Finite Group Databasebeta

← C5×#9969 #11932689

Subgroups — C5×#9969 #11932689

Order 1280.

658 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#484C211yesmaximal, characteristic, complemented
2C2×C5×#481C211yesmaximal, characteristic
3C5×#2639C211yesmaximal, characteristic
4C2×C5×#328C211yesmaximal, characteristic, complemented
5C2×C5×#327C211yesmaximal, characteristic
6C5×#1445C211yesmaximal, characteristic, complemented
7C5×#1280C211yesmaximal, characteristic, complemented
8C2×C5×C22⋊Q8C2211yescharacteristic
9C2×C5×#121C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C5×#484—22no—
12C5×#484—22no—
13C5×#481—22no—
14C5×#481—22no—
15C2×C5×#107—21no—
16C2×C5×#106—21no—
17C2×C5×#103—21no—
18C2×C5×#102—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#9969C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×Q8D411yescharacteristic
33C22×C5×D4—21no—
34C22×C5×D4D411yescharacteristic
35C23×C4×C5—21no—
36C23×C4×C5—21no—
37C23×C4×C5D412yes—
38C23×C4×C5C2311yescharacteristic
39C22×C5×C8—21no—
40C22×C5×C8—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8—21no—
43C5×C22⋊Q8—21no—
44C5×C22⋊Q8—21no—
45C5×#121—21no—
46C5×#121—21no—
47C5×#121—21no—
48C5×#121—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4D411yescharacteristic
56C2×C5×C4⋊C4D411yescharacteristic
57C2×C5×C4⋊C4D412yes—
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—22no—
61C2×C5×C22⋊C4—22no—
62C5×#107—24no—
63C5×#106—24no—
64C5×#103—24no—
65C5×#102—24no—
66C5×C22⋊C8—21no—
67C5×C22⋊C8—21no—
68C5×C22⋊C8D412yes—
69C5×C22⋊C8D412yes—
70C5×#95—22no—
71C5×#95—22no—
72C5×#95—21no—
73C5×#95—21no—
74C5×#95—21no—
75C5×#95—21no—
76C5×#95—44no—
77C2×#484C2×C511yescharacteristic, complemented
78C2×#481C2×C511yescharacteristic
79#2639C2×C511yescharacteristic
80C2×#328C2×C511yescharacteristic, complemented
81C2×#327C2×C511yescharacteristic
82#1445C2×C511yescharacteristic, complemented
83#1280C2×C511yescharacteristic, complemented
84C24×C5—21no—
85C24×C5C2×D411yescharacteristic
86C2×C5×Q8—21no—
87C2×C5×Q8—21no—
88C2×C5×Q8—42no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—42no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—42no—
95C2×C5×D4—42no—
96C22×C4×C5—22no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—22no—
100C22×C4×C5—21no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—42no—
105C22×C4×C5—42no—
106C22×C4×C5—42no—
107C22×C4×C5—41no—
108C22×C4×C5—42no—
109C22×C4×C5—42no—
110C22×C4×C5—42no—
111C22×C4×C5—41no—
112C22×C4×C5—41no—
113C22×C4×C5—41no—
114C22×C4×C5—42no—
115C22×C4×C5C2×D411yescharacteristic
116C22×C4×C5C2×D411yescharacteristic
117C22×C4×C5C2×D411yescharacteristic
118C22×C4×C5C2×D411yescharacteristic
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5#4111yescharacteristic
121C2×C5×C8—22no—
122C2×C5×C8—22no—
123C2×C5×C8—42no—
124C2×C5×C8—42no—
125C5×C4⋊C4—22no—
126C5×C4⋊C4—22no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—41no—
132C5×C4⋊C4—41no—
133C5×C4⋊C4—41no—
134C5×C4⋊C4—41no—
135C5×C22⋊C4—41no—
136C5×C22⋊C4—41no—
137C5×C22⋊C4—41no—
138C5×C22⋊C4—41no—
139C5×C22⋊C4—82no—
140C5×C22⋊C4—82no—
141C2×C22⋊Q8C22×C511yescharacteristic
142C2×#121C22×C511yescharacteristic
143C22×C4⋊C4C22×C511yescharacteristic
144#484—22no—
145#484—22no—
146#481—22no—
147#481—22no—
148C2×#107—21no—
149C2×#106—21no—
150C2×#103—21no—
151C2×#102—21no—
152C2×C22⋊C8C22×C511yescharacteristic
153C2×C22⋊C8C22×C511yescharacteristic
154#400—21no—
155#397—21no—
156#394—21no—
157#393—21no—
158#386—22no—
159C2×#95—22no—
160C2×#95C22×C511yescharacteristic
161C2×#95C22×C511yescharacteristic
162#328—22no—
163#327—22no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—22no—
167C23×C5—41no—
168C23×C5—42no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—42no—
172C23×C5#12011yescharacteristic
173C23×C5#12111yescharacteristic
174C23×C5#12711yescharacteristic
175C23×C5#13512yes—
176C23×C5#13712yes—
177C5×Q8—42no—
178C5×Q8—81no—
179C5×D4—42no—
180C5×D4—81no—
181C5×D4—82no—
182C5×D4—81no—
183C5×D4—81no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—44no—
191C2×C4×C5—42no—
192C2×C4×C5—44no—
193C2×C4×C5—44no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5—42no—
199C2×C4×C5—42no—
200C2×C4×C5—41no—
201C2×C4×C5—42no—
202C2×C4×C5—41no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—82no—
206C2×C4×C5—81no—
207C2×C4×C5—82no—
208C2×C4×C5—81no—
209C2×C4×C5—81no—
210C2×C4×C5—81no—
211C2×C4×C5—82no—
212C2×C4×C5#12011yescharacteristic
213C2×C4×C5#12011yescharacteristic
214C2×C4×C5#12111yescharacteristic
215C2×C4×C5#12111yescharacteristic
216C5×C8—42no—
217C5×C8—42no—
218C22×Q8C5×D411yescharacteristic
219C22×D4—21no—
220C22×D4C5×D411yescharacteristic
221C23×C4—21no—
222C23×C4—21no—
223C23×C4C5×D412yes—
224C23×C4C23×C511yescharacteristic
225C22×C8—21no—
226C22×C8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—21no—
232#121—21no—
233#121—21no—
234#121—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C5×D412yes—
242C2×C4⋊C4C5×D411yescharacteristic
243C2×C4⋊C4C5×D411yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248#107—24no—
249#106—24no—
250#103—24no—
251#102—24no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8C5×D412yes—
255C22⋊C8C5×D412yes—
256#95—22no—
257#95—22no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—44no—
263C22×C5—22no—
264C22×C5—22no—
265C22×C5—22no—
266C22×C5—22no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—82no—
272C22×C5—82no—
273C22×C5—81no—
274C22×C5—81no—
275C22×C5—81no—
276C22×C5#39211yescharacteristic
277C22×C5#45212yes—
278C22×C5#45311yescharacteristic
279C22×C5#45411yescharacteristic
280C22×C5#45812yes—
281C22×C5#46412yes—
282C22×C5#49511yescharacteristic
283C22×C5#49711yescharacteristic
284C4×C5—21no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—82no—
289C4×C5—82no—
290C4×C5—81no—
291C4×C5—82no—
292C4×C5—81no—
293C4×C5—81no—
294C24—21no—
295C24C2×C5×D411yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—42no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—42no—
325C22×C4C2×C5×D411yescharacteristic
326C22×C4C2×C5×D411yescharacteristic
327C22×C4C2×C5×D411yescharacteristic
328C22×C4C2×C5×D411yescharacteristic
329C22×C4C2×C5×D411yescharacteristic
330C22×C4C5×#4111yescharacteristic
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—82no—
350C22⋊C4—82no—
351C2×C5—21no—
352C2×C5—22no—
353C2×C5—21no—
354C2×C5—161no—
355C2×C5#161512yes—
356C2×C5#161812yes—
357C2×C5#200611yescharacteristic
358C2×C5#201511yescharacteristic
359C2×C5#202211yescharacteristic
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—42no—
368C23C5×#12011yescharacteristic
369C23C5×#12111yescharacteristic
370C23C5×#12711yescharacteristic
371C23C5×#13512yes—
372C23C5×#13712yes—
373Q8—42no—
374Q8—81no—
375D4—42no—
376D4—81no—
377D4—82no—
378D4—81no—
379D4—81no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—44no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4C5×#12011yescharacteristic
409C2×C4C5×#12011yescharacteristic
410C2×C4C5×#12111yescharacteristic
411C2×C4C5×#12111yescharacteristic
412C8—42no—
413C8—42no—
414C5#996911yescharacteristic, direct product factor, Sylow
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—21no—
422C22—21no—
423C22—81no—
424C22—81no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22C5×#39211yescharacteristic
429C22C5×#45212yes—
430C22C5×#45311yescharacteristic
431C22C5×#45411yescharacteristic
432C22C5×#45812yes—
433C22C5×#46412yes—
434C22C5×#49511yescharacteristic
435C22C5×#49711yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—81no—
442C4—81no—
443C4—82no—
444C4—82no—
445C4—81no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—161no—
450C2C5×#161512yes—
451C2C5×#161812yes—
452C2C5×#200611yescharacteristic
453C2C5×#201511yescharacteristic
454C2C5×#202211yescharacteristic
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×#484C2semidirect
4. C2×C5×#328C2semidirect
6. C5×#1445C2semidirect
7. C5×#1280C2semidirect
31. #9969C5direct (N × H)
77. C2×#484C2×C5semidirect
80. C2×#328C2×C5semidirect
82. #1445C2×C5semidirect
83. #1280C2×C5semidirect
414. C5#9969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4842
C2×C5×#4812
C5×#26392
C2×C5×#3282
C2×C5×#3272
C5×#14452
C5×#12802
#99695