Finite Group Databasebeta

← #14438695

Subgroups — #14438695

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4036C211yesmaximal, characteristic, complemented
2#11754572C211yesmaximal, characteristic
3#11751067C211yesmaximal, characteristic, complemented
4C5×#4966C211yesmaximal, characteristic, complemented
5#11748413C211yesmaximal, characteristic, complemented
6#11748384C211yesmaximal, characteristic, complemented
7Dic5×#208C211yesmaximal, characteristic, complemented
8#11747401C212yesmaximal, complemented
9#11747156C212yesmaximal, complemented
10#11747145C212yesmaximal, complemented
11#11747142C212yesmaximal, complemented
12#10610610—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×C4⋊Dic5—21no—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#683—21no—
21C2×C3×C4×Dic5C2211yescharacteristic
22C3×#4036—21no—
23C3×#4036—21no—
24C3×#4036C2212yes—
25C3×#4036C2212yes—
26#91566—21no—
27#91566—21no—
28#91451C2211yescharacteristic
29C4×#1203—21no—
30C4×#1203—21no—
31#91376C2211yescharacteristic
32#91375C2211yescharacteristic
33#91373C2211yescharacteristic
34#91094C2212yes—
35#91093C2212yes—
36C5×#810C2212yes—
37C5×#809C2212yes—
38#90974C2212yes—
39#90972C2212yes—
40#90968C2212yes—
41#90966C2212yes—
42#90952C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83012—51nomaximal, Hall
45#66166—31no—
46C2×#4036D311yescharacteristic, complemented
47C5×#417—31no—
48#65521—31no—
49#65422—31no—
50M16×Dic5—31no—
51#65255—31no—
52#65089—32no—
53#65086—32no—
54#65057—32no—
55#65053—32no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5—21no—
71C22×C3×Dic5D411yescharacteristic
72C22×C3×Dic5D411yescharacteristic
73C2×#1203—21no—
74C2×#1203—21no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yes—
77#6710—22no—
78C2×C3⋊#168C2312yes—
79C5×#208—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5—22no—
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5C2312yes—
85C3×#683—22no—
86C3×#683—22no—
87C3×C4×Dic5D411yescharacteristic
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5C2311yescharacteristic
90C3×C4×Dic5C2311yescharacteristic
91#6668—21no—
92#6668—21no—
93#6667—21no—
94#6667—21no—
95(C2×D3)⋊Dic5—21no—
96(C2×D3)⋊Dic5—21no—
97C2×C3×#125—51no—
98#5477—51no—
99#5069—52no—
100#5068—52no—
101#5068—52no—
102#5067—52no—
103#4966—51no—
104#4966—51no—
105#4966—51no—
106#4966D511yescharacteristic, complemented
107C4×#208—51no—
108C2×C5×#41—31no—
109C2×#709—31no—
110C2×C5×M16—31no—
111C2×C5×C4⋊C4C2×D311yescharacteristic
112#4093—31no—
113#4090—31no—
114#4086—31no—
115#4085—61no—
116#4085—61no—
117#4082—31no—
118C4×C22⋊D5—61no—
119C4×C22⋊D5—61no—
120C2×C4⋊Dic5—21no—
121C2×C4⋊Dic5C2×D311yescharacteristic
122C2×#683—21no—
123C2×C4×Dic5C2×D311yescharacteristic
124C2×#681—31no—
125#4036—21no—
126#4036—21no—
127#4036C2×D312yes—
128#4036C2×D312yes—
129C5×#103—32no—
130C5×#102—32no—
131#3967—32no—
132#3964—32no—
133#3953—32no—
134#3948—32no—
135#3947—32no—
136C8×Dic5—32no—
137#3942—32no—
138#3941—32no—
139#3142—151noSylow
140C23×C3×C5C2×D411yescharacteristic
141C22×D15—21no—
142C22×C5×D3—21no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—42no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5#4112yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—42no—
150C2×Dic15—21no—
151D60—21no—
152D60—21no—
153C4×D15—42no—
154Dic30—21no—
155Dic30—21no—
156C5×#67—42no—
157C2×C5×Dic3—21no—
158C5×D12—21no—
159C5×D12—21no—
160C4×C5×D3—42no—
161C5×Dic6—21no—
162C5×Dic6—21no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—41no—
165C2×C3×Dic5—41no—
166C2×C3×Dic5—42no—
167C2×C3×Dic5C2×D411yescharacteristic
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2×D411yescharacteristic
171#1203—42no—
172#1203—42no—
173C3⋊#168—22no—
174C5×C3⋊C8—22no—
175C2×#235—51no—
176C2×#235C2×D511yescharacteristic
177C3×#125—52no—
178C3×#125—52no—
179C3×#125—101no—
180C3×#125—101no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—101no—
183C2×C3×C4⋊C4—101no—
184C2×C3×C4⋊C4C2×D511yescharacteristic
185C2×C3×C42—51no—
186#930—101no—
187#930—101no—
188C2×#208—51no—
189C2×#208C2×D511yescharacteristic
190#875—51no—
191#875—51no—
192#874—51no—
193C4×D12—101no—
194C4×D12—101no—
195#869—51no—
196#810—52no—
197#810—52no—
198#810—52no—
199#810C2×D512yes—
200#809—52no—
201#809—52no—
202#809—52no—
203#809C2×D512yes—
204#803—52no—
205C4×C3⋊C8—52no—
206C5×#41—62no—
207C5×#41—62no—
208C2×C5×Q8—31no—
209C2×C5×D4—31no—
210C2×C5×D4—61no—
211C22×C4×C5—21no—
212C22×C4×C5—61no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—61no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—61no—
217C22×Dic5—21no—
218C22×Dic5#6711yescharacteristic
219C22×Dic5#6711yescharacteristic
220#709—62no—
221#709—62no—
222C2×D20—31no—
223C2×C4×D5—61no—
224C2×Dic10—31no—
225C5×M16—62no—
226C2×C5×C8—32no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4C22×D312yes—
229C22⋊Dic5—61no—
230C22⋊Dic5—61no—
231#685—61no—
232#685—61no—
233C4⋊Dic5—21no—
234C4⋊Dic5—22no—
235C4⋊Dic5—22no—
236C4⋊Dic5C22×D312yes—
237#683—22no—
238#683—22no—
239#683—61no—
240#683—61no—
241C4×Dic5#6711yescharacteristic
242C4×Dic5#6711yescharacteristic
243C4×Dic5C22×D311yescharacteristic
244C4×Dic5C22×D311yescharacteristic
245#681—62no—
246C2×#168—32no—
247#532—151no—
248C2×#125—51no—
249#491—152no—
250#490—152no—
251#488—152no—
252#488—152no—
253#417—31no—
254#417—151no—
255#417—151no—
256#417—151no—
257C4×M16—151no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12412yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×D15—41no—
263C2×D15—41no—
264C2×D15—41no—
265C2×C5×D3—41no—
266C2×C5×D3—41no—
267C2×C5×D3—41no—
268C3×C4×C5—42no—
269C3×C4×C5#12412yes—
270C3×C4×C5C2×#4111yescharacteristic
271C3×C4×C5C2×#4111yescharacteristic
272Dic15—41no—
273C3×Dic5—21no—
274C3×Dic5—21no—
275C3×Dic5—21no—
276C3×Dic5—21no—
277C3×Dic5—42no—
278C5×Dic3—41no—
279C22×C3×C4—21no—
280C22×C3×C4—51no—
281C22×C3×C4—51no—
282C22×C3×C4—101no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—21no—
285C2×#67—101no—
286#235—22no—
287#235—22no—
288#235—102no—
289#235—102no—
290C2×D12—51no—
291C2×D12—101no—
292C2×D12—101no—
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—101no—
296C2×Dic6—51no—
297C2×Dic6C22×D511yescharacteristic
298C3×C4⋊C4—21no—
299C3×C4⋊C4—52no—
300C3×C4⋊C4—102no—
301C3×C4⋊C4—102no—
302C3×C4⋊C4—102no—
303C3×C4⋊C4—102no—
304C3×C4⋊C4—101no—
305C3×C4⋊C4C22×D512yes—
306C3×C42—51no—
307C3×C42—51no—
308C3×C42—51no—
309C3×C42—51no—
310(C2×D3)⋊C4—101no—
311(C2×D3)⋊C4—101no—
312(C2×D3)⋊C4—101no—
313(C2×D3)⋊C4—101no—
314C4⋊Dic3—101no—
315C4⋊Dic3—101no—
316#208—22no—
317#208—102no—
318C2×C3⋊C8—52no—
319C2×C3⋊C8C22×D512yes—
320C23×C5—61no—
321C23×C5C2×#6711yescharacteristic
322C22×D5—61no—
323C5×Q8—61no—
324C5×Q8—61no—
325C5×D4—61no—
326C5×D4—61no—
327C5×D4—122no—
328C2×C4×C5—22no—
329C2×C4×C5—42no—
330C2×C4×C5—61no—
331C2×C4×C5—122no—
332C2×C4×C5#23912yes—
333C2×C4×C5#23912yes—
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—122no—
337C22⋊D5—122no—
338C22⋊D5—122no—
339C2×Dic5—22no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342C2×Dic5—42no—
343C2×Dic5—61no—
344C2×Dic5C2×#6711yescharacteristic
345C2×Dic5C2×#6711yescharacteristic
346C2×Dic5C2×#6711yescharacteristic
347C2×Dic5C2×#6711yescharacteristic
348D20—61no—
349D20—61no—
350C4×D5—122no—
351Dic10—61no—
352Dic10—61no—
353C5×C8—62no—
354#168—62no—
355C2×#41—31no—
356C2×#41—151no—
357C2×M16—31no—
358C2×M16—151no—
359C4⋊Q8—151no—
360#127—151no—
361#125—52no—
362#125—52no—
363#125—101no—
364#125—101no—
365#124—151no—
366#124—151no—
367#121—301no—
368#121—301no—
369C4×D4—301no—
370C4×D4—301no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—101no—
373C2×C4⋊C4—101no—
374C2×C4⋊C4D3×D511yescharacteristic
375C2×C42—51no—
376#103—32no—
377#103—152no—
378#103—152no—
379#103—152no—
380#102—32no—
381#102—152no—
382#102—152no—
383#102—152no—
384#97—152no—
385C4×C8—152no—
386C2×C3×C5—22no—
387C2×C3×C5C2×#12411yescharacteristic
388C2×C3×C5#57511yescharacteristic
389C2×C3×C5#57511yescharacteristic
390D15—81no—
391C5×D3—81no—
392C23×C3D4×D511yescharacteristic
393C22×D3—21no—
394C22×D3—101no—
395C2×C3×C4—22no—
396C2×C3×C4—42no—
397C2×C3×C4—51no—
398C2×C3×C4—51no—
399C2×C3×C4—51no—
400C2×C3×C4—51no—
401C2×C3×C4—102no—
402C2×C3×C4—201no—
403C2×C3×C4—201no—
404C2×C3×C4—202no—
405C2×C3×C4#70912yes—
406C2×C3×C4D4×D511yescharacteristic
407C2×C3×C4#71112yes—
408C2×C3×C4C23×D511yescharacteristic
409#67—42no—
410#67—202no—
411C2×Dic3—21no—
412C2×Dic3—101no—
413D12—21no—
414D12—21no—
415D12—101no—
416D12—101no—
417D12—202no—
418D12—202no—
419C4×D3—42no—
420C4×D3—202no—
421Dic6—21no—
422Dic6—21no—
423Dic6—101no—
424Dic6—101no—
425C3⋊C8—22no—
426C3⋊C8—102no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—121no—
430C22×C5—121no—
431C22×C5—121no—
432C22×C5#94712yes—
433C22×C5C22×#6711yescharacteristic
434C2×D5—121no—
435C2×D5—121no—
436C2×D5—121no—
437C4×C5—42no—
438C4×C5—121no—
439C4×C5#94712yes—
440C4×C5C2×#23911yescharacteristic
441C4×C5C2×#23911yescharacteristic
442Dic5—21no—
443Dic5—21no—
444Dic5—21no—
445Dic5—21no—
446Dic5—42no—
447Dic5—121no—
448#41—62no—
449#41—62no—
450#41—302no—
451#41—302no—
452C2×Q8—31no—
453C2×Q8—151no—
454C2×D4—31no—
455C2×D4—61no—
456C2×D4—151no—
457C2×D4—301no—
458C2×D4—301no—
459C2×D4—301no—
460C22×C4—21no—
461C22×C4—51no—
462C22×C4—51no—
463C22×C4—61no—
464C22×C4—101no—
465C22×C4—301no—
466C22×C4C2×D3×D511yescharacteristic
467M16—62no—
468M16—302no—
469C2×C8—32no—
470C2×C8—152no—
471C4⋊C4—21no—
472C4⋊C4—52no—
473C4⋊C4—102no—
474C4⋊C4—102no—
475C4⋊C4—102no—
476C4⋊C4—102no—
477C4⋊C4—101no—
478C4⋊C4—301no—
479C4⋊C4—301no—
480C4⋊C4C2×D3×D512yes—
481C22⋊C4—301no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C42—51no—
486C42—51no—
487C42—51no—
488C42—51no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3#403112yes—
493C22×C3C2×D4×D511yescharacteristic
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—201no—
498C2×D3—201no—
499C2×D3—201no—
500C3×C4—42no—
501C3×C4—101no—
502C3×C4—101no—
503C3×C4—101no—
504C3×C4—101no—
505C3×C4—202no—
506C3×C4#403112yes—
507C3×C4C2×#70911yescharacteristic
508C3×C4C2×#71111yescharacteristic
509Dic3—41no—
510Dic3—201no—
511C2×C5—22no—
512C2×C5—241no—
513C2×C5C2×#94711yescharacteristic
514C2×C5#582211yescharacteristic
515C2×C5#582211yescharacteristic
516D5—241no—
517C23—61no—
518C23—301no—
519C23D5×#6711yescharacteristic
520Q8—61no—
521Q8—61no—
522Q8—301no—
523Q8—301no—
524D4—61no—
525D4—61no—
526D4—122no—
527D4—301no—
528D4—301no—
529D4—602no—
530D4—602no—
531D4—602no—
532C2×C4—22no—
533C2×C4—42no—
534C2×C4—51no—
535C2×C4—51no—
536C2×C4—51no—
537C2×C4—51no—
538C2×C4—61no—
539C2×C4—102no—
540C2×C4—122no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—202no—
544C2×C4—301no—
545C2×C4—602no—
546C2×C4#676812yes—
547C2×C4#676912yes—
548C2×C4D5×#6711yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—22no—
553C2×C3C2×#403111yescharacteristic
554C2×C3#6610711yescharacteristic
555C2×C3#6611111yescharacteristic
556D3—81no—
557D3—401no—
558C5#8301211yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—601no—
565C22—601no—
566C22—601no—
567C22#9132612yes—
568C22C2×D5×#6711yescharacteristic
569C4—42no—
570C4—101no—
571C4—101no—
572C4—101no—
573C4—101no—
574C4—121no—
575C4—202no—
576C4—601no—
577C4#9132612yes—
578C4C2×#676811yescharacteristic
579C4C2×#676911yescharacteristic
580C3#1061061011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—241no—
583C2—1201no—
584C2C2×#9132611yescharacteristic
585C2#1175469011yescharacteristic
586C2#1175508411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#11754572C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4036C2semidirect
3. #11751067C2semidirect
4. C5×#4966C2semidirect
5. #11748413C2semidirect
6. #11748384C2semidirect
7. Dic5×#208C2semidirect
8. #11747401C2semidirect
9. #11747156C2semidirect
10. #11747145C2semidirect
11. #11747142C2semidirect
46. C2×#4036D3semidirect
106. #4966D5semidirect
489. C3×C5#3142semidirect
558. C5#83012semidirect
580. C3#10610610semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40362
#117545722
#117510672
C5×#49662
#117484132
#117483842
Dic5×#2082
#117474012
#117471562
#117471452
#117471422
#106106103
#830125