Finite Group Databasebeta

← C5×#11755 #11934475

Subgroups — C5×#11755 #11934475

Order 1280.

586 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2482C211yesmaximal, characteristic
2C2×C5×#342C211yesmaximal, characteristic
3C5×#1462C211yesmaximal, characteristic
4C5×#1352C212yesmaximal, complemented
5C5×#1344C212yesmaximal, complemented
6C2×C5×#117C411yescharacteristic, complemented
7C22×C5×C22⋊C4—21no—
8C22×C5×C22⋊C4C2211yescharacteristic
9C5×#407—21no—
10C5×#399C411yescharacteristic, complemented
11C5×#399C2211yescharacteristic
12C5×#397C411yescharacteristic, complemented
13C5×#397C2211yescharacteristic
14C5×#388—21no—
15C5×#388—21no—
16C5×#385—21no—
17C5×#381C411yescharacteristic, complemented
18C5×#379—21no—
19C5×#342—21no—
20C5×#342C2212yes—
21C5×#323—21no—
22C5×#323C2212yes—
23#11755C511yesmaximal, characteristic, direct product factor, Sylow
24C25×C5D411yescharacteristic
25C23×C4×C5—41no—
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C2×C5×M16—41no—
29C5×#117—41no—
30C5×#117—41no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
34C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
35C2×C5×C22⋊C4—24no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—41no—
44C2×C5×C22⋊C4—41no—
45C2×C5×C22⋊C4—41no—
46C2×C5×C22⋊C4—42no—
47C2×C5×C22⋊C4C2×C411yescharacteristic
48C2×C5×C22⋊C4D411yescharacteristic
49C2×C5×C22⋊C4D411yescharacteristic
50C2×C5×C22⋊C4C2311yescharacteristic
51C2×C42×C5—21no—
52C5×C22⋊C8—22no—
53C5×C22⋊C8—41no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95C2×C411yescharacteristic, complemented
58C5×#95C2×C411yescharacteristic, complemented
59#2482C2×C511yescharacteristic
60C2×#342C2×C511yescharacteristic
61#1462C2×C511yescharacteristic
62#1352C2×C512yescomplemented
63#1344C2×C512yescomplemented
64C24×C5—21no—
65C24×C5—21no—
66C24×C5—22no—
67C24×C5—21no—
68C24×C5—21no—
69C24×C5—42no—
70C24×C5—81no—
71C24×C5C22⋊C411yescharacteristic
72C24×C5C22⋊C411yescharacteristic
73C24×C5C2×D411yescharacteristic
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—42no—
83C22×C4×C5—44no—
84C22×C4×C5—42no—
85C22×C4×C5—81no—
86C22×C4×C5—82no—
87C22×C4×C5—82no—
88C22×C4×C5C22⋊C411yescharacteristic
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C5×M16—82no—
93C2×C5×C8—42no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—81no—
97C5×C4⋊C4—81no—
98C5×C22⋊C4—24no—
99C5×C22⋊C4—41no—
100C5×C22⋊C4—41no—
101C5×C22⋊C4—41no—
102C5×C22⋊C4—41no—
103C5×C22⋊C4—42no—
104C5×C22⋊C4—44no—
105C5×C22⋊C4—41no—
106C5×C22⋊C4—41no—
107C5×C22⋊C4—42no—
108C5×C22⋊C4—41no—
109C5×C22⋊C4—42no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—81no—
112C5×C22⋊C4—81no—
113C42×C5—42no—
114C2×#117C4×C511yescharacteristic, complemented
115C22×C22⋊C4—21no—
116C22×C22⋊C4C22×C511yescharacteristic
117#407—21no—
118#399C4×C511yescharacteristic, complemented
119#399C22×C511yescharacteristic
120#397C4×C511yescharacteristic, complemented
121#397C22×C511yescharacteristic
122#388—21no—
123#388—21no—
124#385—21no—
125#381C4×C511yescharacteristic, complemented
126#379—21no—
127#342—21no—
128#342C22×C512yes—
129#323—21no—
130#323C22×C512yes—
131C23×C5—22no—
132C23×C5—22no—
133C23×C5—22no—
134C23×C5—22no—
135C23×C5—22no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—41no—
143C23×C5—42no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5—42no—
149C23×C5—81no—
150C23×C5—81no—
151C23×C5—84no—
152C23×C5—82no—
153C23×C5—82no—
154C23×C5#9911yescharacteristic
155C23×C5#9911yescharacteristic
156C23×C5#10412yes—
157C23×C5C2×C22⋊C411yescharacteristic
158C23×C5AGL(1,ℤ/8)11yescharacteristic
159C23×C5#13711yescharacteristic
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—42no—
165C2×C4×C5—42no—
166C2×C4×C5—42no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—44no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—81no—
185C2×C4×C5—88no—
186C2×C4×C5—82no—
187C2×C4×C5—82no—
188C5×C8—82no—
189C25C5×D411yescharacteristic
190C23×C4—41no—
191C23×C4C2×C4×C511yescharacteristic
192C23×C4C5×D411yescharacteristic
193C2×M16—41no—
194#117—41no—
195#117—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×C4×C511yescharacteristic, complemented
199C2×C4⋊C4C2×C4×C511yescharacteristic, complemented
200C2×C22⋊C4—24no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—41no—
209C2×C22⋊C4—41no—
210C2×C22⋊C4—41no—
211C2×C22⋊C4—42no—
212C2×C22⋊C4C2×C4×C511yescharacteristic
213C2×C22⋊C4C5×D411yescharacteristic
214C2×C22⋊C4C5×D411yescharacteristic
215C2×C22⋊C4C23×C511yescharacteristic
216C2×C42—21no—
217C22⋊C8—22no—
218C22⋊C8—41no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×C4×C511yescharacteristic, complemented
223#95C2×C4×C511yescharacteristic, complemented
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—22no—
233C22×C5—21no—
234C22×C5—42no—
235C22×C5—42no—
236C22×C5—42no—
237C22×C5—41no—
238C22×C5—41no—
239C22×C5—44no—
240C22×C5—44no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—41no—
244C22×C5—41no—
245C22×C5—81no—
246C22×C5—81no—
247C22×C5—82no—
248C22×C5—82no—
249C22×C5#35212yes—
250C22×C5C2×#9911yescharacteristic
251C22×C5#41711yescharacteristic
252C22×C5C2×#10411yescharacteristic
253C4×C5—41no—
254C4×C5—41no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—81no—
258C4×C5—81no—
259C4×C5—84no—
260C4×C5—81no—
261C4×C5—81no—
262C24—21no—
263C24—21no—
264C24—21no—
265C24—21no—
266C24—22no—
267C24—42no—
268C24—81no—
269C24C5×C22⋊C411yescharacteristic
270C24C5×C22⋊C411yescharacteristic
271C24C2×C5×D411yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—44no—
282C22×C4—42no—
283C22×C4—81no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4C5×C22⋊C411yescharacteristic
287C22×C4C5×C22⋊C411yescharacteristic
288C22×C4C22×C4×C511yescharacteristic
289C22×C4C2×C5×D411yescharacteristic
290M16—82no—
291C2×C8—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C22⋊C4—24no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—44no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C42—42no—
312C2×C5—21no—
313C2×C5—21no—
314C2×C5—22no—
315C2×C5—41no—
316C2×C5—41no—
317C2×C5—42no—
318C2×C5—41no—
319C2×C5#150411yescharacteristic
320C2×C5C2×#35211yescharacteristic
321C2×C5#212711yescharacteristic
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—22no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—42no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—84no—
345C23C5×#9911yescharacteristic
346C23C5×#9911yescharacteristic
347C23C5×#10412yes—
348C23C2×C5×C22⋊C411yescharacteristic
349C23C5×AGL(1,ℤ/8)11yescharacteristic
350C23C5×#13711yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—88no—
377C2×C4—82no—
378C2×C4—82no—
379C8—82no—
380C5#1175511yescharacteristic, direct product factor, Sylow
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—44no—
397C22—44no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—82no—
405C22—82no—
406C22C5×#35212yes—
407C22C2×C5×#9911yescharacteristic
408C22C5×#41711yescharacteristic
409C22C2×C5×#10411yescharacteristic
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4—81no—
416C4—84no—
417C4—81no—
418C4—81no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—41no—
423C2—41no—
424C2—41no—
425C2—42no—
426C2C5×#150411yescharacteristic
427C2C2×C5×#35211yescharacteristic
428C2C5×#212711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC25×C5D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1352C2semidirect
5. C5×#1344C2semidirect
6. C2×C5×#117C4semidirect
10. C5×#399C4semidirect
12. C5×#397C4semidirect
17. C5×#381C4semidirect
23. #11755C5direct (N × H)
33. C2×C5×C4⋊C4C2×C4semidirect
34. C2×C5×C4⋊C4C2×C4semidirect
57. C5×#95C2×C4semidirect
58. C5×#95C2×C4semidirect
62. #1352C2×C5semidirect
63. #1344C2×C5semidirect
114. C2×#117C4×C5semidirect
118. #399C4×C5semidirect
120. #397C4×C5semidirect
125. #381C4×C5semidirect
198. C2×C4⋊C4C2×C4×C5semidirect
199. C2×C4⋊C4C2×C4×C5semidirect
222. #95C2×C4×C5semidirect
223. #95C2×C4×C5semidirect
380. C5#11755direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24822
C2×C5×#3422
C5×#14622
C5×#13522
C5×#13442
#117555