Finite Group Databasebeta

← #14300745

Subgroups — #14300745

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic, complemented
2C2×#91466C211yesmaximal, characteristic
3C2×C5×#809C211yesmaximal, characteristic, complemented
4C2×#90967C211yesmaximal, characteristic, complemented
5C2×#90957C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10600994—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C22×#1203—21no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×#6714—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4×Dic15—21no—
16#91781—22no—
17#91781—22no—
18C22×C5×C3⋊C8C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C2×(C2×D3)⋊Dic5—21no—
22#91466—22no—
23#91466C414yescomplemented
24C5×#809—22no—
25#90967—22no—
26#90957—22no—
27#68881—51nomaximal, Hall
28C2×#4084—31no—
29C2×#4038—31no—
30C2×C5×#102—31no—
31C2×#3964—31no—
32C2×#3952—31no—
33#64771—31no—
34#64749D311yescharacteristic, complemented
35C23×D15D411yescharacteristic
36C23×C5×D3—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15C2×C412yes—
46C2×C4×D15D412yes—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12C2×C412yes—
53C22×C3×Dic5—21no—
54C2×#1203—24no—
55C2×#1203—42no—
56C2×#1203—42no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4D412yescomplemented
59#6714—24no—
60C4⋊Dic15—21no—
61C4⋊Dic15D412yescomplemented
62C4×Dic15—24no—
63C2×C5×C3⋊C8—21no—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C3×C4⋊Dic5—21no—
67C3×C4⋊Dic5C2×C412yes—
68C2×C3×#168—21no—
69C2×C3×#168—21no—
70C2×C3×#168—21no—
71(C2×D3)⋊Dic5—24no—
72C2×#895—51no—
73C2×#892—51no—
74C2×#821—51no—
75C2×(C2×D3)⋊C8—51no—
76C2×#809D511yescharacteristic, complemented
77C3×#340—51no—
78#4529—51no—
79C22×C5×D4—31no—
80C22×C22⋊D5—61no—
81C22×C4×D5—31no—
82C22×C5×C8—31no—
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×C22⋊Dic5—61no—
85#4084—34no—
86#4084—62no—
87C2×#685—61no—
88C2×C4⋊Dic5—31no—
89C2×C4⋊Dic5C2×D311yescharacteristic
90C2×C4×Dic5—61no—
91C22×#168C2×D311yescharacteristic
92#4038—62no—
93#4038—62no—
94C5×#102—62no—
95#3964—62no—
96#3952—62no—
97#1875—151noSylow
98C23×C3×C5C2×D411yescharacteristic
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—21no—
102C22×D15—21no—
103C22×D15—21no—
104C22×D15—21no—
105C22×D15C22⋊C412yes—
106C22×C5×D3—22no—
107C22×C5×D3—41no—
108C22×C5×D3—41no—
109C22×C5×D3—41no—
110C22×C5×D3—41no—
111C22×C5×D3—41no—
112C22×C5×D3—41no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C2×C3×C4×C5#4111yescharacteristic
122C2×Dic15—21no—
123C2×Dic15—21no—
124C2×Dic15—22no—
125C2×Dic15—41no—
126C2×Dic15—41no—
127C2×Dic15C22⋊C412yes—
128C4×D15—22no—
129C4×D15—22no—
130C4×D15—22no—
131C4×D15—22no—
132C5×D12—22no—
133C5×D12—22no—
134C5×D12—41no—
135C5×D12—41no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—41no—
138C2×C3×Dic5—41no—
139#1203—48no—
140C3×#168—41no—
141C5×C3⋊C8—41no—
142C22×D12—101no—
143C22×D12C2×D511yescharacteristic
144C22×C4×D3—51no—
145C22×C3×C8—51no—
146C2×C3×C4⋊C4—51no—
147C2×C3×C4⋊C4C2×D511yescharacteristic
148C2×(C2×D3)⋊C4—101no—
149C2×(C2×D3)⋊C4—101no—
150C2×C4⋊Dic3—51no—
151C2×C4×Dic3—101no—
152C22×C3⋊C8C2×D511yescharacteristic
153#895—54no—
154#895—102no—
155#892—102no—
156#892—102no—
157#821—102no—
158(C2×D3)⋊C8—102no—
159#809—22no—
160C24×C5—61no—
161C23×D5—31no—
162C2×C5×D4—32no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—61no—
167C2×C5×D4—61no—
168C22×C4×C5—21no—
169C22×C4×C5C22×D311yescharacteristic
170C2×C22⋊D5—64no—
171C2×C22⋊D5—122no—
172C2×C22⋊D5—122no—
173C22×Dic5—21no—
174C22×Dic5—31no—
175C22×Dic5—61no—
176C2×C4×D5—32no—
177C2×C4×D5—32no—
178C2×C4×D5—61no—
179C2×C4×D5—61no—
180C2×C4×D5—61no—
181C2×C4×D5—61no—
182C2×C5×C8—61no—
183C2×C5×C8—61no—
184C2×C5×C8—61no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4D1212yescomplemented
187C22⋊Dic5—64no—
188#685—64no—
189C4⋊Dic5—21no—
190C4⋊Dic5—32no—
191C4⋊Dic5—61no—
192C4⋊Dic5C4×D312yes—
193C4×Dic5—64no—
194C2×#168—21no—
195C2×#168—21no—
196C2×#168—21no—
197C2×#121—151no—
198C2×#117—151no—
199C2×#102—31no—
200C2×#102—151no—
201C2×C22⋊C8—151no—
202#340—51no—
203#340—151no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12311yescharacteristic
207C22×C3×C5#13511yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
211C2×D15—22no—
212C2×D15—22no—
213C2×D15—22no—
214C2×D15—41no—
215C2×D15—41no—
216C2×D15—41no—
217C2×D15—41no—
218C2×C5×D3—42no—
219C2×C5×D3—42no—
220C2×C5×D3—42no—
221C2×C5×D3—81no—
222C2×C5×D3—81no—
223C2×C5×D3—81no—
224C2×C5×D3—81no—
225C3×C4×C5—42no—
226C3×C4×C5C4×D411yescharacteristic
227C3×C4×C5C4×D411yescharacteristic
228C3×C4×C5#12111yescharacteristic
229C3×C4×C5#12111yescharacteristic
230Dic15—22no—
231Dic15—42no—
232C3×Dic5—42no—
233C23×D3—21no—
234C23×D3—51no—
235C22×C3×C4—21no—
236C22×C3×C4—101no—
237C22×C3×C4C22×D511yescharacteristic
238C22×Dic3—51no—
239C22×Dic3—101no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—104no—
246C2×D12—202no—
247C2×D12—202no—
248C2×D12C4×D512yes—
249C2×C4×D3—52no—
250C2×C4×D3—52no—
251C2×C4×D3—101no—
252C2×C4×D3—101no—
253C2×C4×D3—101no—
254C2×C4×D3—101no—
255C2×C3×C8—101no—
256C2×C3×C8—101no—
257C2×C3×C8—101no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—52no—
260C3×C4⋊C4—101no—
261C3×C4⋊C4C22⋊D512yescomplemented
262(C2×D3)⋊C4—104no—
263(C2×D3)⋊C4—104no—
264C4⋊Dic3—52no—
265C4⋊Dic3—101no—
266C4×Dic3—104no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C23×C5—62no—
271C23×C5—121no—
272C23×C5—121no—
273C23×C5—121no—
274C23×C5—121no—
275C23×C5—121no—
276C23×C5—121no—
277C23×C5D3×D411yescharacteristic
278C22×D5—32no—
279C22×D5—61no—
280C22×D5—61no—
281C22×D5—61no—
282C22×D5—61no—
283C22×D5—61no—
284C22×D5—61no—
285C5×D4—62no—
286C5×D4—62no—
287C5×D4—121no—
288C5×D4—121no—
289C2×C4×C5—22no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5C2×C4×D311yescharacteristic
293C2×C4×C5C2×D1211yescharacteristic
294C2×C4×C5#23511yescharacteristic
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5#23911yescharacteristic
298C22⋊D5—128no—
299C2×Dic5—22no—
300C2×Dic5—32no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—61no—
304C2×Dic5—61no—
305C2×Dic5—62no—
306C2×Dic5—121no—
307C2×Dic5—121no—
308C4×D5—62no—
309C4×D5—62no—
310C4×D5—62no—
311C4×D5—62no—
312C5×C8—121no—
313#168—41no—
314C22×D4—31no—
315C22×D4—301no—
316C23×C4—151no—
317C22×C8—31no—
318C22×C8—51no—
319#121—154no—
320#121—302no—
321#117—302no—
322#117—302no—
323C2×C4⋊C4—51no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4D3×D511yescharacteristic
326C2×C22⋊C4—301no—
327C2×C22⋊C4—301no—
328C2×C42—301no—
329#102—62no—
330#102—302no—
331C22⋊C8—302no—
332C2×C3×C5#38611yescharacteristic
333C2×C3×C5#41611yescharacteristic
334C2×C3×C5#41811yescharacteristic
335C2×C3×C5#44911yescharacteristic
336C2×C3×C5#44911yescharacteristic
337C2×C3×C5#48211yescharacteristic
338C2×C3×C5#48211yescharacteristic
339D15—42no—
340C5×D3—82no—
341C23×C3D4×D511yescharacteristic
342C22×D3—22no—
343C22×D3—41no—
344C22×D3—41no—
345C22×D3—41no—
346C22×D3—41no—
347C22×D3—41no—
348C22×D3—41no—
349C22×D3—52no—
350C22×D3—101no—
351C22×D3—101no—
352C22×D3—101no—
353C22×D3—101no—
354C22×D3—101no—
355C22×D3—101no—
356C2×C3×C4—22no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—102no—
360C2×C3×C4—201no—
361C2×C3×C4—201no—
362C2×C3×C4C2×C4×D511yescharacteristic
363C2×C3×C4#70911yescharacteristic
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4D4×D511yescharacteristic
366C2×C3×C4#71111yescharacteristic
367C2×C3×C4C2×C22⋊D511yescharacteristic
368C2×Dic3—52no—
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—102no—
372C2×Dic3—201no—
373C2×Dic3—201no—
374D12—22no—
375D12—22no—
376D12—41no—
377D12—41no—
378D12—208no—
379C4×D3—102no—
380C4×D3—102no—
381C4×D3—102no—
382C4×D3—102no—
383C3×C8—201no—
384C3⋊C8—41no—
385C22×C5—122no—
386C22×C5—122no—
387C22×C5—122no—
388C22×C5—241no—
389C22×C5—241no—
390C22×C5—241no—
391C22×C5—241no—
392C22×C5D3×C22⋊C411yescharacteristic
393C22×C5#88211yescharacteristic
394C22×C5#89411yescharacteristic
395C22×C5#91111yescharacteristic
396C22×C5#91411yescharacteristic
397C22×C5#91611yescharacteristic
398C22×C5#91911yescharacteristic
399C2×D5—62no—
400C2×D5—62no—
401C2×D5—62no—
402C2×D5—121no—
403C2×D5—121no—
404C2×D5—121no—
405C2×D5—121no—
406C4×C5—42no—
407C4×C5C4×D1211yescharacteristic
408C4×C5#88411yescharacteristic
409C4×C5#89311yescharacteristic
410C4×C5#89511yescharacteristic
411Dic5—42no—
412Dic5—62no—
413Dic5—122no—
414C24—61no—
415C24—151no—
416C2×D4—32no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—304no—
423C2×D4—602no—
424C2×D4—602no—
425C22×C4—21no—
426C22×C4—101no—
427C22×C4—151no—
428C22×C4—152no—
429C22×C4—152no—
430C22×C4—301no—
431C22×C4—301no—
432C22×C4—301no—
433C22×C4—301no—
434C22×C4—301no—
435C22×C4C2×D3×D511yescharacteristic
436C2×C8—61no—
437C2×C8—61no—
438C2×C8—61no—
439C2×C8—101no—
440C2×C8—101no—
441C2×C8—101no—
442C4⋊C4—21no—
443C4⋊C4—52no—
444C4⋊C4—101no—
445C4⋊C4—152no—
446C4⋊C4—301no—
447C4⋊C4#120312yescomplemented
448C22⋊C4—304no—
449C22⋊C4—304no—
450C42—304no—
451C3×C5#187511yescharacteristic, complemented, Hall
452C22×C3D5×C22⋊C411yescharacteristic
453C22×C3#402911yescharacteristic
454C22×C3#405711yescharacteristic
455C22×C3#405811yescharacteristic
456C22×C3#406011yescharacteristic
457C22×C3#406211yescharacteristic
458C22×C3#408311yescharacteristic
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—81no—
463C2×D3—81no—
464C2×D3—81no—
465C2×D3—81no—
466C2×D3—102no—
467C2×D3—102no—
468C2×D3—102no—
469C2×D3—201no—
470C2×D3—201no—
471C2×D3—201no—
472C2×D3—201no—
473C3×C4—42no—
474C3×C4—202no—
475C3×C4#402711yescharacteristic
476C3×C4#403011yescharacteristic
477C3×C4C4×C22⋊D511yescharacteristic
478C3×C4#408411yescharacteristic
479Dic3—102no—
480Dic3—202no—
481C2×C5—242no—
482C2×C5#466511yescharacteristic
483C2×C5#477011yescharacteristic
484C2×C5#478111yescharacteristic
485C2×C5#480411yescharacteristic
486C2×C5#481011yescharacteristic
487C2×C5#486611yescharacteristic
488C2×C5#488511yescharacteristic
489D5—122no—
490C23—62no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23—152no—
498C23—301no—
499C23—301no—
500C23—301no—
501C23—301no—
502C23—301no—
503C23—301no—
504C23#679011yescharacteristic
505D4—62no—
506D4—62no—
507D4—121no—
508D4—121no—
509D4—608no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—102no—
514C2×C4—152no—
515C2×C4—201no—
516C2×C4—201no—
517C2×C4—301no—
518C2×C4—301no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—601no—
525C2×C4—601no—
526C2×C4#676811yescharacteristic
527C2×C4#677111yescharacteristic
528C2×C4C4×D3×D511yescharacteristic
529C2×C4#677711yescharacteristic
530C2×C4C2×#120311yescharacteristic
531C2×C4#679011yescharacteristic
532C8—121no—
533C8—201no—
534C2×C3#6505911yescharacteristic
535C2×C3#6506111yescharacteristic
536C2×C3#6506811yescharacteristic
537C2×C3#6507311yescharacteristic
538C2×C3#6524511yescharacteristic
539C2×C3#6544711yescharacteristic
540C2×C3#6546111yescharacteristic
541D3—82no—
542D3—202no—
543C5#6888111yescharacteristic, complemented, Sylow
544C22—122no—
545C22—122no—
546C22—122no—
547C22—241no—
548C22—241no—
549C22—241no—
550C22—241no—
551C22—302no—
552C22—302no—
553C22—302no—
554C22—601no—
555C22—601no—
556C22—601no—
557C22—601no—
558C22#9135511yescharacteristic
559C22#9147311yescharacteristic
560C22#9148211yescharacteristic
561C22#9149911yescharacteristic
562C22#9150611yescharacteristic
563C22#9152311yescharacteristic
564C22#9157311yescharacteristic
565C4—42no—
566C4—202no—
567C4—302no—
568C4—602no—
569C4#9140611yescharacteristic
570C4C4×#120311yescharacteristic
571C4#9146111yescharacteristic
572C4#9146611yescharacteristic
573C3#1060099411yescharacteristic, complemented, Sylow
574C2—242no—
575C2—602no—
576C2#1174733511yescharacteristic
577C2#1174733711yescharacteristic
578C2#1174747911yescharacteristic
579C2#1174750811yescharacteristic
580C2#1174891811yescharacteristic
581C2#1174904311yescharacteristic
582C2#1174928911yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×#91466C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1875
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91781C2semidirect
3. C2×C5×#809C2semidirect
4. C2×#90967C2semidirect
5. C2×#90957C2semidirect
6. C3×#64749C2semidirect
7. #11745980C2semidirect
23. #91466C4semidirect
34. #64749D3semidirect
58. C3×C5×C4⋊C4D4semidirect
61. C4⋊Dic15D4semidirect
76. C2×#809D5semidirect
186. C5×C4⋊C4D12semidirect
261. C3×C4⋊C4C22⋊D5semidirect
447. C4⋊C4#1203semidirect
451. C3×C5#1875semidirect
543. C5#68881semidirect
573. C3#10600994semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×#914662
C2×C5×#8092
C2×#909672
C2×#909572
C3×#647492
#117459802
#106009943
#688815