Finite Group Databasebeta

← C5×#19023 #11941743

Subgroups — C5×#19023 #11941743

Order 1280.

880 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3559C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3141C211yesmaximal, characteristic, complemented
4C2×C5×#491C211yesmaximal, characteristic, complemented
5C5×#1664C214yesmaximal, complemented
6C5×#1662C214yesmaximal, complemented
7C5×#1530C211yesmaximal, characteristic, complemented
8C5×#1528C211yesmaximal, characteristic, complemented
9C5×#1524C211yesmaximal, characteristic, complemented
10C5×#563C2212yes—
11C5×#562C2212yes—
12C5×#554—21no—
13C5×#553—21no—
14C5×#553—21no—
15C5×#547—22no—
16C5×#547—21no—
17C5×#544—21no—
18C5×#540—21no—
19C5×#539—22no—
20C5×#539—21no—
21C5×#537—21no—
22C5×#532C2211yescharacteristic
23C2×C5×C4⋊Q8C2211yescharacteristic
24C5×#529C2211yescharacteristic
25C2×C5×#125C2211yescharacteristic
26C5×#501C2212yes—
27C5×#491—22no—
28C5×#491C2214yes—
29C5×#489C2212yes—
30C5×#489C2214yes—
31C5×#487—21no—
32C5×#486—21no—
33C5×#484—21no—
34C5×#481—21no—
35C5×#475—21no—
36C5×#474—21no—
37C5×#432C2211yescharacteristic
38C5×#417—22no—
39C2×C5×#103—21no—
40C2×C5×#103—21no—
41C4×C5×M16C2211yescharacteristic
42C2×C5×#97C2211yescharacteristic
43C5×#330C2212yes—
44C5×#330C2214yes—
45C5×#329C2212yes—
46C5×#329C2214yes—
47#19023C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41—22no—
49C2×C5×#41D412yes—
50C22×C5×Q8—21no—
51C2×C5×M16—21no—
52C22×C5×C8—21no—
53C5×C4⋊Q8—21no—
54C5×C4⋊Q8—22no—
55C5×C4⋊Q8—21no—
56C5×C4⋊Q8—21no—
57C5×C4⋊Q8—21no—
58C5×C4⋊Q8D411yescharacteristic
59C5×C4⋊Q8C2312yes—
60C5×#127D411yescharacteristic
61C5×#126—22no—
62C5×#126—22no—
63C5×#126—21no—
64C5×#125—22no—
65C5×#125—21no—
66C5×#125—21no—
67C5×#125—21no—
68C5×#125D412yes—
69C5×#125C2312yes—
70C5×#125C2311yescharacteristic
71C5×#124C2311yescharacteristic
72C5×#124C2312yes—
73C5×#123—22no—
74C5×#123—22no—
75C5×#123—22no—
76C5×#123—22no—
77C5×#123—21no—
78C5×#123—22no—
79C5×#123—22no—
80C5×C22⋊Q8—22no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8D411yescharacteristic
87C5×#121—22no—
88C5×#121—22no—
89C5×#121—21no—
90C5×#121—21no—
91C5×#121—22no—
92C5×#121—22no—
93C5×#121—21no—
94C5×#121—21no—
95C5×#121D411yescharacteristic
96C4×C5×Q8D411yescharacteristic
97C4×C5×D4—22no—
98C4×C5×D4—22no—
99C4×C5×D4—21no—
100C4×C5×D4—21no—
101C4×C5×D4—21no—
102C4×C5×D4—21no—
103C4×C5×D4—21no—
104C4×C5×D4D411yescharacteristic
105C5×#117—21no—
106C5×#117—21no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C5×#107—22no—
117C5×#106—22no—
118C5×C4⋊C8—21no—
119C5×#103—24no—
120C5×#103—22no—
121C5×#103—24no—
122C5×#103—24no—
123C5×#102—24no—
124C5×#102—22no—
125C5×C22⋊C8—21no—
126C5×#97—21no—
127C5×#97C2312yes—
128C5×#97C2312yes—
129C5×#97C2312yes—
130C4×C5×C8—21no—
131#3559C2×C511yescharacteristic
132#3239C2×C511yescharacteristic, complemented
133#3141C2×C511yescharacteristic, complemented
134C2×#491C2×C511yescharacteristic, complemented
135#1664C2×C514yescomplemented
136#1662C2×C514yescomplemented
137#1530C2×C511yescharacteristic, complemented
138#1528C2×C511yescharacteristic, complemented
139#1524C2×C511yescharacteristic, complemented
140C5×#41—44no—
141C5×#41—84no—
142C2×C5×Q8—22no—
143C2×C5×Q8—22no—
144C2×C5×Q8—44no—
145C2×C5×Q8—41no—
146C2×C5×Q8C2×D411yescharacteristic
147C2×C5×Q8C2×D412yes—
148C2×C5×D4—22no—
149C2×C5×D4—21no—
150C2×C5×D4—22no—
151C2×C5×D4—22no—
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4C2×D411yescharacteristic
155C2×C5×D4C2×D412yes—
156C22×C4×C5—21no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—22no—
163C22×C4×C5—41no—
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C5×M16—42no—
168C2×C5×C8—22no—
169C2×C5×C8—22no—
170C2×C5×C8—22no—
171C2×C5×C8—42no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—41no—
191C5×C4⋊C4—41no—
192C5×C4⋊C4C2×D412yes—
193C5×C4⋊C4C2×D412yes—
194C5×C4⋊C4C2×D411yescharacteristic
195C5×C4⋊C4C2×D411yescharacteristic
196C5×C22⋊C4—22no—
197C5×C22⋊C4—22no—
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—21no—
205C5×C22⋊C4—22no—
206C5×C22⋊C4—22no—
207C5×C22⋊C4—21no—
208C42×C5—22no—
209C42×C5—21no—
210C42×C5C2×D411yescharacteristic
211C42×C5C2×D411yescharacteristic
212C42×C5C2×D411yescharacteristic
213C42×C5C2411yescharacteristic
214#563C22×C512yes—
215#562C22×C512yes—
216#554—21no—
217#553—21no—
218#553—21no—
219#547—22no—
220#547—21no—
221#544—21no—
222#540—21no—
223#539—22no—
224#539—21no—
225#537—21no—
226#532C22×C511yescharacteristic
227C2×C4⋊Q8C22×C511yescharacteristic
228#529C22×C511yescharacteristic
229C2×#125C22×C511yescharacteristic
230#501C22×C512yes—
231#491—22no—
232#491C22×C514yes—
233#489C22×C514yes—
234#489C22×C512yes—
235#487—21no—
236#486—21no—
237#484—21no—
238#481—21no—
239#475—21no—
240#474—21no—
241#432C22×C511yescharacteristic
242#417—22no—
243C2×#103—21no—
244C2×#103—21no—
245C4×M16C22×C511yescharacteristic
246C2×#97C22×C511yescharacteristic
247#330C22×C514yes—
248#330C22×C512yes—
249#329C22×C512yes—
250#329C22×C514yes—
251C23×C5—22no—
252C23×C5—21no—
253C23×C5#12011yescharacteristic
254C5×Q8—41no—
255C5×Q8—42no—
256C5×Q8—44no—
257C5×Q8—82no—
258C5×Q8—82no—
259C5×D4—41no—
260C5×D4—42no—
261C5×D4—44no—
262C5×D4—42no—
263C5×D4—42no—
264C5×D4—81no—
265C5×D4—82no—
266C5×D4—82no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—41no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—82no—
280C2×C4×C5—81no—
281C2×C4×C5—82no—
282C2×C4×C5—82no—
283C2×C4×C5—82no—
284C2×C4×C5—82no—
285C2×C4×C5#12011yescharacteristic
286C2×C4×C5#12011yescharacteristic
287C2×C4×C5#12011yescharacteristic
288C2×C4×C5C22×D411yescharacteristic
289C2×C4×C5C22×D411yescharacteristic
290C2×C4×C5C22×D411yescharacteristic
291C5×C8—42no—
292C5×C8—42no—
293C5×C8—42no—
294C2×#41—22no—
295C2×#41C5×D412yes—
296C22×Q8—21no—
297C2×M16—21no—
298C22×C8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—22no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C5×D411yescharacteristic
305C4⋊Q8C23×C512yes—
306#127C5×D411yescharacteristic
307#126—22no—
308#126—22no—
309#126—21no—
310#125—22no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125C5×D412yes—
315#125C23×C512yes—
316#125C23×C511yescharacteristic
317#124C23×C511yescharacteristic
318#124C23×C512yes—
319#123—22no—
320#123—22no—
321#123—22no—
322#123—22no—
323#123—21no—
324#123—22no—
325#123—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8C5×D411yescharacteristic
333#121—22no—
334#121—22no—
335#121—21no—
336#121—21no—
337#121—22no—
338#121—22no—
339#121—21no—
340#121—21no—
341#121C5×D411yescharacteristic
342C4×Q8C5×D411yescharacteristic
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4C5×D411yescharacteristic
351#117—21no—
352#117—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4C5×D411yescharacteristic
360C2×C4⋊C4C5×D411yescharacteristic
361C2×C42C23×C511yescharacteristic
362#107—22no—
363#106—22no—
364C4⋊C8—21no—
365#103—24no—
366#103—22no—
367#103—24no—
368#103—24no—
369#102—24no—
370#102—22no—
371C22⋊C8—21no—
372#97—21no—
373#97C23×C512yes—
374#97C23×C512yes—
375#97C23×C512yes—
376C4×C8—21no—
377C22×C5—21no—
378C22×C5—21no—
379C22×C5—42no—
380C22×C5—41no—
381C22×C5—41no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5—41no—
385C22×C5#45512yes—
386C22×C5C2×#12011yescharacteristic
387C4×C5—21no—
388C4×C5—21no—
389C4×C5—21no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—42no—
393C4×C5—42no—
394C4×C5—41no—
395C4×C5—41no—
396C4×C5—42no—
397C4×C5—41no—
398C4×C5—82no—
399C4×C5#45412yes—
400#41—44no—
401#41—84no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—44no—
405C2×Q8—41no—
406C2×Q8C2×C5×D411yescharacteristic
407C2×Q8C2×C5×D412yes—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4C2×C5×D411yescharacteristic
415C2×D4C2×C5×D412yes—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4C2×C5×D411yescharacteristic
425C22×C4C2×C5×D411yescharacteristic
426C22×C4C2×C5×D411yescharacteristic
427M16—42no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—42no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4C2×C5×D412yes—
453C4⋊C4C2×C5×D412yes—
454C4⋊C4C2×C5×D411yescharacteristic
455C4⋊C4C2×C5×D411yescharacteristic
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—21no—
468C42—22no—
469C42—21no—
470C42C2×C5×D411yescharacteristic
471C42C2×C5×D411yescharacteristic
472C42C2×C5×D411yescharacteristic
473C42C24×C511yescharacteristic
474C2×C5—22no—
475C2×C5—82no—
476C2×C5—81no—
477C2×C5C2×#45511yescharacteristic
478C2×C5C2×#45411yescharacteristic
479C2×C5#302211yescharacteristic
480C23—22no—
481C23—21no—
482C23C5×#12011yescharacteristic
483Q8—42no—
484Q8—41no—
485Q8—44no—
486Q8—82no—
487Q8—82no—
488D4—42no—
489D4—41no—
490D4—44no—
491D4—42no—
492D4—42no—
493D4—81no—
494D4—82no—
495D4—82no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4—81no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4C5×#12011yescharacteristic
515C2×C4C5×#12011yescharacteristic
516C2×C4C5×#12011yescharacteristic
517C2×C4C22×C5×D411yescharacteristic
518C2×C4C22×C5×D411yescharacteristic
519C2×C4C22×C5×D411yescharacteristic
520C8—42no—
521C8—42no—
522C8—42no—
523C5#1902311yescharacteristic, direct product factor, Sylow
524C22—21no—
525C22—21no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22C5×#45512yes—
533C22C2×C5×#12011yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—42no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—41no—
545C4—82no—
546C4C5×#45412yes—
547C2—22no—
548C2—82no—
549C2—81no—
550C2C2×C5×#45511yescharacteristic
551C2C2×C5×#45411yescharacteristic
552C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3559C2
LCSG ▷ C42 ▷ 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×#3239C2semidirect
3. C5×#3141C2semidirect
4. C2×C5×#491C2semidirect
5. C5×#1664C2semidirect
6. C5×#1662C2semidirect
7. C5×#1530C2semidirect
8. C5×#1528C2semidirect
9. C5×#1524C2semidirect
47. #19023C5direct (N × H)
132. #3239C2×C5semidirect
133. #3141C2×C5semidirect
134. C2×#491C2×C5semidirect
135. #1664C2×C5semidirect
136. #1662C2×C5semidirect
137. #1530C2×C5semidirect
138. #1528C2×C5semidirect
139. #1524C2×C5semidirect
523. C5#19023direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35592
C5×#32392
C5×#31412
C2×C5×#4912
C5×#16642
C5×#16622
C5×#15302
C5×#15282
C5×#15242
#190235