Finite Group Databasebeta

← #14511687

Subgroups — #14511687

Order 1920.

236 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 37 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
1SL(2,𝔽3)×D20C211yesmaximal, characteristic
2C4⋊(C5⋊#226)C211yesmaximal, characteristic, complemented
3C5×SL(2,𝔽3)⋊C8C211yesmaximal, characteristic, complemented
4#10599066—31nomaximal, Hall
5C2×D5×SL(2,𝔽3)—21no—
6C2×C5⋊#226—21no—
7C4×C5×SL(2,𝔽3)C2211yescharacteristic
8#90965—41nomaximal
9#73085—51nomaximal, Hall
10Q8×D20D311yescharacteristic
11#65320—31no—
12#65135—31no—
13#64971—31no—
14C5×Q8⋊C8—31no—
15#64706—31no—
16#64679—31no—
17C2×C3×D20—41no—
18C2×C5×SL(2,𝔽3)D411yescharacteristic
19D5×SL(2,𝔽3)—41no—
20C5⋊#226—41no—
21C4⋊Dic15—41no—
22C2×C5×C3⋊C8—41no—
23D4×SL(2,𝔽3)—51no—
24C4⋊#226—51no—
25SL(2,𝔽3)⋊C8D511yescharacteristic, complemented
26C2×Q8×D5—21no—
27C4×C5×Q8C2×D311yescharacteristic
28C2×#689—61no—
29#4043—61no—
30C4×D20—31no—
31#4015—31no—
32#4015—31no—
33C5×C4⋊C8—31no—
34C4×C5×C8—31no—
35#3953—61no—
36#3950—61no—
37#3950—62no—
38#3942—61no—
39C4⋊#168—31no—
40#1649—151noSylow
41C22×C3×D5—81no—
42C2×C3×C4×C5—41no—
43C2×Dic15—81no—
44C3×D20—42no—
45C3×D20—81no—
46C5×SL(2,𝔽3)D811yescharacteristic
47C5×C3⋊C8—81no—
48C22×SL(2,𝔽3)—101no—
49C2×#226—101no—
50C4×SL(2,𝔽3)C2×D511yescharacteristic
51#832—201no—
52C2×C5×Q8#6711yescharacteristic
53Q8×D5—41no—
54Q8×D5—121no—
55C2×D20S411yescharacteristic
56C2×C4×D5—61no—
57C2×Dic10—61no—
58C2×Dic10—61no—
59C2×C5×C8—61no—
60C2×C5×C8—61no—
61C5×C4⋊C4—31no—
62C42×C5—31no—
63#689—121no—
64#689—121no—
65#685—61no—
66C4⋊Dic5—32no—
67C4⋊Dic5—31no—
68C4⋊Dic5—61no—
69C4⋊Dic5—61no—
70C2×#168—61no—
71D4×Q8—51no—
72#500—151no—
73#474—151no—
74#462—151no—
75#332—151no—
76Q8⋊C8—31no—
77D4⋊C8—151no—
78C22×C3×C5—41no—
79C2×C3×D5—82no—
80C2×C3×D5—161no—
81C2×C3×D5—161no—
82C3×C4×C5—41no—
83C3×C4×C5—41no—
84Dic15—161no—
85C2×C3×D4—201no—
86C2×SL(2,𝔽3)—201no—
87C2×SL(2,𝔽3)D2011yescharacteristic
88#226—201no—
89C4⋊Dic3—201no—
90C2×C3⋊C8—41no—
91C22×D5—21no—
92C5×Q8—31no—
93C5×Q8#21311yescharacteristic
94C2×C4×C5—31no—
95C2×C4×C5—31no—
96C2×C4×C5C2×S411yescharacteristic
97C2×Dic5—61no—
98C2×Dic5—121no—
99D20—21no—
100D20#22612yescomplemented
101C4×D5—121no—
102C4×D5—121no—
103Dic10—121no—
104Dic10—121no—
105Dic10—121no—
106Dic10—121no—
107C5×C8—62no—
108C5×C8—121no—
109#168—121no—
110C22×Q8—101no—
111C2×Q16—301no—
112C4⋊Q8—151no—
113C4⋊Q8—151no—
114C22⋊Q8—301no—
115C4×Q8D3×D511yescharacteristic
116C4×D4—151no—
117#107—301no—
118#107—302no—
119C4⋊C8—31no—
120C4⋊C8—151no—
121#103—301no—
122#102—301no—
123C4×C8—31no—
124C2×C3×C5—41no—
125C2×C3×C5—41no—
126C2×C3×C5—41no—
127C3×D5—162no—
128C23×C3—401no—
129C3×D4—202no—
130C3×D4—401no—
131C2×C3×C4—41no—
132C2×Dic3—401no—
133SL(2,𝔽3)D4011yescharacteristic
134C3⋊C8—81no—
135C22×C5GL(2,ℤ/4)11yescharacteristic
136C2×D5—22no—
137C2×D5—41no—
138C2×D5—41no—
139C4×C5—31no—
140C4×C5—31no—
141C4×C5—61no—
142C4×C5C2×#22611yescharacteristic
143C4×C5#98311yescharacteristic
144Dic5—121no—
145Dic5—241no—
146C2×Q8—201no—
147C2×Q8—301no—
148C2×Q8—301no—
149C2×Q8—601no—
150C2×Q8#120211yescharacteristic
151C2×D4—51no—
152C22×C4—301no—
153Q16—601no—
154Q16—601no—
155C2×C8—61no—
156C2×C8—61no—
157C2×C8—301no—
158C4⋊C4—31no—
159C4⋊C4—152no—
160C4⋊C4—151no—
161C4⋊C4—301no—
162C4⋊C4—301no—
163C22⋊C4—301no—
164C42—31no—
165C3×C5—41noHall
166C22×C3—41no—
167C22×C3—402no—
168C22×C3—801no—
169C22×C3—801no—
170C3×C4—41no—
171C3×C4—41no—
172Dic3—801no—
173C2×C5#541511yescharacteristic
174C2×C5#541911yescharacteristic
175C2×C5#543011yescharacteristic
176D5—42no—
177C23—101no—
178Q8—31no—
179Q8—601no—
180Q8—601no—
181Q8—601no—
182Q8—601no—
183Q8#665311yescharacteristic
184D4—52no—
185D4—101no—
186C2×C4—31no—
187C2×C4—31no—
188C2×C4—301no—
189C2×C4—601no—
190C2×C4—601no—
191C2×C4—601no—
192C2×C4D5×S411yescharacteristic
193C8—62no—
194C8—121no—
195C8—601no—
196C2×C3—41no—
197C2×C3—41no—
198C2×C3—41no—
199C2×C3—802no—
200C5#7308511yescharacteristic, complemented, Sylow
201C22—102no—
202C22—201no—
203C22—201no—
204C22#9190511yescharacteristic
205C4—31no—
206C4—31no—
207C4—61no—
208C4—601no—
209C4—1201no—
210C4D5×#22611yescharacteristic
211C4#9189611yescharacteristic
212C3—41noSylow
213C2—202no—
214C2#1175158011yescharacteristic
215C2#1175160711yescharacteristic
216C2#1175162811yescharacteristic
subgroupG/H
centerC22#91905
commutator, cosocleC4×C5×SL(2,𝔽3)C22
Frattini, hypercenterC2×C4D5×S4
FittingC4×C5×Q8C2×D3
socleC22×C5GL(2,ℤ/4)
prime radicalSL(2,𝔽3)×D20C2
hypocenterC5×SL(2,𝔽3)D8
LCSG ▷ C4×C5×SL(2,𝔽3) ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4⋊(C5⋊#226)C2semidirect
3. C5×SL(2,𝔽3)⋊C8C2semidirect
25. SL(2,𝔽3)⋊C8D5semidirect
100. D20#226semidirect
200. C5#73085semidirect

Maximal subgroups

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

subgroupindex
SL(2,𝔽3)×D202
C4⋊(C5⋊#226)2
C5×SL(2,𝔽3)⋊C82
#105990663
#909654
#730855