Finite Group Databasebeta

← #14305949

Subgroups — #14305949

Order 1920.

616 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 130 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
1D5×#869C211yesmaximal, characteristic
2#11752335C211yesmaximal, characteristic
3C3×#65689C211yesmaximal, characteristic
4C2×#91153C214yesmaximal
5#10604673—31nomaximal, Hall
6C2×D5×Dic6C2212yes—
7C2×D5⋊(C3⋊C8)C2212yes—
8C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
9#91758C411yescharacteristic, complemented
10C5×#869C411yescharacteristic, complemented
11C3×C42×D5C2211yescharacteristic
12#91468—22no—
13D5×C4⋊Dic3—22no—
14#91376C412yescomplemented
15#91231—22no—
16C3×(C2×AGL(1,𝔽5))⋊C4—22no—
17#91153—28no—
18#69552—51nomaximal, Hall
19D5×C4⋊Q8—31no—
20C2×#4009—34no—
21#65689D311yescharacteristic
22#65676—31no—
23C22×C3×AGL(1,𝔽5)—22no—
24C2×Dic30C2×C412yes—
25C2×C5×Dic6C2×C412yes—
26C2×C3×C4×D5D412yes—
27C2×C3×C4×D5C2311yescharacteristic
28C2×#1204—22no—
29C2×D5×Dic3—22no—
30D5×Dic6—24no—
31D5×Dic6—24no—
32C2×C3⋊#170—22no—
33D5⋊(C3⋊C8)—22no—
34D5⋊(C3⋊C8)D414yes—
35C3×C4⋊AGL(1,𝔽5)—24no—
36C3×C42×C5C2×C411yescharacteristic
37C4⋊Dic15—22no—
38C5×C4⋊Dic3—22no—
39C3×C4×Dic5C2×C411yescharacteristic
40C3×C4×Dic5D412yes—
41#6668—24no—
42C2×#869—51no—
43C3×#382—51no—
44C2×#810—54no—
45C2×#803—51no—
46C2×Q8×D5—32no—
47C2×C4⋊AGL(1,𝔽5)C2×D312yes—
48C2×D5⋊C8—32no—
49C5×C4⋊Q8—31no—
50#4090—32no—
51D5×C4⋊C4—62no—
52#4034—62no—
53C42×D5C2×D311yescharacteristic
54#4015—31no—
55#4009—68no—
56(C2×AGL(1,𝔽5))⋊C4—22no—
57#4002—62no—
58#1960—151noSylow
59C22×C3×D5C2×D411yescharacteristic
60C2×C3×AGL(1,𝔽5)—42no—
61C2×C3×AGL(1,𝔽5)—44no—
62C2×C3×C4×C5C22⋊C412yes—
63C2×C3×C4×C5C22×C411yescharacteristic
64C2×Dic15—22no—
65Dic30—24no—
66C2×C5×Dic3—22no—
67C5×Dic6—24no—
68C2×C3×Dic5C22⋊C412yes—
69C2×C3×Dic5C2×D411yescharacteristic
70C3×C4×D5—24no—
71C3×C4×D5C2×D412yes—
72C3×C4×D5#4112yes—
73#1204—44no—
74D5×Dic3—42no—
75D5×Dic3—42no—
76C3⋊#170—24no—
77C22×Dic6—52no—
78C2×C3×C4⋊C4—52no—
79C2×C3×C42—51no—
80C2×C4⋊Dic3—102no—
81C22×C3⋊C8—52no—
82#869—52no—
83#869—51no—
84#869—102no—
85#869AGL(1,𝔽5)11yescharacteristic, complemented
86C3×#95—102no—
87#810—108no—
88#803—102no—
89C22×AGL(1,𝔽5)—22no—
90C2×C5×Q8—32no—
91Q8×D5—64no—
92Q8×D5—64no—
93C2×C4×D5—62no—
94C2×C4×D5#6712yes—
95C2×C4×D5C22×D311yescharacteristic
96C2×Dic10—32no—
97C2×Dic10—62no—
98C2×#170—62no—
99C4⋊AGL(1,𝔽5)—24no—
100D5⋊C8—34no—
101D5⋊C8—62no—
102C5×C4⋊C4—62no—
103C42×C5C4×D311yescharacteristic
104C4⋊Dic5—62no—
105#683—64no—
106C4×Dic5C4×D311yescharacteristic
107C4×Dic5D1212yes—
108C2×C4⋊Q8—151no—
109C2×#103—154no—
110C2×#97—151no—
111#382—51no—
112C22×C3×C5C2×C22⋊C411yescharacteristic
113C2×C3×D5#12411yescharacteristic
114C2×C3×D5#12711yescharacteristic
115C2×C3×D5#13714yes—
116C3×AGL(1,𝔽5)—82no—
117C3×C4×C5—22no—
118C3×C4×C5C4×D412yes—
119Dic15—42no—
120C3×Dic5—22no—
121C3×Dic5#12112yes—
122C5×Dic3—42no—
123C22×C3×C4—51no—
124C22×C3×C4—52no—
125C22×C3×C4—102no—
126C22×Dic3—102no—
127C2×Dic6—52no—
128C2×Dic6—104no—
129C2×Dic6—104no—
130C2×Dic6—102no—
131C2×Dic6C2×AGL(1,𝔽5)12yes—
132C3×C4⋊C4—104no—
133C3×C42—52no—
134C3×C42—51no—
135C3×C42C2×AGL(1,𝔽5)11yescharacteristic
136C4⋊Dic3—22no—
137C4⋊Dic3—104no—
138C4⋊Dic3—102no—
139C2×C3⋊C8—54no—
140C2×C3⋊C8—102no—
141C2×C3⋊C8—102no—
142C22×D5C2×#6711yescharacteristic
143C2×AGL(1,𝔽5)—42no—
144C2×AGL(1,𝔽5)—44no—
145C5×Q8—64no—
146C2×C4×C5—62no—
147C2×C4×C5(C2×D3)⋊C412yes—
148C2×C4×C5C2×C4×D311yescharacteristic
149C2×Dic5—62no—
150C2×Dic5(C2×D3)⋊C412yes—
151C2×Dic5C2×D1211yescharacteristic
152C4×D5—24no—
153C4×D5—122no—
154C4×D5—122no—
155C4×D5D3×D412yes—
156C4×D5#23912yes—
157Dic10—64no—
158Dic10—124no—
159#170—64no—
160C22×Q8—152no—
161C22×C8—152no—
162C4⋊Q8—31no—
163C4⋊Q8—152no—
164C4⋊Q8—151no—
165C4⋊Q8—302no—
166C2×C4⋊C4—52no—
167C2×C4⋊C4—302no—
168C2×C42—51no—
169#103—308no—
170#97—302no—
171#95—102no—
172C2×C3×C5#39011yescharacteristic
173C2×C3×C5#41912yes—
174C3×D5#49112yes—
175C3×D5#49712yes—
176C23×C3—51no—
177C2×C3×C4—51no—
178C2×C3×C4—52no—
179C2×C3×C4—52no—
180C2×C3×C4—52no—
181C2×C3×C4—104no—
182C2×C3×C4—202no—
183C2×C3×C4—204no—
184C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
185C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
186C2×Dic3—22no—
187C2×Dic3—102no—
188C2×Dic3—202no—
189C2×Dic3—202no—
190Dic6—24no—
191Dic6—104no—
192Dic6—204no—
193C3⋊C8—104no—
194C22×C5C2×(C2×D3)⋊C411yescharacteristic
195C2×D5#94011yescharacteristic
196C2×D5#94711yescharacteristic
197C2×D5#95114yes—
198AGL(1,𝔽5)—82no—
199C4×C5—22no—
200C4×C5—122no—
201C4×C5#89312yes—
202Dic5—22no—
203Dic5—122no—
204Dic5#89512yes—
205C2×Q8—32no—
206C2×Q8—152no—
207C2×Q8—302no—
208C2×Q8—304no—
209C2×Q8—304no—
210C22×C4—51no—
211C22×C4—52no—
212C22×C4—102no—
213C22×C4—302no—
214C2×C8—154no—
215C2×C8—302no—
216C2×C8—302no—
217C4⋊C4—62no—
218C4⋊C4—104no—
219C4⋊C4—304no—
220C4⋊C4—302no—
221C42—52no—
222C42—51no—
223C42D3×AGL(1,𝔽5)11yescharacteristic
224C3×C5#196011yescharacteristic, complemented, Hall
225C22×C3—51no—
226C22×C3—51no—
227C22×C3—54no—
228C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
229C3×C4—22no—
230C3×C4—52no—
231C3×C4—102no—
232C3×C4—402no—
233C3×C4D4×AGL(1,𝔽5)12yes—
234Dic3—42no—
235Dic3—202no—
236C2×C5#498811yescharacteristic
237C2×C5#500412yes—
238D5#506012yes—
239D5#506912yes—
240C23—51no—
241Q8—64no—
242Q8—304no—
243Q8—604no—
244C2×C4—51no—
245C2×C4—52no—
246C2×C4—52no—
247C2×C4—52no—
248C2×C4—62no—
249C2×C4—104no—
250C2×C4—202no—
251C2×C4—204no—
252C2×C4—302no—
253C2×C4—602no—
254C2×C4—602no—
255C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
256C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
257C8—304no—
258C2×C3—52no—
259C2×C3—52no—
260C2×C3#6578011yescharacteristic
261C2×C3#6578212yes—
262C5#6955211yescharacteristic, complemented, Sylow
263C22—54no—
264C22—51no—
265C22—51no—
266C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
267C4—22no—
268C4—52no—
269C4—102no—
270C4—122no—
271C4—402no—
272C4—602no—
273C4#9192112yes—
274C3#1060467311yescharacteristic, complemented, Sylow
275C2—52no—
276C2—52no—
277C2#1175171112yes—
278C2#1175185711yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1960
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #91758C4semidirect
10. C5×#869C4semidirect
14. #91376C4semidirect
85. #869AGL(1,𝔽5)semidirect
224. C3×C5#1960semidirect
262. C5#69552semidirect
274. C3#10604673semidirect

Maximal subgroups

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

subgroupindex
D5×#8692
#117523352
C3×#656892
C2×#911532
#106046733
#695525