Finite Group Databasebeta

← #14305261

Subgroups — #14305261

Order 1920.

416 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 118 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×#91224C211yesmaximal, characteristic
2C2×C3×C8×AGL(1,𝔽5)C211yesmaximal, characteristic
3#11751822C212yesmaximal
4#11747671C211yesmaximal, characteristic
5#11746526C212yesmaximal
6#10604057—31nomaximal, Hall
7C2×#6758C2212yes—
8C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
9C2×C3×D5⋊C8C2211yescharacteristic
10C2×C3×C8×D5C2211yescharacteristic
11#91358C2212yes—
12#91224—22no—
13C3×C8×AGL(1,𝔽5)—22no—
14#91177—22no—
15Dic3⋊#170—22no—
16#91101C411yescharacteristic, complemented
17C5×#817C411yescharacteristic, complemented
18#90988C412yescomplemented
19#69794—51nomaximal, Hall
20C2×#3995—31no—
21C2×C8×AGL(1,𝔽5)D311yescharacteristic
22#65708—32no—
23#65149—31no—
24#64875—32no—
25C22×C3×AGL(1,𝔽5)—21no—
26C2×C3×C4×D5C2311yescharacteristic
27C2×C3⋊#170—22no—
28#6758—22no—
29#6758—22no—
30C2×C3×#170D412yes—
31C3×C4×AGL(1,𝔽5)—21no—
32C3×C4×AGL(1,𝔽5)Q812yes—
33C3×D5⋊C8—21no—
34C3×D5⋊C8—21no—
35C2×C3×C5×C8C2×C411yescharacteristic
36C4⋊Dic15C2×C412yes—
37C5×C4⋊Dic3C2×C412yes—
38C2×C3×#168C2×C411yescharacteristic
39C3×C8×D5D412yes—
40C3×C8×D5Q812yes—
41#6665—22no—
42Dic3×Dic5—22no—
43C2×C3×C4×C8—51no—
44C2×#819—51no—
45#5106—51no—
46#5102—52no—
47#4523—52no—
48C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
49C2×#700—32no—
50C2×D5⋊C8C2×D311yescharacteristic
51C2×C8×D5C2×D311yescharacteristic
52#4038—32no—
53#4004—62no—
54C4⋊#170—62no—
55#3995—62no—
56C8×AGL(1,𝔽5)—22no—
57C5×#106—31no—
58#3949—31no—
59#3939—32no—
60#1945—151noSylow
61C22×C3×D5#4111yescharacteristic
62C2×C3×AGL(1,𝔽5)—24no—
63C2×C3×AGL(1,𝔽5)—22no—
64C2×C3×C4×C5C22×C411yescharacteristic
65C2×Dic15—22no—
66C2×C5×Dic3—22no—
67C2×C3×Dic5C2×D411yescharacteristic
68C3×C4×D5C2×D411yescharacteristic
69C3×C4×D5C2×Q811yescharacteristic
70C3×C4×D5C2×Q811yescharacteristic
71C3×C4×D5#4111yescharacteristic
72C3⋊#170—42no—
73C3×#170—22no—
74C3×C5×C8C4⋊C412yes—
75C3×#168C4⋊C412yes—
76C22×C3×C8—51no—
77C22×C3×C8—51no—
78C2×C3×C42—51no—
79#926—52no—
80C2×#208—52no—
81C3×C4×C8—102no—
82#819—102no—
83#818—52no—
84#817—51no—
85#817AGL(1,𝔽5)11yescharacteristic, complemented
86Dic3⋊C8—102no—
87Dic3⋊C8—102no—
88C22×AGL(1,𝔽5)—21no—
89C2×C4×D5C22×D311yescharacteristic
90C2×#170—62no—
91C2×#170D1212yes—
92C4×AGL(1,𝔽5)—21no—
93C4×AGL(1,𝔽5)Dic612yes—
94#700—62no—
95#700—62no—
96D5⋊C8—21no—
97D5⋊C8—21no—
98C2×C5×C8C4×D311yescharacteristic
99C5×C4⋊C4—32no—
100#685—62no—
101C4⋊Dic5—32no—
102C4×Dic5—62no—
103C2×#168C4×D311yescharacteristic
104C8×D5Dic612yes—
105C8×D5#6712yes—
106C2×#108—151no—
107#427—151no—
108#424—152no—
109C2×C4×C8—51no—
110#339—152no—
111C22×C3×C5C4×D411yescharacteristic
112C2×C3×D5—22no—
113C2×C3×D5C22⋊Q811yescharacteristic
114C2×C3×D5#12511yescharacteristic
115C3×AGL(1,𝔽5)—24no—
116C3×C4×C5C2×C4⋊C411yescharacteristic
117C3×C4×C5C4×Q811yescharacteristic
118Dic15—42no—
119C3×Dic5#12111yescharacteristic
120C3×Dic5C4⋊Q811yescharacteristic
121C5×Dic3—42no—
122C22×C3×C4—51no—
123C22×C3×C4—101no—
124C2×C3×C8—51no—
125C2×C3×C8—52no—
126C2×C3×C8—52no—
127C2×C3×C8—52no—
128C2×C3×C8—101no—
129C2×C3×C8—101no—
130C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
131C3×C42—52no—
132C3×C42—101no—
133#217—102no—
134C4⋊Dic3—52no—
135C4⋊Dic3C2×AGL(1,𝔽5)12yes—
136C4×Dic3—102no—
137#208—102no—
138#208—102no—
139C2×C3⋊C8—102no—
140C22×D5#23511yescharacteristic
141C2×AGL(1,𝔽5)—24no—
142C2×AGL(1,𝔽5)—22no—
143C2×C4×C5—62no—
144C2×C4×C5C2×C4×D311yescharacteristic
145C2×Dic5—62no—
146C2×Dic5C2×D1211yescharacteristic
147C4×D5C2×Dic611yescharacteristic
148C4×D5C2×Dic611yescharacteristic
149C4×D5#23511yescharacteristic
150C4×D5C2×#6711yescharacteristic
151#170—22no—
152#170—122no—
153C5×C8Dic3⋊C412yes—
154#168Dic3⋊C412yes—
155C2×M16—152no—
156C22×C8—51no—
157C22×C8—51no—
158#117—152no—
159C2×C42—51no—
160#108—302no—
161#107—152no—
162#106—31no—
163#106—151no—
164C4⋊C8—302no—
165C4⋊C8—302no—
166C4×C8—102no—
167C2×C3×C5#38911yescharacteristic
168C2×C3×C5#44312yes—
169C3×D5—21no—
170C3×D5—21no—
171C23×C3—51no—
172C2×C3×C4—51no—
173C2×C3×C4—51no—
174C2×C3×C4—51no—
175C2×C3×C4—51no—
176C2×C3×C4—51no—
177C2×C3×C4—102no—
178C2×C3×C4—104no—
179C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
180C2×Dic3—22no—
181C2×Dic3—102no—
182C3×C8—52no—
183C3×C8—102no—
184C3×C8C4⋊AGL(1,𝔽5)12yes—
185C3⋊C8—202no—
186C22×C5C4×D1211yescharacteristic
187C2×D5—22no—
188C2×D5#87011yescharacteristic
189C2×D5#92411yescharacteristic
190AGL(1,𝔽5)—24no—
191C4×C5—122no—
192C4×C5C4×Dic611yescharacteristic
193C4×C5C2×Dic3⋊C411yescharacteristic
194Dic5—122no—
195Dic5#86911yescharacteristic
196Dic5#93011yescharacteristic
197C22×C4—51no—
198C22×C4—101no—
199M16—302no—
200M16—302no—
201C2×C8—51no—
202C2×C8—52no—
203C2×C8—52no—
204C2×C8—52no—
205C2×C8—101no—
206C2×C8—101no—
207C2×C8—302no—
208C2×C8D3×AGL(1,𝔽5)11yescharacteristic
209C4⋊C4—32no—
210C4⋊C4—152no—
211C22⋊C4—302no—
212C42—52no—
213C42—101no—
214C42—302no—
215C3×C5#194511yescharacteristic, complemented, Hall
216C22×C3—51no—
217C22×C3—51no—
218C22×C3—102no—
219C22×C3D4×AGL(1,𝔽5)11yescharacteristic
220C3×C4—51no—
221C3×C4—51no—
222C3×C4—104no—
223C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
224C3×C4Q8×AGL(1,𝔽5)11yescharacteristic
225Dic3—42no—
226Dic3—202no—
227C2×C5#470012yes—
228C2×C5#492811yescharacteristic
229D5—21no—
230D5—21no—
231C23—51no—
232C2×C4—51no—
233C2×C4—51no—
234C2×C4—51no—
235C2×C4—51no—
236C2×C4—51no—
237C2×C4—62no—
238C2×C4—102no—
239C2×C4—104no—
240C2×C4—302no—
241C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
242C8—52no—
243C8—102no—
244C8—602no—
245C8Dic3⋊AGL(1,𝔽5)12yes—
246C2×C3—101no—
247C2×C3—101no—
248C2×C3#6571211yescharacteristic
249C2×C3#6573612yes—
250C5#6979411yescharacteristic, complemented, Sylow
251C22—51no—
252C22—51no—
253C22—102no—
254C22AGL(1,𝔽5)×D1211yescharacteristic
255C4—51no—
256C4—51no—
257C4—104no—
258C4—122no—
259C4—602no—
260C4AGL(1,𝔽5)×Dic611yescharacteristic
261C4C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
262C3#1060405711yescharacteristic, complemented, Sylow
263C2—101no—
264C2—101no—
265C2#1175167912yes—
266C2#1175185911yescharacteristic
subgroupG/H
centerC22AGL(1,𝔽5)×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5#41
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#1945
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
16. #91101C4semidirect
17. C5×#817C4semidirect
18. #90988C4semidirect
85. #817AGL(1,𝔽5)semidirect
215. C3×C5#1945semidirect
250. C5#69794semidirect
262. C3#10604057semidirect

Maximal subgroups

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

subgroupindex
C2×#912242
C2×C3×C8×AGL(1,𝔽5)2
#117518222
#117476712
#117465262
#106040573
#697945