Finite Group Databasebeta

← #14303003

Subgroups — #14303003

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
1#11756245C211yesmaximal, characteristic, complemented
2#11755428C211yesmaximal, characteristic
3C2×C5×#806C211yesmaximal, characteristic, complemented
4C2×#90997C211yesmaximal, characteristic, complemented
5C2×#90996C211yesmaximal, characteristic, complemented
6C3×#64747C211yesmaximal, characteristic, complemented
7#11746018C211yesmaximal, characteristic, complemented
8#10600827—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C22×C5×#67C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C4×#1220—22no—
14#91770—22no—
15C22⋊C4×D15—21no—
16#91766—21no—
17C2×C5×#217C2211yescharacteristic
18C2×C3×C22⋊Dic5C2211yescharacteristic
19C2×C3×C22⋊Dic5C2211yescharacteristic
20#91573—21no—
21#91570C412yescomplemented
22#91566—22no—
23#91543—21no—
24#91542C412yescomplemented
25C5×#806—22no—
26#90997—22no—
27#90996—22no—
28#68964—51nomaximal, Hall
29#66138—31no—
30#65820—31no—
31C2×C5×#99—31no—
32C2×#3966—31no—
33C2×#3938—31no—
34#64747D311yescharacteristic, complemented
35#64746—31no—
36C24×C3×C5C2311yescharacteristic
37C23×D15D411yescharacteristic
38C23×C5×D3C2×C411yescharacteristic, complemented
39C22×C3×C4×C5—21no—
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220C2×C412yes—
45C2×#1220D412yes—
46C22×Dic15—21no—
47C22×Dic15D411yescharacteristic
48C2×C4×D15—22no—
49C2×C5×#67—21no—
50C2×C5×#67—21no—
51C2×C5×#67—21no—
52C2×C5×#67—21no—
53C2×C5×#67—21no—
54C2×C5×#67—21no—
55C22×C5×Dic3—21no—
56C22×C5×Dic3C2×C411yescharacteristic, complemented
57C22×C3×Dic5—21no—
58C22×C3×Dic5—21no—
59C2×#1203—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4D412yescomplemented
62#6719—21no—
63#6719D412yescomplemented
64#6714—22no—
65#6712—22no—
66C4×Dic15—22no—
67C5×#217—21no—
68C5×#217—21no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×C22⋊Dic5—21no—
72C3×C22⋊Dic5C2×C412yescomplemented
73#6668—22no—
74#6667—22no—
75(C2×D3)⋊Dic5—22no—
76#5493—51no—
77#5486—51no—
78C2×#806—51no—
79C2×#806—51no—
80C2×#806D511yescharacteristic, complemented
81C3×#342—51no—
82#4527—51no—
83C22×C5×D4—31no—
84C22×C22⋊D5—31no—
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊C4C2×D311yescharacteristic
87#4099—32no—
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5C2×D311yescharacteristic
90C2×C22⋊Dic5C2×D311yescharacteristic
91#4085—62no—
92#4083—61no—
93#4081—61no—
94#4075—32no—
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—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×D15—21no—
112C22×D15—21no—
113C22×D15—81no—
114C22×D15C22⋊C412yes—
115C22×C5×D3—21no—
116C22×C5×D3—21no—
117C22×C5×D3—21no—
118C22×C5×D3—81no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—81no—
121#1220—22no—
122#1220—22no—
123#1220—22no—
124#1220—22no—
125C2×Dic15—21no—
126C2×Dic15—21no—
127C2×Dic15—22no—
128C2×Dic15—81no—
129C2×Dic15C22⋊C412yes—
130C4×D15—82no—
131C5×#67—41no—
132C5×#67—41no—
133C5×#67—41no—
134C5×#67—41no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—41no—
139C2×C5×Dic3—81no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—41no—
142C2×C3×Dic5—81no—
143C2×C3×Dic5—81no—
144#1203—82no—
145C22×#67—51no—
146C22×#67C2×D511yescharacteristic
147C2×C3×C22⋊C4—51no—
148C2×C3×C22⋊C4—51no—
149C2×C3×C22⋊C4C2×D511yescharacteristic
150C2×#217—51no—
151C2×#217C2×D511yescharacteristic
152#930—102no—
153C4×#67—102no—
154#886—52no—
155#886—101no—
156#882—52no—
157#882—101no—
158#67⋊C4—102no—
159D3×C22⋊C4—101no—
160#877—101no—
161#806—22no—
162#806—102no—
163#806—102no—
164C24×C5—31no—
165C24×C5C22×D311yescharacteristic
166C23×D5—31no—
167C2×C5×D4—61no—
168C2×C5×D4—61no—
169C2×C5×D4—61no—
170C2×C5×D4—61no—
171C2×C5×D4—61no—
172C2×C5×D4—61no—
173C22×C4×C5—21no—
174C22×C4×C5—31no—
175C22×C4×C5—61no—
176C2×C22⋊D5—32no—
177C2×C22⋊D5—32no—
178C2×C22⋊D5—62no—
179C2×C22⋊D5—61no—
180C2×C22⋊D5—61no—
181C2×C22⋊D5—61no—
182C2×C22⋊D5—61no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—31no—
186C22×Dic5—61no—
187C2×C4×D5—62no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—61no—
190C5×C22⋊C4—61no—
191C5×C22⋊C4D1212yescomplemented
192C22⋊Dic5—21no—
193C22⋊Dic5—21no—
194C22⋊Dic5—21no—
195C22⋊Dic5—32no—
196C22⋊Dic5—62no—
197C22⋊Dic5—61no—
198C22⋊Dic5C4×D312yescomplemented
199#685—62no—
200#685—62no—
201#683—62no—
202#683—62no—
203C4×Dic5—62no—
204#534—151no—
205#518—151no—
206C2×#99—31no—
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×D15—22no—
226C2×D15—42no—
227C2×D15—42no—
228C2×D15—81no—
229C2×C5×D3—42no—
230C2×C5×D3—41no—
231C2×C5×D3—81no—
232C2×C5×D3—81no—
233C3×C4×C5—42no—
234Dic15—22no—
235Dic15—42no—
236C3×Dic5—42no—
237C3×Dic5—81no—
238C5×Dic3—41no—
239C5×Dic3—81no—
240C24×C3C22×D511yescharacteristic
241C23×D3—51no—
242C23×D3C4×D511yescharacteristic, complemented
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—52no—
253C2×#67—52no—
254C2×#67—101no—
255C2×#67—101no—
256C2×#67—101no—
257C2×#67—101no—
258C22×Dic3—21no—
259C22×Dic3—51no—
260C22×Dic3—101no—
261C22×Dic3C4×D511yescharacteristic, complemented
262C2×D12—102no—
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⋊C4C22⋊D512yescomplemented
270#217—21no—
271#217—21no—
272#217—52no—
273#217—101no—
274(C2×D3)⋊C4—102no—
275(C2×D3)⋊C4—102no—
276(C2×D3)⋊C4—102no—
277C4⋊Dic3—102no—
278Dic3⋊C4—102no—
279C4×Dic3—102no—
280C23×C5—61no—
281C23×C5—61no—
282C23×C5—61no—
283C23×C5—81no—
284C23×C5—241no—
285C23×C5C2×C4×D311yescharacteristic
286C23×C5C2×D1211yescharacteristic
287C23×C5#23511yescharacteristic
288C23×C5D3×D411yescharacteristic
289C23×C5D3×D411yescharacteristic
290C23×C5D3×D411yescharacteristic
291C23×C5#23911yescharacteristic
292C22×D5—32no—
293C22×D5—61no—
294C22×D5—61no—
295C22×D5—241no—
296C5×D4—121no—
297C5×D4—121no—
298C5×D4—121no—
299C5×D4—121no—
300C2×C4×C5—22no—
301C2×C4×C5—61no—
302C2×C4×C5—61no—
303C2×C4×C5—61no—
304C2×C4×C5—81no—
305C2×C4×C5—121no—
306C2×C4×C5—241no—
307C22⋊D5—62no—
308C22⋊D5—62no—
309C22⋊D5—62no—
310C22⋊D5—62no—
311C22⋊D5—242no—
312C2×Dic5—22no—
313C2×Dic5—32no—
314C2×Dic5—41no—
315C2×Dic5—61no—
316C2×Dic5—61no—
317C2×Dic5—62no—
318C2×Dic5—81no—
319C2×Dic5—81no—
320C2×Dic5—241no—
321C4×D5—242no—
322C22×D4—31no—
323C22×D4—151no—
324#123—152no—
325#123—301no—
326#121—302no—
327#120—152no—
328#120—301no—
329C4×D4—302no—
330C4×D4—302no—
331#117—301no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—51no—
334C2×C22⋊C4—51no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—301no—
337C2×C22⋊C4D3×D511yescharacteristic
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#38611yescharacteristic
349D15—42no—
350C5×D3—81no—
351C23×C3—81no—
352C23×C3C2×C4×D511yescharacteristic
353C23×C3#70911yescharacteristic
354C23×C3D4×D511yescharacteristic
355C23×C3D4×D511yescharacteristic
356C23×C3D4×D511yescharacteristic
357C23×C3#71111yescharacteristic
358C23×C3C2×C22⋊D511yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—52no—
363C22×D3—81no—
364C22×D3—101no—
365C22×D3—101no—
366C22×D3—401no—
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—41no—
374#67—41no—
375#67—41no—
376#67—41no—
377#67—102no—
378#67—102no—
379#67—102no—
380#67—102no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—41no—
385C2×Dic3—52no—
386C2×Dic3—81no—
387C2×Dic3—101no—
388C2×Dic3—101no—
389C2×Dic3—102no—
390C2×Dic3—401no—
391D12—402no—
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—122no—
401C22×C5—121no—
402C22×C5—241no—
403C22×C5—241no—
404C22×C5C4×D1211yescharacteristic
405C22×C5D3×C22⋊C411yescharacteristic
406C22×C5#88211yescharacteristic
407C22×C5#88411yescharacteristic
408C22×C5#89311yescharacteristic
409C22×C5#89411yescharacteristic
410C22×C5#89511yescharacteristic
411C2×D5—62no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—241no—
415C4×C5—42no—
416C4×C5—121no—
417C4×C5—241no—
418Dic5—42no—
419Dic5—62no—
420Dic5—81no—
421Dic5—122no—
422C24—31no—
423C24—151no—
424C24C2×D3×D511yescharacteristic
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—152no—
432C2×D4—152no—
433C2×D4—302no—
434C2×D4—301no—
435C2×D4—301no—
436C2×D4—301no—
437C2×D4—301no—
438C22×C4—21no—
439C22×C4—31no—
440C22×C4—61no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—151no—
444C22×C4—302no—
445C22×C4—301no—
446C4⋊C4—302no—
447C4⋊C4—302no—
448C22⋊C4—21no—
449C22⋊C4—52no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—101no—
453C22⋊C4—101no—
454C22⋊C4—101no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C22⋊C4—301no—
460C22⋊C4#120312yescomplemented
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×C3D5×C22⋊C411yescharacteristic
471C22×C3#402711yescharacteristic
472C22×C3#402911yescharacteristic
473C22×C3#403011yescharacteristic
474C22×C3C4×C22⋊D511yescharacteristic
475C22×C3#408311yescharacteristic
476C22×C3#408411yescharacteristic
477C2×D3—42no—
478C2×D3—41no—
479C2×D3—81no—
480C2×D3—81no—
481C2×D3—102no—
482C2×D3—202no—
483C2×D3—202no—
484C2×D3—401no—
485C3×C4—42no—
486C3×C4—202no—
487C3×C4—401no—
488Dic3—41no—
489Dic3—81no—
490Dic3—102no—
491Dic3—202no—
492C2×C5—21no—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—21no—
499C2×C5—241no—
500C2×C5#466511yescharacteristic
501D5—122no—
502C23—61no—
503C23—61no—
504C23—61no—
505C23—81no—
506C23—152no—
507C23—241no—
508C23—301no—
509C23—301no—
510C23—1201no—
511C23#676811yescharacteristic
512C23#677111yescharacteristic
513C23C4×D3×D511yescharacteristic
514C23#677711yescharacteristic
515C23C2×#120311yescharacteristic
516C23#679011yescharacteristic
517C23#679011yescharacteristic
518D4—121no—
519D4—121no—
520D4—121no—
521D4—121no—
522D4—302no—
523D4—302no—
524D4—302no—
525D4—302no—
526D4—1202no—
527C2×C4—22no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—81no—
532C2×C4—102no—
533C2×C4—121no—
534C2×C4—152no—
535C2×C4—201no—
536C2×C4—241no—
537C2×C4—301no—
538C2×C4—301no—
539C2×C4—302no—
540C2×C4—401no—
541C2×C4—401no—
542C2×C4—1202no—
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#6524511yescharacteristic
552D3—81no—
553D3—202no—
554C5#6896411yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—122no—
563C22—121no—
564C22—241no—
565C22—241no—
566C22—302no—
567C22—602no—
568C22—602no—
569C22—1201no—
570C22#9135511yescharacteristic
571C22#9140611yescharacteristic
572C22C4×#120311yescharacteristic
573C22#9146111yescharacteristic
574C22#9146611yescharacteristic
575C22#9147311yescharacteristic
576C22#9157311yescharacteristic
577C4—42no—
578C4—121no—
579C4—202no—
580C4—241no—
581C4—302no—
582C4—401no—
583C4—602no—
584C3#1060082711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—241no—
593C2—602no—
594C2#1174891811yescharacteristic
subgroupG/H
centerC2#11748918
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5#386
prime radical#11755428C2
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
1. #11756245C2semidirect
3. C2×C5×#806C2semidirect
4. C2×#90997C2semidirect
5. C2×#90996C2semidirect
6. C3×#64747C2semidirect
7. #11746018C2semidirect
21. #91570C4semidirect
24. #91542C4semidirect
34. #64747D3semidirect
38. C23×C5×D3C2×C4semidirect
56. C22×C5×Dic3C2×C4semidirect
61. C3×C5×C22⋊C4D4semidirect
63. #6719D4semidirect
72. C3×C22⋊Dic5C2×C4semidirect
80. C2×#806D5semidirect
191. C5×C22⋊C4D12semidirect
198. C22⋊Dic5C4×D3semidirect
242. C23×D3C4×D5semidirect
261. C22×Dic3C4×D5semidirect
269. C3×C22⋊C4C22⋊D5semidirect
460. C22⋊C4#1203semidirect
462. C3×C5#1913semidirect
554. C5#68964semidirect
584. C3#10600827semidirect

Maximal subgroups

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

subgroupindex
#117562452
#117554282
C2×C5×#8062
C2×#909972
C2×#909962
C3×#647472
#117460182
#106008273
#689645