Finite Group Databasebeta

← #14283987

Subgroups — #14283987

Order 1920.

540 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 117 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×#66059C211yesmaximal, characteristic
2C4×#6758C212yesmaximal, complemented
3#11746798C214yesmaximal, complemented
4#10604633—31nomaximal, Hall
5C2×C3×#713C412yes—
6C2×#6758—22no—
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×#4093C2212yes—
9C3×#4041—22no—
10C3×#4039—22no—
11C3×#4020C411yescharacteristic
12C3×C42×D5C2211yescharacteristic
13#91231C2214yes—
14C4×C3⋊#170—22no—
15#71797—51nomaximal, Hall
16#66059D311yescharacteristic
17C4×#700—32no—
18#64927—34no—
19C2×C3×C5×Q8C2×C412yes—
20C3×#713—44no—
21C2×C3×D20—22no—
22C2×C3×D20—22no—
23C2×C3×D20C2×C412yes—
24C2×C3×C4×D5—22no—
25C2×C3×C4×D5C2×C411yescharacteristic
26C2×C3×C4×D5D412yes—
27C2×C3⋊#170—24no—
28#6758—28no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2×C411yescharacteristic
31C3×#685—24no—
32C3×C4×Dic5D412yes—
33C3×C4×Dic5C2311yescharacteristic
34C3×#532—51no—
35C4×#208—52no—
36#4540—54no—
37C2×#713Dic312yes—
38C2×#700—62no—
39C5×C4⋊Q8Dic311yescharacteristic
40#4093C2×D312yes—
41#4041—22no—
42#4039—22no—
43#4020Dic311yescharacteristic
44C42×D5C2×D311yescharacteristic
45#4002—34no—
46C4×#170—62no—
47#1525—151noSylow
48C22×C3×D5—22no—
49C22×C3×D5C22⋊C411yescharacteristic
50C3×C5×Q8—42no—
51C2×C3×C4×C5—22no—
52C2×C3×C4×C5C22⋊C412yes—
53C2×C3×C4×C5C22×C411yescharacteristic
54C2×C3×Dic5C22⋊C411yescharacteristic
55C2×C3×Dic5C2×D412yes—
56C3×D20—42no—
57C3×D20—44no—
58C3×D20—44no—
59C3×C4×D5—24no—
60C3×C4×D5—22no—
61C3×C4×D5—44no—
62C3⋊#170—28no—
63C2×C3×#41—52no—
64C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
65C3×#127—51no—
66C3×#124—52no—
67C3×#121—102no—
68C3×C4×D4—102no—
69C2×C3×C42—51no—
70C2×#208—102no—
71#803—54no—
72C4×C3⋊C8—102no—
73C2×C5×Q8C2×Dic312yes—
74#713—44no—
75C2×D20—22no—
76C2×D20—22no—
77C2×D20C2×Dic312yes—
78C2×C4×D5—22no—
79C2×C4×D5C2×Dic311yescharacteristic
80C2×C4×D5#6712yes—
81C2×#170—64no—
82#700—68no—
83C5×C4⋊C4—22no—
84C42×C5C2×Dic311yescharacteristic
85#685—24no—
86C4×Dic5#6712yes—
87C4×Dic5C22×D311yescharacteristic
88#532—51no—
89C4×M16—152no—
90#329—154no—
91C22×C3×C5C2×C22⋊C411yescharacteristic
92C2×C3×D5—21no—
93C2×C3×D5—22no—
94C2×C3×D5—42no—
95C2×C3×D5—44no—
96C3×C4×C5—21no—
97C3×C4×C5—42no—
98C3×C4×C5#10414yes—
99C3×Dic5—22no—
100C3×Dic5#10012yes—
101C3×#41—204no—
102C2×C3×Q8C2×AGL(1,𝔽5)12yes—
103C2×C3×D4—52no—
104C2×C3×D4—102no—
105C2×C3×D4—102no—
106C22×C3×C4—52no—
107C22×C3×C4—51no—
108C22×C3×C4—102no—
109C3×C4⋊C4—22no—
110C3×C22⋊C4—104no—
111C3×C42—52no—
112C3×C42—51no—
113C3×C42C2×AGL(1,𝔽5)11yescharacteristic
114#208—108no—
115C2×C3⋊C8—104no—
116C22×D5—22no—
117C22×D5#21711yescharacteristic
118C5×Q8—42no—
119C2×C4×C5—22no—
120C2×C4×C5#21712yes—
121C2×C4×C5C22×Dic311yescharacteristic
122C2×Dic5#21711yescharacteristic
123C2×Dic5C2×#6712yes—
124D20—42no—
125D20—44no—
126D20—44no—
127C4×D5—24no—
128C4×D5—22no—
129C4×D5—44no—
130#170—68no—
131C2×#41—52no—
132C2×M16—302no—
133C4⋊Q8ΓL(1,𝔽16)11yescharacteristic
134#127—51no—
135#124—52no—
136#121—102no—
137C4×D4—102no—
138C2×C42—51no—
139#97—154no—
140C4×C8—302no—
141C2×C3×C5C2×#10011yescharacteristic
142C2×C3×C5C2×#10412yes—
143C3×D5—41no—
144C3×D5—82no—
145C23×C3—51no—
146C23×C3—102no—
147C3×Q8—42no—
148C3×D4—202no—
149C3×D4—204no—
150C3×D4—204no—
151C2×C3×C4—22no—
152C2×C3×C4—51no—
153C2×C3×C4—52no—
154C2×C3×C4—102no—
155C2×C3×C4—104no—
156C2×C3×C4—204no—
157C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
158C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
159C3⋊C8—108no—
160C22×C5C2×#21711yescharacteristic
161C2×D5—21no—
162C2×D5—22no—
163C2×D5—42no—
164C2×D5—44no—
165C4×C5—21no—
166C4×C5—42no—
167C4×C5#83714yes—
168Dic5—22no—
169Dic5#83312yes—
170#41—204no—
171C2×Q8C2×ΓL(1,𝔽16)12yes—
172C2×D4—52no—
173C2×D4—102no—
174C2×D4—102no—
175C22×C4—52no—
176C22×C4—51no—
177C22×C4—102no—
178M16—308no—
179C2×C8—304no—
180C4⋊C4—22no—
181C22⋊C4—104no—
182C42—52no—
183C42—51no—
184C42C2×ΓL(1,𝔽16)11yescharacteristic
185C3×C5#152511yescharacteristic, complemented, Hall
186C22×C3—101no—
187C22×C3—102no—
188C22×C3—202no—
189C22×C3—204no—
190C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
191C3×C4—21no—
192C3×C4—42no—
193C3×C4—52no—
194C3×C4—102no—
195C3×C4#401014yes—
196C2×C5C2×#83311yescharacteristic
197C2×C5C2×#83712yes—
198D5—41no—
199D5—82no—
200C23—51no—
201C23—102no—
202Q8—42no—
203D4—202no—
204D4—204no—
205D4—204no—
206C2×C4—22no—
207C2×C4—51no—
208C2×C4—52no—
209C2×C4—102no—
210C2×C4—104no—
211C2×C4—204no—
212C2×C4#676312yes—
213C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
214C8—308no—
215C2×C3—201no—
216C2×C3—402no—
217C2×C3D5⋊#10011yescharacteristic
218C2×C3C2×#401012yes—
219C5#7179711yescharacteristic, complemented, Sylow
220C22—101no—
221C22—102no—
222C22—202no—
223C22—204no—
224C22C2×#676311yescharacteristic
225C4—21no—
226C4—42no—
227C4—52no—
228C4—102no—
229C4#9123914yes—
230C3#1060463311yescharacteristic, complemented, Sylow
231C2—201no—
232C2—402no—
233C2D5⋊#83311yescharacteristic
234C2C2×#9123912yes—
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66059C2
cosocleC3×C4×Dic5C23
hypercenterC4⋊Q8ΓL(1,𝔽16)
hypocenterC3×C5#1525
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
2. C4×#6758C2semidirect
3. #11746798C2semidirect
185. C3×C5#1525semidirect
219. C5#71797semidirect
230. C3#10604633semidirect

Maximal subgroups

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

subgroupindex
C3×#660592
C4×#67582
#117467982
#106046333
#717975