Finite Group Databasebeta

← #14292602

Subgroups — #14292602

Order 1920.

304 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 97 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#11750952C212yesmaximal
2#11750800C211yesmaximal, characteristic
3#11750780C211yesmaximal, characteristic
4C3×C5×#334C211yesmaximal, characteristic
5#11746307C212yesmaximal
6#10599344—31nomaximal, Hall
7C2×Dic60—21no—
8C2×Dic60—21no—
9#91758C2212yes—
10C4×Dic30C2211yescharacteristic
11C3×C5×C4⋊C8C2212yes—
12C3×C4×C5×C8C2211yescharacteristic
13#91101—22no—
14#91100—22no—
15#91099—21no—
16#91098—21no—
17C4⋊(C3⋊#168)C2211yescharacteristic
18#68551—51nomaximal, Hall
19#65140—32no—
20#64988—31no—
21#64968—31no—
22C5×#334D311yescharacteristic
23#64706—32no—
24C2×Dic30—22no—
25C2×Dic30D411yescharacteristic
26C2×C3×C5×C8—22no—
27C2×C3×C5×C8D411yescharacteristic
28C2×C3×C5×C8D411yescharacteristic
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15—22no—
31C4⋊Dic15—22no—
32C4⋊Dic15D411yescharacteristic
33#6712—21no—
34C4×Dic15—21no—
35C2×C3⋊#168—21no—
36Dic60—42no—
37Dic60—42no—
38#4851—52no—
39#4699—51no—
40#4679—51no—
41C3×#334D511yescharacteristic
42#4486—52no—
43C2×Dic20—61no—
44C2×Dic20—61no—
45#4015—32no—
46C4×Dic10—31no—
47C5×C4⋊C8C2×D312yes—
48C4×C5×C8C2×D311yescharacteristic
49#3949—62no—
50#3948—62no—
51#3947—61no—
52#3946—61no—
53C4⋊#168—31no—
54#1690—151noSylow
55C2×C3×C4×C5C2×D411yescharacteristic
56C2×C3×C4×C5C2×D411yescharacteristic
57C2×C3×C4×C5#4111yescharacteristic
58C2×Dic15—21no—
59C2×Dic15—21no—
60C2×Dic15—42no—
61Dic30—22no—
62Dic30—42no—
63Dic30—42no—
64C3×C5×C8—21no—
65C3×C5×C8—42no—
66C3×C5×C8SD1612yes—
67C3⋊#168—41no—
68C2×Dic12—101no—
69C2×Dic12—101no—
70#869—52no—
71C4×Dic6—51no—
72C3×C4⋊C8C2×D512yes—
73C3×C4×C8C2×D511yescharacteristic
74#817—102no—
75#816—102no—
76#815—101no—
77Dic3⋊C8—101no—
78C4⋊(C3⋊C8)—51no—
79C2×Dic10—31no—
80C2×Dic10—62no—
81C2×C5×C8—22no—
82C2×C5×C8D1211yescharacteristic
83C2×C5×C8D1211yescharacteristic
84C42×C5C22×D311yescharacteristic
85C4⋊Dic5—31no—
86C4⋊Dic5—62no—
87C4⋊Dic5—62no—
88#683—61no—
89C4×Dic5—61no—
90C2×#168—61no—
91Dic20—122no—
92Dic20—122no—
93#494—151no—
94#475—152no—
95#446—151no—
96#334D1511yescharacteristic
97#332—152no—
98C22×C3×C5#12111yescharacteristic
99C3×C4×C5—21no—
100C3×C4×C5C2×SD1611yescharacteristic
101C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
102C3×C4×C5#13712yes—
103Dic15—41no—
104Dic15—41no—
105Dic15—82no—
106C2×Dic6—51no—
107C2×Dic6—102no—
108C2×C3×C8—22no—
109C2×C3×C8D2011yescharacteristic
110C2×C3×C8D2011yescharacteristic
111C3×C42C22×D511yescharacteristic
112C4⋊Dic3—51no—
113C4⋊Dic3—102no—
114C4⋊Dic3—102no—
115Dic3⋊C4—101no—
116C4×Dic3—101no—
117C2×C3⋊C8—101no—
118Dic12—202no—
119Dic12—202no—
120C2×C4×C5C2×D1211yescharacteristic
121C2×C4×C5D3×D411yescharacteristic
122C2×C4×C5#23911yescharacteristic
123C2×Dic5—61no—
124C2×Dic5—61no—
125C2×Dic5—122no—
126Dic10—62no—
127Dic10—122no—
128Dic10—122no—
129C5×C8—21no—
130C5×C8—42no—
131C5×C8#20412yes—
132#168—121no—
133C2×Q16—301no—
134C2×Q16—301no—
135C4⋊Q8—152no—
136C4×Q8—151no—
137#106—302no—
138C4⋊C8—151no—
139C4⋊C8—301no—
140C4⋊C8C2×D1512yes—
141#103—302no—
142#97—301no—
143C4×C8C2×D1511yescharacteristic
144C2×C3×C5#46011yescharacteristic
145C2×C3×C5#47011yescharacteristic
146C2×C3×C5#47311yescharacteristic
147C2×C3×C4C2×D2011yescharacteristic
148C2×C3×C4D4×D511yescharacteristic
149C2×C3×C4#71311yescharacteristic
150C2×Dic3—101no—
151C2×Dic3—101no—
152C2×Dic3—202no—
153Dic6—102no—
154Dic6—202no—
155Dic6—202no—
156C3×C8—21no—
157C3×C8—42no—
158C3×C8#67712yes—
159C3⋊C8—201no—
160C22×C5#89511yescharacteristic
161C4×C5—21no—
162C4×C5C2×#20411yescharacteristic
163C4×C5#90811yescharacteristic
164C4×C5#91512yes—
165Dic5—121no—
166Dic5—121no—
167Dic5—242no—
168C2×Q8—151no—
169C2×Q8—302no—
170Q16—602no—
171Q16—602no—
172C2×C8—22no—
173C2×C8—301no—
174C2×C8D6011yescharacteristic
175C2×C8D6011yescharacteristic
176C4⋊C4—151no—
177C4⋊C4—301no—
178C4⋊C4—302no—
179C4⋊C4—302no—
180C42—301no—
181C42C22×D1511yescharacteristic
182C3×C5#169011yescharacteristic, complemented, Hall
183C22×C3#404111yescharacteristic
184C3×C4—21no—
185C3×C4C2×#67711yescharacteristic
186C3×C4#405411yescharacteristic
187C3×C4#406112yes—
188Dic3—201no—
189Dic3—201no—
190Dic3—402no—
191C2×C5#484811yescharacteristic
192C2×C5#486711yescharacteristic
193C2×C5#489611yescharacteristic
194Q8—302no—
195Q8—602no—
196Q8—602no—
197C2×C4—301no—
198C2×C4—301no—
199C2×C4—602no—
200C2×C4C2×D6011yescharacteristic
201C2×C4D4×D1511yescharacteristic
202C2×C4#682111yescharacteristic
203C8—21no—
204C8—42no—
205C8—601no—
206C8#670612yes—
207C2×C3#6513711yescharacteristic
208C2×C3#6515711yescharacteristic
209C2×C3#6518511yescharacteristic
210C5#6855111yescharacteristic, complemented, Sylow
211C22#9178411yescharacteristic
212C4—21no—
213C4—601no—
214C4—601no—
215C4—1202no—
216C4C2×#670611yescharacteristic
217C4#9179711yescharacteristic
218C4#9180412yes—
219C3#1059934411yescharacteristic, complemented, Sylow
220C2#1175094911yescharacteristic
221C2#1175096811yescharacteristic
222C2#1175099711yescharacteristic
subgroupG/H
centerC22#91784
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#334C2
socle, prime radicalC22×C3×C5#121
hypercenter#334D15
hypocenterC3×C5#1690
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
182. C3×C5#1690semidirect
210. C5#68551semidirect
219. C3#10599344semidirect

Maximal subgroups

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

subgroupindex
#117509522
#117508002
#117507802
C3×C5×#3342
#117463072
#105993443
#685515