Finite Group Databasebeta

← C5×#13101 #11935821

Subgroups — C5×#13101 #11935821

Order 1280.

630 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3011C211yesmaximal, characteristic
2C5×#2884C211yesmaximal, characteristic
3C5×#2129C211yesmaximal, characteristic, complemented
4C5×#2123C211yesmaximal, characteristic, complemented
5C5×#1796C211yesmaximal, characteristic
6C5×#1395C211yesmaximal, characteristic, complemented
7C5×#1391C211yesmaximal, characteristic, complemented
8C2×C5×2−1+4C2211yescharacteristic
9C2×C5×#137C411yescharacteristic, complemented
10C22×C5×Q16C411yescharacteristic, complemented
11C5×#536C2211yescharacteristic
12C5×#519—21no—
13C5×#452—21no—
14C5×#452—21no—
15C5×#451—21no—
16C5×#451—21no—
17C5×#421—21no—
18C5×#419—21no—
19C5×#419C411yescharacteristic, complemented
20C5×#416C411yescharacteristic, complemented
21C5×#413C2211yescharacteristic
22C5×#410—22no—
23C5×#410—22no—
24C5×#410—21no—
25C5×#410C2211yescharacteristic
26C5×#410C2211yescharacteristic
27C5×#410C2211yescharacteristic
28C5×#408C2211yescharacteristic
29C5×#354—22no—
30C5×#352—22no—
31#13101C511yesmaximal, characteristic, direct product factor, Sylow
32C5×2−1+4—42no—
33C5×2−1+4—42no—
34C2×C5×#41—21no—
35C2×C5×#41—21no—
36C2×C5×#41—21no—
37C2×C5×#41C2×C411yescharacteristic
38C2×C5×#41D411yescharacteristic
39C2×C5×#41D411yescharacteristic
40C2×C5×#41C2311yescharacteristic
41C22×C5×Q8—21no—
42C22×C5×Q8C2×C411yescharacteristic
43C22×C5×Q8C2×C411yescharacteristic
44C22×C5×Q8D411yescharacteristic
45C22×C5×Q8D411yescharacteristic
46C5×#137—42no—
47C2×C5×Q16—21no—
48C2×C5×Q16—21no—
49C2×C5×Q16—21no—
50C2×C5×Q16—42no—
51C2×C5×SD16—21no—
52C2×C5×M16—21no—
53C2×C5×M16C2×C411yescharacteristic
54C22×C5×C8C2×C411yescharacteristic
55C5×C4⋊Q8—21no—
56C5×#124—21no—
57C5×#123—21no—
58C5×#123—21no—
59C5×C22⋊Q8—21no—
60C5×C22⋊Q8—21no—
61C4×C5×Q8—42no—
62C4×C5×Q8—42no—
63C5×#117—24no—
64C5×#117—21no—
65C5×#117—21no—
66C5×#117—21no—
67C5×#117C2×C411yescharacteristic
68C5×#104—42no—
69C5×#103—21no—
70C5×#103—21no—
71C5×#103—21no—
72C5×#103—42no—
73C5×#102—21no—
74C5×#101—21no—
75C5×#100—21no—
76C5×#99—24no—
77C5×#99—21no—
78C5×#99—21no—
79C5×#99—21no—
80C5×#99—21no—
81C5×#99D412yes—
82C5×#99D412yes—
83C5×C22⋊C8—21no—
84C5×C22⋊C8—21no—
85#3011C2×C511yescharacteristic
86#2884C2×C511yescharacteristic
87#2129C2×C511yescharacteristic, complemented
88#2123C2×C511yescharacteristic, complemented
89#1796C2×C511yescharacteristic
90#1395C2×C511yescharacteristic, complemented
91#1391C2×C511yescharacteristic, complemented
92C5×#41—22no—
93C5×#41—22no—
94C5×#41—41no—
95C5×#41—41no—
96C5×#41—41no—
97C5×#41—41no—
98C5×#41—41no—
99C5×#41—41no—
100C5×#41—44no—
101C5×#41—44no—
102C5×#41—44no—
103C2×C5×Q8—22no—
104C2×C5×Q8—22no—
105C2×C5×Q8—21no—
106C2×C5×Q8—21no—
107C2×C5×Q8—21no—
108C2×C5×Q8—22no—
109C2×C5×Q8—22no—
110C2×C5×Q8—21no—
111C2×C5×Q8—21no—
112C2×C5×Q8—41no—
113C2×C5×Q8—41no—
114C2×C5×Q8—41no—
115C2×C5×Q8—41no—
116C2×C5×Q8—44no—
117C2×C5×Q8C22⋊C411yescharacteristic
118C2×C5×Q8C22⋊C411yescharacteristic
119C2×C5×Q8C22⋊C411yescharacteristic
120C2×C5×Q8#4111yescharacteristic
121C2×C5×D4—21no—
122C2×C5×D4—21no—
123C2×C5×D4—21no—
124C2×C5×D4C22⋊C411yescharacteristic
125C2×C5×D4C2×D411yescharacteristic
126C2×C5×D4C2×D411yescharacteristic
127C2×C5×D4#4111yescharacteristic
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5C22×C411yescharacteristic
136C22×C4×C5C2×D411yescharacteristic
137C22×C4×C5C2×D411yescharacteristic
138C5×Q16—42no—
139C5×Q16—42no—
140C5×Q16—42no—
141C5×SD16—42no—
142C5×M16—41no—
143C5×M16—41no—
144C5×M16—41no—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8—41no—
148C2×C5×C8—41no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—44no—
151C5×C4⋊C4—41no—
152C5×C4⋊C4—41no—
153C5×C4⋊C4—41no—
154C5×C4⋊C4—41no—
155C5×C4⋊C4—41no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—22no—
158C5×C22⋊C4—22no—
159C5×C22⋊C4—41no—
160C5×C22⋊C4—41no—
161C5×C22⋊C4—41no—
162C42×C5—21no—
163C42×C5—44no—
164C42×C5—41no—
165C42×C5—41no—
166C42×C5—41no—
167C2×2−1+4C22×C511yescharacteristic
168C2×#137C4×C511yescharacteristic, complemented
169C22×Q16C4×C511yescharacteristic, complemented
170#536C22×C511yescharacteristic
171#519—21no—
172#452—21no—
173#452—21no—
174#451—21no—
175#451—21no—
176#421—21no—
177#419—21no—
178#419C4×C511yescharacteristic, complemented
179#416C4×C511yescharacteristic, complemented
180#413C22×C511yescharacteristic
181#410—21no—
182#410—22no—
183#410—22no—
184#410C22×C511yescharacteristic
185#410C22×C511yescharacteristic
186#410C22×C511yescharacteristic
187#408C22×C511yescharacteristic
188#354—22no—
189#352—22no—
190C23×C5—21no—
191C23×C5C4×D411yescharacteristic
192C23×C5#12011yescharacteristic
193C23×C5#12111yescharacteristic
194C5×Q8—24no—
195C5×Q8—21no—
196C5×Q8—21no—
197C5×Q8—21no—
198C5×Q8—21no—
199C5×Q8—41no—
200C5×Q8—42no—
201C5×Q8—42no—
202C5×Q8—41no—
203C5×Q8—41no—
204C5×Q8—81no—
205C5×Q8#9912yes—
206C5×Q8#9912yes—
207C5×D4—21no—
208C5×D4—21no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—42no—
213C5×D4—42no—
214C5×D4—42no—
215C2×C4×C5—24no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—42no—
228C2×C4×C5—42no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—81no—
235C2×C4×C5—81no—
236C2×C4×C5C2×C22⋊C411yescharacteristic
237C2×C4×C5C4×D411yescharacteristic
238C2×C4×C5#12111yescharacteristic
239C2×C4×C5#12311yescharacteristic
240C5×C8—41no—
241C5×C8—41no—
242C5×C8—81no—
2432−1+4—42no—
2442−1+4—42no—
245C2×#41—21no—
246C2×#41—21no—
247C2×#41—21no—
248C2×#41C2×C4×C511yescharacteristic
249C2×#41C5×D411yescharacteristic
250C2×#41C5×D411yescharacteristic
251C2×#41C23×C511yescharacteristic
252C22×Q8—21no—
253C22×Q8C2×C4×C511yescharacteristic
254C22×Q8C2×C4×C511yescharacteristic
255C22×Q8C5×D411yescharacteristic
256C22×Q8C5×D411yescharacteristic
257#137—42no—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16—42no—
262C2×SD16—21no—
263C2×M16—21no—
264C2×M16C2×C4×C511yescharacteristic
265C22×C8C2×C4×C511yescharacteristic
266C4⋊Q8—21no—
267#124—21no—
268#123—21no—
269#123—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C4×Q8—42no—
273C4×Q8—42no—
274#117—24no—
275#117—21no—
276#117—21no—
277#117—21no—
278#117C2×C4×C511yescharacteristic
279#104—42no—
280#103—21no—
281#103—21no—
282#103—21no—
283#103—42no—
284#102—21no—
285#101—21no—
286#100—21no—
287#99—24no—
288#99—21no—
289#99—21no—
290#99—21no—
291#99—21no—
292#99C5×D412yes—
293#99C5×D412yes—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—81no—
304C22×C5#38611yescharacteristic
305C4×C5—21no—
306C4×C5—22no—
307C4×C5—22no—
308C4×C5—21no—
309C4×C5—21no—
310C4×C5—41no—
311C4×C5—81no—
312C4×C5—82no—
313C4×C5—82no—
314C4×C5—81no—
315C4×C5—161no—
316C4×C5C2×#9911yescharacteristic
317C4×C5C2×#9911yescharacteristic
318#41—22no—
319#41—22no—
320#41—41no—
321#41—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—44no—
327#41—44no—
328#41—44no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—44no—
343C2×Q8C5×C22⋊C411yescharacteristic
344C2×Q8C5×C22⋊C411yescharacteristic
345C2×Q8C5×C22⋊C411yescharacteristic
346C2×Q8C5×#4111yescharacteristic
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C5×C22⋊C411yescharacteristic
351C2×D4C2×C5×D411yescharacteristic
352C2×D4C2×C5×D411yescharacteristic
353C2×D4C5×#4111yescharacteristic
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4C22×C4×C511yescharacteristic
362C22×C4C2×C5×D411yescharacteristic
363C22×C4C2×C5×D411yescharacteristic
364Q16—42no—
365Q16—42no—
366Q16—42no—
367SD16—42no—
368M16—41no—
369M16—41no—
370M16—41no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—41no—
374C2×C8—41no—
375C4⋊C4—21no—
376C4⋊C4—44no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C22⋊C4—21no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C42—21no—
389C42—44no—
390C42—41no—
391C42—41no—
392C42—41no—
393C2×C5—21no—
394C2×C5—41no—
395C2×C5—41no—
396C2×C5—41no—
397C2×C5—81no—
398C2×C5#189811yescharacteristic
399C23—21no—
400C23C4×C5×D411yescharacteristic
401C23C5×#12011yescharacteristic
402C23C5×#12111yescharacteristic
403Q8—24no—
404Q8—21no—
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—41no—
409Q8—42no—
410Q8—42no—
411Q8—41no—
412Q8—41no—
413Q8—81no—
414Q8C5×#9912yes—
415Q8C5×#9912yes—
416D4—21no—
417D4—21no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—42no—
422D4—42no—
423D4—42no—
424C2×C4—24no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4C2×C5×C22⋊C411yescharacteristic
446C2×C4C4×C5×D411yescharacteristic
447C2×C4C5×#12111yescharacteristic
448C2×C4C5×#12311yescharacteristic
449C8—41no—
450C8—41no—
451C8—81no—
452C5#1310111yescharacteristic, direct product factor, Sylow
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22C5×#38611yescharacteristic
462C4—21no—
463C4—22no—
464C4—22no—
465C4—21no—
466C4—21no—
467C4—41no—
468C4—81no—
469C4—82no—
470C4—82no—
471C4—81no—
472C4—161no—
473C4C2×C5×#9911yescharacteristic
474C4C2×C5×#9911yescharacteristic
475C2—21no—
476C2—41no—
477C2—41no—
478C2—41no—
479C2—81no—
480C2C5×#189811yescharacteristic
subgroupG/H
center, socleC2×C5#1898
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×#41C23×C5
prime radicalC2×C5×2−1+4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×2−1+4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2129C2semidirect
4. C5×#2123C2semidirect
6. C5×#1395C2semidirect
7. C5×#1391C2semidirect
9. C2×C5×#137C4semidirect
10. C22×C5×Q16C4semidirect
19. C5×#419C4semidirect
20. C5×#416C4semidirect
31. #13101C5direct (N × H)
87. #2129C2×C5semidirect
88. #2123C2×C5semidirect
90. #1395C2×C5semidirect
91. #1391C2×C5semidirect
168. C2×#137C4×C5semidirect
169. C22×Q16C4×C5semidirect
178. #419C4×C5semidirect
179. #416C4×C5semidirect
452. C5#13101direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30112
C5×#28842
C5×#21292
C5×#21232
C5×#17962
C5×#13952
C5×#13912
#131015