Finite Group Databasebeta

← #14430960

Subgroups — #14430960

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752661C211yesmaximal, characteristic
2#11752523C211yesmaximal, characteristic
3#11750952C211yesmaximal, characteristic, complemented
4C5×#4839C211yesmaximal, characteristic
5C3×#65118C211yesmaximal, characteristic, complemented
6#11748123C211yesmaximal, characteristic
7#11747871C211yesmaximal, characteristic, complemented
8#11747868C211yesmaximal, characteristic, complemented
9#11747864C211yesmaximal, characteristic, complemented
10#11747861C211yesmaximal, characteristic, complemented
11#11747679C211yesmaximal, characteristic
12#11747630C211yesmaximal, characteristic
13D3×#3948C211yesmaximal, characteristic
14#11746934C211yesmaximal, characteristic, complemented
15#11746916C211yesmaximal, characteristic, complemented
16#10610832—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18#91758C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
21C2×C5×D3×C8C2211yescharacteristic
22C5×#872C2211yescharacteristic
23C3×#4016C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91469C2211yescharacteristic
26#91432—21no—
27D3×C4⋊Dic5C2211yescharacteristic
28#91417—21no—
29#91400—21no—
30#91398—21no—
31#91381C2211yescharacteristic
32#91343—21no—
33#91340C2211yescharacteristic
34#91338C2211yescharacteristic
35#91338C2211yescharacteristic
36Dic3×Dic10C2211yescharacteristic
37#91328—21no—
38#91325—21no—
39#91323—21no—
40C3×C5×C4⋊C8C2211yescharacteristic
41#91101C2211yescharacteristic
42#91101C2211yescharacteristic
43#91100C2211yescharacteristic
44#91100C2211yescharacteristic
45C5×Dic3⋊C8C2211yescharacteristic
46C5×Dic3⋊C8C2211yescharacteristic
47C5×C4⋊(C3⋊C8)C2211yescharacteristic
48C3×#3950C2211yescharacteristic
49C3×#3949C2211yescharacteristic
50C3×#3948C2211yescharacteristic
51C3×#3948C2211yescharacteristic
52#90990C2211yescharacteristic
53#90990C2211yescharacteristic
54#90990C2211yescharacteristic
55#90987C2211yescharacteristic
56#90974C2211yescharacteristic
57#90974C2211yescharacteristic
58#90971C2211yescharacteristic
59#90971C2211yescharacteristic
60#81233—51nomaximal, Hall
61#65853—31no—
62#65850—31no—
63C5×#424—31no—
64#65410—31no—
65#65409—31no—
66#65395—31no—
67C2×#3948—31no—
68#65140—31no—
69#65140—31no—
70#65139—31no—
71#65139—31no—
72#65118—31no—
73#65118—31no—
74#65118—31no—
75#65118D311yescharacteristic, complemented
76C2×Dic30—21no—
77C2×Dic30C2311yescharacteristic
78C2×C4×C5×D3C2311yescharacteristic
79C2×C3×Dic10C2311yescharacteristic
80C2×#1204—21no—
81C2×#1204—21no—
82C2×D3×Dic5—21no—
83C2×D3×Dic5—21no—
84D3×Dic10—22no—
85D3×Dic10Q814yescomplemented
86C2×C3×C5×C8C2311yescharacteristic
87C2×C3×C5×C8C2311yescharacteristic
88C3×C42×C5C2311yescharacteristic
89C4⋊Dic15—21no—
90C4⋊Dic15C2311yescharacteristic
91C4⋊Dic15C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94C4×Dic15—21no—
95C5×(C2×D3)⋊C4D411yescharacteristic
96C5×(C2×D3)⋊C4D411yescharacteristic
97C5×Dic3⋊C4D411yescharacteristic
98C5×Dic3⋊C4D411yescharacteristic
99C4×C5×Dic3C2311yescharacteristic
100C2×C5×C3⋊C8C2311yescharacteristic
101C2×C5×C3⋊C8C2311yescharacteristic
102C5×ΓL(1,𝔽25)—22no—
103C5×D3×C8—22no—
104C3×C4⋊Dic5C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×C4×Dic5—21no—
111Dic3⋊Dic5—21no—
112Dic3⋊Dic5—21no—
113#6669—21no—
114#6669—21no—
115#6668—21no—
116#6668—21no—
117(C2×D3)⋊Dic5—21no—
118(C2×D3)⋊Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#5689—51no—
124#5572—51no—
125C3×#479—51no—
126#5063—51no—
127#5021—51no—
128#4881—51no—
129#4875—51no—
130#4860—51no—
131#4857—51no—
132#4851—51no—
133#4839D511yescharacteristic
134#4802—51no—
135D3×#103—51no—
136#4799—51no—
137#4791—51no—
138C22×Dic10—31no—
139C2×C5×M16—31no—
140C22×C5×C8—31no—
141C5×#117—31no—
142#4072—31no—
143#4072—31no—
144C2×C4⋊Dic5—31no—
145#4036—61no—
146#4034—61no—
147#4033—61no—
148#4033—61no—
149#4024—61no—
150#4024—61no—
151#4023—61no—
152#4023—61no—
153#4016—31no—
154#4016C2×D311yescharacteristic
155#4015—31no—
156#4015—31no—
157C4×Dic10—31no—
158C4×Dic10—31no—
159C4×Dic10—31no—
160C4×Dic10C2×D311yescharacteristic
161C5×C4⋊C8—31no—
162C5×C4⋊C8—31no—
163C5×C4⋊C8—31no—
164C5×C4⋊C8C2×D311yescharacteristic
165#3950—31no—
166#3950—31no—
167#3950—31no—
168#3950C2×D311yescharacteristic
169#3949—31no—
170#3949—31no—
171#3949—31no—
172#3949C2×D311yescharacteristic
173#3948—31no—
174#3948—31no—
175#3948—31no—
176#3948—31no—
177#3948—31no—
178#3948—31no—
179#3948C2×D311yescharacteristic
180#3948C2×D311yescharacteristic
181#3082—151noSylow
182C22×C5×D3C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2411yescharacteristic
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190Dic30—21no—
191Dic30—81no—
192Dic30C2×Q812yes—
193C2×C5×Dic3C2×D411yescharacteristic
194C2×C5×Dic3C2×D411yescharacteristic
195C2×C5×Dic3C2×D411yescharacteristic
196C4×C5×D3C2×Q812yes—
197C4×C5×D3#4112yes—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C3×Dic10—21no—
203C3×Dic10C2×Q812yes—
204#1204—24no—
205#1204—81no—
206D3×Dic5—24no—
207D3×Dic5—81no—
208C3×C5×C8—21no—
209C3×C5×C8—21no—
210C5×C3⋊C8—21no—
211C5×C3⋊C8—21no—
212C2×D3×Q8—51no—
213C3×#125—51no—
214C3×C4×Q8—51no—
215Q8×Dic3—51no—
216C2×ΓL(1,𝔽25)C2×D511yescharacteristic
217C2×D3×C8C2×D511yescharacteristic
218#897—101no—
219#896—101no—
220#892—51no—
221#892—51no—
222#892—101no—
223D3×C4⋊C4—51no—
224#890—51no—
225#889—101no—
226#888—51no—
227#888—101no—
228#887—51no—
229#887—101no—
230#872—101no—
231#872C2×D511yescharacteristic
232#869—51no—
233C4×Dic6—51no—
234C4×Dic6—101no—
235C3×#107—51no—
236C3×#106—51no—
237C3×C4⋊C8C2×D511yescharacteristic
238C3×#103—51no—
239C3×#103—51no—
240#835—51no—
241#835—51no—
242#817—51no—
243#817—51no—
244#816—51no—
245#816—51no—
246Dic3⋊C8C2×D511yescharacteristic
247Dic3⋊C8C2×D511yescharacteristic
248#810—51no—
249#810—51no—
250#808—51no—
251#807—51no—
252#807—51no—
253#807—51no—
254C4⋊(C3⋊C8)C2×D511yescharacteristic
255C22×C4×C5—31no—
256C22×Dic5—61no—
257C22×Dic5—61no—
258C2×Dic10—31no—
259C2×Dic10—34no—
260C2×Dic10—62no—
261C2×Dic10—61no—
262C2×Dic10—61no—
263C2×Dic10—61no—
264C2×Dic10C22×D311yescharacteristic
265C5×M16—62no—
266C2×C5×C8—31no—
267C2×C5×C8—31no—
268C2×C5×C8—62no—
269C2×C5×C8C22×D311yescharacteristic
270C2×C5×C8C22×D311yescharacteristic
271C5×C4⋊C4—31no—
272C5×C4⋊C4—31no—
273C5×C22⋊C4—31no—
274C5×C22⋊C4—31no—
275C42×C5—31no—
276C42×C5C22×D311yescharacteristic
277C22⋊Dic5—61no—
278C22⋊Dic5—61no—
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—31no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284C4⋊Dic5—61no—
285C4⋊Dic5C22×D311yescharacteristic
286C4⋊Dic5C22×D311yescharacteristic
287C4⋊Dic5C22×D311yescharacteristic
288#683—21no—
289#683—21no—
290#683—21no—
291#683—61no—
292#683—61no—
293#683—61no—
294#683—61no—
295#683—61no—
296C4×Dic5—21no—
297C4×Dic5—61no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C4×Dic5—61no—
301C4×Dic5—61no—
302#544—151no—
303#519—151no—
304#479—51no—
305#479—151no—
306#479—151no—
307#479—151no—
308#477—151no—
309#477—151no—
310#475—151no—
311#475—151no—
312#428—151no—
313#427—151no—
314#424—31no—
315#419—151no—
316C2×#103—151no—
317C22×C3×C5C22×D411yescharacteristic
318C2×C5×D3—21no—
319C2×C5×D3—21no—
320C2×C5×D3C22⋊Q812yes—
321C3×C4×C5—21no—
322C3×C4×C5—21no—
323C3×C4×C5C22×Q811yescharacteristic
324C3×C4×C5C2×#4111yescharacteristic
325Dic15—22no—
326Dic15—41no—
327Dic15—41no—
328Dic15—41no—
329C3×Dic5—22no—
330C3×Dic5—41no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C5×Dic3—21no—
334C5×Dic3—21no—
335C5×Dic3C22⋊Q812yes—
336C2×C3×Q8—51no—
337D3×Q8—54no—
338D3×Q8—102no—
339C2×C4×D3—101no—
340C2×C4×D3—101no—
341C2×C4×D3C22×D511yescharacteristic
342C2×Dic6—51no—
343C2×Dic6—101no—
344C2×Dic6—101no—
345C2×Dic6—101no—
346C2×C3×C8C22×D511yescharacteristic
347C2×C3×C8C22×D511yescharacteristic
348C3×C4⋊C4—51no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4—51no—
351C3×C4⋊C4—101no—
352C3×C4⋊C4—101no—
353C3×C4⋊C4—101no—
354C3×C42—101no—
355C3×C42C22×D511yescharacteristic
356(C2×D3)⋊C4—101no—
357(C2×D3)⋊C4—101no—
358(C2×D3)⋊C4D2011yescharacteristic
359(C2×D3)⋊C4D2011yescharacteristic
360C4⋊Dic3—51no—
361C4⋊Dic3—51no—
362C4⋊Dic3—51no—
363C4⋊Dic3—101no—
364C4⋊Dic3—101no—
365C4⋊Dic3—101no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4D2011yescharacteristic
372Dic3⋊C4D2011yescharacteristic
373C4×Dic3—101no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3C22×D511yescharacteristic
379C2×C3⋊C8C22×D511yescharacteristic
380C2×C3⋊C8C22×D511yescharacteristic
381ΓL(1,𝔽25)—22no—
382D3×C8—22no—
383C23×C5—31no—
384C2×C4×C5—31no—
385C2×C4×C5—32no—
386C2×C4×C5—32no—
387C2×C4×C5—31no—
388C2×C4×C5—31no—
389C2×C4×C5D3×D411yescharacteristic
390C2×C4×C5D3×D411yescharacteristic
391C2×C4×C5C23×D311yescharacteristic
392C2×Dic5—21no—
393C2×Dic5—21no—
394C2×Dic5—21no—
395C2×Dic5—21no—
396C2×Dic5—64no—
397C2×Dic5—61no—
398C2×Dic5—61no—
399C2×Dic5—61no—
400C2×Dic5—61no—
401C2×Dic5—241no—
402Dic10—21no—
403Dic10—32no—
404Dic10—64no—
405Dic10—61no—
406Dic10—241no—
407Dic10—241no—
408Dic10D3×Q812yes—
409C5×C8—21no—
410C5×C8—21no—
411C5×C8—61no—
412C5×C8—61no—
413C22×Q8—151no—
414C2×M16—31no—
415C22×C8—31no—
416C4⋊Q8—151no—
417C4⋊Q8—151no—
418C4⋊Q8—301no—
419#125—51no—
420#125—151no—
421#125—301no—
422C22⋊Q8—301no—
423C22⋊Q8—301no—
424C4×Q8—51no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—301no—
429C4×Q8—301no—
430#117—31no—
431#117—151no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—151no—
436#107—51no—
437#107—151no—
438#107—151no—
439#107—151no—
440#106—51no—
441#106—151no—
442#106—151no—
443#106—151no—
444C4⋊C8—31no—
445C4⋊C8—31no—
446C4⋊C8—31no—
447C4⋊C8D3×D511yescharacteristic
448#103—51no—
449#103—51no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#103—151no—
455#103—151no—
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459C5×D3—22no—
460C22×D3C2×D2011yescharacteristic
461C3×Q8—52no—
462C3×Q8—101no—
463C2×C3×C4—101no—
464C2×C3×C4—101no—
465C2×C3×C4—101no—
466C2×C3×C4—101no—
467C2×C3×C4C2×D2011yescharacteristic
468C2×C3×C4C2×D2011yescharacteristic
469C2×C3×C4C23×D511yescharacteristic
470C2×Dic3—101no—
471C2×Dic3—101no—
472C2×Dic3—101no—
473C2×Dic3—101no—
474C2×Dic3C2×D2011yescharacteristic
475C2×Dic3C2×D2011yescharacteristic
476C2×Dic3C2×D2011yescharacteristic
477C4×D3—104no—
478C4×D3—401no—
479C4×D3#71112yes—
480C4×D3Q8×D512yes—
481Dic6—52no—
482Dic6—101no—
483Dic6—104no—
484Dic6—401no—
485Dic6—401no—
486C3×C8—21no—
487C3×C8—21no—
488C3⋊C8—21no—
489C3⋊C8—21no—
490C22×C5—32no—
491C22×C5—61no—
492C22×C5—61no—
493C22×C5C2×D3×D411yescharacteristic
494C4×C5—21no—
495C4×C5—21no—
496C4×C5—32no—
497C4×C5—61no—
498C4×C5—61no—
499C4×C5C2×D3×Q811yescharacteristic
500C4×C5D3×#4111yescharacteristic
501Dic5—22no—
502Dic5—41no—
503Dic5—41no—
504Dic5—41no—
505Dic5—62no—
506Dic5—121no—
507Dic5—121no—
508Dic5—121no—
509C2×Q8—51no—
510C2×Q8—154no—
511C2×Q8—151no—
512C2×Q8—301no—
513C2×Q8—301no—
514C2×Q8—302no—
515C2×Q8—301no—
516C22×C4—31no—
517C22×C4—301no—
518C22×C4—301no—
519M16—62no—
520C2×C8—31no—
521C2×C8—31no—
522C2×C8—62no—
523C2×C8C2×D3×D511yescharacteristic
524C2×C8C2×D3×D511yescharacteristic
525C4⋊C4—31no—
526C4⋊C4—31no—
527C4⋊C4—51no—
528C4⋊C4—51no—
529C4⋊C4—51no—
530C4⋊C4—101no—
531C4⋊C4—101no—
532C4⋊C4—101no—
533C4⋊C4—151no—
534C4⋊C4—151no—
535C4⋊C4—151no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4—301no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4—301no—
542C4⋊C4—301no—
543C4⋊C4—301no—
544C22⋊C4—31no—
545C22⋊C4—31no—
546C22⋊C4—301no—
547C22⋊C4—301no—
548C42—31no—
549C42—101no—
550C42—301no—
551C42—301no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42C2×D3×D511yescharacteristic
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3C22×D2011yescharacteristic
558C2×D3—21no—
559C2×D3—21no—
560C2×D3#404312yes—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—102no—
564C3×C4—201no—
565C3×C4—201no—
566C3×C4—201no—
567C3×C4C2×#71111yescharacteristic
568C3×C4C2×Q8×D511yescharacteristic
569Dic3—21no—
570Dic3—21no—
571Dic3—102no—
572Dic3—201no—
573Dic3—201no—
574Dic3—201no—
575Dic3#404312yes—
576C2×C5—62no—
577C2×C5D3×C22⋊Q811yescharacteristic
578C2×C5#577011yescharacteristic
579C2×C5#577911yescharacteristic
580C23—31no—
581Q8—52no—
582Q8—101no—
583Q8—152no—
584Q8—304no—
585Q8—301no—
586Q8—1201no—
587Q8—1201no—
588C2×C4—31no—
589C2×C4—32no—
590C2×C4—32no—
591C2×C4—31no—
592C2×C4—31no—
593C2×C4—101no—
594C2×C4—101no—
595C2×C4—101no—
596C2×C4—101no—
597C2×C4—304no—
598C2×C4—301no—
599C2×C4—301no—
600C2×C4—301no—
601C2×C4—301no—
602C2×C4—1201no—
603C2×C4D3×D2011yescharacteristic
604C2×C4D3×D2011yescharacteristic
605C2×C4C22×D3×D511yescharacteristic
606C8—21no—
607C8—21no—
608C8—61no—
609C8—61no—
610C2×C3C2×#404311yescharacteristic
611C2×C3#6608511yescharacteristic
612C2×C3#6608711yescharacteristic
613D3—22no—
614C5#8123311yescharacteristic, complemented, Sylow
615C22—32no—
616C22—61no—
617C22—61no—
618C22C2×D3×D2011yescharacteristic
619C4—21no—
620C4—21no—
621C4—32no—
622C4—61no—
623C4—61no—
624C4—102no—
625C4—201no—
626C4—201no—
627C4—201no—
628C4—302no—
629C4—601no—
630C4—601no—
631C4—601no—
632C4D3×#71111yescharacteristic
633C4D3×Q8×D511yescharacteristic
634C3#1061083211yescharacteristic, complemented, Sylow
635C2—62no—
636C2D3×#404311yescharacteristic
637C2#1175397211yescharacteristic
638C2#1175404211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11750952C2semidirect
5. C3×#65118C2semidirect
7. #11747871C2semidirect
8. #11747868C2semidirect
9. #11747864C2semidirect
10. #11747861C2semidirect
14. #11746934C2semidirect
15. #11746916C2semidirect
75. #65118D3semidirect
85. D3×Dic10Q8semidirect
556. C3×C5#3082semidirect
614. C5#81233semidirect
634. C3#10610832semidirect

Maximal subgroups

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

subgroupindex
#117526612
#117525232
#117509522
C5×#48392
C3×#651182
#117481232
#117478712
#117478682
#117478642
#117478612
#117476792
#117476302
D3×#39482
#117469342
#117469162
#106108323
#812335