Finite Group Databasebeta

← C5×#10434 #11933154

Subgroups — C5×#10434 #11933154

Order 1280.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2538C211yesmaximal, characteristic
2C5×#1845C211yesmaximal, 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×#107—22no—
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C5×#103—21no—
15C2×C5×#102—21no—
16C2×C4×C5×C8C2211yescharacteristic
17C5×#396—22no—
18C5×#390—21no—
19C5×#389—21no—
20C5×#384C2211yescharacteristic
21C5×#384C2211yescharacteristic
22C5×#380—21no—
23C5×#340—21no—
24C5×#340—21no—
25C5×Q8⋊C8—22no—
26C5×D4⋊C8—22no—
27#10434C511yesmaximal, 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×#107—44no—
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8—21no—
63C5×C4⋊C8—21no—
64C5×#103—42no—
65C5×#102—42no—
66C4×C5×C8—21no—
67C4×C5×C8D412yes—
68C5×#95—22no—
69#2538C2×C511yescharacteristic
70#1845C2×C511yescharacteristic, complemented
71#1803C2×C511yescharacteristic, complemented
72#1802C2×C511yescharacteristic
73C2×Q8⋊C8C2×C511yescharacteristic, complemented
74C2×D4⋊C8C2×C511yescharacteristic
75#1296C2×C511yescharacteristic, complemented
76C24×C5—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8—21no—
82C2×C5×Q8D812yes—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4Q1612yes—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—22no—
92C22×C4×C5—21no—
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×C5—41no—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C2×C5×C8—22no—
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—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—42no—
117C5×C4⋊C4—44no—
118C5×C4⋊C4—42no—
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×C4⋊C4—41no—
129C5×C22⋊C4—44no—
130C5×C22⋊C4—41no—
131C5×C22⋊C4—41no—
132C5×C22⋊C4—82no—
133C42×C5—41no—
134C42×C5—41no—
135C42×C5C2×D411yescharacteristic
136C42×C5#4111yescharacteristic
137C42×C5#4111yescharacteristic
138C42×C5#4111yescharacteristic
139C2×C22⋊Q8—21no—
140C2×C4×Q8C22×C511yescharacteristic
141C2×C4×D4C22×C511yescharacteristic
142C2×#107—22no—
143C2×C4⋊C8C22×C511yescharacteristic
144C2×C4⋊C8C22×C511yescharacteristic
145C2×#103—21no—
146C2×#102—21no—
147C2×C4×C8C22×C511yescharacteristic
148#396—22no—
149#390—21no—
150#389—21no—
151#384C22×C511yescharacteristic
152#384C22×C511yescharacteristic
153#380—21no—
154#340—21no—
155#340—21no—
156Q8⋊C8—22no—
157D4⋊C8—22no—
158C23×C5—22no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—41no—
165C23×C5#12011yescharacteristic
166C5×Q8—22no—
167C5×Q8—22no—
168C5×Q8—41no—
169C5×Q8—41no—
170C5×D4—22no—
171C5×D4—22no—
172C5×D4—41no—
173C5×D4—41no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—22no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—41no—
183C2×C4×C5—42no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—42no—
187C2×C4×C5—41no—
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—81no—
195C2×C4×C5#12111yescharacteristic
196C2×C4×C5#12111yescharacteristic
197C2×C4×C5#12111yescharacteristic
198C2×C4×C5#12311yescharacteristic
199C2×C4×C5#12311yescharacteristic
200C2×C4×C5#12411yescharacteristic
201C2×C4×C5C2×D811yescharacteristic
202C2×C4×C5C2×Q1611yescharacteristic
203C2×C4×C5#13511yescharacteristic
204C2×C4×C5#13511yescharacteristic
205C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C5#13711yescharacteristic
208C2×C4×C5#13711yescharacteristic
209C5×C8—24no—
210C5×C8—81no—
211C5×C8—81no—
212C22×Q8C5×D411yescharacteristic
213C22×D4C5×D411yescharacteristic
214C23×C4—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22⋊Q8—42no—
219C22⋊Q8—42no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C5×D411yescharacteristic
236C2×C4⋊C4C5×D411yescharacteristic
237C2×C4⋊C4C5×D412yes—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—22no—
241C2×C42—21no—
242C2×C42C23×C511yescharacteristic
243#107—44no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248#103—42no—
249#102—42no—
250C4×C8—21no—
251C4×C8C5×D412yes—
252#95—22no—
253C22×C5—42no—
254C22×C5—42no—
255C22×C5—42no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5—81no—
259C22×C5—81no—
260C22×C5#39411yescharacteristic
261C22×C5#44711yescharacteristic
262C22×C5#44911yescharacteristic
263C22×C5#45111yescharacteristic
264C22×C5#45211yescharacteristic
265C22×C5#45311yescharacteristic
266C22×C5#45611yescharacteristic
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—42no—
270C4×C5—82no—
271C4×C5—81no—
272C4×C5—81no—
273C4×C5—161no—
274C4×C5#46611yescharacteristic
275C4×C5#46711yescharacteristic
276C4×C5#46811yescharacteristic
277C4×C5#46811yescharacteristic
278C4×C5#48011yescharacteristic
279C4×C5#48211yescharacteristic
280C4×C5#48411yescharacteristic
281C4×C5#48511yescharacteristic
282C24—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8C5×D812yes—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4C5×Q1612yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4C2×C5×D411yescharacteristic
307C22×C4C2×C5×D411yescharacteristic
308C22×C4C2×C5×D411yescharacteristic
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—44no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—82no—
339C42—41no—
340C42—41no—
341C42C2×C5×D411yescharacteristic
342C42C5×#4111yescharacteristic
343C42C5×#4111yescharacteristic
344C42C5×#4111yescharacteristic
345C2×C5—82no—
346C2×C5#162111yescharacteristic
347C2×C5#163211yescharacteristic
348C2×C5#164911yescharacteristic
349C2×C5#165011yescharacteristic
350C2×C5#203311yescharacteristic
351C2×C5#203611yescharacteristic
352C2×C5#203911yescharacteristic
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23C5×#12011yescharacteristic
361Q8—22no—
362Q8—22no—
363Q8—41no—
364Q8—41no—
365D4—22no—
366D4—22no—
367D4—41no—
368D4—41no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4C5×#12111yescharacteristic
391C2×C4C5×#12111yescharacteristic
392C2×C4C5×#12111yescharacteristic
393C2×C4C5×#12311yescharacteristic
394C2×C4C5×#12311yescharacteristic
395C2×C4C5×#12411yescharacteristic
396C2×C4C2×C5×D811yescharacteristic
397C2×C4C2×C5×Q1611yescharacteristic
398C2×C4C5×#13511yescharacteristic
399C2×C4C5×#13511yescharacteristic
400C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
401C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C5×#13711yescharacteristic
403C2×C4C5×#13711yescharacteristic
404C8—24no—
405C8—81no—
406C8—81no—
407C5#1043411yescharacteristic, direct product factor, Sylow
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C5×#39411yescharacteristic
416C22C5×#44711yescharacteristic
417C22C5×#44911yescharacteristic
418C22C5×#45111yescharacteristic
419C22C5×#45211yescharacteristic
420C22C5×#45311yescharacteristic
421C22C5×#45611yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—81no—
427C4—82no—
428C4—161no—
429C4C5×#46611yescharacteristic
430C4C5×#46711yescharacteristic
431C4C5×#46811yescharacteristic
432C4C5×#46811yescharacteristic
433C4C5×#48011yescharacteristic
434C4C5×#48211yescharacteristic
435C4C5×#48411yescharacteristic
436C4C5×#48511yescharacteristic
437C2—82no—
438C2C5×#162111yescharacteristic
439C2C5×#163211yescharacteristic
440C2C5×#164911yescharacteristic
441C2C5×#165011yescharacteristic
442C2C5×#203311yescharacteristic
443C2C5×#203611yescharacteristic
444C2C5×#203911yescharacteristic
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×#1845C2semidirect
3. C5×#1803C2semidirect
5. C2×C5×Q8⋊C8C2semidirect
7. C5×#1296C2semidirect
27. #10434C5direct (N × H)
70. #1845C2×C5semidirect
71. #1803C2×C5semidirect
73. C2×Q8⋊C8C2×C5semidirect
75. #1296C2×C5semidirect
407. C5#10434direct (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×#18452
C5×#18032
C5×#18022
C2×C5×Q8⋊C82
C2×C5×D4⋊C82
C5×#12962
#104345