Finite Group Databasebeta

← #14280798

Subgroups — #14280798

Order 1920.

528 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 117 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×#91766C211yesmaximal, characteristic
2#11750819C212yesmaximal, complemented
3C3×C5×#323C211yesmaximal, characteristic
4#11746346C211yesmaximal, characteristic
5#11746290C212yesmaximal, complemented
6#10598893—31nomaximal, Hall
7C23×Dic15C411yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C411yescharacteristic
10C2×#6712C411yescharacteristic
11C2×#6712C2211yescharacteristic
12C2×C4×Dic15C411yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14#91766—22no—
15#91766—22no—
16C3×C5×C22⋊C8C2212yes—
17#91114C2212yes—
18#91098—22no—
19C8×Dic15—22no—
20#68100—51nomaximal, Hall
21C2×#4023—31no—
22#65007—32no—
23C5×#323D311yescharacteristic
24#64745—31no—
25#64689—32no—
26C24×C3×C5C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×Dic15—21no—
30C22×Dic15—21no—
31C22×Dic15—22no—
32C22×Dic15C814yescomplemented
33C22×Dic15C2×C411yescharacteristic
34C22×Dic15C2×C411yescharacteristic
35C22×Dic15C2×C411yescharacteristic
36C22×Dic15C2×C411yescharacteristic
37C2×C3×C5×C8—22no—
38C3×C5×C22⋊C4—22no—
39#6719—22no—
40#6712—22no—
41#6712—22no—
42C4×Dic15—21no—
43C4×Dic15—21no—
44C4×Dic15D412yes—
45C4×Dic15D412yes—
46C2×C3⋊#168—22no—
47C2×#877—51no—
48#4718—52no—
49C3×#323D511yescharacteristic
50#4525—51no—
51#4469—52no—
52C23×Dic5—31no—
53C2×C5×C22⋊C4C2×D311yescharacteristic
54C2×C22⋊Dic5—31no—
55C2×#683—31no—
56C2×#683—31no—
57C2×C4×Dic5—31no—
58C2×C4×Dic5—31no—
59#4023—62no—
60#4023—62no—
61C5×C22⋊C8C2×D312yes—
62C22⋊#168—32no—
63#3946—62no—
64C8×Dic5—62no—
65#1458—151noSylow
66C23×C3×C5—21no—
67C23×C3×C5—21no—
68C23×C3×C5—41no—
69C23×C3×C5—41no—
70C23×C3×C5C2×C812yes—
71C23×C3×C5C22×C411yescharacteristic
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D412yes—
76C2×Dic15—21no—
77C2×Dic15—21no—
78C2×Dic15—24no—
79C2×Dic15—24no—
80C2×Dic15—21no—
81C2×Dic15—41no—
82C2×Dic15—41no—
83C2×Dic15C22⋊C412yes—
84C2×Dic15C22⋊C411yescharacteristic
85C2×Dic15C22⋊C411yescharacteristic
86C2×Dic15C2×C812yes—
87C2×Dic15C2×C812yes—
88C2×Dic15M1612yes—
89C3×C5×C8—42no—
90C3⋊#168—42no—
91C23×Dic3—51no—
92C2×C3×C22⋊C4C2×D511yescharacteristic
93C2×#217—51no—
94C2×Dic3⋊C4—51no—
95C2×Dic3⋊C4—51no—
96C2×C4×Dic3—51no—
97C2×C4×Dic3—51no—
98#877—102no—
99#877—102no—
100C3×C22⋊C8C2×D512yes—
101#830—52no—
102Dic3⋊C8—102no—
103C8×Dic3—102no—
104C24×C5C4×D311yescharacteristic
105C22×C4×C5C4×D311yescharacteristic
106C22×C4×C5C22×D311yescharacteristic
107C22×Dic5—31no—
108C22×Dic5—34no—
109C22×Dic5—31no—
110C22×Dic5—31no—
111C22×Dic5—31no—
112C22×Dic5—62no—
113C22×Dic5—61no—
114C22×Dic5—61no—
115C2×C5×C8—22no—
116C5×C22⋊C4—22no—
117C22⋊Dic5—62no—
118#683—62no—
119#683—62no—
120C4×Dic5—32no—
121C4×Dic5—32no—
122C4×Dic5—61no—
123C4×Dic5—61no—
124C2×#168—62no—
125C2×#117—151no—
126#431—152no—
127#324—152no—
128#323—151no—
129#323D1511yescharacteristic
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×C5C22×C811yescharacteristic
139C22×C3×C5C2×M1611yescharacteristic
140C3×C4×C5—22no—
141C3×C4×C5—41no—
142Dic15—22no—
143Dic15—22no—
144Dic15—41no—
145Dic15C22⋊C812yes—
146Dic15C22⋊C812yes—
147C24×C3C4×D511yescharacteristic
148C22×C3×C4C4×D511yescharacteristic
149C22×C3×C4C22×D511yescharacteristic
150C22×Dic3—51no—
151C22×Dic3—54no—
152C22×Dic3—51no—
153C22×Dic3—51no—
154C22×Dic3—51no—
155C22×Dic3—101no—
156C22×Dic3—101no—
157C22×Dic3—102no—
158C2×C3×C8—22no—
159C3×C22⋊C4—22no—
160#217—102no—
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×C5D3×C812yes—
173C23×C5C2×C4×D311yescharacteristic
174C2×C4×C5—21no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5D3×D412yes—
178C2×Dic5—31no—
179C2×Dic5—31no—
180C2×Dic5—32no—
181C2×Dic5—32no—
182C2×Dic5—32no—
183C2×Dic5—32no—
184C2×Dic5—64no—
185C2×Dic5—64no—
186C2×Dic5—61no—
187C2×Dic5—61no—
188C2×Dic5—61no—
189C2×Dic5—121no—
190C2×Dic5—121no—
191C5×C8—42no—
192#168—122no—
193C23×C4—151no—
194#117—302no—
195#117—302no—
196C2×C4⋊C4—151no—
197C2×C4⋊C4—151no—
198C2×C22⋊C4—151no—
199C2×C22⋊C4C2×D1511yescharacteristic
200C2×C42—151no—
201C2×C42—151no—
202C4⋊C8—302no—
203C22⋊C8—152no—
204C22⋊C8C2×D1512yes—
205C4×C8—302no—
206C2×C3×C5—21no—
207C2×C3×C5—21no—
208C2×C3×C5—42no—
209C2×C3×C5C2×C22⋊C811yescharacteristic
210C2×C3×C5#41011yescharacteristic
211C2×C3×C5#41311yescharacteristic
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3C8×D512yes—
217C23×C3C2×C4×D511yescharacteristic
218C2×C3×C4—21no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4D4×D512yes—
222C2×Dic3—51no—
223C2×Dic3—51no—
224C2×Dic3—52no—
225C2×Dic3—52no—
226C2×Dic3—52no—
227C2×Dic3—52no—
228C2×Dic3—104no—
229C2×Dic3—104no—
230C2×Dic3—101no—
231C2×Dic3—101no—
232C2×Dic3—101no—
233C2×Dic3—201no—
234C2×Dic3—201no—
235C3×C8—42no—
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×D3×C811yescharacteristic
246C22×C5D3×M1611yescharacteristic
247C4×C5—22no—
248C4×C5—41no—
249Dic5—32no—
250Dic5—32no—
251Dic5—62no—
252Dic5—62no—
253Dic5—121no—
254C24C4×D1511yescharacteristic
255C22×C4—151no—
256C22×C4—154no—
257C22×C4—151no—
258C22×C4—151no—
259C22×C4—151no—
260C22×C4—301no—
261C22×C4—301no—
262C22×C4—302no—
263C22×C4C4×D1511yescharacteristic
264C22×C4C22×D1511yescharacteristic
265C2×C8—22no—
266C2×C8—302no—
267C4⋊C4—302no—
268C4⋊C4—302no—
269C22⋊C4—22no—
270C22⋊C4—302no—
271C42—152no—
272C42—152no—
273C42—301no—
274C42—301no—
275C3×C5#145811yescharacteristic, complemented, Hall
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—42no—
280C22×C3—42no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3D5×C22⋊C411yescharacteristic
284C22×C3C2×C8×D511yescharacteristic
285C22×C3D5×M1611yescharacteristic
286C3×C4—22no—
287C3×C4—41no—
288Dic3—52no—
289Dic3—52no—
290Dic3—102no—
291Dic3—102no—
292Dic3—201no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5—42no—
296C2×C5D3×C22⋊C811yescharacteristic
297C2×C5#474011yescharacteristic
298C2×C5#474511yescharacteristic
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23C8×D1512yes—
304C23C2×C4×D1511yescharacteristic
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—151no—
309C2×C4—151no—
310C2×C4—152no—
311C2×C4—152no—
312C2×C4—152no—
313C2×C4—152no—
314C2×C4—304no—
315C2×C4—304no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4—601no—
320C2×C4—601no—
321C2×C4D4×D1512yes—
322C8—42no—
323C8—602no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—42no—
327C2×C3D5×C22⋊C811yescharacteristic
328C2×C3#6502911yescharacteristic
329C2×C3#6503411yescharacteristic
330C5#6810011yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22C22⋊C4×D1511yescharacteristic
339C22C2×C8×D1511yescharacteristic
340C22M16×D1511yescharacteristic
341C4—22no—
342C4—41no—
343C4—152no—
344C4—152no—
345C4—302no—
346C4—302no—
347C4—601no—
348C3#1059889311yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—42no—
352C2D15×C22⋊C811yescharacteristic
353C2#1175084111yescharacteristic
354C2#1175084611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C22×D15
FittingC3×C5×#323C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4×C5C23
hypercenter#323D15
hypocenterC3×C5#1458
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #11750819C2semidirect
5. #11746290C2semidirect
32. C22×Dic15C8semidirect
275. C3×C5#1458semidirect
330. C5#68100semidirect
348. C3#10598893semidirect

Maximal subgroups

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

subgroupindex
C2×#917662
#117508192
C3×C5×#3232
#117463462
#117462902
#105988933
#681005