Finite Group Databasebeta

← #14281141

Subgroups — #14281141

Order 1920.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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×#91776C211yesmaximal, characteristic
2#11750820C212yesmaximal
3C3×C5×#324C211yesmaximal, characteristic
4#11746349C211yesmaximal, characteristic
5#11746290C212yesmaximal
6#10598920—31nomaximal, Hall
7C22×Dic30C411yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6712C411yescharacteristic
10C2×#6712C2211yescharacteristic
11C2×C4×Dic15C411yescharacteristic
12C2×C4×Dic15C411yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14#91776—22no—
15#91776—22no—
16C3×C5×C22⋊C8C2212yes—
17#91114C2212yes—
18#91099—22no—
19#91098—22no—
20#68127—51nomaximal, Hall
21C2×#4033—31no—
22#65008—32no—
23C5×#324D311yescharacteristic
24#64748—31no—
25#64689—32no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C22×Dic15C2×C411yescharacteristic
31C22×Dic15C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C2×Dic30—22no—
34C2×Dic30—22no—
35C2×Dic30—22no—
36C2×C3×C5×C8—22no—
37C3×C5×C4⋊C4—22no—
38#6712—22no—
39#6712—22no—
40C4×Dic15—21no—
41C4×Dic15—21no—
42C4×Dic15—21no—
43C4×Dic15—21no—
44C4×Dic15D412yes—
45C4×Dic15D412yes—
46C2×C3⋊#168—22no—
47C2×#887—51no—
48#4719—52no—
49C3×#324D511yescharacteristic
50#4528—51no—
51#4469—52no—
52C22×Dic10—31no—
53C2×C5×C4⋊C4C2×D311yescharacteristic
54C2×#683—31no—
55C2×#683—31no—
56C2×C4×Dic5—31no—
57C2×C4×Dic5—31no—
58C2×C4×Dic5—31no—
59#4033—62no—
60#4033—62no—
61C5×C22⋊C8C2×D312yes—
62C22⋊#168—32no—
63#3947—62no—
64#3946—62no—
65#1467—151noSylow
66C23×C3×C5C22×C411yescharacteristic
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5M1612yes—
73C2×C3×C4×C5C2×D412yes—
74C2×Dic15—21no—
75C2×Dic15—21no—
76C2×Dic15—21no—
77C2×Dic15—21no—
78C2×Dic15—22no—
79C2×Dic15—21no—
80C2×Dic15—41no—
81C2×Dic15C22⋊C411yescharacteristic
82C2×Dic15C22⋊C412yes—
83C2×Dic15C22⋊C411yescharacteristic
84C2×Dic15M1612yes—
85Dic30—28no—
86C3×C5×C8—42no—
87C3⋊#168—42no—
88C22×Dic6—51no—
89C2×C3×C4⋊C4C2×D511yescharacteristic
90C2×Dic3⋊C4—51no—
91C2×Dic3⋊C4—51no—
92C2×C4×Dic3—51no—
93C2×C4×Dic3—51no—
94C2×C4×Dic3—51no—
95#887—102no—
96#887—102no—
97C3×C22⋊C8C2×D512yes—
98#830—52no—
99#815—102no—
100Dic3⋊C8—102no—
101C22×C4×C5C4×D311yescharacteristic
102C22×C4×C5C4×D311yescharacteristic
103C22×C4×C5C22×D311yescharacteristic
104C22×Dic5—31no—
105C22×Dic5—31no—
106C22×Dic5—31no—
107C22×Dic5—31no—
108C2×Dic10—62no—
109C2×Dic10—62no—
110C2×Dic10—62no—
111C2×C5×C8—22no—
112C5×C4⋊C4—22no—
113#683—62no—
114#683—62no—
115C4×Dic5—32no—
116C4×Dic5—32no—
117C4×Dic5—61no—
118C4×Dic5—61no—
119C4×Dic5—61no—
120C4×Dic5—61no—
121C2×#168—62no—
122C2×C4×Q8—151no—
123#432—152no—
124#324—151no—
125#324—152no—
126#324D1511yescharacteristic
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5C2×M1611yescharacteristic
131C22×C3×C5C2×M1611yescharacteristic
132C3×C4×C5—22no—
133C3×C4×C5—22no—
134C3×C4×C5—41no—
135Dic15—22no—
136Dic15—22no—
137Dic15—21no—
138Dic15—41no—
139Dic15#10112yes—
140C22×C3×C4C4×D511yescharacteristic
141C22×C3×C4C4×D511yescharacteristic
142C22×C3×C4C22×D511yescharacteristic
143C22×Dic3—51no—
144C22×Dic3—51no—
145C22×Dic3—51no—
146C22×Dic3—51no—
147C2×Dic6—102no—
148C2×Dic6—102no—
149C2×Dic6—102no—
150C2×C3×C8—22no—
151C3×C4⋊C4—22no—
152Dic3⋊C4—102no—
153Dic3⋊C4—102no—
154C4×Dic3—52no—
155C4×Dic3—52no—
156C4×Dic3—101no—
157C4×Dic3—101no—
158C4×Dic3—101no—
159C4×Dic3—101no—
160C2×C3⋊C8—102no—
161C23×C5C2×C4×D311yescharacteristic
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5ΓL(1,𝔽25)12yes—
168C2×C4×C5D3×D412yes—
169C2×Dic5—31no—
170C2×Dic5—31no—
171C2×Dic5—32no—
172C2×Dic5—32no—
173C2×Dic5—62no—
174C2×Dic5—61no—
175C2×Dic5—61no—
176C2×Dic5—61no—
177C2×Dic5—61no—
178C2×Dic5—61no—
179C2×Dic5—121no—
180Dic10—68no—
181C5×C8—42no—
182#168—122no—
183C22×Q8—151no—
184C4×Q8—302no—
185C4×Q8—302no—
186C2×C4⋊C4—151no—
187C2×C4⋊C4—151no—
188C2×C4⋊C4C2×D1511yescharacteristic
189C2×C42—151no—
190C2×C42—151no—
191C2×C42—151no—
192C4⋊C8—302no—
193C22⋊C8—152no—
194C22⋊C8C2×D1512yes—
195#97—302no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5#40711yescharacteristic
199C2×C3×C5#41011yescharacteristic
200C2×C3×C5C2×#10111yescharacteristic
201C23×C3C2×C4×D511yescharacteristic
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4#67612yes—
208C2×C3×C4D4×D512yes—
209C2×Dic3—51no—
210C2×Dic3—51no—
211C2×Dic3—52no—
212C2×Dic3—52no—
213C2×Dic3—102no—
214C2×Dic3—101no—
215C2×Dic3—101no—
216C2×Dic3—101no—
217C2×Dic3—101no—
218C2×Dic3—101no—
219C2×Dic3—201no—
220Dic6—108no—
221C3×C8—42no—
222C3⋊C8—202no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5D3×C22⋊C411yescharacteristic
226C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
227C22×C5D3×M1611yescharacteristic
228C4×C5—22no—
229C4×C5—22no—
230C4×C5—41no—
231Dic5—32no—
232Dic5—62no—
233Dic5—62no—
234Dic5—61no—
235Dic5—121no—
236C2×Q8—302no—
237C2×Q8—302no—
238C2×Q8—302no—
239C22×C4—151no—
240C22×C4—151no—
241C22×C4—151no—
242C22×C4—151no—
243C22×C4C4×D1511yescharacteristic
244C22×C4C4×D1511yescharacteristic
245C22×C4C22×D1511yescharacteristic
246C2×C8—22no—
247C2×C8—302no—
248C4⋊C4—22no—
249C4⋊C4—302no—
250C4⋊C4—302no—
251C42—152no—
252C42—152no—
253C42—301no—
254C42—301no—
255C42—301no—
256C42—301no—
257C3×C5#146711yescharacteristic, complemented, Hall
258C22×C3—21no—
259C22×C3—21no—
260C22×C3D5×C22⋊C411yescharacteristic
261C22×C3C2×#67611yescharacteristic
262C22×C3D5×M1611yescharacteristic
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—41no—
266Dic3—52no—
267Dic3—101no—
268Dic3—102no—
269Dic3—102no—
270Dic3—201no—
271C2×C5—21no—
272C2×C5—21no—
273C2×C5#472611yescharacteristic
274C2×C5#474011yescharacteristic
275C2×C5D3×#10111yescharacteristic
276C23C2×C4×D1511yescharacteristic
277Q8—308no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—151no—
284C2×C4—151no—
285C2×C4—152no—
286C2×C4—152no—
287C2×C4—302no—
288C2×C4—301no—
289C2×C4—301no—
290C2×C4—301no—
291C2×C4—301no—
292C2×C4—301no—
293C2×C4—601no—
294C2×C4#670512yes—
295C2×C4D4×D1512yes—
296C8—42no—
297C8—602no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3#6501511yescharacteristic
301C2×C3#6502911yescharacteristic
302C2×C3D5×#10111yescharacteristic
303C5#6812711yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22C22⋊C4×D1511yescharacteristic
307C22C2×#670511yescharacteristic
308C22M16×D1511yescharacteristic
309C4—22no—
310C4—22no—
311C4—41no—
312C4—152no—
313C4—302no—
314C4—302no—
315C4—301no—
316C4—601no—
317C3#1059892011yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2#1175082711yescharacteristic
321C2#1175084111yescharacteristic
322C2D15×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#324C2
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×C4×C5C23
hypercenter#324D15
hypocenterC3×C5#1467
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
257. C3×C5#1467semidirect
303. C5#68127semidirect
317. C3#10598920semidirect

Maximal subgroups

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

subgroupindex
C2×#917762
#117508202
C3×C5×#3242
#117463492
#117462902
#105989203
#681275