Finite Group Databasebeta

← #14313722

Subgroups — #14313722

Order 1920.

524 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 135 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×#535C211yesmaximal, characteristic
2#11751338C212yesmaximal, complemented
3#11746363C214yesmaximal, complemented
4#10602655—31nomaximal, Hall
5C2×C3×C5×#41C2211yescharacteristic
6C22×C3×C5×D4C411yescharacteristic
7C3×C5×#127C412yes—
8C3×C5×#124C2212yes—
9C3×C5×#121—22no—
10C3×C5×#120—22no—
11C3×C5×#117C411yescharacteristic
12C2×#6710—22no—
13#91120C2214yescomplemented
14#91117—22no—
15#71862—51nomaximal, Hall
16C5×#535D311yescharacteristic
17#65526—32no—
18#64762—34no—
19C24×C3×C5—21no—
20C3×C5×#41—42no—
21C2×C3×C5×Q8C2311yescharacteristic
22C2×C3×C5×D4—24no—
23C2×C3×C5×D4—21no—
24C2×C3×C5×D4—42no—
25C2×C3×C5×D4C2×C412yes—
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×C3×C5×D4D412yes—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5D412yes—
30C3×C5×C4⋊C4—21no—
31C3×C5×C22⋊C4—21no—
32C3×C5×C22⋊C4—24no—
33C3×C42×C5C2×C412yes—
34#6710—24no—
35#6710—42no—
36C2×C3⋊#168—42no—
37C3×#535D511yescharacteristic
38#5237—52no—
39#4542—54no—
40C2×C5×#41C2×D311yescharacteristic
41C22×C5×D4Dic311yescharacteristic
42C5×#127Dic312yes—
43C5×#124C2×D312yes—
44C5×#121—22no—
45C5×#120—22no—
46C5×#117Dic311yescharacteristic
47C2×#681—62no—
48#3968—34no—
49#3965—62no—
50#2134—151noSylow
51C23×C3×C5—22no—
52C23×C3×C5—42no—
53C23×C3×C5—82no—
54C23×C3×C5C22⋊C411yescharacteristic
55C23×C3×C5C22⋊C412yes—
56C3×C5×Q8—41no—
57C3×C5×D4—41no—
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—84no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—22no—
66C2×C3×C4×C5C22⋊C411yescharacteristic
67C2×C3×C4×C5C22×C411yescharacteristic
68C2×C3×C4×C5C2×D412yes—
69C3⋊#168—44no—
70C2×C3×#41C2×D511yescharacteristic
71C22×C3×D4Dic511yescharacteristic
72C3×#127Dic512yes—
73C3×#124C2×D512yes—
74C3×#121—22no—
75C3×#120—22no—
76C3×#117Dic511yescharacteristic
77C2×#208—102no—
78#836—54no—
79#833—102no—
80C24×C5—21no—
81C5×#41—42no—
82C2×C5×Q8C22×D311yescharacteristic
83C2×C5×D4—24no—
84C2×C5×D4—21no—
85C2×C5×D4—42no—
86C2×C5×D4C2×Dic312yes—
87C2×C5×D4C2×Dic311yescharacteristic
88C2×C5×D4#6712yes—
89C22×C4×C5C2×Dic311yescharacteristic
90C22×C4×C5#6712yes—
91C5×C4⋊C4—21no—
92C5×C22⋊C4—21no—
93C5×C22⋊C4—24no—
94C42×C5C2×Dic312yes—
95#681—64no—
96#681—122no—
97C2×#168—122no—
98#535D1511yescharacteristic
99#413—152no—
100#355—154no—
101C22×C3×C5—21no—
102C22×C3×C5—22no—
103C22×C3×C5—42no—
104C22×C3×C5—41no—
105C22×C3×C5—44no—
106C22×C3×C5—42no—
107C22×C3×C5—84no—
108C22×C3×C5C2×C22⋊C411yescharacteristic
109C3×C4×C5—22no—
110C3×C4×C5—21no—
111C3×C4×C5—42no—
112C3×C4×C5#9912yes—
113C24×C3—21no—
114C3×#41—42no—
115C2×C3×Q8C22×D511yescharacteristic
116C2×C3×D4—24no—
117C2×C3×D4—21no—
118C2×C3×D4—42no—
119C2×C3×D4C2×Dic512yes—
120C2×C3×D4C2×Dic511yescharacteristic
121C2×C3×D4C22⋊D512yes—
122C22×C3×C4C2×Dic511yescharacteristic
123C22×C3×C4C22⋊D512yes—
124C3×C4⋊C4—21no—
125C3×C22⋊C4—21no—
126C3×C22⋊C4—24no—
127C3×C42C2×Dic512yes—
128#208—104no—
129#208—202no—
130C2×C3⋊C8—202no—
131C23×C5—22no—
132C23×C5—42no—
133C23×C5—82no—
134C23×C5#21711yescharacteristic
135C23×C5#21712yes—
136C5×Q8—41no—
137C5×D4—41no—
138C5×D4—42no—
139C5×D4—42no—
140C5×D4—42no—
141C5×D4—84no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5#21711yescharacteristic
147C2×C4×C5C22×Dic311yescharacteristic
148C2×C4×C5C2×#6712yes—
149#168—124no—
150C2×#41C2×D1511yescharacteristic
151C22×D4Dic1511yescharacteristic
152C2×M16—302no—
153#127Dic1512yes—
154#124C2×D1512yes—
155#121—22no—
156#120—22no—
157#117Dic1511yescharacteristic
158#101—154no—
159#100—302no—
160C2×C3×C5—21no—
161C2×C3×C5—42no—
162C2×C3×C5—41no—
163C2×C3×C5—82no—
164C2×C3×C5C2×#9911yescharacteristic
165C23×C3—22no—
166C23×C3—42no—
167C23×C3—82no—
168C23×C3C22⋊Dic511yescharacteristic
169C23×C3C22⋊Dic512yes—
170C3×Q8—41no—
171C3×D4—41no—
172C3×D4—42no—
173C3×D4—42no—
174C3×D4—42no—
175C3×D4—84no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4C22⋊Dic511yescharacteristic
181C2×C3×C4C22×Dic511yescharacteristic
182C2×C3×C4C2×C22⋊D512yes—
183C3⋊C8—204no—
184C22×C5—21no—
185C22×C5—22no—
186C22×C5—42no—
187C22×C5—41no—
188C22×C5—44no—
189C22×C5—42no—
190C22×C5—84no—
191C22×C5C2×#21711yescharacteristic
192C4×C5—22no—
193C4×C5—21no—
194C4×C5—42no—
195C4×C5#83412yes—
196C24—21no—
197#41—42no—
198C2×Q8C22×D1511yescharacteristic
199C2×D4—24no—
200C2×D4—21no—
201C2×D4—42no—
202C2×D4C2×Dic1512yes—
203C2×D4C2×Dic1511yescharacteristic
204C2×D4#122012yes—
205C22×C4C2×Dic1511yescharacteristic
206C22×C4#122012yes—
207M16—304no—
208M16—602no—
209C2×C8—602no—
210C4⋊C4—21no—
211C22⋊C4—21no—
212C22⋊C4—24no—
213C42C2×Dic1512yes—
214C3×C5#213411yescharacteristic, complemented, Hall
215C22×C3—21no—
216C22×C3—22no—
217C22×C3—42no—
218C22×C3—41no—
219C22×C3—44no—
220C22×C3—42no—
221C22×C3—84no—
222C22×C3C2×C22⋊Dic511yescharacteristic
223C3×C4—22no—
224C3×C4—21no—
225C3×C4—42no—
226C3×C4#396612yes—
227C2×C5—21no—
228C2×C5—41no—
229C2×C5—42no—
230C2×C5—82no—
231C2×C5C2×#83411yescharacteristic
232C23—22no—
233C23—42no—
234C23—82no—
235C23#671911yescharacteristic
236C23#671912yes—
237Q8—41no—
238D4—41no—
239D4—42no—
240D4—42no—
241D4—42no—
242D4—84no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4#671911yescharacteristic
248C2×C4C22×Dic1511yescharacteristic
249C2×C4C2×#122012yes—
250C8—604no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3—42no—
254C2×C3—82no—
255C2×C3C2×#396611yescharacteristic
256C5#7186211yescharacteristic, complemented, Sylow
257C22—21no—
258C22—22no—
259C22—42no—
260C22—41no—
261C22—44no—
262C22—42no—
263C22—84no—
264C22C2×#671911yescharacteristic
265C4—22no—
266C4—21no—
267C4—42no—
268C4#9111812yes—
269C3#1060265511yescharacteristic, complemented, Sylow
270C2—21no—
271C2—41no—
272C2—42no—
273C2—82no—
274C2C2×#9111811yescharacteristic
subgroupG/H
centerC2C2×#91118
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C22×D15
Fitting, prime radicalC3×C5×#535C2
socleC2×C3×C5C2×#99
cosocleC2×C3×C5×Q8C23
hypercenter#535D15
hypocenterC3×C5#2134
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
2. #11751338C2semidirect
3. #11746363C2semidirect
13. #91120C22semidirect
214. C3×C5#2134semidirect
256. C5#71862semidirect
269. C3#10602655semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5352
#117513382
#117463632
#106026553
#718625