Finite Group Databasebeta

← #12963122

Subgroups — #12963122

Order 1280.

2038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617735C211yesmaximal, characteristic
2C5×#2906C211yesmaximal, characteristic, complemented
3#10615524C211yesmaximal, characteristic
4#10615524C211yesmaximal, characteristic
5#10615513C211yesmaximal, characteristic, complemented
6Dic5×#131C211yesmaximal, characteristic, complemented
7#10614243C211yesmaximal, characteristic, complemented
8#10610803C213yesmaximal, complemented
9#10610803C213yesmaximal, complemented
10#10610802C213yesmaximal, complemented
11#10610801C213yesmaximal, complemented
12#10610771C213yesmaximal, complemented
13#10610770C213yesmaximal, complemented
14#10610731C213yesmaximal, complemented
15C2×#65129C213yesmaximal, complemented
16C2×D5×#41C2211yescharacteristic
17C2×C5×#131C2211yescharacteristic
18C2×C5×#131C2211yescharacteristic
19C4×C5×#41C2211yescharacteristic
20#41×Dic5C2211yescharacteristic
21C2×#4094C2211yescharacteristic
22C2×#4094C2211yescharacteristic
23#65908C411yescharacteristic
24#65908C411yescharacteristic
25#65906C411yescharacteristic
26#65906C411yescharacteristic
27#65880C413yes—
28#65880C413yes—
29#65879C413yes—
30#65879C413yes—
31#65856C2213yes—
32D5×#117C2213yes—
33C4×#709C2213yes—
34C2×#4018C2213yes—
35C5×#424C2213yescomplemented
36C5×#424C2213yescomplemented
37C5×#423C2213yescomplemented
38C2×C5×C4⋊C8C2213yescomplemented
39#65418C2213yes—
40#65418C2213yes—
41#65415C2213yes—
42#65415C2213yes—
43#65411C2213yescomplemented
44#65411C2213yescomplemented
45M16×Dic5C2213yescomplemented
46M16×Dic5C2213yescomplemented
47#65399C2213yes—
48#65399C2213yes—
49C2×#3952C2213yes—
50C2×#3952C2213yes—
51#65390C2213yescomplemented
52#65390C2213yescomplemented
53C2×#3947C2213yescomplemented
54C2×C8×Dic5C2213yescomplemented
55#65288C2213yescomplemented
56#65288C2213yescomplemented
57#65213C2213yescomplemented
58C2×C4⋊#168C2213yescomplemented
59#65129C2211yescharacteristic
60#65129C2213yes—
61#65129C2213yes—
62#65129C2213yes—
63#65129C2216yes—
64#65129C2213yescomplemented
65#65129C2213yescomplemented
66#65129C2213yescomplemented
67#65129C2213yescomplemented
68#65129C2216yescomplemented
69#65129C2216yescomplemented
70#65124C2216yescomplemented
71#65124C2216yescomplemented
72#65122C2216yescomplemented
73#65122C2216yescomplemented
74#60129—51nomaximal, Sylow
75C2×C5×#41C2311yescharacteristic
76D5×#41—24no—
77D5×#41—24no—
78C2×#713C2×C411yescharacteristic
79C2×Q8×D5C2×C411yescharacteristic
80C2×#711C2×C413yes—
81C2×D4×D5C2×C413yes—
82C2×#709C2313yes—
83C22×C4×D5C2313yes—
84C5×#131—24no—
85C5×#131—24no—
86C2×C5×M16C2313yes—
87C2×C5×M16C2313yes—
88C22×C5×C8C2313yes—
89C22×C5×C8C2313yes—
90C4×C5×Q8C2×C411yescharacteristic
91C4×C5×Q8C2×C411yescharacteristic
92C4×C5×D4C2×C413yes—
93C4×C5×D4C2×C413yes—
94C5×#117C2313yes—
95C2×C42×C5C2313yes—
96#4094—24no—
97#4094—24no—
98Q8×Dic5C2×C411yescharacteristic
99Q8×Dic5C2×C411yescharacteristic
100D4×Dic5C2×C413yes—
101D4×Dic5C2×C413yes—
102C4×C22⋊D5C2×C416yes—
103C4×C22⋊D5C2×C416yes—
104C2×#685C2×C413yes—
105C2×#685C2×C413yes—
106#4072C2313yes—
107C2×#683C2×C413yes—
108C2×#683C2×C413yes—
109C2×C4×Dic5C2313yes—
110C2×#681C2313yes—
111C2×#681C2313yes—
112C22×#168C2313yes—
113C22×#168C2313yes—
114#4039C2×C413yes—
115#4039C2×C413yes—
116#4038C2×C413yes—
117#4038C2×C413yes—
118D5×C4⋊C4C2×C413yes—
119D5×C4⋊C4C2×C413yes—
120#4033C2×C413yes—
121#4033C2×C413yes—
122#4027C2×C416yes—
123#4027C2×C416yes—
124D5×C22⋊C4C2×C416yes—
125#4023C2×C416yes—
126C4×D20C2×C413yes—
127C4×D20C2×C413yes—
128#4018C2×C413yes—
129#4018C2×C413yes—
130#4018C2×C413yes—
131#4018C2×C413yes—
132#4018C2311yescharacteristic
133#4018C2313yes—
134#4018C2313yes—
135#4018C2313yes—
136C42×D5C2316yes—
137C4×Dic10C2×C413yes—
138C4×Dic10C2×C413yes—
139C5×C4⋊C8C2311yescharacteristic
140C5×C4⋊C8C2313yes—
141C5×C4⋊C8C2313yes—
142C5×C4⋊C8C2313yes—
143C5×C4⋊C8C2316yes—
144#3952C2313yes—
145#3952C2313yes—
146#3952C2316yes—
147#3952C2316yes—
148#3952C2313yes—
149#3952C2313yes—
150#3952C2311yescharacteristic
151#3952C2311yescharacteristic
152#3952C2313yes—
153#3952C2313yes—
154#3947C2313yes—
155#3947C2313yes—
156#3947C2316yes—
157#3947C2311yescharacteristic
158#3947C2313yes—
159C8×Dic5C2313yes—
160C8×Dic5C2313yes—
161C8×Dic5C2316yes—
162C8×Dic5C2311yescharacteristic
163C8×Dic5C2313yes—
164C4⋊#168C2313yes—
165C4⋊#168C2316yes—
166C4⋊#168C2313yes—
167C4⋊#168C2311yescharacteristic
168C4⋊#168C2313yes—
169#3428—51no—
170#2925—53no—
171#2925—53no—
172#2924—53no—
173#2924—53no—
174#2923—53no—
175#2922—53no—
176#2921—53no—
177C2×#433—53no—
178#2906—51no—
179#2906D511yescharacteristic, complemented
180#2880—51no—
181#2880—51no—
182#2875—51no—
183C4×#131—51no—
184C23×D5C22×C413yes—
185C5×#41#4114yes—
186C5×#41#4114yes—
187C2×C5×Q8C22×C411yescharacteristic
188C2×C5×D4C22×C413yes—
189C22×C4×C5C22×C413yes—
190C22×C4×C5C22×C413yes—
191C22×C4×C5C2413yes—
192C2×C22⋊D5C22×C416yes—
193C22×Dic5C22×C413yes—
194C22×Dic5C22×C413yes—
195C22×Dic5C22×C413yes—
196#713—24no—
197Q8×D5—24no—
198#711—212no—
199D4×D5—212no—
200#709—26no—
201#709—26no—
202C2×D20C22×C413yes—
203C2×C4×D5—26no—
204C2×C4×D5—26no—
205C2×C4×D5C22×C413yes—
206C2×C4×D5C22×C413yes—
207C2×C4×D5C22×C416yes—
208C2×C4×D5C22×C416yes—
209C2×C4×D5C2411yescharacteristic
210C2×C4×D5C2413yes—
211C2×Dic10C22×C413yes—
212C5×M16—26no—
213C5×M16—26no—
214C2×C5×C8—26no—
215C2×C5×C8—26no—
216C2×C5×C8C2411yescharacteristic
217C2×C5×C8C2411yescharacteristic
218C2×C5×C8C2413yes—
219C2×C5×C8C2413yes—
220C5×C4⋊C4C22×C413yes—
221C5×C4⋊C4C22×C413yes—
222C5×C22⋊C4C22×C416yes—
223C42×C5C22×C413yes—
224C42×C5C22×C413yes—
225C42×C5C2411yescharacteristic
226C42×C5C2413yes—
227C22⋊Dic5C22×C416yes—
228#685C22×C411yescharacteristic
229#685C22×C411yescharacteristic
230#685C22×C413yes—
231#685C22×C413yes—
232#685C22×C413yes—
233#685C22×C413yes—
234#685C22×C413yes—
235#685C22×C413yes—
236C4⋊Dic5C22×C413yes—
237C4⋊Dic5C22×C413yes—
238#683C22×C413yes—
239#683C22×C413yes—
240#683C22×C411yescharacteristic
241#683C22×C411yescharacteristic
242#683C22×C413yes—
243#683C22×C413yes—
244#683C22×C413yes—
245#683C22×C413yes—
246C4×Dic5C22×C416yes—
247C4×Dic5C22×C416yes—
248C4×Dic5C22×C413yes—
249C4×Dic5C22×C413yes—
250C4×Dic5C2413yes—
251C4×Dic5C2411yescharacteristic
252#681—26no—
253#681—26no—
254C2×#168—26no—
255C2×#168—26no—
256C2×#168C2411yescharacteristic
257C2×#168C2413yes—
258C2×#168C2413yes—
259C2×#168C2411yescharacteristic
260C22×#41—51no—
261C2×#131—51no—
262C2×#131—51no—
263C2×#131C2×D511yescharacteristic
264C2×#131C2×D511yescharacteristic
265#520—51no—
266#520—51no—
267#520—53no—
268#520—53no—
269#519—51no—
270#519—51no—
271#518—53no—
272#518—53no—
273C4×#41—51no—
274C4×#41—53no—
275C4×#41—53no—
276C4×#41C2×D511yescharacteristic
277C2×#117—53no—
278C2×#117—53no—
279#433—51no—
280#433—53no—
281#433—53no—
282#433—53no—
283#433—53no—
284#433—53no—
285#433—53no—
286#433—53no—
287#433—56no—
288#433—56no—
289#433—56no—
290#432—56no—
291#432—56no—
292#431—56no—
293#431—56no—
294#424—53no—
295#424—53no—
296#424C2×D513yescomplemented
297#424C2×D513yescomplemented
298#423—53no—
299#423C2×D513yescomplemented
300C2×C4⋊C8—53no—
301C2×C4⋊C8C2×D513yescomplemented
302#408—53no—
303#408—53no—
304#408—53no—
305#408—53no—
306#407—53no—
307#407—53no—
308C2×C22⋊C8—53no—
309C2×C22⋊C8—53no—
310#405—53no—
311#405—53no—
312#405—53no—
313#405—53no—
314C4×M16—53no—
315C4×M16—53no—
316C2×#97—53no—
317C2×C4×C8—53no—
318C23×C5C23×C413yes—
319C22×D5—26no—
320C22×D5—43no—
321C22×D5—43no—
322C22×D5C23×C411yescharacteristic
323C22×D5C23×C413yes—
324C5×Q8#11714yes—
325C5×D4#117112yes—
326C2×C4×C5—43no—
327C2×C4×C5—43no—
328C2×C4×C5C23×C413yes—
329C2×C4×C5C23×C413yes—
330C2×C4×C5C23×C411yescharacteristic
331C2×C4×C5C23×C411yescharacteristic
332C2×C4×C5C23×C413yes—
333C2×C4×C5C2×#4116yes—
334C2×C4×C5C2×#4116yes—
335C2×C4×C5C2511yescharacteristic
336C22⋊D5—212no—
337C2×Dic5—26no—
338C2×Dic5—43no—
339C2×Dic5—43no—
340C2×Dic5C23×C413yes—
341C2×Dic5C23×C411yescharacteristic
342C2×Dic5C23×C411yescharacteristic
343C2×Dic5C23×C413yes—
344C2×Dic5C23×C413yes—
345C2×Dic5C23×C411yescharacteristic
346D20—26no—
347C4×D5—26no—
348C4×D5—26no—
349C4×D5—21no—
350C4×D5—21no—
351C4×D5—23no—
352C4×D5—23no—
353C4×D5—46no—
354C4×D5—46no—
355Dic10—26no—
356C5×C8—21no—
357C5×C8—21no—
358C5×C8—23no—
359C5×C8—23no—
360#168—21no—
361#168—21no—
362#168—23no—
363#168—23no—
364C2×#41—51no—
365C2×#41—53no—
366C2×#41—53no—
367C2×#41—104no—
368C2×#41—104no—
369C2×#41C22×D511yescharacteristic
370C22×Q8—51no—
371C22×D4—53no—
372C23×C4—53no—
373#131—24no—
374#131—24no—
375#131—104no—
376#131—104no—
377C2×M16—53no—
378C2×M16—53no—
379C2×M16C22×D513yes—
380C2×M16C22×D513yes—
381C22×C8—53no—
382C22×C8—53no—
383C22×C8C22×D513yes—
384C22×C8C22×D513yes—
385C4×Q8—51no—
386C4×Q8—51no—
387C4×Q8—53no—
388C4×Q8—53no—
389C4×Q8—53no—
390C4×Q8—53no—
391C4×Q8C4×D511yescharacteristic
392C4×Q8C4×D511yescharacteristic
393C4×D4—53no—
394C4×D4—53no—
395C4×D4—56no—
396C4×D4—56no—
397C4×D4—53no—
398C4×D4—53no—
399C4×D4—56no—
400C4×D4—56no—
401C4×D4—53no—
402C4×D4—53no—
403C4×D4C4×D513yes—
404C4×D4C4×D513yes—
405#117—53no—
406#117—53no—
407#117—53no—
408#117—56no—
409#117—53no—
410#117—53no—
411#117—53no—
412#117—53no—
413#117—53no—
414#117—51no—
415#117—53no—
416#117—53no—
417#117C22×D513yes—
418C2×C4⋊C4—53no—
419C2×C4⋊C4—53no—
420C2×C4⋊C4—53no—
421C2×C4⋊C4—53no—
422C2×C22⋊C4—53no—
423C2×C22⋊C4—53no—
424C2×C22⋊C4—56no—
425C2×C42—53no—
426C2×C42—56no—
427C2×C42C22×D513yes—
428C4⋊C8—51no—
429C4⋊C8—53no—
430C4⋊C8—53no—
431C4⋊C8—53no—
432C4⋊C8—56no—
433C4⋊C8C22×D511yescharacteristic
434C4⋊C8C22×D513yes—
435C4⋊C8C22×D513yes—
436C4⋊C8C22×D513yes—
437C4⋊C8C22×D516yes—
438C22⋊C8—51no—
439C22⋊C8—51no—
440C22⋊C8—53no—
441C22⋊C8—53no—
442C22⋊C8—53no—
443C22⋊C8—53no—
444C22⋊C8—53no—
445C22⋊C8—53no—
446C22⋊C8—56no—
447C22⋊C8—56no—
448#97—51no—
449#97—53no—
450#97—53no—
451#97—53no—
452#97—56no—
453C4×C8—51no—
454C4×C8—53no—
455C4×C8—53no—
456C4×C8—53no—
457C4×C8—56no—
458C22×C5—23no—
459C22×C5—23no—
460C22×C5C2×#11716yes—
461C22×C5C24×C411yescharacteristic
462C2×D5—21no—
463C2×D5—23no—
464C2×D5—23no—
465C2×D5—23no—
466C2×D5—21no—
467C2×D5—21no—
468C2×D5—86no—
469C4×C5—23no—
470C4×C5—23no—
471C4×C5—21no—
472C4×C5—21no—
473C4×C5C2×#11716yes—
474C4×C5C22×#4111yescharacteristic
475C4×C5C22×#4111yescharacteristic
476Dic5—23no—
477Dic5—21no—
478Dic5—23no—
479Dic5—23no—
480Dic5—21no—
481Dic5—21no—
482C24—53no—
483#41—104no—
484#41—1012no—
485#41—106no—
486#41—106no—
487#41#71114yes—
488#41#71314yes—
489C2×Q8—53no—
490C2×Q8—104no—
491C2×Q8C2×C4×D511yescharacteristic
492C2×D4—56no—
493C2×D4—53no—
494C2×D4—1012no—
495C2×D4C2×C4×D513yes—
496C22×C4—53no—
497C22×C4—53no—
498C22×C4—53no—
499C22×C4—53no—
500C22×C4—53no—
501C22×C4—53no—
502C22×C4—51no—
503C22×C4—56no—
504C22×C4—56no—
505C22×C4—106no—
506C22×C4—106no—
507C22×C4C2×C4×D513yes—
508C22×C4C2×C4×D513yes—
509C22×C4C23×D513yes—
510M16—26no—
511M16—26no—
512M16—106no—
513M16—106no—
514C2×C8—26no—
515C2×C8—26no—
516C2×C8—51no—
517C2×C8—53no—
518C2×C8—53no—
519C2×C8—51no—
520C2×C8—106no—
521C2×C8—106no—
522C2×C8C23×D511yescharacteristic
523C2×C8C23×D513yes—
524C2×C8C23×D513yes—
525C2×C8C23×D511yescharacteristic
526C4⋊C4—53no—
527C4⋊C4—53no—
528C4⋊C4—51no—
529C4⋊C4—51no—
530C4⋊C4—53no—
531C4⋊C4—53no—
532C4⋊C4—53no—
533C4⋊C4—53no—
534C4⋊C4—53no—
535C4⋊C4—53no—
536C4⋊C4C2×C4×D513yes—
537C4⋊C4C2×C4×D513yes—
538C22⋊C4—56no—
539C22⋊C4—53no—
540C22⋊C4—53no—
541C22⋊C4—51no—
542C22⋊C4—51no—
543C22⋊C4—53no—
544C22⋊C4—53no—
545C22⋊C4—53no—
546C22⋊C4—53no—
547C22⋊C4C2×C4×D516yes—
548C42—53no—
549C42—53no—
550C42—56no—
551C42—56no—
552C42—51no—
553C42—53no—
554C42C2×C4×D513yes—
555C42C2×C4×D513yes—
556C42C23×D513yes—
557C42C23×D511yescharacteristic
558C2×C5—26no—
559C2×C5C22×#11711yescharacteristic
560C2×C5#357311yescharacteristic
561C2×C5#357311yescharacteristic
562D5—43no—
563D5—41no—
564C23—51no—
565C23—53no—
566C23—106no—
567C23—203no—
568C23—203no—
569C23C22×C4×D513yes—
570Q8—106no—
571Q8#403814yes—
572D4—1012no—
573D4—106no—
574D4#4038112yes—
575C2×C4—43no—
576C2×C4—43no—
577C2×C4—53no—
578C2×C4—51no—
579C2×C4—53no—
580C2×C4—51no—
581C2×C4—53no—
582C2×C4—51no—
583C2×C4—106no—
584C2×C4—106no—
585C2×C4—106no—
586C2×C4—101no—
587C2×C4—103no—
588C2×C4—101no—
589C2×C4—103no—
590C2×C4—206no—
591C2×C4—206no—
592C2×C4—203no—
593C2×C4—203no—
594C2×C4C22×C4×D513yes—
595C2×C4C22×C4×D513yes—
596C2×C4C22×C4×D511yescharacteristic
597C2×C4C22×C4×D511yescharacteristic
598C2×C4C22×C4×D513yes—
599C2×C4C2×#71116yes—
600C2×C4C2×#71316yes—
601C2×C4C24×D511yescharacteristic
602C8—21no—
603C8—21no—
604C8—23no—
605C8—23no—
606C8—101no—
607C8—101no—
608C8—103no—
609C8—103no—
610C5#6012911yescharacteristic, complemented, Sylow
611C22—23no—
612C22—23no—
613C22—103no—
614C22—101no—
615C22—103no—
616C22—101no—
617C22—101no—
618C22—103no—
619C22—406no—
620C22C2×#403816yes—
621C22C23×C4×D511yescharacteristic
622C4—21no—
623C4—23no—
624C4—21no—
625C4—23no—
626C4—103no—
627C4—101no—
628C4—103no—
629C4—101no—
630C4—101no—
631C4—103no—
632C4C2×#403816yes—
633C4C22×#71111yescharacteristic
634C4C22×#71311yescharacteristic
635C2—26no—
636C2—201no—
637C2—203no—
638C2C22×#403811yescharacteristic
639C2#1061906111yescharacteristic
640C2#1061906711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D5
commutator, socleC22×C5C24×C4
FittingC5×#2906C2
prime radicalC2×D5×#41C22
cosocleC2×C4×C5C25
hypercenter#2906D5
hypocenterC5#60129
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. C5×#2906C2semidirect
5. #10615513C2semidirect
6. Dic5×#131C2semidirect
7. #10614243C2semidirect
8. #10610803C2semidirect
9. #10610803C2semidirect
10. #10610802C2semidirect
11. #10610801C2semidirect
12. #10610771C2semidirect
13. #10610770C2semidirect
14. #10610731C2semidirect
15. C2×#65129C2semidirect
35. C5×#424C22semidirect
36. C5×#424C22semidirect
37. C5×#423C22semidirect
38. C2×C5×C4⋊C8C22semidirect
43. #65411C22semidirect
44. #65411C22semidirect
45. M16×Dic5C22semidirect
46. M16×Dic5C22semidirect
51. #65390C22semidirect
52. #65390C22semidirect
53. C2×#3947C22semidirect
54. C2×C8×Dic5C22semidirect
55. #65288C22semidirect
56. #65288C22semidirect
57. #65213C22semidirect
58. C2×C4⋊#168C22semidirect
64. #65129C22semidirect
65. #65129C22semidirect
66. #65129C22semidirect
67. #65129C22semidirect
68. #65129C22semidirect
69. #65129C22semidirect
70. #65124C22semidirect
71. #65124C22semidirect
72. #65122C22semidirect
73. #65122C22semidirect
179. #2906D5semidirect
296. #424C2×D5semidirect
297. #424C2×D5semidirect
299. #423C2×D5semidirect
301. C2×C4⋊C8C2×D5semidirect
610. C5#60129semidirect

Maximal subgroups

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

subgroupindex
#106177352
C5×#29062
#106155242
#106155132
Dic5×#1312
#106142432
#106108032
#106108022
#106108012
#106107712
#106107702
#106107312
C2×#651292
#601295