Finite Group Databasebeta

← C5×#10410 #11933130

Subgroups — C5×#10410 #11933130

Order 1280.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2548C211yesmaximal, characteristic
2C5×#1957C211yesmaximal, characteristic
3C5×#1948C211yesmaximal, characteristic, complemented
4C5×#1803C211yesmaximal, characteristic, complemented
5C2×C5×#331C211yesmaximal, characteristic
6C2×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
7C5×#1279C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×C5×#124—21no—
10C2×C4×C5×Q8C2211yescharacteristic
11C2×C5×#106—21no—
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×#103—21no—
15C2×C5×#102—22no—
16C2×C4×C5×C8C2211yescharacteristic
17C5×#394—22no—
18C5×#390—21no—
19C5×#390—21no—
20C5×#390—21no—
21C5×#384C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C5×#340—21no—
24C5×#340—21no—
25C5×#331—22no—
26C5×Q8⋊C8—22no—
27#10410C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×Q8D411yescharacteristic
29C22×C5×D4—21no—
30C22×C5×D4—21no—
31C22×C5×D4D412yes—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C22×C5×C8—21no—
35C5×#127—21no—
36C5×#127—21no—
37C5×#127—21no—
38C5×#127—21no—
39C5×#124—42no—
40C5×#124—42no—
41C4×C5×Q8—21no—
42C4×C5×Q8—21no—
43C4×C5×Q8—21no—
44C4×C5×Q8—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C5×C4⋊C4D411yescharacteristic
51C2×C5×C4⋊C4D411yescharacteristic
52C2×C5×C22⋊C4—22no—
53C2×C5×C22⋊C4—22no—
54C2×C5×C22⋊C4—22no—
55C2×C5×C22⋊C4—22no—
56C2×C42×C5—21no—
57C2×C42×C5—21no—
58C2×C42×C5C2311yescharacteristic
59C5×#106—42no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8D412yes—
64C5×#103—42no—
65C5×#102—44no—
66C4×C5×C8—21no—
67C4×C5×C8—21no—
68C5×#95—21no—
69#2548C2×C511yescharacteristic
70#1957C2×C511yescharacteristic
71#1948C2×C511yescharacteristic, complemented
72#1803C2×C511yescharacteristic, complemented
73C2×#331C2×C511yescharacteristic
74C2×Q8⋊C8C2×C511yescharacteristic, complemented
75#1279C2×C511yescharacteristic, complemented
76C24×C5—22no—
77C2×C5×Q8—21no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8—21no—
82C2×C5×Q8SD1612yes—
83C2×C5×D4—22no—
84C2×C5×D4—22no—
85C2×C5×D4—42no—
86C2×C5×D4—42no—
87C2×C5×D4—41no—
88C2×C5×D4—41no—
89C2×C5×D4—41no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—41no—
104C22×C4×C5C2×D411yescharacteristic
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5C2×D411yescharacteristic
107C2×C5×C8—22no—
108C2×C5×C8—22no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C2×C5×C8—41no—
113C2×C5×C8—41no—
114C2×C5×C8—41no—
115C2×C5×C8—41no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—21no—
119C5×C4⋊C4—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—42no—
123C5×C4⋊C4—41no—
124C5×C4⋊C4—41no—
125C5×C4⋊C4—41no—
126C5×C4⋊C4—41no—
127C5×C4⋊C4—41no—
128C5×C4⋊C4—41no—
129C5×C22⋊C4—44no—
130C5×C22⋊C4—44no—
131C5×C22⋊C4—82no—
132C5×C22⋊C4—82no—
133C42×C5—41no—
134C42×C5—41no—
135C42×C5—41no—
136C42×C5—41no—
137C42×C5C2×D411yescharacteristic
138C42×C5#4111yescharacteristic
139C42×C5#4111yescharacteristic
140C42×C5#4111yescharacteristic
141C2×#127C22×C511yescharacteristic
142C2×#124—21no—
143C2×C4×Q8C22×C511yescharacteristic
144C2×#106—21no—
145C2×C4⋊C8C22×C511yescharacteristic
146C2×C4⋊C8C22×C511yescharacteristic
147C2×#103—21no—
148C2×#102—22no—
149C2×C4×C8C22×C511yescharacteristic
150#394—22no—
151#390—21no—
152#390—21no—
153#390—21no—
154#384C22×C511yescharacteristic
155C4×C4⋊C4C22×C511yescharacteristic
156#340—21no—
157#340—21no—
158#331—22no—
159Q8⋊C8—22no—
160C23×C5—42no—
161C23×C5—42no—
162C23×C5—42no—
163C23×C5—42no—
164C23×C5—42no—
165C23×C5—42no—
166C23×C5—42no—
167C23×C5#12011yescharacteristic
168C5×Q8—22no—
169C5×Q8—22no—
170C5×Q8—41no—
171C5×Q8—41no—
172C5×D4—44no—
173C5×D4—82no—
174C5×D4—81no—
175C5×D4—81no—
176C5×D4—81no—
177C5×D4—81no—
178C5×D4—81no—
179C5×D4—81no—
180C5×D4—81no—
181C5×D4—81no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—22no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—81no—
197C2×C4×C5—81no—
198C2×C4×C5—81no—
199C2×C4×C5#12111yescharacteristic
200C2×C4×C5#12111yescharacteristic
201C2×C4×C5#12111yescharacteristic
202C2×C4×C5#12311yescharacteristic
203C2×C4×C5#12311yescharacteristic
204C2×C4×C5#12411yescharacteristic
205C2×C4×C5C2×SD1611yescharacteristic
206C2×C4×C5#13511yescharacteristic
207C2×C4×C5#13511yescharacteristic
208C2×C4×C5#13511yescharacteristic
209C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C5#13711yescharacteristic
213C5×C8—42no—
214C5×C8—42no—
215C5×C8—81no—
216C22×Q8C5×D411yescharacteristic
217C22×D4—21no—
218C22×D4—21no—
219C22×D4C5×D412yes—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223#127—21no—
224#127—21no—
225#127—21no—
226#127—21no—
227#124—42no—
228#124—42no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C5×D411yescharacteristic
238C2×C4⋊C4C5×D411yescharacteristic
239C2×C4⋊C4C5×D411yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42C23×C511yescharacteristic
247#106—42no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8C5×D412yes—
252#103—42no—
253#102—44no—
254C4×C8—21no—
255C4×C8—21no—
256#95—21no—
257C22×C5—82no—
258C22×C5—82no—
259C22×C5—82no—
260C22×C5—82no—
261C22×C5—82no—
262C22×C5—82no—
263C22×C5—82no—
264C22×C5#39411yescharacteristic
265C22×C5#44911yescharacteristic
266C22×C5#44911yescharacteristic
267C22×C5#45011yescharacteristic
268C22×C5#45211yescharacteristic
269C22×C5#45311yescharacteristic
270C22×C5#45511yescharacteristic
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—42no—
274C4×C5—81no—
275C4×C5—81no—
276C4×C5—81no—
277C4×C5—161no—
278C4×C5#46311yescharacteristic
279C4×C5#46411yescharacteristic
280C4×C5#46511yescharacteristic
281C4×C5#46911yescharacteristic
282C4×C5#48111yescharacteristic
283C4×C5#48211yescharacteristic
284C4×C5#48811yescharacteristic
285C4×C5#48911yescharacteristic
286C24—22no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C5×SD1612yes—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4C2×C5×D411yescharacteristic
315C22×C4C2×C5×D411yescharacteristic
316C22×C4C2×C5×D411yescharacteristic
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C22⋊C4—82no—
342C22⋊C4—82no—
343C42—41no—
344C42—41no—
345C42—41no—
346C42—41no—
347C42C2×C5×D411yescharacteristic
348C42C5×#4111yescharacteristic
349C42C5×#4111yescharacteristic
350C42C5×#4111yescharacteristic
351C2×C5—162no—
352C2×C5#162011yescharacteristic
353C2×C5#163111yescharacteristic
354C2×C5#164011yescharacteristic
355C2×C5#164211yescharacteristic
356C2×C5#203411yescharacteristic
357C2×C5#203711yescharacteristic
358C2×C5#204211yescharacteristic
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23C5×#12011yescharacteristic
367Q8—22no—
368Q8—22no—
369Q8—41no—
370Q8—41no—
371D4—44no—
372D4—82no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C5×#12111yescharacteristic
399C2×C4C5×#12111yescharacteristic
400C2×C4C5×#12111yescharacteristic
401C2×C4C5×#12311yescharacteristic
402C2×C4C5×#12311yescharacteristic
403C2×C4C5×#12411yescharacteristic
404C2×C4C2×C5×SD1611yescharacteristic
405C2×C4C5×#13511yescharacteristic
406C2×C4C5×#13511yescharacteristic
407C2×C4C5×#13511yescharacteristic
408C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
409C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
410C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
411C2×C4C5×#13711yescharacteristic
412C8—42no—
413C8—42no—
414C8—81no—
415C5#1041011yescharacteristic, direct product factor, Sylow
416C22—82no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C5×#39411yescharacteristic
424C22C5×#44911yescharacteristic
425C22C5×#44911yescharacteristic
426C22C5×#45011yescharacteristic
427C22C5×#45211yescharacteristic
428C22C5×#45311yescharacteristic
429C22C5×#45511yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—161no—
437C4C5×#46311yescharacteristic
438C4C5×#46411yescharacteristic
439C4C5×#46511yescharacteristic
440C4C5×#46911yescharacteristic
441C4C5×#48111yescharacteristic
442C4C5×#48211yescharacteristic
443C4C5×#48811yescharacteristic
444C4C5×#48911yescharacteristic
445C2—162no—
446C2C5×#162011yescharacteristic
447C2C5×#163111yescharacteristic
448C2C5×#164011yescharacteristic
449C2C5×#164211yescharacteristic
450C2C5×#203411yescharacteristic
451C2C5×#203711yescharacteristic
452C2C5×#204211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#127C22
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
3. C5×#1948C2semidirect
4. C5×#1803C2semidirect
6. C2×C5×Q8⋊C8C2semidirect
7. C5×#1279C2semidirect
27. #10410C5direct (N × H)
71. #1948C2×C5semidirect
72. #1803C2×C5semidirect
74. C2×Q8⋊C8C2×C5semidirect
75. #1279C2×C5semidirect
415. C5#10410direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25482
C5×#19572
C5×#19482
C5×#18032
C2×C5×#3312
C2×C5×Q8⋊C82
C5×#12792
#104105