Finite Group Databasebeta

← #14512488

Subgroups — #14512488

Order 1920.

244 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 50 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×Dic5×SL(2,𝔽3)C211yesmaximal, characteristic
2SL(2,𝔽3)⋊#170C212yesmaximal, complemented
3#10604967—31nomaximal, Hall
4C22×C5×SL(2,𝔽3)C411yescharacteristic
5#91241—41nomaximal
6Dic5×SL(2,𝔽3)C411yescharacteristic
7Dic5×SL(2,𝔽3)C2211yescharacteristic
8#73056—51nomaximal, Hall
9C2×Q8×Dic5D311yescharacteristic
10#65748—31no—
11#65748—31no—
12Q8⋊#170—32no—
13Q8⋊#170—32no—
14C22×C3×Dic5—41no—
15C2×C5×SL(2,𝔽3)C812yescomplemented
16C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
17C2×C3⋊#170—42no—
18C2×C4×SL(2,𝔽3)—51no—
19SL(2,𝔽3)⋊C8—52no—
20C22×C5×Q8Dic311yescharacteristic
21Q8×Dic5—31no—
22Q8×Dic5—31no—
23Q8×Dic5Dic311yescharacteristic
24Q8×Dic5C2×D311yescharacteristic
25C2×C4⋊Dic5—31no—
26C2×C4×Dic5—31no—
27C22⋊#170—61no—
28C22⋊#170—61no—
29C4⋊#170—32no—
30C4⋊#170—61no—
31C4×#170—32no—
32C4×#170—61no—
33#1479—151noSylow
34C23×C3×C5—41no—
35C2×C3×Dic5—41no—
36C2×C3×Dic5—41no—
37C2×C3×Dic5—82no—
38C5×SL(2,𝔽3)C2×C811yescharacteristic
39C3⋊#170—82no—
40C22×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic
41C4×SL(2,𝔽3)—51no—
42C4×SL(2,𝔽3)—51no—
43#830—201no—
44C2×C5×Q8—32no—
45C2×C5×Q8—31no—
46C2×C5×Q8C3⋊C812yescomplemented
47C2×C5×Q8C2×Dic311yescharacteristic
48C22×C4×C5—31no—
49C22×Dic5—31no—
50C22×Dic5S411yescharacteristic
51C2×#170—62no—
52C2×#170—62no—
53C4⋊Dic5—31no—
54C4⋊Dic5—31no—
55C4⋊Dic5—61no—
56C4×Dic5—31no—
57C4×Dic5—31no—
58C4×Dic5—31no—
59C4×Dic5—31no—
60C2×C4×Q8—51no—
61#431—151no—
62#431—151no—
63Q8⋊C8—152no—
64Q8⋊C8—152no—
65C22×C3×C5—42no—
66C22×C3×C5—41no—
67C22×C3×C5—81no—
68C22×C3×C5—81no—
69C3×Dic5—42no—
70C3×Dic5—81no—
71C22×C3×C4—201no—
72C2×SL(2,𝔽3)#17012yescomplemented
73C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
74C2×C3⋊C8—202no—
75C23×C5SL(2,ℤ/4)11yescharacteristic
76C5×Q8—32no—
77C5×Q8—31no—
78C5×Q8—61no—
79C5×Q8C2×C3⋊C811yescharacteristic
80C2×C4×C5—32no—
81C2×C4×C5—32no—
82C2×C4×C5—31no—
83C2×C4×C5—31no—
84C2×Dic5—22no—
85C2×Dic5—31no—
86C2×Dic5—31no—
87C2×Dic5—121no—
88C2×Dic5SL(2,ℤ/4)11yescharacteristic
89C2×Dic5C2×S411yescharacteristic
90#170—122no—
91#170—122no—
92C22×Q8ΓL(1,𝔽16)11yescharacteristic
93C4×Q8—51no—
94C4×Q8—51no—
95C4×Q8—151no—
96C4×Q8—151no—
97C2×C4⋊C4—151no—
98C2×C42—151no—
99C4⋊C8—152no—
100C4⋊C8—301no—
101C22⋊C8—301no—
102C22⋊C8—301no—
103C4×C8—152no—
104C4×C8—301no—
105C2×C3×C5—41no—
106C2×C3×C5—41no—
107C2×C3×C5—41no—
108C2×C3×C5—82no—
109C23×C3—41no—
110C2×C3×C4—201no—
111C2×C3×C4—201no—
112C2×C3×C4—402no—
113SL(2,𝔽3)C2×#17011yescharacteristic
114C3⋊C8—402no—
115C22×C5—21no—
116C22×C5—21no—
117C22×C5A4⋊C812yes—
118C22×C5C2×SL(2,ℤ/4)11yescharacteristic
119C4×C5—31no—
120C4×C5—31no—
121C4×C5—32no—
122Dic5—21no—
123Dic5—61no—
124Dic5—61no—
125Dic5#98312yes—
126C2×Q8—31no—
127C2×Q8—32no—
128C2×Q8C3⋊#17012yescomplemented
129C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
130C22×C4—31no—
131C22×C4—51no—
132C22×C4—151no—
133C2×C8—302no—
134C2×C8—302no—
135C4⋊C4—151no—
136C4⋊C4—151no—
137C4⋊C4—301no—
138C42—151no—
139C42—151no—
140C42—151no—
141C42—151no—
142C3×C5—41noHall
143C22×C3—41no—
144C22×C3—42no—
145C22×C3—81no—
146C22×C3—81no—
147C3×C4—202no—
148C3×C4—401no—
149C2×C5—22no—
150C2×C5C2×A4⋊C811yescharacteristic
151C2×C5#542011yescharacteristic
152C2×C5#542311yescharacteristic
153C23A4⋊AGL(1,𝔽5)11yescharacteristic
154Q8—32no—
155Q8—31no—
156Q8—61no—
157Q8C2×C3⋊#17011yescharacteristic
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—32no—
161C2×C4—32no—
162C2×C4—51no—
163C2×C4—51no—
164C2×C4—102no—
165C2×C4—151no—
166C2×C4—151no—
167C2×C4—601no—
168C8—602no—
169C8—602no—
170C2×C3—41no—
171C2×C3—41no—
172C2×C3—41no—
173C2×C3—82no—
174C5#7305611yescharacteristic, complemented, Sylow
175C22—21no—
176C22—21no—
177C22A4⋊#17012yes—
178C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
179C4—31no—
180C4—31no—
181C4—32no—
182C4—52no—
183C4—101no—
184C4—301no—
185C4—301no—
186C3—41noSylow
187C2—22no—
188C2#1175672011yescharacteristic
189C2#1175672211yescharacteristic
190C2C2×A4⋊#17011yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C2×C8
FittingC22×C5×Q8Dic3
socleC22×C5C2×SL(2,ℤ/4)
prime radicalC22×C5×SL(2,𝔽3)C4
cosocleDic5×SL(2,𝔽3)C22
hypercenterC23A4⋊AGL(1,𝔽5)
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. SL(2,𝔽3)⋊#170C2semidirect
15. C2×C5×SL(2,𝔽3)C8semidirect
46. C2×C5×Q8C3⋊C8semidirect
72. C2×SL(2,𝔽3)#170semidirect
128. C2×Q8C3⋊#170semidirect
174. C5#73056semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×SL(2,𝔽3)2
SL(2,𝔽3)⋊#1702
#106049673
#912414
#730565