Finite Group Databasebeta

← C5×#18151 #11940871

Subgroups — C5×#18151 #11940871

Order 1280.

994 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3460C211yesmaximal, characteristic
2C5×#3092C212yesmaximal, complemented
3C5×#2487C211yesmaximal, characteristic, complemented
4C5×#1618C214yesmaximal, complemented
5C5×#1617C212yesmaximal, complemented
6C5×#1616C212yesmaximal, 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—
20C4×C5×#41—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#484C2214yes—
24C5×#483—22no—
25C5×#481C2214yes—
26C5×#480—22no—
27C5×#428—22no—
28C5×#417—22no—
29C5×#407C2212yes—
30C5×#400C2212yes—
31C5×#399C2212yes—
32C5×#389—21no—
33C5×#386—21no—
34C5×#385—21no—
35C5×#380—21no—
36C5×#380C2211yescharacteristic
37C5×#328C2214yes—
38C5×#327C2214yes—
39C5×#324C2212yes—
40C5×#323C2212yes—
41#18151C511yesmaximal, 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×C22⋊Q8—21no—
63C5×C22⋊Q8—21no—
64C5×C22⋊Q8—22no—
65C5×C22⋊Q8D412yes—
66C5×C22⋊Q8C2312yes—
67C5×#121—21no—
68C5×#121—22no—
69C5×#121—22no—
70C5×#121—22no—
71C5×#121—22no—
72C5×#121—22no—
73C5×#121—21no—
74C5×#121D412yes—
75C5×#121C2312yes—
76C5×#120—22no—
77C5×#120—22no—
78C4×C5×Q8—21no—
79C4×C5×Q8—21no—
80C4×C5×D4—21no—
81C4×C5×D4—21no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
84C4×C5×D4—22no—
85C4×C5×D4—22no—
86C4×C5×D4—22no—
87C4×C5×D4—22no—
88C5×#117—22no—
89C5×#117—21no—
90C5×#117—21no—
91C5×#117D412yes—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—22no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4C2312yes—
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—22no—
101C2×C5×C22⋊C4D411yescharacteristic
102C2×C5×C22⋊C4C2311yescharacteristic
103C2×C42×C5—22no—
104C2×C42×C5D411yescharacteristic
105C5×#107—24no—
106C5×#106—24no—
107C5×#103—24no—
108C5×#102—24no—
109C5×C22⋊C8—22no—
110C5×C22⋊C8C2314yes—
111C5×#95—22no—
112C5×#95—22no—
113C5×#95C2312yes—
114#3460C2×C511yescharacteristic
115#3092C2×C512yescomplemented
116#2487C2×C511yescharacteristic, complemented
117#1618C2×C514yescomplemented
118#1617C2×C512yescomplemented
119#1616C2×C512yescomplemented
120#1513C2×C512yescomplemented
121#1465C2×C511yescharacteristic, complemented
122C24×C5C2×D411yescharacteristic
123C24×C5C2×D411yescharacteristic
124C5×#41—42no—
125C5×#41—44no—
126C5×#41—42no—
127C5×#41—82no—
128C2×C5×Q8—21no—
129C2×C5×Q8—21no—
130C2×C5×Q8C2×D412yes—
131C2×C5×D4—21no—
132C2×C5×D4—22no—
133C2×C5×D4—22no—
134C2×C5×D4—22no—
135C2×C5×D4—22no—
136C2×C5×D4—21no—
137C2×C5×D4—22no—
138C2×C5×D4—22no—
139C2×C5×D4—22no—
140C2×C5×D4—41no—
141C2×C5×D4C2×D412yes—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—42no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5—82no—
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D412yes—
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D412yes—
159C22×C4×C5C2411yescharacteristic
160C5×M16—44no—
161C2×C5×C8—24no—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—22no—
171C5×C4⋊C4—24no—
172C5×C4⋊C4—42no—
173C5×C4⋊C4—41no—
174C5×C4⋊C4—41no—
175C5×C4⋊C4—82no—
176C5×C4⋊C4C2×D412yes—
177C5×C4⋊C4C2×D412yes—
178C5×C22⋊C4—22no—
179C5×C22⋊C4—22no—
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—42no—
190C5×C22⋊C4—82no—
191C42×C5—22no—
192C42×C5—22no—
193C42×C5—21no—
194C42×C5—22no—
195C42×C5—21no—
196#544C22×C511yescharacteristic
197#542—22no—
198#540—22no—
199#538—21no—
200#538C22×C512yes—
201#537C22×C511yescharacteristic
202#535—21no—
203#532—22no—
204#529—22no—
205#525—21no—
206#525C22×C512yes—
207C4×#41—21no—
208C2×C4×D4C22×C511yescharacteristic
209C22×C4⋊C4C22×C511yescharacteristic
210#484C22×C514yes—
211#483—22no—
212#481C22×C514yes—
213#480—22no—
214#428—22no—
215#417—22no—
216#407C22×C512yes—
217#400C22×C512yes—
218#399C22×C512yes—
219#389—21no—
220#386—21no—
221#385—21no—
222#380—21no—
223#380C22×C511yescharacteristic
224#328C22×C514yes—
225#327C22×C514yes—
226#324C22×C512yes—
227#323C22×C512yes—
228C23×C5—21no—
229C23×C5—21no—
230C23×C5—21no—
231C23×C5—22no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5—41no—
235C23×C5—41no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5#12012yes—
239C23×C5C22×D411yescharacteristic
240C5×Q8—42no—
241C5×Q8—42no—
242C5×Q8—81no—
243C5×D4—44no—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—42no—
247C5×D4—42no—
248C5×D4—82no—
249C5×D4—82no—
250C5×D4—82no—
251C5×D4—81no—
252C5×D4—82no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—22no—
256C2×C4×C5—24no—
257C2×C4×C5—21no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—21no—
262C2×C4×C5—42no—
263C2×C4×C5—41no—
264C2×C4×C5—44no—
265C2×C4×C5—42no—
266C2×C4×C5—44no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—81no—
276C2×C4×C5—82no—
277C2×C4×C5—84no—
278C2×C4×C5#12011yescharacteristic
279C2×C4×C5#12011yescharacteristic
280C2×C4×C5#13712yes—
281C2×C4×C5C22×D412yes—
282C5×C8—44no—
283C2×#41—21no—
284C2×#41—21no—
285C2×#41C5×D412yes—
286C22×D4C5×D411yescharacteristic
287C23×C4—21no—
288C23×C4C5×D411yescharacteristic
289C23×C4C23×C511yescharacteristic
290C2×M16—22no—
291C4⋊Q8—22no—
292#127—22no—
293#126—22no—
294#126—22no—
295#125—22no—
296#124—22no—
297#124—22no—
298#124—22no—
299#123—22no—
300#123—22no—
301#123—22no—
302#123—22no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—22no—
306C22⋊Q8C5×D412yes—
307C22⋊Q8C23×C512yes—
308#121—21no—
309#121—22no—
310#121—22no—
311#121—22no—
312#121—22no—
313#121—22no—
314#121—21no—
315#121C5×D412yes—
316#121C23×C512yes—
317#120—22no—
318#120—22no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329#117—22no—
330#117—21no—
331#117—21no—
332#117C5×D412yes—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4C23×C512yes—
339C2×C4⋊C4C23×C511yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4C5×D411yescharacteristic
343C2×C22⋊C4C23×C511yescharacteristic
344C2×C42—22no—
345C2×C42C5×D411yescharacteristic
346#107—24no—
347#106—24no—
348#103—24no—
349#102—24no—
350C22⋊C8—22no—
351C22⋊C8C23×C514yes—
352#95—22no—
353#95—22no—
354#95C23×C512yes—
355C22×C5—21no—
356C22×C5—21no—
357C22×C5—22no—
358C22×C5—22no—
359C22×C5—22no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—42no—
364C22×C5—41no—
365C22×C5—42no—
366C22×C5—41no—
367C22×C5—41no—
368C22×C5—42no—
369C22×C5—81no—
370C22×C5C2×#12011yescharacteristic
371C22×C5C2×#13711yescharacteristic
372C22×C5#57511yescharacteristic
373C4×C5—22no—
374C4×C5—22no—
375C4×C5—21no—
376C4×C5—42no—
377C4×C5—41no—
378C4×C5—42no—
379C4×C5—41no—
380C4×C5—42no—
381C4×C5—82no—
382C4×C5—82no—
383C4×C5#45812yes—
384C24C2×C5×D411yescharacteristic
385C24C2×C5×D411yescharacteristic
386#41—42no—
387#41—44no—
388#41—42no—
389#41—82no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8C2×C5×D412yes—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—41no—
403C2×D4C2×C5×D412yes—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—82no—
415C22×C4C2×C5×D411yescharacteristic
416C22×C4C2×C5×D412yes—
417C22×C4C2×C5×D411yescharacteristic
418C22×C4C2×C5×D411yescharacteristic
419C22×C4C2×C5×D411yescharacteristic
420C22×C4C2×C5×D412yes—
421C22×C4C24×C511yescharacteristic
422M16—44no—
423C2×C8—24no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—42no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—82no—
438C4⋊C4C2×C5×D412yes—
439C4⋊C4C2×C5×D412yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—42no—
452C22⋊C4—82no—
453C42—22no—
454C42—22no—
455C42—21no—
456C42—22no—
457C42—21no—
458C2×C5—21no—
459C2×C5—21no—
460C2×C5—42no—
461C2×C5—82no—
462C2×C5—81no—
463C2×C5#300711yescharacteristic
464C2×C5#302111yescharacteristic
465C2×C5C2×#45811yescharacteristic
466C23—21no—
467C23—21no—
468C23—21no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C5×#12012yes—
477C23C22×C5×D411yescharacteristic
478Q8—42no—
479Q8—42no—
480Q8—81no—
481D4—44no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—82no—
487D4—82no—
488D4—81no—
489D4—82no—
490D4—82no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—81no—
514C2×C4—82no—
515C2×C4—84no—
516C2×C4C5×#12011yescharacteristic
517C2×C4C5×#12011yescharacteristic
518C2×C4C5×#13712yes—
519C2×C4C22×C5×D412yes—
520C8—44no—
521C5#1815111yescharacteristic, direct product factor, Sylow
522C22—21no—
523C22—21no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—81no—
537C22C2×C5×#12011yescharacteristic
538C22C2×C5×#13711yescharacteristic
539C22C5×#57511yescharacteristic
540C4—22no—
541C4—22no—
542C4—21no—
543C4—42no—
544C4—41no—
545C4—42no—
546C4—41no—
547C4—42no—
548C4—82no—
549C4—82no—
550C4C5×#45812yes—
551C2—21no—
552C2—21no—
553C2—42no—
554C2—81no—
555C2—82no—
556C2C5×#300711yescharacteristic
557C2C5×#302111yescharacteristic
558C2C2×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×#2487C2semidirect
4. C5×#1618C2semidirect
5. C5×#1617C2semidirect
6. C5×#1616C2semidirect
7. C5×#1513C2semidirect
8. C5×#1465C2semidirect
41. #18151C5direct (N × H)
115. #3092C2×C5semidirect
116. #2487C2×C5semidirect
117. #1618C2×C5semidirect
118. #1617C2×C5semidirect
119. #1616C2×C5semidirect
120. #1513C2×C5semidirect
121. #1465C2×C5semidirect
521. C5#18151direct (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×#24872
C5×#16182
C5×#16172
C5×#16162
C5×#15132
C5×#14652
#181515