Finite Group Databasebeta

← C5×#9519 #11932239

Subgroups — C5×#9519 #11932239

Order 1280.

644 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3004C211yesmaximal, characteristic
2C5×#2976C211yesmaximal, characteristic
3C5×#1787C211yesmaximal, characteristic, complemented
4C5×#1784C211yesmaximal, characteristic, complemented
5C5×#1513C211yesmaximal, characteristic
6C5×#1305C211yesmaximal, characteristic, complemented
7C5×#1293C211yesmaximal, characteristic, complemented
8C23×C5×Q8C2211yescharacteristic
9C2×C5×#137—21no—
10C5×#525C2211yescharacteristic
11C5×#451—21no—
12C5×#451C412yescomplemented
13C5×#448—21no—
14C5×#448C412yescomplemented
15C5×#436—21no—
16C5×#435—21no—
17C5×#435—21no—
18C5×C8×D4—21no—
19C5×#433—21no—
20C5×#419—21no—
21C2×C5×#103—21no—
22C2×C5×#103—21no—
23C2×C5×#101—21no—
24C2×C5×#101—21no—
25C5×#408—21no—
26C5×#407C2211yescharacteristic
27C5×#407C2211yescharacteristic
28C5×#407C2211yescharacteristic
29C2×C5×C22⋊C8C2211yescharacteristic
30C5×#380C2211yescharacteristic
31C5×#328—21no—
32C5×#327—21no—
33#9519C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41D411yescharacteristic
35C22×C5×Q8—21no—
36C22×C5×Q8—21no—
37C22×C5×Q8—21no—
38C22×C5×Q8—21no—
39C22×C5×Q8—21no—
40C22×C5×Q8—42no—
41C22×C5×Q8—42no—
42C22×C5×Q8C2×C412yes—
43C23×C4×C5—21no—
44C23×C4×C5C2311yescharacteristic
45C5×#137—42no—
46C5×#137—42no—
47C2×C5×Q16—22no—
48C2×C5×SD16—22no—
49C2×C5×M16—21no—
50C2×C5×M16—21no—
51C2×C5×M16—21no—
52C2×C5×M16D411yescharacteristic
53C2×C5×M16D411yescharacteristic
54C22×C5×C8—21no—
55C22×C5×C8D411yescharacteristic
56C22×C5×C8D411yescharacteristic
57C5×#123—21no—
58C5×C22⋊Q8C2×C411yescharacteristic
59C5×C22⋊Q8D411yescharacteristic
60C5×#121C2×C411yescharacteristic
61C5×#121D411yescharacteristic
62C5×#120—21no—
63C4×C5×D4—21no—
64C4×C5×D4—21no—
65C5×#117D411yescharacteristic
66C2×C5×C4⋊C4—21no—
67C2×C5×C22⋊C4—21no—
68C5×C4⋊C8—21no—
69C5×C4⋊C8—21no—
70C5×#103—22no—
71C5×#103—22no—
72C5×#103—42no—
73C5×#103—42no—
74C5×#101—42no—
75C5×#101—42no—
76C5×C22⋊C8—21no—
77C5×C22⋊C8—21no—
78C5×C22⋊C8—21no—
79C5×C22⋊C8—21no—
80C5×C22⋊C8—21no—
81C5×C22⋊C8—21no—
82C5×C22⋊C8—21no—
83C5×C22⋊C8—21no—
84C5×C22⋊C8—21no—
85C5×C22⋊C8C2×C412yes—
86C5×#97—21no—
87C4×C5×C8—21no—
88C5×#95—21no—
89#3004C2×C511yescharacteristic
90#2976C2×C511yescharacteristic
91#1787C2×C511yescharacteristic, complemented
92#1784C2×C511yescharacteristic, complemented
93#1513C2×C511yescharacteristic
94#1305C2×C511yescharacteristic, complemented
95#1293C2×C511yescharacteristic, complemented
96C24×C5#4111yescharacteristic
97C5×#41—41no—
98C5×#41—41no—
99C2×C5×Q8—22no—
100C2×C5×Q8—22no—
101C2×C5×Q8—22no—
102C2×C5×Q8—22no—
103C2×C5×Q8—22no—
104C2×C5×Q8—22no—
105C2×C5×Q8—22no—
106C2×C5×Q8—22no—
107C2×C5×Q8—44no—
108C2×C5×Q8—41no—
109C2×C5×Q8—41no—
110C2×C5×Q8—41no—
111C2×C5×Q8—41no—
112C2×C5×Q8—41no—
113C2×C5×Q8—41no—
114C2×C5×Q8—44no—
115C2×C5×Q8—44no—
116C2×C5×Q8—41no—
117C2×C5×Q8—41no—
118C2×C5×Q8C22⋊C411yescharacteristic
119C2×C5×D4—21no—
120C2×C5×D4—21no—
121C2×C5×D4—21no—
122C2×C5×D4C22⋊C411yescharacteristic
123C22×C4×C5—22no—
124C22×C4×C5—21no—
125C22×C4×C5—41no—
126C22×C4×C5—41no—
127C22×C4×C5—44no—
128C22×C4×C5—41no—
129C22×C4×C5—41no—
130C22×C4×C5—41no—
131C22×C4×C5C22×C411yescharacteristic
132C22×C4×C5C2×D411yescharacteristic
133C22×C4×C5C2×D411yescharacteristic
134C22×C4×C5C2×D411yescharacteristic
135C22×C4×C5C2×D411yescharacteristic
136C22×C4×C5#4111yescharacteristic
137C5×Q16—44no—
138C5×SD16—44no—
139C5×M16—41no—
140C5×M16—41no—
141C5×M16—41no—
142C5×M16—41no—
143C5×M16—41no—
144C5×M16—41no—
145C5×M16—81no—
146C2×C5×C8—22no—
147C2×C5×C8—21no—
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C2×C5×C8—21no—
151C2×C5×C8—41no—
152C2×C5×C8—41no—
153C2×C5×C8—41no—
154C2×C5×C8—81no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—41no—
158C5×C4⋊C4—41no—
159C5×C4⋊C4C22⋊C411yescharacteristic
160C5×C4⋊C4C22⋊C411yescharacteristic
161C5×C22⋊C4—21no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4—21no—
164C5×C22⋊C4—21no—
165C5×C22⋊C4—21no—
166C5×C22⋊C4—81no—
167C42×C5—21no—
168C23×Q8C22×C511yescharacteristic
169C2×#137—21no—
170#525C22×C511yescharacteristic
171#451—21no—
172#451C4×C512yescomplemented
173#448—21no—
174#448C4×C512yescomplemented
175#436—21no—
176#435—21no—
177#435—21no—
178C8×D4—21no—
179#433—21no—
180#419—21no—
181C2×#103—21no—
182C2×#103—21no—
183C2×#101—21no—
184C2×#101—21no—
185#408—21no—
186#407C22×C511yescharacteristic
187#407C22×C511yescharacteristic
188#407C22×C511yescharacteristic
189C2×C22⋊C8C22×C511yescharacteristic
190#380C22×C511yescharacteristic
191#328—21no—
192#327—21no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—21no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5C4×D411yescharacteristic
199C23×C5#12111yescharacteristic
200C23×C5#12311yescharacteristic
201C5×Q8—24no—
202C5×Q8—24no—
203C5×Q8—41no—
204C5×Q8—42no—
205C5×Q8—42no—
206C5×Q8—42no—
207C5×Q8—42no—
208C5×Q8—42no—
209C5×Q8—42no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C5×D4—81no—
214C5×D4—81no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—24no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—42no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—81no—
237C2×C4×C5—81no—
238C2×C4×C5—81no—
239C2×C4×C5C2×C22⋊C411yescharacteristic
240C2×C4×C5C4×D411yescharacteristic
241C2×C4×C5#12011yescharacteristic
242C2×C4×C5#12111yescharacteristic
243C5×C8—42no—
244C5×C8—41no—
245C5×C8—41no—
246C5×C8—41no—
247C5×C8—41no—
248C5×C8—81no—
249C2×#41C5×D411yescharacteristic
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—42no—
256C22×Q8—42no—
257C22×Q8C2×C4×C512yes—
258C23×C4—21no—
259C23×C4C23×C511yescharacteristic
260#137—42no—
261#137—42no—
262C2×Q16—22no—
263C2×SD16—22no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16C5×D411yescharacteristic
268C2×M16C5×D411yescharacteristic
269C22×C8—21no—
270C22×C8C5×D411yescharacteristic
271C22×C8C5×D411yescharacteristic
272#123—21no—
273C22⋊Q8C2×C4×C511yescharacteristic
274C22⋊Q8C5×D411yescharacteristic
275#121C2×C4×C511yescharacteristic
276#121C5×D411yescharacteristic
277#120—21no—
278C4×D4—21no—
279C4×D4—21no—
280#117C5×D411yescharacteristic
281C2×C4⋊C4—21no—
282C2×C22⋊C4—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285#103—22no—
286#103—22no—
287#103—42no—
288#103—42no—
289#101—42no—
290#101—42no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8C2×C4×C512yes—
301#97—21no—
302C4×C8—21no—
303#95—21no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—42no—
313C22×C5—42no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—41no—
317C22×C5#38611yescharacteristic
318C22×C5#47111yescharacteristic
319C22×C5#47311yescharacteristic
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—44no—
324C4×C5—41no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5—161no—
328C4×C5B(4,𝔽2)11yescharacteristic
329C4×C5B(4,𝔽2)11yescharacteristic
330C24C5×#4111yescharacteristic
331#41—41no—
332#41—41no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—44no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—44no—
349C2×Q8—44no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8C5×C22⋊C411yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4C5×C22⋊C411yescharacteristic
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—44no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4C22×C4×C511yescharacteristic
366C22×C4C2×C5×D411yescharacteristic
367C22×C4C2×C5×D411yescharacteristic
368C22×C4C2×C5×D411yescharacteristic
369C22×C4C2×C5×D411yescharacteristic
370C22×C4C5×#4111yescharacteristic
371Q16—44no—
372SD16—44no—
373M16—41no—
374M16—41no—
375M16—41no—
376M16—41no—
377M16—41no—
378M16—41no—
379M16—81no—
380C2×C8—22no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—81no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4C5×C22⋊C411yescharacteristic
394C4⋊C4C5×C22⋊C411yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—81no—
401C42—21no—
402C2×C5—21no—
403C2×C5—21no—
404C2×C5—41no—
405C2×C5—41no—
406C2×C5—81no—
407C2×C5#188911yescharacteristic
408C2×C5#190211yescharacteristic
409C2×C5#190811yescharacteristic
410C23—21no—
411C23—21no—
412C23—21no—
413C23—41no—
414C23—41no—
415C23C4×C5×D411yescharacteristic
416C23C5×#12111yescharacteristic
417C23C5×#12311yescharacteristic
418Q8—24no—
419Q8—24no—
420Q8—41no—
421Q8—42no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426Q8—42no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—81no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4C2×C5×C22⋊C411yescharacteristic
457C2×C4C4×C5×D411yescharacteristic
458C2×C4C5×#12011yescharacteristic
459C2×C4C5×#12111yescharacteristic
460C8—42no—
461C8—41no—
462C8—41no—
463C8—41no—
464C8—41no—
465C8—81no—
466C5#951911yescharacteristic, direct product factor, Sylow
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22C5×#38611yescharacteristic
481C22C5×#47111yescharacteristic
482C22C5×#47311yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—44no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—161no—
491C4C5×B(4,𝔽2)11yescharacteristic
492C4C5×B(4,𝔽2)11yescharacteristic
493C2—21no—
494C2—21no—
495C2—41no—
496C2—41no—
497C2—81no—
498C2C5×#188911yescharacteristic
499C2C5×#190211yescharacteristic
500C2C5×#190811yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC5×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1787C2semidirect
4. C5×#1784C2semidirect
6. C5×#1305C2semidirect
7. C5×#1293C2semidirect
12. C5×#451C4semidirect
14. C5×#448C4semidirect
33. #9519C5direct (N × H)
91. #1787C2×C5semidirect
92. #1784C2×C5semidirect
94. #1305C2×C5semidirect
95. #1293C2×C5semidirect
172. #451C4×C5semidirect
174. #448C4×C5semidirect
466. C5#9519direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30042
C5×#29762
C5×#17872
C5×#17842
C5×#15132
C5×#13052
C5×#12932
#95195