Finite Group Databasebeta

← #14284022

Subgroups — #14284022

Order 1920.

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

normal subgroups only

This group has 452 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
1C5×#5688C211yesmaximal, characteristic
2#11747005C212yesmaximal
3#11746364C211yesmaximal, characteristic, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745850C212yesmaximal, complemented
6#10602614—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#896—22no—
9C5×#892C412yes—
10C5×#888C412yes—
11C5×#887—22no—
12C42×C5×D3C2211yescharacteristic
13C5×#870C2211yescharacteristic
14C2×#6650—22no—
15#91087C2212yes—
16C3×#3935C2212yes—
17Dic3×#168—22no—
18#68362—51nomaximal, Hall
19C5×#533—31no—
20C4×#681—32no—
21#64763—32no—
22#64763—31no—
23#64763D311yescharacteristic, complemented
24C2×C4×C5×D3C2×C411yescharacteristic
25C2×C4×C5×D3D412yes—
26C2×C5×Dic6—22no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4C2×C412yes—
29C3×C42×C5C2311yescharacteristic
30C2×C3⋊#168—22no—
31C5×(C2×D3)⋊C4—22no—
32C5×C4⋊Dic3C2×C412yes—
33C5×Dic3⋊C4—22no—
34C5×Dic3⋊C4—22no—
35C4×C5×Dic3—22no—
36C4×C5×Dic3C2×C411yescharacteristic
37C4×C5×Dic3D412yes—
38C2×C3×#168—22no—
39#6650—28no—
40#5688D511yescharacteristic
41#4707—52no—
42C3×#330—51no—
43#4543—51no—
44#4465—52no—
45C5×C4⋊Q8—32no—
46C5×#125—31no—
47C5×#125C2×D311yescharacteristic
48C5×C22⋊Q8—62no—
49C4×C5×Q8—62no—
50C5×#117—32no—
51C2×C42×C5—31no—
52C2×#681—62no—
53#3935—32no—
54#3935C2×D312yes—
55C4×#168—62no—
56#1526—151noSylow
57C22×C5×D3C22⋊C411yescharacteristic
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C5×Dic3—22no—
62C2×C5×Dic3C22⋊C411yescharacteristic
63C2×C5×Dic3C22⋊C412yes—
64C4×C5×D3—22no—
65C4×C5×D3—24no—
66C5×Dic6—44no—
67C3⋊#168—24no—
68C3×#168—24no—
69C3×#125C2×D511yescharacteristic
70C2×ΓL(1,𝔽25)—102no—
71#896—22no—
72#892Dic512yes—
73#888Dic512yes—
74#887—22no—
75C42×D3C2×D511yescharacteristic
76#870C2×D511yescharacteristic
77C3×#97—52no—
78C8×Dic3—102no—
79#803—52no—
80C2×C5×Q8—62no—
81C22×C4×C5—31no—
82C22×C4×C5—32no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—32no—
85C5×C4⋊C4—62no—
86C5×C4⋊C4—62no—
87C5×C4⋊C4C4×D312yes—
88C5×C22⋊C4—62no—
89C42×C5—31no—
90C42×C5—32no—
91C42×C5—62no—
92C42×C5C22×D311yescharacteristic
93#681—68no—
94C2×#168—22no—
95C2×#168—62no—
96#533—31no—
97C4×M16—152no—
98#330—51no—
99#330—152no—
100#330—151no—
101C22×C3×C5C2×C22⋊C411yescharacteristic
102C2×C5×D3—21no—
103C2×C5×D3—22no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C5×Dic3—42no—
108C5×Dic3#10112yes—
109C5×Dic3#10414yes—
110C2×C4×D3C2×Dic511yescharacteristic
111C2×C4×D3C22⋊D512yes—
112C2×Dic6—22no—
113C2×C3×C8—102no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4C2×Dic512yes—
116C3×C42C22×D511yescharacteristic
117(C2×D3)⋊C4—22no—
118C4⋊Dic3C2×Dic512yes—
119Dic3⋊C4—22no—
120Dic3⋊C4—22no—
121C4×Dic3—22no—
122C4×Dic3C2×Dic511yescharacteristic
123C4×Dic3C22⋊D512yes—
124C2×C3⋊C8—102no—
125ΓL(1,𝔽25)—108no—
126C23×C5—31no—
127C5×Q8—124no—
128C2×C4×C5—22no—
129C2×C4×C5—31no—
130C2×C4×C5—32no—
131C2×C4×C5—64no—
132C2×C4×C5—62no—
133C2×C4×C5—62no—
134C2×C4×C5C2×C4×D311yescharacteristic
135C2×C4×C5D3×D412yes—
136#168—24no—
137#168—64no—
138C2×M16—302no—
139C4⋊Q8—32no—
140#125—31no—
141#125D3×D511yescharacteristic
142C22⋊Q8—62no—
143C4×Q8—62no—
144#117—32no—
145C2×C42—31no—
146#97—52no—
147#97—152no—
148C4×C8—302no—
149C2×C3×C5C2×#10111yescharacteristic
150C2×C3×C5C2×#10412yes—
151C5×D3—41no—
152C22×D3C22⋊Dic511yescharacteristic
153C2×C3×C4—22no—
154C2×C3×C4C22×Dic511yescharacteristic
155C2×C3×C4C2×C22⋊D512yes—
156C2×Dic3—22no—
157C2×Dic3C22⋊Dic511yescharacteristic
158C2×Dic3C22⋊Dic512yes—
159C4×D3—22no—
160C4×D3—24no—
161Dic6—44no—
162C3×C8—104no—
163C3⋊C8—104no—
164C22×C5—61no—
165C22×C5—62no—
166C22×C5D3×C22⋊C411yescharacteristic
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—32no—
170C4×C5—34no—
171C4×C5—42no—
172C4×C5—122no—
173C2×Q8—62no—
174C22×C4—31no—
175C22×C4—32no—
176M16—308no—
177C2×C8—102no—
178C2×C8—302no—
179C4⋊C4—22no—
180C4⋊C4—32no—
181C4⋊C4—62no—
182C4⋊C4—62no—
183C4⋊C4D3×Dic512yes—
184C22⋊C4—62no—
185C42—31no—
186C42—32no—
187C42—62no—
188C42C2×D3×D511yescharacteristic
189C3×C5#152611yescharacteristic, complemented, Hall
190C22×C3C2×C22⋊Dic511yescharacteristic
191C2×D3—21no—
192C2×D3—22no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196Dic3—42no—
197Dic3#396812yes—
198Dic3#396914yes—
199C2×C5—121no—
200C2×C5D3×#10111yescharacteristic
201C2×C5D3×#10412yes—
202C23—31no—
203Q8—124no—
204C2×C4—22no—
205C2×C4—31no—
206C2×C4—32no—
207C2×C4—64no—
208C2×C4—62no—
209C2×C4—62no—
210C2×C4C2×D3×Dic511yescharacteristic
211C2×C4D3×C22⋊D512yes—
212C8—104no—
213C8—304no—
214C2×C3C2×#396811yescharacteristic
215C2×C3C2×#396912yes—
216D3—41no—
217C5#6836211yescharacteristic, complemented, Sylow
218C22—62no—
219C22—61no—
220C22D3×C22⋊Dic511yescharacteristic
221C4—22no—
222C4—21no—
223C4—34no—
224C4—32no—
225C4—42no—
226C4—122no—
227C3#1060261411yescharacteristic, complemented, Sylow
228C2—121no—
229C2D3×#396811yescharacteristic
230C2D3×#396912yes—
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11746364C2semidirect
4. C3×#64763C2semidirect
5. #11745850C2semidirect
23. #64763D3semidirect
189. C3×C5#1526semidirect
217. C5#68362semidirect
227. C3#10602614semidirect

Maximal subgroups

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

subgroupindex
C5×#56882
#117470052
#117463642
C3×#647632
#117458502
#106026143
#683625