Finite Group Databasebeta

← #14471647

Subgroups — #14471647

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65873C211yesmaximal, characteristic, complemented
2#11752590C211yesmaximal, characteristic, complemented
3#11751117C211yesmaximal, characteristic
4C4×C5×#214C211yesmaximal, characteristic, complemented
5#11749103C211yesmaximal, characteristic, complemented
6#11749068C211yesmaximal, characteristic
7#11748998C211yesmaximal, characteristic, complemented
8#11748975C211yesmaximal, characteristic
9#11747286C211yesmaximal, characteristic, complemented
10#11747240C211yesmaximal, characteristic, complemented
11#11747145C211yesmaximal, characteristic, complemented
12#11747140C211yesmaximal, characteristic, complemented
13#11746933C211yesmaximal, characteristic, complemented
14#11746926C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
16#10611351—31nomaximal, Hall
17C3×C4×C5×D4C2211yescharacteristic
18C2×#6716C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20#91764C2211yescharacteristic
21C2×C5×#214C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×D4×Dic5C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C3×#4070—21no—
26C2×C3×#683—21no—
27C3×#4036C2211yescharacteristic
28C3×#4034C2211yescharacteristic
29C3×#4024—21no—
30C3×#4024—21no—
31C3×#4016C2211yescharacteristic
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×#832C2211yescharacteristic
45C5×#810C2211yescharacteristic
46C5×#808C2211yescharacteristic
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#83637—51nomaximal, Hall
61#65902—31no—
62#65873D311yescharacteristic, complemented
63C4×C5×SD16—31no—
64#65454—31no—
65#65451—31no—
66#65311—31no—
67#65305—31no—
68#65159—31no—
69#65146—31no—
70#65089—31no—
71#65081—31no—
72#65047—31no—
73#65045—31no—
74#64986—31no—
75C8×Dic10—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×D60C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C2×C5×Dic6C2311yescharacteristic
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C2×C3×Dic10—21no—
84C2×C3×Dic10D411yescharacteristic
85C2×#1200—21no—
86C3×C5×C4⋊C4C2311yescharacteristic
87C3×C5×C22⋊C4—21no—
88C3×C42×C5C2311yescharacteristic
89#6716—22no—
90#6715—22no—
91#6714—21no—
92#6714—21no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#214—22no—
96C5×C4⋊Dic3C2311yescharacteristic
97C5×Dic3⋊C4—21no—
98C4×C5×Dic3—21no—
99C2×C5×C3⋊C8C2311yescharacteristic
100C2×C5×C3⋊C8C2311yescharacteristic
101C3×C22⋊Dic5—21no—
102C3×C22⋊Dic5—21no—
103C3×C4⋊Dic5—21no—
104C3×C4⋊Dic5D411yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×#683D411yescharacteristic
112C3×#683D411yescharacteristic
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×#554—51no—
123#5584—51no—
124#5093—51no—
125#5084—51no—
126#5068—51no—
127#5068—51no—
128#5063—51no—
129#5063—51no—
130Q8×C3⋊C8—51no—
131#5019—51no—
132C4×#214—51no—
133C4×#214D511yescharacteristic, complemented
134#5016—51no—
135#5016—51no—
136C4×#213—51no—
137C2×C5×SD16—31no—
138C4×C5×Q8—31no—
139C4×C5×D4C2×D311yescharacteristic
140#4093—31no—
141#4090—31no—
142D4×Dic5C2×D311yescharacteristic
143D4×Dic5C2×D311yescharacteristic
144C2×#687—31no—
145C2×#686—31no—
146#4070—21no—
147C2×#683—21no—
148#4044—61no—
149#4042—61no—
150#4039—31no—
151#4036C2×D311yescharacteristic
152#4034C2×D311yescharacteristic
153#4033—31no—
154#4024—21no—
155#4024—21no—
156#4022—61no—
157#4021—31no—
158#4018—61no—
159#4016C2×D311yescharacteristic
160C4×Dic10C2×D311yescharacteristic
161C5×#106—31no—
162C5×#103—31no—
163C5×#102—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#3360—151noSylow
181C23×C3×C5—21no—
182C22×D15—21no—
183C3×C5×D4—21no—
184C3×C5×D4#4112yes—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—81no—
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—21no—
191D60—21no—
192D60—21no—
193Dic30—21no—
194Dic30—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C5×Dic6—21no—
198C5×Dic6—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—42no—
202C2×C3×Dic5—81no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C3×Dic10—22no—
208C3×Dic10—81no—
209#1200—42no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C5×C3⋊C8—21no—
213C5×C3⋊C8—21no—
214C3×C4⋊Q8—51no—
215C3×#125—51no—
216C3×#125—51no—
217C3×C22⋊Q8—101no—
218C3×C22⋊Q8—101no—
219C3×C22⋊Q8—101no—
220C3×C4×Q8—51no—
221C3×C4×D4—51no—
222C3×C4×D4—51no—
223C3×C4×D4C2×D511yescharacteristic
224C2×C3×C4⋊C4—101no—
225#946—101no—
226C2×#214—51no—
227C2×#214C2×D511yescharacteristic
228C2×#213—51no—
229#898—101no—
230#898—101no—
231#892—101no—
232#875—51no—
233#875—51no—
234C4×D12—51no—
235#869—51no—
236C4×Dic6—51no—
237C4×Dic6C2×D511yescharacteristic
238#832C2×D511yescharacteristic
239#810—51no—
240#810—51no—
241#810—51no—
242#810—51no—
243#810—51no—
244#810C2×D511yescharacteristic
245#809—51no—
246#809—51no—
247#809—51no—
248#808—51no—
249#808C2×D511yescharacteristic
250#807—51no—
251C4⋊(C3⋊C8)—51no—
252C4⋊(C3⋊C8)—51no—
253C4⋊(C3⋊C8)—51no—
254C4×C3⋊C8—51no—
255C4×C3⋊C8—51no—
256C4×C3⋊C8C2×D511yescharacteristic
257C2×C5×Q8—31no—
258C2×C5×D4C22×D311yescharacteristic
259C22×C4×C5—21no—
260C22×Dic5—21no—
261C22×Dic5—21no—
262C2×D20—31no—
263C2×C4×D5—61no—
264C2×Dic10—21no—
265C2×Dic10—31no—
266C2×Dic10#6711yescharacteristic
267C5×SD16—62no—
268C2×C5×C8—31no—
269C2×C5×C8—31no—
270C5×C4⋊C4—31no—
271C5×C4⋊C4—61no—
272C5×C4⋊C4C22×D311yescharacteristic
273C5×C22⋊C4—21no—
274C42×C5—61no—
275C42×C5C22×D311yescharacteristic
276C22⋊Dic5—21no—
277C22⋊Dic5—21no—
278#687—62no—
279#686—62no—
280#685—61no—
281#685—61no—
282#685—61no—
283#685—61no—
284#685—61no—
285C4⋊Dic5—21no—
286C4⋊Dic5#6711yescharacteristic
287C4⋊Dic5C22×D311yescharacteristic
288C4⋊Dic5C22×D311yescharacteristic
289#683—21no—
290#683—21no—
291#683—21no—
292#683—21no—
293#683—61no—
294#683—61no—
295#683—61no—
296#683#6711yescharacteristic
297#683#6711yescharacteristic
298C4×Dic5—61no—
299C4×Dic5C22×D311yescharacteristic
300C4×Dic5C22×D311yescharacteristic
301C2×#168—31no—
302C2×#168—31no—
303#556—151no—
304#554—51no—
305#488—151no—
306#488—151no—
307#487—151no—
308#479—151no—
309#479—151no—
310#476—151no—
311#463—151no—
312#463—151no—
313#461—151no—
314C8×Q8—151no—
315C4×SD16—31no—
316C4×SD16—151no—
317C4×D8—151no—
318C22×C3×C5—22no—
319C22×C3×C5—41no—
320C22×C3×C5—41no—
321C22×C3×C5C22×D411yescharacteristic
322C2×D15—41no—
323C2×D15—41no—
324C2×D15—41no—
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327C3×C4×C5—41no—
328C3×C4×C5C2×#4111yescharacteristic
329C3×C4×C52−1+411yescharacteristic
330Dic15—41no—
331C3×Dic5—21no—
332C3×Dic5—21no—
333C3×Dic5—21no—
334C3×Dic5—41no—
335C3×Dic5—41no—
336C3×Dic5#13512yes—
337C5×Dic3—41no—
338C5×Dic3—41no—
339C2×C3×Q8—51no—
340C2×C3×Q8—101no—
341C2×C3×D4C22×D511yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—101no—
344C22×C3×C4—101no—
345C2×D12—51no—
346C2×C4×D3—101no—
347C2×Dic6—51no—
348C2×Dic6C22×D511yescharacteristic
349C3×C4⋊C4—51no—
350C3×C4⋊C4—51no—
351C3×C4⋊C4—51no—
352C3×C4⋊C4—51no—
353C3×C4⋊C4—51no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4—101no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4C22×D511yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—101no—
362C3×C22⋊C4—101no—
363C3×C42—51no—
364C3×C42—51no—
365C3×C42C22×D511yescharacteristic
366#214—22no—
367#214—102no—
368#213—102no—
369(C2×D3)⋊C4—101no—
370(C2×D3)⋊C4—101no—
371(C2×D3)⋊C4—101no—
372(C2×D3)⋊C4—101no—
373(C2×D3)⋊C4—101no—
374C4⋊Dic3—101no—
375C4⋊Dic3—101no—
376C4⋊Dic3C22×D511yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—101no—
379C4×Dic3—21no—
380C4×Dic3—101no—
381C2×C3⋊C8—51no—
382C2×C3⋊C8—51no—
383C2×C3⋊C8C22×D511yescharacteristic
384C2×C3⋊C8C22×D511yescharacteristic
385C23×C5—21no—
386C22×D5—61no—
387C5×Q8—61no—
388C5×Q8—61no—
389C5×D4—21no—
390C5×D4#23912yes—
391C2×C4×C5—21no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—81no—
395C2×C4×C5C2×#6711yescharacteristic
396C2×C4×C5C2×#6711yescharacteristic
397C2×C4×C5C23×D311yescharacteristic
398C2×Dic5—21no—
399C2×Dic5—21no—
400C2×Dic5—42no—
401C2×Dic5—61no—
402C2×Dic5—81no—
403C2×Dic5C2×#6711yescharacteristic
404C2×Dic5C2×#6711yescharacteristic
405C2×Dic5C2×#6711yescharacteristic
406C2×Dic5C2×#6711yescharacteristic
407D20—61no—
408D20—61no—
409C4×D5—122no—
410Dic10—22no—
411Dic10—61no—
412Dic10—61no—
413Dic10—81no—
414C5×C8—61no—
415C5×C8—61no—
416#168—61no—
417#168—61no—
418C2×SD16—31no—
419C2×SD16—151no—
420C2×D8—151no—
421C4⋊Q8—51no—
422C4⋊Q8—151no—
423#126—301no—
424#126—301no—
425#125—51no—
426#125—51no—
427#124—151no—
428#124—151no—
429C22⋊Q8—101no—
430C22⋊Q8—101no—
431C22⋊Q8—101no—
432C22⋊Q8—301no—
433C4×Q8—31no—
434C4×Q8—51no—
435C4×Q8—151no—
436C4×D4—51no—
437C4×D4—51no—
438C4×D4—151no—
439C4×D4D3×D511yescharacteristic
440#117—301no—
441C2×C4⋊C4—101no—
442#107—151no—
443#106—31no—
444#106—151no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—31no—
449#103—151no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#102—31no—
455#102—151no—
456#102—151no—
457#102—151no—
458C4×C8—31no—
459C4×C8—151no—
460C4×C8—151no—
461C2×C3×C5—42no—
462C2×C3×C5#54811yescharacteristic
463C2×C3×C5C2×#13511yescharacteristic
464C2×C3×C5#57711yescharacteristic
465D15—81no—
466C23×C3—21no—
467C22×D3—101no—
468C3×Q8—102no—
469C3×Q8—401no—
470C3×D4—21no—
471C3×D4#70912yes—
472C2×C3×C4—21no—
473C2×C3×C4—51no—
474C2×C3×C4—51no—
475C2×C3×C4—51no—
476C2×C3×C4—51no—
477C2×C3×C4—81no—
478C2×C3×C4—101no—
479C2×C3×C4—101no—
480C2×C3×C4—202no—
481C2×C3×C4—401no—
482C2×C3×C4D4×D511yescharacteristic
483C2×C3×C4D4×D511yescharacteristic
484C2×C3×C4C23×D511yescharacteristic
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—101no—
488D12—101no—
489D12—101no—
490C4×D3—202no—
491Dic6—21no—
492Dic6—21no—
493Dic6—101no—
494Dic6—101no—
495C3⋊C8—21no—
496C3⋊C8—21no—
497C3⋊C8—101no—
498C3⋊C8—101no—
499C22×C5—22no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5C22×#6711yescharacteristic
503C2×D5—121no—
504C2×D5—121no—
505C2×D5—121no—
506C4×C5—21no—
507C4×C5—21no—
508C4×C5—41no—
509C4×C5—121no—
510C4×C5—121no—
511C4×C5C2×#23911yescharacteristic
512C4×C5#100711yescharacteristic
513Dic5—21no—
514Dic5—21no—
515Dic5—21no—
516Dic5—41no—
517Dic5—41no—
518Dic5—121no—
519Dic5#95012yes—
520C2×Q8—31no—
521C2×Q8—51no—
522C2×Q8—101no—
523C2×Q8—151no—
524C2×D4—151no—
525C2×D4C2×D3×D511yescharacteristic
526C22×C4—21no—
527C22×C4—101no—
528C22×C4—101no—
529C22×C4—301no—
530SD16—62no—
531SD16—302no—
532D8—302no—
533C2×C8—31no—
534C2×C8—31no—
535C2×C8—151no—
536C2×C8—151no—
537C4⋊C4—31no—
538C4⋊C4—51no—
539C4⋊C4—51no—
540C4⋊C4—51no—
541C4⋊C4—51no—
542C4⋊C4—51no—
543C4⋊C4—61no—
544C4⋊C4—101no—
545C4⋊C4—101no—
546C4⋊C4—101no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C22⋊C4—21no—
554C22⋊C4—101no—
555C22⋊C4—101no—
556C22⋊C4—301no—
557C22⋊C4—301no—
558C22⋊C4—301no—
559C22⋊C4—301no—
560C22⋊C4—301no—
561C42—51no—
562C42—51no—
563C42—61no—
564C42—301no—
565C42C2×D3×D511yescharacteristic
566C3×C5#336011yescharacteristic, complemented, Hall
567C22×C3—22no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3C2×D4×D511yescharacteristic
571C2×D3—201no—
572C2×D3—201no—
573C2×D3—201no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—41no—
577C3×C4—52no—
578C3×C4—101no—
579C3×C4—101no—
580C3×C4—101no—
581C3×C4—201no—
582C3×C4—201no—
583C3×C4C2×#70911yescharacteristic
584C3×C4#415011yescharacteristic
585Dic3—41no—
586Dic3—41no—
587Dic3—201no—
588C2×C5—42no—
589C2×C5#581711yescharacteristic
590C2×C5C2×#95011yescharacteristic
591C2×C5#583611yescharacteristic
592D5—241no—
593C23—21no—
594C23—301no—
595Q8—61no—
596Q8—61no—
597Q8—102no—
598Q8—301no—
599Q8—301no—
600Q8—401no—
601D4—21no—
602D4—301no—
603D4—301no—
604D4#676912yes—
605C2×C4—21no—
606C2×C4—51no—
607C2×C4—51no—
608C2×C4—51no—
609C2×C4—51no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—81no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—202no—
616C2×C4—301no—
617C2×C4—401no—
618C2×C4—602no—
619C2×C4D5×#6711yescharacteristic
620C2×C4D5×#6711yescharacteristic
621C2×C4C22×D3×D511yescharacteristic
622C8—61no—
623C8—61no—
624C8—301no—
625C8—301no—
626C2×C3—42no—
627C2×C3#6588611yescharacteristic
628C2×C3#6609611yescharacteristic
629C2×C3D5×#13511yescharacteristic
630D3—401no—
631C5#8363711yescharacteristic, complemented, Sylow
632C22—22no—
633C22—41no—
634C22—41no—
635C22—601no—
636C22—601no—
637C22—601no—
638C22C2×D5×#6711yescharacteristic
639C4—21no—
640C4—21no—
641C4—41no—
642C4—52no—
643C4—101no—
644C4—101no—
645C4—101no—
646C4—121no—
647C4—121no—
648C4—201no—
649C4—201no—
650C4—601no—
651C4#9200411yescharacteristic
652C4C2×#676911yescharacteristic
653C3#1061135111yescharacteristic, complemented, Sylow
654C2—42no—
655C2—1201no—
656C2#1175432111yescharacteristic
657C2#1175470711yescharacteristic
658C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65873C2semidirect
2. #11752590C2semidirect
4. C4×C5×#214C2semidirect
5. #11749103C2semidirect
7. #11748998C2semidirect
9. #11747286C2semidirect
10. #11747240C2semidirect
11. #11747145C2semidirect
12. #11747140C2semidirect
13. #11746933C2semidirect
14. #11746926C2semidirect
15. C3⋊C8×Dic10C2semidirect
62. #65873D3semidirect
133. C4×#214D5semidirect
566. C3×C5#3360semidirect
631. C5#83637semidirect
653. C3#10611351semidirect

Maximal subgroups

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

subgroupindex
C3×#658732
#117525902
#117511172
C4×C5×#2142
#117491032
#117490682
#117489982
#117489752
#117472862
#117472402
#117471452
#117471402
#117469332
#117469262
C3⋊C8×Dic102
#106113513
#836375