Finite Group Databasebeta

← C5×#69598 #14297131

Subgroups — C5×#69598 #14297131

Order 1920.

1340 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
1C2×C5×#1004C211yesmaximal, characteristic
2C3×C5×#386C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C5×#5213C212yesmaximal, complemented
5C2×C5×#806C212yesmaximal, complemented
6C5×#1790—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic, complemented
9C22×C5×#67—21no—
10C22×C5×#67C2212yes—
11C5×#1004—22no—
12C5×#1004—24no—
13C5×#1004C414yescomplemented
14C2×C5×#237—22no—
15C2×C5×D3×D4—22no—
16C2×C5×#235—21no—
17C2×C3×C5×C22⋊C4—21no—
18C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
19C2×C5×#217C2212yescomplemented
20C2×C5×(C2×D3)⋊C4—22no—
21C3×C5×#95—21no—
22C5×#834—22no—
23C5×C3⋊#95—22no—
24C5×#806—24no—
25#69598C511yesmaximal, characteristic, direct product factor, Hall
26C2×C5×H(5,𝔽2)—31no—
27C2×C5×#99—31no—
28C2×C5×#99—32no—
29C5×#386—32no—
30C5×#386D311yescharacteristic, complemented
31C24×C3×C5D411yescharacteristic
32C24×C3×C5C2311yescharacteristic
33C23×C5×D3—21no—
34C23×C5×D3D412yes—
35C2×C3×C5×D4—22no—
36C2×C3×C5×D4—22no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—42no—
43C22×C3×C4×C5D411yescharacteristic
44C2×C5×#67—22no—
45C2×C5×#67—24no—
46C2×C5×#67—24no—
47C2×C5×#67—22no—
48C2×C5×#67—22no—
49C2×C5×#67—22no—
50C2×C5×#67—22no—
51C2×C5×#67C2×C414yes—
52C2×C5×#67D414yes—
53C22×C5×Dic3—21no—
54C22×C5×Dic3—22no—
55C22×C5×Dic3D412yes—
56C5×#237—28no—
57C5×#237—28no—
58C5×D3×D4—28no—
59C5×D3×D4—28no—
60C5×#235—24no—
61C5×#235—24no—
62C2×C5×D12—21no—
63C2×C4×C5×D3—22no—
64C2×C5×Dic6—21no—
65C3×C5×C22⋊C4—22no—
66C3×C5×C22⋊C4—42no—
67C5×#217—22no—
68C5×#217—22no—
69C5×(C2×D3)⋊C4—44no—
70C2×#1004C2×C511yescharacteristic
71C3×#386C2×C511yescharacteristic, complemented
72C2×#834C2×C511yescharacteristic, complemented
73#5213C2×C512yescomplemented
74C2×#806C2×C512yescomplemented
75C5×H(5,𝔽2)—34no—
76C5×H(5,𝔽2)—64no—
77C5×H(5,𝔽2)—62no—
78C2×C5×#41—62no—
79C2×C5×#41—61no—
80C22×C5×D4—32no—
81C22×C5×D4—62no—
82C22×C5×D4—61no—
83C22×C5×D4C2×D311yescharacteristic
84C23×C4×C5C2×D311yescharacteristic, complemented
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4—32no—
87C2×C5×C22⋊C4—62no—
88C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
89C5×#99—64no—
90C5×#99—62no—
91C5×#95—21no—
92C5×#95—62no—
93#1790—31noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5C22⋊C412yescomplemented
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D412yes—
103C23×C3×C5C2×D411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D412yes—
106C22×C5×D3—22no—
107C22×C5×D3—24no—
108C22×C5×D3—22no—
109C22×C5×D3—42no—
110C22×C5×D3—42no—
111C22×C5×D3—81no—
112C22×C5×D3—81no—
113C22×C5×D3C22⋊C414yescomplemented
114C3×C5×D4—24no—
115C3×C5×D4—24no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—24no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5C22⋊C412yescomplemented
127C5×#67—28no—
128C5×#67—24no—
129C5×#67—24no—
130C5×#67—24no—
131C5×#67—24no—
132C2×C5×Dic3—24no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—42no—
136C2×C5×Dic3—42no—
137C2×C5×Dic3—42no—
138C2×C5×Dic3C22⋊C414yescomplemented
139C5×D12—24no—
140C4×C5×D3—28no—
141C5×Dic6—24no—
142C22×C3×D4C22×C511yescharacteristic
143C23×C3×C4C22×C511yescharacteristic, complemented
144C22×#67—21no—
145C22×#67C22×C512yes—
146#1004—22no—
147#1004—24no—
148#1004C4×C514yescomplemented
149C2×#237—22no—
150C2×D3×D4—22no—
151C2×#235—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4C22×C511yescharacteristic, complemented
154C2×#217C22×C512yescomplemented
155C2×(C2×D3)⋊C4—22no—
156C3×#95—21no—
157#834—22no—
158C3⋊#95—22no—
159#806—24no—
160C24×C5—32no—
161C24×C5—61no—
162C24×C5#6711yescharacteristic
163C24×C5C22×D311yescharacteristic
164C5×#41—64no—
165C5×#41—68no—
166C5×#41—68no—
167C5×#41—64no—
168C2×C5×Q8—61no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4—34no—
172C2×C5×D4—34no—
173C2×C5×D4—61no—
174C2×C5×D4—68no—
175C2×C5×D4—68no—
176C2×C5×D4—62no—
177C2×C5×D4—64no—
178C2×C5×D4—64no—
179C2×C5×D4—62no—
180C2×C5×D4—62no—
181C2×C5×D4—62no—
182C2×C5×D4—62no—
183C2×C5×D4C4×D312yes—
184C2×C5×D4D1212yes—
185C22×C4×C5—22no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—32no—
189C22×C4×C5—42no—
190C22×C4×C5—62no—
191C22×C4×C5—61no—
192C22×C4×C5—62no—
193C22×C4×C5#6711yescharacteristic
194C5×C22⋊C4—22no—
195C5×C22⋊C4—42no—
196C5×C22⋊C4—62no—
197C5×C22⋊C4—62no—
198C5×C22⋊C4—124no—
199C2×H(5,𝔽2)—31no—
200C2×#99—31no—
201C2×#99—32no—
202#386—32no—
203#386C5×D311yescharacteristic, complemented
204C22×C3×C5—22no—
205C22×C3×C5—21no—
206C22×C3×C5—22no—
207C22×C3×C5—21no—
208C22×C3×C5—22no—
209C22×C3×C5—41no—
210C22×C3×C5—41no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—81no—
216C22×C3×C5C2×C22⋊C412yes—
217C22×C3×C5C2×C22⋊C411yescharacteristic
218C22×C3×C5#12012yes—
219C22×C3×C5#12011yescharacteristic
220C22×C3×C5#12011yescharacteristic
221C2×C5×D3—24no—
222C2×C5×D3—42no—
223C2×C5×D3—42no—
224C2×C5×D3—44no—
225C2×C5×D3—82no—
226C2×C5×D3—84no—
227C3×C4×C5—22no—
228C3×C4×C5—42no—
229C3×C4×C5—81no—
230C5×Dic3—24no—
231C5×Dic3—82no—
232C24×C3C5×D411yescharacteristic
233C24×C3C23×C511yescharacteristic
234C23×D3—21no—
235C23×D3C5×D412yes—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4C2×C4×C512yes—
239C2×C3×D4C5×D412yes—
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—42no—
244C22×C3×C4C5×D411yescharacteristic
245C2×#67—22no—
246C2×#67—24no—
247C2×#67—24no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—22no—
251C2×#67—22no—
252C2×#67C2×C4×C514yes—
253C2×#67C5×D414yes—
254C22×Dic3—21no—
255C22×Dic3—22no—
256C22×Dic3C5×D412yes—
257#237—28no—
258#237—28no—
259D3×D4—28no—
260D3×D4—28no—
261#235—24no—
262#235—24no—
263C2×D12—21no—
264C2×C4×D3—22no—
265C2×Dic6—21no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—42no—
268#217—22no—
269#217—22no—
270(C2×D3)⋊C4—44no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—34no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5—64no—
279C23×C5—62no—
280C23×C5—62no—
281C23×C5—122no—
282C23×C5—122no—
283C23×C5—241no—
284C23×C5—241no—
285C23×C5(C2×D3)⋊C412yescomplemented
286C23×C5C2×C4×D311yescharacteristic
287C23×C5C2×D1211yescharacteristic
288C23×C5D3×D412yes—
289C23×C5D3×D412yes—
290C23×C5C2×#6711yescharacteristic
291C5×Q8—64no—
292C5×D4—24no—
293C5×D4—24no—
294C5×D4—64no—
295C5×D4—68no—
296C5×D4—64no—
297C5×D4—64no—
298C5×D4—64no—
299C5×D4—64no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—22no—
303C2×C4×C5—24no—
304C2×C4×C5—34no—
305C2×C4×C5—41no—
306C2×C4×C5—42no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—68no—
312C2×C4×C5—64no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—122no—
316C2×C4×C5—122no—
317C2×C4×C5—122no—
318C2×C4×C5(C2×D3)⋊C412yescomplemented
319H(5,𝔽2)—34no—
320H(5,𝔽2)—64no—
321H(5,𝔽2)—62no—
322C2×#41—62no—
323C2×#41—61no—
324C22×D4—32no—
325C22×D4—62no—
326C22×D4—61no—
327C22×D4C2×C5×D311yescharacteristic
328C23×C4C2×C5×D311yescharacteristic, complemented
329C2×C22⋊C4—21no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—62no—
332C2×C22⋊C4C2×C5×D311yescharacteristic, complemented
333#99—64no—
334#99—62no—
335#95—21no—
336#95—62no—
337C2×C3×C5—22no—
338C2×C3×C5—21no—
339C2×C3×C5—22no—
340C2×C3×C5—21no—
341C2×C3×C5—42no—
342C2×C3×C5#37911yescharacteristic
343C2×C3×C5B(4,𝔽2)11yescharacteristic
344C2×C3×C5#45811yescharacteristic
345C5×D3—44no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3C5×C22⋊C412yescomplemented
353C23×C3C22×C4×C511yescharacteristic
354C23×C3C2×C5×D411yescharacteristic
355C23×C3C2×C5×D412yes—
356C23×C3C2×C5×D412yes—
357C23×C3C2×C5×D411yescharacteristic
358C22×D3—22no—
359C22×D3—24no—
360C22×D3—22no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—81no—
364C22×D3—81no—
365C22×D3C5×C22⋊C414yescomplemented
366C3×D4—24no—
367C3×D4—24no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—42no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4C5×C22⋊C412yescomplemented
379#67—28no—
380#67—24no—
381#67—24no—
382#67—24no—
383#67—24no—
384C2×Dic3—24no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—42no—
388C2×Dic3—42no—
389C2×Dic3—42no—
390C2×Dic3C5×C22⋊C414yescomplemented
391D12—24no—
392C4×D3—28no—
393Dic6—24no—
394C22×C5—21no—
395C22×C5—22no—
396C22×C5—21no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—42no—
402C22×C5—42no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—64no—
406C22×C5—81no—
407C22×C5—124no—
408C22×C5—122no—
409C22×C5—122no—
410C22×C5—242no—
411C22×C5—244no—
412C22×C5D3×C22⋊C412yes—
413C22×C5#88212yes—
414C22×C5C2×(C2×D3)⋊C411yescharacteristic
415C22×C5#93711yescharacteristic
416C22×C5#93711yescharacteristic
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—64no—
420C4×C5—81no—
421C4×C5—242no—
422C24—32no—
423C24—61no—
424C24C5×#6711yescharacteristic
425C24C22×C5×D311yescharacteristic
426#41—64no—
427#41—68no—
428#41—68no—
429#41—64no—
430C2×Q8—61no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—34no—
434C2×D4—34no—
435C2×D4—61no—
436C2×D4—68no—
437C2×D4—68no—
438C2×D4—62no—
439C2×D4—64no—
440C2×D4—64no—
441C2×D4—62no—
442C2×D4—62no—
443C2×D4—62no—
444C2×D4—62no—
445C2×D4C4×C5×D312yes—
446C2×D4C5×D1212yes—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—32no—
451C22×C4—42no—
452C22×C4—62no—
453C22×C4—61no—
454C22×C4—62no—
455C22×C4C5×#6711yescharacteristic
456C22⋊C4—22no—
457C22⋊C4—42no—
458C22⋊C4—62no—
459C22⋊C4—62no—
460C22⋊C4—124no—
461C3×C5#179011yescharacteristic, complemented, Hall
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—22no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—81no—
474C22×C3C2×C5×C22⋊C412yes—
475C22×C3C2×C5×C22⋊C411yescharacteristic
476C22×C3C5×#12012yes—
477C22×C3C5×#12011yescharacteristic
478C22×C3C5×#12011yescharacteristic
479C2×D3—24no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—44no—
483C2×D3—82no—
484C2×D3—84no—
485C3×C4—22no—
486C3×C4—42no—
487C3×C4—81no—
488Dic3—24no—
489Dic3—82no—
490C2×C5—21no—
491C2×C5—22no—
492C2×C5—21no—
493C2×C5—22no—
494C2×C5—42no—
495C2×C5—124no—
496C2×C5#495511yescharacteristic
497C2×C5#503211yescharacteristic
498C2×C5#505311yescharacteristic
499C23—21no—
500C23—21no—
501C23—34no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—64no—
507C23—62no—
508C23—62no—
509C23—122no—
510C23—122no—
511C23—241no—
512C23—241no—
513C23C5×(C2×D3)⋊C412yescomplemented
514C23C2×C4×C5×D311yescharacteristic
515C23C2×C5×D1211yescharacteristic
516C23C5×D3×D412yes—
517C23C5×D3×D412yes—
518C23C2×C5×#6711yescharacteristic
519Q8—64no—
520D4—24no—
521D4—24no—
522D4—64no—
523D4—68no—
524D4—64no—
525D4—64no—
526D4—64no—
527D4—64no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—34no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—68no—
540C2×C4—64no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—122no—
544C2×C4—122no—
545C2×C4—122no—
546C2×C4C5×(C2×D3)⋊C412yescomplemented
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—42no—
552C2×C3C5×#37911yescharacteristic
553C2×C3C5×B(4,𝔽2)11yescharacteristic
554C2×C3C5×#45811yescharacteristic
555D3—44no—
556C5#6959811yescharacteristic, direct product factor, Sylow
557C22—21no—
558C22—22no—
559C22—21no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—64no—
569C22—81no—
570C22—124no—
571C22—122no—
572C22—122no—
573C22—242no—
574C22—244no—
575C22C5×D3×C22⋊C412yes—
576C22C5×#88212yes—
577C22C2×C5×(C2×D3)⋊C411yescharacteristic
578C22C5×#93711yescharacteristic
579C22C5×#93711yescharacteristic
580C4—22no—
581C4—42no—
582C4—64no—
583C4—81no—
584C4—242no—
585C3C5×#179011yescharacteristic, complemented, Sylow
586C2—21no—
587C2—22no—
588C2—21no—
589C2—22no—
590C2—42no—
591C2—124no—
592C2C5×#495511yescharacteristic
593C2C5×#503211yescharacteristic
594C2C5×#505311yescharacteristic
subgroupG/H
centerC22×C5#937
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC3×C5×#386C2
socleC22×C3×C5#120
prime radicalC2×C5×#1004C2
cosocleC24×C3C23×C5
hypercenterC5×#386D3
hypocenterC3C5×#1790
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C5×#386

Complements

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

NH ≅ G/Ntype
2. C3×C5×#386C2semidirect
3. C2×C5×#834C2semidirect
4. C5×#5213C2semidirect
5. C2×C5×#806C2semidirect
8. C23×C3×C4×C5C22semidirect
13. C5×#1004C4semidirect
18. C2×C3×C5×C22⋊C4C22semidirect
19. C2×C5×#217C22semidirect
25. #69598C5direct (N × H)
30. C5×#386D3semidirect
71. C3×#386C2×C5semidirect
72. C2×#834C2×C5semidirect
73. #5213C2×C5semidirect
74. C2×#806C2×C5semidirect
84. C23×C4×C5C2×D3semidirect
88. C2×C5×C22⋊C4C2×D3semidirect
100. C23×C3×C5C22⋊C4semidirect
113. C22×C5×D3C22⋊C4semidirect
126. C2×C3×C4×C5C22⋊C4semidirect
138. C2×C5×Dic3C22⋊C4semidirect
143. C23×C3×C4C22×C5semidirect
148. #1004C4×C5semidirect
153. C2×C3×C22⋊C4C22×C5semidirect
154. C2×#217C22×C5semidirect
203. #386C5×D3semidirect
285. C23×C5(C2×D3)⋊C4semidirect
318. C2×C4×C5(C2×D3)⋊C4semidirect
328. C23×C4C2×C5×D3semidirect
332. C2×C22⋊C4C2×C5×D3semidirect
352. C23×C3C5×C22⋊C4semidirect
365. C22×D3C5×C22⋊C4semidirect
378. C2×C3×C4C5×C22⋊C4semidirect
390. C2×Dic3C5×C22⋊C4semidirect
461. C3×C5#1790semidirect
513. C23C5×(C2×D3)⋊C4semidirect
546. C2×C4C5×(C2×D3)⋊C4semidirect
556. C5#69598direct (N × H)
585. C3C5×#1790semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10042
C3×C5×#3862
C2×C5×#8342
C5×#52132
C2×C5×#8062
C5×#17903
#695985