Finite Group Databasebeta

← #14277585

Subgroups — #14277585

Order 1920.

340 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C3×#65228C211yesmaximal, characteristic
2#11746784C212yesmaximal, complemented
3#10598686—31nomaximal, Hall
4C22×C3×D20C411yescharacteristic
5C2×C3×C42×C5C411yescharacteristic
6C2×C3×#685—22no—
7C2×C3×C4⋊Dic5C2211yescharacteristic
8#91241—22no—
9#67640—51nomaximal, Hall
10#65228D311yescharacteristic
11#64913—32no—
12C23×C3×D5—21no—
13C22×C3×C4×C5—21no—
14C22×C3×C4×C5C2×C411yescharacteristic
15C22×C3×Dic5D412yes—
16C2×C3×D20—21no—
17C2×C3×D20—41no—
18C2×C3×D20—41no—
19C2×C3×D20C812yescomplemented
20C2×C3⋊#170—42no—
21C3×C42×C5—41no—
22C3×#685—44no—
23C3×C4⋊Dic5—41no—
24C3×#390—51no—
25#4528—52no—
26C22×D20Dic311yescharacteristic
27C2×C42×C5Dic311yescharacteristic
28C2×#685—22no—
29C2×C4⋊Dic5C2×D311yescharacteristic
30C22⋊#170—62no—
31#1318—151noSylow
32C23×C3×C5C22⋊C411yescharacteristic
33C22×C3×D5—22no—
34C22×C3×D5—42no—
35C22×C3×D5—42no—
36C22×C3×D5—41no—
37C22×C3×D5—41no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5—22no—
41C2×C3×C4×C5—41no—
42C2×C3×C4×C5—41no—
43C2×C3×C4×C5C2×C811yescharacteristic
44C2×C3×C4×C5M1611yescharacteristic
45C2×C3×Dic5—22no—
46C2×C3×Dic5—42no—
47C3×D20—42no—
48C3×D20—42no—
49C3⋊#170—82no—
50C22×C3×D4—51no—
51C2×C3×C4⋊C4—51no—
52C2×C3×C22⋊C4—102no—
53C2×C3×C42AGL(1,𝔽5)11yescharacteristic
54#830—102no—
55C23×D5—21no—
56C22×C4×C5—21no—
57C22×C4×C5C2×Dic311yescharacteristic
58C22×Dic5#6712yes—
59C2×D20—21no—
60C2×D20—41no—
61C2×D20—41no—
62C2×D20C3⋊C812yescomplemented
63C2×#170—122no—
64C42×C5—41no—
65#685—44no—
66C4⋊Dic5—41no—
67#390—51no—
68#324—152no—
69C22×C3×C5—21no—
70C22×C3×C5—21no—
71C22×C3×C5C22⋊C811yescharacteristic
72C22×C3×C5#9911yescharacteristic
73C22×C3×C5#10011yescharacteristic
74C2×C3×D5—44no—
75C2×C3×D5—42no—
76C2×C3×D5—82no—
77C2×C3×D5—81no—
78C2×C3×D5—81no—
79C3×C4×C5—21no—
80C3×C4×C5—21no—
81C3×C4×C5—42no—
82C3×Dic5—42no—
83C24×C3—101no—
84C2×C3×D4—52no—
85C2×C3×D4—101no—
86C2×C3×D4—201no—
87C2×C3×D4—201no—
88C22×C3×C4—21no—
89C22×C3×C4—52no—
90C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
91C3×C4⋊C4—201no—
92C3×C22⋊C4—204no—
93C3×C42—41no—
94C2×C3⋊C8—202no—
95C23×C5#21711yescharacteristic
96C22×D5—22no—
97C22×D5—42no—
98C22×D5—42no—
99C22×D5—41no—
100C22×D5—41no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5C2×C3⋊C811yescharacteristic
107C2×C4×C5#20811yescharacteristic
108C2×Dic5—22no—
109C2×Dic5—42no—
110D20—42no—
111D20—42no—
112#170—242no—
113C22×D4—51no—
114C2×C4⋊C4—51no—
115C2×C22⋊C4—102no—
116C2×C42ΓL(1,𝔽16)11yescharacteristic
117C22⋊C8—302no—
118C2×C3×C5—21no—
119C2×C3×C5—21no—
120C2×C3×C5#32311yescharacteristic
121C2×C3×C5#35311yescharacteristic
122C2×C3×C5#35511yescharacteristic
123C3×D5—82no—
124C23×C3—102no—
125C23×C3—202no—
126C23×C3—202no—
127C23×C3—201no—
128C23×C3—201no—
129C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
130C3×D4—202no—
131C3×D4—202no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—22no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×C3×C4—102no—
138C2×C3×C4—202no—
139C2×C3×C4D5⋊C811yescharacteristic
140C2×C3×C4#70011yescharacteristic
141C3⋊C8—402no—
142C22×C5—21no—
143C22×C5—21no—
144C22×C5#83011yescharacteristic
145C22×C5#83311yescharacteristic
146C22×C5#83411yescharacteristic
147C2×D5—44no—
148C2×D5—42no—
149C2×D5—82no—
150C2×D5—81no—
151C2×D5—81no—
152C4×C5—21no—
153C4×C5—21no—
154C4×C5—42no—
155Dic5—42no—
156C24—101no—
157C2×D4—52no—
158C2×D4—101no—
159C2×D4—201no—
160C2×D4—201no—
161C22×C4—21no—
162C22×C4—52no—
163C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
164C2×C8—602no—
165C4⋊C4—201no—
166C22⋊C4—204no—
167C42—41no—
168C3×C5#131811yescharacteristic, complemented, Hall
169C22×C3—21no—
170C22×C3—21no—
171C22×C3—204no—
172C22×C3—202no—
173C22×C3—402no—
174C22×C3—401no—
175C22×C3—401no—
176C22×C3#399911yescharacteristic
177C22×C3#400311yescharacteristic
178C22×C3#401311yescharacteristic
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—42no—
182C3×C4—202no—
183C2×C5—21no—
184C2×C5—21no—
185C2×C5#452511yescharacteristic
186C2×C5#454211yescharacteristic
187C2×C5#454511yescharacteristic
188D5—82no—
189C23—102no—
190C23—202no—
191C23—202no—
192C23—201no—
193C23—201no—
194C23#676311yescharacteristic
195D4—202no—
196D4—202no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—102no—
203C2×C4—202no—
204C2×C4D5⋊(C3⋊C8)11yescharacteristic
205C2×C4#675811yescharacteristic
206C8—1202no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—402no—
210C2×C3#6485311yescharacteristic
211C2×C3#6485611yescharacteristic
212C2×C3#6491511yescharacteristic
213C5#6764011yescharacteristic, complemented, Sylow
214C22—21no—
215C22—21no—
216C22—204no—
217C22—202no—
218C22—402no—
219C22—401no—
220C22—401no—
221C22#9122811yescharacteristic
222C22#9123211yescharacteristic
223C22#9124211yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—202no—
228C3#1059868611yescharacteristic, complemented, Sylow
229C2—21no—
230C2—21no—
231C2—402no—
232C2#1174672411yescharacteristic
233C2#1174672711yescharacteristic
234C2#1174678611yescharacteristic
subgroupG/H
centerC22#91228
commutatorC2×C3×C4×C5C2×C8
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC22×C3×C5#99
prime radicalC22×C3×D20C4
cosocleC2×C3×C4⋊Dic5C22
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5#1318
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11746784C2semidirect
19. C2×C3×D20C8semidirect
62. C2×D20C3⋊C8semidirect
168. C3×C5#1318semidirect
213. C5#67640semidirect
228. C3#10598686semidirect

Maximal subgroups

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

subgroupindex
C3×#652282
#117467842
#105986863
#676405