Finite Group Databasebeta

← #14293926

Subgroups — #14293926

Order 1920.

372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 111 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#11750795C211yesmaximal, characteristic
2#11750795C211yesmaximal, characteristic
3#11750794C211yesmaximal, characteristic
4#11750783C211yesmaximal, characteristic, complemented
5#11750782C211yesmaximal, characteristic, complemented
6#11750782C211yesmaximal, characteristic, complemented
7C3×C5×#322C211yesmaximal, characteristic, complemented
8#10598886—31nomaximal, Hall
9C2×#6706—22no—
10#91763C2211yescharacteristic
11#91758C2211yescharacteristic
12#91758C2211yescharacteristic
13#91758C2211yescharacteristic
14C3×C4×C5×C8C2211yescharacteristic
15C3×C4×C5×C8C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17#91105—22no—
18#91105—22no—
19#91102—22no—
20#91100—22no—
21#91100—22no—
22#68093—51nomaximal, Hall
23#64983—31no—
24#64983—31no—
25#64982—31no—
26#64971—31no—
27#64970—31no—
28#64970—31no—
29C5×#322D311yescharacteristic, complemented
30C2×D60—21no—
31C2×D60—21no—
32C2×D60—21no—
33C2×Dic30—21no—
34C2×Dic30—21no—
35C2×Dic30—21no—
36C2×C3×C5×C8D412yes—
37C2×C3×C5×C8D412yes—
38C2×C3×C5×C8D412yes—
39C3×C42×C5C2311yescharacteristic
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46#6706—44no—
47#4694—51no—
48#4694—51no—
49#4693—51no—
50#4682—51no—
51#4681—51no—
52#4681—51no—
53C3×#322D511yescharacteristic, complemented
54C2×#677—62no—
55#4020—31no—
56#4015—31no—
57#4015—31no—
58#4015—31no—
59C4×C5×C8C2×D311yescharacteristic
60C4×C5×C8C2×D311yescharacteristic
61C4×C5×C8C2×D311yescharacteristic
62#3953—62no—
63#3953—62no—
64#3950—62no—
65#3948—62no—
66#3948—62no—
67#1719—151noSylow
68C22×D15—41no—
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×Dic15—41no—
73C2×Dic15—41no—
74C2×Dic15—41no—
75D60—42no—
76D60—42no—
77D60—42no—
78Dic30—42no—
79Dic30—42no—
80Dic30—42no—
81C3×C5×C8—22no—
82C3×C5×C8—22no—
83C3×C5×C8—22no—
84C2×#204—102no—
85#874—51no—
86#869—51no—
87#869—51no—
88#869—51no—
89C3×C4×C8C2×D511yescharacteristic
90C3×C4×C8C2×D511yescharacteristic
91C3×C4×C8C2×D511yescharacteristic
92#821—102no—
93#821—102no—
94#818—102no—
95#816—102no—
96#816—102no—
97C2×D20—61no—
98C2×D20—61no—
99C2×D20—61no—
100C2×Dic10—61no—
101C2×Dic10—61no—
102C2×Dic10—61no—
103C2×C5×C8D1212yes—
104C2×C5×C8D1212yes—
105C2×C5×C8D1212yes—
106C42×C5C22×D311yescharacteristic
107C4⋊Dic5—61no—
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C4⋊Dic5—61no—
111C4⋊Dic5—61no—
112C4⋊Dic5—61no—
113#677—124no—
114#500—151no—
115#492—151no—
116#487—151no—
117#487—151no—
118#486—151no—
119#486—151no—
120#322D1511yescharacteristic, complemented
121C22×C3×C5#12711yescharacteristic
122C2×D15—81no—
123C2×D15—81no—
124C2×D15—81no—
125C3×C4×C5#13512yes—
126C3×C4×C5AGL(1,ℤ/8)12yes—
127C3×C4×C5#13712yes—
128Dic15—81no—
129Dic15—81no—
130Dic15—81no—
131C2×D12—101no—
132C2×D12—101no—
133C2×D12—101no—
134C2×Dic6—101no—
135C2×Dic6—101no—
136C2×Dic6—101no—
137C2×C3×C8D2012yes—
138C2×C3×C8D2012yes—
139C2×C3×C8D2012yes—
140C3×C42C22×D511yescharacteristic
141C4⋊Dic3—101no—
142C4⋊Dic3—101no—
143C4⋊Dic3—101no—
144C4⋊Dic3—101no—
145C4⋊Dic3—101no—
146C4⋊Dic3—101no—
147#204—204no—
148C22×D5—121no—
149C2×C4×C5C2×D1211yescharacteristic
150C2×C4×C5C2×D1211yescharacteristic
151C2×C4×C5C2×D1211yescharacteristic
152C2×Dic5—121no—
153C2×Dic5—121no—
154C2×Dic5—121no—
155D20—122no—
156D20—122no—
157D20—122no—
158Dic10—122no—
159Dic10—122no—
160Dic10—122no—
161C5×C8—22no—
162C5×C8—22no—
163C5×C8—22no—
164C2×SD16—302no—
165C4⋊Q8—151no—
166C4⋊Q8—151no—
167C4⋊Q8—151no—
168#127—151no—
169#107—302no—
170#103—302no—
171#103—302no—
172#102—302no—
173#102—302no—
174C4×C8C2×D1511yescharacteristic
175C4×C8C2×D1511yescharacteristic
176C4×C8C2×D1511yescharacteristic
177C2×C3×C5#49511yescharacteristic
178C2×C3×C5#49611yescharacteristic
179C2×C3×C5#49711yescharacteristic
180D15—161no—
181C22×D3—201no—
182C2×C3×C4C2×D2011yescharacteristic
183C2×C3×C4C2×D2011yescharacteristic
184C2×C3×C4C2×D2011yescharacteristic
185C2×Dic3—201no—
186C2×Dic3—201no—
187C2×Dic3—201no—
188D12—202no—
189D12—202no—
190D12—202no—
191Dic6—202no—
192Dic6—202no—
193Dic6—202no—
194C3×C8—22no—
195C3×C8—22no—
196C3×C8—22no—
197C22×C5#87411yescharacteristic
198C2×D5—241no—
199C2×D5—241no—
200C2×D5—241no—
201C4×C5#90412yes—
202C4×C5#90812yes—
203C4×C5#90912yes—
204Dic5—241no—
205Dic5—241no—
206Dic5—241no—
207C2×Q8—301no—
208C2×Q8—301no—
209C2×Q8—301no—
210C2×D4—301no—
211C2×D4—301no—
212C2×D4—301no—
213SD16—604no—
214C2×C8D6012yes—
215C2×C8D6012yes—
216C2×C8D6012yes—
217C4⋊C4—301no—
218C4⋊C4—301no—
219C4⋊C4—301no—
220C4⋊C4—301no—
221C4⋊C4—301no—
222C4⋊C4—301no—
223C42C22×D1511yescharacteristic
224C3×C5#171911yescharacteristic, complemented, Hall
225C22×C3#402011yescharacteristic
226C2×D3—401no—
227C2×D3—401no—
228C2×D3—401no—
229C3×C4#405012yes—
230C3×C4#405412yes—
231C3×C4#405512yes—
232Dic3—401no—
233Dic3—401no—
234Dic3—401no—
235C2×C5#469611yescharacteristic
236C2×C5#471211yescharacteristic
237C2×C5#471511yescharacteristic
238D5—481no—
239C23—601no—
240Q8—602no—
241Q8—602no—
242Q8—602no—
243D4—602no—
244D4—602no—
245D4—602no—
246C2×C4—601no—
247C2×C4—601no—
248C2×C4—601no—
249C2×C4C2×D6011yescharacteristic
250C2×C4C2×D6011yescharacteristic
251C2×C4C2×D6011yescharacteristic
252C8—22no—
253C8—22no—
254C8—22no—
255C2×C3#6498511yescharacteristic
256C2×C3#6500111yescharacteristic
257C2×C3#6500411yescharacteristic
258D3—801no—
259C5#6809311yescharacteristic, complemented, Sylow
260C22—1201no—
261C22—1201no—
262C22—1201no—
263C22#9176311yescharacteristic
264C4—1201no—
265C4—1201no—
266C4—1201no—
267C4#9179312yes—
268C4#9179712yes—
269C4#9179812yes—
270C3#1059888611yescharacteristic, complemented, Sylow
271C2—2401no—
272C2#1175079711yescharacteristic
273C2#1175081311yescharacteristic
274C2#1175081611yescharacteristic
subgroupG/H
centerC22#91763
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#322C2
socleC22×C3×C5#127
prime radical#91763C22
hypercenter#322D15
hypocenterC3×C5#1719
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #322

Complements

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

NH ≅ G/Ntype
4. #11750783C2semidirect
5. #11750782C2semidirect
6. #11750782C2semidirect
7. C3×C5×#322C2semidirect
29. C5×#322D3semidirect
53. C3×#322D5semidirect
120. #322D15semidirect
224. C3×C5#1719semidirect
259. C5#68093semidirect
270. C3#10598886semidirect

Maximal subgroups

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

subgroupindex
#117507952
#117507942
#117507832
#117507822
C3×C5×#3222
#105988863
#680935