Finite Group Databasebeta

← C5×#74060 #14326560

Subgroups — C5×#74060 #14326560

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#926C211yesmaximal, characteristic
2C22×C5×Dic3⋊C4C211yesmaximal, characteristic
3C2×C5×#877C211yesmaximal, characteristic
4C3×C5×#381C211yesmaximal, characteristic
5C5×#4943C211yesmaximal, characteristic
6C5×#4942C211yesmaximal, characteristic
7C5×Dic3×C22⋊C4C211yesmaximal, characteristic
8C5×#4655C212yesmaximal, complemented
9C5×#4652C212yesmaximal, complemented
10C5×#4649C212yesmaximal, complemented
11C5×#4647C212yesmaximal, complemented
12C5×#2344—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×C5×#217C2211yescharacteristic
19C2×C5×#217C2211yescharacteristic
20C5×#926—24no—
21C2×C5×C4⋊Dic3C2212yes—
22C2×C5×Dic3⋊C4C418yescomplemented
23C2×C5×Dic3⋊C4C2212yes—
24C2×C5×Dic3⋊C4C2212yes—
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2212yes—
30C2×C4×C5×Dic3C2212yes—
31C2×C4×C5×Dic3C2212yes—
32C5×#877—24no—
33C3×C5×#95C2212yes—
34C3×C5×#95C2212yes—
35C5×C3⋊#95C2212yes—
36C5×C3⋊#95C2212yes—
37C5×C3⋊#95C2212yes—
38C5×C3⋊#95C2212yes—
39#74060C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#117—31no—
41C2×C5×#117—31no—
42C22×C5×C4⋊C4—31no—
43C5×#389—32no—
44C5×#387—32no—
45C5×#387—32no—
46C5×#381—31no—
47C5×#381D311yescharacteristic
48C5×#380—31no—
49C4×C5×C4⋊C4—32no—
50C4×C5×C22⋊C4—31no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5C2×C414yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C5×Dic3—22no—
60C22×C5×Dic3—22no—
61C22×C5×Dic3—24no—
62C22×C5×Dic3C2×C414yes—
63C22×C5×Dic3C2×C414yes—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2311yescharacteristic
67C22×C5×Dic3C2311yescharacteristic
68C22×C5×Dic3C2312yes—
69C22×C5×Dic3C2311yescharacteristic
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4—22no—
72C5×#217—22no—
73C5×#217D414yes—
74C5×C4⋊Dic3—24no—
75C5×Dic3⋊C4—24no—
76C5×Dic3⋊C4—24no—
77C5×Dic3⋊C4C2×C414yes—
78C5×Dic3⋊C4C2×C414yes—
79C5×Dic3⋊C4C2×C414yes—
80C5×Dic3⋊C4C2×C414yes—
81C4×C5×Dic3—24no—
82C4×C5×Dic3—24no—
83C4×C5×Dic3—24no—
84C2×#926C2×C511yescharacteristic
85C22×Dic3⋊C4C2×C511yescharacteristic
86C2×#877C2×C511yescharacteristic
87C3×#381C2×C511yescharacteristic
88#4943C2×C511yescharacteristic
89#4942C2×C511yescharacteristic
90Dic3×C22⋊C4C2×C511yescharacteristic
91#4655C2×C512yescomplemented
92#4652C2×C512yescomplemented
93#4649C2×C512yescomplemented
94#4647C2×C512yescomplemented
95C23×C4×C5—31no—
96C23×C4×C5—31no—
97C23×C4×C5C2×D311yescharacteristic
98C5×#117—64no—
99C5×#117—64no—
100C2×C5×C4⋊C4—38no—
101C2×C5×C4⋊C4—31no—
102C2×C5×C4⋊C4—31no—
103C2×C5×C4⋊C4—31no—
104C2×C5×C4⋊C4—31no—
105C2×C5×C4⋊C4—32no—
106C2×C5×C4⋊C4—32no—
107C2×C5×C4⋊C4—32no—
108C2×C5×C22⋊C4—31no—
109C2×C5×C22⋊C4—31no—
110C2×C5×C22⋊C4C2×D311yescharacteristic
111C2×C5×C22⋊C4C2×D311yescharacteristic
112C2×C42×C5—32no—
113C2×C42×C5—32no—
114C2×C42×C5—32no—
115C5×#95—32no—
116C5×#95—32no—
117C5×#95—32no—
118C5×#95—32no—
119C5×#95C2×D312yes—
120C5×#95C2×D312yes—
121#2344—31noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5C2411yescharacteristic
128C2×C3×C4×C5—28no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C5×Dic3—28no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—28no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3C22×C412yes—
154C2×C5×Dic3C22×C412yes—
155C2×C5×Dic3C22×C412yes—
156C2×C5×Dic3C22×C412yes—
157C2×C5×Dic3C2×D414yes—
158C2×C5×Dic3#4114yes—
159C23×C3×C4C22×C511yescharacteristic
160C23×Dic3C22×C511yescharacteristic
161C23×Dic3C22×C511yescharacteristic
162C2×C3×C22⋊C4C22×C511yescharacteristic
163C2×C3×C22⋊C4C22×C511yescharacteristic
164C2×#217C22×C511yescharacteristic
165C2×#217C22×C511yescharacteristic
166#926—24no—
167C2×C4⋊Dic3C22×C512yes—
168C2×Dic3⋊C4C4×C518yescomplemented
169C2×Dic3⋊C4C22×C512yes—
170C2×Dic3⋊C4C22×C512yes—
171C2×Dic3⋊C4C22×C511yescharacteristic
172C2×Dic3⋊C4C22×C511yescharacteristic
173C2×Dic3⋊C4C22×C511yescharacteristic
174C2×Dic3⋊C4C22×C511yescharacteristic
175C2×C4×Dic3C22×C512yes—
176C2×C4×Dic3C22×C512yes—
177C2×C4×Dic3C22×C512yes—
178#877—24no—
179C3×#95C22×C512yes—
180C3×#95C22×C512yes—
181C3⋊#95C22×C512yes—
182C3⋊#95C22×C512yes—
183C3⋊#95C22×C512yes—
184C3⋊#95C22×C512yes—
185C24×C5C22×D311yescharacteristic
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—31no—
189C22×C4×C5—34no—
190C22×C4×C5—34no—
191C22×C4×C5—32no—
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5—31no—
195C22×C4×C5—32no—
196C22×C4×C5—64no—
197C22×C4×C5—62no—
198C22×C4×C5—62no—
199C22×C4×C5C4×D314yes—
200C22×C4×C5C22×D312yes—
201C22×C4×C5C22×D312yes—
202C22×C4×C5C22×D311yescharacteristic
203C22×C4×C5C22×D311yescharacteristic
204C5×C4⋊C4—34no—
205C5×C4⋊C4—34no—
206C5×C4⋊C4—34no—
207C5×C4⋊C4—34no—
208C5×C4⋊C4—64no—
209C5×C4⋊C4—64no—
210C5×C4⋊C4—64no—
211C5×C22⋊C4—22no—
212C5×C22⋊C4—22no—
213C5×C22⋊C4—34no—
214C5×C22⋊C4—62no—
215C42×C5—64no—
216C42×C5—64no—
217C42×C5—64no—
218C2×#117—31no—
219C2×#117—31no—
220C22×C4⋊C4—31no—
221#389—32no—
222#387—32no—
223#387—32no—
224#381—31no—
225#381C5×D311yescharacteristic
226#380—31no—
227C4×C4⋊C4—32no—
228C4×C22⋊C4—31no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5C4×D414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C22×C3×C5C2×#4112yes—
238C22×C3×C52−1+412yes—
239C3×C4×C5—22no—
240C3×C4×C5—22no—
241C3×C4×C5—42no—
242C3×C4×C5—42no—
243C5×Dic3—22no—
244C5×Dic3—22no—
245C5×Dic3—22no—
246C5×Dic3—24no—
247C5×Dic3—42no—
248C5×Dic3#11714yescomplemented
249C24×C3C23×C511yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4C2×C4×C514yes—
253C22×C3×C4C23×C512yes—
254C22×C3×C4C23×C512yes—
255C22×C3×C4C23×C511yescharacteristic
256C22×C3×C4C23×C511yescharacteristic
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—24no—
260C22×Dic3C2×C4×C514yes—
261C22×Dic3C2×C4×C514yes—
262C22×Dic3C23×C512yes—
263C22×Dic3C23×C511yescharacteristic
264C22×Dic3C23×C511yescharacteristic
265C22×Dic3C23×C511yescharacteristic
266C22×Dic3C23×C512yes—
267C22×Dic3C23×C511yescharacteristic
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270#217—22no—
271#217C5×D414yes—
272C4⋊Dic3—24no—
273Dic3⋊C4—24no—
274Dic3⋊C4—24no—
275Dic3⋊C4C2×C4×C514yes—
276Dic3⋊C4C2×C4×C514yes—
277Dic3⋊C4C2×C4×C514yes—
278Dic3⋊C4C2×C4×C514yes—
279C4×Dic3—24no—
280C4×Dic3—24no—
281C4×Dic3—24no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5C2×C4×D312yes—
285C23×C5D3×D412yes—
286C23×C5#23712yes—
287C23×C5C23×D311yescharacteristic
288C2×C4×C5—28no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—32no—
300C2×C4×C5—34no—
301C2×C4×C5—32no—
302C2×C4×C5—32no—
303C2×C4×C5—32no—
304C2×C4×C5—34no—
305C2×C4×C5—68no—
306C2×C4×C5—68no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—62no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5C2×C4×D312yes—
318C2×C4×C5C2×C4×D312yes—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4C2×C5×D311yescharacteristic
322#117—64no—
323#117—64no—
324C2×C4⋊C4—38no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—31no—
327C2×C4⋊C4—31no—
328C2×C4⋊C4—31no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—32no—
331C2×C4⋊C4—32no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4C2×C5×D311yescharacteristic
335C2×C22⋊C4C2×C5×D311yescharacteristic
336C2×C42—32no—
337C2×C42—32no—
338C2×C42—32no—
339#95—32no—
340#95—32no—
341#95—32no—
342#95—32no—
343#95C2×C5×D312yes—
344#95C2×C5×D312yes—
345C2×C3×C5—24no—
346C2×C3×C5C2×#11711yescharacteristic
347C2×C3×C5C2×C4×D411yescharacteristic
348C2×C3×C5#51911yescharacteristic
349C2×C3×C5#54712yes—
350C2×C3×C5#55212yes—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3C22×C4×C512yes—
354C23×C3C2×C5×D412yes—
355C23×C3C5×#4112yes—
356C23×C3C24×C511yescharacteristic
357C2×C3×C4—28no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4C22×C4×C512yes—
369C2×C3×C4C22×C4×C512yes—
370C2×Dic3—28no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—22no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—28no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3C22×C4×C512yes—
383C2×Dic3C22×C4×C512yes—
384C2×Dic3C22×C4×C512yes—
385C2×Dic3C22×C4×C512yes—
386C2×Dic3C2×C5×D414yes—
387C2×Dic3C5×#4114yes—
388C22×C5—24no—
389C22×C5—24no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5#67⋊C414yes—
393C22×C5C22×C4×D311yescharacteristic
394C22×C5C2×D3×D411yescharacteristic
395C22×C5C2×#23711yescharacteristic
396C22×C5D3×#4112yes—
397C22×C5#101012yes—
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—34no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—64no—
404C4×C5—62no—
405C4×C5—62no—
406C4×C5—62no—
407C4×C5—122no—
408C24C22×C5×D311yescharacteristic
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—31no—
412C22×C4—34no—
413C22×C4—34no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—32no—
418C22×C4—32no—
419C22×C4—64no—
420C22×C4—62no—
421C22×C4—62no—
422C22×C4C4×C5×D314yes—
423C22×C4C22×C5×D312yes—
424C22×C4C22×C5×D312yes—
425C22×C4C22×C5×D311yescharacteristic
426C22×C4C22×C5×D311yescharacteristic
427C4⋊C4—34no—
428C4⋊C4—34no—
429C4⋊C4—34no—
430C4⋊C4—34no—
431C4⋊C4—64no—
432C4⋊C4—64no—
433C4⋊C4—64no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—34no—
437C22⋊C4—62no—
438C42—64no—
439C42—64no—
440C42—64no—
441C3×C5#234411yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3C4×C5×D414yes—
447C22×C3C23×C4×C511yescharacteristic
448C22×C3C22×C5×D411yescharacteristic
449C22×C3C2×C5×#4111yescharacteristic
450C22×C3C2×C5×#4112yes—
451C22×C3C5×2−1+412yes—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—42no—
455C3×C4—42no—
456Dic3—22no—
457Dic3—22no—
458Dic3—22no—
459Dic3—24no—
460Dic3—42no—
461Dic3C5×#11714yescomplemented
462C2×C5—24no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#551611yescharacteristic
465C2×C5D3×#11711yescharacteristic
466C2×C5#565012yes—
467C2×C5#565512yes—
468C23—22no—
469C23—22no—
470C23C2×C4×C5×D312yes—
471C23C5×D3×D412yes—
472C23C5×#23712yes—
473C23C23×C5×D311yescharacteristic
474C2×C4—28no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—32no—
486C2×C4—34no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—34no—
491C2×C4—68no—
492C2×C4—68no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4C2×C4×C5×D312yes—
504C2×C4C2×C4×C5×D312yes—
505C2×C3—24no—
506C2×C3C2×C5×#11711yescharacteristic
507C2×C3C2×C4×C5×D411yescharacteristic
508C2×C3C5×#51911yescharacteristic
509C2×C3C5×#54712yes—
510C2×C3C5×#55212yes—
511C5#7406011yescharacteristic, direct product factor, Sylow
512C22—24no—
513C22—24no—
514C22—22no—
515C22—22no—
516C22C5×#67⋊C414yes—
517C22C22×C4×C5×D311yescharacteristic
518C22C2×C5×D3×D411yescharacteristic
519C22C2×C5×#23711yescharacteristic
520C22C5×D3×#4112yes—
521C22C5×#101012yes—
522C4—22no—
523C4—22no—
524C4—34no—
525C4—42no—
526C4—42no—
527C4—64no—
528C4—62no—
529C4—62no—
530C4—62no—
531C4—122no—
532C3C5×#234411yescharacteristic, complemented, Sylow
533C2—24no—
534C2C2×C5×#67⋊C411yescharacteristic
535C2C5×#551611yescharacteristic
536C2C5×D3×#11711yescharacteristic
537C2C5×#565012yes—
538C2C5×#565512yes—
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#381C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC5×#381D3
hypocenterC3C5×#2344
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#381

Complements

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

NH ≅ G/Ntype
8. C5×#4655C2semidirect
9. C5×#4652C2semidirect
10. C5×#4649C2semidirect
11. C5×#4647C2semidirect
22. C2×C5×Dic3⋊C4C4semidirect
39. #74060C5direct (N × H)
91. #4655C2×C5semidirect
92. #4652C2×C5semidirect
93. #4649C2×C5semidirect
94. #4647C2×C5semidirect
168. C2×Dic3⋊C4C4×C5semidirect
248. C5×Dic3#117semidirect
441. C3×C5#2344semidirect
461. Dic3C5×#117semidirect
511. C5#74060direct (N × H)
532. C3C5×#2344semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9262
C22×C5×Dic3⋊C42
C2×C5×#8772
C3×C5×#3812
C5×#49432
C5×#49422
C5×Dic3×C22⋊C42
C5×#46552
C5×#46522
C5×#46492
C5×#46472
C5×#23443
#740605