Finite Group Databasebeta

← #12111491

Subgroups — #12111491

Order 1280.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#478C211yesmaximal, characteristic
2#10614754C211yesmaximal, characteristic, complemented
3#10614056C211yesmaximal, characteristic
4#10602531C211yesmaximal, characteristic, complemented
5#10602397C211yesmaximal, characteristic
6#10601406C211yesmaximal, characteristic, complemented
7#10601402C211yesmaximal, characteristic, complemented
8#10601353C211yesmaximal, characteristic, complemented
9#10601351C211yesmaximal, characteristic, complemented
10#10601247C211yesmaximal, characteristic, complemented
11#10601235C211yesmaximal, characteristic, complemented
12#10600980C211yesmaximal, characteristic
13#10600978C211yesmaximal, characteristic
14#10600949C211yesmaximal, characteristic
15#10600949C211yesmaximal, characteristic
16C2×C5×#125C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C5×#478C418yescomplemented
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×#102C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24#65510C2211yescharacteristic
25#65510C2211yescharacteristic
26C2×#3964C2211yescharacteristic
27C2×#3964C2211yescharacteristic
28#65501—21no—
29#65500—21no—
30C2×#3949C2211yescharacteristic
31C2×#3949C2211yescharacteristic
32C2×#3947C2211yescharacteristic
33C2×C8×Dic5C2211yescharacteristic
34#65274—21no—
35#65274—21no—
36#65274C2211yescharacteristic
37#65274C2211yescharacteristic
38#65274C2211yescharacteristic
39#65274C2211yescharacteristic
40#65270—21no—
41#65270—21no—
42C4⋊C4×Dic5C2211yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44#65240—21no—
45#65240—21no—
46#65224C2211yescharacteristic
47C4×C4⋊Dic5C2211yescharacteristic
48#65221C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50#64771C2211yescharacteristic
51#64771C2211yescharacteristic
52#64770C2211yescharacteristic
53#64770C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#22122—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C5×#125—22no—
66C5×#125C2×C414yes—
67C4×C5×D4—22no—
68C4×C5×D4C2×C414yes—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C22⋊C4—21no—
75C2×C42×C5C2311yescharacteristic
76C2×C22⋊Dic5—21no—
77C2×C22⋊Dic5—21no—
78C2×C22⋊Dic5—21no—
79C2×C22⋊Dic5—21no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C5×#107C2×C414yes—
98C5×#106C2×C414yes—
99C5×C4⋊C8C2×C414yes—
100C5×#102C2×C414yes—
101C5×#102C2×C414yes—
102#3964—41no—
103#3964—41no—
104#3963—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963D411yescharacteristic
112#3963D411yescharacteristic
113#3963D411yescharacteristic
114#3963D411yescharacteristic
115#3949—41no—
116#3949—41no—
117#3947—41no—
118C8×Dic5—41no—
119C4⋊#168—22no—
120C2×#478D511yescharacteristic
121#2330—51no—
122#2319—51no—
123#1989—51no—
124#1948—51no—
125#1943—51no—
126#1941—51no—
127#1936—51no—
128#1934—51no—
129#1926—51no—
130#1926—51no—
131#1920—51no—
132#1918—51no—
133#1802—51no—
134#1768—51no—
135C24×C5—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4C22×C412yes—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—24no—
146C22×C4×C5—81no—
147C22×C4×C5—81no—
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2411yescharacteristic
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5C2×D411yescharacteristic
156C22×Dic5C2×D411yescharacteristic
157C22×Dic5C2×D411yescharacteristic
158C22×Dic5C2×D411yescharacteristic
159C2×C5×C8—21no—
160C2×C5×C8—21no—
161C2×C5×C8—21no—
162C2×C5×C8—21no—
163C2×C5×C8C22×C412yes—
164C2×C5×C8C22×C412yes—
165C5×C4⋊C4—24no—
166C5×C4⋊C4—24no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4C22×C412yes—
171C5×C4⋊C4C22×C412yes—
172C5×C4⋊C4C22×C412yes—
173C5×C22⋊C4—24no—
174C42×C5C22×C412yes—
175C42×C5#4112yes—
176C22⋊Dic5—81no—
177C22⋊Dic5—81no—
178C22⋊Dic5—81no—
179C22⋊Dic5—81no—
180C4⋊Dic5—21no—
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183C4⋊Dic5—21no—
184C4⋊Dic5—21no—
185C4⋊Dic5—21no—
186C4⋊Dic5—21no—
187C4⋊Dic5—21no—
188C4⋊Dic5—81no—
189C4⋊Dic5—81no—
190C4⋊Dic5—81no—
191C4⋊Dic5—81no—
192C4⋊Dic5—81no—
193C4⋊Dic5—81no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5—21no—
197C4×Dic5—21no—
198C4×Dic5—81no—
199C4×Dic5—81no—
200C4×Dic5—81no—
201C2×#168—21no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#125C2×D511yescharacteristic
208C2×C4×D4C2×D511yescharacteristic
209#478Dic518yescomplemented
210C2×#107C2×D511yescharacteristic
211C2×#106—51no—
212C2×#106—51no—
213C2×#106C2×D511yescharacteristic
214C2×C4⋊C8—51no—
215C2×C4⋊C8C2×D511yescharacteristic
216C2×#102—51no—
217C2×#102—51no—
218C2×#102C2×D511yescharacteristic
219C2×#102C2×D511yescharacteristic
220C2×#97—51no—
221C2×C4×C8—51no—
222#390—51no—
223#390—51no—
224#389—51no—
225#389—51no—
226#389—51no—
227#389—51no—
228#389—101no—
229#389—101no—
230#388—101no—
231#388—101no—
232#387—101no—
233#387—101no—
234#384—51no—
235#381—101no—
236#380—101no—
237C4×C4⋊C4—51no—
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240#376—51no—
241#340—51no—
242#340—51no—
243#340—51no—
244#340—51no—
245#340—51no—
246#340—51no—
247#340—51no—
248#340—51no—
249#336—51no—
250#336—51no—
251C23×C5—22no—
252C23×C5—41no—
253C23×C5—41no—
254C23×C5—41no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5C22×D411yescharacteristic
259C5×D4—22no—
260C5×D4—22no—
261C5×D4—41no—
262C5×D4—41no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—84no—
277C2×C4×C5C4×D412yes—
278C2×C4×C5C4×D412yes—
279C2×C4×C5C23×C411yescharacteristic
280C2×C4×C5C2×#4111yescharacteristic
281C2×C4×C5H(5,𝔽2)11yescharacteristic
282C2×C4×C52−1+411yescharacteristic
283C2×C4×C52−1+411yescharacteristic
284C2×C4×C52−1+411yescharacteristic
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C5×C8—22no—
310C5×C8—22no—
311#168—41no—
312#168—41no—
313C22×D4C22×D511yescharacteristic
314C23×C4—21no—
315C22×C8—51no—
316C22×C8—51no—
317C22×C8C22×D511yescharacteristic
318C22×C8C22×D511yescharacteristic
319#125—22no—
320#125C2×Dic514yes—
321C4×D4—22no—
322C4×D4C2×Dic514yes—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—101no—
330C2×C4⋊C4—101no—
331C2×C4⋊C4—101no—
332C2×C4⋊C4—101no—
333C2×C4⋊C4—101no—
334C2×C4⋊C4—101no—
335C2×C4⋊C4C22×D511yescharacteristic
336C2×C4⋊C4C22×D511yescharacteristic
337C2×C4⋊C4C22×D511yescharacteristic
338C2×C22⋊C4—21no—
339C2×C22⋊C4—101no—
340C2×C22⋊C4—101no—
341C2×C22⋊C4—101no—
342C2×C22⋊C4—101no—
343C2×C42—51no—
344C2×C42—51no—
345C2×C42—101no—
346C2×C42—101no—
347C2×C42—101no—
348C2×C42C22×D511yescharacteristic
349#107C2×Dic514yes—
350#106—201no—
351#106—201no—
352#106C2×Dic514yes—
353C4⋊C8—102no—
354C4⋊C8C2×Dic514yes—
355#102—201no—
356#102—201no—
357#102C2×Dic514yes—
358#102C2×Dic514yes—
359#97—201no—
360C4×C8—201no—
361#95—51no—
362#95—51no—
363#95—51no—
364#95—51no—
365#95—101no—
366#95—101no—
367#95—101no—
368#95—101no—
369#95—101no—
370#95—101no—
371#95—101no—
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5—81no—
376C22×C5—81no—
377C22×C5—81no—
378C22×C5—81no—
379C22×C5C2×C4×D411yescharacteristic
380C22×C5#53611yescharacteristic
381C22×C5#53711yescharacteristic
382C22×C5#57611yescharacteristic
383C22×C5#57711yescharacteristic
384C22×C5#57711yescharacteristic
385C22×C5#57711yescharacteristic
386C4×C5—22no—
387C4×C5—22no—
388C4×C5—42no—
389C4×C5—42no—
390C4×C5—42no—
391C4×C5#51911yescharacteristic
392C4×C5#52011yescharacteristic
393C4×C5#54111yescharacteristic
394C4×C5#54211yescharacteristic
395Dic5—41no—
396Dic5—41no—
397Dic5—41no—
398Dic5—41no—
399Dic5—81no—
400Dic5—81no—
401Dic5—81no—
402Dic5—81no—
403C24—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4C22×Dic512yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—81no—
419C22×C4—81no—
420C22×C4—101no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4D4×D511yescharacteristic
425C22×C4D4×D511yescharacteristic
426C22×C4C23×D511yescharacteristic
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—101no—
432C2×C8—101no—
433C2×C8—101no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8—101no—
437C2×C8C22×Dic512yes—
438C2×C8C22×Dic512yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—101no—
445C4⋊C4—101no—
446C4⋊C4—101no—
447C4⋊C4—101no—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C4⋊C4—101no—
451C4⋊C4—101no—
452C4⋊C4—401no—
453C4⋊C4—401no—
454C4⋊C4—401no—
455C4⋊C4—401no—
456C4⋊C4—401no—
457C4⋊C4—401no—
458C4⋊C4C22×Dic512yes—
459C4⋊C4C22×Dic512yes—
460C4⋊C4C22×Dic512yes—
461C22⋊C4—24no—
462C22⋊C4—401no—
463C22⋊C4—401no—
464C22⋊C4—401no—
465C22⋊C4—401no—
466C42—101no—
467C42—101no—
468C42—101no—
469C42—101no—
470C42—401no—
471C42—401no—
472C42—401no—
473C42#71112yes—
474C42C22×Dic512yes—
475C2×C5—82no—
476C2×C5#232311yescharacteristic
477C2×C5#294611yescharacteristic
478C2×C5#295211yescharacteristic
479C2×C5#324111yescharacteristic
480C2×C5#324411yescharacteristic
481C2×C5#325711yescharacteristic
482C2×C5#326011yescharacteristic
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×D4×D511yescharacteristic
491D4—22no—
492D4—22no—
493D4—41no—
494D4—41no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—84no—
509C2×C4—101no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—101no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—201no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4D4×Dic512yes—
534C2×C4D4×Dic512yes—
535C2×C4C2×#71111yescharacteristic
536C2×C4#414711yescharacteristic
537C2×C4#414711yescharacteristic
538C2×C4#414911yescharacteristic
539C2×C4#415011yescharacteristic
540C2×C4C23×Dic511yescharacteristic
541C8—22no—
542C8—22no—
543C8—201no—
544C8—201no—
545C5#2212211yescharacteristic, complemented, Sylow
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#6596211yescharacteristic
554C22#6596311yescharacteristic
555C22#6610411yescharacteristic
556C22#6610411yescharacteristic
557C22#6610811yescharacteristic
558C22#6610911yescharacteristic
559C22C2×D4×Dic511yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—201no—
566C4—201no—
567C4—201no—
568C4—201no—
569C4—401no—
570C4—401no—
571C4—401no—
572C4—401no—
573C4#6595911yescharacteristic
574C4#6597711yescharacteristic
575C4#6614611yescharacteristic
576C4#6616111yescharacteristic
577C2—82no—
578C2#1061290811yescharacteristic
579C2#1061291011yescharacteristic
580C2#1061291311yescharacteristic
581C2#1061291611yescharacteristic
582C2#1061447511yescharacteristic
583C2#1061563011yescharacteristic
584C2#1061566111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#478C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenterC2×#478D5
hypocenterC5#22122
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. #10614754C2semidirect
4. #10602531C2semidirect
6. #10601406C2semidirect
7. #10601402C2semidirect
8. #10601353C2semidirect
9. #10601351C2semidirect
10. #10601247C2semidirect
11. #10601235C2semidirect
18. C5×#478C4semidirect
209. #478Dic5semidirect
545. C5#22122semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4782
#106147542
#106140562
#106025312
#106023972
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