Finite Group Databasebeta

← #14282017

Subgroups — #14282017

Order 1920.

524 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 106 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#11752672C211yesmaximal, characteristic
2C4×#6758C211yesmaximal, characteristic, complemented
3C3×#65680C211yesmaximal, characteristic, complemented
4#11746488C214yesmaximal, complemented
5#10604605—31nomaximal, Hall
6C2×#6772—21no—
7C2×#6758—21no—
8#91758C411yescharacteristic
9C5×#874C411yescharacteristic
10C3×C42×D5C2211yescharacteristic
11#91449—21no—
12#91449C412yes—
13Dic5×D12—21no—
14Dic5×D12C2212yes—
15#91373—21no—
16#91231—21no—
17C4×C3⋊#170C2212yes—
18C3×#4003—21no—
19C3×C4⋊#170C2212yes—
20C3×C4×#170—21no—
21#70761—51nomaximal, Hall
22#66050—31no—
23#65680D311yescharacteristic, complemented
24C4×#700—31no—
25D4⋊#170—34no—
26C2×Dic30—21no—
27C2×C5×D12—21no—
28C2×C5×D12—21no—
29C2×C5×D12C2×C412yes—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×#1201—22no—
34C2×D3×Dic5—22no—
35#6772—44no—
36C2×C3⋊#170—22no—
37#6758—24no—
38C2×C3×#170—22no—
39C3×C42×C5C2×C411yescharacteristic
40C4⋊Dic15—21no—
41C4⋊Dic15C2×C412yes—
42C3×C4×Dic5D411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5C2311yescharacteristic
45(C2×D3)⋊Dic5—22no—
46(C2×D3)⋊Dic5—22no—
47#5477—51no—
48C3×#431—51no—
49C4×#208—51no—
50#4483—54no—
51C2×#711—61no—
52C2×#700—61no—
53C5×#127—31no—
54#4084—32no—
55#4084—61no—
56#4082—61no—
57D4×Dic5—32no—
58D4×Dic5—61no—
59C42×D5C2×D311yescharacteristic
60#4015—31no—
61#4003—21no—
62#4002—61no—
63C4⋊#170C2×D312yes—
64C4×#170—21no—
65C4×#170—32no—
66#1484—151noSylow
67C22×C5×D3—22no—
68C22×C3×D5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×Dic15—22no—
73Dic30—42no—
74C5×D12—24no—
75C5×D12—42no—
76C5×D12—42no—
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80C3×C4×D5—22no—
81C3×C4×D5—22no—
82C3×C4×D5—22no—
83#1201—44no—
84D3×Dic5—44no—
85C3⋊#170—24no—
86C3×#170—42no—
87C2×#235—101no—
88C2×C3×C42—51no—
89#930—52no—
90#930—101no—
91C2×#208—101no—
92#875—101no—
93#874AGL(1,𝔽5)11yescharacteristic
94C4×D12—52no—
95C4×D12—101no—
96#869—51no—
97C3×C4⋊C8—52no—
98C3×C22⋊C8—101no—
99C3×C4×C8—101no—
100#803—101no—
101C4×C3⋊C8—52no—
102C2×C5×D4—32no—
103C2×C5×D4—61no—
104C2×C5×D4—61no—
105C2×C22⋊D5—62no—
106C22×Dic5—62no—
107#711—124no—
108C2×C4×D5C4×D311yescharacteristic
109C2×C4×D5D1211yescharacteristic
110C2×C4×D5#6711yescharacteristic
111C2×Dic10—61no—
112C2×#170—22no—
113C2×#170—62no—
114#700—64no—
115C42×C5C4×D311yescharacteristic
116C22⋊Dic5—62no—
117C22⋊Dic5—62no—
118C4⋊Dic5—32no—
119C4⋊Dic5—61no—
120C4×Dic5D1211yescharacteristic
121C4×Dic5#6711yescharacteristic
122C4×Dic5C22×D311yescharacteristic
123#532—151no—
124#431—51no—
125C4×M16—151no—
126D4⋊C8—154no—
127C22×C3×C5C2×C22⋊C411yescharacteristic
128C2×C5×D3—42no—
129C2×C5×D3—42no—
130C2×C5×D3—42no—
131C2×C3×D5—21no—
132C2×C3×D5—21no—
133C2×C3×D5—21no—
134C3×C4×C5—21no—
135C3×C4×C5#10412yes—
136C3×C4×C5#13112yes—
137Dic15—42no—
138C3×Dic5—21no—
139C3×Dic5—21no—
140C3×Dic5AGL(1,ℤ/8)12yes—
141C22×C3×C4—51no—
142C22×C3×C4—51no—
143C22×C3×C4—51no—
144C2×#67—102no—
145#235—204no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12C2×AGL(1,𝔽5)12yes—
149C2×C4×D3—102no—
150C2×Dic6—101no—
151C2×C3×C8—102no—
152C3×C42—51no—
153C3×C42—51no—
154C3×C42—51no—
155C3×C42C2×AGL(1,𝔽5)11yescharacteristic
156(C2×D3)⋊C4—102no—
157(C2×D3)⋊C4—102no—
158C4⋊Dic3—52no—
159C4⋊Dic3—101no—
160#208—104no—
161C2×C3⋊C8—102no—
162C23×C5—62no—
163C22×D5(C2×D3)⋊C411yescharacteristic
164C5×D4—64no—
165C5×D4—122no—
166C5×D4—122no—
167C2×C4×C5(C2×D3)⋊C411yescharacteristic
168C2×C4×C5(C2×D3)⋊C411yescharacteristic
169C2×C4×C5C2×C4×D311yescharacteristic
170C22⋊D5—124no—
171C2×Dic5—62no—
172C2×Dic5—124no—
173C2×Dic5(C2×D3)⋊C411yescharacteristic
174C2×Dic5C2×D1211yescharacteristic
175C2×Dic5C2×#6711yescharacteristic
176C4×D5—22no—
177C4×D5—22no—
178C4×D5—22no—
179Dic10—122no—
180#170—42no—
181#170—64no—
182C2×#41—301no—
183C2×M16—301no—
184C4⋊Q8—151no—
185#127—31no—
186#124—301no—
187#121—152no—
188#121—301no—
189C4×D4—152no—
190C4×D4—301no—
191C2×C42—51no—
192C4⋊C8—52no—
193C22⋊C8—101no—
194#97—301no—
195C4×C8—101no—
196C4×C8—152no—
197C2×C3×C5#40811yescharacteristic
198C2×C3×C5#41811yescharacteristic
199C2×C3×C5C2×#10411yescharacteristic
200C3×D5—41no—
201C5×D3—82no—
202C23×C3—51no—
203C22×D3—22no—
204C2×C3×C4—51no—
205C2×C3×C4—51no—
206C2×C3×C4—51no—
207C2×C3×C4—102no—
208C2×C3×C4—102no—
209C2×C3×C4—102no—
210C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
211C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
212C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
213#67—204no—
214C2×Dic3—102no—
215D12—24no—
216D12—42no—
217D12—42no—
218C4×D3—204no—
219Dic6—202no—
220C3×C8—202no—
221C3⋊C8—104no—
222C22×C5—122no—
223C22×C5—122no—
224C22×C5—122no—
225C22×C5C2×(C2×D3)⋊C411yescharacteristic
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—21no—
229C4×C5—21no—
230C4×C5#82512yes—
231C4×C5#90112yes—
232Dic5—21no—
233Dic5—21no—
234Dic5—122no—
235Dic5#94912yes—
236#41—604no—
237C2×Q8—301no—
238C2×D4—32no—
239C2×D4—61no—
240C2×D4—61no—
241C2×D4—302no—
242C22×C4—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—302no—
246M16—304no—
247C2×C8—102no—
248C2×C8—302no—
249C4⋊C4—152no—
250C4⋊C4—301no—
251C22⋊C4—302no—
252C22⋊C4—302no—
253C42—51no—
254C42—51no—
255C42—51no—
256C42D3×AGL(1,𝔽5)11yescharacteristic
257C3×C5#148411yescharacteristic, complemented, Hall
258C22×C3—101no—
259C22×C3—101no—
260C22×C3—101no—
261C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
262C2×D3—42no—
263C2×D3—42no—
264C2×D3—42no—
265C3×C4—21no—
266C3×C4—52no—
267C3×C4—101no—
268C3×C4—101no—
269C3×C4#400812yes—
270C3×C4#413112yes—
271Dic3—202no—
272C2×C5—242no—
273C2×C5#500111yescharacteristic
274C2×C5#511011yescharacteristic
275C2×C5C2×#82511yescharacteristic
276D5—41no—
277C23—51no—
278C23—62no—
279Q8—602no—
280D4—64no—
281D4—122no—
282D4—122no—
283D4—604no—
284C2×C4—51no—
285C2×C4—51no—
286C2×C4—51no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—302no—
291C2×C4—604no—
292C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
293C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
294C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
295C8—202no—
296C8—304no—
297C2×C3—201no—
298C2×C3#6576711yescharacteristic
299C2×C3C2×#400811yescharacteristic
300C2×C3#6577611yescharacteristic
301D3—82no—
302C5#7076111yescharacteristic, complemented, Sylow
303C22—101no—
304C22—101no—
305C22—101no—
306C22—122no—
307C22—122no—
308C22—122no—
309C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
310C4—21no—
311C4—52no—
312C4—101no—
313C4—101no—
314C4—602no—
315C4#9115512yes—
316C4#9191112yes—
317C3#1060460511yescharacteristic, complemented, Sylow
318C2—201no—
319C2—242no—
320C2#1175170611yescharacteristic
321C2C2×#9115511yescharacteristic
322C2#1175180111yescharacteristic
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#11752672C2
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1484
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#6758C2semidirect
3. C3×#65680C2semidirect
4. #11746488C2semidirect
23. #65680D3semidirect
257. C3×C5#1484semidirect
302. C5#70761semidirect
317. C3#10604605semidirect

Maximal subgroups

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

subgroupindex
#117526722
C4×#67582
C3×#656802
#117464882
#106046053
#707615