Finite Group Databasebeta

← #14317265

Subgroups — #14317265

Order 1920.

316 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 77 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#11751292C211yesmaximal, characteristic
2C2×#91113C211yesmaximal, characteristic, complemented
3C2×#91084C211yesmaximal, characteristic
4#11750974C211yesmaximal, characteristic, complemented
5C3×C5×#358C211yesmaximal, characteristic, complemented
6#11746322C211yesmaximal, characteristic, complemented
7#11746312C211yesmaximal, characteristic
8#10600030—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91836—21no—
11C2×#6717—21no—
12C2×Dic60C2211yescharacteristic
13C2×D120C2211yescharacteristic
14#91776—21no—
15C2×C3×C5×C16C2211yescharacteristic
16C3×C5×#107C2211yescharacteristic
17#91113—22no—
18C8×Dic15C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20#91094—21no—
21#91084—22no—
22#69237—51nomaximal, Hall
23#65480—31no—
24C2×#3961—31no—
25C2×#3932—31no—
26#65162—31no—
27C5×#358D311yescharacteristic, complemented
28#64721—31no—
29#64711—31no—
30C2×C3×C5×Q8—21no—
31C2×D60—21no—
32C2×Dic30—21no—
33C3×C5×Q16—21no—
34C3×C5×Q16—21no—
35C2×C3×C5×C8C2311yescharacteristic
36C3×C5×C4⋊C4—21no—
37#6717—42no—
38#6714—41no—
39#6714—41no—
40#6712—41no—
41C4×Dic15—41no—
42C4×Dic15D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44Dic60—21no—
45Dic60D412yes—
46D120—21no—
47D120—21no—
48C3×C5×C16—21no—
49C3⋊#672—21no—
50#5191—51no—
51C2×#829—51no—
52C2×#800—51no—
53#4873—51no—
54C3×#358D511yescharacteristic, complemented
55Dic3⋊C16—51no—
56#4491—51no—
57C2×C5×Q16C2×D311yescharacteristic
58#4093—61no—
59C2×#688—61no—
60C2×Dic20—31no—
61C2×D40—31no—
62#4033—61no—
63C2×C5×C16C2×D311yescharacteristic
64C5×#107C2×D311yescharacteristic
65#3961—62no—
66C8×Dic5—31no—
67C2×#672—31no—
68#3942—61no—
69#3932—62no—
70#2211—151noSylow
71C22×D15—41no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—41no—
78C2×Dic15D811yescharacteristic
79C2×Dic15D811yescharacteristic
80D60—41no—
81D60—41no—
82Dic30—22no—
83Dic30—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3⋊#168—21no—
87C2×C3×Q16C2×D511yescharacteristic
88#947—101no—
89C2×#215—101no—
90C2×Dic12—51no—
91C2×D24—51no—
92#887—101no—
93C2×C3×C16C2×D511yescharacteristic
94C3×#107C2×D511yescharacteristic
95#829—102no—
96C8×Dic3—51no—
97C2×C3⋊C16—51no—
98#810—101no—
99#800—102no—
100C2×C5×Q8—21no—
101C2×D20—61no—
102C2×Dic10—61no—
103C5×Q16—21no—
104C5×Q16—21no—
105C2×C5×C8C22×D311yescharacteristic
106C5×C4⋊C4—21no—
107#688—122no—
108#685—121no—
109#685—121no—
110#683—121no—
111C4×Dic5—31no—
112C4×Dic5—121no—
113C2×#168—31no—
114Dic20—32no—
115Dic20—61no—
116D40—61no—
117D40—61no—
118C5×C16—21no—
119#672—61no—
120C2×Q32—151no—
121C2×SD32—151no—
122#495—151no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358D1511yescharacteristic, complemented
126#357—151no—
127C22×C3×C5C2×D811yescharacteristic
128C2×D15—81no—
129C2×D15—81no—
130C2×D15—81no—
131C3×C4×C5—81no—
132C3×C4×C5—81no—
133C3×C4×C5#12111yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135Dic15—21no—
136Dic15—21no—
137Dic15—42no—
138C2×C3×Q8—21no—
139C2×D12—101no—
140C2×Dic6—101no—
141C3×Q16—21no—
142C3×Q16—21no—
143C2×C3×C8C22×D511yescharacteristic
144C3×C4⋊C4—21no—
145#215—202no—
146(C2×D3)⋊C4—201no—
147(C2×D3)⋊C4—201no—
148Dic3⋊C4—201no—
149C4×Dic3—51no—
150C4×Dic3—201no—
151C2×C3⋊C8—51no—
152Dic12—52no—
153Dic12—101no—
154D24—101no—
155D24—101no—
156C3×C16—21no—
157C3⋊C16—101no—
158C22×D5—121no—
159C5×Q8—41no—
160C5×Q8—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5D3×D411yescharacteristic
164C2×Dic5—31no—
165C2×Dic5—31no—
166C2×Dic5—121no—
167D20—121no—
168D20—121no—
169Dic10—62no—
170Dic10—121no—
171C5×C8#23511yescharacteristic
172C5×C8D3×D411yescharacteristic
173#168—61no—
174C2×Q16—151no—
175C2×Q16C2×D1511yescharacteristic
176C2×SD16—301no—
177C2×D8—151no—
178#124—301no—
179C4×Q8—301no—
180Q32—302no—
181SD32—302no—
182C2×C16—151no—
183C2×C16C2×D1511yescharacteristic
184#107C2×D1511yescharacteristic
185#103—301no—
186C4×C8—151no—
187C2×C3×C5#45911yescharacteristic
188C2×C3×C5#50811yescharacteristic
189C2×C3×C5#51011yescharacteristic
190D15—161no—
191C22×D3—201no—
192C3×Q8—41no—
193C3×Q8—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4D4×D511yescharacteristic
197C2×Dic3—51no—
198C2×Dic3—51no—
199C2×Dic3—201no—
200D12—201no—
201D12—201no—
202Dic6—102no—
203Dic6—201no—
204C3×C8#70911yescharacteristic
205C3×C8D4×D511yescharacteristic
206C3⋊C8—101no—
207C22×C5D3×D811yescharacteristic
208C2×D5—241no—
209C2×D5—241no—
210C2×D5—241no—
211C4×C5—81no—
212C4×C5—81no—
213C4×C5#88411yescharacteristic
214C4×C5#91411yescharacteristic
215Dic5—61no—
216Dic5—61no—
217Dic5—122no—
218C2×Q8—21no—
219C2×Q8—301no—
220C2×D4—301no—
221Q16—21no—
222Q16—21no—
223Q16—152no—
224Q16—301no—
225SD16—602no—
226D8—301no—
227D8—301no—
228C2×C8—151no—
229C2×C8C22×D1511yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—601no—
232C22⋊C4—601no—
233C22⋊C4—601no—
234C42—151no—
235C42—601no—
236C16—21no—
237C16—301no—
238C3×C5#221111yescharacteristic, complemented, Hall
239C22×C3D5×D811yescharacteristic
240C2×D3—401no—
241C2×D3—401no—
242C2×D3—401no—
243C3×C4—81no—
244C3×C4—81no—
245C3×C4#403011yescharacteristic
246C3×C4#406011yescharacteristic
247Dic3—101no—
248Dic3—101no—
249Dic3—202no—
250C2×C5#478611yescharacteristic
251C2×C5#491611yescharacteristic
252C2×C5#491811yescharacteristic
253D5—481no—
254C23—601no—
255Q8—41no—
256Q8—41no—
257Q8—302no—
258Q8—601no—
259D4—601no—
260D4—601no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—151no—
264C2×C4—151no—
265C2×C4—601no—
266C2×C4D4×D1511yescharacteristic
267C8—301no—
268C8#681711yescharacteristic
269C8D4×D1511yescharacteristic
270C2×C3#6507511yescharacteristic
271C2×C3#6520511yescharacteristic
272C2×C3#6520711yescharacteristic
273D3—801no—
274C5#6923711yescharacteristic, complemented, Sylow
275C22—1201no—
276C22—1201no—
277C22—1201no—
278C22D8×D1511yescharacteristic
279C4—81no—
280C4—81no—
281C4—301no—
282C4—301no—
283C4—602no—
284C4#9177311yescharacteristic
285C4#9180311yescharacteristic
286C3#1060003011yescharacteristic, complemented, Sylow
287C2—2401no—
288C2#1175088711yescharacteristic
289C2#1175101711yescharacteristic
290C2#1175101911yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#358C2
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
hypercenter#358D15
hypocenterC3×C5#2211
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
2. C2×#91113C2semidirect
4. #11750974C2semidirect
5. C3×C5×#358C2semidirect
6. #11746322C2semidirect
27. C5×#358D3semidirect
54. C3×#358D5semidirect
125. #358D15semidirect
238. C3×C5#2211semidirect
274. C5#69237semidirect
286. C3#10600030semidirect

Maximal subgroups

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

subgroupindex
#117512922
C2×#911132
C2×#910842
#117509742
C3×C5×#3582
#117463222
#117463122
#106000303
#692375