Finite Group Databasebeta

← #14430980

Subgroups — #14430980

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#11755140C211yesmaximal, characteristic
2#11753369C211yesmaximal, characteristic
3#11750892C211yesmaximal, characteristic, complemented
4C5×#4799C211yesmaximal, characteristic, complemented
5C3×D5×#103C211yesmaximal, characteristic
6#11749359C211yesmaximal, characteristic, complemented
7#11749337C211yesmaximal, characteristic, complemented
8#11749208C211yesmaximal, characteristic
9#11747877C211yesmaximal, characteristic, complemented
10#11747861C211yesmaximal, characteristic, complemented
11#11747671C211yesmaximal, characteristic
12#11747647C211yesmaximal, characteristic
13#11747452C211yesmaximal, characteristic
14#11747303C211yesmaximal, characteristic, complemented
15#11747295C211yesmaximal, characteristic, complemented
16#10612964—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18Q8×Dic15C2211yescharacteristic
19#91777C2211yescharacteristic
20C5×Q8×Dic3C2211yescharacteristic
21C5×#890C2211yescharacteristic
22C2×C3×C8×D5C2211yescharacteristic
23C3×D5×C4⋊C4C2211yescharacteristic
24#91469C2211yescharacteristic
25#91384C2211yescharacteristic
26#91360—21no—
27#91358—21no—
28#91358C2211yescharacteristic
29#91358C2211yescharacteristic
30#91357—21no—
31#91357C2211yescharacteristic
32#91349—21no—
33#91335—21no—
34#91331—21no—
35#91331C2211yescharacteristic
36Dic3×Dic10—21no—
37Dic3×Dic10C2211yescharacteristic
38#91328—21no—
39C2×#6649C2211yescharacteristic
40C3×C5×#103C2211yescharacteristic
41#91119C2211yescharacteristic
42#91101C2211yescharacteristic
43#91098C2211yescharacteristic
44#91092C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#817C2211yescharacteristic
47C5×Dic3⋊C8C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50C3×#3948C2211yescharacteristic
51C3×#3942C2211yescharacteristic
52#90989C2211yescharacteristic
53#90988C2211yescharacteristic
54#90988C2211yescharacteristic
55#90987C2211yescharacteristic
56Dic3⋊#168C2211yescharacteristic
57#90983C2211yescharacteristic
58#90971C2211yescharacteristic
59#90970C2211yescharacteristic
60#78779—51nomaximal, Hall
61#66023—31no—
62#65906—31no—
63C5×#479—31no—
64#65352—31no—
65#65310—31no—
66#65170—31no—
67#65164—31no—
68#65149—31no—
69#65146—31no—
70#65140—31no—
71#65128—31no—
72#65091—31no—
73D5×#103D311yescharacteristic
74#65088—31no—
75#65080—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30—21no—
78C3×Q8×D5—22no—
79C3×Q8×D5Q814yescomplemented
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5C2311yescharacteristic
83C2×C3×Dic10—21no—
84C2×C3×Dic10C2311yescharacteristic
85C2×#1204—21no—
86C2×C3×C5×C8C2311yescharacteristic
87C3×C5×C4⋊C4C2311yescharacteristic
88C4⋊Dic15—21no—
89C4⋊Dic15C2311yescharacteristic
90C4⋊Dic15C2311yescharacteristic
91#6712—21no—
92C4×Dic15—21no—
93C4×Dic15C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×C4⋊Dic3—21no—
96C5×C4⋊Dic3—21no—
97C5×C4⋊Dic3C2311yescharacteristic
98C5×C4⋊Dic3C2311yescharacteristic
99C5×Dic3⋊C4—21no—
100C4×C5×Dic3—21no—
101C4×C5×Dic3C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C3×C4⋊Dic5C2311yescharacteristic
104C3×#683—21no—
105C2×C3×#168C2311yescharacteristic
106C3×C8×D5—22no—
107Dic3⋊Dic5—21no—
108Dic3⋊Dic5—21no—
109#6668—21no—
110#6668—21no—
111#6668—21no—
112#6668D411yescharacteristic
113#6668D411yescharacteristic
114#6665—21no—
115#6665—21no—
116#6665D411yescharacteristic
117#6665D411yescharacteristic
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5—21no—
122#6649—22no—
123#5812—51no—
124#5500—51no—
125C2×C3×#103—51no—
126#5225—51no—
127#5106—51no—
128#5102—51no—
129#4964—51no—
130#4799—51no—
131#4799D511yescharacteristic, complemented
132#4796—51no—
133#4796—51no—
134#4793—51no—
135#4793—51no—
136#4791—51no—
137#4791—51no—
138C2×Q8×D5C2×D311yescharacteristic
139C5×#125—31no—
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142C2×#676—31no—
143C2×C8×D5C2×D311yescharacteristic
144#4043—61no—
145#4042—61no—
146#4038—31no—
147#4038—31no—
148#4038—61no—
149D5×C4⋊C4C2×D311yescharacteristic
150#4036—31no—
151#4035—61no—
152#4034—31no—
153#4034—61no—
154#4033—31no—
155#4033—61no—
156#4018—31no—
157#4018—61no—
158#4015—31no—
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103C2×D311yescharacteristic
166#3967—31no—
167#3967C2×D311yescharacteristic
168#3949—31no—
169#3949—31no—
170#3948—31no—
171#3948C2×D311yescharacteristic
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942C2×D311yescharacteristic
176#3940—31no—
177#3939—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3082—151noSylow
182C22×C3×D5C2×D411yescharacteristic
183C3×C5×Q8—21no—
184C3×C5×Q8C2×Q812yes—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15C2×D411yescharacteristic
191C2×Dic15C2×D411yescharacteristic
192Dic30—81no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3C2×D411yescharacteristic
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5C2×D411yescharacteristic
200C3×C4×D5—24no—
201C3×C4×D5—81no—
202C3×C4×D5C2×Q812yes—
203C3×C4×D5#4112yes—
204C3×Dic10—21no—
205C3×Dic10—24no—
206C3×Dic10C2×Q812yes—
207#1204—81no—
208C3×C5×C8—21no—
209C3⋊#168—21no—
210C3×#168—21no—
211C5×C3⋊C8—21no—
212C22×C3×Q8—51no—
213C22×C3×C8—51no—
214C2×C3×C4⋊C4—51no—
215Q8×Dic3—51no—
216Q8×Dic3—51no—
217Q8×Dic3—51no—
218Q8×Dic3—101no—
219Q8×Dic3—101no—
220Q8×Dic3C2×D511yescharacteristic
221#926—51no—
222#926—51no—
223#926—51no—
224#926—101no—
225#926—101no—
226#924—101no—
227#924—101no—
228C2×#208—51no—
229#890—51no—
230#890—101no—
231#890C2×D511yescharacteristic
232#888—51no—
233#888—51no—
234#888—101no—
235C3×#103—51no—
236C3×#103—51no—
237C3×#103—51no—
238C3×#103C2×D511yescharacteristic
239#835—51no—
240#835—51no—
241#835—51no—
242#835C2×D511yescharacteristic
243#818—51no—
244#818—51no—
245#817—51no—
246#817C2×D511yescharacteristic
247Dic3⋊C8—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250Dic3⋊C8C2×D511yescharacteristic
251#808—51no—
252#808—51no—
253#807—51no—
254#807C2×D511yescharacteristic
255C2×C5×Q8C22×D311yescharacteristic
256Q8×D5—22no—
257Q8×D5Dic614yescomplemented
258C2×C4×D5—21no—
259C2×C4×D5—21no—
260C2×C4×D5C22×D311yescharacteristic
261C2×Dic10—21no—
262C2×Dic10—61no—
263C2×Dic10—61no—
264C2×Dic10C22×D311yescharacteristic
265C2×C5×C8—31no—
266C2×C5×C8C22×D311yescharacteristic
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—61no—
270C5×C4⋊C4—61no—
271C5×C4⋊C4—61no—
272C5×C4⋊C4C22×D311yescharacteristic
273C42×C5—31no—
274C42×C5—61no—
275#685—31no—
276#685—31no—
277#685—61no—
278#685—61no—
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284C4⋊Dic5C22×D311yescharacteristic
285#683—21no—
286#683—31no—
287#683—31no—
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×#168C22×D311yescharacteristic
300#676—62no—
301C8×D5—22no—
302#544—151no—
303#519—151no—
304#479—31no—
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—151no—
315#419—151no—
316C2×#103—51no—
317C22×C3×C5C22×D411yescharacteristic
318C2×C3×D5—21no—
319C2×C3×D5—21no—
320C2×C3×D5C22⋊Q812yes—
321C3×C4×C5—22no—
322C3×C4×C5—41no—
323C3×C4×C5C22×Q811yescharacteristic
324C3×C4×C5C2×#4111yescharacteristic
325Dic15—21no—
326Dic15—21no—
327Dic15—41no—
328Dic15—41no—
329C3×Dic5—22no—
330C3×Dic5—41no—
331C3×Dic5C22⋊Q812yes—
332C5×Dic3—21no—
333C5×Dic3—21no—
334C5×Dic3—41no—
335C5×Dic3—41no—
336C2×C3×Q8—54no—
337C2×C3×Q8—51no—
338C2×C3×Q8—101no—
339C2×C3×Q8—102no—
340C2×C3×Q8C22×D511yescharacteristic
341C22×C3×C4—51no—
342C22×C3×C4—101no—
343C22×C3×C4—101no—
344C2×Dic6—101no—
345C2×Dic6—101no—
346C2×C3×C8—51no—
347C2×C3×C8—102no—
348C2×C3×C8C22×D511yescharacteristic
349C3×C4⋊C4—51no—
350C3×C4⋊C4—101no—
351C3×C4⋊C4C22×D511yescharacteristic
352#217—51no—
353#217—51no—
354#217—101no—
355#217—101no—
356C4⋊Dic3—21no—
357C4⋊Dic3—21no—
358C4⋊Dic3—51no—
359C4⋊Dic3—51no—
360C4⋊Dic3—51no—
361C4⋊Dic3—51no—
362C4⋊Dic3—101no—
363C4⋊Dic3—101no—
364C4⋊Dic3—101no—
365C4⋊Dic3—101no—
366C4⋊Dic3C22×D511yescharacteristic
367C4⋊Dic3C22×D511yescharacteristic
368Dic3⋊C4—21no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372C4×Dic3—21no—
373C4×Dic3—51no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C4×Dic3—101no—
379C4×Dic3C22×D511yescharacteristic
380#208—102no—
381C2×C3⋊C8—51no—
382C2×C3⋊C8C22×D511yescharacteristic
383C22×D5D3×D411yescharacteristic
384C5×Q8—21no—
385C5×Q8C2×Dic612yes—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—31no—
389C2×C4×C5—31no—
390C2×C4×C5—61no—
391C2×C4×C5—61no—
392C2×C4×C5C23×D311yescharacteristic
393C2×Dic5—21no—
394C2×Dic5—21no—
395C2×Dic5—31no—
396C2×Dic5—31no—
397C2×Dic5—61no—
398C2×Dic5—61no—
399C2×Dic5D3×D411yescharacteristic
400C4×D5—24no—
401C4×D5—81no—
402C4×D5C2×Dic612yes—
403C4×D5#23712yes—
404Dic10—21no—
405Dic10—24no—
406Dic10—241no—
407Dic10—241no—
408Dic10C2×Dic612yes—
409C5×C8—21no—
410C5×C8—61no—
411#168—21no—
412#168—61no—
413C22×Q8—51no—
414C2×M16—151no—
415C22×C8—51no—
416C4⋊Q8—151no—
417C4⋊Q8—151no—
418C4⋊Q8—301no—
419#125—31no—
420#125—151no—
421#125—301no—
422C22⋊Q8—301no—
423C22⋊Q8—301no—
424C4×Q8—31no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—301no—
429C4×Q8—301no—
430#117—151no—
431#117—151no—
432#117—151no—
433#117—301no—
434#117—301no—
435C2×C4⋊C4—51no—
436#107—31no—
437#107—151no—
438#107—151no—
439#107—151no—
440#106—31no—
441#106—151no—
442#106—151no—
443#106—151no—
444C4⋊C8—31no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—31no—
449#103—51no—
450#103—51no—
451#103—51no—
452#103—151no—
453#103—151no—
454#103—151no—
455#103D3×D511yescharacteristic
456C2×C3×C5C2×C22⋊Q811yescharacteristic
457C2×C3×C5#57711yescharacteristic
458C2×C3×C5#57811yescharacteristic
459C3×D5—22no—
460C23×C3—51no—
461C3×Q8—21no—
462C3×Q8—52no—
463C3×Q8—104no—
464C3×Q8—101no—
465C3×Q8Q8×D512yes—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—51no—
469C2×C3×C4—52no—
470C2×C3×C4—52no—
471C2×C3×C4—104no—
472C2×C3×C4—101no—
473C2×C3×C4—101no—
474C2×C3×C4—401no—
475C2×C3×C4C23×D511yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—51no—
479C2×Dic3—51no—
480C2×Dic3—101no—
481C2×Dic3—101no—
482C2×Dic3D4×D511yescharacteristic
483C2×Dic3D4×D511yescharacteristic
484Dic6—401no—
485Dic6—401no—
486C3×C8—21no—
487C3×C8—101no—
488C3⋊C8—21no—
489C3⋊C8—101no—
490C22×C5C2×D3×D411yescharacteristic
491C2×D5—21no—
492C2×D5—21no—
493C2×D5#87812yes—
494C4×C5—22no—
495C4×C5—41no—
496C4×C5—61no—
497C4×C5—61no—
498C4×C5—121no—
499C4×C5—121no—
500C4×C5C22×Dic611yescharacteristic
501C4×C5C2×#23711yescharacteristic
502Dic5—22no—
503Dic5—41no—
504Dic5—61no—
505Dic5—61no—
506Dic5—121no—
507Dic5—121no—
508Dic5#87812yes—
509C2×Q8—54no—
510C2×Q8—51no—
511C2×Q8—101no—
512C2×Q8—102no—
513C2×Q8—301no—
514C2×Q8—301no—
515C2×Q8C2×D3×D511yescharacteristic
516C22×C4—51no—
517C22×C4—101no—
518C22×C4—101no—
519M16—302no—
520C2×C8—31no—
521C2×C8—51no—
522C2×C8—102no—
523C2×C8—151no—
524C2×C8C2×D3×D511yescharacteristic
525C4⋊C4—31no—
526C4⋊C4—31no—
527C4⋊C4—51no—
528C4⋊C4—61no—
529C4⋊C4—61no—
530C4⋊C4—61no—
531C4⋊C4—101no—
532C4⋊C4—151no—
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⋊C4C2×D3×D511yescharacteristic
544C22⋊C4—151no—
545C22⋊C4—151no—
546C22⋊C4—301no—
547C22⋊C4—301no—
548C42—31no—
549C42—61no—
550C42—151no—
551C42—301no—
552C42—301no—
553C42—301no—
554C42—301no—
555C42—301no—
556C3×C5#308211yescharacteristic, complemented, Hall
557C22×C3—52no—
558C22×C3—101no—
559C22×C3—101no—
560C22×C3C2×D4×D511yescharacteristic
561C3×C4—22no—
562C3×C4—41no—
563C3×C4—52no—
564C3×C4—102no—
565C3×C4—201no—
566C3×C4C2×Q8×D511yescharacteristic
567C3×C4D5×#4111yescharacteristic
568Dic3—21no—
569Dic3—21no—
570Dic3—41no—
571Dic3—41no—
572Dic3—101no—
573Dic3—101no—
574Dic3—201no—
575Dic3—201no—
576C2×C5C2×#87811yescharacteristic
577C2×C5#576211yescharacteristic
578C2×C5#576611yescharacteristic
579D5—22no—
580C23—51no—
581Q8—21no—
582Q8—52no—
583Q8—104no—
584Q8—101no—
585Q8—1201no—
586Q8—1201no—
587Q8D5×Dic612yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—51no—
593C2×C4—52no—
594C2×C4—52no—
595C2×C4—61no—
596C2×C4—61no—
597C2×C4—104no—
598C2×C4—101no—
599C2×C4—101no—
600C2×C4—151no—
601C2×C4—151no—
602C2×C4—301no—
603C2×C4—301no—
604C2×C4—401no—
605C2×C4C22×D3×D511yescharacteristic
606C8—21no—
607C8—61no—
608C8—101no—
609C8—301no—
610C2×C3—102no—
611C2×C3D5×C22⋊Q811yescharacteristic
612C2×C3#6610411yescharacteristic
613C2×C3#6611311yescharacteristic
614C5#7877911yescharacteristic, complemented, Sylow
615C22—52no—
616C22—101no—
617C22—101no—
618C22D3×D4×D511yescharacteristic
619C4—22no—
620C4—41no—
621C4—52no—
622C4—61no—
623C4—61no—
624C4—102no—
625C4—121no—
626C4—121no—
627C4—201no—
628C4—301no—
629C4—301no—
630C4—601no—
631C4—601no—
632C4C2×D5×Dic611yescharacteristic
633C4D5×#23711yescharacteristic
634C3#1061296411yescharacteristic, complemented, Sylow
635C2—102no—
636C2D5×#87811yescharacteristic
637C2#1175408711yescharacteristic
638C2#1175410711yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenter#103D3×D5
hypocenterC3×C5#3082
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #11750892C2semidirect
4. C5×#4799C2semidirect
6. #11749359C2semidirect
7. #11749337C2semidirect
9. #11747877C2semidirect
10. #11747861C2semidirect
14. #11747303C2semidirect
15. #11747295C2semidirect
79. C3×Q8×D5Q8semidirect
131. #4799D5semidirect
257. Q8×D5Dic6semidirect
556. C3×C5#3082semidirect
614. C5#78779semidirect
634. C3#10612964semidirect

Maximal subgroups

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

subgroupindex
#117551402
#117533692
#117508922
C5×#47992
C3×D5×#1032
#117493592
#117493372
#117492082
#117478772
#117478612
#117476712
#117476472
#117474522
#117473032
#117472952
#106129643
#787795