Finite Group Databasebeta

← #14284240

Subgroups — #14284240

Order 1920.

424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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×#66062C211yesmaximal, characteristic
2#11752342C211yesmaximal, characteristic
3#11752335C211yesmaximal, characteristic
4#11746741C214yesmaximal, complemented
5#10604637—31nomaximal, Hall
6C2×D5⋊(C3⋊C8)—21no—
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×#4092—21no—
9C3×Q8×Dic5—21no—
10C3×#4043—21no—
11C3×#4038C412yes—
12C3×#4036C2212yes—
13C3×#4033—21no—
14C3×C42×D5C2211yescharacteristic
15C3×#4015C411yescharacteristic
16#91232—21no—
17#91231—21no—
18#91231C2212yes—
19#91231C2212yes—
20C4⋊(C3⋊#170)—21no—
21#71822—51nomaximal, Hall
22#66062D311yescharacteristic
23#65683—31no—
24#65676—31no—
25#64870—34no—
26C2×C3×C5×Q8—21no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×Dic10—21no—
31C2×C3⋊#170—22no—
32C2×C3⋊#170—22no—
33D5⋊(C3⋊C8)—24no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4C2×C412yes—
36C3×C42×C5C2×C411yescharacteristic
37C3×#685—22no—
38C3×C4⋊Dic5—21no—
39C3×C4⋊Dic5—22no—
40C3×C4⋊Dic5C2×C412yes—
41C3×#683—22no—
42C3×C4×Dic5—22no—
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46C3×#533—51no—
47#4926—51no—
48C2×#803—51no—
49#4543—54no—
50C2×D5⋊C8—61no—
51C5×C4⋊Q8Dic311yescharacteristic
52#4092—21no—
53Q8×Dic5—21no—
54#4043—21no—
55#4038Dic312yes—
56#4036C2×D312yes—
57#4033—21no—
58C42×D5C2×D311yescharacteristic
59#4015Dic311yescharacteristic
60#4003—61no—
61#4002—32no—
62#4002—32no—
63#4002—61no—
64C4⋊#170—61no—
65#1531—151noSylow
66C22×C3×D5C22⋊C411yescharacteristic
67C3×C5×Q8—42no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×C3×Dic5—22no—
73C2×C3×Dic5C22⋊C411yescharacteristic
74C2×C3×Dic5C2×D411yescharacteristic
75C2×C3×Dic5C2×D411yescharacteristic
76C3×C4×D5—22no—
77C3×C4×D5—22no—
78C3×C4×D5—41no—
79C3×Dic10—42no—
80C3⋊#170—24no—
81C3⋊#170—42no—
82C3×C4⋊Q8—51no—
83C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
84C3×#125—52no—
85C3×C22⋊Q8—101no—
86C3×C22⋊Q8—101no—
87C3×C4×Q8—101no—
88C3×C4×Q8—101no—
89C3×#117—52no—
90C2×C3×C42—51no—
91C22×C3⋊C8—101no—
92#830—101no—
93C4⋊(C3⋊C8)—101no—
94#803—52no—
95#803—52no—
96#803—101no—
97C2×C5×Q8—21no—
98C2×C4×D5C2×Dic311yescharacteristic
99C2×C4×D5#6711yescharacteristic
100C2×C4×D5#6711yescharacteristic
101C2×Dic10—21no—
102C2×#170—62no—
103C2×#170—62no—
104D5⋊C8—64no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4C2×Dic312yes—
107C42×C5C2×Dic311yescharacteristic
108#685—22no—
109C4⋊Dic5—21no—
110C4⋊Dic5—22no—
111C4⋊Dic5C2×Dic312yes—
112#683—22no—
113C4×Dic5—22no—
114C4×Dic5#6711yescharacteristic
115C4×Dic5#6711yescharacteristic
116C4×Dic5C22×D311yescharacteristic
117#533—51no—
118#432—151no—
119C2×#97—151no—
120#330—154no—
121C22×C3×C5C2×C22⋊C411yescharacteristic
122C2×C3×D5—21no—
123C2×C3×D5—21no—
124C2×C3×D5#10112yes—
125C3×C4×C5—21no—
126C3×C4×C5—21no—
127C3×C4×C5—42no—
128C3×C4×C5#10412yes—
129C3×Dic5—21no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C3×Dic5—42no—
133C2×C3×Q8—21no—
134C2×C3×Q8—101no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—52no—
140C3×C4⋊C4—102no—
141C3×C4⋊C4—102no—
142C3×C4⋊C4—101no—
143C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
144C3×C22⋊C4—102no—
145C3×C42—51no—
146C3×C42—51no—
147C3×C42—51no—
148C3×C42—102no—
149C3×C42C2×AGL(1,𝔽5)11yescharacteristic
150C2×C3⋊C8—102no—
151C2×C3⋊C8—104no—
152C2×C3⋊C8—102no—
153C22×D5#21711yescharacteristic
154C5×Q8—42no—
155C2×C4×C5—22no—
156C2×C4×C5#21711yescharacteristic
157C2×C4×C5#21711yescharacteristic
158C2×C4×C5C22×Dic311yescharacteristic
159C2×Dic5—22no—
160C2×Dic5#21711yescharacteristic
161C2×Dic5C2×#6711yescharacteristic
162C2×Dic5C2×#6711yescharacteristic
163C4×D5—22no—
164C4×D5—22no—
165C4×D5—41no—
166Dic10—42no—
167#170—64no—
168#170—122no—
169C22×C8—301no—
170C4⋊Q8—51no—
171C4⋊Q8ΓL(1,𝔽16)11yescharacteristic
172#125—52no—
173C22⋊Q8—101no—
174C22⋊Q8—101no—
175C4×Q8—101no—
176C4×Q8—101no—
177#117—52no—
178C2×C42—51no—
179C4⋊C8—301no—
180C22⋊C8—301no—
181#97—152no—
182#97—152no—
183#97—301no—
184C2×C3×C5C2×#10111yescharacteristic
185C2×C3×C5C2×#10411yescharacteristic
186C2×C3×C5#42111yescharacteristic
187C3×D5—22no—
188C23×C3—51no—
189C3×Q8—42no—
190C3×Q8—202no—
191C2×C3×C4—22no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—102no—
196C2×C3×C4—102no—
197C2×C3×C4—102no—
198C2×C3×C4—201no—
199C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
200C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
201C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
202C3⋊C8—104no—
203C3⋊C8—202no—
204C22×C5C2×#21711yescharacteristic
205C2×D5—21no—
206C2×D5—21no—
207C2×D5#83612yes—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—42no—
211C4×C5#83712yes—
212Dic5—21no—
213Dic5—21no—
214Dic5—21no—
215Dic5—42no—
216C2×Q8—21no—
217C2×Q8—101no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—51no—
221C2×C8—302no—
222C2×C8—304no—
223C2×C8—302no—
224C4⋊C4—21no—
225C4⋊C4—52no—
226C4⋊C4—102no—
227C4⋊C4—102no—
228C4⋊C4—101no—
229C4⋊C4C2×ΓL(1,𝔽16)12yes—
230C22⋊C4—102no—
231C42—51no—
232C42—51no—
233C42—51no—
234C42—102no—
235C42C2×ΓL(1,𝔽16)11yescharacteristic
236C3×C5#153111yescharacteristic, complemented, Hall
237C22×C3—52no—
238C22×C3—101no—
239C22×C3—101no—
240C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—42no—
244C3×C4—101no—
245C3×C4—101no—
246C3×C4—101no—
247C3×C4—202no—
248C3×C4#401012yes—
249C2×C5C2×#83611yescharacteristic
250C2×C5C2×#83711yescharacteristic
251C2×C5#523611yescharacteristic
252D5—22no—
253C23—51no—
254Q8—42no—
255Q8—202no—
256C2×C4—22no—
257C2×C4—51no—
258C2×C4—51no—
259C2×C4—51no—
260C2×C4—102no—
261C2×C4—102no—
262C2×C4—102no—
263C2×C4—201no—
264C2×C4#676311yescharacteristic
265C2×C4#676311yescharacteristic
266C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
267C8—304no—
268C8—602no—
269C2×C3—102no—
270C2×C3#6576911yescharacteristic
271C2×C3C2×#401011yescharacteristic
272C2×C3D5⋊#10111yescharacteristic
273C5#7182211yescharacteristic, complemented, Sylow
274C22—52no—
275C22—101no—
276C22—101no—
277C22C2×#676311yescharacteristic
278C4—21no—
279C4—21no—
280C4—42no—
281C4—101no—
282C4—101no—
283C4—101no—
284C4—202no—
285C4#9123912yes—
286C3#1060463711yescharacteristic, complemented, Sylow
287C2—102no—
288C2#1175242811yescharacteristic
289C2C2×#9123911yescharacteristic
290C2D5⋊#83611yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×C4⋊Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊Q8ΓL(1,𝔽16)
hypocenterC3×C5#1531
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11746741C2semidirect
236. C3×C5#1531semidirect
273. C5#71822semidirect
286. C3#10604637semidirect

Maximal subgroups

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

subgroupindex
C3×#660622
#117523422
#117523352
#117467412
#106046373
#718225