Finite Group Databasebeta

← C3×#10599523 #14307121

Subgroups — C3×#10599523 #14307121

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65851C211yesmaximal, characteristic
2C3×M16×Dic5C211yesmaximal, characteristic
3C3×C4×#683C211yesmaximal, characteristic
4C3×C5×#339C211yesmaximal, characteristic
5C3×#64775C211yesmaximal, characteristic
6C3×#64752C211yesmaximal, characteristic
7C3×#64743C211yesmaximal, characteristic
8#10599523C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×M16C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C3×#4072C2211yescharacteristic
13C2×C3×#683—21no—
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C3×#4036C411yescharacteristic, complemented
18C3×#4036C411yescharacteristic, complemented
19C3×#4034C411yescharacteristic, complemented
20C3×#4034C411yescharacteristic, complemented
21C3×#4024—21no—
22C3×#4024—21no—
23C3×C4×Dic10—21no—
24C3×C4×Dic10—21no—
25C3×#3963—21no—
26C3×#3947—21no—
27C3×C8×Dic5—21no—
28C3×#1986—51nomaximal, Hall
29#65851C2×C311yescharacteristic
30M16×Dic5C2×C311yescharacteristic
31C4×#683C2×C311yescharacteristic
32C5×#339C2×C311yescharacteristic
33#64775C2×C311yescharacteristic
34#64752C2×C311yescharacteristic
35#64743C2×C311yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×C3×Dic5—21no—
39C22×C3×Dic5D411yescharacteristic
40C22×C3×Dic5D411yescharacteristic
41C2×C3×Dic10—21no—
42C2×C3×Dic10—21no—
43C3×C5×M16—21no—
44C3×C5×M16Q812yescomplemented
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51C3×C42×C5—21no—
52C3×C22⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—24no—
58C3×#683—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5—21no—
64C3×C4×Dic5—21no—
65C3×C4×Dic5C2×C411yescharacteristic
66C3×C4×Dic5C2×C411yescharacteristic
67C3×C4×Dic5D411yescharacteristic
68C3×C4×Dic5D411yescharacteristic
69C3×#681—21no—
70C3×#681Q812yescomplemented
71C2×C3×#168—21no—
72C3×#533—51no—
73C3×C4×M16—51no—
74C3×C4×C4⋊C4—51no—
75C3×#339—51no—
76C3×#339—51no—
77C3×#339—51no—
78C3×#339D511yescharacteristic
79C2×C5×M16C22×C311yescharacteristic
80C5×#117C22×C311yescharacteristic
81C2×C42×C5C22×C311yescharacteristic
82#4072C22×C311yescharacteristic
83C2×#683—21no—
84C2×C4×Dic5C22×C311yescharacteristic
85C2×C4×Dic5C22×C311yescharacteristic
86C2×#681C22×C311yescharacteristic
87#4036C3×C411yescharacteristic, complemented
88#4036C3×C411yescharacteristic, complemented
89#4034C3×C411yescharacteristic, complemented
90#4034C3×C411yescharacteristic, complemented
91#4024—21no—
92#4024—21no—
93C4×Dic10—21no—
94C4×Dic10—21no—
95#3963—21no—
96#3947—21no—
97C8×Dic5—21no—
98#1986—51noSylow
99C23×C3×C5C2×D411yescharacteristic
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×Q811yescharacteristic
108C2×C3×C4×C5C2×Q811yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×Dic5—22no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×Dic10—42no—
123C3×Dic10—42no—
124C3×C5×C8—22no—
125C3×#168—22no—
126C2×C3×M16—51no—
127C2×C3×M16C2×D511yescharacteristic
128C3×C4⋊Q8—51no—
129C3×C4⋊Q8—51no—
130C3×#125—51no—
131C3×#125—51no—
132C3×C22⋊Q8—101no—
133C3×C22⋊Q8—101no—
134C3×C4×Q8—101no—
135C3×C4×Q8—101no—
136C3×#117—51no—
137C3×#117C2×D511yescharacteristic
138C2×C3×C4⋊C4—101no—
139C2×C3×C42—51no—
140C2×C3×C42—51no—
141C2×C3×C42C2×D511yescharacteristic
142C3×#97—101no—
143C3×C4×C8—101no—
144C3×#95—101no—
145C22×C4×C5—21no—
146C22×C4×C5C23×C311yescharacteristic
147C22×Dic5—21no—
148C22×Dic5C3×D411yescharacteristic
149C22×Dic5C3×D411yescharacteristic
150C2×Dic10—21no—
151C2×Dic10—21no—
152C5×M16—21no—
153C5×M16C3×Q812yescomplemented
154C2×C5×C8—21no—
155C5×C4⋊C4C2×C3×C411yescharacteristic
156C5×C4⋊C4C2×C3×C411yescharacteristic
157C5×C22⋊C4—21no—
158C42×C5—21no—
159C42×C5—21no—
160C42×C5—21no—
161C22⋊Dic5—21no—
162C4⋊Dic5—21no—
163C4⋊Dic5—21no—
164C4⋊Dic5C2×C3×C411yescharacteristic
165C4⋊Dic5C2×C3×C411yescharacteristic
166#683—24no—
167#683—21no—
168#683—21no—
169#683—21no—
170#683—21no—
171C4×Dic5—21no—
172C4×Dic5—21no—
173C4×Dic5—21no—
174C4×Dic5C2×C3×C411yescharacteristic
175C4×Dic5C2×C3×C411yescharacteristic
176C4×Dic5C3×D411yescharacteristic
177C4×Dic5C3×D411yescharacteristic
178#681—21no—
179#681C3×Q812yescomplemented
180C2×#168—21no—
181#533—51no—
182C4×M16—51no—
183C4×C4⋊C4—51no—
184#339—51no—
185#339—51no—
186#339—51no—
187#339C3×D511yescharacteristic
188C22×C3×C5—21no—
189C22×C3×C5—21no—
190C22×C3×C5C2×C22⋊C411yescharacteristic
191C22×C3×C5#12411yescharacteristic
192C22×C3×C5C4⋊Q811yescharacteristic
193C3×C4×C5—42no—
194C3×C4×C5—41no—
195C3×C4×C5—41no—
196C3×C4×C5C4×Q811yescharacteristic
197C3×C4×C5C4×Q811yescharacteristic
198C3×C4×C5C22⋊Q811yescharacteristic
199C3×C4×C5C22⋊Q811yescharacteristic
200C3×Dic5—21no—
201C3×Dic5—21no—
202C3×Dic5—21no—
203C3×Dic5—42no—
204C3×Dic5—41no—
205C3×Dic5—41no—
206C3×Dic5#10412yes—
207C2×C3×Q8—101no—
208C2×C3×Q8—101no—
209C22×C3×C4—21no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—101no—
213C22×C3×C4C22×D511yescharacteristic
214C3×M16—21no—
215C3×M16—52no—
216C3×M16—101no—
217C3×M16Dic1012yescomplemented
218C2×C3×C8—21no—
219C2×C3×C8—101no—
220C3×C4⋊C4—51no—
221C3×C4⋊C4—51no—
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4—101no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—104no—
229C3×C4⋊C4C4×D511yescharacteristic
230C3×C4⋊C4C4×D511yescharacteristic
231C3×C22⋊C4—21no—
232C3×C22⋊C4—101no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—51no—
237C3×C42—51no—
238C3×C42—51no—
239C3×C42—51no—
240C3×C42—101no—
241C3×C42—101no—
242C3×C42—101no—
243C23×C5C2×C3×D411yescharacteristic
244C2×C4×C5—22no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—41no—
248C2×C4×C5—41no—
249C2×C4×C5C22×C3×C411yescharacteristic
250C2×C4×C5C2×C3×D411yescharacteristic
251C2×C4×C5C2×C3×Q811yescharacteristic
252C2×C4×C5C2×C3×Q811yescharacteristic
253C2×C4×C5C3×#4111yescharacteristic
254C2×C4×C5C3×#4111yescharacteristic
255C2×Dic5—22no—
256C2×Dic5—22no—
257C2×Dic5—21no—
258C2×Dic5—21no—
259C2×Dic5—41no—
260C2×Dic5—41no—
261C2×Dic5—41no—
262C2×Dic5C3×C22⋊C411yescharacteristic
263C2×Dic5C3×C22⋊C411yescharacteristic
264C2×Dic5C3×C22⋊C411yescharacteristic
265C2×Dic5C3×C22⋊C411yescharacteristic
266Dic10—42no—
267Dic10—42no—
268C5×C8—22no—
269#168—22no—
270C2×M16—51no—
271C2×M16C2×C3×D511yescharacteristic
272C4⋊Q8—51no—
273C4⋊Q8—51no—
274#125—51no—
275#125—51no—
276C22⋊Q8—101no—
277C22⋊Q8—101no—
278C4×Q8—101no—
279C4×Q8—101no—
280#117—51no—
281#117C2×C3×D511yescharacteristic
282C2×C4⋊C4—101no—
283C2×C42—51no—
284C2×C42—51no—
285C2×C42C2×C3×D511yescharacteristic
286#97—101no—
287C4×C8—101no—
288#95—101no—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5#39111yescharacteristic
292C2×C3×C5C2×#10411yescharacteristic
293C2×C3×C5#42111yescharacteristic
294C23×C3D4×D511yescharacteristic
295C3×Q8—202no—
296C3×Q8—202no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—51no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—51no—
306C2×C3×C4—102no—
307C2×C3×C4—102no—
308C2×C3×C4—101no—
309C2×C3×C4—101no—
310C2×C3×C4—201no—
311C2×C3×C4—201no—
312C2×C3×C4—201no—
313C2×C3×C4C2×Dic1011yescharacteristic
314C2×C3×C4C2×C4×D511yescharacteristic
315C2×C3×C4#70911yescharacteristic
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4#71111yescharacteristic
318C2×C3×C4Q8×D511yescharacteristic
319C3×C8—22no—
320C3×C8—102no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5C2×C3×C22⋊C411yescharacteristic
324C22×C5C3×#12411yescharacteristic
325C22×C5C3×C4⋊Q811yescharacteristic
326C4×C5—42no—
327C4×C5—41no—
328C4×C5—41no—
329C4×C5C3×C4×Q811yescharacteristic
330C4×C5C3×C4×Q811yescharacteristic
331C4×C5C3×C22⋊Q811yescharacteristic
332C4×C5C3×C22⋊Q811yescharacteristic
333Dic5—21no—
334Dic5—21no—
335Dic5—21no—
336Dic5—42no—
337Dic5—41no—
338Dic5—41no—
339Dic5C3×#10412yes—
340C2×Q8—101no—
341C2×Q8—101no—
342C22×C4—21no—
343C22×C4—51no—
344C22×C4—51no—
345C22×C4—101no—
346C22×C4C22×C3×D511yescharacteristic
347M16—21no—
348M16—52no—
349M16—101no—
350M16C3×Dic1012yescomplemented
351C2×C8—21no—
352C2×C8—101no—
353C4⋊C4—51no—
354C4⋊C4—51no—
355C4⋊C4—101no—
356C4⋊C4—101no—
357C4⋊C4—101no—
358C4⋊C4—101no—
359C4⋊C4—101no—
360C4⋊C4—101no—
361C4⋊C4—104no—
362C4⋊C4C3×C4×D511yescharacteristic
363C4⋊C4C3×C4×D511yescharacteristic
364C22⋊C4—21no—
365C22⋊C4—101no—
366C42—21no—
367C42—21no—
368C42—21no—
369C42—51no—
370C42—51no—
371C42—51no—
372C42—51no—
373C42—101no—
374C42—101no—
375C42—101no—
376C3×C5#198611yescharacteristic, complemented, Hall
377C22×C3—21no—
378C22×C3—21no—
379C22×C3D5×C22⋊C411yescharacteristic
380C22×C3#403111yescharacteristic
381C22×C3#403411yescharacteristic
382C3×C4—42no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—52no—
386C3×C4—101no—
387C3×C4—101no—
388C3×C4—101no—
389C3×C4—202no—
390C3×C4—201no—
391C3×C4—201no—
392C3×C4C4×Dic1011yescharacteristic
393C3×C4#402411yescharacteristic
394C3×C4#403311yescharacteristic
395C3×C4#404211yescharacteristic
396C2×C5—21no—
397C2×C5—21no—
398C2×C5C3×#39111yescharacteristic
399C2×C5C2×C3×#10411yescharacteristic
400C2×C5C3×#42111yescharacteristic
401C23C3×D4×D511yescharacteristic
402Q8—202no—
403Q8—202no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—51no—
410C2×C4—51no—
411C2×C4—51no—
412C2×C4—51no—
413C2×C4—102no—
414C2×C4—102no—
415C2×C4—101no—
416C2×C4—101no—
417C2×C4—201no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4C2×C3×Dic1011yescharacteristic
421C2×C4C2×C3×C4×D511yescharacteristic
422C2×C4C3×#70911yescharacteristic
423C2×C4C3×D4×D511yescharacteristic
424C2×C4C3×#71111yescharacteristic
425C2×C4C3×Q8×D511yescharacteristic
426C8—22no—
427C8—102no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3#6493511yescharacteristic
431C2×C3D5×#10411yescharacteristic
432C2×C3#6511011yescharacteristic
433C5C3×#198611yescharacteristic, complemented, Sylow
434C22—21no—
435C22—21no—
436C22C3×D5×C22⋊C411yescharacteristic
437C22C3×#403111yescharacteristic
438C22C3×#403411yescharacteristic
439C4—42no—
440C4—41no—
441C4—41no—
442C4—52no—
443C4—101no—
444C4—101no—
445C4—101no—
446C4—202no—
447C4—201no—
448C4—201no—
449C4C3×C4×Dic1011yescharacteristic
450C4C3×#402411yescharacteristic
451C4C3×#403311yescharacteristic
452C4C3×#404211yescharacteristic
453C3#1059952311yescharacteristic, direct product factor, Sylow
454C2—21no—
455C2—21no—
456C2C3×#6493511yescharacteristic
457C2C3×D5×#10411yescharacteristic
458C2C3×#6511011yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#339D5
hypocenterC5C3×#1986
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
8. #10599523C3direct (N × H)
17. C3×#4036C4semidirect
18. C3×#4036C4semidirect
19. C3×#4034C4semidirect
20. C3×#4034C4semidirect
44. C3×C5×M16Q8semidirect
70. C3×#681Q8semidirect
87. #4036C3×C4semidirect
88. #4036C3×C4semidirect
89. #4034C3×C4semidirect
90. #4034C3×C4semidirect
153. C5×M16C3×Q8semidirect
179. #681C3×Q8semidirect
217. C3×M16Dic10semidirect
350. M16C3×Dic10semidirect
376. C3×C5#1986semidirect
433. C5C3×#1986semidirect
453. C3#10599523direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658512
C3×M16×Dic52
C3×C4×#6832
C3×C5×#3392
C3×#647752
C3×#647522
C3×#647432
#105995233
C3×#19865