Finite Group Databasebeta

← C3×#10605790 #14326417

Subgroups — C3×#10605790 #14326417

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×#4072C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic
3C2×C3×#3963C211yesmaximal, characteristic
4C3×#65235C212yesmaximal
5C3×C22⋊C4×Dic5C212yesmaximal
6C3×#64943C212yesmaximal, complemented
7C3×#64942C212yesmaximal, complemented
8C3×#64940C211yesmaximal, characteristic, complemented
9C3×#64939C211yesmaximal, characteristic, complemented
10C3×#64938C211yesmaximal, characteristic, complemented
11C3×#64937C211yesmaximal, characteristic, complemented
12#10605790C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×Dic5C2212yes—
15C2×C3×C5×C22⋊C4C2212yes—
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C3×#4072C418yescomplemented
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×C3×#683C2212yes—
22C2×C3×#683C2212yes—
23C2×C3×C4×Dic5C2212yes—
24C2×C3×C4×Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C3×C5×#95C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2212yes—
30C3×#3963C2211yescharacteristic
31C3×#3963C2212yes—
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#2343—51nomaximal, Hall
38C2×#4072C2×C311yescharacteristic
39C5×#381C2×C311yescharacteristic
40C2×#3963C2×C311yescharacteristic
41#65235C2×C312yes—
42C22⋊C4×Dic5C2×C312yes—
43#64943C2×C312yescomplemented
44#64942C2×C312yescomplemented
45#64940C2×C311yescharacteristic, complemented
46#64939C2×C311yescharacteristic, complemented
47#64938C2×C311yescharacteristic, complemented
48#64937C2×C311yescharacteristic, complemented
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—24no—
51C22×C3×C4×C5C2×C414yes—
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×Dic5—24no—
57C22×C3×Dic5—24no—
58C22×C3×Dic5—42no—
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C3×C5×C22⋊C4—24no—
66C3×C22⋊Dic5C2×C414yes—
67C3×C22⋊Dic5C2×C414yes—
68C3×C4⋊Dic5C2×C414yescomplemented
69C3×C4⋊Dic5C2×C414yescomplemented
70C3×#683—24no—
71C3×#683—42no—
72C3×C4×Dic5—24no—
73C3×C4×Dic5—42no—
74C3×C4×Dic5C2×C414yescomplemented
75C3×C4×Dic5C2×C414yescomplemented
76C2×C3×#117—51no—
77C3×#387—52no—
78C3×#387—52no—
79C3×#385—52no—
80C3×#383—51no—
81C3×#382—51no—
82C3×#381D511yescharacteristic
83C3×C4×C4⋊C4—51no—
84C3×C4×C22⋊C4—52no—
85C3×#376—51no—
86C2×C3×#95—51no—
87C23×C4×C5C22×C311yescharacteristic
88C23×Dic5C22×C312yes—
89C2×C5×C22⋊C4C22×C312yes—
90C2×C22⋊Dic5C22×C311yescharacteristic
91C2×C22⋊Dic5C22×C311yescharacteristic
92#4072C3×C418yescomplemented
93C2×C4⋊Dic5C22×C311yescharacteristic
94C2×C4⋊Dic5C22×C311yescharacteristic
95C2×#683C22×C312yes—
96C2×#683C22×C312yes—
97C2×C4×Dic5C22×C312yes—
98C2×C4×Dic5C22×C312yes—
99C2×C4×Dic5C22×C311yescharacteristic
100C2×C4×Dic5C22×C311yescharacteristic
101C5×#95C22×C311yescharacteristic
102C5×#95C22×C311yescharacteristic
103C5×#95C22×C312yes—
104#3963C22×C311yescharacteristic
105#3963C22×C312yes—
106#3963C22×C311yescharacteristic
107#3963C22×C312yes—
108#3963C22×C312yes—
109#3963C22×C312yes—
110#3963C22×C312yes—
111#2343—51noSylow
112C23×C3×C5—22no—
113C23×C3×C5—21no—
114C23×C3×C5—21no—
115C23×C3×C5C22×C412yes—
116C23×C3×C5#4114yes—
117C23×C3×C5C2411yescharacteristic
118C2×C3×C4×C5—28no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
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×Dic5—22no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—21no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—21no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—22no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—48no—
141C2×C3×Dic5C22×C412yes—
142C2×C3×Dic5C22×C412yes—
143C2×C3×Dic5C22×C412yes—
144C2×C3×Dic5C22×C412yes—
145C2×C3×Dic5#4114yes—
146C23×C3×C4—52no—
147C23×C3×C4C2×D511yescharacteristic
148C3×#117—58no—
149C2×C3×C4⋊C4—51no—
150C2×C3×C4⋊C4—51no—
151C2×C3×C4⋊C4—52no—
152C2×C3×C4⋊C4—52no—
153C2×C3×C22⋊C4—51no—
154C2×C3×C22⋊C4—51no—
155C2×C3×C22⋊C4C2×D512yes—
156C2×C3×C42—51no—
157C2×C3×C42—51no—
158C2×C3×C42—52no—
159C2×C3×C42—52no—
160C3×#95—51no—
161C3×#95—51no—
162C3×#95—52no—
163C3×#95—52no—
164C3×#95—52no—
165C3×#95—52no—
166C3×#95—52no—
167C3×#95C2×D511yescharacteristic
168C3×#95C2×D511yescharacteristic
169C3×#95C2×D512yes—
170C24×C5C23×C311yescharacteristic
171C22×C4×C5—24no—
172C22×C4×C5C2×C3×C414yes—
173C22×C4×C5C23×C312yes—
174C22×C4×C5C23×C312yes—
175C22×C4×C5C23×C311yescharacteristic
176C22×C4×C5C23×C311yescharacteristic
177C22×Dic5—24no—
178C22×Dic5—24no—
179C22×Dic5—42no—
180C22×Dic5C23×C312yes—
181C22×Dic5C23×C311yescharacteristic
182C22×Dic5C23×C311yescharacteristic
183C22×Dic5C23×C311yescharacteristic
184C22×Dic5C23×C311yescharacteristic
185C22×Dic5C23×C312yes—
186C5×C22⋊C4—24no—
187C22⋊Dic5C2×C3×C414yes—
188C22⋊Dic5C2×C3×C414yes—
189C4⋊Dic5C2×C3×C414yescomplemented
190C4⋊Dic5C2×C3×C414yescomplemented
191#683—24no—
192#683—42no—
193C4×Dic5—24no—
194C4×Dic5—42no—
195C4×Dic5C2×C3×C414yescomplemented
196C4×Dic5C2×C3×C414yescomplemented
197C2×#117—51no—
198#387—52no—
199#387—52no—
200#385—52no—
201#383—51no—
202#382—51no—
203#381C3×D511yescharacteristic
204C4×C4⋊C4—51no—
205C4×C22⋊C4—52no—
206#376—51no—
207C2×#95—51no—
208C22×C3×C5—22no—
209C22×C3×C5—22no—
210C22×C3×C5—24no—
211C22×C3×C5—24no—
212C22×C3×C5#11714yes—
213C22×C3×C5C23×C411yescharacteristic
214C22×C3×C5C2×#4112yes—
215C22×C3×C5C2×#4112yes—
216C22×C3×C5H(5,𝔽2)11yescharacteristic
217C22×C3×C52−1+411yescharacteristic
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220C3×C4×C5—42no—
221C3×C4×C5—42no—
222C3×Dic5—22no—
223C3×Dic5—22no—
224C3×Dic5—22no—
225C3×Dic5—22no—
226C3×Dic5—24no—
227C3×Dic5—42no—
228C24×C3C22×D511yescharacteristic
229C22×C3×C4—24no—
230C22×C3×C4—52no—
231C22×C3×C4—51no—
232C22×C3×C4—51no—
233C22×C3×C4—51no—
234C22×C3×C4—51no—
235C22×C3×C4—52no—
236C22×C3×C4—104no—
237C22×C3×C4—104no—
238C22×C3×C4—202no—
239C22×C3×C4C4×D514yes—
240C22×C3×C4C22×D512yes—
241C22×C3×C4C22×D512yes—
242C22×C3×C4C22×D511yescharacteristic
243C22×C3×C4C22×D511yescharacteristic
244C3×C4⋊C4—54no—
245C3×C4⋊C4—54no—
246C3×C4⋊C4—104no—
247C3×C4⋊C4—202no—
248C3×C22⋊C4—24no—
249C3×C22⋊C4—54no—
250C3×C22⋊C4—54no—
251C3×C42—54no—
252C3×C42—54no—
253C3×C42—104no—
254C3×C42—202no—
255C23×C5—22no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5C22×C3×C412yes—
259C23×C5C3×#4114yes—
260C23×C5C24×C311yescharacteristic
261C2×C4×C5—28no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5C22×C3×C412yes—
271C2×C4×C5C22×C3×C412yes—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—21no—
276C2×Dic5—22no—
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—48no—
284C2×Dic5C22×C3×C412yes—
285C2×Dic5C22×C3×C412yes—
286C2×Dic5C22×C3×C412yes—
287C2×Dic5C22×C3×C412yes—
288C2×Dic5C3×#4114yes—
289C23×C4—52no—
290C23×C4C2×C3×D511yescharacteristic
291#117—58no—
292C2×C4⋊C4—51no—
293C2×C4⋊C4—51no—
294C2×C4⋊C4—52no—
295C2×C4⋊C4—52no—
296C2×C22⋊C4—51no—
297C2×C22⋊C4—51no—
298C2×C22⋊C4C2×C3×D512yes—
299C2×C42—51no—
300C2×C42—51no—
301C2×C42—52no—
302C2×C42—52no—
303#95—51no—
304#95—51no—
305#95—52no—
306#95—52no—
307#95—52no—
308#95—52no—
309#95—52no—
310#95C2×C3×D511yescharacteristic
311#95C2×C3×D511yescharacteristic
312#95C2×C3×D512yes—
313C2×C3×C5—24no—
314C2×C3×C5C2×#11711yescharacteristic
315C2×C3×C5C4×#4111yescharacteristic
316C2×C3×C5#52011yescharacteristic
317C2×C3×C5#55112yes—
318C2×C3×C5#55212yes—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3C2×C4×D512yes—
323C23×C3#71114yes—
324C23×C3C23×D511yescharacteristic
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—28no—
328C2×C3×C4—22no—
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—52no—
338C2×C3×C4—54no—
339C2×C3×C4—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4—101no—
343C2×C3×C4—102no—
344C2×C3×C4—101no—
345C2×C3×C4—101no—
346C2×C3×C4—101no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4—208no—
351C2×C3×C4C2×C4×D512yes—
352C2×C3×C4C2×C4×D512yes—
353C22×C5—22no—
354C22×C5—22no—
355C22×C5—24no—
356C22×C5—24no—
357C22×C5C3×#11714yes—
358C22×C5C23×C3×C411yescharacteristic
359C22×C5C2×C3×#4112yes—
360C22×C5C2×C3×#4112yes—
361C22×C5C3×H(5,𝔽2)11yescharacteristic
362C22×C5C3×2−1+411yescharacteristic
363C4×C5—22no—
364C4×C5—22no—
365C4×C5—42no—
366C4×C5—42no—
367Dic5—22no—
368Dic5—22no—
369Dic5—22no—
370Dic5—22no—
371Dic5—24no—
372Dic5—42no—
373C24C22×C3×D511yescharacteristic
374C22×C4—24no—
375C22×C4—52no—
376C22×C4—51no—
377C22×C4—51no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—52no—
381C22×C4—104no—
382C22×C4—104no—
383C22×C4—202no—
384C22×C4C3×C4×D514yes—
385C22×C4C22×C3×D512yes—
386C22×C4C22×C3×D512yes—
387C22×C4C22×C3×D511yescharacteristic
388C22×C4C22×C3×D511yescharacteristic
389C4⋊C4—54no—
390C4⋊C4—54no—
391C4⋊C4—104no—
392C4⋊C4—202no—
393C22⋊C4—24no—
394C22⋊C4—54no—
395C22⋊C4—54no—
396C42—54no—
397C42—54no—
398C42—104no—
399C42—202no—
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—24no—
404C22×C3—24no—
405C22×C3#402314yes—
406C22×C3C22×C4×D511yescharacteristic
407C22×C3C2×#71112yes—
408C22×C3D5×#4112yes—
409C22×C3#414911yescharacteristic
410C22×C3#415011yescharacteristic
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—102no—
416C3×C4—102no—
417C3×C4—102no—
418C3×C4—102no—
419C3×C4—104no—
420C3×C4—202no—
421C2×C5—24no—
422C2×C5C2×C3×#11711yescharacteristic
423C2×C5C3×C4×#4111yescharacteristic
424C2×C5C3×#52011yescharacteristic
425C2×C5C3×#55112yes—
426C2×C5C3×#55212yes—
427C23—22no—
428C23—21no—
429C23—21no—
430C23C2×C3×C4×D512yes—
431C23C3×#71114yes—
432C23C23×C3×D511yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—28no—
436C2×C4—22no—
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—52no—
446C2×C4—54no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—101no—
451C2×C4—102no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—101no—
455C2×C4—102no—
456C2×C4—102no—
457C2×C4—102no—
458C2×C4—208no—
459C2×C4C2×C3×C4×D512yes—
460C2×C4C2×C3×C4×D512yes—
461C2×C3—24no—
462C2×C3C2×#402311yescharacteristic
463C2×C3#6585611yescharacteristic
464C2×C3#6585711yescharacteristic
465C2×C3#6598412yes—
466C2×C3#6599212yes—
467C5C3×#234311yescharacteristic, complemented, Sylow
468C22—22no—
469C22—22no—
470C22—24no—
471C22—24no—
472C22C3×#402314yes—
473C22C22×C3×C4×D511yescharacteristic
474C22C2×C3×#71112yes—
475C22C3×D5×#4112yes—
476C22C3×#414911yescharacteristic
477C22C3×#415011yescharacteristic
478C4—22no—
479C4—22no—
480C4—42no—
481C4—42no—
482C4—102no—
483C4—102no—
484C4—102no—
485C4—102no—
486C4—104no—
487C4—202no—
488C3#1060579011yescharacteristic, direct product factor, Sylow
489C2—24no—
490C2C2×C3×#402311yescharacteristic
491C2C3×#6585611yescharacteristic
492C2C3×#6585711yescharacteristic
493C2C3×#6598412yes—
494C2C3×#6599212yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#381C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC3×#381D5
hypocenterC5C3×#2343
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
6. C3×#64943C2semidirect
7. C3×#64942C2semidirect
8. C3×#64940C2semidirect
9. C3×#64939C2semidirect
10. C3×#64938C2semidirect
11. C3×#64937C2semidirect
12. #10605790C3direct (N × H)
18. C3×#4072C4semidirect
43. #64943C2×C3semidirect
44. #64942C2×C3semidirect
45. #64940C2×C3semidirect
46. #64939C2×C3semidirect
47. #64938C2×C3semidirect
48. #64937C2×C3semidirect
68. C3×C4⋊Dic5C2×C4semidirect
69. C3×C4⋊Dic5C2×C4semidirect
74. C3×C4×Dic5C2×C4semidirect
75. C3×C4×Dic5C2×C4semidirect
92. #4072C3×C4semidirect
189. C4⋊Dic5C2×C3×C4semidirect
190. C4⋊Dic5C2×C3×C4semidirect
195. C4×Dic5C2×C3×C4semidirect
196. C4×Dic5C2×C3×C4semidirect
400. C3×C5#2343semidirect
467. C5C3×#2343semidirect
488. C3#10605790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40722
C3×C5×#3812
C2×C3×#39632
C3×#652352
C3×C22⋊C4×Dic52
C3×#649432
C3×#649422
C3×#649402
C3×#649392
C3×#649382
C3×#649372
#106057903
C3×#23435