Finite Group Databasebeta

← #14436101

Subgroups — #14436101

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
1#11756282C211yesmaximal, characteristic
2#11756277C211yesmaximal, characteristic, complemented
3C3×C5×#433C211yesmaximal, characteristic, complemented
4#11750950C211yesmaximal, characteristic, complemented
5#11750948C211yesmaximal, characteristic, complemented
6#11750942C211yesmaximal, characteristic, complemented
7#11750930C211yesmaximal, characteristic, complemented
8#11750834C211yesmaximal, characteristic
9#11750834C211yesmaximal, characteristic
10#11750823C211yesmaximal, characteristic, complemented
11#11750822C211yesmaximal, characteristic, complemented
12#11750817C211yesmaximal, characteristic, complemented
13#11750811C211yesmaximal, characteristic, complemented
14C4×Dic60C211yesmaximal, characteristic, complemented
15C4×#6706C211yesmaximal, characteristic, complemented
16#10611116—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20#91813C2211yescharacteristic
21#91813C2211yescharacteristic
22C2×Dic60C2211yescharacteristic
23C2×Dic60C2211yescharacteristic
24C2×#6706C2211yescharacteristic
25C2×#6706C2211yescharacteristic
26#91781—21no—
27C4⋊C4×D15—21no—
28#91778—21no—
29#91778—21no—
30#91770—21no—
31#91770—21no—
32#91768—21no—
33#91768—21no—
34C4×D60C2211yescharacteristic
35C4×D60C2211yescharacteristic
36#91759C2211yescharacteristic
37#91758C2211yescharacteristic
38C4×Dic30C2211yescharacteristic
39C4×Dic30C2211yescharacteristic
40C4×Dic30C2211yescharacteristic
41C4×Dic30C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43C3×C5×C4⋊C8C2211yescharacteristic
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×C5×C22⋊C8C2211yescharacteristic
46C3×C5×#97C2211yescharacteristic
47C3×C4×C5×C8C2211yescharacteristic
48#91105C2211yescharacteristic
49#91105C2211yescharacteristic
50#91102C2211yescharacteristic
51#91102C2211yescharacteristic
52#91101C2211yescharacteristic
53#91101C2211yescharacteristic
54#91100C2211yescharacteristic
55#91100C2211yescharacteristic
56#91100C2211yescharacteristic
57#91100C2211yescharacteristic
58#91100C2211yescharacteristic
59#91100C2211yescharacteristic
60#79385—51nomaximal, Hall
61#65857—31no—
62#65852—31no—
63C5×#433D311yescharacteristic, complemented
64#65138—31no—
65#65136—31no—
66#65130—31no—
67#65118—31no—
68#65022—31no—
69#65022—31no—
70#65011—31no—
71#65010—31no—
72#65005—31no—
73#64999—31no—
74C4×Dic20—31no—
75C4×#677—31no—
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220—21no—
78C22×Dic15—21no—
79#6817—22no—
80#6817—22no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×Dic30C2311yescharacteristic
86C2×Dic30C2311yescharacteristic
87C2×Dic30C2311yescharacteristic
88C2×C3×C5×C8C2311yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C22⋊C4D411yescharacteristic
95C3×C5×C22⋊C4D411yescharacteristic
96C3×C42×C5C2311yescharacteristic
97C3×C42×C5C2311yescharacteristic
98#6719—21no—
99#6719—21no—
100#6714—21no—
101#6714—21no—
102C4⋊Dic15—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15—21no—
105C4⋊Dic15C2311yescharacteristic
106C4⋊Dic15C2311yescharacteristic
107C4⋊Dic15C2311yescharacteristic
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110#6712—21no—
111#6712—21no—
112#6712—21no—
113#6712—21no—
114#6712—21no—
115#6712—21no—
116#6712—21no—
117C4×Dic15—21no—
118C4×Dic15—21no—
119C4×Dic15—21no—
120C4×Dic15—21no—
121Dic60—22no—
122Dic60—22no—
123#6706—22no—
124#6706—22no—
125#5523—51no—
126#5518—51no—
127C3×#433D511yescharacteristic, complemented
128#4849—51no—
129#4847—51no—
130#4841—51no—
131#4829—51no—
132#4733—51no—
133#4733—51no—
134#4722—51no—
135#4721—51no—
136#4716—51no—
137#4710—51no—
138C4×Dic12—51no—
139C4×#204—51no—
140C2×#709—31no—
141C5×#117C2×D311yescharacteristic
142C2×C4⋊Dic5—31no—
143#4070—31no—
144#4070—31no—
145C2×Dic20—31no—
146C2×Dic20—31no—
147C2×#677—31no—
148C2×#677—31no—
149#4038—61no—
150D5×C4⋊C4—61no—
151#4035—61no—
152#4035—61no—
153#4027—61no—
154#4027—61no—
155#4025—61no—
156#4025—61no—
157C4×D20—31no—
158C4×D20—31no—
159#4016—31no—
160#4015—31no—
161C4×Dic10—31no—
162C4×Dic10—31no—
163C4×Dic10—31no—
164C4×Dic10—31no—
165C5×C4⋊C8C2×D311yescharacteristic
166C5×C4⋊C8C2×D311yescharacteristic
167C5×C22⋊C8C2×D311yescharacteristic
168C5×C22⋊C8C2×D311yescharacteristic
169C5×#97C2×D311yescharacteristic
170C4×C5×C8C2×D311yescharacteristic
171#3953—31no—
172#3953—31no—
173#3950—31no—
174#3950—31no—
175#3949—31no—
176#3949—31no—
177#3948—31no—
178#3948—31no—
179#3948—31no—
180#3948—31no—
181#3948—31no—
182#3948—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×D15—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194#1220—24no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—81no—
203D60—21no—
204D60#4112yes—
205C4×D15—24no—
206C4×D15—81no—
207C4×D15—81no—
208Dic30—21no—
209Dic30—21no—
210Dic30—21no—
211Dic30—21no—
212Dic30—21no—
213Dic30#4112yes—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C2×#235—51no—
219C3×#117C2×D511yescharacteristic
220C2×C4⋊Dic3—51no—
221#924—51no—
222#924—51no—
223C2×Dic12—51no—
224C2×Dic12—51no—
225C2×#204—51no—
226C2×#204—51no—
227#892—101no—
228D3×C4⋊C4—101no—
229#889—101no—
230#889—101no—
231#67⋊C4—101no—
232#67⋊C4—101no—
233#879—101no—
234#879—101no—
235C4×D12—51no—
236C4×D12—51no—
237#870—51no—
238#869—51no—
239C4×Dic6—51no—
240C4×Dic6—51no—
241C4×Dic6—51no—
242C4×Dic6—51no—
243C3×C4⋊C8C2×D511yescharacteristic
244C3×C4⋊C8C2×D511yescharacteristic
245C3×C22⋊C8C2×D511yescharacteristic
246C3×C22⋊C8C2×D511yescharacteristic
247C3×#97C2×D511yescharacteristic
248C3×C4×C8C2×D511yescharacteristic
249#821—51no—
250#821—51no—
251#818—51no—
252#818—51no—
253#817—51no—
254#817—51no—
255#816—51no—
256#816—51no—
257#816—51no—
258#816—51no—
259#816—51no—
260#816—51no—
261C22×C4×C5C22×D311yescharacteristic
262C2×C22⋊D5—61no—
263C22×Dic5—61no—
264#709—62no—
265#709—62no—
266C2×D20—31no—
267C2×C4×D5—61no—
268C2×C4×D5—61no—
269C2×C4×D5—61no—
270C2×Dic10—31no—
271C2×Dic10—31no—
272C2×Dic10—31no—
273C2×C5×C8C22×D311yescharacteristic
274C2×C5×C8C22×D311yescharacteristic
275C2×C5×C8C22×D311yescharacteristic
276C2×C5×C8C22×D311yescharacteristic
277C5×C4⋊C4D1211yescharacteristic
278C5×C4⋊C4D1211yescharacteristic
279C5×C22⋊C4D1211yescharacteristic
280C5×C22⋊C4D1211yescharacteristic
281C42×C5C22×D311yescharacteristic
282C42×C5C22×D311yescharacteristic
283C22⋊Dic5—61no—
284C22⋊Dic5—61no—
285#685—61no—
286#685—61no—
287C4⋊Dic5—31no—
288C4⋊Dic5—31no—
289C4⋊Dic5—31no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5—61no—
293C4⋊Dic5—61no—
294#683—61no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302C4×Dic5—61no—
303C4×Dic5—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306Dic20—62no—
307Dic20—62no—
308#677—62no—
309#677—62no—
310#541—151no—
311#520—151no—
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—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433D1511yescharacteristic, complemented
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339Dic15—22no—
340Dic15—41no—
341Dic15—41no—
342Dic15—41no—
343Dic15—41no—
344Dic15—41no—
345Dic15—41no—
346C22×C3×C4C22×D511yescharacteristic
347C2×#67—101no—
348C22×Dic3—101no—
349#235—102no—
350#235—102no—
351C2×D12—51no—
352C2×C4×D3—101no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×Dic6—51no—
356C2×Dic6—51no—
357C2×Dic6—51no—
358C2×C3×C8C22×D511yescharacteristic
359C2×C3×C8C22×D511yescharacteristic
360C2×C3×C8C22×D511yescharacteristic
361C2×C3×C8C22×D511yescharacteristic
362C3×C4⋊C4D2011yescharacteristic
363C3×C4⋊C4D2011yescharacteristic
364C3×C22⋊C4D2011yescharacteristic
365C3×C22⋊C4D2011yescharacteristic
366C3×C42C22×D511yescharacteristic
367C3×C42C22×D511yescharacteristic
368#217—101no—
369#217—101no—
370(C2×D3)⋊C4—101no—
371(C2×D3)⋊C4—101no—
372C4⋊Dic3—51no—
373C4⋊Dic3—51no—
374C4⋊Dic3—51no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3—101no—
378C4⋊Dic3—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—101no—
388C4×Dic3—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391Dic12—102no—
392Dic12—102no—
393#204—102no—
394#204—102no—
395C23×C5C2×D1211yescharacteristic
396C22×D5—61no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5C2×D1211yescharacteristic
400C2×C4×C5C2×D1211yescharacteristic
401C2×C4×C5C2×D1211yescharacteristic
402C2×C4×C5C2×D1211yescharacteristic
403C2×C4×C5C2×D1211yescharacteristic
404C2×C4×C5C23×D311yescharacteristic
405C22⋊D5—64no—
406C2×Dic5—61no—
407C2×Dic5—61no—
408C2×Dic5—61no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—241no—
414D20—32no—
415D20—61no—
416C4×D5—64no—
417C4×D5—241no—
418C4×D5—241no—
419Dic10—32no—
420Dic10—61no—
421Dic10—61no—
422Dic10—61no—
423Dic10—61no—
424Dic10—61no—
425C5×C8—21no—
426C5×C8—21no—
427C5×C8—21no—
428C5×C8—21no—
429C2×#41—151no—
430C2×Q16—151no—
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—151no—
443C4×Q8—151no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—301no—
451#117C2×D1511yescharacteristic
452C2×C4⋊C4—151no—
453C2×C4⋊C4—301no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8C2×D1511yescharacteristic
459C4⋊C8C2×D1511yescharacteristic
460#103—151no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8C2×D1511yescharacteristic
469C22⋊C8C2×D1511yescharacteristic
470#97C2×D1511yescharacteristic
471C4×C8C2×D1511yescharacteristic
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476D15—42no—
477C23×C3C2×D2011yescharacteristic
478C22×D3—101no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4C2×D2011yescharacteristic
482C2×C3×C4C2×D2011yescharacteristic
483C2×C3×C4C2×D2011yescharacteristic
484C2×C3×C4C2×D2011yescharacteristic
485C2×C3×C4C2×D2011yescharacteristic
486C2×C3×C4C23×D511yescharacteristic
487#67—104no—
488C2×Dic3—101no—
489C2×Dic3—101no—
490C2×Dic3—101no—
491C2×Dic3—101no—
492C2×Dic3—101no—
493C2×Dic3—101no—
494C2×Dic3—101no—
495C2×Dic3—401no—
496D12—52no—
497D12—101no—
498C4×D3—104no—
499C4×D3—401no—
500C4×D3—401no—
501Dic6—52no—
502Dic6—101no—
503Dic6—101no—
504Dic6—101no—
505Dic6—101no—
506Dic6—101no—
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—21no—
510C3×C8—21no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×D1211yescharacteristic
515C2×D5—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5D3×#4111yescharacteristic
524C4×C5D3×#4111yescharacteristic
525Dic5—62no—
526Dic5—121no—
527Dic5—121no—
528Dic5—121no—
529Dic5—121no—
530Dic5—121no—
531Dic5—121no—
532#41—302no—
533#41—302no—
534C2×Q8—151no—
535C2×Q8—151no—
536C2×Q8—151no—
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—301no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4C22×D1511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8C22×D1511yescharacteristic
549C2×C8C22×D1511yescharacteristic
550C2×C8C22×D1511yescharacteristic
551C2×C8C22×D1511yescharacteristic
552C4⋊C4—151no—
553C4⋊C4—151no—
554C4⋊C4—151no—
555C4⋊C4—151no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4—301no—
560C4⋊C4—301no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4D6011yescharacteristic
568C4⋊C4D6011yescharacteristic
569C22⋊C4—301no—
570C22⋊C4—301no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C22⋊C4D6011yescharacteristic
574C22⋊C4D6011yescharacteristic
575C42—301no—
576C42—301no—
577C42—301no—
578C42—301no—
579C42C22×D1511yescharacteristic
580C42C22×D1511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C22×D2011yescharacteristic
586C2×D3—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4D5×#4111yescharacteristic
595C3×C4D5×#4111yescharacteristic
596Dic3—102no—
597Dic3—201no—
598Dic3—201no—
599Dic3—201no—
600Dic3—201no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#552411yescharacteristic
605C2×C5#575111yescharacteristic
606C2×C5#575311yescharacteristic
607D5—122no—
608C23—301no—
609C23C2×D6011yescharacteristic
610Q8—152no—
611Q8—301no—
612Q8—301no—
613Q8—301no—
614Q8—301no—
615Q8—301no—
616D4—152no—
617D4—304no—
618D4—301no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—304no—
622C2×C4—301no—
623C2×C4—301no—
624C2×C4—301no—
625C2×C4—301no—
626C2×C4—301no—
627C2×C4—301no—
628C2×C4—301no—
629C2×C4—1201no—
630C2×C4—1201no—
631C2×C4—1201no—
632C2×C4C2×D6011yescharacteristic
633C2×C4C2×D6011yescharacteristic
634C2×C4C2×D6011yescharacteristic
635C2×C4C2×D6011yescharacteristic
636C2×C4C2×D6011yescharacteristic
637C2×C4C23×D1511yescharacteristic
638C8—21no—
639C8—21no—
640C8—21no—
641C8—21no—
642C2×C3—41no—
643C2×C3#6585811yescharacteristic
644C2×C3#6608511yescharacteristic
645C2×C3#6608711yescharacteristic
646D3—202no—
647C5#7938511yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C22×D6011yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—302no—
661C4—601no—
662C4—601no—
663C4—601no—
664C4—601no—
665C4—601no—
666C4—601no—
667C4#41×D1511yescharacteristic
668C4#41×D1511yescharacteristic
669C3#1061111611yescharacteristic, complemented, Sylow
670C2—41no—
671C2—602no—
672C2#1175628311yescharacteristic
673C2#1175651011yescharacteristic
674C2#1175651211yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#433C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenter#433D15
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11756277C2semidirect
3. C3×C5×#433C2semidirect
4. #11750950C2semidirect
5. #11750948C2semidirect
6. #11750942C2semidirect
7. #11750930C2semidirect
10. #11750823C2semidirect
11. #11750822C2semidirect
12. #11750817C2semidirect
13. #11750811C2semidirect
14. C4×Dic60C2semidirect
15. C4×#6706C2semidirect
63. C5×#433D3semidirect
127. C3×#433D5semidirect
324. #433D15semidirect
581. C3×C5#3120semidirect
647. C5#79385semidirect
669. C3#10611116semidirect

Maximal subgroups

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

subgroupindex
#117562822
#117562772
C3×C5×#4332
#117509502
#117509482
#117509422
#117509302
#117508342
#117508232
#117508222
#117508172
#117508112
C4×Dic602
C4×#67062
#106111163
#793855