Finite Group Databasebeta

← #12029591

Subgroups — #12029591

Order 1280.

1194 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#398C211yesmaximal, characteristic
2C2×#65270C212yesmaximal
3#10602358C211yesmaximal, characteristic
4#10602357C212yesmaximal
5#10602357C212yesmaximal
6#10602356C211yesmaximal, characteristic
7#10600209C212yesmaximal
8#10600209C212yesmaximal
9#10600200C212yesmaximal
10C22×C5×C4⋊C4C2212yes—
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic5C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4×Dic5C2212yes—
16C22×C4×Dic5C2211yescharacteristic
17C5×#398C418yescomplemented
18C2×C5×#95C2212yes—
19C2×C5×#95C2211yescharacteristic
20C2×#3963C2212yes—
21C2×#3963C2212yes—
22C2×#3963C2212yes—
23C2×#3963C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2211yescharacteristic
31C2×#3963C2212yes—
32#65270—28no—
33#14590—51nomaximal, Sylow
34C23×C4×C5C2311yescharacteristic
35C23×C4×C5C2312yes—
36C23×C4×C5C2312yes—
37C23×C4×C5C2311yescharacteristic
38C23×C4×C5C2311yescharacteristic
39C23×Dic5C2312yes—
40C23×Dic5C2312yes—
41C23×Dic5C2312yes—
42C23×Dic5C2312yes—
43C2×C5×C4⋊C4—24no—
44C2×C5×C4⋊C4—24no—
45C2×C5×C4⋊C4—41no—
46C2×C5×C4⋊C4—41no—
47C2×C5×C4⋊C4—41no—
48C2×C5×C4⋊C4—41no—
49C2×C5×C4⋊C4C2×C418yes—
50C2×C5×C4⋊C4C2×C414yes—
51C2×C5×C4⋊C4C2×C414yes—
52C2×C4⋊Dic5—24no—
53C2×C4⋊Dic5—41no—
54C2×C4⋊Dic5—41no—
55C2×C4⋊Dic5—41no—
56C2×C4⋊Dic5D414yes—
57C2×C4×Dic5—22no—
58C2×C4×Dic5—24no—
59C2×C4×Dic5—42no—
60C2×C4×Dic5—42no—
61C2×C4×Dic5—41no—
62C2×C4×Dic5—41no—
63C5×#95C2×C418yes—
64C5×#95C2×C414yes—
65#3963—24no—
66#3963—24no—
67#3963—24no—
68#3963—24no—
69#3963—24no—
70#3963—24no—
71#3963—24no—
72#3963—24no—
73#3963—24no—
74#3963—42no—
75#3963—42no—
76#3963—41no—
77C2×#398D511yescharacteristic
78C2×#387—52no—
79#1443—52no—
80#1443—52no—
81#1441—51no—
82#1436—52no—
83#1436—52no—
84#1436—52no—
85C4⋊#95—51no—
86C24×C5C2411yescharacteristic
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—22no—
92C22×C4×C5—22no—
93C22×C4×C5—22no—
94C22×C4×C5—22no—
95C22×C4×C5—22no—
96C22×C4×C5—22no—
97C22×C4×C5—22no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—22no—
104C22×C4×C5—21no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5C22×C414yes—
112C22×C4×C5C22×C412yes—
113C22×C4×C5C22×C414yes—
114C22×C4×C5C22×C412yes—
115C22×C4×C5C22×C412yes—
116C22×C4×C5C2×D412yes—
117C22×C4×C5#4112yes—
118C22×Dic5—22no—
119C22×Dic5—22no—
120C22×Dic5—22no—
121C22×Dic5—22no—
122C22×Dic5—22no—
123C22×Dic5—22no—
124C22×Dic5—22no—
125C22×Dic5—22no—
126C22×Dic5—22no—
127C22×Dic5—22no—
128C22×Dic5—22no—
129C22×Dic5—22no—
130C22×Dic5—22no—
131C22×Dic5—22no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5C2×D414yes—
144C22×Dic5#4114yes—
145C22×Dic5#4114yes—
146C5×C4⋊C4—216no—
147C5×C4⋊C4—44no—
148C5×C4⋊C4—44no—
149C4⋊Dic5—44no—
150C4⋊Dic5—44no—
151C4×Dic5—48no—
152C4×Dic5—44no—
153C22×C4⋊C4—51no—
154C22×C4⋊C4—51no—
155C22×C4⋊C4C2×D512yes—
156C22×C4⋊C4C2×D511yescharacteristic
157C22×C4⋊C4C2×D511yescharacteristic
158C22×C42—51no—
159C22×C42—52no—
160#398Dic518yescomplemented
161#387—108no—
162C2×#95—52no—
163C2×#95—52no—
164C2×#95—52no—
165C2×#95—52no—
166C2×#95—52no—
167C2×#95—52no—
168C2×#95—52no—
169C2×#95—52no—
170C2×#95—52no—
171C2×#95—52no—
172C2×#95—52no—
173C2×#95—51no—
174C2×#95C2×D512yes—
175C2×#95C2×D511yescharacteristic
176C23×C5C23×C411yescharacteristic
177C23×C5C22×D411yescharacteristic
178C23×C5C2×#4111yescharacteristic
179C23×C5C2×#4112yes—
180C23×C5C2×#4112yes—
181C23×C5H(5,𝔽2)11yescharacteristic
182C23×C5H(5,𝔽2)11yescharacteristic
183C23×C5H(5,𝔽2)11yescharacteristic
184C23×C52−1+412yes—
185C23×C52−1+412yes—
186C23×C52−1+411yescharacteristic
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—22no—
191C2×C4×C5—22no—
192C2×C4×C5—22no—
193C2×C4×C5—24no—
194C2×C4×C5—24no—
195C2×C4×C5—24no—
196C2×C4×C5—24no—
197C2×C4×C5—24no—
198C2×C4×C5—22no—
199C2×C4×C5—24no—
200C2×C4×C5—22no—
201C2×C4×C5—24no—
202C2×C4×C5—24no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—42no—
207C2×C4×C5—42no—
208C2×C4×C5—42no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5—42no—
214C2×C4×C5—42no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5C4×D414yes—
218C2×Dic5—24no—
219C2×Dic5—24no—
220C2×Dic5—24no—
221C2×Dic5—24no—
222C2×Dic5—24no—
223C2×Dic5—24no—
224C2×Dic5—24no—
225C2×Dic5—24no—
226C2×Dic5—24no—
227C2×Dic5—42no—
228C2×Dic5—42no—
229C2×Dic5—42no—
230C2×Dic5—42no—
231C2×Dic5—42no—
232C2×Dic5—42no—
233C2×Dic5—42no—
234C2×Dic5—42no—
235C2×Dic5—42no—
236C2×Dic5—42no—
237C2×Dic5—42no—
238C2×Dic5—42no—
239C2×Dic5—42no—
240C2×Dic5—42no—
241C2×Dic5—42no—
242C2×Dic5—42no—
243C2×Dic5—42no—
244C2×Dic5—42no—
245C2×Dic5—42no—
246C23×C4—52no—
247C23×C4—52no—
248C23×C4—52no—
249C23×C4—52no—
250C23×C4C22×D511yescharacteristic
251C23×C4C22×D511yescharacteristic
252C23×C4C22×D512yes—
253C23×C4C22×D512yes—
254C23×C4C22×D511yescharacteristic
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—41no—
259C2×C4⋊C4—41no—
260C2×C4⋊C4—41no—
261C2×C4⋊C4—54no—
262C2×C4⋊C4—104no—
263C2×C4⋊C4—201no—
264C2×C4⋊C4—201no—
265C2×C4⋊C4—201no—
266C2×C4⋊C4C2×Dic518yes—
267C2×C4⋊C4C2×Dic514yes—
268C2×C4⋊C4C2×Dic514yes—
269C2×C42—104no—
270C2×C42—102no—
271C2×C42—201no—
272C2×C42—201no—
273C2×C42—202no—
274C2×C42—202no—
275#95—104no—
276#95—104no—
277#95—104no—
278#95—104no—
279#95—104no—
280#95—104no—
281#95—104no—
282#95—104no—
283#95—104no—
284#95—202no—
285#95—201no—
286#95—202no—
287#95C2×Dic518yes—
288#95C2×Dic514yes—
289C22×C5C2×C4×D411yescharacteristic
290C22×C5C4×#4112yes—
291C22×C5#51811yescharacteristic
292C22×C5#51912yes—
293C22×C5#52011yescharacteristic
294C22×C5#53411yescharacteristic
295C22×C5#53711yescharacteristic
296C22×C5#53811yescharacteristic
297C22×C5#53911yescharacteristic
298C22×C5#53912yes—
299C22×C5#53912yes—
300C22×C5#54112yes—
301C22×C5#54112yes—
302C22×C5#54712yes—
303C22×C5#54812yes—
304C22×C5#55111yescharacteristic
305C22×C5#55212yes—
306C22×C5#55312yes—
307C22×C5#55612yes—
308C22×C5#55911yescharacteristic
309C22×C5#56311yescharacteristic
310C22×C5#56312yes—
311C22×C5#56311yescharacteristic
312C4×C5—24no—
313C4×C5—44no—
314C4×C5—44no—
315C4×C5—42no—
316C4×C5—42no—
317Dic5—44no—
318Dic5—44no—
319Dic5—44no—
320Dic5—82no—
321C24C23×D511yescharacteristic
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—54no—
347C22×C4—54no—
348C22×C4—54no—
349C22×C4—102no—
350C22×C4—102no—
351C22×C4—102no—
352C22×C4—102no—
353C22×C4—102no—
354C22×C4—102no—
355C22×C4—102no—
356C22×C4—102no—
357C22×C4—102no—
358C22×C4—102no—
359C22×C4—102no—
360C22×C4—102no—
361C22×C4—102no—
362C22×C4—102no—
363C22×C4—102no—
364C22×C4—102no—
365C22×C4—102no—
366C22×C4—102no—
367C22×C4—102no—
368C22×C4—102no—
369C22×C4—102no—
370C22×C4—102no—
371C22×C4—102no—
372C22×C4—102no—
373C22×C4—102no—
374C22×C4D4×D512yes—
375C22×C4#71112yes—
376C22×C4C22×Dic514yes—
377C22×C4C22×Dic512yes—
378C22×C4C22×Dic514yes—
379C22×C4C22×Dic512yes—
380C22×C4C22×Dic512yes—
381C4⋊C4—216no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—204no—
385C4⋊C4—204no—
386C42—204no—
387C42—208no—
388C2×C5#232511yescharacteristic
389C2×C5#233612yes—
390C2×C5#236212yes—
391C2×C5#237411yescharacteristic
392C2×C5#238111yescharacteristic
393C2×C5#272411yescharacteristic
394C2×C5#272512yes—
395C2×C5#272811yescharacteristic
396C2×C5#278712yes—
397C2×C5#278911yescharacteristic
398C2×C5#279411yescharacteristic
399C23C2×D4×D511yescharacteristic
400C23C2×#71111yescharacteristic
401C23#414411yescharacteristic
402C23#414411yescharacteristic
403C23#414712yes—
404C23#414712yes—
405C23D5×#4112yes—
406C23D5×#4112yes—
407C23#414911yescharacteristic
408C23#415011yescharacteristic
409C23C23×Dic511yescharacteristic
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—104no—
441C2×C4—104no—
442C2×C4—104no—
443C2×C4—104no—
444C2×C4—104no—
445C2×C4—104no—
446C2×C4—104no—
447C2×C4—104no—
448C2×C4—104no—
449C2×C4—202no—
450C2×C4—202no—
451C2×C4—202no—
452C2×C4—202no—
453C2×C4—202no—
454C2×C4—202no—
455C2×C4—202no—
456C2×C4—202no—
457C2×C4—202no—
458C2×C4—202no—
459C2×C4—202no—
460C2×C4—202no—
461C2×C4—202no—
462C2×C4—202no—
463C2×C4—202no—
464C2×C4—202no—
465C2×C4—202no—
466C2×C4—202no—
467C2×C4—202no—
468C2×C4D4×Dic514yes—
469C5#1459011yescharacteristic, complemented, Sylow
470C22#6593111yescharacteristic
471C22#6593611yescharacteristic
472C22#6593911yescharacteristic
473C22#6595111yescharacteristic
474C22#6596512yes—
475C22#6596712yes—
476C22#6597312yes—
477C22#6597512yes—
478C22#6599311yescharacteristic
479C22#6599512yes—
480C22#6599811yescharacteristic
481C22#6602612yes—
482C22#6602612yes—
483C22#6603012yes—
484C22#6603012yes—
485C22#6606911yescharacteristic
486C22#6606912yes—
487C22#6606911yescharacteristic
488C22C2×D4×Dic511yescharacteristic
489C22#6613211yescharacteristic
490C22#6614612yes—
491C22#41×Dic512yes—
492C22#6616111yescharacteristic
493C4—24no—
494C4—42no—
495C4—42no—
496C4—44no—
497C4—44no—
498C4—204no—
499C4—204no—
500C4—204no—
501C4—402no—
502C2#1060959712yes—
503C2#1060960111yescharacteristic
504C2#1060963411yescharacteristic
505C2#1060964611yescharacteristic
506C2#1060971511yescharacteristic
507C2#1060973312yes—
508C2#1061436511yescharacteristic
509C2#1061447912yes—
510C2#1061457011yescharacteristic
511C2#1061475512yes—
512C2#1061496211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#398C2
socle, prime radical, cosocleC24×C5C24
hypercenterC2×#398D5
hypocenterC5#14590
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
17. C5×#398C4semidirect
160. #398Dic5semidirect
469. C5#14590semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C2×#652702
#106023582
#106023572
#106023562
#106002092
#106002002
#145905