Finite Group Databasebeta

← #14436186

Subgroups — #14436186

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
2C5×#5523C211yesmaximal, characteristic
3C3×#65289C211yesmaximal, characteristic, complemented
4#11748464C211yesmaximal, characteristic, complemented
5#11748444C211yesmaximal, characteristic, complemented
6#11748361C211yesmaximal, characteristic
7#11748361C211yesmaximal, characteristic
8#11747101C211yesmaximal, characteristic, complemented
9#11747093C211yesmaximal, characteristic, complemented
10C4×#6663C211yesmaximal, characteristic, complemented
11#11747077C211yesmaximal, characteristic, complemented
12#11747056C211yesmaximal, characteristic, complemented
13C4×#6659C211yesmaximal, characteristic, complemented
14#11746965C211yesmaximal, characteristic, complemented
15#11746894C211yesmaximal, characteristic, complemented
16#10614306—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
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×C5×C4⋊Dic3C2211yescharacteristic
30C5×#892—21no—
31C5×D3×C4⋊C4—21no—
32C5×#67⋊C4—21no—
33C5×#67⋊C4—21no—
34C4×C5×D12C2211yescharacteristic
35C4×C5×D12C2211yescharacteristic
36C4×C5×Dic6C2211yescharacteristic
37C4×C5×Dic6C2211yescharacteristic
38C2×#6663C2211yescharacteristic
39C2×#6663C2211yescharacteristic
40C2×#6659C2211yescharacteristic
41C2×#6659C2211yescharacteristic
42C3×C22⋊#168C2211yescharacteristic
43C3×C22⋊#168C2211yescharacteristic
44C3×C4⋊#168C2211yescharacteristic
45C3×C4⋊#168C2211yescharacteristic
46C3×#3935C2211yescharacteristic
47C3×C4×#168C2211yescharacteristic
48#90988C2211yescharacteristic
49#90988C2211yescharacteristic
50#90985C2211yescharacteristic
51#90985C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90975C2211yescharacteristic
55#90975C2211yescharacteristic
56#90973C2211yescharacteristic
57#90973C2211yescharacteristic
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic
60#79385—51nomaximal, Hall
61C5×#520—31no—
62#65852—31no—
63#65528—31no—
64#65528—31no—
65#65320—31no—
66#65319—31no—
67C4×#689—31no—
68#65311—31no—
69#65308—31no—
70#65307—31no—
71C4×#687—31no—
72#65298—31no—
73#65289D311yescharacteristic, complemented
74#65260—31no—
75#65259—31no—
76C22×C3×C4×C5C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×#67—21no—
80C22×C5×Dic3—21no—
81C5×#235—22no—
82C5×#235—22no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C5×Dic6C2311yescharacteristic
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—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4—21no—
115C4×C5×Dic3—21no—
116C4×C5×Dic3—21no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121#6663—22no—
122#6663—22no—
123#6659—22no—
124#6659—22no—
125#5523D511yescharacteristic
126#5518—51no—
127C3×#433—51no—
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×C5×#41—31no—
141C4×C5×Q8—31no—
142C4×C5×Q8—31no—
143C4×C5×D4—31no—
144C4×C5×D4—31no—
145C4×C5×D4—61no—
146C4×C5×D4—61no—
147C5×#117—61no—
148C5×#117C2×D311yescharacteristic
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4—61no—
151C2×#689—31no—
152C2×#689—31no—
153C2×#687—31no—
154C2×#687—31no—
155#4070—31no—
156#4070—31no—
157#4035—61no—
158#4035—61no—
159#4025—61no—
160#4025—61no—
161#4016—31no—
162#4015—31no—
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964—31no—
169C22⋊#168C2×D311yescharacteristic
170C22⋊#168C2×D311yescharacteristic
171#3942—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168C2×D311yescharacteristic
180C4⋊#168C2×D311yescharacteristic
181#3935C2×D311yescharacteristic
182C4×#168C2×D311yescharacteristic
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C5×D3—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—
202C5×#67—24no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—81no—
207C5×D12—21no—
208C5×D12#4112yes—
209C4×C5×D3—24no—
210C4×C5×D3—81no—
211C4×C5×D3—81no—
212C5×Dic6—21no—
213C5×Dic6#4112yes—
214C3×#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×#235C2×D511yescharacteristic
219C3×#117C2×D511yescharacteristic
220C2×C4⋊Dic3C2×D511yescharacteristic
221#924—51no—
222#924—51no—
223C2×Dic12—51no—
224C2×Dic12—51no—
225C2×#204—51no—
226C2×#204—51no—
227#892—21no—
228D3×C4⋊C4—21no—
229#889—101no—
230#889—101no—
231#67⋊C4—21no—
232#67⋊C4—21no—
233#879—101no—
234#879—101no—
235C4×D12C2×D511yescharacteristic
236C4×D12C2×D511yescharacteristic
237#870—51no—
238#869—51no—
239C4×Dic6—51no—
240C4×Dic6—51no—
241C4×Dic6C2×D511yescharacteristic
242C4×Dic6C2×D511yescharacteristic
243C3×C4⋊C8—51no—
244C3×C4⋊C8—51no—
245C3×C22⋊C8—51no—
246C3×C22⋊C8—51no—
247C3×#97—51no—
248C3×C4×C8—51no—
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—
261C5×#41—62no—
262C5×#41—62no—
263C2×C5×Q8—31no—
264C2×C5×D4—31no—
265C2×C5×D4—61no—
266C22×C4×C5—61no—
267C22×C4×C5—61no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5C22×D311yescharacteristic
271C2×Dic10—31no—
272C2×Dic10—31no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4D1211yescharacteristic
279C5×C4⋊C4D1211yescharacteristic
280C5×C22⋊C4—61no—
281C5×C22⋊C4—61no—
282C5×C22⋊C4D1211yescharacteristic
283C5×C22⋊C4D1211yescharacteristic
284C42×C5—61no—
285C42×C5—61no—
286C42×C5C22×D311yescharacteristic
287C42×C5C22×D311yescharacteristic
288C22⋊Dic5—61no—
289C22⋊Dic5—61no—
290#689—62no—
291#689—62no—
292#687—62no—
293#687—62no—
294C4⋊Dic5—31no—
295C4⋊Dic5—31no—
296C4⋊Dic5—61no—
297C4⋊Dic5—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303#683—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C2×#168C22×D311yescharacteristic
307C2×#168C22×D311yescharacteristic
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310#541—151no—
311#520—31no—
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—51no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3—22no—
330C2×C5×D3—41no—
331C2×C5×D3—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—
343C5×Dic3—22no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C22×C3×C4C22×D511yescharacteristic
347C2×#67—21no—
348C22×Dic3—21no—
349#235—22no—
350#235—22no—
351C2×D12C22×D511yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×Dic6—51no—
356C2×Dic6—51no—
357C2×Dic6C22×D511yescharacteristic
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4C22⋊D511yescharacteristic
363C3×C4⋊C4C22⋊D511yescharacteristic
364C3×C22⋊C4C22⋊D511yescharacteristic
365C3×C22⋊C4C22⋊D511yescharacteristic
366C3×C42C22×D511yescharacteristic
367C3×C42C22×D511yescharacteristic
368#217—101no—
369#217—101no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—51no—
374C4⋊Dic3—51no—
375C4⋊Dic3—101no—
376C4⋊Dic3—101no—
377C4⋊Dic3C22×D511yescharacteristic
378C4⋊Dic3C22×D511yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391Dic12—102no—
392Dic12—102no—
393#204—102no—
394#204—102no—
395C23×C5—61no—
396C23×C5C2×D1211yescharacteristic
397C5×Q8—32no—
398C5×Q8—61no—
399C5×D4—32no—
400C5×D4—64no—
401C5×D4—61no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—64no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—241no—
409C2×C4×C5—241no—
410C2×C4×C5—241no—
411C2×C4×C5C2×D1211yescharacteristic
412C2×C4×C5C2×D1211yescharacteristic
413C2×C4×C5C2×D1211yescharacteristic
414C2×C4×C5C2×D1211yescharacteristic
415C2×C4×C5C2×D1211yescharacteristic
416C2×C4×C5C23×D311yescharacteristic
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421Dic10—61no—
422Dic10—61no—
423Dic10—61no—
424Dic10—61no—
425#168—21no—
426#168—21no—
427#168—21no—
428#168—21no—
429C2×#41—31no—
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—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450#117—61no—
451#117D3×D511yescharacteristic
452C2×C4⋊C4—31no—
453C2×C4⋊C4—61no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—51no—
459C4⋊C8—51no—
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—51no—
469C22⋊C8—51no—
470#97—51no—
471C4×C8—51no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C5×D3—42no—
477C23×C3C2×C22⋊D511yescharacteristic
478C22×D3—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4C2×C22⋊D511yescharacteristic
482C2×C3×C4C2×C22⋊D511yescharacteristic
483C2×C3×C4C2×C22⋊D511yescharacteristic
484C2×C3×C4C2×C22⋊D511yescharacteristic
485C2×C3×C4C2×C22⋊D511yescharacteristic
486C2×C3×C4C23×D511yescharacteristic
487#67—24no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—81no—
492C2×Dic3—101no—
493C2×Dic3—101no—
494C2×Dic3—101no—
495C2×Dic3—101no—
496D12—21no—
497D12#70912yes—
498C4×D3—24no—
499C4×D3—81no—
500C4×D3—81no—
501Dic6—21no—
502Dic6—101no—
503Dic6—101no—
504Dic6—101no—
505Dic6—101no—
506Dic6#70912yes—
507C3×C8—101no—
508C3×C8—101no—
509C3×C8—101no—
510C3×C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—62no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C22×D1211yescharacteristic
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—62no—
524C4×C5—121no—
525C4×C5—121no—
526C4×C5D3×#4111yescharacteristic
527C4×C5D3×#4111yescharacteristic
528Dic5—121no—
529Dic5—121no—
530Dic5—121no—
531Dic5—121no—
532#41—62no—
533#41—62no—
534C2×Q8—31no—
535C2×Q8—151no—
536C2×Q8—151no—
537C2×D4—31no—
538C2×D4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—51no—
551C2×C8—51no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
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#120311yescharacteristic
568C4⋊C4#120311yescharacteristic
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C22⋊C4#120311yescharacteristic
574C22⋊C4#120311yescharacteristic
575C42—61no—
576C42—61no—
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×C3C22×C22⋊D511yescharacteristic
586C2×D3—22no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4C2×#70911yescharacteristic
595C3×C4C2×#70911yescharacteristic
596Dic3—22no—
597Dic3—41no—
598Dic3—41no—
599Dic3—201no—
600Dic3—201no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5—122no—
605C2×C5#552411yescharacteristic
606C2×C5#575111yescharacteristic
607C2×C5#575311yescharacteristic
608C23—61no—
609C23C2×#120311yescharacteristic
610Q8—32no—
611Q8—61no—
612Q8—301no—
613Q8—301no—
614Q8—301no—
615Q8—301no—
616D4—32no—
617D4—64no—
618D4—61no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—64no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—241no—
626C2×C4—241no—
627C2×C4—241no—
628C2×C4—301no—
629C2×C4—301no—
630C2×C4—301no—
631C2×C4—301no—
632C2×C4C2×#120311yescharacteristic
633C2×C4C2×#120311yescharacteristic
634C2×C4C2×#120311yescharacteristic
635C2×C4C2×#120311yescharacteristic
636C2×C4C2×#120311yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—101no—
641C8—101no—
642C2×C3—41no—
643C2×C3#6612511yescharacteristic
644C2×C3#6617011yescharacteristic
645C2×C3#6617211yescharacteristic
646D3—42no—
647C5#7938511yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—62no—
652C22—121no—
653C22—121no—
654C22C22×#120311yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—62no—
661C4—121no—
662C4—121no—
663C4—601no—
664C4—601no—
665C4—601no—
666C4—601no—
667C4D3×#70911yescharacteristic
668C4D3×#70911yescharacteristic
669C3#1061430611yescharacteristic, complemented, Sylow
670C2—41no—
671C2—122no—
672C2#1175458411yescharacteristic
673C2#1175530611yescharacteristic
674C2#1175530711yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
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. C3×#65289C2semidirect
4. #11748464C2semidirect
5. #11748444C2semidirect
8. #11747101C2semidirect
9. #11747093C2semidirect
10. C4×#6663C2semidirect
11. #11747077C2semidirect
12. #11747056C2semidirect
13. C4×#6659C2semidirect
14. #11746965C2semidirect
15. #11746894C2semidirect
73. #65289D3semidirect
581. C3×C5#3120semidirect
647. C5#79385semidirect
669. C3#10614306semidirect

Maximal subgroups

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

subgroupindex
#117562772
C5×#55232
C3×#652892
#117484642
#117484442
#117483612
#117471012
#117470932
C4×#66632
#117470772
#117470562
C4×#66592
#117469652
#117468942
#106143063
#793855