Finite Group Databasebeta

← #14298420

Subgroups — #14298420

Order 1920.

544 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#91403C211yesmaximal, characteristic
2#11752003C212yesmaximal
3#11746790C211yesmaximal, characteristic, complemented
4C3×#64919C211yesmaximal, characteristic, complemented
5#11746574C212yesmaximal, complemented
6#10604195—31nomaximal, Hall
7C22×#1200C2211yescharacteristic
8C2×#6762C2212yes—
9C2×C3×#704C2212yes—
10C2×#6714C411yescharacteristic
11C2×C4×C5×Dic3C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×#6668C2211yescharacteristic
14C2×#6667C411yescharacteristic
15C2×Dic3×Dic5C411yescharacteristic
16#91403—24no—
17#91171—24no—
18#68991—51nomaximal, Hall
19C2×#4018—31no—
20#65755—32no—
21#64919—31no—
22#64919—32no—
23#64919D311yescharacteristic, complemented
24C23×D15C2×C411yescharacteristic
25C22×C3×C4×C5C2×C411yescharacteristic
26C22×Dic15C2×C411yescharacteristic
27C22×C5×Dic3C2×C411yescharacteristic
28C22×C5×Dic3C2×C411yescharacteristic
29C22×C3×Dic5C2×C411yescharacteristic
30C22×C3×Dic5C2311yescharacteristic
31C2×#1200—22no—
32C2×#1200—21no—
33C2×#1200—21no—
34C2×#1200D414yes—
35#6762—22no—
36#6762—22no—
37C2×C3⋊#170—22no—
38C3×#704—22no—
39C3×#704—22no—
40C2×C3×#170—22no—
41#6714—22no—
42C4×C5×Dic3—22no—
43C3×#683—22no—
44#6668—22no—
45#6667—22no—
46Dic3×Dic5—22no—
47C2×#892—51no—
48#5126—52no—
49C3×#343—51no—
50#4554—52no—
51#4530—51no—
52C22×C4×D5—31no—
53C2×#704—32no—
54C2×#704C2×D312yes—
55C2×C42×C5—31no—
56C2×#685—31no—
57C2×#685—31no—
58C2×#683—31no—
59C2×#683C2×D311yescharacteristic
60C2×C4×Dic5—31no—
61#4018—64no—
62#4003—64no—
63#1822—151noSylow
64C23×C3×C5C22×C411yescharacteristic
65C22×D15—21no—
66C22×D15—21no—
67C22×D15—41no—
68C22×D15—41no—
69C22×D15C22⋊C412yes—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×Dic15—21no—
73C2×Dic15—41no—
74C2×C5×Dic3—21no—
75C2×C5×Dic3—21no—
76C2×C5×Dic3—21no—
77C2×C5×Dic3—41no—
78C2×C5×Dic3C22⋊C412yes—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—41no—
81C2×C3×Dic5C2×D412yes—
82C2×C3×Dic5#4112yes—
83C2×C3×Dic5#4111yescharacteristic
84C2×C3×Dic5#4111yescharacteristic
85#1200—24no—
86#1200—24no—
87C3⋊#170—42no—
88C3×#170—42no—
89C22×C4×D3—51no—
90C2×C3×M16—52no—
91C2×C3×C4⋊C4—51no—
92C2×(C2×D3)⋊C4—51no—
93C2×(C2×D3)⋊C4—51no—
94C2×C4⋊Dic3—51no—
95C2×C4×Dic3—51no—
96C2×C4×Dic3AGL(1,𝔽5)11yescharacteristic
97C2×#208—52no—
98#892—104no—
99(C2×D3)⋊C8—104no—
100C23×D5—31no—
101C22×C4×C5—31no—
102C22×C4×C5—31no—
103C22×C4×C5C4×D311yescharacteristic
104C22×Dic5—31no—
105C22×Dic5C4×D311yescharacteristic
106C22×Dic5C22×D311yescharacteristic
107C2×C4×D5—34no—
108C2×C4×D5—62no—
109C2×C4×D5—61no—
110C2×C4×D5—61no—
111#704—22no—
112#704—22no—
113#704—62no—
114#704—62no—
115C2×#170—22no—
116C2×#170—62no—
117C42×C5—62no—
118#685—62no—
119#685—62no—
120#683—22no—
121#683—62no—
122C4×Dic5—62no—
123C2×#117—151no—
124#407—152no—
125#343—51no—
126#343—151no—
127#343—152no—
128C22×C3×C5—21no—
129C22×C3×C5—21no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C22×C3×C5#11711yescharacteristic
132C22×C3×C5#11711yescharacteristic
133C2×D15—22no—
134C2×D15—22no—
135C2×D15—22no—
136C2×D15—42no—
137C2×D15—42no—
138C3×C4×C5—41no—
139Dic15—41no—
140C3×Dic5—41no—
141C3×Dic5#12312yes—
142C3×Dic5#12312yes—
143C5×Dic3—22no—
144C5×Dic3—41no—
145C23×D3—51no—
146C22×C3×C4—51no—
147C22×C3×C4—51no—
148C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
149C22×Dic3—51no—
150C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
151C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
152C2×C4×D3—54no—
153C2×C4×D3—101no—
154C2×C4×D3—102no—
155C2×C4×D3—101no—
156C3×M16—102no—
157C3×M16—102no—
158C2×C3×C8—102no—
159C3×C4⋊C4—102no—
160(C2×D3)⋊C4—102no—
161(C2×D3)⋊C4—102no—
162C4⋊Dic3—102no—
163C4×Dic3—22no—
164C4×Dic3—102no—
165#208—102no—
166#208—102no—
167C2×C3⋊C8—102no—
168C23×C5C2×C4×D311yescharacteristic
169C22×D5—32no—
170C22×D5—61no—
171C22×D5—61no—
172C22×D5—121no—
173C22×D5—121no—
174C2×C4×C5—21no—
175C2×C4×C5—32no—
176C2×C4×C5—41no—
177C2×C4×C5—61no—
178C2×C4×C5—61no—
179C2×C4×C5—61no—
180C2×C4×C5—121no—
181C2×Dic5—21no—
182C2×Dic5—41no—
183C2×Dic5—61no—
184C2×Dic5—121no—
185C2×Dic5#23512yes—
186C2×Dic5D3×D412yes—
187C2×Dic5#23711yescharacteristic
188C2×Dic5#23911yescharacteristic
189C4×D5—64no—
190C4×D5—64no—
191#170—42no—
192#170—122no—
193C23×C4—151no—
194C2×M16—52no—
195C2×M16—152no—
196#117—304no—
197C2×C4⋊C4—51no—
198C2×C4⋊C4—151no—
199C2×C22⋊C4—151no—
200C2×C22⋊C4—151no—
201C2×C42—31no—
202C2×C42—151no—
203C22⋊C8—304no—
204C2×C3×C5—21no—
205C2×C3×C5—21no—
206C2×C3×C5#38111yescharacteristic
207C2×C3×C5#41311yescharacteristic
208C2×C3×C5#41311yescharacteristic
209D15—42no—
210C23×C3C22×AGL(1,𝔽5)11yescharacteristic
211C22×D3—52no—
212C22×D3—101no—
213C22×D3—101no—
214C22×D3—201no—
215C22×D3—201no—
216C2×C3×C4—21no—
217C2×C3×C4—41no—
218C2×C3×C4—51no—
219C2×C3×C4—52no—
220C2×C3×C4—51no—
221C2×C3×C4—52no—
222C2×C3×C4—101no—
223C2×C3×C4—201no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—41no—
228C2×Dic3—101no—
229C2×Dic3—201no—
230C2×Dic3C22⋊AGL(1,𝔽5)12yes—
231C4×D3—104no—
232C4×D3—104no—
233C3×C8—202no—
234C3⋊C8—202no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5#87211yescharacteristic
238C22×C5D3×C22⋊C411yescharacteristic
239C22×C5#89211yescharacteristic
240C2×D5—62no—
241C2×D5—62no—
242C2×D5—62no—
243C2×D5—122no—
244C2×D5—122no—
245C4×C5—41no—
246C4×C5—62no—
247C4×C5—121no—
248Dic5—41no—
249Dic5—121no—
250Dic5#88312yes—
251Dic5#89412yes—
252C24—151no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—51no—
256C22×C4—51no—
257C22×C4—154no—
258C22×C4—151no—
259C22×C4—301no—
260C22×C4—301no—
261C22×C4—302no—
262C22×C4D3×AGL(1,𝔽5)11yescharacteristic
263M16—102no—
264M16—102no—
265M16—302no—
266M16—302no—
267C2×C8—102no—
268C2×C8—302no—
269C4⋊C4—102no—
270C4⋊C4—302no—
271C22⋊C4—302no—
272C22⋊C4—302no—
273C42—62no—
274C42—302no—
275C3×C5#182211yescharacteristic, complemented, Hall
276C22×C3—21no—
277C22×C3—21no—
278C22×C3#413011yescharacteristic
279C22×C3#413011yescharacteristic
280C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
281C2×D3—102no—
282C2×D3—102no—
283C2×D3—102no—
284C2×D3—202no—
285C2×D3—202no—
286C3×C4—41no—
287C3×C4—52no—
288C3×C4—52no—
289C3×C4—201no—
290Dic3—22no—
291Dic3—41no—
292Dic3—201no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5#466411yescharacteristic
296C2×C5#474511yescharacteristic
297C2×C5#475111yescharacteristic
298D5—122no—
299C23—152no—
300C23—301no—
301C23—301no—
302C23—601no—
303C23—601no—
304C23C2×D3×AGL(1,𝔽5)11yescharacteristic
305C2×C4—21no—
306C2×C4—32no—
307C2×C4—41no—
308C2×C4—51no—
309C2×C4—51no—
310C2×C4—52no—
311C2×C4—52no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—101no—
316C2×C4—121no—
317C2×C4—201no—
318C2×C4—304no—
319C2×C4—304no—
320C2×C4—301no—
321C2×C4—601no—
322C8—202no—
323C8—602no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3#6576111yescharacteristic
327C2×C3#6576111yescharacteristic
328C2×C3#6576411yescharacteristic
329D3—202no—
330C5#6899111yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—302no—
334C22—302no—
335C22—302no—
336C22—602no—
337C22—602no—
338C22#9190711yescharacteristic
339C22#9190911yescharacteristic
340C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
341C4—41no—
342C4—52no—
343C4—52no—
344C4—62no—
345C4—121no—
346C4—201no—
347C4—601no—
348C3#1060419511yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—602no—
352C2#1175185311yescharacteristic
353C2#1175191711yescharacteristic
354C2#1175204911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
4. C3×#64919C2semidirect
5. #11746574C2semidirect
23. #64919D3semidirect
275. C3×C5#1822semidirect
330. C5#68991semidirect
348. C3#10604195semidirect

Maximal subgroups

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

subgroupindex
C2×#914032
#117520032
#117467902
C3×#649192
#117465742
#106041953
#689915