Finite Group Databasebeta

← #12117066

Subgroups — #12117066

Order 1280.

782 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×#65410C211yesmaximal, characteristic
2#10605613C211yesmaximal, characteristic
3#10605610C211yesmaximal, characteristic
4C5×#1809C211yesmaximal, characteristic
5#10602776C211yesmaximal, characteristic
6#10601407C211yesmaximal, characteristic, complemented
7Dic5×#107C211yesmaximal, characteristic, complemented
8#10601352C211yesmaximal, characteristic, complemented
9#10601346C211yesmaximal, characteristic, complemented
10#10600296C211yesmaximal, characteristic
11#10600294C211yesmaximal, characteristic
12#10599613C211yesmaximal, characteristic, complemented
13#10599611C211yesmaximal, characteristic, complemented
14#10599609C211yesmaximal, characteristic, complemented
15#10599607C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×#4072C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C2×C5×#107C2211yescharacteristic
20C2×C5×#106C2211yescharacteristic
21C5×#380C2211yescharacteristic
22C5×#380C2211yescharacteristic
23C4×C22⋊Dic5C2211yescharacteristic
24C2×C22⋊#168C2211yescharacteristic
25#65410C418yescomplemented
26C2×#3950C2211yescharacteristic
27C2×#3950C2211yescharacteristic
28C2×#3949C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×#3947C2211yescharacteristic
31C2×C8×Dic5C2211yescharacteristic
32C4⋊C4×Dic5C2211yescharacteristic
33C4⋊C4×Dic5C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36#65262C2211yescharacteristic
37#65262C2211yescharacteristic
38#65262C2211yescharacteristic
39#65262C2211yescharacteristic
40#65233—21no—
41#65233—21no—
42#65231—21no—
43C22⋊C4×Dic5—21no—
44#64942—21no—
45#64942—21no—
46#64940—21no—
47#64938—21no—
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50#64770C2211yescharacteristic
51#64770C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#22623—51nomaximal, Sylow
61C23×C4×C5C2311yescharacteristic
62C23×Dic5—21no—
63C2×C5×M16—22no—
64C2×C5×M16—22no—
65C2×C5×M16C2×C414yes—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C22⋊C4—21no—
73C2×C5×C22⋊C4—21no—
74C2×C22⋊Dic5—21no—
75C2×C22⋊Dic5D411yescharacteristic
76C2×C22⋊Dic5D411yescharacteristic
77#4072—22no—
78#4072C2×C414yes—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5C2×C414yes—
82C2×C4⋊Dic5C2311yescharacteristic
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×#683—21no—
87C2×#683—21no—
88C2×#683—21no—
89C2×#683—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5C2311yescharacteristic
96C2×C4×Dic5C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C5×#107—22no—
100C5×#106—22no—
101C5×#95—21no—
102C5×#95—21no—
103#3963—21no—
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
113C22⋊#168—22no—
114#3950C2×C414yes—
115#3950C2×C414yes—
116#3949C2×C414yes—
117#3949C2×C414yes—
118#3947—22no—
119C8×Dic5—22no—
120C2×#428—51no—
121#2347—51no—
122#2345—51no—
123#1944—51no—
124#1941—51no—
125#1921—51no—
126#1920—51no—
127#1919—51no—
128#1918—51no—
129#1825—51no—
130#1823—51no—
131#1809D511yescharacteristic
132#1776—51no—
133C4×#107—51no—
134#1753—51no—
135C24×C5C2×D411yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5#4112yes—
147C22×C4×C5C2411yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—24no—
153C22×Dic5—81no—
154C22×Dic5—81no—
155C22×Dic5C2×D411yescharacteristic
156C22×Dic5C2×D411yescharacteristic
157C22×Dic5C2×D411yescharacteristic
158C22×Dic5C2×D411yescharacteristic
159C5×M16—28no—
160C2×C5×C8—21no—
161C2×C5×C8—21no—
162C2×C5×C8C22×C412yes—
163C2×C5×C8C22×C412yes—
164C2×C5×C8#4112yes—
165C2×C5×C8#4112yes—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C22⋊C4—42no—
175C5×C22⋊C4—81no—
176C22⋊Dic5—24no—
177C22⋊Dic5—22no—
178C22⋊Dic5—41no—
179C4⋊Dic5—24no—
180C4⋊Dic5—21no—
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183C4⋊Dic5—21no—
184C4⋊Dic5C22×C412yes—
185C4⋊Dic5C22×C412yes—
186C4⋊Dic5C22×C412yes—
187C4⋊Dic5C22×C412yes—
188#683—42no—
189#683—42no—
190#683—81no—
191#683—81no—
192C4×Dic5—24no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—21no—
196C4×Dic5—21no—
197C4×Dic5—81no—
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—
207C22×M16C2×D511yescharacteristic
208C2×#117—51no—
209C22×C4⋊C4—51no—
210#428—58no—
211C2×#107—51no—
212C2×#107—51no—
213C2×#107C2×D511yescharacteristic
214C2×#106—51no—
215C2×#106—51no—
216C2×#106C2×D511yescharacteristic
217C2×C22⋊C8—51no—
218C2×#97—51no—
219C2×C4×C8—51no—
220#389—51no—
221#389—51no—
222#389—51no—
223#389—51no—
224#388—101no—
225#388—101no—
226#387—101no—
227#387—101no—
228#383—101no—
229#380—101no—
230#380C2×D511yescharacteristic
231#380C2×D511yescharacteristic
232C4×C4⋊C4—51no—
233C4×C4⋊C4—51no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
236C4×C4⋊C4—101no—
237C4×C22⋊C4—51no—
238C4×C22⋊C4—101no—
239#340—51no—
240#340—51no—
241#340—51no—
242#340—51no—
243#340—51no—
244#340—51no—
245#340—51no—
246#340—51no—
247#340C2×D511yescharacteristic
248#340C2×D511yescharacteristic
249#336—51no—
250#336—51no—
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—21no—
257C23×C5C4×D412yes—
258C23×C5C22×D411yescharacteristic
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
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—41no—
277C2×C4×C5C4×D412yes—
278C2×C4×C5C23×C411yescharacteristic
279C2×C4×C5C2×#4111yescharacteristic
280C2×C4×C5C2×#4111yescharacteristic
281C2×C4×C5C2×#4111yescharacteristic
282C2×C4×C52−1+411yescharacteristic
283C2×C4×C52−1+411yescharacteristic
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
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—84no—
308C2×Dic5#13712yes—
309C5×C8—22no—
310C5×C8#11714yes—
311#168—41no—
312#168—41no—
313C23×C4—101no—
314C23×C4C22×D511yescharacteristic
315C2×M16—22no—
316C2×M16—22no—
317C2×M16C4×D514yes—
318C22×C8—51no—
319C22×C8—51no—
320C22×C8C22×D511yescharacteristic
321C22×C8C22×D511yescharacteristic
322#117—54no—
323#117—102no—
324C2×C4⋊C4—54no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—101no—
330C2×C4⋊C4—102no—
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×C4⋊C4C22×D511yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—51no—
342C2×C22⋊C4—51no—
343C2×C22⋊C4—101no—
344C2×C42—51no—
345C2×C42—51no—
346C2×C42—101no—
347C2×C42—101no—
348C2×C42—101no—
349C2×C42—101no—
350C2×C42—101no—
351#107—22no—
352#107—54no—
353#107—54no—
354#106—22no—
355#106—54no—
356#106—54no—
357C22⋊C8—102no—
358#97—102no—
359C4×C8—102no—
360#95—21no—
361#95—21no—
362#95—51no—
363#95—51no—
364#95—101no—
365#95—101no—
366#95—101no—
367#95—101no—
368#95—101no—
369#95—101no—
370#95—101no—
371#95—101no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5—41no—
379C22×C5C2×C4×D411yescharacteristic
380C22×C5#54711yescharacteristic
381C22×C5#54711yescharacteristic
382C22×C5C2×#13711yescharacteristic
383C22×C5#57511yescharacteristic
384C22×C5#57611yescharacteristic
385C22×C5#57711yescharacteristic
386C4×C5—22no—
387C4×C5—81no—
388C4×C5—81no—
389C4×C5—81no—
390C4×C5—81no—
391C4×C5C2×#11711yescharacteristic
392C4×C5#51911yescharacteristic
393C4×C5#55211yescharacteristic
394C4×C5#55211yescharacteristic
395Dic5—22no—
396Dic5—41no—
397Dic5—41no—
398Dic5—41no—
399Dic5—42no—
400Dic5—42no—
401Dic5—42no—
402Dic5—42no—
403C24D4×D511yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—101no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—104no—
421C22×C4—401no—
422C22×C4—401no—
423C22×C4C2×C4×D512yes—
424C22×C4D4×D511yescharacteristic
425C22×C4#71312yes—
426C22×C4C23×D511yescharacteristic
427M16—28no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—101no—
431C2×C8—101no—
432C2×C8—101no—
433C2×C8—101no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8C2×C4×D512yes—
437C2×C8C2×C4×D512yes—
438C2×C8#71112yes—
439C2×C8#71112yes—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—52no—
449C4⋊C4—52no—
450C4⋊C4—52no—
451C4⋊C4—52no—
452C4⋊C4—101no—
453C4⋊C4—101no—
454C4⋊C4—101no—
455C4⋊C4—101no—
456C4⋊C4—104no—
457C4⋊C4—202no—
458C4⋊C4—202no—
459C4⋊C4—401no—
460C4⋊C4—401no—
461C22⋊C4—42no—
462C22⋊C4—81no—
463C22⋊C4—102no—
464C22⋊C4—104no—
465C22⋊C4—201no—
466C42—101no—
467C42—101no—
468C42—101no—
469C42—101no—
470C42—104no—
471C42—401no—
472C42—401no—
473C42—401no—
474C42—401no—
475C2×C5—42no—
476C2×C5#234411yescharacteristic
477C2×C5C4×#13711yescharacteristic
478C2×C5#294611yescharacteristic
479C2×C5#334611yescharacteristic
480C2×C5#335011yescharacteristic
481C2×C5#335511yescharacteristic
482C2×C5#335611yescharacteristic
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23#403912yes—
490C23C2×D4×D511yescharacteristic
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—52no—
510C2×C4—101no—
511C2×C4—101no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
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×C4—404no—
534C2×C4#403912yes—
535C2×C4C22×C4×D511yescharacteristic
536C2×C4C2×#71111yescharacteristic
537C2×C4C2×#71111yescharacteristic
538C2×C4C2×#71311yescharacteristic
539C2×C4#415011yescharacteristic
540C2×C4#415011yescharacteristic
541C8—22no—
542C8—201no—
543C8—201no—
544C8#402314yes—
545C5#2262311yescharacteristic, complemented, Sylow
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×#403911yescharacteristic
554C22#6594511yescharacteristic
555C22#6594511yescharacteristic
556C22#6610711yescharacteristic
557C22#6610811yescharacteristic
558C22D5×#13711yescharacteristic
559C22#6611211yescharacteristic
560C4—22no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—102no—
566C4—201no—
567C4—201no—
568C4—201no—
569C4—202no—
570C4—202no—
571C4—202no—
572C4—202no—
573C4C2×#402311yescharacteristic
574C4#6585011yescharacteristic
575C4#6597611yescharacteristic
576C4#6597611yescharacteristic
577C2—42no—
578C2#1060560911yescharacteristic
579C2#1061093111yescharacteristic
580C2#1061093211yescharacteristic
581C2#1061256111yescharacteristic
582C2#1061256311yescharacteristic
583C2#1061259211yescharacteristic
584C2#1061263211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1809C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenter#1809D5
hypocenterC5#22623
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
6. #10601407C2semidirect
7. Dic5×#107C2semidirect
8. #10601352C2semidirect
9. #10601346C2semidirect
12. #10599613C2semidirect
13. #10599611C2semidirect
14. #10599609C2semidirect
15. #10599607C2semidirect
25. #65410C4semidirect
545. C5#22623semidirect

Maximal subgroups

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

subgroupindex
C2×#654102
#106056132
#106056102
C5×#18092
#106027762
#106014072
Dic5×#1072
#106013522
#106013462
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