Finite Group Databasebeta

← #14438689

Subgroups — #14438689

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
1C3×#66166C211yesmaximal, characteristic
2C2×#91388C211yesmaximal, characteristic, complemented
3#11751333C211yesmaximal, characteristic, complemented
4C5×#5232C211yesmaximal, characteristic, complemented
5#11749331C212yesmaximal, complemented
6#11749330C212yesmaximal, complemented
7#11749085C212yesmaximal, complemented
8#11749084C212yesmaximal, complemented
9#11748369C211yesmaximal, characteristic, complemented
10#11748368C211yesmaximal, characteristic, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10610610—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C3×#4093C2211yescharacteristic
20C3×#4090C2211yescharacteristic
21C3×#4086C2211yescharacteristic
22C3×#4085—21no—
23C3×#4085—21no—
24C3×#4082C2211yescharacteristic
25C3×C4×C22⋊D5—21no—
26C3×C4×C22⋊D5—21no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5—21no—
29C2×#6669—21no—
30#91388—21no—
31#91388—21no—
32#91388C2212yes—
33#91388C2212yes—
34#91119C2212yes—
35#91116C2212yes—
36C5×#835C2212yes—
37C5×#832C2212yes—
38#90971C2212yes—
39#90970C2212yes—
40#90965C2212yes—
41#90964C2212yes—
42#90952C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83284—51nomaximal, Hall
45#66166D311yescharacteristic
46C2×#4036—31no—
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—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15—21no—
64C22×C5×Dic3—21no—
65C2×C3×C22⋊D5—21no—
66C2×C3×C22⋊D5—21no—
67C2×C3×C22⋊D5—21no—
68C22×C3×Dic5D411yescharacteristic
69C22×C3×Dic5D411yescharacteristic
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10C2311yescharacteristic
75C4⋊Dic15—21no—
76C4⋊Dic15C2312yes—
77#6710—22no—
78C2×C3⋊#168C2312yes—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C5×#208—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×C22⋊Dic5—21no—
84C3×C22⋊Dic5—21no—
85C3×#685—21no—
86C3×#685—21no—
87C3×#683—21no—
88C3×#683—21no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92C3×C4×Dic5C2311yescharacteristic
93Dic3⋊Dic5—22no—
94Dic3⋊Dic5—22no—
95#6669—22no—
96#6669—22no—
97C3×#532—51no—
98C2×#870—51no—
99#5232—51no—
100#5232—51no—
101#5232—51no—
102#5232D511yescharacteristic, complemented
103#5082—52no—
104#5071—52no—
105#5056—52no—
106#5056—52no—
107C4×#208—51no—
108C2×C5×#41C2×D311yescharacteristic
109C2×#709C2×D311yescharacteristic
110C2×C5×M16—31no—
111C2×C5×C4⋊C4—31no—
112#4093C2×D311yescharacteristic
113#4090C2×D311yescharacteristic
114#4086C2×D311yescharacteristic
115#4085—21no—
116#4085—21no—
117#4082C2×D311yescharacteristic
118C4×C22⋊D5—21no—
119C4×C22⋊D5—21no—
120C2×C4⋊Dic5—31no—
121C2×C4⋊Dic5—61no—
122C2×#683—61no—
123C2×C4×Dic5C2×D311yescharacteristic
124C2×#681—31no—
125#4036—32no—
126#4036—32no—
127#4036—61no—
128#4036—61no—
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×C5—21no—
141C23×C3×C5C2×D411yescharacteristic
142C22×C3×D5—21no—
143C3×C5×Q8—21no—
144C3×C5×Q8—21no—
145C3×C5×D4—21no—
146C3×C5×D4—21no—
147C3×C5×D4—42no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—42no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15—22no—
155C2×Dic15—42no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—42no—
158C3×C22⋊D5—42no—
159C3×C22⋊D5—42no—
160C3×C22⋊D5—42no—
161C2×C3×Dic5—21no—
162C2×C3×Dic5—41no—
163C2×C3×Dic5—41no—
164C2×C3×Dic5C2×D411yescharacteristic
165C2×C3×Dic5C2×D411yescharacteristic
166C2×C3×Dic5C2×D411yescharacteristic
167C2×C3×Dic5C2×D411yescharacteristic
168C3×D20—21no—
169C3×D20—21no—
170C3×C4×D5—42no—
171C3×Dic10—21no—
172C3×Dic10—21no—
173C3⋊#168—22no—
174C5×C3⋊C8—22no—
175C2×C3×#41—51no—
176C2×C3×#41C2×D511yescharacteristic
177C3×C4⋊Q8—51no—
178C3×#127—51no—
179C3×#124—51no—
180C3×#124—51no—
181C3×#121—101no—
182C3×#121—101no—
183C3×C4×D4—101no—
184C3×C4×D4—101no—
185C2×C3×C42—51no—
186C2×C4⋊Dic3—51no—
187C2×C4⋊Dic3C2×D511yescharacteristic
188C2×Dic3⋊C4—101no—
189C2×Dic3⋊C4—101no—
190C2×#208—51no—
191C2×#208C2×D511yescharacteristic
192#870—52no—
193#870—52no—
194#870—101no—
195#870—101no—
196#835—52no—
197#835—52no—
198#835—52no—
199#835C2×D512yes—
200#832—52no—
201#832—52no—
202#832—52no—
203#832C2×D512yes—
204#803—52no—
205C4×C3⋊C8—52no—
206C5×#41—22no—
207C5×#41—22no—
208C2×C5×Q8C22×D311yescharacteristic
209C2×C5×D4—21no—
210C2×C5×D4C22×D311yescharacteristic
211C22×C4×C5—21no—
212C22×C4×C5—61no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—21no—
215C2×C22⋊D5—21no—
216C2×C22⋊D5—21no—
217C22×Dic5—61no—
218C22×Dic5#6711yescharacteristic
219C22×Dic5#6711yescharacteristic
220#709—22no—
221#709—22no—
222C2×D20C22×D311yescharacteristic
223C2×C4×D5—21no—
224C2×Dic10C22×D311yescharacteristic
225C5×M16—62no—
226C2×C5×C8—32no—
227C5×C4⋊C4—32no—
228C5×C4⋊C4—61no—
229C22⋊Dic5—21no—
230C22⋊Dic5—21no—
231#685—21no—
232#685—21no—
233C4⋊Dic5—32no—
234C4⋊Dic5—61no—
235C4⋊Dic5—62no—
236C4⋊Dic5—62no—
237#683—21no—
238#683—21no—
239#683—62no—
240#683—62no—
241C4×Dic5#6711yescharacteristic
242C4×Dic5#6711yescharacteristic
243C4×Dic5C22×D311yescharacteristic
244C4×Dic5C22×D311yescharacteristic
245#681—62no—
246C2×#168—32no—
247#532—51no—
248C2×#125—151no—
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—41no—
261C22×C3×C5—41no—
262C22×C3×C5—41no—
263C22×C3×C5#12412yes—
264C22×C3×C5C22×D411yescharacteristic
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C2×C3×D5—41no—
268C3×C4×C5—41no—
269C3×C4×C5#12412yes—
270C3×C4×C5C2×#4111yescharacteristic
271C3×C4×C5C2×#4111yescharacteristic
272Dic15—42no—
273C3×Dic5—21no—
274C3×Dic5—21no—
275C3×Dic5—21no—
276C3×Dic5—21no—
277C3×Dic5—41no—
278C5×Dic3—42no—
279C3×#41—22no—
280C3×#41—22no—
281C3×#41—102no—
282C3×#41—102no—
283C2×C3×Q8—51no—
284C2×C3×Q8C22×D511yescharacteristic
285C2×C3×D4—21no—
286C2×C3×D4—51no—
287C2×C3×D4—101no—
288C2×C3×D4—101no—
289C2×C3×D4—101no—
290C2×C3×D4C22×D511yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—51no—
293C22×C3×C4—51no—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C22×Dic3—21no—
297C22×Dic3—101no—
298C3×C4⋊C4—101no—
299C3×C4⋊C4—101no—
300C3×C22⋊C4—101no—
301C3×C22⋊C4—101no—
302C3×C22⋊C4—101no—
303C3×C22⋊C4—101no—
304C3×C42—51no—
305C3×C42—51no—
306C3×C42—51no—
307C3×C42—51no—
308C4⋊Dic3—21no—
309C4⋊Dic3—52no—
310C4⋊Dic3—101no—
311C4⋊Dic3C22×D512yes—
312Dic3⋊C4—102no—
313Dic3⋊C4—102no—
314Dic3⋊C4—102no—
315Dic3⋊C4—102no—
316#208—22no—
317#208—102no—
318C2×C3⋊C8—52no—
319C2×C3⋊C8C22×D512yes—
320C23×C5—21no—
321C23×C5C2×#6711yescharacteristic
322C22×D5—21no—
323C5×Q8—21no—
324C5×Q8—21no—
325C5×D4—21no—
326C5×D4—21no—
327C5×D4—42no—
328C2×C4×C5—21no—
329C2×C4×C5—42no—
330C2×C4×C5—62no—
331C2×C4×C5—122no—
332C2×C4×C5#23712yes—
333C2×C4×C5#23712yes—
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—42no—
337C22⋊D5—42no—
338C22⋊D5—42no—
339C2×Dic5—21no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342C2×Dic5—62no—
343C2×Dic5—122no—
344C2×Dic5C2×#6711yescharacteristic
345C2×Dic5C2×#6711yescharacteristic
346C2×Dic5C2×#6711yescharacteristic
347C2×Dic5C2×#6711yescharacteristic
348D20—21no—
349D20—21no—
350C4×D5—42no—
351Dic10—21no—
352Dic10—21no—
353C5×C8—62no—
354#168—62no—
355C2×#41—51no—
356C2×#41D3×D511yescharacteristic
357C2×M16—31no—
358C2×M16—151no—
359C4⋊Q8—51no—
360#127—51no—
361#125—152no—
362#125—152no—
363#125—301no—
364#125—301no—
365#124—51no—
366#124—51no—
367#121—101no—
368#121—101no—
369C4×D4—101no—
370C4×D4—101no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—151no—
373C2×C4⋊C4—301no—
374C2×C4⋊C4—301no—
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×C5—81no—
388C2×C3×C5C2×#12411yescharacteristic
389C2×C3×C5#57511yescharacteristic
390C2×C3×C5#57511yescharacteristic
391C3×D5—81no—
392C23×C3—21no—
393C23×C3—101no—
394C23×C3D4×D511yescharacteristic
395C3×Q8—21no—
396C3×Q8—21no—
397C3×Q8—101no—
398C3×Q8—101no—
399C3×D4—21no—
400C3×D4—21no—
401C3×D4—42no—
402C3×D4—101no—
403C3×D4—101no—
404C3×D4—202no—
405C3×D4—202no—
406C3×D4—202no—
407C2×C3×C4—21no—
408C2×C3×C4—42no—
409C2×C3×C4—51no—
410C2×C3×C4—51no—
411C2×C3×C4—51no—
412C2×C3×C4—51no—
413C2×C3×C4—101no—
414C2×C3×C4—201no—
415C2×C3×C4—201no—
416C2×C3×C4—202no—
417C2×C3×C4#70912yes—
418C2×C3×C4D4×D511yescharacteristic
419C2×C3×C4#71112yes—
420C2×C3×C4C23×D511yescharacteristic
421C2×Dic3—22no—
422C2×Dic3—42no—
423C2×Dic3—102no—
424C2×Dic3—202no—
425C3⋊C8—22no—
426C3⋊C8—102no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5#93612yes—
433C22×C5C22×#6711yescharacteristic
434C2×D5—41no—
435C2×D5—41no—
436C2×D5—41no—
437C4×C5—41no—
438C4×C5—122no—
439C4×C5#93612yes—
440C4×C5C2×#23711yescharacteristic
441C4×C5C2×#23711yescharacteristic
442Dic5—21no—
443Dic5—21no—
444Dic5—21no—
445Dic5—21no—
446Dic5—41no—
447Dic5—122no—
448#41—22no—
449#41—22no—
450#41—102no—
451#41—102no—
452C2×Q8—51no—
453C2×Q8C2×D3×D511yescharacteristic
454C2×D4—21no—
455C2×D4—51no—
456C2×D4—101no—
457C2×D4—101no—
458C2×D4—101no—
459C2×D4C2×D3×D511yescharacteristic
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—32no—
472C4⋊C4—61no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—152no—
476C4⋊C4—302no—
477C4⋊C4—302no—
478C4⋊C4—302no—
479C4⋊C4—302no—
480C4⋊C4—301no—
481C22⋊C4—101no—
482C22⋊C4—101no—
483C22⋊C4—101no—
484C22⋊C4—101no—
485C42—51no—
486C42—51no—
487C42—51no—
488C42—51no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—201no—
496C22×C3—201no—
497C22×C3—201no—
498C22×C3#403112yes—
499C22×C3C2×D4×D511yescharacteristic
500C3×C4—41no—
501C3×C4—101no—
502C3×C4—101no—
503C3×C4—101no—
504C3×C4—101no—
505C3×C4—201no—
506C3×C4#403112yes—
507C3×C4C2×#70911yescharacteristic
508C3×C4C2×#71111yescharacteristic
509Dic3—42no—
510Dic3—202no—
511C2×C5—22no—
512C2×C5—81no—
513C2×C5C2×#93611yescharacteristic
514C2×C5#582211yescharacteristic
515C2×C5#582211yescharacteristic
516D5—81no—
517C23—21no—
518C23—101no—
519C23D5×#6711yescharacteristic
520Q8—21no—
521Q8—21no—
522Q8—101no—
523Q8—101no—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—101no—
528D4—101no—
529D4—202no—
530D4—202no—
531D4—202no—
532C2×C4—21no—
533C2×C4—42no—
534C2×C4—51no—
535C2×C4—51no—
536C2×C4—51no—
537C2×C4—51no—
538C2×C4—62no—
539C2×C4—101no—
540C2×C4—122no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—202no—
544C2×C4—302no—
545C2×C4—602no—
546C2×C4#677912yes—
547C2×C4#678012yes—
548C2×C4D5×#6711yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—22no—
553C2×C3—81no—
554C2×C3—401no—
555C2×C3C2×#403111yescharacteristic
556C2×C3#6610711yescharacteristic
557C2×C3#6611111yescharacteristic
558C5#8328411yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—201no—
565C22—201no—
566C22—201no—
567C22#9153412yes—
568C22C2×D5×#6711yescharacteristic
569C4—41no—
570C4—101no—
571C4—101no—
572C4—101no—
573C4—101no—
574C4—122no—
575C4—201no—
576C4—602no—
577C4#9153412yes—
578C4C2×#677911yescharacteristic
579C4C2×#678011yescharacteristic
580C3#1061061011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—81no—
583C2—401no—
584C2#1175534311yescharacteristic
585C2#1175534411yescharacteristic
586C2C2×#9153411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC3×#66166C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91388C2semidirect
3. #11751333C2semidirect
4. C5×#5232C2semidirect
5. #11749331C2semidirect
6. #11749330C2semidirect
7. #11749085C2semidirect
8. #11749084C2semidirect
9. #11748369C2semidirect
10. #11748368C2semidirect
11. Dic5×#208C2semidirect
102. #5232D5semidirect
489. C3×C5#3142semidirect
558. C5#83284semidirect
580. C3#10610610semidirect

Maximal subgroups

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

subgroupindex
C3×#661662
C2×#913882
#117513332
C5×#52322
#117493312
#117493302
#117490852
#117490842
#117483692
#117483682
Dic5×#2082
#106106103
#832845