Finite Group Databasebeta

← #14280949

Subgroups — #14280949

Order 1920.

496 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 112 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×#91325C211yesmaximal, characteristic
2#11751986C212yesmaximal
3#11746785C211yesmaximal, characteristic
4C3×#64914C211yesmaximal, characteristic
5#11746569C212yesmaximal
6#10604291—31nomaximal, Hall
7C22×#1204C411yescharacteristic
8C2×C4×Dic15C411yescharacteristic
9C2×C5×Dic3⋊C4C411yescharacteristic
10C2×C3×#683C2211yescharacteristic
11C2×#6669C2211yescharacteristic
12C2×Dic3×Dic5C411yescharacteristic
13C2×Dic3×Dic5C2211yescharacteristic
14#91325—22no—
15#91325—22no—
16#91241C2212yes—
17C3×C22⋊#170C2212yes—
18Dic3⋊#170—22no—
19Dic3×#170—22no—
20#68125—51nomaximal, Hall
21C2×#4033—31no—
22#65748—32no—
23#64914—31no—
24#64914—32no—
25#64914D311yescharacteristic
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×Dic15C2×C411yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C22×C5×Dic3C2×C411yescharacteristic
30C22×C5×Dic3C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2311yescharacteristic
33C2×#1204—22no—
34C2×#1204—22no—
35C2×#1204C814yescomplemented
36C2×C3⋊#170—22no—
37C2×C3×#170—22no—
38C4×Dic15—21no—
39C4×Dic15—21no—
40C5×Dic3⋊C4—22no—
41C3×#683—22no—
42#6669—22no—
43Dic3×Dic5—21no—
44Dic3×Dic5—21no—
45Dic3×Dic5D412yes—
46Dic3×Dic5D412yes—
47C2×#887—51no—
48#4718—52no—
49C3×#324—51no—
50#4528—51no—
51#4469—52no—
52C22×Dic10—31no—
53C2×C5×C4⋊C4—31no—
54C2×#683—31no—
55C2×#683C2×D311yescharacteristic
56C2×C4×Dic5—31no—
57C2×C4×Dic5—31no—
58C2×C4×Dic5—31no—
59#4033—62no—
60#4033—62no—
61C22⋊#170—32no—
62C22⋊#170C2×D312yes—
63C4⋊#170—62no—
64C4×#170—62no—
65#1461—151noSylow
66C23×C3×C5C22×C411yescharacteristic
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—41no—
69C2×Dic15—21no—
70C2×Dic15—21no—
71C2×Dic15—22no—
72C2×Dic15C22⋊C411yescharacteristic
73C2×Dic15C22⋊C411yescharacteristic
74C2×Dic15C2×C812yes—
75C2×C5×Dic3—21no—
76C2×C5×Dic3—41no—
77C2×C5×Dic3C22⋊C412yes—
78C2×C5×Dic3C2×C812yes—
79C2×C5×Dic3M1612yes—
80C2×C3×Dic5—21no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5C2×C812yes—
84C2×C3×Dic5C2×D412yes—
85#1204—28no—
86C3⋊#170—42no—
87C3×#170—42no—
88C22×Dic6—51no—
89C2×C3×C4⋊C4—51no—
90C2×Dic3⋊C4—51no—
91C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic
92C2×C4×Dic3—51no—
93C2×C4×Dic3—51no—
94C2×C4×Dic3—51no—
95#887—102no—
96#887—102no—
97C3×C22⋊C8—52no—
98#830—52no—
99Dic3⋊C8—102no—
100C8×Dic3—102no—
101C22×C4×C5—31no—
102C22×C4×C5—31no—
103C22×C4×C5C4×D311yescharacteristic
104C22×Dic5—31no—
105C22×Dic5—31no—
106C22×Dic5C4×D311yescharacteristic
107C22×Dic5C22×D311yescharacteristic
108C2×Dic10—34no—
109C2×Dic10—62no—
110C2×Dic10—62no—
111C2×#170—22no—
112C2×#170—62no—
113C5×C4⋊C4—62no—
114#683—22no—
115#683—62no—
116C4×Dic5—32no—
117C4×Dic5—32no—
118C4×Dic5—61no—
119C4×Dic5—61no—
120C4×Dic5—61no—
121C4×Dic5—61no—
122C2×C4×Q8—151no—
123#431—152no—
124#324—51no—
125#324—152no—
126#324—151no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5C22×C811yescharacteristic
131C22×C3×C5C2×M1611yescharacteristic
132C3×C4×C5—41no—
133Dic15—22no—
134Dic15—21no—
135Dic15#10112yes—
136C3×Dic5—22no—
137C3×Dic5—22no—
138C5×Dic3—41no—
139C5×Dic3C22⋊C814yes—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
143C22×Dic3—51no—
144C22×Dic3—51no—
145C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
146C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
147C2×Dic6—54no—
148C2×Dic6—102no—
149C2×Dic6—102no—
150C2×C3×C8—102no—
151C3×C4⋊C4—102no—
152Dic3⋊C4—22no—
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—32no—
164C2×C4×C5—32no—
165C2×C4×C5—32no—
166C2×C4×C5—41no—
167C2×C4×C5—61no—
168C2×C4×C5—121no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—31no—
172C2×Dic5—31no—
173C2×Dic5—32no—
174C2×Dic5—41no—
175C2×Dic5—62no—
176C2×Dic5—61no—
177C2×Dic5—61no—
178C2×Dic5D3×C812yes—
179C2×Dic5D3×D412yes—
180Dic10—68no—
181#170—42no—
182#170—122no—
183C22×Q8—151no—
184C4×Q8—302no—
185C4×Q8—302no—
186C2×C4⋊C4—31no—
187C2×C4⋊C4—51no—
188C2×C4⋊C4—151no—
189C2×C42—151no—
190C2×C42—151no—
191C2×C42—151no—
192C4⋊C8—302no—
193C22⋊C8—52no—
194C22⋊C8—152no—
195C4×C8—302no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5C2×C22⋊C811yescharacteristic
199C2×C3×C5#41011yescharacteristic
200C2×C3×C5C2×#10111yescharacteristic
201C23×C3C22×AGL(1,𝔽5)11yescharacteristic
202C2×C3×C4—21no—
203C2×C3×C4—41no—
204C2×C3×C4—52no—
205C2×C3×C4—52no—
206C2×C3×C4—101no—
207C2×C3×C4—101no—
208C2×C3×C4—201no—
209C2×Dic3—21no—
210C2×Dic3—41no—
211C2×Dic3—51no—
212C2×Dic3—52no—
213C2×Dic3—51no—
214C2×Dic3—102no—
215C2×Dic3—101no—
216C2×Dic3—101no—
217C2×Dic3D5⋊C812yes—
218C2×Dic3#70012yes—
219C2×Dic3C22⋊AGL(1,𝔽5)12yes—
220Dic6—108no—
221C3×C8—202no—
222C3⋊C8—202no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5D3×C22⋊C411yescharacteristic
226C22×C5C2×D3×C811yescharacteristic
227C22×C5D3×M1611yescharacteristic
228C4×C5—34no—
229C4×C5—41no—
230C4×C5—121no—
231Dic5—22no—
232Dic5—22no—
233Dic5—32no—
234Dic5—62no—
235Dic5—61no—
236C2×Q8—154no—
237C2×Q8—302no—
238C2×Q8—302no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4—151no—
244C22×C4—151no—
245C22×C4D3×AGL(1,𝔽5)11yescharacteristic
246C2×C8—102no—
247C2×C8—302no—
248C4⋊C4—62no—
249C4⋊C4—102no—
250C4⋊C4—302no—
251C42—152no—
252C42—152no—
253C42—301no—
254C42—301no—
255C42—301no—
256C42—301no—
257C3×C5#146111yescharacteristic, complemented, Hall
258C22×C3—21no—
259C22×C3—21no—
260C22×C3C2×D5⋊C811yescharacteristic
261C22×C3C2×#70011yescharacteristic
262C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C3×C4—41no—
264C3×C4—102no—
265C3×C4—102no—
266Dic3—41no—
267Dic3—52no—
268Dic3—102no—
269Dic3—101no—
270Dic3#400314yes—
271C2×C5—21no—
272C2×C5—21no—
273C2×C5D3×C22⋊C811yescharacteristic
274C2×C5#474011yescharacteristic
275C2×C5D3×#10111yescharacteristic
276C23C2×D3×AGL(1,𝔽5)11yescharacteristic
277Q8—308no—
278C2×C4—21no—
279C2×C4—32no—
280C2×C4—32no—
281C2×C4—32no—
282C2×C4—41no—
283C2×C4—52no—
284C2×C4—52no—
285C2×C4—61no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—121no—
289C2×C4—151no—
290C2×C4—152no—
291C2×C4—151no—
292C2×C4—201no—
293C2×C4—302no—
294C2×C4—301no—
295C2×C4—301no—
296C8—202no—
297C8—602no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3C2×#400311yescharacteristic
301C2×C3#6577111yescharacteristic
302C2×C3D5⋊#10111yescharacteristic
303C5#6812511yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22D3×D5⋊C811yescharacteristic
307C22D3×#70011yescharacteristic
308C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
309C4—34no—
310C4—41no—
311C4—102no—
312C4—102no—
313C4—121no—
314C4—152no—
315C4—302no—
316C4—301no—
317C3#1060429111yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2D3×#400311yescharacteristic
321C2#1175191811yescharacteristic
322C2#1175203111yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C22×C8
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1461
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
35. C2×#1204C8semidirect
257. C3×C5#1461semidirect
303. C5#68125semidirect
317. C3#10604291semidirect

Maximal subgroups

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

subgroupindex
C2×#913252
#117519862
#117467852
C3×#649142
#117465692
#106042913
#681255