Finite Group Databasebeta

← #14511686

Subgroups — #14511686

Order 1920.

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

normal subgroups only

This group has 228 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
2#11752110C211yesmaximal, characteristic, complemented
3C5×SL(2,𝔽3)⋊C8C211yesmaximal, characteristic, complemented
4#10599062—31nomaximal, Hall
5C2×D5×SL(2,𝔽3)—21no—
6C4×C5×SL(2,𝔽3)C2211yescharacteristic
7#91184—21no—
8#90965—41nomaximal
9#73086—51nomaximal, Hall
10Q8×D20D311yescharacteristic
11#65310—31no—
12#65131—31no—
13#64970—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—
20C4⋊Dic15—41no—
21C2×C5×C3⋊C8—41no—
22D4×SL(2,𝔽3)—51no—
23#5391—51no—
24SL(2,𝔽3)⋊C8D511yescharacteristic, complemented
25C2×Q8×D5—21no—
26C4×C5×Q8C2×D311yescharacteristic
27#4043—61no—
28C4×D20—31no—
29#4015—31no—
30#4015—31no—
31C5×C4⋊C8—31no—
32C4×C5×C8—31no—
33#3967—61no—
34#3953—61no—
35#3949—61no—
36#3948—62no—
37#3939—61no—
38C4⋊#168—31no—
39#1637—151noSylow
40C22×C3×D5—81no—
41C2×C3×C4×C5—41no—
42C2×Dic15—81no—
43C3×D20—42no—
44C3×D20—81no—
45C5×SL(2,𝔽3)SD1611yescharacteristic
46C5×C3⋊C8—81no—
47C22×SL(2,𝔽3)—101no—
48C4×SL(2,𝔽3)C2×D511yescharacteristic
49#859—101no—
50#832—201no—
51C2×C5×Q8#6711yescharacteristic
52Q8×D5—41no—
53Q8×D5—121no—
54C2×D20S411yescharacteristic
55C2×C4×D5—61no—
56C2×Dic10—61no—
57C2×Dic10—61no—
58C2×C5×C8—61no—
59C2×C5×C8—61no—
60C5×C4⋊C4—31no—
61C42×C5—31no—
62#685—61no—
63C4⋊Dic5—32no—
64C4⋊Dic5—31no—
65C4⋊Dic5—61no—
66C4⋊Dic5—61no—
67C2×#168—61no—
68D4×Q8—51no—
69#487—151no—
70#477—151no—
71#476—151no—
72#332—151no—
73Q8⋊C8—31no—
74D4⋊C8—151no—
75C22×C3×C5—41no—
76C2×C3×D5—82no—
77C2×C3×D5—161no—
78C2×C3×D5—161no—
79C3×C4×C5—41no—
80C3×C4×C5—41no—
81Dic15—161no—
82C2×C3×D4—201no—
83C2×SL(2,𝔽3)—201no—
84C2×SL(2,𝔽3)D2011yescharacteristic
85C4⋊Dic3—201no—
86C2×C3⋊C8—41no—
87C22×D5—21no—
88C5×Q8—31no—
89C5×Q8#21411yescharacteristic
90C2×C4×C5—31no—
91C2×C4×C5—31no—
92C2×C4×C5C2×S411yescharacteristic
93C2×Dic5—61no—
94C2×Dic5—121no—
95D20—21no—
96D20#22612yes—
97C4×D5—121no—
98C4×D5—121no—
99Dic10—121no—
100Dic10—121no—
101Dic10—122no—
102C5×C8—121no—
103C5×C8—121no—
104#168—121no—
105C22×Q8—101no—
106C4⋊Q8—151no—
107C4⋊Q8—151no—
108C22⋊Q8—301no—
109C4×Q8D3×D511yescharacteristic
110C4×D4—151no—
111#107—301no—
112#106—301no—
113C4⋊C8—31no—
114C4⋊C8—151no—
115#103—302no—
116#103—301no—
117#102—301no—
118C4×C8—31no—
119C2×C3×C5—41no—
120C2×C3×C5—41no—
121C2×C3×C5—41no—
122C3×D5—162no—
123C23×C3—401no—
124C3×D4—202no—
125C3×D4—401no—
126C2×C3×C4—41no—
127C2×Dic3—401no—
128SL(2,𝔽3)#67711yescharacteristic
129C3⋊C8—81no—
130C22×C5GL(2,ℤ/4)11yescharacteristic
131C2×D5—22no—
132C2×D5—41no—
133C2×D5—41no—
134C4×C5—31no—
135C4×C5—31no—
136C4×C5—61no—
137C4×C5C2×#22611yescharacteristic
138C4×C5#98311yescharacteristic
139Dic5—121no—
140Dic5—241no—
141C2×Q8—201no—
142C2×Q8—301no—
143C2×Q8—301no—
144C2×Q8—601no—
145C2×Q8#120211yescharacteristic
146C2×D4—51no—
147C22×C4—301no—
148C2×C8—61no—
149C2×C8—61no—
150C2×C8—301no—
151C4⋊C4—31no—
152C4⋊C4—152no—
153C4⋊C4—151no—
154C4⋊C4—301no—
155C4⋊C4—301no—
156C22⋊C4—301no—
157C42—31no—
158C3×C5—41noHall
159C22×C3—41no—
160C22×C3—402no—
161C22×C3—801no—
162C22×C3—801no—
163C3×C4—41no—
164C3×C4—41no—
165Dic3—801no—
166C2×C5#541411yescharacteristic
167C2×C5#541911yescharacteristic
168C2×C5#543111yescharacteristic
169D5—42no—
170C23—101no—
171Q8—31no—
172Q8—601no—
173Q8—601no—
174Q8—602no—
175Q8#665711yescharacteristic
176D4—52no—
177D4—101no—
178C2×C4—31no—
179C2×C4—31no—
180C2×C4—301no—
181C2×C4—601no—
182C2×C4—601no—
183C2×C4—601no—
184C2×C4D5×S411yescharacteristic
185C8—121no—
186C8—121no—
187C8—601no—
188C2×C3—41no—
189C2×C3—41no—
190C2×C3—41no—
191C2×C3—802no—
192C5#7308611yescharacteristic, complemented, Sylow
193C22—102no—
194C22—201no—
195C22—201no—
196C22#9190511yescharacteristic
197C4—31no—
198C4—31no—
199C4—61no—
200C4—601no—
201C4—1201no—
202C4D5×#22611yescharacteristic
203C4#9189611yescharacteristic
204C3—41noSylow
205C2—202no—
206C2#1175158211yescharacteristic
207C2#1175160711yescharacteristic
208C2#1175162611yescharacteristic
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)SD16
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. #11752110C2semidirect
3. C5×SL(2,𝔽3)⋊C8C2semidirect
24. SL(2,𝔽3)⋊C8D5semidirect
192. C5#73086semidirect

Maximal subgroups

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

subgroupindex
SL(2,𝔽3)×D202
#117521102
C5×SL(2,𝔽3)⋊C82
#105990623
#909654
#730865