Finite Group Databasebeta

← C5×#9522 #11932242

Subgroups — C5×#9522 #11932242

Order 1280.

472 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3092C211yesmaximal, characteristic
2C5×#2976C211yesmaximal, characteristic
3C5×#1823C211yesmaximal, characteristic, complemented
4C5×#1821C211yesmaximal, characteristic, complemented
5C5×#1513C211yesmaximal, characteristic
6C5×#1305C211yesmaximal, characteristic, complemented
7C5×#1293C211yesmaximal, characteristic, complemented
8C5×#525C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C5×#484C412yescomplemented
11C5×#483—21no—
12C5×#481C412yescomplemented
13C5×#480—21no—
14C5×#436—21no—
15C5×#435—21no—
16C5×#435—21no—
17C5×C8×D4—21no—
18C5×#433—21no—
19C5×#428—21no—
20C5×#417—21no—
21C5×#408—21no—
22C5×#407C2211yescharacteristic
23C5×#407C2211yescharacteristic
24C5×#407C2211yescharacteristic
25C2×C5×C22⋊C8C2211yescharacteristic
26C5×#380C2211yescharacteristic
27C5×#343—21no—
28C5×#343—21no—
29C5×#340—21no—
30C5×#340—21no—
31C5×#328—21no—
32C5×#327—21no—
33#9522C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41D411yescharacteristic
35C23×C4×C5—21no—
36C23×C4×C5C2311yescharacteristic
37C2×C5×M16—21no—
38C2×C5×M16—21no—
39C2×C5×M16—21no—
40C2×C5×M16D411yescharacteristic
41C2×C5×M16D411yescharacteristic
42C22×C5×C8—21no—
43C22×C5×C8D411yescharacteristic
44C22×C5×C8D411yescharacteristic
45C5×#123—21no—
46C5×C22⋊Q8C2×C411yescharacteristic
47C5×C22⋊Q8D411yescharacteristic
48C5×#121C2×C411yescharacteristic
49C5×#121D411yescharacteristic
50C5×#120—21no—
51C4×C5×D4—21no—
52C4×C5×D4—21no—
53C5×#117D411yescharacteristic
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4C2×C412yes—
61C2×C5×C22⋊C4—21no—
62C5×#107—22no—
63C5×#106—22no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8—21no—
66C5×#103—22no—
67C5×#102—22no—
68C5×C22⋊C8—21no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8—21no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8—21no—
75C5×C22⋊C8—21no—
76C5×C22⋊C8—21no—
77C5×C22⋊C8C2×C412yes—
78C5×#97—21no—
79C4×C5×C8—21no—
80C5×#95—21no—
81#3092C2×C511yescharacteristic
82#2976C2×C511yescharacteristic
83#1823C2×C511yescharacteristic, complemented
84#1821C2×C511yescharacteristic, complemented
85#1513C2×C511yescharacteristic
86#1305C2×C511yescharacteristic, complemented
87#1293C2×C511yescharacteristic, complemented
88C24×C5#4111yescharacteristic
89C5×#41—41no—
90C5×#41—41no—
91C2×C5×Q8C22⋊C411yescharacteristic
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—21no—
95C2×C5×D4C22⋊C411yescharacteristic
96C22×C4×C5—21no—
97C22×C4×C5—22no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—81no—
104C22×C4×C5—81no—
105C22×C4×C5C22×C411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C22×C4×C5C2×D411yescharacteristic
108C22×C4×C5C2×D411yescharacteristic
109C22×C4×C5C2×D411yescharacteristic
110C22×C4×C5#4111yescharacteristic
111C5×M16—41no—
112C5×M16—41no—
113C5×M16—41no—
114C5×M16—41no—
115C5×M16—41no—
116C5×M16—41no—
117C5×M16—81no—
118C2×C5×C8—22no—
119C2×C5×C8—21no—
120C2×C5×C8—21no—
121C2×C5×C8—21no—
122C2×C5×C8—21no—
123C2×C5×C8—41no—
124C2×C5×C8—41no—
125C2×C5×C8—41no—
126C2×C5×C8—81no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—22no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—41no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—41no—
134C5×C4⋊C4—41no—
135C5×C4⋊C4C22⋊C411yescharacteristic
136C5×C4⋊C4C22⋊C411yescharacteristic
137C5×C22⋊C4—21no—
138C5×C22⋊C4—21no—
139C5×C22⋊C4—21no—
140C5×C22⋊C4—21no—
141C5×C22⋊C4—21no—
142C5×C22⋊C4—81no—
143C42×C5—21no—
144#525C22×C511yescharacteristic
145C22×C4⋊C4C22×C511yescharacteristic
146#484C4×C512yescomplemented
147#483—21no—
148#481C4×C512yescomplemented
149#480—21no—
150#436—21no—
151#435—21no—
152#435—21no—
153C8×D4—21no—
154#433—21no—
155#428—21no—
156#417—21no—
157#408—21no—
158#407C22×C511yescharacteristic
159#407C22×C511yescharacteristic
160#407C22×C511yescharacteristic
161C2×C22⋊C8C22×C511yescharacteristic
162#380C22×C511yescharacteristic
163#343—21no—
164#343—21no—
165#340—21no—
166#340—21no—
167#328—21no—
168#327—21no—
169C23×C5—21no—
170C23×C5—21no—
171C23×C5—21no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5C4×D411yescharacteristic
175C23×C5#12111yescharacteristic
176C23×C5#12311yescharacteristic
177C5×Q8—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—81no—
182C5×D4—81no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5—82no—
199C2×C4×C5—81no—
200C2×C4×C5—81no—
201C2×C4×C5—82no—
202C2×C4×C5—81no—
203C2×C4×C5—81no—
204C2×C4×C5—81no—
205C2×C4×C5C2×C22⋊C411yescharacteristic
206C2×C4×C5C4×D411yescharacteristic
207C2×C4×C5#12011yescharacteristic
208C2×C4×C5#12111yescharacteristic
209C5×C8—42no—
210C5×C8—41no—
211C5×C8—41no—
212C5×C8—41no—
213C5×C8—41no—
214C5×C8—81no—
215C2×#41C5×D411yescharacteristic
216C23×C4—21no—
217C23×C4C23×C511yescharacteristic
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16C5×D411yescharacteristic
222C2×M16C5×D411yescharacteristic
223C22×C8—21no—
224C22×C8C5×D411yescharacteristic
225C22×C8C5×D411yescharacteristic
226#123—21no—
227C22⋊Q8C2×C4×C511yescharacteristic
228C22⋊Q8C5×D411yescharacteristic
229#121C2×C4×C511yescharacteristic
230#121C5×D411yescharacteristic
231#120—21no—
232C4×D4—21no—
233C4×D4—21no—
234#117C5×D411yescharacteristic
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×C4×C512yes—
242C2×C22⋊C4—21no—
243#107—22no—
244#106—22no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247#103—22no—
248#102—22no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8C2×C4×C512yes—
259#97—21no—
260C4×C8—21no—
261#95—21no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—42no—
271C22×C5—42no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5#38611yescharacteristic
276C22×C5#47111yescharacteristic
277C22×C5#47211yescharacteristic
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—41no—
282C4×C5—41no—
283C4×C5—41no—
284C4×C5—82no—
285C4×C5—161no—
286C4×C5#45811yescharacteristic
287C4×C5#45811yescharacteristic
288C24C5×#4111yescharacteristic
289#41—41no—
290#41—41no—
291C2×Q8C5×C22⋊C411yescharacteristic
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4C5×C22⋊C411yescharacteristic
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—81no—
304C22×C4—81no—
305C22×C4C22×C4×C511yescharacteristic
306C22×C4C2×C5×D411yescharacteristic
307C22×C4C2×C5×D411yescharacteristic
308C22×C4C2×C5×D411yescharacteristic
309C22×C4C2×C5×D411yescharacteristic
310C22×C4C5×#4111yescharacteristic
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315M16—41no—
316M16—41no—
317M16—81no—
318C2×C8—22no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—81no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4C5×C22⋊C411yescharacteristic
336C4⋊C4C5×C22⋊C411yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—81no—
343C42—21no—
344C2×C5—21no—
345C2×C5—21no—
346C2×C5—41no—
347C2×C5—41no—
348C2×C5—81no—
349C2×C5#189011yescharacteristic
350C2×C5#190211yescharacteristic
351C2×C5#190711yescharacteristic
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23C4×C5×D411yescharacteristic
358C23C5×#12111yescharacteristic
359C23C5×#12311yescharacteristic
360Q8—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4C2×C5×C22⋊C411yescharacteristic
389C2×C4C4×C5×D411yescharacteristic
390C2×C4C5×#12011yescharacteristic
391C2×C4C5×#12111yescharacteristic
392C8—42no—
393C8—41no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—81no—
398C5#952211yescharacteristic, direct product factor, Sylow
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22C5×#38611yescharacteristic
413C22C5×#47111yescharacteristic
414C22C5×#47211yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4—161no—
423C4C5×#45811yescharacteristic
424C4C5×#45811yescharacteristic
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2C5×#189011yescharacteristic
431C2C5×#190211yescharacteristic
432C2C5×#190711yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC5×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1823C2semidirect
4. C5×#1821C2semidirect
6. C5×#1305C2semidirect
7. C5×#1293C2semidirect
10. C5×#484C4semidirect
12. C5×#481C4semidirect
33. #9522C5direct (N × H)
83. #1823C2×C5semidirect
84. #1821C2×C5semidirect
86. #1305C2×C5semidirect
87. #1293C2×C5semidirect
146. #484C4×C5semidirect
148. #481C4×C5semidirect
398. C5#9522direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30922
C5×#29762
C5×#18232
C5×#18212
C5×#15132
C5×#13052
C5×#12932
#95225