Finite Group Databasebeta

← C3×#10605855 #14330856

Subgroups — C3×#10605855 #14330856

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic, complemented
3C3×#65501C211yesmaximal, characteristic, complemented
4C3×#65246C212yesmaximal, complemented
5C3×#65245C212yesmaximal, complemented
6C3×#64959C212yesmaximal, complemented
7C3×#64957C212yesmaximal, complemented
8C3×#64954C212yesmaximal, complemented
9C3×#64943C212yesmaximal, complemented
10#10605855C311yesmaximal, characteristic, direct product factor, Hall
11C23×C3×C4×C5C2211yescharacteristic
12C22×C3×C22⋊D5C2212yes—
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C2×C3×C5×C22⋊C4C2212yes—
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C3×#4076C418yescomplemented
19C2×C3×#685C2212yes—
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×#685C2212yes—
23C2×C3×C4⋊Dic5C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×#683C2212yes—
26C2×C3×C4×Dic5C2212yes—
27C3×C5×#95C2212yes—
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2211yescharacteristic
30C3×#3963C2212yes—
31C3×#3963C2212yes—
32C3×#3963C2212yes—
33C3×#2377—51nomaximal, Hall
34C2×#4076C2×C311yescharacteristic
35C5×#381C2×C311yescharacteristic, complemented
36#65501C2×C311yescharacteristic, complemented
37#65246C2×C312yescomplemented
38#65245C2×C312yescomplemented
39#64959C2×C312yescomplemented
40#64957C2×C312yescomplemented
41#64954C2×C312yescomplemented
42#64943C2×C312yescomplemented
43C24×C3×C5C2311yescharacteristic
44C23×C3×D5C2312yes—
45C22×C3×C4×C5—42no—
46C22×C3×C4×C5C2×C414yescomplemented
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C2×C3×C22⋊D5—42no—
52C2×C3×C22⋊D5—42no—
53C2×C3×C22⋊D5C2×C418yescomplemented
54C22×C3×Dic5C2312yes—
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2312yes—
57C2×C3×D20—42no—
58C2×C3×D20C2×C414yes—
59C2×C3×C4×D5—42no—
60C2×C3×C4×D5—42no—
61C2×C3×C4×D5—42no—
62C3×C5×C22⋊C4—42no—
63C3×C22⋊Dic5—41no—
64C3×C22⋊Dic5—41no—
65C3×#685—42no—
66C3×#685—42no—
67C3×#685—42no—
68C3×#685C2×C418yescomplemented
69C3×C4⋊Dic5—42no—
70C3×C4⋊Dic5C2×C414yescomplemented
71C3×#683—42no—
72C3×C4×Dic5—42no—
73C2×C3×#121—51no—
74C3×#390—52no—
75C3×#388—52no—
76C3×#387—52no—
77C3×#386—52no—
78C3×#386—52no—
79C3×#385—52no—
80C3×#381D511yescharacteristic, complemented
81C3×#380—51no—
82C23×C4×C5C22×C311yescharacteristic
83C22×C22⋊D5C22×C312yes—
84C22×D20C22×C311yescharacteristic
85C22×C4×D5C22×C312yes—
86C2×C5×C22⋊C4C22×C312yes—
87C2×C22⋊Dic5C22×C311yescharacteristic
88C2×C22⋊Dic5C22×C311yescharacteristic
89#4076C3×C418yescomplemented
90C2×#685C22×C312yes—
91C2×#685C22×C312yes—
92C2×#685C22×C312yes—
93C2×#685C22×C312yes—
94C2×C4⋊Dic5C22×C312yes—
95C2×C4⋊Dic5C22×C311yescharacteristic
96C2×#683C22×C312yes—
97C2×C4×Dic5C22×C312yes—
98C5×#95C22×C312yes—
99C5×#95C22×C311yescharacteristic
100C5×#95C22×C311yescharacteristic
101#3963C22×C312yes—
102#3963C22×C312yes—
103#3963C22×C312yes—
104#2377—51noSylow
105C23×C3×C5—21no—
106C23×C3×C5—22no—
107C23×C3×C5—22no—
108C23×C3×C5—21no—
109C23×C3×C5C22×C412yes—
110C23×C3×C5C2411yescharacteristic
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—22no—
116C22×C3×D5—22no—
117C22×C3×D5C22×C414yes—
118C2×C3×C4×C5—22no—
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—44no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C412yes—
129C3×C22⋊D5—48no—
130C2×C3×Dic5—22no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C22×C414yes—
139C3×D20—44no—
140C3×C4×D5—48no—
141C22×C3×D4—52no—
142C22×C3×D4—51no—
143C23×C3×C4—52no—
144C23×C3×C4C2×D511yescharacteristic
145C3×#121—58no—
146C2×C3×C4⋊C4—51no—
147C2×C3×C4⋊C4—52no—
148C2×C3×C4⋊C4—52no—
149C2×C3×C22⋊C4—52no—
150C2×C3×C22⋊C4—51no—
151C2×C3×C22⋊C4—51no—
152C2×C3×C22⋊C4—52no—
153C2×C3×C22⋊C4—52no—
154C2×C3×C22⋊C4—52no—
155C2×C3×C22⋊C4C2×D512yes—
156C2×C3×C42—52no—
157C3×#95—52no—
158C3×#95—52no—
159C3×#95—52no—
160C3×#95C2×D511yescharacteristic
161C3×#95C2×D512yes—
162C3×#95C2×D511yescharacteristic
163C24×C5C23×C311yescharacteristic
164C23×D5C23×C312yes—
165C22×C4×C5—42no—
166C22×C4×C5C2×C3×C414yescomplemented
167C22×C4×C5C23×C312yes—
168C22×C4×C5C23×C312yes—
169C22×C4×C5C23×C311yescharacteristic
170C22×C4×C5C23×C311yescharacteristic
171C2×C22⋊D5—42no—
172C2×C22⋊D5—42no—
173C2×C22⋊D5C2×C3×C418yescomplemented
174C22×Dic5C23×C312yes—
175C22×Dic5C23×C312yes—
176C22×Dic5C23×C312yes—
177C2×D20—42no—
178C2×D20C2×C3×C414yes—
179C2×C4×D5—42no—
180C2×C4×D5—42no—
181C2×C4×D5—42no—
182C5×C22⋊C4—42no—
183C22⋊Dic5—41no—
184C22⋊Dic5—41no—
185#685—42no—
186#685—42no—
187#685—42no—
188#685C2×C3×C418yescomplemented
189C4⋊Dic5—42no—
190C4⋊Dic5C2×C3×C414yescomplemented
191#683—42no—
192C4×Dic5—42no—
193C2×#121—51no—
194#390—52no—
195#388—52no—
196#387—52no—
197#386—52no—
198#386—52no—
199#385—52no—
200#381C3×D511yescharacteristic, complemented
201#380—51no—
202C22×C3×C5—22no—
203C22×C3×C5—22no—
204C22×C3×C5—22no—
205C22×C3×C5—42no—
206C22×C3×C5—42no—
207C22×C3×C5C23×C411yescharacteristic
208C22×C3×C5H(5,𝔽2)12yes—
209C22×C3×C5H(5,𝔽2)12yes—
210C22×C3×C5H(5,𝔽2)11yescharacteristic
211C22×C3×C52−1+411yescharacteristic
212C2×C3×D5—24no—
213C2×C3×D5—24no—
214C2×C3×D5—24no—
215C2×C3×D5—42no—
216C2×C3×D5—42no—
217C2×C3×D5—42no—
218C2×C3×D5—42no—
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221C3×C4×C5—42no—
222C3×C4×C5—42no—
223C3×Dic5—24no—
224C3×Dic5—42no—
225C3×Dic5—42no—
226C24×C3—52no—
227C24×C3C22×D511yescharacteristic
228C2×C3×D4—58no—
229C2×C3×D4—54no—
230C2×C3×D4—202no—
231C2×C3×D4—202no—
232C2×C3×D4—202no—
233C22×C3×C4—42no—
234C22×C3×C4—52no—
235C22×C3×C4—52no—
236C22×C3×C4—52no—
237C22×C3×C4—202no—
238C22×C3×C4—202no—
239C22×C3×C4—202no—
240C22×C3×C4C4×D514yescomplemented
241C22×C3×C4C22×D512yes—
242C22×C3×C4C22×D512yes—
243C22×C3×C4C22×D511yescharacteristic
244C22×C3×C4C22×D511yescharacteristic
245C3×C4⋊C4—54no—
246C3×C4⋊C4—202no—
247C3×C4⋊C4—202no—
248C3×C22⋊C4—42no—
249C3×C22⋊C4—58no—
250C3×C22⋊C4—202no—
251C3×C22⋊C4—202no—
252C3×C22⋊C4—202no—
253C3×C22⋊C4—201no—
254C3×C22⋊C4—201no—
255C3×C42—202no—
256C23×C5—21no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—21no—
260C23×C5C22×C3×C412yes—
261C23×C5C24×C311yescharacteristic
262C22×D5—22no—
263C22×D5—22no—
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—22no—
267C22×D5—22no—
268C22×D5C22×C3×C414yes—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—44no—
278C2×C4×C5C22×C3×C412yes—
279C2×C4×C5C22×C3×C412yes—
280C22⋊D5—48no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5C22×C3×C414yes—
290D20—44no—
291C4×D5—48no—
292C22×D4—52no—
293C22×D4—51no—
294C23×C4—52no—
295C23×C4C2×C3×D511yescharacteristic
296#121—58no—
297C2×C4⋊C4—51no—
298C2×C4⋊C4—52no—
299C2×C4⋊C4—52no—
300C2×C22⋊C4—52no—
301C2×C22⋊C4—51no—
302C2×C22⋊C4—51no—
303C2×C22⋊C4—52no—
304C2×C22⋊C4—52no—
305C2×C22⋊C4—52no—
306C2×C22⋊C4C2×C3×D512yes—
307C2×C42—52no—
308#95—52no—
309#95—52no—
310#95—52no—
311#95C2×C3×D511yescharacteristic
312#95C2×C3×D512yes—
313#95C2×C3×D511yescharacteristic
314C2×C3×C5—42no—
315C2×C3×C5#51811yescharacteristic
316C2×C3×C5#51811yescharacteristic
317C2×C3×C5#52011yescharacteristic
318C2×C3×C5#56012yes—
319C2×C3×C5#56212yes—
320C3×D5—44no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—21no—
325C23×C3—54no—
326C23×C3—102no—
327C23×C3—102no—
328C23×C3—102no—
329C23×C3—102no—
330C23×C3—102no—
331C23×C3—102no—
332C23×C3C2×C4×D512yes—
333C23×C3C23×D511yescharacteristic
334C3×D4—204no—
335C3×D4—208no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—44no—
345C2×C3×C4—54no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—102no—
354C2×C3×C4—208no—
355C2×C3×C4C2×C4×D512yes—
356C2×C3×C4C2×C4×D512yes—
357C22×C5—22no—
358C22×C5—22no—
359C22×C5—22no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5C23×C3×C411yescharacteristic
363C22×C5C3×H(5,𝔽2)12yes—
364C22×C5C3×H(5,𝔽2)11yescharacteristic
365C22×C5C3×H(5,𝔽2)12yes—
366C22×C5C3×2−1+411yescharacteristic
367C2×D5—24no—
368C2×D5—24no—
369C2×D5—24no—
370C2×D5—42no—
371C2×D5—42no—
372C2×D5—42no—
373C2×D5—42no—
374C4×C5—22no—
375C4×C5—22no—
376C4×C5—42no—
377C4×C5—42no—
378Dic5—24no—
379Dic5—42no—
380Dic5—42no—
381C24—52no—
382C24C22×C3×D511yescharacteristic
383C2×D4—58no—
384C2×D4—54no—
385C2×D4—202no—
386C2×D4—202no—
387C2×D4—202no—
388C22×C4—42no—
389C22×C4—52no—
390C22×C4—52no—
391C22×C4—52no—
392C22×C4—202no—
393C22×C4—202no—
394C22×C4—202no—
395C22×C4C3×C4×D514yescomplemented
396C22×C4C22×C3×D512yes—
397C22×C4C22×C3×D512yes—
398C22×C4C22×C3×D511yescharacteristic
399C22×C4C22×C3×D511yescharacteristic
400C4⋊C4—54no—
401C4⋊C4—202no—
402C4⋊C4—202no—
403C22⋊C4—42no—
404C22⋊C4—58no—
405C22⋊C4—202no—
406C22⋊C4—202no—
407C22⋊C4—202no—
408C22⋊C4—201no—
409C22⋊C4—201no—
410C42—202no—
411C3×C5#237711yescharacteristic, complemented, Hall
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—104no—
418C22×C3—104no—
419C22×C3—104no—
420C22×C3—202no—
421C22×C3—202no—
422C22×C3—202no—
423C22×C3—202no—
424C22×C3C22×C4×D511yescharacteristic
425C22×C3#414412yes—
426C22×C3#414912yes—
427C22×C3#414911yescharacteristic
428C22×C3#415011yescharacteristic
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—104no—
434C3×C4—202no—
435C3×C4—202no—
436C2×C5—42no—
437C2×C5C3×#51811yescharacteristic
438C2×C5C3×#51811yescharacteristic
439C2×C5C3×#52011yescharacteristic
440C2×C5C3×#56012yes—
441C2×C5C3×#56212yes—
442D5—44no—
443C23—22no—
444C23—21no—
445C23—22no—
446C23—21no—
447C23—54no—
448C23—102no—
449C23—102no—
450C23—102no—
451C23—102no—
452C23—102no—
453C23—102no—
454C23C2×C3×C4×D512yes—
455C23C23×C3×D511yescharacteristic
456D4—204no—
457D4—208no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—44no—
467C2×C4—54no—
468C2×C4—102no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—102no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—208no—
477C2×C4C2×C3×C4×D512yes—
478C2×C4C2×C3×C4×D512yes—
479C2×C3—42no—
480C2×C3—204no—
481C2×C3#6582011yescharacteristic
482C2×C3#6585511yescharacteristic
483C2×C3#6585711yescharacteristic
484C2×C3#6600012yes—
485C2×C3#6600112yes—
486C5C3×#237711yescharacteristic, complemented, Sylow
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—104no—
493C22—104no—
494C22—104no—
495C22—202no—
496C22—202no—
497C22—202no—
498C22—202no—
499C22C22×C3×C4×D511yescharacteristic
500C22C3×#414412yes—
501C22C3×#414912yes—
502C22C3×#414911yescharacteristic
503C22C3×#415011yescharacteristic
504C4—22no—
505C4—22no—
506C4—42no—
507C4—42no—
508C4—104no—
509C4—202no—
510C4—202no—
511C3#1060585511yescharacteristic, direct product factor, Sylow
512C2—42no—
513C2—204no—
514C2C3×#6582011yescharacteristic
515C2C3×#6585511yescharacteristic
516C2C3×#6585711yescharacteristic
517C2C3×#6600012yes—
518C2C3×#6600112yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#381C2
socleC23×C3×C5C24
prime radicalC2×C3×#4076C2
cosocleC23×C5C24×C3
hypercenterC3×#381D5
hypocenterC5C3×#2377
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
2. C3×C5×#381C2semidirect
3. C3×#65501C2semidirect
4. C3×#65246C2semidirect
5. C3×#65245C2semidirect
6. C3×#64959C2semidirect
7. C3×#64957C2semidirect
8. C3×#64954C2semidirect
9. C3×#64943C2semidirect
10. #10605855C3direct (N × H)
18. C3×#4076C4semidirect
35. C5×#381C2×C3semidirect
36. #65501C2×C3semidirect
37. #65246C2×C3semidirect
38. #65245C2×C3semidirect
39. #64959C2×C3semidirect
40. #64957C2×C3semidirect
41. #64954C2×C3semidirect
42. #64943C2×C3semidirect
46. C22×C3×C4×C5C2×C4semidirect
53. C2×C3×C22⋊D5C2×C4semidirect
68. C3×#685C2×C4semidirect
70. C3×C4⋊Dic5C2×C4semidirect
80. C3×#381D5semidirect
89. #4076C3×C4semidirect
166. C22×C4×C5C2×C3×C4semidirect
173. C2×C22⋊D5C2×C3×C4semidirect
188. #685C2×C3×C4semidirect
190. C4⋊Dic5C2×C3×C4semidirect
200. #381C3×D5semidirect
240. C22×C3×C4C4×D5semidirect
395. C22×C4C3×C4×D5semidirect
411. C3×C5#2377semidirect
486. C5C3×#2377semidirect
511. C3#10605855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40762
C3×C5×#3812
C3×#655012
C3×#652462
C3×#652452
C3×#649592
C3×#649572
C3×#649542
C3×#649432
#106058553
C3×#23775