Finite Group Databasebeta

← #14513739

Subgroups — #14513739

Order 1920.

434 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic
2#11752145C212yesmaximal
3#11752110C212yesmaximal, complemented
4#11752105C212yesmaximal, complemented
5#10614239—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#91758—41nomaximal
8C4×C5×SL(2,𝔽3)C2211yescharacteristic
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10#91184C2214yes—
11#85337—51nomaximal, Hall
12C4×C5×#41D311yescharacteristic
13C2×#4015—31no—
14#65521—32no—
15#65310—32no—
16#65309—32no—
17#65297—32no—
18#65296—32no—
19#65284—32no—
20#65213—31no—
21C2×Dic30—42no—
22C5×#41⋊C3Q812yescomplemented
23C2×C5×SL(2,𝔽3)C2311yescharacteristic
24C3×C42×C5—41no—
25C4⋊Dic15—42no—
26C4⋊Dic15—42no—
27C4×#41⋊C3D511yescharacteristic
28#5426—52no—
29#5391—52no—
30#5386—52no—
31C2×C5×#41C2×D311yescharacteristic
32C22×Dic10—61no—
33C4×C5×Q8C2×D311yescharacteristic
34C4×C5×Q8C2×D311yescharacteristic
35C4×C5×D4—31no—
36C4×C5×D4—31no—
37C5×#117—31no—
38C2×C42×C5—31no—
39C2×C4⋊Dic5—32no—
40C2×C4⋊Dic5—61no—
41C2×#681—32no—
42#4015—32no—
43#4015—32no—
44#4015—61no—
45#4015—61no—
46#3967—34no—
47#3964—34no—
48#3940—34no—
49#3939—34no—
50C4⋊#168—32no—
51C4⋊#168—32no—
52#3079—151noSylow
53C2×C3×C4×C5—41no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—41no—
56C2×Dic15—44no—
57Dic30—84no—
58C5×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
59C2×#41⋊C3C2×D511yescharacteristic
60#869—201no—
61C4×SL(2,𝔽3)C2×D511yescharacteristic
62C4×SL(2,𝔽3)C2×D511yescharacteristic
63#859—54no—
64C5×#41—32no—
65C5×#41Dic612yescomplemented
66C2×C5×Q8C22×D311yescharacteristic
67C2×C5×D4—31no—
68C22×C4×C5—31no—
69C22×C4×C5—31no—
70C22×C4×C5—31no—
71C22×Dic5—62no—
72C2×Dic10—62no—
73C2×Dic10—62no—
74C2×Dic10—124no—
75C5×C4⋊C4—31no—
76C5×C4⋊C4—31no—
77C5×C22⋊C4—61no—
78C42×C5—31no—
79C42×C5—31no—
80C42×C5—31no—
81C42×C5S411yescharacteristic
82C4⋊Dic5—34no—
83C4⋊Dic5—62no—
84C4⋊Dic5—62no—
85C4⋊Dic5—62no—
86#681—64no—
87C2×#168—34no—
88C2×C4⋊Q8—151no—
89C4×#41D1511yescharacteristic
90#477—152no—
91#476—152no—
92#475—152no—
93#474—152no—
94#428—152no—
95#423—151no—
96#417—152no—
97C22×C3×C5—41no—
98C3×C4×C5—42no—
99C3×C4×C5—42no—
100C3×C4×C5—42no—
101Dic15—84no—
102C2×Dic6—202no—
103#41⋊C3Dic1012yescomplemented
104C2×SL(2,𝔽3)C22×D511yescharacteristic
105C3×C42—41no—
106C4⋊Dic3—202no—
107C4⋊Dic3—202no—
108C23×C5—31no—
109C5×Q8—31no—
110C5×Q8C2×Dic611yescharacteristic
111C5×D4—32no—
112C5×D4—61no—
113C2×C4×C5—31no—
114C2×C4×C5—32no—
115C2×C4×C5—32no—
116C2×C4×C5—31no—
117C2×C4×C5—31no—
118C2×C4×C5—62no—
119C2×C4×C5—62no—
120C2×C4×C5C2×S411yescharacteristic
121C2×C4×C5C2×S411yescharacteristic
122C2×C4×C5C2×S411yescharacteristic
123C2×Dic5—64no—
124C2×Dic5—124no—
125Dic10—124no—
126Dic10—124no—
127#168—64no—
128C2×#41C2×D1511yescharacteristic
129C22×Q8—301no—
130C2×M16—152no—
131C4⋊Q8—152no—
132C4⋊Q8—152no—
133C4⋊Q8—301no—
134C4⋊Q8—301no—
135C4×Q8C2×D1511yescharacteristic
136C4×Q8C2×D1511yescharacteristic
137C4×D4—31no—
138C4×D4—31no—
139#117—31no—
140C2×C4⋊C4—152no—
141C2×C4⋊C4—301no—
142C2×C42—31no—
143#107—154no—
144#106—154no—
145C4⋊C8—152no—
146C4⋊C8—152no—
147#103—154no—
148#102—154no—
149C2×C3×C5—41no—
150C2×C3×C5—41no—
151C2×C3×C5—41no—
152C2×C3×C4—41no—
153C2×C3×C4—41no—
154C2×C3×C4—41no—
155C2×Dic3—204no—
156Dic6—404no—
157SL(2,𝔽3)C2×Dic1011yescharacteristic, complemented
158C22×C5—32no—
159C22×C5—61no—
160C22×C5—61no—
161C22×C5C22×S411yescharacteristic
162C4×C5—31no—
163C4×C5—31no—
164C4×C5—61no—
165C4×C5—61no—
166C4×C5A4⋊Q812yes—
167C4×C5#98412yes—
168C4×C5#98612yes—
169Dic5—124no—
170#41—32no—
171#41Dic3012yescomplemented
172C2×Q8—302no—
173C2×Q8—302no—
174C2×Q8—604no—
175C2×Q8C22×D1511yescharacteristic
176C2×D4—31no—
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—31no—
180C22×C4—302no—
181M16—304no—
182C2×C8—154no—
183C4⋊C4—31no—
184C4⋊C4—31no—
185C4⋊C4—154no—
186C4⋊C4—302no—
187C4⋊C4—302no—
188C4⋊C4—302no—
189C22⋊C4—61no—
190C42—31no—
191C42—31no—
192C42—31no—
193C42C5⋊S411yescharacteristic
194C3×C5—41noHall
195C22×C3—41no—
196C3×C4—42no—
197C3×C4—42no—
198C3×C4—42no—
199Dic3—404no—
200C2×C5—62no—
201C2×C5C2×A4⋊Q811yescharacteristic
202C2×C5C2×#98411yescharacteristic
203C2×C5C2×#98611yescharacteristic
204C23—31no—
205Q8—31no—
206Q8—604no—
207Q8—604no—
208Q8C2×Dic3011yescharacteristic
209D4—32no—
210D4—61no—
211C2×C4—31no—
212C2×C4—32no—
213C2×C4—32no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—62no—
217C2×C4—62no—
218C2×C4—304no—
219C2×C4—604no—
220C2×C4C2×C5⋊S411yescharacteristic
221C2×C4C2×C5⋊S411yescharacteristic
222C2×C4C2×C5⋊S411yescharacteristic
223C8—304no—
224C2×C3—41no—
225C2×C3—41no—
226C2×C3—41no—
227C5#8533711yescharacteristic, complemented, Sylow
228C22—32no—
229C22—61no—
230C22—61no—
231C22C22×C5⋊S411yescharacteristic
232C4—31no—
233C4—31no—
234C4—61no—
235C4—61no—
236C4—604no—
237C4#9194812yes—
238C4#9195412yes—
239C4#9195612yes—
240C3—41noSylow
241C2—62no—
242C2C2×#9194811yescharacteristic
243C2C2×#9195411yescharacteristic
244C2C2×#9195611yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)C2×Q8
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11752110C2semidirect
4. #11752105C2semidirect
22. C5×#41⋊C3Q8semidirect
58. C5×SL(2,𝔽3)C2×Q8semidirect
65. C5×#41Dic6semidirect
103. #41⋊C3Dic10semidirect
157. SL(2,𝔽3)C2×Dic10semidirect
171. #41Dic30semidirect
227. C5#85337semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#117521452
#117521102
#117521052
#106142393
#917584
#853375