Finite Group Databasebeta

← #11986325

Subgroups — #11986325

Order 1280.

560 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1437C211yesmaximal, characteristic
2#10602335C211yesmaximal, characteristic
3#10602332C211yesmaximal, characteristic
4C22×C5×C22⋊C4—21no—
5C22×C5×C22⋊C4C2211yescharacteristic
6C22×C42×C5C411yescharacteristic, complemented
7C2×C5×#95—21no—
8C2×C5×#95C411yescharacteristic, complemented
9#65536—21no—
10#65496—21no—
11#64746—21no—
12#64746C412yescomplemented
13#64745—21no—
14#64745C412yescomplemented
15#7213—51nomaximal, Sylow
16C25×C5D411yescharacteristic
17C23×C4×C5—21no—
18C23×C4×C5—21no—
19C23×C4×C5C2×C411yescharacteristic
20C23×C4×C5D411yescharacteristic
21C2×C5×C22⋊C4—24no—
22C2×C5×C22⋊C4—41no—
23C2×C5×C22⋊C4—41no—
24C2×C5×C22⋊C4—42no—
25C2×C5×C22⋊C4—42no—
26C2×C5×C22⋊C4C2×C411yescharacteristic
27C2×C5×C22⋊C4C2×C411yescharacteristic
28C2×C5×C22⋊C4D411yescharacteristic
29C2×C5×C22⋊C4Q811yescharacteristic
30C2×C42×C5—41no—
31C2×C42×C5—42no—
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—41no—
34C2×C22⋊Dic5—41no—
35C2×#681—41no—
36C5×#95—41no—
37C5×#95—42no—
38C22⋊#168—22no—
39C22⋊#168—41no—
40#1819—51no—
41#1462—51no—
42#1437D511yescharacteristic
43C24×C5—22no—
44C24×C5—21no—
45C24×C5—21no—
46C24×C5—41no—
47C24×C5—41no—
48C24×C5—41no—
49C24×C5—41no—
50C24×C5—41no—
51C24×C5C22⋊C411yescharacteristic
52C24×C5C22⋊C411yescharacteristic
53C24×C5C4⋊C411yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—22no—
62C22×C4×C5—41no—
63C22×C4×C5—41no—
64C22×C4×C5—41no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5C4211yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C4⋊C411yescharacteristic
79C22×C4×C5C4⋊C411yescharacteristic
80C22×Dic5—42no—
81C5×C22⋊C4—41no—
82C5×C22⋊C4—41no—
83C5×C22⋊C4—41no—
84C5×C22⋊C4—41no—
85C5×C22⋊C4—48no—
86C42×C5—42no—
87C42×C5—42no—
88C22⋊Dic5—42no—
89C22⋊Dic5—42no—
90C22⋊Dic5—81no—
91C22⋊Dic5—81no—
92C22⋊Dic5—81no—
93C22⋊Dic5—81no—
94#681—81no—
95#681—81no—
96C2×#168—42no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4C2×D511yescharacteristic
99C22×C42Dic511yescharacteristic, complemented
100#407—101no—
101#379—101no—
102C2×#95—21no—
103C2×#95Dic511yescharacteristic, complemented
104#342—52no—
105#342—101no—
106#323—52no—
107#323—101no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—21no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—42no—
120C23×C5—42no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5—41no—
125C23×C5—42no—
126C23×C5—42no—
127C23×C5—42no—
128C23×C5—42no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—41no—
133C23×C5—81no—
134C23×C5—81no—
135C23×C5—81no—
136C23×C5—81no—
137C23×C5—81no—
138C23×C5—81no—
139C23×C5#9511yescharacteristic
140C23×C5#9911yescharacteristic
141C23×C5#9911yescharacteristic
142C23×C5#10412yes—
143C2×C4×C5—24no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—41no—
155C2×C4×C5—42no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—42no—
164C2×C4×C5—42no—
165C2×C4×C5—42no—
166C2×C4×C5—81no—
167C2×C4×C5—81no—
168C2×C4×C5—81no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×Dic5—82no—
172C2×Dic5—82no—
173C2×Dic5—82no—
174#168—82no—
175C25C22⋊D511yescharacteristic
176C23×C4—21no—
177C23×C4—21no—
178C23×C4C2×Dic511yescharacteristic
179C23×C4C22⋊D511yescharacteristic
180C2×M16—201no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—42no—
185C2×C22⋊C4—42no—
186C2×C22⋊C4—102no—
187C2×C22⋊C4—201no—
188C2×C22⋊C4—201no—
189C2×C22⋊C4Dic1011yescharacteristic
190C2×C22⋊C4C4×D511yescharacteristic
191C2×C22⋊C4C4×D511yescharacteristic
192C2×C22⋊C4D2011yescharacteristic
193C2×C42—41no—
194C2×C42—42no—
195C22⋊C8—102no—
196C22⋊C8—201no—
197#95—41no—
198#95—42no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—22no—
214C22×C5—42no—
215C22×C5—42no—
216C22×C5—41no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—81no—
222C22×C5—82no—
223C22×C5—82no—
224C22×C5—82no—
225C22×C5—82no—
226C22×C5—81no—
227C22×C5H(3,ℤ/4)11yescharacteristic
228C22×C5#33911yescharacteristic
229C22×C5#34211yescharacteristic
230C22×C5AΣL(1,𝔽16)11yescharacteristic
231C22×C5#35211yescharacteristic
232C22×C5#35311yescharacteristic
233C22×C5#35411yescharacteristic
234C4×C5—44no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—41no—
238C4×C5—41no—
239C4×C5—82no—
240Dic5—162no—
241C24—22no—
242C24—21no—
243C24—21no—
244C24—41no—
245C24—41no—
246C24—41no—
247C24—41no—
248C24—41no—
249C24#68311yescharacteristic
250C24#68511yescharacteristic
251C24C22⋊Dic511yescharacteristic
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—202no—
275C22×C4C4×Dic511yescharacteristic
276C22×C4#68311yescharacteristic
277C22×C4C4⋊Dic511yescharacteristic
278C22×C4#68511yescharacteristic
279M16—401no—
280M16—401no—
281C2×C8—202no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—48no—
287C22⋊C4—202no—
288C22⋊C4—202no—
289C22⋊C4—401no—
290C22⋊C4—401no—
291C22⋊C4—401no—
292C22⋊C4—401no—
293C42—42no—
294C42—42no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5—21no—
298C2×C5—21no—
299C2×C5—21no—
300C2×C5—21no—
301C2×C5—42no—
302C2×C5—81no—
303C2×C5#128411yescharacteristic
304C2×C5#139011yescharacteristic
305C2×C5#139311yescharacteristic
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—81no—
335C23—81no—
336C23—81no—
337C23#393712yes—
338C23#396311yescharacteristic
339C23#396611yescharacteristic
340C23#396611yescharacteristic
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—402no—
370C2×C4—402no—
371C2×C4—402no—
372C8—402no—
373C5#721311yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—42no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—81no—
402C22#6474311yescharacteristic
403C22#6474611yescharacteristic
404C22#6475111yescharacteristic
405C22#6475611yescharacteristic
406C22#6475911yescharacteristic
407C22#6476111yescharacteristic
408C22#6476511yescharacteristic
409C4—44no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—82no—
415C4—802no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—81no—
424C2#1059810711yescharacteristic
425C2#1059812811yescharacteristic
426C2#1059813211yescharacteristic
subgroupG/H
centerC22#64746
commutatorC22×C4×C5C42
FrattiniC22×C22⋊C4C2×D5
FittingC5×#1437C2
socleC22×C5#342
prime radicalC25×C5D4
cosocleC22×C5×C22⋊C4C22
hypercenter#1437D5
hypocenterC5#7213
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1437

Complements

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

NH ≅ G/Ntype
6. C22×C42×C5C4semidirect
8. C2×C5×#95C4semidirect
12. #64746C4semidirect
14. #64745C4semidirect
99. C22×C42Dic5semidirect
103. C2×#95Dic5semidirect
373. C5#7213semidirect

Maximal subgroups

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

subgroupindex
C5×#14372
#106023352
#106023322
#72135