no—
32C5×#323—31no—
33#64745—31no—
34#64688—31no—
35#64688D311yescharacteristic, complemented
36C23×D15C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C22×D3×D5—21no—
40C22×D3×D5—21no—
41C22×D3×D5—22no—
42C22×D3×D5—22no—
43C22×D3×D5—42no—
44C22×D3×D5—42no—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15C2×C411yescharacteristic
47C2×C4×D15—42no—
48C2×C4×D15D411yescharacteristic
49C2×C4×D15D411yescharacteristic
50C2×C4×D15D411yescharacteristic
51C2×C4×D15D411yescharacteristic
52C22×C5×Dic3C2×C411yescharacteristic
53C22×C3×Dic5C2×C411yescharacteristic
54C2×#1200—21no—
55C2×#1200—21no—
56C2×#1200—42no—
57C2×C3×C5×C8—21no—
58C2×C3⋊#168—21no—
59#6705—42no—
60C5×(C2×D3)⋊C4—21no—
61C5×(C2×D3)⋊C4—21no—
62C2×C5×C3⋊C8—21no—
63C3×#685—21no—
64C3×#685—21no—
65C2×C3×#168—21no—
66(C2×D3)⋊Dic5—21no—
67(C2×D3)⋊Dic5—21no—
68#6665—21no—
69#6665—21no—
70#6651—42no—
71C2×D3×C22⋊C4—51no—
72#4726—51no—
73#4726—51no—
74C3×#323—51no—
75#4525—51no—
76#4468—51no—
77#4468D511yescharacteristic, complemented
78C24×D5—31no—
79C22×C4×D5—31no—
80C22×C4×D5—31no—
81C2×C5×C22⋊C4—31no—
82C2×C22⋊Dic5—31no—
83C2×#685—31no—
84C2×#685C2×D311yescharacteristic
85C2×#676—61no—
86C2×#676—61no—
87D5×C22⋊C4—61no—
88D5×C22⋊C4—61no—
89D5×C22⋊C4—61no—
90D5×C22⋊C4—61no—
91C5×C22⋊C8—31no—
92C5×C22⋊C8C2×D311yescharacteristic, complemented
93C22⋊#168—31no—
94C22⋊#168C2×D311yescharacteristic, complemented
95#3952—61no—
96#3952—61no—
97#1462—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—22no—
102C22×D15—22no—
103C22×D15C22⋊C411yescharacteristic
104C22×D15C22⋊C411yescharacteristic
105C22×C5×D3—21no—
106C22×C5×D3—21no—
107C22×C5×D3—41no—
108C22×C5×D3—41no—
109C22×C5×D3M1612yescomplemented
110C22×C3×D5—21no—
111C22×C3×D5—21no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C22×C3×D5M1612yescomplemented
115C2×D3×D5—24no—
116C2×D3×D5—24no—
117C2×D3×D5—48no—
118C2×D3×D5—42no—
119C2×D3×D5—42no—
120C2×D3×D5—48no—
121C2×D3×D5—42no—
122C2×D3×D5—42no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×Dic15—41no—
127C2×Dic15C22⋊C411yescharacteristic
128C2×Dic15C22⋊C411yescharacteristic
129C4×D15—22no—
130C4×D15—22no—
131C4×D15—41no—
132C4×D15—41no—
133C2×C5×Dic3—21no—
134C2×C5×Dic3—41no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—41no—
137#1200—42no—
138#1200—42no—
139C3×C5×C8—41no—
140C3⋊#168—41no—
141C3×#168—41no—
142C5×C3⋊C8—41no—
143C24×D3—51no—
144C22×C4×D3—51no—
145C22×C4×D3—51no—
146C2×C3×C22⋊C4—51no—
147C2×#217—51no—
148C2×(C2×D3)⋊C4—51no—
149C2×(C2×D3)⋊C4C2×D511yescharacteristic
150C2×ΓL(1,𝔽25)—101no—
151C2×ΓL(1,𝔽25)—101no—
152D3×C22⋊C4—101no—
153D3×C22⋊C4—101no—
154D3×C22⋊C4—101no—
155D3×C22⋊C4—101no—
156C3×C22⋊C8—51no—
157C3×C22⋊C8C2×D511yescharacteristic, complemented
158#830—51no—
159#830C2×D511yescharacteristic, complemented
160(C2×D3)⋊C8—101no—
161(C2×D3)⋊C8—101no—
162C24×C5—31no—
163C23×D5—31no—
164C23×D5—61no—
165C23×D5—61no—
166C23×D5—62no—
167C23×D5—62no—
168C23×D5—122no—
169C23×D5—122no—
170C23×D5C4×D311yescharacteristic
171C22×C4×C5—31no—
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—31no—
174C22×Dic5C4×D311yescharacteristic
175C2×C4×D5—31no—
176C2×C4×D5—31no—
177C2×C4×D5—31no—
178C2×C4×D5—31no—
179C2×C4×D5—61no—
180C2×C4×D5—61no—
181C2×C4×D5—122no—
182C2×C4×D5—122no—
183C2×C5×C8—21no—
184C2×C5×C8—61no—
185C5×C22⋊C4—61no—
186C5×C22⋊C4—61no—
187C22⋊Dic5—61no—
188C22⋊Dic5—61no—
189#685—21no—
190#685—21no—
191#685—61no—
192#685—61no—
193C2×#168—21no—
194C2×#168—61no—
195#676—122no—
196#676—122no—
197C22×C22⋊C4—151no—
198#407—151no—
199#407—151no—
200#323—31no—
201#323—51no—
202#323—151no—
203#323—151no—
204C22×C3×C5—21no—
205C22×C3×C5—21no—
206C22×C3×C5C2×C22⋊C411yescharacteristic
207C22×C3×C5C2×M1611yescharacteristic
208C22×C3×C5C2×M1611yescharacteristic
209C2×D15—24no—
210C2×D15—24no—
211C2×D15—21no—
212C2×D15—21no—
213C2×D15—21no—
214C2×D15—21no—
215C2×D15#9912yes—
216C2×D15#10012yes—
217C2×C5×D3—22no—
218C2×C5×D3—42no—
219C2×C5×D3—41no—
220C2×C5×D3—41no—
221C2×C5×D3—42no—
222C2×C3×D5—22no—
223C2×C3×D5—42no—
224C2×C3×D5—41no—
225C2×C3×D5—41no—
226C2×C3×D5—42no—
227D3×D5—48no—
228D3×D5—48no—
229C3×C4×C5—21no—
230C3×C4×C5—21no—
231Dic15—21no—
232Dic15—21no—
233C3×Dic5—41no—
234C5×Dic3—41no—
235C24×C3—51no—
236C23×D3—51no—
237C23×D3—101no—
238C23×D3—101no—
239C23×D3—102no—
240C23×D3—102no—
241C23×D3—202no—
242C23×D3—202no—
243C23×D3C4×D511yescharacteristic
244C22×C3×C4—51no—
245C22×C3×C4C22×D511yescharacteristic
246C22×Dic3—51no—
247C22×Dic3C4×D511yescharacteristic
248C2×C4×D3—51no—
249C2×C4×D3—51no—
250C2×C4×D3—51no—
251C2×C4×D3—51no—
252C2×C4×D3—101no—
253C2×C4×D3—101no—
254C2×C4×D3—202no—
255C2×C4×D3—202no—
256C2×C3×C8—21no—
257C2×C3×C8—101no—
258C3×C22⋊C4—101no—
259C3×C22⋊C4—101no—
260#217—101no—
261#217—101no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—21no—
264(C2×D3)⋊C4—101no—
265(C2×D3)⋊C4—101no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—101no—
268ΓL(1,𝔽25)—202no—
269ΓL(1,𝔽25)—202no—
270C23×C5—32no—
271C23×C5—61no—
272C23×C5—61no—
273C23×C5—121no—
274C23×C5—121no—
275C23×C5C2×C4×D311yescharacteristic
276C22×D5—21no—
277C22×D5—21no—
278C22×D5—31no—
279C22×D5—31no—
280C22×D5—41no—
281C22×D5—41no—
282C22×D5—64no—
283C22×D5—64no—
284C22×D5—62no—
285C22×D5—62no—
286C22×D5—61no—
287C22×D5—61no—
288C22×D5—122no—
289C22×D5—122no—
290C22×D5—128no—
291C22×D5—122no—
292C22×D5—122no—
293C22×D5—128no—
294C22×D5ΓL(1,𝔽25)12yescomplemented
295C2×C4×C5—41no—
296C2×C4×C5—61no—
297C2×C4×C5—121no—
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5D3×D411yescharacteristic
300C2×Dic5—21no—
301C2×Dic5—31no—
302C2×Dic5—31no—
303C2×Dic5—41no—
304C2×Dic5—121no—
305C4×D5—62no—
306C4×D5—62no—
307C4×D5—122no—
308C4×D5—122no—
309C4×D5—121no—
310C4×D5—121no—
311C5×C8—41no—
312C5×C8—121no—
313#168—41no—
314#168—121no—
315C25—151no—
316C23×C4—151no—
317C23×C4—151no—
318C2×M16—301no—
319C2×M16—301no—
320C2×C22⋊C4—31no—
321C2×C22⋊C4—51no—
322C2×C22⋊C4—151no—
323C2×C22⋊C4—151no—
324C2×C22⋊C4—301no—
325C2×C22⋊C4—301no—
326C2×C22⋊C4—301no—
327C2×C22⋊C4—301no—
328C22⋊C8—31no—
329C22⋊C8—51no—
330C22⋊C8—151no—
331C22⋊C8—301no—
332C22⋊C8—301no—
333C22⋊C8D3×D511yescharacteristic, complemented
334C2×C3×C5—21no—
335C2×C3×C5—21no—
336C2×C3×C5#40711yescharacteristic
337C2×C3×C5C2×#9911yescharacteristic
338C2×C3×C5C2×#10011yescharacteristic
339D15—22no—
340D15—22no—
341C3×D5—42no—
342C5×D3—42no—
343C23×C3—52no—
344C23×C3—101no—
345C23×C3—101no—
346C23×C3—201no—
347C23×C3—201no—
348C23×C3C2×C4×D511yescharacteristic
349C22×D3—21no—
350C22×D3—21no—
351C22×D3—41no—
352C22×D3—41no—
353C22×D3—51no—
354C22×D3—51no—
355C22×D3—104no—
356C22×D3—104no—
357C22×D3—102no—
358C22×D3—102no—
359C22×D3—101no—
360C22×D3—101no—
361C22×D3—202no—
362C22×D3—202no—
363C22×D3—208no—
364C22×D3—202no—
365C22×D3—202no—
366C22×D3—208no—
367C22×D3#67612yescomplemented
368C2×C3×C4—41no—
369C2×C3×C4—101no—
370C2×C3×C4—201no—
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4D4×D511yescharacteristic
373C2×Dic3—21no—
374C2×Dic3—41no—
375C2×Dic3—51no—
376C2×Dic3—51no—
377C2×Dic3—201no—
378C4×D3—102no—
379C4×D3—102no—
380C4×D3—202no—
381C4×D3—202no—
382C4×D3—201no—
383C4×D3—201no—
384C3×C8—41no—
385C3×C8—201no—
386C3⋊C8—41no—
387C3⋊C8—201no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—122no—
392C22×C5—122no—
393C22×C5—121no—
394C22×C5—121no—
395C22×C5D3×C22⋊C411yescharacteristic
396C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
397C22×C5D3×M1611yescharacteristic
398C2×D5—22no—
399C2×D5—32no—
400C2×D5—32no—
401C2×D5—42no—
402C2×D5—41no—
403C2×D5—41no—
404C2×D5—42no—
405C2×D5—64no—
406C2×D5—64no—
407C2×D5—61no—
408C2×D5—61no—
409C2×D5—61no—
410C2×D5—61no—
411C2×D5—128no—
412C2×D5—128no—
413C4×C5—21no—
414C4×C5—21no—
415C4×C5—121no—
416Dic5—41no—
417Dic5—61no—
418Dic5—61no—
419C24—31no—
420C24—51no—
421C24—151no—
422C24—302no—
423C24—302no—
424C24—301no—
425C24—301no—
426C24—602no—
427C24—602no—
428C22×C4—31no—
429C22×C4—51no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—301no—
436C22×C4—301no—
437C22×C4—602no—
438C22×C4—602no—
439C22×C4C2×D3×D511yescharacteristic
440M16—602no—
441M16—602no—
442C2×C8—21no—
443C2×C8—61no—
444C2×C8—101no—
445C2×C8—301no—
446C22⋊C4—61no—
447C22⋊C4—61no—
448C22⋊C4—101no—
449C22⋊C4—101no—
450C22⋊C4—301no—
451C22⋊C4—301no—
452C22⋊C4—301no—
453C22⋊C4—301no—
454C3×C5#146211yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—102no—
458C22×C3—202no—
459C22×C3—202no—
460C22×C3—201no—
461C22×C3—201no—
462C22×C3D5×C22⋊C411yescharacteristic
463C22×C3C2×#67611yescharacteristic
464C22×C3D5×M1611yescharacteristic
465C2×D3—22no—
466C2×D3—42no—
467C2×D3—41no—
468C2×D3—41no—
469C2×D3—42no—
470C2×D3—52no—
471C2×D3—52no—
472C2×D3—104no—
473C2×D3—104no—
474C2×D3—101no—
475C2×D3—101no—
476C2×D3—101no—
477C2×D3—101no—
478C2×D3—208no—
479C2×D3—208no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—201no—
483Dic3—41no—
484Dic3—101no—
485Dic3—101no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—122no—
489C2×C5#472611yescharacteristic
490C2×C5D3×#9911yescharacteristic
491C2×C5D3×#10011yescharacteristic
492D5—42no—
493D5—62no—
494D5—62no—
495C23—32no—
496C23—52no—
497C23—61no—
498C23—61no—
499C23—101no—
500C23—101no—
501C23—121no—
502C23—121no—
503C23—151no—
504C23—151no—
505C23—201no—
506C23—201no—
507C23—302no—
508C23—302no—
509C23—304no—
510C23—304no—
511C23—301no—
512C23—301no—
513C23—602no—
514C23—602no—
515C23—608no—
516C23—608no—
517C23—602no—
518C23—602no—
519C23C4×D3×D511yescharacteristic
520C2×C4—41no—
521C2×C4—61no—
522C2×C4—101no—
523C2×C4—121no—
524C2×C4—151no—
525C2×C4—151no—
526C2×C4—201no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—601no—
530C2×C4—601no—
531C2×C4—602no—
532C2×C4—602no—
533C2×C4—601no—
534C2×C4#677711yescharacteristic
535C2×C4#679011yescharacteristic
536C8—41no—
537C8—121no—
538C8—201no—
539C8—601no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—202no—
543C2×C3#6501511yescharacteristic
544C2×C3D5×#9911yescharacteristic
545C2×C3D5×#10011yescharacteristic
546D3—42no—
547D3—102no—
548D3—102no—
549C5#6812011yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—62no—
553C22—102no—
554C22—122no—
555C22—122no—
556C22—121no—
557C22—121no—
558C22—152no—
559C22—152no—
560C22—202no—
561C22—202no—
562C22—201no—
563C22—201no—
564C22—304no—
565C22—304no—
566C22—301no—
567C22—301no—
568C22—301no—
569C22—301no—
570C22—608no—
571C22—608no—
572C22D5×ΓL(1,𝔽25)11yescharacteristic
573C22D3×#67611yescharacteristic
574C22#9147311yescharacteristic
575C4—21no—
576C4—21no—
577C4—121no—
578C4—201no—
579C4—301no—
580C4—301no—
581C3#1059891311yescharacteristic, complemented, Sylow
582C2—21no—
583C2—21no—
584C2—122no—
585C2—202no—
586C2—302no—
587C2—302no—
588C2#1174712811yescharacteristic
589C2#1174810311yescharacteristic
590C2#1174822411yescharacteristic
subgroupG/H
centerC22#91473
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D3×D5C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1462
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750827C2semidirect
3. #11748509C2semidirect
4. C5×#4468C2semidirect
5. C3×#64688C2semidirect
6. #11745949C2semidirect
7. #11745948C2semidirect
22. C3×C5×C22⋊C8C22semidirect
23. #91114C22semidirect
25. C5×#830C22semidirect
26. C3×C22⋊#168C22semidirect
35. #64688D3semidirect
77. #4468D5semidirect
92. C5×C22⋊C8C2×D3semidirect
94. C22⋊#168C2×D3semidirect
109. C22×C5×D3M16semidirect
114. C22×C3×D5M16semidirect
157. C3×C22⋊C8C2×D5semidirect
159. #830C2×D5semidirect
294. C22×D5ΓL(1,𝔽25)semidirect
333. C22⋊C8D3×D5semidirect
367. C22×D3#676semidirect
454. C3×C5#1462semidirect
549. C5#68120semidirect
581. C3#10598913semidirect

Maximal subgroups

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

subgroupindex
C2×#914732
#117508272
#117485092
C5×#44682
C3×#646882
#117459492
#117459482
#105989133
#681205