Finite Group Databasebeta

← #14513738

Subgroups — #14513738

Order 1920.

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

normal subgroups only

This group has 514 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
1C2×#91954C212yesmaximal
2C4×C5×#41⋊C3C211yesmaximal, characteristic
3C4⋊(C5⋊#226)C214yesmaximal, complemented
4#10614264—31nomaximal, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6#91954—24no—
7C2×C5⋊#226C2214yes—
8#91758—41nomaximal
9C4×C5×SL(2,𝔽3)C2212yes—
10#85336—51nomaximal, Hall
11C4×C5×#41D311yescharacteristic
12C2×#4097—32no—
13C2×#4015—31no—
14#65320—34no—
15#65308—34no—
16#65293—32no—
17#65213—31no—
18C2×Dic30—42no—
19C5×#41⋊C3D412yes—
20C2×C5×SL(2,𝔽3)C2311yescharacteristic
21C5⋊#226—24no—
22C3×C42×C5—41no—
23C4⋊Dic15—44no—
24C2×#984—52no—
25C4×#41⋊C3D511yescharacteristic
26C4⋊#226—54no—
27C2×C5×#41C2×D311yescharacteristic
28C22×Dic10—32no—
29C4×C5×Q8C2×D312yes—
30C4×C5×D4—32no—
31C5×#117—31no—
32C2×C42×C5—31no—
33#4097—64no—
34#4097—64no—
35C2×#689—34no—
36C2×#687—34no—
37C2×C4⋊Dic5—62no—
38C2×#681—32no—
39#4015—34no—
40#4015—61no—
41#4015—61no—
42#3942—38no—
43C4⋊#168—34no—
44#3039—151noSylow
45C2×C3×C4×C5—42no—
46C2×C3×C4×C5—41no—
47C2×Dic15—44no—
48Dic30—84no—
49C5×SL(2,𝔽3)C2×D411yescharacteristic
50C2×#41⋊C3C2×D511yescharacteristic
51#984—104no—
52C2×#226—54no—
53#869—201no—
54C4×SL(2,𝔽3)C2×D512yes—
55C5×#41—32no—
56C5×#41D1212yes—
57C2×C5×Q8C22×D311yescharacteristic
58C2×C5×D4—31no—
59C22×C4×C5—31no—
60C22×C4×C5—32no—
61C22×Dic5—62no—
62C2×Dic10—34no—
63C2×Dic10—64no—
64C2×Dic10—64no—
65C2×Dic10—62no—
66C5×C4⋊C4—32no—
67C5×C22⋊C4—61no—
68C42×C5—31no—
69C42×C5—32no—
70C42×C5S411yescharacteristic
71#689—64no—
72#689—64no—
73#687—68no—
74C4⋊Dic5—64no—
75C4⋊Dic5—64no—
76#681—64no—
77C2×#168—34no—
78C2×#137—152no—
79C2×C4⋊Q8—151no—
80C4×#41D1511yescharacteristic
81#462—154no—
82#461—154no—
83#423—151no—
84#419—152no—
85C22×C3×C5—41no—
86C3×C4×C5—42no—
87C3×C4×C5—44no—
88Dic15—84no—
89C2×Dic6—202no—
90#41⋊C3D2012yes—
91C2×SL(2,𝔽3)C22×D511yescharacteristic
92#226—104no—
93C3×C42—41no—
94C4⋊Dic3—204no—
95C23×C5—31no—
96C5×Q8—31no—
97C5×Q8C2×D1211yescharacteristic
98C5×D4—32no—
99C5×D4—61no—
100C2×C4×C5—31no—
101C2×C4×C5—32no—
102C2×C4×C5—32no—
103C2×C4×C5—32no—
104C2×C4×C5—64no—
105C2×C4×C5C2×S411yescharacteristic
106C2×C4×C5C2×S412yes—
107C2×Dic5—64no—
108C2×Dic5—124no—
109Dic10—64no—
110Dic10—64no—
111Dic10—124no—
112#168—64no—
113C2×#41C2×D1511yescharacteristic
114C22×Q8—152no—
115#137—304no—
116#137—304no—
117C2×Q16—154no—
118C2×SD16—154no—
119C2×M16—152no—
120C4⋊Q8—154no—
121C4⋊Q8—301no—
122C4⋊Q8—301no—
123C4×Q8C2×D1512yes—
124C4×D4—32no—
125#117—31no—
126C2×C4⋊C4—302no—
127C2×C42—31no—
128C4⋊C8—154no—
129#103—158no—
130C2×C3×C5—41no—
131C2×C3×C5—42no—
132C2×C3×C4—42no—
133C2×C3×C4—41no—
134C2×Dic3—204no—
135Dic6—404no—
136SL(2,𝔽3)C2×D2011yescharacteristic
137C22×C5—32no—
138C22×C5—62no—
139C22×C5C22×S411yescharacteristic
140C4×C5—31no—
141C4×C5—31no—
142C4×C5—62no—
143C4×C5C4⋊S412yes—
144C4×C5#98414yescomplemented
145Dic5—124no—
146#41—32no—
147#41D6012yes—
148C2×Q8—154no—
149C2×Q8—304no—
150C2×Q8—304no—
151C2×Q8—302no—
152C2×Q8C22×D1511yescharacteristic
153C2×D4—31no—
154C22×C4—31no—
155C22×C4—32no—
156C22×C4—302no—
157Q16—304no—
158Q16—304no—
159SD16—308no—
160M16—304no—
161C2×C8—154no—
162C4⋊C4—32no—
163C4⋊C4—304no—
164C4⋊C4—304no—
165C22⋊C4—61no—
166C42—32no—
167C42—31no—
168C42C5⋊S411yescharacteristic
169C3×C5—41noHall
170C22×C3—41no—
171C3×C4—42no—
172C3×C4—44no—
173Dic3—404no—
174C2×C5—62no—
175C2×C5C2×C4⋊S411yescharacteristic
176C2×C5C2×#98412yes—
177C23—31no—
178Q8—31no—
179Q8—304no—
180Q8—304no—
181Q8—604no—
182Q8C2×D6011yescharacteristic
183D4—32no—
184D4—61no—
185C2×C4—31no—
186C2×C4—32no—
187C2×C4—32no—
188C2×C4—32no—
189C2×C4—64no—
190C2×C4—304no—
191C2×C4—604no—
192C2×C4C2×C5⋊S411yescharacteristic
193C2×C4C2×C5⋊S412yes—
194C8—304no—
195C2×C3—41no—
196C2×C3—42no—
197C5#8533611yescharacteristic, complemented, Sylow
198C22—32no—
199C22—62no—
200C22C22×C5⋊S411yescharacteristic
201C4—31no—
202C4—31no—
203C4—62no—
204C4—604no—
205C4C4⋊(C5⋊S4)12yes—
206C4#9195414yescomplemented
207C3—41noSylow
208C2—62no—
209C2C2×C4⋊(C5⋊S4)11yescharacteristic
210C2C2×#9195412yes—
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×D4
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. C4⋊(C5⋊#226)C2semidirect
144. C4×C5#984semidirect
197. C5#85336semidirect
206. C4#91954semidirect

Maximal subgroups

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

subgroupindex
C2×#919542
C4×C5×#41⋊C32
C4⋊(C5⋊#226)2
#106142643
#917584
#853365