Finite Group Databasebeta

← #14292590

Subgroups — #14292590

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
1C3×C5×#494C211yesmaximal, characteristic
2#11751195C212yesmaximal
3#11750780C211yesmaximal, characteristic
4#11746368C212yesmaximal
5#11746278C211yesmaximal, characteristic
6#10602102—31nomaximal, Hall
7C2×C3×C5×Q16—21no—
8C2×C3×C5×Q16—21no—
9C3×C5×C4⋊Q8C2212yes—
10C4×Dic30C2211yescharacteristic
11C3×C4×C5×C8C2211yescharacteristic
12#91099—21no—
13#91098—21no—
14#91094—22no—
15#91092—22no—
16C4⋊(C3⋊#168)C2212yes—
17C4⋊(C3⋊#168)C2211yescharacteristic
18#71309—51nomaximal, Hall
19C5×#494D311yescharacteristic
20#65383—32no—
21#64968—31no—
22#64767—32no—
23#64677—31no—
24C2×C3×C5×Q8—22no—
25C2×Dic30D411yescharacteristic
26C3×C5×Q16—42no—
27C3×C5×Q16—42no—
28C2×C3×C5×C8D411yescharacteristic
29C2×C3×C5×C8D411yescharacteristic
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C4⋊Dic15D411yescharacteristic
34#6712—21no—
35C4×Dic15—21no—
36C2×C3⋊#168—22no—
37C2×C3⋊#168—21no—
38C3×#494D511yescharacteristic
39#5094—52no—
40#4679—51no—
41#4547—52no—
42#4457—51no—
43C2×C5×Q16—21no—
44C2×C5×Q16—21no—
45C5×C4⋊Q8C2×D312yes—
46C4×Dic10—31no—
47C4×C5×C8C2×D311yescharacteristic
48#3947—61no—
49#3946—61no—
50#3942—62no—
51#3940—62no—
52C4⋊#168—32no—
53C4⋊#168—31no—
54#1690—151noSylow
55C3×C5×Q8—42no—
56C3×C5×Q8—42no—
57C2×C3×C4×C5—42no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5#4111yescharacteristic
61C2×Dic15—21no—
62C2×Dic15—21no—
63Dic30—22no—
64C3×C5×C8—21no—
65C3×C5×C8SD1612yes—
66C3⋊#168—41no—
67C3⋊#168—42no—
68C2×C3×Q16—21no—
69C2×C3×Q16—21no—
70C3×C4⋊Q8C2×D512yes—
71C4×Dic6—51no—
72C3×C4×C8C2×D511yescharacteristic
73#815—101no—
74Dic3⋊C8—101no—
75#810—102no—
76#808—102no—
77C4⋊(C3⋊C8)—51no—
78C4⋊(C3⋊C8)—52no—
79C2×C5×Q8—22no—
80C2×Dic10—31no—
81C5×Q16—42no—
82C5×Q16—42no—
83C2×C5×C8#6711yescharacteristic
84C2×C5×C8#6711yescharacteristic
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C42×C5C22×D311yescharacteristic
88C4⋊Dic5—31no—
89#683—61no—
90C4×Dic5—61no—
91C2×#168—62no—
92C2×#168—61no—
93#494D1511yescharacteristic
94#475—152no—
95#446—151no—
96#334—151no—
97#332—152no—
98C22×C3×C5#12111yescharacteristic
99C3×C4×C5—21no—
100C3×C4×C5—82no—
101C3×C4×C5C2×SD1611yescharacteristic
102C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
103C3×C4×C5#13712yes—
104Dic15—41no—
105Dic15—41no—
106C2×C3×Q8—22no—
107C2×Dic6—51no—
108C3×Q16—42no—
109C3×Q16—42no—
110C2×C3×C8C22⋊D511yescharacteristic
111C2×C3×C8C22⋊D511yescharacteristic
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C42C22×D511yescharacteristic
115C4⋊Dic3—51no—
116Dic3⋊C4—101no—
117C4×Dic3—101no—
118C2×C3⋊C8—102no—
119C2×C3⋊C8—101no—
120C5×Q8—42no—
121C5×Q8—42no—
122C2×C4×C5—42no—
123C2×C4×C5D3×D411yescharacteristic
124C2×C4×C5#23711yescharacteristic
125C2×C4×C5C2×#6711yescharacteristic
126C2×Dic5—61no—
127C2×Dic5—61no—
128Dic10—62no—
129C5×C8—21no—
130C5×C8#21412yes—
131#168—122no—
132#168—121no—
133C2×Q16—21no—
134C2×Q16—21no—
135C4⋊Q8C2×D1512yes—
136C4×Q8—151no—
137#106—302no—
138C4⋊C8—151no—
139C4⋊C8—152no—
140C4⋊C8—301no—
141#103—302no—
142#97—301no—
143C4×C8C2×D1511yescharacteristic
144C2×C3×C5#46011yescharacteristic
145C2×C3×C5#47011yescharacteristic
146C2×C3×C5#47311yescharacteristic
147C3×Q8—42no—
148C3×Q8—42no—
149C2×C3×C4—42no—
150C2×C3×C4D4×D511yescharacteristic
151C2×C3×C4#71111yescharacteristic
152C2×C3×C4C2×C22⋊D511yescharacteristic
153C2×Dic3—101no—
154C2×Dic3—101no—
155Dic6—102no—
156C3×C8—21no—
157C3×C8#68712yes—
158C3⋊C8—202no—
159C3⋊C8—201no—
160C22×C5#93811yescharacteristic
161C4×C5—21no—
162C4×C5—82no—
163C4×C5#91812yes—
164C4×C5#93211yescharacteristic
165C4×C5C2×#21411yescharacteristic
166Dic5—121no—
167Dic5—121no—
168C2×Q8—22no—
169C2×Q8—151no—
170Q16—42no—
171Q16—42no—
172C2×C8—302no—
173C2×C8—301no—
174C2×C8#122011yescharacteristic
175C2×C8#122011yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—151no—
179C4⋊C4—301no—
180C42—301no—
181C42C22×D1511yescharacteristic
182C3×C5#169011yescharacteristic, complemented, Hall
183C22×C3#408411yescharacteristic
184C3×C4—21no—
185C3×C4—82no—
186C3×C4#406412yes—
187C3×C4#407811yescharacteristic
188C3×C4C2×#68711yescharacteristic
189Dic3—201no—
190Dic3—201no—
191C2×C5#507511yescharacteristic
192C2×C5#518911yescharacteristic
193C2×C5#519211yescharacteristic
194Q8—42no—
195Q8—42no—
196Q8—302no—
197C2×C4—42no—
198C2×C4—301no—
199C2×C4—301no—
200C2×C4D4×D1511yescharacteristic
201C2×C4#681911yescharacteristic
202C2×C4C2×#122011yescharacteristic
203C8—21no—
204C8—602no—
205C8—601no—
206C8#671612yes—
207C2×C3#6536411yescharacteristic
208C2×C3#6547811yescharacteristic
209C2×C3#6548111yescharacteristic
210C5#7130911yescharacteristic, complemented, Sylow
211C22#9182711yescharacteristic
212C4—21no—
213C4—82no—
214C4—601no—
215C4—601no—
216C4#9180712yes—
217C4#9182111yescharacteristic
218C4C2×#671611yescharacteristic
219C3#1060210211yescharacteristic, complemented, Sylow
220C2#1175117611yescharacteristic
221C2#1175129011yescharacteristic
222C2#1175129311yescharacteristic
subgroupG/H
centerC22#91827
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#494C2
socle, prime radicalC22×C3×C5#121
hypercenter#494D15
hypocenterC3×C5#1690
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
182. C3×C5#1690semidirect
210. C5#71309semidirect
219. C3#10602102semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4942
#117511952
#117507802
#117463682
#117462782
#106021023
#713095