Finite Group Databasebeta

← #14436188

Subgroups — #14436188

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#11756277C211yesmaximal, characteristic, complemented
2C3×#65857C211yesmaximal, characteristic
3C5×#5000C211yesmaximal, characteristic, complemented
4#11748531C211yesmaximal, characteristic
5#11748531C211yesmaximal, characteristic
6#11748450C211yesmaximal, characteristic, complemented
7#11748414C211yesmaximal, characteristic, complemented
8#11747095C211yesmaximal, characteristic, complemented
9#11747091C211yesmaximal, characteristic, complemented
10C4×#6662C211yesmaximal, characteristic, complemented
11#11747062C211yesmaximal, characteristic, complemented
12#11747052C211yesmaximal, characteristic, complemented
13C4×#6657C211yesmaximal, characteristic, complemented
14#11746944C211yesmaximal, characteristic, complemented
15#11746888C211yesmaximal, characteristic, complemented
16#10611116—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19#91813C2211yescharacteristic
20#91813C2211yescharacteristic
21#91778—21no—
22#91778—21no—
23#91768—21no—
24#91768—21no—
25#91759C2211yescharacteristic
26#91758C2211yescharacteristic
27C4×Dic30C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C3×#4038—21no—
31C3×D5×C4⋊C4—21no—
32C3×#4027—21no—
33C3×#4027—21no—
34C3×C4×D20C2211yescharacteristic
35C3×C4×D20C2211yescharacteristic
36C3×C4×Dic10C2211yescharacteristic
37C3×C4×Dic10C2211yescharacteristic
38C2×#6662C2211yescharacteristic
39C2×#6662C2211yescharacteristic
40C2×#6657C2211yescharacteristic
41C2×#6657C2211yescharacteristic
42C5×#830C2211yescharacteristic
43C5×#830C2211yescharacteristic
44C5×C4⋊(C3⋊C8)C2211yescharacteristic
45C5×C4⋊(C3⋊C8)C2211yescharacteristic
46C5×#803C2211yescharacteristic
47C4×C5×C3⋊C8C2211yescharacteristic
48#90990C2211yescharacteristic
49#90990C2211yescharacteristic
50#90987C2211yescharacteristic
51#90987C2211yescharacteristic
52#90974C2211yescharacteristic
53#90974C2211yescharacteristic
54#90974C2211yescharacteristic
55#90974C2211yescharacteristic
56#90971C2211yescharacteristic
57#90971C2211yescharacteristic
58#90965C2211yescharacteristic
59#90965C2211yescharacteristic
60#82575—51nomaximal, Hall
61#65857D311yescharacteristic
62#65852—31no—
63C5×#433—31no—
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×Dic30C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C3×C22⋊D5—21no—
80C22×C3×Dic5—21no—
81C3×#709—22no—
82C3×#709—22no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4D411yescharacteristic
89C3×C5×C4⋊C4D411yescharacteristic
90C3×C5×C22⋊C4D411yescharacteristic
91C3×C5×C22⋊C4D411yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C3×C42×C5C2311yescharacteristic
94#6719—21no—
95#6719—21no—
96C4⋊Dic15—21no—
97C4⋊Dic15—21no—
98C4⋊Dic15C2311yescharacteristic
99C4⋊Dic15C2311yescharacteristic
100#6712—21no—
101#6712—21no—
102#6712—21no—
103#6712—21no—
104#6712—21no—
105#6712—21no—
106C4×Dic15—21no—
107C4×Dic15—21no—
108C2×C5×C3⋊C8C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C2×C5×C3⋊C8C2311yescharacteristic
112C3×#685—21no—
113C3×#685—21no—
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121#6662—22no—
122#6662—22no—
123#6657—22no—
124#6657—22no—
125C3×#520—51no—
126#5518—51no—
127#5239—51no—
128#5239—51no—
129#5031—51no—
130#5030—51no—
131C4×#216—51no—
132#5022—51no—
133#5019—51no—
134#5018—51no—
135C4×#214—51no—
136#5009—51no—
137#5000D511yescharacteristic, complemented
138#4971—51no—
139#4970—51no—
140C2×#709C2×D311yescharacteristic
141C5×#117C2×D311yescharacteristic
142C2×C4⋊Dic5C2×D311yescharacteristic
143#4070—31no—
144#4070—31no—
145C2×Dic20—31no—
146C2×Dic20—31no—
147C2×#677—31no—
148C2×#677—31no—
149#4038—21no—
150D5×C4⋊C4—21no—
151#4035—61no—
152#4035—61no—
153#4027—21no—
154#4027—21no—
155#4025—61no—
156#4025—61no—
157C4×D20C2×D311yescharacteristic
158C4×D20C2×D311yescharacteristic
159#4016—31no—
160#4015—31no—
161C4×Dic10—31no—
162C4×Dic10—31no—
163C4×Dic10C2×D311yescharacteristic
164C4×Dic10C2×D311yescharacteristic
165C5×C4⋊C8—31no—
166C5×C4⋊C8—31no—
167C5×C22⋊C8—31no—
168C5×C22⋊C8—31no—
169C5×#97—31no—
170C4×C5×C8—31no—
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×C3×D5—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
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198Dic30—21no—
199Dic30—21no—
200Dic30—21no—
201Dic30—21no—
202C3×C22⋊D5—24no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—81no—
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—24no—
210C3×C4×D5—81no—
211C3×C4×D5—81no—
212C3×Dic10—21no—
213C3×Dic10#4112yes—
214C5×C3⋊C8—21no—
215C5×C3⋊C8—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×C3×#41—51no—
219C3×C4×Q8—51no—
220C3×C4×Q8—51no—
221C3×C4×D4—51no—
222C3×C4×D4—51no—
223C3×C4×D4—101no—
224C3×C4×D4—101no—
225C3×#117—101no—
226C3×#117C2×D511yescharacteristic
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—101no—
229C2×#216—51no—
230C2×#216—51no—
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×Dic6—51no—
243#835—51no—
244#835—51no—
245#832—51no—
246#832—51no—
247#830C2×D511yescharacteristic
248#830C2×D511yescharacteristic
249#810—51no—
250#810—51no—
251#810—51no—
252#810—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)C2×D511yescharacteristic
258C4⋊(C3⋊C8)C2×D511yescharacteristic
259#803C2×D511yescharacteristic
260C4×C3⋊C8C2×D511yescharacteristic
261C22×C4×C5C22×D311yescharacteristic
262C2×C22⋊D5—21no—
263C22×Dic5—21no—
264#709—22no—
265#709—22no—
266C2×D20C22×D311yescharacteristic
267C2×C4×D5—21no—
268C2×C4×D5—21no—
269C2×C4×D5—21no—
270C2×Dic10—31no—
271C2×Dic10—31no—
272C2×Dic10C22×D311yescharacteristic
273C2×C5×C8—31no—
274C2×C5×C8—31no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4#6711yescharacteristic
278C5×C4⋊C4#6711yescharacteristic
279C5×C22⋊C4#6711yescharacteristic
280C5×C22⋊C4#6711yescharacteristic
281C42×C5C22×D311yescharacteristic
282C42×C5C22×D311yescharacteristic
283C22⋊Dic5—61no—
284C22⋊Dic5—61no—
285#685—21no—
286#685—21no—
287C4⋊Dic5—21no—
288C4⋊Dic5—31no—
289C4⋊Dic5—31no—
290C4⋊Dic5—61no—
291C4⋊Dic5—61no—
292C4⋊Dic5C22×D311yescharacteristic
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—21no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302C4×Dic5—21no—
303C4×Dic5—21no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306Dic20—62no—
307Dic20—62no—
308#677—62no—
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—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—31no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—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—41no—
340Dic15—41no—
341Dic15—41no—
342Dic15—41no—
343C3×Dic5—22no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×D4—51no—
350C2×C3×D4—101no—
351C22×C3×C4—101no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4C22×D511yescharacteristic
356C2×Dic6—51no—
357C2×Dic6—51no—
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4D2011yescharacteristic
364C3×C4⋊C4D2011yescharacteristic
365C3×C22⋊C4—101no—
366C3×C22⋊C4—101no—
367C3×C22⋊C4D2011yescharacteristic
368C3×C22⋊C4D2011yescharacteristic
369C3×C42—101no—
370C3×C42—101no—
371C3×C42C22×D511yescharacteristic
372C3×C42C22×D511yescharacteristic
373#217—101no—
374#217—101no—
375#216—102no—
376#216—102no—
377#214—102no—
378#214—102no—
379C4⋊Dic3—51no—
380C4⋊Dic3—51no—
381C4⋊Dic3—101no—
382C4⋊Dic3—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8C22×D511yescharacteristic
392C2×C3⋊C8C22×D511yescharacteristic
393C2×C3⋊C8C22×D511yescharacteristic
394C2×C3⋊C8C22×D511yescharacteristic
395C23×C5C2×#6711yescharacteristic
396C22×D5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5C2×#6711yescharacteristic
400C2×C4×C5C2×#6711yescharacteristic
401C2×C4×C5C2×#6711yescharacteristic
402C2×C4×C5C2×#6711yescharacteristic
403C2×C4×C5C2×#6711yescharacteristic
404C2×C4×C5C23×D311yescharacteristic
405C22⋊D5—24no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—81no—
414D20—21no—
415D20#23512yes—
416C4×D5—24no—
417C4×D5—81no—
418C4×D5—81no—
419Dic10—21no—
420Dic10—61no—
421Dic10—61no—
422Dic10—61no—
423Dic10—61no—
424Dic10#23512yes—
425C5×C8—61no—
426C5×C8—61no—
427C5×C8—61no—
428C5×C8—61no—
429C2×#41—51no—
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—51no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—101no—
451#117D3×D511yescharacteristic
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—31no—
459C4⋊C8—31no—
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⋊C8—31no—
469C22⋊C8—31no—
470#97—31no—
471C4×C8—31no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—42no—
477C23×C3—101no—
478C23×C3C2×D2011yescharacteristic
479C3×Q8—52no—
480C3×Q8—101no—
481C3×D4—52no—
482C3×D4—104no—
483C3×D4—101no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—104no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—401no—
491C2×C3×C4—401no—
492C2×C3×C4—401no—
493C2×C3×C4C2×D2011yescharacteristic
494C2×C3×C4C2×D2011yescharacteristic
495C2×C3×C4C2×D2011yescharacteristic
496C2×C3×C4C2×D2011yescharacteristic
497C2×C3×C4C2×D2011yescharacteristic
498C2×C3×C4C23×D511yescharacteristic
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3—101no—
502C2×Dic3—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×#6711yescharacteristic
515C2×D5—22no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5C2×#23511yescharacteristic
524C4×C5C2×#23511yescharacteristic
525Dic5—22no—
526Dic5—41no—
527Dic5—41no—
528Dic5—121no—
529Dic5—121no—
530Dic5—121no—
531Dic5—121no—
532#41—102no—
533#41—102no—
534C2×Q8—51no—
535C2×Q8—151no—
536C2×Q8—151no—
537C2×D4—51no—
538C2×D4—101no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—31no—
552C4⋊C4—51no—
553C4⋊C4—51no—
554C4⋊C4—101no—
555C4⋊C4—101no—
556C4⋊C4—101no—
557C4⋊C4—151no—
558C4⋊C4—151no—
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⋊C4#120211yescharacteristic
568C4⋊C4#120211yescharacteristic
569C22⋊C4—101no—
570C22⋊C4—101no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C22⋊C4#120211yescharacteristic
574C22⋊C4#120211yescharacteristic
575C42—101no—
576C42—101no—
577C42—301no—
578C42—301no—
579C42C2×D3×D511yescharacteristic
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—102no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C22×D2011yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—102no—
595C3×C4—201no—
596C3×C4—201no—
597C3×C4D5×#4111yescharacteristic
598C3×C4D5×#4111yescharacteristic
599Dic3—201no—
600Dic3—201no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#579111yescharacteristic
605C2×C5#583611yescharacteristic
606C2×C5#583811yescharacteristic
607D5—42no—
608C23—101no—
609C23C2×#120211yescharacteristic
610Q8—52no—
611Q8—101no—
612Q8—301no—
613Q8—301no—
614Q8—301no—
615Q8—301no—
616D4—52no—
617D4—104no—
618D4—101no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—104no—
622C2×C4—101no—
623C2×C4—101no—
624C2×C4—101no—
625C2×C4—301no—
626C2×C4—301no—
627C2×C4—301no—
628C2×C4—301no—
629C2×C4—401no—
630C2×C4—401no—
631C2×C4—401no—
632C2×C4C2×#120211yescharacteristic
633C2×C4C2×#120211yescharacteristic
634C2×C4C2×#120211yescharacteristic
635C2×C4C2×#120211yescharacteristic
636C2×C4C2×#120211yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—61no—
641C8—61no—
642C2×C3—41no—
643C2×C3—202no—
644C2×C3#6585811yescharacteristic
645C2×C3#6608511yescharacteristic
646C2×C3#6608711yescharacteristic
647C5#8257511yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—102no—
652C22—201no—
653C22—201no—
654C22C22×#120211yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—102no—
661C4—201no—
662C4—201no—
663C4—601no—
664C4—601no—
665C4—601no—
666C4—601no—
667C4D5×#23511yescharacteristic
668C4D5×#23511yescharacteristic
669C3#1061111611yescharacteristic, complemented, Sylow
670C2—41no—
671C2—202no—
672C2#1175456411yescharacteristic
673C2#1175530911yescharacteristic
674C2#1175531211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenter#117D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756277C2semidirect
3. C5×#5000C2semidirect
6. #11748450C2semidirect
7. #11748414C2semidirect
8. #11747095C2semidirect
9. #11747091C2semidirect
10. C4×#6662C2semidirect
11. #11747062C2semidirect
12. #11747052C2semidirect
13. C4×#6657C2semidirect
14. #11746944C2semidirect
15. #11746888C2semidirect
137. #5000D5semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10611116semidirect

Maximal subgroups

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

subgroupindex
#117562772
C3×#658572
C5×#50002
#117485312
#117484502
#117484142
#117470952
#117470912
C4×#66622
#117470622
#117470522
C4×#66572
#117469442
#117468882
#106111163
#825755