Finite Group Databasebeta

← #12046800

Subgroups — #12046800

Order 1280.

1082 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#382C211yesmaximal, characteristic
2C2×#65272C211yesmaximal, characteristic
3#10602359C212yesmaximal
4#10602357C211yesmaximal, characteristic
5#10602329C212yesmaximal
6#10600210C212yesmaximal
7#10600210C212yesmaximal
8#10600208C212yesmaximal
9#10600196C212yesmaximal
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C42×C5C2211yescharacteristic
13C22×C4⋊Dic5C2211yescharacteristic
14C22×#683C2212yes—
15C22×C4×Dic5C2211yescharacteristic
16C5×#382—24no—
17C2×C5×#95C2212yes—
18C2×C5×#95C2212yes—
19C2×#3963C2212yes—
20C2×#3963C2212yes—
21C2×#3963C2212yes—
22C2×#3963C2212yes—
23C2×#3963C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32#65272—24no—
33#15945—51nomaximal, Sylow
34C23×C4×C5C2312yes—
35C23×C4×C5C2311yescharacteristic
36C23×C4×C5C2311yescharacteristic
37C23×C4×C5C2312yes—
38C23×C4×C5C2311yescharacteristic
39C23×Dic5C2312yes—
40C23×Dic5C2312yes—
41C23×Dic5C2312yes—
42C23×Dic5C2312yes—
43C2×C5×C4⋊C4—22no—
44C2×C5×C4⋊C4—41no—
45C2×C5×C4⋊C4—41no—
46C2×C5×C4⋊C4—41no—
47C2×C5×C4⋊C4—41no—
48C2×C5×C4⋊C4D414yes—
49C2×C42×C5—22no—
50C2×C42×C5—24no—
51C2×C4⋊Dic5—22no—
52C2×C4⋊Dic5—41no—
53C2×C4⋊Dic5—41no—
54C2×#683—24no—
55C2×#683—24no—
56C2×#683—24no—
57C2×C4×Dic5—24no—
58C2×C4×Dic5—41no—
59C5×#95—24no—
60C5×#95—24no—
61#3963—22no—
62#3963—24no—
63#3963—24no—
64#3963—24no—
65#3963—24no—
66#3963—24no—
67#3963—24no—
68#3963—24no—
69#3963—24no—
70#3963—24no—
71#3963—42no—
72#3963—41no—
73#3963—42no—
74C2×#398—51no—
75C2×#382D511yescharacteristic
76#1443—52no—
77#1443—52no—
78#1442—52no—
79#1441—52no—
80#1436—52no—
81#1436—51no—
82#1434—52no—
83C24×C5C2411yescharacteristic
84C22×C4×C5—22no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—22no—
88C22×C4×C5—22no—
89C22×C4×C5—22no—
90C22×C4×C5—22no—
91C22×C4×C5—22no—
92C22×C4×C5—22no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5—22no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5C2×D412yes—
109C22×C4×C5C2×D412yes—
110C22×C4×C5C2×D412yes—
111C22×C4×C5#4114yes—
112C22×C4×C5#4114yes—
113C22×Dic5—22no—
114C22×Dic5—22no—
115C22×Dic5—22no—
116C22×Dic5—22no—
117C22×Dic5—22no—
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#4114yes—
140C22×Dic5#4114yes—
141C5×C4⋊C4—44no—
142C5×C4⋊C4—44no—
143C42×C5—28no—
144C4⋊Dic5—44no—
145#683—48no—
146C4×Dic5—44no—
147C22×C4⋊C4—52no—
148C22×C4⋊C4—51no—
149C22×C4⋊C4C2×D511yescharacteristic
150C22×C4⋊C4C2×D511yescharacteristic
151C22×C42—51no—
152C22×C42C2×D511yescharacteristic
153#398—104no—
154#382—24no—
155C2×#95—52no—
156C2×#95—51no—
157C2×#95—52no—
158C2×#95—52no—
159C2×#95—52no—
160C2×#95—52no—
161C2×#95—52no—
162C2×#95—52no—
163C2×#95—52no—
164C2×#95—52no—
165C2×#95—52no—
166C2×#95—51no—
167C2×#95—52no—
168C2×#95C2×D512yes—
169C2×#95C2×D512yes—
170C23×C5C22×D411yescharacteristic
171C23×C5C2×#4112yes—
172C23×C5C2×#4112yes—
173C23×C5C2×#4112yes—
174C23×C5C2×#4112yes—
175C23×C5H(5,𝔽2)11yescharacteristic
176C23×C5H(5,𝔽2)11yescharacteristic
177C23×C52−1+412yes—
178C23×C52−1+412yes—
179C2×C4×C5—22no—
180C2×C4×C5—22no—
181C2×C4×C5—24no—
182C2×C4×C5—24no—
183C2×C4×C5—24no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—24no—
187C2×C4×C5—24no—
188C2×C4×C5—24no—
189C2×C4×C5—24no—
190C2×C4×C5—42no—
191C2×C4×C5—42no—
192C2×C4×C5—42no—
193C2×C4×C5—42no—
194C2×C4×C5—42no—
195C2×C4×C5—42no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—42no—
201C2×C4×C5—42no—
202C2×C4×C5—42no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—42no—
207C2×C4×C5#12414yes—
208C2×Dic5—24no—
209C2×Dic5—24no—
210C2×Dic5—24no—
211C2×Dic5—24no—
212C2×Dic5—24no—
213C2×Dic5—24no—
214C2×Dic5—42no—
215C2×Dic5—42no—
216C2×Dic5—42no—
217C2×Dic5—42no—
218C2×Dic5—42no—
219C2×Dic5—42no—
220C2×Dic5—42no—
221C2×Dic5—42no—
222C2×Dic5—42no—
223C2×Dic5—42no—
224C2×Dic5—42no—
225C2×Dic5—42no—
226C2×Dic5—42no—
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—
236C23×C4—52no—
237C23×C4—52no—
238C23×C4—52no—
239C23×C4—52no—
240C23×C4C22×D512yes—
241C23×C4C22×D512yes—
242C23×C4C22×D511yescharacteristic
243C23×C4C22×D511yescharacteristic
244C23×C4C22×D511yescharacteristic
245C2×C4⋊C4—22no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4—104no—
251C2×C4⋊C4—104no—
252C2×C4⋊C4—104no—
253C2×C4⋊C4—102no—
254C2×C4⋊C4—201no—
255C2×C4⋊C4—201no—
256C2×C4⋊C4C22⋊D514yes—
257C2×C42—24no—
258C2×C42—22no—
259C2×C42—104no—
260C2×C42—201no—
261#95—24no—
262#95—24no—
263#95—104no—
264#95—104no—
265#95—104no—
266#95—104no—
267#95—104no—
268#95—104no—
269#95—104no—
270#95—104no—
271#95—102no—
272#95—104no—
273#95—201no—
274#95—202no—
275#95—202no—
276C22×C5#52511yescharacteristic
277C22×C5C2×#12411yescharacteristic
278C22×C5#52912yes—
279C22×C5#52912yes—
280C22×C5#53411yescharacteristic
281C22×C5#54112yes—
282C22×C5#54112yes—
283C22×C5#54212yes—
284C22×C5#54212yes—
285C22×C5#54712yes—
286C22×C5#54812yes—
287C22×C5#55111yescharacteristic
288C22×C5#55212yes—
289C22×C5#55212yes—
290C22×C5#55212yes—
291C22×C5#55212yes—
292C22×C5#55312yes—
293C22×C5#55312yes—
294C22×C5#55511yescharacteristic
295C22×C5#56311yescharacteristic
296C22×C5#56311yescharacteristic
297C4×C5—24no—
298C4×C5—42no—
299C4×C5—42no—
300C4×C5—44no—
301C4×C5—82no—
302Dic5—44no—
303Dic5—44no—
304Dic5—82no—
305Dic5—82no—
306C24C23×D511yescharacteristic
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—54no—
332C22×C4—54no—
333C22×C4—102no—
334C22×C4—102no—
335C22×C4—102no—
336C22×C4—102no—
337C22×C4—102no—
338C22×C4—102no—
339C22×C4—102no—
340C22×C4—102no—
341C22×C4—102no—
342C22×C4—102no—
343C22×C4—102no—
344C22×C4—102no—
345C22×C4—102no—
346C22×C4—102no—
347C22×C4—102no—
348C22×C4—102no—
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#70914yes—
360C22×C4#71314yes—
361C22×C4C2×C22⋊D512yes—
362C22×C4C2×C22⋊D512yes—
363C22×C4C2×C22⋊D512yes—
364C4⋊C4—44no—
365C4⋊C4—44no—
366C4⋊C4—204no—
367C4⋊C4—208no—
368C42—28no—
369C42—204no—
370C2×C5#247512yes—
371C2×C5#248912yes—
372C2×C5#251512yes—
373C2×C5#252912yes—
374C2×C5#259111yescharacteristic
375C2×C5#271711yescharacteristic
376C2×C5#273111yescharacteristic
377C2×C5#276612yes—
378C2×C5#276612yes—
379C23C2×#70912yes—
380C23#414411yescharacteristic
381C23#414411yescharacteristic
382C23C2×#71312yes—
383C23D5×#4112yes—
384C23D5×#4112yes—
385C23#415012yes—
386C23#415012yes—
387C23C22×C22⋊D511yescharacteristic
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—104no—
417C2×C4—104no—
418C2×C4—104no—
419C2×C4—104no—
420C2×C4—104no—
421C2×C4—104no—
422C2×C4—202no—
423C2×C4—202no—
424C2×C4—202no—
425C2×C4—202no—
426C2×C4—202no—
427C2×C4—202no—
428C2×C4—202no—
429C2×C4—202no—
430C2×C4—202no—
431C2×C4—202no—
432C2×C4—202no—
433C2×C4—202no—
434C2×C4—202no—
435C2×C4—202no—
436C2×C4—202no—
437C2×C4—202no—
438C2×C4—202no—
439C2×C4—202no—
440C2×C4—202no—
441C2×C4—202no—
442C2×C4—202no—
443C2×C4—202no—
444C2×C4#409314yes—
445C5#1594511yescharacteristic, complemented, Sylow
446C22#6584812yes—
447C22#6584812yes—
448C22#6585212yes—
449C22#6586212yes—
450C22#6586512yes—
451C22#6586512yes—
452C22#6600312yes—
453C22#6600312yes—
454C22#6600411yescharacteristic
455C22#6600611yescharacteristic
456C22#6600611yescharacteristic
457C22#6601311yescharacteristic
458C22#6602512yes—
459C22#6602812yes—
460C22#6602812yes—
461C22#6603112yes—
462C22#6612511yescharacteristic
463C22#6613811yescharacteristic
464C22C2×#409311yescharacteristic
465C22#6615812yes—
466C22#6616512yes—
467C4—24no—
468C4—42no—
469C4—42no—
470C4—44no—
471C4—82no—
472C4—204no—
473C4—204no—
474C4—402no—
475C4—402no—
476C2#1060590512yes—
477C2#1060591012yes—
478C2#1060593612yes—
479C2#1060593612yes—
480C2#1061391311yescharacteristic
481C2#1061398212yes—
482C2#1061472011yescharacteristic
483C2#1061472111yescharacteristic
484C2#1061479112yes—
subgroupG/H
center, FrattiniC24C23×D5
commutator, socle, prime radical, cosocleC24×C5C24
FittingC2×C5×#382C2
hypercenterC2×#382D5
hypocenterC5#15945
LCSG ▷ C24×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
445. C5#15945semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3822
C2×#652722
#106023592
#106023572
#106023292
#106002102
#106002082
#106001962
#159455