Finite Group Databasebeta

← #14430920

Subgroups — #14430920

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#11756488C211yesmaximal, characteristic
2#11756331C211yesmaximal, characteristic
3C3×C5×#475C211yesmaximal, characteristic, complemented
4#11751192C211yesmaximal, characteristic, complemented
5#11751123C211yesmaximal, characteristic, complemented
6#11750962C211yesmaximal, characteristic
7#11750961C211yesmaximal, characteristic
8#11750958C211yesmaximal, characteristic, complemented
9#11750955C211yesmaximal, characteristic, complemented
10#11750940C211yesmaximal, characteristic
11#11750930C211yesmaximal, characteristic, complemented
12#11750903C211yesmaximal, characteristic
13D15×#103C211yesmaximal, characteristic
14#11750900C211yesmaximal, characteristic, complemented
15#11750894C211yesmaximal, characteristic, complemented
16#10612744—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20#91835—21no—
21Q8×Dic15C2211yescharacteristic
22#91833—21no—
23C2×#6705C2211yescharacteristic
24C2×C8×D15C2211yescharacteristic
25#91785—21no—
26#91781—21no—
27#91781C2211yescharacteristic
28#91781C2211yescharacteristic
29C4⋊C4×D15C2211yescharacteristic
30#91779C2211yescharacteristic
31#91778—21no—
32#91777C2211yescharacteristic
33#91776—21no—
34#91776C2211yescharacteristic
35#91761—21no—
36#91761C2211yescharacteristic
37#91759C2211yescharacteristic
38C4×Dic30—21no—
39C4×Dic30C2211yescharacteristic
40C3×C5×#106C2211yescharacteristic
41C3×C5×#106C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45#91119C2211yescharacteristic
46#91119C2211yescharacteristic
47#91102C2211yescharacteristic
48#91101C2211yescharacteristic
49#91100C2211yescharacteristic
50#91100C2211yescharacteristic
51#91098C2211yescharacteristic
52#91098C2211yescharacteristic
53#91094C2211yescharacteristic
54#91094C2211yescharacteristic
55#91092C2211yescharacteristic
56#91091C2211yescharacteristic
57#91091C2211yescharacteristic
58#91091C2211yescharacteristic
59C4⋊(C3⋊#168)C2211yescharacteristic
60#81013—51nomaximal, Hall
61#66063—31no—
62#65906—31no—
63C5×#475D311yescharacteristic, complemented
64#65380—31no—
65#65311—31no—
66#65150—31no—
67#65149—31no—
68#65146—31no—
69#65143—31no—
70#65128—31no—
71#65118—31no—
72#65091—31no—
73D5×#103—31no—
74#65088—31no—
75#65083—31no—
76C2×C3×C5×Q8—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78Q8×D15—22no—
79Q8×D15Q814yescomplemented
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C4×D15C2311yescharacteristic
83C2×Dic30—21no—
84C2×Dic30—21no—
85C2×Dic30C2311yescharacteristic
86C2×C3×C5×C8C2311yescharacteristic
87C2×C3×C5×C8C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C42×C5—21no—
94C3×C42×C5C2311yescharacteristic
95#6714—21no—
96#6714—21no—
97#6714D411yescharacteristic
98#6714D411yescharacteristic
99C4⋊Dic15—21no—
100C4⋊Dic15—21no—
101C4⋊Dic15C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105#6712—21no—
106#6712—21no—
107#6712—21no—
108#6712—21no—
109#6712—21no—
110#6712—21no—
111#6712D411yescharacteristic
112#6712D411yescharacteristic
113C4×Dic15—21no—
114C4×Dic15—21no—
115C4×Dic15—21no—
116C4×Dic15—21no—
117C4×Dic15—21no—
118C4×Dic15C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C2×C3⋊#168C2311yescharacteristic
121#6705—22no—
122C8×D15—22no—
123#5729—51no—
124#5572—51no—
125C3×#475D511yescharacteristic, complemented
126#5091—51no—
127#5022—51no—
128#4861—51no—
129#4860—51no—
130#4857—51no—
131#4854—51no—
132#4839—51no—
133#4829—51no—
134#4802—51no—
135D3×#103—51no—
136#4799—51no—
137#4793—51no—
138C2×Q8×D5—31no—
139C5×C4⋊Q8C2×D311yescharacteristic
140C4×C5×Q8C2×D311yescharacteristic
141#4092—61no—
142Q8×Dic5—31no—
143#4090—61no—
144C2×#676—31no—
145C2×C8×D5—31no—
146#4042—61no—
147#4038—31no—
148#4038—31no—
149#4038—61no—
150D5×C4⋊C4—31no—
151#4036—31no—
152#4035—61no—
153#4034—31no—
154#4033—31no—
155#4033—61no—
156#4018—31no—
157#4018—61no—
158#4016—31no—
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#106C2×D311yescharacteristic
162C5×#106C2×D311yescharacteristic
163C5×C4⋊C8C2×D311yescharacteristic
164C5×#103C2×D311yescharacteristic
165C5×#103C2×D311yescharacteristic
166#3967—31no—
167#3967—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3082—151noSylow
182C22×D15C2×D411yescharacteristic
183C3×C5×Q8—21no—
184C3×C5×Q8—81no—
185C3×C5×Q8C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15C2×D411yescharacteristic
198C2×Dic15C2×D411yescharacteristic
199C2×Dic15C2×D411yescharacteristic
200C4×D15—24no—
201C4×D15—81no—
202C4×D15C2×Q812yes—
203C4×D15#4112yes—
204Dic30—21no—
205Dic30—24no—
206Dic30—81no—
207Dic30C2×Q812yes—
208C3×C5×C8—21no—
209C3×C5×C8—21no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C2×D3×Q8—51no—
213C3×C4⋊Q8C2×D511yescharacteristic
214C3×C4×Q8C2×D511yescharacteristic
215#946—101no—
216Q8×Dic3—51no—
217#944—101no—
218C2×ΓL(1,𝔽25)—51no—
219C2×D3×C8—51no—
220#896—101no—
221#892—51no—
222#892—51no—
223#892—101no—
224D3×C4⋊C4—51no—
225#890—51no—
226#889—101no—
227#888—51no—
228#887—51no—
229#887—101no—
230#872—51no—
231#872—101no—
232#870—51no—
233C4×Dic6—51no—
234C4×Dic6—101no—
235C3×#106C2×D511yescharacteristic
236C3×#106C2×D511yescharacteristic
237C3×C4⋊C8C2×D511yescharacteristic
238C3×#103C2×D511yescharacteristic
239C3×#103C2×D511yescharacteristic
240#835—51no—
241#835—51no—
242#818—51no—
243#817—51no—
244#816—51no—
245#816—51no—
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248#810—51no—
249#810—51no—
250#808—51no—
251#807—51no—
252#807—51no—
253#807—51no—
254C4⋊(C3⋊C8)—51no—
255C2×C5×Q8—21no—
256C2×C5×Q8C22×D311yescharacteristic
257Q8×D5—34no—
258Q8×D5—62no—
259C2×C4×D5—31no—
260C2×C4×D5—61no—
261C2×C4×D5—61no—
262C2×Dic10—31no—
263C2×Dic10—61no—
264C2×Dic10—61no—
265C2×C5×C8C22×D311yescharacteristic
266C2×C5×C8C22×D311yescharacteristic
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4C22×D311yescharacteristic
270C5×C4⋊C4C22×D311yescharacteristic
271C5×C4⋊C4C22×D311yescharacteristic
272C42×C5—21no—
273C42×C5C22×D311yescharacteristic
274#685—31no—
275#685—31no—
276#685—61no—
277#685—61no—
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283#683—31no—
284#683—31no—
285#683—61no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292C4×Dic5—31no—
293C4×Dic5—61no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C2×#168—31no—
299C2×#168—31no—
300#676—62no—
301C8×D5—62no—
302#544—151no—
303#519—151no—
304#479—151no—
305#479—151no—
306#479—151no—
307#479—151no—
308#477—151no—
309#477—151no—
310#475—151no—
311#475D1511yescharacteristic, complemented
312#428—151no—
313#427—151no—
314#424—151no—
315#419—151no—
316C2×#103—151no—
317C22×C3×C5C22×D411yescharacteristic
318C2×D15—21no—
319C2×D15—21no—
320C2×D15C22⋊Q812yes—
321C3×C4×C5—22no—
322C3×C4×C5—21no—
323C3×C4×C5—21no—
324C3×C4×C5—41no—
325C3×C4×C5—41no—
326C3×C4×C5—41no—
327C3×C4×C5C22×Q811yescharacteristic
328C3×C4×C5C2×#4111yescharacteristic
329Dic15—22no—
330Dic15—21no—
331Dic15—21no—
332Dic15—41no—
333Dic15—41no—
334Dic15—41no—
335Dic15C22⋊Q812yes—
336C2×C3×Q8—21no—
337C2×C3×Q8C22×D511yescharacteristic
338D3×Q8—54no—
339D3×Q8—102no—
340C2×C4×D3—51no—
341C2×C4×D3—101no—
342C2×C4×D3—101no—
343C2×Dic6—51no—
344C2×Dic6—101no—
345C2×Dic6—101no—
346C2×C3×C8C22×D511yescharacteristic
347C2×C3×C8C22×D511yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4C22×D511yescharacteristic
351C3×C4⋊C4C22×D511yescharacteristic
352C3×C4⋊C4C22×D511yescharacteristic
353C3×C42—21no—
354C3×C42C22×D511yescharacteristic
355(C2×D3)⋊C4—51no—
356(C2×D3)⋊C4—51no—
357(C2×D3)⋊C4—101no—
358(C2×D3)⋊C4—101no—
359C4⋊Dic3—51no—
360C4⋊Dic3—51no—
361C4⋊Dic3—51no—
362C4⋊Dic3—101no—
363C4⋊Dic3—101no—
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373C4×Dic3—51no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3—101no—
379C2×C3⋊C8—51no—
380C2×C3⋊C8—51no—
381ΓL(1,𝔽25)—102no—
382D3×C8—102no—
383C22×D5—31no—
384C5×Q8—21no—
385C5×Q8—81no—
386C5×Q8D3×Q812yes—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5D3×D411yescharacteristic
392C2×C4×C5D3×D411yescharacteristic
393C2×C4×C5C23×D311yescharacteristic
394C2×Dic5—31no—
395C2×Dic5—31no—
396C2×Dic5—31no—
397C2×Dic5—61no—
398C2×Dic5—61no—
399C2×Dic5—61no—
400C2×Dic5—61no—
401C4×D5—32no—
402C4×D5—32no—
403C4×D5—64no—
404C4×D5—241no—
405Dic10—32no—
406Dic10—64no—
407Dic10—61no—
408Dic10—241no—
409C5×C8—21no—
410C5×C8—21no—
411#168—61no—
412#168—61no—
413C22×Q8—151no—
414C2×M16—151no—
415C22×C8—151no—
416C4⋊Q8—151no—
417C4⋊Q8—301no—
418C4⋊Q8C2×D1511yescharacteristic
419#125—151no—
420#125—151no—
421#125—301no—
422C22⋊Q8—301no—
423C22⋊Q8—301no—
424C4×Q8—151no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—301no—
428C4×Q8—301no—
429C4×Q8C2×D1511yescharacteristic
430#117—151no—
431#117—151no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—151no—
436#107—151no—
437#107—151no—
438#107—151no—
439#107—151no—
440#106—151no—
441#106—151no—
442#106C2×D1511yescharacteristic
443#106C2×D1511yescharacteristic
444C4⋊C8—151no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8C2×D1511yescharacteristic
448#103—151no—
449#103—151no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#103C2×D1511yescharacteristic
455#103C2×D1511yescharacteristic
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459D15—22no—
460C22×D3—51no—
461C3×Q8—21no—
462C3×Q8—81no—
463C3×Q8Q8×D512yes—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4D4×D511yescharacteristic
469C2×C3×C4D4×D511yescharacteristic
470C2×C3×C4C23×D511yescharacteristic
471C2×Dic3—51no—
472C2×Dic3—51no—
473C2×Dic3—51no—
474C2×Dic3—101no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3—101no—
478C4×D3—52no—
479C4×D3—52no—
480C4×D3—104no—
481C4×D3—401no—
482Dic6—52no—
483Dic6—104no—
484Dic6—101no—
485Dic6—401no—
486C3×C8—21no—
487C3×C8—21no—
488C3⋊C8—101no—
489C3⋊C8—101no—
490C22×C5C2×D3×D411yescharacteristic
491C2×D5—32no—
492C2×D5—61no—
493C2×D5—61no—
494C4×C5—21no—
495C4×C5—21no—
496C4×C5—22no—
497C4×C5—41no—
498C4×C5—41no—
499C4×C5—41no—
500C4×C5C2×D3×Q811yescharacteristic
501C4×C5D3×#4111yescharacteristic
502Dic5—32no—
503Dic5—61no—
504Dic5—61no—
505Dic5—62no—
506Dic5—121no—
507Dic5—121no—
508Dic5—121no—
509C2×Q8—21no—
510C2×Q8—154no—
511C2×Q8—151no—
512C2×Q8—301no—
513C2×Q8—301no—
514C2×Q8—302no—
515C2×Q8C22×D1511yescharacteristic
516C22×C4—151no—
517C22×C4—301no—
518C22×C4—301no—
519M16—302no—
520C2×C8—151no—
521C2×C8—151no—
522C2×C8—302no—
523C2×C8C22×D1511yescharacteristic
524C2×C8C22×D1511yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—151no—
528C4⋊C4—151no—
529C4⋊C4—151no—
530C4⋊C4—151no—
531C4⋊C4—151no—
532C4⋊C4—301no—
533C4⋊C4—301no—
534C4⋊C4—301no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4—301no—
539C4⋊C4—301no—
540C4⋊C4—301no—
541C4⋊C4C22×D1511yescharacteristic
542C4⋊C4C22×D1511yescharacteristic
543C4⋊C4C22×D1511yescharacteristic
544C22⋊C4—151no—
545C22⋊C4—151no—
546C22⋊C4—301no—
547C22⋊C4—301no—
548C42—21no—
549C42—151no—
550C42—301no—
551C42—301no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42C22×D1511yescharacteristic
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3C2×D4×D511yescharacteristic
558C2×D3—52no—
559C2×D3—101no—
560C2×D3—101no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—22no—
564C3×C4—41no—
565C3×C4—41no—
566C3×C4—41no—
567C3×C4C2×Q8×D511yescharacteristic
568C3×C4D5×#4111yescharacteristic
569Dic3—52no—
570Dic3—101no—
571Dic3—101no—
572Dic3—102no—
573Dic3—201no—
574Dic3—201no—
575Dic3—201no—
576C2×C5D3×C22⋊Q811yescharacteristic
577C2×C5#576211yescharacteristic
578C2×C5#577911yescharacteristic
579D5—62no—
580C23—151no—
581Q8—21no—
582Q8—81no—
583Q8—152no—
584Q8—304no—
585Q8—301no—
586Q8—1201no—
587Q8Q8×D1512yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—151no—
593C2×C4—152no—
594C2×C4—152no—
595C2×C4—151no—
596C2×C4—151no—
597C2×C4—304no—
598C2×C4—301no—
599C2×C4—301no—
600C2×C4—301no—
601C2×C4—301no—
602C2×C4—1201no—
603C2×C4D4×D1511yescharacteristic
604C2×C4D4×D1511yescharacteristic
605C2×C4C23×D1511yescharacteristic
606C8—21no—
607C8—21no—
608C8—301no—
609C8—301no—
610C2×C3D5×C22⋊Q811yescharacteristic
611C2×C3#6609611yescharacteristic
612C2×C3#6611311yescharacteristic
613D3—102no—
614C5#8101311yescharacteristic, complemented, Sylow
615C22—152no—
616C22—301no—
617C22—301no—
618C22C2×D4×D1511yescharacteristic
619C4—22no—
620C4—21no—
621C4—21no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—152no—
626C4—302no—
627C4—301no—
628C4—301no—
629C4—601no—
630C4—601no—
631C4—601no—
632C4C2×Q8×D1511yescharacteristic
633C4#41×D1511yescharacteristic
634C3#1061274411yescharacteristic, complemented, Sylow
635C2—302no—
636C2D15×C22⋊Q811yescharacteristic
637C2#1175652111yescharacteristic
638C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#475C2
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#475D15
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C3×C5×#475C2semidirect
4. #11751192C2semidirect
5. #11751123C2semidirect
8. #11750958C2semidirect
9. #11750955C2semidirect
11. #11750930C2semidirect
14. #11750900C2semidirect
15. #11750894C2semidirect
63. C5×#475D3semidirect
79. Q8×D15Q8semidirect
125. C3×#475D5semidirect
311. #475D15semidirect
556. C3×C5#3082semidirect
614. C5#81013semidirect
634. C3#10612744semidirect

Maximal subgroups

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

subgroupindex
#117564882
#117563312
C3×C5×#4752
#117511922
#117511232
#117509622
#117509612
#117509582
#117509552
#117509402
#117509302
#117509032
D15×#1032
#117509002
#117508942
#106127443
#810135