Finite Group Databasebeta

← C5×#68964 #14302983

Subgroups — C5×#68964 #14302983

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5493C211yesmaximal, characteristic
2C5×#5486C211yesmaximal, characteristic, complemented
3C2×C5×#806C211yesmaximal, characteristic, complemented
4C2×C5×#806C211yesmaximal, characteristic, complemented
5C2×C5×#806C211yesmaximal, characteristic, complemented
6C3×C5×#342C211yesmaximal, characteristic, complemented
7C5×#4527C211yesmaximal, characteristic, complemented
8C5×#1913—31nomaximal, Hall
9C22×C5×#67C2211yescharacteristic
10C22×C5×#67C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C5×#930—22no—
17C4×C5×#67—22no—
18C5×#886—21no—
19C5×#886C412yescomplemented
20C5×#882—21no—
21C5×#882C412yescomplemented
22C5×#67⋊C4—22no—
23C5×D3×C22⋊C4—21no—
24C5×#877—21no—
25C5×#806—22no—
26C5×#806—22no—
27C5×#806—22no—
28#68964C511yesmaximal, characteristic, direct product factor, Hall
29C5×#534—31no—
30C5×#518—31no—
31C2×C5×#99—31no—
32C2×C5×#99—31no—
33C2×C5×#99—31no—
34C5×#342—31no—
35C5×#342D311yescharacteristic, complemented
36C24×C3×C5C2311yescharacteristic
37C23×C5×D3C2×C411yescharacteristic, complemented
38C23×C5×D3D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—21no—
45C2×C5×#67—21no—
46C2×C5×#67—21no—
47C2×C5×#67—21no—
48C2×C5×#67—21no—
49C2×C5×#67—21no—
50C2×C5×#67—21no—
51C2×C5×#67—21no—
52C2×C5×#67C2×C412yes—
53C2×C5×#67D412yes—
54C22×C5×Dic3—21no—
55C22×C5×Dic3—21no—
56C22×C5×Dic3C2×C411yescharacteristic, complemented
57C22×C5×Dic3D411yescharacteristic
58C2×C5×D12—22no—
59C2×C4×C5×D3—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4—21no—
63C3×C5×C22⋊C4—21no—
64C3×C5×C22⋊C4C2×C412yescomplemented
65C3×C5×C22⋊C4D412yescomplemented
66C5×#217—21no—
67C5×#217—21no—
68C5×#217—21no—
69C5×#217D412yescomplemented
70C5×(C2×D3)⋊C4—22no—
71C5×(C2×D3)⋊C4—22no—
72C5×(C2×D3)⋊C4—22no—
73C5×C4⋊Dic3—22no—
74C5×Dic3⋊C4—22no—
75C4×C5×Dic3—22no—
76#5493C2×C511yescharacteristic
77#5486C2×C511yescharacteristic, complemented
78C2×#806C2×C511yescharacteristic, complemented
79C2×#806C2×C511yescharacteristic, complemented
80C2×#806C2×C511yescharacteristic, complemented
81C3×#342C2×C511yescharacteristic, complemented
82#4527C2×C511yescharacteristic, complemented
83C22×C5×D4—31no—
84C22×C5×D4—31no—
85C5×#123—32no—
86C5×#123—61no—
87C5×#121—62no—
88C5×#120—32no—
89C5×#120—61no—
90C4×C5×D4—62no—
91C4×C5×D4—62no—
92C5×#117—61no—
93C2×C5×C22⋊C4—31no—
94C2×C5×C22⋊C4—31no—
95C2×C5×C22⋊C4—61no—
96C2×C5×C22⋊C4C2×D311yescharacteristic
97C2×C5×C22⋊C4C2×D311yescharacteristic
98C2×C5×C22⋊C4C2×D311yescharacteristic
99C5×#99—62no—
100C5×#99—62no—
101C5×#99—62no—
102#1913—31noSylow
103C23×C3×C5—81no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5C2×D411yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C22×C5×D3—21no—
112C22×C5×D3—21no—
113C22×C5×D3—21no—
114C22×C5×D3—21no—
115C22×C5×D3—21no—
116C22×C5×D3—81no—
117C22×C5×D3—81no—
118C22×C5×D3C22⋊C412yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—81no—
123C2×C3×C4×C5—81no—
124C2×C3×C4×C5—81no—
125C5×#67—22no—
126C5×#67—22no—
127C5×#67—22no—
128C5×#67—22no—
129C5×#67—41no—
130C5×#67—41no—
131C5×#67—41no—
132C5×#67—41no—
133C2×C5×Dic3—21no—
134C2×C5×Dic3—21no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—41no—
140C2×C5×Dic3—81no—
141C2×C5×Dic3—81no—
142C2×C5×Dic3C22⋊C412yes—
143C5×D12—82no—
144C4×C5×D3—82no—
145C22×#67C22×C511yescharacteristic
146C22×#67C22×C511yescharacteristic
147C2×C3×C22⋊C4C22×C511yescharacteristic
148C2×C3×C22⋊C4C22×C511yescharacteristic
149C2×C3×C22⋊C4C22×C511yescharacteristic
150C2×#217C22×C511yescharacteristic
151C2×#217C22×C511yescharacteristic
152#930—22no—
153C4×#67—22no—
154#886—21no—
155#886C4×C512yescomplemented
156#882—21no—
157#882C4×C512yescomplemented
158#67⋊C4—22no—
159D3×C22⋊C4—21no—
160#877—21no—
161#806—22no—
162#806—22no—
163#806—22no—
164C24×C5—31no—
165C24×C5—31no—
166C24×C5C22×D311yescharacteristic
167C2×C5×D4—32no—
168C2×C5×D4—32no—
169C2×C5×D4—62no—
170C2×C5×D4—61no—
171C2×C5×D4—61no—
172C2×C5×D4—61no—
173C2×C5×D4—61no—
174C2×C5×D4—61no—
175C2×C5×D4—61no—
176C2×C5×D4—61no—
177C2×C5×D4—61no—
178C2×C5×D4—61no—
179C2×C5×D4—61no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—31no—
184C22×C4×C5—31no—
185C22×C4×C5—62no—
186C22×C4×C5—61no—
187C22×C4×C5—61no—
188C5×C4⋊C4—62no—
189C5×C4⋊C4—62no—
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C5×C22⋊C4—21no—
193C5×C22⋊C4—21no—
194C5×C22⋊C4—32no—
195C5×C22⋊C4—62no—
196C5×C22⋊C4—62no—
197C5×C22⋊C4—62no—
198C5×C22⋊C4—61no—
199C5×C22⋊C4—61no—
200C5×C22⋊C4—61no—
201C5×C22⋊C4C4×D312yescomplemented
202C5×C22⋊C4D1212yescomplemented
203C42×C5—62no—
204#534—31no—
205#518—31no—
206C2×#99—31no—
207C2×#99—31no—
208C2×#99—31no—
209#342—31no—
210#342C5×D311yescharacteristic, complemented
211C22×C3×C5—41no—
212C22×C3×C5—41no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×D411yescharacteristic
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5#12111yescharacteristic
223C22×C3×C5#12111yescharacteristic
224C22×C3×C5#12311yescharacteristic
225C2×C5×D3—22no—
226C2×C5×D3—42no—
227C2×C5×D3—42no—
228C2×C5×D3—42no—
229C2×C5×D3—41no—
230C2×C5×D3—81no—
231C2×C5×D3—81no—
232C2×C5×D3—81no—
233C3×C4×C5—42no—
234C3×C4×C5—42no—
235C3×C4×C5—81no—
236C5×Dic3—22no—
237C5×Dic3—42no—
238C5×Dic3—41no—
239C5×Dic3—81no—
240C24×C3C23×C511yescharacteristic
241C23×D3C2×C4×C511yescharacteristic, complemented
242C23×D3C5×D411yescharacteristic
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C2×#67—21no—
247C2×#67—21no—
248C2×#67—21no—
249C2×#67—21no—
250C2×#67—21no—
251C2×#67—21no—
252C2×#67—21no—
253C2×#67—21no—
254C2×#67—21no—
255C2×#67—21no—
256C2×#67C2×C4×C512yes—
257C2×#67C5×D412yes—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3C2×C4×C511yescharacteristic, complemented
261C22×Dic3C5×D411yescharacteristic
262C2×D12—22no—
263C2×C4×D3—22no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4C2×C4×C512yescomplemented
269C3×C22⋊C4C5×D412yescomplemented
270#217—21no—
271#217—21no—
272#217—21no—
273#217C5×D412yescomplemented
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277C4⋊Dic3—22no—
278Dic3⋊C4—22no—
279C4×Dic3—22no—
280C23×C5—32no—
281C23×C5—61no—
282C23×C5—61no—
283C23×C5—61no—
284C23×C5—61no—
285C23×C5—61no—
286C23×C5—81no—
287C23×C5—241no—
288C23×C5—241no—
289C23×C5C2×C4×D311yescharacteristic
290C23×C5C2×D1211yescharacteristic
291C23×C5#23511yescharacteristic
292C23×C5D3×D411yescharacteristic
293C23×C5D3×D411yescharacteristic
294C23×C5D3×D411yescharacteristic
295C23×C5#23911yescharacteristic
296C5×D4—62no—
297C5×D4—62no—
298C5×D4—62no—
299C5×D4—62no—
300C5×D4—121no—
301C5×D4—121no—
302C5×D4—121no—
303C5×D4—121no—
304C5×D4—242no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—32no—
308C2×C4×C5—41no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5—61no—
313C2×C4×C5—62no—
314C2×C4×C5—61no—
315C2×C4×C5—81no—
316C2×C4×C5—81no—
317C2×C4×C5—81no—
318C2×C4×C5—121no—
319C2×C4×C5—242no—
320C2×C4×C5—241no—
321C2×C4×C5—241no—
322C22×D4—31no—
323C22×D4—31no—
324#123—32no—
325#123—61no—
326#121—62no—
327#120—32no—
328#120—61no—
329C4×D4—62no—
330C4×D4—62no—
331#117—61no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—61no—
335C2×C22⋊C4C2×C5×D311yescharacteristic
336C2×C22⋊C4C2×C5×D311yescharacteristic
337C2×C22⋊C4C2×C5×D311yescharacteristic
338#99—62no—
339#99—62no—
340#99—62no—
341C2×C3×C5—21no—
342C2×C3×C5—21no—
343C2×C3×C5—21no—
344C2×C3×C5—21no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5—21no—
348C2×C3×C5#38611yescharacteristic
349C5×D3—42no—
350C5×D3—81no—
351C23×C3—81no—
352C23×C3C22×C4×C511yescharacteristic
353C23×C3C2×C5×D411yescharacteristic
354C23×C3C2×C5×D411yescharacteristic
355C23×C3C2×C5×D411yescharacteristic
356C23×C3C2×C5×D411yescharacteristic
357C23×C3C5×#4111yescharacteristic
358C23×C3C5×#4111yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—21no—
364C22×D3—81no—
365C22×D3—81no—
366C22×D3C5×C22⋊C412yes—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—41no—
370C2×C3×C4—81no—
371C2×C3×C4—81no—
372C2×C3×C4—81no—
373#67—22no—
374#67—22no—
375#67—22no—
376#67—22no—
377#67—41no—
378#67—41no—
379#67—41no—
380#67—41no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—41no—
388C2×Dic3—81no—
389C2×Dic3—81no—
390C2×Dic3C5×C22⋊C412yes—
391D12—82no—
392C4×D3—82no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—62no—
401C22×C5—122no—
402C22×C5—122no—
403C22×C5—122no—
404C22×C5—121no—
405C22×C5—241no—
406C22×C5—241no—
407C22×C5—241no—
408C22×C5C4×D1211yescharacteristic
409C22×C5D3×C22⋊C411yescharacteristic
410C22×C5#88211yescharacteristic
411C22×C5#88411yescharacteristic
412C22×C5#89311yescharacteristic
413C22×C5#89411yescharacteristic
414C22×C5#89511yescharacteristic
415C4×C5—42no—
416C4×C5—42no—
417C4×C5—62no—
418C4×C5—81no—
419C4×C5—122no—
420C4×C5—121no—
421C4×C5—241no—
422C24—31no—
423C24—31no—
424C24C22×C5×D311yescharacteristic
425C2×D4—32no—
426C2×D4—32no—
427C2×D4—62no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—62no—
444C22×C4—61no—
445C22×C4—61no—
446C4⋊C4—62no—
447C4⋊C4—62no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—32no—
453C22⋊C4—62no—
454C22⋊C4—62no—
455C22⋊C4—62no—
456C22⋊C4—61no—
457C22⋊C4—61no—
458C22⋊C4—61no—
459C22⋊C4C4×C5×D312yescomplemented
460C22⋊C4C5×D1212yescomplemented
461C42—62no—
462C3×C5#191311yescharacteristic, complemented, Hall
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3C2×C5×C22⋊C411yescharacteristic
471C22×C3C4×C5×D411yescharacteristic
472C22×C3C4×C5×D411yescharacteristic
473C22×C3C5×#12011yescharacteristic
474C22×C3C5×#12111yescharacteristic
475C22×C3C5×#12111yescharacteristic
476C22×C3C5×#12311yescharacteristic
477C2×D3—22no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—41no—
482C2×D3—81no—
483C2×D3—81no—
484C2×D3—81no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—81no—
488Dic3—22no—
489Dic3—42no—
490Dic3—41no—
491Dic3—81no—
492C2×C5—21no—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—21no—
499C2×C5—122no—
500C2×C5—241no—
501C2×C5#466511yescharacteristic
502C23—32no—
503C23—61no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23—61no—
508C23—81no—
509C23—241no—
510C23—241no—
511C23C2×C4×C5×D311yescharacteristic
512C23C2×C5×D1211yescharacteristic
513C23C5×#23511yescharacteristic
514C23C5×D3×D411yescharacteristic
515C23C5×D3×D411yescharacteristic
516C23C5×D3×D411yescharacteristic
517C23C5×#23911yescharacteristic
518D4—62no—
519D4—62no—
520D4—62no—
521D4—62no—
522D4—121no—
523D4—121no—
524D4—121no—
525D4—121no—
526D4—242no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—32no—
530C2×C4—41no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—121no—
541C2×C4—242no—
542C2×C4—241no—
543C2×C4—241no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3C5×#38611yescharacteristic
552D3—42no—
553D3—81no—
554C5#6896411yescharacteristic, direct product factor, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—62no—
563C22—122no—
564C22—122no—
565C22—122no—
566C22—121no—
567C22—241no—
568C22—241no—
569C22—241no—
570C22C4×C5×D1211yescharacteristic
571C22C5×D3×C22⋊C411yescharacteristic
572C22C5×#88211yescharacteristic
573C22C5×#88411yescharacteristic
574C22C5×#89311yescharacteristic
575C22C5×#89411yescharacteristic
576C22C5×#89511yescharacteristic
577C4—42no—
578C4—42no—
579C4—62no—
580C4—81no—
581C4—122no—
582C4—121no—
583C4—241no—
584C3C5×#191311yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—122no—
593C2—241no—
594C2C5×#466511yescharacteristic
subgroupG/H
centerC2×C5#4665
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#342C2
socleC2×C3×C5#386
prime radicalC5×#5493C2
cosocleC24×C3C23×C5
hypercenterC5×#342D3
hypocenterC3C5×#1913
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C24×C5 ◁ C5×#342

Complements

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

NH ≅ G/Ntype
2. C5×#5486C2semidirect
3. C2×C5×#806C2semidirect
4. C2×C5×#806C2semidirect
5. C2×C5×#806C2semidirect
6. C3×C5×#342C2semidirect
7. C5×#4527C2semidirect
19. C5×#886C4semidirect
21. C5×#882C4semidirect
28. #68964C5direct (N × H)
35. C5×#342D3semidirect
37. C23×C5×D3C2×C4semidirect
56. C22×C5×Dic3C2×C4semidirect
64. C3×C5×C22⋊C4C2×C4semidirect
65. C3×C5×C22⋊C4D4semidirect
69. C5×#217D4semidirect
77. #5486C2×C5semidirect
78. C2×#806C2×C5semidirect
79. C2×#806C2×C5semidirect
80. C2×#806C2×C5semidirect
81. C3×#342C2×C5semidirect
82. #4527C2×C5semidirect
155. #886C4×C5semidirect
157. #882C4×C5semidirect
201. C5×C22⋊C4C4×D3semidirect
202. C5×C22⋊C4D12semidirect
210. #342C5×D3semidirect
241. C23×D3C2×C4×C5semidirect
260. C22×Dic3C2×C4×C5semidirect
268. C3×C22⋊C4C2×C4×C5semidirect
269. C3×C22⋊C4C5×D4semidirect
273. #217C5×D4semidirect
459. C22⋊C4C4×C5×D3semidirect
460. C22⋊C4C5×D12semidirect
462. C3×C5#1913semidirect
554. C5#68964direct (N × H)
584. C3C5×#1913semidirect

Maximal subgroups

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

subgroupindex
C5×#54932
C5×#54862
C2×C5×#8062
C3×C5×#3422
C5×#45272
C5×#19133
#689645