Finite Group Databasebeta

← #14322765

Subgroups — #14322765

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4018C211yesmaximal, characteristic
2#11751036C211yesmaximal, characteristic, complemented
3C5×#4936C211yesmaximal, characteristic, complemented
4#11748772C214yesmaximal
5#11748759C212yesmaximal
6#11748691C214yesmaximal, complemented
7Dic5×C4⋊Dic3C212yesmaximal, complemented
8#10605955—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×C4⋊Dic15C2212yes—
12C2×C4⋊Dic15C2214yes—
13C2×C5×C4⋊Dic3C2212yes—
14C2×C3×#685C2212yes—
15C2×C3×#683C2212yes—
16C2×C3×C4×Dic5C2211yescharacteristic
17C3×#4018C418yescomplemented
18C2×#6665C2214yes—
19C2×Dic3×Dic5C2214yes—
20C5×C3⋊#95C2214yes—
21#90994C2214yes—
22#90994C2214yes—
23#82231—51nomaximal, Hall
24C2×#4018D311yescharacteristic
25C5×#382—31no—
26#65276—32no—
27C4⋊C4×Dic5—32no—
28#65224—31no—
29#64959—34no—
30#64944—34no—
31C23×C3×D5C2311yescharacteristic
32C22×C3×C4×C5C2312yes—
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15C2314yes—
35C22×C5×Dic3C2314yes—
36C22×C3×Dic5C2311yescharacteristic
37C22×C3×Dic5C2312yes—
38C2×C3×C4×D5—22no—
39C2×C3×C4×D5—22no—
40C2×C3×C4×D5C2×C414yes—
41C3×C42×C5C2×C414yes—
42C4⋊Dic15—24no—
43C4⋊Dic15—44no—
44C5×C4⋊Dic3—24no—
45C3×#685C2×C418yes—
46C3×#683C2×C418yes—
47C3×C4×Dic5C2×C414yes—
48#6665—44no—
49Dic3×Dic5—44no—
50C2×C3×#117—51no—
51#5212—52no—
52#4980—54no—
53#4951—54no—
54#4936D511yescharacteristic, complemented
55#4935—51no—
56C4×C4⋊Dic3—52no—
57C22×C4×D5C2×D311yescharacteristic
58C2×C5×C4⋊C4—32no—
59C2×C42×C5C2×D311yescharacteristic
60C2×#685—34no—
61C2×#685C2×D312yes—
62C2×C4⋊Dic5—32no—
63C2×C4⋊Dic5—34no—
64C2×#683C2×D312yes—
65C2×C4×Dic5—34no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4018Dic318yescomplemented
68C5×#95—34no—
69#3963—34no—
70#3963—34no—
71#2314—151noSylow
72C23×C3×C5C2411yescharacteristic
73C22×C3×D5—21no—
74C22×C3×D5—21no—
75C22×C3×D5—22no—
76C22×C3×D5—22no—
77C22×C3×D5C22×C412yes—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5C22×C414yes—
81C2×C3×C4×C5C22×C412yes—
82C2×C3×C4×C5#4112yes—
83C2×C3×C4×C5#4112yes—
84C2×Dic15—24no—
85C2×Dic15—24no—
86C2×Dic15—24no—
87C2×C5×Dic3—24no—
88C2×C5×Dic3—24no—
89C2×C5×Dic3—24no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5C22×C414yes—
95C2×C3×Dic5C22×C412yes—
96C3×C4×D5—28no—
97C23×C3×C4—51no—
98C3×#117—58no—
99C2×C3×C4⋊C4—52no—
100C2×C3×C22⋊C4—52no—
101C2×C3×C42—51no—
102C2×C3×C42C2×D511yescharacteristic
103C2×#217—54no—
104C2×C4⋊Dic3—52no—
105C2×C4⋊Dic3—54no—
106C2×C4⋊Dic3C2×D512yes—
107C2×C4×Dic3—54no—
108C3⋊#95—54no—
109C3⋊#95—54no—
110C3⋊#95C2×D514yes—
111C23×D5C22×D311yescharacteristic
112C22×C4×C5—34no—
113C22×C4×C5C22×D312yes—
114C22×C4×C5C22×D311yescharacteristic
115C22×Dic5—34no—
116C22×Dic5C22×D311yescharacteristic
117C22×Dic5C22×D312yes—
118C2×C4×D5—22no—
119C2×C4×D5—22no—
120C2×C4×D5C2×Dic314yes—
121C5×C4⋊C4—64no—
122C42×C5C2×Dic314yes—
123#685—124no—
124#685C2×Dic318yes—
125C4⋊Dic5—64no—
126C4⋊Dic5—124no—
127#683C2×Dic318yes—
128C4×Dic5—124no—
129C4×Dic5C2×Dic314yes—
130C2×#117—51no—
131#388—154no—
132#387—154no—
133#384—151no—
134#382—31no—
135#380—152no—
136C4×C4⋊C4—152no—
137C22×C3×C5C23×C411yescharacteristic
138C22×C3×C5C2×#4111yescharacteristic
139C22×C3×C5C2×#4111yescharacteristic
140C22×C3×C5H(5,𝔽2)12yes—
141C22×C3×C52−1+412yes—
142C2×C3×D5—22no—
143C2×C3×D5—24no—
144C2×C3×D5—41no—
145C2×C3×D5—41no—
146C2×C3×D5—42no—
147C3×C4×C5—24no—
148C3×C4×C5#11714yes—
149Dic15—44no—
150C3×Dic5—22no—
151C3×Dic5—24no—
152C5×Dic3—44no—
153C24×C3—51no—
154C22×C3×C4—51no—
155C22×C3×C4—52no—
156C22×C3×C4—54no—
157C22×C3×C4—102no—
158C22×C3×C4—102no—
159C22×C3×C4C22×D512yes—
160C22×C3×C4C22×D511yescharacteristic
161C22×Dic3—54no—
162C22×Dic3C22×D514yes—
163C3×C4⋊C4—58no—
164C3×C22⋊C4—58no—
165C3×C42—54no—
166C3×C42C4×D514yes—
167#217—204no—
168C4⋊Dic3—24no—
169C4⋊Dic3—104no—
170C4⋊Dic3—204no—
171C4×Dic3—204no—
172C23×C5C23×D311yescharacteristic
173C22×D5—21no—
174C22×D5—21no—
175C22×D5—22no—
176C22×D5—22no—
177C22×D5C22×Dic312yes—
178C2×C4×C5—22no—
179C2×C4×C5—22no—
180C2×C4×C5—64no—
181C2×C4×C5—64no—
182C2×C4×C5—64no—
183C2×C4×C5#23512yes—
184C2×C4×C5#23512yes—
185C2×C4×C5C22×Dic314yes—
186C2×C4×C5C22×Dic312yes—
187C2×Dic5—21no—
188C2×Dic5—21no—
189C2×Dic5—22no—
190C2×Dic5—22no—
191C2×Dic5—64no—
192C2×Dic5—64no—
193C2×Dic5—64no—
194C2×Dic5C22×Dic314yes—
195C2×Dic5C22×Dic312yes—
196C4×D5—28no—
197C23×C4—51no—
198#117—58no—
199C2×C4⋊C4—32no—
200C2×C4⋊C4—52no—
201C2×C4⋊C4—152no—
202C2×C4⋊C4—154no—
203C2×C22⋊C4—52no—
204C2×C22⋊C4—154no—
205C2×C42—51no—
206C2×C42—154no—
207C2×C42D3×D511yescharacteristic
208#95—34no—
209#95—154no—
210#95—154no—
211C2×C3×C5C2×#11711yescharacteristic
212C2×C3×C5#52012yes—
213C2×C3×C5#54011yescharacteristic
214C2×C3×C5#54111yescharacteristic
215C2×C3×C5#54212yes—
216C3×D5—42no—
217C23×C3—52no—
218C23×C3—101no—
219C23×C3—101no—
220C23×C3—102no—
221C23×C3—102no—
222C23×C3C23×D511yescharacteristic
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—54no—
226C2×C3×C4—52no—
227C2×C3×C4—101no—
228C2×C3×C4—101no—
229C2×C3×C4—102no—
230C2×C3×C4—102no—
231C2×C3×C4—108no—
232C2×C3×C4C2×C4×D514yes—
233C2×C3×C4C2×C4×D512yes—
234C2×C3×C4#71112yes—
235C2×C3×C4#71312yes—
236C2×Dic3—24no—
237C2×Dic3—24no—
238C2×Dic3—24no—
239C2×Dic3—104no—
240C2×Dic3—104no—
241C2×Dic3—104no—
242C22×C5C2×#23511yescharacteristic
243C22×C5C2×#23511yescharacteristic
244C22×C5#100912yes—
245C22×C5#101012yes—
246C22×C5C23×Dic311yescharacteristic
247C2×D5—22no—
248C2×D5—24no—
249C2×D5—41no—
250C2×D5—42no—
251C2×D5—41no—
252C4×C5—24no—
253C4×C5—124no—
254C4×C5#92614yes—
255Dic5—22no—
256Dic5—24no—
257Dic5—124no—
258C24—51no—
259C22×C4—34no—
260C22×C4—51no—
261C22×C4—52no—
262C22×C4—54no—
263C22×C4—102no—
264C22×C4—102no—
265C22×C4—154no—
266C22×C4C2×D3×D512yes—
267C22×C4C2×D3×D511yescharacteristic
268C4⋊C4—58no—
269C4⋊C4—64no—
270C4⋊C4—304no—
271C4⋊C4—604no—
272C22⋊C4—58no—
273C22⋊C4—604no—
274C42—54no—
275C42—604no—
276C42D5×Dic314yes—
277C3×C5#231411yescharacteristic, complemented, Hall
278C22×C3—102no—
279C22×C3—104no—
280C22×C3—202no—
281C22×C3—201no—
282C22×C3—201no—
283C22×C3C22×C4×D511yescharacteristic
284C22×C3C2×#71111yescharacteristic
285C22×C3C2×#71311yescharacteristic
286C22×C3#414912yes—
287C22×C3#415012yes—
288C3×C4—24no—
289C3×C4—102no—
290C3×C4—104no—
291C3×C4#403814yes—
292Dic3—44no—
293Dic3—204no—
294C2×C5#551811yescharacteristic
295C2×C5#553412yes—
296C2×C5#553511yescharacteristic
297C2×C5C2×#92611yescharacteristic
298C2×C5#582712yes—
299D5—42no—
300C23—52no—
301C23—102no—
302C23—101no—
303C23—101no—
304C23—102no—
305C23C22×D3×D511yescharacteristic
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—54no—
309C2×C4—52no—
310C2×C4—64no—
311C2×C4—64no—
312C2×C4—64no—
313C2×C4—102no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—102no—
317C2×C4—108no—
318C2×C4—304no—
319C2×C4—304no—
320C2×C4—304no—
321C2×C4#677212yes—
322C2×C4#677312yes—
323C2×C4C2×D5×Dic314yes—
324C2×C4C2×D5×Dic312yes—
325C2×C3—202no—
326C2×C3C2×#403811yescharacteristic
327C2×C3#6585712yes—
328C2×C3#6601612yes—
329C2×C3#6603111yescharacteristic
330C2×C3#6603211yescharacteristic
331C5#8223111yescharacteristic, complemented, Sylow
332C22—104no—
333C22—102no—
334C22—202no—
335C22—201no—
336C22—201no—
337C22#9200112yes—
338C22C2×#677211yescharacteristic
339C22C2×#677311yescharacteristic
340C22#9201912yes—
341C22C22×D5×Dic311yescharacteristic
342C4—24no—
343C4—104no—
344C4—102no—
345C4—124no—
346C4—604no—
347C4#9135814yes—
348C3#1060595511yescharacteristic, complemented, Sylow
349C2—202no—
350C2#1175251011yescharacteristic
351C2#1175271712yes—
352C2#1175271911yescharacteristic
353C2C2×#9135811yescharacteristic
354C2#1175450912yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2314
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751036C2semidirect
3. C5×#4936C2semidirect
6. #11748691C2semidirect
7. Dic5×C4⋊Dic3C2semidirect
17. C3×#4018C4semidirect
54. #4936D5semidirect
67. #4018Dic3semidirect
277. C3×C5#2314semidirect
331. C5#82231semidirect
348. C3#10605955semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
#117510362
C5×#49362
#117487722
#117487592
#117486912
Dic5×C4⋊Dic32
#106059553
#822315