Finite Group Databasebeta

← #14281048

Subgroups — #14281048

Order 1920.

504 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 120 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×C5×#892C211yesmaximal, characteristic
2#11748337C212yesmaximal, complemented
3#11746349C211yesmaximal, characteristic, complemented
4C3×#64748C211yesmaximal, characteristic, complemented
5#11745949C212yesmaximal
6#10602365—31nomaximal, Hall
7C22×C4×C5×D3C411yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C5×(C2×D3)⋊C4C411yescharacteristic
10C2×C5×(C2×D3)⋊C4C2211yescharacteristic
11C2×C5×C4⋊Dic3C411yescharacteristic
12C2×C4×C5×Dic3C411yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C5×#892—22no—
15C5×#892—22no—
16#91114C2212yes—
17C3×C22⋊#168C2212yes—
18Dic3⋊#168—22no—
19#90953—22no—
20#68126—51nomaximal, Hall
21C2×C5×#117—31no—
22#65215—32no—
23#64748—31no—
24#64748D311yescharacteristic, complemented
25#64745—32no—
26C23×C5×D3C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C22×C5×Dic3C2×C411yescharacteristic
31C22×C5×Dic3C2×C411yescharacteristic
32C22×C5×Dic3C2×C411yescharacteristic
33C2×C4×C5×D3—22no—
34C2×C4×C5×D3—22no—
35C2×C4×C5×D3—21no—
36C2×C4×C5×D3—21no—
37C3×C5×C4⋊C4—22no—
38C2×C3⋊#168—22no—
39C5×(C2×D3)⋊C4—22no—
40C5×(C2×D3)⋊C4—22no—
41C5×C4⋊Dic3—22no—
42C4×C5×Dic3—21no—
43C4×C5×Dic3—21no—
44C4×C5×Dic3D412yes—
45C4×C5×Dic3D412yes—
46C2×C3×#168—22no—
47C2×#892D511yescharacteristic
48#4719—52no—
49C3×#324—51no—
50#4528—51no—
51#4468—52no—
52C23×C4×C5—31no—
53C5×#117—62no—
54C5×#117—62no—
55C2×C5×C4⋊C4—31no—
56C2×C5×C4⋊C4C2×D311yescharacteristic
57C2×C5×C22⋊C4—31no—
58C2×C5×C22⋊C4—31no—
59C2×C42×C5—31no—
60C2×C42×C5—31no—
61C22⋊#168—32no—
62C22⋊#168C2×D312yes—
63C4⋊#168—62no—
64#3935—62no—
65#1464—151noSylow
66C23×C3×C5C22×C411yescharacteristic
67C22×C5×D3—21no—
68C22×C5×D3—21no—
69C22×C5×D3—41no—
70C22×C5×D3—41no—
71C22×C5×D3M1612yes—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5M1612yes—
78C2×C3×C4×C5C2×D412yes—
79C2×C5×Dic3—21no—
80C2×C5×Dic3—21no—
81C2×C5×Dic3—21no—
82C2×C5×Dic3—41no—
83C2×C5×Dic3—41no—
84C2×C5×Dic3C22⋊C411yescharacteristic
85C2×C5×Dic3C22⋊C411yescharacteristic
86C2×C5×Dic3C22⋊C412yes—
87C4×C5×D3—24no—
88C4×C5×D3—24no—
89C3⋊#168—42no—
90C3×#168—42no—
91C22×C4×D3Dic511yescharacteristic
92C2×C3×C4⋊C4C2×D511yescharacteristic
93C2×(C2×D3)⋊C4Dic511yescharacteristic
94C2×(C2×D3)⋊C4C2×D511yescharacteristic
95C2×C4⋊Dic3Dic511yescharacteristic
96C2×C4×Dic3Dic511yescharacteristic
97C2×C4×Dic3C2×D511yescharacteristic
98#892—22no—
99#892—22no—
100C3×C22⋊C8—52no—
101#830—52no—
102#815—102no—
103Dic3⋊C8—102no—
104C24×C5—31no—
105C22×C4×C5—31no—
106C22×C4×C5—31no—
107C22×C4×C5—31no—
108C22×C4×C5—61no—
109C22×C4×C5—61no—
110C22×C4×C5—62no—
111C22×C4×C5—62no—
112C22×C4×C5C4×D311yescharacteristic
113C22×C4×C5C4×D311yescharacteristic
114C22×C4×C5C22×D311yescharacteristic
115C5×C4⋊C4—22no—
116C5×C4⋊C4—62no—
117C5×C22⋊C4—62no—
118C5×C22⋊C4—62no—
119C42×C5—32no—
120C42×C5—32no—
121C42×C5—61no—
122C42×C5—61no—
123C2×#168—22no—
124C2×#168—62no—
125C2×#117—31no—
126#432—152no—
127#324—51no—
128#324—151no—
129#323—152no—
130C22×C3×C5—21no—
131C22×C3×C5—21no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5C2×M1611yescharacteristic
134C22×C3×C5C2×M1611yescharacteristic
135C2×C5×D3—22no—
136C2×C5×D3—42no—
137C2×C5×D3—41no—
138C2×C5×D3—41no—
139C2×C5×D3—42no—
140C3×C4×C5—22no—
141C3×C4×C5—22no—
142C3×C4×C5—41no—
143C5×Dic3—21no—
144C5×Dic3—21no—
145C5×Dic3—22no—
146C5×Dic3—41no—
147C23×D3C2×Dic511yescharacteristic
148C22×C3×C4C2×Dic511yescharacteristic
149C22×C3×C4C2×Dic511yescharacteristic
150C22×C3×C4C22×D511yescharacteristic
151C22×Dic3C2×Dic511yescharacteristic
152C22×Dic3C2×Dic511yescharacteristic
153C22×Dic3C2×Dic511yescharacteristic
154C2×C4×D3—22no—
155C2×C4×D3—22no—
156C2×C4×D3—21no—
157C2×C4×D3—21no—
158C2×C3×C8—102no—
159C3×C4⋊C4—22no—
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—22no—
162C4⋊Dic3—22no—
163C4×Dic3—21no—
164C4×Dic3—21no—
165C4×Dic3C22⋊D512yes—
166C4×Dic3C22⋊D512yes—
167C2×C3⋊C8—102no—
168C23×C5—32no—
169C23×C5—61no—
170C23×C5—61no—
171C23×C5—121no—
172C23×C5—121no—
173C23×C5C2×C4×D311yescharacteristic
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—31no—
178C2×C4×C5—31no—
179C2×C4×C5—32no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—64no—
183C2×C4×C5—64no—
184C2×C4×C5—61no—
185C2×C4×C5—61no—
186C2×C4×C5—61no—
187C2×C4×C5—121no—
188C2×C4×C5—121no—
189C2×C4×C5ΓL(1,𝔽25)12yes—
190C2×C4×C5D3×D412yes—
191#168—42no—
192#168—122no—
193C23×C4—31no—
194#117—62no—
195#117—62no—
196C2×C4⋊C4—31no—
197C2×C4⋊C4D3×D511yescharacteristic
198C2×C22⋊C4—31no—
199C2×C22⋊C4—31no—
200C2×C42—31no—
201C2×C42—31no—
202C4⋊C8—302no—
203C22⋊C8—52no—
204C22⋊C8—152no—
205#97—302no—
206C2×C3×C5—21no—
207C2×C3×C5—21no—
208C2×C3×C5#40711yescharacteristic
209C2×C3×C5#41011yescharacteristic
210C2×C3×C5#41311yescharacteristic
211C5×D3—42no—
212C23×C3C22×Dic511yescharacteristic
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—41no—
216C22×D3—41no—
217C22×D3#68112yes—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4#68112yes—
224C2×C3×C4C2×C22⋊D512yes—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—41no—
229C2×Dic3—41no—
230C2×Dic3C22⋊Dic511yescharacteristic
231C2×Dic3C22⋊Dic511yescharacteristic
232C2×Dic3C22⋊Dic512yes—
233C4×D3—24no—
234C4×D3—24no—
235C3×C8—202no—
236C3⋊C8—202no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—62no—
240C22×C5—122no—
241C22×C5—122no—
242C22×C5—121no—
243C22×C5—121no—
244C22×C5D3×C22⋊C411yescharacteristic
245C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
246C22×C5D3×M1611yescharacteristic
247C4×C5—22no—
248C4×C5—22no—
249C4×C5—41no—
250C4×C5—61no—
251C4×C5—61no—
252C4×C5—62no—
253C4×C5—121no—
254C24—31no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—61no—
259C22×C4—61no—
260C22×C4—62no—
261C22×C4—62no—
262C22×C4D3×Dic511yescharacteristic
263C22×C4D3×Dic511yescharacteristic
264C22×C4C2×D3×D511yescharacteristic
265C2×C8—102no—
266C2×C8—302no—
267C4⋊C4—22no—
268C4⋊C4—62no—
269C22⋊C4—62no—
270C22⋊C4—62no—
271C42—32no—
272C42—32no—
273C42—61no—
274C42—61no—
275C3×C5#146411yescharacteristic, complemented, Hall
276C22×C3—21no—
277C22×C3—21no—
278C22×C3C2×#68111yescharacteristic
279C22×C3C2×#68111yescharacteristic
280C22×C3C2×C22⋊Dic511yescharacteristic
281C2×D3—22no—
282C2×D3—42no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—42no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—41no—
289Dic3—21no—
290Dic3—21no—
291Dic3—22no—
292Dic3—41no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5—122no—
296C2×C5#472611yescharacteristic
297C2×C5#474011yescharacteristic
298C2×C5#475111yescharacteristic
299C23—32no—
300C23—61no—
301C23—61no—
302C23—121no—
303C23—121no—
304C23C2×D3×Dic511yescharacteristic
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—32no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—64no—
314C2×C4—64no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—121no—
319C2×C4—121no—
320C2×C4#665012yes—
321C2×C4D3×C22⋊D512yes—
322C8—202no—
323C8—602no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3#6549611yescharacteristic
327C2×C3#6552611yescharacteristic
328C2×C3#6552911yescharacteristic
329D3—42no—
330C5#6812611yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—62no—
334C22—122no—
335C22—122no—
336C22—121no—
337C22—121no—
338C22D3×#68111yescharacteristic
339C22C2×#665011yescharacteristic
340C22D3×C22⋊Dic511yescharacteristic
341C4—22no—
342C4—22no—
343C4—41no—
344C4—61no—
345C4—61no—
346C4—62no—
347C4—121no—
348C3#1060236511yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—122no—
352C2#1174850511yescharacteristic
353C2#1174917311yescharacteristic
354C2#1174937211yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1464
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11748337C2semidirect
3. #11746349C2semidirect
4. C3×#64748C2semidirect
24. #64748D3semidirect
275. C3×C5#1464semidirect
330. C5#68126semidirect
348. C3#10602365semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8922
#117483372
#117463492
C3×#647482
#117459492
#106023653
#681265