Finite Group Databasebeta

← C3×#10601136 #14301430

Subgroups — C3×#10601136 #14301430

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
1C2×C3×#4093C211yesmaximal, characteristic
2C3×#65855C211yesmaximal, characteristic
3C3×C5×#419C211yesmaximal, characteristic, complemented
4C3×#65514C211yesmaximal, characteristic, complemented
5C2×C3×#3955C211yesmaximal, characteristic
6C3×#64775C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10601136C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C3×#4093—22no—
14C3×#4093C414yescomplemented
15C2×C3×#685—22no—
16C3×#4072C2211yescharacteristic
17C2×C3×C4×Dic5C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C3×#4039—22no—
20C3×D5×C22⋊C4—22no—
21C3×C4×D20—22no—
22C3×C5×#103—22no—
23C3×#3967—22no—
24C3×#3955—22no—
25C3×#1885—51nomaximal, Hall
26C2×#4093C2×C311yescharacteristic
27#65855C2×C311yescharacteristic
28C5×#419C2×C311yescharacteristic, complemented
29#65514C2×C311yescharacteristic, complemented
30C2×#3955C2×C311yescharacteristic
31#64775C2×C311yescharacteristic, complemented
32#64752C2×C311yescharacteristic, complemented
33C23×C3×D5D412yes—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8C2×C412yescomplemented
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×Dic5—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20C2×C412yes—
48C2×C3×D20D412yes—
49C2×C3×C4×D5—24no—
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×C22⋊Dic5—21no—
57C3×#685—24no—
58C3×#685—28no—
59C3×C4⋊Dic5D412yes—
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5C2×C412yescomplemented
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66C2×C3×#124—51no—
67C3×#518—51no—
68C3×#419—51no—
69C3×#419D511yescharacteristic, complemented
70C2×C3×#100—51no—
71C3×#339—51no—
72C3×#339—51no—
73C22×C5×Q8C22×C311yescharacteristic
74C22×D20C22×C311yescharacteristic
75C2×C5×M16C22×C311yescharacteristic
76C5×#117C22×C311yescharacteristic
77#4093—22no—
78#4093C3×C414yescomplemented
79C2×#685—22no—
80#4072C22×C311yescharacteristic
81C2×C4×Dic5C22×C311yescharacteristic
82C2×#681C22×C311yescharacteristic
83#4039—22no—
84D5×C22⋊C4—22no—
85C4×D20—22no—
86C5×#103—22no—
87#3967—22no—
88#3955—22no—
89#1885—51noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5—44no—
94C22×C3×D5C22⋊C414yes—
95C3×C5×Q8—22no—
96C3×C5×Q8—22no—
97C3×C5×Q8—41no—
98C3×C5×Q8—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×Dic5—22no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—42no—
112C3×D20—22no—
113C3×D20—22no—
114C3×D20—22no—
115C3×D20—22no—
116C3×C4×D5—84no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C22×C3×Q8C2×D511yescharacteristic
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×C42—51no—
132C3×#103—22no—
133C3×#103—102no—
134C3×#100—102no—
135C23×D5C3×D412yes—
136C2×C5×Q8—21no—
137C2×C5×Q8—21no—
138C2×C5×Q8—21no—
139C2×C5×Q8—21no—
140C2×C5×Q8—21no—
141C2×C5×Q8C2×C3×C412yescomplemented
142C22×C4×C5—21no—
143C22×C4×C5C23×C311yescharacteristic
144C22×Dic5—21no—
145C2×D20—21no—
146C2×D20—21no—
147C2×D20—21no—
148C2×D20—21no—
149C2×D20C2×C3×C412yes—
150C2×D20C3×D412yes—
151C2×C4×D5—24no—
152C5×M16—21no—
153C5×M16—21no—
154C2×C5×C8—21no—
155C5×C4⋊C4C3×D412yes—
156C5×C22⋊C4—21no—
157C42×C5—21no—
158C22⋊Dic5—21no—
159#685—24no—
160#685—28no—
161C4⋊Dic5C3×D412yes—
162C4×Dic5—21no—
163C4×Dic5—21no—
164C4×Dic5C2×C3×C412yescomplemented
165#681—21no—
166#681—21no—
167C2×#168—21no—
168C2×#124—51no—
169#518—51no—
170#419—51no—
171#419C3×D511yescharacteristic, complemented
172C2×#100—51no—
173#339—51no—
174#339—51no—
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—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8C4×D512yescomplemented
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⋊C4C22⋊D512yes—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—108no—
218C3×C22⋊C4—104no—
219C3×C22⋊C4—101no—
220C3×C42—21no—
221C3×C42—52no—
222C3×C42—101no—
223C3×C42—101no—
224C23×C5C2×C3×D411yescharacteristic
225C22×D5—22no—
226C22×D5—22no—
227C22×D5—44no—
228C22×D5C3×C22⋊C414yes—
229C5×Q8—22no—
230C5×Q8—22no—
231C5×Q8—41no—
232C5×Q8—41no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5C22×C3×C411yescharacteristic
238C2×C4×C5C2×C3×D411yescharacteristic
239C2×C4×C5C2×C3×D411yescharacteristic
240C2×C4×C5C2×C3×D411yescharacteristic
241C2×C4×C5C3×#4111yescharacteristic
242C2×C4×C5C3×#4111yescharacteristic
243C2×Dic5—22no—
244C2×Dic5—22no—
245C2×Dic5—42no—
246D20—22no—
247D20—22no—
248D20—22no—
249D20—22no—
250C4×D5—84no—
251C5×C8—41no—
252#168—41no—
253C22×Q8C2×C3×D511yescharacteristic
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×C42—51no—
266#103—22no—
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—22no—
280C3×Q8—22no—
281C3×Q8—41no—
282C3×Q8—41no—
283C3×D4—102no—
284C3×D4—102no—
285C3×D4—102no—
286C3×D4—102no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—102no—
292C2×C3×C4—102no—
293C2×C3×C4—202no—
294C2×C3×C4—404no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4#70911yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4#71111yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
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—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8C3×C4×D512yescomplemented
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×C22⋊D512yes—
344C22⋊C4—21no—
345C22⋊C4—108no—
346C22⋊C4—104no—
347C22⋊C4—101no—
348C42—21no—
349C42—52no—
350C42—101no—
351C42—101no—
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#402911yescharacteristic
360C22×C3#408311yescharacteristic
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—202no—
364C3×C4—202no—
365C3×C4#402711yescharacteristic
366C3×C4#403011yescharacteristic
367C3×C4C4×C22⋊D511yescharacteristic
368C3×C4#408411yescharacteristic
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—22no—
380Q8—22no—
381Q8—41no—
382Q8—41no—
383D4—102no—
384D4—102no—
385D4—102no—
386D4—102no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—102no—
392C2×C4—102no—
393C2×C4—202no—
394C2×C4—404no—
395C2×C4C2×C3×C4×D511yescharacteristic
396C2×C4C3×#70911yescharacteristic
397C2×C4C3×D4×D511yescharacteristic
398C2×C4C3×D4×D511yescharacteristic
399C2×C4C3×#71111yescharacteristic
400C2×C4C2×C3×C22⋊D511yescharacteristic
401C8—41no—
402C8—201no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—204no—
406C2×C3#6524511yescharacteristic
407C2×C3#6549112yes—
408C5C3×#188511yescharacteristic, complemented, Sylow
409C22—22no—
410C22—104no—
411C22—204no—
412C22—204no—
413C22—402no—
414C22C3×D5×C22⋊C411yescharacteristic
415C22C3×#402911yescharacteristic
416C22C3×#408311yescharacteristic
417C4—42no—
418C4—42no—
419C4—202no—
420C4—202no—
421C4C3×#402711yescharacteristic
422C4C3×#403011yescharacteristic
423C4C3×C4×C22⋊D511yescharacteristic
424C4C3×#408411yescharacteristic
425C3#1060113611yescharacteristic, direct product factor, Sylow
426C2—21no—
427C2—21no—
428C2—204no—
429C2C3×#6524511yescharacteristic
430C2C3×#6549112yes—
subgroupG/H
centerC22×C3#4083
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#419C2
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#419D5
hypocenterC5C3×#1885
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
3. C3×C5×#419C2semidirect
4. C3×#65514C2semidirect
6. C3×#64775C2semidirect
7. C3×#64752C2semidirect
8. #10601136C3direct (N × H)
14. C3×#4093C4semidirect
28. C5×#419C2×C3semidirect
29. #65514C2×C3semidirect
31. #64775C2×C3semidirect
32. #64752C2×C3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
62. C3×C4×Dic5C2×C4semidirect
69. C3×#419D5semidirect
78. #4093C3×C4semidirect
141. C2×C5×Q8C2×C3×C4semidirect
164. C4×Dic5C2×C3×C4semidirect
171. #419C3×D5semidirect
197. C2×C3×Q8C4×D5semidirect
325. C2×Q8C3×C4×D5semidirect
352. C3×C5#1885semidirect
408. C5C3×#1885semidirect
425. C3#10601136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40932
C3×#658552
C3×C5×#4192
C3×#655142
C2×C3×#39552
C3×#647752
C3×#647522
#106011363
C3×#18855