Finite Group Databasebeta

← #14315835

Subgroups — #14315835

Order 1920.

308 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 81 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
1#11751298C211yesmaximal, characteristic, complemented
2#11751294C211yesmaximal, characteristic
3#11750970C211yesmaximal, characteristic, complemented
4C3×C5×#360C211yesmaximal, characteristic, complemented
5#11746337C211yesmaximal, characteristic, complemented
6#11746333C211yesmaximal, characteristic, complemented
7#11746308C211yesmaximal, characteristic, complemented
8#10600042—31nomaximal, Hall
9C3×C5×#135C2211yescharacteristic
10#91837—21no—
11C2×D120C2211yescharacteristic
12#91782—21no—
13C3×C5×M32C2211yescharacteristic
14C3×C5×#106C2211yescharacteristic
15#91121—21no—
16#91112C412yescomplemented
17#91110C412yescomplemented
18#91103C2211yescharacteristic
19#91099C2211yescharacteristic
20#91096C2211yescharacteristic
21#91093—21no—
22#69249—51nomaximal, Hall
23#65486—31no—
24#65482—31no—
25#65158—31no—
26C5×#360D311yescharacteristic, complemented
27#64736—31no—
28#64732—31no—
29#64707—31no—
30C3×C5×#41—21no—
31C2×D60—21no—
32C2×C4×D15—41no—
33C3×C5×Q16C2×C411yescharacteristic, complemented
34C3×C5×SD16—21no—
35C3×C5×D8C2×C411yescharacteristic, complemented
36C2×C3×C5×C8C2311yescharacteristic
37C3×C5×C4⋊C4—21no—
38#6714—41no—
39C4×Dic15D411yescharacteristic
40#6710—21no—
41#6710—41no—
42C2×C3⋊#168—41no—
43C2×C3⋊#168D411yescharacteristic
44D120—21no—
45D120C2×C412yes—
46C3×C5×C16—21no—
47C3⋊#672C2×C412yescomplemented
48#5197—51no—
49#5193—51no—
50#4869—51no—
51C3×#360D511yescharacteristic, complemented
52#4516—51no—
53#4512—51no—
54#4487—51no—
55C5×#135C2×D311yescharacteristic
56#4094—61no—
57C2×D40—31no—
58#4039—61no—
59C5×M32C2×D311yescharacteristic
60C5×#106C2×D311yescharacteristic
61#3969—61no—
62#3960—32no—
63#3958—32no—
64#3951—31no—
65#3947—31no—
66#3944—31no—
67#3941—61no—
68AGL(1,ℤ/16)—151noSylow
69C22×D15—41no—
70C3×C5×Q8—21no—
71C3×C5×D4—21no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15—21no—
77D60—22no—
78D60—41no—
79C4×D15—82no—
80C3×C5×C8C22×C411yescharacteristic
81C3×C5×C8#4111yescharacteristic
82C3⋊#168—21no—
83C3⋊#168—41no—
84C3×#135C2×D511yescharacteristic
85#948—101no—
86C2×D24—51no—
87#893—101no—
88C3×M32C2×D511yescharacteristic
89C3×#106C2×D511yescharacteristic
90#837—101no—
91#828—52no—
92#826—52no—
93#819—51no—
94#815—51no—
95#812—51no—
96#809—101no—
97C5×#41—21no—
98C2×D20—61no—
99C2×C4×D5—121no—
100C5×Q16C4×D311yescharacteristic, complemented
101C5×SD16—21no—
102C5×D8C4×D311yescharacteristic, complemented
103C2×C5×C8C22×D311yescharacteristic
104C5×C4⋊C4—21no—
105#685—121no—
106C4×Dic5—31no—
107#681—61no—
108#681—121no—
109C2×#168—31no—
110C2×#168—121no—
111D40—32no—
112D40—61no—
113C5×C16—21no—
114#672—32no—
115#509—151no—
116#444—151no—
117#442—151no—
118#365—151no—
119#361—151no—
120#360D1511yescharacteristic, complemented
121#347—151no—
122C22×C3×C5—41no—
123C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
124C2×D15—42no—
125C2×D15—81no—
126C2×D15—81no—
127C3×C4×C5—41no—
128C3×C4×C5—81no—
129C3×C4×C5C4×D411yescharacteristic
130C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
131Dic15—41no—
132C3×#41—21no—
133C2×D12—101no—
134C2×C4×D3—201no—
135C3×Q16C4×D511yescharacteristic, complemented
136C3×SD16—21no—
137C3×D8C4×D511yescharacteristic, complemented
138C2×C3×C8C22×D511yescharacteristic
139C3×C4⋊C4—21no—
140(C2×D3)⋊C4—201no—
141C4×Dic3—51no—
142#208—101no—
143#208—201no—
144C2×C3⋊C8—51no—
145C2×C3⋊C8—201no—
146D24—52no—
147D24—101no—
148C3×C16—21no—
149C3⋊C16—52no—
150C22×D5—121no—
151C5×Q8—21no—
152C5×D4—21no—
153C5×D4—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5D3×D411yescharacteristic
157C2×Dic5—61no—
158D20—62no—
159D20—121no—
160C4×D5—242no—
161C5×C8C2×C4×D311yescharacteristic
162C5×C8#23711yescharacteristic
163#168—61no—
164#168—121no—
165#135C2×D1511yescharacteristic
166C2×D8—151no—
167#131—301no—
168C4×D4—301no—
169SD32—152no—
170D16—152no—
171M32—151no—
172M32C2×D1511yescharacteristic
173#108—151no—
174#106C2×D1511yescharacteristic
175#104—301no—
176#102—301no—
177#97—151no—
178C2×C3×C5—21no—
179C2×C3×C5—81no—
180C2×C3×C5#44211yescharacteristic
181D15—82no—
182C22×D3—201no—
183C3×Q8—21no—
184C3×D4—21no—
185C3×D4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4D4×D511yescharacteristic
189C2×Dic3—101no—
190D12—102no—
191D12—201no—
192C4×D3—402no—
193C3×C8C2×C4×D511yescharacteristic
194C3×C8#71111yescharacteristic
195C3⋊C8—101no—
196C3⋊C8—201no—
197C22×C5—41no—
198C22×C5#91111yescharacteristic
199C2×D5—122no—
200C2×D5—241no—
201C2×D5—241no—
202C4×C5—41no—
203C4×C5—81no—
204C4×C5#67⋊C411yescharacteristic
205C4×C5#91411yescharacteristic
206Dic5—121no—
207#41—21no—
208C2×D4—301no—
209C22×C4—601no—
210Q16C4×D1511yescharacteristic, complemented
211SD16—21no—
212D8—152no—
213D8—301no—
214D8C4×D1511yescharacteristic, complemented
215M16—301no—
216M16—601no—
217C2×C8—151no—
218C2×C8—601no—
219C2×C8C22×D1511yescharacteristic
220C4⋊C4—21no—
221C22⋊C4—601no—
222C42—151no—
223C16—21no—
224C16—152no—
225C3×C5AGL(1,ℤ/16)11yescharacteristic, complemented, Hall
226C22×C3—41no—
227C22×C3#405711yescharacteristic
228C2×D3—202no—
229C2×D3—401no—
230C2×D3—401no—
231C3×C4—41no—
232C3×C4—81no—
233C3×C4#402711yescharacteristic
234C3×C4#406011yescharacteristic
235Dic3—201no—
236C2×C5—21no—
237C2×C5—81no—
238C2×C5#478511yescharacteristic
239D5—242no—
240C23—601no—
241Q8—21no—
242D4—21no—
243D4—41no—
244D4—302no—
245D4—601no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—301no—
249C2×C4—1202no—
250C2×C4D4×D1511yescharacteristic
251C8—301no—
252C8—601no—
253C8C2×C4×D1511yescharacteristic
254C8#681911yescharacteristic
255C2×C3—21no—
256C2×C3—81no—
257C2×C3#6507411yescharacteristic
258D3—402no—
259C5#6924911yescharacteristic, complemented, Sylow
260C22—41no—
261C22—602no—
262C22—1201no—
263C22—1201no—
264C22#9180011yescharacteristic
265C4—41no—
266C4—81no—
267C4—601no—
268C4#9177011yescharacteristic
269C4#9180311yescharacteristic
270C3#1060004211yescharacteristic, complemented, Sylow
271C2—21no—
272C2—81no—
273C2—1202no—
274C2#1175088611yescharacteristic
subgroupG/H
centerC2#11750886
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C22×D15
FittingC3×C5×#360C2
socleC2×C3×C5#442
prime radical#11751294C2
cosocleC2×C3×C5×C8C23
hypercenter#360D15
hypocenterC3×C5AGL(1,ℤ/16)
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #11751298C2semidirect
3. #11750970C2semidirect
4. C3×C5×#360C2semidirect
5. #11746337C2semidirect
6. #11746333C2semidirect
7. #11746308C2semidirect
16. #91112C4semidirect
17. #91110C4semidirect
26. C5×#360D3semidirect
33. C3×C5×Q16C2×C4semidirect
35. C3×C5×D8C2×C4semidirect
47. C3⋊#672C2×C4semidirect
51. C3×#360D5semidirect
100. C5×Q16C4×D3semidirect
102. C5×D8C4×D3semidirect
120. #360D15semidirect
135. C3×Q16C4×D5semidirect
137. C3×D8C4×D5semidirect
210. Q16C4×D15semidirect
214. D8C4×D15semidirect
225. C3×C5AGL(1,ℤ/16)semidirect
259. C5#69249semidirect
270. C3#10600042semidirect

Maximal subgroups

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

subgroupindex
#117512982
#117512942
#117509702
C3×C5×#3602
#117463372
#117463332
#117463082
#106000423
#692495