Finite Group Databasebeta

← C5×#18150 #11940870

Subgroups — C5×#18150 #11940870

Order 1280.

1014 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3460C211yesmaximal, characteristic
2C5×#3092C212yesmaximal, complemented
3C5×#2486C211yesmaximal, characteristic, complemented
4C5×#1612C214yesmaximal, complemented
5C5×#1611C212yesmaximal, complemented
6C5×#1610C212yesmaximal, complemented
7C5×#1513C212yesmaximal, complemented
8C5×#1465C211yesmaximal, characteristic, complemented
9C5×#544C2211yescharacteristic
10C5×#542—22no—
11C5×#540—22no—
12C5×#538—21no—
13C5×#538C2212yes—
14C5×#537C2211yescharacteristic
15C5×#535—21no—
16C5×#532—22no—
17C5×#529—22no—
18C5×#525—21no—
19C5×#525C2212yes—
20C2×C5×#123—21no—
21C4×C5×#41—21no—
22C2×C4×C5×D4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#484—22no—
25C5×#483C2214yes—
26C5×#481—22no—
27C5×#480C2214yes—
28C5×#428—22no—
29C5×#417—22no—
30C5×#407C2212yes—
31C5×#398C2212yes—
32C5×#397C2212yes—
33C5×#389—21no—
34C5×#381—21no—
35C5×#380—21no—
36C5×#380C2211yescharacteristic
37C5×#328C2214yes—
38C5×#327C2214yes—
39C5×#324C2212yes—
40C5×#323C2212yes—
41#18150C511yesmaximal, characteristic, direct product factor, Sylow
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41D412yes—
45C22×C5×D4D411yescharacteristic
46C23×C4×C5—21no—
47C23×C4×C5D411yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C2×C5×M16—22no—
50C5×C4⋊Q8—22no—
51C5×#127—22no—
52C5×#126—22no—
53C5×#126—22no—
54C5×#125—22no—
55C5×#124—22no—
56C5×#124—22no—
57C5×#124—22no—
58C5×#123—22no—
59C5×#123—22no—
60C5×#123—22no—
61C5×#123—22no—
62C5×#123—44no—
63C5×C22⋊Q8—21no—
64C5×C22⋊Q8—21no—
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8D412yes—
67C5×C22⋊Q8C2312yes—
68C5×#121—21no—
69C5×#121—22no—
70C5×#121—22no—
71C5×#121—22no—
72C5×#121—22no—
73C5×#121—22no—
74C5×#121—21no—
75C5×#121D412yes—
76C5×#121C2312yes—
77C5×#120—22no—
78C5×#120—22no—
79C4×C5×Q8—21no—
80C4×C5×Q8—21no—
81C4×C5×D4—21no—
82C4×C5×D4—21no—
83C4×C5×D4—22no—
84C4×C5×D4—22no—
85C4×C5×D4—22no—
86C4×C5×D4—22no—
87C4×C5×D4—22no—
88C4×C5×D4—22no—
89C5×#117—22no—
90C5×#117—21no—
91C5×#117—21no—
92C5×#117D412yes—
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—22no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4C2312yes—
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4D411yescharacteristic
103C2×C5×C22⋊C4C2311yescharacteristic
104C2×C42×C5—22no—
105C2×C42×C5D411yescharacteristic
106C5×#107—24no—
107C5×#106—24no—
108C5×#103—24no—
109C5×#102—24no—
110C5×C22⋊C8—22no—
111C5×C22⋊C8C2314yes—
112C5×#95—22no—
113C5×#95—22no—
114C5×#95C2312yes—
115#3460C2×C511yescharacteristic
116#3092C2×C512yescomplemented
117#2486C2×C511yescharacteristic, complemented
118#1612C2×C514yescomplemented
119#1611C2×C512yescomplemented
120#1610C2×C512yescomplemented
121#1513C2×C512yescomplemented
122#1465C2×C511yescharacteristic, complemented
123C24×C5C2×D411yescharacteristic
124C24×C5C2×D411yescharacteristic
125C5×#41—42no—
126C5×#41—44no—
127C5×#41—42no—
128C5×#41—82no—
129C2×C5×Q8—21no—
130C2×C5×Q8—21no—
131C2×C5×Q8C2×D412yes—
132C2×C5×D4—21no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—22no—
137C2×C5×D4—21no—
138C2×C5×D4—22no—
139C2×C5×D4—22no—
140C2×C5×D4—22no—
141C2×C5×D4—41no—
142C2×C5×D4C2×D412yes—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5—42no—
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2411yescharacteristic
162C5×M16—44no—
163C2×C5×C8—24no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—24no—
174C5×C4⋊C4—42no—
175C5×C4⋊C4—41no—
176C5×C4⋊C4—41no—
177C5×C4⋊C4—44no—
178C5×C4⋊C4C2×D412yes—
179C5×C4⋊C4C2×D412yes—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—42no—
192C5×C22⋊C4—44no—
193C42×C5—22no—
194C42×C5—22no—
195C42×C5—21no—
196C42×C5—22no—
197C42×C5—21no—
198#544C22×C511yescharacteristic
199#542—22no—
200#540—22no—
201#538—21no—
202#538C22×C512yes—
203#537C22×C511yescharacteristic
204#535—21no—
205#532—22no—
206#529—22no—
207#525—21no—
208#525C22×C512yes—
209C2×#123—21no—
210C4×#41—21no—
211C2×C4×D4C22×C511yescharacteristic
212C22×C4⋊C4C22×C511yescharacteristic
213#484—22no—
214#483C22×C514yes—
215#481—22no—
216#480C22×C514yes—
217#428—22no—
218#417—22no—
219#407C22×C512yes—
220#398C22×C512yes—
221#397C22×C512yes—
222#389—21no—
223#381—21no—
224#380—21no—
225#380C22×C511yescharacteristic
226#328C22×C514yes—
227#327C22×C514yes—
228#324C22×C512yes—
229#323C22×C512yes—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—22no—
234C23×C5—21no—
235C23×C5—21no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5#12012yes—
241C23×C5C22×D411yescharacteristic
242C5×Q8—42no—
243C5×Q8—42no—
244C5×Q8—81no—
245C5×D4—44no—
246C5×D4—42no—
247C5×D4—42no—
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—82no—
251C5×D4—82no—
252C5×D4—82no—
253C5×D4—81no—
254C5×D4—82no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—22no—
258C2×C4×C5—24no—
259C2×C4×C5—21no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—42no—
265C2×C4×C5—41no—
266C2×C4×C5—44no—
267C2×C4×C5—42no—
268C2×C4×C5—44no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—81no—
278C2×C4×C5—82no—
279C2×C4×C5—84no—
280C2×C4×C5#12011yescharacteristic
281C2×C4×C5#12011yescharacteristic
282C2×C4×C5AGL(1,ℤ/8)12yes—
283C2×C4×C5C22×D412yes—
284C5×C8—44no—
285C2×#41—21no—
286C2×#41—21no—
287C2×#41C5×D412yes—
288C22×D4C5×D411yescharacteristic
289C23×C4—21no—
290C23×C4C5×D411yescharacteristic
291C23×C4C23×C511yescharacteristic
292C2×M16—22no—
293C4⋊Q8—22no—
294#127—22no—
295#126—22no—
296#126—22no—
297#125—22no—
298#124—22no—
299#124—22no—
300#124—22no—
301#123—22no—
302#123—22no—
303#123—22no—
304#123—22no—
305#123—44no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—22no—
309C22⋊Q8C5×D412yes—
310C22⋊Q8C23×C512yes—
311#121—21no—
312#121—22no—
313#121—22no—
314#121—22no—
315#121—22no—
316#121—22no—
317#121—21no—
318#121C5×D412yes—
319#121C23×C512yes—
320#120—22no—
321#120—22no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332#117—22no—
333#117—21no—
334#117—21no—
335#117C5×D412yes—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C23×C512yes—
342C2×C4⋊C4C23×C511yescharacteristic
343C2×C22⋊C4—22no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4C5×D411yescharacteristic
346C2×C22⋊C4C23×C511yescharacteristic
347C2×C42—22no—
348C2×C42C5×D411yescharacteristic
349#107—24no—
350#106—24no—
351#103—24no—
352#102—24no—
353C22⋊C8—22no—
354C22⋊C8C23×C514yes—
355#95—22no—
356#95—22no—
357#95C23×C512yes—
358C22×C5—21no—
359C22×C5—21no—
360C22×C5—22no—
361C22×C5—22no—
362C22×C5—22no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—42no—
367C22×C5—41no—
368C22×C5—42no—
369C22×C5—41no—
370C22×C5—41no—
371C22×C5—42no—
372C22×C5—81no—
373C22×C5C2×#12011yescharacteristic
374C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C5#57511yescharacteristic
376C4×C5—22no—
377C4×C5—22no—
378C4×C5—21no—
379C4×C5—42no—
380C4×C5—41no—
381C4×C5—42no—
382C4×C5—41no—
383C4×C5—42no—
384C4×C5—82no—
385C4×C5—82no—
386C4×C5#45812yes—
387C24C2×C5×D411yescharacteristic
388C24C2×C5×D411yescharacteristic
389#41—42no—
390#41—44no—
391#41—42no—
392#41—82no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8C2×C5×D412yes—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—41no—
406C2×D4C2×C5×D412yes—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4C2×C5×D411yescharacteristic
420C22×C4C2×C5×D412yes—
421C22×C4C2×C5×D411yescharacteristic
422C22×C4C2×C5×D411yescharacteristic
423C22×C4C2×C5×D411yescharacteristic
424C22×C4C2×C5×D412yes—
425C22×C4C24×C511yescharacteristic
426M16—44no—
427C2×C8—24no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—24no—
438C4⋊C4—42no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—44no—
442C4⋊C4C2×C5×D412yes—
443C4⋊C4C2×C5×D412yes—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—42no—
456C22⋊C4—44no—
457C42—22no—
458C42—22no—
459C42—21no—
460C42—22no—
461C42—21no—
462C2×C5—21no—
463C2×C5—21no—
464C2×C5—42no—
465C2×C5—82no—
466C2×C5—81no—
467C2×C5#300611yescharacteristic
468C2×C5#302211yescharacteristic
469C2×C5C2×#45811yescharacteristic
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23—21no—
475C23—21no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23C5×#12012yes—
481C23C22×C5×D411yescharacteristic
482Q8—42no—
483Q8—42no—
484Q8—81no—
485D4—44no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—82no—
491D4—82no—
492D4—81no—
493D4—82no—
494D4—82no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—44no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—81no—
518C2×C4—82no—
519C2×C4—84no—
520C2×C4C5×#12011yescharacteristic
521C2×C4C5×#12011yescharacteristic
522C2×C4C5×AGL(1,ℤ/8)12yes—
523C2×C4C22×C5×D412yes—
524C8—44no—
525C5#1815011yescharacteristic, direct product factor, Sylow
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—41no—
536C22—42no—
537C22—41no—
538C22—41no—
539C22—42no—
540C22—81no—
541C22C2×C5×#12011yescharacteristic
542C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
543C22C5×#57511yescharacteristic
544C4—22no—
545C4—22no—
546C4—21no—
547C4—42no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—42no—
552C4—82no—
553C4—82no—
554C4C5×#45812yes—
555C2—21no—
556C2—21no—
557C2—42no—
558C2—81no—
559C2—82no—
560C2C5×#300611yescharacteristic
561C2C5×#302211yescharacteristic
562C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3460C2
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
2. C5×#3092C2semidirect
3. C5×#2486C2semidirect
4. C5×#1612C2semidirect
5. C5×#1611C2semidirect
6. C5×#1610C2semidirect
7. C5×#1513C2semidirect
8. C5×#1465C2semidirect
41. #18150C5direct (N × H)
116. #3092C2×C5semidirect
117. #2486C2×C5semidirect
118. #1612C2×C5semidirect
119. #1611C2×C5semidirect
120. #1610C2×C5semidirect
121. #1513C2×C5semidirect
122. #1465C2×C5semidirect
525. C5#18150direct (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×#30922
C5×#24862
C5×#16122
C5×#16112
C5×#16102
C5×#15132
C5×#14652
#181505