Finite Group Databasebeta

← #72231442

Subgroups — #72231442

Order 2400.

286 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 34 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
1C2×C5×D5×A4C211yesmaximal, characteristic, complemented
2C2×C5×C5⋊S4C211yesmaximal, characteristic, complemented
3A4⋊#1039C211yesmaximal, characteristic, complemented
4#11717094—31nomaximal, Hall
5C2×C52×A4C2211yescharacteristic
6C5×D5×A4—21no—
7C5×C5⋊S4—21no—
8#10597121—41nomaximal
9#91958—51nomaximal
10#91904—51nomaximal
11C23×C5×D5D311yescharacteristic, complemented
12C2×C5×C22⋊D5—31no—
13C2×#6037—31no—
14C2×#6037—31no—
15C22⋊#1039—31no—
16#87778—31no—
17#87778—31no—
18C2×C5×D15—41no—
19C2×C3×C5×D5—41no—
20C52×A4D411yescharacteristic, complemented
21C3⋊#1039—41no—
22C22×C5×A4—51no—
23C2×D5×A4D511yescharacteristic, complemented
24C2×C5⋊S4D511yescharacteristic, complemented
25C2×C5×S4—51no—
26A4⋊Dic5—51no—
27A4⋊Dic5—51no—
28A4⋊Dic5—102no—
29C23×C52C2×D311yescharacteristic
30C22×C5×D5—21no—
31C22×C5×D5—31no—
32C22×C5×D5—31no—
33C22×C5×D5—31no—
34C22×C5×D5—61no—
35C2×#1039—31no—
36C2×#1039—31no—
37C5×C22⋊D5—61no—
38C5×C22⋊D5—61no—
39C2×C5×Dic5—31no—
40#6037—62no—
41#6037—61no—
42#6037—61no—
43#4099—151no—
44#4083—151no—
45C2×C3×C52—41no—
46C5×D15—81no—
47C3×C5×D5—81no—
48C2×C5×A4—22no—
49C2×C5×A4—101no—
50C2×C5×A4C2×D511yescharacteristic
51C2×C5×A4C2×D511yescharacteristic
52D5×A4—21no—
53C5⋊S4—21no—
54C5×S4—101no—
55#1220—201no—
56#1201—201no—
57C22×C52—31no—
58C22×C52—31no—
59C22×C52#6711yescharacteristic, complemented
60C2×C5×D5—32no—
61C2×C5×D5—31no—
62C2×C5×D5—61no—
63C2×C5×D5—61no—
64C2×C5×D5—61no—
65C2×C5×D5—61no—
66C2×C5×D5—61no—
67C2×C5×D5—61no—
68C2×C5×D5S411yescharacteristic, complemented
69#1039—61no—
70#1039—61no—
71C5×Dic5—61no—
72GL(2,ℤ/4)—251noHall
73C24×C5—51no—
74C23×D5D1511yescharacteristic, complemented
75C2×C5×D4—151no—
76C2×C22⋊D5—31no—
77C2×C22⋊D5—151no—
78C2×C22⋊D5—151no—
79C2×C22⋊D5—151no—
80C2×C22⋊D5—151no—
81C22⋊Dic5—151no—
82C22⋊Dic5—151no—
83C22⋊Dic5—151no—
84C22⋊Dic5—151no—
85C22⋊Dic5—302no—
86#685—151no—
87#685—151no—
88C3×C52—41noHall
89C22×C3×C5—201no—
90C2×D15—41no—
91C2×C5×D3—201no—
92C2×C3×D5—41no—
93C5×A4—22no—
94C5×A4C22⋊D511yescharacteristic, complemented
95C5×A4C22⋊D511yescharacteristic, complemented
96Dic15—201no—
97Dic15—201no—
98Dic15—402no—
99C2×C52—31no—
100C2×C52—31no—
101C2×C52C2×S411yescharacteristic
102C5×D5—21no—
103C5×D5—61no—
104C5×D5—121no—
105C22×A4—51no—
106C2×S4—51no—
107SL(2,ℤ/4)—251no—
108C23×C5—22no—
109C23×C5—101no—
110C23×C5—151no—
111C23×C5—151no—
112C23×C5—151no—
113C23×C5—301no—
114C23×C5D3×D511yescharacteristic
115C23×C5C2×D1511yescharacteristic
116C22×D5—21no—
117C22×D5—31no—
118C22×D5—31no—
119C22×D5—31no—
120C22×D5—61no—
121C5×D4—301no—
122C5×D4—301no—
123C2×C4×C5—151no—
124C22⋊D5—61no—
125C22⋊D5—61no—
126C22⋊D5—302no—
127C22⋊D5—301no—
128C22⋊D5—301no—
129C22⋊D5—302no—
130C22⋊D5—301no—
131C22⋊D5—301no—
132C2×Dic5—31no—
133C2×Dic5—151no—
134C2×Dic5—151no—
135C2×Dic5—151no—
136C2×Dic5—151no—
137C2×Dic5—302no—
138C2×Dic5—302no—
139#120—751noSylow
140C2×C3×C5—41no—
141C2×C3×C5—41no—
142C2×C3×C5—82no—
143C2×C3×C5—401no—
144D15—81no—
145C3×D5—81no—
146C5×D3—401no—
147C52GL(2,ℤ/4)11yescharacteristic, complemented, Sylow
148C2×A4—101no—
149C2×A4D5211yescharacteristic
150S4—101no—
151#67—1001no—
152C22×C5—22no—
153C22×C5—31no—
154C22×C5—31no—
155C22×C5—31no—
156C22×C5—31no—
157C22×C5—51no—
158C22×C5—62no—
159C22×C5—62no—
160C22×C5—152no—
161C22×C5—151no—
162C22×C5—301no—
163C22×C5—301no—
164C22×C5—301no—
165C22×C5—301no—
166C22×C5—301no—
167C22×C5—301no—
168C22×C5#120111yescharacteristic, complemented
169C22×C5#122011yescharacteristic, complemented
170C2×D5—32no—
171C2×D5—31no—
172C2×D5—61no—
173C2×D5—61no—
174C2×D5—61no—
175C2×D5—61no—
176C2×D5—61no—
177C2×D5—61no—
178C2×D5C5⋊S411yescharacteristic, complemented
179C4×C5—301no—
180Dic5—61no—
181Dic5—301no—
182Dic5—301no—
183Dic5—301no—
184Dic5—301no—
185Dic5—602no—
186Dic5—602no—
187C24—51no—
188C2×D4—151no—
189C2×D4—751no—
190C2×D4—751no—
191C22⋊C4—751no—
192C22⋊C4—751no—
193C22⋊C4—751no—
194C3×C5—41no—
195C3×C5—41no—
196C3×C5—82no—
197C22×C3—201no—
198C2×D3—201no—
199A4#603711yescharacteristic, complemented
200Dic3—1001no—
201C2×C5—22no—
202C2×C5—31no—
203C2×C5—31no—
204C2×C5—31no—
205C2×C5—31no—
206C2×C5—62no—
207C2×C5—62no—
208C2×C5—101no—
209C2×C5—301no—
210C2×C5—601no—
211C2×C5D5×S411yescharacteristic
212C2×C5C2×C5⋊S411yescharacteristic
213D5—21no—
214D5—61no—
215D5—121no—
216C23—101no—
217C23—151no—
218C23—151no—
219C23—151no—
220C23—301no—
221C23D5×D1511yescharacteristic
222D4—301no—
223D4—301no—
224D4—1501no—
225D4—1502no—
226D4—1501no—
227C2×C4—151no—
228C2×C4—751no—
229C2×C4—751no—
230C2×C3—41no—
231C2×C3—401no—
232D3—401no—
233C5—22no—
234C5#9190411yescharacteristic, complemented
235C5#9195811yescharacteristic, complemented
236C22—31no—
237C22—31no—
238C22—51no—
239C22—152no—
240C22—151no—
241C22—301no—
242C22—301no—
243C22—301no—
244C22—301no—
245C22—301no—
246C22—301no—
247C22#1059712111yescharacteristic, complemented
248C4—301no—
249C4—1501no—
250C4—1501no—
251C3—41noSylow
252C2—31no—
253C2—31no—
254C2—101no—
255C2—301no—
256C2—601no—
257C2D5×C5⋊S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D5×C5⋊S4
commutator, cosocleC2×C52×A4C22
Fitting, socleC23×C52C2×D3
hypocenterC52×A4D4
LCSG ▷ C2×C52×A4 ▷ C52×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5×D5×A4C2semidirect
2. C2×C5×C5⋊S4C2semidirect
3. A4⋊#1039C2semidirect
11. C23×C5×D5D3semidirect
20. C52×A4D4semidirect
23. C2×D5×A4D5semidirect
24. C2×C5⋊S4D5semidirect
59. C22×C52#67semidirect
68. C2×C5×D5S4semidirect
74. C23×D5D15semidirect
94. C5×A4C22⋊D5semidirect
95. C5×A4C22⋊D5semidirect
147. C52GL(2,ℤ/4)semidirect
168. C22×C5#1201semidirect
169. C22×C5#1220semidirect
178. C2×D5C5⋊S4semidirect
199. A4#6037semidirect
234. C5#91904semidirect
235. C5#91958semidirect
247. C22#10597121semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D5×A42
C2×C5×C5⋊S42
A4⋊#10392
#117170943
#105971214
#919585
#919045