Finite Group Databasebeta

← C5×#8713 #11931433

Subgroups — C5×#8713 #11931433

Order 1280.

940 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#380C211yesmaximal, characteristic
2C5×#1779C211yesmaximal, characteristic
3C5×C22⋊#95C211yesmaximal, characteristic
4C5×#1294C214yesmaximal, complemented
5C24×C4×C5C2211yescharacteristic
6C22×C5×C4⋊C4C411yescharacteristic, complemented
7C22×C5×C4⋊C4C411yescharacteristic, complemented
8C22×C5×C22⋊C4—21no—
9C22×C5×C22⋊C4—21no—
10C2×C5×C22⋊C8—21no—
11C2×C5×C22⋊C8—21no—
12C2×C5×C22⋊C8C2212yes—
13C5×#380—21no—
14C5×#380—21no—
15C5×#380C412yescomplemented
16C5×#380C2212yes—
17C2×C5×#95—21no—
18C2×C5×#95—21no—
19C2×C5×#95C2212yes—
20#8713C511yesmaximal, characteristic, direct product factor, Sylow
21C25×C5D411yescharacteristic
22C23×C4×C5—24no—
23C23×C4×C5—21no—
24C23×C4×C5—21no—
25C23×C4×C5—22no—
26C23×C4×C5—42no—
27C23×C4×C5—42no—
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C23×C4×C5D411yescharacteristic
32C23×C4×C5D411yescharacteristic
33C23×C4×C5C2311yescharacteristic
34C22×C5×C8—22no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—42no—
38C2×C5×C4⋊C4—42no—
39C2×C5×C4⋊C4C2×C412yes—
40C2×C5×C4⋊C4C2×C412yes—
41C2×C5×C22⋊C4—24no—
42C2×C5×C22⋊C4—22no—
43C2×C5×C22⋊C4—22no—
44C2×C5×C22⋊C4—42no—
45C2×C5×C22⋊C4—44no—
46C2×C5×C22⋊C4—42no—
47C5×C22⋊C8—24no—
48C5×C22⋊C8—42no—
49C5×C22⋊C8—42no—
50C5×#95—22no—
51C5×#95—22no—
52C5×#95—24no—
53C5×#95—42no—
54C2×#380C2×C511yescharacteristic
55#1779C2×C511yescharacteristic
56C22⋊#95C2×C511yescharacteristic
57#1294C2×C514yescomplemented
58C24×C5—22no—
59C24×C5—22no—
60C24×C5—22no—
61C24×C5—22no—
62C24×C5—41no—
63C24×C5—41no—
64C24×C5C22⋊C411yescharacteristic
65C24×C5C22⋊C411yescharacteristic
66C24×C5SD1612yes—
67C24×C5Q1612yes—
68C24×C5C2×D411yescharacteristic
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—22no—
79C22×C4×C5—24no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5—416no—
90C22×C4×C5—42no—
91C22×C4×C5—42no—
92C22×C4×C5—42no—
93C22×C4×C5—42no—
94C22×C4×C5—42no—
95C22×C4×C5—42no—
96C22×C4×C5—42no—
97C22×C4×C5—42no—
98C22×C4×C5—42no—
99C22×C4×C5—42no—
100C22×C4×C5—42no—
101C22×C4×C5—42no—
102C22×C4×C5C22⋊C411yescharacteristic
103C22×C4×C5C22⋊C411yescharacteristic
104C22×C4×C5C22×C411yescharacteristic
105C22×C4×C5C2×D411yescharacteristic
106C22×C4×C5#4114yes—
107C2×C5×C8—42no—
108C2×C5×C8—42no—
109C2×C5×C8—42no—
110C5×C4⋊C4—42no—
111C5×C4⋊C4—42no—
112C5×C4⋊C4—42no—
113C5×C4⋊C4—42no—
114C5×C22⋊C4—48no—
115C5×C22⋊C4—44no—
116C5×C22⋊C4—44no—
117C24×C4C22×C511yescharacteristic
118C22×C4⋊C4C4×C511yescharacteristic, complemented
119C22×C4⋊C4C4×C511yescharacteristic, complemented
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8C22×C512yes—
125#380—21no—
126#380—21no—
127#380C4×C512yescomplemented
128#380C22×C512yes—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95C22×C512yes—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—24no—
141C23×C5—24no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5—21no—
146C23×C5—21no—
147C23×C5—21no—
148C23×C5—24no—
149C23×C5—24no—
150C23×C5—42no—
151C23×C5—42no—
152C23×C5—44no—
153C23×C5—44no—
154C23×C5—44no—
155C23×C5—44no—
156C23×C5#9912yes—
157C23×C5#10312yes—
158C23×C5#10312yes—
159C23×C5#10412yes—
160C23×C5C2×C22⋊C411yescharacteristic
161C23×C5#12312yes—
162C23×C5C2×SD1611yescharacteristic
163C23×C5C2×Q1611yescharacteristic
164C23×C5AGL(1,ℤ/8)12yes—
165C2×C4×C5—28no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—44no—
176C2×C4×C5—44no—
177C2×C4×C5—44no—
178C2×C4×C5—44no—
179C2×C4×C5—44no—
180C2×C4×C5—44no—
181C2×C4×C5—44no—
182C2×C4×C5—44no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5—42no—
187C2×C4×C5—42no—
188C2×C4×C5—42no—
189C2×C4×C5—82no—
190C2×C4×C5—82no—
191C2×C4×C5—82no—
192C2×C4×C5—84no—
193C2×C4×C5—84no—
194C2×C4×C5—82no—
195C2×C4×C5#9912yes—
196C2×C4×C5#11712yes—
197C2×C4×C5#12312yes—
198C5×C8—82no—
199C25C5×D411yescharacteristic
200C23×C4—24no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4C2×C4×C511yescharacteristic
207C23×C4C2×C4×C511yescharacteristic
208C23×C4C5×D411yescharacteristic
209C23×C4C5×D411yescharacteristic
210C23×C4C5×D411yescharacteristic
211C23×C4C23×C511yescharacteristic
212C22×C8—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—42no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4C2×C4×C512yes—
218C2×C4⋊C4C2×C4×C512yes—
219C2×C22⋊C4—24no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—42no—
223C2×C22⋊C4—44no—
224C2×C22⋊C4—42no—
225C22⋊C8—24no—
226C22⋊C8—42no—
227C22⋊C8—42no—
228#95—22no—
229#95—22no—
230#95—24no—
231#95—42no—
232C22×C5—22no—
233C22×C5—22no—
234C22×C5—22no—
235C22×C5—22no—
236C22×C5—22no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—22no—
240C22×C5—22no—
241C22×C5—22no—
242C22×C5—22no—
243C22×C5—21no—
244C22×C5—22no—
245C22×C5—21no—
246C22×C5—22no—
247C22×C5—22no—
248C22×C5—22no—
249C22×C5—48no—
250C22×C5—48no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5#32814yes—
256C22×C5#38111yescharacteristic
257C22×C5C2×#9911yescharacteristic
258C22×C5C2×#9911yescharacteristic
259C22×C5C2×#10311yescharacteristic
260C22×C5#41811yescharacteristic
261C22×C5C2×#10411yescharacteristic
262C22×C5#42111yescharacteristic
263C22×C5#48112yes—
264C22×C5#48412yes—
265C4×C5—22no—
266C4×C5—22no—
267C4×C5—22no—
268C4×C5—41no—
269C4×C5—84no—
270C4×C5—82no—
271C4×C5—82no—
272C24—22no—
273C24—22no—
274C24—22no—
275C24—22no—
276C24—41no—
277C24—41no—
278C24C5×C22⋊C411yescharacteristic
279C24C5×C22⋊C411yescharacteristic
280C24C5×SD1612yes—
281C24C5×Q1612yes—
282C24C2×C5×D411yescharacteristic
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—416no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4C5×C22⋊C411yescharacteristic
317C22×C4C5×C22⋊C411yescharacteristic
318C22×C4C22×C4×C511yescharacteristic
319C22×C4C2×C5×D411yescharacteristic
320C22×C4C5×#4114yes—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C22⋊C4—48no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C2×C5—22no—
332C2×C5—24no—
333C2×C5—22no—
334C2×C5—42no—
335C2×C5C2×#32811yescharacteristic
336C2×C5#150711yescharacteristic
337C2×C5#151011yescharacteristic
338C2×C5#152011yescharacteristic
339C2×C5#181911yescharacteristic
340C2×C5#182411yescharacteristic
341C2×C5#182611yescharacteristic
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—24no—
352C23—24no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—24no—
359C23—24no—
360C23—42no—
361C23—42no—
362C23—44no—
363C23—44no—
364C23—44no—
365C23—44no—
366C23C5×#9912yes—
367C23C5×#10312yes—
368C23C5×#10312yes—
369C23C5×#10412yes—
370C23C2×C5×C22⋊C411yescharacteristic
371C23C5×#12312yes—
372C23C2×C5×SD1611yescharacteristic
373C23C2×C5×Q1611yescharacteristic
374C23C5×AGL(1,ℤ/8)12yes—
375C2×C4—28no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4—82no—
405C2×C4C5×#9912yes—
406C2×C4C5×#11712yes—
407C2×C4C5×#12312yes—
408C8—82no—
409C5#871311yescharacteristic, direct product factor, Sylow
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—21no—
423C22—21no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—48no—
428C22—48no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22C5×#32814yes—
434C22C5×#38111yescharacteristic
435C22C2×C5×#9911yescharacteristic
436C22C2×C5×#9911yescharacteristic
437C22C2×C5×#10311yescharacteristic
438C22C5×#41811yescharacteristic
439C22C2×C5×#10411yescharacteristic
440C22C5×#42111yescharacteristic
441C22C5×#48112yes—
442C22C5×#48412yes—
443C4—22no—
444C4—22no—
445C4—22no—
446C4—41no—
447C4—84no—
448C4—82no—
449C4—82no—
450C2—22no—
451C2—24no—
452C2—22no—
453C2—42no—
454C2C2×C5×#32811yescharacteristic
455C2C5×#150711yescharacteristic
456C2C5×#151011yescharacteristic
457C2C5×#152011yescharacteristic
458C2C5×#181911yescharacteristic
459C2C5×#182411yescharacteristic
460C2C5×#182611yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC25×C5D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C24×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1294C2semidirect
6. C22×C5×C4⋊C4C4semidirect
7. C22×C5×C4⋊C4C4semidirect
15. C5×#380C4semidirect
20. #8713C5direct (N × H)
57. #1294C2×C5semidirect
118. C22×C4⋊C4C4×C5semidirect
119. C22×C4⋊C4C4×C5semidirect
127. #380C4×C5semidirect
409. C5#8713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3802
C5×#17792
C5×C22⋊#952
C5×#12942
#87135