Finite Group Databasebeta

← C3×#10611906 #14435422

Subgroups — C3×#10611906 #14435422

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
2C3×#65958C211yesmaximal, characteristic
3C3×C5×#451C211yesmaximal, characteristic, complemented
4C3×#65516C211yesmaximal, characteristic
5C3×#65474C212yesmaximal, complemented
6C3×#65473C212yesmaximal, complemented
7C3×#65333C211yesmaximal, characteristic, complemented
8C3×#65106C212yesmaximal, complemented
9C3×#65088C212yesmaximal, complemented
10C3×#65024C211yesmaximal, characteristic
11C3×#65008C211yesmaximal, characteristic, complemented
12#10611906C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C3×C5×Q16C2212yes—
15C3×C5×C22⋊Q8C2211yescharacteristic
16C3×#4093C2211yescharacteristic
17C3×Q8×Dic5—21no—
18C3×Q8×Dic5—21no—
19C3×Q8×Dic5C2212yes—
20C3×Q8×Dic5C2212yes—
21C3×Q8×Dic5C2211yescharacteristic
22C2×C3×#688C2212yes—
23C3×#4076C2211yescharacteristic
24C2×C3×C4⋊Dic5—21no—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5—21no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C3×#4044—21no—
29C3×#4039C2211yescharacteristic
30C3×#4038—21no—
31C3×#4036C2211yescharacteristic
32C3×#4032—21no—
33C3×#4027—21no—
34C3×C5×#103C2212yes—
35C3×C5×C22⋊C8C2211yescharacteristic
36C3×#3967C2212yes—
37C3×#3967C2212yes—
38C3×C22⋊#168C2211yescharacteristic
39C3×#3953C2212yes—
40C3×#3949C2212yes—
41C3×#3947C2212yes—
42C3×#3946C2212yes—
43C3×#3939C2212yes—
44C3×#3117—51nomaximal, Hall
45C2×Q8×Dic5C2×C311yescharacteristic, complemented
46#65958C2×C311yescharacteristic
47C5×#451C2×C311yescharacteristic, complemented
48#65516C2×C311yescharacteristic
49#65474C2×C312yescomplemented
50#65473C2×C312yescomplemented
51#65333C2×C311yescharacteristic, complemented
52#65106C2×C312yescomplemented
53#65088C2×C312yescomplemented
54#65024C2×C311yescharacteristic
55#65008C2×C311yescharacteristic, complemented
56C2×C3×C5×Q8—24no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×Q8C2312yes—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×C3×C22⋊D5—21no—
63C22×C3×Dic5—21no—
64C22×C3×Dic5D411yescharacteristic
65C22×C3×Dic5D411yescharacteristic
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C3×C5×Q16—24no—
69C2×C3×C5×C8C2312yes—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C22⋊C4—21no—
73C3×#688—24no—
74C3×#685—21no—
75C3×#685—21no—
76C3×#685—21no—
77C3×#685—21no—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5—22no—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×#683—21no—
86C3×C4×Dic5—22no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5—21no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92C3×C4×Dic5C2311yescharacteristic
93C2×C3×#168C2312yes—
94C3×#529—51no—
95C2×C3×C4×Q8—51no—
96C3×#484—51no—
97C3×#481—51no—
98C3×#479—52no—
99C3×#464—52no—
100C3×#451D511yescharacteristic, complemented
101C3×#448—51no—
102C3×#441—52no—
103C3×#440—52no—
104C3×#432—51no—
105C22×C5×Q8C22×C311yescharacteristic
106C2×C5×Q16C22×C312yes—
107C5×C22⋊Q8C22×C311yescharacteristic
108#4093C22×C311yescharacteristic
109Q8×Dic5—21no—
110Q8×Dic5—21no—
111Q8×Dic5C22×C312yes—
112Q8×Dic5C22×C312yes—
113Q8×Dic5C22×C311yescharacteristic
114C2×#688C22×C312yes—
115#4076C22×C311yescharacteristic
116C2×C4⋊Dic5—21no—
117C2×C4⋊Dic5C22×C311yescharacteristic
118C2×C4×Dic5—21no—
119C2×C4×Dic5C22×C311yescharacteristic
120#4044—21no—
121#4039C22×C311yescharacteristic
122#4038—21no—
123#4036C22×C311yescharacteristic
124#4032—21no—
125#4027—21no—
126C5×#103C22×C312yes—
127C5×C22⋊C8C22×C311yescharacteristic
128#3967C22×C312yes—
129#3967C22×C312yes—
130C22⋊#168C22×C311yescharacteristic
131#3953C22×C312yes—
132#3949C22×C312yes—
133#3947C22×C312yes—
134#3946C22×C312yes—
135#3939C22×C312yes—
136#3117—51noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C3×D5—21no—
139C3×C5×Q8—24no—
140C3×C5×Q8—22no—
141C3×C5×Q8—22no—
142C3×C5×Q8#4114yes—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150C3×C22⋊D5—42no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—41no—
155C2×C3×Dic5—42no—
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C2×C3×Dic5C2×D411yescharacteristic
160C3×D20—22no—
161C3×C4×D5—42no—
162C3×C5×C8—22no—
163C3×#168—22no—
164C22×C3×Q8C2×D511yescharacteristic
165C2×C3×Q16C2×D512yes—
166C2×C3×SD16—52no—
167C3×#126—101no—
168C3×#125—51no—
169C3×#124—51no—
170C3×#123—101no—
171C3×C22⋊Q8C2×D511yescharacteristic
172C3×#121—51no—
173C3×C4×Q8—52no—
174C3×C4×Q8—51no—
175C3×C4×Q8—52no—
176C3×C4×Q8—101no—
177C3×C4×Q8—101no—
178C3×C4×D4—51no—
179C3×C4×D4—101no—
180C3×#117—101no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—101no—
183C2×C3×C42—51no—
184C2×C3×C42—101no—
185C3×#107—52no—
186C3×#106—52no—
187C3×C4⋊C8—52no—
188C3×#103—52no—
189C3×#103—52no—
190C3×#103C2×D512yes—
191C3×#102—52no—
192C3×C22⋊C8—51no—
193C3×C22⋊C8C2×D511yescharacteristic
194C3×#97—52no—
195C2×C5×Q8—24no—
196C2×C5×Q8—21no—
197C2×C5×Q8C23×C311yescharacteristic
198C2×C5×Q8C23×C312yes—
199C22×C4×C5—21no—
200C22×C4×C5C23×C311yescharacteristic
201C2×C22⋊D5—21no—
202C22×Dic5—21no—
203C22×Dic5C3×D411yescharacteristic
204C22×Dic5C3×D411yescharacteristic
205C2×D20C23×C311yescharacteristic
206C2×C4×D5—21no—
207C5×Q16—24no—
208C2×C5×C8C23×C312yes—
209C5×C4⋊C4—21no—
210C5×C4⋊C4C23×C311yescharacteristic
211C5×C22⋊C4—21no—
212#688—24no—
213#685—21no—
214#685—21no—
215#685—21no—
216#685—21no—
217C4⋊Dic5—21no—
218C4⋊Dic5—21no—
219C4⋊Dic5—21no—
220C4⋊Dic5—22no—
221C4⋊Dic5—22no—
222C4⋊Dic5C23×C312yes—
223C4⋊Dic5C23×C311yescharacteristic
224#683—21no—
225C4×Dic5—21no—
226C4×Dic5—22no—
227C4×Dic5—22no—
228C4×Dic5C3×D411yescharacteristic
229C4×Dic5C3×D411yescharacteristic
230C4×Dic5C23×C311yescharacteristic
231C4×Dic5C23×C311yescharacteristic
232C2×#168C23×C312yes—
233#529—51no—
234C2×C4×Q8—51no—
235#484—51no—
236#481—51no—
237#479—52no—
238#464—52no—
239#451C3×D511yescharacteristic, complemented
240#448—51no—
241#441—52no—
242#440—52no—
243#432—51no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×C3×D5—41no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C3×C4×C5—24no—
252C3×C4×C5—21no—
253C3×C4×C5—41no—
254C3×C4×C5—41no—
255C3×C4×C5C2×#4112yes—
256C3×Dic5—21no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C3×Dic5—21no—
260C3×Dic5—41no—
261C3×Dic5—42no—
262C2×C3×Q8—24no—
263C2×C3×Q8—21no—
264C2×C3×Q8C22×D511yescharacteristic
265C2×C3×Q8C22×D512yes—
266C2×C3×D4—51no—
267C2×C3×D4—101no—
268C22×C3×C4—21no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—101no—
272C22×C3×C4—101no—
273C22×C3×C4C22×D511yescharacteristic
274C3×Q16—24no—
275C3×SD16—104no—
276C2×C3×C8—52no—
277C2×C3×C8C22×D512yes—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—52no—
280C3×C4⋊C4—51no—
281C3×C4⋊C4—101no—
282C3×C4⋊C4—102no—
283C3×C4⋊C4—102no—
284C3×C4⋊C4—101no—
285C3×C4⋊C4—101no—
286C3×C4⋊C4—101no—
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C22⋊C4—21no—
289C3×C22⋊C4—101no—
290C3×C22⋊C4—101no—
291C3×C22⋊C4—101no—
292C3×C22⋊C4—101no—
293C3×C42—51no—
294C3×C42—51no—
295C3×C42—51no—
296C3×C42—51no—
297C3×C42—102no—
298C3×C42—102no—
299C3×C42—101no—
300C23×C5C2×C3×D411yescharacteristic
301C22×D5—21no—
302C5×Q8—24no—
303C5×Q8—22no—
304C5×Q8—22no—
305C5×Q8C3×#4114yes—
306C2×C4×C5—24no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5C2×C3×D411yescharacteristic
312C2×C4×C5C24×C311yescharacteristic
313C22⋊D5—42no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—21no—
317C2×Dic5—41no—
318C2×Dic5—42no—
319C2×Dic5C2×C3×D411yescharacteristic
320C2×Dic5C2×C3×D411yescharacteristic
321C2×Dic5C2×C3×D411yescharacteristic
322C2×Dic5C2×C3×D411yescharacteristic
323D20—22no—
324C4×D5—42no—
325C5×C8—22no—
326#168—22no—
327C22×Q8C2×C3×D511yescharacteristic
328C2×Q16C2×C3×D512yes—
329C2×SD16—52no—
330#126—101no—
331#125—51no—
332#124—51no—
333#123—101no—
334C22⋊Q8C2×C3×D511yescharacteristic
335#121—51no—
336C4×Q8—52no—
337C4×Q8—52no—
338C4×Q8—51no—
339C4×Q8—101no—
340C4×Q8—101no—
341C4×D4—51no—
342C4×D4—101no—
343#117—101no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C42—51no—
347C2×C42—101no—
348#107—52no—
349#106—52no—
350C4⋊C8—52no—
351#103—52no—
352#103—52no—
353#103C2×C3×D512yes—
354#102—52no—
355C22⋊C8—51no—
356C22⋊C8C2×C3×D511yescharacteristic
357#97—52no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362C3×D5—81no—
363C23×C3—101no—
364C23×C3D4×D511yescharacteristic
365C3×Q8—24no—
366C3×Q8—22no—
367C3×Q8—22no—
368C3×Q8#71114yes—
369C3×D4—102no—
370C3×D4—202no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—51no—
377C2×C3×C4—51no—
378C2×C3×C4—51no—
379C2×C3×C4—51no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—101no—
383C2×C3×C4—202no—
384C2×C3×C4—201no—
385C2×C3×C4—202no—
386C2×C3×C4D4×D511yescharacteristic
387C2×C3×C4C23×D511yescharacteristic
388C3×C8—22no—
389C3×C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5C3×#13712yes—
393C22×C5C22×C3×D411yescharacteristic
394C2×D5—41no—
395C2×D5—41no—
396C2×D5—41no—
397C4×C5—24no—
398C4×C5—21no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5C2×C3×#4112yes—
402Dic5—21no—
403Dic5—21no—
404Dic5—21no—
405Dic5—21no—
406Dic5—41no—
407Dic5—42no—
408C2×Q8—24no—
409C2×Q8—21no—
410C2×Q8C22×C3×D511yescharacteristic
411C2×Q8C22×C3×D512yes—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—21no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4C22×C3×D511yescharacteristic
420Q16—24no—
421SD16—104no—
422C2×C8—52no—
423C2×C8C22×C3×D512yes—
424C4⋊C4—21no—
425C4⋊C4—52no—
426C4⋊C4—51no—
427C4⋊C4—102no—
428C4⋊C4—102no—
429C4⋊C4—101no—
430C4⋊C4—101no—
431C4⋊C4—101no—
432C4⋊C4—101no—
433C4⋊C4C22×C3×D511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—101no—
436C22⋊C4—101no—
437C22⋊C4—101no—
438C22⋊C4—101no—
439C42—51no—
440C42—51no—
441C42—51no—
442C42—51no—
443C42—102no—
444C42—102no—
445C42—101no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3#406412yes—
453C22×C3C2×D4×D511yescharacteristic
454C3×C4—24no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—101no—
459C3×C4—101no—
460C3×C4—101no—
461C3×C4—101no—
462C3×C4—201no—
463C3×C4—202no—
464C3×C4C2×#71112yes—
465C2×C5—22no—
466C2×C5C3×#52511yescharacteristic
467C2×C5C2×C3×#13711yescharacteristic
468C2×C5C3×#57511yescharacteristic
469D5—81no—
470C23—101no—
471C23C3×D4×D511yescharacteristic
472Q8—24no—
473Q8—22no—
474Q8—22no—
475Q8C3×#71114yes—
476D4—102no—
477D4—202no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—101no—
490C2×C4—202no—
491C2×C4—201no—
492C2×C4—202no—
493C2×C4C3×D4×D511yescharacteristic
494C2×C4C23×C3×D511yescharacteristic
495C8—22no—
496C8—102no—
497C2×C3—22no—
498C2×C3—401no—
499C2×C3#6592011yescharacteristic
500C2×C3C2×#406411yescharacteristic
501C2×C3#6611111yescharacteristic
502C5C3×#311711yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—201no—
506C22—201no—
507C22—201no—
508C22C3×#406412yes—
509C22C2×C3×D4×D511yescharacteristic
510C4—24no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—101no—
515C4—101no—
516C4—101no—
517C4—101no—
518C4—202no—
519C4—201no—
520C4C2×C3×#71112yes—
521C3#1061190611yescharacteristic, direct product factor, Sylow
522C2—22no—
523C2—401no—
524C2C3×#6592011yescharacteristic
525C2C2×C3×#406411yescharacteristic
526C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#451C2
socleC22×C3×C5C22×D4
prime radicalC3×#4076C22
hypercenterC3×#451D5
hypocenterC5C3×#3117
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic5C2semidirect
3. C3×C5×#451C2semidirect
5. C3×#65474C2semidirect
6. C3×#65473C2semidirect
7. C3×#65333C2semidirect
8. C3×#65106C2semidirect
9. C3×#65088C2semidirect
11. C3×#65008C2semidirect
12. #10611906C3direct (N × H)
45. C2×Q8×Dic5C2×C3semidirect
47. C5×#451C2×C3semidirect
49. #65474C2×C3semidirect
50. #65473C2×C3semidirect
51. #65333C2×C3semidirect
52. #65106C2×C3semidirect
53. #65088C2×C3semidirect
55. #65008C2×C3semidirect
100. C3×#451D5semidirect
239. #451C3×D5semidirect
446. C3×C5#3117semidirect
502. C5C3×#3117semidirect
521. C3#10611906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic52
C3×#659582
C3×C5×#4512
C3×#655162
C3×#654742
C3×#654732
C3×#653332
C3×#651062
C3×#650882
C3×#650242
C3×#650082
#106119063
C3×#31175