Finite Group Databasebeta

← #12157364

Subgroups — #12157364

Order 1280.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2442C211yesmaximal, characteristic
2#10605190C211yesmaximal, characteristic
3#10602532C211yesmaximal, characteristic, complemented
4#10602531C211yesmaximal, characteristic, complemented
5#10602351C211yesmaximal, characteristic
6#10602349C211yesmaximal, characteristic
7#10600403C211yesmaximal, characteristic, complemented
8#10600403C211yesmaximal, characteristic, complemented
9#10600394C211yesmaximal, characteristic, complemented
10#10600394C211yesmaximal, characteristic, complemented
11#10600335C211yesmaximal, characteristic, complemented
12#10600333C211yesmaximal, characteristic, complemented
13#10600306C211yesmaximal, characteristic
14#10600296C211yesmaximal, characteristic
15#10600243C211yesmaximal, characteristic
16C2×C5×#125C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C2×#4072C2211yescharacteristic
19C22×#681C2211yescharacteristic
20C5×#400—21no—
21C5×#398—21no—
22C5×#389C2211yescharacteristic
23C5×#389C2211yescharacteristic
24C5×#385—21no—
25C5×#382C2211yescharacteristic
26C5×#380—21no—
27C5×#380C2211yescharacteristic
28C4×C5×C22⋊C4C2211yescharacteristic
29#65501C2211yescharacteristic
30C2×C22⋊#168C2211yescharacteristic
31C2×#3940C2211yescharacteristic
32C2×#3940C2211yescharacteristic
33C2×#3940C2211yescharacteristic
34C2×#3939C2211yescharacteristic
35#65233—21no—
36#65233—21no—
37C4×C4⋊Dic5C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39#65217C2211yescharacteristic
40#65217C2211yescharacteristic
41C2×C4⋊#168C2211yescharacteristic
42C2×C4⋊#168C2211yescharacteristic
43#64939—21no—
44#64937—21no—
45#64749C2211yescharacteristic
46#64749C2211yescharacteristic
47#64749C2211yescharacteristic
48#64749C2211yescharacteristic
49#64749C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#26019—51nomaximal, Sylow
60C23×C4×C5—21no—
61C23×C4×C5C2311yescharacteristic
62C5×#125—22no—
63C5×#125—41no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—41no—
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4D411yescharacteristic
77C2×C5×C22⋊C4D411yescharacteristic
78C2×C42×C5C2311yescharacteristic
79C2×C42×C5C2311yescharacteristic
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—21no—
82#4072—22no—
83#4072Q814yes—
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×#683—21no—
89C2×#683—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×#681—22no—
94C2×#681—22no—
95C2×#681—41no—
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C5×#95—21no—
101C5×#95—21no—
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105C5×#95D411yescharacteristic
106C5×#95D411yescharacteristic
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112C22⋊#168—22no—
113#3940—22no—
114#3940—22no—
115#3940—41no—
116#3939—41no—
117C4⋊#168—22no—
118C4⋊#168—41no—
119#2442D511yescharacteristic
120#2346—51no—
121#2101—51no—
122#2088—51no—
123#2088—51no—
124#2059—51no—
125#1989—51no—
126#1949—51no—
127#1919—51no—
128#1919—51no—
129#1853—51no—
130#1851—51no—
131#1825—51no—
132#1809—51no—
133#1736—51no—
134C24×C5C2×D411yescharacteristic
135C22×C4×C5—21no—
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—42no—
144C22×C4×C5—42no—
145C22×C4×C5—81no—
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×Q812yes—
152C22×C4×C5#4112yes—
153C22×C4×C5C2411yescharacteristic
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—42no—
166C5×C4⋊C4—42no—
167C5×C4⋊C4—42no—
168C5×C4⋊C4—81no—
169C5×C4⋊C4—81no—
170C5×C4⋊C4#4112yes—
171C5×C22⋊C4—41no—
172C5×C22⋊C4—41no—
173C5×C22⋊C4—42no—
174C42×C5—21no—
175C42×C5—21no—
176C42×C5—21no—
177C42×C5—21no—
178C22⋊Dic5—24no—
179C22⋊Dic5—81no—
180C4⋊Dic5—21no—
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183C4⋊Dic5—21no—
184C4⋊Dic5—21no—
185C4⋊Dic5—21no—
186C4⋊Dic5C2×Q812yes—
187C4⋊Dic5C2×Q812yes—
188#683—81no—
189#683—81no—
190C4×Dic5—24no—
191C4×Dic5—42no—
192C4×Dic5—42no—
193#681—44no—
194C2×#168—21no—
195C2×#168—21no—
196C2×#168—21no—
197C2×#168—21no—
198C2×#168—21no—
199C2×#168—21no—
200C2×#168—21no—
201C2×#168—21no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168#4112yes—
206C22×M16—51no—
207C2×#125C2×D511yescharacteristic
208C2×#117—51no—
209C22×C4⋊C4C2×D511yescharacteristic
210C2×#107—51no—
211C2×#106—51no—
212C2×#106—51no—
213C2×#106—51no—
214C2×C4⋊C8—51no—
215C2×C4⋊C8—51no—
216C2×C22⋊C8—51no—
217#400—21no—
218#398—21no—
219#389—51no—
220#389—51no—
221#389C2×D511yescharacteristic
222#389C2×D511yescharacteristic
223#388—101no—
224#388—101no—
225#385—21no—
226#382—101no—
227#382C2×D511yescharacteristic
228#380—21no—
229#380—51no—
230#380C2×D511yescharacteristic
231C4×C4⋊C4—51no—
232C4×C4⋊C4—51no—
233C4×C22⋊C4C2×D511yescharacteristic
234#376—101no—
235#340—51no—
236#340—51no—
237#340—51no—
238#340—51no—
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#336—51no—
248#336—51no—
249C23×C5—21no—
250C23×C5—21no—
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5C22⋊Q812yes—
256C23×C5C22×D411yescharacteristic
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—84no—
288C2×C4×C5C22⋊Q812yes—
289C2×C4×C5C22×Q811yescharacteristic
290C2×C4×C5C2×#4111yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×C4×C5H(5,𝔽2)11yescharacteristic
294C2×C4×C52−1+411yescharacteristic
295C2×Dic5—22no—
296C2×Dic5—22no—
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—
307#168—22no—
308#168—41no—
309#168—41no—
310#168—41no—
311C23×C4—21no—
312C23×C4C22×D511yescharacteristic
313C2×M16—102no—
314C2×M16—102no—
315C2×M16—201no—
316C22×C8—51no—
317C22×C8—51no—
318C22×C8—51no—
319C22×C8—51no—
320#125—22no—
321#125—41no—
322#117—54no—
323#117—102no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—101no—
336C2×C4⋊C4—101no—
337C2×C4⋊C4C22×D511yescharacteristic
338C2×C4⋊C4C22×D511yescharacteristic
339C2×C4⋊C4C22×D511yescharacteristic
340C2×C4⋊C4C22×D511yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—101no—
343C2×C22⋊C4—101no—
344C2×C22⋊C4C22⋊D511yescharacteristic
345C2×C22⋊C4C22⋊D511yescharacteristic
346C2×C42—101no—
347C2×C42—101no—
348C2×C42—101no—
349C2×C42C22×D511yescharacteristic
350C2×C42C22×D511yescharacteristic
351#107—201no—
352#106—102no—
353#106—102no—
354#106—201no—
355C4⋊C8—102no—
356C4⋊C8—201no—
357C22⋊C8—102no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—101no—
364#95—101no—
365#95—101no—
366#95—101no—
367#95—101no—
368#95C22⋊D511yescharacteristic
369#95C22⋊D511yescharacteristic
370C22×C5—22no—
371C22×C5—22no—
372C22×C5—22no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5C2×C22⋊Q811yescharacteristic
378C22×C5#54611yescharacteristic
379C22×C5#54711yescharacteristic
380C22×C5#57511yescharacteristic
381C22×C5#57511yescharacteristic
382C22×C5#57711yescharacteristic
383C22×C5#57711yescharacteristic
384C4×C5—22no—
385C4×C5—41no—
386C4×C5—41no—
387C4×C5—41no—
388C4×C5—41no—
389C4×C5—42no—
390C4×C5—81no—
391C4×C5—81no—
392C4×C5—81no—
393C4×C5#53311yescharacteristic
394C4×C5#54411yescharacteristic
395C4×C5#55111yescharacteristic
396C4×C5#55211yescharacteristic
397Dic5—42no—
398Dic5—42no—
399Dic5—81no—
400Dic5—81no—
401C24C2×C22⋊D511yescharacteristic
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—81no—
413C22×C4—101no—
414C22×C4—101no—
415C22×C4—101no—
416C22×C4—101no—
417C22×C4Q8×D512yes—
418C22×C4#71312yes—
419C22×C4C2×C22⋊D511yescharacteristic
420C22×C4C2×C22⋊D511yescharacteristic
421C22×C4C2×C22⋊D511yescharacteristic
422C22×C4C2×C22⋊D511yescharacteristic
423C22×C4C2×C22⋊D511yescharacteristic
424C22×C4C23×D511yescharacteristic
425M16—204no—
426C2×C8—52no—
427C2×C8—101no—
428C2×C8—101no—
429C2×C8—101no—
430C2×C8—101no—
431C2×C8—101no—
432C2×C8—101no—
433C2×C8—101no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8—101no—
437C2×C8—101no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4—52no—
449C4⋊C4—52no—
450C4⋊C4—81no—
451C4⋊C4—81no—
452C4⋊C4—101no—
453C4⋊C4—101no—
454C4⋊C4—101no—
455C4⋊C4—101no—
456C4⋊C4—101no—
457C4⋊C4—101no—
458C4⋊C4—401no—
459C4⋊C4—401no—
460C4⋊C4#71112yes—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—42no—
464C22⋊C4—104no—
465C22⋊C4—401no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—104no—
471C42—202no—
472C42—202no—
473C2×C5—42no—
474C2×C5#243811yescharacteristic
475C2×C5#308011yescharacteristic
476C2×C5#308411yescharacteristic
477C2×C5#332111yescharacteristic
478C2×C5#332311yescharacteristic
479C2×C5#334811yescharacteristic
480C2×C5#335111yescharacteristic
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23#409212yes—
488C23C22×C22⋊D511yescharacteristic
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—84no—
520C2×C4—102no—
521C2×C4—102no—
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#409212yes—
533C2×C4C2×#71111yescharacteristic
534C2×C4#414411yescharacteristic
535C2×C4C2×Q8×D511yescharacteristic
536C2×C4C2×#71311yescharacteristic
537C2×C4D5×#4111yescharacteristic
538C2×C4#415011yescharacteristic
539C8—102no—
540C8—201no—
541C8—201no—
542C8—201no—
543C5#2601911yescharacteristic, complemented, Sylow
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22#6614011yescharacteristic
552C22C2×#409211yescharacteristic
553C22#6615611yescharacteristic
554C22#6615611yescharacteristic
555C22#6615811yescharacteristic
556C22#6617011yescharacteristic
557C22#6617111yescharacteristic
558C4—22no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—202no—
568C4—202no—
569C4—401no—
570C4—401no—
571C4#6595611yescharacteristic
572C4#6595711yescharacteristic
573C4#6597111yescharacteristic
574C4#6597611yescharacteristic
575C2—42no—
576C2#1061449311yescharacteristic
577C2#1061474811yescharacteristic
578C2#1061520711yescharacteristic
579C2#1061523211yescharacteristic
580C2#1061527011yescharacteristic
581C2#1061532511yescharacteristic
582C2#1061534311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2442C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenter#2442D5
hypocenterC5#26019
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
3. #10602532C2semidirect
4. #10602531C2semidirect
7. #10600403C2semidirect
8. #10600403C2semidirect
9. #10600394C2semidirect
10. #10600394C2semidirect
11. #10600335C2semidirect
12. #10600333C2semidirect
543. C5#26019semidirect

Maximal subgroups

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

subgroupindex
C5×#24422
#106051902
#106025322
#106025312
#106023512
#106023492
#106004032
#106003942
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