Finite Group Databasebeta

← #14513424

Subgroups — #14513424

Order 1920.

514 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#91954C211yesmaximal, characteristic
2C2×C5×#984C211yesmaximal, characteristic
3Dic5×#41⋊C3C211yesmaximal, characteristic
4#11751597C214yesmaximal, complemented
5#10615698—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#91954—22no—
8C2×C5⋊#226C2212yes—
9C5×#984—22no—
10C2×C5×#226C2212yes—
11#91376—41nomaximal
12Dic5×SL(2,𝔽3)C2212yes—
13#85336—51nomaximal, Hall
14C2×C5×#137—31no—
15#41×Dic5D311yescharacteristic
16C2×#4097—31no—
17C2×#4090—31no—
18#65514—31no—
19#65471—34no—
20#65451—34no—
21#65409—31no—
22#65407—31no—
23C2×Dic30—41no—
24C2×C5×Dic6—41no—
25C5×#41⋊C3D412yes—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊#226—22no—
28C5×#226—22no—
29C3×C4×Dic5—41no—
30#6668—44no—
31C2×#984—51no—
32C2×#984D511yescharacteristic
33C4×#41⋊C3—51no—
34C4⋊#226—54no—
35C2×C5×#41C2×D311yescharacteristic
36C22×C5×Q8—31no—
37C22×Dic10—31no—
38C5×#137—62no—
39C5×#137—62no—
40C2×C5×Q16—32no—
41C2×C5×SD16—32no—
42C2×C5×M16—31no—
43#4097—62no—
44#4097—62no—
45Q8×Dic5C2×D312yes—
46#4090—34no—
47#4090—61no—
48#4090—61no—
49C2×#689—32no—
50D4×Dic5—32no—
51C2×#687—32no—
52#4072—31no—
53C2×#683—62no—
54C2×C4×Dic5—31no—
55C2×#681—31no—
56#3967—34no—
57#3948—34no—
58#3946—34no—
59#3039—151noSylow
60C2×C3×C4×C5—41no—
61C2×Dic15—42no—
62Dic30—82no—
63C2×C5×Dic3—42no—
64C5×Dic6—82no—
65C2×C3×Dic5—42no—
66C5×SL(2,𝔽3)C2×D411yescharacteristic
67C2×#41⋊C3C2×D511yescharacteristic
68#984—22no—
69#984—102no—
70C2×#226—52no—
71C2×#226C2×D512yes—
72#869—201no—
73C4×SL(2,𝔽3)—52no—
74C5×#41—32no—
75C5×#41D1212yes—
76C2×C5×Q8—32no—
77C2×C5×Q8—62no—
78C2×C5×Q8—62no—
79C2×C5×Q8—61no—
80C2×C5×Q8C22×D311yescharacteristic
81C2×C5×D4—31no—
82C22×C4×C5—31no—
83C22×C4×C5—61no—
84C22×Dic5—32no—
85C22×Dic5—61no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C2×Dic10—62no—
89C2×Dic10—61no—
90C5×Q16—62no—
91C5×Q16—62no—
92C5×SD16—64no—
93C5×M16—62no—
94C2×C5×C8—32no—
95C22⋊Dic5—61no—
96#689—62no—
97#689—62no—
98#687—64no—
99C4⋊Dic5—32no—
100#683—64no—
101#683—64no—
102C4×Dic5—31no—
103C4×Dic5—32no—
104C4×Dic5S411yescharacteristic
105#681—62no—
106C2×#168—32no—
107C2×#137—31no—
108C2×#137—151no—
109C2×C4⋊Q8—151no—
110C4×#41—51no—
111#462—154no—
112#461—154no—
113#423—151no—
114#419—151no—
115#419—151no—
116C22×C3×C5—41no—
117C3×C4×C5—42no—
118Dic15—82no—
119C3×Dic5—44no—
120C5×Dic3—82no—
121C2×Dic6—41no—
122C2×Dic6—201no—
123#41⋊C3C22⋊D512yes—
124C2×SL(2,𝔽3)C22×D511yescharacteristic
125#226—22no—
126#226—102no—
127C3×C42—201no—
128C4⋊Dic3—204no—
129C23×C5—31no—
130C5×Q8—31no—
131C5×Q8—62no—
132C5×Q8—62no—
133C5×Q8—122no—
134C5×Q8C2×D1211yescharacteristic
135C5×D4—32no—
136C5×D4—61no—
137C2×C4×C5—31no—
138C2×C4×C5—32no—
139C2×C4×C5—32no—
140C2×C4×C5—62no—
141C2×C4×C5—122no—
142C2×C4×C5C2×S411yescharacteristic
143C2×Dic5—32no—
144C2×Dic5—64no—
145C2×Dic5—62no—
146C2×Dic5—122no—
147C2×Dic5C2×S412yes—
148Dic10—62no—
149Dic10—62no—
150Dic10—122no—
151C5×C8—62no—
152#168—62no—
153C2×#41D3×D511yescharacteristic
154C22×Q8—31no—
155C22×Q8—151no—
156#137—62no—
157#137—62no—
158#137—302no—
159#137—302no—
160C2×Q16—32no—
161C2×Q16—152no—
162C2×SD16—32no—
163C2×SD16—152no—
164C2×M16—31no—
165C2×M16—151no—
166C4⋊Q8—154no—
167C4⋊Q8—301no—
168C4⋊Q8—301no—
169C4×Q8—52no—
170C4×D4—152no—
171#117—151no—
172C2×C4⋊C4—302no—
173C2×C42—151no—
174C4⋊C8—154no—
175#103—154no—
176#103—154no—
177C2×C3×C5—41no—
178C2×C3×C5—42no—
179C2×C3×C4—41no—
180C2×C3×C4—202no—
181C2×Dic3—42no—
182C2×Dic3—202no—
183Dic6—82no—
184Dic6—402no—
185SL(2,𝔽3)C2×C22⋊D511yescharacteristic
186C22×C5—32no—
187C22×C5—62no—
188C22×C5C22×S411yescharacteristic
189C4×C5—31no—
190C4×C5—31no—
191C4×C5—122no—
192C4×C5C4⋊S412yes—
193Dic5—62no—
194Dic5—122no—
195Dic5#98414yescomplemented
196#41—32no—
197#41#120312yes—
198C2×Q8—32no—
199C2×Q8—62no—
200C2×Q8—62no—
201C2×Q8—61no—
202C2×Q8—152no—
203C2×Q8—302no—
204C2×Q8—302no—
205C2×Q8—301no—
206C2×Q8C2×D3×D511yescharacteristic
207C2×D4—31no—
208C22×C4—31no—
209C22×C4—61no—
210C22×C4—152no—
211C22×C4—301no—
212Q16—62no—
213Q16—62no—
214Q16—302no—
215Q16—302no—
216SD16—64no—
217SD16—304no—
218M16—62no—
219M16—302no—
220C2×C8—32no—
221C2×C8—152no—
222C4⋊C4—152no—
223C4⋊C4—304no—
224C4⋊C4—304no—
225C22⋊C4—301no—
226C42—51no—
227C42—152no—
228C42—151no—
229C3×C5—41noHall
230C22×C3—41no—
231C3×C4—42no—
232C3×C4—204no—
233Dic3—82no—
234Dic3—402no—
235C2×C5—62no—
236C2×C5C2×C4⋊S411yescharacteristic
237C2×C5C2×#98412yes—
238C23—31no—
239Q8—31no—
240Q8—62no—
241Q8—62no—
242Q8—122no—
243Q8—302no—
244Q8—302no—
245Q8—602no—
246Q8C2×#120311yescharacteristic
247D4—32no—
248D4—61no—
249C2×C4—31no—
250C2×C4—32no—
251C2×C4—32no—
252C2×C4—52no—
253C2×C4—62no—
254C2×C4—122no—
255C2×C4—152no—
256C2×C4—304no—
257C2×C4—302no—
258C2×C4—602no—
259C2×C4D5×S411yescharacteristic
260C8—62no—
261C8—302no—
262C2×C3—42no—
263C2×C3—41no—
264C5#8533611yescharacteristic, complemented, Sylow
265C22—32no—
266C22—62no—
267C22C2×D5×S411yescharacteristic
268C4—31no—
269C4—31no—
270C4—54no—
271C4—122no—
272C4—302no—
273C4—602no—
274C4#9190212yes—
275C3—41noSylow
276C2—62no—
277C2D5×#98412yes—
278C2C2×#9190211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #11751597C2semidirect
195. Dic5#984semidirect
264. C5#85336semidirect

Maximal subgroups

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

subgroupindex
C2×#919542
C2×C5×#9842
Dic5×#41⋊C32
#117515972
#106156983
#913764
#853365