Finite Group Databasebeta

← C3×C5×#1442 #14274476

Subgroups — C3×C5×#1442 #14274476

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C4⋊C4C211yesmaximal, characteristic
2C2×C3×C5×#95C212yesmaximal
3C2×C3×C5×#95C212yesmaximal
4C2×C3×C5×#95C211yesmaximal, characteristic
5C2×C3×C5×#95C211yesmaximal, characteristic
6C5×#1442C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2212yes—
8C23×C3×C4×C5C2212yes—
9C23×C3×C4×C5C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C2×C3×C5×C4⋊C4—24no—
13C2×C3×C5×C4⋊C4—22no—
14C3×C5×#95—24no—
15C3×C5×#95—24no—
16C3×C5×#95—22no—
17C3×C5×#95C414yescomplemented
18C3×#1442C511yesmaximal, characteristic, direct product factor, Hall
19C22×C5×C4⋊C4C2×C311yescharacteristic
20C2×C5×#95C2×C312yes—
21C2×C5×#95C2×C312yes—
22C2×C5×#95C2×C311yescharacteristic
23C2×C5×#95C2×C311yescharacteristic
24C24×C3×C5C2311yescharacteristic
25C22×C3×C4×C5—22no—
26C22×C3×C4×C5—22no—
27C22×C3×C4×C5—22no—
28C22×C3×C4×C5—22no—
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5—22no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5—22no—
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—21no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—22no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5C2×C414yes—
48C22×C3×C4×C5C2×C412yes—
49C22×C3×C4×C5D414yes—
50C22×C3×C4×C5D412yes—
51C22×C3×C4×C5D412yes—
52C22×C3×C4×C5Q812yes—
53C22×C3×C4×C5Q812yes—
54C3×C5×C4⋊C4—28no—
55C22×C3×C4⋊C4C2×C511yescharacteristic
56C2×C3×#95C2×C512yes—
57C2×C3×#95C2×C512yes—
58C2×C3×#95C2×C511yescharacteristic
59C2×C3×#95C2×C511yescharacteristic
60C23×C4×C5C22×C312yes—
61C23×C4×C5C22×C311yescharacteristic
62C23×C4×C5C22×C312yes—
63C23×C4×C5C22×C311yescharacteristic
64C23×C4×C5C22×C311yescharacteristic
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—22no—
67C5×#95—24no—
68C5×#95—24no—
69C5×#95—22no—
70C5×#95C3×C414yescomplemented
71#1442C3×C511yescharacteristic, direct product factor, Sylow
72C23×C3×C5C22×C411yescharacteristic
73C23×C3×C5C2×D411yescharacteristic
74C23×C3×C5C2×D412yes—
75C23×C3×C5C2×D411yescharacteristic
76C23×C3×C5C2×Q811yescharacteristic
77C23×C3×C5C2×Q811yescharacteristic
78C23×C3×C5#4112yes—
79C23×C3×C5#4112yes—
80C23×C3×C5#4112yes—
81C23×C3×C5#4111yescharacteristic
82C23×C3×C5#4111yescharacteristic
83C2×C3×C4×C5—24no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—24no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—24no—
88C2×C3×C4×C5—24no—
89C2×C3×C4×C5—24no—
90C2×C3×C4×C5—24no—
91C2×C3×C4×C5—24no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—24no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—24no—
96C2×C3×C4×C5—24no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—42no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—42no—
102C2×C3×C4×C5—42no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—42no—
110C2×C3×C4×C5—42no—
111C2×C3×C4×C5C4⋊C414yes—
112C23×C3×C4C22×C512yes—
113C23×C3×C4C22×C511yescharacteristic
114C23×C3×C4C22×C512yes—
115C23×C3×C4C22×C511yescharacteristic
116C23×C3×C4C22×C511yescharacteristic
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4—22no—
119C3×#95—24no—
120C3×#95—24no—
121C3×#95—22no—
122C3×#95C4×C514yescomplemented
123C24×C5C23×C311yescharacteristic
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5C2×C3×C414yes—
147C22×C4×C5C2×C3×C412yes—
148C22×C4×C5C3×D414yes—
149C22×C4×C5C3×D412yes—
150C22×C4×C5C3×D412yes—
151C22×C4×C5C3×Q812yes—
152C22×C4×C5C3×Q812yes—
153C5×C4⋊C4—28no—
154C22×C4⋊C4C2×C3×C511yescharacteristic
155C2×#95C2×C3×C512yes—
156C2×#95C2×C3×C512yes—
157C2×#95C2×C3×C511yescharacteristic
158C2×#95C2×C3×C511yescharacteristic
159C22×C3×C5C2×C4⋊C411yescharacteristic
160C22×C3×C5#11712yes—
161C22×C3×C5C4×D412yes—
162C22×C3×C5C4×D411yescharacteristic
163C22×C3×C5C4×Q811yescharacteristic
164C22×C3×C5#12011yescharacteristic
165C22×C3×C5#12112yes—
166C22×C3×C5#12111yescharacteristic
167C22×C3×C5C22⋊Q812yes—
168C22×C3×C5C22⋊Q812yes—
169C22×C3×C5C22⋊Q811yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C22×C3×C5#12312yes—
172C22×C3×C5#12312yes—
173C22×C3×C5#12411yescharacteristic
174C22×C3×C5#12411yescharacteristic
175C22×C3×C5#12412yes—
176C22×C3×C5#12512yes—
177C22×C3×C5#12512yes—
178C22×C3×C5#12511yescharacteristic
179C22×C3×C5#12612yes—
180C22×C3×C5#12612yes—
181C22×C3×C5C4⋊Q811yescharacteristic
182C3×C4×C5—24no—
183C3×C4×C5—44no—
184C3×C4×C5—42no—
185C3×C4×C5—44no—
186C3×C4×C5—42no—
187C24×C3C23×C511yescharacteristic
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4C2×C4×C514yes—
211C22×C3×C4C2×C4×C512yes—
212C22×C3×C4C5×D412yes—
213C22×C3×C4C5×D414yes—
214C22×C3×C4C5×D412yes—
215C22×C3×C4C5×Q812yes—
216C22×C3×C4C5×Q812yes—
217C3×C4⋊C4—28no—
218C23×C5C22×C3×C411yescharacteristic
219C23×C5C2×C3×D411yescharacteristic
220C23×C5C2×C3×D412yes—
221C23×C5C2×C3×D411yescharacteristic
222C23×C5C2×C3×Q811yescharacteristic
223C23×C5C2×C3×Q811yescharacteristic
224C23×C5C3×#4112yes—
225C23×C5C3×#4112yes—
226C23×C5C3×#4112yes—
227C23×C5C3×#4111yescharacteristic
228C23×C5C3×#4111yescharacteristic
229C2×C4×C5—24no—
230C2×C4×C5—22no—
231C2×C4×C5—24no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—24no—
237C2×C4×C5—24no—
238C2×C4×C5—22no—
239C2×C4×C5—24no—
240C2×C4×C5—22no—
241C2×C4×C5—24no—
242C2×C4×C5—24no—
243C2×C4×C5—41no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—41no—
250C2×C4×C5—42no—
251C2×C4×C5—41no—
252C2×C4×C5—42no—
253C2×C4×C5—42no—
254C2×C4×C5—41no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5C3×C4⋊C414yes—
258C23×C4C22×C3×C512yes—
259C23×C4C22×C3×C512yes—
260C23×C4C22×C3×C511yescharacteristic
261C23×C4C22×C3×C511yescharacteristic
262C23×C4C22×C3×C511yescharacteristic
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265#95—24no—
266#95—24no—
267#95—22no—
268#95C3×C4×C514yescomplemented
269C2×C3×C5#38211yescharacteristic
270C2×C3×C5#38511yescharacteristic
271C2×C3×C5#38712yes—
272C2×C3×C5#38812yes—
273C2×C3×C5#38911yescharacteristic
274C2×C3×C5#39311yescharacteristic
275C2×C3×C5#39411yescharacteristic
276C2×C3×C5#39711yescharacteristic
277C2×C3×C5#39812yes—
278C2×C3×C5#40012yes—
279C2×C3×C5#40011yescharacteristic
280C23×C3C22×C4×C511yescharacteristic
281C23×C3C2×C5×D411yescharacteristic
282C23×C3C2×C5×D412yes—
283C23×C3C2×C5×D411yescharacteristic
284C23×C3C2×C5×Q811yescharacteristic
285C23×C3C2×C5×Q811yescharacteristic
286C23×C3C5×#4112yes—
287C23×C3C5×#4112yes—
288C23×C3C5×#4112yes—
289C23×C3C5×#4111yescharacteristic
290C23×C3C5×#4111yescharacteristic
291C2×C3×C4—24no—
292C2×C3×C4—22no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—24no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—24no—
304C2×C3×C4—24no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—41no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4C5×C4⋊C414yes—
320C22×C5C2×C3×C4⋊C411yescharacteristic
321C22×C5C3×#11712yes—
322C22×C5C3×C4×D412yes—
323C22×C5C3×C4×D411yescharacteristic
324C22×C5C3×C4×Q811yescharacteristic
325C22×C5C3×#12011yescharacteristic
326C22×C5C3×#12112yes—
327C22×C5C3×#12111yescharacteristic
328C22×C5C3×C22⋊Q812yes—
329C22×C5C3×C22⋊Q812yes—
330C22×C5C3×C22⋊Q811yescharacteristic
331C22×C5C3×#12311yescharacteristic
332C22×C5C3×#12312yes—
333C22×C5C3×#12312yes—
334C22×C5C3×#12411yescharacteristic
335C22×C5C3×#12411yescharacteristic
336C22×C5C3×#12412yes—
337C22×C5C3×#12512yes—
338C22×C5C3×#12512yes—
339C22×C5C3×#12511yescharacteristic
340C22×C5C3×#12612yes—
341C22×C5C3×#12612yes—
342C22×C5C3×C4⋊Q811yescharacteristic
343C4×C5—24no—
344C4×C5—44no—
345C4×C5—42no—
346C4×C5—44no—
347C4×C5—42no—
348C24C23×C3×C511yescharacteristic
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4C2×C3×C4×C514yes—
372C22×C4C2×C3×C4×C512yes—
373C22×C4C3×C5×D412yes—
374C22×C4C3×C5×D414yes—
375C22×C4C3×C5×D412yes—
376C22×C4C3×C5×Q812yes—
377C22×C4C3×C5×Q812yes—
378C4⋊C4—28no—
379C3×C5#144211yescharacteristic, direct product factor, Hall
380C22×C3C2×C5×C4⋊C411yescharacteristic
381C22×C3C5×#11712yes—
382C22×C3C4×C5×D412yes—
383C22×C3C4×C5×D411yescharacteristic
384C22×C3C4×C5×Q811yescharacteristic
385C22×C3C5×#12011yescharacteristic
386C22×C3C5×#12112yes—
387C22×C3C5×#12111yescharacteristic
388C22×C3C5×C22⋊Q812yes—
389C22×C3C5×C22⋊Q812yes—
390C22×C3C5×C22⋊Q811yescharacteristic
391C22×C3C5×#12311yescharacteristic
392C22×C3C5×#12312yes—
393C22×C3C5×#12312yes—
394C22×C3C5×#12411yescharacteristic
395C22×C3C5×#12411yescharacteristic
396C22×C3C5×#12412yes—
397C22×C3C5×#12512yes—
398C22×C3C5×#12512yes—
399C22×C3C5×#12511yescharacteristic
400C22×C3C5×#12612yes—
401C22×C3C5×#12612yes—
402C22×C3C5×C4⋊Q811yescharacteristic
403C3×C4—24no—
404C3×C4—44no—
405C3×C4—42no—
406C3×C4—44no—
407C3×C4—42no—
408C2×C5C3×#38211yescharacteristic
409C2×C5C3×#38511yescharacteristic
410C2×C5C3×#38712yes—
411C2×C5C3×#38812yes—
412C2×C5C3×#38911yescharacteristic
413C2×C5C3×#39311yescharacteristic
414C2×C5C3×#39411yescharacteristic
415C2×C5C3×#39711yescharacteristic
416C2×C5C3×#39812yes—
417C2×C5C3×#40012yes—
418C2×C5C3×#40011yescharacteristic
419C23C22×C3×C4×C511yescharacteristic
420C23C2×C3×C5×D411yescharacteristic
421C23C2×C3×C5×D412yes—
422C23C2×C3×C5×D411yescharacteristic
423C23C2×C3×C5×Q811yescharacteristic
424C23C2×C3×C5×Q811yescharacteristic
425C23C3×C5×#4112yes—
426C23C3×C5×#4112yes—
427C23C3×C5×#4112yes—
428C23C3×C5×#4111yescharacteristic
429C23C3×C5×#4111yescharacteristic
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4C3×C5×C4⋊C414yes—
459C2×C3C5×#38211yescharacteristic
460C2×C3C5×#38511yescharacteristic
461C2×C3C5×#38712yes—
462C2×C3C5×#38812yes—
463C2×C3C5×#38911yescharacteristic
464C2×C3C5×#39311yescharacteristic
465C2×C3C5×#39411yescharacteristic
466C2×C3C5×#39711yescharacteristic
467C2×C3C5×#39812yes—
468C2×C3C5×#40012yes—
469C2×C3C5×#40011yescharacteristic
470C5C3×#144211yescharacteristic, direct product factor, Sylow
471C22C2×C3×C5×C4⋊C411yescharacteristic
472C22C3×C5×#11712yes—
473C22C3×C4×C5×D412yes—
474C22C3×C4×C5×D411yescharacteristic
475C22C3×C4×C5×Q811yescharacteristic
476C22C3×C5×#12011yescharacteristic
477C22C3×C5×#12112yes—
478C22C3×C5×#12111yescharacteristic
479C22C3×C5×C22⋊Q812yes—
480C22C3×C5×C22⋊Q812yes—
481C22C3×C5×C22⋊Q811yescharacteristic
482C22C3×C5×#12311yescharacteristic
483C22C3×C5×#12312yes—
484C22C3×C5×#12312yes—
485C22C3×C5×#12411yescharacteristic
486C22C3×C5×#12411yescharacteristic
487C22C3×C5×#12412yes—
488C22C3×C5×#12512yes—
489C22C3×C5×#12512yes—
490C22C3×C5×#12511yescharacteristic
491C22C3×C5×#12612yes—
492C22C3×C5×#12612yes—
493C22C3×C5×C4⋊Q811yescharacteristic
494C4—24no—
495C4—44no—
496C4—42no—
497C4—44no—
498C4—42no—
499C3C5×#144211yescharacteristic, direct product factor, Sylow
500C2C3×C5×#38211yescharacteristic
501C2C3×C5×#38511yescharacteristic
502C2C3×C5×#38712yes—
503C2C3×C5×#38812yes—
504C2C3×C5×#38911yescharacteristic
505C2C3×C5×#39311yescharacteristic
506C2C3×C5×#39411yescharacteristic
507C2C3×C5×#39711yescharacteristic
508C2C3×C5×#39812yes—
509C2C3×C5×#40012yes—
510C2C3×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×#1442C3direct (N × H)
17. C3×C5×#95C4semidirect
18. C3×#1442C5direct (N × H)
70. C5×#95C3×C4semidirect
71. #1442C3×C5direct (N × H)
122. C3×#95C4×C5semidirect
268. #95C3×C4×C5semidirect
379. C3×C5#1442direct (N × H)
470. C5C3×#1442direct (N × H)
499. C3C5×#1442direct (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×#14423
C3×#14425