Finite Group Databasebeta

← C3×#10606090 #14322882

Subgroups — C3×#10606090 #14322882

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
3C2×C3×#4018C211yesmaximal, characteristic
4C3×C5×#384C211yesmaximal, characteristic, complemented
5C3×#65278C214yesmaximal
6C3×#65266C211yesmaximal, characteristic, complemented
7C3×#65265C211yesmaximal, characteristic, complemented
8C3×#65261C214yesmaximal, complemented
9C3×#65225C211yesmaximal, characteristic, complemented
10#10606090C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C4×D5C2212yes—
12C22×C3×C4×D5C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2214yes—
16C2×C3×C42×C5C2211yescharacteristic
17C2×C3×#685C2212yes—
18C2×C3×#685C2212yes—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×C3×#683C2212yes—
22C2×C3×#683C2214yes—
23C2×C3×#683C2212yes—
24C2×C3×C4×Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C3×#4038—24no—
27C3×D5×C4⋊C4—24no—
28C3×#4018C418yescomplemented
29C3×#3963C2214yes—
30C3×#3963C2214yes—
31C3×#2317—51nomaximal, Hall
32C2×#4038C2×C311yescharacteristic
33C2×D5×C4⋊C4C2×C311yescharacteristic
34C2×#4018C2×C311yescharacteristic
35C5×#384C2×C311yescharacteristic, complemented
36#65278C2×C314yes—
37#65266C2×C311yescharacteristic, complemented
38#65265C2×C311yescharacteristic, complemented
39#65261C2×C314yescomplemented
40#65225C2×C311yescharacteristic, complemented
41C23×C3×D5C2311yescharacteristic
42C22×C3×C4×C5C2312yes—
43C22×C3×C4×C5C2312yes—
44C22×C3×C4×C5C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×C3×Dic5C2312yes—
47C22×C3×Dic5C2312yes—
48C22×C3×Dic5C2312yes—
49C22×C3×Dic5C2311yescharacteristic
50C2×C3×C4×D5—24no—
51C2×C3×C4×D5—44no—
52C2×C3×C4×D5C2×C414yes—
53C2×C3×C4×D5D414yes—
54C2×C3×C4×D5Q814yes—
55C3×C5×C4⋊C4—22no—
56C3×C5×C4⋊C4—22no—
57C3×C5×C4⋊C4—44no—
58C3×C42×C5C2×C414yescomplemented
59C3×#685—24no—
60C3×#685C2×C418yes—
61C3×C4⋊Dic5—22no—
62C3×C4⋊Dic5—22no—
63C3×#683—24no—
64C3×#683—44no—
65C3×#683C2×C418yescomplemented
66C3×C4×Dic5—24no—
67C3×C4×Dic5C2×C414yescomplemented
68C2×C3×#117—51no—
69C2×C3×#117—51no—
70C22×C3×C4⋊C4—51no—
71C3×#389—54no—
72C3×#385—54no—
73C3×#384—51no—
74C3×#384D511yescharacteristic, complemented
75C3×#382—51no—
76C3×#382—51no—
77C22×C4×D5C22×C312yes—
78C22×C4×D5C22×C311yescharacteristic
79C2×C5×C4⋊C4C22×C311yescharacteristic
80C2×C5×C4⋊C4C22×C311yescharacteristic
81C2×C5×C4⋊C4C22×C314yes—
82C2×C42×C5C22×C311yescharacteristic
83C2×#685C22×C312yes—
84C2×#685C22×C312yes—
85C2×C4⋊Dic5C22×C311yescharacteristic
86C2×C4⋊Dic5C22×C311yescharacteristic
87C2×#683C22×C312yes—
88C2×#683C22×C314yes—
89C2×#683C22×C312yes—
90C2×C4×Dic5C22×C312yes—
91C2×C4×Dic5C22×C311yescharacteristic
92#4038—24no—
93D5×C4⋊C4—24no—
94#4018C3×C418yescomplemented
95#3963C22×C314yes—
96#3963C22×C314yes—
97#2317—51noSylow
98C23×C3×C5C2411yescharacteristic
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5C22×C412yes—
102C22×C3×D5C2×D412yes—
103C22×C3×D5C2×Q812yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—22no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—24no—
109C2×C3×C4×C5—24no—
110C2×C3×C4×C5C22×C414yes—
111C2×C3×C4×C5C22×C412yes—
112C2×C3×C4×C5C2×D412yes—
113C2×C3×C4×C5C2×Q812yes—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5—24no—
119C2×C3×Dic5—24no—
120C2×C3×Dic5C22×C414yes—
121C2×C3×Dic5C22×C412yes—
122C2×C3×Dic5C2×D412yes—
123C2×C3×Dic5C2×Q812yes—
124C3×C4×D5—48no—
125C3×C4×D5C4⋊C4116yescomplemented
126C23×C3×C4—51no—
127C23×C3×C4—52no—
128C3×#117—58no—
129C3×#117—104no—
130C2×C3×C4⋊C4—52no—
131C2×C3×C4⋊C4—51no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4—52no—
134C2×C3×C4⋊C4—54no—
135C2×C3×C4⋊C4—104no—
136C2×C3×C4⋊C4C2×D511yescharacteristic
137C2×C3×C4⋊C4C2×D511yescharacteristic
138C2×C3×C4⋊C4C2×D514yes—
139C2×C3×C22⋊C4—52no—
140C2×C3×C22⋊C4—52no—
141C2×C3×C42—51no—
142C2×C3×C42—52no—
143C2×C3×C42C2×D511yescharacteristic
144C3×#95—54no—
145C3×#95—54no—
146C23×D5C23×C311yescharacteristic
147C22×C4×C5C23×C312yes—
148C22×C4×C5C23×C312yes—
149C22×C4×C5C23×C312yes—
150C22×C4×C5C23×C311yescharacteristic
151C22×Dic5C23×C312yes—
152C22×Dic5C23×C312yes—
153C22×Dic5C23×C312yes—
154C22×Dic5C23×C311yescharacteristic
155C2×C4×D5—24no—
156C2×C4×D5—44no—
157C2×C4×D5C2×C3×C414yes—
158C2×C4×D5C3×D414yes—
159C2×C4×D5C3×Q814yes—
160C5×C4⋊C4—22no—
161C5×C4⋊C4—22no—
162C5×C4⋊C4—44no—
163C42×C5C2×C3×C414yescomplemented
164#685—24no—
165#685C2×C3×C418yes—
166C4⋊Dic5—22no—
167C4⋊Dic5—22no—
168#683—24no—
169#683—44no—
170#683C2×C3×C418yescomplemented
171C4×Dic5—24no—
172C4×Dic5C2×C3×C414yescomplemented
173C2×#117—51no—
174C2×#117—51no—
175C22×C4⋊C4—51no—
176#389—54no—
177#385—54no—
178#384—51no—
179#384C3×D511yescharacteristic, complemented
180#382—51no—
181#382—51no—
182C22×C3×C5C23×C411yescharacteristic
183C22×C3×C5C22×D411yescharacteristic
184C22×C3×C5C22×Q811yescharacteristic
185C22×C3×C5H(5,𝔽2)12yes—
186C22×C3×C52−1+412yes—
187C2×C3×D5—24no—
188C2×C3×D5—22no—
189C2×C3×D5—22no—
190C2×C3×D5—24no—
191C2×C3×D5C2×C4⋊C414yes—
192C3×C4×C5—24no—
193C3×C4×C5—42no—
194C3×C4×C5—42no—
195C3×C4×C5C2×C4⋊C414yes—
196C3×Dic5—24no—
197C3×Dic5—42no—
198C3×Dic5—42no—
199C3×Dic5C2×C4⋊C414yes—
200C24×C3—51no—
201C22×C3×C4—51no—
202C22×C3×C4—54no—
203C22×C3×C4—54no—
204C22×C3×C4—54no—
205C22×C3×C4—52no—
206C22×C3×C4—52no—
207C22×C3×C4—52no—
208C22×C3×C4—104no—
209C22×C3×C4—204no—
210C22×C3×C4C22×D512yes—
211C22×C3×C4C22×D512yes—
212C22×C3×C4C22×D512yes—
213C22×C3×C4C22×D511yescharacteristic
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—44no—
217C3×C4⋊C4—58no—
218C3×C4⋊C4—104no—
219C3×C4⋊C4—102no—
220C3×C4⋊C4—102no—
221C3×C4⋊C4—204no—
222C3×C22⋊C4—58no—
223C3×C22⋊C4—104no—
224C3×C42—54no—
225C3×C42—104no—
226C3×C42C4×D514yescomplemented
227C23×C5C24×C311yescharacteristic
228C22×D5—22no—
229C22×D5—22no—
230C22×D5C22×C3×C412yes—
231C22×D5C2×C3×D412yes—
232C22×D5C2×C3×Q812yes—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—24no—
238C2×C4×C5—24no—
239C2×C4×C5C22×C3×C414yes—
240C2×C4×C5C22×C3×C412yes—
241C2×C4×C5C2×C3×D412yes—
242C2×C4×C5C2×C3×Q812yes—
243C2×Dic5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5—24no—
248C2×Dic5—24no—
249C2×Dic5C22×C3×C414yes—
250C2×Dic5C22×C3×C412yes—
251C2×Dic5C2×C3×D412yes—
252C2×Dic5C2×C3×Q812yes—
253C4×D5—48no—
254C4×D5C3×C4⋊C4116yescomplemented
255C23×C4—51no—
256C23×C4—52no—
257#117—58no—
258#117—104no—
259C2×C4⋊C4—52no—
260C2×C4⋊C4—51no—
261C2×C4⋊C4—52no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—54no—
264C2×C4⋊C4—104no—
265C2×C4⋊C4C2×C3×D511yescharacteristic
266C2×C4⋊C4C2×C3×D511yescharacteristic
267C2×C4⋊C4C2×C3×D514yes—
268C2×C22⋊C4—52no—
269C2×C22⋊C4—52no—
270C2×C42—51no—
271C2×C42—52no—
272C2×C42C2×C3×D511yescharacteristic
273#95—54no—
274#95—54no—
275C2×C3×C5C22×C4⋊C411yescharacteristic
276C2×C3×C5#52012yes—
277C2×C3×C5#53511yescharacteristic
278C2×C3×C5#53611yescharacteristic
279C2×C3×C5#54412yes—
280C3×D5—24no—
281C23×C3—52no—
282C23×C3—52no—
283C23×C3—52no—
284C23×C3—102no—
285C23×C3—102no—
286C23×C3C23×D511yescharacteristic
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—24no—
292C2×C3×C4—24no—
293C2×C3×C4—52no—
294C2×C3×C4—52no—
295C2×C3×C4—52no—
296C2×C3×C4—516no—
297C2×C3×C4—54no—
298C2×C3×C4—102no—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4—102no—
302C2×C3×C4—104no—
303C2×C3×C4—104no—
304C2×C3×C4—208no—
305C2×C3×C4C2×C4×D514yes—
306C2×C3×C4C2×C4×D512yes—
307C2×C3×C4D4×D512yes—
308C2×C3×C4Q8×D512yes—
309C22×C5C23×C3×C411yescharacteristic
310C22×C5C22×C3×D411yescharacteristic
311C22×C5C22×C3×Q811yescharacteristic
312C22×C5C3×H(5,𝔽2)12yes—
313C22×C5C3×2−1+412yes—
314C2×D5—24no—
315C2×D5—22no—
316C2×D5—22no—
317C2×D5—24no—
318C2×D5C2×C3×C4⋊C414yes—
319C4×C5—24no—
320C4×C5—42no—
321C4×C5—42no—
322C4×C5C2×C3×C4⋊C414yes—
323Dic5—24no—
324Dic5—42no—
325Dic5—42no—
326Dic5C2×C3×C4⋊C414yes—
327C24—51no—
328C22×C4—51no—
329C22×C4—54no—
330C22×C4—54no—
331C22×C4—54no—
332C22×C4—52no—
333C22×C4—52no—
334C22×C4—52no—
335C22×C4—104no—
336C22×C4—204no—
337C22×C4C22×C3×D512yes—
338C22×C4C22×C3×D512yes—
339C22×C4C22×C3×D512yes—
340C22×C4C22×C3×D511yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—44no—
344C4⋊C4—58no—
345C4⋊C4—104no—
346C4⋊C4—102no—
347C4⋊C4—102no—
348C4⋊C4—204no—
349C22⋊C4—58no—
350C22⋊C4—104no—
351C42—54no—
352C42—104no—
353C42C3×C4×D514yescomplemented
354C3×C5#231711yescharacteristic, complemented, Hall
355C22×C3—54no—
356C22×C3—102no—
357C22×C3—102no—
358C22×C3—104no—
359C22×C3—104no—
360C22×C3C22×C4×D511yescharacteristic
361C22×C3C2×D4×D511yescharacteristic
362C22×C3#414412yes—
363C22×C3C2×Q8×D511yescharacteristic
364C22×C3#414712yes—
365C3×C4—24no—
366C3×C4—42no—
367C3×C4—42no—
368C3×C4—54no—
369C3×C4—104no—
370C3×C4—202no—
371C3×C4—202no—
372C3×C4D5×C4⋊C414yes—
373C2×C5C22×C3×C4⋊C411yescharacteristic
374C2×C5C3×#52012yes—
375C2×C5C3×#53511yescharacteristic
376C2×C5C3×#53611yescharacteristic
377C2×C5C3×#54412yes—
378D5—24no—
379C23—52no—
380C23—52no—
381C23—52no—
382C23—102no—
383C23—102no—
384C23C23×C3×D511yescharacteristic
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—52no—
392C2×C4—52no—
393C2×C4—52no—
394C2×C4—516no—
395C2×C4—54no—
396C2×C4—102no—
397C2×C4—102no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—104no—
401C2×C4—104no—
402C2×C4—208no—
403C2×C4C2×C3×C4×D514yes—
404C2×C4C2×C3×C4×D512yes—
405C2×C4C3×D4×D512yes—
406C2×C4C3×Q8×D512yes—
407C2×C3—104no—
408C2×C3C2×D5×C4⋊C411yescharacteristic
409C2×C3#6583812yes—
410C2×C3#6604911yescharacteristic
411C2×C3#6605811yescharacteristic
412C2×C3#6606312yes—
413C5C3×#231711yescharacteristic, complemented, Sylow
414C22—54no—
415C22—102no—
416C22—102no—
417C22—104no—
418C22—104no—
419C22C22×C3×C4×D511yescharacteristic
420C22C2×C3×D4×D511yescharacteristic
421C22C3×#414412yes—
422C22C2×C3×Q8×D511yescharacteristic
423C22C3×#414712yes—
424C4—24no—
425C4—42no—
426C4—42no—
427C4—54no—
428C4—104no—
429C4—202no—
430C4—202no—
431C4C3×D5×C4⋊C414yes—
432C3#1060609011yescharacteristic, direct product factor, Sylow
433C2—104no—
434C2C2×C3×D5×C4⋊C411yescharacteristic
435C2C3×#6583812yes—
436C2C3×#6604911yescharacteristic
437C2C3×#6605811yescharacteristic
438C2C3×#6606312yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#384C2
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC23×C5C24×C3
hypercenterC3×#384D5
hypocenterC5C3×#2317
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
4. C3×C5×#384C2semidirect
6. C3×#65266C2semidirect
7. C3×#65265C2semidirect
8. C3×#65261C2semidirect
9. C3×#65225C2semidirect
10. #10606090C3direct (N × H)
28. C3×#4018C4semidirect
35. C5×#384C2×C3semidirect
37. #65266C2×C3semidirect
38. #65265C2×C3semidirect
39. #65261C2×C3semidirect
40. #65225C2×C3semidirect
58. C3×C42×C5C2×C4semidirect
65. C3×#683C2×C4semidirect
67. C3×C4×Dic5C2×C4semidirect
74. C3×#384D5semidirect
94. #4018C3×C4semidirect
125. C3×C4×D5C4⋊C4semidirect
163. C42×C5C2×C3×C4semidirect
170. #683C2×C3×C4semidirect
172. C4×Dic5C2×C3×C4semidirect
179. #384C3×D5semidirect
226. C3×C42C4×D5semidirect
254. C4×D5C3×C4⋊C4semidirect
353. C42C3×C4×D5semidirect
354. C3×C5#2317semidirect
413. C5C3×#2317semidirect
432. C3#10606090direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×C3×D5×C4⋊C42
C2×C3×#40182
C3×C5×#3842
C3×#652782
C3×#652662
C3×#652652
C3×#652612
C3×#652252
#106060903
C3×#23175