Finite Group Databasebeta

← C5×#10431 #11933151

Subgroups — C5×#10431 #11933151

Order 1280.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2537C211yesmaximal, characteristic
2C5×#1834C211yesmaximal, characteristic, complemented
3C5×#1802C211yesmaximal, characteristic, complemented
4C5×#1802C211yesmaximal, characteristic, complemented
5C2×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C2×C5×D4⋊C8C211yesmaximal, characteristic, complemented
7C5×#1296C211yesmaximal, characteristic, complemented
8C2×C5×#121—21no—
9C2×C5×#121—21no—
10C2×C4×C5×D4C2211yescharacteristic
11C2×C4×C5×D4C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×#102—21no—
15C2×C5×#102—21no—
16C2×C4×C5×C8C2211yescharacteristic
17C5×#394—22no—
18C5×#384C2211yescharacteristic
19C5×#384C2211yescharacteristic
20C5×#380—21no—
21C5×#380—21no—
22C5×#340—21no—
23C5×#340—21no—
24C5×#340—22no—
25C5×D4⋊C8—22no—
26C5×D4⋊C8—22no—
27#10431C511yesmaximal, characteristic, direct product factor, Sylow
28C22×C5×D4—22no—
29C22×C5×D4D411yescharacteristic
30C22×C5×D4D411yescharacteristic
31C23×C4×C5—21no—
32C23×C4×C5—21no—
33C22×C5×C8—21no—
34C22×C5×C8—21no—
35C22×C5×C8—21no—
36C5×#121—42no—
37C5×#121—42no—
38C5×#121—42no—
39C5×#121—42no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4D411yescharacteristic
54C2×C5×C4⋊C4D411yescharacteristic
55C2×C5×C4⋊C4D412yes—
56C2×C5×C22⋊C4—22no—
57C2×C5×C22⋊C4—22no—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C42×C5C2311yescharacteristic
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8—21no—
65C5×#102—42no—
66C5×#102—42no—
67C4×C5×C8—21no—
68C4×C5×C8D412yescomplemented
69C5×#95—22no—
70#2537C2×C511yescharacteristic
71#1834C2×C511yescharacteristic, complemented
72#1802C2×C511yescharacteristic, complemented
73#1802C2×C511yescharacteristic, complemented
74C2×D4⋊C8C2×C511yescharacteristic, complemented
75C2×D4⋊C8C2×C511yescharacteristic, complemented
76#1296C2×C511yescharacteristic, complemented
77C24×C5—21no—
78C24×C5—21no—
79C2×C5×D4—21no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—44no—
90C2×C5×D4—44no—
91C2×C5×D4—82no—
92C2×C5×D4D812yes—
93C2×C5×D4SD1612yes—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—22no—
97C22×C4×C5—41no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5—41no—
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C2×C5×C8—22no—
114C2×C5×C8—41no—
115C2×C5×C8—41no—
116C2×C5×C8—41no—
117C2×C5×C8—41no—
118C2×C5×C8—41no—
119C2×C5×C8—41no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—42no—
127C5×C4⋊C4—42no—
128C5×C4⋊C4—41no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4—41no—
131C5×C4⋊C4—41no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—41no—
134C5×C4⋊C4—41no—
135C5×C4⋊C4—41no—
136C5×C22⋊C4—44no—
137C5×C22⋊C4—44no—
138C5×C22⋊C4—41no—
139C5×C22⋊C4—41no—
140C5×C22⋊C4—41no—
141C5×C22⋊C4—41no—
142C42×C5C2×D411yescharacteristic
143C42×C5#4111yescharacteristic
144C42×C5#4111yescharacteristic
145C42×C5#4111yescharacteristic
146C2×#121—21no—
147C2×#121—21no—
148C2×C4×D4C22×C511yescharacteristic
149C2×C4×D4C22×C511yescharacteristic
150C2×C4⋊C8C22×C511yescharacteristic
151C2×C4⋊C8C22×C511yescharacteristic
152C2×#102—21no—
153C2×#102—21no—
154C2×C4×C8C22×C511yescharacteristic
155#394—22no—
156#384C22×C511yescharacteristic
157#384C22×C511yescharacteristic
158#380—21no—
159#380—21no—
160#340—21no—
161#340—21no—
162#340—22no—
163D4⋊C8—22no—
164D4⋊C8—22no—
165C23×C5—22no—
166C23×C5—22no—
167C23×C5—41no—
168C23×C5—41no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5#12011yescharacteristic
180C5×D4—22no—
181C5×D4—22no—
182C5×D4—22no—
183C5×D4—22no—
184C5×D4—41no—
185C5×D4—41no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—88no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—42no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5—41no—
199C2×C4×C5—42no—
200C2×C4×C5—81no—
201C2×C4×C5—81no—
202C2×C4×C5—81no—
203C2×C4×C5—81no—
204C2×C4×C5—81no—
205C2×C4×C5—81no—
206C2×C4×C5—81no—
207C2×C4×C5—81no—
208C2×C4×C5—81no—
209C2×C4×C5—81no—
210C2×C4×C5—81no—
211C2×C4×C5#12111yescharacteristic
212C2×C4×C5#12111yescharacteristic
213C2×C4×C5#12111yescharacteristic
214C2×C4×C5#12311yescharacteristic
215C2×C4×C5#12311yescharacteristic
216C2×C4×C5#12411yescharacteristic
217C2×C4×C5C2×D811yescharacteristic
218C2×C4×C5C2×SD1611yescharacteristic
219C2×C4×C5#13511yescharacteristic
220C2×C4×C5#13511yescharacteristic
221C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
222C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
223C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C5#13711yescharacteristic
225C5×C8—42no—
226C5×C8—81no—
227C5×C8—81no—
228C22×D4—22no—
229C22×D4C5×D411yescharacteristic
230C22×D4C5×D411yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236#121—42no—
237#121—42no—
238#121—42no—
239#121—42no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4C5×D411yescharacteristic
254C2×C4⋊C4C5×D411yescharacteristic
255C2×C4⋊C4C5×D412yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42C23×C511yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265#102—42no—
266#102—42no—
267C4×C8—21no—
268C4×C8C5×D412yescomplemented
269#95—22no—
270C22×C5—42no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5—81no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5—81no—
284C22×C5#39411yescharacteristic
285C22×C5#44711yescharacteristic
286C22×C5#44911yescharacteristic
287C22×C5#45011yescharacteristic
288C22×C5#45211yescharacteristic
289C22×C5#45411yescharacteristic
290C22×C5#45511yescharacteristic
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—82no—
294C4×C5—81no—
295C4×C5—81no—
296C4×C5—161no—
297C4×C5#46511yescharacteristic
298C4×C5#46611yescharacteristic
299C4×C5#46811yescharacteristic
300C4×C5#46911yescharacteristic
301C4×C5#48011yescharacteristic
302C4×C5#48111yescharacteristic
303C4×C5#48211yescharacteristic
304C4×C5#48211yescharacteristic
305C24—21no—
306C24—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4—82no—
320C2×D4C5×D812yes—
321C2×D4C5×SD1612yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4C2×C5×D411yescharacteristic
339C22×C4C2×C5×D411yescharacteristic
340C22×C4C2×C5×D411yescharacteristic
341C2×C8—22no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C22⋊C4—44no—
365C22⋊C4—44no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C42C2×C5×D411yescharacteristic
371C42C5×#4111yescharacteristic
372C42C5×#4111yescharacteristic
373C42C5×#4111yescharacteristic
374C2×C5—82no—
375C2×C5—82no—
376C2×C5#162511yescharacteristic
377C2×C5#163511yescharacteristic
378C2×C5#163911yescharacteristic
379C2×C5#164611yescharacteristic
380C2×C5#203311yescharacteristic
381C2×C5#203411yescharacteristic
382C2×C5#204011yescharacteristic
383C23—22no—
384C23—22no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23C5×#12011yescharacteristic
398D4—22no—
399D4—22no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—88no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4C5×#12111yescharacteristic
430C2×C4C5×#12111yescharacteristic
431C2×C4C5×#12111yescharacteristic
432C2×C4C5×#12311yescharacteristic
433C2×C4C5×#12311yescharacteristic
434C2×C4C5×#12411yescharacteristic
435C2×C4C2×C5×D811yescharacteristic
436C2×C4C2×C5×SD1611yescharacteristic
437C2×C4C5×#13511yescharacteristic
438C2×C4C5×#13511yescharacteristic
439C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
440C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
441C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
442C2×C4C5×#13711yescharacteristic
443C8—42no—
444C8—81no—
445C8—81no—
446C5#1043111yescharacteristic, direct product factor, Sylow
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22C5×#39411yescharacteristic
462C22C5×#44711yescharacteristic
463C22C5×#44911yescharacteristic
464C22C5×#45011yescharacteristic
465C22C5×#45211yescharacteristic
466C22C5×#45411yescharacteristic
467C22C5×#45511yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—81no—
472C4—82no—
473C4—161no—
474C4C5×#46511yescharacteristic
475C4C5×#46611yescharacteristic
476C4C5×#46811yescharacteristic
477C4C5×#46911yescharacteristic
478C4C5×#48011yescharacteristic
479C4C5×#48111yescharacteristic
480C4C5×#48211yescharacteristic
481C4C5×#48211yescharacteristic
482C2—82no—
483C2—82no—
484C2C5×#162511yescharacteristic
485C2C5×#163511yescharacteristic
486C2C5×#163911yescharacteristic
487C2C5×#164611yescharacteristic
488C2C5×#203311yescharacteristic
489C2C5×#203411yescharacteristic
490C2C5×#204011yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC5×#2537C2
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×#1802C2semidirect
4. C5×#1802C2semidirect
5. C2×C5×D4⋊C8C2semidirect
6. C2×C5×D4⋊C8C2semidirect
7. C5×#1296C2semidirect
27. #10431C5direct (N × H)
68. C4×C5×C8D4semidirect
71. #1834C2×C5semidirect
72. #1802C2×C5semidirect
73. #1802C2×C5semidirect
74. C2×D4⋊C8C2×C5semidirect
75. C2×D4⋊C8C2×C5semidirect
76. #1296C2×C5semidirect
268. C4×C8C5×D4semidirect
446. C5#10431direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25372
C5×#18342
C5×#18022
C2×C5×D4⋊C82
C5×#12962
#104315