Finite Group Databasebeta

← C5×#12794 #11935514

Subgroups — C5×#12794 #11935514

Order 1280.

540 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#123C211yesmaximal, characteristic
2C2×C5×#352C212yesmaximal
3C5×#1800C211yesmaximal, characteristic
4C5×#1799C211yesmaximal, characteristic
5C5×#1390C212yesmaximal
6C2×C5×#123C2211yescharacteristic
7C2×C4×C5×D4C2211yescharacteristic
8C22×C42×C5C411yescharacteristic, complemented
9C5×#423—21no—
10C2×C5×#100C2212yes—
11C2×C5×#99C2212yes—
12C5×#388—21no—
13C5×#387—21no—
14C5×#386C2211yescharacteristic
15C5×#385C411yescharacteristic, complemented
16C5×#381C411yescharacteristic, complemented
17C5×#380—21no—
18C4×C5×C4⋊C4—21no—
19C4×C5×C22⋊C4—21no—
20C4×C5×C22⋊C4C411yescharacteristic, complemented
21C5×#352—24no—
22C5×#343—21no—
23C5×#342—21no—
24#12794C511yesmaximal, characteristic, direct product factor, Sylow
25C22×C5×D4C2311yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C2×C5×M16—22no—
31C5×#123—21no—
32C5×#123—21no—
33C5×#123D412yes—
34C5×#123Q812yes—
35C4×C5×D4—41no—
36C4×C5×D4—41no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—41no—
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—22no—
44C2×C5×C22⋊C4C2×C411yescharacteristic
45C2×C5×C22⋊C4C2×C411yescharacteristic
46C2×C5×C22⋊C4C2×C411yescharacteristic
47C2×C5×C22⋊C4D411yescharacteristic
48C2×C42×C5—21no—
49C2×C42×C5—21no—
50C2×C42×C5—21no—
51C2×C42×C5—41no—
52C2×C42×C5—41no—
53C2×C42×C5D411yescharacteristic
54C5×C4⋊C8—41no—
55C5×C4⋊C8—41no—
56C5×#100—22no—
57C5×#100—22no—
58C5×#99—22no—
59C5×#99—22no—
60C5×#95—21no—
61C5×#95—21no—
62C5×#95—21no—
63C5×#95—21no—
64C5×#95—21no—
65C5×#95—41no—
66C4×#123C2×C511yescharacteristic
67C2×#352C2×C512yes—
68#1800C2×C511yescharacteristic
69#1799C2×C511yescharacteristic
70#1390C2×C512yes—
71C24×C5C22×C411yescharacteristic
72C24×C5C2×D411yescharacteristic
73C2×C5×D4—41no—
74C2×C5×D4—41no—
75C2×C5×D4C2×D411yescharacteristic
76C2×C5×D4C2×Q811yescharacteristic
77C2×C5×D4#4111yescharacteristic
78C2×C5×D4#4111yescharacteristic
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—42no—
89C22×C4×C5—42no—
90C22×C4×C5—42no—
91C22×C4×C5—41no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5—42no—
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C22⋊C411yescharacteristic
97C22×C4×C5C22⋊C411yescharacteristic
98C22×C4×C5C22⋊C411yescharacteristic
99C22×C4×C5C4⋊C412yescomplemented
100C22×C4×C5C2×D411yescharacteristic
101C5×M16—42no—
102C5×M16—42no—
103C2×C5×C8—42no—
104C5×C4⋊C4—22no—
105C5×C4⋊C4—22no—
106C5×C4⋊C4—41no—
107C5×C4⋊C4—42no—
108C5×C4⋊C4—82no—
109C5×C22⋊C4—21no—
110C5×C22⋊C4—22no—
111C5×C22⋊C4—22no—
112C5×C22⋊C4—41no—
113C5×C22⋊C4—41no—
114C5×C22⋊C4—42no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—42no—
117C5×C22⋊C4—42no—
118C5×C22⋊C4C4⋊C412yescomplemented
119C42×C5—21no—
120C42×C5—21no—
121C42×C5—42no—
122C42×C5—42no—
123C42×C5—41no—
124C42×C5—41no—
125C2×#123C22×C511yescharacteristic
126C2×C4×D4C22×C511yescharacteristic
127C22×C42C4×C511yescharacteristic, complemented
128#423—21no—
129C2×#100C22×C512yes—
130C2×#99C22×C512yes—
131#388—21no—
132#387—21no—
133#386C22×C511yescharacteristic
134#385C4×C511yescharacteristic, complemented
135#381C4×C511yescharacteristic, complemented
136#380—21no—
137C4×C4⋊C4—21no—
138C4×C22⋊C4—21no—
139C4×C22⋊C4C4×C511yescharacteristic, complemented
140#352—24no—
141#343—21no—
142#342—21no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5—21no—
146C23×C5—21no—
147C23×C5—41no—
148C23×C5—41no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5C2×C22⋊C411yescharacteristic
152C23×C5C2×C4⋊C411yescharacteristic
153C23×C5#11711yescharacteristic
154C23×C5#12111yescharacteristic
155C23×C5C22⋊Q811yescharacteristic
156C5×D4—41no—
157C5×D4—41no—
158C5×D4—41no—
159C5×D4—41no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—42no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—42no—
173C2×C4×C5—41no—
174C2×C4×C5—42no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—42no—
179C2×C4×C5—42no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—81no—
189C2×C4×C5—82no—
190C2×C4×C5—82no—
191C2×C4×C5—82no—
192C2×C4×C5#9911yescharacteristic
193C2×C4×C5#9911yescharacteristic
194C2×C4×C5#12111yescharacteristic
195C2×C4×C5C22⋊Q811yescharacteristic
196C5×C8—82no—
197C22×D4C23×C511yescharacteristic
198C23×C4C2×C4×C511yescharacteristic
199C23×C4C2×C4×C511yescharacteristic
200C23×C4C2×C4×C511yescharacteristic
201C23×C4C5×D411yescharacteristic
202C2×M16—22no—
203#123—21no—
204#123—21no—
205#123C5×D412yes—
206#123C5×Q812yes—
207C4×D4—41no—
208C4×D4—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4C5×D411yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4C2×C4×C511yescharacteristic
217C2×C22⋊C4C2×C4×C511yescharacteristic
218C2×C22⋊C4C2×C4×C511yescharacteristic
219C2×C22⋊C4C5×D411yescharacteristic
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—41no—
224C2×C42—41no—
225C2×C42C5×D411yescharacteristic
226C4⋊C8—41no—
227C4⋊C8—41no—
228#100—22no—
229#100—22no—
230#99—22no—
231#99—22no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—41no—
238C22×C5—21no—
239C22×C5—21no—
240C22×C5—21no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5—21no—
244C22×C5—41no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5—41no—
248C22×C5—42no—
249C22×C5—41no—
250C22×C5—41no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5—81no—
254C22×C5#38011yescharacteristic
255C22×C5C2×#9911yescharacteristic
256C22×C5#41011yescharacteristic
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—42no—
261C4×C5—42no—
262C4×C5—41no—
263C4×C5—41no—
264C4×C5—41no—
265C4×C5—42no—
266C4×C5—81no—
267C4×C5—162no—
268C4×C5#35212yescomplemented
269C24C22×C4×C511yescharacteristic
270C24C2×C5×D411yescharacteristic
271C2×D4—41no—
272C2×D4—41no—
273C2×D4C2×C5×D411yescharacteristic
274C2×D4C2×C5×Q811yescharacteristic
275C2×D4C5×#4111yescharacteristic
276C2×D4C5×#4111yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4C5×C22⋊C411yescharacteristic
294C22×C4C5×C22⋊C411yescharacteristic
295C22×C4C5×C22⋊C411yescharacteristic
296C22×C4C5×C22⋊C411yescharacteristic
297C22×C4C5×C4⋊C412yescomplemented
298C22×C4C2×C5×D411yescharacteristic
299M16—42no—
300M16—42no—
301C2×C8—42no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—82no—
307C22⋊C4—21no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4C5×C4⋊C412yescomplemented
317C42—21no—
318C42—21no—
319C42—42no—
320C42—42no—
321C42—41no—
322C42—41no—
323C2×C5—21no—
324C2×C5—21no—
325C2×C5—41no—
326C2×C5—41no—
327C2×C5—41no—
328C2×C5—41no—
329C2×C5#179911yescharacteristic
330C2×C5C2×#35211yescharacteristic
331C2×C5#212011yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C2×C5×C22⋊C411yescharacteristic
341C23C2×C5×C4⋊C411yescharacteristic
342C23C5×#11711yescharacteristic
343C23C5×#12111yescharacteristic
344C23C5×C22⋊Q811yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4C5×#9911yescharacteristic
382C2×C4C5×#9911yescharacteristic
383C2×C4C5×#12111yescharacteristic
384C2×C4C5×C22⋊Q811yescharacteristic
385C8—82no—
386C5#1279411yescharacteristic, direct product factor, Sylow
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22C5×#38011yescharacteristic
404C22C2×C5×#9911yescharacteristic
405C22C5×#41011yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—42no—
414C4—41no—
415C4—81no—
416C4—162no—
417C4C5×#35212yescomplemented
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—41no—
424C2C5×#179911yescharacteristic
425C2C2×C5×#35211yescharacteristic
426C2C5×#212011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC24C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC22×C5×D4C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22×C42×C5C4semidirect
15. C5×#385C4semidirect
16. C5×#381C4semidirect
20. C4×C5×C22⋊C4C4semidirect
24. #12794C5direct (N × H)
99. C22×C4×C5C4⋊C4semidirect
118. C5×C22⋊C4C4⋊C4semidirect
127. C22×C42C4×C5semidirect
134. #385C4×C5semidirect
135. #381C4×C5semidirect
139. C4×C22⋊C4C4×C5semidirect
268. C4×C5#352semidirect
297. C22×C4C5×C4⋊C4semidirect
316. C22⋊C4C5×C4⋊C4semidirect
386. C5#12794direct (N × H)
417. C4C5×#352semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1232
C2×C5×#3522
C5×#18002
C5×#17992
C5×#13902
#127945