Finite Group Databasebeta

← C5×#10420 #11933140

Subgroups — C5×#10420 #11933140

Order 1280.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2542C211yesmaximal, characteristic
2C5×#1990C211yesmaximal, characteristic, complemented
3C5×#1948C211yesmaximal, characteristic, complemented
4C5×#1802C211yesmaximal, characteristic
5C2×C5×#332C211yesmaximal, characteristic, complemented
6C2×C5×D4⋊C8C211yesmaximal, characteristic
7C5×#1279C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×C5×C22⋊Q8—21no—
10C2×C5×C22⋊Q8—21no—
11C2×C4×C5×D4C2211yescharacteristic
12C2×C5×#106—21no—
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×C4⋊C8C2211yescharacteristic
15C2×C5×#102—21no—
16C2×C4×C5×C8C2211yescharacteristic
17C5×#399—22no—
18C5×#390—21no—
19C5×#384—21no—
20C5×#384C2211yescharacteristic
21C4×C5×C4⋊C4C2211yescharacteristic
22C5×#340—21no—
23C5×#340—21no—
24C5×#340—22no—
25C5×#332—22no—
26C5×D4⋊C8—22no—
27#10420C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8—21no—
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C22×C5×C8—21no—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8—21no—
38C5×C22⋊Q8—42no—
39C5×C22⋊Q8—42no—
40C5×C22⋊Q8—42no—
41C5×C22⋊Q8—42no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C2×C5×C4⋊C4—22no—
47C2×C5×C4⋊C4—22no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4D411yescharacteristic
53C2×C5×C4⋊C4D412yes—
54C2×C5×C4⋊C4D411yescharacteristic
55C2×C5×C4⋊C4D411yescharacteristic
56C2×C5×C22⋊C4—22no—
57C2×C5×C22⋊C4—22no—
58C2×C5×C22⋊C4—21no—
59C2×C42×C5—21no—
60C2×C42×C5C2311yescharacteristic
61C5×#106—42no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×C4⋊C8D412yes—
66C5×#102—42no—
67C4×C5×C8—21no—
68C4×C5×C8—21no—
69C5×#95—21no—
70#2542C2×C511yescharacteristic
71#1990C2×C511yescharacteristic, complemented
72#1948C2×C511yescharacteristic, complemented
73#1802C2×C511yescharacteristic
74C2×#332C2×C511yescharacteristic, complemented
75C2×D4⋊C8C2×C511yescharacteristic
76#1279C2×C511yescharacteristic, complemented
77C24×C5—21no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C2×C5×Q8—41no—
82C2×C5×Q8—41no—
83C2×C5×Q8—41no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4SD1612yes—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—22no—
93C22×C4×C5—21no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—41no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C2×C5×C8—22no—
105C2×C5×C8—22no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—22no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—44no—
120C5×C4⋊C4—44no—
121C5×C4⋊C4—42no—
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×C4⋊C4D812yes—
129C5×C4⋊C4SD1612yes—
130C5×C22⋊C4—44no—
131C5×C22⋊C4—44no—
132C5×C22⋊C4—41no—
133C5×C22⋊C4—41no—
134C42×C5—41no—
135C42×C5—41no—
136C42×C5C2×D411yescharacteristic
137C42×C5#4111yescharacteristic
138C42×C5#4111yescharacteristic
139C42×C5#4111yescharacteristic
140C2×C4⋊Q8C22×C511yescharacteristic
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C4×D4C22×C511yescharacteristic
144C2×#106—21no—
145C2×C4⋊C8C22×C511yescharacteristic
146C2×C4⋊C8C22×C511yescharacteristic
147C2×#102—21no—
148C2×C4×C8C22×C511yescharacteristic
149#399—22no—
150#390—21no—
151#384—21no—
152#384C22×C511yescharacteristic
153C4×C4⋊C4C22×C511yescharacteristic
154#340—21no—
155#340—21no—
156#340—22no—
157#332—22no—
158D4⋊C8—22no—
159C23×C5—22no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5#12011yescharacteristic
167C5×Q8—81no—
168C5×Q8—81no—
169C5×Q8—81no—
170C5×Q8—81no—
171C5×D4—22no—
172C5×D4—22no—
173C5×D4—41no—
174C5×D4—41no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—22no—
178C2×C4×C5—22no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5—41no—
187C2×C4×C5—42no—
188C2×C4×C5—41no—
189C2×C4×C5—81no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5—81no—
195C2×C4×C5—81no—
196C2×C4×C5#12111yescharacteristic
197C2×C4×C5#12111yescharacteristic
198C2×C4×C5#12111yescharacteristic
199C2×C4×C5#12311yescharacteristic
200C2×C4×C5#12311yescharacteristic
201C2×C4×C5#12411yescharacteristic
202C2×C4×C5C2×D811yescharacteristic
203C2×C4×C5C2×SD1611yescharacteristic
204C2×C4×C5C2×SD1611yescharacteristic
205C2×C4×C5#13511yescharacteristic
206C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C5#13711yescharacteristic
209C2×C4×C5#13711yescharacteristic
210C5×C8—42no—
211C5×C8—42no—
212C5×C8—81no—
213C22×Q8—21no—
214C22×D4C5×D411yescharacteristic
215C23×C4—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C22⋊Q8—42no—
224C22⋊Q8—42no—
225C22⋊Q8—42no—
226C22⋊Q8—42no—
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C5×D411yescharacteristic
238C2×C4⋊C4C5×D412yes—
239C2×C4⋊C4C5×D411yescharacteristic
240C2×C4⋊C4C5×D411yescharacteristic
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—21no—
244C2×C42—21no—
245C2×C42C23×C511yescharacteristic
246#106—42no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8C5×D412yes—
251#102—42no—
252C4×C8—21no—
253C4×C8—21no—
254#95—21no—
255C22×C5—42no—
256C22×C5—42no—
257C22×C5—42no—
258C22×C5—81no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5—81no—
262C22×C5#39411yescharacteristic
263C22×C5#44711yescharacteristic
264C22×C5#44811yescharacteristic
265C22×C5#45011yescharacteristic
266C22×C5#45211yescharacteristic
267C22×C5#45411yescharacteristic
268C22×C5#45611yescharacteristic
269C4×C5—21no—
270C4×C5—21no—
271C4×C5—42no—
272C4×C5—42no—
273C4×C5—81no—
274C4×C5—82no—
275C4×C5—161no—
276C4×C5#45911yescharacteristic
277C4×C5#46011yescharacteristic
278C4×C5#46511yescharacteristic
279C4×C5#47011yescharacteristic
280C4×C5#48311yescharacteristic
281C4×C5#48511yescharacteristic
282C4×C5#48611yescharacteristic
283C4×C5#49011yescharacteristic
284C24—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4C5×SD1612yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4C2×C5×D411yescharacteristic
309C22×C4C2×C5×D411yescharacteristic
310C22×C4C2×C5×D411yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—44no—
327C4⋊C4—44no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4C5×D812yes—
336C4⋊C4C5×SD1612yes—
337C22⋊C4—44no—
338C22⋊C4—44no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—41no—
342C42—41no—
343C42C2×C5×D411yescharacteristic
344C42C5×#4111yescharacteristic
345C42C5×#4111yescharacteristic
346C42C5×#4111yescharacteristic
347C2×C5—82no—
348C2×C5#162711yescharacteristic
349C2×C5#163511yescharacteristic
350C2×C5#164711yescharacteristic
351C2×C5#165111yescharacteristic
352C2×C5#203511yescharacteristic
353C2×C5#203811yescharacteristic
354C2×C5#204111yescharacteristic
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23C5×#12011yescharacteristic
363Q8—81no—
364Q8—81no—
365Q8—81no—
366Q8—81no—
367D4—22no—
368D4—22no—
369D4—41no—
370D4—41no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4C5×#12111yescharacteristic
393C2×C4C5×#12111yescharacteristic
394C2×C4C5×#12111yescharacteristic
395C2×C4C5×#12311yescharacteristic
396C2×C4C5×#12311yescharacteristic
397C2×C4C5×#12411yescharacteristic
398C2×C4C2×C5×D811yescharacteristic
399C2×C4C2×C5×SD1611yescharacteristic
400C2×C4C2×C5×SD1611yescharacteristic
401C2×C4C5×#13511yescharacteristic
402C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
403C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
404C2×C4C5×#13711yescharacteristic
405C2×C4C5×#13711yescharacteristic
406C8—42no—
407C8—42no—
408C8—81no—
409C5#1042011yescharacteristic, direct product factor, Sylow
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C5×#39411yescharacteristic
418C22C5×#44711yescharacteristic
419C22C5×#44811yescharacteristic
420C22C5×#45011yescharacteristic
421C22C5×#45211yescharacteristic
422C22C5×#45411yescharacteristic
423C22C5×#45611yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—81no—
429C4—82no—
430C4—161no—
431C4C5×#45911yescharacteristic
432C4C5×#46011yescharacteristic
433C4C5×#46511yescharacteristic
434C4C5×#47011yescharacteristic
435C4C5×#48311yescharacteristic
436C4C5×#48511yescharacteristic
437C4C5×#48611yescharacteristic
438C4C5×#49011yescharacteristic
439C2—82no—
440C2C5×#162711yescharacteristic
441C2C5×#163511yescharacteristic
442C2C5×#164711yescharacteristic
443C2C5×#165111yescharacteristic
444C2C5×#203511yescharacteristic
445C2C5×#203811yescharacteristic
446C2C5×#204111yescharacteristic
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×#1990C2semidirect
3. C5×#1948C2semidirect
5. C2×C5×#332C2semidirect
7. C5×#1279C2semidirect
27. #10420C5direct (N × H)
71. #1990C2×C5semidirect
72. #1948C2×C5semidirect
74. C2×#332C2×C5semidirect
76. #1279C2×C5semidirect
409. C5#10420direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25422
C5×#19902
C5×#19482
C5×#18022
C2×C5×#3322
C2×C5×D4⋊C82
C5×#12792
#104205