Finite Group Databasebeta

← #14436207

Subgroups — #14436207

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65908C211yesmaximal, characteristic
2#11752511C211yesmaximal, characteristic, complemented
3C4×#6718C211yesmaximal, characteristic, complemented
4C5×#5030C211yesmaximal, characteristic, complemented
5#11749350C211yesmaximal, characteristic, complemented
6#11749329C211yesmaximal, characteristic, complemented
7#11749295C211yesmaximal, characteristic
8#11749294C211yesmaximal, characteristic
9#11747414C211yesmaximal, characteristic, complemented
10#11747392C211yesmaximal, characteristic, complemented
11#11747340C211yesmaximal, characteristic, complemented
12#11747168C211yesmaximal, characteristic, complemented
13#11747052C211yesmaximal, characteristic, complemented
14C4×#6655C211yesmaximal, characteristic, complemented
15#11746874C211yesmaximal, characteristic, complemented
16#10611580—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#216C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C3×#4039—21no—
25C3×#4039C2211yescharacteristic
26C3×D5×C4⋊C4—21no—
27C3×D5×C4⋊C4C2211yescharacteristic
28C3×C4×D20—21no—
29C3×C4×D20C2211yescharacteristic
30C3×#4018—21no—
31C3×#4018C2211yescharacteristic
32#91388C2211yescharacteristic
33#91382—21no—
34#91379—21no—
35#91376C2211yescharacteristic
36#91366—21no—
37#91363—21no—
38#91360C2211yescharacteristic
39#91359C2211yescharacteristic
40C2×#6657C2211yescharacteristic
41C2×#6655C2211yescharacteristic
42#91119C2211yescharacteristic
43#91094C2211yescharacteristic
44#91091C2211yescharacteristic
45C4×C3⋊#168C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C5×#808C2211yescharacteristic
49C5×#803C2211yescharacteristic
50#90990C2211yescharacteristic
51#90986C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90974C2211yescharacteristic
55#90972C2211yescharacteristic
56#90965C2211yescharacteristic
57#90964C2211yescharacteristic
58#90955C2211yescharacteristic
59#90955C2211yescharacteristic
60#82575—51nomaximal, Hall
61#65917—31no—
62#65908D311yescharacteristic
63C5×#441—31no—
64#65476—31no—
65#65471—31no—
66C4×#689—31no—
67C4×#688—31no—
68#65160—31no—
69#65151—31no—
70#65107—31no—
71#65099—31no—
72#65098—31no—
73#65085—31no—
74#64999—31no—
75#64998—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C2×C5×Dic6C2311yescharacteristic
79C3×#713—22no—
80C3×#713—22no—
81C2×C3×D20—21no—
82C2×C3×D20C2311yescharacteristic
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C42×C5—21no—
91C3×C42×C5C2311yescharacteristic
92#6718—22no—
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95C4×Dic15—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#216—22no—
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C4×C5×Dic3—21no—
102C2×C5×C3⋊C8C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C3×#685—21no—
105C3×#685—21no—
106C3×#685D411yescharacteristic
107C3×#685D411yescharacteristic
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×#683D411yescharacteristic
112C3×#683D411yescharacteristic
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6669—21no—
119#6668—21no—
120#6668—21no—
121#6665—21no—
122#6665—21no—
123#6657—22no—
124#6655—22no—
125C3×#520—51no—
126#5518—51no—
127#5239—51no—
128#5239—51no—
129#5031—51no—
130#5030D511yescharacteristic, complemented
131C4×#216—51no—
132#5022—51no—
133#5019—51no—
134#5018—51no—
135C4×#214—51no—
136#5009—51no—
137#5000—51no—
138#4971—51no—
139#4970—51no—
140C2×#713C2×D311yescharacteristic
141C2×C5×Q16—31no—
142C4×C5×Q8—31no—
143C4×C5×Q8C2×D311yescharacteristic
144#4092—31no—
145Q8×Dic5C2×D311yescharacteristic
146#4090—31no—
147C2×#689—31no—
148C2×#688—31no—
149C2×#677—31no—
150#4044—61no—
151#4043—31no—
152#4039—21no—
153#4039C2×D311yescharacteristic
154D5×C4⋊C4—21no—
155D5×C4⋊C4C2×D311yescharacteristic
156#4036—31no—
157#4035—61no—
158#4022—61no—
159C4×D20—21no—
160C4×D20C2×D311yescharacteristic
161#4018—21no—
162#4018C2×D311yescharacteristic
163#4016—61no—
164C4×Dic10—31no—
165C5×#106—31no—
166C5×#103—31no—
167C5×#103—31no—
168C5×#97—31no—
169#3967—31no—
170#3967—31no—
171#3953—31no—
172#3952—31no—
173#3952—31no—
174#3950—31no—
175#3948—31no—
176#3946—31no—
177#3946—31no—
178#3942—31no—
179#3941—31no—
180#3940—31no—
181#3939—31no—
182C4×#168—31no—
183#3120—151noSylow
184C22×C3×D5—21no—
185C22×C3×D5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
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—
195Dic30—21no—
196Dic30—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C5×Dic6—21no—
200C5×Dic6—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C3×D20—24no—
206C3×D20—21no—
207C3×D20#4112yes—
208C3×C4×D5—24no—
209C3×C4×D5—21no—
210C3×C4×D5—21no—
211C3×C4×D5—81no—
212C3×C4×D5—81no—
213C3×C4×D5—81no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×C3×#41—51no—
219C3×C4×Q8—51no—
220C3×C4×Q8C2×D511yescharacteristic
221C3×C4×D4—51no—
222C3×C4×D4—51no—
223C3×C4×D4—101no—
224C3×C4×D4—101no—
225C3×#117—51no—
226C3×#117—101no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—101no—
229C2×#216—51no—
230C2×#216C2×D511yescharacteristic
231C2×#214—51no—
232C2×#214—51no—
233#924—51no—
234#924—51no—
235#889—101no—
236#889—101no—
237#879—101no—
238#879—101no—
239#870—51no—
240#869—51no—
241C4×Dic6—51no—
242C4×Dic6C2×D511yescharacteristic
243#835—51no—
244#835C2×D511yescharacteristic
245#832—51no—
246#832—51no—
247#830—51no—
248#830—51no—
249#810—51no—
250#810—51no—
251#810—51no—
252#810C2×D511yescharacteristic
253#808—51no—
254#808C2×D511yescharacteristic
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803C2×D511yescharacteristic
260C4×C3⋊C8—51no—
261C2×C5×Q8—31no—
262C2×C5×Q8C22×D311yescharacteristic
263#713—22no—
264#713—22no—
265C2×D20—21no—
266C2×D20C22×D311yescharacteristic
267C2×C4×D5—21no—
268C2×C4×D5—21no—
269C2×C4×D5—21no—
270C2×C4×D5—21no—
271C2×C4×D5C22×D311yescharacteristic
272C2×Dic10—31no—
273C5×Q16—62no—
274C2×C5×C8—31no—
275C2×C5×C8—31no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4C22×D311yescharacteristic
280C42×C5—21no—
281C42×C5—61no—
282C42×C5C22×D311yescharacteristic
283#689—62no—
284#688—62no—
285#685—21no—
286#685—21no—
287#685—61no—
288#685—61no—
289#685#6711yescharacteristic
290#685#6711yescharacteristic
291C4⋊Dic5—21no—
292C4⋊Dic5—31no—
293C4⋊Dic5—61no—
294C4⋊Dic5—61no—
295C4⋊Dic5C22×D311yescharacteristic
296#683—21no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683#6711yescharacteristic
303#683#6711yescharacteristic
304C4×Dic5—21no—
305C4×Dic5—61no—
306C4×Dic5C22×D311yescharacteristic
307C2×#168—31no—
308C2×#168—31no—
309#677—62no—
310#541—151no—
311#520—51no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
319#452—151no—
320#441—31no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5C22×D411yescharacteristic
326C2×C3×D5—21no—
327C2×C3×D5—22no—
328C2×C3×D5—21no—
329C2×C3×D5—21no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—22no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—41no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—41no—
339Dic15—41no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—41no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8C22×D511yescharacteristic
349C2×C3×D4—51no—
350C2×C3×D4—101no—
351C22×C3×C4—51no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4—101no—
356C2×Dic6—51no—
357C2×Dic6C22×D511yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—51no—
366C3×C22⋊C4—51no—
367C3×C22⋊C4—101no—
368C3×C22⋊C4—101no—
369C3×C42—21no—
370C3×C42—51no—
371C3×C42—101no—
372C3×C42C22×D511yescharacteristic
373#217—101no—
374#217—101no—
375#216—22no—
376#216—102no—
377#214—102no—
378#214—102no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382C4⋊Dic3C22×D511yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—21no—
390C4×Dic3—101no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8C22×D511yescharacteristic
394C2×C3⋊C8C22×D511yescharacteristic
395C22×D5—21no—
396C22×D5C2×#6711yescharacteristic
397C5×Q8—21no—
398C5×Q8—61no—
399C5×Q8—61no—
400C5×Q8#23512yes—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5C2×#6711yescharacteristic
406C2×C4×C5C2×#6711yescharacteristic
407C2×C4×C5C23×D311yescharacteristic
408C2×Dic5—21no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5C2×#6711yescharacteristic
412C2×Dic5C2×#6711yescharacteristic
413C2×Dic5C2×#6711yescharacteristic
414D20—24no—
415D20—21no—
416D20#23512yes—
417C4×D5—24no—
418C4×D5—21no—
419C4×D5—21no—
420C4×D5—81no—
421C4×D5—81no—
422C4×D5—81no—
423Dic10—61no—
424Dic10—61no—
425C5×C8—61no—
426C5×C8—61no—
427#168—61no—
428#168—61no—
429C2×#41—51no—
430C2×Q16—31no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—151no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—151no—
441C22⋊Q8—151no—
442C4×Q8—31no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8D3×D511yescharacteristic
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—51no—
451#117—101no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—151no—
455#107—151no—
456#106—31no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—31no—
461#103—31no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—31no—
471C4×C8—151no—
472C2×C3×C5#52511yescharacteristic
473C2×C3×C5#57711yescharacteristic
474C2×C3×C5#57811yescharacteristic
475C3×D5—41no—
476C3×D5—42no—
477C23×C3—51no—
478C23×C3—101no—
479C3×Q8—21no—
480C3×Q8#70912yes—
481C3×D4—52no—
482C3×D4—104no—
483C3×D4—101no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—51no—
487C2×C3×C4—51no—
488C2×C3×C4—51no—
489C2×C3×C4—104no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4—401no—
494C2×C3×C4—401no—
495C2×C3×C4—401no—
496C2×C3×C4D4×D511yescharacteristic
497C2×C3×C4D4×D511yescharacteristic
498C2×C3×C4C23×D511yescharacteristic
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503Dic6—21no—
504Dic6—21no—
505Dic6—101no—
506Dic6—101no—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5C22×#6711yescharacteristic
512C2×D5—21no—
513C2×D5—22no—
514C2×D5—21no—
515C2×D5—21no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—22no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—41no—
522C4×C5—121no—
523C4×C5—121no—
524C4×C5C2×#23511yescharacteristic
525C4×C5C2×#23511yescharacteristic
526Dic5—21no—
527Dic5—21no—
528Dic5—21no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—102no—
533#41—102no—
534C2×Q8—31no—
535C2×Q8—151no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—51no—
538C2×D4—101no—
539C22×C4—51no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544Q16—62no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—31no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4C2×D3×D511yescharacteristic
569C22⋊C4—51no—
570C22⋊C4—51no—
571C22⋊C4—101no—
572C22⋊C4—101no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C42—21no—
576C42—51no—
577C42—61no—
578C42—101no—
579C42—301no—
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—101no—
583C22×C3—101no—
584C22×C3—102no—
585C22×C3—101no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—41no—
593C3×C4—101no—
594C3×C4—101no—
595C3×C4—101no—
596C3×C4—201no—
597C3×C4C2×#70911yescharacteristic
598C3×C4D5×#4111yescharacteristic
599Dic3—41no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5#579111yescharacteristic
604C2×C5#583611yescharacteristic
605C2×C5#583811yescharacteristic
606D5—41no—
607D5—42no—
608C23—51no—
609C23—101no—
610Q8—21no—
611Q8—61no—
612Q8—61no—
613Q8—301no—
614Q8—301no—
615Q8#677112yes—
616D4—52no—
617D4—104no—
618D4—101no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—51no—
622C2×C4—51no—
623C2×C4—51no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—104no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—301no—
631C2×C4—301no—
632C2×C4—401no—
633C2×C4—401no—
634C2×C4—401no—
635C2×C4D5×#6711yescharacteristic
636C2×C4D5×#6711yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—301no—
641C8—301no—
642C2×C3—201no—
643C2×C3—202no—
644C2×C3#6588111yescharacteristic
645C2×C3#6611211yescharacteristic
646C2×C3#6611311yescharacteristic
647C5#8257511yescharacteristic, complemented, Sylow
648C22—102no—
649C22—101no—
650C22—101no—
651C22—101no—
652C22—201no—
653C22—201no—
654C22C2×D5×#6711yescharacteristic
655C4—22no—
656C4—21no—
657C4—21no—
658C4—41no—
659C4—101no—
660C4—101no—
661C4—101no—
662C4—121no—
663C4—121no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4C2×#677111yescharacteristic
668C4D5×#23511yescharacteristic
669C3#1061158011yescharacteristic, complemented, Sylow
670C2—201no—
671C2—202no—
672C2#1175452511yescharacteristic
673C2#1175510211yescharacteristic
674C2#1175533511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#713C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3120
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
2. #11752511C2semidirect
3. C4×#6718C2semidirect
4. C5×#5030C2semidirect
5. #11749350C2semidirect
6. #11749329C2semidirect
9. #11747414C2semidirect
10. #11747392C2semidirect
11. #11747340C2semidirect
12. #11747168C2semidirect
13. #11747052C2semidirect
14. C4×#6655C2semidirect
15. #11746874C2semidirect
130. #5030D5semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10611580semidirect

Maximal subgroups

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

subgroupindex
C3×#659082
#117525112
C4×#67182
C5×#50302
#117493502
#117493292
#117492952
#117492942
#117474142
#117473922
#117473402
#117471682
#117470522
C4×#66552
#117468742
#106115803
#825755