Finite Group Databasebeta

← C3×#10615615 #14424529

Subgroups — C3×#10615615 #14424529

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4147C211yesmaximal, characteristic
2C22×C3×C5×Q16C211yesmaximal, characteristic, complemented
3C3×#66150C211yesmaximal, characteristic, complemented
4C2×C3×#4088C211yesmaximal, characteristic, complemented
5C3×#65514C211yesmaximal, characteristic, complemented
6C3×#65476C214yesmaximal, complemented
7C3×#65475C214yesmaximal, complemented
8C3×#65402C211yesmaximal, characteristic, complemented
9C3×#65399C211yesmaximal, characteristic, complemented
10#10615615C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×C3×C5×Q8C2211yescharacteristic
13C3×#4147—24no—
14C3×#4147—24no—
15C2×C3×#713—21no—
16C2×C3×#713C2212yes—
17C2×C3×Q8×D5—21no—
18C2×C3×Q8×D5C2212yes—
19C2×C3×#709—22no—
20C2×C3×#709C2211yescharacteristic
21C2×C3×#709C2211yescharacteristic
22C2×C3×C5×Q16—24no—
23C2×C3×C5×Q16C2214yes—
24C22×C3×C5×C8C2211yescharacteristic
25C3×#4093—21no—
26C3×#4092C2214yes—
27C3×#4090—21no—
28C2×C3×#689C2212yes—
29C3×#4088—24no—
30C2×C3×#688C2212yes—
31C3×#4075—22no—
32C3×#4072C2211yescharacteristic
33C2×C3×#681C2211yescharacteristic
34C3×#3967C2214yes—
35C3×#3953C2212yes—
36C3×#3952C2214yes—
37C3×#3948C2212yes—
38C3×#3011—51nomaximal, Hall
39C2×#4147C2×C311yescharacteristic
40C22×C5×Q16C2×C311yescharacteristic, complemented
41#66150C2×C311yescharacteristic, complemented
42C2×#4088C2×C311yescharacteristic, complemented
43#65514C2×C311yescharacteristic, complemented
44#65476C2×C314yescomplemented
45#65475C2×C314yescomplemented
46#65402C2×C311yescharacteristic, complemented
47#65399C2×C311yescharacteristic, complemented
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8D414yes—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×Q8C2312yes—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×C3×C22⋊D5—21no—
60C2×C3×C22⋊D5D412yes—
61C3×#713—28no—
62C3×#713—24no—
63C3×#713—24no—
64C3×Q8×D5—28no—
65C3×Q8×D5—24no—
66C3×Q8×D5—24no—
67C3×#709—216no—
68C3×#709—22no—
69C3×#709—22no—
70C3×#709—22no—
71C3×#709D414yes—
72C2×C3×D20—22no—
73C2×C3×D20D411yescharacteristic
74C2×C3×D20C2311yescharacteristic
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—21no—
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5C2312yes—
79C2×C3×Dic10—22no—
80C2×C3×Dic10D411yescharacteristic
81C2×C3×Dic10C2311yescharacteristic
82C3×C5×Q16—28no—
83C2×C3×C5×C8—22no—
84C2×C3×C5×C8C2312yes—
85C3×C22⋊Dic5—21no—
86C3×#689—24no—
87C3×#688—24no—
88C3×#685—24no—
89C3×C4⋊Dic5C2312yes—
90C3×#683—24no—
91C3×C4×Dic5—21no—
92C3×#681—22no—
93C2×C3×#168C2312yes—
94C2×C3×2−1+4—51no—
95C2×C3×#137—51no—
96C22×C3×Q16D511yescharacteristic, complemented
97C3×#536—51no—
98C3×#452—54no—
99C3×#451—54no—
100C3×#419—51no—
101C3×#416—51no—
102C3×#408—51no—
103C22×C5×Q8C22×C311yescharacteristic
104C22×C5×Q8C22×C311yescharacteristic
105#4147—24no—
106#4147—24no—
107C2×#713—21no—
108C2×#713C22×C312yes—
109C2×Q8×D5—21no—
110C2×Q8×D5C22×C312yes—
111C2×#709—22no—
112C2×#709C22×C311yescharacteristic
113C2×#709C22×C311yescharacteristic
114C2×C5×Q16—24no—
115C2×C5×Q16C22×C314yes—
116C22×C5×C8C22×C311yescharacteristic
117#4093—21no—
118#4092C22×C314yes—
119#4090—21no—
120C2×#689C22×C312yes—
121#4088—24no—
122C2×#688C22×C312yes—
123#4075—22no—
124#4072C22×C311yescharacteristic
125C2×#681C22×C311yescharacteristic
126#3967C22×C314yes—
127#3953C22×C312yes—
128#3952C22×C314yes—
129#3948C22×C312yes—
130#3011—51noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C3×D5—21no—
133C22×C3×D5C2×D412yes—
134C3×C5×Q8—24no—
135C3×C5×Q8—22no—
136C3×C5×Q8—22no—
137C3×C5×Q8—22no—
138C3×C5×Q8—42no—
139C3×C5×Q8C2×D414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—42no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2411yescharacteristic
148C3×C22⋊D5—24no—
149C3×C22⋊D5—24no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5C2×D412yes—
153C3×D20—28no—
154C3×D20—22no—
155C3×D20—21no—
156C3×D20C2×D412yes—
157C3×C4×D5—28no—
158C3×C4×D5—28no—
159C3×C4×D5—24no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—28no—
163C3×Dic10—22no—
164C3×Dic10—21no—
165C3×Dic10C2×D412yes—
166C3×C5×C8—22no—
167C3×#168—22no—
168C3×2−1+4—104no—
169C3×2−1+4—104no—
170C2×C3×#41—51no—
171C2×C3×#41—52no—
172C2×C3×#41—51no—
173C2×C3×#41—102no—
174C2×C3×#41—101no—
175C22×C3×Q8—52no—
176C22×C3×Q8—101no—
177C22×C3×Q8C2×D511yescharacteristic
178C22×C3×Q8C2×D511yescharacteristic
179C3×#137—104no—
180C2×C3×Q16—24no—
181C2×C3×Q16—52no—
182C2×C3×Q16C2×D514yes—
183C2×C3×SD16—52no—
184C2×C3×M16—51no—
185C22×C3×C8C2×D511yescharacteristic
186C3×C4⋊Q8—101no—
187C3×#124—101no—
188C3×#123—102no—
189C3×C22⋊Q8—54no—
190C3×#117—51no—
191C3×#103—54no—
192C3×#103—52no—
193C3×#102—52no—
194C3×C22⋊C8—54no—
195C2×C5×Q8—21no—
196C2×C5×Q8—22no—
197C2×C5×Q8—21no—
198C2×C5×Q8—22no—
199C2×C5×Q8—22no—
200C2×C5×Q8C3×D414yes—
201C2×C5×Q8C23×C312yes—
202C2×C5×Q8C23×C312yes—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5C23×C311yescharacteristic
206C2×C22⋊D5—21no—
207C2×C22⋊D5C3×D412yes—
208#713—28no—
209#713—24no—
210#713—24no—
211Q8×D5—28no—
212Q8×D5—24no—
213Q8×D5—24no—
214#709—216no—
215#709—22no—
216#709—22no—
217#709—22no—
218#709C3×D414yes—
219C2×D20—22no—
220C2×D20C3×D411yescharacteristic
221C2×D20C23×C311yescharacteristic
222C2×C4×D5—22no—
223C2×C4×D5—21no—
224C2×C4×D5—22no—
225C2×C4×D5C23×C312yes—
226C2×Dic10—22no—
227C2×Dic10C3×D411yescharacteristic
228C2×Dic10C23×C311yescharacteristic
229C5×Q16—28no—
230C2×C5×C8—22no—
231C2×C5×C8C23×C312yes—
232C22⋊Dic5—21no—
233#689—24no—
234#688—24no—
235#685—24no—
236C4⋊Dic5C23×C312yes—
237#683—24no—
238C4×Dic5—21no—
239#681—22no—
240C2×#168C23×C312yes—
241C2×2−1+4—51no—
242C2×#137—51no—
243C22×Q16C3×D511yescharacteristic, complemented
244#536—51no—
245#452—54no—
246#451—54no—
247#419—51no—
248#416—51no—
249#408—51no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C3×D5—22no—
254C2×C3×D5—22no—
255C2×C3×D5—24no—
256C2×C3×D5—42no—
257C3×C4×C5—24no—
258C3×C4×C5—42no—
259C3×C4×C5#12012yes—
260C3×C4×C5C22×D411yescharacteristic
261C3×C4×C5C22×D411yescharacteristic
262C3×Dic5—22no—
263C3×Dic5—22no—
264C3×Dic5—42no—
265C3×#41—54no—
266C3×#41—1016no—
267C3×#41—104no—
268C3×#41—108no—
269C3×#41—104no—
270C3×#41—102no—
271C3×#41—102no—
272C3×#41—102no—
273C2×C3×Q8—21no—
274C2×C3×Q8—22no—
275C2×C3×Q8—21no—
276C2×C3×Q8—22no—
277C2×C3×Q8—22no—
278C2×C3×Q8—51no—
279C2×C3×Q8—51no—
280C2×C3×Q8—102no—
281C2×C3×Q8—104no—
282C2×C3×Q8—108no—
283C2×C3×Q8—104no—
284C2×C3×Q8C22⋊D514yes—
285C2×C3×Q8C22×D512yes—
286C2×C3×Q8C22×D512yes—
287C2×C3×D4—52no—
288C2×C3×D4—51no—
289C2×C3×D4—51no—
290C2×C3×D4—102no—
291C2×C3×D4—101no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—52no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C3×Q16—28no—
300C3×Q16—104no—
301C3×SD16—104no—
302C3×M16—102no—
303C2×C3×C8—22no—
304C2×C3×C8—52no—
305C2×C3×C8C22×D512yes—
306C3×C4⋊C4—52no—
307C3×C4⋊C4—104no—
308C3×C22⋊C4—104no—
309C3×C22⋊C4—101no—
310C3×C42—101no—
311C23×C5C2×C3×D411yescharacteristic
312C22×D5—21no—
313C22×D5C2×C3×D412yes—
314C5×Q8—24no—
315C5×Q8—22no—
316C5×Q8—22no—
317C5×Q8—22no—
318C5×Q8—42no—
319C5×Q8C2×C3×D414yes—
320C2×C4×C5—24no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—42no—
324C2×C4×C5C2×C3×D411yescharacteristic
325C2×C4×C5C2×C3×D412yes—
326C2×C4×C5C2×C3×D412yes—
327C2×C4×C5C24×C311yescharacteristic
328C22⋊D5—24no—
329C22⋊D5—24no—
330C2×Dic5—21no—
331C2×Dic5—22no—
332C2×Dic5C2×C3×D412yes—
333D20—28no—
334D20—22no—
335D20—21no—
336D20C2×C3×D412yes—
337C4×D5—28no—
338C4×D5—28no—
339C4×D5—24no—
340C4×D5—22no—
341C4×D5—22no—
342Dic10—28no—
343Dic10—22no—
344Dic10—21no—
345Dic10C2×C3×D412yes—
346C5×C8—22no—
347#168—22no—
3482−1+4—104no—
3492−1+4—104no—
350C2×#41—51no—
351C2×#41—52no—
352C2×#41—51no—
353C2×#41—102no—
354C2×#41—101no—
355C22×Q8—52no—
356C22×Q8—101no—
357C22×Q8C2×C3×D511yescharacteristic
358C22×Q8C2×C3×D511yescharacteristic
359#137—104no—
360C2×Q16—24no—
361C2×Q16—52no—
362C2×Q16C2×C3×D514yes—
363C2×SD16—52no—
364C2×M16—51no—
365C22×C8C2×C3×D511yescharacteristic
366C4⋊Q8—101no—
367#124—101no—
368#123—102no—
369C22⋊Q8—54no—
370#117—51no—
371#103—54no—
372#103—52no—
373#102—52no—
374C22⋊C8—54no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378C3×D5—42no—
379C3×D5—42no—
380C23×C3—52no—
381C23×C3—101no—
382C23×C3D4×D511yescharacteristic
383C3×Q8—22no—
384C3×Q8—24no—
385C3×Q8—22no—
386C3×Q8—22no—
387C3×Q8—42no—
388C3×Q8—52no—
389C3×Q8—108no—
390C3×Q8—101no—
391C3×Q8—102no—
392C3×Q8C2×C22⋊D514yes—
393C3×D4—52no—
394C3×D4—108no—
395C3×D4—104no—
396C3×D4—104no—
397C3×D4—101no—
398C3×D4—102no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—42no—
403C2×C3×C4—52no—
404C2×C3×C4—108no—
405C2×C3×C4—108no—
406C2×C3×C4—101no—
407C2×C3×C4—102no—
408C2×C3×C4—102no—
409C2×C3×C4—104no—
410C2×C3×C4—102no—
411C2×C3×C4D4×D512yes—
412C2×C3×C4D4×D511yescharacteristic
413C2×C3×C4C2×C22⋊D512yes—
414C2×C3×C4C23×D511yescharacteristic
415C3×C8—22no—
416C3×C8—102no—
417C22×C5—22no—
418C22×C5C3×#12012yes—
419C22×C5C22×C3×D411yescharacteristic
420C2×D5—24no—
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—42no—
424C4×C5—24no—
425C4×C5—42no—
426C4×C5C3×#12012yes—
427C4×C5C22×C3×D411yescharacteristic
428C4×C5C22×C3×D411yescharacteristic
429Dic5—22no—
430Dic5—22no—
431Dic5—42no—
432#41—54no—
433#41—1016no—
434#41—104no—
435#41—108no—
436#41—104no—
437#41—102no—
438#41—102no—
439#41—102no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—51no—
446C2×Q8—51no—
447C2×Q8—102no—
448C2×Q8—104no—
449C2×Q8—108no—
450C2×Q8—104no—
451C2×Q8C3×C22⋊D514yes—
452C2×Q8C22×C3×D512yes—
453C2×Q8C22×C3×D512yes—
454C2×D4—52no—
455C2×D4—51no—
456C2×D4—51no—
457C2×D4—102no—
458C2×D4—101no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—52no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—101no—
465C22×C4C22×C3×D511yescharacteristic
466Q16—28no—
467Q16—104no—
468SD16—104no—
469M16—102no—
470C2×C8—22no—
471C2×C8—52no—
472C2×C8C22×C3×D512yes—
473C4⋊C4—52no—
474C4⋊C4—104no—
475C22⋊C4—104no—
476C22⋊C4—101no—
477C42—101no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—104no—
481C22×C3—102no—
482C22×C3—102no—
483C22×C3—202no—
484C22×C3#408312yes—
485C22×C3C2×D4×D511yescharacteristic
486C3×C4—24no—
487C3×C4—42no—
488C3×C4—102no—
489C3×C4—102no—
490C3×C4—202no—
491C3×C4#408312yes—
492C3×C4C2×D4×D511yescharacteristic
493C3×C4C22×C22⋊D511yescharacteristic
494C2×C5—22no—
495C2×C5C2×C3×#12011yescharacteristic
496C2×C5C3×#57812yes—
497D5—42no—
498D5—42no—
499C23—52no—
500C23—101no—
501C23C3×D4×D511yescharacteristic
502Q8—24no—
503Q8—22no—
504Q8—22no—
505Q8—22no—
506Q8—42no—
507Q8—52no—
508Q8—108no—
509Q8—102no—
510Q8—101no—
511Q8C2×C3×C22⋊D514yes—
512D4—52no—
513D4—108no—
514D4—104no—
515D4—104no—
516D4—102no—
517D4—101no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—52no—
523C2×C4—108no—
524C2×C4—108no—
525C2×C4—101no—
526C2×C4—104no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4C3×D4×D511yescharacteristic
531C2×C4C3×D4×D512yes—
532C2×C4C2×C3×C22⋊D512yes—
533C2×C4C23×C3×D511yescharacteristic
534C8—22no—
535C8—102no—
536C2×C3—22no—
537C2×C3—202no—
538C2×C3—202no—
539C2×C3#6610012yes—
540C2×C3C2×#408311yescharacteristic
541C5C3×#301111yescharacteristic, complemented, Sylow
542C22—22no—
543C22—104no—
544C22—102no—
545C22—102no—
546C22—202no—
547C22C3×#408312yes—
548C22C2×C3×D4×D511yescharacteristic
549C4—24no—
550C4—42no—
551C4—102no—
552C4—102no—
553C4—202no—
554C4C3×#408312yes—
555C4C2×C3×D4×D511yescharacteristic
556C4C22×C3×C22⋊D511yescharacteristic
557C3#1061561511yescharacteristic, direct product factor, Sylow
558C2—22no—
559C2—202no—
560C2—202no—
561C2C3×#6610012yes—
562C2C2×C3×#408311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4147C2
hypercenterC22×C3×Q16D5
hypocenterC5C3×#3011
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×Q16

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×Q16C2semidirect
3. C3×#66150C2semidirect
4. C2×C3×#4088C2semidirect
5. C3×#65514C2semidirect
6. C3×#65476C2semidirect
7. C3×#65475C2semidirect
8. C3×#65402C2semidirect
9. C3×#65399C2semidirect
10. #10615615C3direct (N × H)
40. C22×C5×Q16C2×C3semidirect
41. #66150C2×C3semidirect
42. C2×#4088C2×C3semidirect
43. #65514C2×C3semidirect
44. #65476C2×C3semidirect
45. #65475C2×C3semidirect
46. #65402C2×C3semidirect
47. #65399C2×C3semidirect
96. C22×C3×Q16D5semidirect
243. C22×Q16C3×D5semidirect
478. C3×C5#3011semidirect
541. C5C3×#3011semidirect
557. C3#10615615direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41472
C22×C3×C5×Q162
C3×#661502
C2×C3×#40882
C3×#655142
C3×#654762
C3×#654752
C3×#654022
C3×#653992
#106156153
C3×#30115