Finite Group Databasebeta

← #14284499

Subgroups — #14284499

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
1C5×#5688C211yesmaximal, characteristic
2#11746878C212yesmaximal
3#11746364C211yesmaximal, characteristic, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745850C212yesmaximal, complemented
6#10602616—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#896—22no—
9C5×#892C412yes—
10C5×#888C412yes—
11C5×#887—22no—
12C42×C5×D3C2211yescharacteristic
13C5×#870C2211yescharacteristic
14#91087C2212yes—
15C3×#3935C2212yes—
16Dic3⋊#168—22no—
17(C2×D3)⋊#168—22no—
18#68369—51nomaximal, Hall
19C5×#533—31no—
20#65215—32no—
21#64763—32no—
22#64763—31no—
23#64763D311yescharacteristic, complemented
24C2×C4×C5×D3C2×C411yescharacteristic
25C2×C4×C5×D3D412yes—
26C2×C5×Dic6—22no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4C2×C412yes—
29C3×C42×C5C2311yescharacteristic
30C2×C3⋊#168—22no—
31C5×(C2×D3)⋊C4—22no—
32C5×C4⋊Dic3C2×C412yes—
33C5×Dic3⋊C4—22no—
34C5×Dic3⋊C4—22no—
35C4×C5×Dic3—22no—
36C4×C5×Dic3C2×C411yescharacteristic
37C4×C5×Dic3D412yes—
38C2×C3×#168—22no—
39#5688D511yescharacteristic
40#4705—52no—
41C3×#330—51no—
42#4543—51no—
43#4465—52no—
44C5×C4⋊Q8—32no—
45C5×#125—31no—
46C5×#125C2×D311yescharacteristic
47C5×C22⋊Q8—62no—
48C4×C5×Q8—62no—
49C5×#117—32no—
50C2×C42×C5—31no—
51C22⋊#168—62no—
52C4⋊#168—62no—
53#3935—32no—
54#3935C2×D312yes—
55#1537—151noSylow
56C22×C5×D3C22⋊C411yescharacteristic
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C22×C411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×C5×Dic3—22no—
61C2×C5×Dic3C22⋊C412yes—
62C2×C5×Dic3C22⋊C411yescharacteristic
63C4×C5×D3—22no—
64C4×C5×D3—42no—
65C5×Dic6—44no—
66C3⋊#168—42no—
67C3×#168—42no—
68C3×#125C2×D511yescharacteristic
69#896—22no—
70#892Dic512yes—
71#888Dic512yes—
72#887—22no—
73C42×D3C2×D511yescharacteristic
74#870C2×D511yescharacteristic
75C3×#97—52no—
76(C2×D3)⋊C8—102no—
77Dic3⋊C8—102no—
78#803—52no—
79C2×C5×Q8—62no—
80C22×C4×C5—31no—
81C22×C4×C5—32no—
82C5×C4⋊C4—22no—
83C5×C4⋊C4—32no—
84C5×C4⋊C4—62no—
85C5×C4⋊C4—62no—
86C5×C4⋊C4C4×D312yes—
87C5×C22⋊C4—62no—
88C42×C5—31no—
89C42×C5—32no—
90C42×C5—62no—
91C42×C5C22×D311yescharacteristic
92C2×#168—22no—
93C2×#168—62no—
94#533—31no—
95#432—152no—
96#330—51no—
97#330—152no—
98#330—151no—
99C22×C3×C5C2×C22⋊C411yescharacteristic
100C2×C5×D3—21no—
101C2×C5×D3—22no—
102C3×C4×C5—21no—
103C3×C4×C5—22no—
104C3×C4×C5—42no—
105C5×Dic3—22no—
106C5×Dic3—42no—
107C5×Dic3#10112yes—
108C2×C4×D3C2×Dic511yescharacteristic
109C2×C4×D3C22⋊D512yes—
110C2×Dic6—22no—
111C2×C3×C8—102no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4C2×Dic512yes—
114C3×C42C22×D511yescharacteristic
115(C2×D3)⋊C4—22no—
116C4⋊Dic3C2×Dic512yes—
117Dic3⋊C4—22no—
118Dic3⋊C4—22no—
119C4×Dic3—22no—
120C4×Dic3C2×Dic511yescharacteristic
121C4×Dic3C22⋊D512yes—
122C2×C3⋊C8—102no—
123C23×C5—31no—
124C5×Q8—124no—
125C2×C4×C5—22no—
126C2×C4×C5—31no—
127C2×C4×C5—32no—
128C2×C4×C5—62no—
129C2×C4×C5—62no—
130C2×C4×C5—122no—
131C2×C4×C5C2×C4×D311yescharacteristic
132C2×C4×C5D3×D412yes—
133#168—42no—
134#168—122no—
135C4⋊Q8—32no—
136#125—31no—
137#125D3×D511yescharacteristic
138C22⋊Q8—62no—
139C4×Q8—62no—
140#117—32no—
141C2×C42—31no—
142C4⋊C8—302no—
143C22⋊C8—302no—
144#97—52no—
145#97—152no—
146C2×C3×C5C2×#10111yescharacteristic
147C2×C3×C5#42112yes—
148C5×D3—41no—
149C22×D3C22⋊Dic511yescharacteristic
150C2×C3×C4—22no—
151C2×C3×C4C22×Dic511yescharacteristic
152C2×C3×C4C2×C22⋊D512yes—
153C2×Dic3—22no—
154C2×Dic3C22⋊Dic512yes—
155C2×Dic3C22⋊Dic511yescharacteristic
156C4×D3—22no—
157C4×D3—42no—
158Dic6—44no—
159C3×C8—202no—
160C3⋊C8—202no—
161C22×C5—61no—
162C22×C5—62no—
163C22×C5D3×C22⋊C411yescharacteristic
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—32no—
167C4×C5—42no—
168C4×C5—62no—
169C4×C5—122no—
170C2×Q8—62no—
171C22×C4—31no—
172C22×C4—32no—
173C2×C8—102no—
174C2×C8—302no—
175C4⋊C4—22no—
176C4⋊C4—32no—
177C4⋊C4—62no—
178C4⋊C4—62no—
179C4⋊C4D3×Dic512yes—
180C22⋊C4—62no—
181C42—31no—
182C42—32no—
183C42—62no—
184C42C2×D3×D511yescharacteristic
185C3×C5#153711yescharacteristic, complemented, Hall
186C22×C3C2×C22⋊Dic511yescharacteristic
187C2×D3—21no—
188C2×D3—22no—
189C3×C4—21no—
190C3×C4—22no—
191C3×C4—42no—
192Dic3—22no—
193Dic3—42no—
194Dic3#396812yes—
195C2×C5—121no—
196C2×C5D3×#10111yescharacteristic
197C2×C5#482112yes—
198C23—31no—
199Q8—124no—
200C2×C4—22no—
201C2×C4—31no—
202C2×C4—32no—
203C2×C4—62no—
204C2×C4—62no—
205C2×C4—122no—
206C2×C4C2×D3×Dic511yescharacteristic
207C2×C4D3×C22⋊D512yes—
208C8—202no—
209C8—602no—
210C2×C3C2×#396811yescharacteristic
211C2×C3#6552512yes—
212D3—41no—
213C5#6836911yescharacteristic, complemented, Sylow
214C22—62no—
215C22—61no—
216C22D3×C22⋊Dic511yescharacteristic
217C4—22no—
218C4—21no—
219C4—32no—
220C4—42no—
221C4—62no—
222C4—122no—
223C3#1060261611yescharacteristic, complemented, Sylow
224C2—121no—
225C2D3×#396811yescharacteristic
226C2#1174942912yes—
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊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. C3×#64763C2semidirect
5. #11745850C2semidirect
23. #64763D3semidirect
185. C3×C5#1537semidirect
213. C5#68369semidirect
223. C3#10602616semidirect

Maximal subgroups

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

subgroupindex
C5×#56882
#117468782
#117463642
C3×#647632
#117458502
#106026163
#683695