Finite Group Databasebeta

← C3×C4×#3966 #14295364

Subgroups — C3×C4×#3966 #14295364

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×#3966C212yesmaximal
3C3×C4×C22⋊Dic5C212yesmaximal, complemented
4C3×#64746C212yesmaximal, complemented
5C4×#3966C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×D4C2211yescharacteristic
7C23×C3×C4×C5C411yescharacteristic, complemented
8C23×C3×C4×C5C2211yescharacteristic
9C3×C4×C5×D4—22no—
10C3×C4×C5×D4—22no—
11C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
12C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×C3×C42×C5C411yescharacteristic, complemented
15C2×C3×C22⋊Dic5C2214yes—
16C2×C3×C4×Dic5—22no—
17C3×#3966C418yesdirect product factor
18C3×#3963—22no—
19C3×C4×#99—51nomaximal, Hall
20C2×C4×C5×D4C2×C311yescharacteristic
21C2×#3966C2×C312yes—
22C4×C22⋊Dic5C2×C312yescomplemented
23#64746C2×C312yescomplemented
24C24×C3×C5C2×C411yescharacteristic
25C24×C3×C5C2311yescharacteristic
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C414yes—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D412yes—
39C22×C3×C4×C5D412yes—
40C22×C3×Dic5—24no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C22⋊C4—22no—
43C3×C5×C22⋊C4—22no—
44C3×C42×C5—21no—
45C3×C42×C5—21no—
46C3×C22⋊Dic5—24no—
47C3×C22⋊Dic5C2×C418yescomplemented
48C3×C4×Dic5—44no—
49C2×C3×C4×D4D511yescharacteristic
50C2×C3×#99—52no—
51C3×C4×C22⋊C4—52no—
52C3×#342—52no—
53C22×C5×D4C22×C311yescharacteristic
54C23×C4×C5C3×C411yescharacteristic, complemented
55C23×C4×C5C22×C311yescharacteristic
56C4×C5×D4—22no—
57C4×C5×D4—22no—
58C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
59C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
60C2×C5×C22⋊C4C22×C311yescharacteristic
61C2×C42×C5C3×C411yescharacteristic, complemented
62C2×C22⋊Dic5C22×C314yes—
63C2×C4×Dic5—22no—
64#3966C3×C418yesdirect product factor
65#3963—22no—
66C4×#99—51noSylow
67C23×C3×C5—21no—
68C23×C3×C5—21no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5C4212yescomplemented
74C23×C3×C5C22×C411yescharacteristic
75C23×C3×C5C22×C412yes—
76C23×C3×C5C2×D412yes—
77C23×C3×C5#4112yes—
78C3×C5×D4—28no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—24no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—42no—
87C2×C3×C4×C5—42no—
88C2×C3×C4×C5—42no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C4212yescomplemented
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C412yes—
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×Dic5—28no—
96C2×C3×Dic5—44no—
97C2×C3×Dic5—44no—
98C22×C3×D4C2×D511yescharacteristic
99C23×C3×C4Dic511yescharacteristic, complemented
100C23×C3×C4C2×D511yescharacteristic
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C2×C3×C4⋊C4Dic511yescharacteristic, complemented
104C2×C3×C22⋊C4—54no—
105C2×C3×C22⋊C4Dic511yescharacteristic, complemented
106C2×C3×C22⋊C4C2×D511yescharacteristic
107C2×C3×C42—102no—
108C2×C3×C42Dic511yescharacteristic, complemented
109C3×#99—58no—
110C3×#95—102no—
111C24×C5C2×C3×C411yescharacteristic
112C24×C5C23×C311yescharacteristic
113C2×C5×D4—22no—
114C2×C5×D4—22no—
115C2×C5×D4C2×C3×C414yes—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—42no—
119C22×C4×C5—42no—
120C22×C4×C5C2×C3×C411yescharacteristic
121C22×C4×C5C2×C3×C411yescharacteristic
122C22×C4×C5C2×C3×C411yescharacteristic
123C22×C4×C5C2×C3×C411yescharacteristic
124C22×C4×C5C2×C3×C411yescharacteristic
125C22×C4×C5C3×D412yes—
126C22×C4×C5C3×D412yes—
127C22×Dic5—24no—
128C5×C4⋊C4—22no—
129C5×C22⋊C4—22no—
130C5×C22⋊C4—22no—
131C42×C5—21no—
132C42×C5—21no—
133C22⋊Dic5—24no—
134C22⋊Dic5C2×C3×C418yescomplemented
135C4×Dic5—44no—
136C2×C4×D4C3×D511yescharacteristic
137C2×#99—52no—
138C4×C22⋊C4—52no—
139#342—52no—
140C22×C3×C5—22no—
141C22×C3×C5—21no—
142C22×C3×C5—22no—
143C22×C3×C5—21no—
144C22×C3×C5—22no—
145C22×C3×C5—42no—
146C22×C3×C5—42no—
147C22×C3×C5—42no—
148C22×C3×C5—42no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5C2×C4211yescharacteristic
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5#11711yescharacteristic
154C22×C3×C5C4×D414yes—
155C3×C4×C5—22no—
156C3×C4×C5—21no—
157C3×C4×C5—22no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5#9912yescomplemented
161C3×Dic5—48no—
162C24×C3C2×Dic511yescharacteristic
163C24×C3C22×D511yescharacteristic
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4C4×D514yes—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—42no—
170C22×C3×C4—42no—
171C22×C3×C4—104no—
172C22×C3×C4C2×Dic511yescharacteristic
173C22×C3×C4C2×Dic511yescharacteristic
174C22×C3×C4C2×Dic511yescharacteristic
175C22×C3×C4C2×Dic511yescharacteristic
176C22×C3×C4C2×Dic511yescharacteristic
177C22×C3×C4C22⋊D512yes—
178C22×C3×C4C22⋊D512yes—
179C3×C4⋊C4—22no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—58no—
183C3×C22⋊C4—104no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—204no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—41no—
190C23×C5—41no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5C3×C4212yescomplemented
194C23×C5C22×C3×C412yes—
195C23×C5C22×C3×C411yescharacteristic
196C23×C5C2×C3×D412yes—
197C23×C5C3×#4112yes—
198C5×D4—28no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—24no—
202C2×C4×C5—22no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—41no—
206C2×C4×C5—42no—
207C2×C4×C5—42no—
208C2×C4×C5—42no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5C3×C4212yescomplemented
212C2×C4×C5C3×C22⋊C411yescharacteristic
213C2×C4×C5C3×C22⋊C412yes—
214C2×C4×C5C3×C22⋊C411yescharacteristic
215C2×Dic5—28no—
216C2×Dic5—44no—
217C2×Dic5—44no—
218C22×D4C2×C3×D511yescharacteristic
219C23×C4C3×Dic511yescharacteristic, complemented
220C23×C4C2×C3×D511yescharacteristic
221C4×D4—22no—
222C4×D4—22no—
223C2×C4⋊C4C3×Dic511yescharacteristic, complemented
224C2×C22⋊C4—54no—
225C2×C22⋊C4C3×Dic511yescharacteristic, complemented
226C2×C22⋊C4C2×C3×D511yescharacteristic
227C2×C42—102no—
228C2×C42C3×Dic511yescharacteristic, complemented
229#99—58no—
230#95—102no—
231C2×C3×C5—24no—
232C2×C3×C5—21no—
233C2×C3×C5—21no—
234C2×C3×C5—42no—
235C2×C3×C5C4×C22⋊C411yescharacteristic
236C2×C3×C5C2×#9911yescharacteristic
237C2×C3×C5#41011yescharacteristic
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3C4×Dic512yescomplemented
245C23×C3C2×C4×D512yes—
246C23×C3#70912yes—
247C23×C3C22×Dic511yescharacteristic
248C23×C3C2×C22⋊D512yes—
249C3×D4—28no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—24no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—108no—
263C2×C3×C4—204no—
264C2×C3×C4—204no—
265C2×C3×C4C4×Dic512yescomplemented
266C2×C3×C4C22⋊Dic511yescharacteristic
267C2×C3×C4C22⋊Dic512yes—
268C2×C3×C4C22⋊Dic511yescharacteristic
269C22×C5—22no—
270C22×C5—21no—
271C22×C5—22no—
272C22×C5—21no—
273C22×C5—22no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5—42no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5C2×C3×C4211yescharacteristic
281C22×C5C2×C3×C22⋊C411yescharacteristic
282C22×C5C3×#11711yescharacteristic
283C22×C5C3×C4×D414yes—
284C4×C5—22no—
285C4×C5—21no—
286C4×C5—22no—
287C4×C5—41no—
288C4×C5—41no—
289C4×C5C3×#9912yescomplemented
290Dic5—48no—
291C24C2×C3×Dic511yescharacteristic
292C24C22×C3×D511yescharacteristic
293C2×D4—22no—
294C2×D4—22no—
295C2×D4C3×C4×D514yes—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—104no—
301C22×C4C2×C3×Dic511yescharacteristic
302C22×C4C2×C3×Dic511yescharacteristic
303C22×C4C2×C3×Dic511yescharacteristic
304C22×C4C2×C3×Dic511yescharacteristic
305C22×C4C2×C3×Dic511yescharacteristic
306C22×C4C3×C22⋊D512yes—
307C22×C4C3×C22⋊D512yes—
308C4⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—58no—
312C22⋊C4—104no—
313C42—21no—
314C42—21no—
315C42—204no—
316C3×C5C4×#9911yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3C2×C4×Dic511yescharacteristic
329C22×C3#407211yescharacteristic
330C22×C3C4×C22⋊D514yes—
331C22×C3C2×C22⋊Dic511yescharacteristic
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—22no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—208no—
338C3×C4#396612yesdirect product factor
339C2×C5—24no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5—42no—
343C2×C5C3×C4×C22⋊C411yescharacteristic
344C2×C5C2×C3×#9911yescharacteristic
345C2×C5C3×#41011yescharacteristic
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23C3×C4×Dic512yescomplemented
353C23C2×C3×C4×D512yes—
354C23C3×#70912yes—
355C23C22×C3×Dic511yescharacteristic
356C23C2×C3×C22⋊D512yes—
357D4—28no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—108no—
371C2×C4—204no—
372C2×C4—204no—
373C2×C4C3×C4×Dic512yescomplemented
374C2×C4C3×C22⋊Dic511yescharacteristic
375C2×C4C3×C22⋊Dic512yes—
376C2×C4C3×C22⋊Dic511yescharacteristic
377C2×C3—24no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—42no—
381C2×C3C4×C22⋊Dic511yescharacteristic
382C2×C3C2×#396611yescharacteristic
383C2×C3#6552911yescharacteristic
384C5C3×C4×#9911yescharacteristic, complemented, Sylow
385C22—21no—
386C22—22no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22C2×C3×C4×Dic511yescharacteristic
397C22C3×#407211yescharacteristic
398C22C3×C4×C22⋊D514yes—
399C22C2×C3×C22⋊Dic511yescharacteristic
400C4—22no—
401C4—21no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—208no—
406C4C3×#396612yesdirect product factor
407C3C4×#396611yescharacteristic, direct product factor, Sylow
408C2—24no—
409C2—21no—
410C2—21no—
411C2—42no—
412C2C3×C4×C22⋊Dic511yescharacteristic
413C2C2×C3×#396611yescharacteristic
414C2C3×#6552911yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊Dic5
commutatorC22×C5C2×C3×C42
FrattiniC24C22×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C22
cosocleC24×C5C23×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
3. C3×C4×C22⋊Dic5C2semidirect
4. C3×#64746C2semidirect
5. C4×#3966C3direct (N × H)
7. C23×C3×C4×C5C4semidirect
11. C2×C3×C5×C4⋊C4C4semidirect
12. C2×C3×C5×C22⋊C4C4semidirect
14. C2×C3×C42×C5C4semidirect
17. C3×#3966C4direct (N × H)
22. C4×C22⋊Dic5C2×C3semidirect
23. #64746C2×C3semidirect
47. C3×C22⋊Dic5C2×C4semidirect
54. C23×C4×C5C3×C4semidirect
58. C2×C5×C4⋊C4C3×C4semidirect
59. C2×C5×C22⋊C4C3×C4semidirect
61. C2×C42×C5C3×C4semidirect
64. #3966C3×C4direct (N × H)
73. C23×C3×C5C42semidirect
91. C2×C3×C4×C5C42semidirect
99. C23×C3×C4Dic5semidirect
103. C2×C3×C4⋊C4Dic5semidirect
105. C2×C3×C22⋊C4Dic5semidirect
108. C2×C3×C42Dic5semidirect
134. C22⋊Dic5C2×C3×C4semidirect
160. C3×C4×C5#99semidirect
193. C23×C5C3×C42semidirect
211. C2×C4×C5C3×C42semidirect
219. C23×C4C3×Dic5semidirect
223. C2×C4⋊C4C3×Dic5semidirect
225. C2×C22⋊C4C3×Dic5semidirect
228. C2×C42C3×Dic5semidirect
244. C23×C3C4×Dic5semidirect
265. C2×C3×C4C4×Dic5semidirect
289. C4×C5C3×#99semidirect
316. C3×C5C4×#99semidirect
338. C3×C4#3966direct (N × H)
352. C23C3×C4×Dic5semidirect
373. C2×C4C3×C4×Dic5semidirect
384. C5C3×C4×#99semidirect
406. C4C3×#3966direct (N × H)
407. C3C4×#3966direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C3×#39662
C3×C4×C22⋊Dic52
C3×#647462
C4×#39663
C3×C4×#995