Finite Group Databasebeta

← #14284343

Subgroups — #14284343

Order 1920.

496 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C3×D5×#124C211yesmaximal, characteristic
2#11752342C212yesmaximal, complemented
3#11746798C212yesmaximal, complemented
4#11746792C212yesmaximal, complemented
5#10604543—31nomaximal, Hall
6C2×C3×Q8×D5C411yescharacteristic
7C2×C3×D4×D5C411yescharacteristic
8C3×C5×#124C411yescharacteristic
9C3×#4093C2211yescharacteristic
10C3×#4082C2211yescharacteristic
11C3×#4031—22no—
12C3×D5×C22⋊C4—22no—
13C3×#4021C411yescharacteristic
14C3×C42×D5C2211yescharacteristic
15#91232—22no—
16#91231C2214yescomplemented
17C4⋊(C3⋊#170)—22no—
18#71719—51nomaximal, Hall
19D5×#124D311yescharacteristic
20#65683—32no—
21#64927—32no—
22#64921—32no—
23C23×C3×D5—21no—
24C2×C3×C5×Q8C2×C411yescharacteristic
25C2×C3×C5×D4C2×C411yescharacteristic
26C2×C3×C22⋊D5—21no—
27C3×Q8×D5—42no—
28C3×D4×D5—42no—
29C2×C3×D20C2×C411yescharacteristic
30C2×C3×C4×D5—21no—
31C2×C3×C4×D5C2×C411yescharacteristic
32C2×C3×C4×D5D412yes—
33C2×C3×Dic10—21no—
34C2×C3×Dic10C2×C411yescharacteristic
35C2×C3⋊#170—24no—
36C3×C5×C22⋊C4—22no—
37C3×C42×C5C2×C411yescharacteristic
38C3×C22⋊Dic5—22no—
39C3×#685—22no—
40C3×#685—22no—
41C3×C4×Dic5D412yes—
42C3×C4×Dic5C2311yescharacteristic
43C2×C3×#124—51no—
44#4926—52no—
45#4540—52no—
46#4540—52no—
47C2×Q8×D5Dic311yescharacteristic
48C2×D4×D5Dic311yescharacteristic
49C5×#124Dic311yescharacteristic
50#4093C2×D311yescharacteristic
51#4082C2×D311yescharacteristic
52#4031—22no—
53D5×C22⋊C4—22no—
54#4021Dic311yescharacteristic
55C42×D5C2×D311yescharacteristic
56#4003—62no—
57#4002—34no—
58C4⋊#170—62no—
59#1533—151noSylow
60C23×C3×C5—21no—
61C22×C3×D5—21no—
62C22×C3×D5—44no—
63C22×C3×D5—42no—
64C22×C3×D5C22⋊C411yescharacteristic
65C3×C5×Q8—41no—
66C3×C5×D4—41no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5C22⋊C412yes—
69C2×C3×C4×C5C22×C411yescharacteristic
70C3×C22⋊D5—42no—
71C2×C3×Dic5—21no—
72C2×C3×Dic5C22⋊C411yescharacteristic
73C2×C3×Dic5C2×D412yes—
74C3×D20—41no—
75C3×C4×D5—22no—
76C3×C4×D5—42no—
77C3×C4×D5—42no—
78C3×Dic10—42no—
79C3×Dic10—41no—
80C3⋊#170—44no—
81C22×C3×Q8—51no—
82C22×C3×D4—51no—
83C3×#124—51no—
84C3×#124—51no—
85C3×#124—51no—
86C3×#124—102no—
87C3×#124AGL(1,𝔽5)11yescharacteristic
88C2×C3×C22⋊C4—102no—
89C2×C3×C42—51no—
90#830—102no—
91C4⋊(C3⋊C8)—102no—
92#803—54no—
93C23×D5—21no—
94C2×C5×Q8C2×Dic311yescharacteristic
95C2×C5×D4C2×Dic311yescharacteristic
96C2×C22⋊D5—21no—
97Q8×D5—42no—
98D4×D5—42no—
99C2×D20C2×Dic311yescharacteristic
100C2×C4×D5—21no—
101C2×C4×D5C2×Dic311yescharacteristic
102C2×C4×D5#6712yes—
103C2×Dic10—21no—
104C2×Dic10C2×Dic311yescharacteristic
105C2×#170—64no—
106C5×C22⋊C4—22no—
107C42×C5C2×Dic311yescharacteristic
108C22⋊Dic5—22no—
109#685—22no—
110#685—22no—
111C4×Dic5#6712yes—
112C4×Dic5C22×D311yescharacteristic
113C2×#124—51no—
114#432—152no—
115#329—152no—
116#329—152no—
117C22×C3×C5—41no—
118C22×C3×C5—42no—
119C22×C3×C5C2×C22⋊C411yescharacteristic
120C2×C3×D5—22no—
121C2×C3×D5—41no—
122C2×C3×D5—42no—
123C2×C3×D5—84no—
124C2×C3×D5#10012yes—
125C3×C4×C5—21no—
126C3×C4×C5—22no—
127C3×C4×C5—41no—
128C3×Dic5—21no—
129C3×Dic5—22no—
130C3×Dic5—41no—
131C24×C3—101no—
132C2×C3×Q8—51no—
133C2×C3×Q8—101no—
134C2×C3×Q8—202no—
135C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
136C2×C3×D4—51no—
137C2×C3×D4—101no—
138C2×C3×D4—202no—
139C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
140C22×C3×C4—51no—
141C22×C3×C4—52no—
142C22×C3×C4—101no—
143C3×C22⋊C4—22no—
144C3×C22⋊C4—102no—
145C3×C22⋊C4—102no—
146C3×C22⋊C4—102no—
147C3×C42—52no—
148C3×C42—51no—
149C3×C42C2×AGL(1,𝔽5)11yescharacteristic
150C2×C3⋊C8—104no—
151C23×C5—21no—
152C22×D5—21no—
153C22×D5—44no—
154C22×D5—42no—
155C22×D5#21711yescharacteristic
156C5×Q8—41no—
157C5×D4—41no—
158C2×C4×C5—21no—
159C2×C4×C5#21712yes—
160C2×C4×C5C22×Dic311yescharacteristic
161C22⋊D5—42no—
162C2×Dic5—21no—
163C2×Dic5#21711yescharacteristic
164C2×Dic5C2×#6712yes—
165D20—41no—
166C4×D5—22no—
167C4×D5—42no—
168C4×D5—42no—
169Dic10—42no—
170Dic10—41no—
171#170—124no—
172C22×Q8—51no—
173C22×D4—51no—
174#124—51no—
175#124—51no—
176#124—51no—
177#124—102no—
178#124ΓL(1,𝔽16)11yescharacteristic
179C2×C22⋊C4—102no—
180C2×C42—51no—
181C4⋊C8—302no—
182C22⋊C8—302no—
183#97—154no—
184C2×C3×C5—81no—
185C2×C3×C5C2×#10011yescharacteristic
186C2×C3×C5#42112yes—
187C3×D5—22no—
188C3×D5—81no—
189C23×C3—21no—
190C23×C3—51no—
191C23×C3—101no—
192C23×C3—202no—
193C23×C3—204no—
194C3×Q8—41no—
195C3×Q8—201no—
196C3×Q8—202no—
197C3×D4—41no—
198C3×D4—201no—
199C3×D4—202no—
200C2×C3×C4—21no—
201C2×C3×C4—51no—
202C2×C3×C4—52no—
203C2×C3×C4—102no—
204C2×C3×C4—101no—
205C2×C3×C4—202no—
206C2×C3×C4—202no—
207C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
208C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
209C3⋊C8—204no—
210C22×C5—41no—
211C22×C5—42no—
212C22×C5C2×#21711yescharacteristic
213C2×D5—22no—
214C2×D5—41no—
215C2×D5—42no—
216C2×D5—84no—
217C2×D5#83312yes—
218C4×C5—21no—
219C4×C5—22no—
220C4×C5—41no—
221Dic5—21no—
222Dic5—22no—
223Dic5—41no—
224C24—101no—
225C2×Q8—51no—
226C2×Q8—101no—
227C2×Q8—202no—
228C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
229C2×D4—51no—
230C2×D4—101no—
231C2×D4—202no—
232C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
233C22×C4—51no—
234C22×C4—52no—
235C22×C4—101no—
236C2×C8—304no—
237C22⋊C4—22no—
238C22⋊C4—102no—
239C22⋊C4—102no—
240C22⋊C4—102no—
241C42—52no—
242C42—51no—
243C42C2×ΓL(1,𝔽16)11yescharacteristic
244C3×C5#153311yescharacteristic, complemented, Hall
245C22×C3—42no—
246C22×C3—41no—
247C22×C3—52no—
248C22×C3—102no—
249C22×C3—202no—
250C22×C3—201no—
251C22×C3—404no—
252C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
253C3×C4—22no—
254C3×C4—21no—
255C3×C4—41no—
256C3×C4—102no—
257C3×C4—101no—
258C3×C4—201no—
259C2×C5—81no—
260C2×C5C2×#83311yescharacteristic
261C2×C5#523612yes—
262D5—22no—
263D5—81no—
264C23—21no—
265C23—51no—
266C23—101no—
267C23—202no—
268C23—204no—
269Q8—41no—
270Q8—201no—
271Q8—202no—
272D4—41no—
273D4—201no—
274D4—202no—
275C2×C4—21no—
276C2×C4—52no—
277C2×C4—51no—
278C2×C4—102no—
279C2×C4—101no—
280C2×C4—202no—
281C2×C4—202no—
282C2×C4#676312yes—
283C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
284C8—604no—
285C2×C3—81no—
286C2×C3—102no—
287C2×C3—401no—
288C2×C3D5⋊#10011yescharacteristic
289C2×C3#6579512yes—
290C5#7171911yescharacteristic, complemented, Sylow
291C22—42no—
292C22—41no—
293C22—52no—
294C22—102no—
295C22—202no—
296C22—201no—
297C22—404no—
298C22C2×#676311yescharacteristic
299C4—22no—
300C4—21no—
301C4—41no—
302C4—102no—
303C4—101no—
304C4—201no—
305C3#1060454311yescharacteristic, complemented, Sylow
306C2—81no—
307C2—102no—
308C2—401no—
309C2D5⋊#83311yescharacteristic
310C2#1175245412yes—
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#124C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC3×C4×Dic5C23
hypercenter#124ΓL(1,𝔽16)
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11752342C2semidirect
3. #11746798C2semidirect
4. #11746792C2semidirect
16. #91231C22semidirect
244. C3×C5#1533semidirect
290. C5#71719semidirect
305. C3#10604543semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
#117523422
#117467982
#117467922
#106045433
#717195