Finite Group Databasebeta

← #14284497

Subgroups — #14284497

Order 1920.

388 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 104 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#11746870C212yesmaximal
3#11746364C211yesmaximal, characteristic, complemented
4C5×#4543C211yesmaximal, characteristic, complemented
5#11745849C212yesmaximal, complemented
6#10599162—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C3×#4042—22no—
9C3×#4038C412yes—
10C3×#4034C412yes—
11C3×#4033—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4016C2211yescharacteristic
14#91087C2212yes—
15C5×#803C2212yes—
16#90982—22no—
17#90955—22no—
18#71823—51nomaximal, Hall
19#66022D311yescharacteristic
20#64994—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—
39C3×#533—51no—
40#4926—52no—
41#4543—51no—
42#4543—52no—
43#4543D511yescharacteristic, complemented
44C5×#125C2×D311yescharacteristic
45#4042—22no—
46#4038Dic312yes—
47#4034Dic312yes—
48#4033—22no—
49C42×D5C2×D311yescharacteristic
50#4016C2×D311yescharacteristic
51C5×#97—32no—
52#3952—62no—
53#3946—62no—
54#3935—32no—
55#1537—151noSylow
56C22×C3×D5C22⋊C411yescharacteristic
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C22×C411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×C3×Dic5—22no—
61C2×C3×Dic5C22⋊C412yes—
62C2×C3×Dic5C22⋊C411yescharacteristic
63C3×C4×D5—22no—
64C3×C4×D5—42no—
65C3×Dic10—44no—
66C3⋊#168—42no—
67C5×C3⋊C8—42no—
68C3×C4⋊Q8—52no—
69C3×#125—51no—
70C3×#125C2×D511yescharacteristic
71C3×C22⋊Q8—102no—
72C3×C4×Q8—102no—
73C3×#117—52no—
74C2×C3×C42—51no—
75#830—102no—
76C4⋊(C3⋊C8)—102no—
77#803—52no—
78#803C2×D512yes—
79C2×C4×D5C2×Dic311yescharacteristic
80C2×C4×D5#6712yes—
81C2×Dic10—22no—
82C2×C5×C8—62no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4C2×Dic312yes—
85C42×C5C22×D311yescharacteristic
86#685—22no—
87C4⋊Dic5C2×Dic312yes—
88#683—22no—
89#683—22no—
90C4×Dic5—22no—
91C4×Dic5C2×Dic311yescharacteristic
92C4×Dic5#6712yes—
93C2×#168—62no—
94#533—51no—
95#432—152no—
96#330—31no—
97#330—152no—
98#330—151no—
99C22×C3×C5C2×C22⋊C411yescharacteristic
100C2×C3×D5—21no—
101C2×C3×D5—22no—
102C3×C4×C5—21no—
103C3×C4×C5—22no—
104C3×C4×C5—42no—
105C3×Dic5—22no—
106C3×Dic5—42no—
107C3×Dic5#10112yes—
108C2×C3×Q8—102no—
109C22×C3×C4—51no—
110C22×C3×C4—52no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—52no—
113C3×C4⋊C4—102no—
114C3×C4⋊C4—102no—
115C3×C4⋊C4C4×D512yes—
116C3×C22⋊C4—102no—
117C3×C42—51no—
118C3×C42—52no—
119C3×C42—102no—
120C3×C42C22×D511yescharacteristic
121C2×C3⋊C8—22no—
122C2×C3⋊C8—102no—
123C22×D5#21711yescharacteristic
124C2×C4×C5—22no—
125C2×C4×C5C22×Dic311yescharacteristic
126C2×C4×C5C2×#6712yes—
127C2×Dic5—22no—
128C2×Dic5#21712yes—
129C2×Dic5#21711yescharacteristic
130C4×D5—22no—
131C4×D5—42no—
132Dic10—44no—
133C5×C8—122no—
134#168—122no—
135C4⋊Q8—52no—
136#125—51no—
137#125D3×D511yescharacteristic
138C22⋊Q8—102no—
139C4×Q8—102no—
140#117—52no—
141C2×C42—51no—
142C4⋊C8—302no—
143C22⋊C8—302no—
144#97—32no—
145#97—152no—
146C2×C3×C5C2×#10111yescharacteristic
147C2×C3×C5#42112yes—
148C3×D5—41no—
149C23×C3—51no—
150C3×Q8—204no—
151C2×C3×C4—22no—
152C2×C3×C4—51no—
153C2×C3×C4—52no—
154C2×C3×C4—102no—
155C2×C3×C4—102no—
156C2×C3×C4—202no—
157C2×C3×C4C2×C4×D511yescharacteristic
158C2×C3×C4D4×D512yes—
159C3⋊C8—42no—
160C3⋊C8—202no—
161C22×C5C2×#21711yescharacteristic
162C2×D5—21no—
163C2×D5—22no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—42no—
167Dic5—22no—
168Dic5—42no—
169Dic5#83612yes—
170C2×Q8—102no—
171C22×C4—51no—
172C22×C4—52no—
173C2×C8—62no—
174C2×C8—302no—
175C4⋊C4—22no—
176C4⋊C4—52no—
177C4⋊C4—102no—
178C4⋊C4—102no—
179C4⋊C4D5×Dic312yes—
180C22⋊C4—102no—
181C42—51no—
182C42—52no—
183C42—102no—
184C42C2×D3×D511yescharacteristic
185C3×C5#153711yescharacteristic, complemented, Hall
186C22×C3—101no—
187C22×C3—102no—
188C22×C3D5×C22⋊C411yescharacteristic
189C3×C4—21no—
190C3×C4—22no—
191C3×C4—42no—
192C3×C4—52no—
193C3×C4—102no—
194C3×C4—202no—
195C2×C5C2×#83611yescharacteristic
196C2×C5#523612yes—
197D5—41no—
198C23—51no—
199Q8—204no—
200C2×C4—22no—
201C2×C4—51no—
202C2×C4—52no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4—202no—
206C2×C4C2×D5×Dic311yescharacteristic
207C2×C4D5×#6712yes—
208C8—122no—
209C8—602no—
210C2×C3—201no—
211C2×C3D5×#10111yescharacteristic
212C2×C3#6511012yes—
213C5#7182311yescharacteristic, complemented, Sylow
214C22—102no—
215C22—101no—
216C22D5×#21711yescharacteristic
217C4—22no—
218C4—21no—
219C4—42no—
220C4—52no—
221C4—102no—
222C4—202no—
223C3#1059916211yescharacteristic, complemented, Sylow
224C2—201no—
225C2D5×#83611yescharacteristic
226C2#1174942712yes—
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#1537
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
43. #4543D5semidirect
185. C3×C5#1537semidirect
213. C5#71823semidirect
223. C3#10599162semidirect

Maximal subgroups

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

subgroupindex
C3×#660222
#117468702
#117463642
C5×#45432
#117458492
#105991623
#718235