Finite Group Databasebeta

← #14281050

Subgroups — #14281050

Order 1920.

504 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 94 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×#91532C211yesmaximal, characteristic
2#11752013C212yesmaximal, complemented
3#11746804C211yesmaximal, characteristic
4C3×#64933C211yesmaximal, characteristic
5#11746569C212yesmaximal, complemented
6#10604203—31nomaximal, Hall
7C23×Dic15C411yescharacteristic
8C2×C5×#217C411yescharacteristic
9C2×C3×C22⋊Dic5C2211yescharacteristic
10C2×#6669C411yescharacteristic
11C2×#6669C2211yescharacteristic
12#91532—22no—
13#91532—22no—
14C2×Dic3×Dic5C411yescharacteristic
15C2×Dic3×Dic5C2211yescharacteristic
16#91241C2212yes—
17C3×C22⋊#170C2212yes—
18Dic3⋊#170—22no—
19#91169—22no—
20#68102—51nomaximal, Hall
21C2×#4023—31no—
22#65759—32no—
23#64933—31no—
24#64933D311yescharacteristic
25#64914—32no—
26C24×C3×C5C2×C411yescharacteristic
27C22×Dic15—22no—
28C22×Dic15—21no—
29C22×Dic15—21no—
30C22×Dic15—22no—
31C22×Dic15C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C22×C5×Dic3C2×C411yescharacteristic
34C22×C5×Dic3C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2311yescharacteristic
37C2×C3⋊#170—22no—
38C2×C3×#170—22no—
39C5×#217—22no—
40C3×C22⋊Dic5—22no—
41#6669—22no—
42#6669—22no—
43Dic3×Dic5—21no—
44Dic3×Dic5—21no—
45Dic3×Dic5D412yes—
46Dic3×Dic5D412yes—
47C2×#877—51no—
48#4719—52no—
49C3×#323—51no—
50#4525—51no—
51#4469—52no—
52C23×Dic5—31no—
53C2×C5×C22⋊C4—31no—
54C2×C22⋊Dic5C2×D311yescharacteristic
55C2×#683—31no—
56C2×#683—31no—
57C2×C4×Dic5—31no—
58C2×C4×Dic5—31no—
59#4023—62no—
60#4023—62no—
61C22⋊#170—32no—
62C22⋊#170C2×D312yes—
63#4002—62no—
64C4⋊#170—62no—
65#1464—151noSylow
66C23×C3×C5—21no—
67C23×C3×C5—21no—
68C23×C3×C5—41no—
69C23×C3×C5—41no—
70C23×C3×C5M1612yes—
71C23×C3×C5C22×C411yescharacteristic
72C2×Dic15—24no—
73C2×Dic15—24no—
74C2×Dic15—21no—
75C2×Dic15—21no—
76C2×Dic15—21no—
77C2×Dic15—21no—
78C2×Dic15C22⋊C411yescharacteristic
79C2×Dic15C22⋊C411yescharacteristic
80C2×Dic15M1612yes—
81C2×C5×Dic3—21no—
82C2×C5×Dic3—41no—
83C2×C5×Dic3—41no—
84C2×C5×Dic3C22⋊C412yes—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5—41no—
88C2×C3×Dic5C2×D412yes—
89C3⋊#170—42no—
90C3×#170—42no—
91C23×Dic3—51no—
92C2×C3×C22⋊C4—51no—
93C2×#217AGL(1,𝔽5)11yescharacteristic
94C2×Dic3⋊C4—51no—
95C2×Dic3⋊C4—51no—
96C2×C4×Dic3—51no—
97C2×C4×Dic3—51no—
98#877—102no—
99#877—102no—
100C3×C22⋊C8—52no—
101#830—52no—
102#815—102no—
103Dic3⋊C8—102no—
104C24×C5C4×D311yescharacteristic
105C22×C4×C5—31no—
106C22×C4×C5—31no—
107C22×Dic5—31no—
108C22×Dic5—31no—
109C22×Dic5—62no—
110C22×Dic5—61no—
111C22×Dic5—61no—
112C22×Dic5—62no—
113C22×Dic5C4×D311yescharacteristic
114C22×Dic5C22×D311yescharacteristic
115C2×#170—22no—
116C2×#170—62no—
117C5×C22⋊C4—62no—
118C22⋊Dic5—22no—
119#683—62no—
120#683—62no—
121C4×Dic5—32no—
122C4×Dic5—32no—
123C4×Dic5—61no—
124C4×Dic5—61no—
125C2×#117—151no—
126#432—152no—
127#324—152no—
128#323—51no—
129#323—151no—
130C22×C3×C5—21no—
131C22×C3×C5—21no—
132C22×C3×C5—22no—
133C22×C3×C5—42no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C22×C3×C5C2×M1611yescharacteristic
139C22×C3×C5C2×M1611yescharacteristic
140Dic15—21no—
141Dic15—21no—
142Dic15—22no—
143C3×Dic5—22no—
144C3×Dic5—41no—
145C5×Dic3—22no—
146C5×Dic3—41no—
147C24×C3C2×AGL(1,𝔽5)11yescharacteristic
148C22×C3×C4—51no—
149C22×C3×C4—51no—
150C22×Dic3—51no—
151C22×Dic3—51no—
152C22×Dic3—101no—
153C22×Dic3—101no—
154C22×Dic3—102no—
155C22×Dic3—102no—
156C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
157C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
158C2×C3×C8—102no—
159C3×C22⋊C4—102no—
160#217—22no—
161Dic3⋊C4—102no—
162Dic3⋊C4—102no—
163C4×Dic3—52no—
164C4×Dic3—52no—
165C4×Dic3—101no—
166C4×Dic3—101no—
167C2×C3⋊C8—102no—
168C23×C5—21no—
169C23×C5—21no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5ΓL(1,𝔽25)12yes—
173C23×C5C2×C4×D311yescharacteristic
174C2×C4×C5—32no—
175C2×C4×C5—61no—
176C2×C4×C5—121no—
177C2×C4×C5—121no—
178C2×Dic5—21no—
179C2×Dic5—31no—
180C2×Dic5—31no—
181C2×Dic5—32no—
182C2×Dic5—41no—
183C2×Dic5—41no—
184C2×Dic5—64no—
185C2×Dic5—64no—
186C2×Dic5—61no—
187C2×Dic5—61no—
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5D3×D412yes—
191#170—42no—
192#170—122no—
193C23×C4—151no—
194#117—302no—
195#117—302no—
196C2×C4⋊C4—151no—
197C2×C4⋊C4—151no—
198C2×C22⋊C4—31no—
199C2×C22⋊C4—51no—
200C2×C42—151no—
201C2×C42—151no—
202C4⋊C8—302no—
203C22⋊C8—52no—
204C22⋊C8—152no—
205#97—302no—
206C2×C3×C5—21no—
207C2×C3×C5—21no—
208C2×C3×C5—42no—
209C2×C3×C5#40711yescharacteristic
210C2×C3×C5#41011yescharacteristic
211C2×C3×C5#41311yescharacteristic
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3#70012yes—
217C23×C3C22×AGL(1,𝔽5)11yescharacteristic
218C2×C3×C4—52no—
219C2×C3×C4—101no—
220C2×C3×C4—201no—
221C2×C3×C4—201no—
222C2×Dic3—21no—
223C2×Dic3—41no—
224C2×Dic3—41no—
225C2×Dic3—52no—
226C2×Dic3—51no—
227C2×Dic3—51no—
228C2×Dic3—104no—
229C2×Dic3—104no—
230C2×Dic3—101no—
231C2×Dic3—101no—
232C2×Dic3—101no—
233C2×Dic3—101no—
234C2×Dic3C22⋊AGL(1,𝔽5)12yes—
235C3×C8—202no—
236C3⋊C8—202no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—22no—
240C22×C5—42no—
241C22×C5—42no—
242C22×C5—41no—
243C22×C5—41no—
244C22×C5D3×C22⋊C411yescharacteristic
245C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
246C22×C5D3×M1611yescharacteristic
247C4×C5—62no—
248C4×C5—121no—
249Dic5—22no—
250Dic5—41no—
251Dic5—61no—
252Dic5—61no—
253Dic5—62no—
254C24D3×AGL(1,𝔽5)11yescharacteristic
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—151no—
260C22×C4—151no—
261C22×C4—301no—
262C22×C4—301no—
263C22×C4—302no—
264C22×C4—302no—
265C2×C8—102no—
266C2×C8—302no—
267C4⋊C4—302no—
268C4⋊C4—302no—
269C22⋊C4—62no—
270C22⋊C4—102no—
271C42—152no—
272C42—152no—
273C42—301no—
274C42—301no—
275C3×C5#146411yescharacteristic, complemented, Hall
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—42no—
280C22×C3—42no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3C2×#70011yescharacteristic
284C22×C3D5⋊M1611yescharacteristic
285C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
286C3×C4—102no—
287C3×C4—201no—
288Dic3—22no—
289Dic3—41no—
290Dic3—101no—
291Dic3—101no—
292Dic3—102no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5—42no—
296C2×C5#472611yescharacteristic
297C2×C5#474011yescharacteristic
298C2×C5#474511yescharacteristic
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23#674012yes—
304C23C2×D3×AGL(1,𝔽5)11yescharacteristic
305C2×C4—32no—
306C2×C4—52no—
307C2×C4—61no—
308C2×C4—101no—
309C2×C4—121no—
310C2×C4—121no—
311C2×C4—152no—
312C2×C4—151no—
313C2×C4—151no—
314C2×C4—201no—
315C2×C4—201no—
316C2×C4—304no—
317C2×C4—304no—
318C2×C4—301no—
319C2×C4—301no—
320C2×C4—301no—
321C2×C4—301no—
322C8—202no—
323C8—602no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—42no—
327C2×C3#6575611yescharacteristic
328C2×C3#6577111yescharacteristic
329C2×C3#6577711yescharacteristic
330C5#6810211yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22#9193111yescharacteristic
339C22C2×#674011yescharacteristic
340C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
341C4—62no—
342C4—102no—
343C4—121no—
344C4—201no—
345C4—302no—
346C4—301no—
347C4—301no—
348C3#1060420311yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—42no—
352C2#1175203111yescharacteristic
353C2#1175204811yescharacteristic
354C2#1175205211yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
Fitting, prime radicalC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#1464
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. #11752013C2semidirect
5. #11746569C2semidirect
275. C3×C5#1464semidirect
330. C5#68102semidirect
348. C3#10604203semidirect

Maximal subgroups

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

subgroupindex
C2×#915322
#117520132
#117468042
C3×#649332
#117465692
#106042033
#681025