Finite Group Databasebeta

← #14436291

Subgroups — #14436291

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#11752509C211yesmaximal, characteristic, complemented
3#11751123C211yesmaximal, characteristic, complemented
4C5×#5031C211yesmaximal, characteristic, complemented
5#11749294C211yesmaximal, characteristic
6#11749294C211yesmaximal, characteristic
7#11749247C211yesmaximal, characteristic, complemented
8Dic5×#216C211yesmaximal, characteristic, complemented
9#11747471C211yesmaximal, characteristic, complemented
10#11747340C211yesmaximal, characteristic, complemented
11#11747338C211yesmaximal, characteristic, complemented
12#11747261C211yesmaximal, characteristic, complemented
13#11747059C211yesmaximal, characteristic, complemented
14#11746888C211yesmaximal, characteristic, complemented
15#11746873C211yesmaximal, characteristic, complemented
16#10612191—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19#91759C2211yescharacteristic
20C2×C5×#216C2211yescharacteristic
21C2×C5×#216C2211yescharacteristic
22C5×#869C2211yescharacteristic
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#91361—21no—
33#91361—21no—
34#91359C2211yescharacteristic
35#91359C2211yescharacteristic
36#91336—21no—
37#91336—21no—
38Dic5×Dic6C2211yescharacteristic
39Dic5×Dic6C2211yescharacteristic
40C2×#6655C2211yescharacteristic
41C2×#6655C2211yescharacteristic
42#91119C2211yescharacteristic
43#91119C2211yescharacteristic
44#91092C2211yescharacteristic
45#91091C2211yescharacteristic
46C4⋊(C3⋊#168)C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C5×#810C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90990C2211yescharacteristic
51#90987C2211yescharacteristic
52#90972C2211yescharacteristic
53#90972C2211yescharacteristic
54#90965C2211yescharacteristic
55#90965C2211yescharacteristic
56#90955C2211yescharacteristic
57#90955C2211yescharacteristic
58#90952C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#82575—51nomaximal, Hall
61#66065—31no—
62#65908D311yescharacteristic
63C5×#462—31no—
64#65476—31no—
65#65476—31no—
66#65473—31no—
67Q16×Dic5—31no—
68#65372—31no—
69#65311—31no—
70#65136—31no—
71#65129—31no—
72#65106—31no—
73#65098—31no—
74#65094—31no—
75#65077—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C5×Dic6C2311yescharacteristic
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
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95#6712—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#216—22no—
99C5×#216—22no—
100C5×C4⋊Dic3—21no—
101C5×C4⋊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#6665—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6655—22no—
124#6655—22no—
125C3×#520—51no—
126#5518—51no—
127#5239—51no—
128#5239—51no—
129#5031D511yescharacteristic, complemented
130#5030—51no—
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—
142C2×C5×Q16—31no—
143C5×C4⋊Q8—31no—
144C4×C5×Q8C2×D311yescharacteristic
145#4092—31no—
146#4092—31no—
147Q8×Dic5—31no—
148Q8×Dic5—31no—
149Q8×Dic5C2×D311yescharacteristic
150C2×#688—31no—
151C2×#688—31no—
152#4044—61no—
153#4044—61no—
154#4039—21no—
155#4039C2×D311yescharacteristic
156D5×C4⋊C4—21no—
157D5×C4⋊C4C2×D311yescharacteristic
158#4035—61no—
159#4035—61no—
160C4×D20—21no—
161C4×D20C2×D311yescharacteristic
162#4018—21no—
163#4018C2×D311yescharacteristic
164#4016—31no—
165C5×C4⋊C8—31no—
166C5×#103—31no—
167C5×#103—31no—
168#3967—31no—
169#3967—31no—
170#3967—31no—
171#3967—31no—
172#3953—31no—
173#3953—31no—
174#3952—31no—
175#3952—31no—
176#3950—31no—
177#3949—31no—
178#3947—31no—
179C8×Dic5—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—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C5×Dic6—21no—
198C5×Dic6—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×#216C2×D511yescharacteristic
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#869C2×D511yescharacteristic
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835—51no—
245#832—51no—
246#832—51no—
247#830—51no—
248#830—51no—
249#810—51no—
250#810—51no—
251#810C2×D511yescharacteristic
252#810C2×D511yescharacteristic
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)C2×D511yescharacteristic
259#803—51no—
260C4×C3⋊C8—51no—
261C2×C5×Q8—31no—
262C2×C5×Q8—31no—
263C2×C5×Q8C22×D311yescharacteristic
264#713—22no—
265#713—22no—
266C2×D20—21no—
267C2×D20C22×D311yescharacteristic
268C2×C4×D5—21no—
269C2×C4×D5—21no—
270C2×C4×D5—21no—
271C2×C4×D5—21no—
272C2×C4×D5C22×D311yescharacteristic
273C5×Q16—62no—
274C5×Q16—62no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4C22×D311yescharacteristic
281C42×C5—21no—
282C42×C5C22×D311yescharacteristic
283#688—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—31no—
294C4⋊Dic5—61no—
295C4⋊Dic5—61no—
296C4⋊Dic5C22×D311yescharacteristic
297#683—21no—
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×Dic5—61no—
307C4×Dic5C22×D311yescharacteristic
308C2×#168—31no—
309C2×#168—31no—
310#541—151no—
311#520—51no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—31no—
317#461—151no—
318#452—151no—
319#452—151no—
320#441—151no—
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×Dic6C22×D511yescharacteristic
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—22no—
377#214—102no—
378#214—102no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—51no—
382C4⋊Dic3—51no—
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⋊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—61no—
401C5×Q8—61no—
402C5×Q8#23512yes—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5C2×#6711yescharacteristic
408C2×C4×C5C2×#6711yescharacteristic
409C2×C4×C5C23×D311yescharacteristic
410C2×Dic5—21no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5C2×#6711yescharacteristic
414C2×Dic5C2×#6711yescharacteristic
415C2×Dic5C2×#6711yescharacteristic
416D20—24no—
417D20—21no—
418D20#23512yes—
419C4×D5—24no—
420C4×D5—21no—
421C4×D5—21no—
422C4×D5—81no—
423C4×D5—81no—
424C4×D5—81no—
425C5×C8—61no—
426C5×C8—61no—
427#168—61no—
428#168—61no—
429C2×#41—51no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—31no—
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—151no—
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—151no—
457#106—151no—
458C4⋊C8—31no—
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—151no—
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#71112yes—
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—21no—
506Dic6—21no—
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—31no—
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—62no—
546SD16—302no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—21no—
553C4⋊C4—51no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—151no—
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—101no—
578C42—301no—
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×#71111yescharacteristic
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—61no—
614Q8—61no—
615Q8#677212yes—
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#6594011yescharacteristic
645C2×C3#6610011yescharacteristic
646C2×C3#6611211yescharacteristic
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×#677211yescharacteristic
668C4D5×#23511yescharacteristic
669C3#1061219111yescharacteristic, complemented, Sylow
670C2—201no—
671C2—202no—
672C2#1175452611yescharacteristic
673C2#1175510111yescharacteristic
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. #11752509C2semidirect
3. #11751123C2semidirect
4. C5×#5031C2semidirect
7. #11749247C2semidirect
8. Dic5×#216C2semidirect
9. #11747471C2semidirect
10. #11747340C2semidirect
11. #11747338C2semidirect
12. #11747261C2semidirect
13. #11747059C2semidirect
14. #11746888C2semidirect
15. #11746873C2semidirect
129. #5031D5semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10612191semidirect

Maximal subgroups

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

subgroupindex
C3×#659082
#117525092
#117511232
C5×#50312
#117492942
#117492472
Dic5×#2162
#117474712
#117473402
#117473382
#117472612
#117470592
#117468882
#117468732
#106121913
#825755