Finite Group Databasebeta

← #14472123

Subgroups — #14472123

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65903C211yesmaximal, characteristic, complemented
2#11752590C211yesmaximal, characteristic
3#11751129C211yesmaximal, characteristic
4C4×C5×#216C211yesmaximal, characteristic, complemented
5#11749350C211yesmaximal, characteristic, complemented
6#11749314C211yesmaximal, characteristic
7#11749244C211yesmaximal, characteristic, complemented
8#11749221C211yesmaximal, characteristic
9#11747288C211yesmaximal, characteristic, complemented
10#11747238C211yesmaximal, characteristic
11#11747145C211yesmaximal, characteristic
12#11747140C211yesmaximal, characteristic, complemented
13#11746933C211yesmaximal, characteristic
14#11746926C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
16#10611431—31nomaximal, Hall
17C3×C4×C5×Q8C2211yescharacteristic
18C2×#6718C2211yescharacteristic
19C2×#6717C2211yescharacteristic
20#91764C2211yescharacteristic
21C2×C5×#216C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C3×Q8×Dic5C2211yescharacteristic
25C3×#4036—21no—
26C3×#4036C2211yescharacteristic
27C3×#4034—21no—
28C3×#4034C2211yescharacteristic
29C3×#4016—21no—
30C3×#4016C2211yescharacteristic
31C3×C4×Dic10—21no—
32C3×C4×Dic10C2211yescharacteristic
33#91418C2211yescharacteristic
34#91411—21no—
35#91403—21no—
36#91380—21no—
37#91376C2211yescharacteristic
38#91375C2211yescharacteristic
39#91345—21no—
40#91333C2211yescharacteristic
41#91094C2211yescharacteristic
42#91093C2211yescharacteristic
43C4⋊(C3⋊#168)C2211yescharacteristic
44C5×#835C2211yescharacteristic
45C5×#810C2211yescharacteristic
46C5×#807C2211yescharacteristic
47C4×C5×C3⋊C8C2211yescharacteristic
48#90989C2211yescharacteristic
49#90986C2211yescharacteristic
50#90982C2211yescharacteristic
51#90982C2211yescharacteristic
52#90974C2211yescharacteristic
53#90974C2211yescharacteristic
54#90972C2211yescharacteristic
55#90972C2211yescharacteristic
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic
58Dic5×C3⋊C8C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83689—51nomaximal, Hall
61#65903D311yescharacteristic, complemented
62#65902—31no—
63C4×C5×Q16—31no—
64#65474—31no—
65#65471—31no—
66#65317—31no—
67#65311—31no—
68#65179—31no—
69#65166—31no—
70#65089—31no—
71#65081—31no—
72#65079—31no—
73#65077—31no—
74#64986—31no—
75C8×Dic10—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×D60C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×Dic6C2311yescharacteristic
80C2×C3×Dic10—21no—
81C2×C3×Dic10D411yescharacteristic
82C2×#1200—21no—
83C3×C5×C4⋊C4—21no—
84C3×C5×C4⋊C4C2311yescharacteristic
85C3×C42×C5—21no—
86C3×C42×C5C2311yescharacteristic
87#6718—22no—
88#6717—22no—
89#6714—21no—
90#6714—21no—
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93C5×#216—22no—
94C5×C4⋊Dic3C2311yescharacteristic
95C5×Dic3⋊C4—21no—
96C4×C5×Dic3—21no—
97C2×C5×C3⋊C8C2311yescharacteristic
98C2×C5×C3⋊C8C2311yescharacteristic
99C3×C4⋊Dic5—21no—
100C3×C4⋊Dic5—21no—
101C3×C4⋊Dic5—21no—
102C3×C4⋊Dic5D411yescharacteristic
103C3×C4⋊Dic5C2311yescharacteristic
104C3×C4⋊Dic5C2311yescharacteristic
105C3×#683—21no—
106C3×#683—21no—
107C3×#683—21no—
108C3×#683—21no—
109C3×#683D411yescharacteristic
110C3×#683D411yescharacteristic
111C3×C4×Dic5—21no—
112C3×C4×Dic5—21no—
113C3×C4×Dic5C2311yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115#6669—21no—
116#6668—21no—
117#6668—21no—
118#6667—21no—
119#6667—21no—
120#6667—21no—
121Dic3×Dic5—21no—
122C3×#557—51no—
123#5584—51no—
124#5093—51no—
125#5087—51no—
126#5068—51no—
127#5068—51no—
128#5063—51no—
129#5063—51no—
130#5031—51no—
131C4×#216—51no—
132C4×#216D511yescharacteristic, complemented
133#5028—51no—
134#5028—51no—
135C4×#215—51no—
136Q8×C3⋊C8—51no—
137C2×C5×Q16—31no—
138C4×C5×Q8—31no—
139C4×C5×Q8C2×D311yescharacteristic
140#4093—31no—
141Q8×Dic5C2×D311yescharacteristic
142Q8×Dic5C2×D311yescharacteristic
143#4090—31no—
144C2×#689—31no—
145C2×#688—31no—
146#4044—61no—
147#4042—61no—
148#4039—31no—
149#4036—21no—
150#4036C2×D311yescharacteristic
151#4034—21no—
152#4034C2×D311yescharacteristic
153#4033—31no—
154#4022—61no—
155#4021—31no—
156#4018—61no—
157#4016—21no—
158#4016C2×D311yescharacteristic
159C4×Dic10—21no—
160C4×Dic10C2×D311yescharacteristic
161C5×#107—31no—
162C5×#103—31no—
163C5×#103—31no—
164C4×C5×C8—31no—
165#3967—31no—
166#3967—31no—
167#3953—31no—
168#3953—31no—
169#3948—31no—
170#3948—31no—
171#3946—31no—
172#3946—31no—
173C8×Dic5—31no—
174C8×Dic5—31no—
175#3942—31no—
176#3941—31no—
177#3940—31no—
178#3939—31no—
179C4⋊#168—31no—
180#3364—151noSylow
181C22×D15—21no—
182C3×C5×Q8—21no—
183C3×C5×Q8#4112yes—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2411yescharacteristic
189C2×Dic15—21no—
190D60—21no—
191D60—21no—
192Dic30—21no—
193Dic30—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C5×Dic6—21no—
197C5×Dic6—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C3×Dic10—22no—
205C3×Dic10—42no—
206#1200—42no—
207C3⋊#168—21no—
208C3⋊#168—21no—
209C5×C3⋊C8—21no—
210C5×C3⋊C8—21no—
211C3×C4⋊Q8—51no—
212C3×C4⋊Q8—101no—
213C3×#125—51no—
214C3×#125—51no—
215C3×#125—101no—
216C3×#125—101no—
217C3×C4×Q8—51no—
218C3×C4×Q8—51no—
219C3×C4×Q8—51no—
220C3×C4×Q8—101no—
221C3×C4×Q8C2×D511yescharacteristic
222#946—101no—
223C2×#216—51no—
224C2×#216C2×D511yescharacteristic
225C2×#215—51no—
226#898—101no—
227#898—101no—
228#892—101no—
229#875—51no—
230#875—51no—
231C4×D12—51no—
232#869—51no—
233C4×Dic6—51no—
234C4×Dic6C2×D511yescharacteristic
235#835C2×D511yescharacteristic
236#810—51no—
237#810—51no—
238#810—51no—
239#810—51no—
240#810—51no—
241#810C2×D511yescharacteristic
242#809—51no—
243#809—51no—
244#809—51no—
245#808—51no—
246#807—51no—
247#807C2×D511yescharacteristic
248C4⋊(C3⋊C8)—51no—
249C4⋊(C3⋊C8)—51no—
250C4⋊(C3⋊C8)—51no—
251C4×C3⋊C8—51no—
252C4×C3⋊C8—51no—
253C4×C3⋊C8C2×D511yescharacteristic
254C2×C5×Q8—31no—
255C2×C5×Q8C22×D311yescharacteristic
256C2×D20—31no—
257C2×C4×D5—61no—
258C2×Dic10—21no—
259C2×Dic10—31no—
260C2×Dic10#6711yescharacteristic
261C5×Q16—62no—
262C2×C5×C8—31no—
263C2×C5×C8—31no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4—31no—
266C5×C4⋊C4—61no—
267C5×C4⋊C4C22×D311yescharacteristic
268C42×C5—21no—
269C42×C5—61no—
270C42×C5C22×D311yescharacteristic
271#689—62no—
272#688—62no—
273#685—61no—
274#685—61no—
275#685—61no—
276#685—61no—
277#685—61no—
278C4⋊Dic5—21no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5#6711yescharacteristic
282C4⋊Dic5C22×D311yescharacteristic
283C4⋊Dic5C22×D311yescharacteristic
284#683—21no—
285#683—21no—
286#683—21no—
287#683—21no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683#6711yescharacteristic
292#683#6711yescharacteristic
293C4×Dic5—21no—
294C4×Dic5—21no—
295C4×Dic5—61no—
296C4×Dic5C22×D311yescharacteristic
297C4×Dic5C22×D311yescharacteristic
298C2×#168—31no—
299C2×#168—31no—
300#557—51no—
301#556—151no—
302#488—151no—
303#488—151no—
304#487—151no—
305#479—151no—
306#479—151no—
307#474—151no—
308#464—151no—
309#464—151no—
310#462—151no—
311C8×Q8—151no—
312C4×Q16—31no—
313C4×Q16—151no—
314C4×SD16—151no—
315C22×C3×C5C22×D411yescharacteristic
316C2×D15—41no—
317C2×D15—41no—
318C2×D15—41no—
319C3×C4×C5—22no—
320C3×C4×C5—21no—
321C3×C4×C5—21no—
322C3×C4×C5—41no—
323C3×C4×C5C2×#4111yescharacteristic
324C3×C4×C52−1+411yescharacteristic
325Dic15—41no—
326C3×Dic5—21no—
327C3×Dic5—21no—
328C3×Dic5—21no—
329C3×Dic5—41no—
330C3×Dic5—41no—
331C3×Dic5#13512yes—
332C5×Dic3—41no—
333C5×Dic3—41no—
334C2×C3×Q8—51no—
335C2×C3×Q8—101no—
336C2×C3×Q8C22×D511yescharacteristic
337C2×D12—51no—
338C2×C4×D3—101no—
339C2×Dic6—51no—
340C2×Dic6C22×D511yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—51no—
343C3×C4⋊C4—51no—
344C3×C4⋊C4—51no—
345C3×C4⋊C4—51no—
346C3×C4⋊C4—51no—
347C3×C4⋊C4—101no—
348C3×C4⋊C4—101no—
349C3×C4⋊C4—101no—
350C3×C4⋊C4—101no—
351C3×C4⋊C4—101no—
352C3×C4⋊C4—101no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4C22×D511yescharacteristic
355C3×C42—21no—
356C3×C42—51no—
357C3×C42—51no—
358C3×C42—101no—
359C3×C42—101no—
360C3×C42C22×D511yescharacteristic
361#216—22no—
362#216—102no—
363#215—102no—
364(C2×D3)⋊C4—101no—
365(C2×D3)⋊C4—101no—
366(C2×D3)⋊C4—101no—
367(C2×D3)⋊C4—101no—
368(C2×D3)⋊C4—101no—
369C4⋊Dic3—101no—
370C4⋊Dic3—101no—
371C4⋊Dic3C22×D511yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—101no—
374C4×Dic3—21no—
375C4×Dic3—101no—
376C2×C3⋊C8—51no—
377C2×C3⋊C8—51no—
378C2×C3⋊C8C22×D511yescharacteristic
379C2×C3⋊C8C22×D511yescharacteristic
380C22×D5—61no—
381C5×Q8—21no—
382C5×Q8—61no—
383C5×Q8—61no—
384C5×Q8#23912yes—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—61no—
388C2×C4×C5—61no—
389C2×C4×C5C2×#6711yescharacteristic
390C2×C4×C5C2×#6711yescharacteristic
391C2×C4×C5C23×D311yescharacteristic
392C2×Dic5—21no—
393C2×Dic5—21no—
394C2×Dic5—61no—
395C2×Dic5C2×#6711yescharacteristic
396C2×Dic5C2×#6711yescharacteristic
397C2×Dic5C2×#6711yescharacteristic
398C2×Dic5C2×#6711yescharacteristic
399D20—61no—
400D20—61no—
401C4×D5—122no—
402Dic10—22no—
403Dic10—42no—
404Dic10—61no—
405Dic10—61no—
406C5×C8—61no—
407C5×C8—61no—
408#168—61no—
409#168—61no—
410C2×Q16—31no—
411C2×Q16—151no—
412C2×SD16—151no—
413C4⋊Q8—51no—
414C4⋊Q8—101no—
415C4⋊Q8—151no—
416#126—301no—
417#126—301no—
418#125—51no—
419#125—51no—
420#125—101no—
421#125—101no—
422#124—151no—
423#124—151no—
424C22⋊Q8—301no—
425C4×Q8—31no—
426C4×Q8—51no—
427C4×Q8—51no—
428C4×Q8—51no—
429C4×Q8—101no—
430C4×Q8—151no—
431C4×Q8D3×D511yescharacteristic
432C4×D4—151no—
433#117—301no—
434#107—31no—
435#107—151no—
436#106—151no—
437C4⋊C8—151no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440#103—31no—
441#103—31no—
442#103—151no—
443#103—151no—
444#103—151no—
445#103—151no—
446#103—151no—
447#102—151no—
448#102—151no—
449#102—151no—
450C4×C8—31no—
451C4×C8—151no—
452C4×C8—151no—
453C2×C3×C5#54811yescharacteristic
454C2×C3×C5C2×#13511yescharacteristic
455C2×C3×C5#57811yescharacteristic
456D15—81no—
457C22×D3—101no—
458C3×Q8—21no—
459C3×Q8—102no—
460C3×Q8—202no—
461C3×Q8#70912yes—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—51no—
465C2×C3×C4—51no—
466C2×C3×C4—51no—
467C2×C3×C4—51no—
468C2×C3×C4—101no—
469C2×C3×C4—101no—
470C2×C3×C4D4×D511yescharacteristic
471C2×C3×C4D4×D511yescharacteristic
472C2×C3×C4C23×D511yescharacteristic
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—101no—
476D12—101no—
477D12—101no—
478C4×D3—202no—
479Dic6—21no—
480Dic6—21no—
481Dic6—101no—
482Dic6—101no—
483C3⋊C8—21no—
484C3⋊C8—21no—
485C3⋊C8—101no—
486C3⋊C8—101no—
487C22×C5C22×#6711yescharacteristic
488C2×D5—121no—
489C2×D5—121no—
490C2×D5—121no—
491C4×C5—22no—
492C4×C5—21no—
493C4×C5—21no—
494C4×C5—41no—
495C4×C5—121no—
496C4×C5—121no—
497C4×C5C2×#23911yescharacteristic
498C4×C5#100711yescharacteristic
499Dic5—21no—
500Dic5—21no—
501Dic5—21no—
502Dic5—41no—
503Dic5—41no—
504Dic5—121no—
505Dic5#95012yes—
506C2×Q8—31no—
507C2×Q8—51no—
508C2×Q8—101no—
509C2×Q8—151no—
510C2×Q8C2×D3×D511yescharacteristic
511C2×D4—151no—
512C22×C4—301no—
513Q16—62no—
514Q16—302no—
515SD16—302no—
516C2×C8—31no—
517C2×C8—31no—
518C2×C8—151no—
519C2×C8—151no—
520C4⋊C4—21no—
521C4⋊C4—31no—
522C4⋊C4—51no—
523C4⋊C4—51no—
524C4⋊C4—51no—
525C4⋊C4—51no—
526C4⋊C4—51no—
527C4⋊C4—61no—
528C4⋊C4—101no—
529C4⋊C4—101no—
530C4⋊C4—101no—
531C4⋊C4—101no—
532C4⋊C4—101no—
533C4⋊C4—101no—
534C4⋊C4—101no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4C2×D3×D511yescharacteristic
539C22⋊C4—301no—
540C22⋊C4—301no—
541C22⋊C4—301no—
542C22⋊C4—301no—
543C22⋊C4—301no—
544C42—21no—
545C42—51no—
546C42—51no—
547C42—61no—
548C42—101no—
549C42—101no—
550C42—301no—
551C42C2×D3×D511yescharacteristic
552C3×C5#336411yescharacteristic, complemented, Hall
553C22×C3C2×D4×D511yescharacteristic
554C2×D3—201no—
555C2×D3—201no—
556C2×D3—201no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—22no—
560C3×C4—41no—
561C3×C4—52no—
562C3×C4—101no—
563C3×C4—101no—
564C3×C4—101no—
565C3×C4—201no—
566C3×C4—201no—
567C3×C4C2×#70911yescharacteristic
568C3×C4#415011yescharacteristic
569Dic3—41no—
570Dic3—41no—
571Dic3—201no—
572C2×C5#581711yescharacteristic
573C2×C5C2×#95011yescharacteristic
574C2×C5#583811yescharacteristic
575D5—241no—
576C23—301no—
577Q8—21no—
578Q8—61no—
579Q8—61no—
580Q8—102no—
581Q8—202no—
582Q8—301no—
583Q8—301no—
584Q8#676912yes—
585D4—301no—
586D4—301no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—51no—
590C2×C4—51no—
591C2×C4—51no—
592C2×C4—51no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—101no—
596C2×C4—101no—
597C2×C4—301no—
598C2×C4—602no—
599C2×C4D5×#6711yescharacteristic
600C2×C4D5×#6711yescharacteristic
601C2×C4C22×D3×D511yescharacteristic
602C8—61no—
603C8—61no—
604C8—301no—
605C8—301no—
606C2×C3#6588611yescharacteristic
607C2×C3#6610011yescharacteristic
608C2×C3D5×#13511yescharacteristic
609D3—401no—
610C5#8368911yescharacteristic, complemented, Sylow
611C22—601no—
612C22—601no—
613C22—601no—
614C22C2×D5×#6711yescharacteristic
615C4—21no—
616C4—22no—
617C4—21no—
618C4—41no—
619C4—52no—
620C4—101no—
621C4—101no—
622C4—101no—
623C4—121no—
624C4—121no—
625C4—201no—
626C4—201no—
627C4—601no—
628C4#9200411yescharacteristic
629C4C2×#676911yescharacteristic
630C3#1061143111yescharacteristic, complemented, Sylow
631C2—1201no—
632C2#1175432111yescharacteristic
633C2#1175510111yescharacteristic
634C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65903C2semidirect
4. C4×C5×#216C2semidirect
5. #11749350C2semidirect
7. #11749244C2semidirect
9. #11747288C2semidirect
12. #11747140C2semidirect
14. #11746926C2semidirect
15. C3⋊C8×Dic10C2semidirect
61. #65903D3semidirect
132. C4×#216D5semidirect
552. C3×C5#3364semidirect
610. C5#83689semidirect
630. C3#10611431semidirect

Maximal subgroups

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

subgroupindex
C3×#659032
#117525902
#117511292
C4×C5×#2162
#117493502
#117493142
#117492442
#117492212
#117472882
#117472382
#117471452
#117471402
#117469332
#117469262
C3⋊C8×Dic102
#106114313
#836895