Finite Group Databasebeta

← C5×#9965 #11932685

Subgroups — C5×#9965 #11932685

Order 1280.

830 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#451C211yesmaximal, characteristic, complemented
2C2×C5×#448C211yesmaximal, characteristic
3C5×#2639C211yesmaximal, characteristic
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×C5×#327C211yesmaximal, characteristic
6C5×#1446C211yesmaximal, characteristic, complemented
7C5×#1280C211yesmaximal, characteristic, complemented
8C23×C5×Q8C2211yescharacteristic
9C22×C5×Q16—21no—
10C22×C5×SD16—21no—
11C2×C5×C22⋊Q8C2211yescharacteristic
12C2×C5×#121C2211yescharacteristic
13C5×#451—22no—
14C5×#451—22no—
15C5×#448—22no—
16C5×#448—22no—
17C2×C5×#103—21no—
18C2×C5×#103—21no—
19C2×C5×C22⋊C8C2211yescharacteristic
20C2×C5×C22⋊C8C2211yescharacteristic
21C5×#400—21no—
22C5×#397—21no—
23C5×#394—21no—
24C5×#393—21no—
25C5×#386—22no—
26C2×C5×#95—22no—
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C5×#328—22no—
30C5×#327—22no—
31#9965C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8—21no—
33C22×C5×Q8—21no—
34C22×C5×Q8—21no—
35C22×C5×Q8—21no—
36C22×C5×Q8—21no—
37C22×C5×Q8—44no—
38C22×C5×Q8D411yescharacteristic
39C22×C5×Q8D412yes—
40C22×C5×D4—21no—
41C22×C5×D4D411yescharacteristic
42C23×C4×C5—21no—
43C23×C4×C5—21no—
44C23×C4×C5D412yes—
45C23×C4×C5C2311yescharacteristic
46C2×C5×Q16—24no—
47C2×C5×Q16—44no—
48C2×C5×SD16—24no—
49C2×C5×SD16—44no—
50C22×C5×C8—21no—
51C22×C5×C8—21no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8—21no—
54C5×C22⋊Q8—21no—
55C5×C22⋊Q8—21no—
56C5×#121—21no—
57C5×#121—21no—
58C5×#121—21no—
59C5×#121—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4D411yescharacteristic
62C2×C5×C4⋊C4D411yescharacteristic
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4—21no—
65C2×C5×C22⋊C4—22no—
66C2×C5×C22⋊C4—22no—
67C5×#103—24no—
68C5×#103—24no—
69C5×C22⋊C8—21no—
70C5×C22⋊C8—21no—
71C5×C22⋊C8D412yes—
72C5×C22⋊C8D412yes—
73C5×#95—22no—
74C5×#95—22no—
75C5×#95—21no—
76C5×#95—21no—
77C5×#95—21no—
78C5×#95—21no—
79C5×#95—44no—
80C2×#451C2×C511yescharacteristic, complemented
81C2×#448C2×C511yescharacteristic
82#2639C2×C511yescharacteristic
83C2×#328C2×C511yescharacteristic, complemented
84C2×#327C2×C511yescharacteristic
85#1446C2×C511yescharacteristic, complemented
86#1280C2×C511yescharacteristic, complemented
87C24×C5—21no—
88C24×C5C2×D411yescharacteristic
89C2×C5×Q8—24no—
90C2×C5×Q8—24no—
91C2×C5×Q8—22no—
92C2×C5×Q8—22no—
93C2×C5×Q8—21no—
94C2×C5×Q8—21no—
95C2×C5×Q8—44no—
96C2×C5×Q8—42no—
97C2×C5×Q8—42no—
98C2×C5×Q8—44no—
99C2×C5×Q8—42no—
100C2×C5×Q8—44no—
101C2×C5×Q8—44no—
102C2×C5×Q8—41no—
103C2×C5×Q8—41no—
104C2×C5×D4—21no—
105C2×C5×D4—21no—
106C2×C5×D4—42no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4—42no—
110C2×C5×D4—42no—
111C22×C4×C5—24no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—22no—
117C22×C4×C5—21no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—42no—
121C22×C4×C5—42no—
122C22×C4×C5—41no—
123C22×C4×C5—41no—
124C22×C4×C5—42no—
125C22×C4×C5—42no—
126C22×C4×C5—41no—
127C22×C4×C5—42no—
128C22×C4×C5—41no—
129C22×C4×C5—42no—
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5C2×D411yescharacteristic
132C22×C4×C5C2×D411yescharacteristic
133C22×C4×C5C2×D411yescharacteristic
134C22×C4×C5C2×D411yescharacteristic
135C22×C4×C5#4111yescharacteristic
136C5×Q16—48no—
137C5×SD16—48no—
138C2×C5×C8—22no—
139C2×C5×C8—22no—
140C2×C5×C8—42no—
141C2×C5×C8—42no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—41no—
147C5×C4⋊C4—41no—
148C5×C22⋊C4—41no—
149C5×C22⋊C4—41no—
150C5×C22⋊C4—41no—
151C5×C22⋊C4—41no—
152C5×C22⋊C4—82no—
153C5×C22⋊C4—82no—
154C23×Q8C22×C511yescharacteristic
155C22×Q16—21no—
156C22×SD16—21no—
157C2×C22⋊Q8C22×C511yescharacteristic
158C2×#121C22×C511yescharacteristic
159#451—22no—
160#451—22no—
161#448—22no—
162#448—22no—
163C2×#103—21no—
164C2×#103—21no—
165C2×C22⋊C8C22×C511yescharacteristic
166C2×C22⋊C8C22×C511yescharacteristic
167#400—21no—
168#397—21no—
169#394—21no—
170#393—21no—
171#386—22no—
172C2×#95—22no—
173C2×#95C22×C511yescharacteristic
174C2×#95C22×C511yescharacteristic
175#328—22no—
176#327—22no—
177C23×C5—21no—
178C23×C5—21no—
179C23×C5—22no—
180C23×C5—41no—
181C23×C5—42no—
182C23×C5—41no—
183C23×C5—41no—
184C23×C5—42no—
185C23×C5#12011yescharacteristic
186C23×C5#12111yescharacteristic
187C23×C5#12711yescharacteristic
188C23×C5#13512yes—
189C23×C5#13712yes—
190C5×Q8—24no—
191C5×Q8—24no—
192C5×Q8—42no—
193C5×Q8—42no—
194C5×Q8—44no—
195C5×Q8—44no—
196C5×Q8—42no—
197C5×Q8—81no—
198C5×D4—42no—
199C5×D4—81no—
200C5×D4—82no—
201C5×D4—81no—
202C5×D4—81no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—24no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—42no—
211C2×C4×C5—44no—
212C2×C4×C5—42no—
213C2×C4×C5—44no—
214C2×C4×C5—44no—
215C2×C4×C5—42no—
216C2×C4×C5—44no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—41no—
223C2×C4×C5—42no—
224C2×C4×C5—41no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—82no—
228C2×C4×C5—81no—
229C2×C4×C5—81no—
230C2×C4×C5—82no—
231C2×C4×C5#12011yescharacteristic
232C2×C4×C5#12011yescharacteristic
233C2×C4×C5#12111yescharacteristic
234C2×C4×C5#12111yescharacteristic
235C5×C8—42no—
236C5×C8—42no—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—44no—
243C22×Q8C5×D411yescharacteristic
244C22×Q8C5×D412yes—
245C22×D4—21no—
246C22×D4C5×D411yescharacteristic
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C5×D412yes—
250C23×C4C23×C511yescharacteristic
251C2×Q16—24no—
252C2×Q16—44no—
253C2×SD16—24no—
254C2×SD16—44no—
255C22×C8—21no—
256C22×C8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261#121—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C5×D411yescharacteristic
267C2×C4⋊C4C5×D411yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272#103—24no—
273#103—24no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8C5×D412yes—
277C22⋊C8C5×D412yes—
278#95—22no—
279#95—22no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—44no—
285C22×C5—22no—
286C22×C5—22no—
287C22×C5—22no—
288C22×C5—22no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—82no—
294C22×C5—82no—
295C22×C5—81no—
296C22×C5—81no—
297C22×C5—81no—
298C22×C5#39211yescharacteristic
299C22×C5#45212yes—
300C22×C5#45511yescharacteristic
301C22×C5#45611yescharacteristic
302C22×C5B(4,𝔽2)12yes—
303C22×C5#46412yes—
304C22×C5#49511yescharacteristic
305C22×C5#49711yescharacteristic
306C4×C5—21no—
307C4×C5—21no—
308C4×C5—21no—
309C4×C5—21no—
310C4×C5—44no—
311C4×C5—82no—
312C4×C5—82no—
313C4×C5—81no—
314C4×C5—81no—
315C4×C5—81no—
316C24—21no—
317C24C2×C5×D411yescharacteristic
318C2×Q8—24no—
319C2×Q8—24no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—44no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8—44no—
328C2×Q8—42no—
329C2×Q8—44no—
330C2×Q8—44no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—42no—
339C2×D4—42no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—42no—
359C22×C4C2×C5×D411yescharacteristic
360C22×C4C2×C5×D411yescharacteristic
361C22×C4C2×C5×D411yescharacteristic
362C22×C4C2×C5×D411yescharacteristic
363C22×C4C2×C5×D411yescharacteristic
364C22×C4C5×#4111yescharacteristic
365Q16—48no—
366SD16—48no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—42no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—82no—
382C22⋊C4—82no—
383C2×C5—21no—
384C2×C5—22no—
385C2×C5—21no—
386C2×C5—161no—
387C2×C5#160312yes—
388C2×C5#160612yes—
389C2×C5#200711yescharacteristic
390C2×C5#201511yescharacteristic
391C2×C5#202111yescharacteristic
392C23—21no—
393C23—21no—
394C23—22no—
395C23—41no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23C5×#12011yescharacteristic
401C23C5×#12111yescharacteristic
402C23C5×#12711yescharacteristic
403C23C5×#13512yes—
404C23C5×#13712yes—
405Q8—24no—
406Q8—24no—
407Q8—42no—
408Q8—42no—
409Q8—44no—
410Q8—44no—
411Q8—42no—
412Q8—81no—
413D4—42no—
414D4—81no—
415D4—82no—
416D4—81no—
417D4—81no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—82no—
446C2×C4C5×#12011yescharacteristic
447C2×C4C5×#12011yescharacteristic
448C2×C4C5×#12111yescharacteristic
449C2×C4C5×#12111yescharacteristic
450C8—42no—
451C8—42no—
452C5#996511yescharacteristic, direct product factor, Sylow
453C22—21no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—21no—
460C22—21no—
461C22—81no—
462C22—81no—
463C22—82no—
464C22—82no—
465C22—81no—
466C22C5×#39211yescharacteristic
467C22C5×#45212yes—
468C22C5×#45511yescharacteristic
469C22C5×#45611yescharacteristic
470C22C5×B(4,𝔽2)12yes—
471C22C5×#46412yes—
472C22C5×#49511yescharacteristic
473C22C5×#49711yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—44no—
479C4—82no—
480C4—81no—
481C4—81no—
482C4—82no—
483C4—81no—
484C2—21no—
485C2—22no—
486C2—21no—
487C2—161no—
488C2C5×#160312yes—
489C2C5×#160612yes—
490C2C5×#200711yescharacteristic
491C2C5×#201511yescharacteristic
492C2C5×#202111yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#451C2semidirect
4. C2×C5×#328C2semidirect
6. C5×#1446C2semidirect
7. C5×#1280C2semidirect
31. #9965C5direct (N × H)
80. C2×#451C2×C5semidirect
83. C2×#328C2×C5semidirect
85. #1446C2×C5semidirect
86. #1280C2×C5semidirect
452. C5#9965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4512
C2×C5×#4482
C5×#26392
C2×C5×#3282
C2×C5×#3272
C5×#14462
C5×#12802
#99655