Finite Group Databasebeta

← #14278900

Subgroups — #14278900

Order 1920.

272 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 92 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⋊#812C211yesmaximal, characteristic
2C2×C3×#3993C211yesmaximal, characteristic
3D5×#819C211yesmaximal, characteristic
4#10598627—31nomaximal, Hall
5C2×C3×C4⋊AGL(1,𝔽5)—21no—
6C2×C3×C8×D5C2211yescharacteristic
7D5×#208—21no—
8#91227—21no—
9#91219—21no—
10D5⋊(C3⋊C16)C412yescomplemented
11C3×#3993—21no—
12C3×#3993C412yes—
13#91103C411yescharacteristic, complemented
14C5×#819C411yescharacteristic, complemented
15#90991—21no—
16#67720—51nomaximal, Hall
17C2×#3993D311yescharacteristic
18D5⋊M32—31no—
19D5×#108—31no—
20C22×C3×AGL(1,𝔽5)—41no—
21C2×C3×C4×D5D411yescharacteristic
22C3×C4⋊AGL(1,𝔽5)—22no—
23C3×C4⋊AGL(1,𝔽5)—41no—
24C2×C3×C5×C8C2×C411yescharacteristic
25#6710—21no—
26C5×#208—21no—
27C2×C3×#168D411yescharacteristic
28C3×C8×D5C2×C411yescharacteristic
29C3×C8×D5C2×C411yescharacteristic
30C3×C8×D5D411yescharacteristic
31C3×C8×D5Q811yescharacteristic
32#6649—41no—
33D5×C3⋊C8—41no—
34C3⋊#674—22no—
35C2×C3×#106—51no—
36C2×#819—51no—
37C2×#812—51no—
38C2×C4⋊AGL(1,𝔽5)—21no—
39D5×M16—61no—
40C2×C8×D5C2×D311yescharacteristic
41#3998—61no—
42#3993—21no—
43#3993Dic312yes—
44#3990—61no—
45D5⋊C16—32no—
46C5×#108—31no—
47#3954—61no—
48#3951—31no—
49#1383—151noSylow
50C22×C3×D5SD1611yescharacteristic
51C2×C3×AGL(1,𝔽5)—42no—
52C2×C3×AGL(1,𝔽5)—82no—
53C2×C3×C4×C5C22⋊C411yescharacteristic
54C2×C3×Dic5Q1611yescharacteristic
55C3×C4×D5C22⋊C411yescharacteristic
56C3×C4×D5C4⋊C411yescharacteristic
57C3×C4×D5D811yescharacteristic
58C3×C4×D5SD1611yescharacteristic
59C3×C5×C8C4211yescharacteristic
60C3×C5×C8C4⋊C411yescharacteristic
61C3⋊#168—41no—
62C3×#168C22⋊C411yescharacteristic
63C3×#168C4⋊C411yescharacteristic
64C5×C3⋊C8—41no—
65C22×C3×C8—51no—
66C2×C3×C4⋊C4—101no—
67C2×#208—101no—
68C3×#106—52no—
69C3×#106—101no—
70#819—51no—
71#819—101no—
72#819AGL(1,𝔽5)11yescharacteristic, complemented
73#812—101no—
74#812—101no—
75C2×C3⋊C16—52no—
76C22×AGL(1,𝔽5)—41no—
77C2×C4×D5#6711yescharacteristic
78C4⋊AGL(1,𝔽5)—22no—
79C4⋊AGL(1,𝔽5)—41no—
80C5×M16—61no—
81C2×C5×C8C4×D311yescharacteristic
82#681—61no—
83C2×#168D1211yescharacteristic
84#676—121no—
85C8×D5—121no—
86C8×D5Dic611yescharacteristic
87C8×D5C4×D311yescharacteristic
88C8×D5C2×Dic311yescharacteristic
89C8×D5#6711yescharacteristic
90#674—62no—
91C2×M32—151no—
92C2×#108—151no—
93C2×#106—51no—
94C22×C3×C5#10311yescharacteristic
95C2×C3×D5—22no—
96C2×C3×D5#10211yescharacteristic
97C2×C3×D5#10611yescharacteristic
98C3×AGL(1,𝔽5)—82no—
99C3×C4×C5#9511yescharacteristic
100C3×C4×C5#10211yescharacteristic
101C3×Dic5#10311yescharacteristic
102C3×Dic5#10711yescharacteristic
103C22×C3×C4—51no—
104C22×C3×C4—201no—
105C2×C3×C8—51no—
106C2×C3×C8—51no—
107C2×C3×C8—51no—
108C2×C3×C8—51no—
109C2×C3×C8—51no—
110C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
111C3×C4⋊C4—102no—
112C3×C4⋊C4—201no—
113#208—21no—
114#208—101no—
115#208—201no—
116C2×C3⋊C8—201no—
117C3⋊C16—102no—
118C22×D5#21411yescharacteristic
119C2×AGL(1,𝔽5)—42no—
120C2×AGL(1,𝔽5)—82no—
121C2×C4×C5(C2×D3)⋊C411yescharacteristic
122C2×Dic5#21611yescharacteristic
123C4×D5Dic3⋊C411yescharacteristic
124C4×D5#21311yescharacteristic
125C4×D5#21511yescharacteristic
126C4×D5#21711yescharacteristic
127C5×C8—121no—
128C5×C8C4×Dic311yescharacteristic
129C5×C8Dic3⋊C411yescharacteristic
130#168—121no—
131#168C4⋊Dic311yescharacteristic
132#168(C2×D3)⋊C411yescharacteristic
133C2×M16—301no—
134C22×C8—51no—
135C2×C4⋊C4—101no—
136M32—301no—
137M32—301no—
138C2×C16—152no—
139#108—31no—
140#108—151no—
141#108—301no—
142#106—52no—
143#106—101no—
144C2×C3×C5—21no—
145C2×C3×C5#34011yescharacteristic
146C3×D5—21no—
147C3×D5#36512yes—
148C23×C3—51no—
149C2×C3×C4—51no—
150C2×C3×C4—51no—
151C2×C3×C4—51no—
152C2×C3×C4—51no—
153C2×C3×C4—51no—
154C2×C3×C4—202no—
155C2×C3×C4—402no—
156C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
157C3×C8—51no—
158C3×C8—51no—
159C3×C8C4×AGL(1,𝔽5)11yescharacteristic
160C3×C8C4⋊AGL(1,𝔽5)11yescharacteristic
161C3⋊C8—41no—
162C3⋊C8—201no—
163C22×C5#81011yescharacteristic
164C2×D5—22no—
165C2×D5#80811yescharacteristic
166C2×D5#83211yescharacteristic
167AGL(1,𝔽5)—82no—
168C4×C5#80911yescharacteristic
169C4×C5C3⋊#9511yescharacteristic
170Dic5#80711yescharacteristic
171Dic5#83511yescharacteristic
172C22×C4—51no—
173C22×C4—201no—
174M16—61no—
175M16—301no—
176M16—601no—
177C2×C8—51no—
178C2×C8—51no—
179C2×C8—51no—
180C2×C8—51no—
181C2×C8—51no—
182C2×C8—601no—
183C2×C8D3×AGL(1,𝔽5)11yescharacteristic
184C4⋊C4—102no—
185C4⋊C4—201no—
186C16—302no—
187C3×C5#138311yescharacteristic, complemented, Hall
188C22×C3—51no—
189C22×C3—51no—
190C22×C3—102no—
191C22×C3#400911yescharacteristic
192C3×C4—51no—
193C3×C4—51no—
194C3×C4—402no—
195C3×C4(C2×AGL(1,𝔽5))⋊C411yescharacteristic
196C3×C4#400711yescharacteristic
197C2×C5—21no—
198C2×C5#452911yescharacteristic
199D5—21no—
200D5#448712yes—
201C23—51no—
202C2×C4—51no—
203C2×C4—51no—
204C2×C4—51no—
205C2×C4—51no—
206C2×C4—51no—
207C2×C4—202no—
208C2×C4—402no—
209C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
210C8—51no—
211C8—51no—
212C8—121no—
213C8—601no—
214C8Dic3×AGL(1,𝔽5)11yescharacteristic
215C8Dic3⋊AGL(1,𝔽5)11yescharacteristic
216C2×C3—21no—
217C2×C3—52no—
218C2×C3—101no—
219C2×C3#6487411yescharacteristic
220C5#6772011yescharacteristic, complemented, Sylow
221C22—51no—
222C22—51no—
223C22—102no—
224C22#9115311yescharacteristic
225C4—51no—
226C4—51no—
227C4—402no—
228C4#9115111yescharacteristic
229C4(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
230C3#1059862711yescharacteristic, complemented, Sylow
231C2—21no—
232C2—52no—
233C2—101no—
234C2#1174652811yescharacteristic
subgroupG/H
centerC2#11746528
commutatorC3×C5×C8C42
Frattini, hypercenterC2×C8D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC2×C3×C5#340
prime radicalC22×C3×D5SD16
cosocleC2×C3×C8×D5C22
hypocenterC3×C5#1383
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
10. D5⋊(C3⋊C16)C4semidirect
13. #91103C4semidirect
14. C5×#819C4semidirect
72. #819AGL(1,𝔽5)semidirect
187. C3×C5#1383semidirect
220. C5#67720semidirect
230. C3#10598627semidirect

Maximal subgroups

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

subgroupindex
D5⋊#8122
C2×C3×#39932
D5×#8192
#105986273
#677205