Finite Group Databasebeta

← #14303014

Subgroups — #14303014

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66138C211yesmaximal, characteristic
2#11755406C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90995C211yesmaximal, characteristic, complemented
6#11746020C211yesmaximal, characteristic, complemented
7#11746018C211yesmaximal, characteristic, complemented
8#10600827—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C22⋊D5C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×C5×#217C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C3×#4099C412yescomplemented
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C3×#4085—22no—
18C3×#4083—21no—
19C3×#4081—21no—
20C3×#4075C412yescomplemented
21#91559—22no—
22Dic3×C22⋊D5—22no—
23D5×#217—21no—
24#91528—21no—
25#91118—22no—
26C5×#834—22no—
27#90995—22no—
28#71848—51nomaximal, Hall
29#66138D311yescharacteristic
30#65820—31no—
31C2×C5×#99—31no—
32C2×#3966—31no—
33C2×#3938—31no—
34#64747—31no—
35#64746—31no—
36C24×C3×C5C2×C411yescharacteristic, complemented
37C24×C3×C5C2311yescharacteristic
38C23×C3×D5D411yescharacteristic
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C22×C3×C4×C5C2×C411yescharacteristic, complemented
46C22×Dic15—21no—
47C22×Dic15—21no—
48C22×C5×Dic3—21no—
49C22×C5×Dic3—21no—
50C2×C3×C22⋊D5—21no—
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5—21no—
54C2×C3×C22⋊D5—22no—
55C2×C3×C22⋊D5C2×C412yes—
56C2×C3×C22⋊D5D412yes—
57C22×C3×Dic5—21no—
58C22×C3×Dic5D411yescharacteristic
59C2×D5×Dic3—22no—
60#6719—21no—
61#6719—21no—
62#6719—21no—
63#6719D412yescomplemented
64C5×#217—21no—
65C5×#217—21no—
66C5×#217—21no—
67C5×#217D412yescomplemented
68C3×C22⋊Dic5—21no—
69C3×C22⋊Dic5—22no—
70C3×C22⋊Dic5C2×C412yescomplemented
71C3×#685—22no—
72C3×#683—22no—
73#6668—22no—
74#6665—22no—
75Dic3×Dic5—22no—
76C3×#534—51no—
77#5798—51no—
78C2×#834—51no—
79C2×#834—51no—
80C2×#834D511yescharacteristic, complemented
81#4527—51no—
82#4527—51no—
83C22×C5×D4C2×D311yescharacteristic
84C22×C22⋊D5C2×D311yescharacteristic
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊C4—31no—
87#4099Dic312yescomplemented
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5—31no—
90C2×C22⋊Dic5C2×D311yescharacteristic
91#4085—22no—
92#4083—21no—
93#4081—21no—
94#4075Dic312yescomplemented
95C4×C22⋊D5—62no—
96#4027—62no—
97D5×C22⋊C4—61no—
98#4023—61no—
99C5×#99—62no—
100#3966—62no—
101#3938—62no—
102#1913—151noSylow
103C23×C3×C5—21no—
104C23×C3×C5—21no—
105C23×C3×C5—21no—
106C23×C3×C5—81no—
107C23×C3×C5—81no—
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C23×C3×C5#4111yescharacteristic
114C23×C3×C5#4111yescharacteristic
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—81no—
118C22×C3×D5C22⋊C412yes—
119C3×C5×D4—41no—
120C3×C5×D4—41no—
121C3×C5×D4—41no—
122C3×C5×D4—41no—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—21no—
126C2×Dic15—22no—
127C2×Dic15—41no—
128C2×Dic15—81no—
129C2×Dic15—81no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—41no—
132C2×C5×Dic3—81no—
133C2×C5×Dic3—81no—
134C3×C22⋊D5—22no—
135C3×C22⋊D5—22no—
136C3×C22⋊D5—22no—
137C3×C22⋊D5—22no—
138C3×C22⋊D5—82no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—81no—
143C2×C3×Dic5C22⋊C412yes—
144D5×Dic3—82no—
145C22×C3×D4—51no—
146C22×C3×D4C2×D511yescharacteristic
147C3×#123—52no—
148C3×#123—101no—
149C3×#121—102no—
150C3×#120—52no—
151C3×#120—101no—
152C2×C3×C22⋊C4—51no—
153C2×#217—51no—
154C2×#217—51no—
155C2×#217—101no—
156C2×#217C2×D511yescharacteristic
157C2×#217C2×D511yescharacteristic
158D4×Dic3—102no—
159D4×Dic3—102no—
160#926—101no—
161#834—22no—
162#834—102no—
163#834—102no—
164C24×C5C2×Dic311yescharacteristic, complemented
165C24×C5C22×D311yescharacteristic
166C23×D5#6711yescharacteristic
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C22×C4×C5—61no—
174C22×C4×C5—61no—
175C22×C4×C5C2×Dic311yescharacteristic, complemented
176C2×C22⋊D5—21no—
177C2×C22⋊D5—21no—
178C2×C22⋊D5—21no—
179C2×C22⋊D5—21no—
180C2×C22⋊D5—22no—
181C2×C22⋊D5C2×Dic312yes—
182C2×C22⋊D5#6712yes—
183C22×Dic5—21no—
184C22×Dic5—61no—
185C22×Dic5—61no—
186C22×Dic5#6711yescharacteristic
187C2×C4×D5—62no—
188C5×C22⋊C4—32no—
189C5×C22⋊C4—61no—
190C5×C22⋊C4—61no—
191C5×C22⋊C4—61no—
192C22⋊Dic5—21no—
193C22⋊Dic5—22no—
194C22⋊Dic5—32no—
195C22⋊Dic5—61no—
196C22⋊Dic5—61no—
197C22⋊Dic5—61no—
198C22⋊Dic5C2×Dic312yescomplemented
199#685—22no—
200#685—62no—
201#683—22no—
202#683—62no—
203C4×Dic5—62no—
204#534—51no—
205#518—151no—
206C2×#99—31no—
207C2×#99—151no—
208C2×#99—151no—
209#342—151no—
210#342—151no—
211C22×C3×C5—41no—
212C22×C3×C5—41no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5—42no—
219C22×C3×C5—41no—
220C22×C3×C5—81no—
221C22×C3×C5—81no—
222C22×C3×C5C2×C22⋊C411yescharacteristic
223C22×C3×C5C4×D411yescharacteristic
224C22×C3×C5C4×D411yescharacteristic
225C22×C3×C5#12011yescharacteristic
226C22×C3×C5#12111yescharacteristic
227C22×C3×C5#12111yescharacteristic
228C22×C3×C5#12311yescharacteristic
229C2×C3×D5—22no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—81no—
233C3×C4×C5—41no—
234Dic15—42no—
235Dic15—81no—
236C3×Dic5—22no—
237C3×Dic5—42no—
238C5×Dic3—42no—
239C5×Dic3—81no—
240C24×C3—51no—
241C24×C3C4×D511yescharacteristic, complemented
242C24×C3C22×D511yescharacteristic
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—52no—
250C2×C3×D4—52no—
251C2×C3×D4—101no—
252C2×C3×D4—101no—
253C2×C3×D4—101no—
254C2×C3×D4—101no—
255C2×C3×D4—102no—
256C22×C3×C4—51no—
257C22×C3×C4—101no—
258C22×C3×C4C4×D511yescharacteristic, complemented
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—102no—
262C22×Dic3—101no—
263C22×Dic3—101no—
264C3×C4⋊C4—102no—
265C3×C22⋊C4—52no—
266C3×C22⋊C4—102no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4—101no—
269#217—21no—
270#217—21no—
271#217—21no—
272#217—52no—
273#217—102no—
274#217—101no—
275#217—101no—
276#217—101no—
277#217C22⋊D512yescomplemented
278C4⋊Dic3—102no—
279C4×Dic3—102no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—81no—
284C23×C5—81no—
285C23×C5D3×D411yescharacteristic
286C23×C5D3×D411yescharacteristic
287C23×C5#23711yescharacteristic
288C23×C5#23711yescharacteristic
289C23×C5C22×Dic311yescharacteristic
290C23×C5C2×#6711yescharacteristic
291C23×C5C2×#6711yescharacteristic
292C22×D5—21no—
293C22×D5—21no—
294C22×D5—81no—
295C22×D5#21712yes—
296C5×D4—41no—
297C5×D4—41no—
298C5×D4—41no—
299C5×D4—41no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—62no—
304C2×C4×C5—121no—
305C2×C4×C5—241no—
306C2×C4×C5—241no—
307C22⋊D5—22no—
308C22⋊D5—22no—
309C22⋊D5—22no—
310C22⋊D5—22no—
311C22⋊D5—82no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—22no—
315C2×Dic5—62no—
316C2×Dic5—81no—
317C2×Dic5—121no—
318C2×Dic5—241no—
319C2×Dic5—241no—
320C2×Dic5#21712yes—
321C4×D5—242no—
322C22×D4—51no—
323C22×D4D3×D511yescharacteristic
324#123—52no—
325#123—101no—
326#121—102no—
327#120—52no—
328#120—101no—
329C4×D4—302no—
330C4×D4—302no—
331#117—301no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—51no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—151no—
337C2×C22⋊C4—301no—
338#99—62no—
339#99—302no—
340#99—302no—
341C2×C3×C5—21no—
342C2×C3×C5—21no—
343C2×C3×C5—21no—
344C2×C3×C5—21no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5—21no—
348C2×C3×C5—81no—
349C2×C3×C5#38611yescharacteristic
350C3×D5—42no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—52no—
355C23×C3—81no—
356C23×C3—81no—
357C23×C3—101no—
358C23×C3—101no—
359C23×C3—401no—
360C23×C3C2×C4×D511yescharacteristic
361C23×C3#70911yescharacteristic
362C23×C3D4×D511yescharacteristic
363C23×C3D4×D511yescharacteristic
364C23×C3D4×D511yescharacteristic
365C23×C3#71111yescharacteristic
366C23×C3C2×C22⋊D511yescharacteristic
367C3×D4—41no—
368C3×D4—41no—
369C3×D4—41no—
370C3×D4—41no—
371C3×D4—102no—
372C3×D4—102no—
373C3×D4—102no—
374C3×D4—102no—
375C3×D4—402no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—52no—
380C2×C3×C4—101no—
381C2×C3×C4—101no—
382C2×C3×C4—102no—
383C2×C3×C4—401no—
384C2×Dic3—22no—
385C2×Dic3—41no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388C2×Dic3—102no—
389C2×Dic3—201no—
390C2×Dic3—402no—
391C2×Dic3—401no—
392C2×Dic3—401no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—42no—
401C22×C5—41no—
402C22×C5—81no—
403C22×C5—81no—
404C22×C5D4×Dic311yescharacteristic
405C22×C5D4×Dic311yescharacteristic
406C22×C5#93511yescharacteristic
407C22×C5#93711yescharacteristic
408C22×C5#93911yescharacteristic
409C22×C5#93911yescharacteristic
410C22×C5C2×#21711yescharacteristic
411C2×D5—22no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—81no—
415C4×C5—41no—
416C4×C5—122no—
417C4×C5—241no—
418Dic5—22no—
419Dic5—42no—
420Dic5—122no—
421Dic5—241no—
422C24—51no—
423C24D5×Dic311yescharacteristic, complemented
424C24C2×D3×D511yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—52no—
432C2×D4—52no—
433C2×D4—101no—
434C2×D4—101no—
435C2×D4—101no—
436C2×D4—101no—
437C2×D4—102no—
438C22×C4—51no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—101no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4—301no—
445C22×C4D5×Dic311yescharacteristic, complemented
446C4⋊C4—102no—
447C4⋊C4—302no—
448C22⋊C4—32no—
449C22⋊C4—52no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—61no—
453C22⋊C4—102no—
454C22⋊C4—102no—
455C22⋊C4—101no—
456C22⋊C4—152no—
457C22⋊C4—302no—
458C22⋊C4—301no—
459C22⋊C4—301no—
460C22⋊C4—301no—
461C42—302no—
462C3×C5#191311yescharacteristic, complemented, Hall
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3—102no—
475C22×C3—202no—
476C22×C3—202no—
477C22×C3—401no—
478C22×C3D5×C22⋊C411yescharacteristic
479C22×C3#402711yescharacteristic
480C22×C3#402911yescharacteristic
481C22×C3#403011yescharacteristic
482C22×C3C4×C22⋊D511yescharacteristic
483C22×C3#408311yescharacteristic
484C22×C3#408411yescharacteristic
485C3×C4—41no—
486C3×C4—102no—
487C3×C4—202no—
488Dic3—42no—
489Dic3—81no—
490Dic3—202no—
491Dic3—401no—
492C2×C5—21no—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—21no—
499C2×C5—81no—
500C2×C5#522011yescharacteristic
501D5—42no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—52no—
506C23—81no—
507C23—81no—
508C23—101no—
509C23—101no—
510C23—401no—
511C23C2×D5×Dic311yescharacteristic
512C23#677911yescharacteristic
513C23#678011yescharacteristic
514C23D5×#6711yescharacteristic
515C23D5×#6711yescharacteristic
516C23D3×C22⋊D511yescharacteristic
517C23#679011yescharacteristic
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—102no—
523D4—102no—
524D4—102no—
525D4—102no—
526D4—402no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—52no—
531C2×C4—62no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—102no—
535C2×C4—121no—
536C2×C4—241no—
537C2×C4—241no—
538C2×C4—302no—
539C2×C4—401no—
540C2×C4—601no—
541C2×C4—1202no—
542C2×C4—1201no—
543C2×C4—1201no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—81no—
552C2×C3—202no—
553C2×C3#6524511yescharacteristic
554C5#7184811yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22—102no—
567C22—202no—
568C22—202no—
569C22—401no—
570C22D5×#21711yescharacteristic
571C22#9154811yescharacteristic
572C22#9154911yescharacteristic
573C22#9155011yescharacteristic
574C22Dic3×C22⋊D511yescharacteristic
575C22#9155911yescharacteristic
576C22#9157711yescharacteristic
577C4—41no—
578C4—102no—
579C4—122no—
580C4—202no—
581C4—241no—
582C4—602no—
583C4—1201no—
584C3#1060082711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—81no—
593C2—202no—
594C2#1174951811yescharacteristic
subgroupG/H
centerC2#11749518
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radicalC3×#66138C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11755406C2semidirect
3. C2×#91118C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90995C2semidirect
6. #11746020C2semidirect
7. #11746018C2semidirect
15. C3×#4099C4semidirect
20. C3×#4075C4semidirect
36. C24×C3×C5C2×C4semidirect
45. C22×C3×C4×C5C2×C4semidirect
63. #6719D4semidirect
67. C5×#217D4semidirect
70. C3×C22⋊Dic5C2×C4semidirect
80. C2×#834D5semidirect
87. #4099Dic3semidirect
94. #4075Dic3semidirect
164. C24×C5C2×Dic3semidirect
175. C22×C4×C5C2×Dic3semidirect
198. C22⋊Dic5C2×Dic3semidirect
241. C24×C3C4×D5semidirect
258. C22×C3×C4C4×D5semidirect
277. #217C22⋊D5semidirect
423. C24D5×Dic3semidirect
445. C22×C4D5×Dic3semidirect
462. C3×C5#1913semidirect
554. C5#71848semidirect
584. C3#10600827semidirect

Maximal subgroups

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

subgroupindex
C3×#661382
#117554062
C2×#911182
C2×C5×#8342
C2×#909952
#117460202
#117460182
#106008273
#718485