Finite Group Databasebeta

← C3×#10601091 #14299782

Subgroups — C3×#10601091 #14299782

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66161C211yesmaximal, characteristic
2C3×C5×#417C211yesmaximal, characteristic
3C2×C3×#3969C211yesmaximal, characteristic
4C3×#65266C211yesmaximal, characteristic, complemented
5C3×#65253C211yesmaximal, characteristic, complemented
6C3×#64775C211yesmaximal, characteristic, complemented
7C3×#64774C211yesmaximal, characteristic, complemented
8#10601091C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
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⋊Dic5C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C3×C5×#103—21no—
22C3×C5×#102—21no—
23C3×#3969C414yescomplemented
24C3×#3963—22no—
25C3×#3940—21no—
26C3×#3939—21no—
27C3×#1860—51nomaximal, Hall
28#66161C2×C311yescharacteristic
29C5×#417C2×C311yescharacteristic
30C2×#3969C2×C311yescharacteristic
31#65266C2×C311yescharacteristic, complemented
32#65253C2×C311yescharacteristic, complemented
33#64775C2×C311yescharacteristic, complemented
34#64774C2×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—21no—
46C22×C3×Dic5—22no—
47C22×C3×Dic5D412yes—
48C3×C5×M16—21no—
49C3×C5×M16—21no—
50C2×C3×C5×C8—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5—22no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4×Dic5—22no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5C2×C412yescomplemented
64C3×#681—21no—
65C3×#681C2×C412yescomplemented
66C2×C3×#168—21no—
67C3×#520—51no—
68C3×#428—51no—
69C2×C3×#104—51no—
70C3×#417D511yescharacteristic
71C3×#382—51no—
72C3×#343—51no—
73C3×#339—51no—
74C2×C5×#41C22×C311yescharacteristic
75C2×C5×M16C22×C311yescharacteristic
76C2×C5×C4⋊C4C22×C311yescharacteristic
77Q8×Dic5—21no—
78D4×Dic5—21no—
79D4×Dic5—22no—
80#4072—21no—
81#4072C22×C311yescharacteristic
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5C22×C311yescharacteristic
84C2×C4×Dic5C22×C311yescharacteristic
85C2×#681C22×C311yescharacteristic
86C5×#103—21no—
87C5×#102—21no—
88#3969C3×C414yescomplemented
89#3963—22no—
90#3940—21no—
91#3939—21no—
92#1860—51noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×Q8—21no—
96C3×C5×Q8C4⋊C412yes—
97C3×C5×D4—22no—
98C3×C5×D4—22no—
99C3×C5×D4—21no—
100C3×C5×D4C4⋊C412yes—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×Q811yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—42no—
119C2×C3×Dic5—82no—
120C3×C5×C8—41no—
121C3×#168—22no—
122C2×C3×#41C2×D511yescharacteristic
123C2×C3×M16—51no—
124C2×C3×M16C2×D511yescharacteristic
125C3×C4×Q8—101no—
126C3×C4×D4—102no—
127C3×C4×D4—101no—
128C3×#117—51no—
129C3×#117—101no—
130C2×C3×C4⋊C4—51no—
131C2×C3×C4⋊C4—101no—
132C2×C3×C4⋊C4C2×D511yescharacteristic
133C2×C3×C42—51no—
134C3×#107—101no—
135C3×#106—101no—
136C3×#104—54no—
137C3×#103—21no—
138C3×#102—21no—
139C3×#95—102no—
140C5×#41—21no—
141C5×#41—21no—
142C5×#41C2×C3×C412yes—
143C5×#41C3×Q812yes—
144C2×C5×Q8C3×D411yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4C3×D411yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5C23×C311yescharacteristic
150C22×Dic5—21no—
151C22×Dic5—22no—
152C22×Dic5C3×D412yes—
153C5×M16—21no—
154C5×M16—21no—
155C2×C5×C8—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C22⋊Dic5—22no—
159C22⋊Dic5—21no—
160C4⋊Dic5—22no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163C4⋊Dic5C3×D411yescharacteristic
164C4⋊Dic5C3×D411yescharacteristic
165C4×Dic5—22no—
166C4×Dic5—21no—
167C4×Dic5—21no—
168C4×Dic5C2×C3×C412yescomplemented
169#681—21no—
170#681C2×C3×C412yescomplemented
171C2×#168—21no—
172#520—51no—
173#428—51no—
174C2×#104—51no—
175#417C3×D511yescharacteristic
176#382—51no—
177#343—51no—
178#339—51no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—22no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5C4×D411yescharacteristic
185C22×C3×C5#12011yescharacteristic
186C22×C3×C5C22⋊Q811yescharacteristic
187C3×C4×C5—22no—
188C3×C4×C5—81no—
189C3×C4×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12311yescharacteristic
193C3×Dic5—42no—
194C3×Dic5—41no—
195C3×Dic5—42no—
196C3×Dic5—41no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41Dic1012yes—
200C3×#41C4×D512yes—
201C2×C3×Q8C22⋊D511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C22⋊D511yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—52no—
207C22×C3×C4—101no—
208C22×C3×C4—102no—
209C22×C3×C4C22×D511yescharacteristic
210C3×M16—21no—
211C3×M16—21no—
212C3×M16—52no—
213C3×M16—101no—
214C2×C3×C8—21no—
215C2×C3×C8—101no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—51no—
219C3×C4⋊C4—51no—
220C3×C4⋊C4—102no—
221C3×C4⋊C4—101no—
222C3×C4⋊C4—101no—
223C3×C22⋊C4—102no—
224C3×C22⋊C4—101no—
225C3×C42—52no—
226C3×C42—102no—
227C3×C42—101no—
228C3×C42—101no—
229C23×C5—21no—
230C23×C5C2×C3×D411yescharacteristic
231C5×Q8—21no—
232C5×Q8C3×C4⋊C412yes—
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—21no—
236C5×D4C3×C4⋊C412yes—
237C2×C4×C5—21no—
238C2×C4×C5—22no—
239C2×C4×C5—22no—
240C2×C4×C5—42no—
241C2×C4×C5—41no—
242C2×C4×C5C22×C3×C411yescharacteristic
243C2×C4×C5C2×C3×D411yescharacteristic
244C2×C4×C5C2×C3×D411yescharacteristic
245C2×C4×C5C2×C3×Q811yescharacteristic
246C2×C4×C5C3×#4111yescharacteristic
247C2×C4×C5C3×#4111yescharacteristic
248C2×Dic5—22no—
249C2×Dic5—21no—
250C2×Dic5—22no—
251C2×Dic5—21no—
252C2×Dic5—41no—
253C2×Dic5—41no—
254C2×Dic5—42no—
255C2×Dic5—82no—
256C5×C8—41no—
257#168—22no—
258C2×#41C2×C3×D511yescharacteristic
259C2×M16—51no—
260C2×M16C2×C3×D511yescharacteristic
261C4×Q8—101no—
262C4×D4—102no—
263C4×D4—101no—
264#117—51no—
265#117—101no—
266C2×C4⋊C4—51no—
267C2×C4⋊C4—101no—
268C2×C4⋊C4C2×C3×D511yescharacteristic
269C2×C42—51no—
270#107—101no—
271#106—101no—
272#104—54no—
273#103—21no—
274#102—21no—
275#95—102no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5—42no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C2×C3×C5#45511yescharacteristic
282C23×C3—21no—
283C23×C3D4×D511yescharacteristic
284C3×Q8—21no—
285C3×Q8#68312yes—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—21no—
289C3×D4#68312yes—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—42no—
294C2×C3×C4—41no—
295C2×C3×C4—102no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—102no—
299C2×C3×C4—201no—
300C2×C3×C4—201no—
301C2×C3×C4—202no—
302C2×C3×C4—402no—
303C2×C3×C4C2×Dic1011yescharacteristic
304C2×C3×C4C2×C4×D511yescharacteristic
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4#71111yescharacteristic
307C2×C3×C4#71111yescharacteristic
308C2×C3×C4C2×C22⋊D511yescharacteristic
309C3×C8—41no—
310C3×C8—102no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—22no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5C3×C4×D411yescharacteristic
317C22×C5C3×#12011yescharacteristic
318C22×C5C3×C22⋊Q811yescharacteristic
319C4×C5—22no—
320C4×C5—81no—
321C4×C5C2×C3×C4⋊C411yescharacteristic
322C4×C5C3×C4×D411yescharacteristic
323C4×C5C3×C22⋊Q811yescharacteristic
324C4×C5C3×#12311yescharacteristic
325Dic5—42no—
326Dic5—41no—
327Dic5—42no—
328Dic5—41no—
329#41—21no—
330#41—21no—
331#41C3×Dic1012yes—
332#41C3×C4×D512yes—
333C2×Q8C3×C22⋊D511yescharacteristic
334C2×D4—21no—
335C2×D4C3×C22⋊D511yescharacteristic
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—52no—
339C22×C4—101no—
340C22×C4—102no—
341C22×C4C22×C3×D511yescharacteristic
342M16—21no—
343M16—21no—
344M16—52no—
345M16—101no—
346C2×C8—21no—
347C2×C8—101no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—51no—
351C4⋊C4—51no—
352C4⋊C4—102no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C22⋊C4—102no—
356C22⋊C4—101no—
357C42—52no—
358C42—102no—
359C42—101no—
360C42—101no—
361C3×C5#186011yescharacteristic, complemented, Hall
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3#402411yescharacteristic
368C22×C3#402711yescharacteristic
369C22×C3#408311yescharacteristic
370C3×C4—22no—
371C3×C4—81no—
372C3×C4—202no—
373C3×C4—201no—
374C3×C4—202no—
375C3×C4—201no—
376C3×C4#402411yescharacteristic
377C3×C4#402711yescharacteristic
378C3×C4C2×#68311yescharacteristic
379C3×C4#408111yescharacteristic
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—42no—
383C2×C5C3×#38511yescharacteristic
384C2×C5C3×#45411yescharacteristic
385C2×C5C3×#45511yescharacteristic
386C23—21no—
387C23C3×D4×D511yescharacteristic
388Q8—21no—
389Q8C3×#68312yes—
390D4—22no—
391D4—22no—
392D4—21no—
393D4C3×#68312yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—102no—
402C2×C4—102no—
403C2×C4—201no—
404C2×C4—201no—
405C2×C4—202no—
406C2×C4—402no—
407C2×C4C2×C3×Dic1011yescharacteristic
408C2×C4C2×C3×C4×D511yescharacteristic
409C2×C4C3×D4×D511yescharacteristic
410C2×C4C3×#71111yescharacteristic
411C2×C4C3×#71111yescharacteristic
412C2×C4C2×C3×C22⋊D511yescharacteristic
413C8—41no—
414C8—102no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—42no—
418C2×C3#6523511yescharacteristic
419C2×C3#6549011yescharacteristic
420C2×C3#6549111yescharacteristic
421C5C3×#186011yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22C3×#402411yescharacteristic
428C22C3×#402711yescharacteristic
429C22C3×#408311yescharacteristic
430C4—22no—
431C4—81no—
432C4—202no—
433C4—201no—
434C4—202no—
435C4—201no—
436C4C3×#402411yescharacteristic
437C4C3×#402711yescharacteristic
438C4C2×C3×#68311yescharacteristic
439C4C3×#408111yescharacteristic
440C3#1060109111yescharacteristic, direct product factor, Sylow
441C2—21no—
442C2—21no—
443C2—42no—
444C2C3×#6523511yescharacteristic
445C2C3×#6549011yescharacteristic
446C2C3×#6549111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#417C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#417D5
hypocenterC5C3×#1860
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
4. C3×#65266C2semidirect
5. C3×#65253C2semidirect
6. C3×#64775C2semidirect
7. C3×#64774C2semidirect
8. #10601091C3direct (N × H)
23. C3×#3969C4semidirect
31. #65266C2×C3semidirect
32. #65253C2×C3semidirect
33. #64775C2×C3semidirect
34. #64774C2×C3semidirect
63. C3×C4×Dic5C2×C4semidirect
65. C3×#681C2×C4semidirect
88. #3969C3×C4semidirect
168. C4×Dic5C2×C3×C4semidirect
170. #681C2×C3×C4semidirect
361. C3×C5#1860semidirect
421. C5C3×#1860semidirect
440. C3#10601091direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661612
C3×C5×#4172
C2×C3×#39692
C3×#652662
C3×#652532
C3×#647752
C3×#647742
#106010913
C3×#18605