Finite Group Databasebeta

← C3×#10602369 #14299446

Subgroups — C3×#10602369 #14299446

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic
2C3×#65501C211yesmaximal, characteristic
3C2×C3×C22⋊#168C211yesmaximal, characteristic
4C2×C3×#3940C211yesmaximal, characteristic, complemented
5C2×C3×#3939C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10602369C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C3×C5×#117—22no—
11C3×C5×#117—22no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C42×C5—21no—
16C2×C3×C22⋊Dic5—21no—
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C3×#3963—21no—
22C3×C22⋊#168C414yescomplemented
23C3×#3940—22no—
24C3×#3939—22no—
25C3×#1854—51nomaximal, Hall
26C2×C5×#117C2×C311yescharacteristic
27#65501C2×C311yescharacteristic
28C2×C22⋊#168C2×C311yescharacteristic
29C2×#3940C2×C311yescharacteristic, complemented
30C2×#3939C2×C311yescharacteristic, complemented
31#64749C2×C311yescharacteristic, complemented
32#64749C2×C311yescharacteristic, complemented
33C24×C3×C5D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2×C412yes—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5Q812yes—
43C22×C3×C4×C5C2311yescharacteristic
44C22×C3×Dic5—21no—
45C22×C3×Dic5—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C5×C4⋊C4D412yes—
50C3×C5×C22⋊C4—24no—
51C3×C42×C5—24no—
52C3×C22⋊Dic5—42no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168C2×C412yes—
62C2×C3×#168C2×C412yes—
63C2×C3×#117D511yescharacteristic
64C2×C3×#107—51no—
65C2×C3×#106—51no—
66C2×C3×C22⋊C8—51no—
67C3×#380—51no—
68C3×#340—51no—
69C3×#340—51no—
70C23×C4×C5C22×C311yescharacteristic
71C5×#117—22no—
72C5×#117—22no—
73C2×C5×C4⋊C4C22×C311yescharacteristic
74C2×C5×C4⋊C4C22×C311yescharacteristic
75C2×C5×C22⋊C4—21no—
76C2×C42×C5—21no—
77C2×C22⋊Dic5—21no—
78C2×C4⋊Dic5C22×C311yescharacteristic
79C2×C4⋊Dic5C22×C311yescharacteristic
80C22×#168C22×C311yescharacteristic
81C22×#168C22×C311yescharacteristic
82#3963—21no—
83C22⋊#168C3×C414yescomplemented
84#3940—22no—
85#3939—22no—
86#1854—51noSylow
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—21no—
91C23×C3×C5—21no—
92C23×C3×C5—21no—
93C23×C3×C5C4⋊C412yes—
94C23×C3×C5C2×D411yescharacteristic
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—22no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C4⋊C412yes—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×Q811yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C3×#168—22no—
121C3×#168—22no—
122C23×C3×C4C2×D511yescharacteristic
123C22×C3×C8—51no—
124C22×C3×C8—51no—
125C3×#117—22no—
126C3×#117—22no—
127C2×C3×C4⋊C4—51no—
128C2×C3×C4⋊C4—51no—
129C2×C3×C4⋊C4C2×D511yescharacteristic
130C2×C3×C4⋊C4C2×D511yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—101no—
133C2×C3×C42—21no—
134C3×#107—102no—
135C3×#106—102no—
136C3×C22⋊C8—54no—
137C3×#95—101no—
138C24×C5C3×D411yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C2×C3×C412yes—
146C22×C4×C5C3×D411yescharacteristic
147C22×C4×C5C3×Q812yes—
148C22×C4×C5C23×C311yescharacteristic
149C22×Dic5—21no—
150C22×Dic5—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4C3×D412yes—
154C5×C4⋊C4C3×D412yes—
155C5×C22⋊C4—24no—
156C42×C5—24no—
157C22⋊Dic5—42no—
158C4⋊Dic5—21no—
159C4⋊Dic5—21no—
160C4⋊Dic5—21no—
161C4⋊Dic5—21no—
162C2×#168—21no—
163C2×#168—21no—
164C2×#168—21no—
165C2×#168—21no—
166C2×#168C2×C3×C412yes—
167C2×#168C2×C3×C412yes—
168C2×#117C3×D511yescharacteristic
169C2×#107—51no—
170C2×#106—51no—
171C2×C22⋊C8—51no—
172#380—51no—
173#340—51no—
174#340—51no—
175C22×C3×C5—22no—
176C22×C3×C5—22no—
177C22×C3×C5—22no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5C2×C4⋊C411yescharacteristic
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5#12311yescharacteristic
185C22×C3×C5#13511yescharacteristic
186C22×C3×C5#13511yescharacteristic
187C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5—42no—
191C3×C4×C5—42no—
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C4×D411yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195C3×C4×C5C22⋊Q811yescharacteristic
196C3×Dic5—81no—
197C3×Dic5—81no—
198C24×C3C22⋊D511yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C22×C3×C4Dic1012yes—
208C22×C3×C4C4×D512yes—
209C22×C3×C4C22⋊D511yescharacteristic
210C22×C3×C4C22×D511yescharacteristic
211C2×C3×C8—52no—
212C2×C3×C8—52no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C2×C3×C8—101no—
216C2×C3×C8—101no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—101no—
220C3×C4⋊C4—101no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4C22⋊D512yes—
224C3×C4⋊C4C22⋊D512yes—
225C3×C22⋊C4—24no—
226C3×C22⋊C4—202no—
227C3×C42—24no—
228C23×C5—21no—
229C23×C5—21no—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5C3×C4⋊C412yes—
235C23×C5C2×C3×D411yescharacteristic
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5C3×C4⋊C412yes—
249C2×C4×C5C22×C3×C411yescharacteristic
250C2×C4×C5C2×C3×D411yescharacteristic
251C2×C4×C5C2×C3×D411yescharacteristic
252C2×C4×C5C2×C3×Q811yescharacteristic
253C2×C4×C5C3×#4111yescharacteristic
254C2×C4×C5C3×#4111yescharacteristic
255C2×Dic5—41no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—41no—
260C2×Dic5—41no—
261#168—22no—
262#168—22no—
263C23×C4C2×C3×D511yescharacteristic
264C22×C8—51no—
265C22×C8—51no—
266#117—22no—
267#117—22no—
268C2×C4⋊C4—51no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4C2×C3×D511yescharacteristic
271C2×C4⋊C4C2×C3×D511yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—101no—
274C2×C42—21no—
275#107—102no—
276#106—102no—
277C22⋊C8—54no—
278#95—101no—
279C2×C3×C5—42no—
280C2×C3×C5#38511yescharacteristic
281C2×C3×C5#42711yescharacteristic
282C2×C3×C5#42811yescharacteristic
283C2×C3×C5#44911yescharacteristic
284C2×C3×C5#45211yescharacteristic
285C2×C3×C5#48211yescharacteristic
286C2×C3×C5#48511yescharacteristic
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3#68312yes—
294C23×C3C2×C22⋊D511yescharacteristic
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—201no—
308C2×C3×C4—201no—
309C2×C3×C4—201no—
310C2×C3×C4—201no—
311C2×C3×C4—201no—
312C2×C3×C4—201no—
313C2×C3×C4#68312yes—
314C2×C3×C4C2×Dic1011yescharacteristic
315C2×C3×C4C2×C4×D511yescharacteristic
316C2×C3×C4#70911yescharacteristic
317C2×C3×C4#70911yescharacteristic
318C2×C3×C4C2×C22⋊D511yescharacteristic
319C2×C3×C4C2×C22⋊D511yescharacteristic
320C3×C8—102no—
321C3×C8—102no—
322C22×C5—22no—
323C22×C5—22no—
324C22×C5—22no—
325C22×C5—41no—
326C22×C5—41no—
327C22×C5—41no—
328C22×C5—41no—
329C22×C5C2×C3×C4⋊C411yescharacteristic
330C22×C5C3×#12011yescharacteristic
331C22×C5C3×#12311yescharacteristic
332C22×C5C3×#13511yescharacteristic
333C22×C5C3×#13511yescharacteristic
334C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
335C22×C5C3×#13711yescharacteristic
336C4×C5—22no—
337C4×C5—42no—
338C4×C5—42no—
339C4×C5C3×C4×D411yescharacteristic
340C4×C5C3×C4×D411yescharacteristic
341C4×C5C3×C22⋊Q811yescharacteristic
342C4×C5C3×C22⋊Q811yescharacteristic
343Dic5—81no—
344Dic5—81no—
345C24C3×C22⋊D511yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4C3×Dic1012yes—
355C22×C4C3×C4×D512yes—
356C22×C4C3×C22⋊D511yescharacteristic
357C22×C4C22×C3×D511yescharacteristic
358C2×C8—52no—
359C2×C8—52no—
360C2×C8—101no—
361C2×C8—101no—
362C2×C8—101no—
363C2×C8—101no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4C3×C22⋊D512yes—
371C4⋊C4C3×C22⋊D512yes—
372C22⋊C4—24no—
373C22⋊C4—202no—
374C42—24no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3C2×#68311yescharacteristic
384C22×C3#407511yescharacteristic
385C22×C3#409511yescharacteristic
386C22×C3#409611yescharacteristic
387C22×C3#409611yescharacteristic
388C22×C3#409711yescharacteristic
389C22×C3#409911yescharacteristic
390C3×C4—22no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—401no—
394C3×C4—401no—
395C3×C4#407011yescharacteristic
396C3×C4#407011yescharacteristic
397C3×C4C4×C22⋊D511yescharacteristic
398C3×C4C4×C22⋊D511yescharacteristic
399C2×C5—42no—
400C2×C5C3×#38511yescharacteristic
401C2×C5C3×#42711yescharacteristic
402C2×C5C3×#42811yescharacteristic
403C2×C5C3×#44911yescharacteristic
404C2×C5C3×#45211yescharacteristic
405C2×C5C3×#48211yescharacteristic
406C2×C5C3×#48511yescharacteristic
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23C3×#68312yes—
414C23C2×C3×C22⋊D511yescharacteristic
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—201no—
428C2×C4—201no—
429C2×C4—201no—
430C2×C4—201no—
431C2×C4—201no—
432C2×C4—201no—
433C2×C4C3×#68312yes—
434C2×C4C2×C3×Dic1011yescharacteristic
435C2×C4C2×C3×C4×D511yescharacteristic
436C2×C4C3×#70911yescharacteristic
437C2×C4C3×#70911yescharacteristic
438C2×C4C2×C3×C22⋊D511yescharacteristic
439C2×C4C2×C3×C22⋊D511yescharacteristic
440C8—102no—
441C8—102no—
442C2×C3—42no—
443C2×C3#6528411yescharacteristic
444C2×C3#6528511yescharacteristic
445C2×C3#6528711yescharacteristic
446C2×C3#6529211yescharacteristic
447C2×C3#6549911yescharacteristic
448C2×C3#6552711yescharacteristic
449C2×C3#6552811yescharacteristic
450C5C3×#185411yescharacteristic, complemented, Sylow
451C22—22no—
452C22—22no—
453C22—22no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22C2×C3×#68311yescharacteristic
459C22C3×#407511yescharacteristic
460C22C3×#409511yescharacteristic
461C22C3×#409611yescharacteristic
462C22C3×#409611yescharacteristic
463C22C3×#409711yescharacteristic
464C22C3×#409911yescharacteristic
465C4—22no—
466C4—42no—
467C4—42no—
468C4—401no—
469C4—401no—
470C4C3×#407011yescharacteristic
471C4C3×#407011yescharacteristic
472C4C3×C4×C22⋊D511yescharacteristic
473C4C3×C4×C22⋊D511yescharacteristic
474C3#1060236911yescharacteristic, direct product factor, Sylow
475C2—42no—
476C2C3×#6528411yescharacteristic
477C2C3×#6528511yescharacteristic
478C2C3×#6528711yescharacteristic
479C2C3×#6529211yescharacteristic
480C2C3×#6549911yescharacteristic
481C2C3×#6552711yescharacteristic
482C2C3×#6552811yescharacteristic
subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#1854
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3940C2semidirect
5. C2×C3×#3939C2semidirect
6. C3×#64749C2semidirect
7. C3×#64749C2semidirect
8. #10602369C3direct (N × H)
22. C3×C22⋊#168C4semidirect
29. C2×#3940C2×C3semidirect
30. C2×#3939C2×C3semidirect
31. #64749C2×C3semidirect
32. #64749C2×C3semidirect
83. C22⋊#168C3×C4semidirect
375. C3×C5#1854semidirect
450. C5C3×#1854semidirect
474. C3#10602369direct (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×#1172
C3×#655012
C2×C3×C22⋊#1682
C2×C3×#39402
C2×C3×#39392
C3×#647492
#106023693
C3×#18545