Finite Group Databasebeta

← C3×#10602467 #14283263

Subgroups — C3×#10602467 #14283263

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C3×#65500C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C3×#64757C214yesmaximal, complemented
5#10602467C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×D4—21no—
7C22×C3×C5×D4C411yescharacteristic, complemented
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#121—21no—
10C3×C5×#121—21no—
11C3×C5×#121C412yescomplemented
12C3×C5×#121C2212yes—
13C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C22⋊Dic5—21no—
16C2×C3×#681—21no—
17C3×#3963—21no—
18C3×#3963C2212yescomplemented
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yescomplemented
21C3×#1510—51nomaximal, Hall
22C2×C5×#121C2×C311yescharacteristic
23#65500C2×C311yescharacteristic, complemented
24#65496C2×C311yescharacteristic, complemented
25#64757C2×C314yescomplemented
26C24×C3×C5—21no—
27C24×C3×C5D411yescharacteristic
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—42no—
32C2×C3×C5×D4—44no—
33C2×C3×C5×D4C2×C412yes—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—42no—
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×C3×Dic5—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C412yes—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C22⋊Dic5—42no—
48C3×#681—42no—
49C2×C3×#168—22no—
50C2×C3×#121D511yescharacteristic
51C3×#407—51no—
52C3×#381—51no—
53C3×#327—54no—
54C22×C5×D4—21no—
55C22×C5×D4C3×C411yescharacteristic, complemented
56C23×C4×C5C22×C311yescharacteristic
57C5×#121—21no—
58C5×#121—21no—
59C5×#121C3×C412yescomplemented
60C5×#121C22×C312yes—
61C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
62C2×C5×C22⋊C4—21no—
63C2×C22⋊Dic5—21no—
64C2×#681—21no—
65#3963—21no—
66#3963C22×C312yescomplemented
67C22⋊#168—21no—
68C22⋊#168C22×C312yescomplemented
69#1510—51noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—22no—
73C23×C3×C5—41no—
74C23×C3×C5—42no—
75C23×C3×C5—42no—
76C23×C3×C5—42no—
77C23×C3×C5C22⋊C411yescharacteristic
78C23×C3×C5C22⋊C411yescharacteristic
79C23×C3×C5C2×D411yescharacteristic
80C3×C5×D4—42no—
81C3×C5×D4—42no—
82C3×C5×D4—44no—
83C3×C5×D4—44no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×Dic5—42no—
97C2×C3×Dic5—42no—
98C2×C3×Dic5—42no—
99C3×#168—42no—
100C22×C3×D4—21no—
101C22×C3×D4Dic511yescharacteristic, complemented
102C23×C3×C4C2×D511yescharacteristic
103C2×C3×M16—101no—
104C3×#121—21no—
105C3×#121—21no—
106C3×#121Dic512yescomplemented
107C3×#121C2×D512yes—
108C2×C3×C4⋊C4Dic511yescharacteristic, complemented
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—101no—
111C3×C22⋊C8—52no—
112C3×C22⋊C8—101no—
113C3×#95—52no—
114C3×#95—101no—
115C24×C5—21no—
116C24×C5C3×D411yescharacteristic
117C2×C5×D4—22no—
118C2×C5×D4—22no—
119C2×C5×D4—21no—
120C2×C5×D4—42no—
121C2×C5×D4—44no—
122C2×C5×D4C2×C3×C412yes—
123C22×C4×C5—21no—
124C22×C4×C5—42no—
125C22×C4×C5C2×C3×C411yescharacteristic
126C22×C4×C5C2×C3×C411yescharacteristic
127C22×C4×C5C3×D411yescharacteristic
128C22×C4×C5C3×D411yescharacteristic
129C22×C4×C5C3×D411yescharacteristic
130C22×C4×C5C23×C311yescharacteristic
131C22×Dic5—22no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4C2×C3×C412yes—
134C5×C22⋊C4—22no—
135C5×C22⋊C4—22no—
136C22⋊Dic5—42no—
137#681—42no—
138C2×#168—22no—
139C2×#121C3×D511yescharacteristic
140#407—51no—
141#381—51no—
142#327—54no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—44no—
151C22×C3×C5—42no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5—84no—
155C22×C3×C5#9912yes—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5AGL(1,ℤ/8)12yes—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—42no—
163C3×Dic5—82no—
164C24×C3—21no—
165C24×C3C22⋊D511yescharacteristic
166C2×C3×D4—22no—
167C2×C3×D4—22no—
168C2×C3×D4—21no—
169C2×C3×D4—42no—
170C2×C3×D4—44no—
171C2×C3×D4C2×Dic512yes—
172C22×C3×C4—21no—
173C22×C3×C4—42no—
174C22×C3×C4—102no—
175C22×C3×C4C2×Dic511yescharacteristic
176C22×C3×C4C2×Dic511yescharacteristic
177C22×C3×C4C22⋊D511yescharacteristic
178C22×C3×C4C22⋊D511yescharacteristic
179C22×C3×C4C22⋊D511yescharacteristic
180C22×C3×C4C22×D511yescharacteristic
181C3×M16—202no—
182C2×C3×C8—102no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C2×Dic512yes—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—202no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—22no—
191C23×C5—41no—
192C23×C5—42no—
193C23×C5—42no—
194C23×C5—42no—
195C23×C5C3×C22⋊C411yescharacteristic
196C23×C5C3×C22⋊C411yescharacteristic
197C23×C5C2×C3×D411yescharacteristic
198C5×D4—42no—
199C5×D4—42no—
200C5×D4—44no—
201C5×D4—44no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—42no—
210C2×C4×C5C3×C22⋊C411yescharacteristic
211C2×C4×C5C3×C22⋊C411yescharacteristic
212C2×C4×C5C22×C3×C411yescharacteristic
213C2×C4×C5C2×C3×D411yescharacteristic
214C2×Dic5—42no—
215C2×Dic5—42no—
216C2×Dic5—42no—
217#168—42no—
218C22×D4—21no—
219C22×D4C3×Dic511yescharacteristic, complemented
220C23×C4C2×C3×D511yescharacteristic
221C2×M16—101no—
222#121—21no—
223#121—21no—
224#121C3×Dic512yescomplemented
225#121C2×C3×D512yes—
226C2×C4⋊C4C3×Dic511yescharacteristic, complemented
227C2×C22⋊C4—21no—
228C2×C22⋊C4—101no—
229C22⋊C8—52no—
230C22⋊C8—101no—
231#95—52no—
232#95—101no—
233C2×C3×C5—22no—
234C2×C3×C5—22no—
235C2×C3×C5—41no—
236C2×C3×C5—82no—
237C2×C3×C5C2×#9911yescharacteristic
238C2×C3×C5#41811yescharacteristic
239C2×C3×C5#42111yescharacteristic
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—22no—
243C23×C3—41no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3—42no—
247C23×C3C22⋊Dic511yescharacteristic
248C23×C3C22⋊Dic511yescharacteristic
249C23×C3C2×C22⋊D511yescharacteristic
250C3×D4—42no—
251C3×D4—42no—
252C3×D4—44no—
253C3×D4—44no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—202no—
263C2×C3×C4—202no—
264C2×C3×C4—202no—
265C2×C3×C4C22⋊Dic511yescharacteristic
266C2×C3×C4C22⋊Dic511yescharacteristic
267C2×C3×C4C22×Dic511yescharacteristic
268C2×C3×C4C2×C22⋊D511yescharacteristic
269C3×C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—44no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5—42no—
281C22×C5—84no—
282C22×C5C3×#9912yes—
283C22×C5C2×C3×C22⋊C411yescharacteristic
284C22×C5C3×AGL(1,ℤ/8)12yes—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—42no—
290Dic5—82no—
291C24—21no—
292C24C3×C22⋊D511yescharacteristic
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—42no—
297C2×D4—44no—
298C2×D4C2×C3×Dic512yes—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—102no—
302C22×C4C2×C3×Dic511yescharacteristic
303C22×C4C2×C3×Dic511yescharacteristic
304C22×C4C3×C22⋊D511yescharacteristic
305C22×C4C3×C22⋊D511yescharacteristic
306C22×C4C3×C22⋊D511yescharacteristic
307C22×C4C22×C3×D511yescharacteristic
308M16—202no—
309C2×C8—102no—
310C4⋊C4—21no—
311C4⋊C4C2×C3×Dic512yes—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—202no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C22×C3—84no—
328C22×C3#396612yes—
329C22×C3#407812yes—
330C22×C3C2×C22⋊Dic511yescharacteristic
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—42no—
336C3×C4—402no—
337C2×C5—22no—
338C2×C5—22no—
339C2×C5—41no—
340C2×C5—82no—
341C2×C5C2×C3×#9911yescharacteristic
342C2×C5C3×#41811yescharacteristic
343C2×C5C3×#42111yescharacteristic
344C23—22no—
345C23—22no—
346C23—22no—
347C23—41no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23C3×C22⋊Dic511yescharacteristic
352C23C3×C22⋊Dic511yescharacteristic
353C23C2×C3×C22⋊D511yescharacteristic
354D4—42no—
355D4—42no—
356D4—44no—
357D4—44no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4—202no—
369C2×C4C3×C22⋊Dic511yescharacteristic
370C2×C4C3×C22⋊Dic511yescharacteristic
371C2×C4C22×C3×Dic511yescharacteristic
372C2×C4C2×C3×C22⋊D511yescharacteristic
373C8—202no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3—82no—
378C2×C3#6550411yescharacteristic
379C2×C3C2×#396611yescharacteristic
380C2×C3#6552511yescharacteristic
381C5C3×#151011yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—44no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—84no—
394C22C3×#396612yes—
395C22C3×#407812yes—
396C22C2×C3×C22⋊Dic511yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—402no—
403C3#1060246711yescharacteristic, direct product factor, Sylow
404C2—22no—
405C2—22no—
406C2—41no—
407C2—82no—
408C2C3×#6550411yescharacteristic
409C2C2×C3×#396611yescharacteristic
410C2C3×#6552511yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊Dic5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC2×C3×C5×#121C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#121D5
hypocenterC5C3×#1510
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C3×#65500C2semidirect
3. C3×#65496C2semidirect
4. C3×#64757C2semidirect
5. #10602467C3direct (N × H)
7. C22×C3×C5×D4C4semidirect
11. C3×C5×#121C4semidirect
13. C2×C3×C5×C4⋊C4C4semidirect
18. C3×#3963C22semidirect
20. C3×C22⋊#168C22semidirect
23. #65500C2×C3semidirect
24. #65496C2×C3semidirect
25. #64757C2×C3semidirect
55. C22×C5×D4C3×C4semidirect
59. C5×#121C3×C4semidirect
61. C2×C5×C4⋊C4C3×C4semidirect
66. #3963C22×C3semidirect
68. C22⋊#168C22×C3semidirect
101. C22×C3×D4Dic5semidirect
106. C3×#121Dic5semidirect
108. C2×C3×C4⋊C4Dic5semidirect
219. C22×D4C3×Dic5semidirect
224. #121C3×Dic5semidirect
226. C2×C4⋊C4C3×Dic5semidirect
315. C3×C5#1510semidirect
381. C5C3×#1510semidirect
403. C3#10602467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C3×#655002
C3×#654962
C3×#647572
#106024673
C3×#15105