Finite Group Databasebeta

← #14472091

Subgroups — #14472091

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×#66005C211yesmaximal, characteristic
2#11752462C211yesmaximal, characteristic, complemented
3#11751157C211yesmaximal, characteristic
4C5×#5054C211yesmaximal, characteristic
5#11749349C211yesmaximal, characteristic, complemented
6#11749332C211yesmaximal, characteristic, complemented
7#11749245C211yesmaximal, characteristic, complemented
8Dic5×#216C211yesmaximal, characteristic, complemented
9#11749101C211yesmaximal, characteristic
10#11749085C211yesmaximal, characteristic
11#11749003C211yesmaximal, characteristic
12Dic5×#214C211yesmaximal, characteristic
13C4×#6661C211yesmaximal, characteristic, complemented
14#11746944C211yesmaximal, characteristic, complemented
15#11746846C211yesmaximal, characteristic, complemented
16#10612311—31nomaximal, Hall
17C3×C5×#124C2211yescharacteristic
18#91759C2211yescharacteristic
19C2×C5×#216C2211yescharacteristic
20C2×C5×#214C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×#4090C2211yescharacteristic
24C3×#4082C2211yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26C3×#4025—21no—
27C3×#4025—21no—
28C3×#4024—21no—
29C3×#4023—21no—
30C3×C4×Dic10C2211yescharacteristic
31C3×C4×Dic10C2211yescharacteristic
32#91468C2211yescharacteristic
33#91388C2211yescharacteristic
34#91379—21no—
35#91346—21no—
36Dic5×Dic6C2211yescharacteristic
37Dic5×Dic6C2211yescharacteristic
38#91327—21no—
39#91324—21no—
40C2×#6661C2211yescharacteristic
41#91119C2211yescharacteristic
42#91119C2211yescharacteristic
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic
45C4×C3⋊#168C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#832C2211yescharacteristic
48C5×C4⋊(C3⋊C8)C2211yescharacteristic
49#90990C2211yescharacteristic
50#90989C2211yescharacteristic
51#90987C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90972C2211yescharacteristic
55#90971C2211yescharacteristic
56#90971C2211yescharacteristic
57#90970C2211yescharacteristic
58Dic5×C3⋊C8C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83676—51nomaximal, Hall
61#66005D311yescharacteristic
62#65903—31no—
63C5×#464—31no—
64Q16×Dic5—31no—
65#65471—31no—
66#65455—31no—
67SD16×Dic5—31no—
68#65345—31no—
69C4×#689—31no—
70#65119—31no—
71#65118—31no—
72#65088—31no—
73#65081—31no—
74#65057—31no—
75#65048—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×C5×Dic6C2311yescharacteristic
79C22×C3×Dic5—21no—
80C2×C3×Dic10D411yescharacteristic
81C2×C3×Dic10C2311yescharacteristic
82C2×#1204—21no—
83C3×C5×C22⋊C4—21no—
84C3×C5×C22⋊C4—21no—
85C3×C42×C5C2311yescharacteristic
86C4⋊Dic15C2311yescharacteristic
87C4⋊Dic15C2311yescharacteristic
88#6712—21no—
89#6712—21no—
90C2×C3⋊#168C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C5×#216—22no—
93C5×#214—22no—
94C5×C4⋊Dic3C2311yescharacteristic
95C5×Dic3⋊C4—21no—
96C4×C5×Dic3—21no—
97C2×C5×C3⋊C8C2311yescharacteristic
98C2×C5×C3⋊C8C2311yescharacteristic
99C3×C22⋊Dic5—21no—
100C3×C22⋊Dic5—21no—
101C3×C22⋊Dic5—21no—
102C3×C4⋊Dic5—21no—
103C3×C4⋊Dic5D411yescharacteristic
104C3×C4⋊Dic5C2311yescharacteristic
105C3×#683—21no—
106C3×#683—21no—
107C3×#683—21no—
108C3×#683D411yescharacteristic
109C3×#683D411yescharacteristic
110C3×C4×Dic5—21no—
111C3×C4×Dic5—21no—
112C3×C4×Dic5C2311yescharacteristic
113C3×C4×Dic5C2311yescharacteristic
114Dic3⋊Dic5—21no—
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6661—22no—
122C3×#556—51no—
123#5567—51no—
124#5090—51no—
125#5079—51no—
126#5056—51no—
127#5056—51no—
128#5054—51no—
129#5054D511yescharacteristic
130C4×#216—51no—
131C4×#216—51no—
132Q8×C3⋊C8—51no—
133#5022—51no—
134#5022—51no—
135C4×#214—51no—
136#5007—51no—
137C2×C5×Q16—31no—
138C2×C5×SD16—31no—
139C5×#124C2×D311yescharacteristic
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142Q8×Dic5—31no—
143Q8×Dic5C2×D311yescharacteristic
144#4090C2×D311yescharacteristic
145C2×#689—31no—
146#4082C2×D311yescharacteristic
147D4×Dic5C2×D311yescharacteristic
148#4036—31no—
149#4036—61no—
150#4034—31no—
151#4034—61no—
152#4025—21no—
153#4025—21no—
154#4024—21no—
155#4023—21no—
156#4016—31no—
157#4016—61no—
158C4×Dic10—61no—
159C4×Dic10C2×D311yescharacteristic
160C4×Dic10C2×D311yescharacteristic
161C5×C4⋊C8—31no—
162C5×#103—31no—
163C5×#102—31no—
164#3967—31no—
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964—31no—
169#3950—31no—
170#3949—31no—
171#3948—31no—
172#3948—31no—
173#3946—31no—
174#3946—31no—
175C8×Dic5—31no—
176C8×Dic5—31no—
177#3942—31no—
178#3939—31no—
179C4×#168—31no—
180#3364—151noSylow
181C23×C3×C5—21no—
182C3×C5×Q8—21no—
183C3×C5×Q8—21no—
184C3×C5×D4—21no—
185C3×C5×D4—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C5×Dic6—21no—
195C5×Dic6#4112yes—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—42no—
199C2×C3×Dic5C2×D411yescharacteristic
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C2×C3×Dic5C2×D411yescharacteristic
203C3×Dic10—22no—
204C3×Dic10—21no—
205C3×Dic10—21no—
206#1204—42no—
207C3⋊#168—21no—
208C3⋊#168—21no—
209C5×C3⋊C8—21no—
210C5×C3⋊C8—21no—
211C3×C4⋊Q8—51no—
212C3×#126—101no—
213C3×#126—101no—
214C3×#124—51no—
215C3×#124C2×D511yescharacteristic
216C3×C22⋊Q8—101no—
217C3×C4×Q8—51no—
218C3×C4×Q8—51no—
219C3×C4×Q8—51no—
220C3×C4×D4—51no—
221C3×#117—101no—
222#944—101no—
223C2×#216—51no—
224C2×#216C2×D511yescharacteristic
225C2×#214C2×D511yescharacteristic
226#889—101no—
227#889—101no—
228#887—101no—
229#870—51no—
230#870—51no—
231#869—51no—
232C4×Dic6—51no—
233C4×Dic6—51no—
234C4×Dic6C2×D511yescharacteristic
235#835—51no—
236#835—51no—
237#835—51no—
238#835—51no—
239#835—51no—
240#835C2×D511yescharacteristic
241#832—51no—
242#832—51no—
243#832C2×D511yescharacteristic
244#810—51no—
245#808—51no—
246#807—51no—
247#807—51no—
248C4⋊(C3⋊C8)—51no—
249C4⋊(C3⋊C8)—51no—
250C4⋊(C3⋊C8)C2×D511yescharacteristic
251C4×C3⋊C8—51no—
252C4×C3⋊C8—51no—
253C4×C3⋊C8—51no—
254C2×C5×Q8—31no—
255C2×C5×Q8C22×D311yescharacteristic
256C2×C5×D4C22×D311yescharacteristic
257C22×Dic5—21no—
258C2×Dic10—61no—
259C2×Dic10#6711yescharacteristic
260C2×Dic10C22×D311yescharacteristic
261C5×Q16—62no—
262C5×SD16—62no—
263C2×C5×C8—31no—
264C2×C5×C8—31no—
265C5×C4⋊C4—31no—
266C5×C4⋊C4—61no—
267C5×C22⋊C4—21no—
268C5×C22⋊C4—21no—
269C42×C5—61no—
270C42×C5C22×D311yescharacteristic
271C22⋊Dic5—21no—
272C22⋊Dic5—21no—
273C22⋊Dic5—21no—
274#689—62no—
275C4⋊Dic5—21no—
276C4⋊Dic5—31no—
277C4⋊Dic5—31no—
278C4⋊Dic5—61no—
279C4⋊Dic5—61no—
280C4⋊Dic5—61no—
281C4⋊Dic5#6711yescharacteristic
282C4⋊Dic5C22×D311yescharacteristic
283#683—21no—
284#683—21no—
285#683—21no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683#6711yescharacteristic
291#683#6711yescharacteristic
292C4×Dic5—21no—
293C4×Dic5—21no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C4×Dic5C22×D311yescharacteristic
297C4×Dic5C22×D311yescharacteristic
298C2×#168—31no—
299C2×#168—31no—
300#557—151no—
301#556—51no—
302#488—151no—
303#488—151no—
304#487—151no—
305#479—151no—
306#479—151no—
307#474—151no—
308#464—31no—
309#464—151no—
310#462—151no—
311C8×Q8—151no—
312C4×Q16—151no—
313C4×Q16—151no—
314C4×SD16—151no—
315C22×C3×C5—41no—
316C22×C3×C5—41no—
317C22×C3×C5—41no—
318C22×C3×C5C22×D411yescharacteristic
319C3×C4×C5—21no—
320C3×C4×C5—21no—
321C3×C4×C5—41no—
322C3×C4×C5C2×#4111yescharacteristic
323C3×C4×C52−1+411yescharacteristic
324Dic15—41no—
325Dic15—41no—
326C3×Dic5—21no—
327C3×Dic5—21no—
328C3×Dic5—21no—
329C3×Dic5—41no—
330C3×Dic5—41no—
331C3×Dic5#13512yes—
332C5×Dic3—22no—
333C5×Dic3—41no—
334C2×C3×Q8—51no—
335C2×C3×Q8—51no—
336C2×C3×Q8C22×D511yescharacteristic
337C2×C3×D4C22×D511yescharacteristic
338C22×C3×C4—101no—
339C2×Dic6—101no—
340C2×Dic6C22×D511yescharacteristic
341C3×C4⋊C4—51no—
342C3×C4⋊C4—51no—
343C3×C4⋊C4—51no—
344C3×C4⋊C4—51no—
345C3×C4⋊C4—101no—
346C3×C4⋊C4—101no—
347C3×C4⋊C4—101no—
348C3×C4⋊C4—101no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—101no—
352C3×C22⋊C4—101no—
353C3×C22⋊C4—101no—
354C3×C42—51no—
355C3×C42—51no—
356C3×C42—101no—
357C3×C42—101no—
358C3×C42C22×D511yescharacteristic
359#216—22no—
360#216—102no—
361#214—22no—
362C4⋊Dic3—51no—
363C4⋊Dic3—51no—
364C4⋊Dic3—101no—
365C4⋊Dic3C22×D511yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373C4×Dic3—21no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C2×C3⋊C8—51no—
377C2×C3⋊C8—51no—
378C2×C3⋊C8C22×D511yescharacteristic
379C2×C3⋊C8C22×D511yescharacteristic
380C23×C5—21no—
381C5×Q8—21no—
382C5×Q8—21no—
383C5×Q8—32no—
384C5×Q8—61no—
385C5×D4—21no—
386C5×D4—21no—
387C2×C4×C5—21no—
388C2×C4×C5—61no—
389C2×C4×C5—61no—
390C2×C4×C5C2×#6711yescharacteristic
391C2×C4×C5C2×#6711yescharacteristic
392C2×C4×C5C23×D311yescharacteristic
393C2×Dic5—21no—
394C2×Dic5—21no—
395C2×Dic5—42no—
396C2×Dic5—61no—
397C2×Dic5—61no—
398C2×Dic5C2×#6711yescharacteristic
399C2×Dic5C2×#6711yescharacteristic
400C2×Dic5C2×#6711yescharacteristic
401C2×Dic5C2×#6711yescharacteristic
402Dic10—22no—
403Dic10—21no—
404Dic10—21no—
405Dic10—122no—
406C5×C8—61no—
407C5×C8—61no—
408#168—61no—
409#168—61no—
410C2×Q16—31no—
411C2×Q16—151no—
412C2×SD16—31no—
413C4⋊Q8—51no—
414C4⋊Q8—151no—
415C4⋊Q8—301no—
416#126—101no—
417#126—101no—
418#125—151no—
419#125—151no—
420#125—301no—
421#125—301no—
422#124—51no—
423#124D3×D511yescharacteristic
424C22⋊Q8—101no—
425C4×Q8—31no—
426C4×Q8—51no—
427C4×Q8—51no—
428C4×Q8—51no—
429C4×Q8—151no—
430C4×Q8—151no—
431C4×Q8—301no—
432C4×D4—51no—
433#117—101no—
434#107—151no—
435#107—151no—
436#106—151no—
437C4⋊C8—31no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440#103—31no—
441#103—151no—
442#103—151no—
443#103—151no—
444#103—151no—
445#103—151no—
446#103—151no—
447#102—31no—
448#102—151no—
449#102—151no—
450C4×C8—151no—
451C4×C8—151no—
452C4×C8—151no—
453C2×C3×C5—81no—
454C2×C3×C5#54811yescharacteristic
455C2×C3×C5C2×#13511yescharacteristic
456C2×C3×C5#57811yescharacteristic
457C23×C3—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—102no—
461C3×Q8—101no—
462C3×Q8—101no—
463C3×D4—21no—
464C3×D4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—51no—
467C2×C3×C4—51no—
468C2×C3×C4—51no—
469C2×C3×C4—51no—
470C2×C3×C4—101no—
471C2×C3×C4—101no—
472C2×C3×C4—202no—
473C2×C3×C4D4×D511yescharacteristic
474C2×C3×C4D4×D511yescharacteristic
475C2×C3×C4C23×D511yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—101no—
479C2×Dic3—101no—
480Dic6—21no—
481Dic6—202no—
482Dic6#71112yes—
483C3⋊C8—21no—
484C3⋊C8—21no—
485C3⋊C8—101no—
486C3⋊C8—101no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5C22×#6711yescharacteristic
491C4×C5—21no—
492C4×C5—21no—
493C4×C5—41no—
494C4×C5—62no—
495C4×C5—121no—
496C4×C5D3×#4111yescharacteristic
497C4×C5#101011yescharacteristic
498Dic5—21no—
499Dic5—21no—
500Dic5—21no—
501Dic5—41no—
502Dic5—41no—
503Dic5—121no—
504Dic5—121no—
505Dic5#95012yes—
506C2×Q8—31no—
507C2×Q8—51no—
508C2×Q8—51no—
509C2×Q8—301no—
510C2×Q8C2×D3×D511yescharacteristic
511C2×D4C2×D3×D511yescharacteristic
512C22×C4—101no—
513Q16—62no—
514Q16—302no—
515SD16—62no—
516C2×C8—31no—
517C2×C8—31no—
518C2×C8—151no—
519C2×C8—151no—
520C4⋊C4—31no—
521C4⋊C4—51no—
522C4⋊C4—51no—
523C4⋊C4—51no—
524C4⋊C4—51no—
525C4⋊C4—61no—
526C4⋊C4—101no—
527C4⋊C4—101no—
528C4⋊C4—101no—
529C4⋊C4—101no—
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—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—101no—
542C22⋊C4—101no—
543C22⋊C4—101no—
544C42—51no—
545C42—51no—
546C42—61no—
547C42—101no—
548C42—101no—
549C42—301no—
550C42—301no—
551C42C2×D3×D511yescharacteristic
552C3×C5#336411yescharacteristic, complemented, Hall
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3C2×D4×D511yescharacteristic
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—41no—
560C3×C4—52no—
561C3×C4—101no—
562C3×C4—101no—
563C3×C4—101no—
564C3×C4—201no—
565C3×C4—201no—
566C3×C4C2×#71111yescharacteristic
567C3×C4#415011yescharacteristic
568Dic3—22no—
569Dic3—41no—
570Dic3—201no—
571Dic3—201no—
572C2×C5—81no—
573C2×C5C2×#95011yescharacteristic
574C2×C5#583111yescharacteristic
575C2×C5#583811yescharacteristic
576C23—21no—
577Q8—21no—
578Q8—21no—
579Q8—32no—
580Q8—61no—
581Q8—102no—
582Q8—101no—
583Q8—101no—
584Q8—602no—
585D4—21no—
586D4—21no—
587C2×C4—21no—
588C2×C4—51no—
589C2×C4—51no—
590C2×C4—51no—
591C2×C4—51no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—101no—
595C2×C4—101no—
596C2×C4—202no—
597C2×C4—301no—
598C2×C4—301no—
599C2×C4D5×#6711yescharacteristic
600C2×C4D5×#6711yescharacteristic
601C2×C4C22×D3×D511yescharacteristic
602C8—61no—
603C8—61no—
604C8—301no—
605C8—301no—
606C2×C3—81no—
607C2×C3#6593211yescharacteristic
608C2×C3D5×#13511yescharacteristic
609C2×C3#6611311yescharacteristic
610C5#8367611yescharacteristic, complemented, Sylow
611C22—41no—
612C22—41no—
613C22—41no—
614C22C2×D5×#6711yescharacteristic
615C4—21no—
616C4—21no—
617C4—41no—
618C4—52no—
619C4—62no—
620C4—101no—
621C4—101no—
622C4—101no—
623C4—121no—
624C4—201no—
625C4—201no—
626C4—601no—
627C4—601no—
628C4#9202011yescharacteristic
629C4D3×#71111yescharacteristic
630C3#1061231111yescharacteristic, complemented, Sylow
631C2—81no—
632C2#1175479811yescharacteristic
633C2D5×#95011yescharacteristic
634C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenter#124D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752462C2semidirect
5. #11749349C2semidirect
6. #11749332C2semidirect
7. #11749245C2semidirect
8. Dic5×#216C2semidirect
13. C4×#6661C2semidirect
14. #11746944C2semidirect
15. #11746846C2semidirect
552. C3×C5#3364semidirect
610. C5#83676semidirect
630. C3#10612311semidirect

Maximal subgroups

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

subgroupindex
C3×#660052
#117524622
#117511572
C5×#50542
#117493492
#117493322
#117492452
Dic5×#2162
#117491012
#117490852
#117490032
Dic5×#2142
C4×#66612
#117469442
#117468462
#106123113
#836765