Finite Group Databasebeta

← #14298407

Subgroups — #14298407

Order 1920.

544 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 121 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×C3×#4018C211yesmaximal, characteristic
2#11752414C212yesmaximal
3#11746790C214yesmaximal, complemented
4#10604195—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6762C2214yes—
7C2×C3×C42×C5C411yescharacteristic
8C2×C3×#685C412yes—
9C2×C3×#683C2212yes—
10C2×C3×C4×Dic5C411yescharacteristic
11C3×#4018—24no—
12#91232—24no—
13#71589—51nomaximal, Hall
14C2×#4018D311yescharacteristic
15#65755—32no—
16#64919—34no—
17C23×C3×D5C2×C411yescharacteristic
18C22×C3×C4×C5C2×C411yescharacteristic
19C22×C3×C4×C5C2×C412yes—
20C22×C3×Dic5C2×C412yes—
21C22×C3×Dic5C2311yescharacteristic
22C2×C3×C4×D5—24no—
23C2×C3×C4×D5D414yes—
24#6762—28no—
25C2×C3⋊#170—24no—
26C3×C42×C5—22no—
27C3×#685—24no—
28C3×#683—24no—
29C3×C4×Dic5—22no—
30C2×C3×#117—51no—
31#5207—52no—
32#4530—54no—
33C22×C4×D5C2×D311yescharacteristic
34C2×#704—34no—
35C2×C42×C5Dic311yescharacteristic
36C2×#685Dic312yes—
37C2×#683C2×D312yes—
38C2×C4×Dic5Dic311yescharacteristic
39#4018—24no—
40#4003—64no—
41#1822—151noSylow
42C23×C3×C5C22×C411yescharacteristic
43C22×C3×D5—22no—
44C22×C3×D5—42no—
45C22×C3×D5C22⋊C412yes—
46C2×C3×C4×C5—22no—
47C2×C3×C4×C5—22no—
48C2×C3×C4×C5—42no—
49C2×C3×C4×C5C22⋊C412yes—
50C2×C3×Dic5—22no—
51C2×C3×Dic5—42no—
52C2×C3×Dic5C2×D412yes—
53C2×C3×Dic5#4114yes—
54C3×C4×D5—28no—
55C3⋊#170—44no—
56C23×C3×C4—51no—
57C3×#117—104no—
58C2×C3×C4⋊C4—52no—
59C2×C3×C22⋊C4—52no—
60C2×C3×C42—51no—
61C2×C3×C42AGL(1,𝔽5)11yescharacteristic
62C2×#208—54no—
63#830—104no—
64C23×D5C2×Dic311yescharacteristic
65C22×C4×C5C2×Dic312yes—
66C22×C4×C5C2×Dic311yescharacteristic
67C22×Dic5C2×Dic312yes—
68C22×Dic5C22×D311yescharacteristic
69C2×C4×D5—24no—
70C2×C4×D5#6714yes—
71#704—68no—
72C2×#170—64no—
73C42×C5—22no—
74#685—24no—
75#683—24no—
76C4×Dic5—22no—
77C2×#117—51no—
78#407—152no—
79#343—154no—
80C22×C3×C5—22no—
81C22×C3×C5C2×C22⋊C411yescharacteristic
82C22×C3×C5#11712yes—
83C2×C3×D5—22no—
84C2×C3×D5—24no—
85C2×C3×D5—44no—
86C3×C4×C5—22no—
87C3×C4×C5—42no—
88C3×Dic5—42no—
89C3×Dic5#12314yes—
90C24×C3—51no—
91C22×C3×C4—51no—
92C22×C3×C4—54no—
93C22×C3×C4—52no—
94C22×C3×C4—104no—
95C22×C3×C4C2×AGL(1,𝔽5)12yes—
96C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
97C3×C4⋊C4—104no—
98C3×C22⋊C4—104no—
99C3×C42—22no—
100C3×C42—102no—
101#208—108no—
102C2×C3⋊C8—104no—
103C23×C5C22×Dic311yescharacteristic
104C22×D5—22no—
105C22×D5—42no—
106C22×D5#21712yes—
107C2×C4×C5—22no—
108C2×C4×C5—22no—
109C2×C4×C5—42no—
110C2×C4×C5#21712yes—
111C2×Dic5—22no—
112C2×Dic5—42no—
113C2×Dic5#23514yes—
114C2×Dic5C2×#6712yes—
115C4×D5—28no—
116#170—124no—
117C23×C4—51no—
118C2×M16—154no—
119#117—104no—
120C2×C4⋊C4—52no—
121C2×C22⋊C4—52no—
122C2×C42—51no—
123C2×C42ΓL(1,𝔽16)11yescharacteristic
124C22⋊C8—304no—
125C2×C3×C5—22no—
126C2×C3×C5#38111yescharacteristic
127C2×C3×C5#41312yes—
128C3×D5—42no—
129C23×C3—52no—
130C23×C3—102no—
131C23×C3—202no—
132C23×C3C22×AGL(1,𝔽5)11yescharacteristic
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135C2×C3×C4—42no—
136C2×C3×C4—54no—
137C2×C3×C4—52no—
138C2×C3×C4—108no—
139C2×C3×C4—102no—
140C2×C3×C4—202no—
141C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
142C3⋊C8—204no—
143C22×C5—22no—
144C22×C5#92612yes—
145C22×C5C2×#21711yescharacteristic
146C2×D5—22no—
147C2×D5—24no—
148C2×D5—44no—
149C4×C5—22no—
150C4×C5—42no—
151Dic5—42no—
152Dic5#92914yes—
153C24—51no—
154C22×C4—51no—
155C22×C4—54no—
156C22×C4—52no—
157C22×C4—104no—
158C22×C4C2×ΓL(1,𝔽16)12yes—
159C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
160M16—308no—
161C2×C8—304no—
162C4⋊C4—104no—
163C22⋊C4—104no—
164C42—22no—
165C42—102no—
166C3×C5#182211yescharacteristic, complemented, Hall
167C22×C3—22no—
168C22×C3—104no—
169C22×C3—102no—
170C22×C3—204no—
171C22×C3#413012yes—
172C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
173C3×C4—22no—
174C3×C4—42no—
175C3×C4—54no—
176C3×C4—202no—
177C2×C5—22no—
178C2×C5#521111yescharacteristic
179C2×C5#523712yes—
180D5—42no—
181C23—52no—
182C23—102no—
183C23—202no—
184C23C22×ΓL(1,𝔽16)11yescharacteristic
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—42no—
188C2×C4—54no—
189C2×C4—52no—
190C2×C4—108no—
191C2×C4—102no—
192C2×C4—202no—
193C2×C4#676312yes—
194C8—604no—
195C2×C3—22no—
196C2×C3—202no—
197C2×C3#6576112yes—
198C2×C3#6576411yescharacteristic
199C5#7158911yescharacteristic, complemented, Sylow
200C22—22no—
201C22—104no—
202C22—102no—
203C22—204no—
204C22#9198912yes—
205C22C2×#676311yescharacteristic
206C4—22no—
207C4—42no—
208C4—54no—
209C4—202no—
210C3#1060419511yescharacteristic, complemented, Sylow
211C2—22no—
212C2—202no—
213C2#1175242012yes—
214C2#1175242311yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
166. C3×C5#1822semidirect
199. C5#71589semidirect
210. C3#10604195semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
#117524142
#117467902
#106041953
#715895