Finite Group Databasebeta

← #14301989

Subgroups — #14301989

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756283C211yesmaximal, characteristic
2C2×#91761C211yesmaximal, characteristic, complemented
3C2×#91109C211yesmaximal, characteristic, complemented
4#11751227C211yesmaximal, characteristic, complemented
5C2×#91089C211yesmaximal, characteristic, complemented
6C3×C5×#339C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10599550—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C4×D15C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×#6714—21no—
15C2×#6712—21no—
16C2×C4×Dic15C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18#91786C412yescomplemented
19#91784C412yescomplemented
20#91775—21no—
21#91771—21no—
22C4×D60—22no—
23#91761—22no—
24#91761—22no—
25#91109—22no—
26#91104—22no—
27#91089—22no—
28#68757—51nomaximal, Hall
29#65858—31no—
30C2×#4018—31no—
31C2×#3957—31no—
32#65415—31no—
33C2×#3937—31no—
34C5×#339D311yescharacteristic, complemented
35#64752—31no—
36C23×D15D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42#6817—21no—
43#6817—21no—
44#6817—21no—
45#6817—21no—
46C2×D60—22no—
47C2×D60C2×C411yescharacteristic
48C2×C4×D15—21no—
49C2×C4×D15—21no—
50C2×C4×D15—21no—
51C2×C4×D15—21no—
52C2×C4×D15—21no—
53C2×C4×D15C2×C412yes—
54C2×C4×D15D412yes—
55C2×Dic30C2×C411yescharacteristic
56C3×C5×M16—21no—
57C3×C5×M16—21no—
58C2×C3×C5×C8—21no—
59C3×C5×C4⋊C4C2×C412yes—
60C3×C5×C22⋊C4—21no—
61C3×C42×C5—21no—
62C3×C42×C5—21no—
63C3×C42×C5D412yescomplemented
64#6714—24no—
65#6714—22no—
66#6714—22no—
67C4⋊Dic15—22no—
68#6712—24no—
69C4×Dic15—21no—
70C4×Dic15D412yescomplemented
71#6710—21no—
72#6710—21no—
73C2×C3⋊#168—21no—
74#5524—51no—
75C2×#872—51no—
76C2×#825—51no—
77#5126—51no—
78C2×#805—51no—
79C3×#339D511yescharacteristic, complemented
80#4532—51no—
81C2×#709—31no—
82C22×C4×D5—31no—
83C2×C5×M16C2×D311yescharacteristic
84C5×#117C2×D311yescharacteristic
85C2×C42×C5C2×D311yescharacteristic
86C2×#685—61no—
87C2×#683—61no—
88C2×C4×Dic5—31no—
89C2×#681—31no—
90#4043—32no—
91#4041—32no—
92#4032—61no—
93#4028—61no—
94C4×D20—62no—
95#4018—62no—
96#4018—62no—
97#3957—62no—
98#3952—62no—
99#3937—62no—
100#1897—151noSylow
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C22×D15—21no—
104C22×D15—21no—
105C22×D15—42no—
106C22×D15C22⋊C412yes—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—42no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116#1220—41no—
117#1220—41no—
118C2×Dic15—21no—
119C2×Dic15—21no—
120C2×Dic15—21no—
121C2×Dic15—22no—
122C2×Dic15—42no—
123C2×Dic15C22⋊C412yes—
124D60—21no—
125D60—21no—
126D60—44no—
127C4×D15—22no—
128C4×D15—22no—
129C4×D15—22no—
130C4×D15—22no—
131C4×D15—41no—
132C4×D15—41no—
133Dic30—21no—
134Dic30—21no—
135C3×C5×C8—41no—
136C3⋊#168—41no—
137C2×#235—51no—
138C22×C4×D3—51no—
139C2×C3×M16C2×D511yescharacteristic
140C3×#117C2×D511yescharacteristic
141C2×C3×C42C2×D511yescharacteristic
142C2×(C2×D3)⋊C4—101no—
143C2×Dic3⋊C4—101no—
144C2×C4×Dic3—51no—
145C2×#208—51no—
146#897—52no—
147#895—52no—
148#886—101no—
149#882—101no—
150C4×D12—102no—
151#872—102no—
152#872—102no—
153#825—102no—
154(C2×D3)⋊C8—102no—
155#805—102no—
156C23×D5—31no—
157C22×C4×C5—21no—
158C22×C4×C5C22×D311yescharacteristic
159C2×C22⋊D5—61no—
160C22×Dic5—31no—
161C22×Dic5—61no—
162#709—61no—
163#709—61no—
164#709—61no—
165#709—61no—
166C2×D20—31no—
167C2×D20—62no—
168C2×C4×D5—32no—
169C2×C4×D5—32no—
170C2×C4×D5—61no—
171C2×C4×D5—61no—
172C2×C4×D5—61no—
173C2×C4×D5—61no—
174C2×C4×D5—61no—
175C2×Dic10—31no—
176C5×M16—21no—
177C5×M16—21no—
178C2×C5×C8—21no—
179C5×C4⋊C4C4×D312yes—
180C5×C22⋊C4—21no—
181C42×C5—21no—
182C42×C5—21no—
183C42×C5D1212yescomplemented
184#685—62no—
185#685—62no—
186#685—64no—
187C4⋊Dic5—62no—
188#683—64no—
189C4×Dic5—32no—
190C4×Dic5—61no—
191#681—61no—
192#681—61no—
193C2×#168—61no—
194#525—151no—
195C2×#117—151no—
196C2×#104—151no—
197C2×#104—151no—
198#407—151no—
199#339—151no—
200#339D1511yescharacteristic, complemented
201C22×C3×C5—22no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5#12011yescharacteristic
204C22×C3×C5#12311yescharacteristic
205C2×D15—22no—
206C2×D15—22no—
207C2×D15—22no—
208C2×D15—42no—
209C2×D15—42no—
210C2×D15—41no—
211C2×D15—42no—
212C3×C4×C5—42no—
213C3×C4×C5—42no—
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5C4×D411yescharacteristic
216C3×C4×C5#12111yescharacteristic
217C3×C4×C5#12111yescharacteristic
218Dic15—22no—
219Dic15—42no—
220Dic15—41no—
221C23×D3—51no—
222C22×C3×C4—21no—
223C22×C3×C4C22×D511yescharacteristic
224C2×#67—101no—
225C22×Dic3—51no—
226C22×Dic3—101no—
227#235—101no—
228#235—101no—
229#235—101no—
230#235—101no—
231C2×D12—51no—
232C2×D12—102no—
233C2×C4×D3—52no—
234C2×C4×D3—52no—
235C2×C4×D3—101no—
236C2×C4×D3—101no—
237C2×C4×D3—101no—
238C2×C4×D3—101no—
239C2×C4×D3—101no—
240C2×Dic6—51no—
241C3×M16—21no—
242C3×M16—21no—
243C2×C3×C8—21no—
244C3×C4⋊C4C4×D512yes—
245C3×C22⋊C4—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42D2012yescomplemented
249(C2×D3)⋊C4—102no—
250(C2×D3)⋊C4—102no—
251(C2×D3)⋊C4—104no—
252C4⋊Dic3—102no—
253Dic3⋊C4—104no—
254C4×Dic3—52no—
255C4×Dic3—101no—
256#208—101no—
257#208—101no—
258C2×C3⋊C8—101no—
259C23×C5D3×D411yescharacteristic
260C22×D5—32no—
261C22×D5—61no—
262C22×D5—61no—
263C22×D5—61no—
264C22×D5—122no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—42no—
268C2×C4×C5C2×C4×D311yescharacteristic
269C2×C4×C5C2×D1211yescharacteristic
270C2×C4×C5#23511yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5#23911yescharacteristic
274C22⋊D5—121no—
275C22⋊D5—121no—
276C2×Dic5—32no—
277C2×Dic5—61no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281C2×Dic5—122no—
282D20—61no—
283D20—61no—
284D20—124no—
285C4×D5—62no—
286C4×D5—62no—
287C4×D5—62no—
288C4×D5—62no—
289C4×D5—121no—
290C4×D5—121no—
291Dic10—61no—
292Dic10—61no—
293C5×C8—41no—
294#168—121no—
295C2×#41—151no—
296C23×C4—151no—
297C2×M16—151no—
298C2×M16C2×D1511yescharacteristic
299#123—301no—
300C22⋊Q8—152no—
301#121—152no—
302#120—301no—
303C4×D4—302no—
304#117—302no—
305#117—302no—
306#117C2×D1511yescharacteristic
307C2×C4⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—151no—
310C2×C42C2×D1511yescharacteristic
311#104—302no—
312#104—302no—
313C22⋊C8—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C2×C3×C5#42112yes—
318D15—42no—
319D15—81no—
320C23×C3D4×D511yescharacteristic
321C22×D3—52no—
322C22×D3—101no—
323C22×D3—101no—
324C22×D3—101no—
325C22×D3—202no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—42no—
329C2×C3×C4C2×C4×D511yescharacteristic
330C2×C3×C4C2×D2011yescharacteristic
331C2×C3×C4#70911yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4#71311yescharacteristic
335#67—201no—
336#67—201no—
337C2×Dic3—52no—
338C2×Dic3—101no—
339C2×Dic3—101no—
340C2×Dic3—101no—
341C2×Dic3—102no—
342C2×Dic3—202no—
343D12—101no—
344D12—101no—
345D12—204no—
346C4×D3—102no—
347C4×D3—102no—
348C4×D3—102no—
349C4×D3—102no—
350C4×D3—201no—
351C4×D3—201no—
352Dic6—101no—
353Dic6—101no—
354C3×C8—41no—
355C3⋊C8—201no—
356C22×C5—22no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88211yescharacteristic
359C22×C5#89411yescharacteristic
360C2×D5—62no—
361C2×D5—62no—
362C2×D5—62no—
363C2×D5—122no—
364C2×D5—122no—
365C2×D5—121no—
366C2×D5—122no—
367C4×C5—42no—
368C4×C5—42no—
369C4×C5C4×D1211yescharacteristic
370C4×C5#88411yescharacteristic
371C4×C5#89311yescharacteristic
372C4×C5#89511yescharacteristic
373Dic5—62no—
374Dic5—122no—
375Dic5—121no—
376C24—151no—
377#41—301no—
378#41—301no—
379#41—301no—
380#41—301no—
381C2×Q8—151no—
382C2×D4—151no—
383C2×D4—302no—
384C2×D4—301no—
385C22×C4—21no—
386C22×C4—151no—
387C22×C4—152no—
388C22×C4—152no—
389C22×C4—301no—
390C22×C4—301no—
391C22×C4—301no—
392C22×C4—301no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4C22×D1511yescharacteristic
396M16—21no—
397M16—21no—
398M16—301no—
399M16—301no—
400C2×C8—21no—
401C2×C8—301no—
402C4⋊C4—302no—
403C4⋊C4—304no—
404C4⋊C4C4×D1512yes—
405C22⋊C4—21no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—304no—
409C42—21no—
410C42—21no—
411C42—152no—
412C42—301no—
413C42D6012yescomplemented
414C3×C5#189711yescharacteristic, complemented, Hall
415C22×C3—22no—
416C22×C3D5×C22⋊C411yescharacteristic
417C22×C3#402811yescharacteristic
418C22×C3#404011yescharacteristic
419C2×D3—102no—
420C2×D3—102no—
421C2×D3—102no—
422C2×D3—202no—
423C2×D3—202no—
424C2×D3—202no—
425C2×D3—201no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4C4×D2011yescharacteristic
429C3×C4#403011yescharacteristic
430C3×C4#403911yescharacteristic
431C3×C4#404111yescharacteristic
432Dic3—102no—
433Dic3—202no—
434Dic3—201no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#466511yescharacteristic
438C2×C5#482112yes—
439D5—122no—
440D5—241no—
441C23—152no—
442C23—301no—
443C23—301no—
444C23—301no—
445C23—602no—
446C23D4×D1511yescharacteristic
447Q8—301no—
448Q8—301no—
449D4—301no—
450D4—301no—
451D4—604no—
452D4—601no—
453D4—601no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—152no—
458C2×C4—301no—
459C2×C4—301no—
460C2×C4—302no—
461C2×C4—302no—
462C2×C4—302no—
463C2×C4—302no—
464C2×C4—301no—
465C2×C4—302no—
466C2×C4—602no—
467C2×C4—601no—
468C2×C4—601no—
469C2×C4C2×C4×D1511yescharacteristic
470C2×C4C2×D6011yescharacteristic
471C2×C4#681711yescharacteristic
472C2×C4D4×D1511yescharacteristic
473C2×C4D4×D1511yescharacteristic
474C2×C4#682111yescharacteristic
475C8—41no—
476C8—601no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3#6495411yescharacteristic
480C2×C3#6511012yes—
481D3—202no—
482D3—401no—
483C5#6875711yescharacteristic, complemented, Sylow
484C22—22no—
485C22—302no—
486C22—302no—
487C22—302no—
488C22—602no—
489C22—602no—
490C22—602no—
491C22—601no—
492C22C22⋊C4×D1511yescharacteristic
493C22#9177111yescharacteristic
494C22#9178311yescharacteristic
495C4—42no—
496C4—42no—
497C4—302no—
498C4—602no—
499C4—601no—
500C4C4×D6011yescharacteristic
501C4#9177311yescharacteristic
502C4#9178211yescharacteristic
503C4#9178411yescharacteristic
504C3#1059955011yescharacteristic, complemented, Sylow
505C2—21no—
506C2—21no—
507C2—602no—
508C2—1201no—
509C2#1175076611yescharacteristic
510C2#1175092212yes—
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756283C2
cosocleC22×C3×C4×C5C23
hypercenter#339D15
hypocenterC3×C5#1897
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#91761C2semidirect
3. C2×#91109C2semidirect
4. #11751227C2semidirect
5. C2×#91089C2semidirect
6. C3×C5×#339C2semidirect
7. #11746353C2semidirect
18. #91786C4semidirect
19. #91784C4semidirect
34. C5×#339D3semidirect
63. C3×C42×C5D4semidirect
70. C4×Dic15D4semidirect
79. C3×#339D5semidirect
183. C42×C5D12semidirect
200. #339D15semidirect
248. C3×C42D20semidirect
413. C42D60semidirect
414. C3×C5#1897semidirect
483. C5#68757semidirect
504. C3#10599550semidirect

Maximal subgroups

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

subgroupindex
#117562832
C2×#917612
C2×#911092
#117512272
C2×#910892
C3×C5×#3392
#117463532
#105995503
#687575