Finite Group Databasebeta

← #12121397

Subgroups — #12121397

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615080C211yesmaximal, characteristic
2#10615061C211yesmaximal, characteristic, complemented
3#10610780C211yesmaximal, characteristic
4C5×#1995C211yesmaximal, characteristic, complemented
5#10601313C211yesmaximal, characteristic, complemented
6#10600229C211yesmaximal, characteristic, complemented
7#10600223C211yesmaximal, characteristic
8#10599567C211yesmaximal, characteristic
9#10599567C211yesmaximal, characteristic
10#10599541C211yesmaximal, characteristic, complemented
11#10599540C211yesmaximal, characteristic, complemented
12#10599536C211yesmaximal, characteristic, complemented
13#10599536C211yesmaximal, characteristic, complemented
14#10599533C211yesmaximal, characteristic
15#10599532C211yesmaximal, characteristic
16C5×#533C2211yescharacteristic
17C2×#4053C2211yescharacteristic
18C2×#4053C2211yescharacteristic
19C4×#709C2211yescharacteristic
20C5×#423C2211yescharacteristic
21C5×#376C2211yescharacteristic
22C2×#3954C2211yescharacteristic
23C2×#3954C2211yescharacteristic
24#65408C2211yescharacteristic
25#65408C2211yescharacteristic
26#65383C411yescharacteristic, complemented
27#65380C411yescharacteristic, complemented
28#65376C411yescharacteristic, complemented
29#65373C411yescharacteristic, complemented
30#65355C411yescharacteristic, complemented
31#65355C411yescharacteristic, complemented
32#65352C411yescharacteristic, complemented
33#65352C411yescharacteristic, complemented
34#65313—21no—
35#65313—21no—
36#65313—21no—
37Q8×#168—21no—
38#65291C2211yescharacteristic
39#65291C2211yescharacteristic
40#65288C2211yescharacteristic
41#65288C2211yescharacteristic
42#65287C2211yescharacteristic
43#65287C2211yescharacteristic
44#65286C2211yescharacteristic
45#65286C2211yescharacteristic
46C2×#3937C2211yescharacteristic
47C2×#3937C2211yescharacteristic
48C2×C4⋊#168C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50C4×#681C2211yescharacteristic
51C2×#3935C2211yescharacteristic
52C2×C4×#168C2211yescharacteristic
53#65128—21no—
54#65128—21no—
55#65126—21no—
56D5×C4⋊C8—21no—
57C5×#339C2211yescharacteristic
58C5×#339C2211yescharacteristic
59C5×#339C2211yescharacteristic
60C5×#339C2211yescharacteristic
61#64778C2211yescharacteristic
62#64778C2211yescharacteristic
63#64744C2211yescharacteristic
64#64744C2211yescharacteristic
65#64743C2211yescharacteristic
66#64743C2211yescharacteristic
67#22984—51nomaximal, Sylow
68C2×#709C2311yescharacteristic
69C2×C5×M16C2311yescharacteristic
70C2×C5×M16C2311yescharacteristic
71C5×C4⋊Q8C2×C411yescharacteristic
72C5×C4⋊Q8C2×C411yescharacteristic
73C5×#125C2×C411yescharacteristic
74C5×#125C2×C411yescharacteristic
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8—21no—
77C4×C5×Q8—21no—
78C4×C5×Q8—21no—
79C5×#117C2311yescharacteristic
80C5×#117C2311yescharacteristic
81C2×C42×C5C2311yescharacteristic
82C2×C42×C5C2311yescharacteristic
83C2×C42×C5C2311yescharacteristic
84C4×C22⋊D5—21no—
85C4×C22⋊D5—21no—
86#4072C2311yescharacteristic
87C2×#681C2311yescharacteristic
88C2×#681C2311yescharacteristic
89C22×#168C2311yescharacteristic
90C22×#168C2311yescharacteristic
91C22×#168C2311yescharacteristic
92C22×#168C2311yescharacteristic
93#4053—22no—
94#4053—22no—
95#4053—41no—
96#4053—41no—
97C2×#676—21no—
98C2×#676—21no—
99C2×C8×D5—21no—
100C2×C8×D5—21no—
101C4×D20C2×C411yescharacteristic
102C4×D20C2×C411yescharacteristic
103#4018—21no—
104C42×D5—21no—
105C4×Dic10C2×C411yescharacteristic
106C4×Dic10C2×C411yescharacteristic
107C5×C4⋊C8—21no—
108C5×C4⋊C8—21no—
109C5×#95—21no—
110C5×#95—21no—
111#3954—41no—
112#3954—41no—
113#3946—21no—
114#3946—21no—
115#3946—21no—
116#3946—21no—
117#3942C2×C411yescharacteristic
118#3942C2×C411yescharacteristic
119#3942C2×C411yescharacteristic
120#3942C2×C411yescharacteristic
121#3941C2×C411yescharacteristic
122#3941C2×C411yescharacteristic
123#3941C2×C411yescharacteristic
124#3941C2×C411yescharacteristic
125#3940C2×C411yescharacteristic
126#3940C2×C411yescharacteristic
127#3940C2×C411yescharacteristic
128#3940C2×C411yescharacteristic
129#3939C2×C411yescharacteristic
130#3939C2×C411yescharacteristic
131#3939C2×C411yescharacteristic
132#3939C2×C411yescharacteristic
133#3937—22no—
134#3937Q814yescomplemented
135C4⋊#168—21no—
136C4⋊#168—21no—
137C4⋊#168—21no—
138C4⋊#168—21no—
139C4⋊#168C2×C411yescharacteristic
140C4⋊#168C2×C411yescharacteristic
141C4⋊#168C2×C411yescharacteristic
142C4⋊#168C2×C411yescharacteristic
143C4⋊#168D411yescharacteristic
144C4⋊#168D411yescharacteristic
145C4⋊#168D411yescharacteristic
146C4⋊#168D411yescharacteristic
147#3935—21no—
148#3935—21no—
149#3935—21no—
150#3935—41no—
151C4×#168—21no—
152C4×#168—21no—
153C4×#168—21no—
154C4×#168—41no—
155#3076—51no—
156#2962—51no—
157#2906—51no—
158#1995D511yescharacteristic, complemented
159#1950—51no—
160#1946—51no—
161#1945—51no—
162#1922—51no—
163#1922—51no—
164#1866—51no—
165#1866—51no—
166#1768—51no—
167#1765—51no—
168#1764—51no—
169#1759—51no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5#4111yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C22×C4×C5C2411yescharacteristic
177C2×C22⋊D5—21no—
178#709—21no—
179#709—21no—
180#709C2×Q812yes—
181#709#4112yes—
182C2×D20C22×C411yescharacteristic
183C2×C4×D5—21no—
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×Dic10C22×C411yescharacteristic
187C5×M16—21no—
188C5×M16—21no—
189C5×M16—21no—
190C5×M16—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4C22×C411yescharacteristic
200C5×C4⋊C4C22×C411yescharacteristic
201C5×C4⋊C4C22×C411yescharacteristic
202C5×C4⋊C4C22×C411yescharacteristic
203C5×C22⋊C4—21no—
204C5×C22⋊C4—21no—
205C42×C5—21no—
206C42×C5—21no—
207C42×C5—21no—
208C42×C5—21no—
209C42×C5—21no—
210C42×C5C22×C411yescharacteristic
211C42×C5C22×C411yescharacteristic
212C42×C5C2×D411yescharacteristic
213C42×C5C2×D411yescharacteristic
214C42×C5C2×Q812yes—
215C22⋊Dic5—21no—
216#685—21no—
217#685—21no—
218C4⋊Dic5C22×C411yescharacteristic
219C4⋊Dic5C22×C411yescharacteristic
220#683—21no—
221#683—21no—
222C4×Dic5—21no—
223C4×Dic5—21no—
224C4×Dic5—21no—
225#681—21no—
226#681—21no—
227#681—21no—
228#681C2×Q812yes—
229C2×#168—21no—
230C2×#168—21no—
231C2×#168—21no—
232C2×#168—21no—
233C2×#168—21no—
234C2×#168—21no—
235C2×#168—21no—
236C2×#168—21no—
237C2×#168—21no—
238C2×#168—21no—
239C2×#168C22×C411yescharacteristic
240C2×#168C22×C411yescharacteristic
241C2×#168C22×C411yescharacteristic
242C2×#168C22×C411yescharacteristic
243C2×#168C2×D411yescharacteristic
244C2×#168C2×D411yescharacteristic
245C2×#168C2×D411yescharacteristic
246C2×#168C2×D411yescharacteristic
247#676—42no—
248#676—42no—
249C8×D5—42no—
250C8×D5—42no—
251C2×#131—51no—
252C2×#131—51no—
253#533C2×D511yescharacteristic
254C4×#41—51no—
255#479—51no—
256#479—51no—
257#478—51no—
258#478—51no—
259#477—51no—
260#476—51no—
261#475—51no—
262#474—51no—
263#446—101no—
264#446—101no—
265#446—101no—
266C8×Q8—101no—
267C2×#108—51no—
268C2×#108—51no—
269#427—51no—
270#427—51no—
271#424—51no—
272#424—51no—
273#424—51no—
274#424—51no—
275#424—101no—
276#424—101no—
277#423—101no—
278#423C2×D511yescharacteristic
279C2×C4⋊C8—51no—
280C2×C4⋊C8—51no—
281C2×C4⋊C8—101no—
282C2×#104—51no—
283C2×#104—51no—
284#416—51no—
285#416—51no—
286#405—51no—
287#405—51no—
288C4×M16—51no—
289C2×#97—51no—
290C2×C4×C8—51no—
291#376C2×D511yescharacteristic
292#341—51no—
293#341—51no—
294#339—51no—
295#339—51no—
296#339C2×D511yescharacteristic
297#339C2×D511yescharacteristic
298#339C2×D511yescharacteristic
299#339C2×D511yescharacteristic
300#336—51no—
301#336—51no—
302C23×C5C2×#4111yescharacteristic
303C22×D5—21no—
304C5×Q8—42no—
305C5×Q8—81no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—22no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5C4×D411yescharacteristic
319C2×C4×C5C4×D411yescharacteristic
320C2×C4×C5C4×D411yescharacteristic
321C2×C4×C5C4×D411yescharacteristic
322C2×C4×C5C23×C411yescharacteristic
323C2×C4×C5C22×D411yescharacteristic
324C2×C4×C5C22×Q811yescharacteristic
325C2×C4×C5C2×#4111yescharacteristic
326C2×C4×C5H(5,𝔽2)11yescharacteristic
327C2×C4×C52−1+411yescharacteristic
328C22⋊D5—22no—
329C22⋊D5—22no—
330C2×Dic5—21no—
331C2×Dic5—21no—
332C2×Dic5—21no—
333D20—21no—
334D20C4×Q812yes—
335C4×D5—22no—
336C4×D5—22no—
337C4×D5—42no—
338C4×D5—81no—
339Dic10—21no—
340Dic10C4×Q812yes—
341C5×C8—41no—
342C5×C8—41no—
343#168—21no—
344#168—21no—
345#168—21no—
346#168—21no—
347#168—21no—
348#168—21no—
349#168—21no—
350#168—21no—
351#168—22no—
352#168—41no—
353C2×#41—51no—
354#131—102no—
355#131—102no—
356#131—201no—
357#131—201no—
358C2×M16—51no—
359C2×M16—51no—
360C2×M16—101no—
361C2×M16—101no—
362C2×M16C22×D511yescharacteristic
363C2×M16C22×D511yescharacteristic
364C22×C8—51no—
365C22×C8—51no—
366C22×C8—51no—
367C22×C8—51no—
368C22×C8—101no—
369C22×C8—101no—
370C4⋊Q8C4×D511yescharacteristic
371C4⋊Q8C4×D511yescharacteristic
372#125C4×D511yescharacteristic
373#125C4×D511yescharacteristic
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—51no—
379C4×Q8—51no—
380C4×D4—51no—
381C4×D4—51no—
382C4×D4—101no—
383C4×D4—101no—
384#117—51no—
385#117—101no—
386#117C22×D511yescharacteristic
387#117C22×D511yescharacteristic
388C2×C42—101no—
389C2×C42C22×D511yescharacteristic
390C2×C42C22×D511yescharacteristic
391C2×C42C22×D511yescharacteristic
392#108—201no—
393#108—201no—
394#107—51no—
395#107—51no—
396#107—51no—
397#107—51no—
398#106—51no—
399#106—51no—
400#106—51no—
401#106—51no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—51no—
405C4⋊C8—51no—
406C4⋊C8—51no—
407C4⋊C8—51no—
408C4⋊C8—51no—
409C4⋊C8—51no—
410C4⋊C8—51no—
411C4⋊C8—51no—
412C4⋊C8—101no—
413C4⋊C8—101no—
414C4⋊C8—101no—
415C4⋊C8—101no—
416C4⋊C8—101no—
417C4⋊C8—101no—
418C4⋊C8—101no—
419C4⋊C8—101no—
420#104—54no—
421#104—102no—
422#103—51no—
423#103—51no—
424#103—51no—
425#103—51no—
426#102—51no—
427#102—51no—
428#102—51no—
429#102—51no—
430#97—101no—
431#97—101no—
432#97—101no—
433#97—201no—
434C4×C8—101no—
435C4×C8—101no—
436C4×C8—101no—
437C4×C8—201no—
438#95—21no—
439#95—21no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5C2×C4×D411yescharacteristic
443C22×C5#55211yescharacteristic
444C22×C5#55411yescharacteristic
445C2×D5—22no—
446C2×D5—41no—
447C2×D5—41no—
448C4×C5—21no—
449C4×C5—21no—
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—42no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5—81no—
458C4×C5C2×C4×Q811yescharacteristic
459C4×C5#52011yescharacteristic
460C4×C5#54611yescharacteristic
461C4×C5D4×Q811yescharacteristic
462Dic5—22no—
463Dic5—41no—
464Dic5—41no—
465#41—52no—
466#41—52no—
467#41—101no—
468#41—101no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—51no—
472C2×D4—51no—
473C2×D4—101no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4#71111yescharacteristic
480C22×C4#71111yescharacteristic
481C22×C4C23×D511yescharacteristic
482M16—21no—
483M16—21no—
484M16—21no—
485M16—21no—
486M16—52no—
487M16—101no—
488M16—101no—
489M16—101no—
490M16—202no—
491M16—202no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—51no—
495C2×C8—51no—
496C2×C8—51no—
497C2×C8—51no—
498C2×C8—51no—
499C2×C8—51no—
500C2×C8—51no—
501C2×C8—51no—
502C2×C8—101no—
503C2×C8—101no—
504C2×C8—101no—
505C2×C8—101no—
506C2×C8—101no—
507C2×C8—101no—
508C2×C8—101no—
509C2×C8—101no—
510C2×C8—101no—
511C2×C8—101no—
512C2×C8—202no—
513C2×C8—202no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—51no—
521C4⋊C4—51no—
522C4⋊C4—101no—
523C4⋊C4—101no—
524C4⋊C4C2×C4×D511yescharacteristic
525C4⋊C4C2×C4×D511yescharacteristic
526C4⋊C4C2×C4×D511yescharacteristic
527C4⋊C4C2×C4×D511yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—101no—
531C22⋊C4—101no—
532C22⋊C4—101no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—101no—
539C42—101no—
540C42—101no—
541C42C2×C4×D511yescharacteristic
542C42C2×C4×D511yescharacteristic
543C42D4×D511yescharacteristic
544C42D4×D511yescharacteristic
545C42Q8×D512yes—
546C2×C5—21no—
547C2×C5—21no—
548C2×C5#236011yescharacteristic
549C2×C5#295511yescharacteristic
550C2×C5#295711yescharacteristic
551D5—42no—
552C23—101no—
553C23C2×#71111yescharacteristic
554Q8—42no—
555Q8—52no—
556Q8—81no—
557Q8—101no—
558D4—52no—
559D4—102no—
560D4—102no—
561D4—101no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—101no—
575C2×C4—102no—
576C2×C4—102no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—202no—
580C2×C4—401no—
581C2×C4#402711yescharacteristic
582C2×C4#402711yescharacteristic
583C2×C4#402711yescharacteristic
584C2×C4#402711yescharacteristic
585C2×C4C22×C4×D511yescharacteristic
586C2×C4C2×D4×D511yescharacteristic
587C2×C4C2×Q8×D511yescharacteristic
588C2×C4#414711yescharacteristic
589C2×C4D5×#4111yescharacteristic
590C2×C4#414911yescharacteristic
591C8—41no—
592C8—41no—
593C8—102no—
594C8—101no—
595C8—101no—
596C8—101no—
597C8—101no—
598C8—101no—
599C8—101no—
600C8—101no—
601C8—101no—
602C8—201no—
603C5#2298411yescharacteristic, complemented, Sylow
604C22—21no—
605C22—21no—
606C22—102no—
607C22—201no—
608C22—201no—
609C22C2×#402711yescharacteristic
610C22#6596911yescharacteristic
611C22#6597311yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—102no—
623C4—201no—
624C4—201no—
625C4C4×Q8×D511yescharacteristic
626C4#6590811yescharacteristic
627C4#6601011yescharacteristic
628C4#6606111yescharacteristic
629C2—21no—
630C2—21no—
631C2—202no—
632C2#1060834611yescharacteristic
633C2#1061072011yescharacteristic
634C2#1061072111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1995C2
socleC22×C5C2×C4×D4
prime radicalC2×#709C23
cosocleC22×C4×C5C24
hypercenter#1995D5
hypocenterC5#22984
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #10615061C2semidirect
4. C5×#1995C2semidirect
5. #10601313C2semidirect
6. #10600229C2semidirect
10. #10599541C2semidirect
11. #10599540C2semidirect
12. #10599536C2semidirect
13. #10599536C2semidirect
26. #65383C4semidirect
27. #65380C4semidirect
28. #65376C4semidirect
29. #65373C4semidirect
30. #65355C4semidirect
31. #65355C4semidirect
32. #65352C4semidirect
33. #65352C4semidirect
134. #3937Q8semidirect
158. #1995D5semidirect
603. C5#22984semidirect

Maximal subgroups

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

subgroupindex
#106150802
#106150612
#106107802
C5×#19952
#106013132
#106002292
#106002232
#105995672
#105995412
#105995402
#105995362
#105995332
#105995322
#229845