Finite Group Databasebeta

← C3×#10602400 #14300080

Subgroups — C3×#10602400 #14300080

Order 1920.

724 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
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×#3964C211yesmaximal, characteristic
3C2×C3×#3964C211yesmaximal, characteristic
4C2×C3×#3940C211yesmaximal, characteristic, complemented
5C3×#65217C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7C3×#64744C211yesmaximal, characteristic, complemented
8#10602400C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C23×C3×C4×C5—21no—
11C3×C4×C5×D4—22no—
12C3×C4×C5×D4—22no—
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C42×C5C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×#683—21no—
19C22×C3×#168C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C3×#3964—22no—
22C3×#3964C414yescomplemented
23C3×#3963—21no—
24C3×#3940—22no—
25C3×#1864—51nomaximal, Hall
26C2×C4×C5×D4C2×C311yescharacteristic
27C2×#3964C2×C311yescharacteristic
28C2×#3964C2×C311yescharacteristic
29C2×#3940C2×C311yescharacteristic, complemented
30#65217C2×C311yescharacteristic, complemented
31#64749C2×C311yescharacteristic, complemented
32#64744C2×C311yescharacteristic, complemented
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C2×C3×C5×D4Q812yes—
40C22×C3×C4×C5—24no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—42no—
43C22×C3×C4×C5—42no—
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C22×C3×Dic5—21no—
48C22×C3×Dic5—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4D412yes—
51C3×C5×C22⋊C4—24no—
52C3×C42×C5—21no—
53C3×C42×C5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5C2×C412yescomplemented
58C3×#683—42no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168C2×C412yescomplemented
65C2×C3×C4×D4D511yescharacteristic
66C2×C3×#106—51no—
67C2×C3×#102—51no—
68C2×C3×#102—51no—
69C3×#389—51no—
70C3×#340—51no—
71C3×#336—51no—
72C22×C5×D4C22×C311yescharacteristic
73C23×C4×C5—21no—
74C4×C5×D4—22no—
75C4×C5×D4—22no—
76C2×C5×C4⋊C4C22×C311yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C42×C5C22×C311yescharacteristic
79C2×C4⋊Dic5C22×C311yescharacteristic
80C2×C4⋊Dic5C22×C311yescharacteristic
81C2×#683—21no—
82C22×#168C22×C311yescharacteristic
83C22×#168C22×C311yescharacteristic
84#3964—22no—
85#3964C3×C414yescomplemented
86#3963—21no—
87#3940—22no—
88#1864—51noSylow
89C23×C3×C5—22no—
90C23×C3×C5—22no—
91C23×C3×C5—22no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5—41no—
95C23×C3×C5—41no—
96C23×C3×C5C2×D411yescharacteristic
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4C4⋊C414yescomplemented
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—48no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5SD1612yes—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×Q811yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×Dic5—22no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C3×#168—22no—
124C3×#168—41no—
125C22×C3×D4C2×D511yescharacteristic
126C23×C3×C4—21no—
127C22×C3×C8—51no—
128C22×C3×C8—51no—
129C3×C4×D4—22no—
130C3×C4×D4—22no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4—101no—
134C2×C3×C4⋊C4C2×D511yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C42C2×D511yescharacteristic
137C3×#106—102no—
138C3×#102—54no—
139C3×#102—102no—
140C3×#95—101no—
141C24×C5—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4C2×C3×C412yes—
146C2×C5×D4C3×D412yes—
147C2×C5×D4C3×Q812yes—
148C22×C4×C5—24no—
149C22×C4×C5—21no—
150C22×C4×C5—42no—
151C22×C4×C5—42no—
152C22×C4×C5C3×D411yescharacteristic
153C22×C4×C5C3×D411yescharacteristic
154C22×C4×C5C23×C311yescharacteristic
155C22×Dic5—21no—
156C22×Dic5—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4C3×D412yes—
159C5×C22⋊C4—24no—
160C42×C5—21no—
161C42×C5—21no—
162C4⋊Dic5—21no—
163C4⋊Dic5—21no—
164C4⋊Dic5—21no—
165C4⋊Dic5C2×C3×C412yescomplemented
166#683—42no—
167C2×#168—21no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—21no—
171C2×#168—21no—
172C2×#168C2×C3×C412yescomplemented
173C2×C4×D4C3×D511yescharacteristic
174C2×#106—51no—
175C2×#102—51no—
176C2×#102—51no—
177#389—51no—
178#340—51no—
179#336—51no—
180C22×C3×C5—24no—
181C22×C3×C5—42no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—42no—
185C22×C3×C5—42no—
186C22×C3×C5—42no—
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5#12011yescharacteristic
189C22×C3×C5C22⋊Q811yescharacteristic
190C22×C3×C5C2×SD1611yescharacteristic
191C22×C3×C5#13511yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
194C3×C4×C5—22no—
195C3×C4×C5—41no—
196C3×C4×C5—42no—
197C3×C4×C5C2×C4⋊C411yescharacteristic
198C3×C4×C5C4×D411yescharacteristic
199C3×C4×C5C22⋊Q811yescharacteristic
200C3×C4×C5#12311yescharacteristic
201C3×Dic5—42no—
202C3×Dic5—81no—
203C24×C3—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4Dic1012yes—
208C2×C3×D4C4×D512yes—
209C2×C3×D4C22⋊D512yes—
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—101no—
215C22×C3×C4—101no—
216C22×C3×C4C22⋊D511yescharacteristic
217C22×C3×C4C22⋊D511yescharacteristic
218C22×C3×C4C22×D511yescharacteristic
219C2×C3×C8—52no—
220C2×C3×C8—101no—
221C2×C3×C8—101no—
222C2×C3×C8—101no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—52no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—202no—
231C3×C4⋊C4C22⋊D512yes—
232C3×C22⋊C4—24no—
233C3×C42—21no—
234C3×C42—21no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5C2×C3×D411yescharacteristic
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—22no—
246C5×D4C3×C4⋊C414yescomplemented
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—21no—
250C2×C4×C5—22no—
251C2×C4×C5—21no—
252C2×C4×C5—21no—
253C2×C4×C5—48no—
254C2×C4×C5—41no—
255C2×C4×C5—41no—
256C2×C4×C5C3×SD1612yes—
257C2×C4×C5C22×C3×C411yescharacteristic
258C2×C4×C5C2×C3×D411yescharacteristic
259C2×C4×C5C2×C3×D411yescharacteristic
260C2×C4×C5C2×C3×Q811yescharacteristic
261C2×C4×C5C3×#4111yescharacteristic
262C2×C4×C5C3×#4111yescharacteristic
263C2×Dic5—22no—
264C2×Dic5—41no—
265C2×Dic5—41no—
266C2×Dic5—41no—
267C2×Dic5—41no—
268C2×Dic5—41no—
269#168—22no—
270#168—41no—
271C22×D4C2×C3×D511yescharacteristic
272C23×C4—21no—
273C22×C8—51no—
274C22×C8—51no—
275C4×D4—22no—
276C4×D4—22no—
277C2×C4⋊C4—51no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4C2×C3×D511yescharacteristic
281C2×C22⋊C4—21no—
282C2×C42C2×C3×D511yescharacteristic
283#106—102no—
284#102—54no—
285#102—102no—
286#95—101no—
287C2×C3×C5—44no—
288C2×C3×C5#38511yescharacteristic
289C2×C3×C5C4×SD1611yescharacteristic
290C2×C3×C5#44211yescharacteristic
291C2×C3×C5#44911yescharacteristic
292C2×C3×C5#45011yescharacteristic
293C2×C3×C5#47611yescharacteristic
294C2×C3×C5#47811yescharacteristic
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3C2×C22⋊D511yescharacteristic
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4#68314yescomplemented
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—48no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—102no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4#68712yes—
323C2×C3×C4C2×Dic1011yescharacteristic
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4#70911yescharacteristic
326C2×C3×C4#70911yescharacteristic
327C2×C3×C4C2×C22⋊D511yescharacteristic
328C2×C3×C4C2×C22⋊D511yescharacteristic
329C3×C8—102no—
330C3×C8—201no—
331C22×C5—24no—
332C22×C5—42no—
333C22×C5—42no—
334C22×C5—42no—
335C22×C5—42no—
336C22×C5—42no—
337C22×C5—42no—
338C22×C5C3×C4×D411yescharacteristic
339C22×C5C3×#12011yescharacteristic
340C22×C5C3×C22⋊Q811yescharacteristic
341C22×C5C2×C3×SD1611yescharacteristic
342C22×C5C3×#13511yescharacteristic
343C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
344C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
345C4×C5—22no—
346C4×C5—41no—
347C4×C5—42no—
348C4×C5C2×C3×C4⋊C411yescharacteristic
349C4×C5C3×C4×D411yescharacteristic
350C4×C5C3×C22⋊Q811yescharacteristic
351C4×C5C3×#12311yescharacteristic
352Dic5—42no—
353Dic5—81no—
354C24—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4C3×Dic1012yes—
359C2×D4C3×C4×D512yes—
360C2×D4C3×C22⋊D512yes—
361C22×C4—24no—
362C22×C4—21no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—101no—
366C22×C4—101no—
367C22×C4C3×C22⋊D511yescharacteristic
368C22×C4C3×C22⋊D511yescharacteristic
369C22×C4C22×C3×D511yescharacteristic
370C2×C8—52no—
371C2×C8—101no—
372C2×C8—101no—
373C2×C8—101no—
374C2×C8—101no—
375C2×C8—101no—
376C4⋊C4—21no—
377C4⋊C4—52no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—202no—
382C4⋊C4C3×C22⋊D512yes—
383C22⋊C4—24no—
384C42—21no—
385C42—21no—
386C3×C5#186411yescharacteristic, complemented, Hall
387C22×C3—24no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3#407011yescharacteristic
395C22×C3C4×C22⋊D511yescharacteristic
396C22×C3#407811yescharacteristic
397C22×C3C2×#68711yescharacteristic
398C22×C3#409511yescharacteristic
399C22×C3#409611yescharacteristic
400C22×C3#409911yescharacteristic
401C3×C4—22no—
402C3×C4—42no—
403C3×C4—41no—
404C3×C4—202no—
405C3×C4—401no—
406C3×C4C2×#68311yescharacteristic
407C3×C4#407011yescharacteristic
408C3×C4C4×C22⋊D511yescharacteristic
409C3×C4#407511yescharacteristic
410C2×C5—44no—
411C2×C5C3×#38511yescharacteristic
412C2×C5C3×C4×SD1611yescharacteristic
413C2×C5C3×#44211yescharacteristic
414C2×C5C3×#44911yescharacteristic
415C2×C5C3×#45011yescharacteristic
416C2×C5C3×#47611yescharacteristic
417C2×C5C3×#47811yescharacteristic
418C23—22no—
419C23—22no—
420C23—22no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C2×C3×C22⋊D511yescharacteristic
426D4—22no—
427D4—22no—
428D4—22no—
429D4C3×#68314yescomplemented
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—48no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—102no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4C3×#68712yes—
446C2×C4C2×C3×Dic1011yescharacteristic
447C2×C4C2×C3×C4×D511yescharacteristic
448C2×C4C3×#70911yescharacteristic
449C2×C4C3×#70911yescharacteristic
450C2×C4C2×C3×C22⋊D511yescharacteristic
451C2×C4C2×C3×C22⋊D511yescharacteristic
452C8—102no—
453C8—201no—
454C2×C3—44no—
455C2×C3#6529711yescharacteristic
456C2×C3#6529811yescharacteristic
457C2×C3#6530311yescharacteristic
458C2×C3C4×#68711yescharacteristic
459C2×C3#6549911yescharacteristic
460C2×C3#6550711yescharacteristic
461C2×C3#6552711yescharacteristic
462C5C3×#186411yescharacteristic, complemented, Sylow
463C22—24no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C3×#407011yescharacteristic
471C22C3×C4×C22⋊D511yescharacteristic
472C22C3×#407811yescharacteristic
473C22C2×C3×#68711yescharacteristic
474C22C3×#409511yescharacteristic
475C22C3×#409611yescharacteristic
476C22C3×#409911yescharacteristic
477C4—22no—
478C4—42no—
479C4—41no—
480C4—202no—
481C4—401no—
482C4C2×C3×#68311yescharacteristic
483C4C3×#407011yescharacteristic
484C4C3×C4×C22⋊D511yescharacteristic
485C4C3×#407511yescharacteristic
486C3#1060240011yescharacteristic, direct product factor, Sylow
487C2—44no—
488C2C3×#6529711yescharacteristic
489C2C3×#6529811yescharacteristic
490C2C3×#6530311yescharacteristic
491C2C3×C4×#68711yescharacteristic
492C2C3×#6549911yescharacteristic
493C2C3×#6550711yescharacteristic
494C2C3×#6552711yescharacteristic
subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#1864
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3940C2semidirect
5. C3×#65217C2semidirect
6. C3×#64749C2semidirect
7. C3×#64744C2semidirect
8. #10602400C3direct (N × H)
22. C3×#3964C4semidirect
29. C2×#3940C2×C3semidirect
30. #65217C2×C3semidirect
31. #64749C2×C3semidirect
32. #64744C2×C3semidirect
57. C3×C4⋊Dic5C2×C4semidirect
64. C2×C3×#168C2×C4semidirect
85. #3964C3×C4semidirect
100. C3×C5×D4C4⋊C4semidirect
165. C4⋊Dic5C2×C3×C4semidirect
172. C2×#168C2×C3×C4semidirect
246. C5×D4C3×C4⋊C4semidirect
306. C3×D4#683semidirect
386. C3×C5#1864semidirect
429. D4C3×#683semidirect
462. C5C3×#1864semidirect
486. C3#10602400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C3×#39642
C2×C3×#39402
C3×#652172
C3×#647492
C3×#647442
#106024003
C3×#18645