Finite Group Databasebeta

← #14417278

Subgroups — #14417278

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65850C211yesmaximal, characteristic, complemented
2#11754506C211yesmaximal, characteristic
3C2×#91315C211yesmaximal, characteristic
4#11751103C211yesmaximal, characteristic
5C5×#4995C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7#11748320C211yesmaximal, characteristic, complemented
8#11747270C212yesmaximal, complemented
9#11747269C212yesmaximal, complemented
10#11747225C212yesmaximal, complemented
11#11747224C212yesmaximal, complemented
12#10610933—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20C3×#4033C2212yes—
21C3×#4033C2212yes—
22C3×#4023—22no—
23C3×C4×Dic10—21no—
24C3×C4×Dic10—21no—
25#91556—22no—
26#91437—21no—
27#91418C2212yes—
28#91347—21no—
29#91333C2212yes—
30C2×#6662C2212yes—
31#91315C418yescomplemented
32C2×#6658C2212yes—
33#91094C2211yescharacteristic
34#91094C2211yescharacteristic
35#91093C2211yescharacteristic
36#91093C2211yescharacteristic
37C5×#808C2212yes—
38C5×#807C2212yes—
39#90970C2212yes—
40#90970C2212yes—
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82547—51nomaximal, Hall
44C2×#4055—31no—
45#65850D311yescharacteristic, complemented
46#65838—31no—
47C5×#428—31no—
48#65411—31no—
49#65291—31no—
50C2×#3942—31no—
51#65178—32no—
52#65162—32no—
53#65142—32no—
54#65141—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817C2×C414yes—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C22×C5×Dic3—21no—
63C22×C3×Dic5—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—22no—
66C2×C3×Dic10C2×C414yescomplemented
67C2×C3×Dic10C2312yes—
68C2×#1200—22no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73C2×C3⋊#168—22no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C5×#208C2×C414yescomplemented
79C2×C5×C3⋊C8C2312yes—
80C3×C22⋊Dic5D412yes—
81C3×C4⋊Dic5D411yescharacteristic
82C3×C4⋊Dic5D411yescharacteristic
83C3×#683—22no—
84C3×#683—22no—
85C3×C4×Dic5—22no—
86C3×C4×Dic5—22no—
87C3×C4×Dic5C2312yes—
88#6669—22no—
89#6667—22no—
90Dic3×Dic5—22no—
91#6662C2×C418yescomplemented
92#6658C2×C418yescomplemented
93C3×#519—51no—
94C2×#942—51no—
95#5523—51no—
96C2×#835—51no—
97#5030—52no—
98C4×#216—52no—
99#5026—52no—
100C4×#215—52no—
101#5002—51no—
102#4997—51no—
103#4995D511yescharacteristic, complemented
104C2×#709—31no—
105C22×Dic10C2×D311yescharacteristic
106C2×C5×M16—31no—
107C5×#117C2×D311yescharacteristic
108C2×C5×C4⋊C4—31no—
109C4×C22⋊D5—62no—
110#4072C2×D311yescharacteristic
111C22×#168—31no—
112#4055—38no—
113C2×Dic20—32no—
114C2×#677—32no—
115#4039—32no—
116#4038—61no—
117D5×C4⋊C4—61no—
118#4033—32no—
119#4033C2×D312yes—
120#4033C2×D312yes—
121#4023—22no—
122C4×Dic10—21no—
123C4×Dic10—21no—
124C5×#107—32no—
125C5×#106—32no—
126#3947—32no—
127C8×Dic5—32no—
128#3942—32no—
129#3942—32no—
130#3942—31no—
131#3942—31no—
132#3941—31no—
133#3941—31no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4112yes—
142C2×C3×C4×C5C2411yescharacteristic
143#1220—24no—
144C2×Dic15—21no—
145D60—21no—
146D60C22×C412yes—
147C4×D15—24no—
148Dic30—21no—
149Dic30C22×C412yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—81no—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C2×D412yes—
155C2×C3×Dic5C2×D412yes—
156C3×Dic10—24no—
157C3×Dic10—22no—
158C3×Dic10C22×C414yes—
159#1200—82no—
160C3⋊#168—21no—
161C3⋊#168—21no—
162C5×C3⋊C8C22×C414yes—
163C22×C3×Q8—51no—
164C2×#235—51no—
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C3×#117—51no—
170C3×#117—102no—
171C3×#117C2×D511yescharacteristic
172C2×#216—52no—
173#942—58no—
174C2×#215—52no—
175C2×C4⋊Dic3C2×D511yescharacteristic
176C2×#208C2×D511yescharacteristic
177C22×C3⋊C8—51no—
178#892—101no—
179D3×C4⋊C4—101no—
180#67⋊C4—102no—
181C4×D12—52no—
182C4×Dic6—52no—
183#835—52no—
184#835—52no—
185#810—51no—
186#810—51no—
187#809—51no—
188#809—51no—
189#808C2×D512yes—
190#807C2×D512yes—
191#803—52no—
192C4×C3⋊C8—52no—
193C22×C4×C5—61no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—61no—
196C22×Dic5—21no—
197#709—34no—
198#709—62no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×C4×D5—62no—
202C2×Dic10—22no—
203C2×Dic10—21no—
204C2×Dic10—31no—
205C2×Dic10C4×D314yescomplemented
206C2×Dic10C22×D312yes—
207C5×M16—34no—
208C2×C5×C8—32no—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C42×C5—21no—
215C22⋊Dic5#6712yes—
216#685—62no—
217C4⋊Dic5#6711yescharacteristic
218C4⋊Dic5#6711yescharacteristic
219#683—22no—
220#683—22no—
221#683—62no—
222C4×Dic5—22no—
223C4×Dic5—22no—
224C4×Dic5—62no—
225C4×Dic5C22×D312yes—
226C2×#168—31no—
227C2×#168—31no—
228C2×#168—62no—
229Dic20—38no—
230#677—38no—
231C2×#137—151no—
232#520—151no—
233#519—51no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—31no—
239#416—151no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5—41no—
250C3×C4×C5—41no—
251C3×C4×C5C4×D412yes—
252C3×C4×C5C23×C411yescharacteristic
253C3×C4×C5C2×#4111yescharacteristic
254Dic15—22no—
255C3×Dic5—24no—
256C3×Dic5—22no—
257C3×Dic5—22no—
258C5×Dic3—42no—
259C2×C3×Q8—54no—
260C2×C3×Q8—52no—
261C2×C3×Q8—101no—
262C2×C3×Q8—102no—
263C22×C3×C4—101no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—101no—
266C22×Dic3—21no—
267#235—54no—
268#235—102no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×C4×D3—102no—
272C2×Dic6—51no—
273C3×C4⋊C4—51no—
274C3×C4⋊C4—51no—
275C3×C4⋊C4—102no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C4⋊C4C22×D511yescharacteristic
279C3×C22⋊C4—21no—
280C3×C22⋊C4—52no—
281C3×C42—21no—
282C3×C42—52no—
283C3×C42—102no—
284C3×C42—102no—
285#216—58no—
286#215—58no—
287(C2×D3)⋊C4—102no—
288C4⋊Dic3—21no—
289C4⋊Dic3C22×D512yes—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292#208C4×D514yescomplemented
293C2×C3⋊C8—51no—
294C2×C3⋊C8—51no—
295C2×C3⋊C8—102no—
296C2×C3⋊C8C22×D512yes—
297C23×C5C2×#6711yescharacteristic
298C22×D5—61no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—62no—
302C2×C4×C5—241no—
303C2×C4×C5C2×C4×D312yes—
304C2×C4×C5#23512yes—
305C2×C4×C5C2×#6711yescharacteristic
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—64no—
308C2×Dic5—24no—
309C2×Dic5—22no—
310C2×Dic5—61no—
311C2×Dic5C2×#6712yes—
312C2×Dic5C2×#6712yes—
313D20—32no—
314D20—61no—
315C4×D5—64no—
316C4×D5—242no—
317Dic10—24no—
318Dic10—22no—
319Dic10—32no—
320Dic10—61no—
321Dic10C2×C4×D314yes—
322C5×C8—34no—
323#168—61no—
324#168—61no—
325C2×#41—151no—
326C22×Q8—51no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—31no—
331C22×C8—151no—
332C4×Q8—52no—
333C4×Q8—52no—
334C4×Q8—101no—
335C4×Q8—101no—
336C4×Q8—152no—
337C4×D4—152no—
338C4×D4—302no—
339#117—51no—
340#117—102no—
341#117—301no—
342#117D3×D511yescharacteristic
343C2×C4⋊C4—31no—
344C2×C4⋊C4—301no—
345#107—32no—
346#106—32no—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—101no—
362C3×Q8—54no—
363C3×Q8—102no—
364C3×Q8—104no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—52no—
368C2×C3×C4—52no—
369C2×C3×C4—102no—
370C2×C3×C4—104no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71312yes—
374C2×C3×C4C23×D511yescharacteristic
375#67—104no—
376C2×Dic3—22no—
377C2×Dic3—81no—
378C2×Dic3—101no—
379D12—52no—
380D12—101no—
381C4×D3—104no—
382C4×D3—402no—
383Dic6—52no—
384Dic6—101no—
385C3⋊C8—101no—
386C3⋊C8—101no—
387C3⋊C8C2×C4×D514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5C4×#6712yes—
391C22×C5C22×#6711yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—122no—
398C4×C5C4×#6712yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23511yescharacteristic
401Dic5—24no—
402Dic5—22no—
403Dic5—22no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—54no—
408C2×Q8—52no—
409C2×Q8—102no—
410C2×Q8—101no—
411C2×Q8—151no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—34no—
422C2×C8—32no—
423C2×C8—151no—
424C2×C8—151no—
425C2×C8—302no—
426C4⋊C4—32no—
427C4⋊C4—51no—
428C4⋊C4—51no—
429C4⋊C4—61no—
430C4⋊C4—102no—
431C4⋊C4—102no—
432C4⋊C4—302no—
433C4⋊C4C2×D3×D511yescharacteristic
434C4⋊C4C2×D3×D511yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—52no—
437C22⋊C4—302no—
438C42—21no—
439C42—52no—
440C42—102no—
441C42—102no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#403912yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—104no—
454C3×C4—102no—
455C3×C4—102no—
456C3×C4#403912yes—
457C3×C4C22×C4×D511yescharacteristic
458C3×C4C2×#71311yescharacteristic
459Dic3—42no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×C4×#6711yescharacteristic
463C2×C5#583711yescharacteristic
464C2×C5#583811yescharacteristic
465D5—122no—
466C23—301no—
467C23D5×#6711yescharacteristic
468Q8—54no—
469Q8—104no—
470Q8—102no—
471Q8—152no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—52no—
479C2×C4—52no—
480C2×C4—62no—
481C2×C4—104no—
482C2×C4—102no—
483C2×C4—241no—
484C2×C4—301no—
485C2×C4—304no—
486C2×C4—1202no—
487C2×C4#677312yes—
488C2×C4C4×D3×D512yes—
489C2×C4D5×#6711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—34no—
492C8—301no—
493C8—301no—
494C2×C3—22no—
495C2×C3C2×#403911yescharacteristic
496C2×C3#6610911yescharacteristic
497C2×C3#6611311yescharacteristic
498D3—202no—
499C5#8254711yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9144412yes—
506C22C2×D5×#6711yescharacteristic
507C4—41no—
508C4—41no—
509C4—104no—
510C4—102no—
511C4—102no—
512C4—122no—
513C4—302no—
514C4#9144412yes—
515C4C2×#677311yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061093311yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2C2×#9144411yescharacteristic
521C2#1175531711yescharacteristic
522C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#65850C2semidirect
5. C5×#4995C2semidirect
6. C2×#90970C2semidirect
7. #11748320C2semidirect
8. #11747270C2semidirect
9. #11747269C2semidirect
10. #11747225C2semidirect
11. #11747224C2semidirect
31. #91315C4semidirect
45. #65850D3semidirect
66. C2×C3×Dic10C2×C4semidirect
78. C5×#208C2×C4semidirect
91. #6662C2×C4semidirect
92. #6658C2×C4semidirect
103. #4995D5semidirect
205. C2×Dic10C4×D3semidirect
292. #208C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#82547semidirect
517. C3#10610933semidirect

Maximal subgroups

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

subgroupindex
C3×#658502
#117545062
C2×#913152
#117511032
C5×#49952
C2×#909702
#117483202
#117472702
#117472692
#117472252
#117472242
#106109333
#825475