Finite Group Databasebeta

← #14303019

Subgroups — #14303019

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
1C5×#5493C211yesmaximal, characteristic
2#11755410C211yesmaximal, characteristic, complemented
3C2×#90996C211yesmaximal, characteristic, complemented
4C2×#90996C211yesmaximal, characteristic, complemented
5C2×#90996C211yesmaximal, characteristic, complemented
6#11746348C211yesmaximal, characteristic, complemented
7C3×#64747C211yesmaximal, characteristic, complemented
8#10602641—31nomaximal, Hall
9C22×C5×#67C2211yescharacteristic
10C22×C5×#67C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C5×#930—22no—
15C5×#886—21no—
16C5×#886C412yescomplemented
17C5×#882—21no—
18C5×#882C412yescomplemented
19C2×C3×C22⋊Dic5C2211yescharacteristic
20C2×C3×C22⋊Dic5C2211yescharacteristic
21#67⋊Dic5—22no—
22D3×C22⋊Dic5—21no—
23Dic5×#67—22no—
24#91529—21no—
25#90996—22no—
26#90996—22no—
27#90996—22no—
28#68964—51nomaximal, Hall
29C5×#534—31no—
30#66132—31no—
31C2×#3966—31no—
32C2×#3966—31no—
33C2×#3966—31no—
34#64747—31no—
35#64747D311yescharacteristic, complemented
36C24×C3×C5C2311yescharacteristic
37C23×C5×D3C2×C411yescharacteristic, complemented
38C23×C5×D3D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×Dic15—21no—
41C22×Dic15—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C2×C5×#67—21no—
46C2×C5×#67—21no—
47C2×C5×#67—21no—
48C2×C5×#67—21no—
49C2×C5×#67—21no—
50C2×C5×#67—21no—
51C2×C5×#67—21no—
52C2×C5×#67C2×C412yes—
53C2×C5×#67D412yes—
54C22×C5×Dic3C2×C411yescharacteristic, complemented
55C22×C5×Dic3D411yescharacteristic
56C2×C5×D12—22no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5—21no—
59C2×D3×Dic5—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4C2×C412yescomplemented
62#6719—21no—
63#6719—21no—
64#6719—21no—
65#6719D412yescomplemented
66C5×(C2×D3)⋊C4—22no—
67C5×(C2×D3)⋊C4—22no—
68C5×C4⋊Dic3—22no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×C22⋊Dic5—21no—
72C3×C22⋊Dic5D412yescomplemented
73Dic3⋊Dic5—22no—
74(C2×D3)⋊Dic5—22no—
75Dic3×Dic5—22no—
76#5493D511yescharacteristic
77#5486—51no—
78C2×#806—51no—
79C2×#806—51no—
80C2×#806—51no—
81C3×#342—51no—
82#4527—51no—
83C22×C5×D4—31no—
84C22×C5×D4—31no—
85C5×#123—32no—
86C5×#123—61no—
87C5×#121—62no—
88C5×#120—32no—
89C5×#120—61no—
90C2×C5×C22⋊C4C2×D311yescharacteristic
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—31no—
93C2×C22⋊Dic5—61no—
94C2×C22⋊Dic5C2×D311yescharacteristic
95C2×C22⋊Dic5C2×D311yescharacteristic
96D4×Dic5—62no—
97D4×Dic5—62no—
98#4072—61no—
99#3966—62no—
100#3966—62no—
101#3966—62no—
102#1913—151noSylow
103C23×C3×C5—81no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5C2×D411yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C22×C5×D3—21no—
112C22×C5×D3—21no—
113C22×C5×D3—21no—
114C22×C5×D3—21no—
115C22×C5×D3—21no—
116C22×C5×D3—81no—
117C22×C5×D3—81no—
118C22×C5×D3C22⋊C412yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—81no—
121C2×Dic15—22no—
122C2×Dic15—41no—
123C2×Dic15—81no—
124C2×Dic15—81no—
125C5×#67—22no—
126C5×#67—22no—
127C5×#67—22no—
128C5×#67—22no—
129C5×#67—41no—
130C5×#67—41no—
131C5×#67—41no—
132C5×#67—41no—
133C2×C5×Dic3—21no—
134C2×C5×Dic3—21no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3C22⋊C412yes—
139C5×D12—82no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—41no—
142C2×C3×Dic5—81no—
143C2×C3×Dic5—81no—
144D3×Dic5—82no—
145C22×#67C2×D511yescharacteristic
146C22×#67C2×D511yescharacteristic
147C2×C3×C22⋊C4—51no—
148C2×C3×C22⋊C4—51no—
149C2×C3×C22⋊C4C2×D511yescharacteristic
150C2×#217—51no—
151C2×#217—51no—
152#930—22no—
153C4×#67—102no—
154#886—21no—
155#886Dic512yescomplemented
156#882—21no—
157#882Dic512yescomplemented
158#67⋊C4—102no—
159D3×C22⋊C4—101no—
160#877—101no—
161#806—102no—
162#806—102no—
163#806—102no—
164C24×C5—31no—
165C24×C5—31no—
166C24×C5C22×D311yescharacteristic
167C2×C5×D4—32no—
168C2×C5×D4—32no—
169C2×C5×D4—62no—
170C2×C5×D4—61no—
171C2×C5×D4—61no—
172C2×C5×D4—61no—
173C2×C5×D4—61no—
174C2×C5×D4—61no—
175C2×C5×D4—61no—
176C2×C5×D4—61no—
177C2×C5×D4—61no—
178C2×C5×D4—61no—
179C2×C5×D4—61no—
180C22×C4×C5—21no—
181C22×C4×C5—31no—
182C22×C4×C5—31no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—62no—
186C22×Dic5—61no—
187C22×Dic5—61no—
188C5×C4⋊C4—62no—
189C5×C22⋊C4—21no—
190C5×C22⋊C4—62no—
191C5×C22⋊C4—62no—
192C5×C22⋊C4C4×D312yescomplemented
193C22⋊Dic5—21no—
194C22⋊Dic5—21no—
195C22⋊Dic5—21no—
196C22⋊Dic5—32no—
197C22⋊Dic5—62no—
198C22⋊Dic5—61no—
199C22⋊Dic5—61no—
200C22⋊Dic5—61no—
201C22⋊Dic5D1212yescomplemented
202C4⋊Dic5—62no—
203C4×Dic5—62no—
204#534—31no—
205#518—151no—
206C2×#99—151no—
207C2×#99—151no—
208C2×#99—151no—
209#342—51no—
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×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×D411yescharacteristic
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5#12111yescharacteristic
223C22×C3×C5#12111yescharacteristic
224C22×C3×C5#12311yescharacteristic
225C2×C5×D3—22no—
226C2×C5×D3—42no—
227C2×C5×D3—42no—
228C2×C5×D3—42no—
229C2×C5×D3—41no—
230C2×C5×D3—81no—
231C2×C5×D3—81no—
232C2×C5×D3—81no—
233C3×C4×C5—42no—
234Dic15—42no—
235Dic15—81no—
236C3×Dic5—42no—
237C3×Dic5—81no—
238C5×Dic3—22no—
239C5×Dic3—41no—
240C24×C3C22×D511yescharacteristic
241C23×D3C2×Dic511yescharacteristic, complemented
242C23×D3C22⋊D511yescharacteristic
243C22×C3×C4—21no—
244C22×C3×C4—101no—
245C22×C3×C4—101no—
246C2×#67—21no—
247C2×#67—21no—
248C2×#67—21no—
249C2×#67—21no—
250C2×#67—21no—
251C2×#67—21no—
252C2×#67—21no—
253C2×#67—21no—
254C2×#67—21no—
255C2×#67—21no—
256C2×#67C2×Dic512yes—
257C2×#67C22⋊D512yes—
258C22×Dic3—101no—
259C22×Dic3—101no—
260C22×Dic3C2×Dic511yescharacteristic, complemented
261C22×Dic3C22⋊D511yescharacteristic
262C2×D12—22no—
263C2×C4×D3—102no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—52no—
266C3×C22⋊C4—101no—
267C3×C22⋊C4—101no—
268C3×C22⋊C4—101no—
269C3×C22⋊C4C2×Dic512yescomplemented
270#217—52no—
271#217—101no—
272#217—101no—
273#217—101no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—102no—
277C4⋊Dic3—22no—
278Dic3⋊C4—102no—
279C4×Dic3—102no—
280C23×C5—32no—
281C23×C5—61no—
282C23×C5—61no—
283C23×C5—61no—
284C23×C5—61no—
285C23×C5—61no—
286C23×C5—81no—
287C23×C5—241no—
288C23×C5—241no—
289C23×C5C2×C4×D311yescharacteristic
290C23×C5C2×D1211yescharacteristic
291C23×C5#23511yescharacteristic
292C23×C5D3×D411yescharacteristic
293C23×C5D3×D411yescharacteristic
294C23×C5D3×D411yescharacteristic
295C23×C5#23911yescharacteristic
296C5×D4—62no—
297C5×D4—62no—
298C5×D4—62no—
299C5×D4—62no—
300C5×D4—121no—
301C5×D4—121no—
302C5×D4—121no—
303C5×D4—121no—
304C5×D4—242no—
305C2×C4×C5—22no—
306C2×C4×C5—32no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5—81no—
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—62no—
316C2×Dic5—81no—
317C2×Dic5—81no—
318C2×Dic5—121no—
319C2×Dic5—242no—
320C2×Dic5—241no—
321C2×Dic5—241no—
322C22×D4—31no—
323C22×D4—31no—
324#123—32no—
325#123—61no—
326#121—62no—
327#120—32no—
328#120—61no—
329C4×D4—302no—
330C4×D4—302no—
331#117—301no—
332C2×C22⋊C4—51no—
333C2×C22⋊C4—51no—
334C2×C22⋊C4—151no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—301no—
337C2×C22⋊C4D3×D511yescharacteristic
338#99—302no—
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#38611yescharacteristic
349C5×D3—42no—
350C5×D3—81no—
351C23×C3—81no—
352C23×C3D4×D511yescharacteristic
353C23×C3D4×D511yescharacteristic
354C23×C3#71111yescharacteristic
355C23×C3#71111yescharacteristic
356C23×C3C22×Dic511yescharacteristic
357C23×C3C2×C22⋊D511yescharacteristic
358C23×C3C2×C22⋊D511yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—21no—
364C22×D3—81no—
365C22×D3—81no—
366C22×D3C22⋊Dic512yes—
367C2×C3×C4—22no—
368C2×C3×C4—81no—
369C2×C3×C4—102no—
370C2×C3×C4—201no—
371C2×C3×C4—401no—
372C2×C3×C4—401no—
373#67—22no—
374#67—22no—
375#67—22no—
376#67—22no—
377#67—41no—
378#67—41no—
379#67—41no—
380#67—41no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—102no—
387C2×Dic3—201no—
388C2×Dic3—401no—
389C2×Dic3—401no—
390C2×Dic3C22⋊Dic512yes—
391D12—82no—
392C4×D3—402no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—62no—
401C22×C5—122no—
402C22×C5—122no—
403C22×C5—122no—
404C22×C5—121no—
405C22×C5—241no—
406C22×C5—241no—
407C22×C5—241no—
408C22×C5C4×D1211yescharacteristic
409C22×C5D3×C22⋊C411yescharacteristic
410C22×C5#88211yescharacteristic
411C22×C5#88411yescharacteristic
412C22×C5#89311yescharacteristic
413C22×C5#89411yescharacteristic
414C22×C5#89511yescharacteristic
415C4×C5—42no—
416C4×C5—62no—
417C4×C5—121no—
418Dic5—42no—
419Dic5—81no—
420Dic5—122no—
421Dic5—241no—
422C24—31no—
423C24—31no—
424C24C2×D3×D511yescharacteristic
425C2×D4—32no—
426C2×D4—32no—
427C2×D4—62no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C22×C4—21no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—302no—
444C22×C4—301no—
445C22×C4—301no—
446C4⋊C4—62no—
447C4⋊C4—302no—
448C22⋊C4—21no—
449C22⋊C4—52no—
450C22⋊C4—62no—
451C22⋊C4—62no—
452C22⋊C4—101no—
453C22⋊C4—101no—
454C22⋊C4—101no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—301no—
458C22⋊C4—301no—
459C22⋊C4—301no—
460C22⋊C4D3×Dic512yescomplemented
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×C3D4×Dic511yescharacteristic
471C22×C3D4×Dic511yescharacteristic
472C22×C3#408111yescharacteristic
473C22×C3#408311yescharacteristic
474C22×C3#408511yescharacteristic
475C22×C3#408511yescharacteristic
476C22×C3C2×C22⋊Dic511yescharacteristic
477C2×D3—22no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—41no—
482C2×D3—81no—
483C2×D3—81no—
484C2×D3—81no—
485C3×C4—42no—
486C3×C4—202no—
487C3×C4—401no—
488Dic3—22no—
489Dic3—41no—
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—122no—
500C2×C5—241no—
501C2×C5#466511yescharacteristic
502C23—32no—
503C23—61no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23—61no—
508C23—81no—
509C23—241no—
510C23—241no—
511C23#676811yescharacteristic
512C23#677211yescharacteristic
513C23D5×D1211yescharacteristic
514C23#677711yescharacteristic
515C23C2×D3×Dic511yescharacteristic
516C23D3×C22⋊D511yescharacteristic
517C23D3×C22⋊D511yescharacteristic
518D4—62no—
519D4—62no—
520D4—62no—
521D4—62no—
522D4—121no—
523D4—121no—
524D4—121no—
525D4—121no—
526D4—242no—
527C2×C4—22no—
528C2×C4—32no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—81no—
535C2×C4—102no—
536C2×C4—201no—
537C2×C4—302no—
538C2×C4—401no—
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#6550911yescharacteristic
552D3—42no—
553D3—81no—
554C5#6896411yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—62no—
563C22—122no—
564C22—122no—
565C22—122no—
566C22—121no—
567C22—241no—
568C22—241no—
569C22—241no—
570C22Dic5×D1211yescharacteristic
571C22#9141611yescharacteristic
572C22#9142311yescharacteristic
573C22#9143511yescharacteristic
574C22#9145311yescharacteristic
575C22#9147511yescharacteristic
576C22D3×C22⋊Dic511yescharacteristic
577C4—42no—
578C4—62no—
579C4—121no—
580C4—202no—
581C4—401no—
582C4—602no—
583C4—1201no—
584C3#1060264111yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—122no—
593C2—241no—
594C2#1174890111yescharacteristic
subgroupG/H
centerC2#11748901
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5#386
prime radicalC5×#5493C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11755410C2semidirect
3. C2×#90996C2semidirect
4. C2×#90996C2semidirect
5. C2×#90996C2semidirect
6. #11746348C2semidirect
7. C3×#64747C2semidirect
16. C5×#886C4semidirect
18. C5×#882C4semidirect
35. #64747D3semidirect
37. C23×C5×D3C2×C4semidirect
54. C22×C5×Dic3C2×C4semidirect
61. C3×C5×C22⋊C4C2×C4semidirect
65. #6719D4semidirect
72. C3×C22⋊Dic5D4semidirect
155. #886Dic5semidirect
157. #882Dic5semidirect
192. C5×C22⋊C4C4×D3semidirect
201. C22⋊Dic5D12semidirect
241. C23×D3C2×Dic5semidirect
260. C22×Dic3C2×Dic5semidirect
269. C3×C22⋊C4C2×Dic5semidirect
460. C22⋊C4D3×Dic5semidirect
462. C3×C5#1913semidirect
554. C5#68964semidirect
584. C3#10602641semidirect

Maximal subgroups

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

subgroupindex
C5×#54932
#117554102
C2×#909962
#117463482
C3×#647472
#106026413
#689645