Finite Group Databasebeta

← C5×#13092 #11935812

Subgroups — C5×#13092 #11935812

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#101C211yesmaximal, characteristic, complemented
2C5×#2436C211yesmaximal, characteristic
3C2×C5×#355C212yesmaximal, complemented
4C5×#1784C211yesmaximal, characteristic, complemented
5C5×#1394C212yesmaximal, complemented
6C23×C5×Q8C2211yescharacteristic
7C22×C5×M16—21no—
8C2×C5×#124C411yescharacteristic
9C2×C5×#124C2211yescharacteristic
10C2×C5×#121C411yescharacteristic
11C2×C5×#101—24no—
12C2×C5×#101—21no—
13C2×C5×#101—21no—
14C2×C5×#101C2212yes—
15C2×C5×#101C2212yes—
16C5×#407—21no—
17C5×#393—21no—
18C5×#393—21no—
19C5×#391C411yescharacteristic
20C5×#391C2211yescharacteristic
21C5×#386—21no—
22C5×#386—21no—
23C4×C5×C22⋊C4C411yescharacteristic
24C5×#355—24no—
25#13092C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×Q8—22no—
27C22×C5×Q8—22no—
28C22×C5×Q8—41no—
29C22×C5×Q8—41no—
30C22×C5×Q8—42no—
31C22×C5×Q8C2×C411yescharacteristic
32C22×C5×Q8D411yescharacteristic
33C22×C5×Q8D411yescharacteristic
34C22×C5×Q8C2311yescharacteristic
35C22×C5×D4—21no—
36C22×C5×D4C2×C411yescharacteristic
37C23×C4×C5C2×C411yescharacteristic
38C23×C4×C5D411yescharacteristic
39C23×C4×C5D411yescharacteristic
40C2×C5×M16—24no—
41C2×C5×M16—22no—
42C2×C5×M16—22no—
43C2×C5×M16—41no—
44C2×C5×M16—42no—
45C22×C5×C8—41no—
46C5×#124—22no—
47C5×#124—22no—
48C5×#124—42no—
49C5×#121—41no—
50C5×#121—41no—
51C2×C5×C4⋊C4C2×C411yescharacteristic
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C42×C5C2×C411yescharacteristic
59C2×C42×C5C2×C411yescharacteristic
60C5×#101—24no—
61C5×#101—22no—
62C5×#101—22no—
63C5×#101—22no—
64C5×#101—42no—
65C5×#101D414yescomplemented
66C5×C22⋊C8—41no—
67C5×C22⋊C8—41no—
68C5×#95—21no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—21no—
72C5×#95—21no—
73C22×#101C2×C511yescharacteristic, complemented
74#2436C2×C511yescharacteristic
75C2×#355C2×C512yescomplemented
76#1784C2×C511yescharacteristic, complemented
77#1394C2×C512yescomplemented
78C24×C5—21no—
79C24×C5C22⋊C411yescharacteristic
80C2×C5×Q8—22no—
81C2×C5×Q8—22no—
82C2×C5×Q8—22no—
83C2×C5×Q8—21no—
84C2×C5×Q8—22no—
85C2×C5×Q8—21no—
86C2×C5×Q8—41no—
87C2×C5×Q8—41no—
88C2×C5×Q8—41no—
89C2×C5×Q8—41no—
90C2×C5×Q8—41no—
91C2×C5×Q8—41no—
92C2×C5×Q8—44no—
93C2×C5×Q8—44no—
94C2×C5×Q8—44no—
95C2×C5×Q8—44no—
96C2×C5×Q8C2×D412yes—
97C2×C5×Q8#4112yes—
98C2×C5×D4—22no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—44no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—22no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5C22⋊C411yescharacteristic
121C22×C4×C5C22⋊C411yescharacteristic
122C22×C4×C5C22⋊C411yescharacteristic
123C22×C4×C5C22×C411yescharacteristic
124C22×C4×C5C2×D411yescharacteristic
125C22×C4×C5C2×D411yescharacteristic
126C5×M16—24no—
127C5×M16—44no—
128C5×M16—42no—
129C5×M16—42no—
130C5×M16—42no—
131C2×C5×C8—44no—
132C2×C5×C8—42no—
133C2×C5×C8—42no—
134C5×C4⋊C4—41no—
135C5×C22⋊C4—42no—
136C5×C22⋊C4—42no—
137C5×C22⋊C4—42no—
138C5×C22⋊C4—42no—
139C5×C22⋊C4—41no—
140C5×C22⋊C4—42no—
141C5×C22⋊C4—41no—
142C42×C5—22no—
143C42×C5—41no—
144C23×Q8C22×C511yescharacteristic
145C22×M16—21no—
146C2×#124C4×C511yescharacteristic
147C2×#124C22×C511yescharacteristic
148C2×#121C4×C511yescharacteristic
149C2×#101—21no—
150C2×#101—24no—
151C2×#101—21no—
152C2×#101C22×C512yes—
153C2×#101C22×C512yes—
154#407—21no—
155#393—21no—
156#393—21no—
157#391C4×C511yescharacteristic
158#391C22×C511yescharacteristic
159#386—21no—
160#386—21no—
161C4×C22⋊C4C4×C511yescharacteristic
162#355—24no—
163C23×C5—22no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—41no—
167C23×C5—42no—
168C23×C5—42no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5#9911yescharacteristic
173C23×C5#9911yescharacteristic
174C23×C5C2×C22⋊C411yescharacteristic
175C5×Q8—42no—
176C5×Q8—42no—
177C5×Q8—44no—
178C5×Q8—44no—
179C5×Q8—42no—
180C5×Q8—42no—
181C5×D4—82no—
182C5×D4—82no—
183C5×D4—82no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—42no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5—42no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5#9912yes—
215C2×C4×C5C4×D412yes—
216C2×C4×C5#12011yescharacteristic
217C2×C4×C5#12112yes—
218C2×C4×C5#12311yescharacteristic
219C5×C8—44no—
220C5×C8—82no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—41no—
224C22×Q8—41no—
225C22×Q8—42no—
226C22×Q8C2×C4×C511yescharacteristic
227C22×Q8C5×D411yescharacteristic
228C22×Q8C5×D411yescharacteristic
229C22×Q8C23×C511yescharacteristic
230C22×D4—21no—
231C22×D4C2×C4×C511yescharacteristic
232C23×C4C2×C4×C511yescharacteristic
233C23×C4C5×D411yescharacteristic
234C23×C4C5×D411yescharacteristic
235C2×M16—24no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—41no—
239C2×M16—42no—
240C22×C8—41no—
241#124—22no—
242#124—22no—
243#124—42no—
244#121—41no—
245#121—41no—
246C2×C4⋊C4C2×C4×C511yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42C2×C4×C511yescharacteristic
254C2×C42C2×C4×C511yescharacteristic
255#101—24no—
256#101—22no—
257#101—22no—
258#101—22no—
259#101—42no—
260#101C5×D414yescomplemented
261C22⋊C8—41no—
262C22⋊C8—41no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5—82no—
278C22×C5—82no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5#35512yescomplemented
283C22×C5#38611yescharacteristic
284C22×C5C2×#9911yescharacteristic
285C22×C5C2×#9911yescharacteristic
286C4×C5—21no—
287C4×C5—22no—
288C4×C5—22no—
289C4×C5—21no—
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—41no—
293C4×C5—81no—
294C4×C5—81no—
295C4×C5—81no—
296C24—21no—
297C24C5×C22⋊C411yescharacteristic
298C2×Q8—22no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—44no—
314C2×Q8C2×C5×D412yes—
315C2×Q8C5×#4112yes—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—44no—
320C2×D4—41no—
321C2×D4—41no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4C5×C22⋊C411yescharacteristic
339C22×C4C5×C22⋊C411yescharacteristic
340C22×C4C5×C22⋊C411yescharacteristic
341C22×C4C22×C4×C511yescharacteristic
342C22×C4C2×C5×D411yescharacteristic
343C22×C4C2×C5×D411yescharacteristic
344M16—24no—
345M16—44no—
346M16—42no—
347M16—42no—
348M16—42no—
349C2×C8—44no—
350C2×C8—42no—
351C2×C8—42no—
352C4⋊C4—41no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—41no—
357C22⋊C4—42no—
358C22⋊C4—41no—
359C22⋊C4—42no—
360C42—22no—
361C42—41no—
362C2×C5—21no—
363C2×C5—21no—
364C2×C5—22no—
365C2×C5—41no—
366C2×C5—161no—
367C2×C5#189811yescharacteristic
368C2×C5C2×#35511yescharacteristic
369C2×C5#213311yescharacteristic
370C23—21no—
371C23—21no—
372C23—22no—
373C23—41no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C5×#9911yescharacteristic
380C23C5×#9911yescharacteristic
381C23C2×C5×C22⋊C411yescharacteristic
382Q8—42no—
383Q8—42no—
384Q8—44no—
385Q8—44no—
386Q8—42no—
387Q8—42no—
388D4—82no—
389D4—82no—
390D4—82no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4C5×#9912yes—
422C2×C4C4×C5×D412yes—
423C2×C4C5×#12011yescharacteristic
424C2×C4C5×#12112yes—
425C2×C4C5×#12311yescharacteristic
426C8—44no—
427C8—82no—
428C5#1309211yescharacteristic, direct product factor, Sylow
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—82no—
439C22—82no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C5×#35512yescomplemented
444C22C5×#38611yescharacteristic
445C22C2×C5×#9911yescharacteristic
446C22C2×C5×#9911yescharacteristic
447C4—21no—
448C4—22no—
449C4—21no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—81no—
456C4—81no—
457C2—21no—
458C2—21no—
459C2—22no—
460C2—41no—
461C2—161no—
462C2C5×#189811yescharacteristic
463C2C2×C5×#35511yescharacteristic
464C2C5×#213311yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×Q8C23×C5
prime radicalC2×C5×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C23×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C5×#101C2semidirect
3. C2×C5×#355C2semidirect
4. C5×#1784C2semidirect
5. C5×#1394C2semidirect
25. #13092C5direct (N × H)
65. C5×#101D4semidirect
73. C22×#101C2×C5semidirect
75. C2×#355C2×C5semidirect
76. #1784C2×C5semidirect
77. #1394C2×C5semidirect
260. #101C5×D4semidirect
282. C22×C5#355semidirect
428. C5#13092direct (N × H)
443. C22C5×#355semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#1012
C5×#24362
C2×C5×#3552
C5×#17842
C5×#13942
#130925