Finite Group Databasebeta

← C5×#19311 #11942031

Subgroups — C5×#19311 #11942031

Order 1280.

578 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3185C211yesmaximal, characteristic
2C5×#3113C211yesmaximal, characteristic
3C5×#3078C211yesmaximal, characteristic
4C5×Q8×M16C211yesmaximal, characteristic
5C5×#1704C211yesmaximal, characteristic, complemented
6C5×#1700C211yesmaximal, characteristic, complemented
7C5×#1692C211yesmaximal, characteristic, complemented
8C5×#1690C211yesmaximal, characteristic, complemented
9C5×#1684C211yesmaximal, characteristic, complemented
10C5×#1680C211yesmaximal, characteristic, complemented
11C5×#1672C211yesmaximal, characteristic, complemented
12C5×#1670C211yesmaximal, characteristic, complemented
13C5×#1569C211yesmaximal, characteristic
14C5×#1561C211yesmaximal, characteristic
15C5×#1559C211yesmaximal, characteristic
16C5×#533C2211yescharacteristic
17C5×#533C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C5×#498C2211yescharacteristic
20C5×#494C2211yescharacteristic
21C5×#487C2211yescharacteristic
22C5×#487C2211yescharacteristic
23C5×#483—21no—
24C5×#479—21no—
25C5×#479—21no—
26C5×#477C2211yescharacteristic
27C5×#477C2211yescharacteristic
28C5×#475C2211yescharacteristic
29C5×#475C2211yescharacteristic
30C5×#475C2211yescharacteristic
31C5×#475C2211yescharacteristic
32C5×#470—21no—
33C5×#470—21no—
34C5×#462C2211yescharacteristic
35C5×#462C2211yescharacteristic
36C5×#451—21no—
37C5×#446—21no—
38C5×#446—21no—
39C5×#446C2211yescharacteristic
40C5×#446C2211yescharacteristic
41C5×C8×Q8C2211yescharacteristic
42C5×C8×Q8C2211yescharacteristic
43C5×#441—21no—
44C5×#441—21no—
45C5×#441—21no—
46C5×#441—21no—
47C5×#432C2211yescharacteristic
48C5×#428—21no—
49C5×#423—21no—
50C5×#423C2211yescharacteristic
51C5×#423C2211yescharacteristic
52C5×#419—21no—
53C4×C5×M16—21no—
54C4×C5×M16C2211yescharacteristic
55C5×#335C2211yescharacteristic
56C5×#335C2211yescharacteristic
57C5×#334C2211yescharacteristic
58C5×#334C2211yescharacteristic
59C5×#333C2211yescharacteristic
60C5×#333C2211yescharacteristic
61C5×#332C2211yescharacteristic
62C5×#332C2211yescharacteristic
63C5×#332C2211yescharacteristic
64C5×#332C2211yescharacteristic
65C5×#332C2211yescharacteristic
66C5×#332C2211yescharacteristic
67#19311C511yesmaximal, characteristic, direct product factor, Sylow
68C22×C5×Q8D411yescharacteristic
69C2×C5×Q16—21no—
70C2×C5×Q16—21no—
71C2×C5×Q16—21no—
72C2×C5×Q16—21no—
73C2×C5×M16—21no—
74C2×C5×M16—21no—
75C2×C5×M16D411yescharacteristic
76C2×C5×M16D411yescharacteristic
77C5×C4⋊Q8C2311yescharacteristic
78C5×C4⋊Q8C2311yescharacteristic
79C5×C4⋊Q8C2311yescharacteristic
80C5×C4⋊Q8C2311yescharacteristic
81C5×#125—21no—
82C5×#125—21no—
83C5×C22⋊Q8—21no—
84C5×C22⋊Q8—21no—
85C5×C22⋊Q8—21no—
86C5×C22⋊Q8—21no—
87C4×C5×Q8—21no—
88C4×C5×Q8—21no—
89C4×C5×Q8—21no—
90C4×C5×Q8—21no—
91C4×C5×Q8—21no—
92C4×C5×Q8—21no—
93C4×C5×Q8D411yescharacteristic
94C4×C5×Q8D411yescharacteristic
95C4×C5×Q8C2311yescharacteristic
96C4×C5×Q8C2311yescharacteristic
97C5×#117—21no—
98C5×#117—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4D411yescharacteristic
101C2×C42×C5—21no—
102C2×C42×C5C2311yescharacteristic
103C5×#107—21no—
104C5×#107—21no—
105C5×#106—21no—
106C5×#106—21no—
107C5×#106—21no—
108C5×#106—21no—
109C5×#106—21no—
110C5×#106—21no—
111C5×C4⋊C8—21no—
112C5×C4⋊C8—21no—
113C5×C4⋊C8—21no—
114C5×C4⋊C8—21no—
115C5×C4⋊C8—21no—
116C5×C4⋊C8—21no—
117C5×C4⋊C8C2311yescharacteristic
118C5×C4⋊C8C2311yescharacteristic
119C5×C4⋊C8C2311yescharacteristic
120C5×C4⋊C8C2311yescharacteristic
121C5×C4⋊C8C2311yescharacteristic
122C5×C4⋊C8C2311yescharacteristic
123C5×#103—21no—
124C5×#103—21no—
125C5×#103—21no—
126C5×#103—21no—
127C5×#103—21no—
128C5×#103—21no—
129C5×#103—21no—
130C5×#103—21no—
131C5×#103—21no—
132C5×#103—21no—
133C5×#103—21no—
134C5×#103—21no—
135C5×C22⋊C8—21no—
136C5×#97—21no—
137C5×#97—21no—
138C5×#97—21no—
139C5×#97D411yescharacteristic
140C5×#97D411yescharacteristic
141C4×C5×C8—21no—
142C4×C5×C8—21no—
143C4×C5×C8C2311yescharacteristic
144C4×C5×C8C2311yescharacteristic
145#3185C2×C511yescharacteristic
146#3113C2×C511yescharacteristic
147#3078C2×C511yescharacteristic
148Q8×M16C2×C511yescharacteristic
149#1704C2×C511yescharacteristic, complemented
150#1700C2×C511yescharacteristic, complemented
151#1692C2×C511yescharacteristic, complemented
152#1690C2×C511yescharacteristic, complemented
153#1684C2×C511yescharacteristic, complemented
154#1680C2×C511yescharacteristic, complemented
155#1672C2×C511yescharacteristic, complemented
156#1670C2×C511yescharacteristic, complemented
157#1569C2×C511yescharacteristic
158#1561C2×C511yescharacteristic
159#1559C2×C511yescharacteristic
160C2×C5×Q8—21no—
161C2×C5×Q8—22no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—41no—
167C2×C5×Q8C2×D411yescharacteristic
168C2×C5×Q8C2×D411yescharacteristic
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C5×Q16—42no—
175C5×Q16—42no—
176C5×Q16—42no—
177C5×Q16—42no—
178C5×M16—22no—
179C5×M16—41no—
180C5×M16—42no—
181C5×M16—42no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8C2×D411yescharacteristic
189C2×C5×C8C2×D411yescharacteristic
190C2×C5×C8C2×D411yescharacteristic
191C2×C5×C8C2×D411yescharacteristic
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—41no—
206C5×C4⋊C4—41no—
207C5×C4⋊C4—41no—
208C5×C4⋊C4—41no—
209C5×C4⋊C4C2×D411yescharacteristic
210C5×C4⋊C4C2×D411yescharacteristic
211C5×C22⋊C4—41no—
212C5×C22⋊C4—41no—
213C42×C5—21no—
214C42×C5—21no—
215C42×C5—21no—
216C42×C5—21no—
217C42×C5—41no—
218C42×C5—41no—
219C42×C5C2×D411yescharacteristic
220C42×C5C2×D411yescharacteristic
221C42×C5#4111yescharacteristic
222C42×C5C2411yescharacteristic
223#533C22×C511yescharacteristic
224#533C22×C511yescharacteristic
225C2×C4×Q8C22×C511yescharacteristic
226#498C22×C511yescharacteristic
227#494C22×C511yescharacteristic
228#487C22×C511yescharacteristic
229#487C22×C511yescharacteristic
230#483—21no—
231#479—21no—
232#479—21no—
233#477C22×C511yescharacteristic
234#477C22×C511yescharacteristic
235#475C22×C511yescharacteristic
236#475C22×C511yescharacteristic
237#475C22×C511yescharacteristic
238#475C22×C511yescharacteristic
239#470—21no—
240#470—21no—
241#462C22×C511yescharacteristic
242#462C22×C511yescharacteristic
243#451—21no—
244#446—21no—
245#446—21no—
246#446C22×C511yescharacteristic
247#446C22×C511yescharacteristic
248C8×Q8C22×C511yescharacteristic
249C8×Q8C22×C511yescharacteristic
250#441—21no—
251#441—21no—
252#441—21no—
253#441—21no—
254#432C22×C511yescharacteristic
255#428—21no—
256#423—21no—
257#423C22×C511yescharacteristic
258#423C22×C511yescharacteristic
259#419—21no—
260C4×M16—21no—
261C4×M16C22×C511yescharacteristic
262#335C22×C511yescharacteristic
263#335C22×C511yescharacteristic
264#334C22×C511yescharacteristic
265#334C22×C511yescharacteristic
266#333C22×C511yescharacteristic
267#333C22×C511yescharacteristic
268#332C22×C511yescharacteristic
269#332C22×C511yescharacteristic
270#332C22×C511yescharacteristic
271#332C22×C511yescharacteristic
272#332C22×C511yescharacteristic
273#332C22×C511yescharacteristic
274C23×C5#12111yescharacteristic
275C5×Q8—21no—
276C5×Q8—21no—
277C5×Q8—21no—
278C5×Q8—42no—
279C5×Q8—41no—
280C5×Q8—41no—
281C5×Q8—41no—
282C5×Q8—41no—
283C5×Q8—41no—
284C5×Q8—41no—
285C5×Q8—81no—
286C5×Q8#13712yes—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—41no—
296C2×C4×C5—42no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—81no—
302C2×C4×C5#12111yescharacteristic
303C2×C4×C5#12111yescharacteristic
304C2×C4×C5#12111yescharacteristic
305C2×C4×C5C22×D411yescharacteristic
306C2×C4×C5C22×D411yescharacteristic
307C2×C4×C5C2×#4111yescharacteristic
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—21no—
311C5×C8—41no—
312C5×C8—41no—
313C5×C8—41no—
314C5×C8—41no—
315C5×C8—41no—
316C5×C8—41no—
317C5×C8#13712yes—
318C22×Q8C5×D411yescharacteristic
319C2×Q16—21no—
320C2×Q16—21no—
321C2×Q16—21no—
322C2×Q16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16C5×D411yescharacteristic
326C2×M16C5×D411yescharacteristic
327C4⋊Q8C23×C511yescharacteristic
328C4⋊Q8C23×C511yescharacteristic
329C4⋊Q8C23×C511yescharacteristic
330C4⋊Q8C23×C511yescharacteristic
331#125—21no—
332#125—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8C5×D411yescharacteristic
344C4×Q8C5×D411yescharacteristic
345C4×Q8C23×C511yescharacteristic
346C4×Q8C23×C511yescharacteristic
347#117—21no—
348#117—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4C5×D411yescharacteristic
351C2×C42—21no—
352C2×C42C23×C511yescharacteristic
353#107—21no—
354#107—21no—
355#106—21no—
356#106—21no—
357#106—21no—
358#106—21no—
359#106—21no—
360#106—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8C23×C511yescharacteristic
368C4⋊C8C23×C511yescharacteristic
369C4⋊C8C23×C511yescharacteristic
370C4⋊C8C23×C511yescharacteristic
371C4⋊C8C23×C511yescharacteristic
372C4⋊C8C23×C511yescharacteristic
373#103—21no—
374#103—21no—
375#103—21no—
376#103—21no—
377#103—21no—
378#103—21no—
379#103—21no—
380#103—21no—
381#103—21no—
382#103—21no—
383#103—21no—
384#103—21no—
385C22⋊C8—21no—
386#97—21no—
387#97—21no—
388#97—21no—
389#97C5×D411yescharacteristic
390#97C5×D411yescharacteristic
391C4×C8—21no—
392C4×C8—21no—
393C4×C8C23×C511yescharacteristic
394C4×C8C23×C511yescharacteristic
395C22×C5—21no—
396C22×C5—21no—
397C22×C5—21no—
398C22×C5C2×#12111yescharacteristic
399C4×C5—21no—
400C4×C5—21no—
401C4×C5—22no—
402C4×C5—21no—
403C4×C5—21no—
404C4×C5—41no—
405C4×C5—41no—
406C4×C5—41no—
407C4×C5—81no—
408C4×C5—81no—
409C4×C5—81no—
410C4×C5—81no—
411C4×C5C2×#13711yescharacteristic
412C4×C5C2×#13711yescharacteristic
413C4×C5#57511yescharacteristic
414C4×C5#57511yescharacteristic
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8C2×C5×D411yescharacteristic
423C2×Q8C2×C5×D411yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4C2×C5×D411yescharacteristic
427C22×C4C2×C5×D411yescharacteristic
428C22×C4C5×#4111yescharacteristic
429Q16—42no—
430Q16—42no—
431Q16—42no—
432Q16—42no—
433M16—22no—
434M16—41no—
435M16—42no—
436M16—42no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8C2×C5×D411yescharacteristic
444C2×C8C2×C5×D411yescharacteristic
445C2×C8C2×C5×D411yescharacteristic
446C2×C8C2×C5×D411yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×C5×D411yescharacteristic
465C4⋊C4C2×C5×D411yescharacteristic
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—41no—
473C42—41no—
474C42C2×C5×D411yescharacteristic
475C42C2×C5×D411yescharacteristic
476C42C5×#4111yescharacteristic
477C42C24×C511yescharacteristic
478C2×C5—41no—
479C2×C5#303711yescharacteristic
480C2×C5#305611yescharacteristic
481C2×C5#306911yescharacteristic
482C23C5×#12111yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—42no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—81no—
494Q8C5×#13712yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—81no—
510C2×C4C5×#12111yescharacteristic
511C2×C4C5×#12111yescharacteristic
512C2×C4C5×#12111yescharacteristic
513C2×C4C22×C5×D411yescharacteristic
514C2×C4C22×C5×D411yescharacteristic
515C2×C4C2×C5×#4111yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8C5×#13712yes—
526C5#1931111yescharacteristic, direct product factor, Sylow
527C22—21no—
528C22—21no—
529C22—21no—
530C22C2×C5×#12111yescharacteristic
531C4—21no—
532C4—21no—
533C4—22no—
534C4—21no—
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×C5×#13711yescharacteristic
544C4C2×C5×#13711yescharacteristic
545C4C5×#57511yescharacteristic
546C4C5×#57511yescharacteristic
547C2—41no—
548C2C5×#303711yescharacteristic
549C2C5×#305611yescharacteristic
550C2C5×#306911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
prime radicalC23×C5#121
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
5. C5×#1704C2semidirect
6. C5×#1700C2semidirect
7. C5×#1692C2semidirect
8. C5×#1690C2semidirect
9. C5×#1684C2semidirect
10. C5×#1680C2semidirect
11. C5×#1672C2semidirect
12. C5×#1670C2semidirect
67. #19311C5direct (N × H)
149. #1704C2×C5semidirect
150. #1700C2×C5semidirect
151. #1692C2×C5semidirect
152. #1690C2×C5semidirect
153. #1684C2×C5semidirect
154. #1680C2×C5semidirect
155. #1672C2×C5semidirect
156. #1670C2×C5semidirect
526. C5#19311direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31852
C5×#31132
C5×#30782
C5×Q8×M162
C5×#17042
C5×#17002
C5×#16922
C5×#16902
C5×#16842
C5×#16802
C5×#16722
C5×#16702
C5×#15692
C5×#15612
C5×#15592
#193115