Finite Group Databasebeta

← #14284480

Subgroups — #14284480

Order 1920.

476 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752674C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic, complemented
3C3×#65684C211yesmaximal, characteristic, complemented
4#11746505C214yesmaximal, complemented
5#10604638—31nomaximal, Hall
6C2×#6773C412yes—
7#91763C411yescharacteristic
8C5×#869C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91450—21no—
11#91450—21no—
12#91418—21no—
13#91418—21no—
14#91375C2212yes—
15#91233—21no—
16#91232—21no—
17#91231C2212yes—
18C3×#4004—21no—
19C3×#4003—21no—
20C3×#4002C2212yes—
21#70811—51nomaximal, Hall
22#66059—31no—
23#65684—31no—
24#65684D311yescharacteristic, complemented
25#64927—34no—
26C2×D60—21no—
27C2×D60—21no—
28C2×D60C2×C412yes—
29C2×C5×Dic6C2×C412yes—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×#1202—22no—
34C2×#1200—22no—
35#6773—44no—
36C2×C3⋊#170—22no—
37C2×C3×#170—22no—
38C3×C42×C5C2×C411yescharacteristic
39C5×C4⋊Dic3—21no—
40C5×C4⋊Dic3—21no—
41C3×C4×Dic5D411yescharacteristic
42C3×C4×Dic5D411yescharacteristic
43C3×C4×Dic5C2311yescharacteristic
44#6667—22no—
45#6667—22no—
46#5477—51no—
47C3×#432—51no—
48#4926—51no—
49#4464—54no—
50C2×#713—32no—
51C5×C4⋊Q8—31no—
52#4093—32no—
53#4041—61no—
54#4041—61no—
55#4039—61no—
56#4039—61no—
57#4020—31no—
58C42×D5C2×D311yescharacteristic
59#4004—21no—
60#4004—61no—
61#4003—21no—
62#4003—61no—
63#4002—32no—
64#4002C2×D312yes—
65#1536—151noSylow
66C22×D15—22no—
67C22×C3×D5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22×C411yescharacteristic
71D60—42no—
72D60—42no—
73D60—42no—
74C2×C5×Dic3—22no—
75C5×Dic6—42no—
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C2×D411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C3×C4×D5—22no—
80C3×C4×D5—41no—
81C3×C4×D5—41no—
82#1202—44no—
83#1200—44no—
84C3⋊#170—42no—
85C3×#170—42no—
86C2×#235—52no—
87C2×C3×C42—51no—
88#930—101no—
89#930—101no—
90#875—52no—
91#874—51no—
92C4×D12—101no—
93C4×D12—101no—
94#869AGL(1,𝔽5)11yescharacteristic
95C3×C4⋊C8—101no—
96C3×C22⋊C8—101no—
97C3×#97—52no—
98#830—101no—
99C4⋊(C3⋊C8)—101no—
100#803—52no—
101C2×C5×Q8—32no—
102#713—124no—
103C2×D20—32no—
104C2×D20—62no—
105C2×D20—61no—
106C2×D20—61no—
107C2×C4×D5—62no—
108C2×C4×D5C4×D311yescharacteristic
109C2×C4×D5D1211yescharacteristic
110C2×C4×D5#6711yescharacteristic
111C2×#170—22no—
112C2×#170—62no—
113C5×C4⋊C4—61no—
114C5×C4⋊C4—61no—
115C42×C5C4×D311yescharacteristic
116#685—62no—
117#685—62no—
118C4×Dic5D1211yescharacteristic
119C4×Dic5#6711yescharacteristic
120C4×Dic5C22×D311yescharacteristic
121#532—151no—
122#432—51no—
123#432—151no—
124#329—154no—
125C22×C3×C5C2×C22⋊C411yescharacteristic
126C2×D15—42no—
127C2×D15—42no—
128C2×D15—42no—
129C2×C3×D5—21no—
130C2×C3×D5—21no—
131C2×C3×D5—21no—
132C3×C4×C5—21no—
133C3×C4×C5—21no—
134C3×C4×C5—21no—
135C3×Dic5—21no—
136C3×Dic5—21no—
137C3×Dic5#10012yes—
138C5×Dic3—42no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C2×#67—102no—
143#235—204no—
144C2×D12—52no—
145C2×D12—101no—
146C2×D12—101no—
147C2×C4×D3—102no—
148C2×Dic6C2×AGL(1,𝔽5)12yes—
149C2×C3×C8—102no—
150C3×C42—51no—
151C3×C42—51no—
152C3×C42—51no—
153C3×C42C2×AGL(1,𝔽5)11yescharacteristic
154(C2×D3)⋊C4—102no—
155(C2×D3)⋊C4—102no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C2×C3⋊C8—102no—
159C22×D5—62no—
160C22×D5(C2×D3)⋊C411yescharacteristic
161C5×Q8—122no—
162C2×C4×C5—62no—
163C2×C4×C5(C2×D3)⋊C411yescharacteristic
164C2×C4×C5(C2×D3)⋊C411yescharacteristic
165C2×C4×C5C2×C4×D311yescharacteristic
166C2×Dic5(C2×D3)⋊C411yescharacteristic
167C2×Dic5C2×D1211yescharacteristic
168C2×Dic5C2×#6711yescharacteristic
169D20—122no—
170D20—122no—
171D20—122no—
172D20—124no—
173C4×D5—22no—
174C4×D5—41no—
175C4×D5—41no—
176C4×D5—124no—
177#170—42no—
178#170—122no—
179C2×#41—152no—
180C4⋊Q8—31no—
181#127—151no—
182#124—152no—
183#121—301no—
184#121—301no—
185C4×D4—301no—
186C4×D4—301no—
187C2×C42—51no—
188C4⋊C8—101no—
189C4⋊C8—301no—
190C22⋊C8—101no—
191C22⋊C8—301no—
192#97—52no—
193#97—152no—
194C2×C3×C5C2×#10011yescharacteristic
195C2×C3×C5#42111yescharacteristic
196C2×C3×C5#42111yescharacteristic
197D15—82no—
198C3×D5—41no—
199C23×C3—51no—
200C22×D3—102no—
201C2×C3×C4—51no—
202C2×C3×C4—51no—
203C2×C3×C4—51no—
204C2×C3×C4—102no—
205C2×C3×C4—201no—
206C2×C3×C4—201no—
207C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
208C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
209C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
210#67—204no—
211C2×Dic3—22no—
212D12—202no—
213D12—202no—
214D12—202no—
215C4×D3—204no—
216Dic6—42no—
217C3×C8—202no—
218C3⋊C8—202no—
219C22×C5C2×(C2×D3)⋊C411yescharacteristic
220C2×D5—21no—
221C2×D5—21no—
222C2×D5—21no—
223C2×D5—122no—
224C2×D5—122no—
225C2×D5—122no—
226C4×C5—21no—
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—122no—
230Dic5—21no—
231Dic5—21no—
232Dic5#82312yes—
233#41—604no—
234C2×Q8—32no—
235C2×D4—152no—
236C2×D4—302no—
237C2×D4—301no—
238C2×D4—301no—
239C22×C4—51no—
240C22×C4—51no—
241C22×C4—51no—
242C22×C4—302no—
243C2×C8—102no—
244C2×C8—302no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C22⋊C4—302no—
248C22⋊C4—302no—
249C42—51no—
250C42—51no—
251C42—51no—
252C42D3×AGL(1,𝔽5)11yescharacteristic
253C3×C5#153611yescharacteristic, complemented, Hall
254C22×C3—101no—
255C22×C3—101no—
256C22×C3—101no—
257C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
258C2×D3—202no—
259C2×D3—202no—
260C2×D3—202no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—52no—
265C3×C4—101no—
266C3×C4—101no—
267Dic3—42no—
268C2×C5#500511yescharacteristic
269C2×C5C2×#82311yescharacteristic
270C2×C5#513911yescharacteristic
271D5—41no—
272D5—242no—
273C23—51no—
274C23—302no—
275Q8—122no—
276D4—602no—
277D4—602no—
278D4—602no—
279D4—604no—
280C2×C4—51no—
281C2×C4—51no—
282C2×C4—51no—
283C2×C4—62no—
284C2×C4—102no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4—604no—
288C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
289C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
290C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
291C8—202no—
292C8—602no—
293C2×C3—201no—
294C2×C3D5⋊#10011yescharacteristic
295C2×C3#6578411yescharacteristic
296C2×C3#6578411yescharacteristic
297D3—402no—
298C5#7081111yescharacteristic, complemented, Sylow
299C22—101no—
300C22—101no—
301C22—101no—
302C22—602no—
303C22—602no—
304C22—602no—
305C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—52no—
310C4—101no—
311C4—101no—
312C4—122no—
313C3#1060463811yescharacteristic, complemented, Sylow
314C2—201no—
315C2—1202no—
316C2#1175172311yescharacteristic
317C2#1175172411yescharacteristic
318C2D5⋊#82311yescharacteristic
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 radical#11752674C2
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1536
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
2. #11752343C2semidirect
3. C3×#65684C2semidirect
4. #11746505C2semidirect
24. #65684D3semidirect
253. C3×C5#1536semidirect
298. C5#70811semidirect
313. C3#10604638semidirect

Maximal subgroups

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

subgroupindex
#117526742
#117523432
C3×#656842
#117465052
#106046383
#708115