Finite Group Databasebeta

← C3×#10605497 #14326420

Subgroups — C3×#10605497 #14326420

Order 1920.

1064 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×#4018C211yesmaximal, characteristic
2C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#65278C212yesmaximal
4C3×#65267C212yesmaximal, complemented
5C3×C4×#685C212yesmaximal
6C3×#65226C211yesmaximal, characteristic, complemented
7C3×#65222C212yesmaximal, complemented
8C3×#64953C211yesmaximal, characteristic
9C3×D5×#95C211yesmaximal, characteristic
10C3×#64939C211yesmaximal, characteristic, complemented
11C3×#64937C211yesmaximal, characteristic, complemented
12#10605497C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C42×C5C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×#685C2212yes—
19C2×C3×#685C2211yescharacteristic
20C2×C3×#685C2211yescharacteristic
21C2×C3×#683C2212yes—
22C2×C3×#683C2211yescharacteristic
23C2×C3×#683C2211yescharacteristic
24C2×C3×C4×Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C3×#4018C418yescomplemented
27C3×C5×#95C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29C3×#3963C2211yescharacteristic
30C3×#3963C2212yes—
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#2343—51nomaximal, Hall
38C2×#4018C2×C311yescharacteristic
39C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
40#65278C2×C312yes—
41#65267C2×C312yescomplemented
42C4×#685C2×C312yes—
43#65226C2×C311yescharacteristic, complemented
44#65222C2×C312yescomplemented
45#64953C2×C311yescharacteristic
46D5×#95C2×C311yescharacteristic
47#64939C2×C311yescharacteristic, complemented
48#64937C2×C311yescharacteristic, complemented
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×C4×D5—24no—
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5—24no—
63C2×C3×C4×D5—42no—
64C2×C3×C4×D5C2×C414yes—
65C3×C5×C4⋊C4—24no—
66C3×C42×C5—42no—
67C3×C42×C5C2×C414yescomplemented
68C3×#685—24no—
69C3×#685C2×C414yes—
70C3×#685C2×C414yes—
71C3×#683—42no—
72C3×#683C2×C414yescomplemented
73C3×#683C2×C414yescomplemented
74C3×C4×Dic5—24no—
75C3×C4×Dic5C2×C414yescomplemented
76C2×C3×#117—51no—
77C3×#387—52no—
78C3×#387—52no—
79C3×#385—52no—
80C3×#383—51no—
81C3×#382—51no—
82C3×#381—51no—
83C3×C4×C4⋊C4D511yescharacteristic, complemented
84C3×C4×C22⋊C4—52no—
85C3×#376—51no—
86C2×C3×#95—51no—
87C22×C4×D5C22×C312yes—
88C22×C4×D5C22×C311yescharacteristic
89C2×C5×C4⋊C4C22×C312yes—
90C2×C42×C5C22×C312yes—
91C2×C42×C5C22×C311yescharacteristic
92C2×#685C22×C312yes—
93C2×#685C22×C311yescharacteristic
94C2×#685C22×C311yescharacteristic
95C2×#683C22×C312yes—
96C2×#683C22×C311yescharacteristic
97C2×#683C22×C311yescharacteristic
98C2×C4×Dic5C22×C312yes—
99C2×C4×Dic5C22×C311yescharacteristic
100#4018C3×C418yescomplemented
101C5×#95C22×C311yescharacteristic
102C5×#95C22×C311yescharacteristic
103#3963C22×C311yescharacteristic
104#3963C22×C312yes—
105#3963C22×C311yescharacteristic
106#3963C22×C312yes—
107#3963C22×C312yes—
108#3963C22×C312yes—
109#3963C22×C312yes—
110#3963C22×C312yes—
111#2343—51noSylow
112C23×C3×C5C2411yescharacteristic
113C22×C3×D5—22no—
114C22×C3×D5—21no—
115C22×C3×D5—21no—
116C22×C3×D5C22×C412yes—
117C22×C3×D5#4114yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5#4114yes—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—21no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5C22×C412yes—
142C2×C3×Dic5C22×C412yes—
143C2×C3×Dic5C22×C412yes—
144C3×C4×D5—28no—
145C3×C4×D5—48no—
146C23×C3×C4—51no—
147C23×C3×C4—52no—
148C3×#117—58no—
149C2×C3×C4⋊C4—51no—
150C2×C3×C4⋊C4—51no—
151C2×C3×C4⋊C4—52no—
152C2×C3×C4⋊C4C2×D512yes—
153C2×C3×C22⋊C4—51no—
154C2×C3×C22⋊C4—51no—
155C2×C3×C22⋊C4—52no—
156C2×C3×C42—51no—
157C2×C3×C42—52no—
158C2×C3×C42C2×D512yes—
159C2×C3×C42C2×D511yescharacteristic
160C3×#95—51no—
161C3×#95—52no—
162C3×#95—51no—
163C3×#95—52no—
164C3×#95—52no—
165C3×#95—52no—
166C3×#95—52no—
167C3×#95—52no—
168C3×#95C2×D511yescharacteristic
169C3×#95C2×D511yescharacteristic
170C23×D5C23×C311yescharacteristic
171C22×C4×C5C23×C312yes—
172C22×C4×C5C23×C311yescharacteristic
173C22×C4×C5C23×C311yescharacteristic
174C22×C4×C5C23×C311yescharacteristic
175C22×C4×C5C23×C312yes—
176C22×Dic5C23×C312yes—
177C22×Dic5C23×C312yes—
178C22×Dic5C23×C311yescharacteristic
179C22×Dic5C23×C311yescharacteristic
180C22×Dic5C23×C311yescharacteristic
181C2×C4×D5—24no—
182C2×C4×D5—24no—
183C2×C4×D5—24no—
184C2×C4×D5—42no—
185C2×C4×D5C2×C3×C414yes—
186C5×C4⋊C4—24no—
187C42×C5—42no—
188C42×C5C2×C3×C414yescomplemented
189#685—24no—
190#685C2×C3×C414yes—
191#685C2×C3×C414yes—
192#683—42no—
193#683C2×C3×C414yescomplemented
194#683C2×C3×C414yescomplemented
195C4×Dic5—24no—
196C4×Dic5C2×C3×C414yescomplemented
197C2×#117—51no—
198#387—52no—
199#387—52no—
200#385—52no—
201#383—51no—
202#382—51no—
203#381—51no—
204C4×C4⋊C4C3×D511yescharacteristic, complemented
205C4×C22⋊C4—52no—
206#376—51no—
207C2×#95—51no—
208C22×C3×C5C23×C411yescharacteristic
209C22×C3×C5C2×#4112yes—
210C22×C3×C5C2×#4112yes—
211C22×C3×C5H(5,𝔽2)11yescharacteristic
212C22×C3×C52−1+411yescharacteristic
213C2×C3×D5—22no—
214C2×C3×D5—22no—
215C2×C3×D5—24no—
216C2×C3×D5—24no—
217C2×C3×D5#11714yes—
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221C3×C4×C5—24no—
222C3×C4×C5—42no—
223C3×Dic5—22no—
224C3×Dic5—22no—
225C3×Dic5—22no—
226C3×Dic5—42no—
227C3×Dic5—42no—
228C24×C3—51no—
229C22×C3×C4—51no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—54no—
233C22×C3×C4—52no—
234C22×C3×C4—52no—
235C22×C3×C4—104no—
236C22×C3×C4—104no—
237C22×C3×C4—104no—
238C22×C3×C4—202no—
239C22×C3×C4C22×D512yes—
240C22×C3×C4C22×D511yescharacteristic
241C22×C3×C4C22×D511yescharacteristic
242C22×C3×C4C22×D511yescharacteristic
243C22×C3×C4C22×D512yes—
244C3×C4⋊C4—24no—
245C3×C4⋊C4—54no—
246C3×C4⋊C4—54no—
247C3×C4⋊C4—202no—
248C3×C22⋊C4—54no—
249C3×C22⋊C4—54no—
250C3×C22⋊C4—104no—
251C3×C42—42no—
252C3×C42—54no—
253C3×C42—104no—
254C3×C42C4×D514yescomplemented
255C23×C5C24×C311yescharacteristic
256C22×D5—22no—
257C22×D5—21no—
258C22×D5—21no—
259C22×D5C22×C3×C412yes—
260C22×D5C3×#4114yes—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—21no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5C22×C3×C412yes—
271C2×C4×C5C22×C3×C412yes—
272C2×C4×C5C22×C3×C412yes—
273C2×C4×C5C3×#4114yes—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—21no—
277C2×Dic5—21no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5C22×C3×C412yes—
285C2×Dic5C22×C3×C412yes—
286C2×Dic5C22×C3×C412yes—
287C4×D5—28no—
288C4×D5—48no—
289C23×C4—51no—
290C23×C4—52no—
291#117—58no—
292C2×C4⋊C4—51no—
293C2×C4⋊C4—51no—
294C2×C4⋊C4—52no—
295C2×C4⋊C4C2×C3×D512yes—
296C2×C22⋊C4—51no—
297C2×C22⋊C4—51no—
298C2×C22⋊C4—52no—
299C2×C42—51no—
300C2×C42—52no—
301C2×C42C2×C3×D512yes—
302C2×C42C2×C3×D511yescharacteristic
303#95—51no—
304#95—52no—
305#95—51no—
306#95—52no—
307#95—52no—
308#95—52no—
309#95—52no—
310#95—52no—
311#95C2×C3×D511yescharacteristic
312#95C2×C3×D511yescharacteristic
313C2×C3×C5C2×#11711yescharacteristic
314C2×C3×C5C4×#4111yescharacteristic
315C2×C3×C5#52011yescharacteristic
316C2×C3×C5#55112yes—
317C2×C3×C5#55212yes—
318C3×D5—24no—
319C23×C3—52no—
320C23×C3—54no—
321C23×C3—102no—
322C23×C3—101no—
323C23×C3—101no—
324C23×C3C23×D511yescharacteristic
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—52no—
335C2×C3×C4—52no—
336C2×C3×C4—52no—
337C2×C3×C4—108no—
338C2×C3×C4—102no—
339C2×C3×C4—101no—
340C2×C3×C4—101no—
341C2×C3×C4—102no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—208no—
349C2×C3×C4C2×C4×D512yes—
350C2×C3×C4C2×C4×D512yes—
351C2×C3×C4C2×C4×D512yes—
352C2×C3×C4#70914yes—
353C22×C5C23×C3×C411yescharacteristic
354C22×C5C2×C3×#4112yes—
355C22×C5C2×C3×#4112yes—
356C22×C5C3×H(5,𝔽2)11yescharacteristic
357C22×C5C3×2−1+411yescharacteristic
358C2×D5—22no—
359C2×D5—22no—
360C2×D5—24no—
361C2×D5—24no—
362C2×D5C3×#11714yes—
363C4×C5—22no—
364C4×C5—22no—
365C4×C5—22no—
366C4×C5—24no—
367C4×C5—42no—
368Dic5—22no—
369Dic5—22no—
370Dic5—22no—
371Dic5—42no—
372Dic5—42no—
373C24—51no—
374C22×C4—51no—
375C22×C4—51no—
376C22×C4—51no—
377C22×C4—54no—
378C22×C4—52no—
379C22×C4—52no—
380C22×C4—104no—
381C22×C4—104no—
382C22×C4—104no—
383C22×C4—202no—
384C22×C4C22×C3×D512yes—
385C22×C4C22×C3×D511yescharacteristic
386C22×C4C22×C3×D511yescharacteristic
387C22×C4C22×C3×D511yescharacteristic
388C22×C4C22×C3×D512yes—
389C4⋊C4—24no—
390C4⋊C4—54no—
391C4⋊C4—54no—
392C4⋊C4—202no—
393C22⋊C4—54no—
394C22⋊C4—54no—
395C22⋊C4—104no—
396C42—42no—
397C42—54no—
398C42—104no—
399C42C3×C4×D514yescomplemented
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3—54no—
402C22×C3—102no—
403C22×C3—102no—
404C22×C3—104no—
405C22×C3—104no—
406C22×C3C22×C4×D511yescharacteristic
407C22×C3C2×#70912yes—
408C22×C3#414411yescharacteristic
409C22×C3#414711yescharacteristic
410C22×C3D5×#4112yes—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—24no—
415C3×C4—42no—
416C3×C4—102no—
417C3×C4—102no—
418C3×C4—102no—
419C3×C4—202no—
420C3×C4—202no—
421C2×C5C2×C3×#11711yescharacteristic
422C2×C5C3×C4×#4111yescharacteristic
423C2×C5C3×#52011yescharacteristic
424C2×C5C3×#55112yes—
425C2×C5C3×#55212yes—
426D5—24no—
427C23—52no—
428C23—54no—
429C23—102no—
430C23—101no—
431C23—101no—
432C23C23×C3×D511yescharacteristic
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—52no—
443C2×C4—52no—
444C2×C4—52no—
445C2×C4—108no—
446C2×C4—102no—
447C2×C4—101no—
448C2×C4—101no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—102no—
453C2×C4—102no—
454C2×C4—102no—
455C2×C4—102no—
456C2×C4—208no—
457C2×C4C2×C3×C4×D512yes—
458C2×C4C2×C3×C4×D512yes—
459C2×C4C2×C3×C4×D512yes—
460C2×C4C3×#70914yes—
461C2×C3—104no—
462C2×C3C4×#70911yescharacteristic
463C2×C3#6583811yescharacteristic
464C2×C3D5×#11711yescharacteristic
465C2×C3#6589012yes—
466C2×C3#6591512yes—
467C5C3×#234311yescharacteristic, complemented, Sylow
468C22—54no—
469C22—104no—
470C22—104no—
471C22—102no—
472C22—102no—
473C22C22×C3×C4×D511yescharacteristic
474C22C2×C3×#70912yes—
475C22C3×#414411yescharacteristic
476C22C3×#414711yescharacteristic
477C22C3×D5×#4112yes—
478C4—22no—
479C4—24no—
480C4—22no—
481C4—22no—
482C4—42no—
483C4—102no—
484C4—102no—
485C4—102no—
486C4—202no—
487C4—202no—
488C3#1060549711yescharacteristic, direct product factor, Sylow
489C2—104no—
490C2C3×C4×#70911yescharacteristic
491C2C3×#6583811yescharacteristic
492C2C3×D5×#11711yescharacteristic
493C2C3×#6589012yes—
494C2C3×#6591512yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC23×C5C24×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#2343
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C4⋊C4C2semidirect
4. C3×#65267C2semidirect
6. C3×#65226C2semidirect
7. C3×#65222C2semidirect
10. C3×#64939C2semidirect
11. C3×#64937C2semidirect
12. #10605497C3direct (N × H)
26. C3×#4018C4semidirect
39. C4×C5×C4⋊C4C2×C3semidirect
41. #65267C2×C3semidirect
43. #65226C2×C3semidirect
44. #65222C2×C3semidirect
47. #64939C2×C3semidirect
48. #64937C2×C3semidirect
67. C3×C42×C5C2×C4semidirect
72. C3×#683C2×C4semidirect
73. C3×#683C2×C4semidirect
75. C3×C4×Dic5C2×C4semidirect
83. C3×C4×C4⋊C4D5semidirect
100. #4018C3×C4semidirect
188. C42×C5C2×C3×C4semidirect
193. #683C2×C3×C4semidirect
194. #683C2×C3×C4semidirect
196. C4×Dic5C2×C3×C4semidirect
204. C4×C4⋊C4C3×D5semidirect
254. C3×C42C4×D5semidirect
399. C42C3×C4×D5semidirect
400. C3×C5#2343semidirect
467. C5C3×#2343semidirect
488. C3#10605497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40182
C3×C4×C5×C4⋊C42
C3×#652782
C3×#652672
C3×C4×#6852
C3×#652262
C3×#652222
C3×#649532
C3×D5×#952
C3×#649392
C3×#649372
#106054973
C3×#23435