Finite Group Databasebeta

← C3×#10599797 #14301231

Subgroups — C3×#10599797 #14301231

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4055C211yesmaximal, characteristic
2C3×#65838C211yesmaximal, characteristic
3C2×C3×#3957C211yesmaximal, characteristic
4C3×#65409C211yesmaximal, characteristic, complemented
5C3×#65263C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7C3×#64775C211yesmaximal, characteristic, complemented
8#10599797C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C3×C4×C22⋊D5—22no—
15C3×#4072C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17C3×#4055—22no—
18C3×#4055C414yescomplemented
19C2×C3×Dic20—21no—
20C2×C3×#677—21no—
21C3×#4039—21no—
22C3×#4038—21no—
23C3×D5×C4⋊C4—21no—
24C3×#4033—21no—
25C3×#3963—22no—
26C3×#3957—22no—
27C3×#3948—21no—
28C3×#3948—21no—
29C3×#1882—51nomaximal, Hall
30C2×#4055C2×C311yescharacteristic
31#65838C2×C311yescharacteristic
32C2×#3957C2×C311yescharacteristic
33#65409C2×C311yescharacteristic, complemented
34#65263C2×C311yescharacteristic, complemented
35C5×#343C2×C311yescharacteristic, complemented
36#64775C2×C311yescharacteristic, complemented
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C22×C3×Dic5—21no—
41C22×C3×Dic5—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709C2×C412yes—
45C3×#709D412yes—
46C2×C3×D20D411yescharacteristic
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5—22no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10—21no—
54C2×C3×Dic10C2×C412yescomplemented
55C2×C3×Dic10D411yescharacteristic
56C3×C5×M16—21no—
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C3×C5×M16C2×C412yescomplemented
60C2×C3×C5×C8—21no—
61C2×C3×C5×C8—21no—
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C22⋊Dic5—21no—
65C3×#685—22no—
66C3×C4⋊Dic5D411yescharacteristic
67C3×C4⋊Dic5D411yescharacteristic
68C3×#683—22no—
69C3×C4×Dic5—22no—
70C3×C4×Dic5—21no—
71C3×C4×Dic5—21no—
72C3×C4×Dic5—21no—
73C3×Dic20—24no—
74C3×#677—24no—
75C2×C3×#137—51no—
76C3×#520—51no—
77C2×C3×#104—51no—
78C3×#419—51no—
79C3×#391—51no—
80C3×#343D511yescharacteristic, complemented
81C3×#339—51no—
82C2×#709C22×C311yescharacteristic
83C22×Dic10C22×C311yescharacteristic
84C2×C5×M16C22×C311yescharacteristic
85C2×C5×M16C22×C311yescharacteristic
86C2×C5×C4⋊C4C22×C311yescharacteristic
87C4×C22⋊D5—22no—
88#4072C22×C311yescharacteristic
89C2×C4×Dic5C22×C311yescharacteristic
90#4055—22no—
91#4055C3×C414yescomplemented
92C2×Dic20—21no—
93C2×#677—21no—
94#4039—21no—
95#4038—21no—
96D5×C4⋊C4—21no—
97#4033—21no—
98#3963—22no—
99#3957—22no—
100#3948—21no—
101#3948—21no—
102#1882—51noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C3×C22⋊D5—22no—
114C3×C22⋊D5—22no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5—41no—
124C3×D20—21no—
125C3×D20C22⋊C412yes—
126C3×C4×D5—22no—
127C3×C4×D5—22no—
128C3×C4×D5—82no—
129C3×Dic10—21no—
130C3×Dic10—22no—
131C3×Dic10—22no—
132C3×Dic10—41no—
133C3×Dic10—41no—
134C3×Dic10C22⋊C412yes—
135C3×C5×C8—22no—
136C3×C5×C8—41no—
137C2×C3×#41—51no—
138C22×C3×Q8—51no—
139C3×#137—54no—
140C3×#137—102no—
141C2×C3×Q16—101no—
142C2×C3×SD16—101no—
143C2×C3×M16C2×D511yescharacteristic
144C2×C3×M16C2×D511yescharacteristic
145C3×C4×Q8—101no—
146C3×C4×D4—101no—
147C3×C4×D4—102no—
148C3×#117—51no—
149C3×#117—101no—
150C2×C3×C4⋊C4—101no—
151C2×C3×C4⋊C4C2×D511yescharacteristic
152C2×C3×C42—51no—
153C3×#104—102no—
154C3×#103—101no—
155C3×#103—101no—
156C3×#95—102no—
157C22×C4×C5C3×D412yes—
158C22×C4×C5C23×C311yescharacteristic
159C2×C22⋊D5—21no—
160C22×Dic5—21no—
161C22×Dic5—21no—
162#709—21no—
163#709—21no—
164#709C2×C3×C412yes—
165#709C3×D412yes—
166C2×D20C3×D411yescharacteristic
167C2×C4×D5—21no—
168C2×C4×D5—22no—
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10—21no—
172C2×Dic10—21no—
173C2×Dic10—21no—
174C2×Dic10C2×C3×C412yescomplemented
175C2×Dic10C3×D411yescharacteristic
176C5×M16—21no—
177C5×M16—21no—
178C5×M16—21no—
179C5×M16C2×C3×C412yescomplemented
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C22⋊Dic5—21no—
185#685—22no—
186C4⋊Dic5C3×D411yescharacteristic
187C4⋊Dic5C3×D411yescharacteristic
188#683—22no—
189C4×Dic5—22no—
190C4×Dic5—21no—
191C4×Dic5—21no—
192C4×Dic5—21no—
193Dic20—24no—
194#677—24no—
195C2×#137—51no—
196#520—51no—
197C2×#104—51no—
198#419—51no—
199#391—51no—
200#343C3×D511yescharacteristic, complemented
201#339—51no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×C3×D5—22no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C3×C4×C5—42no—
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215C3×Dic5—22no—
216C3×Dic5—42no—
217C3×Dic5—42no—
218C3×Dic5—41no—
219C3×Dic5—41no—
220C3×#41—52no—
221C3×#41—52no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—52no—
225C2×C3×Q8—51no—
226C2×C3×Q8—101no—
227C2×C3×Q8—101no—
228C2×C3×Q8—101no—
229C2×C3×Q8—101no—
230C2×C3×Q8—101no—
231C2×C3×D4—51no—
232C2×C3×D4—101no—
233C22×C3×C4—102no—
234C22×C3×C4—101no—
235C22×C3×C4—101no—
236C22×C3×C4—101no—
237C22×C3×C4D2012yes—
238C22×C3×C4C22×D511yescharacteristic
239C3×Q16—104no—
240C3×SD16—104no—
241C3×M16—21no—
242C3×M16—21no—
243C3×M16—21no—
244C3×M16C4×D512yescomplemented
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—102no—
252C3×C22⋊C4—102no—
253C3×C22⋊C4—101no—
254C3×C42—102no—
255C3×C42—101no—
256C3×C42—101no—
257C3×C42—101no—
258C23×C5C2×C3×D411yescharacteristic
259C22×D5—21no—
260C2×C4×C5—22no—
261C2×C4×C5—42no—
262C2×C4×C5C22×C3×C411yescharacteristic
263C2×C4×C5C2×C3×D411yescharacteristic
264C2×C4×C5C2×C3×D411yescharacteristic
265C2×C4×C5C2×C3×D411yescharacteristic
266C2×C4×C5C3×#4111yescharacteristic
267C2×C4×C5C3×#4111yescharacteristic
268C22⋊D5—22no—
269C22⋊D5—22no—
270C2×Dic5—21no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—21no—
274C2×Dic5—21no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—41no—
278C2×Dic5—41no—
279D20—21no—
280D20C3×C22⋊C412yes—
281C4×D5—22no—
282C4×D5—22no—
283C4×D5—82no—
284Dic10—21no—
285Dic10—22no—
286Dic10—22no—
287Dic10—41no—
288Dic10—41no—
289Dic10C3×C22⋊C412yes—
290C5×C8—22no—
291C5×C8—41no—
292C2×#41—51no—
293C22×Q8—51no—
294#137—54no—
295#137—102no—
296C2×Q16—101no—
297C2×SD16—101no—
298C2×M16C2×C3×D511yescharacteristic
299C2×M16C2×C3×D511yescharacteristic
300C4×Q8—101no—
301C4×D4—101no—
302C4×D4—102no—
303#117—51no—
304#117—101no—
305C2×C4⋊C4—101no—
306C2×C4⋊C4C2×C3×D511yescharacteristic
307C2×C42—51no—
308#104—102no—
309#103—101no—
310#103—101no—
311#95—102no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317C3×D5—42no—
318C23×C3—101no—
319C23×C3C2×D2011yescharacteristic
320C3×Q8—52no—
321C3×Q8—101no—
322C3×Q8—102no—
323C3×Q8—102no—
324C3×Q8—201no—
325C3×Q8—201no—
326C3×D4—52no—
327C3×D4—102no—
328C3×D4—102no—
329C3×D4—101no—
330C2×C3×C4—22no—
331C2×C3×C4—42no—
332C2×C3×C4—101no—
333C2×C3×C4—102no—
334C2×C3×C4—102no—
335C2×C3×C4—102no—
336C2×C3×C4—102no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—201no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4—201no—
343C2×C3×C4—402no—
344C2×C3×C4C2×C4×D511yescharacteristic
345C2×C3×C4#70911yescharacteristic
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4#71311yescharacteristic
350C3×C8—22no—
351C3×C8—41no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5C3×C4×D411yescharacteristic
355C22×C5C3×#12011yescharacteristic
356C22×C5C3×#12111yescharacteristic
357C2×D5—22no—
358C2×D5—41no—
359C2×D5—41no—
360C4×C5—42no—
361C4×C5C2×C3×C22⋊C411yescharacteristic
362C4×C5C3×C4×D411yescharacteristic
363C4×C5C3×#12111yescharacteristic
364C4×C5C3×#12311yescharacteristic
365Dic5—22no—
366Dic5—42no—
367Dic5—42no—
368Dic5—41no—
369Dic5—41no—
370#41—52no—
371#41—52no—
372#41—101no—
373#41—101no—
374C2×Q8—52no—
375C2×Q8—51no—
376C2×Q8—101no—
377C2×Q8—101no—
378C2×Q8—101no—
379C2×Q8—101no—
380C2×Q8—101no—
381C2×D4—51no—
382C2×D4—101no—
383C22×C4—102no—
384C22×C4—101no—
385C22×C4—101no—
386C22×C4—101no—
387C22×C4C3×D2012yes—
388C22×C4C22×C3×D511yescharacteristic
389Q16—104no—
390SD16—104no—
391M16—21no—
392M16—21no—
393M16—21no—
394M16C3×C4×D512yescomplemented
395C2×C8—21no—
396C2×C8—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—51no—
400C4⋊C4—51no—
401C4⋊C4—102no—
402C22⋊C4—102no—
403C22⋊C4—101no—
404C42—102no—
405C42—101no—
406C42—101no—
407C42—101no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—102no—
412C22×C3—201no—
413C22×C3—201no—
414C22×C3C4×D2011yescharacteristic
415C22×C3#402811yescharacteristic
416C22×C3#404111yescharacteristic
417C3×C4—42no—
418C3×C4—102no—
419C3×C4—202no—
420C3×C4—201no—
421C3×C4—201no—
422C3×C4—202no—
423C3×C4D5×C22⋊C411yescharacteristic
424C3×C4#403011yescharacteristic
425C3×C4#403911yescharacteristic
426C3×C4#404011yescharacteristic
427C2×C5—21no—
428C2×C5—21no—
429C2×C5C3×#38611yescharacteristic
430C2×C5C3×#45511yescharacteristic
431C2×C5C3×#45611yescharacteristic
432D5—42no—
433C23—101no—
434C23C2×C3×D2011yescharacteristic
435Q8—52no—
436Q8—101no—
437Q8—102no—
438Q8—102no—
439Q8—201no—
440Q8—201no—
441D4—52no—
442D4—102no—
443D4—102no—
444D4—101no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—101no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—201no—
455C2×C4—201no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—402no—
459C2×C4C2×C3×C4×D511yescharacteristic
460C2×C4C3×#70911yescharacteristic
461C2×C4C3×D4×D511yescharacteristic
462C2×C4C3×D4×D511yescharacteristic
463C2×C4C3×D4×D511yescharacteristic
464C2×C4C3×#71311yescharacteristic
465C8—22no—
466C8—41no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—202no—
470C2×C3#6495411yescharacteristic
471C2×C3#6503511yescharacteristic
472C2×C3#6504111yescharacteristic
473C5C3×#188211yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—102no—
477C22—201no—
478C22—201no—
479C22C3×C4×D2011yescharacteristic
480C22C3×#402811yescharacteristic
481C22C3×#404111yescharacteristic
482C4—42no—
483C4—102no—
484C4—202no—
485C4—201no—
486C4—201no—
487C4—202no—
488C4C3×D5×C22⋊C411yescharacteristic
489C4C3×#403011yescharacteristic
490C4C3×#403911yescharacteristic
491C4C3×#404011yescharacteristic
492C3#1059979711yescharacteristic, direct product factor, Sylow
493C2—21no—
494C2—21no—
495C2—202no—
496C2C3×#6495411yescharacteristic
497C2C3×#6503511yescharacteristic
498C2C3×#6504111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#343D5
hypocenterC5C3×#1882
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
4. C3×#65409C2semidirect
5. C3×#65263C2semidirect
6. C3×C5×#343C2semidirect
7. C3×#64775C2semidirect
8. #10599797C3direct (N × H)
18. C3×#4055C4semidirect
33. #65409C2×C3semidirect
34. #65263C2×C3semidirect
35. C5×#343C2×C3semidirect
36. #64775C2×C3semidirect
54. C2×C3×Dic10C2×C4semidirect
59. C3×C5×M16C2×C4semidirect
80. C3×#343D5semidirect
91. #4055C3×C4semidirect
174. C2×Dic10C2×C3×C4semidirect
179. C5×M16C2×C3×C4semidirect
200. #343C3×D5semidirect
244. C3×M16C4×D5semidirect
394. M16C3×C4×D5semidirect
408. C3×C5#1882semidirect
473. C5C3×#1882semidirect
492. C3#10599797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40552
C3×#658382
C2×C3×#39572
C3×#654092
C3×#652632
C3×C5×#3432
C3×#647752
#105997973
C3×#18825