Finite Group Databasebeta

← #14512447

Subgroups — #14512447

Order 1920.

236 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 44 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⋊C3)C211yesmaximal, characteristic
2SL(2,𝔽3)⋊#170C212yesmaximal, complemented
3#10604437—31nomaximal, Hall
4C2×C5⋊(#41⋊C3)C411yescharacteristic
5C4×C5×SL(2,𝔽3)C411yescharacteristic
6#91233—41nomaximal
7Dic5×SL(2,𝔽3)C2211yescharacteristic
8#73071—51nomaximal, Hall
9C4×#713D311yescharacteristic
10D5⋊(C4⋊C8)—31no—
11#65678—31no—
12Q8⋊#170—32no—
13#64871—32no—
14C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
15C2×C3⋊#170—42no—
16C5⋊(#41⋊C3)C812yescomplemented
17C3×C4×Dic5—41no—
18C4×#41⋊C3—51no—
19SL(2,𝔽3)⋊C8—52no—
20C2×#713Dic311yescharacteristic
21C2×D5⋊C8—61no—
22C4×C5×Q8Dic311yescharacteristic
23Q8×Dic5C2×D311yescharacteristic
24#4039—31no—
25#4038—31no—
26C4×D20—31no—
27C42×D5—31no—
28#4004—61no—
29#4004—61no—
30#4003—61no—
31C4⋊#170—32no—
32C4×#170—32no—
33#1477—151noSylow
34C2×C3×C4×C5—41no—
35C2×C3×Dic5—41no—
36C2×C3×Dic5—41no—
37C5×SL(2,𝔽3)C2×C811yescharacteristic, complemented
38C3⋊#170—82no—
39C2×#41⋊C3—51no—
40C4×SL(2,𝔽3)—51no—
41C4×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic
42C4⋊(C3⋊C8)—201no—
43C2×C5×Q8C2×Dic311yescharacteristic
44#713—32no—
45#713C3⋊C812yescomplemented
46C2×D20—31no—
47C2×C4×D5—31no—
48C2×C4×D5—31no—
49C2×C4×D5—31no—
50C2×#170—62no—
51C2×#170—62no—
52D5⋊C8—122no—
53C5×C4⋊C4—31no—
54C42×C5—31no—
55#685—61no—
56C4⋊Dic5—31no—
57C4×Dic5—31no—
58C4×Dic5—31no—
59C4×Dic5S411yescharacteristic
60C4×#41—51no—
61#431—151no—
62C2×C4⋊C8—151no—
63Q8⋊C8—152no—
64D4⋊C8—152no—
65C22×C3×C5—41no—
66C3×C4×C5—81no—
67C3×Dic5—42no—
68C3×Dic5—41no—
69C3×Dic5—41no—
70#41⋊C3—52no—
71C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
72C3×C42—201no—
73C2×C3⋊C8—202no—
74C22×D5—31no—
75C5×Q8—31no—
76C5×Q8C2×C3⋊C811yescharacteristic
77C2×C4×C5—31no—
78C2×C4×C5—31no—
79C2×C4×C5SL(2,ℤ/4)11yescharacteristic
80C2×Dic5—31no—
81C2×Dic5SL(2,ℤ/4)11yescharacteristic
82C2×Dic5C2×S411yescharacteristic
83D20—32no—
84D20—61no—
85C4×D5—32no—
86C4×D5—32no—
87C4×D5—61no—
88C4×D5—61no—
89C4×D5—121no—
90#170—122no—
91#170—122no—
92C2×#41—51no—
93C22×C8—301no—
94C4×Q8—51no—
95C4×Q8ΓL(1,𝔽16)11yescharacteristic
96C4×D4—151no—
97C4×D4—151no—
98#117—151no—
99C2×C42—151no—
100C4⋊C8—152no—
101C4⋊C8—301no—
102C4⋊C8—301no—
103C22⋊C8—301no—
104C4×C8—152no—
105C2×C3×C5—41no—
106C2×C3×C5—41no—
107C2×C3×C5—41no—
108C2×C3×C4—41no—
109C2×C3×C4—201no—
110C2×C3×C4—201no—
111SL(2,𝔽3)D5⋊C811yescharacteristic, complemented
112C3⋊C8—402no—
113C22×C5C2×SL(2,ℤ/4)11yescharacteristic
114C2×D5—32no—
115C2×D5—61no—
116C2×D5—61no—
117C4×C5—21no—
118C4×C5—31no—
119C4×C5—31no—
120C4×C5—61no—
121Dic5—61no—
122Dic5A4⋊C812yes—
123Dic5#98411yescharacteristic
124Dic5#98611yescharacteristic
125#41—52no—
126#41—152no—
127C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
128C2×D4—151no—
129C22×C4—151no—
130C22×C4—151no—
131C22×C4—151no—
132C2×C8—302no—
133C2×C8—302no—
134C2×C8—602no—
135C4⋊C4—31no—
136C4⋊C4—151no—
137C22⋊C4—301no—
138C42—31no—
139C42—51no—
140C42—151no—
141C42—151no—
142C3×C5—41noHall
143C22×C3—41no—
144C3×C4—81no—
145C3×C4—201no—
146C3×C4—201no—
147C3×C4—202no—
148C2×C5C2×A4⋊C811yescharacteristic
149C2×C5#542311yescharacteristic
150C2×C5#542611yescharacteristic
151D5—62no—
152C23—151no—
153Q8—31no—
154Q8D5⋊(C3⋊C8)11yescharacteristic
155D4—152no—
156D4—301no—
157C2×C4—31no—
158C2×C4—31no—
159C2×C4—51no—
160C2×C4—51no—
161C2×C4—152no—
162C2×C4—152no—
163C2×C4—151no—
164C2×C4—301no—
165C2×C4—301no—
166C2×C4—601no—
167C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
168C8—602no—
169C8—602no—
170C2×C3—41no—
171C2×C3—41no—
172C2×C3—41no—
173C5#7307111yescharacteristic, complemented, Sylow
174C22—152no—
175C22—301no—
176C22—301no—
177C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
178C4—21no—
179C4—31no—
180C4—31no—
181C4—52no—
182C4—51no—
183C4—51no—
184C4—61no—
185C4—301no—
186C3—41noSylow
187C2—302no—
188C2D5⋊(A4⋊C8)11yescharacteristic
189C2#1175672011yescharacteristic
190C2#1175672611yescharacteristic
subgroupG/H
center, FrattiniC22C2×A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C2×C8
FittingC4×C5×Q8Dic3
socleC22×C5C2×SL(2,ℤ/4)
prime radicalC2×C5⋊(#41⋊C3)C4
cosocleDic5×SL(2,𝔽3)C22
hypercenterC2×C4A4⋊AGL(1,𝔽5)
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. SL(2,𝔽3)⋊#170C2semidirect
16. C5⋊(#41⋊C3)C8semidirect
37. C5×SL(2,𝔽3)C2×C8semidirect
45. #713C3⋊C8semidirect
111. SL(2,𝔽3)D5⋊C8semidirect
173. C5#73071semidirect

Maximal subgroups

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

subgroupindex
C4×C5⋊(#41⋊C3)2
SL(2,𝔽3)⋊#1702
#106044373
#912334
#730715