Finite Group Databasebeta

← C3×#10599552 #14301436

Subgroups — C3×#10599552 #14301436

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65855C211yesmaximal, characteristic
2C2×C3×#4021C211yesmaximal, characteristic
3C2×C3×#3955C211yesmaximal, characteristic
4C3×#65409C211yesmaximal, characteristic, complemented
5C3×#65293C211yesmaximal, characteristic, complemented
6C3×C5×#339C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599552C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×C3×#685—22no—
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4039—22no—
18C3×D5×C22⋊C4—22no—
19C3×#4021—22no—
20C3×#4021C414yescomplemented
21C3×C4×D20—22no—
22C3×#3955—22no—
23C3×#3948—22no—
24C3×#3942—22no—
25C3×#1885—51nomaximal, Hall
26#65855C2×C311yescharacteristic
27C2×#4021C2×C311yescharacteristic
28C2×#3955C2×C311yescharacteristic
29#65409C2×C311yescharacteristic, complemented
30#65293C2×C311yescharacteristic, complemented
31C5×#339C2×C311yescharacteristic, complemented
32#64743C2×C311yescharacteristic, complemented
33C23×C3×D5D412yes—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×Dic5—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20C2×C412yes—
42C2×C3×D20D412yes—
43C2×C3×C4×D5—24no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10C2×C412yescomplemented
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4D412yes—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5—21no—
56C3×C42×C5—21no—
57C3×C42×C5C2×C412yescomplemented
58C3×C22⋊Dic5—21no—
59C3×#685—24no—
60C3×#685—28no—
61C3×C4⋊Dic5D412yes—
62C3×C4×Dic5—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66C2×C3×#124—51no—
67C3×#518—51no—
68C3×#419—51no—
69C3×#419—51no—
70C2×C3×#100—51no—
71C3×#339—51no—
72C3×#339D511yescharacteristic, complemented
73C22×D20C22×C311yescharacteristic
74C22×Dic10C22×C311yescharacteristic
75C2×C5×M16C22×C311yescharacteristic
76C5×#117C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78C2×#685—22no—
79#4072C22×C311yescharacteristic
80C2×#681C22×C311yescharacteristic
81#4039—22no—
82D5×C22⋊C4—22no—
83#4021—22no—
84#4021C3×C414yescomplemented
85C4×D20—22no—
86#3955—22no—
87#3948—22no—
88#3942—22no—
89#1885—51noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5—44no—
94C22×C3×D5C22⋊C414yes—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5—42no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×Dic5—22no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—41no—
108C3×D20—22no—
109C3×D20—22no—
110C3×D20—22no—
111C3×D20—22no—
112C3×C4×D5—84no—
113C3×Dic10—22no—
114C3×Dic10—22no—
115C3×Dic10—41no—
116C3×Dic10—41no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C22×C3×Q8—51no—
120C22×C3×D4—51no—
121C2×C3×M16—51no—
122C2×C3×M16C2×D511yescharacteristic
123C3×#124—54no—
124C3×#124—102no—
125C3×C4×D4—102no—
126C3×C4×D4—102no—
127C3×#117—51no—
128C3×#117C2×D511yescharacteristic
129C2×C3×C22⋊C4—102no—
130C2×C3×C22⋊C4—102no—
131C2×C3×C42C2×D511yescharacteristic
132C3×#103—102no—
133C3×#103—102no—
134C3×#100—102no—
135C23×D5C3×D412yes—
136C22×C4×C5—21no—
137C22×C4×C5C23×C311yescharacteristic
138C22×Dic5—21no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20C2×C3×C412yes—
144C2×D20C3×D412yes—
145C2×C4×D5—24no—
146C2×Dic10—21no—
147C2×Dic10—21no—
148C2×Dic10—21no—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10C2×C3×C412yescomplemented
152C5×M16—21no—
153C5×M16—21no—
154C2×C5×C8—21no—
155C5×C4⋊C4C3×D412yes—
156C5×C22⋊C4—21no—
157C42×C5—21no—
158C42×C5—21no—
159C42×C5C2×C3×C412yescomplemented
160C22⋊Dic5—21no—
161#685—24no—
162#685—28no—
163C4⋊Dic5C3×D412yes—
164C4×Dic5—21no—
165#681—21no—
166#681—21no—
167C2×#168—21no—
168C2×#124—51no—
169#518—51no—
170#419—51no—
171#419—51no—
172C2×#100—51no—
173#339—51no—
174#339C3×D511yescharacteristic, complemented
175C22×C3×C5—22no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12011yescharacteristic
178C22×C3×C5#12311yescharacteristic
179C2×C3×D5—24no—
180C2×C3×D5—44no—
181C2×C3×D5—44no—
182C2×C3×D5—82no—
183C3×C4×C5—42no—
184C3×C4×C5—42no—
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5#12111yescharacteristic
188C3×C4×C5#12111yescharacteristic
189C3×Dic5—42no—
190C3×Dic5—42no—
191C24×C3—52no—
192C2×C3×Q8—52no—
193C2×C3×Q8—101no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C2×C3×D4—52no—
199C2×C3×D4—52no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—101no—
204C22×C3×C4—21no—
205C22×C3×C4—104no—
206C22×C3×C4—101no—
207C22×C3×C4C22×D511yescharacteristic
208C3×M16—21no—
209C3×M16—21no—
210C3×M16—101no—
211C3×M16—101no—
212C2×C3×C8—21no—
213C2×C3×C8—101no—
214C3×C4⋊C4—52no—
215C3×C4⋊C4D2012yes—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—108no—
218C3×C22⋊C4—104no—
219C3×C22⋊C4—101no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—101no—
223C3×C42C4×D512yescomplemented
224C23×C5C2×C3×D411yescharacteristic
225C22×D5—22no—
226C22×D5—22no—
227C22×D5—44no—
228C22×D5C3×C22⋊C414yes—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—42no—
232C2×C4×C5C22×C3×C411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C2×C4×C5C2×C3×D411yescharacteristic
236C2×C4×C5C3×#4111yescharacteristic
237C2×C4×C5C3×#4111yescharacteristic
238C2×Dic5—22no—
239C2×Dic5—22no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242D20—22no—
243D20—22no—
244D20—22no—
245D20—22no—
246C4×D5—84no—
247Dic10—22no—
248Dic10—22no—
249Dic10—41no—
250Dic10—41no—
251C5×C8—41no—
252#168—41no—
253C22×Q8—51no—
254C22×D4—51no—
255C2×M16—51no—
256C2×M16C2×C3×D511yescharacteristic
257#124—54no—
258#124—102no—
259C4×D4—102no—
260C4×D4—102no—
261#117—51no—
262#117C2×C3×D511yescharacteristic
263C2×C22⋊C4—102no—
264C2×C22⋊C4—102no—
265C2×C42C2×C3×D511yescharacteristic
266#103—102no—
267#103—102no—
268#100—102no—
269C2×C3×C5—21no—
270C2×C3×C5—21no—
271C2×C3×C5#38611yescharacteristic
272C2×C3×C5#45512yes—
273C3×D5—44no—
274C23×C3—54no—
275C23×C3—102no—
276C23×C3—102no—
277C23×C3—204no—
278C23×C3D4×D511yescharacteristic
279C3×Q8—102no—
280C3×Q8—102no—
281C3×Q8—201no—
282C3×Q8—201no—
283C3×D4—102no—
284C3×D4—102no—
285C3×D4—102no—
286C3×D4—102no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—42no—
290C2×C3×C4—102no—
291C2×C3×C4—102no—
292C2×C3×C4—201no—
293C2×C3×C4—201no—
294C2×C3×C4—404no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4#70911yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4#71311yescharacteristic
301C3×C8—41no—
302C3×C8—201no—
303C22×C5—22no—
304C22×C5C2×C3×C22⋊C411yescharacteristic
305C22×C5C3×#12011yescharacteristic
306C22×C5C3×#12311yescharacteristic
307C2×D5—24no—
308C2×D5—44no—
309C2×D5—44no—
310C2×D5—82no—
311C4×C5—42no—
312C4×C5—42no—
313C4×C5C3×C4×D411yescharacteristic
314C4×C5C3×C4×D411yescharacteristic
315C4×C5C3×#12111yescharacteristic
316C4×C5C3×#12111yescharacteristic
317Dic5—42no—
318Dic5—42no—
319C24—52no—
320C2×Q8—52no—
321C2×Q8—101no—
322C2×Q8—101no—
323C2×Q8—101no—
324C2×Q8—101no—
325C2×Q8—101no—
326C2×D4—52no—
327C2×D4—52no—
328C2×D4—101no—
329C2×D4—101no—
330C2×D4—101no—
331C2×D4—101no—
332C22×C4—21no—
333C22×C4—104no—
334C22×C4—101no—
335C22×C4C22×C3×D511yescharacteristic
336M16—21no—
337M16—21no—
338M16—101no—
339M16—101no—
340C2×C8—21no—
341C2×C8—101no—
342C4⋊C4—52no—
343C4⋊C4C3×D2012yes—
344C22⋊C4—21no—
345C22⋊C4—108no—
346C22⋊C4—104no—
347C22⋊C4—101no—
348C42—21no—
349C42—21no—
350C42—101no—
351C42C3×C4×D512yescomplemented
352C3×C5#188511yescharacteristic, complemented, Hall
353C22×C3—22no—
354C22×C3—104no—
355C22×C3—204no—
356C22×C3—204no—
357C22×C3—402no—
358C22×C3D5×C22⋊C411yescharacteristic
359C22×C3#402811yescharacteristic
360C22×C3#404011yescharacteristic
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—202no—
364C3×C4—202no—
365C3×C4C4×D2011yescharacteristic
366C3×C4#403011yescharacteristic
367C3×C4#403911yescharacteristic
368C3×C4#404111yescharacteristic
369C2×C5—21no—
370C2×C5—21no—
371C2×C5C3×#38611yescharacteristic
372C2×C5C3×#45512yes—
373D5—44no—
374C23—54no—
375C23—102no—
376C23—102no—
377C23—204no—
378C23C3×D4×D511yescharacteristic
379Q8—102no—
380Q8—102no—
381Q8—201no—
382Q8—201no—
383D4—102no—
384D4—102no—
385D4—102no—
386D4—102no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—102no—
391C2×C4—102no—
392C2×C4—201no—
393C2×C4—201no—
394C2×C4—404no—
395C2×C4C2×C3×C4×D511yescharacteristic
396C2×C4C2×C3×D2011yescharacteristic
397C2×C4C3×#70911yescharacteristic
398C2×C4C3×D4×D511yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C2×C4C3×#71311yescharacteristic
401C8—41no—
402C8—201no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—204no—
406C2×C3#6495411yescharacteristic
407C2×C3#6511412yes—
408C5C3×#188511yescharacteristic, complemented, Sylow
409C22—22no—
410C22—104no—
411C22—204no—
412C22—204no—
413C22—402no—
414C22C3×D5×C22⋊C411yescharacteristic
415C22C3×#402811yescharacteristic
416C22C3×#404011yescharacteristic
417C4—42no—
418C4—42no—
419C4—202no—
420C4—202no—
421C4C3×C4×D2011yescharacteristic
422C4C3×#403011yescharacteristic
423C4C3×#403911yescharacteristic
424C4C3×#404111yescharacteristic
425C3#1059955211yescharacteristic, direct product factor, Sylow
426C2—21no—
427C2—21no—
428C2—204no—
429C2C3×#6495411yescharacteristic
430C2C3×#6511412yes—
subgroupG/H
centerC22×C3#4028
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#339D5
hypocenterC5C3×#1885
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
4. C3×#65409C2semidirect
5. C3×#65293C2semidirect
6. C3×C5×#339C2semidirect
7. C3×#64743C2semidirect
8. #10599552C3direct (N × H)
20. C3×#4021C4semidirect
29. #65409C2×C3semidirect
30. #65293C2×C3semidirect
31. C5×#339C2×C3semidirect
32. #64743C2×C3semidirect
49. C2×C3×Dic10C2×C4semidirect
57. C3×C42×C5C2×C4semidirect
72. C3×#339D5semidirect
84. #4021C3×C4semidirect
151. C2×Dic10C2×C3×C4semidirect
159. C42×C5C2×C3×C4semidirect
174. #339C3×D5semidirect
223. C3×C42C4×D5semidirect
351. C42C3×C4×D5semidirect
352. C3×C5#1885semidirect
408. C5C3×#1885semidirect
425. C3#10599552direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658552
C2×C3×#40212
C2×C3×#39552
C3×#654092
C3×#652932
C3×C5×#3392
C3×#647432
#105995523
C3×#18855