Finite Group Databasebeta

← #14281011

Subgroups — #14281011

Order 1920.

624 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 98 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×D3×#683C211yesmaximal, characteristic
2#11752051C212yesmaximal
3#11746785C211yesmaximal, characteristic, complemented
4C3×#64914C211yesmaximal, characteristic, complemented
5#11746569C212yesmaximal, complemented
6#10604882—31nomaximal, Hall
7C22×C4×C5×D3C411yescharacteristic
8C22×D3×Dic5C411yescharacteristic
9C22×D3×Dic5C2211yescharacteristic
10C2×#6739—22no—
11C2×#6712C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×#6669C2211yescharacteristic
14C2×#6668C411yescharacteristic
15D3×#683—22no—
16D3×#683—22no—
17#91241C2212yes—
18C3×C22⋊#170C2212yes—
19(C2×D3)⋊#170—22no—
20#68144—51nomaximal, Hall
21C22×#683—31no—
22#65798—32no—
23#64914—31no—
24#64914—32no—
25#64914D311yescharacteristic, complemented
26C23×C5×D3C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×Dic15C2×C411yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C22×C5×Dic3C2×C411yescharacteristic
31C2×C4×C5×D3—21no—
32C2×C4×C5×D3—21no—
33C2×C4×C5×D3—42no—
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C2×D3×Dic5—21no—
37C2×D3×Dic5—21no—
38C2×D3×Dic5—22no—
39C2×D3×Dic5—22no—
40C2×D3×Dic5—42no—
41C2×D3×Dic5D412yes—
42C2×D3×Dic5D412yes—
43C2×C3⋊#170—22no—
44C2×C3×#170—22no—
45#6739—44no—
46#6712—22no—
47C3×#683—22no—
48#6669—22no—
49#6668—22no—
50C2×D3×C4⋊C4—51no—
51#4726—52no—
52C3×#324—51no—
53#4528—51no—
54#4469—52no—
55C23×C4×C5—31no—
56C23×Dic5—31no—
57C23×Dic5—31no—
58C2×#704—62no—
59C2×#683—31no—
60C2×#683—31no—
61C2×#683—31no—
62C2×#683—62no—
63C2×#683—62no—
64C2×#683C2×D311yescharacteristic
65C22⋊#170—32no—
66C22⋊#170—62no—
67C22⋊#170C2×D312yes—
68#1463—151noSylow
69C23×C3×C5C22×C411yescharacteristic
70C22×C5×D3—21no—
71C22×C5×D3—21no—
72C22×C5×D3—22no—
73C22×C5×D3—22no—
74C22×C5×D3C22⋊C411yescharacteristic
75C22×C5×D3C22⋊C411yescharacteristic
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—41no—
78C2×Dic15—21no—
79C2×Dic15—21no—
80C2×Dic15—41no—
81C2×Dic15C22⋊C412yes—
82C2×Dic15M1612yescomplemented
83C2×C5×Dic3—21no—
84C2×C5×Dic3—41no—
85C4×C5×D3—42no—
86C4×C5×D3—42no—
87C2×C3×Dic5—21no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—41no—
90C2×C3×Dic5M1612yescomplemented
91C2×C3×Dic5C2×D412yes—
92D3×Dic5—24no—
93D3×Dic5—24no—
94D3×Dic5—24no—
95D3×Dic5—42no—
96C3⋊#170—42no—
97C3×#170—42no—
98C22×C4×D3—51no—
99C22×C4×D3—51no—
100C22×C4×D3AGL(1,𝔽5)11yescharacteristic
101C2×C3×C4⋊C4—51no—
102C2×C4⋊Dic3—51no—
103C2×Dic3⋊C4—51no—
104C2×Dic3⋊C4—51no—
105C2×ΓL(1,𝔽25)—102no—
106D3×C4⋊C4—102no—
107D3×C4⋊C4—102no—
108C3×C22⋊C8—52no—
109#830—52no—
110(C2×D3)⋊C8—102no—
111C24×C5—31no—
112C22×C4×C5—31no—
113C22×C4×C5—61no—
114C22×C4×C5—61no—
115C22×C4×C5—122no—
116C22×C4×C5C4×D311yescharacteristic
117C22×Dic5—31no—
118C22×Dic5—31no—
119C22×Dic5—32no—
120C22×Dic5—32no—
121C22×Dic5—62no—
122C22×Dic5—61no—
123C22×Dic5—61no—
124C22×Dic5—62no—
125C22×Dic5—122no—
126C22×Dic5C4×D311yescharacteristic
127C22×Dic5C22×D311yescharacteristic
128#704—124no—
129C2×#170—22no—
130C2×#170—62no—
131#683—22no—
132#683—62no—
133#683—62no—
134#683—62no—
135C22×C4⋊C4—151no—
136#407—152no—
137#324—51no—
138#324—152no—
139#324—151no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5C2×C22⋊C411yescharacteristic
143C22×C3×C5C2×M1611yescharacteristic
144C22×C3×C5C2×M1611yescharacteristic
145C2×C5×D3—24no—
146C2×C5×D3—24no—
147C2×C5×D3—21no—
148C2×C5×D3—21no—
149C2×C5×D3—21no—
150C2×C5×D3—21no—
151C2×C5×D3#9912yes—
152C2×C5×D3#10112yes—
153C3×C4×C5—41no—
154Dic15—22no—
155Dic15—22no—
156C3×Dic5—22no—
157C3×Dic5—22no—
158C5×Dic3—41no—
159C23×D3C2×AGL(1,𝔽5)11yescharacteristic
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
163C22×Dic3—51no—
164C22×Dic3—51no—
165C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—21no—
168C2×C4×D3—42no—
169C2×C4×D3—52no—
170C2×C4×D3—52no—
171C2×C4×D3—102no—
172C2×C4×D3—102no—
173C2×C4×D3—101no—
174C2×C4×D3—101no—
175C2×C4×D3—202no—
176C2×C3×C8—102no—
177C3×C4⋊C4—102no—
178C4⋊Dic3—102no—
179Dic3⋊C4—102no—
180Dic3⋊C4—102no—
181C2×C3⋊C8—102no—
182ΓL(1,𝔽25)—204no—
183C23×C5—31no—
184C23×C5—31no—
185C23×C5—62no—
186C23×C5—62no—
187C23×C5—61no—
188C23×C5—61no—
189C23×C5C2×C4×D311yescharacteristic
190C2×C4×C5—21no—
191C2×C4×C5—41no—
192C2×C4×C5—61no—
193C2×C4×C5—122no—
194C2×C4×C5—122no—
195C2×C4×C5—121no—
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5—32no—
199C2×Dic5—32no—
200C2×Dic5—41no—
201C2×Dic5—64no—
202C2×Dic5—64no—
203C2×Dic5—64no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—122no—
207C2×Dic5—121no—
208C2×Dic5ΓL(1,𝔽25)12yescomplemented
209C2×Dic5D3×D412yes—
210#170—42no—
211#170—122no—
212C23×C4—31no—
213C23×C4—151no—
214C23×C4—151no—
215C2×M16—302no—
216C2×C4⋊C4—51no—
217C2×C4⋊C4—151no—
218C2×C4⋊C4—151no—
219C2×C4⋊C4—151no—
220C2×C4⋊C4—302no—
221C2×C4⋊C4—302no—
222C22⋊C8—52no—
223C22⋊C8—152no—
224C22⋊C8—302no—
225C2×C3×C5—21no—
226C2×C3×C5—21no—
227C2×C3×C5#40711yescharacteristic
228C2×C3×C5C2×#9911yescharacteristic
229C2×C3×C5C2×#10111yescharacteristic
230C5×D3—22no—
231C5×D3—22no—
232C23×C3C22×AGL(1,𝔽5)11yescharacteristic
233C22×D3—21no—
234C22×D3—21no—
235C22×D3—22no—
236C22×D3—22no—
237C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
238C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—52no—
242C2×C3×C4—52no—
243C2×C3×C4—101no—
244C2×C3×C4—101no—
245C2×C3×C4—201no—
246C2×Dic3—21no—
247C2×Dic3—41no—
248C2×Dic3—52no—
249C2×Dic3—52no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252C2×Dic3—201no—
253C4×D3—42no—
254C4×D3—42no—
255C4×D3—104no—
256C4×D3—104no—
257C4×D3—104no—
258C4×D3—202no—
259C3×C8—202no—
260C3⋊C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—32no—
264C22×C5—32no—
265C22×C5—64no—
266C22×C5—64no—
267C22×C5—61no—
268C22×C5—61no—
269C22×C5—61no—
270C22×C5—61no—
271C22×C5D3×C22⋊C411yescharacteristic
272C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
273C22×C5D3×M1611yescharacteristic
274C4×C5—41no—
275C4×C5—121no—
276Dic5—22no—
277Dic5—22no—
278Dic5—62no—
279Dic5—62no—
280C24—31no—
281C22×C4—31no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4—61no—
285C22×C4—61no—
286C22×C4—122no—
287C22×C4—152no—
288C22×C4—152no—
289C22×C4—151no—
290C22×C4—151no—
291C22×C4—302no—
292C22×C4—302no—
293C22×C4—301no—
294C22×C4—301no—
295C22×C4—602no—
296C22×C4D3×AGL(1,𝔽5)11yescharacteristic
297M16—604no—
298C2×C8—102no—
299C2×C8—302no—
300C4⋊C4—102no—
301C4⋊C4—302no—
302C4⋊C4—302no—
303C4⋊C4—302no—
304C3×C5#146311yescharacteristic, complemented, Hall
305C22×C3—21no—
306C22×C3—21no—
307C22×C3D5⋊M1611yescharacteristic
308C22×C3D5⋊M1611yescharacteristic
309C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C2×D3—24no—
311C2×D3—24no—
312C2×D3—21no—
313C2×D3—21no—
314C2×D3—21no—
315C2×D3—21no—
316C2×D3#400512yes—
317C2×D3#401112yes—
318C3×C4—41no—
319C3×C4—102no—
320C3×C4—102no—
321Dic3—41no—
322Dic3—102no—
323Dic3—102no—
324C2×C5—21no—
325C2×C5—21no—
326C2×C5—62no—
327C2×C5—62no—
328C2×C5#472611yescharacteristic
329C2×C5D3×#9911yescharacteristic
330C2×C5D3×#10111yescharacteristic
331C23—31no—
332C23—31no—
333C23—62no—
334C23—62no—
335C23—61no—
336C23—61no—
337C23C2×D3×AGL(1,𝔽5)11yescharacteristic
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—52no—
341C2×C4—52no—
342C2×C4—61no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—122no—
346C2×C4—122no—
347C2×C4—121no—
348C2×C4—152no—
349C2×C4—152no—
350C2×C4—201no—
351C2×C4—304no—
352C2×C4—304no—
353C2×C4—304no—
354C2×C4—301no—
355C2×C4—301no—
356C2×C4—602no—
357C2×C4—601no—
358C8—202no—
359C8—602no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3#6575511yescharacteristic
363C2×C3C2×#400511yescharacteristic
364C2×C3C2×#401111yescharacteristic
365D3—22no—
366D3—22no—
367C5#6814411yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—32no—
371C22—32no—
372C22—64no—
373C22—64no—
374C22—61no—
375C22—61no—
376C22—61no—
377C22—61no—
378C22#9191511yescharacteristic
379C22D5⋊ΓL(1,𝔽25)11yescharacteristic
380C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
381C4—41no—
382C4—102no—
383C4—102no—
384C4—121no—
385C4—302no—
386C4—302no—
387C3#1060488211yescharacteristic, complemented, Sylow
388C2—21no—
389C2—21no—
390C2—62no—
391C2—62no—
392C2D3×#400511yescharacteristic
393C2#1175191911yescharacteristic
394C2D3×#401111yescharacteristic
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×C5×D3C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1463
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. #11746785C2semidirect
4. C3×#64914C2semidirect
5. #11746569C2semidirect
25. #64914D3semidirect
82. C2×Dic15M16semidirect
90. C2×C3×Dic5M16semidirect
208. C2×Dic5ΓL(1,𝔽25)semidirect
304. C3×C5#1463semidirect
367. C5#68144semidirect
387. C3#10604882semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6832
#117520512
#117467852
C3×#649142
#117465692
#106048823
#681445