Finite Group Databasebeta

← #14285351

Subgroups — #14285351

Order 1920.

456 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 120 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×D3×C4⋊Q8C211yesmaximal, characteristic
2#11746875C212yesmaximal
3#11746367C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745862C212yesmaximal, complemented
6#10602570—31nomaximal, Hall
7C2×C5×D3×Q8C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C5×#944C412yes—
10C5×D3×C4⋊C4—22no—
11C5×#888—22no—
12C42×C5×D3C2211yescharacteristic
13C5×#869C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yes—
15C3×C4⋊#168C2212yes—
16(C2×D3)⋊#168—22no—
17#90953—22no—
18#68487—51nomaximal, Hall
19C2×C5×C4⋊Q8—31no—
20#65215—32no—
21#64766—32no—
22#64766—31no—
23#64766D311yescharacteristic, complemented
24C2×C3×C5×Q8C2×C412yes—
25C5×D3×Q8—44no—
26C2×C4×C5×D3—22no—
27C2×C4×C5×D3C2×C411yescharacteristic
28C2×C4×C5×D3D412yes—
29C2×C5×Dic6—22no—
30C2×C5×Dic6C2×C412yes—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—22no—
34C5×C4⋊Dic3—22no—
35C5×Dic3⋊C4—24no—
36C4×C5×Dic3C2×C411yescharacteristic
37C4×C5×Dic3D412yes—
38C2×C3×#168—22no—
39D3×C4⋊Q8D511yescharacteristic
40#4835—52no—
41C3×#333—51no—
42#4546—51no—
43#4481—52no—
44C22×C5×Q8—32no—
45C5×C4⋊Q8—32no—
46C5×C4⋊Q8—31no—
47C5×C4⋊Q8—62no—
48C5×C4⋊Q8C2×D311yescharacteristic
49C2×C5×C4⋊C4—62no—
50C2×C42×C5—31no—
51C22⋊#168—62no—
52C4⋊#168—32no—
53C4⋊#168C2×D312yes—
54#3935—62no—
55#1558—151noSylow
56C22×C5×D3C22⋊C411yescharacteristic
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C5×Dic3—22no—
62C2×C5×Dic3C22⋊C412yes—
63C2×C5×Dic3C22⋊C411yescharacteristic
64C4×C5×D3—22no—
65C4×C5×D3—22no—
66C4×C5×D3—22no—
67C4×C5×D3—44no—
68C5×Dic6—44no—
69C5×Dic6—42no—
70C3⋊#168—42no—
71C3×#168—42no—
72C2×D3×Q8Dic512yes—
73C3×C4⋊Q8C2×D511yescharacteristic
74#944Dic512yes—
75D3×C4⋊C4—22no—
76#888—22no—
77C42×D3C2×D511yescharacteristic
78#869C2×D511yescharacteristic
79C3×C4⋊C8—52no—
80(C2×D3)⋊C8—102no—
81#815—102no—
82C4⋊(C3⋊C8)—52no—
83C2×C5×Q8—32no—
84C2×C5×Q8—62no—
85C2×C5×Q8—124no—
86C2×C5×Q8C4×D312yes—
87C22×C4×C5—31no—
88C22×C4×C5—32no—
89C22×C4×C5—62no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—64no—
92C5×C4⋊C4—62no—
93C42×C5—31no—
94C42×C5—32no—
95C42×C5C22×D311yescharacteristic
96C2×#168—22no—
97C2×#168—62no—
98C2×C4⋊Q8—31no—
99#432—152no—
100#333—51no—
101#333—152no—
102#333—151no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C2×C5×D3—22no—
105C2×C5×D3#10012yes—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13712yes—
109C3×C4×C5#13712yes—
110C5×Dic3—21no—
111C5×Dic3—22no—
112C5×Dic3—42no—
113C2×C3×Q8C2×Dic512yes—
114D3×Q8—44no—
115C2×C4×D3—22no—
116C2×C4×D3C2×Dic511yescharacteristic
117C2×C4×D3C22⋊D512yes—
118C2×Dic6—22no—
119C2×Dic6C2×Dic512yes—
120C2×C3×C8—102no—
121C3×C4⋊C4—22no—
122C3×C42C22×D511yescharacteristic
123C4⋊Dic3—22no—
124Dic3⋊C4—24no—
125C4×Dic3C2×Dic511yescharacteristic
126C4×Dic3C22⋊D512yes—
127C2×C3⋊C8—102no—
128C23×C5—31no—
129C5×Q8—42no—
130C5×Q8—122no—
131C5×Q8—124no—
132C2×C4×C5—22no—
133C2×C4×C5—32no—
134C2×C4×C5—31no—
135C2×C4×C5—62no—
136C2×C4×C5—62no—
137C2×C4×C5—62no—
138C2×C4×C5—62no—
139C2×C4×C5—124no—
140C2×C4×C5C2×C4×D311yescharacteristic
141C2×C4×C5D3×D412yes—
142#168—42no—
143#168—122no—
144C22×Q8—32no—
145C4⋊Q8—32no—
146C4⋊Q8—31no—
147C4⋊Q8—62no—
148C4⋊Q8D3×D511yescharacteristic
149C2×C4⋊C4—62no—
150C2×C42—31no—
151C4⋊C8—52no—
152C4⋊C8—152no—
153C22⋊C8—302no—
154#97—302no—
155C2×C3×C5C2×#10011yescharacteristic
156C2×C3×C5#41912yes—
157C5×D3—22no—
158C22×D3C22⋊Dic511yescharacteristic
159C3×Q8—42no—
160C2×C3×C4—22no—
161C2×C3×C4C22×Dic511yescharacteristic
162C2×C3×C4C2×C22⋊D512yes—
163C2×Dic3—22no—
164C2×Dic3C22⋊Dic512yes—
165C2×Dic3C22⋊Dic511yescharacteristic
166C4×D3—22no—
167C4×D3—22no—
168C4×D3—22no—
169C4×D3—44no—
170Dic6—44no—
171Dic6—42no—
172C3×C8—202no—
173C3⋊C8—202no—
174C22×C5—32no—
175C22×C5—62no—
176C22×C5D3×C22⋊C411yescharacteristic
177C4×C5—21no—
178C4×C5—42no—
179C4×C5—61no—
180C4×C5—62no—
181C4×C5—122no—
182C4×C5#91512yes—
183C4×C5#91812yes—
184C2×Q8—32no—
185C2×Q8—62no—
186C2×Q8—124no—
187C2×Q8D3×Dic512yes—
188C22×C4—31no—
189C22×C4—32no—
190C22×C4—62no—
191C2×C8—102no—
192C2×C8—302no—
193C4⋊C4—22no—
194C4⋊C4—64no—
195C4⋊C4—62no—
196C42—31no—
197C42—32no—
198C42C2×D3×D511yescharacteristic
199C3×C5#155811yescharacteristic, complemented, Hall
200C22×C3C2×C22⋊Dic511yescharacteristic
201C2×D3—22no—
202C2×D3#396512yes—
203C3×C4—21no—
204C3×C4—42no—
205C3×C4#408812yes—
206C3×C4#408812yes—
207Dic3—21no—
208Dic3—22no—
209Dic3—42no—
210C2×C5—62no—
211C2×C5D3×#10011yescharacteristic
212C2×C5#480212yes—
213C23—31no—
214Q8—42no—
215Q8—122no—
216Q8—124no—
217C2×C4—22no—
218C2×C4—32no—
219C2×C4—31no—
220C2×C4—62no—
221C2×C4—62no—
222C2×C4—62no—
223C2×C4—62no—
224C2×C4—124no—
225C2×C4C2×D3×Dic511yescharacteristic
226C2×C4D3×C22⋊D512yes—
227C8—202no—
228C8—602no—
229C2×C3C2×#396511yescharacteristic
230C2×C3#6551412yes—
231D3—22no—
232C5#6848711yescharacteristic, complemented, Sylow
233C22—32no—
234C22—62no—
235C22D3×C22⋊Dic511yescharacteristic
236C4—21no—
237C4—42no—
238C4—61no—
239C4—62no—
240C4—122no—
241C4#9151812yes—
242C4#9152012yes—
243C3#1060257011yescharacteristic, complemented, Sylow
244C2—62no—
245C2D3×#396511yescharacteristic
246C2#1174921312yes—
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1558
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11746367C2semidirect
4. C3×#64766C2semidirect
5. #11745862C2semidirect
23. #64766D3semidirect
199. C3×C5#1558semidirect
232. C5#68487semidirect
243. C3#10602570semidirect

Maximal subgroups

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

subgroupindex
C5×D3×C4⋊Q82
#117468752
#117463672
C3×#647662
#117458622
#106025703
#684875