Finite Group Databasebeta

← #11755437

Subgroups — #11755437

Order 960.

856 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1220C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#6790C211yesmaximal, characteristic, complemented
4C2×D5×#67C211yesmaximal, characteristic, complemented
5C5×#953C211yesmaximal, characteristic, complemented
6#91577C211yesmaximal, characteristic, complemented
7#91572C211yesmaximal, characteristic, complemented
8#91571C211yesmaximal, characteristic, complemented
9#91567C211yesmaximal, characteristic, complemented
10#91566C211yesmaximal, characteristic, complemented
11#91564C211yesmaximal, characteristic, complemented
12#91559C211yesmaximal, characteristic, complemented
13#91552C211yesmaximal, characteristic, complemented
14#91550C211yesmaximal, characteristic, complemented
15#91533C211yesmaximal, characteristic, complemented
16#65924—31nomaximal, Hall
17C24×C3×C5C2211yescharacteristic, complemented
18C23×D15C2211yescharacteristic, complemented
19C23×C3×D5C2211yescharacteristic, complemented
20C22×D3×D5C2211yescharacteristic, complemented
21C2×#1220—24no—
22C2×#1220C2211yescharacteristic
23C2×#1220C2211yescharacteristic, complemented
24C2×#1220C2211yescharacteristic, complemented
25C2×#1220C2211yescharacteristic, complemented
26C22×Dic15C2211yescharacteristic, complemented
27C2×C5×#67C2211yescharacteristic, complemented
28C2×C5×#67C2211yescharacteristic, complemented
29C2×C5×#67C2211yescharacteristic, complemented
30C2×C3×C22⋊D5—24no—
31C2×C3×C22⋊D5C2211yescharacteristic
32C2×C3×C22⋊D5C2211yescharacteristic, complemented
33C2×C3×C22⋊D5C2211yescharacteristic, complemented
34C2×C3×C22⋊D5C2211yescharacteristic, complemented
35C22×C3×Dic5C2211yescharacteristic, complemented
36#6790—24no—
37D5×#67—24no—
38C2×#1203C2211yescharacteristic, complemented
39C2×#1202C2211yescharacteristic, complemented
40C2×#1202C2211yescharacteristic, complemented
41C2×#1202C2211yescharacteristic, complemented
42C2×#1201C2211yescharacteristic, complemented
43C2×#1200C2211yescharacteristic, complemented
44C2×D5×Dic3C2211yescharacteristic, complemented
45C5×#217C2211yescharacteristic, complemented
46C5×#217C2211yescharacteristic, complemented
47C5×#217C2211yescharacteristic, complemented
48#6669C2211yescharacteristic, complemented
49#6668C2211yescharacteristic, complemented
50#6667C2211yescharacteristic, complemented
51#6667C2211yescharacteristic, complemented
52(C2×D3)⋊Dic5C2211yescharacteristic, complemented
53#6665C2211yescharacteristic, complemented
54#6665C2211yescharacteristic, complemented
55Dic3×Dic5C2211yescharacteristic, complemented
56D4×#67—51nomaximal, Hall
57C22×C22⋊D5—31no—
58C22×C22⋊D5D311yescharacteristic, complemented
59C2×D4×D5—31no—
60C2×D4×D5—31no—
61C5×#120—31no—
62#4086—31no—
63#4085—31no—
64#4085—31no—
65#4083—31no—
66#4030—31no—
67#4030—31no—
68#4028—31no—
69#4028—31no—
70#4027—31no—
71#4027—31no—
72C23×C3×C5—22no—
73C23×C3×C5—22no—
74C23×C3×C5—41no—
75C23×C3×C5C2311yescharacteristic
76C23×C3×C5C2311yescharacteristic
77C23×C3×C5C2311yescharacteristic
78C22×D15—22no—
79C22×D15—22no—
80C22×D15—41no—
81C22×D15C2311yescharacteristic
82C22×D15C2311yescharacteristic
83C22×C5×D3C2311yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—22no—
86C22×C3×D5—41no—
87C22×C3×D5C2311yescharacteristic
88C22×C3×D5C2311yescharacteristic
89C2×D3×D5—22no—
90C2×D3×D5—22no—
91C2×D3×D5—41no—
92#1220—22no—
93#1220—22no—
94#1220—22no—
95#1220D414yescomplemented
96C2×Dic15—22no—
97C2×Dic15C2311yescharacteristic
98C2×Dic15C2311yescharacteristic
99C5×#67—22no—
100C5×#67—22no—
101C5×#67—41no—
102C2×C5×Dic3C2311yescharacteristic
103C2×C5×Dic3C2311yescharacteristic
104C2×C5×Dic3C2311yescharacteristic
105C3×C22⋊D5—22no—
106C3×C22⋊D5—22no—
107C3×C22⋊D5—22no—
108C3×C22⋊D5D414yescomplemented
109C2×C3×Dic5—22no—
110C2×C3×Dic5C2311yescharacteristic
111C2×C3×Dic5C2311yescharacteristic
112#1203—22no—
113#1202—22no—
114#1202—22no—
115#1202—41no—
116#1201—22no—
117#1200—22no—
118D5×Dic3—22no—
119C22×C3×D4—51no—
120C22×#67—51no—
121C22×#67—51no—
122C2×D3×D4—51no—
123#953—51no—
124#953D511yescharacteristic, complemented
125#940—51no—
126#939—51no—
127#939—51no—
128#938—51no—
129#937—51no—
130#937—51no—
131D4×Dic3—51no—
132#930—51no—
133C4×#67—51no—
134C24×C5C2×D311yescharacteristic, complemented
135C23×D5—31no—
136C23×D5—31no—
137C23×D5C2×D311yescharacteristic, complemented
138C2×C5×D4—31no—
139C2×C5×D4—31no—
140C2×C5×D4—31no—
141C2×C22⋊D5—24no—
142C2×C22⋊D5—31no—
143C2×C22⋊D5—31no—
144C2×C22⋊D5—31no—
145C2×C22⋊D5—31no—
146C2×C22⋊D5—31no—
147C2×C22⋊D5—31no—
148C2×C22⋊D5—64no—
149C2×C22⋊D5C2×D311yescharacteristic
150C2×C22⋊D5C2×D311yescharacteristic, complemented
151C2×C22⋊D5C2×D311yescharacteristic, complemented
152C2×C22⋊D5C2×D311yescharacteristic, complemented
153C22×Dic5—31no—
154C22×Dic5C2×D311yescharacteristic, complemented
155D4×D5—64no—
156D4×D5—64no—
157C2×D20—31no—
158C2×D20—31no—
159C2×D20—31no—
160C2×C4×D5—31no—
161C2×C4×D5—31no—
162C5×C22⋊C4—31no—
163C5×C22⋊C4—31no—
164C5×C22⋊C4—31no—
165C22⋊Dic5—31no—
166#685—31no—
167#685—31no—
168#685—31no—
169#685—31no—
170#683—31no—
171#683—31no—
172C4×Dic5—31no—
173D42—151noSylow
174C22×C3×C5—21no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—44no—
182C22×C3×C5C2×D412yescomplemented
183C22×C3×C5C2×D412yescomplemented
184C22×C3×C5C2411yescharacteristic
185C2×D15—21no—
186C2×D15—21no—
187C2×D15—21no—
188C2×D15—21no—
189C2×D15—21no—
190C2×D15—44no—
191C2×D15C2×D412yescomplemented
192C2×C5×D3—21no—
193C2×C5×D3—21no—
194C2×C5×D3—21no—
195C2×C3×D5—21no—
196C2×C3×D5—21no—
197C2×C3×D5—21no—
198C2×C3×D5—21no—
199C2×C3×D5—21no—
200C2×C3×D5—44no—
201C2×C3×D5C2×D412yescomplemented
202D3×D5—44no—
203Dic15—21no—
204Dic15C2×D412yescomplemented
205C3×Dic5—21no—
206C3×Dic5C2×D412yescomplemented
207C5×Dic3—21no—
208C5×Dic3—21no—
209C5×Dic3—21no—
210C24×C3—51no—
211C24×C3C2×D511yescharacteristic, complemented
212C23×D3—51no—
213C23×D3—51no—
214C2×C3×D4—51no—
215C2×C3×D4—51no—
216C2×C3×D4—51no—
217C2×C3×D4—51no—
218C2×C3×D4—104no—
219C22×C3×C4—51no—
220C2×#67—51no—
221C2×#67—51no—
222C2×#67—51no—
223C2×#67—51no—
224C2×#67—51no—
225C2×#67—51no—
226C2×#67—51no—
227C2×#67—51no—
228C2×#67—104no—
229C2×#67—104no—
230C2×#67C2×D511yescharacteristic, complemented
231C2×#67C2×D511yescharacteristic, complemented
232C2×#67C2×D511yescharacteristic, complemented
233C22×Dic3—51no—
234C22×Dic3—51no—
235D3×D4—104no—
236C2×D12—51no—
237C2×C4×D3—51no—
238#217—51no—
239#217—51no—
240#217C2×D511yescharacteristic, complemented
241#217C2×D511yescharacteristic, complemented
242#217C2×D511yescharacteristic, complemented
243(C2×D3)⋊C4—51no—
244(C2×D3)⋊C4—51no—
245(C2×D3)⋊C4—51no—
246C4⋊Dic3—51no—
247Dic3⋊C4—51no—
248C4×Dic3—51no—
249C23×C5—22no—
250C23×C5—22no—
251C23×C5—31no—
252C23×C5—41no—
253C23×C5C22×D311yescharacteristic
254C23×C5C22×D311yescharacteristic
255C23×C5C22×D311yescharacteristic
256C22×D5—22no—
257C22×D5—22no—
258C22×D5—31no—
259C22×D5—31no—
260C22×D5—41no—
261C22×D5—62no—
262C22×D5—62no—
263C22×D5—62no—
264C22×D5—62no—
265C22×D5—121no—
266C22×D5—121no—
267C22×D5C22×D311yescharacteristic
268C22×D5C22×D311yescharacteristic
269C5×D4—62no—
270C5×D4—62no—
271C5×D4—121no—
272C2×C4×C5—31no—
273C2×C4×C5—31no—
274C2×C4×C5—31no—
275C22⋊D5—22no—
276C22⋊D5—22no—
277C22⋊D5—22no—
278C22⋊D5—34no—
279C22⋊D5—62no—
280C22⋊D5—62no—
281C22⋊D5—62no—
282C22⋊D5—62no—
283C22⋊D5—62no—
284C22⋊D5#6714yescomplemented
285C2×Dic5—22no—
286C2×Dic5—31no—
287C2×Dic5—31no—
288C2×Dic5—62no—
289C2×Dic5C22×D311yescharacteristic
290C2×Dic5C22×D311yescharacteristic
291D20—62no—
292D20—62no—
293D20—121no—
294C4×D5—62no—
295C4×D5—62no—
296C22×D4—51no—
297C22×D4—151no—
298C22×D4—151no—
299C22×D4—151no—
300#127—151no—
301#121—151no—
302#121—151no—
303#121—151no—
304#121—151no—
305#120—31no—
306#120—151no—
307#120—151no—
308#120—151no—
309C4×D4—151no—
310C4×D4—151no—
311C2×C3×C5—22no—
312C2×C3×C5—22no—
313C2×C3×C5—41no—
314C2×C3×C5C22×D411yescharacteristic
315C2×C3×C5C22×D411yescharacteristic
316C2×C3×C5H(5,𝔽2)11yescharacteristic
317D15—22no—
318D15—41no—
319C3×D5—22no—
320C3×D5—41no—
321C5×D3—41no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—41no—
325C23×C3—51no—
326C23×C3—51no—
327C23×C3—102no—
328C23×C3—102no—
329C23×C3—201no—
330C23×C3C22×D511yescharacteristic
331C23×C3C22×D511yescharacteristic
332C23×C3C22×D511yescharacteristic
333C22×D3—51no—
334C22×D3—51no—
335C22×D3—102no—
336C22×D3—102no—
337C22×D3—102no—
338C22×D3—102no—
339C22×D3—201no—
340C22×D3—201no—
341C22×D3C22×D511yescharacteristic
342C3×D4—54no—
343C3×D4—102no—
344C3×D4—102no—
345C3×D4—102no—
346C2×C3×C4—51no—
347C2×C3×C4—51no—
348C2×C3×C4—102no—
349#67—22no—
350#67—22no—
351#67—41no—
352#67—54no—
353#67—102no—
354#67—102no—
355#67—102no—
356#67—102no—
357#67—102no—
358#67—102no—
359#67—201no—
360C2×Dic3—51no—
361C2×Dic3—51no—
362C2×Dic3—102no—
363C2×Dic3—102no—
364C2×Dic3C22×D511yescharacteristic
365C2×Dic3C22×D511yescharacteristic
366C2×Dic3C22×D511yescharacteristic
367D12—102no—
368C4×D3—102no—
369C22×C5—21no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—21no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—21no—
376C22×C5—44no—
377C22×C5—61no—
378C22×C5—61no—
379C22×C5—61no—
380C22×C5D3×D412yescomplemented
381C22×C5C2×#6712yescomplemented
382C22×C5C23×D311yescharacteristic
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—21no—
386C2×D5—21no—
387C2×D5—21no—
388C2×D5—32no—
389C2×D5—44no—
390C2×D5—61no—
391C2×D5—61no—
392C2×D5—61no—
393C2×D5—61no—
394C2×D5—61no—
395C2×D5—124no—
396C2×D5—124no—
397C2×D5C2×#6712yescomplemented
398C4×C5—61no—
399C4×C5—61no—
400C4×C5—61no—
401Dic5—21no—
402Dic5—32no—
403Dic5—61no—
404Dic5C2×#6712yescomplemented
405C24—51no—
406C24—151no—
407C24—151no—
408C24D3×D511yescharacteristic, complemented
409C2×D4—31no—
410C2×D4—31no—
411C2×D4—31no—
412C2×D4—51no—
413C2×D4—51no—
414C2×D4—51no—
415C2×D4—51no—
416C2×D4—104no—
417C2×D4—151no—
418C2×D4—151no—
419C2×D4—151no—
420C2×D4—151no—
421C2×D4—151no—
422C2×D4—151no—
423C2×D4—151no—
424C2×D4—151no—
425C2×D4—151no—
426C2×D4—304no—
427C2×D4—304no—
428C2×D4—304no—
429C22×C4—51no—
430C22×C4—151no—
431C22×C4—151no—
432C22×C4—151no—
433C4⋊C4—151no—
434C4⋊C4—151no—
435C22⋊C4—31no—
436C22⋊C4—31no—
437C22⋊C4—31no—
438C22⋊C4—151no—
439C22⋊C4—151no—
440C22⋊C4—151no—
441C22⋊C4—151no—
442C22⋊C4—151no—
443C42—151no—
444C3×C5D4211yescharacteristic, complemented, Hall
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—44no—
453C22×C3—52no—
454C22×C3—101no—
455C22×C3—101no—
456C22×C3—101no—
457C22×C3—101no—
458C22×C3—101no—
459C22×C3—204no—
460C22×C3D4×D512yescomplemented
461C22×C3D4×D512yescomplemented
462C22×C3C23×D511yescharacteristic
463C2×D3—21no—
464C2×D3—21no—
465C2×D3—21no—
466C2×D3—52no—
467C2×D3—101no—
468C2×D3—101no—
469C2×D3—101no—
470C2×D3—101no—
471C2×D3—101no—
472C2×D3—204no—
473C2×D3—204no—
474C3×C4—52no—
475C3×C4—101no—
476Dic3—21no—
477Dic3—21no—
478Dic3—21no—
479Dic3—52no—
480Dic3—101no—
481C2×C5—22no—
482C2×C5—22no—
483C2×C5—41no—
484C2×C5—121no—
485C2×C5C2×D3×D411yescharacteristic
486C2×C5#100411yescharacteristic
487C2×C5C22×#6711yescharacteristic
488D5—22no—
489D5—41no—
490D5—62no—
491D5—121no—
492C23—22no—
493C23—22no—
494C23—31no—
495C23—41no—
496C23—51no—
497C23—51no—
498C23—102no—
499C23—102no—
500C23—151no—
501C23—151no—
502C23—201no—
503C23—302no—
504C23—302no—
505C23—302no—
506C23—302no—
507C23—601no—
508C23—601no—
509C23C2×D3×D511yescharacteristic
510C23C2×D3×D511yescharacteristic
511C23C2×D3×D511yescharacteristic
512D4—54no—
513D4—62no—
514D4—62no—
515D4—102no—
516D4—102no—
517D4—102no—
518D4—121no—
519D4—154no—
520D4—302no—
521D4—302no—
522D4—302no—
523D4—302no—
524D4—302no—
525D4—302no—
526D4—302no—
527D4—601no—
528C2×C4—31no—
529C2×C4—31no—
530C2×C4—31no—
531C2×C4—51no—
532C2×C4—51no—
533C2×C4—102no—
534C2×C4—151no—
535C2×C4—151no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C3—22no—
540C2×C3—22no—
541C2×C3—41no—
542C2×C3—102no—
543C2×C3—201no—
544C2×C3C2×D4×D511yescharacteristic
545C2×C3C2×D4×D511yescharacteristic
546C2×C3#414411yescharacteristic
547D3—41no—
548D3—102no—
549D3—201no—
550C5D4×#6711yescharacteristic, complemented, Sylow
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—52no—
560C22—61no—
561C22—61no—
562C22—61no—
563C22—101no—
564C22—101no—
565C22—101no—
566C22—101no—
567C22—101no—
568C22—152no—
569C22—204no—
570C22—301no—
571C22—301no—
572C22—301no—
573C22—301no—
574C22—301no—
575C22—604no—
576C22—604no—
577C22D5×#6712yescomplemented
578C22#679012yescomplemented
579C22C22×D3×D511yescharacteristic
580C4—52no—
581C4—61no—
582C4—61no—
583C4—61no—
584C4—101no—
585C4—152no—
586C4—301no—
587C3#6592411yescharacteristic, complemented, Sylow
588C2—22no—
589C2—22no—
590C2—41no—
591C2—102no—
592C2—121no—
593C2—201no—
594C2—302no—
595C2—601no—
596C2C2×D5×#6711yescharacteristic
597C2C2×#679011yescharacteristic
598C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
hypercenterC24D3×D5
hypocenterC3×C5D42
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#1220C2semidirect
2. C22×C3×C22⋊D5C2semidirect
3. C2×#6790C2semidirect
4. C2×D5×#67C2semidirect
5. C5×#953C2semidirect
6. #91577C2semidirect
7. #91572C2semidirect
8. #91571C2semidirect
9. #91567C2semidirect
10. #91566C2semidirect
11. #91564C2semidirect
12. #91559C2semidirect
13. #91552C2semidirect
14. #91550C2semidirect
15. #91533C2semidirect
17. C24×C3×C5C22semidirect
18. C23×D15C22semidirect
19. C23×C3×D5C22semidirect
20. C22×D3×D5C22semidirect
23. C2×#1220C22semidirect
24. C2×#1220C22semidirect
25. C2×#1220C22semidirect
26. C22×Dic15C22semidirect
27. C2×C5×#67C22semidirect
28. C2×C5×#67C22semidirect
29. C2×C5×#67C22semidirect
32. C2×C3×C22⋊D5C22semidirect
33. C2×C3×C22⋊D5C22semidirect
34. C2×C3×C22⋊D5C22semidirect
35. C22×C3×Dic5C22semidirect
38. C2×#1203C22semidirect
39. C2×#1202C22semidirect
40. C2×#1202C22semidirect
41. C2×#1202C22semidirect
42. C2×#1201C22semidirect
43. C2×#1200C22semidirect
44. C2×D5×Dic3C22semidirect
45. C5×#217C22semidirect
46. C5×#217C22semidirect
47. C5×#217C22semidirect
48. #6669C22semidirect
49. #6668C22semidirect
50. #6667C22semidirect
51. #6667C22semidirect
52. (C2×D3)⋊Dic5C22semidirect
53. #6665C22semidirect
54. #6665C22semidirect
55. Dic3×Dic5C22semidirect
58. C22×C22⋊D5D3semidirect
95. #1220D4semidirect
108. C3×C22⋊D5D4semidirect
124. #953D5semidirect
134. C24×C5C2×D3semidirect
137. C23×D5C2×D3semidirect
150. C2×C22⋊D5C2×D3semidirect
151. C2×C22⋊D5C2×D3semidirect
152. C2×C22⋊D5C2×D3semidirect
154. C22×Dic5C2×D3semidirect
182. C22×C3×C5C2×D4semidirect
183. C22×C3×C5C2×D4semidirect
191. C2×D15C2×D4semidirect
201. C2×C3×D5C2×D4semidirect
204. Dic15C2×D4semidirect
206. C3×Dic5C2×D4semidirect
211. C24×C3C2×D5semidirect
230. C2×#67C2×D5semidirect
231. C2×#67C2×D5semidirect
232. C2×#67C2×D5semidirect
240. #217C2×D5semidirect
241. #217C2×D5semidirect
242. #217C2×D5semidirect
284. C22⋊D5#67semidirect
380. C22×C5D3×D4semidirect
381. C22×C5C2×#67semidirect
397. C2×D5C2×#67semidirect
404. Dic5C2×#67semidirect
408. C24D3×D5semidirect
444. C3×C5D42semidirect
460. C22×C3D4×D5semidirect
461. C22×C3D4×D5semidirect
550. C5D4×#67semidirect
577. C22D5×#67semidirect
578. C22#6790semidirect
587. C3#65924semidirect

Maximal subgroups

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

subgroupindex
C22×#12202
C22×C3×C22⋊D52
C2×#67902
C2×D5×#672
C5×#9532
#915772
#915722
#915712
#915672
#915662
#915642
#915592
#915522
#915502
#915332
#659243
D4×#675