Finite Group Databasebeta

← C3×C5×#2409 #14275443

Subgroups — C3×C5×#2409 #14275443

Order 1920.

1680 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5×Q8C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊Q8C212yesmaximal, complemented
3C2×C3×C4×C5×D4C211yesmaximal, characteristic
4C3×C5×#395C212yesmaximal, complemented
5C3×C5×#393C212yesmaximal, complemented
6C3×C5×#391C212yesmaximal, complemented
7C3×C5×#386C212yesmaximal
8C3×C5×#385C212yesmaximal, complemented
9C3×C5×#380C211yesmaximal, characteristic, complemented
10C5×#2409C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×Q8—28no—
12C22×C3×C5×Q8—24no—
13C22×C3×C5×Q8C2212yes—
14C22×C3×C5×Q8C2212yes—
15C22×C3×C5×D4C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C23×C3×C4×C5C2212yes—
18C23×C3×C4×C5C2211yescharacteristic
19C3×C5×C22⋊Q8—28no—
20C3×C4×C5×D4—24no—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C4⋊C4C2214yes—
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2214yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C42×C5C2211yescharacteristic
29C3×C5×#95C2212yes—
30C3×C5×#95C2214yes—
31C3×C5×#95C2214yes—
32C3×#2409C511yesmaximal, characteristic, direct product factor, Hall
33C23×C5×Q8C2×C311yescharacteristic, complemented
34C2×C5×C22⋊Q8C2×C312yescomplemented
35C2×C4×C5×D4C2×C311yescharacteristic
36C5×#395C2×C312yescomplemented
37C5×#393C2×C312yescomplemented
38C5×#391C2×C312yescomplemented
39C5×#386C2×C312yes—
40C5×#385C2×C312yescomplemented
41C5×#380C2×C311yescharacteristic, complemented
42C24×C3×C5C2311yescharacteristic
43C24×C3×C5C2311yescharacteristic
44C2×C3×C5×Q8—232no—
45C2×C3×C5×Q8—28no—
46C2×C3×C5×Q8—24no—
47C2×C3×C5×Q8—24no—
48C2×C3×C5×Q8—24no—
49C2×C3×C5×Q8D418yescomplemented
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4Q814yescomplemented
53C22×C3×C4×C5—24no—
54C22×C3×C4×C5—28no—
55C22×C3×C4×C5—24no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—24no—
58C22×C3×C4×C5D414yes—
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2314yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2314yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4—24no—
68C3×C5×C4⋊C4—28no—
69C3×C5×C22⋊C4—22no—
70C3×C5×C22⋊C4—24no—
71C3×C5×C22⋊C4—22no—
72C3×C5×C22⋊C4—28no—
73C3×C42×C5—22no—
74C23×C3×Q8C2×C511yescharacteristic, complemented
75C2×C3×C22⋊Q8C2×C512yescomplemented
76C2×C3×C4×D4C2×C511yescharacteristic
77C3×#395C2×C512yescomplemented
78C3×#393C2×C512yescomplemented
79C3×#391C2×C512yescomplemented
80C3×#386C2×C512yes—
81C3×#385C2×C512yescomplemented
82C3×#380C2×C511yescharacteristic, complemented
83C22×C5×Q8—28no—
84C22×C5×Q8—24no—
85C22×C5×Q8C22×C312yes—
86C22×C5×Q8C22×C312yes—
87C22×C5×D4C22×C311yescharacteristic
88C23×C4×C5C22×C312yes—
89C23×C4×C5C22×C311yescharacteristic
90C23×C4×C5C22×C311yescharacteristic
91C5×C22⋊Q8—28no—
92C4×C5×D4—24no—
93C2×C5×C4⋊C4C22×C312yes—
94C2×C5×C4⋊C4C22×C314yes—
95C2×C5×C4⋊C4C22×C311yescharacteristic
96C2×C5×C22⋊C4C22×C312yes—
97C2×C5×C22⋊C4C22×C311yescharacteristic
98C2×C5×C22⋊C4C22×C314yes—
99C2×C5×C22⋊C4C22×C311yescharacteristic
100C2×C42×C5C22×C311yescharacteristic
101C5×#95C22×C312yes—
102C5×#95C22×C314yes—
103C5×#95C22×C314yes—
104#2409C3×C511yescharacteristic, direct product factor, Sylow
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5—22no—
108C23×C3×C5—21no—
109C23×C3×C5—21no—
110C23×C3×C5—22no—
111C23×C3×C5C2×D412yes—
112C23×C3×C5C2×Q812yes—
113C23×C3×C5C2×Q812yescomplemented
114C23×C3×C5#4112yes—
115C23×C3×C5C2411yescharacteristic
116C3×C5×Q8—216no—
117C3×C5×Q8—216no—
118C3×C5×D4—28no—
119C2×C3×C4×C5—216no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—24no—
122C2×C3×C4×C5—24no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—28no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—24no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—24no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—24no—
133C2×C3×C4×C5—44no—
134C2×C3×C4×C5C2×D418yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D414yes—
138C2×C3×C4×C5C2×Q812yescomplemented
139C22×C3×Q8—28no—
140C22×C3×Q8—24no—
141C22×C3×Q8C22×C512yes—
142C22×C3×Q8C22×C512yes—
143C22×C3×D4C22×C511yescharacteristic
144C23×C3×C4C22×C512yes—
145C23×C3×C4C22×C511yescharacteristic
146C23×C3×C4C22×C511yescharacteristic
147C3×C22⋊Q8—28no—
148C3×C4×D4—24no—
149C2×C3×C4⋊C4C22×C512yes—
150C2×C3×C4⋊C4C22×C514yes—
151C2×C3×C4⋊C4C22×C511yescharacteristic
152C2×C3×C22⋊C4C22×C512yes—
153C2×C3×C22⋊C4C22×C511yescharacteristic
154C2×C3×C22⋊C4C22×C514yes—
155C2×C3×C22⋊C4C22×C511yescharacteristic
156C2×C3×C42C22×C511yescharacteristic
157C3×#95C22×C512yes—
158C3×#95C22×C514yes—
159C3×#95C22×C514yes—
160C24×C5C23×C311yescharacteristic
161C24×C5C23×C311yescharacteristic
162C2×C5×Q8—232no—
163C2×C5×Q8—28no—
164C2×C5×Q8—24no—
165C2×C5×Q8—24no—
166C2×C5×Q8—24no—
167C2×C5×Q8C3×D418yescomplemented
168C2×C5×D4—22no—
169C2×C5×D4—22no—
170C2×C5×D4C3×Q814yescomplemented
171C22×C4×C5—24no—
172C22×C4×C5—28no—
173C22×C4×C5—24no—
174C22×C4×C5—22no—
175C22×C4×C5—24no—
176C22×C4×C5C3×D414yes—
177C22×C4×C5C23×C311yescharacteristic
178C22×C4×C5C23×C314yes—
179C22×C4×C5C23×C311yescharacteristic
180C22×C4×C5C23×C314yes—
181C22×C4×C5C23×C311yescharacteristic
182C22×C4×C5C23×C311yescharacteristic
183C22×C4×C5C23×C311yescharacteristic
184C5×C4⋊C4—22no—
185C5×C4⋊C4—24no—
186C5×C4⋊C4—28no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—24no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—28no—
191C42×C5—22no—
192C23×Q8C2×C3×C511yescharacteristic, complemented
193C2×C22⋊Q8C2×C3×C512yescomplemented
194C2×C4×D4C2×C3×C511yescharacteristic
195#395C2×C3×C512yescomplemented
196#393C2×C3×C512yescomplemented
197#391C2×C3×C512yescomplemented
198#386C2×C3×C512yes—
199#385C2×C3×C512yescomplemented
200#380C2×C3×C511yescharacteristic, complemented
201C22×C3×C5—22no—
202C22×C3×C5—22no—
203C22×C3×C5—24no—
204C22×C3×C5—24no—
205C22×C3×C5—22no—
206C22×C3×C5—24no—
207C22×C3×C5—41no—
208C22×C3×C5—41no—
209C22×C3×C5—42no—
210C22×C3×C5C22⋊Q814yescomplemented
211C22×C3×C5C22×D411yescharacteristic
212C22×C3×C5C22×D412yes—
213C22×C3×C5C22×Q811yescharacteristic
214C22×C3×C5C2×#4111yescharacteristic
215C22×C3×C52−1+412yes—
216C3×C4×C5—28no—
217C3×C4×C5—22no—
218C3×C4×C5—22no—
219C3×C4×C5—41no—
220C3×C4×C5—41no—
221C3×C4×C5—44no—
222C3×C4×C5#12014yes—
223C24×C3C23×C511yescharacteristic
224C24×C3C23×C511yescharacteristic
225C2×C3×Q8—232no—
226C2×C3×Q8—28no—
227C2×C3×Q8—24no—
228C2×C3×Q8—24no—
229C2×C3×Q8—24no—
230C2×C3×Q8C5×D418yescomplemented
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4C5×Q814yescomplemented
234C22×C3×C4—24no—
235C22×C3×C4—28no—
236C22×C3×C4—24no—
237C22×C3×C4—22no—
238C22×C3×C4—24no—
239C22×C3×C4C5×D414yes—
240C22×C3×C4C23×C511yescharacteristic
241C22×C3×C4C23×C514yes—
242C22×C3×C4C23×C511yescharacteristic
243C22×C3×C4C23×C514yes—
244C22×C3×C4C23×C511yescharacteristic
245C22×C3×C4C23×C511yescharacteristic
246C22×C3×C4C23×C511yescharacteristic
247C3×C4⋊C4—22no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4—28no—
250C3×C22⋊C4—22no—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—28no—
254C3×C42—22no—
255C23×C5—22no—
256C23×C5—22no—
257C23×C5—22no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—22no—
261C23×C5C2×C3×D412yes—
262C23×C5C2×C3×Q812yes—
263C23×C5C2×C3×Q812yescomplemented
264C23×C5C3×#4112yes—
265C23×C5C24×C311yescharacteristic
266C5×Q8—216no—
267C5×Q8—216no—
268C5×D4—28no—
269C2×C4×C5—216no—
270C2×C4×C5—21no—
271C2×C4×C5—24no—
272C2×C4×C5—24no—
273C2×C4×C5—22no—
274C2×C4×C5—21no—
275C2×C4×C5—28no—
276C2×C4×C5—21no—
277C2×C4×C5—24no—
278C2×C4×C5—21no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—24no—
283C2×C4×C5—44no—
284C2×C4×C5C2×C3×D418yes—
285C2×C4×C5C2×C3×D412yes—
286C2×C4×C5C2×C3×D412yes—
287C2×C4×C5C2×C3×D414yes—
288C2×C4×C5C2×C3×Q812yescomplemented
289C22×Q8—28no—
290C22×Q8—24no—
291C22×Q8C22×C3×C512yes—
292C22×Q8C22×C3×C512yes—
293C22×D4C22×C3×C511yescharacteristic
294C23×C4C22×C3×C511yescharacteristic
295C23×C4C22×C3×C512yes—
296C23×C4C22×C3×C511yescharacteristic
297C22⋊Q8—28no—
298C4×D4—24no—
299C2×C4⋊C4C22×C3×C511yescharacteristic
300C2×C4⋊C4C22×C3×C512yes—
301C2×C4⋊C4C22×C3×C514yes—
302C2×C22⋊C4C22×C3×C511yescharacteristic
303C2×C22⋊C4C22×C3×C511yescharacteristic
304C2×C22⋊C4C22×C3×C514yes—
305C2×C22⋊C4C22×C3×C512yes—
306C2×C42C22×C3×C511yescharacteristic
307#95C22×C3×C512yes—
308#95C22×C3×C514yes—
309#95C22×C3×C514yes—
310C2×C3×C5—24no—
311C2×C3×C5—42no—
312C2×C3×C5C2×#12011yescharacteristic
313C2×C3×C5C2×C22⋊Q811yescharacteristic
314C2×C3×C5#53611yescharacteristic
315C2×C3×C5#54812yes—
316C2×C3×C5D4×Q812yes—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3C2×C5×D412yes—
324C23×C3C2×C5×Q812yes—
325C23×C3C2×C5×Q812yescomplemented
326C23×C3C5×#4112yes—
327C23×C3C24×C511yescharacteristic
328C3×Q8—216no—
329C3×Q8—216no—
330C3×D4—28no—
331C2×C3×C4—216no—
332C2×C3×C4—21no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—28no—
338C2×C3×C4—21no—
339C2×C3×C4—24no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—24no—
345C2×C3×C4—44no—
346C2×C3×C4C2×C5×D418yes—
347C2×C3×C4C2×C5×D412yes—
348C2×C3×C4C2×C5×D412yes—
349C2×C3×C4C2×C5×D414yes—
350C2×C3×C4C2×C5×Q812yescomplemented
351C22×C5—22no—
352C22×C5—22no—
353C22×C5—24no—
354C22×C5—24no—
355C22×C5—22no—
356C22×C5—24no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—42no—
360C22×C5C3×C22⋊Q814yescomplemented
361C22×C5C22×C3×D411yescharacteristic
362C22×C5C22×C3×D412yes—
363C22×C5C22×C3×Q811yescharacteristic
364C22×C5C2×C3×#4111yescharacteristic
365C22×C5C3×2−1+412yes—
366C4×C5—28no—
367C4×C5—22no—
368C4×C5—22no—
369C4×C5—41no—
370C4×C5—41no—
371C4×C5—44no—
372C4×C5C3×#12014yes—
373C24C23×C3×C511yescharacteristic
374C24C23×C3×C511yescharacteristic
375C2×Q8—232no—
376C2×Q8—28no—
377C2×Q8—24no—
378C2×Q8—24no—
379C2×Q8—24no—
380C2×Q8C3×C5×D418yescomplemented
381C2×D4—22no—
382C2×D4—22no—
383C2×D4C3×C5×Q814yescomplemented
384C22×C4—24no—
385C22×C4—28no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4C3×C5×D414yes—
390C22×C4C23×C3×C511yescharacteristic
391C22×C4C23×C3×C514yes—
392C22×C4C23×C3×C511yescharacteristic
393C22×C4C23×C3×C514yes—
394C22×C4C23×C3×C511yescharacteristic
395C22×C4C23×C3×C511yescharacteristic
396C22×C4C23×C3×C511yescharacteristic
397C4⋊C4—22no—
398C4⋊C4—24no—
399C4⋊C4—28no—
400C22⋊C4—22no—
401C22⋊C4—24no—
402C22⋊C4—22no—
403C22⋊C4—28no—
404C42—22no—
405C3×C5#240911yescharacteristic, direct product factor, Hall
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—22no—
411C22×C3—24no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—42no—
415C22×C3C5×C22⋊Q814yescomplemented
416C22×C3C22×C5×D411yescharacteristic
417C22×C3C22×C5×D412yes—
418C22×C3C22×C5×Q811yescharacteristic
419C22×C3C2×C5×#4111yescharacteristic
420C22×C3C5×2−1+412yes—
421C3×C4—28no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—44no—
427C3×C4C5×#12014yes—
428C2×C5—24no—
429C2×C5—42no—
430C2×C5C2×C3×#12011yescharacteristic
431C2×C5C2×C3×C22⋊Q811yescharacteristic
432C2×C5C3×#53611yescharacteristic
433C2×C5C3×#54812yes—
434C2×C5C3×D4×Q812yes—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—21no—
439C23—21no—
440C23—22no—
441C23C2×C3×C5×D412yes—
442C23C2×C3×C5×Q812yes—
443C23C2×C3×C5×Q812yescomplemented
444C23C3×C5×#4112yes—
445C23C24×C3×C511yescharacteristic
446Q8—216no—
447Q8—216no—
448D4—28no—
449C2×C4—216no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—28no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—44no—
464C2×C4C2×C3×C5×D418yes—
465C2×C4C2×C3×C5×D412yes—
466C2×C4C2×C3×C5×D412yes—
467C2×C4C2×C3×C5×D414yes—
468C2×C4C2×C3×C5×Q812yescomplemented
469C2×C3—24no—
470C2×C3—42no—
471C2×C3C2×C5×#12011yescharacteristic
472C2×C3C2×C5×C22⋊Q811yescharacteristic
473C2×C3C5×#53611yescharacteristic
474C2×C3C5×#54812yes—
475C2×C3C5×D4×Q812yes—
476C5C3×#240911yescharacteristic, direct product factor, Sylow
477C22—22no—
478C22—22no—
479C22—24no—
480C22—24no—
481C22—22no—
482C22—24no—
483C22—41no—
484C22—41no—
485C22—42no—
486C22C3×C5×C22⋊Q814yescomplemented
487C22C22×C3×C5×D411yescharacteristic
488C22C22×C3×C5×D412yes—
489C22C22×C3×C5×Q811yescharacteristic
490C22C2×C3×C5×#4111yescharacteristic
491C22C3×C5×2−1+412yes—
492C4—28no—
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—44no—
498C4C3×C5×#12014yes—
499C3C5×#240911yescharacteristic, direct product factor, Sylow
500C2—24no—
501C2—42no—
502C2C2×C3×C5×#12011yescharacteristic
503C2C2×C3×C5×C22⋊Q811yescharacteristic
504C2C3×C5×#53611yescharacteristic
505C2C3×C5×#54812yes—
506C2C3×C5×D4×Q812yes—
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×Q8C2semidirect
2. C2×C3×C5×C22⋊Q8C2semidirect
4. C3×C5×#395C2semidirect
5. C3×C5×#393C2semidirect
6. C3×C5×#391C2semidirect
8. C3×C5×#385C2semidirect
9. C3×C5×#380C2semidirect
10. C5×#2409C3direct (N × H)
32. C3×#2409C5direct (N × H)
33. C23×C5×Q8C2×C3semidirect
34. C2×C5×C22⋊Q8C2×C3semidirect
36. C5×#395C2×C3semidirect
37. C5×#393C2×C3semidirect
38. C5×#391C2×C3semidirect
40. C5×#385C2×C3semidirect
41. C5×#380C2×C3semidirect
49. C2×C3×C5×Q8D4semidirect
52. C2×C3×C5×D4Q8semidirect
74. C23×C3×Q8C2×C5semidirect
75. C2×C3×C22⋊Q8C2×C5semidirect
77. C3×#395C2×C5semidirect
78. C3×#393C2×C5semidirect
79. C3×#391C2×C5semidirect
81. C3×#385C2×C5semidirect
82. C3×#380C2×C5semidirect
104. #2409C3×C5direct (N × H)
113. C23×C3×C5C2×Q8semidirect
138. C2×C3×C4×C5C2×Q8semidirect
167. C2×C5×Q8C3×D4semidirect
170. C2×C5×D4C3×Q8semidirect
192. C23×Q8C2×C3×C5semidirect
193. C2×C22⋊Q8C2×C3×C5semidirect
195. #395C2×C3×C5semidirect
196. #393C2×C3×C5semidirect
197. #391C2×C3×C5semidirect
199. #385C2×C3×C5semidirect
200. #380C2×C3×C5semidirect
210. C22×C3×C5C22⋊Q8semidirect
230. C2×C3×Q8C5×D4semidirect
233. C2×C3×D4C5×Q8semidirect
263. C23×C5C2×C3×Q8semidirect
288. C2×C4×C5C2×C3×Q8semidirect
325. C23×C3C2×C5×Q8semidirect
350. C2×C3×C4C2×C5×Q8semidirect
360. C22×C5C3×C22⋊Q8semidirect
380. C2×Q8C3×C5×D4semidirect
383. C2×D4C3×C5×Q8semidirect
405. C3×C5#2409direct (N × H)
415. C22×C3C5×C22⋊Q8semidirect
443. C23C2×C3×C5×Q8semidirect
468. C2×C4C2×C3×C5×Q8semidirect
476. C5C3×#2409direct (N × H)
486. C22C3×C5×C22⋊Q8semidirect
499. C3C5×#2409direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×Q82
C2×C3×C5×C22⋊Q82
C2×C3×C4×C5×D42
C3×C5×#3952
C3×C5×#3932
C3×C5×#3912
C3×C5×#3862
C3×C5×#3852
C3×C5×#3802
C5×#24093
C3×#24095