Finite Group Databasebeta

← C5×#18442 #11941162

Subgroups — C5×#18442 #11941162

Order 1280.

848 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3563C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic
3C5×#3229C211yesmaximal, characteristic, complemented
4C5×#2660C211yesmaximal, characteristic, complemented
5C5×#1611C214yesmaximal, complemented
6C5×#1609C214yesmaximal
7C5×#1506C211yesmaximal, characteristic, complemented
8C5×#1500C211yesmaximal, characteristic
9C5×#1470C211yesmaximal, characteristic, complemented
10C5×#564—21no—
11C5×#563—21no—
12C5×#557—21no—
13C5×#554—21no—
14C5×#552—21no—
15C5×#552—21no—
16C5×#552—22no—
17C5×#544—21no—
18C5×#544C2212yes—
19C5×#541—21no—
20C5×#541—22no—
21C5×#539C2212yes—
22C5×#533C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#125C2211yescharacteristic
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×#398C2214yes—
39C5×#395—22no—
40C5×#384—21no—
41C5×#382—21no—
42C5×#376C2211yescharacteristic
43C5×#328C2212yes—
44C5×#328C2214yes—
45C5×#327C2212yes—
46C5×#324C2214yes—
47#18442C511yesmaximal, characteristic, direct product factor, Sylow
48C22×C5×Q8—21no—
49C5×C4⋊Q8—21no—
50C5×C4⋊Q8—22no—
51C5×C4⋊Q8—22no—
52C5×C4⋊Q8—21no—
53C5×C4⋊Q8—21no—
54C5×C4⋊Q8—21no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8D411yescharacteristic
57C5×C4⋊Q8D411yescharacteristic
58C5×#126—22no—
59C5×#126—22no—
60C5×#126—22no—
61C5×#126—22no—
62C5×#126—21no—
63C5×#125—22no—
64C5×#125—22no—
65C5×#125—22no—
66C5×#125—22no—
67C5×#125—21no—
68C5×#125—22no—
69C5×#125—22no—
70C5×#125—22no—
71C5×#125—22no—
72C5×#125—21no—
73C5×#125—21no—
74C5×#125—21no—
75C5×#125—21no—
76C5×#125—21no—
77C5×#125D411yescharacteristic
78C5×#124D411yescharacteristic
79C5×#123—22no—
80C5×#123—21no—
81C5×#123—22no—
82C5×C22⋊Q8—21no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—21no—
88C5×C22⋊Q8—22no—
89C5×C22⋊Q8C2311yescharacteristic
90C5×C22⋊Q8C2312yes—
91C5×#121C2311yescharacteristic
92C4×C5×Q8—21no—
93C4×C5×Q8—22no—
94C4×C5×Q8—21no—
95C4×C5×Q8—21no—
96C4×C5×Q8D412yes—
97C4×C5×Q8D411yescharacteristic
98C4×C5×D4—21no—
99C4×C5×D4—22no—
100C4×C5×D4D411yescharacteristic
101C5×#117—22no—
102C5×#117—21no—
103C5×#117—21no—
104C5×#117—22no—
105C5×#117—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—24no—
109C2×C5×C4⋊C4D411yescharacteristic
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D412yes—
112C2×C5×C4⋊C4C2312yes—
113C2×C5×C4⋊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#3563C2×C511yescharacteristic
132#3238C2×C511yescharacteristic
133#3229C2×C511yescharacteristic, complemented
134#2660C2×C511yescharacteristic, complemented
135#1611C2×C514yescomplemented
136#1609C2×C514yes—
137#1506C2×C511yescharacteristic, complemented
138#1500C2×C511yescharacteristic
139#1470C2×C511yescharacteristic, complemented
140C2×C5×Q8—22no—
141C2×C5×Q8—21no—
142C2×C5×Q8—41no—
143C2×C5×Q8—41no—
144C2×C5×Q8—82no—
145C2×C5×Q8C2×D412yes—
146C2×C5×Q8C2×D411yescharacteristic
147C2×C5×D4—21no—
148C2×C5×D4C2×D411yescharacteristic
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2411yescharacteristic
158C2×C5×C8—22no—
159C2×C5×C8—22no—
160C5×C4⋊C4—22no—
161C5×C4⋊C4—22no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—22no—
167C5×C4⋊C4—22no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
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⋊C4—84no—
190C5×C4⋊C4C2×D411yescharacteristic
191C5×C4⋊C4C2×D411yescharacteristic
192C5×C4⋊C4C2×D412yes—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—22no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4—21no—
201C5×C22⋊C4—21no—
202C42×C5—24no—
203C42×C5—22no—
204C42×C5—22no—
205C42×C5—22no—
206C42×C5—22no—
207C42×C5—21no—
208C42×C5C2×D411yescharacteristic
209C42×C5C2×D411yescharacteristic
210C42×C5C2×D411yescharacteristic
211C42×C5C2×D411yescharacteristic
212#564—21no—
213#563—21no—
214#557—21no—
215#554—21no—
216#552—21no—
217#552—21no—
218#552—22no—
219#544—21no—
220#544C22×C512yes—
221#541—21no—
222#541—22no—
223#539C22×C512yes—
224#533C22×C511yescharacteristic
225C2×C4⋊Q8C22×C511yescharacteristic
226#529C22×C511yescharacteristic
227C2×#125C22×C511yescharacteristic
228#501—21no—
229#498—21no—
230#489—21no—
231#487—21no—
232#483C22×C514yes—
233#483C22×C512yes—
234#480C22×C512yes—
235#477—21no—
236#476—21no—
237#475—22no—
238#432C22×C511yescharacteristic
239#431C22×C511yescharacteristic
240#398C22×C514yes—
241#395—22no—
242#384—21no—
243#382—21no—
244#376C22×C511yescharacteristic
245#328C22×C514yes—
246#328C22×C512yes—
247#327C22×C512yes—
248#324C22×C514yes—
249C23×C5—21no—
250C23×C5C22×D411yescharacteristic
251C5×Q8—41no—
252C5×Q8—42no—
253C5×Q8—42no—
254C5×Q8—82no—
255C5×Q8—82no—
256C5×Q8—82no—
257C5×D4—41no—
258C5×D4—42no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—24no—
262C2×C4×C5—22no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
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—44no—
277C2×C4×C5—82no—
278C2×C4×C5#12011yescharacteristic
279C2×C4×C5#12011yescharacteristic
280C2×C4×C5#12011yescharacteristic
281C2×C4×C5#12011yescharacteristic
282C2×C4×C5C22×D411yescharacteristic
283C2×C4×C5C22×D411yescharacteristic
284C5×C8—42no—
285C5×C8—42no—
286C22×Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C5×D411yescharacteristic
295C4⋊Q8C5×D411yescharacteristic
296#126—22no—
297#126—22no—
298#126—22no—
299#126—22no—
300#126—21no—
301#125—22no—
302#125—22no—
303#125—22no—
304#125—22no—
305#125—21no—
306#125—22no—
307#125—22no—
308#125—22no—
309#125—22no—
310#125—21no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125—21no—
315#125C5×D411yescharacteristic
316#124C5×D411yescharacteristic
317#123—22no—
318#123—21no—
319#123—22no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—21no—
326C22⋊Q8—22no—
327C22⋊Q8C23×C511yescharacteristic
328C22⋊Q8C23×C512yes—
329#121C23×C511yescharacteristic
330C4×Q8—21no—
331C4×Q8—22no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8C5×D411yescharacteristic
335C4×Q8C5×D412yes—
336C4×D4—21no—
337C4×D4—22no—
338C4×D4C5×D411yescharacteristic
339#117—22no—
340#117—21no—
341#117—21no—
342#117—22no—
343#117—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4C5×D411yescharacteristic
348C2×C4⋊C4C5×D412yes—
349C2×C4⋊C4C5×D411yescharacteristic
350C2×C4⋊C4C23×C512yes—
351C2×C4⋊C4C23×C512yes—
352C2×C42—21no—
353C2×C42C23×C511yescharacteristic
354#107—22no—
355#106—24no—
356#106—22no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359#103—24no—
360#103—22no—
361#102—22no—
362C22⋊C8C23×C512yes—
363C22⋊C8C23×C512yes—
364#97—21no—
365C4×C8—21no—
366#95—21no—
367#95—24no—
368#95C23×C512yes—
369C22×C5—21no—
370C22×C5—21no—
371C22×C5—41no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5C2×#12011yescharacteristic
375C22×C5#57712yes—
376C4×C5—21no—
377C4×C5—21no—
378C4×C5—21no—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—44no—
382C4×C5—42no—
383C4×C5—41no—
384C4×C5—41no—
385C4×C5—42no—
386C4×C5—42no—
387C4×C5—42no—
388C4×C5—41no—
389C4×C5—82no—
390C4×C5#45612yes—
391C2×Q8—22no—
392C2×Q8—21no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—82no—
396C2×Q8C2×C5×D412yes—
397C2×Q8C2×C5×D411yescharacteristic
398C2×D4—21no—
399C2×D4C2×C5×D411yescharacteristic
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4C2×C5×D412yes—
405C22×C4C2×C5×D411yescharacteristic
406C22×C4C2×C5×D411yescharacteristic
407C22×C4C2×C5×D412yes—
408C22×C4C24×C511yescharacteristic
409C2×C8—22no—
410C2×C8—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—84no—
441C4⋊C4C2×C5×D411yescharacteristic
442C4⋊C4C2×C5×D412yes—
443C4⋊C4C2×C5×D411yescharacteristic
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C42—24no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42—21no—
459C42C2×C5×D411yescharacteristic
460C42C2×C5×D411yescharacteristic
461C42C2×C5×D411yescharacteristic
462C42C2×C5×D411yescharacteristic
463C2×C5—22no—
464C2×C5—81no—
465C2×C5#301011yescharacteristic
466C2×C5C2×#45611yescharacteristic
467C2×C5#302811yescharacteristic
468C23—21no—
469C23C22×C5×D411yescharacteristic
470Q8—41no—
471Q8—42no—
472Q8—42no—
473Q8—82no—
474Q8—82no—
475Q8—82no—
476D4—41no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—82no—
497C2×C4C5×#12011yescharacteristic
498C2×C4C5×#12011yescharacteristic
499C2×C4C5×#12011yescharacteristic
500C2×C4C5×#12011yescharacteristic
501C2×C4C22×C5×D411yescharacteristic
502C2×C4C22×C5×D411yescharacteristic
503C8—42no—
504C8—42no—
505C5#1844211yescharacteristic, direct product factor, Sylow
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22C2×C5×#12011yescharacteristic
512C22C5×#57712yes—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—44no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—82no—
527C4C5×#45612yes—
528C2—22no—
529C2—81no—
530C2C5×#301011yescharacteristic
531C2C2×C5×#45611yescharacteristic
532C2C5×#302811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#121C23
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
3. C5×#3229C2semidirect
4. C5×#2660C2semidirect
5. C5×#1611C2semidirect
7. C5×#1506C2semidirect
9. C5×#1470C2semidirect
47. #18442C5direct (N × H)
133. #3229C2×C5semidirect
134. #2660C2×C5semidirect
135. #1611C2×C5semidirect
137. #1506C2×C5semidirect
139. #1470C2×C5semidirect
505. C5#18442direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35632
C5×#32382
C5×#32292
C5×#26602
C5×#16112
C5×#16092
C5×#15062
C5×#15002
C5×#14702
#184425