Finite Group Databasebeta

← C5×#24081 #11946801

Subgroups — C5×#24081 #11946801

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3493C211yesmaximal, characteristic
2C5×#3092C212yesmaximal, complemented
3C5×#2317C211yesmaximal, characteristic, complemented
4C5×#2061C212yesmaximal, complemented
5C5×#2040C212yesmaximal, complemented
6C5×#1897C212yesmaximal, complemented
7C5×#1859C214yesmaximal, complemented
8C5×#1822C211yesmaximal, characteristic, complemented
9C5×#556—22no—
10C5×#555—22no—
11C5×#553—22no—
12C5×#552—22no—
13C5×#544C2211yescharacteristic
14C5×#538—22no—
15C5×#537C2211yescharacteristic
16C5×#529—22no—
17C5×#525C2212yes—
18C5×#520C2212yes—
19C2×C5×#117C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C5×#484—22no—
23C5×#483—22no—
24C5×#481—22no—
25C5×#480—22no—
26C5×#428C2214yes—
27C2×C5×#104C2214yes—
28C5×#417C2214yes—
29C5×#407C2212yes—
30C5×#389—22no—
31C5×#385—22no—
32C5×#384C2212yes—
33C5×#382C2212yes—
34C5×#343C2212yes—
35C5×#343C2212yes—
36C5×#339C2214yes—
37#24081C511yesmaximal, characteristic, direct product factor, Sylow
38C2×C5×#41C2312yes—
39C23×C4×C5—21no—
40C23×C4×C5C2311yescharacteristic
41C2×C5×M16C2314yes—
42C5×C4⋊Q8—22no—
43C5×#126—24no—
44C5×#126—24no—
45C5×#125—22no—
46C5×#125—22no—
47C5×#124—22no—
48C5×#124—24no—
49C5×#123—24no—
50C5×#123—22no—
51C5×C22⋊Q8—22no—
52C5×C22⋊Q8—22no—
53C5×C22⋊Q8D412yes—
54C5×C22⋊Q8D412yes—
55C5×#121—24no—
56C5×#121—22no—
57C5×#121—22no—
58C5×#121D412yes—
59C5×#121D412yes—
60C5×#120—22no—
61C4×C5×Q8—22no—
62C4×C5×Q8—22no—
63C4×C5×D4—22no—
64C4×C5×D4—22no—
65C4×C5×D4—24no—
66C4×C5×D4—22no—
67C4×C5×D4—22no—
68C5×#117—24no—
69C5×#117—22no—
70C5×#117—22no—
71C5×#117—22no—
72C5×#117—24no—
73C5×#117C2312yes—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—24no—
80C2×C5×C4⋊C4C2312yes—
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2311yescharacteristic
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4D412yes—
85C2×C42×C5D412yes—
86C2×C42×C5C2312yes—
87C5×#107—24no—
88C5×#106—24no—
89C5×#104—28no—
90C5×#103—24no—
91C5×#102—24no—
92C5×C22⋊C8—22no—
93C5×C22⋊C8—22no—
94C5×#95—24no—
95#3493C2×C511yescharacteristic
96#3092C2×C512yescomplemented
97#2317C2×C511yescharacteristic, complemented
98#2061C2×C512yescomplemented
99#2040C2×C512yescomplemented
100#1897C2×C512yescomplemented
101#1859C2×C514yescomplemented
102#1822C2×C511yescharacteristic, complemented
103C24×C5C2×D411yescharacteristic
104C5×#41—24no—
105C5×#41—24no—
106C2×C5×Q8—22no—
107C2×C5×Q8C2×D412yes—
108C2×C5×D4—22no—
109C2×C5×D4—22no—
110C2×C5×D4—22no—
111C2×C5×D4—22no—
112C2×C5×D4C2×D412yes—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—24no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—42no—
120C22×C4×C5—82no—
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2×D412yes—
123C22×C4×C5C2×D412yes—
124C22×C4×C5C2×D412yes—
125C22×C4×C5C2×D412yes—
126C22×C4×C5C2411yescharacteristic
127C5×M16—24no—
128C5×M16—24no—
129C2×C5×C8—24no—
130C5×C4⋊C4—24no—
131C5×C4⋊C4—24no—
132C5×C4⋊C4—24no—
133C5×C4⋊C4—22no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—22no—
136C5×C4⋊C4—22no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4—22no—
139C5×C4⋊C4—24no—
140C5×C4⋊C4—41no—
141C5×C4⋊C4—41no—
142C5×C4⋊C4—84no—
143C5×C4⋊C4C2×D412yes—
144C5×C4⋊C4C2×D412yes—
145C5×C22⋊C4—24no—
146C5×C22⋊C4—24no—
147C5×C22⋊C4—24no—
148C5×C22⋊C4—24no—
149C5×C22⋊C4—22no—
150C5×C22⋊C4—22no—
151C5×C22⋊C4—22no—
152C5×C22⋊C4—22no—
153C5×C22⋊C4—22no—
154C42×C5—24no—
155C42×C5—22no—
156C42×C5—22no—
157C42×C5—22no—
158C42×C5—22no—
159C42×C5#4114yes—
160#556—22no—
161#555—22no—
162#553—22no—
163#552—22no—
164#544C22×C511yescharacteristic
165#538—22no—
166#537C22×C511yescharacteristic
167#529—22no—
168#525C22×C512yes—
169#520C22×C512yes—
170C2×#117C22×C511yescharacteristic
171C2×#117C22×C511yescharacteristic
172C22×C4⋊C4C22×C511yescharacteristic
173#484—22no—
174#483—22no—
175#481—22no—
176#480—22no—
177#428C22×C514yes—
178C2×#104C22×C514yes—
179#417C22×C514yes—
180#407C22×C512yes—
181#389—22no—
182#385—22no—
183#384C22×C512yes—
184#382C22×C512yes—
185#343C22×C512yes—
186#343C22×C512yes—
187#339C22×C514yes—
188C23×C5—21no—
189C23×C5—21no—
190C23×C5—22no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5#12012yes—
194C23×C5C22×D411yescharacteristic
195C5×Q8—24no—
196C5×Q8—82no—
197C5×D4—24no—
198C5×D4—42no—
199C5×D4—42no—
200C5×D4—82no—
201C5×D4—82no—
202C5×D4—82no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—24no—
206C2×C4×C5—24no—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—22no—
210C2×C4×C5—22no—
211C2×C4×C5—22no—
212C2×C4×C5—24no—
213C2×C4×C5—42no—
214C2×C4×C5—42no—
215C2×C4×C5—44no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5—44no—
219C2×C4×C5—42no—
220C2×C4×C5—84no—
221C2×C4×C5—84no—
222C2×C4×C5#12011yescharacteristic
223C2×C4×C5#12011yescharacteristic
224C2×C4×C5C22×D412yes—
225C2×C4×C5C2×#4112yes—
226C2×C4×C52−1+412yes—
227C5×C8—44no—
228C2×#41C23×C512yes—
229C23×C4—21no—
230C23×C4C23×C511yescharacteristic
231C2×M16C23×C514yes—
232C4⋊Q8—22no—
233#126—24no—
234#126—24no—
235#125—22no—
236#125—22no—
237#124—22no—
238#124—24no—
239#123—24no—
240#123—22no—
241C22⋊Q8—22no—
242C22⋊Q8—22no—
243C22⋊Q8C5×D412yes—
244C22⋊Q8C5×D412yes—
245#121—24no—
246#121—22no—
247#121—22no—
248#121C5×D412yes—
249#121C5×D412yes—
250#120—22no—
251C4×Q8—22no—
252C4×Q8—22no—
253C4×D4—22no—
254C4×D4—22no—
255C4×D4—24no—
256C4×D4—22no—
257C4×D4—22no—
258#117—24no—
259#117—22no—
260#117—22no—
261#117—22no—
262#117—24no—
263#117C23×C512yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4C23×C512yes—
271C2×C4⋊C4C23×C511yescharacteristic
272C2×C4⋊C4C23×C511yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4C5×D412yes—
275C2×C42C5×D412yes—
276C2×C42C23×C512yes—
277#107—24no—
278#106—24no—
279#104—28no—
280#103—24no—
281#102—24no—
282C22⋊C8—22no—
283C22⋊C8—22no—
284#95—24no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—22no—
288C22×C5—22no—
289C22×C5—22no—
290C22×C5—42no—
291C22×C5—42no—
292C22×C5—42no—
293C22×C5—42no—
294C22×C5—42no—
295C22×C5C2×#12011yescharacteristic
296C22×C5#52511yescharacteristic
297C22×C5#53611yescharacteristic
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—44no—
301C4×C5—42no—
302C4×C5—42no—
303C4×C5—42no—
304C4×C5—42no—
305C4×C5—42no—
306C4×C5—82no—
307C4×C5#54714yes—
308C24C2×C5×D411yescharacteristic
309#41—24no—
310#41—24no—
311C2×Q8—22no—
312C2×Q8C2×C5×D412yes—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4C2×C5×D412yes—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—42no—
325C22×C4—82no—
326C22×C4C2×C5×D411yescharacteristic
327C22×C4C2×C5×D412yes—
328C22×C4C2×C5×D412yes—
329C22×C4C2×C5×D412yes—
330C22×C4C2×C5×D412yes—
331C22×C4C24×C511yescharacteristic
332M16—24no—
333M16—24no—
334C2×C8—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—24no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—84no—
348C4⋊C4C2×C5×D412yes—
349C4⋊C4C2×C5×D412yes—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C42—24no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42C5×#4114yes—
365C2×C5—21no—
366C2×C5—21no—
367C2×C5—42no—
368C2×C5—82no—
369C2×C5#240611yescharacteristic
370C2×C5#302111yescharacteristic
371C2×C5#302211yescharacteristic
372C23—21no—
373C23—21no—
374C23—22no—
375C23—41no—
376C23—41no—
377C23C5×#12012yes—
378C23C22×C5×D411yescharacteristic
379Q8—24no—
380Q8—82no—
381D4—24no—
382D4—42no—
383D4—42no—
384D4—82no—
385D4—82no—
386D4—82no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—84no—
405C2×C4—84no—
406C2×C4C5×#12011yescharacteristic
407C2×C4C5×#12011yescharacteristic
408C2×C4C22×C5×D412yes—
409C2×C4C2×C5×#4112yes—
410C2×C4C5×2−1+412yes—
411C8—44no—
412C5#2408111yescharacteristic, direct product factor, Sylow
413C22—21no—
414C22—21no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22C2×C5×#12011yescharacteristic
424C22C5×#52511yescharacteristic
425C22C5×#53611yescharacteristic
426C4—21no—
427C4—21no—
428C4—44no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—82no—
435C4C5×#54714yes—
436C2—21no—
437C2—21no—
438C2—42no—
439C2—82no—
440C2C5×#240611yescharacteristic
441C2C5×#302111yescharacteristic
442C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3493C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3092C2semidirect
3. C5×#2317C2semidirect
4. C5×#2061C2semidirect
5. C5×#2040C2semidirect
6. C5×#1897C2semidirect
7. C5×#1859C2semidirect
8. C5×#1822C2semidirect
37. #24081C5direct (N × H)
96. #3092C2×C5semidirect
97. #2317C2×C5semidirect
98. #2061C2×C5semidirect
99. #2040C2×C5semidirect
100. #1897C2×C5semidirect
101. #1859C2×C5semidirect
102. #1822C2×C5semidirect
412. C5#24081direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34932
C5×#30922
C5×#23172
C5×#20612
C5×#20402
C5×#18972
C5×#18592
C5×#18222
#240815