Finite Group Databasebeta

← C3×#10602482 #14283306

Subgroups — C3×#10602482 #14283306

Order 1920.

548 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C3×#65500C211yesmaximal, characteristic
3C3×#65496C211yesmaximal, characteristic
4C3×#64758C214yesmaximal, complemented
5#10602482C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×Q8C411yescharacteristic, complemented
7C23×C3×C4×C5C2211yescharacteristic
8C3×C5×C22⋊Q8—21no—
9C3×C5×C22⋊Q8—21no—
10C3×C5×C22⋊Q8C412yescomplemented
11C3×C5×C22⋊Q8C2212yes—
12C2×C3×C5×C4⋊C4—21no—
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×#3963C2212yes—
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yes—
21C3×#1511—51nomaximal, Hall
22C2×C5×C22⋊Q8C2×C311yescharacteristic
23#65500C2×C311yescharacteristic
24#65496C2×C311yescharacteristic
25#64758C2×C314yescomplemented
26C24×C3×C5D411yescharacteristic
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8—42no—
29C2×C3×C5×Q8C2×C412yes—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5—42no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×Dic5—22no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4C2×C412yes—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C22⋊Dic5—42no—
47C3×#681—42no—
48C2×C3×#168—22no—
49C2×C3×C22⋊Q8D511yescharacteristic
50C3×#407—51no—
51C3×#381—51no—
52C3×#328—54no—
53C22×C5×Q8C3×C411yescharacteristic, complemented
54C23×C4×C5C22×C311yescharacteristic
55C5×C22⋊Q8—21no—
56C5×C22⋊Q8—21no—
57C5×C22⋊Q8C3×C412yescomplemented
58C5×C22⋊Q8C22×C312yes—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
61C2×C5×C22⋊C4—21no—
62C2×C22⋊Dic5—21no—
63C2×#681—21no—
64#3963—21no—
65#3963C22×C312yes—
66C22⋊#168—21no—
67C22⋊#168C22×C312yes—
68#1511—51noSylow
69C23×C3×C5—22no—
70C23×C3×C5—22no—
71C23×C3×C5—41no—
72C23×C3×C5C22⋊C411yescharacteristic
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C3×C5×Q8—42no—
76C3×C5×Q8—42no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—42no—
86C2×C3×C4×C5—42no—
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×Dic5—42no—
92C2×C3×Dic5—42no—
93C2×C3×Dic5—42no—
94C3×#168—42no—
95C22×C3×Q8Dic511yescharacteristic, complemented
96C23×C3×C4C2×D511yescharacteristic
97C2×C3×M16—101no—
98C3×C22⋊Q8—21no—
99C3×C22⋊Q8—21no—
100C3×C22⋊Q8Dic512yescomplemented
101C3×C22⋊Q8C2×D512yes—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4Dic511yescharacteristic, complemented
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—101no—
106C3×C22⋊C8—52no—
107C3×C22⋊C8—101no—
108C3×#95—52no—
109C3×#95—101no—
110C24×C5C3×D411yescharacteristic
111C2×C5×Q8—21no—
112C2×C5×Q8—42no—
113C2×C5×Q8C2×C3×C412yes—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—42no—
117C22×C4×C5C2×C3×C411yescharacteristic
118C22×C4×C5C2×C3×C411yescharacteristic
119C22×C4×C5C3×D411yescharacteristic
120C22×C4×C5C3×D411yescharacteristic
121C22×C4×C5C3×D411yescharacteristic
122C22×C4×C5C23×C311yescharacteristic
123C22×Dic5—22no—
124C5×C4⋊C4—22no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—22no—
127C5×C4⋊C4C2×C3×C412yes—
128C5×C22⋊C4—22no—
129C5×C22⋊C4—22no—
130C22⋊Dic5—42no—
131#681—42no—
132C2×#168—22no—
133C2×C22⋊Q8C3×D511yescharacteristic
134#407—51no—
135#381—51no—
136#328—54no—
137C22×C3×C5—21no—
138C22×C3×C5—21no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—44no—
145C22×C3×C5#9912yes—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C22×C3×C5#13712yes—
148C3×C4×C5—21no—
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151C3×C4×C5—21no—
152C3×C4×C5—42no—
153C3×C4×C5—42no—
154C3×Dic5—82no—
155C24×C3C22⋊D511yescharacteristic
156C2×C3×Q8—21no—
157C2×C3×Q8—42no—
158C2×C3×Q8C2×Dic512yes—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—42no—
162C22×C3×C4—102no—
163C22×C3×C4C2×Dic511yescharacteristic
164C22×C3×C4C2×Dic511yescharacteristic
165C22×C3×C4C22⋊D511yescharacteristic
166C22×C3×C4C22⋊D511yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C22×C3×C4C22×D511yescharacteristic
169C3×M16—202no—
170C2×C3×C8—102no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4C2×Dic512yes—
175C3×C22⋊C4—22no—
176C3×C22⋊C4—22no—
177C3×C22⋊C4—202no—
178C23×C5—22no—
179C23×C5—22no—
180C23×C5—41no—
181C23×C5C3×C22⋊C411yescharacteristic
182C23×C5C3×C22⋊C411yescharacteristic
183C23×C5C2×C3×D411yescharacteristic
184C5×Q8—42no—
185C5×Q8—42no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—42no—
195C2×C4×C5—42no—
196C2×C4×C5C3×C22⋊C411yescharacteristic
197C2×C4×C5C3×C22⋊C411yescharacteristic
198C2×C4×C5C22×C3×C411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×Dic5—42no—
201C2×Dic5—42no—
202C2×Dic5—42no—
203#168—42no—
204C22×Q8C3×Dic511yescharacteristic, complemented
205C23×C4C2×C3×D511yescharacteristic
206C2×M16—101no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8C3×Dic512yescomplemented
210C22⋊Q8C2×C3×D512yes—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C3×Dic511yescharacteristic, complemented
213C2×C22⋊C4—21no—
214C2×C22⋊C4—101no—
215C22⋊C8—52no—
216C22⋊C8—101no—
217#95—52no—
218#95—101no—
219C2×C3×C5—22no—
220C2×C3×C5—22no—
221C2×C3×C5—41no—
222C2×C3×C5C2×#9911yescharacteristic
223C2×C3×C5#41911yescharacteristic
224C2×C3×C5#42111yescharacteristic
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—41no—
228C23×C3C22⋊Dic511yescharacteristic
229C23×C3C22⋊Dic511yescharacteristic
230C23×C3C2×C22⋊D511yescharacteristic
231C3×Q8—42no—
232C3×Q8—42no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—202no—
244C2×C3×C4—202no—
245C2×C3×C4—202no—
246C2×C3×C4C22⋊Dic511yescharacteristic
247C2×C3×C4C22⋊Dic511yescharacteristic
248C2×C3×C4C22×Dic511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C3×C8—202no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—44no—
259C22×C5C3×#9912yes—
260C22×C5C2×C3×C22⋊C411yescharacteristic
261C22×C5C3×#13712yes—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—42no—
267C4×C5—42no—
268Dic5—82no—
269C24C3×C22⋊D511yescharacteristic
270C2×Q8—21no—
271C2×Q8—42no—
272C2×Q8C2×C3×Dic512yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—102no—
277C22×C4C2×C3×Dic511yescharacteristic
278C22×C4C2×C3×Dic511yescharacteristic
279C22×C4C3×C22⋊D511yescharacteristic
280C22×C4C3×C22⋊D511yescharacteristic
281C22×C4C3×C22⋊D511yescharacteristic
282C22×C4C22×C3×D511yescharacteristic
283M16—202no—
284C2×C8—102no—
285C4⋊C4—22no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4C2×C3×Dic512yes—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—202no—
292C3×C5#151111yescharacteristic, complemented, Hall
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—44no—
301C22×C3#396612yes—
302C22×C3#408812yes—
303C22×C3C2×C22⋊Dic511yescharacteristic
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—42no—
309C3×C4—42no—
310C3×C4—402no—
311C2×C5—22no—
312C2×C5—22no—
313C2×C5—41no—
314C2×C5C2×C3×#9911yescharacteristic
315C2×C5C3×#41911yescharacteristic
316C2×C5C3×#42111yescharacteristic
317C23—22no—
318C23—22no—
319C23—41no—
320C23C3×C22⋊Dic511yescharacteristic
321C23C3×C22⋊Dic511yescharacteristic
322C23C2×C3×C22⋊D511yescharacteristic
323Q8—42no—
324Q8—42no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—202no—
336C2×C4—202no—
337C2×C4—202no—
338C2×C4C3×C22⋊Dic511yescharacteristic
339C2×C4C3×C22⋊Dic511yescharacteristic
340C2×C4C22×C3×Dic511yescharacteristic
341C2×C4C2×C3×C22⋊D511yescharacteristic
342C8—202no—
343C2×C3—22no—
344C2×C3—22no—
345C2×C3—41no—
346C2×C3C2×#396611yescharacteristic
347C2×C3#6551411yescharacteristic
348C2×C3#6552511yescharacteristic
349C5C3×#151111yescharacteristic, complemented, Sylow
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—44no—
358C22C3×#396612yes—
359C22C3×#408812yes—
360C22C2×C3×C22⋊Dic511yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—402no—
368C3#1060248211yescharacteristic, direct product factor, Sylow
369C2—22no—
370C2—22no—
371C2—41no—
372C2C2×C3×#396611yescharacteristic
373C2C3×#6551411yescharacteristic
374C2C3×#6552511yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊Dic5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×C22⋊Q8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C22⋊Q8D5
hypocenterC5C3×#1511
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#64758C2semidirect
5. #10602482C3direct (N × H)
6. C22×C3×C5×Q8C4semidirect
10. C3×C5×C22⋊Q8C4semidirect
13. C2×C3×C5×C4⋊C4C4semidirect
25. #64758C2×C3semidirect
53. C22×C5×Q8C3×C4semidirect
57. C5×C22⋊Q8C3×C4semidirect
60. C2×C5×C4⋊C4C3×C4semidirect
95. C22×C3×Q8Dic5semidirect
100. C3×C22⋊Q8Dic5semidirect
103. C2×C3×C4⋊C4Dic5semidirect
204. C22×Q8C3×Dic5semidirect
209. C22⋊Q8C3×Dic5semidirect
212. C2×C4⋊C4C3×Dic5semidirect
292. C3×C5#1511semidirect
349. C5C3×#1511semidirect
368. C3#10602482direct (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×C22⋊Q82
C3×#655002
C3×#654962
C3×#647582
#106024823
C3×#15115