Finite Group Databasebeta

← #14514921

Subgroups — #14514921

Order 1920.

324 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 34 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×C4×SL(2,𝔽5)C211yesmaximal, characteristic
2C2×#91143C212yesmaximal
3C22×SL(2,𝔽5)C2211yescharacteristic
4C4×SL(2,𝔽5)C412yescomplemented
5#91143C414yescomplemented
6#73063—51nomaximal, Hall
7C2×#4002—61nomaximal
8C2×SL(2,𝔽5)C2×C412yes—
9C2×SL(2,𝔽5)C2×C411yescharacteristic
10C2×C4×SL(2,𝔽3)—51no—
11C2×#859—52no—
12#4649—101nomaximal
13C22×#170—62no—
14C2×C4×Dic5—61no—
15#4002—64no—
16#1763—151noSylow
17SL(2,𝔽5)C4211yescharacteristic, complemented
18C22×SL(2,𝔽3)—51no—
19C2×Dic3⋊C4—102no—
20C2×C4×Dic3—101no—
21C2×C4×Dic3—102no—
22C4×SL(2,𝔽3)—52no—
23#859—54no—
24C3×#95—101no—
25C3⋊#95—101no—
26C22×C4×C5—61no—
27C22×Dic5—61no—
28C22×Dic5—61no—
29C2×#170—64no—
30C2×#170—64no—
31C2×#170—64no—
32C4×Dic5—62no—
33C4×Dic5—62no—
34C2×C4×Q8—51no—
35C2×#103—152no—
36C2×#97—151no—
37C4×C4⋊C4—151no—
38#340—152no—
39C22×C3×C4—102no—
40C22×C3×C4—101no—
41C22×Dic3—102no—
42C22×Dic3—101no—
43C22×Dic3—101no—
44C2×SL(2,𝔽3)—52no—
45C2×SL(2,𝔽3)—51no—
46Dic3⋊C4—104no—
47Dic3⋊C4—104no—
48C4×Dic3—102no—
49C4×Dic3—102no—
50C4×Dic3—204no—
51C23×C5—61no—
52C2×C4×C5—62no—
53C2×C4×C5—122no—
54C2×Dic5—61no—
55C2×Dic5—62no—
56C2×Dic5—61no—
57C2×Dic5—62no—
58C2×Dic5—62no—
59C2×Dic5—121no—
60C2×Dic5—121no—
61#170—68no—
62C22×Q8—51no—
63C22×C8—152no—
64C4×Q8—52no—
65C4×Q8—152no—
66C2×C4⋊C4—152no—
67C2×C4⋊C4—151no—
68C2×C42—151no—
69C2×C42—301no—
70#103—154no—
71#103—154no—
72#97—302no—
73#95—101no—
74C23×C3—101no—
75C2×C3×C4—104no—
76C2×C3×C4—102no—
77C2×C3×C4—202no—
78C2×C3×C4—202no—
79C2×C3×C4—202no—
80C2×Dic3—104no—
81C2×Dic3—101no—
82C2×Dic3—102no—
83C2×Dic3—101no—
84C2×Dic3—102no—
85C2×Dic3—102no—
86C2×Dic3—102no—
87C2×Dic3—102no—
88C2×Dic3—202no—
89C2×Dic3—202no—
90SL(2,𝔽3)—51no—
91C22×C5—62no—
92C22×C5—61no—
93C22×C5—61no—
94C22×C5—61no—
95C22×C5—62no—
96C4×C5—122no—
97Dic5—62no—
98Dic5—61no—
99Dic5—61no—
100Dic5—122no—
101C2×Q8—52no—
102C2×Q8—51no—
103C2×Q8—152no—
104C2×Q8—151no—
105C22×C4—102no—
106C22×C4—151no—
107C22×C4—151no—
108C22×C4S511yescharacteristic
109C2×C8—154no—
110C2×C8—302no—
111C2×C8—302no—
112C4⋊C4—154no—
113C4⋊C4—152no—
114C4⋊C4—302no—
115C4⋊C4—301no—
116C42—152no—
117C42—152no—
118C42—602no—
119C22×C3—102no—
120C22×C3—101no—
121C22×C3—101no—
122C22×C3—101no—
123C22×C3—102no—
124C3×C4—202no—
125C3×C4—204no—
126Dic3—102no—
127Dic3—101no—
128Dic3—101no—
129Dic3—104no—
130Dic3—204no—
131C2×C5—61no—
132C2×C5—62no—
133C2×C5—62no—
134C2×C5—61no—
135C2×C5—61no—
136C23C2×S511yescharacteristic
137Q8—51no—
138Q8—152no—
139Q8—151no—
140Q8—301no—
141C2×C4—22no—
142C2×C4—104no—
143C2×C4—152no—
144C2×C4—152no—
145C2×C4—151no—
146C2×C4—151no—
147C2×C4—152no—
148C2×C4—202no—
149C2×C4—202no—
150C2×C4—301no—
151C2×C4—301no—
152C2×C4A5⋊C412yes—
153C8—304no—
154C2×C3—101no—
155C2×C3—102no—
156C2×C3—102no—
157C2×C3—101no—
158C2×C3—101no—
159C5—61noSylow
160C22C4×S512yes—
161C22#9187111yescharacteristic
162C22#9187211yescharacteristic
163C22C2×A5⋊C411yescharacteristic
164C22#9187712yes—
165C4—22no—
166C4—152no—
167C4—151no—
168C4—151no—
169C4—204no—
170C4—302no—
171C3—101noSylow
172C2C4×A5⋊C411yescharacteristic
173C2#1175150912yes—
174C2#1175151012yes—
175C2#1175151611yescharacteristic
176C2#1175153011yescharacteristic
subgroupG/H
center, Frattini, socleC23C2×S5
commutator, hypocenterSL(2,𝔽5)C42
Fitting, hypercenterC22×C4S5
prime radical, cosocleC22×SL(2,𝔽5)C22
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C4×SL(2,𝔽5)C4semidirect
5. #91143C4semidirect
17. SL(2,𝔽5)C42semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SL(2,𝔽5)2
C2×#911432
#730635
C2×#40026
#464910