Finite Group Databasebeta

← #14284262

Subgroups — #14284262

Order 1920.

424 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 98 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#11752506C211yesmaximal, characteristic
2#11752342C211yesmaximal, characteristic
3C3×#65676C211yesmaximal, characteristic
4#11746507C214yesmaximal, complemented
5#10604636—31nomaximal, Hall
6C2×C3×D5⋊C8—21no—
7#91758C411yescharacteristic
8C5×#869C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91388C2212yes—
11#91360—21no—
12#91359—21no—
13#91358C412yes—
14#91333—21no—
15Dic5×Dic6—21no—
16#91232—21no—
17#91231C2212yes—
18C4⋊(C3⋊#170)—21no—
19C3×#4002—21no—
20C3×#4002C2212yes—
21#69801—51nomaximal, Hall
22#66062—31no—
23#65683—31no—
24#65676D311yescharacteristic
25#64870—34no—
26C2×Dic30—21no—
27C2×C5×Dic6—21no—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3⋊#170—22no—
32C2×C3×#170—22no—
33C3×D5⋊C8—24no—
34C3×C42×C5C2×C411yescharacteristic
35C4⋊Dic15—21no—
36C4⋊Dic15C2×C412yes—
37C5×C4⋊Dic3—21no—
38C5×C4⋊Dic3C2×C412yes—
39C3×C4×Dic5D411yescharacteristic
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5C2311yescharacteristic
42Dic3⋊Dic5—22no—
43#6669—22no—
44#6665—22no—
45Dic3×Dic5—22no—
46#5470—51no—
47C2×C3×#97—51no—
48#4926—51no—
49#4465—54no—
50C2×D5⋊C8—21no—
51C5×C4⋊Q8—31no—
52#4092—61no—
53Q8×Dic5—61no—
54#4043—61no—
55#4038—32no—
56#4036—32no—
57#4033—61no—
58C42×D5C2×D311yescharacteristic
59#4015—31no—
60#4003—61no—
61#4002—21no—
62#4002—32no—
63#4002C2×D312yes—
64C4⋊#170—61no—
65#1531—151noSylow
66C22×C3×D5C22⋊C411yescharacteristic
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22×C411yescharacteristic
70C2×Dic15—22no—
71Dic30—42no—
72C2×C5×Dic3—22no—
73C5×Dic6—42no—
74C2×C3×Dic5C22⋊C411yescharacteristic
75C2×C3×Dic5C2×D411yescharacteristic
76C2×C3×Dic5C2×D411yescharacteristic
77C3×C4×D5—22no—
78C3×C4×D5—22no—
79C3×C4×D5—41no—
80C3⋊#170—42no—
81C3×#170—24no—
82C22×C3×C8—101no—
83C2×C3×C42—51no—
84#926—52no—
85#924—101no—
86#924—101no—
87#870—52no—
88#869—51no—
89#869AGL(1,𝔽5)11yescharacteristic
90C4×Dic6—101no—
91C4×Dic6—101no—
92C3×#97—52no—
93C3×#97—101no—
94#830—101no—
95C4⋊(C3⋊C8)—101no—
96#803—52no—
97C2×C5×Q8—61no—
98C2×C4×D5C4×D311yescharacteristic
99C2×C4×D5D1211yescharacteristic
100C2×C4×D5#6711yescharacteristic
101C2×Dic10—61no—
102C2×#170—22no—
103C2×#170—62no—
104D5⋊C8—24no—
105C5×C4⋊C4—32no—
106C5×C4⋊C4—61no—
107C42×C5C4×D311yescharacteristic
108#685—62no—
109C4⋊Dic5—32no—
110C4⋊Dic5—61no—
111C4⋊Dic5—62no—
112#683—62no—
113C4×Dic5—62no—
114C4×Dic5D1211yescharacteristic
115C4×Dic5#6711yescharacteristic
116C4×Dic5C22×D311yescharacteristic
117#533—151no—
118#432—151no—
119C2×#97—51no—
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#10412yes—
128Dic15—42no—
129C3×Dic5—21no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C5×Dic3—42no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C2×Dic6—21no—
137C2×Dic6—101no—
138C2×C3×C8—102no—
139C2×C3×C8—104no—
140C3×C42—51no—
141C3×C42—51no—
142C3×C42—51no—
143C3×C42C2×AGL(1,𝔽5)11yescharacteristic
144#217—102no—
145C4⋊Dic3—21no—
146C4⋊Dic3—52no—
147C4⋊Dic3—101no—
148C4⋊Dic3C2×AGL(1,𝔽5)12yes—
149Dic3⋊C4—102no—
150Dic3⋊C4—102no—
151C4×Dic3—102no—
152C2×C3⋊C8—102no—
153C22×D5(C2×D3)⋊C411yescharacteristic
154C5×Q8—122no—
155C2×C4×C5—62no—
156C2×C4×C5(C2×D3)⋊C411yescharacteristic
157C2×C4×C5(C2×D3)⋊C411yescharacteristic
158C2×C4×C5C2×C4×D311yescharacteristic
159C2×Dic5—62no—
160C2×Dic5(C2×D3)⋊C411yescharacteristic
161C2×Dic5C2×D1211yescharacteristic
162C2×Dic5C2×#6711yescharacteristic
163C4×D5—22no—
164C4×D5—22no—
165C4×D5—41no—
166Dic10—122no—
167#170—24no—
168#170—122no—
169C22×C8—101no—
170C4⋊Q8—31no—
171C4⋊Q8—151no—
172#125—152no—
173C22⋊Q8—301no—
174C22⋊Q8—301no—
175C4×Q8—301no—
176C4×Q8—301no—
177#117—152no—
178C2×C42—51no—
179C4⋊C8—301no—
180C22⋊C8—301no—
181#97—52no—
182#97—101no—
183#97—152no—
184C2×C3×C5C2×#10111yescharacteristic
185C2×C3×C5C2×#10411yescharacteristic
186C2×C3×C5#42111yescharacteristic
187C3×D5—22no—
188C23×C3—51no—
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—51no—
192C2×C3×C4—102no—
193C2×C3×C4—102no—
194C2×C3×C4—201no—
195C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
197C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
198C2×Dic3—22no—
199C2×Dic3—102no—
200Dic6—42no—
201Dic6—202no—
202C3×C8—104no—
203C3⋊C8—202no—
204C22×C5C2×(C2×D3)⋊C411yescharacteristic
205C2×D5—21no—
206C2×D5—21no—
207C2×D5#82412yes—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—122no—
211C4×C5#80512yes—
212Dic5—21no—
213Dic5—21no—
214Dic5—21no—
215Dic5—122no—
216C2×Q8—61no—
217C2×Q8—301no—
218C22×C4—51no—
219C22×C4—51no—
220C22×C4—51no—
221C2×C8—102no—
222C2×C8—104no—
223C2×C8—302no—
224C4⋊C4—32no—
225C4⋊C4—61no—
226C4⋊C4—152no—
227C4⋊C4—302no—
228C4⋊C4—302no—
229C4⋊C4—301no—
230C22⋊C4—302no—
231C42—51no—
232C42—51no—
233C42—51no—
234C42—302no—
235C42D3×AGL(1,𝔽5)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—101no—
244C3×C4—101no—
245C3×C4—101no—
246C3×C4#400812yes—
247Dic3—42no—
248Dic3—202no—
249C2×C5C2×#80511yescharacteristic
250C2×C5C2×#82411yescharacteristic
251C2×C5#513911yescharacteristic
252D5—22no—
253C23—51no—
254Q8—122no—
255Q8—602no—
256C2×C4—51no—
257C2×C4—51no—
258C2×C4—51no—
259C2×C4—62no—
260C2×C4—102no—
261C2×C4—102no—
262C2×C4—201no—
263C2×C4—302no—
264C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
265C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
266C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
267C8—104no—
268C8—602no—
269C2×C3—102no—
270C2×C3C2×#400811yescharacteristic
271C2×C3#6578411yescharacteristic
272C2×C3D5⋊#10111yescharacteristic
273C5#6980111yescharacteristic, complemented, Sylow
274C22—52no—
275C22—101no—
276C22—101no—
277C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
278C4—21no—
279C4—21no—
280C4—101no—
281C4—101no—
282C4—101no—
283C4—122no—
284C4—602no—
285C4#9115612yes—
286C3#1060463611yescharacteristic, complemented, Sylow
287C2—102no—
288C2C2×#9115611yescharacteristic
289C2#1175172311yescharacteristic
290C2D5⋊#82411yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1531
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11746507C2semidirect
236. C3×C5#1531semidirect
273. C5#69801semidirect
286. C3#10604636semidirect

Maximal subgroups

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

subgroupindex
#117525062
#117523422
C3×#656762
#117465072
#106046363
#698015