Finite Group Databasebeta

← #14284006

Subgroups — #14284006

Order 1920.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756447C211yesmaximal, characteristic
2#11750808C212yesmaximal
3C3×C5×#330C211yesmaximal, characteristic, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11746286C212yesmaximal, complemented
6#10599155—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C2×#6705—22no—
9#91785—22no—
10#91781C412yes—
11#91777C412yes—
12#91776—22no—
13C42×D15C2211yescharacteristic
14#91759C2211yescharacteristic
15C3×C5×#97C2212yes—
16C8×Dic15—22no—
17#91087C2212yes—
18#68362—51nomaximal, Hall
19#66022—31no—
20#64996—32no—
21C5×#330D311yescharacteristic, complemented
22#64763—31no—
23#64685—32no—
24C2×C4×D15C2×C411yescharacteristic
25C2×C4×D15D412yes—
26C2×Dic30—22no—
27C2×C3×C5×C8—22no—
28C3×C5×C4⋊C4—22no—
29C3×C5×C4⋊C4C2×C412yes—
30C3×C42×C5C2311yescharacteristic
31#6714—22no—
32C4⋊Dic15C2×C412yes—
33#6712—22no—
34#6712—22no—
35C4×Dic15—22no—
36C4×Dic15C2×C411yescharacteristic
37C4×Dic15D412yes—
38C2×C3⋊#168—22no—
39#6705—28no—
40#5688—51no—
41#4707—52no—
42C3×#330D511yescharacteristic, complemented
43#4543—51no—
44#4465—52no—
45C5×#125C2×D311yescharacteristic
46C2×#676—62no—
47#4042—62no—
48#4038—32no—
49#4034—32no—
50#4033—62no—
51C42×D5—31no—
52#4016—31no—
53C5×#97C2×D312yes—
54C8×Dic5—62no—
55#3935—32no—
56#1526—151noSylow
57C22×D15C22⋊C411yescharacteristic
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×Dic15—22no—
62C2×Dic15C22⋊C411yescharacteristic
63C2×Dic15C22⋊C412yes—
64C4×D15—22no—
65C4×D15—24no—
66Dic30—44no—
67C3×C5×C8—24no—
68C3⋊#168—24no—
69C3×#125C2×D511yescharacteristic
70C2×ΓL(1,𝔽25)—102no—
71#896—102no—
72#892—52no—
73#888—52no—
74#887—102no—
75C42×D3—51no—
76#870—51no—
77C3×#97C2×D512yes—
78C8×Dic3—102no—
79#803—52no—
80C2×C4×D5—31no—
81C2×C4×D5—32no—
82C2×Dic10—62no—
83C2×C5×C8—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4C4×D312yes—
86C42×C5C22×D311yescharacteristic
87#685—62no—
88C4⋊Dic5—32no—
89#683—62no—
90#683—62no—
91C4×Dic5—31no—
92C4×Dic5—32no—
93C4×Dic5—62no—
94C2×#168—62no—
95#676—68no—
96#533—151no—
97C4×M16—152no—
98#330—151no—
99#330—152no—
100#330D1511yescharacteristic, complemented
101C22×C3×C5C2×C22⋊C411yescharacteristic
102C2×D15—21no—
103C2×D15—22no—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107Dic15—42no—
108Dic15#10112yes—
109Dic15#10414yes—
110C2×C4×D3—51no—
111C2×C4×D3—52no—
112C2×Dic6—102no—
113C2×C3×C8—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4C4×D512yes—
116C3×C42C22×D511yescharacteristic
117(C2×D3)⋊C4—102no—
118C4⋊Dic3—52no—
119Dic3⋊C4—102no—
120Dic3⋊C4—102no—
121C4×Dic3—51no—
122C4×Dic3—52no—
123C4×Dic3—102no—
124C2×C3⋊C8—102no—
125ΓL(1,𝔽25)—108no—
126C22×D5—31no—
127C2×C4×C5—22no—
128C2×C4×C5C2×C4×D311yescharacteristic
129C2×C4×C5D3×D412yes—
130C2×Dic5—31no—
131C2×Dic5—32no—
132C2×Dic5—62no—
133C4×D5—64no—
134C4×D5—62no—
135Dic10—124no—
136C5×C8—24no—
137#168—64no—
138C2×M16—302no—
139C4⋊Q8—152no—
140#125—151no—
141#125C2×D1511yescharacteristic
142C22⋊Q8—302no—
143C4×Q8—302no—
144#117—152no—
145C2×C42—151no—
146#97—152no—
147#97C2×D1512yes—
148C4×C8—302no—
149C2×C3×C5C2×#10111yescharacteristic
150C2×C3×C5C2×#10412yes—
151D15—41no—
152C22×D3—51no—
153C2×C3×C4—22no—
154C2×C3×C4C2×C4×D511yescharacteristic
155C2×C3×C4D4×D512yes—
156C2×Dic3—51no—
157C2×Dic3—52no—
158C2×Dic3—102no—
159C4×D3—104no—
160C4×D3—102no—
161Dic6—204no—
162C3×C8—24no—
163C3⋊C8—104no—
164C22×C5D3×C22⋊C411yescharacteristic
165C2×D5—61no—
166C2×D5—62no—
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—42no—
170Dic5—32no—
171Dic5—34no—
172Dic5—122no—
173C2×Q8—302no—
174C22×C4—151no—
175C22×C4—152no—
176M16—308no—
177C2×C8—22no—
178C2×C8—302no—
179C4⋊C4—22no—
180C4⋊C4—152no—
181C4⋊C4—302no—
182C4⋊C4—302no—
183C4⋊C4C4×D1512yes—
184C22⋊C4—302no—
185C42—151no—
186C42—152no—
187C42—302no—
188C42C22×D1511yescharacteristic
189C3×C5#152611yescharacteristic, complemented, Hall
190C22×C3D5×C22⋊C411yescharacteristic
191C2×D3—101no—
192C2×D3—102no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196Dic3—52no—
197Dic3—54no—
198Dic3—202no—
199C2×C5D3×#10111yescharacteristic
200C2×C5D3×#10412yes—
201D5—121no—
202C23—151no—
203Q8—604no—
204C2×C4—22no—
205C2×C4—151no—
206C2×C4—152no—
207C2×C4—304no—
208C2×C4—302no—
209C2×C4—302no—
210C2×C4C2×C4×D1511yescharacteristic
211C2×C4D4×D1512yes—
212C8—24no—
213C8—304no—
214C2×C3D5×#10111yescharacteristic
215C2×C3D5×#10412yes—
216D3—201no—
217C5#6836211yescharacteristic, complemented, Sylow
218C22—302no—
219C22—301no—
220C22C22⋊C4×D1511yescharacteristic
221C4—22no—
222C4—21no—
223C4—42no—
224C4—154no—
225C4—152no—
226C4—602no—
227C3#1059915511yescharacteristic, complemented, Sylow
228C2—601no—
229C2D15×#10111yescharacteristic
230C2D15×#10412yes—
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#330D15
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. C3×C5×#330C2semidirect
4. #11746364C2semidirect
5. #11746286C2semidirect
21. C5×#330D3semidirect
42. C3×#330D5semidirect
100. #330D15semidirect
189. C3×C5#1526semidirect
217. C5#68362semidirect
227. C3#10599155semidirect

Maximal subgroups

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

subgroupindex
#117564472
#117508082
C3×C5×#3302
#117463642
#117462862
#105991553
#683625