Finite Group Databasebeta

← C5×#18438 #11941158

Subgroups — C5×#18438 #11941158

Order 1280.

908 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3561C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic, complemented
3C5×#3229C211yesmaximal, characteristic, complemented
4C5×#2640C211yesmaximal, characteristic, complemented
5C5×#1612C214yesmaximal, complemented
6C5×#1608C214yesmaximal, complemented
7C5×#1506C211yesmaximal, characteristic, complemented
8C5×#1500C211yesmaximal, characteristic, complemented
9C5×#1469C211yesmaximal, characteristic, complemented
10C5×#563—21no—
11C5×#562—21no—
12C5×#556—21no—
13C5×#551—22no—
14C5×D4×Q8—21no—
15C5×#548—21no—
16C5×#546—21no—
17C5×#543C2212yes—
18C5×#542—21no—
19C5×#542—22no—
20C5×#538C2212yes—
21C5×#536—21no—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#124C2211yescharacteristic
26C5×#501—21no—
27C5×#498—21no—
28C5×#489—21no—
29C5×#487—21no—
30C5×#483C2212yes—
31C5×#483C2214yes—
32C5×#480C2212yes—
33C5×#477—21no—
34C5×#476—21no—
35C5×#475—22no—
36C5×#432C2211yescharacteristic
37C5×#431C2211yescharacteristic
38C5×#397C2214yes—
39C5×#393—22no—
40C5×#391—21no—
41C5×#390—21no—
42C5×#376C2211yescharacteristic
43C5×#328C2212yes—
44C5×#328C2214yes—
45C5×#327C2212yes—
46C5×#323C2214yes—
47#18438C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—21no—
49C22×C5×Q8—21no—
50C22×C5×Q8—21no—
51C22×C5×Q8D411yescharacteristic
52C22×C5×D4D411yescharacteristic
53C5×C4⋊Q8—21no—
54C5×C4⋊Q8—22no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8—21no—
58C5×C4⋊Q8—21no—
59C5×C4⋊Q8D411yescharacteristic
60C5×C4⋊Q8D411yescharacteristic
61C5×#126—22no—
62C5×#126—22no—
63C5×#126—22no—
64C5×#126—21no—
65C5×#125—21no—
66C5×#125D411yescharacteristic
67C5×#124—21no—
68C5×#124—22no—
69C5×#124—22no—
70C5×#124—21no—
71C5×#124—21no—
72C5×#124—21no—
73C5×#124—21no—
74C5×#124D411yescharacteristic
75C5×#123—22no—
76C5×#123—22no—
77C5×#123—22no—
78C5×#123—21no—
79C5×#123—22no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8C2311yescharacteristic
90C5×C22⋊Q8C2312yes—
91C5×#121—21no—
92C5×#121—22no—
93C5×#121—22no—
94C5×#121C2311yescharacteristic
95C5×#120—22no—
96C4×C5×Q8—21no—
97C4×C5×Q8—21no—
98C4×C5×Q8D412yes—
99C4×C5×Q8D411yescharacteristic
100C4×C5×D4—21no—
101C4×C5×D4—22no—
102C4×C5×D4—21no—
103C4×C5×D4—22no—
104C4×C5×D4D411yescharacteristic
105C5×#117—22no—
106C5×#117—21no—
107C5×#117—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4C2312yes—
110C2×C5×C22⋊C4—22no—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4D412yes—
113C2×C5×C22⋊C4C2312yes—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C5×#107—22no—
117C5×#106—24no—
118C5×#106—22no—
119C5×C4⋊C8—21no—
120C5×C4⋊C8—21no—
121C5×#103—24no—
122C5×#103—22no—
123C5×#102—22no—
124C5×C22⋊C8C2312yes—
125C5×C22⋊C8C2312yes—
126C5×#97—21no—
127C4×C5×C8—21no—
128C5×#95—21no—
129C5×#95—24no—
130C5×#95C2312yes—
131#3561C2×C511yescharacteristic
132#3238C2×C511yescharacteristic, complemented
133#3229C2×C511yescharacteristic, complemented
134#2640C2×C511yescharacteristic, complemented
135#1612C2×C514yescomplemented
136#1608C2×C514yescomplemented
137#1506C2×C511yescharacteristic, complemented
138#1500C2×C511yescharacteristic, complemented
139#1469C2×C511yescharacteristic, complemented
140C24×C5C2×D412yes—
141C5×#41—82no—
142C2×C5×Q8—22no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8—42no—
147C2×C5×Q8—41no—
148C2×C5×Q8—41no—
149C2×C5×Q8—82no—
150C2×C5×Q8—82no—
151C2×C5×Q8C2×D411yescharacteristic
152C2×C5×Q8C2×D412yes—
153C2×C5×D4—21no—
154C2×C5×D4—22no—
155C2×C5×D4—22no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—42no—
159C2×C5×D4C2×D411yescharacteristic
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—21no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D412yes—
169C22×C4×C5C2411yescharacteristic
170C2×C5×C8—22no—
171C2×C5×C8—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—22no—
187C5×C4⋊C4—41no—
188C5×C4⋊C4—41no—
189C5×C4⋊C4C2×D411yescharacteristic
190C5×C4⋊C4C2×D411yescharacteristic
191C5×C4⋊C4C2×D412yes—
192C5×C22⋊C4—22no—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—22no—
201C5×C22⋊C4—21no—
202C5×C22⋊C4—21no—
203C5×C22⋊C4—21no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—22no—
206C5×C22⋊C4—21no—
207C5×C22⋊C4—84no—
208C42×C5—22no—
209C42×C5—22no—
210C42×C5—21no—
211C42×C5—42no—
212C42×C5C2×D411yescharacteristic
213C42×C5C2×D411yescharacteristic
214C42×C5C2×D411yescharacteristic
215C42×C5C2×D411yescharacteristic
216#563—21no—
217#562—21no—
218#556—21no—
219#551—22no—
220D4×Q8—21no—
221#548—21no—
222#546—21no—
223#543C22×C512yes—
224#542—21no—
225#542—22no—
226#538C22×C512yes—
227#536—21no—
228#533C22×C511yescharacteristic
229C2×C4⋊Q8C22×C511yescharacteristic
230#529C22×C511yescharacteristic
231C2×#124C22×C511yescharacteristic
232#501—21no—
233#498—21no—
234#489—21no—
235#487—21no—
236#483C22×C512yes—
237#483C22×C514yes—
238#480C22×C512yes—
239#477—21no—
240#476—21no—
241#475—22no—
242#432C22×C511yescharacteristic
243#431C22×C511yescharacteristic
244#397C22×C514yes—
245#393—22no—
246#391—21no—
247#390—21no—
248#376C22×C511yescharacteristic
249#328C22×C512yes—
250#328C22×C514yes—
251#327C22×C512yes—
252#323C22×C514yes—
253C23×C5—22no—
254C23×C5—21no—
255C23×C5—24no—
256C23×C5—42no—
257C23×C5—42no—
258C23×C5C22×D411yescharacteristic
259C5×Q8—41no—
260C5×Q8—42no—
261C5×Q8—42no—
262C5×Q8—42no—
263C5×Q8—81no—
264C5×Q8—82no—
265C5×Q8—82no—
266C5×Q8—82no—
267C5×D4—41no—
268C5×D4—42no—
269C5×D4—42no—
270C5×D4—81no—
271C5×D4—82no—
272C5×D4—82no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—21no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—41no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—42no—
288C2×C4×C5—44no—
289C2×C4×C5—82no—
290C2×C4×C5—82no—
291C2×C4×C5—82no—
292C2×C4×C5#12011yescharacteristic
293C2×C4×C5#12011yescharacteristic
294C2×C4×C5#12011yescharacteristic
295C2×C4×C5#12011yescharacteristic
296C2×C4×C5C22×D411yescharacteristic
297C2×C4×C5C22×D411yescharacteristic
298C5×C8—42no—
299C5×C8—42no—
300C2×#41—21no—
301C22×Q8—21no—
302C22×Q8—21no—
303C22×Q8C5×D411yescharacteristic
304C22×D4C5×D411yescharacteristic
305C4⋊Q8—21no—
306C4⋊Q8—22no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C5×D411yescharacteristic
312C4⋊Q8C5×D411yescharacteristic
313#126—22no—
314#126—22no—
315#126—22no—
316#126—21no—
317#125—21no—
318#125C5×D411yescharacteristic
319#124—21no—
320#124—22no—
321#124—22no—
322#124—21no—
323#124—21no—
324#124—21no—
325#124—21no—
326#124C5×D411yescharacteristic
327#123—22no—
328#123—22no—
329#123—22no—
330#123—21no—
331#123—22no—
332C22⋊Q8—22no—
333C22⋊Q8—21no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—21no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8C23×C511yescharacteristic
342C22⋊Q8C23×C512yes—
343#121—21no—
344#121—22no—
345#121—22no—
346#121C23×C511yescharacteristic
347#120—22no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8C5×D411yescharacteristic
351C4×Q8C5×D412yes—
352C4×D4—21no—
353C4×D4—22no—
354C4×D4—21no—
355C4×D4—22no—
356C4×D4C5×D411yescharacteristic
357#117—22no—
358#117—21no—
359#117—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C512yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4C5×D412yes—
365C2×C22⋊C4C23×C512yes—
366C2×C42—21no—
367C2×C42C23×C511yescharacteristic
368#107—22no—
369#106—24no—
370#106—22no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373#103—24no—
374#103—22no—
375#102—22no—
376C22⋊C8C23×C512yes—
377C22⋊C8C23×C512yes—
378#97—21no—
379C4×C8—21no—
380#95—21no—
381#95—24no—
382#95C23×C512yes—
383C22×C5—21no—
384C22×C5—21no—
385C22×C5—41no—
386C22×C5—42no—
387C22×C5—41no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—41no—
391C22×C5—84no—
392C22×C5C2×#12011yescharacteristic
393C22×C5#57712yes—
394C4×C5—21no—
395C4×C5—21no—
396C4×C5—21no—
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—41no—
404C4×C5—42no—
405C4×C5—82no—
406C4×C5—82no—
407C4×C5#45512yes—
408C24C2×C5×D412yes—
409#41—82no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—82no—
418C2×Q8—82no—
419C2×Q8C2×C5×D411yescharacteristic
420C2×Q8C2×C5×D412yes—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—42no—
427C2×D4C2×C5×D411yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4C2×C5×D411yescharacteristic
435C22×C4C2×C5×D411yescharacteristic
436C22×C4C2×C5×D412yes—
437C22×C4C24×C511yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4C2×C5×D411yescharacteristic
458C4⋊C4C2×C5×D412yes—
459C4⋊C4C2×C5×D411yescharacteristic
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—21no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C22⋊C4—84no—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—42no—
480C42C2×C5×D411yescharacteristic
481C42C2×C5×D411yescharacteristic
482C42C2×C5×D411yescharacteristic
483C42C2×C5×D411yescharacteristic
484C2×C5—22no—
485C2×C5—81no—
486C2×C5—82no—
487C2×C5#301011yescharacteristic
488C2×C5C2×#45511yescharacteristic
489C2×C5#302811yescharacteristic
490C23—22no—
491C23—21no—
492C23—24no—
493C23—42no—
494C23—42no—
495C23C22×C5×D411yescharacteristic
496Q8—41no—
497Q8—42no—
498Q8—42no—
499Q8—42no—
500Q8—81no—
501Q8—82no—
502Q8—82no—
503Q8—82no—
504D4—41no—
505D4—42no—
506D4—42no—
507D4—81no—
508D4—82no—
509D4—82no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C5×#12011yescharacteristic
530C2×C4C5×#12011yescharacteristic
531C2×C4C5×#12011yescharacteristic
532C2×C4C5×#12011yescharacteristic
533C2×C4C22×C5×D411yescharacteristic
534C2×C4C22×C5×D411yescharacteristic
535C8—42no—
536C8—42no—
537C5#1843811yescharacteristic, direct product factor, Sylow
538C22—21no—
539C22—21no—
540C22—41no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—42no—
545C22—41no—
546C22—84no—
547C22C2×C5×#12011yescharacteristic
548C22C5×#57712yes—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—42no—
560C4—82no—
561C4—82no—
562C4C5×#45512yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C5×#301011yescharacteristic
567C2C2×C5×#45511yescharacteristic
568C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3561C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3238C2semidirect
3. C5×#3229C2semidirect
4. C5×#2640C2semidirect
5. C5×#1612C2semidirect
6. C5×#1608C2semidirect
7. C5×#1506C2semidirect
8. C5×#1500C2semidirect
9. C5×#1469C2semidirect
47. #18438C5direct (N × H)
132. #3238C2×C5semidirect
133. #3229C2×C5semidirect
134. #2640C2×C5semidirect
135. #1612C2×C5semidirect
136. #1608C2×C5semidirect
137. #1506C2×C5semidirect
138. #1500C2×C5semidirect
139. #1469C2×C5semidirect
537. C5#18438direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35612
C5×#32382
C5×#32292
C5×#26402
C5×#16122
C5×#16082
C5×#15062
C5×#15002
C5×#14692
#184385