Finite Group Databasebeta

← #14282404

Subgroups — #14282404

Order 1920.

552 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 126 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#11752340C211yesmaximal, characteristic, complemented
3C3×C4×D5⋊C8C211yesmaximal, characteristic, complemented
4#11746491C214yesmaximal, complemented
5#10604650—31nomaximal, Hall
6C2×#6773—21no—
7C2×#6758—21no—
8C2×C3×D5⋊C8—21no—
9#91763C411yescharacteristic
10C5×#869C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91450—21no—
13#91450C412yes—
14#91418—21no—
15#91418C2212yes—
16#91375—21no—
17C4⋊(C3⋊#170)—21no—
18C4⋊(C3⋊#170)C2212yes—
19C3×C4×#170—21no—
20C3×C4×#170C2212yes—
21#69735—51nomaximal, Hall
22#66059—31no—
23#65681—31no—
24C4×D5⋊C8D311yescharacteristic, complemented
25#64871—34no—
26C2×D60—21no—
27C2×D60—21no—
28C2×D60C2×C412yes—
29C2×C5×Dic6—21no—
30C2×C3×C4×D5C2×C411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5D411yescharacteristic
33C2×#1202—22no—
34C2×#1200—22no—
35#6773—42no—
36#6773—42no—
37C2×C3⋊#170—22no—
38#6758—42no—
39C2×C3×#170—22no—
40C3×D5⋊C8—24no—
41C3×C42×C5C2×C411yescharacteristic
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3C2×C412yes—
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5D411yescharacteristic
46C3×C4×Dic5C2311yescharacteristic
47#6667—22no—
48#6667—22no—
49#5477—51no—
50C2×C3×C4×C8—51no—
51#4924—51no—
52#4459—54no—
53C2×#713—61no—
54C2×#700—61no—
55C2×D5⋊C8—21no—
56C5×C4⋊Q8—31no—
57#4093—61no—
58#4041—32no—
59#4041—61no—
60#4039—32no—
61#4039—61no—
62#4020—31no—
63C42×D5C2×D311yescharacteristic
64C4⋊#170—32no—
65C4⋊#170—61no—
66C4×#170—21no—
67C4×#170C2×D312yes—
68#1492—151noSylow
69C22×D15—22no—
70C22×C3×D5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22⋊C411yescharacteristic
72C2×C3×C4×C5C22⋊C411yescharacteristic
73C2×C3×C4×C5C22×C411yescharacteristic
74D60—24no—
75D60—42no—
76D60—42no—
77C2×C5×Dic3—22no—
78C5×Dic6—42no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C2×D411yescharacteristic
81C2×C3×Dic5C2×D411yescharacteristic
82C3×C4×D5—22no—
83C3×C4×D5—22no—
84C3×C4×D5D812yes—
85C3×C4×D5SD1612yes—
86#1202—44no—
87#1200—42no—
88#1200—42no—
89C3⋊#170—42no—
90C3×#170—24no—
91C2×#235—101no—
92C22×C3×C8—101no—
93C2×C3×C42—51no—
94#930—52no—
95#930—101no—
96C2×#208—101no—
97#875—101no—
98#874—51no—
99C4×D12—52no—
100C4×D12—101no—
101#869AGL(1,𝔽5)11yescharacteristic
102C3×C4×C8—52no—
103C3×C4×C8—101no—
104C4⋊(C3⋊C8)—52no—
105C4⋊(C3⋊C8)—101no—
106C2×C5×Q8—61no—
107#713—122no—
108#713—122no—
109C2×D20—32no—
110C2×D20—62no—
111C2×D20—61no—
112C2×D20—61no—
113C2×C4×D5—62no—
114C2×C4×D5C4×D311yescharacteristic
115C2×C4×D5D1211yescharacteristic
116C2×C4×D5#6711yescharacteristic
117C2×#170—22no—
118C2×#170—62no—
119#700—122no—
120D5⋊C8—24no—
121C5×C4⋊C4—32no—
122C5×C4⋊C4—61no—
123C42×C5C4×D311yescharacteristic
124#685—62no—
125#685—62no—
126C4×Dic5D1211yescharacteristic
127C4×Dic5#6711yescharacteristic
128C4×Dic5C22×D311yescharacteristic
129#532—151no—
130#423—151no—
131C2×C4×C8—51no—
132D4⋊C8—154no—
133C22×C3×C5C2×C22⋊C411yescharacteristic
134C2×D15—42no—
135C2×D15—42no—
136C2×D15—42no—
137C2×C3×D5—21no—
138C2×C3×D5—21no—
139C2×C3×D5#10212yes—
140C3×C4×C5#10212yes—
141C3×C4×C5#10412yes—
142C3×C4×C5#13112yes—
143C3×Dic5—21no—
144C3×Dic5—21no—
145C3×Dic5C2×D811yescharacteristic
146C3×Dic5C2×SD1611yescharacteristic
147C5×Dic3—42no—
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×C3×C4—51no—
151C2×#67—102no—
152#235—202no—
153#235—202no—
154C2×D12—52no—
155C2×D12—101no—
156C2×D12—101no—
157C2×C4×D3—102no—
158C2×Dic6—21no—
159C2×C3×C8—102no—
160C2×C3×C8—104no—
161C3×C42—51no—
162C3×C42—51no—
163C3×C42—51no—
164C3×C42C2×AGL(1,𝔽5)11yescharacteristic
165(C2×D3)⋊C4—102no—
166(C2×D3)⋊C4—102no—
167C4⋊Dic3—21no—
168C4⋊Dic3C2×AGL(1,𝔽5)12yes—
169#208—202no—
170C2×C3⋊C8—102no—
171C22×D5—62no—
172C22×D5(C2×D3)⋊C411yescharacteristic
173C5×Q8—122no—
174C2×C4×C5—62no—
175C2×C4×C5(C2×D3)⋊C411yescharacteristic
176C2×C4×C5(C2×D3)⋊C411yescharacteristic
177C2×C4×C5C2×C4×D311yescharacteristic
178C2×Dic5(C2×D3)⋊C411yescharacteristic
179C2×Dic5C2×D1211yescharacteristic
180C2×Dic5C2×#6711yescharacteristic
181D20—64no—
182D20—124no—
183D20—122no—
184D20—122no—
185C4×D5—22no—
186C4×D5—22no—
187C4×D5—122no—
188C4×D5—122no—
189C4×D5#20412yes—
190C4×D5D2412yes—
191#170—24no—
192#170—122no—
193C2×#41—301no—
194C2×M16—301no—
195C22×C8—101no—
196C4⋊Q8—31no—
197#127—151no—
198#124—301no—
199#121—152no—
200#121—301no—
201C4×D4—152no—
202C4×D4—301no—
203C2×C42—51no—
204C4⋊C8—152no—
205C4⋊C8—301no—
206C4×C8—52no—
207C4×C8—101no—
208C2×C3×C5#40811yescharacteristic
209C2×C3×C5C2×#10211yescharacteristic
210C2×C3×C5C2×#10411yescharacteristic
211D15—82no—
212C3×D5—22no—
213C23×C3—51no—
214C22×D3—102no—
215C2×C3×C4—51no—
216C2×C3×C4—52no—
217C2×C3×C4—52no—
218C2×C3×C4—51no—
219C2×C3×C4—51no—
220C2×C3×C4—102no—
221C2×C3×C4—102no—
222C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
223C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
224C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
225#67—204no—
226C2×Dic3—22no—
227D12—104no—
228D12—202no—
229D12—202no—
230C4×D3—202no—
231C4×D3—202no—
232Dic6—42no—
233C3×C8—104no—
234C3⋊C8—202no—
235C22×C5C2×(C2×D3)⋊C411yescharacteristic
236C2×D5—21no—
237C2×D5—21no—
238C2×D5—122no—
239C2×D5—122no—
240C2×D5—122no—
241C2×D5#82112yes—
242C4×C5—122no—
243C4×C5#80512yes—
244C4×C5#82112yes—
245C4×C5#90112yes—
246Dic5—21no—
247Dic5—21no—
248Dic5C2×#20411yescharacteristic
249Dic5C2×D2411yescharacteristic
250#41—602no—
251#41—602no—
252C2×Q8—61no—
253C2×D4—152no—
254C2×D4—302no—
255C2×D4—301no—
256C2×D4—301no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—51no—
260C22×C4—302no—
261M16—602no—
262C2×C8—102no—
263C2×C8—104no—
264C2×C8—302no—
265C4⋊C4—32no—
266C4⋊C4—61no—
267C22⋊C4—302no—
268C22⋊C4—302no—
269C42—51no—
270C42—51no—
271C42—51no—
272C42D3×AGL(1,𝔽5)11yescharacteristic
273C3×C5#149211yescharacteristic, complemented, Hall
274C22×C3—52no—
275C22×C3—101no—
276C22×C3—101no—
277C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
278C2×D3—202no—
279C2×D3—202no—
280C2×D3—202no—
281C3×C4—51no—
282C3×C4—51no—
283C3×C4—101no—
284C3×C4—101no—
285C3×C4#400712yes—
286C3×C4#401012yes—
287C3×C4#413312yes—
288Dic3—42no—
289C2×C5C2×#80511yescharacteristic
290C2×C5#511011yescharacteristic
291C2×C5C2×#82111yescharacteristic
292D5—22no—
293D5—242no—
294C23—51no—
295C23—302no—
296Q8—122no—
297D4—304no—
298D4—604no—
299D4—602no—
300D4—602no—
301C2×C4—51no—
302C2×C4—52no—
303C2×C4—52no—
304C2×C4—51no—
305C2×C4—51no—
306C2×C4—62no—
307C2×C4—102no—
308C2×C4—102no—
309C2×C4—602no—
310C2×C4—602no—
311C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
312C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
313C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
314C8—104no—
315C8—602no—
316C2×C3—102no—
317C2×C3C2×#400711yescharacteristic
318C2×C3C2×#401011yescharacteristic
319C2×C3#6578711yescharacteristic
320D3—402no—
321C5#6973511yescharacteristic, complemented, Sylow
322C22—52no—
323C22—101no—
324C22—101no—
325C22—602no—
326C22—602no—
327C22—602no—
328C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
329C4—51no—
330C4—51no—
331C4—101no—
332C4—101no—
333C4—122no—
334C4#9115212yes—
335C4#9115812yes—
336C4#9191412yes—
337C3#1060465011yescharacteristic, complemented, Sylow
338C2—102no—
339C2—1202no—
340C2C2×#9115211yescharacteristic
341C2C2×#9115811yescharacteristic
342C2#1175181311yescharacteristic
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#1492
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. #11752340C2semidirect
3. C3×C4×D5⋊C8C2semidirect
4. #11746491C2semidirect
24. C4×D5⋊C8D3semidirect
273. C3×C5#1492semidirect
321. C5#69735semidirect
337. C3#10604650semidirect

Maximal subgroups

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

subgroupindex
#117526742
#117523402
C3×C4×D5⋊C82
#117464912
#106046503
#697355