Finite Group Databasebeta

← #14284020

Subgroups — #14284020

Order 1920.

452 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 112 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×#66022C211yesmaximal, characteristic
2#11747003C212yesmaximal
3#11746364C211yesmaximal, characteristic, complemented
4C5×#4543C211yesmaximal, characteristic, complemented
5#11745849C212yesmaximal, complemented
6#10599155—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C3×#4042—22no—
9C3×#4038C412yes—
10C3×#4034C412yes—
11C3×#4033—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4016C2211yescharacteristic
14C2×#6649—22no—
15#91087C2212yes—
16C5×#803C2212yes—
17Dic5×C3⋊C8—22no—
18#71821—51nomaximal, Hall
19#66022D311yescharacteristic
20#64996—32no—
21C5×#330—31no—
22#64763—31no—
23#64685—32no—
24C2×C3×C4×D5C2×C411yescharacteristic
25C2×C3×C4×D5D412yes—
26C2×C3×Dic10—22no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4C2×C412yes—
29C3×C42×C5C2311yescharacteristic
30C2×C3⋊#168—22no—
31C2×C5×C3⋊C8—22no—
32C3×#685—22no—
33C3×C4⋊Dic5C2×C412yes—
34C3×#683—22no—
35C3×#683—22no—
36C3×C4×Dic5—22no—
37C3×C4×Dic5C2×C411yescharacteristic
38C3×C4×Dic5D412yes—
39#6649—28no—
40C3×#533—51no—
41C4×#208—52no—
42#4543—51no—
43#4543—52no—
44#4543D511yescharacteristic, complemented
45C5×#125C2×D311yescharacteristic
46C2×#676—62no—
47#4042—22no—
48#4038Dic312yes—
49#4034Dic312yes—
50#4033—22no—
51C42×D5C2×D311yescharacteristic
52#4016C2×D311yescharacteristic
53C5×#97—32no—
54C8×Dic5—62no—
55#3935—32no—
56#1526—151noSylow
57C22×C3×D5C22⋊C411yescharacteristic
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C3×Dic5—22no—
62C2×C3×Dic5C22⋊C411yescharacteristic
63C2×C3×Dic5C22⋊C412yes—
64C3×C4×D5—22no—
65C3×C4×D5—24no—
66C3×Dic10—44no—
67C3⋊#168—24no—
68C5×C3⋊C8—24no—
69C3×C4⋊Q8—52no—
70C3×#125—51no—
71C3×#125C2×D511yescharacteristic
72C3×C22⋊Q8—102no—
73C3×C4×Q8—102no—
74C3×#117—52no—
75C2×C3×C42—51no—
76C2×#208—102no—
77#803—52no—
78#803C2×D512yes—
79C4×C3⋊C8—102no—
80C2×C4×D5C2×Dic311yescharacteristic
81C2×C4×D5#6712yes—
82C2×Dic10—22no—
83C2×C5×C8—62no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4C2×Dic312yes—
86C42×C5C22×D311yescharacteristic
87#685—22no—
88C4⋊Dic5C2×Dic312yes—
89#683—22no—
90#683—22no—
91C4×Dic5—22no—
92C4×Dic5C2×Dic311yescharacteristic
93C4×Dic5#6712yes—
94C2×#168—62no—
95#676—68no—
96#533—51no—
97C4×M16—152no—
98#330—31no—
99#330—152no—
100#330—151no—
101C22×C3×C5C2×C22⋊C411yescharacteristic
102C2×C3×D5—21no—
103C2×C3×D5—22no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×Dic5—42no—
108C3×Dic5#10112yes—
109C3×Dic5#10414yes—
110C2×C3×Q8—102no—
111C22×C3×C4—51no—
112C22×C3×C4—52no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—52no—
115C3×C4⋊C4—102no—
116C3×C4⋊C4—102no—
117C3×C4⋊C4C4×D512yes—
118C3×C22⋊C4—102no—
119C3×C42—51no—
120C3×C42—52no—
121C3×C42—102no—
122C3×C42C22×D511yescharacteristic
123#208—108no—
124C2×C3⋊C8—22no—
125C2×C3⋊C8—102no—
126C22×D5#21711yescharacteristic
127C2×C4×C5—22no—
128C2×C4×C5C22×Dic311yescharacteristic
129C2×C4×C5C2×#6712yes—
130C2×Dic5—22no—
131C2×Dic5#21711yescharacteristic
132C2×Dic5#21712yes—
133C4×D5—22no—
134C4×D5—24no—
135Dic10—44no—
136C5×C8—64no—
137#168—64no—
138C2×M16—302no—
139C4⋊Q8—52no—
140#125—51no—
141#125D3×D511yescharacteristic
142C22⋊Q8—102no—
143C4×Q8—102no—
144#117—52no—
145C2×C42—51no—
146#97—32no—
147#97—152no—
148C4×C8—302no—
149C2×C3×C5C2×#10111yescharacteristic
150C2×C3×C5C2×#10412yes—
151C3×D5—41no—
152C23×C3—51no—
153C3×Q8—204no—
154C2×C3×C4—22no—
155C2×C3×C4—51no—
156C2×C3×C4—52no—
157C2×C3×C4—104no—
158C2×C3×C4—102no—
159C2×C3×C4—102no—
160C2×C3×C4C2×C4×D511yescharacteristic
161C2×C3×C4D4×D512yes—
162C3⋊C8—24no—
163C3⋊C8—104no—
164C22×C5C2×#21711yescharacteristic
165C2×D5—21no—
166C2×D5—22no—
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—42no—
170Dic5—42no—
171Dic5#83612yes—
172Dic5#83714yes—
173C2×Q8—102no—
174C22×C4—51no—
175C22×C4—52no—
176M16—308no—
177C2×C8—62no—
178C2×C8—302no—
179C4⋊C4—22no—
180C4⋊C4—52no—
181C4⋊C4—102no—
182C4⋊C4—102no—
183C4⋊C4D5×Dic312yes—
184C22⋊C4—102no—
185C42—51no—
186C42—52no—
187C42—102no—
188C42C2×D3×D511yescharacteristic
189C3×C5#152611yescharacteristic, complemented, Hall
190C22×C3—101no—
191C22×C3—102no—
192C22×C3D5×C22⋊C411yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—52no—
197C3×C4—54no—
198C3×C4—202no—
199C2×C5C2×#83611yescharacteristic
200C2×C5C2×#83712yes—
201D5—41no—
202C23—51no—
203Q8—204no—
204C2×C4—22no—
205C2×C4—51no—
206C2×C4—52no—
207C2×C4—104no—
208C2×C4—102no—
209C2×C4—102no—
210C2×C4C2×D5×Dic311yescharacteristic
211C2×C4D5×#6712yes—
212C8—64no—
213C8—304no—
214C2×C3—201no—
215C2×C3D5×#10111yescharacteristic
216C2×C3D5×#10412yes—
217C5#7182111yescharacteristic, complemented, Sylow
218C22—102no—
219C22—101no—
220C22D5×#21711yescharacteristic
221C4—22no—
222C4—21no—
223C4—42no—
224C4—54no—
225C4—52no—
226C4—202no—
227C3#1059915511yescharacteristic, complemented, Sylow
228C2—201no—
229C2D5×#83611yescharacteristic
230C2D5×#83712yes—
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #11746364C2semidirect
4. C5×#4543C2semidirect
5. #11745849C2semidirect
44. #4543D5semidirect
189. C3×C5#1526semidirect
217. C5#71821semidirect
227. C3#10599155semidirect

Maximal subgroups

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

subgroupindex
C3×#660222
#117470032
#117463642
C5×#45432
#117458492
#105991553
#718215