Finite Group Databasebeta

← C3×#10601156 #14299723

Subgroups — C3×#10601156 #14299723

Order 1920.

604 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66161C211yesmaximal, characteristic
2C2×C3×C5×#104C211yesmaximal, characteristic
3C3×#65521C211yesmaximal, characteristic
4C3×#65410C211yesmaximal, characteristic, complemented
5C3×#65224C211yesmaximal, characteristic, complemented
6C3×#64774C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10601156C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C3×Q8×Dic5—21no—
13C3×D4×Dic5—21no—
14C3×D4×Dic5—22no—
15C3×#4072—21no—
16C3×#4072C2211yescharacteristic
17C2×C3×C4⋊Dic5—21no—
18C2×C3×C4⋊Dic5—22no—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22C3×C5×#104C414yescomplemented
23C3×#3967—21no—
24C3×#3964—21no—
25C3×#3950—21no—
26C3×#3949—21no—
27C3×#1859—51nomaximal, Hall
28#66161C2×C311yescharacteristic
29C2×C5×#104C2×C311yescharacteristic
30#65521C2×C311yescharacteristic
31#65410C2×C311yescharacteristic, complemented
32#65224C2×C311yescharacteristic, complemented
33#64774C2×C311yescharacteristic, complemented
34#64743C2×C311yescharacteristic, complemented
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41C2×C412yes—
38C3×C5×#41Q812yes—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×C3×Dic5—22no—
46C22×C3×Dic5—21no—
47C22×C3×Dic5D412yes—
48C3×C5×M16—21no—
49C3×C5×M16C2×C412yescomplemented
50C2×C3×C5×C8—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2×C412yescomplemented
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5—22no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—44no—
61C3×C4⋊Dic5D411yescharacteristic
62C3×C4⋊Dic5D411yescharacteristic
63C3×C4×Dic5—22no—
64C3×C4×Dic5—21no—
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68C3×#520—51no—
69C3×#428—51no—
70C2×C3×#104D511yescharacteristic
71C3×#417—51no—
72C3×#384—51no—
73C3×#343—51no—
74C3×#339—51no—
75C2×C5×#41C22×C311yescharacteristic
76C2×C5×M16C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78Q8×Dic5—21no—
79D4×Dic5—21no—
80D4×Dic5—22no—
81#4072—21no—
82#4072C22×C311yescharacteristic
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5C22×C311yescharacteristic
86C2×C4⋊Dic5C22×C311yescharacteristic
87C2×#681C22×C311yescharacteristic
88C5×#104C3×C414yescomplemented
89#3967—21no—
90#3964—21no—
91#3950—21no—
92#3949—21no—
93#1859—51noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—21no—
97C3×C5×Q8C4⋊C412yescomplemented
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4—21no—
101C3×C5×D4C4⋊C412yescomplemented
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×Q811yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×Dic5—21no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5—42no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—82no—
121C3×C5×C8—22no—
122C3×#168—41no—
123C2×C3×#41C2×D511yescharacteristic
124C2×C3×M16—51no—
125C2×C3×M16C2×D511yescharacteristic
126C3×C4×Q8—101no—
127C3×C4×D4—102no—
128C3×C4×D4—101no—
129C3×#117—51no—
130C3×#117—101no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4—101no—
134C2×C3×C4⋊C4—102no—
135C2×C3×C42C2×D511yescharacteristic
136C3×#107—101no—
137C3×#106—101no—
138C3×#104Dic514yescomplemented
139C3×#103—101no—
140C3×#102—101no—
141C5×#41—21no—
142C5×#41—21no—
143C5×#41C2×C3×C412yes—
144C5×#41C3×Q812yes—
145C2×C5×Q8C3×D411yescharacteristic
146C2×C5×D4—21no—
147C2×C5×D4C3×D411yescharacteristic
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5C23×C311yescharacteristic
151C22×Dic5—22no—
152C22×Dic5—21no—
153C22×Dic5C3×D412yes—
154C5×M16—21no—
155C5×M16C2×C3×C412yescomplemented
156C2×C5×C8—21no—
157C42×C5—21no—
158C42×C5C2×C3×C412yescomplemented
159C22⋊Dic5—22no—
160C22⋊Dic5—21no—
161C4⋊Dic5—22no—
162C4⋊Dic5—21no—
163C4⋊Dic5—21no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166C4⋊Dic5—44no—
167C4⋊Dic5C3×D411yescharacteristic
168C4⋊Dic5C3×D411yescharacteristic
169C4×Dic5—22no—
170C4×Dic5—21no—
171#681—21no—
172#681—21no—
173C2×#168—21no—
174#520—51no—
175#428—51no—
176C2×#104C3×D511yescharacteristic
177#417—51no—
178#384—51no—
179#343—51no—
180#339—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—22no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5C4×D411yescharacteristic
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5C22⋊Q811yescharacteristic
189C3×C4×C5—24no—
190C3×C4×C5—22no—
191C3×C4×C5C2×C4⋊C411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5#12311yescharacteristic
195C3×Dic5—42no—
196C3×Dic5—41no—
197C3×Dic5—41no—
198C3×Dic5—81no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41Dic1012yes—
202C3×#41C2×Dic512yes—
203C2×C3×Q8D2011yescharacteristic
204C2×C3×D4—21no—
205C2×C3×D4D2011yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—52no—
209C22×C3×C4—102no—
210C22×C3×C4—101no—
211C22×C3×C4C22×D511yescharacteristic
212C3×M16—21no—
213C3×M16—101no—
214C3×M16—101no—
215C3×M16C2×Dic512yescomplemented
216C2×C3×C8—21no—
217C2×C3×C8—101no—
218C3×C4⋊C4—51no—
219C3×C4⋊C4—51no—
220C3×C4⋊C4—102no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—204no—
226C3×C22⋊C4—102no—
227C3×C22⋊C4—101no—
228C3×C42—21no—
229C3×C42—102no—
230C3×C42—101no—
231C3×C42C2×Dic512yescomplemented
232C23×C5—21no—
233C23×C5C2×C3×D411yescharacteristic
234C5×Q8—21no—
235C5×Q8C3×C4⋊C412yescomplemented
236C5×D4—22no—
237C5×D4—22no—
238C5×D4—21no—
239C5×D4C3×C4⋊C412yescomplemented
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—21no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5C22×C3×C411yescharacteristic
247C2×C4×C5C2×C3×D411yescharacteristic
248C2×C4×C5C2×C3×D411yescharacteristic
249C2×C4×C5C2×C3×Q811yescharacteristic
250C2×C4×C5C3×#4111yescharacteristic
251C2×C4×C5C3×#4111yescharacteristic
252C2×Dic5—21no—
253C2×Dic5—22no—
254C2×Dic5—21no—
255C2×Dic5—42no—
256C2×Dic5—42no—
257C2×Dic5—41no—
258C2×Dic5—82no—
259C5×C8—22no—
260#168—41no—
261C2×#41C2×C3×D511yescharacteristic
262C2×M16—51no—
263C2×M16C2×C3×D511yescharacteristic
264C4×Q8—101no—
265C4×D4—102no—
266C4×D4—101no—
267#117—51no—
268#117—101no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—101no—
272C2×C4⋊C4—102no—
273C2×C42C2×C3×D511yescharacteristic
274#107—101no—
275#106—101no—
276#104C3×Dic514yescomplemented
277#103—101no—
278#102—101no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5—42no—
282C2×C3×C5#38511yescharacteristic
283C2×C3×C5#45311yescharacteristic
284C2×C3×C5#45611yescharacteristic
285C23×C3—21no—
286C23×C3D4×D511yescharacteristic
287C3×Q8—21no—
288C3×Q8C4⋊Dic512yescomplemented
289C3×D4—22no—
290C3×D4—22no—
291C3×D4—21no—
292C3×D4C4⋊Dic512yescomplemented
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—102no—
302C2×C3×C4—202no—
303C2×C3×C4—202no—
304C2×C3×C4—201no—
305C2×C3×C4—402no—
306C2×C3×C4C2×Dic1011yescharacteristic
307C2×C3×C4C2×D2011yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4#71111yescharacteristic
310C2×C3×C4#71111yescharacteristic
311C2×C3×C4C22×Dic511yescharacteristic
312C3×C8—22no—
313C3×C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—22no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5C3×C4×D411yescharacteristic
320C22×C5C3×#12011yescharacteristic
321C22×C5C3×C22⋊Q811yescharacteristic
322C4×C5—24no—
323C4×C5—22no—
324C4×C5C2×C3×C4⋊C411yescharacteristic
325C4×C5C3×C4×D411yescharacteristic
326C4×C5C3×C22⋊Q811yescharacteristic
327C4×C5C3×#12311yescharacteristic
328Dic5—42no—
329Dic5—41no—
330Dic5—41no—
331Dic5—81no—
332#41—21no—
333#41—21no—
334#41C3×Dic1012yes—
335#41C2×C3×Dic512yes—
336C2×Q8C3×D2011yescharacteristic
337C2×D4—21no—
338C2×D4C3×D2011yescharacteristic
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—52no—
342C22×C4—102no—
343C22×C4—101no—
344C22×C4C22×C3×D511yescharacteristic
345M16—21no—
346M16—101no—
347M16—101no—
348M16C2×C3×Dic512yescomplemented
349C2×C8—21no—
350C2×C8—101no—
351C4⋊C4—51no—
352C4⋊C4—51no—
353C4⋊C4—102no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C4⋊C4—101no—
357C4⋊C4—101no—
358C4⋊C4—204no—
359C22⋊C4—102no—
360C22⋊C4—101no—
361C42—21no—
362C42—102no—
363C42—101no—
364C42C2×C3×Dic512yescomplemented
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3#402411yescharacteristic
372C22×C3#402811yescharacteristic
373C22×C3D4×Dic511yescharacteristic
374C3×C4—24no—
375C3×C4—22no—
376C3×C4—202no—
377C3×C4—201no—
378C3×C4—201no—
379C3×C4—401no—
380C3×C4#402411yescharacteristic
381C3×C4#403211yescharacteristic
382C3×C4C2×C4⋊Dic511yescharacteristic
383C3×C4D4×Dic511yescharacteristic
384C2×C5—21no—
385C2×C5—21no—
386C2×C5—42no—
387C2×C5C3×#38511yescharacteristic
388C2×C5C3×#45311yescharacteristic
389C2×C5C3×#45611yescharacteristic
390C23—21no—
391C23C3×D4×D511yescharacteristic
392Q8—21no—
393Q8C3×C4⋊Dic512yescomplemented
394D4—22no—
395D4—22no—
396D4—21no—
397D4C3×C4⋊Dic512yescomplemented
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—101no—
405C2×C4—101no—
406C2×C4—102no—
407C2×C4—202no—
408C2×C4—202no—
409C2×C4—201no—
410C2×C4—402no—
411C2×C4C2×C3×Dic1011yescharacteristic
412C2×C4C2×C3×D2011yescharacteristic
413C2×C4C3×D4×D511yescharacteristic
414C2×C4C3×#71111yescharacteristic
415C2×C4C3×#71111yescharacteristic
416C2×C4C22×C3×Dic511yescharacteristic
417C8—22no—
418C8—201no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—42no—
422C2×C3#6511111yescharacteristic
423C2×C3#6511511yescharacteristic
424C2×C3#6523911yescharacteristic
425C5C3×#185911yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—22no—
429C22—41no—
430C22—41no—
431C22C3×#402411yescharacteristic
432C22C3×#402811yescharacteristic
433C22C3×D4×Dic511yescharacteristic
434C4—24no—
435C4—22no—
436C4—202no—
437C4—201no—
438C4—201no—
439C4—401no—
440C4C3×#402411yescharacteristic
441C4C3×#403211yescharacteristic
442C4C2×C3×C4⋊Dic511yescharacteristic
443C4C3×D4×Dic511yescharacteristic
444C3#1060115611yescharacteristic, direct product factor, Sylow
445C2—21no—
446C2—21no—
447C2—42no—
448C2C3×#6511111yescharacteristic
449C2C3×#6511511yescharacteristic
450C2C3×#6523911yescharacteristic
subgroupG/H
centerC22×C3#4028
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#104D5
hypocenterC5C3×#1859
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C3×#65410C2semidirect
5. C3×#65224C2semidirect
6. C3×#64774C2semidirect
7. C3×#64743C2semidirect
8. #10601156C3direct (N × H)
22. C3×C5×#104C4semidirect
31. #65410C2×C3semidirect
32. #65224C2×C3semidirect
33. #64774C2×C3semidirect
34. #64743C2×C3semidirect
49. C3×C5×M16C2×C4semidirect
52. C3×C42×C5C2×C4semidirect
88. C5×#104C3×C4semidirect
97. C3×C5×Q8C4⋊C4semidirect
101. C3×C5×D4C4⋊C4semidirect
138. C3×#104Dic5semidirect
155. C5×M16C2×C3×C4semidirect
158. C42×C5C2×C3×C4semidirect
215. C3×M16C2×Dic5semidirect
231. C3×C42C2×Dic5semidirect
235. C5×Q8C3×C4⋊C4semidirect
239. C5×D4C3×C4⋊C4semidirect
276. #104C3×Dic5semidirect
288. C3×Q8C4⋊Dic5semidirect
292. C3×D4C4⋊Dic5semidirect
348. M16C2×C3×Dic5semidirect
364. C42C2×C3×Dic5semidirect
365. C3×C5#1859semidirect
393. Q8C3×C4⋊Dic5semidirect
397. D4C3×C4⋊Dic5semidirect
425. C5C3×#1859semidirect
444. C3#10601156direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661612
C2×C3×C5×#1042
C3×#655212
C3×#654102
C3×#652242
C3×#647742
C3×#647432
#106011563
C3×#18595