Finite Group Databasebeta

← #14425749

Subgroups — #14425749

Order 1920.

1544 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1544 conjugacy classes of subgroups — too many to draw. Only its 271 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×C5×#585C211yesmaximal, characteristic, complemented
2#11756589C213yesmaximal, complemented
3#11751345C218yesmaximal, complemented
4#11751341C213yesmaximal, complemented
5#10615857—31nomaximal, Hall
6C3×C5×2−1+4—23no—
7C3×C5×H(5,𝔽2)—23no—
8C3×C5×H(5,𝔽2)C2214yes—
9C2×C3×C5×#41—26no—
10C2×C3×C5×#41C2213yes—
11C22×D60C2211yescharacteristic, complemented
12#91836—23no—
13#91829—23no—
14#91826C22112yescomplemented
15#91819—26no—
16#91815C2213yescomplemented
17#91118C22112yescomplemented
18#84126—51nomaximal, Hall
19C5×#585D311yescharacteristic, complemented
20#66164—33no—
21#65533—38no—
22#65529—33no—
23C23×D15C2312yes—
24C3×C5×#41—24no—
25C3×C5×#41—212no—
26C3×C5×#41—26no—
27C3×C5×#41—212no—
28C3×C5×#41—26no—
29C2×C3×C5×Q8—26no—
30C2×C3×C5×Q8D413yescomplemented
31C2×C3×C5×D4—26no—
32C2×C3×C5×D4—212no—
33C2×C3×C5×D4D413yescomplemented
34C2×C3×C5×D4C2316yes—
35C22×C3×C4×C5—24no—
36C22×C3×C4×C5D416yescomplemented
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—212no—
39C2×D60—23no—
40C2×D60—23no—
41#6719C2316yes—
42#6714—212no—
43C4⋊Dic15—23no—
44C4×Dic15—23no—
45C3×#585D511yescharacteristic, complemented
46#5830—53no—
47#5244—58no—
48#5240—53no—
49C5×2−1+4—23no—
50C5×H(5,𝔽2)—23no—
51C5×H(5,𝔽2)C2×D314yes—
52C2×C5×#41—26no—
53C2×C5×#41C2×D313yes—
54C22×D20—31no—
55#4093—63no—
56#4086—63no—
57#4083—312no—
58#4076—66no—
59#4072—33no—
60#3966—312no—
61#3027—151noSylow
62C23×C3×C5—24no—
63C23×C3×C5C2×D416yes—
64C23×C3×C5C2411yescharacteristic
65C22×D15—26no—
66C22×D15—82no—
67C3×C5×Q8—24no—
68C3×C5×Q8—26no—
69C3×C5×D4—212no—
70C3×C5×D4—212no—
71C3×C5×D4—26no—
72C2×C3×C4×C5—212no—
73C2×C3×C4×C5—26no—
74C2×C3×C4×C5—26no—
75C2×C3×C4×C5C2×D416yes—
76C2×C3×C4×C5C2×D413yes—
77C2×C3×C4×C5C2×D413yes—
78#1220—812no—
79C2×Dic15—26no—
80D60—41no—
81D60—43no—
82C3×2−1+4—23no—
83C3×H(5,𝔽2)—23no—
84C3×H(5,𝔽2)C2×D514yes—
85C2×C3×#41—26no—
86C2×C3×#41C2×D513yes—
87C22×D12—51no—
88#947—103no—
89#940—103no—
90#937—512no—
91#930—106no—
92#926—53no—
93#834—512no—
94C23×D5—32no—
95C5×#41—24no—
96C5×#41—212no—
97C5×#41—26no—
98C5×#41—212no—
99C5×#41—26no—
100C2×C5×Q8—26no—
101C2×C5×Q8#6713yescomplemented
102C2×C5×D4—26no—
103C2×C5×D4—212no—
104C2×C5×D4#6713yescomplemented
105C2×C5×D4C22×D316yes—
106C22×C4×C5—24no—
107C22×C4×C5#6716yescomplemented
108C22×C4×C5C22×D311yescharacteristic
109C2×C22⋊D5—612no—
110C2×D20—63no—
111C2×D20—63no—
112C22⋊Dic5—36no—
113#685—612no—
114C4⋊Dic5—63no—
115C4×Dic5—63no—
116#585D1511yescharacteristic, complemented
117#535—153no—
118B(4,𝔽2)—158no—
119#410—153no—
120C22×C3×C5—26no—
121C22×C3×C5—41no—
122C22×C3×C5—46no—
123C22×C3×C5—84no—
124C22×C3×C5C22×D413yes—
125C2×D15—412no—
126C2×D15—42no—
127C3×C4×C5—26no—
128C3×C4×C5#12011yescharacteristic
129C3×C4×C5#12013yes—
130Dic15—46no—
131C23×D3—52no—
132C3×#41—24no—
133C3×#41—212no—
134C3×#41—26no—
135C3×#41—212no—
136C3×#41—26no—
137C2×C3×Q8—26no—
138C2×C3×Q8C22⋊D513yescomplemented
139C2×C3×D4—26no—
140C2×C3×D4—212no—
141C2×C3×D4C22⋊D513yescomplemented
142C2×C3×D4C22×D516yes—
143C22×C3×C4—24no—
144C22×C3×C4C22⋊D516yescomplemented
145C22×C3×C4C22×D511yescharacteristic
146C2×#67—1012no—
147C2×D12—103no—
148C2×D12—103no—
149#217—56no—
150(C2×D3)⋊C4—1012no—
151C4⋊Dic3—103no—
152C4×Dic3—103no—
153C23×C5—24no—
154C23×C5C2×#6716yes—
155C23×C5C23×D311yescharacteristic
156C22×D5—66no—
157C22×D5—242no—
158C5×Q8—24no—
159C5×Q8—26no—
160C5×D4—212no—
161C5×D4—212no—
162C5×D4—26no—
163C2×C4×C5—212no—
164C2×C4×C5—26no—
165C2×C4×C5—26no—
166C2×C4×C5C2×#6716yes—
167C2×C4×C5C2×#6713yes—
168C2×C4×C5C2×#6713yes—
169C22⋊D5—2412no—
170C2×Dic5—66no—
171D20—121no—
172D20—123no—
1732−1+4—23no—
174H(5,𝔽2)—23no—
175H(5,𝔽2)C2×D1514yes—
176C2×#41—26no—
177C2×#41C2×D1513yes—
178C22×D4—151no—
179#127—303no—
180#124—303no—
181#121—306no—
182#120—1512no—
183#117—153no—
184#99—1512no—
185C2×C3×C5—23no—
186C2×C3×C5—46no—
187C2×C3×C5C2×#12011yescharacteristic
188D15—82no—
189C23×C3—24no—
190C23×C3C2×C22⋊D516yes—
191C23×C3C23×D511yescharacteristic
192C22×D3—106no—
193C22×D3—402no—
194C3×Q8—24no—
195C3×Q8—26no—
196C3×D4—212no—
197C3×D4—212no—
198C3×D4—26no—
199C2×C3×C4—212no—
200C2×C3×C4—26no—
201C2×C3×C4—26no—
202C2×C3×C4C2×C22⋊D516yes—
203C2×C3×C4C2×C22⋊D513yes—
204C2×C3×C4C2×C22⋊D513yes—
205#67—4012no—
206C2×Dic3—106no—
207D12—201no—
208D12—203no—
209C22×C5—26no—
210C22×C5—41no—
211C22×C5—46no—
212C22×C5—84no—
213C22×C5C22×#6713yes—
214C2×D5—1212no—
215C2×D5—122no—
216C4×C5—26no—
217C4×C5#95311yescharacteristic
218C4×C5#95313yes—
219Dic5—126no—
220C24—152no—
221#41—24no—
222#41—212no—
223#41—26no—
224#41—212no—
225#41—26no—
226C2×Q8—26no—
227C2×Q8#122013yescomplemented
228C2×D4—26no—
229C2×D4—212no—
230C2×D4—3012no—
231C2×D4—303no—
232C2×D4—303no—
233C2×D4#122013yescomplemented
234C2×D4C22×D1516yes—
235C22×C4—24no—
236C22×C4#122016yescomplemented
237C22×C4C22×D1511yescharacteristic
238C4⋊C4—303no—
239C22⋊C4—156no—
240C22⋊C4—3012no—
241C42—303no—
242C3×C5#302711yescharacteristic, complemented, Hall
243C22×C3—26no—
244C22×C3—41no—
245C22×C3—46no—
246C22×C3—84no—
247C22×C3C22×C22⋊D513yes—
248C2×D3—2012no—
249C2×D3—202no—
250C3×C4—26no—
251C3×C4#409911yescharacteristic
252C3×C4#409913yes—
253Dic3—206no—
254C2×C5—23no—
255C2×C5—46no—
256C2×C5C2×#95311yescharacteristic
257D5—242no—
258C23—24no—
259C23—306no—
260C23—1202no—
261C23C2×#122016yes—
262C23C23×D1511yescharacteristic
263Q8—24no—
264Q8—26no—
265D4—212no—
266D4—212no—
267D4—26no—
268D4—601no—
269D4—603no—
270D4—12012no—
271C2×C4—212no—
272C2×C4—26no—
273C2×C4—26no—
274C2×C4—306no—
275C2×C4C2×#122016yes—
276C2×C4C2×#122013yes—
277C2×C4C2×#122013yes—
278C2×C3—23no—
279C2×C3—46no—
280C2×C3C2×#409911yescharacteristic
281D3—402no—
282C5#8412611yescharacteristic, complemented, Sylow
283C22—26no—
284C22—41no—
285C22—46no—
286C22—84no—
287C22—6012no—
288C22—602no—
289C22C22×#122013yes—
290C4—26no—
291C4—606no—
292C4#9184211yescharacteristic
293C4#9184213yes—
294C3#1061585711yescharacteristic, complemented, Sylow
295C2—23no—
296C2—46no—
297C2—1202no—
298C2C2×#9184211yescharacteristic
subgroupG/H
centerC2C2×#91842
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC3×C5×#585C2
socleC2×C3×C5C2×#120
hypercenter#585D15
hypocenterC3×C5#3027
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C3×C5×#585C2semidirect
2. #11756589C2semidirect
3. #11751345C2semidirect
4. #11751341C2semidirect
11. C22×D60C22semidirect
14. #91826C22semidirect
16. #91815C22semidirect
17. #91118C22semidirect
19. C5×#585D3semidirect
30. C2×C3×C5×Q8D4semidirect
33. C2×C3×C5×D4D4semidirect
36. C22×C3×C4×C5D4semidirect
45. C3×#585D5semidirect
101. C2×C5×Q8#67semidirect
104. C2×C5×D4#67semidirect
107. C22×C4×C5#67semidirect
116. #585D15semidirect
138. C2×C3×Q8C22⋊D5semidirect
141. C2×C3×D4C22⋊D5semidirect
144. C22×C3×C4C22⋊D5semidirect
227. C2×Q8#1220semidirect
233. C2×D4#1220semidirect
236. C22×C4#1220semidirect
242. C3×C5#3027semidirect
282. C5#84126semidirect
294. C3#10615857semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5852
#117565892
#117513452
#117513412
#106158573
#841265