Finite Group Databasebeta

← C5×#69657 #14301021

Subgroups — C5×#69657 #14301021

Order 1920.

876 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#213C211yesmaximal, characteristic
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C3×C5×#390C211yesmaximal, characteristic, complemented
4C2×C5×#832C211yesmaximal, characteristic, complemented
5C2×C5×#809C211yesmaximal, characteristic, complemented
6C5×#4529C211yesmaximal, characteristic, complemented
7C5×#4524C211yesmaximal, characteristic, complemented
8C5×#1879—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C22×C4×C5×D3—21no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C42×C5C2211yescharacteristic
16C2×C5×#213—22no—
17C2×C5×#213—22no—
18C2×C5×#213C414yescomplemented
19C2×C5×(C2×D3)⋊C4—21no—
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C22×C5×C3⋊C8C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C4×C5×D12—22no—
24C4×C5×D12—22no—
25C5×#832—22no—
26C5×#809—22no—
27#69657C511yesmaximal, characteristic, direct product factor, Hall
28C22×C5×D8—31no—
29C2×C4×C5×D4—31no—
30C2×C5×#102—31no—
31C2×C5×#102—31no—
32C5×#390D311yescharacteristic, complemented
33C5×#340—31no—
34C5×#336—31no—
35C24×C3×C5—21no—
36C23×C5×D3—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C412yescomplemented
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C22×C5×Dic3—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12C2×C412yes—
52C2×C5×D12D412yes—
53C2×C5×D12D412yes—
54C2×C4×C5×D3—24no—
55C2×C4×C5×D3—42no—
56C2×C4×C5×D3—42no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—42no—
60C3×C5×C22⋊C4—42no—
61C3×C42×C5—21no—
62C3×C42×C5—21no—
63C5×#213—28no—
64C5×(C2×D3)⋊C4—24no—
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3D412yes—
67C2×C5×C3⋊C8—21no—
68C2×C5×C3⋊C8—21no—
69C2×C5×C3⋊C8—21no—
70C2×C5×C3⋊C8—21no—
71C2×C5×C3⋊C8—21no—
72C2×C5×C3⋊C8C2×C412yescomplemented
73C22×#213C2×C511yescharacteristic
74C2×C4×D12C2×C511yescharacteristic, complemented
75C3×#390C2×C511yescharacteristic, complemented
76C2×#832C2×C511yescharacteristic, complemented
77C2×#809C2×C511yescharacteristic, complemented
78#4529C2×C511yescharacteristic, complemented
79#4524C2×C511yescharacteristic, complemented
80C22×C5×D4—31no—
81C22×C5×D4C2×D311yescharacteristic
82C23×C4×C5—61no—
83C2×C5×D8—34no—
84C2×C5×D8—62no—
85C2×C5×D8—62no—
86C22×C5×C8—31no—
87C22×C5×C8—31no—
88C4×C5×D4—62no—
89C4×C5×D4—62no—
90C2×C5×C4⋊C4—31no—
91C2×C5×C4⋊C4C2×D311yescharacteristic
92C2×C5×C22⋊C4—21no—
93C2×C5×C22⋊C4—21no—
94C2×C5×C22⋊C4—61no—
95C2×C42×C5C2×D311yescharacteristic
96C5×#102—62no—
97C5×#102—62no—
98#1879—31noSylow
99C23×C3×C5—22no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5—41no—
106C23×C3×C5C2×D411yescharacteristic
107C22×C5×D3—22no—
108C22×C5×D3—22no—
109C22×C5×D3—22no—
110C22×C5×D3—41no—
111C22×C5×D3—41no—
112C22×C5×D3—41no—
113C22×C5×D3—41no—
114C3×C5×D4—22no—
115C3×C5×D4—22no—
116C3×C5×D4—41no—
117C3×C5×D4—41no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5D812yescomplemented
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5#4111yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×C5×Dic3—22no—
134C2×C5×Dic3—41no—
135C2×C5×Dic3—41no—
136C5×D12—22no—
137C5×D12—22no—
138C5×D12—22no—
139C5×D12C22⋊C414yescomplemented
140C4×C5×D3—48no—
141C5×C3⋊C8—22no—
142C5×C3⋊C8—41no—
143C22×C3×D4C22×C511yescharacteristic
144C22×D12C22×C511yescharacteristic
145C22×C4×D3—21no—
146C2×C3×C4⋊C4C22×C511yescharacteristic
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C42C22×C511yescharacteristic
150C2×#213—22no—
151C2×#213—22no—
152C2×#213C4×C514yescomplemented
153C2×(C2×D3)⋊C4—21no—
154C2×C4⋊Dic3C22×C511yescharacteristic
155C22×C3⋊C8C22×C511yescharacteristic
156C22×C3⋊C8C22×C511yescharacteristic
157C4×D12—22no—
158C4×D12—22no—
159#832—22no—
160#809—22no—
161C24×C5—21no—
162C24×C5—61no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—32no—
169C2×C5×D4—32no—
170C2×C5×D4—32no—
171C2×C5×D4—61no—
172C2×C5×D4—61no—
173C2×C5×D4—61no—
174C2×C5×D4C4×D312yescomplemented
175C22×C4×C5—21no—
176C22×C4×C5—64no—
177C22×C4×C5—61no—
178C22×C4×C5—122no—
179C22×C4×C5—122no—
180C22×C4×C5#6711yescharacteristic
181C22×C4×C5#6711yescharacteristic
182C22×C4×C5C22×D311yescharacteristic
183C5×D8—68no—
184C2×C5×C8—32no—
185C2×C5×C8—61no—
186C2×C5×C8—61no—
187C2×C5×C8—61no—
188C2×C5×C8—61no—
189C2×C5×C8—61no—
190C5×C4⋊C4—21no—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—32no—
193C5×C4⋊C4—61no—
194C5×C22⋊C4—42no—
195C5×C22⋊C4—42no—
196C5×C22⋊C4—64no—
197C42×C5—21no—
198C42×C5—21no—
199C22×D8—31no—
200C2×C4×D4—31no—
201C2×#102—31no—
202C2×#102—31no—
203#390C5×D311yescharacteristic, complemented
204#340—31no—
205#336—31no—
206C22×C3×C5—42no—
207C22×C3×C5—42no—
208C22×C3×C5—42no—
209C22×C3×C5—81no—
210C22×C3×C5—81no—
211C22×C3×C5—81no—
212C22×C3×C5—81no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C22×C3×C5C2×D811yescharacteristic
217C22×C3×C5#13511yescharacteristic
218C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
219C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
220C2×C5×D3—24no—
221C2×C5×D3—42no—
222C2×C5×D3—42no—
223C2×C5×D3—42no—
224C2×C5×D3—42no—
225C2×C5×D3—42no—
226C2×C5×D3—42no—
227C3×C4×C5—22no—
228C3×C4×C5—41no—
229C3×C4×C5—81no—
230C3×C4×C5C2×C22⋊C411yescharacteristic
231C3×C4×C5C4×D411yescharacteristic
232C3×C4×C5#12111yescharacteristic
233C3×C4×C5#12311yescharacteristic
234C5×Dic3—42no—
235C24×C3—21no—
236C23×D3—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4C2×C4×C512yescomplemented
243C22×C3×C4—21no—
244C22×C3×C4C5×D411yescharacteristic
245C22×C3×C4C5×D411yescharacteristic
246C22×C3×C4C23×C511yescharacteristic
247C22×Dic3—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12C2×C4×C512yes—
252C2×D12C5×D412yes—
253C2×D12C5×D412yes—
254C2×C4×D3—24no—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C22⋊C4—42no—
260C3×C22⋊C4—42no—
261C3×C42—21no—
262C3×C42—21no—
263#213—28no—
264(C2×D3)⋊C4—24no—
265C4⋊Dic3—21no—
266C4⋊Dic3C5×D412yes—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8C2×C4×C512yescomplemented
273C23×C5—22no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—62no—
281C23×C5—62no—
282C23×C5—62no—
283C23×C5—121no—
284C23×C5—121no—
285C23×C5—121no—
286C23×C5—121no—
287C23×C5C2×#6711yescharacteristic
288C5×D4—22no—
289C5×D4—22no—
290C5×D4—34no—
291C5×D4—41no—
292C5×D4—41no—
293C5×D4—62no—
294C5×D4—62no—
295C5×D4—62no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—62no—
305C2×C4×C5—128no—
306C2×C4×C5—121no—
307C2×C4×C5—121no—
308C2×C4×C5#21312yescomplemented
309C2×C4×C5C2×C4×D311yescharacteristic
310C2×C4×C5#23511yescharacteristic
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5#23711yescharacteristic
315C5×C8—62no—
316C5×C8—121no—
317C22×D4—31no—
318C22×D4C2×C5×D311yescharacteristic
319C23×C4—61no—
320C2×D8—34no—
321C2×D8—62no—
322C2×D8—62no—
323C22×C8—31no—
324C22×C8—31no—
325C4×D4—62no—
326C4×D4—62no—
327C2×C4⋊C4—31no—
328C2×C4⋊C4C2×C5×D311yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—61no—
332C2×C42C2×C5×D311yescharacteristic
333#102—62no—
334#102—62no—
335C2×C3×C5—82no—
336C2×C3×C5#38611yescharacteristic
337C2×C3×C5C4×D811yescharacteristic
338C2×C3×C5#44211yescharacteristic
339C2×C3×C5#44711yescharacteristic
340C2×C3×C5#44911yescharacteristic
341C2×C3×C5#45911yescharacteristic
342C2×C3×C5#46311yescharacteristic
343C5×D3—44no—
344C23×C3—22no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3C2×C5×D411yescharacteristic
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—41no—
356C22×D3—41no—
357C22×D3—41no—
358C22×D3—41no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—41no—
362C3×D4—41no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4C5×D812yescomplemented
372C2×C3×C4C22×C4×C511yescharacteristic
373C2×C3×C4C2×C5×D411yescharacteristic
374C2×C3×C4C2×C5×D411yescharacteristic
375C2×C3×C4C2×C5×D411yescharacteristic
376C2×C3×C4C5×#4111yescharacteristic
377C2×C3×C4C5×#4111yescharacteristic
378C2×Dic3—22no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381D12—22no—
382D12—22no—
383D12—22no—
384D12C5×C22⋊C414yescomplemented
385C4×D3—48no—
386C3⋊C8—22no—
387C3⋊C8—41no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—64no—
392C22×C5—81no—
393C22×C5—81no—
394C22×C5—81no—
395C22×C5—81no—
396C22×C5—122no—
397C22×C5—122no—
398C22×C5—122no—
399C22×C5—122no—
400C22×C5—122no—
401C22×C5—122no—
402C22×C5C4×#6711yescharacteristic
403C22×C5C2×#21311yescharacteristic
404C22×C5#93211yescharacteristic
405C22×C5#93711yescharacteristic
406C22×C5#93811yescharacteristic
407C22×C5#94911yescharacteristic
408C22×C5#95011yescharacteristic
409C4×C5—22no—
410C4×C5—41no—
411C4×C5—81no—
412C4×C5—122no—
413C4×C5D3×C22⋊C411yescharacteristic
414C4×C5#67⋊C411yescharacteristic
415C4×C5#88311yescharacteristic
416C4×C5#88411yescharacteristic
417C24—21no—
418C24—61no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—32no—
425C2×D4—32no—
426C2×D4—32no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4C4×C5×D312yescomplemented
431C22×C4—21no—
432C22×C4—64no—
433C22×C4—61no—
434C22×C4—122no—
435C22×C4—122no—
436C22×C4C5×#6711yescharacteristic
437C22×C4C5×#6711yescharacteristic
438C22×C4C22×C5×D311yescharacteristic
439D8—68no—
440C2×C8—32no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—32no—
449C4⋊C4—61no—
450C22⋊C4—42no—
451C22⋊C4—42no—
452C22⋊C4—64no—
453C42—21no—
454C42—21no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3C4×C5×D411yescharacteristic
464C22×C3C5×#12011yescharacteristic
465C22×C3C5×#12111yescharacteristic
466C22×C3C2×C5×D811yescharacteristic
467C22×C3C5×#13511yescharacteristic
468C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
469C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
470C2×D3—24no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—42no—
477C3×C4—22no—
478C3×C4—41no—
479C3×C4—81no—
480C3×C4C2×C5×C22⋊C411yescharacteristic
481C3×C4C4×C5×D411yescharacteristic
482C3×C4C5×#12111yescharacteristic
483C3×C4C5×#12311yescharacteristic
484Dic3—42no—
485C2×C5—82no—
486C2×C5—124no—
487C2×C5#495611yescharacteristic
488C2×C5C4×#21311yescharacteristic
489C2×C5#501411yescharacteristic
490C2×C5#503611yescharacteristic
491C2×C5#503711yescharacteristic
492C2×C5#505711yescharacteristic
493C2×C5#507211yescharacteristic
494C23—22no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—62no—
502C23—62no—
503C23—62no—
504C23—121no—
505C23—121no—
506C23—121no—
507C23—121no—
508C23C2×C5×#6711yescharacteristic
509D4—22no—
510D4—22no—
511D4—34no—
512D4—41no—
513D4—41no—
514D4—62no—
515D4—62no—
516D4—62no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—62no—
526C2×C4—128no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4C5×#21312yescomplemented
530C2×C4C2×C4×C5×D311yescharacteristic
531C2×C4C5×#23511yescharacteristic
532C2×C4C5×D3×D411yescharacteristic
533C2×C4C5×D3×D411yescharacteristic
534C2×C4C5×D3×D411yescharacteristic
535C2×C4C5×#23711yescharacteristic
536C8—62no—
537C8—121no—
538C2×C3—82no—
539C2×C3C5×#38611yescharacteristic
540C2×C3C4×C5×D811yescharacteristic
541C2×C3C5×#44211yescharacteristic
542C2×C3C5×#44711yescharacteristic
543C2×C3C5×#44911yescharacteristic
544C2×C3C5×#45911yescharacteristic
545C2×C3C5×#46311yescharacteristic
546D3—44no—
547C5#6965711yescharacteristic, direct product factor, Sylow
548C22—42no—
549C22—42no—
550C22—42no—
551C22—64no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—122no—
557C22—122no—
558C22—122no—
559C22—122no—
560C22—122no—
561C22—122no—
562C22C4×C5×#6711yescharacteristic
563C22C2×C5×#21311yescharacteristic
564C22C5×#93211yescharacteristic
565C22C5×#93711yescharacteristic
566C22C5×#93811yescharacteristic
567C22C5×#94911yescharacteristic
568C22C5×#95011yescharacteristic
569C4—22no—
570C4—41no—
571C4—81no—
572C4—122no—
573C4C5×D3×C22⋊C411yescharacteristic
574C4C5×#67⋊C411yescharacteristic
575C4C5×#88311yescharacteristic
576C4C5×#88411yescharacteristic
577C3C5×#187911yescharacteristic, complemented, Sylow
578C2—82no—
579C2—124no—
580C2C5×#495611yescharacteristic
581C2C4×C5×#21311yescharacteristic
582C2C5×#501411yescharacteristic
583C2C5×#503611yescharacteristic
584C2C5×#503711yescharacteristic
585C2C5×#505711yescharacteristic
586C2C5×#507211yescharacteristic
subgroupG/H
centerC23×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#390C2
socleC23×C3×C5C2×D4
prime radicalC22×C5×#213C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#390D3
hypocenterC3C5×#1879
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C5×#390

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×D12C2semidirect
3. C3×C5×#390C2semidirect
4. C2×C5×#832C2semidirect
5. C2×C5×#809C2semidirect
6. C5×#4529C2semidirect
7. C5×#4524C2semidirect
18. C2×C5×#213C4semidirect
27. #69657C5direct (N × H)
32. C5×#390D3semidirect
42. C2×C3×C5×D4C2×C4semidirect
72. C2×C5×C3⋊C8C2×C4semidirect
74. C2×C4×D12C2×C5semidirect
75. C3×#390C2×C5semidirect
76. C2×#832C2×C5semidirect
77. C2×#809C2×C5semidirect
78. #4529C2×C5semidirect
79. #4524C2×C5semidirect
126. C2×C3×C4×C5D8semidirect
139. C5×D12C22⋊C4semidirect
152. C2×#213C4×C5semidirect
174. C2×C5×D4C4×D3semidirect
203. #390C5×D3semidirect
242. C2×C3×D4C2×C4×C5semidirect
272. C2×C3⋊C8C2×C4×C5semidirect
308. C2×C4×C5#213semidirect
371. C2×C3×C4C5×D8semidirect
384. D12C5×C22⋊C4semidirect
430. C2×D4C4×C5×D3semidirect
455. C3×C5#1879semidirect
529. C2×C4C5×#213semidirect
547. C5#69657direct (N × H)
577. C3C5×#1879semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2132
C2×C4×C5×D122
C3×C5×#3902
C2×C5×#8322
C2×C5×#8092
C5×#45292
C5×#45242
C5×#18793
#696575