Finite Group Databasebeta

← C3×C5×#1880 #14274914

Subgroups — C3×C5×#1880 #14274914

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic
2C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
3C2×C3×C5×#103C211yesmaximal, characteristic, complemented
4C2×C3×C5×#102C211yesmaximal, characteristic
5C3×C5×#390C211yesmaximal, characteristic
6C3×C5×#340C211yesmaximal, characteristic, complemented
7C3×C5×#336C211yesmaximal, characteristic, complemented
8C5×#1880C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C2×C3×C5×SD16—22no—
12C2×C3×C5×SD16—22no—
13C2×C3×C5×SD16C414yescomplemented
14C22×C3×C5×C8C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C3×C4×C5×Q8—22no—
17C3×C4×C5×Q8—22no—
18C2×C3×C5×C4⋊C4—21no—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4—21no—
22C2×C3×C5×C22⋊C4—21no—
23C2×C3×C42×C5—21no—
24C2×C3×C42×C5C2211yescharacteristic
25C3×C5×#103—22no—
26C3×C5×#102—22no—
27C3×#1880C511yesmaximal, characteristic, direct product factor, Hall
28C22×C5×SD16C2×C311yescharacteristic
29C2×C4×C5×Q8C2×C311yescharacteristic, complemented
30C2×C5×#103C2×C311yescharacteristic, complemented
31C2×C5×#102C2×C311yescharacteristic
32C5×#390C2×C311yescharacteristic
33C5×#340C2×C311yescharacteristic, complemented
34C5×#336C2×C311yescharacteristic, complemented
35C24×C3×C5—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yes—
40C2×C3×C5×Q8D412yes—
41C2×C3×C5×Q8D412yes—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4C2×C412yes—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5D411yescharacteristic
52C22×C3×C4×C5D411yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C3×C5×SD16—28no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C2×C3×C5×C8C2×C412yes—
61C3×C5×C4⋊C4—24no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4D412yes—
66C3×C5×C22⋊C4—42no—
67C3×C5×C22⋊C4—42no—
68C3×C42×C5—24no—
69C3×C42×C5—21no—
70C3×C42×C5—21no—
71C22×C3×SD16C2×C511yescharacteristic
72C2×C3×C4×Q8C2×C511yescharacteristic, complemented
73C2×C3×#103C2×C511yescharacteristic, complemented
74C2×C3×#102C2×C511yescharacteristic
75C3×#390C2×C511yescharacteristic
76C3×#340C2×C511yescharacteristic, complemented
77C3×#336C2×C511yescharacteristic, complemented
78C22×C5×Q8C22×C311yescharacteristic
79C22×C5×D4C22×C311yescharacteristic
80C2×C5×SD16—22no—
81C2×C5×SD16—22no—
82C2×C5×SD16C3×C414yescomplemented
83C22×C5×C8C22×C311yescharacteristic
84C22×C5×C8C22×C311yescharacteristic
85C4×C5×Q8—22no—
86C4×C5×Q8—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4C22×C311yescharacteristic
89C2×C5×C4⋊C4C22×C311yescharacteristic
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—21no—
92C2×C42×C5—21no—
93C2×C42×C5C22×C311yescharacteristic
94C5×#103—22no—
95C5×#102—22no—
96#1880C3×C511yescharacteristic, direct product factor, Sylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×Q8—22no—
106C3×C5×Q8—22no—
107C3×C5×Q8—22no—
108C3×C5×Q8C22⋊C414yescomplemented
109C3×C5×D4—22no—
110C3×C5×D4—22no—
111C3×C5×D4—41no—
112C3×C5×D4—41no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5SD1612yescomplemented
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×C3×C4×C5#4111yescharacteristic
134C3×C5×C8—22no—
135C3×C5×C8—41no—
136C22×C3×Q8C22×C511yescharacteristic
137C22×C3×D4C22×C511yescharacteristic
138C2×C3×SD16—22no—
139C2×C3×SD16—22no—
140C2×C3×SD16C4×C514yescomplemented
141C22×C3×C8C22×C511yescharacteristic
142C22×C3×C8C22×C511yescharacteristic
143C3×C4×Q8—22no—
144C3×C4×Q8—22no—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4C22×C511yescharacteristic
147C2×C3×C4⋊C4C22×C511yescharacteristic
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C42—21no—
151C2×C3×C42C22×C511yescharacteristic
152C3×#103—22no—
153C3×#102—22no—
154C24×C5—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8C2×C3×C412yes—
159C2×C5×Q8C3×D412yes—
160C2×C5×Q8C3×D412yes—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4C2×C3×C412yes—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5C3×D411yescharacteristic
171C22×C4×C5C3×D411yescharacteristic
172C22×C4×C5C23×C311yescharacteristic
173C5×SD16—28no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8—21no—
179C2×C5×C8C2×C3×C412yes—
180C5×C4⋊C4—24no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C3×D412yes—
185C5×C22⋊C4—42no—
186C5×C22⋊C4—42no—
187C42×C5—24no—
188C42×C5—21no—
189C42×C5—21no—
190C22×SD16C2×C3×C511yescharacteristic
191C2×C4×Q8C2×C3×C511yescharacteristic, complemented
192C2×#103C2×C3×C511yescharacteristic, complemented
193C2×#102C2×C3×C511yescharacteristic
194#390C2×C3×C511yescharacteristic
195#340C2×C3×C511yescharacteristic, complemented
196#336C2×C3×C511yescharacteristic, complemented
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—81no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5C2×SD1611yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5#13711yescharacteristic
211C3×C4×C5—24no—
212C3×C4×C5—22no—
213C3×C4×C5—41no—
214C3×C4×C5—42no—
215C3×C4×C5—81no—
216C3×C4×C5C2×C22⋊C411yescharacteristic
217C3×C4×C5C4×D411yescharacteristic
218C3×C4×C5#12111yescharacteristic
219C3×C4×C5#12311yescharacteristic
220C24×C3—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C2×C4×C512yes—
225C2×C3×Q8C5×D412yes—
226C2×C3×Q8C5×D412yes—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4C2×C4×C512yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4C5×D411yescharacteristic
237C22×C3×C4C5×D411yescharacteristic
238C22×C3×C4C23×C511yescharacteristic
239C3×SD16—28no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8C2×C4×C512yes—
246C3×C4⋊C4—24no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4C5×D412yes—
251C3×C22⋊C4—42no—
252C3×C22⋊C4—42no—
253C3×C42—24no—
254C3×C42—21no—
255C3×C42—21no—
256C23×C5—22no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5C2×C3×D411yescharacteristic
264C5×Q8—22no—
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8C3×C22⋊C414yescomplemented
268C5×D4—22no—
269C5×D4—22no—
270C5×D4—41no—
271C5×D4—41no—
272C2×C4×C5—22no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5C3×SD1612yescomplemented
287C2×C4×C5C22×C3×C411yescharacteristic
288C2×C4×C5C2×C3×D411yescharacteristic
289C2×C4×C5C2×C3×D411yescharacteristic
290C2×C4×C5C2×C3×D411yescharacteristic
291C2×C4×C5C3×#4111yescharacteristic
292C2×C4×C5C3×#4111yescharacteristic
293C5×C8—22no—
294C5×C8—41no—
295C22×Q8C22×C3×C511yescharacteristic
296C22×D4C22×C3×C511yescharacteristic
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16C3×C4×C514yescomplemented
300C22×C8C22×C3×C511yescharacteristic
301C22×C8C22×C3×C511yescharacteristic
302C4×Q8—22no—
303C4×Q8—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C22×C3×C511yescharacteristic
306C2×C4⋊C4C22×C3×C511yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C42—21no—
310C2×C42C22×C3×C511yescharacteristic
311#103—22no—
312#102—22no—
313C2×C3×C5—82no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5C4×SD1611yescharacteristic
316C2×C3×C5#44011yescharacteristic
317C2×C3×C5#44811yescharacteristic
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#46011yescharacteristic
320C2×C3×C5#46411yescharacteristic
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3C2×C5×D411yescharacteristic
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8C5×C22⋊C414yescomplemented
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4—41no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4C5×SD1612yescomplemented
352C2×C3×C4C22×C4×C511yescharacteristic
353C2×C3×C4C2×C5×D411yescharacteristic
354C2×C3×C4C2×C5×D411yescharacteristic
355C2×C3×C4C2×C5×D411yescharacteristic
356C2×C3×C4C5×#4111yescharacteristic
357C2×C3×C4C5×#4111yescharacteristic
358C3×C8—22no—
359C3×C8—41no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5C3×C4×D411yescharacteristic
368C22×C5C3×#12011yescharacteristic
369C22×C5C3×#12111yescharacteristic
370C22×C5C2×C3×SD1611yescharacteristic
371C22×C5C3×#13511yescharacteristic
372C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
373C22×C5C3×#13711yescharacteristic
374C4×C5—24no—
375C4×C5—22no—
376C4×C5—41no—
377C4×C5—42no—
378C4×C5—81no—
379C4×C5C2×C3×C22⋊C411yescharacteristic
380C4×C5C3×C4×D411yescharacteristic
381C4×C5C3×#12111yescharacteristic
382C4×C5C3×#12311yescharacteristic
383C24—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8C2×C3×C4×C512yes—
388C2×Q8C3×C5×D412yes—
389C2×Q8C3×C5×D412yes—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C2×C3×C4×C512yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4C3×C5×D411yescharacteristic
400C22×C4C3×C5×D411yescharacteristic
401C22×C4C23×C3×C511yescharacteristic
402SD16—28no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8C2×C3×C4×C512yes—
409C4⋊C4—24no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4C3×C5×D412yes—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C42—24no—
417C42—21no—
418C42—21no—
419C3×C5#188011yescharacteristic, direct product factor, Hall
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3C4×C5×D411yescharacteristic
428C22×C3C5×#12011yescharacteristic
429C22×C3C5×#12111yescharacteristic
430C22×C3C2×C5×SD1611yescharacteristic
431C22×C3C5×#13511yescharacteristic
432C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
433C22×C3C5×#13711yescharacteristic
434C3×C4—24no—
435C3×C4—22no—
436C3×C4—41no—
437C3×C4—42no—
438C3×C4—81no—
439C3×C4C2×C5×C22⋊C411yescharacteristic
440C3×C4C4×C5×D411yescharacteristic
441C3×C4C5×#12111yescharacteristic
442C3×C4C5×#12311yescharacteristic
443C2×C5—82no—
444C2×C5C3×#38611yescharacteristic
445C2×C5C3×C4×SD1611yescharacteristic
446C2×C5C3×#44011yescharacteristic
447C2×C5C3×#44811yescharacteristic
448C2×C5C3×#44911yescharacteristic
449C2×C5C3×#46011yescharacteristic
450C2×C5C3×#46411yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C2×C3×C5×D411yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—22no—
462Q8C3×C5×C22⋊C414yescomplemented
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4C3×C5×SD1612yescomplemented
482C2×C4C22×C3×C4×C511yescharacteristic
483C2×C4C2×C3×C5×D411yescharacteristic
484C2×C4C2×C3×C5×D411yescharacteristic
485C2×C4C2×C3×C5×D411yescharacteristic
486C2×C4C3×C5×#4111yescharacteristic
487C2×C4C3×C5×#4111yescharacteristic
488C8—22no—
489C8—41no—
490C2×C3—82no—
491C2×C3C5×#38611yescharacteristic
492C2×C3C4×C5×SD1611yescharacteristic
493C2×C3C5×#44011yescharacteristic
494C2×C3C5×#44811yescharacteristic
495C2×C3C5×#44911yescharacteristic
496C2×C3C5×#46011yescharacteristic
497C2×C3C5×#46411yescharacteristic
498C5C3×#188011yescharacteristic, direct product factor, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C3×C4×C5×D411yescharacteristic
507C22C3×C5×#12011yescharacteristic
508C22C3×C5×#12111yescharacteristic
509C22C2×C3×C5×SD1611yescharacteristic
510C22C3×C5×#13511yescharacteristic
511C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
512C22C3×C5×#13711yescharacteristic
513C4—24no—
514C4—22no—
515C4—41no—
516C4—42no—
517C4—81no—
518C4C2×C3×C5×C22⋊C411yescharacteristic
519C4C3×C4×C5×D411yescharacteristic
520C4C3×C5×#12111yescharacteristic
521C4C3×C5×#12311yescharacteristic
522C3C5×#188011yescharacteristic, direct product factor, Sylow
523C2—82no—
524C2C3×C5×#38611yescharacteristic
525C2C3×C4×C5×SD1611yescharacteristic
526C2C3×C5×#44011yescharacteristic
527C2C3×C5×#44811yescharacteristic
528C2C3×C5×#44911yescharacteristic
529C2C3×C5×#46011yescharacteristic
530C2C3×C5×#46411yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutatorC2×C4C22×C3×C4×C5
Frattini, cosocleC22×C4C23×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5×Q8C2semidirect
3. C2×C3×C5×#103C2semidirect
6. C3×C5×#340C2semidirect
7. C3×C5×#336C2semidirect
8. C5×#1880C3direct (N × H)
13. C2×C3×C5×SD16C4semidirect
27. C3×#1880C5direct (N × H)
29. C2×C4×C5×Q8C2×C3semidirect
30. C2×C5×#103C2×C3semidirect
33. C5×#340C2×C3semidirect
34. C5×#336C2×C3semidirect
72. C2×C3×C4×Q8C2×C5semidirect
73. C2×C3×#103C2×C5semidirect
76. C3×#340C2×C5semidirect
77. C3×#336C2×C5semidirect
82. C2×C5×SD16C3×C4semidirect
96. #1880C3×C5direct (N × H)
108. C3×C5×Q8C22⋊C4semidirect
127. C2×C3×C4×C5SD16semidirect
140. C2×C3×SD16C4×C5semidirect
191. C2×C4×Q8C2×C3×C5semidirect
192. C2×#103C2×C3×C5semidirect
195. #340C2×C3×C5semidirect
196. #336C2×C3×C5semidirect
267. C5×Q8C3×C22⋊C4semidirect
286. C2×C4×C5C3×SD16semidirect
299. C2×SD16C3×C4×C5semidirect
332. C3×Q8C5×C22⋊C4semidirect
351. C2×C3×C4C5×SD16semidirect
419. C3×C5#1880direct (N × H)
462. Q8C3×C5×C22⋊C4semidirect
481. C2×C4C3×C5×SD16semidirect
498. C5C3×#1880direct (N × H)
522. C3C5×#1880direct (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×SD162
C2×C3×C4×C5×Q82
C2×C3×C5×#1032
C2×C3×C5×#1022
C3×C5×#3902
C3×C5×#3402
C3×C5×#3362
C5×#18803
C3×#18805