Finite Group Databasebeta

← #14512443

Subgroups — #14512443

Order 1920.

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

normal subgroups only

This group has 244 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×D5×SL(2,𝔽3)C211yesmaximal, characteristic
2SL(2,𝔽3)⋊#170C212yesmaximal, complemented
3#10604438—31nomaximal, Hall
4C2×D5×SL(2,𝔽3)C411yescharacteristic
5C4×C5×SL(2,𝔽3)C411yescharacteristic
6#91232—41nomaximal
7Dic5×SL(2,𝔽3)C2211yescharacteristic
8#73056—51nomaximal, Hall
9C4×Q8×D5D311yescharacteristic
10#65680—31no—
11#65678—31no—
12Q8⋊#170—32no—
13#64872—32no—
14C2×C3×C4×D5—41no—
15C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
16C2×C3⋊#170—42no—
17D5×SL(2,𝔽3)C812yescomplemented
18C2×C4×SL(2,𝔽3)—51no—
19SL(2,𝔽3)⋊C8—52no—
20C2×Q8×D5Dic311yescharacteristic
21C4×C5×Q8Dic311yescharacteristic
22Q8×Dic5C2×D311yescharacteristic
23D5×C4⋊C4—31no—
24#4033—31no—
25C42×D5—31no—
26C4×Dic10—31no—
27#4004—61no—
28#4003—61no—
29#4003—61no—
30C4⋊#170—32no—
31C4×#170—32no—
32C4×#170—61no—
33#1479—151noSylow
34C22×C3×D5—41no—
35C2×C3×C4×C5—41no—
36C2×C3×Dic5—41no—
37C3×C4×D5—82no—
38C5×SL(2,𝔽3)C2×C811yescharacteristic
39C3⋊#170—82no—
40C22×SL(2,𝔽3)—51no—
41C4×SL(2,𝔽3)—51no—
42C4×SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic
43#830—201no—
44C2×C5×Q8C2×Dic311yescharacteristic
45Q8×D5—32no—
46Q8×D5C3⋊C812yescomplemented
47C2×C4×D5—31no—
48C2×C4×D5—31no—
49C2×C4×D5S411yescharacteristic
50C2×Dic10—31no—
51C2×#170—62no—
52C2×#170—62no—
53C5×C4⋊C4—31no—
54C42×C5—31no—
55C4⋊Dic5—31no—
56#683—61no—
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—41no—
66C2×C3×D5—42no—
67C2×C3×D5—81no—
68C2×C3×D5—81no—
69C3×C4×C5—81no—
70C3×Dic5—42no—
71C22×C3×C4—201no—
72C2×SL(2,𝔽3)—52no—
73C2×SL(2,𝔽3)C2×AGL(1,𝔽5)11yescharacteristic
74C2×C3⋊C8—202no—
75C22×D5SL(2,ℤ/4)11yescharacteristic
76C5×Q8—31no—
77C5×Q8C2×C3⋊C811yescharacteristic
78C2×C4×C5—31no—
79C2×C4×C5—31no—
80C2×C4×C5SL(2,ℤ/4)11yescharacteristic
81C2×Dic5—31no—
82C2×Dic5—31no—
83C2×Dic5C2×S411yescharacteristic
84C4×D5—22no—
85C4×D5—32no—
86C4×D5—32no—
87C4×D5—121no—
88Dic10—32no—
89Dic10—61no—
90#170—122no—
91#170—122no—
92C22×Q8—51no—
93C4×Q8—51no—
94C4×Q8—151no—
95C4×Q8—151no—
96C4×Q8ΓL(1,𝔽16)11yescharacteristic
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—
108C3×D5—82no—
109C23×C3—201no—
110C2×C3×C4—41no—
111C2×C3×C4—201no—
112C2×C3×C4—402no—
113SL(2,𝔽3)D5⋊C811yescharacteristic
114C3⋊C8—402no—
115C22×C5C2×SL(2,ℤ/4)11yescharacteristic
116C2×D5—21no—
117C2×D5—21no—
118C2×D5A4⋊C812yes—
119C4×C5—21no—
120C4×C5—31no—
121C4×C5—31no—
122C4×C5—61no—
123Dic5—32no—
124Dic5—61no—
125Dic5#98312yes—
126C2×Q8—52no—
127C2×Q8—151no—
128C2×Q8—152no—
129C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
130C22×C4—51no—
131C22×C4—151no—
132C22×C4—151no—
133C2×C8—302no—
134C2×C8—302no—
135C4⋊C4—31no—
136C4⋊C4—151no—
137C4⋊C4—301no—
138C42—31no—
139C42—151no—
140C42—151no—
141C42—151no—
142C3×C5—41noHall
143C22×C3—41no—
144C22×C3—202no—
145C22×C3—401no—
146C22×C3—401no—
147C3×C4—81no—
148C3×C4—202no—
149C2×C5C2×A4⋊C811yescharacteristic
150C2×C5#542011yescharacteristic
151C2×C5#542311yescharacteristic
152D5—22no—
153C23—51no—
154Q8—31no—
155Q8—152no—
156Q8—301no—
157Q8D5⋊(C3⋊C8)11yescharacteristic
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—51no—
161C2×C4—102no—
162C2×C4—152no—
163C2×C4—152no—
164C2×C4—151no—
165C2×C4—151no—
166C2×C4—601no—
167C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
168C8—602no—
169C8—602no—
170C2×C3—41no—
171C2×C3—41no—
172C2×C3—41no—
173C2×C3—402no—
174C5#7305611yescharacteristic, complemented, Sylow
175C22—52no—
176C22—101no—
177C22—101no—
178C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
179C4—21no—
180C4—31no—
181C4—31no—
182C4—52no—
183C4—61no—
184C4—152no—
185C4—301no—
186C3—41noSylow
187C2—102no—
188C2D5⋊(A4⋊C8)11yescharacteristic
189C2#1175672211yescharacteristic
190C2#1175672411yescharacteristic
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×D5×SL(2,𝔽3)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
17. D5×SL(2,𝔽3)C8semidirect
46. Q8×D5C3⋊C8semidirect
174. C5#73056semidirect

Maximal subgroups

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

subgroupindex
C4×D5×SL(2,𝔽3)2
SL(2,𝔽3)⋊#1702
#106044383
#912324
#730565