Finite Group Databasebeta

← C5×#10433 #11933153

Subgroups — C5×#10433 #11933153

Order 1280.

530 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×#2538C211yesmaximal, characteristic
2C5×#1834C211yesmaximal, characteristic, complemented
3C5×#1803C211yesmaximal, characteristic, complemented
4C5×#1802C211yesmaximal, characteristic
5C2×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C5×D4⋊C8C211yesmaximal, characteristic
7C5×#1296C211yesmaximal, characteristic, complemented
8C2×C5×C22⋊Q8—21no—
9C2×C4×C5×Q8C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×#103—21no—
14C2×C5×#102—21no—
15C2×C4×C5×C8C2211yescharacteristic
16C5×#396—22no—
17C5×#390—21no—
18C5×#389—21no—
19C5×#384C2211yescharacteristic
20C5×#384C2211yescharacteristic
21C5×#380—21no—
22C5×#340—21no—
23C5×#340—21no—
24C5×#340—22no—
25C5×Q8⋊C8—22no—
26C5×D4⋊C8—22no—
27#10433C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8D411yescharacteristic
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C22×C5×C8—21no—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C5×C22⋊Q8—42no—
35C5×C22⋊Q8—42no—
36C4×C5×Q8—21no—
37C4×C5×Q8—21no—
38C4×C5×Q8—21no—
39C4×C5×Q8—21no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C2×C5×C4⋊C4—22no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4D411yescharacteristic
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C4⋊C4D412yes—
54C2×C5×C22⋊C4—22no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—22no—
57C2×C42×C5—21no—
58C2×C42×C5C2311yescharacteristic
59C5×C4⋊C8—21no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×#103—42no—
64C5×#102—42no—
65C4×C5×C8—21no—
66C4×C5×C8D412yes—
67C5×#95—22no—
68#2538C2×C511yescharacteristic
69#1834C2×C511yescharacteristic, complemented
70#1803C2×C511yescharacteristic, complemented
71#1802C2×C511yescharacteristic
72C2×Q8⋊C8C2×C511yescharacteristic, complemented
73C2×D4⋊C8C2×C511yescharacteristic
74#1296C2×C511yescharacteristic, complemented
75C24×C5—21no—
76C2×C5×Q8—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8D812yes—
82C2×C5×D4—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4SD1612yes—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—22no—
91C22×C4×C5—21no—
92C22×C4×C5—41no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C2×C5×C8—22no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—42no—
116C5×C4⋊C4—44no—
117C5×C4⋊C4—42no—
118C5×C4⋊C4—41no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C4⋊C4—41no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C5×C4⋊C4—41no—
126C5×C4⋊C4—41no—
127C5×C4⋊C4—41no—
128C5×C22⋊C4—44no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—82no—
132C42×C5—41no—
133C42×C5—41no—
134C42×C5C2×D411yescharacteristic
135C42×C5#4111yescharacteristic
136C42×C5#4111yescharacteristic
137C42×C5#4111yescharacteristic
138C2×C22⋊Q8—21no—
139C2×C4×Q8C22×C511yescharacteristic
140C2×C4×D4C22×C511yescharacteristic
141C2×C4⋊C8C22×C511yescharacteristic
142C2×C4⋊C8C22×C511yescharacteristic
143C2×#103—21no—
144C2×#102—21no—
145C2×C4×C8C22×C511yescharacteristic
146#396—22no—
147#390—21no—
148#389—21no—
149#384C22×C511yescharacteristic
150#384C22×C511yescharacteristic
151#380—21no—
152#340—21no—
153#340—21no—
154#340—22no—
155Q8⋊C8—22no—
156D4⋊C8—22no—
157C23×C5—22no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5#12011yescharacteristic
165C5×Q8—22no—
166C5×Q8—22no—
167C5×Q8—41no—
168C5×Q8—41no—
169C5×D4—22no—
170C5×D4—22no—
171C5×D4—41no—
172C5×D4—41no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—22no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—42no—
181C2×C4×C5—41no—
182C2×C4×C5—42no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—42no—
187C2×C4×C5—81no—
188C2×C4×C5—81no—
189C2×C4×C5—81no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5#12111yescharacteristic
195C2×C4×C5#12111yescharacteristic
196C2×C4×C5#12111yescharacteristic
197C2×C4×C5#12311yescharacteristic
198C2×C4×C5#12311yescharacteristic
199C2×C4×C5#12411yescharacteristic
200C2×C4×C5C2×D811yescharacteristic
201C2×C4×C5C2×SD1611yescharacteristic
202C2×C4×C5#13511yescharacteristic
203C2×C4×C5#13511yescharacteristic
204C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C5#13711yescharacteristic
206C2×C4×C5#13711yescharacteristic
207C2×C4×C5#13711yescharacteristic
208C5×C8—42no—
209C5×C8—81no—
210C5×C8—81no—
211C22×Q8C5×D411yescharacteristic
212C22×D4C5×D411yescharacteristic
213C23×C4—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22⋊Q8—42no—
218C22⋊Q8—42no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C5×D411yescharacteristic
235C2×C4⋊C4C5×D411yescharacteristic
236C2×C4⋊C4C5×D412yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—22no—
240C2×C42—21no—
241C2×C42C23×C511yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246#103—42no—
247#102—42no—
248C4×C8—21no—
249C4×C8C5×D412yes—
250#95—22no—
251C22×C5—42no—
252C22×C5—42no—
253C22×C5—42no—
254C22×C5—81no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5#39411yescharacteristic
259C22×C5#44711yescharacteristic
260C22×C5#44811yescharacteristic
261C22×C5#45211yescharacteristic
262C22×C5#45211yescharacteristic
263C22×C5#45411yescharacteristic
264C22×C5#45511yescharacteristic
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—42no—
268C4×C5—82no—
269C4×C5—81no—
270C4×C5—81no—
271C4×C5—161no—
272C4×C5#46511yescharacteristic
273C4×C5#46611yescharacteristic
274C4×C5#46811yescharacteristic
275C4×C5#47011yescharacteristic
276C4×C5#48011yescharacteristic
277C4×C5#48211yescharacteristic
278C4×C5#48311yescharacteristic
279C4×C5#48511yescharacteristic
280C24—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8C5×D812yes—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C5×SD1612yes—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×C5×D411yescharacteristic
305C22×C4C2×C5×D411yescharacteristic
306C22×C4C2×C5×D411yescharacteristic
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—42no—
321C4⋊C4—44no—
322C4⋊C4—42no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C22⋊C4—44no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—82no—
337C42—41no—
338C42—41no—
339C42C2×C5×D411yescharacteristic
340C42C5×#4111yescharacteristic
341C42C5×#4111yescharacteristic
342C42C5×#4111yescharacteristic
343C2×C5—82no—
344C2×C5#162711yescharacteristic
345C2×C5#163811yescharacteristic
346C2×C5#164111yescharacteristic
347C2×C5#164311yescharacteristic
348C2×C5#203311yescharacteristic
349C2×C5#203511yescharacteristic
350C2×C5#204011yescharacteristic
351C23—22no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23C5×#12011yescharacteristic
359Q8—22no—
360Q8—22no—
361Q8—41no—
362Q8—41no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4C5×#12111yescharacteristic
389C2×C4C5×#12111yescharacteristic
390C2×C4C5×#12111yescharacteristic
391C2×C4C5×#12311yescharacteristic
392C2×C4C5×#12311yescharacteristic
393C2×C4C5×#12411yescharacteristic
394C2×C4C2×C5×D811yescharacteristic
395C2×C4C2×C5×SD1611yescharacteristic
396C2×C4C5×#13511yescharacteristic
397C2×C4C5×#13511yescharacteristic
398C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
399C2×C4C5×#13711yescharacteristic
400C2×C4C5×#13711yescharacteristic
401C2×C4C5×#13711yescharacteristic
402C8—42no—
403C8—81no—
404C8—81no—
405C5#1043311yescharacteristic, direct product factor, Sylow
406C22—42no—
407C22—42no—
408C22—42no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22C5×#39411yescharacteristic
414C22C5×#44711yescharacteristic
415C22C5×#44811yescharacteristic
416C22C5×#45211yescharacteristic
417C22C5×#45211yescharacteristic
418C22C5×#45411yescharacteristic
419C22C5×#45511yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—81no—
425C4—82no—
426C4—161no—
427C4C5×#46511yescharacteristic
428C4C5×#46611yescharacteristic
429C4C5×#46811yescharacteristic
430C4C5×#47011yescharacteristic
431C4C5×#48011yescharacteristic
432C4C5×#48211yescharacteristic
433C4C5×#48311yescharacteristic
434C4C5×#48511yescharacteristic
435C2—82no—
436C2C5×#162711yescharacteristic
437C2C5×#163811yescharacteristic
438C2C5×#164111yescharacteristic
439C2C5×#164311yescharacteristic
440C2C5×#203311yescharacteristic
441C2C5×#203511yescharacteristic
442C2C5×#204011yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1834C2semidirect
3. C5×#1803C2semidirect
5. C2×C5×Q8⋊C8C2semidirect
7. C5×#1296C2semidirect
27. #10433C5direct (N × H)
69. #1834C2×C5semidirect
70. #1803C2×C5semidirect
72. C2×Q8⋊C8C2×C5semidirect
74. #1296C2×C5semidirect
405. C5#10433direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25382
C5×#18342
C5×#18032
C5×#18022
C2×C5×Q8⋊C82
C2×C5×D4⋊C82
C5×#12962
#104335