Finite Group Databasebeta

← C5×#29680 #11952400

Subgroups — C5×#29680 #11952400

Order 1280.

1102 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×#3460C211yesmaximal, characteristic
2C5×#3039C212yesmaximal, complemented
3C5×#2547C211yesmaximal, characteristic, complemented
4C5×#2028C212yesmaximal, complemented
5C5×#2007C212yesmaximal, complemented
6C5×#2004C214yesmaximal, complemented
7C5×#1806C212yesmaximal, complemented
8C5×#1800C211yesmaximal, characteristic, complemented
9C2×C5×#137C2214yes—
10C5×#544C2211yescharacteristic
11C5×#542—22no—
12C5×#540—22no—
13C5×#538—22no—
14C5×#537C2211yescharacteristic
15C5×#535C2212yes—
16C5×#532—22no—
17C2×C5×C4⋊Q8C2211yescharacteristic
18C5×#529—22no—
19C2×C5×#124C2212yes—
20C5×#525—22no—
21C4×C5×#41C2212yes—
22C2×C4×C5×D4C2211yescharacteristic
23C5×#462—22no—
24C5×#462—22no—
25C5×#461—22no—
26C5×#461—22no—
27C5×#423C2212yes—
28C2×C5×#104C2214yes—
29C5×#419C2214yes—
30C2×C5×#100C2212yes—
31C5×#397—22no—
32C5×#391C2212yes—
33C5×#380—22no—
34C4×C5×C4⋊C4C2211yescharacteristic
35C5×#343C2212yes—
36C5×#339C2214yes—
37#29680C511yesmaximal, characteristic, direct product factor, Sylow
38C2×C5×#41—22no—
39C2×C5×#41C2312yes—
40C22×C5×Q8C2312yes—
41C22×C5×D4C2311yescharacteristic
42C23×C4×C5D412yes—
43C5×#137—44no—
44C5×#137—44no—
45C2×C5×Q16—24no—
46C2×C5×SD16—24no—
47C2×C5×M16C2314yes—
48C5×C4⋊Q8—22no—
49C5×C4⋊Q8—22no—
50C5×C4⋊Q8—22no—
51C5×#127—22no—
52C5×#126—24no—
53C5×#125—22no—
54C5×#124—24no—
55C5×#124—22no—
56C5×#124—44no—
57C5×#123—24no—
58C5×#123—24no—
59C5×C22⋊Q8—22no—
60C5×C22⋊Q8—22no—
61C5×C22⋊Q8—22no—
62C5×#121—22no—
63C5×#121—24no—
64C5×#121—22no—
65C5×#121—22no—
66C5×#121—22no—
67C5×#121—22no—
68C5×#120—24no—
69C4×C5×Q8D412yes—
70C4×C5×Q8D412yes—
71C4×C5×D4—24no—
72C4×C5×D4—22no—
73C4×C5×D4—22no—
74C4×C5×D4—22no—
75C4×C5×D4—22no—
76C4×C5×D4D412yes—
77C4×C5×D4D412yes—
78C5×#117—22no—
79C5×#117—22no—
80C5×#117C2312yes—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C22⋊C4—24no—
86C2×C5×C22⋊C4D412yes—
87C2×C42×C5—22no—
88C2×C42×C5C2312yes—
89C2×C42×C5C2311yescharacteristic
90C5×C4⋊C8—22no—
91C5×C4⋊C8—22no—
92C5×#104—44no—
93C5×#103—24no—
94C5×#103—24no—
95C5×#100—42no—
96C5×#95—21no—
97C5×#95—24no—
98#3460C2×C511yescharacteristic
99#3039C2×C512yescomplemented
100#2547C2×C511yescharacteristic, complemented
101#2028C2×C512yescomplemented
102#2007C2×C512yescomplemented
103#2004C2×C514yescomplemented
104#1806C2×C512yescomplemented
105#1800C2×C511yescharacteristic, complemented
106C24×C5C2×D412yes—
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—84no—
112C2×C5×Q8—22no—
113C2×C5×Q8—24no—
114C2×C5×Q8—24no—
115C2×C5×Q8—22no—
116C2×C5×Q8—22no—
117C2×C5×Q8C2×D412yes—
118C2×C5×D4—22no—
119C2×C5×D4—24no—
120C2×C5×D4—24no—
121C2×C5×D4—22no—
122C2×C5×D4—22no—
123C2×C5×D4—22no—
124C2×C5×D4—21no—
125C2×C5×D4—21no—
126C2×C5×D4C2×D412yes—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—44no—
135C22×C4×C5C2×D411yescharacteristic
136C22×C4×C5C2×D412yes—
137C22×C4×C5C2×D411yescharacteristic
138C22×C4×C5C2411yescharacteristic
139C5×Q16—48no—
140C5×SD16—48no—
141C5×M16—24no—
142C5×M16—24no—
143C2×C5×C8—24no—
144C5×C4⋊C4—22no—
145C5×C4⋊C4—22no—
146C5×C4⋊C4—24no—
147C5×C4⋊C4—22no—
148C5×C4⋊C4—22no—
149C5×C4⋊C4—22no—
150C5×C4⋊C4—42no—
151C5×C4⋊C4—42no—
152C5×C4⋊C4—41no—
153C5×C4⋊C4—41no—
154C5×C4⋊C4C2×D412yes—
155C5×C4⋊C4C2×D412yes—
156C5×C22⋊C4—24no—
157C5×C22⋊C4—24no—
158C5×C22⋊C4—24no—
159C5×C22⋊C4—22no—
160C5×C22⋊C4—24no—
161C5×C22⋊C4—22no—
162C5×C22⋊C4—22no—
163C5×C22⋊C4—48no—
164C42×C5—22no—
165C42×C5—22no—
166C42×C5—22no—
167C42×C5—24no—
168C42×C5C2×D412yes—
169C42×C5C2×D412yes—
170C2×#137C22×C514yes—
171#544C22×C511yescharacteristic
172#542—22no—
173#540—22no—
174#538—22no—
175#537C22×C511yescharacteristic
176#535C22×C512yes—
177#532—22no—
178C2×C4⋊Q8C22×C511yescharacteristic
179#529—22no—
180C2×#124C22×C512yes—
181#525—22no—
182C4×#41C22×C512yes—
183C2×C4×D4C22×C511yescharacteristic
184#462—22no—
185#462—22no—
186#461—22no—
187#461—22no—
188#423C22×C512yes—
189C2×#104C22×C514yes—
190#419C22×C514yes—
191C2×#100C22×C512yes—
192#397—22no—
193#391C22×C512yes—
194#380—22no—
195C4×C4⋊C4C22×C511yescharacteristic
196#343C22×C512yes—
197#339C22×C514yes—
198C23×C5—22no—
199C23×C5—22no—
200C23×C5—22no—
201C23×C5—22no—
202C23×C5—42no—
203C23×C5—42no—
204C23×C5C22×D411yescharacteristic
205C5×Q8—22no—
206C5×Q8—22no—
207C5×Q8—44no—
208C5×Q8—44no—
209C5×Q8—82no—
210C5×D4—22no—
211C5×D4—22no—
212C5×D4—42no—
213C5×D4—42no—
214C5×D4—42no—
215C5×D4—42no—
216C5×D4—84no—
217C5×D4—82no—
218C5×D4—84no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—22no—
224C2×C4×C5—41no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—44no—
228C2×C4×C5—44no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—82no—
237C2×C4×C5—82no—
238C2×C4×C5#12012yes—
239C2×C4×C5#12011yescharacteristic
240C2×C4×C5#12011yescharacteristic
241C2×C4×C5C22×D412yes—
242C2×C4×C5H(5,𝔽2)11yescharacteristic
243C2×C4×C5H(5,𝔽2)12yes—
244C2×C4×C52−1+411yescharacteristic
245C5×C8—44no—
246C2×#41—22no—
247C2×#41C23×C512yes—
248C22×Q8C23×C512yes—
249C22×D4C23×C511yescharacteristic
250C23×C4C5×D412yes—
251#137—44no—
252#137—44no—
253C2×Q16—24no—
254C2×SD16—24no—
255C2×M16C23×C514yes—
256C4⋊Q8—22no—
257C4⋊Q8—22no—
258C4⋊Q8—22no—
259#127—22no—
260#126—24no—
261#125—22no—
262#124—24no—
263#124—22no—
264#124—44no—
265#123—24no—
266#123—24no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—22no—
270#121—22no—
271#121—24no—
272#121—22no—
273#121—22no—
274#121—22no—
275#121—22no—
276#120—24no—
277C4×Q8C5×D412yes—
278C4×Q8C5×D412yes—
279C4×D4—24no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—22no—
284C4×D4C5×D412yes—
285C4×D4C5×D412yes—
286#117—22no—
287#117—22no—
288#117C23×C512yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4C23×C511yescharacteristic
293C2×C22⋊C4—24no—
294C2×C22⋊C4C5×D412yes—
295C2×C42—22no—
296C2×C42C23×C512yes—
297C2×C42C23×C511yescharacteristic
298C4⋊C8—22no—
299C4⋊C8—22no—
300#104—44no—
301#103—24no—
302#103—24no—
303#100—42no—
304#95—21no—
305#95—24no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—44no—
309C22×C5—42no—
310C22×C5—42no—
311C22×C5—42no—
312C22×C5—42no—
313C22×C5—42no—
314C22×C5—42no—
315C22×C5—82no—
316C22×C5C2×#12011yescharacteristic
317C22×C5#53511yescharacteristic
318C22×C5#53711yescharacteristic
319C4×C5—21no—
320C4×C5—22no—
321C4×C5—42no—
322C4×C5—42no—
323C4×C5—42no—
324C4×C5—42no—
325C4×C5—82no—
326C4×C5—82no—
327C4×C5#45512yes—
328C4×C5#53512yes—
329C4×C5#53712yes—
330C24C2×C5×D412yes—
331#41—22no—
332#41—22no—
333#41—22no—
334#41—22no—
335#41—84no—
336C2×Q8—22no—
337C2×Q8—24no—
338C2×Q8—24no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8C2×C5×D412yes—
342C2×D4—22no—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—21no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4C2×C5×D412yes—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—44no—
359C22×C4C2×C5×D411yescharacteristic
360C22×C4C2×C5×D412yes—
361C22×C4C2×C5×D411yescharacteristic
362C22×C4C24×C511yescharacteristic
363Q16—48no—
364SD16—48no—
365M16—24no—
366M16—24no—
367C2×C8—24no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4C2×C5×D412yes—
379C4⋊C4C2×C5×D412yes—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—24no—
383C22⋊C4—22no—
384C22⋊C4—24no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—48no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42—24no—
392C42C2×C5×D412yes—
393C42C2×C5×D412yes—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—82no—
397C2×C5—82no—
398C2×C5#261511yescharacteristic
399C2×C5C2×#45511yescharacteristic
400C2×C5#302211yescharacteristic
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—42no—
406C23—42no—
407C23C22×C5×D411yescharacteristic
408Q8—22no—
409Q8—22no—
410Q8—44no—
411Q8—44no—
412Q8—82no—
413D4—22no—
414D4—22no—
415D4—42no—
416D4—42no—
417D4—42no—
418D4—42no—
419D4—82no—
420D4—84no—
421D4—84no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4C5×#12012yes—
442C2×C4C5×#12011yescharacteristic
443C2×C4C5×#12011yescharacteristic
444C2×C4C22×C5×D412yes—
445C2×C4C5×H(5,𝔽2)11yescharacteristic
446C2×C4C5×H(5,𝔽2)12yes—
447C2×C4C5×2−1+411yescharacteristic
448C8—44no—
449C5#2968011yescharacteristic, direct product factor, Sylow
450C22—21no—
451C22—21no—
452C22—44no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—82no—
460C22C2×C5×#12011yescharacteristic
461C22C5×#53511yescharacteristic
462C22C5×#53711yescharacteristic
463C4—21no—
464C4—22no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—82no—
471C4C5×#45512yes—
472C4C5×#53512yes—
473C4C5×#53712yes—
474C2—21no—
475C2—21no—
476C2—82no—
477C2—82no—
478C2C5×#261511yescharacteristic
479C2C2×C5×#45511yescharacteristic
480C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3039C2semidirect
3. C5×#2547C2semidirect
4. C5×#2028C2semidirect
5. C5×#2007C2semidirect
6. C5×#2004C2semidirect
7. C5×#1806C2semidirect
8. C5×#1800C2semidirect
37. #29680C5direct (N × H)
99. #3039C2×C5semidirect
100. #2547C2×C5semidirect
101. #2028C2×C5semidirect
102. #2007C2×C5semidirect
103. #2004C2×C5semidirect
104. #1806C2×C5semidirect
105. #1800C2×C5semidirect
449. C5#29680direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34602
C5×#30392
C5×#25472
C5×#20282
C5×#20072
C5×#20042
C5×#18062
C5×#18002
#296805