Finite Group Databasebeta

← #14298417

Subgroups — #14298417

Order 1920.

544 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic
2#11748351C212yesmaximal
3C5×#4530C211yesmaximal, characteristic, complemented
4C3×#64750C211yesmaximal, characteristic, complemented
5#11745987C212yesmaximal, complemented
6#10599784—31nomaximal, Hall
7C22×C4×D15C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6714C412yes—
10C2×C4⋊Dic15C2211yescharacteristic
11C2×C4×Dic15C412yes—
12#91781—24no—
13C2×C5×#208C2212yes—
14C2×C3×#681C2212yes—
15#90957—24no—
16#68991—51nomaximal, Hall
17C2×#4038—31no—
18#65415—32no—
19C5×#343—31no—
20#64774—32no—
21#64750D311yescharacteristic, complemented
22C23×D15C2×C411yescharacteristic
23C22×C3×C4×C5C2×C412yes—
24C22×C3×C4×C5C2311yescharacteristic
25C22×Dic15C2×C411yescharacteristic
26C22×Dic15C2×C412yes—
27C2×C4×D15—22no—
28C2×C4×D15—21no—
29C2×C4×D15—21no—
30C2×C4×D15D414yes—
31C3×C5×C4⋊C4—22no—
32#6714—24no—
33C4⋊Dic15—22no—
34C4×Dic15—24no—
35C5×#208—22no—
36C5×#208—22no—
37C2×C5×C3⋊C8—22no—
38C3×#681—22no—
39C3×#681—22no—
40C2×C3×#168—22no—
41C2×#892—51no—
42#5126—52no—
43C3×#343—51no—
44#4554—52no—
45#4530D511yescharacteristic, complemented
46C22×C4×D5—31no—
47C2×C5×M16—32no—
48C2×C5×C4⋊C4C2×D311yescharacteristic
49C2×#685—32no—
50C2×C4⋊Dic5—31no—
51C2×C4×Dic5—32no—
52C2×#681C2×D312yes—
53#4038—64no—
54#3952—64no—
55#1822—151noSylow
56C23×C3×C5C22×C411yescharacteristic
57C22×D15—21no—
58C22×D15—21no—
59C22×D15—41no—
60C22×D15—41no—
61C22×D15C22⋊C412yes—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5#4112yes—
66C2×C3×C4×C5#4111yescharacteristic
67C2×C3×C4×C5#4111yescharacteristic
68C2×Dic15—21no—
69C2×Dic15—21no—
70C2×Dic15—22no—
71C2×Dic15—42no—
72C2×Dic15C22⋊C412yes—
73C4×D15—24no—
74C4×D15—24no—
75C3×#168—42no—
76C5×C3⋊C8—42no—
77C22×C4×D3—51no—
78C2×C3×M16—52no—
79C2×C3×C4⋊C4C2×D511yescharacteristic
80C2×(C2×D3)⋊C4—52no—
81C2×C4⋊Dic3—51no—
82C2×C4×Dic3—52no—
83C2×#208C2×D512yes—
84#892—104no—
85(C2×D3)⋊C8—104no—
86C23×D5—31no—
87C22×C4×C5C4×D312yes—
88C22×C4×C5C22×D311yescharacteristic
89C22×Dic5—31no—
90C22×Dic5—32no—
91C2×C4×D5—34no—
92C2×C4×D5—62no—
93C2×C4×D5—61no—
94C2×C4×D5—61no—
95C5×M16—62no—
96C5×M16—62no—
97C2×C5×C8—62no—
98C5×C4⋊C4—22no—
99#685—64no—
100C4⋊Dic5—62no—
101C4×Dic5—64no—
102#681—22no—
103#681—22no—
104C2×#168—22no—
105C2×#117—151no—
106#407—152no—
107#343—31no—
108#343—51no—
109#343—152no—
110C22×C3×C5—21no—
111C22×C3×C5—21no—
112C22×C3×C5C2×C22⋊C411yescharacteristic
113C22×C3×C5#11711yescharacteristic
114C22×C3×C5#11711yescharacteristic
115C2×D15—22no—
116C2×D15—22no—
117C2×D15—22no—
118C2×D15—42no—
119C2×D15—42no—
120C3×C4×C5—42no—
121C3×C4×C5#12312yes—
122C3×C4×C5#12312yes—
123Dic15—22no—
124Dic15—42no—
125C23×D3—51no—
126C22×C3×C4C4×D512yes—
127C22×C3×C4C22×D511yescharacteristic
128C22×Dic3—51no—
129C22×Dic3—52no—
130C2×C4×D3—54no—
131C2×C4×D3—102no—
132C2×C4×D3—101no—
133C2×C4×D3—101no—
134C3×M16—102no—
135C3×M16—102no—
136C2×C3×C8—102no—
137C3×C4⋊C4—22no—
138(C2×D3)⋊C4—104no—
139C4⋊Dic3—102no—
140C4×Dic3—104no—
141#208—22no—
142#208—22no—
143C2×C3⋊C8—22no—
144C23×C5C2×C4×D311yescharacteristic
145C22×D5—32no—
146C22×D5—61no—
147C22×D5—61no—
148C22×D5—121no—
149C22×D5—121no—
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5#23512yes—
153C2×C4×C5D3×D412yes—
154C2×C4×C5#23711yescharacteristic
155C2×C4×C5#23911yescharacteristic
156C2×Dic5—32no—
157C2×Dic5—61no—
158C2×Dic5—61no—
159C2×Dic5—62no—
160C2×Dic5—122no—
161C4×D5—64no—
162C4×D5—64no—
163C5×C8—122no—
164#168—42no—
165C23×C4—151no—
166C2×M16—32no—
167C2×M16—52no—
168#117—304no—
169C2×C4⋊C4—151no—
170C2×C4⋊C4D3×D511yescharacteristic
171C2×C22⋊C4—152no—
172C2×C42—152no—
173C22⋊C8—304no—
174C2×C3×C5—21no—
175C2×C3×C5—21no—
176C2×C3×C5#38111yescharacteristic
177C2×C3×C5#41311yescharacteristic
178C2×C3×C5#41311yescharacteristic
179D15—42no—
180C23×C3C2×C4×D511yescharacteristic
181C22×D3—52no—
182C22×D3—101no—
183C22×D3—101no—
184C22×D3—201no—
185C22×D3—201no—
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188C2×C3×C4#70912yes—
189C2×C3×C4D4×D512yes—
190C2×C3×C4#71111yescharacteristic
191C2×C3×C4#71311yescharacteristic
192C2×Dic3—52no—
193C2×Dic3—101no—
194C2×Dic3—101no—
195C2×Dic3—102no—
196C2×Dic3—202no—
197C4×D3—104no—
198C4×D3—104no—
199C3×C8—202no—
200C3⋊C8—42no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5#87211yescharacteristic
204C22×C5D3×C22⋊C411yescharacteristic
205C22×C5#89211yescharacteristic
206C2×D5—62no—
207C2×D5—62no—
208C2×D5—62no—
209C2×D5—122no—
210C2×D5—122no—
211C4×C5—42no—
212C4×C5#88312yes—
213C4×C5#89412yes—
214Dic5—62no—
215Dic5—122no—
216C24—151no—
217C22×C4—151no—
218C22×C4—154no—
219C22×C4—152no—
220C22×C4—301no—
221C22×C4—301no—
222C22×C4—302no—
223C22×C4#120012yes—
224C22×C4C2×D3×D511yescharacteristic
225M16—62no—
226M16—62no—
227M16—102no—
228M16—102no—
229C2×C8—62no—
230C2×C8—102no—
231C4⋊C4—22no—
232C4⋊C4—302no—
233C22⋊C4—304no—
234C42—304no—
235C3×C5#182211yescharacteristic, complemented, Hall
236C22×C3—21no—
237C22×C3—21no—
238C22×C3#401811yescharacteristic
239C22×C3D5×C22⋊C411yescharacteristic
240C22×C3#403811yescharacteristic
241C2×D3—102no—
242C2×D3—102no—
243C2×D3—102no—
244C2×D3—202no—
245C2×D3—202no—
246C3×C4—42no—
247C3×C4#402912yes—
248C3×C4#404012yes—
249Dic3—102no—
250Dic3—202no—
251C2×C5—21no—
252C2×C5—21no—
253C2×C5#466411yescharacteristic
254C2×C5#474511yescharacteristic
255C2×C5#475111yescharacteristic
256D5—122no—
257C23—152no—
258C23—301no—
259C23—301no—
260C23—601no—
261C23—601no—
262C23C2×#120011yescharacteristic
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—152no—
266C2×C4—301no—
267C2×C4—301no—
268C2×C4—304no—
269C2×C4—304no—
270C2×C4—302no—
271C2×C4—602no—
272C2×C4#676611yescharacteristic
273C2×C4#676811yescharacteristic
274C2×C4#677112yes—
275C2×C4#679012yes—
276C8—122no—
277C8—202no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3#6495311yescharacteristic
281C2×C3#6503411yescharacteristic
282C2×C3#6504011yescharacteristic
283D3—202no—
284C5#6899111yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22—302no—
288C22—302no—
289C22—302no—
290C22—602no—
291C22—602no—
292C22#9134711yescharacteristic
293C22#9138611yescharacteristic
294C22#9156111yescharacteristic
295C4—42no—
296C4—302no—
297C4—602no—
298C4#9135412yes—
299C4#9135512yes—
300C3#1059978411yescharacteristic, complemented, Sylow
301C2—21no—
302C2—21no—
303C2—602no—
304C2#1174860611yescharacteristic
305C2#1174912811yescharacteristic
306C2#1174937411yescharacteristic
subgroupG/H
centerC22#91561
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×#4530C2semidirect
4. C3×#64750C2semidirect
5. #11745987C2semidirect
21. #64750D3semidirect
45. #4530D5semidirect
235. C3×C5#1822semidirect
284. C5#68991semidirect
300. C3#10599784semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
#117483512
C5×#45302
C3×#647502
#117459872
#105997843
#689915