Finite Group Databasebeta

← #14283274

Subgroups — #14283274

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#930C211yesmaximal, characteristic
2C3×#64953C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C5×#4451C211yesmaximal, characteristic, complemented
6#11745958C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10599097—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×D5×#67—21no—
11C2×D5×D12C411yescharacteristic, complemented
12#91819C2211yescharacteristic
13C5×#930C2211yescharacteristic
14C2×C3×#685—21no—
15#91566—21no—
16D5×(C2×D3)⋊C4—21no—
17#91450C411yescharacteristic, complemented
18#91449C411yescharacteristic, complemented
19#91448—21no—
20D5×C4⋊Dic3C411yescharacteristic, complemented
21C2×#6649—21no—
22C3×C5×#95C2211yescharacteristic, complemented
23#91114C2211yescharacteristic, complemented
24C5×#830C2211yescharacteristic, complemented
25C3×#3963—21no—
26C3×#3963C2211yescharacteristic, complemented
27#90955—21no—
28#69531—51nomaximal, Hall
29D5×#121—31no—
30#65015—31no—
31#64953D311yescharacteristic, complemented
32C5×#327—31no—
33#64757—31no—
34#64690—31no—
35#64671—31no—
36C23×C3×D5D411yescharacteristic
37C22×D3×D5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C2×D60C2×C411yescharacteristic
42C2×C5×#67—21no—
43C2×C5×D12C2×C411yescharacteristic
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C2×C3×C4×D5—42no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51D5×#67—42no—
52D5×#67—42no—
53C2×#1203—21no—
54C2×#1202—21no—
55C2×#1201—21no—
56C2×D5×Dic3—21no—
57D5×D12—42no—
58#6714—21no—
59C4⋊Dic15C2×C411yescharacteristic
60C2×C3⋊#168—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×C4⋊Dic3C2×C411yescharacteristic
63C2×C5×C3⋊C8—21no—
64C3×#685—42no—
65#6668—21no—
66#6667—21no—
67(C2×D3)⋊Dic5—21no—
68#6649—42no—
69C2×#930—51no—
70C3×#381—51no—
71#5207—51no—
72#4451—51no—
73#4451—51no—
74#4451—51no—
75#4451D511yescharacteristic, complemented
76C2×D4×D5—31no—
77C2×D4×D5—61no—
78C22×C4×D5C2×D311yescharacteristic
79C5×#121—31no—
80#4085—61no—
81#4084—31no—
82#4076—31no—
83C2×#685—21no—
84C2×#676—61no—
85#4041—31no—
86D5×C4⋊C4—31no—
87#4030—61no—
88D5×C22⋊C4—61no—
89C5×C22⋊C8—31no—
90C5×#95C2×D311yescharacteristic, complemented
91#3963—21no—
92#3963C2×D311yescharacteristic, complemented
93C22⋊#168—31no—
94#3952—61no—
95#1510—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×C5×D3—21no—
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—22no—
102C22×C3×D5—41no—
103C22×C3×D5C22⋊C411yescharacteristic
104C22×C3×D5C22⋊C411yescharacteristic
105C2×D3×D5—42no—
106C2×D3×D5—42no—
107C2×D3×D5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114#1220—41no—
115#1220—41no—
116C2×Dic15—21no—
117D60—41no—
118C5×#67—41no—
119C5×#67—41no—
120C2×C5×Dic3—21no—
121C5×D12—41no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5—41no—
125C2×C3×Dic5—41no—
126C2×C3×Dic5C22⋊C411yescharacteristic
127C2×C3×Dic5C22⋊C411yescharacteristic
128C3×C4×D5—22no—
129C3×C4×D5—22no—
130C3×C4×D5—41no—
131C3×C4×D5—41no—
132#1203—42no—
133#1202—42no—
134#1201—42no—
135D5×Dic3—42no—
136C3⋊#168—41no—
137C5×C3⋊C8—41no—
138C23×C3×C4—51no—
139C22×#67—101no—
140C22×D12—51no—
141C2×C3×C22⋊C4—101no—
142#930—51no—
143#930—51no—
144#930—51no—
145#930—101no—
146#930—101no—
147#930C2×D511yescharacteristic
148C2×(C2×D3)⋊C4—101no—
149C2×C4⋊Dic3—51no—
150C2×#208—101no—
151C3×#95—51no—
152C3×#95—101no—
153C3×#95C2×D511yescharacteristic, complemented
154#830—51no—
155#830—101no—
156#830C2×D511yescharacteristic, complemented
157C23×D5—61no—
158C23×D5#6711yescharacteristic
159C2×C5×D4—31no—
160C2×C5×D4—61no—
161C22×C4×C5—21no—
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—61no—
164C2×C22⋊D5—61no—
165C2×C22⋊D5—61no—
166C22×Dic5—21no—
167C22×Dic5#6711yescharacteristic
168D4×D5—122no—
169D4×D5—122no—
170D4×D5—122no—
171C2×D20—31no—
172C2×D20—61no—
173C2×C4×D5—42no—
174C2×C4×D5—61no—
175C2×C4×D5C4×D311yescharacteristic
176C2×C4×D5C4×D311yescharacteristic
177C2×C4×D5D1211yescharacteristic
178C2×C4×D5D1211yescharacteristic
179C2×C5×C8—61no—
180C5×C4⋊C4—31no—
181C5×C22⋊C4—61no—
182C22⋊Dic5—61no—
183#685—42no—
184#685—61no—
185#685—61no—
186C4⋊Dic5—31no—
187#683—61no—
188C2×#168—61no—
189#676—122no—
190C2×#121—151no—
191#407—151no—
192#381—51no—
193#327—31no—
194#327—151no—
195#327—151no—
196#327—151no—
197C22×C3×C5—21no—
198C22×C3×C5—21no—
199C22×C3×C5C2×C22⋊C411yescharacteristic
200C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
201C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
202C2×D15—41no—
203C2×D15—41no—
204C2×D15—41no—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C3×D5—21no—
209C2×C3×D5—21no—
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—21no—
213C2×C3×D5—42no—
214C2×C3×D5—42no—
215C2×C3×D5#9912yes—
216D3×D5—84no—
217C3×C4×C5—21no—
218C3×C4×C5—21no—
219C3×C4×C5—81no—
220Dic15—41no—
221C3×Dic5—21no—
222C3×Dic5—21no—
223C3×Dic5—81no—
224C5×Dic3—41no—
225C24×C3—51no—
226C23×D3—101no—
227C22×C3×C4—21no—
228C22×C3×C4—51no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—101no—
234C22×C3×C4—202no—
235C22×C3×C4C22×D511yescharacteristic
236C2×#67—21no—
237C2×#67—101no—
238C2×#67—101no—
239C2×#67—101no—
240C2×#67—202no—
241C2×#67—202no—
242C22×Dic3—101no—
243C2×D12—51no—
244C2×D12—101no—
245C2×D12—202no—
246C2×D12C4×D511yescharacteristic
247C3×C22⋊C4—202no—
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—101no—
250(C2×D3)⋊C4—101no—
251(C2×D3)⋊C4—101no—
252C4⋊Dic3—51no—
253C4⋊Dic3—101no—
254C4⋊Dic3C4×D511yescharacteristic
255#208—202no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—101no—
258C23×C5—61no—
259C23×C5C2×#6711yescharacteristic
260C22×D5—21no—
261C22×D5—21no—
262C22×D5—22no—
263C22×D5—41no—
264C22×D5—61no—
265C22×D5—122no—
266C22×D5—122no—
267C22×D5—122no—
268C22×D5(C2×D3)⋊C411yescharacteristic
269C22×D5(C2×D3)⋊C411yescharacteristic
270C5×D4—121no—
271C5×D4—121no—
272C5×D4—121no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—61no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5C2×D1211yescharacteristic
280C22⋊D5—122no—
281C22⋊D5—122no—
282C22⋊D5—121no—
283C22⋊D5—121no—
284C2×Dic5—41no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287C2×Dic5—41no—
288C2×Dic5—61no—
289C2×Dic5(C2×D3)⋊C411yescharacteristic
290C2×Dic5(C2×D3)⋊C411yescharacteristic
291D20—121no—
292D20—122no—
293C4×D5—22no—
294C4×D5—22no—
295C4×D5—41no—
296C4×D5—41no—
297C4×D5—122no—
298C5×C8—121no—
299#168—121no—
300C22×D4—151no—
301C22×D4—301no—
302C23×C4—51no—
303C2×M16—301no—
304#121—31no—
305#121—151no—
306#121—151no—
307#121—151no—
308#121—301no—
309#121—301no—
310C2×C4⋊C4—151no—
311C2×C22⋊C4—101no—
312C2×C22⋊C4—301no—
313C22⋊C8—31no—
314C22⋊C8—151no—
315C22⋊C8—301no—
316#95—51no—
317#95—101no—
318#95D3×D511yescharacteristic, complemented
319C2×C3×C5—21no—
320C2×C3×C5—21no—
321C2×C3×C5C2×#9911yescharacteristic
322C2×C3×C5#41811yescharacteristic
323C2×C3×C5#42111yescharacteristic
324D15—81no—
325C3×D5—22no—
326C3×D5—41no—
327C5×D3—81no—
328C23×C3—51no—
329C23×C3—51no—
330C23×C3—102no—
331C23×C3—101no—
332C23×C3—101no—
333C23×C3—201no—
334C23×C3D4×D511yescharacteristic
335C22×D3—21no—
336C22×D3—101no—
337C22×D3—202no—
338C22×D3—202no—
339C22×D3—202no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—51no—
345C2×C3×C4—51no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—201no—
349C2×C3×C4—201no—
350C2×C3×C4—201no—
351C2×C3×C4—201no—
352C2×C3×C4—201no—
353C2×C3×C4—201no—
354C2×C3×C4C2×C4×D511yescharacteristic
355C2×C3×C4D4×D511yescharacteristic
356#67—41no—
357#67—41no—
358#67—202no—
359#67—202no—
360#67—201no—
361#67—201no—
362C2×Dic3—21no—
363C2×Dic3—101no—
364C2×Dic3—202no—
365D12—41no—
366D12—201no—
367D12—202no—
368C3⋊C8—41no—
369C3⋊C8—201no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C2×(C2×D3)⋊C411yescharacteristic
376C22×C5#94911yescharacteristic
377C22×C5#94911yescharacteristic
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—42no—
384C2×D5—42no—
385C2×D5—121no—
386C2×D5—121no—
387C2×D5—121no—
388C2×D5—244no—
389C2×D5#80612yes—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—81no—
393C4×C5—121no—
394Dic5—21no—
395Dic5—21no—
396Dic5—81no—
397Dic5—121no—
398C24—51no—
399C24—301no—
400C2×D4—31no—
401C2×D4—61no—
402C2×D4—151no—
403C2×D4—301no—
404C2×D4—301no—
405C2×D4—301no—
406C2×D4—301no—
407C2×D4—602no—
408C2×D4—602no—
409C2×D4—602no—
410C22×C4—21no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—101no—
417C22×C4—202no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420M16—602no—
421C2×C8—61no—
422C2×C8—301no—
423C4⋊C4—31no—
424C4⋊C4—151no—
425C4⋊C4—301no—
426C22⋊C4—61no—
427C22⋊C4—202no—
428C22⋊C4—301no—
429C22⋊C4—301no—
430C22⋊C4—301no—
431C3×C5#151011yescharacteristic, complemented, Hall
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—52no—
435C22×C3—101no—
436C22×C3—101no—
437C22×C3—101no—
438C22×C3—101no—
439C22×C3—101no—
440C22×C3—202no—
441C22×C3—202no—
442C22×C3D5×C22⋊C411yescharacteristic
443C22×C3#405711yescharacteristic
444C22×C3#406011yescharacteristic
445C2×D3—41no—
446C2×D3—41no—
447C2×D3—41no—
448C2×D3—201no—
449C2×D3—201no—
450C2×D3—201no—
451C2×D3—404no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—81no—
455C3×C4—101no—
456C3×C4—101no—
457C3×C4—401no—
458Dic3—41no—
459Dic3—201no—
460C2×C5—21no—
461C2×C5—21no—
462C2×C5—241no—
463C2×C5C2×#80611yescharacteristic
464C2×C5#500111yescharacteristic
465C2×C5#500511yescharacteristic
466D5—22no—
467D5—41no—
468D5—241no—
469C23—51no—
470C23—51no—
471C23—61no—
472C23—102no—
473C23—101no—
474C23—101no—
475C23—201no—
476C23—301no—
477C23—602no—
478C23—602no—
479C23—602no—
480C23D5×#6711yescharacteristic
481D4—121no—
482D4—121no—
483D4—121no—
484D4—601no—
485D4—602no—
486D4—602no—
487D4—602no—
488D4—601no—
489D4—601no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—51no—
495C2×C4—51no—
496C2×C4—61no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—201no—
500C2×C4—201no—
501C2×C4—201no—
502C2×C4—201no—
503C2×C4—201no—
504C2×C4—201no—
505C2×C4—301no—
506C2×C4—602no—
507C2×C4C4×D3×D511yescharacteristic
508C2×C4D5×D1211yescharacteristic
509C8—121no—
510C8—601no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—102no—
514C2×C3—201no—
515C2×C3D5×#9911yescharacteristic
516C2×C3#6505911yescharacteristic
517C2×C3#6511011yescharacteristic
518D3—81no—
519D3—401no—
520C5#6953111yescharacteristic, complemented, Sylow
521C22—21no—
522C22—21no—
523C22—52no—
524C22—101no—
525C22—101no—
526C22—101no—
527C22—101no—
528C22—101no—
529C22—121no—
530C22—121no—
531C22—121no—
532C22—202no—
533C22—202no—
534C22—601no—
535C22—601no—
536C22—601no—
537C22—1204no—
538C22D5×(C2×D3)⋊C411yescharacteristic
539C22#9147811yescharacteristic
540C22#9150211yescharacteristic
541C4—21no—
542C4—21no—
543C4—81no—
544C4—101no—
545C4—101no—
546C4—121no—
547C4—401no—
548C4—601no—
549C3#1059909711yescharacteristic, complemented, Sylow
550C2—21no—
551C2—21no—
552C2—102no—
553C2—201no—
554C2—241no—
555C2—1201no—
556C2#1174710911yescharacteristic
557C2D5×#80611yescharacteristic
558C2#1174747511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalD5×#930C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#64953C2semidirect
3. #11748499C2semidirect
4. #11746272C2semidirect
5. C5×#4451C2semidirect
6. #11745958C2semidirect
7. #11745956C2semidirect
11. C2×D5×D12C4semidirect
17. #91450C4semidirect
18. #91449C4semidirect
20. D5×C4⋊Dic3C4semidirect
22. C3×C5×#95C22semidirect
23. #91114C22semidirect
24. C5×#830C22semidirect
26. C3×#3963C22semidirect
31. #64953D3semidirect
75. #4451D5semidirect
90. C5×#95C2×D3semidirect
92. #3963C2×D3semidirect
153. C3×#95C2×D5semidirect
156. #830C2×D5semidirect
318. #95D3×D5semidirect
431. C3×C5#1510semidirect
520. C5#69531semidirect
549. C3#10599097semidirect

Maximal subgroups

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

subgroupindex
D5×#9302
C3×#649532
#117484992
#117462722
C5×#44512
#117459582
#117459562
#105990973
#695315