Finite Group Databasebeta

← C2×C3×C5×#482 #14276121

Subgroups — C2×C3×C5×#482 #14276121

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic, complemented
3C3×C5×#482C218yesmaximal, direct product factor
4C2×C3×C5×#107C211yesmaximal, characteristic, complemented
5C2×C3×C5×#106C211yesmaximal, characteristic, complemented
6C2×C3×C5×#102C211yesmaximal, characteristic, complemented
7C2×C3×C5×#102C211yesmaximal, characteristic, complemented
8C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
9C2×C5×#482C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×D4—21no—
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C22×C3×C5×C8C2211yescharacteristic
15C3×C5×#121—22no—
16C3×C5×#121C2214yes—
17C3×C5×#117—22no—
18C3×C5×#117C2214yescomplemented
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4—21no—
23C2×C3×C5×C22⋊C4—21no—
24C2×C3×C42×C5—21no—
25C3×C5×#107C2214yescomplemented
26C3×C5×#106C2214yescomplemented
27C3×C5×#102C2214yescomplemented
28C3×C5×#102C2214yescomplemented
29C3×C5×C22⋊C8C2214yescomplemented
30C2×C3×#482C511yesmaximal, characteristic, direct product factor, Hall
31C2×C5×#121C2×C311yescharacteristic
32C2×C5×#117C2×C311yescharacteristic, complemented
33C5×#482C2×C318yesdirect product factor
34C2×C5×#107C2×C311yescharacteristic, complemented
35C2×C5×#106C2×C311yescharacteristic, complemented
36C2×C5×#102C2×C311yescharacteristic, complemented
37C2×C5×#102C2×C311yescharacteristic, complemented
38C2×C5×C22⋊C8C2×C311yescharacteristic, complemented
39C24×C3×C5—21no—
40C24×C3×C5D411yescharacteristic
41C2×C3×C5×D4—24no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4—22no—
45C2×C3×C5×D4—44no—
46C2×C3×C5×D4C2312yes—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5D412yes—
53C22×C3×C4×C5D411yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C3×C5×C8—22no—
57C2×C3×C5×C8—22no—
58C2×C3×C5×C8C2312yes—
59C2×C3×C5×C8C2312yes—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4—21no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4C2312yes—
64C3×C5×C4⋊C4C2312yes—
65C3×C5×C4⋊C4C2312yes—
66C3×C5×C22⋊C4—24no—
67C3×C5×C22⋊C4—24no—
68C3×C42×C5—24no—
69C2×C3×#121C2×C511yescharacteristic
70C2×C3×#117C2×C511yescharacteristic, complemented
71C3×#482C2×C518yesdirect product factor
72C2×C3×#107C2×C511yescharacteristic, complemented
73C2×C3×#106C2×C511yescharacteristic, complemented
74C2×C3×#102C2×C511yescharacteristic, complemented
75C2×C3×#102C2×C511yescharacteristic, complemented
76C2×C3×C22⋊C8C2×C511yescharacteristic, complemented
77C22×C5×D4—21no—
78C22×C5×D4C22×C311yescharacteristic
79C23×C4×C5C22×C311yescharacteristic
80C22×C5×C8C22×C311yescharacteristic
81C22×C5×C8C22×C311yescharacteristic
82C5×#121—22no—
83C5×#121C22×C314yes—
84C5×#117—22no—
85C5×#117C22×C314yescomplemented
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C2×C5×C4⋊C4C22×C311yescharacteristic
88C2×C5×C4⋊C4C22×C311yescharacteristic
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C42×C5—21no—
92C5×#107C22×C314yescomplemented
93C5×#106C22×C314yescomplemented
94C5×#102C22×C314yescomplemented
95C5×#102C22×C314yescomplemented
96C5×C22⋊C8C22×C314yescomplemented
97C2×#482C3×C511yescharacteristic, direct product factor, Sylow
98C23×C3×C5—22no—
99C23×C3×C5—22no—
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5—42no—
103C23×C3×C5—42no—
104C23×C3×C5—42no—
105C23×C3×C5C2×D412yes—
106C23×C3×C5C2×D411yescharacteristic
107C3×C5×D4—22no—
108C3×C5×D4—22no—
109C3×C5×D4—48no—
110C3×C5×D4—42no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—24no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—42no—
119C2×C3×C4×C5—42no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5#4112yes—
124C2×C3×C4×C5#4112yes—
125C2×C3×C4×C5C2411yescharacteristic
126C3×C5×C8—22no—
127C3×C5×C8—22no—
128C22×C3×D4—21no—
129C22×C3×D4C22×C511yescharacteristic
130C23×C3×C4C22×C511yescharacteristic
131C22×C3×C8C22×C511yescharacteristic
132C22×C3×C8C22×C511yescharacteristic
133C3×#121—22no—
134C3×#121C22×C514yes—
135C3×#117—22no—
136C3×#117C22×C514yescomplemented
137C2×C3×C4⋊C4C22×C511yescharacteristic
138C2×C3×C4⋊C4C22×C511yescharacteristic
139C2×C3×C4⋊C4C22×C511yescharacteristic
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C42—21no—
143C3×#107C22×C514yescomplemented
144C3×#106C22×C514yescomplemented
145C3×#102C22×C514yescomplemented
146C3×#102C22×C514yescomplemented
147C3×C22⋊C8C22×C514yescomplemented
148C24×C5—21no—
149C24×C5C3×D411yescharacteristic
150C2×C5×D4—24no—
151C2×C5×D4—21no—
152C2×C5×D4—22no—
153C2×C5×D4—22no—
154C2×C5×D4—44no—
155C2×C5×D4C23×C312yes—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5C3×D411yescharacteristic
162C22×C4×C5C3×D412yes—
163C22×C4×C5C23×C312yes—
164C22×C4×C5C23×C311yescharacteristic
165C2×C5×C8—22no—
166C2×C5×C8—22no—
167C2×C5×C8C23×C312yes—
168C2×C5×C8C23×C312yes—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—21no—
172C5×C4⋊C4C23×C312yes—
173C5×C4⋊C4C23×C312yes—
174C5×C4⋊C4C23×C312yes—
175C5×C22⋊C4—24no—
176C5×C22⋊C4—24no—
177C42×C5—24no—
178C2×#121C2×C3×C511yescharacteristic
179C2×#117C2×C3×C511yescharacteristic, complemented
180#482C2×C3×C518yesdirect product factor
181C2×#107C2×C3×C511yescharacteristic, complemented
182C2×#106C2×C3×C511yescharacteristic, complemented
183C2×#102C2×C3×C511yescharacteristic, complemented
184C2×#102C2×C3×C511yescharacteristic, complemented
185C2×C22⋊C8C2×C3×C511yescharacteristic, complemented
186C22×C3×C5—22no—
187C22×C3×C5—22no—
188C22×C3×C5—22no—
189C22×C3×C5—44no—
190C22×C3×C5—42no—
191C22×C3×C5—42no—
192C22×C3×C5—42no—
193C22×C3×C5—84no—
194C22×C3×C5#12312yes—
195C22×C3×C5#13512yes—
196C22×C3×C5AGL(1,ℤ/8)12yes—
197C22×C3×C5C22×D411yescharacteristic
198C3×C4×C5—22no—
199C3×C4×C5—42no—
200C3×C4×C5—42no—
201C3×C4×C5—42no—
202C3×C4×C5#12312yes—
203C3×C4×C5C2×#4111yescharacteristic
204C3×C4×C5C2×#4111yescharacteristic
205C24×C3—21no—
206C24×C3C5×D411yescharacteristic
207C2×C3×D4—24no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—44no—
212C2×C3×D4C23×C512yes—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4C5×D411yescharacteristic
219C22×C3×C4C5×D412yes—
220C22×C3×C4C23×C512yes—
221C22×C3×C4C23×C511yescharacteristic
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8C23×C512yes—
225C2×C3×C8C23×C512yes—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4C23×C512yes—
230C3×C4⋊C4C23×C512yes—
231C3×C4⋊C4C23×C512yes—
232C3×C22⋊C4—24no—
233C3×C22⋊C4—24no—
234C3×C42—24no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—22no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5C2×C3×D412yes—
243C23×C5C2×C3×D411yescharacteristic
244C5×D4—22no—
245C5×D4—22no—
246C5×D4—48no—
247C5×D4—42no—
248C2×C4×C5—22no—
249C2×C4×C5—24no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5C2×C3×D412yes—
259C2×C4×C5C2×C3×D411yescharacteristic
260C2×C4×C5C3×#4112yes—
261C2×C4×C5C3×#4112yes—
262C2×C4×C5C24×C311yescharacteristic
263C5×C8—22no—
264C5×C8—22no—
265C22×D4—21no—
266C22×D4C22×C3×C511yescharacteristic
267C23×C4C22×C3×C511yescharacteristic
268C22×C8C22×C3×C511yescharacteristic
269C22×C8C22×C3×C511yescharacteristic
270#121—22no—
271#121C22×C3×C514yes—
272#117—22no—
273#117C22×C3×C514yescomplemented
274C2×C4⋊C4C22×C3×C511yescharacteristic
275C2×C4⋊C4C22×C3×C511yescharacteristic
276C2×C4⋊C4C22×C3×C511yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C42—21no—
280#107C22×C3×C514yescomplemented
281#106C22×C3×C514yescomplemented
282#102C22×C3×C514yescomplemented
283#102C22×C3×C514yescomplemented
284C22⋊C8C22×C3×C514yescomplemented
285C2×C3×C5—42no—
286C2×C3×C5—82no—
287C2×C3×C5#48214yesdirect product factor
288C2×C3×C5C2×#12311yescharacteristic
289C2×C3×C5C2×#13511yescharacteristic
290C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3C2×C5×D412yes—
299C23×C3C2×C5×D411yescharacteristic
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—48no—
303C3×D4—42no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4C2×C5×D412yes—
315C2×C3×C4C2×C5×D411yescharacteristic
316C2×C3×C4C5×#4112yes—
317C2×C3×C4C5×#4112yes—
318C2×C3×C4C24×C511yescharacteristic
319C3×C8—22no—
320C3×C8—22no—
321C22×C5—22no—
322C22×C5—22no—
323C22×C5—22no—
324C22×C5—44no—
325C22×C5—42no—
326C22×C5—42no—
327C22×C5—42no—
328C22×C5—84no—
329C22×C5C3×#12312yes—
330C22×C5C3×#13512yes—
331C22×C5C3×AGL(1,ℤ/8)12yes—
332C22×C5C22×C3×D411yescharacteristic
333C4×C5—22no—
334C4×C5—42no—
335C4×C5—42no—
336C4×C5—42no—
337C4×C5C3×#12312yes—
338C4×C5C2×C3×#4111yescharacteristic
339C4×C5C2×C3×#4111yescharacteristic
340C24—21no—
341C24C3×C5×D411yescharacteristic
342C2×D4—24no—
343C2×D4—21no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—44no—
347C2×D4C23×C3×C512yes—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4C3×C5×D411yescharacteristic
354C22×C4C3×C5×D412yes—
355C22×C4C23×C3×C512yes—
356C22×C4C23×C3×C511yescharacteristic
357C2×C8—22no—
358C2×C8—22no—
359C2×C8C23×C3×C512yes—
360C2×C8C23×C3×C512yes—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4C23×C3×C512yes—
365C4⋊C4C23×C3×C512yes—
366C4⋊C4C23×C3×C512yes—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C42—24no—
370C3×C5C2×#48211yescharacteristic, direct product factor, Hall
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—44no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—84no—
379C22×C3C5×#12312yes—
380C22×C3C5×#13512yes—
381C22×C3C5×AGL(1,ℤ/8)12yes—
382C22×C3C22×C5×D411yescharacteristic
383C3×C4—22no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4C5×#12312yes—
388C3×C4C2×C5×#4111yescharacteristic
389C3×C4C2×C5×#4111yescharacteristic
390C2×C5—42no—
391C2×C5—82no—
392C2×C5C3×#48214yesdirect product factor
393C2×C5C2×C3×#12311yescharacteristic
394C2×C5C2×C3×#13511yescharacteristic
395C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23C2×C3×C5×D412yes—
404C23C2×C3×C5×D411yescharacteristic
405D4—22no—
406D4—22no—
407D4—48no—
408D4—42no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4C2×C3×C5×D412yes—
420C2×C4C2×C3×C5×D411yescharacteristic
421C2×C4C3×C5×#4112yes—
422C2×C4C3×C5×#4112yes—
423C2×C4C24×C3×C511yescharacteristic
424C8—22no—
425C8—22no—
426C2×C3—42no—
427C2×C3—82no—
428C2×C3C5×#48214yesdirect product factor
429C2×C3C2×C5×#12311yescharacteristic
430C2×C3C2×C5×#13511yescharacteristic
431C2×C3C2×C5×AGL(1,ℤ/8)11yescharacteristic
432C5C2×C3×#48211yescharacteristic, direct product factor, Sylow
433C22—22no—
434C22—22no—
435C22—22no—
436C22—44no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—84no—
441C22C3×C5×#12312yes—
442C22C3×C5×#13512yes—
443C22C3×C5×AGL(1,ℤ/8)12yes—
444C22C22×C3×C5×D411yescharacteristic
445C4—22no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4C3×C5×#12312yes—
450C4C2×C3×C5×#4111yescharacteristic
451C4C2×C3×C5×#4111yescharacteristic
452C3C2×C5×#48211yescharacteristic, direct product factor, Sylow
453C2—42no—
454C2—82no—
455C2C3×C5×#48214yesdirect product factor
456C2C2×C3×C5×#12311yescharacteristic
457C2C2×C3×C5×#13511yescharacteristic
458C2C2×C3×C5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
center, socleC23×C3×C5C2×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C23×C3×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#117C2semidirect
3. C3×C5×#482C2direct (N × H)
4. C2×C3×C5×#107C2semidirect
5. C2×C3×C5×#106C2semidirect
6. C2×C3×C5×#102C2semidirect
7. C2×C3×C5×#102C2semidirect
8. C2×C3×C5×C22⋊C8C2semidirect
9. C2×C5×#482C3direct (N × H)
18. C3×C5×#117C22semidirect
25. C3×C5×#107C22semidirect
26. C3×C5×#106C22semidirect
27. C3×C5×#102C22semidirect
28. C3×C5×#102C22semidirect
29. C3×C5×C22⋊C8C22semidirect
30. C2×C3×#482C5direct (N × H)
32. C2×C5×#117C2×C3semidirect
33. C5×#482C2×C3direct (N × H)
34. C2×C5×#107C2×C3semidirect
35. C2×C5×#106C2×C3semidirect
36. C2×C5×#102C2×C3semidirect
37. C2×C5×#102C2×C3semidirect
38. C2×C5×C22⋊C8C2×C3semidirect
70. C2×C3×#117C2×C5semidirect
71. C3×#482C2×C5direct (N × H)
72. C2×C3×#107C2×C5semidirect
73. C2×C3×#106C2×C5semidirect
74. C2×C3×#102C2×C5semidirect
75. C2×C3×#102C2×C5semidirect
76. C2×C3×C22⋊C8C2×C5semidirect
85. C5×#117C22×C3semidirect
92. C5×#107C22×C3semidirect
93. C5×#106C22×C3semidirect
94. C5×#102C22×C3semidirect
95. C5×#102C22×C3semidirect
96. C5×C22⋊C8C22×C3semidirect
97. C2×#482C3×C5direct (N × H)
136. C3×#117C22×C5semidirect
143. C3×#107C22×C5semidirect
144. C3×#106C22×C5semidirect
145. C3×#102C22×C5semidirect
146. C3×#102C22×C5semidirect
147. C3×C22⋊C8C22×C5semidirect
179. C2×#117C2×C3×C5semidirect
180. #482C2×C3×C5direct (N × H)
181. C2×#107C2×C3×C5semidirect
182. C2×#106C2×C3×C5semidirect
183. C2×#102C2×C3×C5semidirect
184. C2×#102C2×C3×C5semidirect
185. C2×C22⋊C8C2×C3×C5semidirect
273. #117C22×C3×C5semidirect
280. #107C22×C3×C5semidirect
281. #106C22×C3×C5semidirect
282. #102C22×C3×C5semidirect
283. #102C22×C3×C5semidirect
284. C22⋊C8C22×C3×C5semidirect
287. C2×C3×C5#482direct (N × H)
370. C3×C5C2×#482direct (N × H)
392. C2×C5C3×#482direct (N × H)
428. C2×C3C5×#482direct (N × H)
432. C5C2×C3×#482direct (N × H)
452. C3C2×C5×#482direct (N × H)
455. C2C3×C5×#482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C2×C3×C5×#1172
C3×C5×#4822
C2×C3×C5×#1072
C2×C3×C5×#1062
C2×C3×C5×#1022
C2×C3×C5×C22⋊C82
C2×C5×#4823
C2×C3×#4825