Finite Group Databasebeta

← C2×C3×C5×#463 #14276065

Subgroups — C2×C3×C5×#463 #14276065

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
2C22×C3×C5×D8C211yesmaximal, characteristic
3C2×C3×C5×#124C211yesmaximal, characteristic, complemented
4C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
5C3×C5×#463C218yesmaximal, direct product factor
6C2×C3×C5×C4⋊C8C211yesmaximal, characteristic, complemented
7C2×C3×C5×#103C211yesmaximal, characteristic, complemented
8C2×C3×C5×#102C211yesmaximal, characteristic, complemented
9C2×C5×#463C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic
13C23×C3×C4×C5—21no—
14C2×C3×C5×SD16—24no—
15C2×C3×C5×SD16C2214yescomplemented
16C2×C3×C5×D8—24no—
17C2×C3×C5×D8C2214yes—
18C22×C3×C5×C8C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic
20C3×C5×#124—22no—
21C3×C5×#124C2214yescomplemented
22C3×C4×C5×D4—22no—
23C3×C4×C5×D4C2214yescomplemented
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4—21no—
26C2×C3×C5×C22⋊C4—21no—
27C2×C3×C5×C22⋊C4—21no—
28C2×C3×C42×C5C2211yescharacteristic
29C3×C5×C4⋊C8C2214yescomplemented
30C3×C5×#103C2214yescomplemented
31C3×C5×#102C2214yescomplemented
32C2×C3×#463C511yesmaximal, characteristic, direct product factor, Hall
33C22×C5×SD16C2×C311yescharacteristic, complemented
34C22×C5×D8C2×C311yescharacteristic
35C2×C5×#124C2×C311yescharacteristic, complemented
36C2×C4×C5×D4C2×C311yescharacteristic, complemented
37C5×#463C2×C318yesdirect product factor
38C2×C5×C4⋊C8C2×C311yescharacteristic, complemented
39C2×C5×#103C2×C311yescharacteristic, complemented
40C2×C5×#102C2×C311yescharacteristic, complemented
41C24×C3×C5—21no—
42C24×C3×C5—21no—
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8C2312yes—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—22no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4D414yes—
53C2×C3×C5×D4C2312yes—
54C2×C3×C5×D4C2312yes—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—24no—
58C22×C3×C4×C5—44no—
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5D411yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C3×C5×SD16—28no—
63C3×C5×D8—28no—
64C2×C3×C5×C8—22no—
65C2×C3×C5×C8—22no—
66C2×C3×C5×C8C2312yes—
67C2×C3×C5×C8C2312yes—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2312yes—
70C3×C5×C22⋊C4—24no—
71C3×C5×C22⋊C4—24no—
72C3×C5×C22⋊C4—24no—
73C3×C42×C5D412yes—
74C3×C42×C5C2312yes—
75C22×C3×SD16C2×C511yescharacteristic, complemented
76C22×C3×D8C2×C511yescharacteristic
77C2×C3×#124C2×C511yescharacteristic, complemented
78C2×C3×C4×D4C2×C511yescharacteristic, complemented
79C3×#463C2×C518yesdirect product factor
80C2×C3×C4⋊C8C2×C511yescharacteristic, complemented
81C2×C3×#103C2×C511yescharacteristic, complemented
82C2×C3×#102C2×C511yescharacteristic, complemented
83C22×C5×Q8C22×C311yescharacteristic
84C22×C5×D4C22×C311yescharacteristic
85C22×C5×D4C22×C311yescharacteristic
86C23×C4×C5—21no—
87C2×C5×SD16—24no—
88C2×C5×SD16C22×C314yescomplemented
89C2×C5×D8—24no—
90C2×C5×D8C22×C314yes—
91C22×C5×C8C22×C311yescharacteristic
92C22×C5×C8C22×C311yescharacteristic
93C5×#124—22no—
94C5×#124C22×C314yescomplemented
95C4×C5×D4—22no—
96C4×C5×D4C22×C314yescomplemented
97C2×C5×C4⋊C4C22×C311yescharacteristic
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C42×C5C22×C311yescharacteristic
102C5×C4⋊C8C22×C314yescomplemented
103C5×#103C22×C314yescomplemented
104C5×#102C22×C314yescomplemented
105C2×#463C3×C511yescharacteristic, direct product factor, Sylow
106C23×C3×C5—24no—
107C23×C3×C5—22no—
108C23×C3×C5—22no—
109C23×C3×C5—42no—
110C23×C3×C5—42no—
111C23×C3×C5—42no—
112C23×C3×C5—42no—
113C23×C3×C5—42no—
114C23×C3×C5C2×D411yescharacteristic
115C3×C5×Q8—22no—
116C3×C5×Q8—22no—
117C3×C5×Q8—42no—
118C3×C5×D4—24no—
119C3×C5×D4—22no—
120C3×C5×D4—22no—
121C3×C5×D4—22no—
122C3×C5×D4—42no—
123C3×C5×D4C2×D414yes—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—48no—
129C2×C3×C4×C5—42no—
130C2×C3×C4×C5—42no—
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5C2411yescharacteristic
137C3×C5×C8—22no—
138C3×C5×C8—22no—
139C22×C3×Q8C22×C511yescharacteristic
140C22×C3×D4C22×C511yescharacteristic
141C22×C3×D4C22×C511yescharacteristic
142C23×C3×C4—21no—
143C2×C3×SD16—24no—
144C2×C3×SD16C22×C514yescomplemented
145C2×C3×D8—24no—
146C2×C3×D8C22×C514yes—
147C22×C3×C8C22×C511yescharacteristic
148C22×C3×C8C22×C511yescharacteristic
149C3×#124—22no—
150C3×#124C22×C514yescomplemented
151C3×C4×D4—22no—
152C3×C4×D4C22×C514yescomplemented
153C2×C3×C4⋊C4C22×C511yescharacteristic
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C42C22×C511yescharacteristic
158C3×C4⋊C8C22×C514yescomplemented
159C3×#103C22×C514yescomplemented
160C3×#102C22×C514yescomplemented
161C24×C5—21no—
162C24×C5—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—22no—
165C2×C5×Q8—22no—
166C2×C5×Q8C23×C312yes—
167C2×C5×D4—21no—
168C2×C5×D4—22no—
169C2×C5×D4—21no—
170C2×C5×D4—22no—
171C2×C5×D4—22no—
172C2×C5×D4C3×D414yes—
173C2×C5×D4C23×C312yes—
174C2×C5×D4C23×C312yes—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—24no—
178C22×C4×C5—44no—
179C22×C4×C5C3×D411yescharacteristic
180C22×C4×C5C3×D411yescharacteristic
181C22×C4×C5C23×C311yescharacteristic
182C5×SD16—28no—
183C5×D8—28no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8C23×C312yes—
187C2×C5×C8C23×C312yes—
188C5×C4⋊C4—21no—
189C5×C4⋊C4C23×C312yes—
190C5×C22⋊C4—24no—
191C5×C22⋊C4—24no—
192C5×C22⋊C4—24no—
193C42×C5C3×D412yes—
194C42×C5C23×C312yes—
195C22×SD16C2×C3×C511yescharacteristic, complemented
196C22×D8C2×C3×C511yescharacteristic
197C2×#124C2×C3×C511yescharacteristic, complemented
198C2×C4×D4C2×C3×C511yescharacteristic, complemented
199#463C2×C3×C518yesdirect product factor
200C2×C4⋊C8C2×C3×C511yescharacteristic, complemented
201C2×#103C2×C3×C511yescharacteristic, complemented
202C2×#102C2×C3×C511yescharacteristic, complemented
203C22×C3×C5—24no—
204C22×C3×C5—42no—
205C22×C3×C5—42no—
206C22×C3×C5—48no—
207C22×C3×C5—42no—
208C22×C3×C5—42no—
209C22×C3×C5—42no—
210C22×C3×C5—84no—
211C22×C3×C5#12112yes—
212C22×C3×C5#13512yes—
213C22×C3×C5AGL(1,ℤ/8)12yes—
214C22×C3×C5C22×D411yescharacteristic
215C3×C4×C5—22no—
216C3×C4×C5—22no—
217C3×C4×C5—42no—
218C3×C4×C5—42no—
219C3×C4×C5#12112yes—
220C3×C4×C5C22×D411yescharacteristic
221C3×C4×C5C2×#4111yescharacteristic
222C24×C3—21no—
223C24×C3—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C2×C3×Q8C23×C512yes—
228C2×C3×D4—21no—
229C2×C3×D4—22no—
230C2×C3×D4—21no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4C5×D414yes—
234C2×C3×D4C23×C512yes—
235C2×C3×D4C23×C512yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—24no—
239C22×C3×C4—44no—
240C22×C3×C4C5×D411yescharacteristic
241C22×C3×C4C5×D411yescharacteristic
242C22×C3×C4C23×C511yescharacteristic
243C3×SD16—28no—
244C3×D8—28no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8C23×C512yes—
248C2×C3×C8C23×C512yes—
249C3×C4⋊C4—21no—
250C3×C4⋊C4C23×C512yes—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—24no—
253C3×C22⋊C4—24no—
254C3×C42C5×D412yes—
255C3×C42C23×C512yes—
256C23×C5—24no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—42no—
260C23×C5—42no—
261C23×C5—42no—
262C23×C5—42no—
263C23×C5—42no—
264C23×C5C2×C3×D411yescharacteristic
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8—42no—
268C5×D4—24no—
269C5×D4—22no—
270C5×D4—22no—
271C5×D4—22no—
272C5×D4—42no—
273C5×D4C2×C3×D414yes—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—48no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5C2×C3×D412yes—
282C2×C4×C5C2×C3×D412yes—
283C2×C4×C5C2×C3×D411yescharacteristic
284C2×C4×C5C2×C3×D412yes—
285C2×C4×C5C3×#4112yes—
286C2×C4×C5C24×C311yescharacteristic
287C5×C8—22no—
288C5×C8—22no—
289C22×Q8C22×C3×C511yescharacteristic
290C22×D4C22×C3×C511yescharacteristic
291C22×D4C22×C3×C511yescharacteristic
292C23×C4—21no—
293C2×SD16—24no—
294C2×SD16C22×C3×C514yescomplemented
295C2×D8—24no—
296C2×D8C22×C3×C514yes—
297C22×C8C22×C3×C511yescharacteristic
298C22×C8C22×C3×C511yescharacteristic
299#124—22no—
300#124C22×C3×C514yescomplemented
301C4×D4—22no—
302C4×D4C22×C3×C514yescomplemented
303C2×C4⋊C4C22×C3×C511yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C42C22×C3×C511yescharacteristic
308C4⋊C8C22×C3×C514yescomplemented
309#103C22×C3×C514yescomplemented
310#102C22×C3×C514yescomplemented
311C2×C3×C5—44no—
312C2×C3×C5—82no—
313C2×C3×C5#46314yesdirect product factor
314C2×C3×C5C2×#12111yescharacteristic
315C2×C3×C5C2×#13511yescharacteristic
316C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
317C23×C3—24no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3C2×C5×D411yescharacteristic
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—42no—
329C3×D4—24no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—42no—
334C3×D4C2×C5×D414yes—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—48no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4C2×C5×D412yes—
343C2×C3×C4C2×C5×D412yes—
344C2×C3×C4C2×C5×D411yescharacteristic
345C2×C3×C4C2×C5×D412yes—
346C2×C3×C4C5×#4112yes—
347C2×C3×C4C24×C511yescharacteristic
348C3×C8—22no—
349C3×C8—22no—
350C22×C5—24no—
351C22×C5—42no—
352C22×C5—42no—
353C22×C5—48no—
354C22×C5—42no—
355C22×C5—42no—
356C22×C5—42no—
357C22×C5—84no—
358C22×C5C3×#12112yes—
359C22×C5C3×#13512yes—
360C22×C5C3×AGL(1,ℤ/8)12yes—
361C22×C5C22×C3×D411yescharacteristic
362C4×C5—22no—
363C4×C5—22no—
364C4×C5—42no—
365C4×C5—42no—
366C4×C5C3×#12112yes—
367C4×C5C22×C3×D411yescharacteristic
368C4×C5C2×C3×#4111yescharacteristic
369C24—21no—
370C24—21no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8C23×C3×C512yes—
375C2×D4—21no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4C3×C5×D414yes—
381C2×D4C23×C3×C512yes—
382C2×D4C23×C3×C512yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—44no—
387C22×C4C3×C5×D411yescharacteristic
388C22×C4C3×C5×D411yescharacteristic
389C22×C4C23×C3×C511yescharacteristic
390SD16—28no—
391D8—28no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8C23×C3×C512yes—
395C2×C8C23×C3×C512yes—
396C4⋊C4—21no—
397C4⋊C4C23×C3×C512yes—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C42C3×C5×D412yes—
402C42C23×C3×C512yes—
403C3×C5C2×#46311yescharacteristic, direct product factor, Hall
404C22×C3—24no—
405C22×C3—48no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—84no—
412C22×C3C5×#12112yes—
413C22×C3C5×#13512yes—
414C22×C3C5×AGL(1,ℤ/8)12yes—
415C22×C3C22×C5×D411yescharacteristic
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—42no—
419C3×C4—42no—
420C3×C4C5×#12112yes—
421C3×C4C22×C5×D411yescharacteristic
422C3×C4C2×C5×#4111yescharacteristic
423C2×C5—44no—
424C2×C5—82no—
425C2×C5C3×#46314yesdirect product factor
426C2×C5C2×C3×#12111yescharacteristic
427C2×C5C2×C3×#13511yescharacteristic
428C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
429C23—22no—
430C23—24no—
431C23—22no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23C2×C3×C5×D411yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—42no—
441D4—22no—
442D4—24no—
443D4—22no—
444D4—22no—
445D4—42no—
446D4C2×C3×C5×D414yes—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—48no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4C2×C3×C5×D412yes—
455C2×C4C2×C3×C5×D412yes—
456C2×C4C2×C3×C5×D412yes—
457C2×C4C2×C3×C5×D411yescharacteristic
458C2×C4C3×C5×#4112yes—
459C2×C4C24×C3×C511yescharacteristic
460C8—22no—
461C8—22no—
462C2×C3—44no—
463C2×C3—82no—
464C2×C3C5×#46314yesdirect product factor
465C2×C3C2×C5×#12111yescharacteristic
466C2×C3C2×C5×#13511yescharacteristic
467C2×C3C2×C5×AGL(1,ℤ/8)11yescharacteristic
468C5C2×C3×#46311yescharacteristic, direct product factor, Sylow
469C22—24no—
470C22—48no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22C3×C5×#12112yes—
478C22C3×C5×#13512yes—
479C22C3×C5×AGL(1,ℤ/8)12yes—
480C22C22×C3×C5×D411yescharacteristic
481C4—22no—
482C4—22no—
483C4—42no—
484C4—42no—
485C4C3×C5×#12112yes—
486C4C22×C3×C5×D411yescharacteristic
487C4C2×C3×C5×#4111yescharacteristic
488C3C2×C5×#46311yescharacteristic, direct product factor, Sylow
489C2—44no—
490C2—82no—
491C2C3×C5×#46314yesdirect product factor
492C2C2×C3×C5×#12111yescharacteristic
493C2C2×C3×C5×#13511yescharacteristic
494C2C2×C3×C5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
prime radicalC22×C3×C5×D8C2
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
1. C22×C3×C5×SD16C2semidirect
3. C2×C3×C5×#124C2semidirect
4. C2×C3×C4×C5×D4C2semidirect
5. C3×C5×#463C2direct (N × H)
6. C2×C3×C5×C4⋊C8C2semidirect
7. C2×C3×C5×#103C2semidirect
8. C2×C3×C5×#102C2semidirect
9. C2×C5×#463C3direct (N × H)
15. C2×C3×C5×SD16C22semidirect
21. C3×C5×#124C22semidirect
23. C3×C4×C5×D4C22semidirect
29. C3×C5×C4⋊C8C22semidirect
30. C3×C5×#103C22semidirect
31. C3×C5×#102C22semidirect
32. C2×C3×#463C5direct (N × H)
33. C22×C5×SD16C2×C3semidirect
35. C2×C5×#124C2×C3semidirect
36. C2×C4×C5×D4C2×C3semidirect
37. C5×#463C2×C3direct (N × H)
38. C2×C5×C4⋊C8C2×C3semidirect
39. C2×C5×#103C2×C3semidirect
40. C2×C5×#102C2×C3semidirect
75. C22×C3×SD16C2×C5semidirect
77. C2×C3×#124C2×C5semidirect
78. C2×C3×C4×D4C2×C5semidirect
79. C3×#463C2×C5direct (N × H)
80. C2×C3×C4⋊C8C2×C5semidirect
81. C2×C3×#103C2×C5semidirect
82. C2×C3×#102C2×C5semidirect
88. C2×C5×SD16C22×C3semidirect
94. C5×#124C22×C3semidirect
96. C4×C5×D4C22×C3semidirect
102. C5×C4⋊C8C22×C3semidirect
103. C5×#103C22×C3semidirect
104. C5×#102C22×C3semidirect
105. C2×#463C3×C5direct (N × H)
144. C2×C3×SD16C22×C5semidirect
150. C3×#124C22×C5semidirect
152. C3×C4×D4C22×C5semidirect
158. C3×C4⋊C8C22×C5semidirect
159. C3×#103C22×C5semidirect
160. C3×#102C22×C5semidirect
195. C22×SD16C2×C3×C5semidirect
197. C2×#124C2×C3×C5semidirect
198. C2×C4×D4C2×C3×C5semidirect
199. #463C2×C3×C5direct (N × H)
200. C2×C4⋊C8C2×C3×C5semidirect
201. C2×#103C2×C3×C5semidirect
202. C2×#102C2×C3×C5semidirect
294. C2×SD16C22×C3×C5semidirect
300. #124C22×C3×C5semidirect
302. C4×D4C22×C3×C5semidirect
308. C4⋊C8C22×C3×C5semidirect
309. #103C22×C3×C5semidirect
310. #102C22×C3×C5semidirect
313. C2×C3×C5#463direct (N × H)
403. C3×C5C2×#463direct (N × H)
425. C2×C5C3×#463direct (N × H)
464. C2×C3C5×#463direct (N × H)
468. C5C2×C3×#463direct (N × H)
488. C3C2×C5×#463direct (N × H)
491. C2C3×C5×#463direct (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
C22×C3×C5×D82
C2×C3×C5×#1242
C2×C3×C4×C5×D42
C3×C5×#4632
C2×C3×C5×C4⋊C82
C2×C3×C5×#1032
C2×C3×C5×#1022
C2×C5×#4633
C2×C3×#4635