Finite Group Databasebeta

← #14438694

Subgroups — #14438694

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×#91779C211yesmaximal, characteristic, complemented
2#11754586C211yesmaximal, characteristic
3C5×#4966C211yesmaximal, characteristic, complemented
4C3×#65255C211yesmaximal, characteristic, complemented
5#11748390C211yesmaximal, characteristic, complemented
6#11748369C211yesmaximal, characteristic, complemented
7#11748328C211yesmaximal, characteristic, complemented
8#11747429C212yesmaximal, complemented
9#11747409C212yesmaximal, complemented
10#11747387C212yesmaximal, complemented
11#11747382C212yesmaximal, complemented
12#10610610—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15—21no—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×#6712—21no—
19C2×C4×Dic15C2211yescharacteristic
20#91779—21no—
21#91779—21no—
22#91779C2212yes—
23#91779C2212yes—
24C2×C5×#208C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91571—21no—
27#91571—21no—
28#91463C2211yescharacteristic
29C4×#1201—21no—
30C4×#1201—21no—
31#91385C2211yescharacteristic
32#91370C2211yescharacteristic
33#91368C2211yescharacteristic
34C5×#810C2212yes—
35C5×#809C2212yes—
36C3×#3942C2212yes—
37C3×#3941C2212yes—
38#90973C2212yes—
39#90971C2212yes—
40#90967C2212yes—
41#90965C2212yes—
42#90954C2212yes—
43#90951C2212yes—
44#78879—51nomaximal, Hall
45#66166—31no—
46C2×#4036—31no—
47C5×#417—31no—
48#65521—31no—
49#65422—31no—
50M16×Dic5—31no—
51#65255D311yescharacteristic, complemented
52#65089—32no—
53#65086—32no—
54#65057—32no—
55#65053—32no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15—21no—
59C22×Dic15D411yescharacteristic
60C22×Dic15D411yescharacteristic
61C2×C5×#67—21no—
62C5×#235—22no—
63C5×#235—22no—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2311yescharacteristic
67C2×C3×C22⋊D5—21no—
68C3×#709—22no—
69C3×#709—22no—
70C2×C3×D20C2311yescharacteristic
71C2×C3×C4×D5—21no—
72C2×C3×Dic10C2311yescharacteristic
73C2×#1201—21no—
74C2×#1201—21no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yes—
77C4⋊Dic15—21no—
78C4⋊Dic15—22no—
79C4⋊Dic15—22no—
80C4⋊Dic15C2312yes—
81#6712—22no—
82#6712—22no—
83C4×Dic15D411yescharacteristic
84C4×Dic15D411yescharacteristic
85C4×Dic15C2311yescharacteristic
86C4×Dic15C2311yescharacteristic
87C5×#208—22no—
88C2×C5×C3⋊C8C2312yes—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6669—21no—
92#6669—21no—
93(C2×D3)⋊Dic5—21no—
94(C2×D3)⋊Dic5—21no—
95#6665—21no—
96#6665—21no—
97#5832—51no—
98C2×#890—51no—
99C3×#417—51no—
100#5232—51no—
101#5133—51no—
102Dic3×M16—51no—
103#4966D511yescharacteristic, complemented
104#4800—52no—
105#4797—52no—
106#4768—52no—
107#4764—52no—
108C2×C5×#41—31no—
109C2×#709C2×D311yescharacteristic
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—31no—
121C2×C4⋊Dic5—61no—
122C2×#683—61no—
123C2×C4×Dic5—31no—
124C2×#681C2×D311yescharacteristic
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#3942C2×D312yes—
138#3941C2×D312yes—
139#3142—151noSylow
140C23×C3×C5C2×D411yescharacteristic
141C22×C5×D3—21no—
142C22×C3×D5—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
149C2×Dic15—22no—
150C2×Dic15—41no—
151C2×Dic15—41no—
152C2×Dic15—42no—
153C2×Dic15C2×D411yescharacteristic
154C2×Dic15C2×D411yescharacteristic
155C2×Dic15C2×D411yescharacteristic
156C2×Dic15C2×D411yescharacteristic
157C5×#67—42no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12—21no—
161C4×C5×D3—42no—
162C5×Dic6—21no—
163C5×Dic6—21no—
164C3×C22⋊D5—42no—
165C2×C3×Dic5—21no—
166C3×D20—21no—
167C3×D20—21no—
168C3×C4×D5—42no—
169C3×Dic10—21no—
170C3×Dic10—21no—
171#1201—42no—
172#1201—42no—
173C3×#168—22no—
174C5×C3⋊C8—22no—
175C2×C3×#41—51no—
176C2×#235C2×D511yescharacteristic
177C2×C3×M16—51no—
178C2×C3×C4⋊C4C2×D511yescharacteristic
179#947—51no—
180#944—51no—
181#940—51no—
182#939—101no—
183#939—101no—
184#936—51no—
185C4×#67—101no—
186C4×#67—101no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—101no—
189C2×Dic3⋊C4—101no—
190C2×C4×Dic3—51no—
191C2×#208C2×D511yescharacteristic
192#890—52no—
193#890—52no—
194#890—101no—
195#890—101no—
196C3×#103—52no—
197C3×#102—52no—
198#835—52no—
199#832—52no—
200#821—52no—
201#816—52no—
202#815—52no—
203C8×Dic3—52no—
204#810C2×D512yes—
205#809C2×D512yes—
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—21no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—61no—
217C22×Dic5—31no—
218C22×Dic5—31no—
219C22×Dic5—61no—
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—21no—
228C5×C4⋊C4C22×D312yes—
229C22⋊Dic5—61no—
230C22⋊Dic5—61no—
231#685—61no—
232#685—61no—
233C4⋊Dic5—32no—
234C4⋊Dic5—62no—
235C4⋊Dic5—62no—
236C4⋊Dic5—61no—
237#683—61no—
238#683—61no—
239#683—62no—
240#683—62no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245#681—22no—
246C2×#168C22×D312yes—
247#532—151no—
248C2×#125—151no—
249#491—152no—
250#490—152no—
251#488—152no—
252#488—152no—
253#417—31no—
254#417—51no—
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×C5×D3—41no—
263C2×C5×D3—41no—
264C2×C5×D3—41no—
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C2×C3×D5—41no—
268C3×C4×C5—42no—
269C3×C4×C5#12412yes—
270C3×C4×C5C2×#4111yescharacteristic
271C3×C4×C5C2×#4111yescharacteristic
272Dic15—21no—
273Dic15—21no—
274Dic15—21no—
275Dic15—21no—
276Dic15—42no—
277C3×Dic5—41no—
278C5×Dic3—41no—
279C3×#41—102no—
280C3×#41—102no—
281C2×C3×Q8—51no—
282C2×C3×D4—51no—
283C2×C3×D4—101no—
284C22×C3×C4—21no—
285C22×C3×C4—101no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—21no—
288C2×#67—101no—
289C2×#67—101no—
290C22×Dic3—51no—
291C22×Dic3—51no—
292C22×Dic3—101no—
293#235—22no—
294#235—22no—
295C2×D12C22×D511yescharacteristic
296C2×C4×D3—21no—
297C2×Dic6C22×D511yescharacteristic
298C3×M16—102no—
299C2×C3×C8—52no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4C22×D512yes—
302#217—101no—
303#217—101no—
304(C2×D3)⋊C4—101no—
305(C2×D3)⋊C4—101no—
306C4⋊Dic3—52no—
307C4⋊Dic3—102no—
308C4⋊Dic3—102no—
309C4⋊Dic3—101no—
310Dic3⋊C4—101no—
311Dic3⋊C4—101no—
312Dic3⋊C4—102no—
313Dic3⋊C4—102no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—51no—
317C4×Dic3—51no—
318#208—22no—
319C2×C3⋊C8C22×D512yes—
320C23×C5—61no—
321C23×C5D3×D411yescharacteristic
322C22×D5—21no—
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#23512yes—
333C2×C4×C5D3×D411yescharacteristic
334C2×C4×C5#23712yes—
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—42no—
337C22⋊D5—122no—
338C22⋊D5—122no—
339C2×Dic5—21no—
340C2×Dic5—31no—
341C2×Dic5—31no—
342C2×Dic5—31no—
343C2×Dic5—31no—
344C2×Dic5—62no—
345C2×Dic5—121no—
346C2×Dic5—121no—
347C2×Dic5—122no—
348D20—21no—
349D20—21no—
350C4×D5—42no—
351Dic10—21no—
352Dic10—21no—
353C5×C8—62no—
354#168—22no—
355C2×#41—31no—
356C2×#41—51no—
357C2×M16—31no—
358C2×M16—51no—
359C4⋊Q8—151no—
360#127—151no—
361#125—152no—
362#125—152no—
363#125—301no—
364#125—301no—
365#124—151no—
366#124—151no—
367#121—301no—
368#121—301no—
369C4×D4—301no—
370C4×D4—301no—
371C2×C4⋊C4—151no—
372C2×C4⋊C4—301no—
373C2×C4⋊C4—301no—
374C2×C4⋊C4D3×D511yescharacteristic
375C2×C42—151no—
376#103—32no—
377#103—52no—
378#103—152no—
379#103—152no—
380#102—32no—
381#102—52no—
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
390C3×D5—81no—
391C5×D3—81no—
392C23×C3—101no—
393C23×C3D4×D511yescharacteristic
394C22×D3—21no—
395C3×Q8—101no—
396C3×Q8—101no—
397C3×D4—101no—
398C3×D4—101no—
399C3×D4—202no—
400C2×C3×C4—22no—
401C2×C3×C4—42no—
402C2×C3×C4—101no—
403C2×C3×C4—202no—
404C2×C3×C4#70912yes—
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4#71112yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—42no—
409#67—202no—
410#67—202no—
411C2×Dic3—21no—
412C2×Dic3—51no—
413C2×Dic3—51no—
414C2×Dic3—51no—
415C2×Dic3—51no—
416C2×Dic3—102no—
417C2×Dic3—201no—
418C2×Dic3—201no—
419C2×Dic3—202no—
420D12—21no—
421D12—21no—
422C4×D3—42no—
423Dic6—21no—
424Dic6—21no—
425C3×C8—102no—
426C3⋊C8—22no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—121no—
430C22×C5—121no—
431C22×C5—121no—
432C22×C5#88512yes—
433C22×C5C2×D3×D411yescharacteristic
434C2×D5—41no—
435C2×D5—41no—
436C2×D5—41no—
437C4×C5—42no—
438C4×C5—121no—
439C4×C5#88512yes—
440C4×C5C2×#23511yescharacteristic
441C4×C5C2×#23711yescharacteristic
442Dic5—41no—
443Dic5—61no—
444Dic5—61no—
445Dic5—61no—
446Dic5—61no—
447Dic5—122no—
448#41—62no—
449#41—62no—
450#41—102no—
451#41—102no—
452C2×Q8—31no—
453C2×Q8—51no—
454C2×D4—31no—
455C2×D4—51no—
456C2×D4—61no—
457C2×D4—101no—
458C2×D4—301no—
459C2×D4—301no—
460C22×C4—21no—
461C22×C4—61no—
462C22×C4—101no—
463C22×C4—151no—
464C22×C4—151no—
465C22×C4—301no—
466C22×C4C2×D3×D511yescharacteristic
467M16—62no—
468M16—102no—
469C2×C8—32no—
470C2×C8—52no—
471C4⋊C4—21no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—302no—
477C4⋊C4—301no—
478C4⋊C4—301no—
479C4⋊C4—301no—
480C4⋊C4C2×D3×D512yes—
481C22⋊C4—301no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C42—151no—
486C42—151no—
487C42—151no—
488C42—151no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—201no—
493C22×C3—201no—
494C22×C3—201no—
495C22×C3#403112yes—
496C22×C3C2×D4×D511yescharacteristic
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C3×C4—42no—
501C3×C4—201no—
502C3×C4#403112yes—
503C3×C4C2×#70911yescharacteristic
504C3×C4C2×#71111yescharacteristic
505Dic3—41no—
506Dic3—101no—
507Dic3—101no—
508Dic3—101no—
509Dic3—101no—
510Dic3—202no—
511C2×C5—22no—
512C2×C5—241no—
513C2×C5C2×#88511yescharacteristic
514C2×C5#577311yescharacteristic
515C2×C5#577711yescharacteristic
516D5—81no—
517C23—61no—
518C23—101no—
519C23#679011yescharacteristic
520Q8—61no—
521Q8—61no—
522Q8—101no—
523Q8—101no—
524D4—61no—
525D4—61no—
526D4—101no—
527D4—101no—
528D4—122no—
529D4—202no—
530D4—602no—
531D4—602no—
532C2×C4—22no—
533C2×C4—42no—
534C2×C4—61no—
535C2×C4—101no—
536C2×C4—122no—
537C2×C4—151no—
538C2×C4—151no—
539C2×C4—151no—
540C2×C4—151no—
541C2×C4—202no—
542C2×C4—302no—
543C2×C4—601no—
544C2×C4—601no—
545C2×C4—602no—
546C2×C4#676512yes—
547C2×C4#677212yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—22no—
553C2×C3—401no—
554C2×C3C2×#403111yescharacteristic
555C2×C3#6610711yescharacteristic
556C2×C3#6611111yescharacteristic
557D3—81no—
558C5#7887911yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—201no—
565C22—201no—
566C22—201no—
567C22#9146212yes—
568C22C2×#679011yescharacteristic
569C4—42no—
570C4—121no—
571C4—201no—
572C4—301no—
573C4—301no—
574C4—301no—
575C4—301no—
576C4—602no—
577C4#9146212yes—
578C4C2×#676511yescharacteristic
579C4C2×#677211yescharacteristic
580C3#1061061011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—241no—
583C2—401no—
584C2C2×#9146211yescharacteristic
585C2#1175470211yescharacteristic
586C2#1175509611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#11754586C2
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×#91779C2semidirect
3. C5×#4966C2semidirect
4. C3×#65255C2semidirect
5. #11748390C2semidirect
6. #11748369C2semidirect
7. #11748328C2semidirect
8. #11747429C2semidirect
9. #11747409C2semidirect
10. #11747387C2semidirect
11. #11747382C2semidirect
51. #65255D3semidirect
103. #4966D5semidirect
489. C3×C5#3142semidirect
558. C5#78879semidirect
580. C3#10610610semidirect

Maximal subgroups

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

subgroupindex
C2×#917792
#117545862
C5×#49662
C3×#652552
#117483902
#117483692
#117483282
#117474292
#117474092
#117473872
#117473822
#106106103
#788795