Finite Group Databasebeta

← C3×C5×#1441 #14274475

Subgroups — C3×C5×#1441 #14274475

Order 1920.

1128 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
1C22×C3×C5×C4⋊C4C211yesmaximal, characteristic
2C22×C3×C5×C4⋊C4C211yesmaximal, characteristic
3C2×C3×C5×#95C212yesmaximal
4C2×C3×C5×#95C212yesmaximal
5C2×C3×C5×#95C211yesmaximal, characteristic
6C5×#1441C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C23×C3×C4×C5C2212yes—
9C23×C3×C4×C5C2212yes—
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C2×C3×C5×C4⋊C4—24no—
13C2×C3×C5×C4⋊C4—22no—
14C2×C3×C5×C4⋊C4—22no—
15C2×C3×C5×C4⋊C4—22no—
16C2×C3×C5×C4⋊C4C414yescomplemented
17C3×C5×#95—24no—
18C3×C5×#95—22no—
19C3×C5×#95—24no—
20C3×#1441C511yesmaximal, characteristic, direct product factor, Hall
21C22×C5×C4⋊C4C2×C311yescharacteristic
22C22×C5×C4⋊C4C2×C311yescharacteristic
23C2×C5×#95C2×C312yes—
24C2×C5×#95C2×C312yes—
25C2×C5×#95C2×C311yescharacteristic
26C24×C3×C5C2311yescharacteristic
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—22no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—22no—
36C22×C3×C4×C5—22no—
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—22no—
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—22no—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—22no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5C2×C412yes—
50C22×C3×C4×C5C2×C412yes—
51C22×C3×C4×C5C2×C412yes—
52C22×C3×C4×C5D414yes—
53C22×C3×C4×C5D412yes—
54C22×C3×C4×C5D412yes—
55C22×C3×C4×C5D412yes—
56C22×C3×C4×C5Q814yes—
57C22×C3×C4×C5Q812yes—
58C3×C5×C4⋊C4—28no—
59C3×C5×C4⋊C4—28no—
60C22×C3×C4⋊C4C2×C511yescharacteristic
61C22×C3×C4⋊C4C2×C511yescharacteristic
62C2×C3×#95C2×C512yes—
63C2×C3×#95C2×C512yes—
64C2×C3×#95C2×C511yescharacteristic
65C23×C4×C5C22×C311yescharacteristic
66C23×C4×C5C22×C312yes—
67C23×C4×C5C22×C312yes—
68C23×C4×C5C22×C311yescharacteristic
69C23×C4×C5C22×C311yescharacteristic
70C2×C5×C4⋊C4—24no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4C3×C414yescomplemented
75C5×#95—24no—
76C5×#95—22no—
77C5×#95—24no—
78#1441C3×C511yescharacteristic, direct product factor, Sylow
79C23×C3×C5C22×C411yescharacteristic
80C23×C3×C5C2×D411yescharacteristic
81C23×C3×C5C2×D411yescharacteristic
82C23×C3×C5C2×D411yescharacteristic
83C23×C3×C5C2×D412yes—
84C23×C3×C5C2×Q811yescharacteristic
85C23×C3×C5C2×Q812yes—
86C23×C3×C5#4111yescharacteristic
87C23×C3×C5#4111yescharacteristic
88C23×C3×C5#4112yes—
89C23×C3×C5#4112yes—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—24no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—24no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—24no—
102C2×C3×C4×C5—24no—
103C2×C3×C4×C5—24no—
104C2×C3×C4×C5—24no—
105C2×C3×C4×C5—24no—
106C2×C3×C4×C5—24no—
107C2×C3×C4×C5—24no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—42no—
110C2×C3×C4×C5—42no—
111C2×C3×C4×C5—42no—
112C2×C3×C4×C5—42no—
113C2×C3×C4×C5—42no—
114C2×C3×C4×C5—42no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—42no—
117C2×C3×C4×C5—42no—
118C2×C3×C4×C5—42no—
119C2×C3×C4×C5C22⋊C414yes—
120C2×C3×C4×C5C4⋊C414yescomplemented
121C23×C3×C4C22×C511yescharacteristic
122C23×C3×C4C22×C512yes—
123C23×C3×C4C22×C512yes—
124C23×C3×C4C22×C511yescharacteristic
125C23×C3×C4C22×C511yescharacteristic
126C2×C3×C4⋊C4—24no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4C4×C514yescomplemented
131C3×#95—24no—
132C3×#95—22no—
133C3×#95—24no—
134C24×C5C23×C311yescharacteristic
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5C2×C3×C412yes—
158C22×C4×C5C2×C3×C412yes—
159C22×C4×C5C2×C3×C412yes—
160C22×C4×C5C3×D414yes—
161C22×C4×C5C3×D412yes—
162C22×C4×C5C3×D412yes—
163C22×C4×C5C3×D412yes—
164C22×C4×C5C3×Q814yes—
165C22×C4×C5C3×Q812yes—
166C5×C4⋊C4—28no—
167C5×C4⋊C4—28no—
168C22×C4⋊C4C2×C3×C511yescharacteristic
169C22×C4⋊C4C2×C3×C511yescharacteristic
170C2×#95C2×C3×C512yes—
171C2×#95C2×C3×C512yes—
172C2×#95C2×C3×C511yescharacteristic
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C22×C3×C5C2×C4⋊C411yescharacteristic
175C22×C3×C5#11711yescharacteristic
176C22×C3×C5C4×D412yes—
177C22×C3×C5C4×Q812yes—
178C22×C3×C5#12011yescharacteristic
179C22×C3×C5#12111yescharacteristic
180C22×C3×C5#12111yescharacteristic
181C22×C3×C5#12112yes—
182C22×C3×C5#12112yes—
183C22×C3×C5C22⋊Q811yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5C22⋊Q812yes—
186C22×C3×C5C22⋊Q812yes—
187C22×C3×C5C22⋊Q812yes—
188C22×C3×C5#12311yescharacteristic
189C22×C3×C5#12312yes—
190C22×C3×C5#12411yescharacteristic
191C22×C3×C5#12512yes—
192C22×C3×C5#12512yes—
193C22×C3×C5#12612yes—
194C22×C3×C5C4⋊Q812yes—
195C22×C3×C5C4⋊Q811yescharacteristic
196C3×C4×C5—24no—
197C3×C4×C5—24no—
198C3×C4×C5—42no—
199C3×C4×C5—44no—
200C3×C4×C5—44no—
201C24×C3C23×C511yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4C2×C4×C512yes—
225C22×C3×C4C2×C4×C512yes—
226C22×C3×C4C2×C4×C512yes—
227C22×C3×C4C5×D414yes—
228C22×C3×C4C5×D412yes—
229C22×C3×C4C5×D412yes—
230C22×C3×C4C5×D412yes—
231C22×C3×C4C5×Q814yes—
232C22×C3×C4C5×Q812yes—
233C3×C4⋊C4—28no—
234C3×C4⋊C4—28no—
235C23×C5C22×C3×C411yescharacteristic
236C23×C5C2×C3×D411yescharacteristic
237C23×C5C2×C3×D411yescharacteristic
238C23×C5C2×C3×D411yescharacteristic
239C23×C5C2×C3×D412yes—
240C23×C5C2×C3×Q811yescharacteristic
241C23×C5C2×C3×Q812yes—
242C23×C5C3×#4111yescharacteristic
243C23×C5C3×#4111yescharacteristic
244C23×C5C3×#4112yes—
245C23×C5C3×#4112yes—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—24no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—24no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—24no—
258C2×C4×C5—24no—
259C2×C4×C5—24no—
260C2×C4×C5—24no—
261C2×C4×C5—24no—
262C2×C4×C5—24no—
263C2×C4×C5—24no—
264C2×C4×C5—41no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—41no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5C3×C22⋊C414yes—
276C2×C4×C5C3×C4⋊C414yescomplemented
277C23×C4C22×C3×C511yescharacteristic
278C23×C4C22×C3×C512yes—
279C23×C4C22×C3×C512yes—
280C23×C4C22×C3×C511yescharacteristic
281C23×C4C22×C3×C511yescharacteristic
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4C3×C4×C514yescomplemented
287#95—24no—
288#95—22no—
289#95—24no—
290C2×C3×C5#38011yescharacteristic
291C2×C3×C5#38611yescharacteristic
292C2×C3×C5#38712yes—
293C2×C3×C5#38912yes—
294C2×C3×C5#39111yescharacteristic
295C2×C3×C5#39411yescharacteristic
296C2×C3×C5#39511yescharacteristic
297C2×C3×C5#39612yes—
298C2×C3×C5#39811yescharacteristic
299C2×C3×C5#39812yes—
300C2×C3×C5#40011yescharacteristic
301C23×C3C22×C4×C511yescharacteristic
302C23×C3C2×C5×D411yescharacteristic
303C23×C3C2×C5×D411yescharacteristic
304C23×C3C2×C5×D411yescharacteristic
305C23×C3C2×C5×D412yes—
306C23×C3C2×C5×Q811yescharacteristic
307C23×C3C2×C5×Q812yes—
308C23×C3C5×#4111yescharacteristic
309C23×C3C5×#4111yescharacteristic
310C23×C3C5×#4112yes—
311C23×C3C5×#4112yes—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—24no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—41no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4C5×C22⋊C414yes—
342C2×C3×C4C5×C4⋊C414yescomplemented
343C22×C5C2×C3×C22⋊C411yescharacteristic
344C22×C5C2×C3×C4⋊C411yescharacteristic
345C22×C5C3×#11711yescharacteristic
346C22×C5C3×C4×D412yes—
347C22×C5C3×C4×Q812yes—
348C22×C5C3×#12011yescharacteristic
349C22×C5C3×#12111yescharacteristic
350C22×C5C3×#12111yescharacteristic
351C22×C5C3×#12112yes—
352C22×C5C3×#12112yes—
353C22×C5C3×C22⋊Q811yescharacteristic
354C22×C5C3×C22⋊Q811yescharacteristic
355C22×C5C3×C22⋊Q812yes—
356C22×C5C3×C22⋊Q812yes—
357C22×C5C3×C22⋊Q812yes—
358C22×C5C3×#12311yescharacteristic
359C22×C5C3×#12312yes—
360C22×C5C3×#12411yescharacteristic
361C22×C5C3×#12512yes—
362C22×C5C3×#12512yes—
363C22×C5C3×#12612yes—
364C22×C5C3×C4⋊Q812yes—
365C22×C5C3×C4⋊Q811yescharacteristic
366C4×C5—24no—
367C4×C5—24no—
368C4×C5—42no—
369C4×C5—44no—
370C4×C5—44no—
371C24C23×C3×C511yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4C2×C3×C4×C512yes—
395C22×C4C2×C3×C4×C512yes—
396C22×C4C2×C3×C4×C512yes—
397C22×C4C3×C5×D414yes—
398C22×C4C3×C5×D412yes—
399C22×C4C3×C5×D412yes—
400C22×C4C3×C5×D412yes—
401C22×C4C3×C5×Q814yes—
402C22×C4C3×C5×Q812yes—
403C4⋊C4—28no—
404C4⋊C4—28no—
405C3×C5#144111yescharacteristic, direct product factor, Hall
406C22×C3C2×C5×C22⋊C411yescharacteristic
407C22×C3C2×C5×C4⋊C411yescharacteristic
408C22×C3C5×#11711yescharacteristic
409C22×C3C4×C5×D412yes—
410C22×C3C4×C5×Q812yes—
411C22×C3C5×#12011yescharacteristic
412C22×C3C5×#12111yescharacteristic
413C22×C3C5×#12111yescharacteristic
414C22×C3C5×#12112yes—
415C22×C3C5×#12112yes—
416C22×C3C5×C22⋊Q811yescharacteristic
417C22×C3C5×C22⋊Q811yescharacteristic
418C22×C3C5×C22⋊Q812yes—
419C22×C3C5×C22⋊Q812yes—
420C22×C3C5×C22⋊Q812yes—
421C22×C3C5×#12311yescharacteristic
422C22×C3C5×#12312yes—
423C22×C3C5×#12411yescharacteristic
424C22×C3C5×#12512yes—
425C22×C3C5×#12512yes—
426C22×C3C5×#12612yes—
427C22×C3C5×C4⋊Q812yes—
428C22×C3C5×C4⋊Q811yescharacteristic
429C3×C4—24no—
430C3×C4—24no—
431C3×C4—42no—
432C3×C4—44no—
433C3×C4—44no—
434C2×C5C3×#38011yescharacteristic
435C2×C5C3×#38611yescharacteristic
436C2×C5C3×#38712yes—
437C2×C5C3×#38912yes—
438C2×C5C3×#39111yescharacteristic
439C2×C5C3×#39411yescharacteristic
440C2×C5C3×#39511yescharacteristic
441C2×C5C3×#39612yes—
442C2×C5C3×#39811yescharacteristic
443C2×C5C3×#39812yes—
444C2×C5C3×#40011yescharacteristic
445C23C22×C3×C4×C511yescharacteristic
446C23C2×C3×C5×D411yescharacteristic
447C23C2×C3×C5×D411yescharacteristic
448C23C2×C3×C5×D411yescharacteristic
449C23C2×C3×C5×D412yes—
450C23C2×C3×C5×Q811yescharacteristic
451C23C2×C3×C5×Q812yes—
452C23C3×C5×#4111yescharacteristic
453C23C3×C5×#4111yescharacteristic
454C23C3×C5×#4112yes—
455C23C3×C5×#4112yes—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4C3×C5×C22⋊C414yes—
486C2×C4C3×C5×C4⋊C414yescomplemented
487C2×C3C5×#38011yescharacteristic
488C2×C3C5×#38611yescharacteristic
489C2×C3C5×#38712yes—
490C2×C3C5×#38912yes—
491C2×C3C5×#39111yescharacteristic
492C2×C3C5×#39411yescharacteristic
493C2×C3C5×#39511yescharacteristic
494C2×C3C5×#39612yes—
495C2×C3C5×#39811yescharacteristic
496C2×C3C5×#39812yes—
497C2×C3C5×#40011yescharacteristic
498C5C3×#144111yescharacteristic, direct product factor, Sylow
499C22C2×C3×C5×C22⋊C411yescharacteristic
500C22C2×C3×C5×C4⋊C411yescharacteristic
501C22C3×C5×#11711yescharacteristic
502C22C3×C4×C5×D412yes—
503C22C3×C4×C5×Q812yes—
504C22C3×C5×#12011yescharacteristic
505C22C3×C5×#12111yescharacteristic
506C22C3×C5×#12111yescharacteristic
507C22C3×C5×#12112yes—
508C22C3×C5×#12112yes—
509C22C3×C5×C22⋊Q811yescharacteristic
510C22C3×C5×C22⋊Q811yescharacteristic
511C22C3×C5×C22⋊Q812yes—
512C22C3×C5×C22⋊Q812yes—
513C22C3×C5×C22⋊Q812yes—
514C22C3×C5×#12311yescharacteristic
515C22C3×C5×#12312yes—
516C22C3×C5×#12411yescharacteristic
517C22C3×C5×#12512yes—
518C22C3×C5×#12512yes—
519C22C3×C5×#12612yes—
520C22C3×C5×C4⋊Q812yes—
521C22C3×C5×C4⋊Q811yescharacteristic
522C4—24no—
523C4—24no—
524C4—42no—
525C4—44no—
526C4—44no—
527C3C5×#144111yescharacteristic, direct product factor, Sylow
528C2C3×C5×#38011yescharacteristic
529C2C3×C5×#38611yescharacteristic
530C2C3×C5×#38712yes—
531C2C3×C5×#38912yes—
532C2C3×C5×#39111yescharacteristic
533C2C3×C5×#39411yescharacteristic
534C2C3×C5×#39511yescharacteristic
535C2C3×C5×#39612yes—
536C2C3×C5×#39811yescharacteristic
537C2C3×C5×#39812yes—
538C2C3×C5×#40011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3×C5C23
commutatorC23C22×C3×C4×C5
Frattini, cosocleC24C23×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C5×#1441C3direct (N × H)
16. C2×C3×C5×C4⋊C4C4semidirect
20. C3×#1441C5direct (N × H)
74. C2×C5×C4⋊C4C3×C4semidirect
78. #1441C3×C5direct (N × H)
120. C2×C3×C4×C5C4⋊C4semidirect
130. C2×C3×C4⋊C4C4×C5semidirect
276. C2×C4×C5C3×C4⋊C4semidirect
286. C2×C4⋊C4C3×C4×C5semidirect
342. C2×C3×C4C5×C4⋊C4semidirect
405. C3×C5#1441direct (N × H)
486. C2×C4C3×C5×C4⋊C4semidirect
498. C5C3×#1441direct (N × H)
527. C3C5×#1441direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C4⋊C42
C2×C3×C5×#952
C5×#14413
C3×#14415