Finite Group Databasebeta

← #14330669

Subgroups — #14330669

Order 1920.

1376 conjugacy classes of subgroups; only the 284 normal subgroups are shown.

normal subgroups only

This group has 1376 conjugacy classes of subgroups — too many to draw. Only its 284 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×#953C211yesmaximal, characteristic
2#11751348C211yesmaximal, characteristic, complemented
3C3×#65536C211yesmaximal, characteristic, complemented
4#11749519C213yesmaximal, complemented
5#11749482C213yesmaximal, complemented
6#11749479C213yesmaximal, complemented
7#11749478C213yesmaximal, complemented
8#10614311—31nomaximal, Hall
9C25×C3×C5C2211yescharacteristic
10C22×C5×#67C2213yes—
11C22×D3×Dic5C2211yescharacteristic, complemented
12C2×#6719C2213yes—
13C2×#6719C2213yes—
14C5×#953C418yescomplemented
15C2×C5×#217C2213yes—
16C2×C3×C22⋊Dic5C2213yes—
17C2×C3×C22⋊Dic5C2213yes—
18C2×Dic3⋊Dic5C2213yescomplemented
19C2×(C2×D3)⋊Dic5C2213yescomplemented
20C2×Dic3×Dic5C2213yescomplemented
21#90994C2213yescomplemented
22#90994C2213yescomplemented
23#73851—51nomaximal, Hall
24C2×C5×#120—31no—
25#65536—31no—
26#65536D311yescharacteristic, complemented
27#65510—33no—
28#65509—33no—
29#65240—33no—
30#65240—33no—
31C24×C3×C5—43no—
32C24×C3×C5—43no—
33C24×C3×C5C2×C414yescomplemented
34C24×C3×C5C2313yes—
35C23×C5×D3C2311yescharacteristic
36C22×Dic15C2311yescharacteristic
37C22×Dic15C2313yes—
38C2×C5×#67—43no—
39C2×C5×#67—43no—
40C2×C5×#67C2×C4112yes—
41C22×C5×Dic3C2313yes—
42C22×C3×Dic5C2311yescharacteristic
43C22×C3×Dic5C2313yes—
44C2×D3×Dic5—43no—
45#6719—43no—
46#6719—43no—
47C5×#217C2×C4112yescomplemented
48C3×C22⋊Dic5—43no—
49C3×C22⋊Dic5—43no—
50Dic3⋊Dic5—43no—
51(C2×D3)⋊Dic5—43no—
52Dic3×Dic5—43no—
53C2×#953D511yescharacteristic
54C3×#379—51no—
55#5247—51no—
56#4957—53no—
57#4956—53no—
58#4945—53no—
59#4944—53no—
60C25×C5C2×D311yescharacteristic
61C22×C5×D4—33no—
62C23×Dic5—31no—
63C5×#120—38no—
64C2×C5×C22⋊C4—33no—
65C2×C22⋊Dic5—33no—
66C2×C22⋊Dic5—33no—
67C2×C22⋊Dic5—33no—
68C2×C22⋊Dic5C2×D313yes—
69C2×C22⋊Dic5C2×D313yes—
70C2×C4⋊Dic5—33no—
71C2×C4×Dic5—33no—
72#3963—33no—
73#3963—33no—
74#2375—151noSylow
75C23×C3×C5—23no—
76C23×C3×C5—23no—
77C23×C3×C5—23no—
78C23×C3×C5—23no—
79C23×C3×C5—23no—
80C23×C3×C5—23no—
81C23×C3×C5—412no—
82C23×C3×C5—412no—
83C23×C3×C5—44no—
84C23×C3×C5C22×C416yes—
85C23×C3×C5C2411yescharacteristic
86C22×C5×D3—23no—
87C22×C5×D3—23no—
88C22×C5×D3C22×C412yes—
89C2×Dic15—23no—
90C2×Dic15—23no—
91C2×Dic15—23no—
92C2×Dic15—23no—
93C5×#67—412no—
94C2×C5×Dic3—23no—
95C2×C5×Dic3—23no—
96C2×C5×Dic3C22×C416yes—
97C2×C3×Dic5—23no—
98C2×C3×Dic5—23no—
99C2×C3×Dic5—23no—
100C2×C3×Dic5—23no—
101D3×Dic5—44no—
102C25×C3C2×D511yescharacteristic
103C22×#67C2×D513yes—
104C22×C4×D3—51no—
105C2×C3×C22⋊C4—53no—
106C2×C3×C22⋊C4—53no—
107#953Dic518yescomplemented
108C2×#217—53no—
109C2×#217—53no—
110C2×#217C2×D513yes—
111C2×(C2×D3)⋊C4—53no—
112C2×Dic3⋊C4—53no—
113C2×C4×Dic3—53no—
114C3⋊#95—53no—
115C3⋊#95—53no—
116C24×C5—31no—
117C24×C5—43no—
118C24×C5—43no—
119C24×C5C4×D314yescomplemented
120C24×C5C22×D313yes—
121C2×C5×D4—312no—
122C2×C5×D4—123no—
123C2×C5×D4—123no—
124C22×C4×C5—33no—
125C22×Dic5—33no—
126C22×Dic5—31no—
127C22×Dic5—123no—
128C22×Dic5C22×D313yes—
129C22×Dic5C22×D311yescharacteristic
130C5×C22⋊C4—312no—
131C22⋊Dic5—43no—
132C22⋊Dic5—43no—
133C22⋊Dic5—123no—
134C22⋊Dic5—123no—
135C22⋊Dic5—123no—
136C4⋊Dic5—123no—
137C4×Dic5—123no—
138C2×#120—31no—
139#390—153no—
140#388—153no—
141#388—153no—
142#386—153no—
143#379—51no—
144#379—151no—
145C22×C3×C5—26no—
146C22×C3×C5—26no—
147C22×C3×C5—26no—
148C22×C3×C5—416no—
149C22×C3×C5—43no—
150C22×C3×C5—43no—
151C22×C3×C5—43no—
152C22×C3×C5—43no—
153C22×C3×C5C23×C411yescharacteristic
154C22×C3×C5H(5,𝔽2)13yes—
155C22×C3×C5H(5,𝔽2)13yes—
156C2×C5×D3—26no—
157C2×C5×D3—43no—
158C2×C5×D3—41no—
159Dic15—43no—
160Dic15—41no—
161C3×Dic5—43no—
162C3×Dic5—41no—
163C5×Dic3—26no—
164C24×C3—43no—
165C24×C3—43no—
166C24×C3C2×Dic514yescomplemented
167C24×C3C22×D513yes—
168C23×D3C22×D511yescharacteristic
169C22×C3×C4—51no—
170C22×C3×C4—53no—
171C2×#67—43no—
172C2×#67—43no—
173C2×#67C2×Dic5112yes—
174C22×Dic3—51no—
175C22×Dic3—53no—
176C22×Dic3C22×D513yes—
177C2×C4×D3—203no—
178C3×C22⋊C4—203no—
179C3×C22⋊C4—203no—
180#217—203no—
181#217—203no—
182#217C2×Dic5112yescomplemented
183(C2×D3)⋊C4—203no—
184Dic3⋊C4—203no—
185C4×Dic3—203no—
186C23×C5—23no—
187C23×C5—23no—
188C23×C5—23no—
189C23×C5—23no—
190C23×C5—23no—
191C23×C5—23no—
192C23×C5—32no—
193C23×C5—412no—
194C23×C5—44no—
195C23×C5—412no—
196C23×C5—63no—
197C23×C5—63no—
198C23×C5C2×C4×D316yes—
199C23×C5C23×D311yescharacteristic
200C5×D4—1212no—
201C2×C4×C5—36no—
202C2×C4×C5—63no—
203C2×C4×C5—63no—
204C2×Dic5—23no—
205C2×Dic5—23no—
206C2×Dic5—23no—
207C2×Dic5—23no—
208C2×Dic5—63no—
209C2×Dic5—63no—
210C2×Dic5—63no—
211C2×Dic5—63no—
212C2×Dic5—124no—
213C25D3×D511yescharacteristic
214C22×D4—33no—
215C23×C4—151no—
216#120—38no—
217C2×C4⋊C4—153no—
218C2×C22⋊C4—33no—
219C2×C22⋊C4—53no—
220C2×C22⋊C4—53no—
221C2×C22⋊C4—153no—
222C2×C22⋊C4—153no—
223C2×C22⋊C4—153no—
224C2×C42—153no—
225#95—153no—
226#95—153no—
227C2×C3×C5—46no—
228C2×C3×C5#51813yes—
229C2×C3×C5#56013yes—
230C2×C3×C5H(3,𝔽4)11yescharacteristic
231C5×D3—42no—
232C23×C3—23no—
233C23×C3—23no—
234C23×C3—23no—
235C23×C3—23no—
236C23×C3—23no—
237C23×C3—23no—
238C23×C3—412no—
239C23×C3—44no—
240C23×C3—412no—
241C23×C3C22×Dic516yes—
242C23×C3C23×D511yescharacteristic
243C22×D3—23no—
244C22×D3—23no—
245C22×D3C22×Dic512yes—
246C2×C3×C4—103no—
247C2×C3×C4—103no—
248C2×C3×C4—103no—
249C2×C3×C4—103no—
250#67—412no—
251C2×Dic3—23no—
252C2×Dic3—23no—
253C2×Dic3—103no—
254C2×Dic3—103no—
255C2×Dic3—103no—
256C2×Dic3—103no—
257C2×Dic3C22×Dic516yes—
258C4×D3—204no—
259C22×C5—26no—
260C22×C5—26no—
261C22×C5—26no—
262C22×C5—416no—
263C22×C5—43no—
264C22×C5—43no—
265C22×C5—43no—
266C22×C5—43no—
267C22×C5—66no—
268C22×C5—121no—
269C22×C5—123no—
270C22×C5C22×C4×D311yescharacteristic
271C22×C5#100413yes—
272C22×C5#100413yes—
273C4×C5—66no—
274Dic5—41no—
275Dic5—43no—
276Dic5—121no—
277Dic5—123no—
278C24—31no—
279C24—43no—
280C24—43no—
281C24D3×Dic514yescomplemented
282C24C2×D3×D513yes—
283C2×D4—312no—
284C2×D4—123no—
285C2×D4—123no—
286C22×C4—33no—
287C22×C4—51no—
288C22×C4—53no—
289C22×C4—151no—
290C22×C4—153no—
291C22×C4—603no—
292C4⋊C4—603no—
293C22⋊C4—312no—
294C22⋊C4—203no—
295C22⋊C4—203no—
296C22⋊C4—603no—
297C22⋊C4—603no—
298C22⋊C4—603no—
299C42—603no—
300C3×C5#237511yescharacteristic, complemented, Hall
301C22×C3—26no—
302C22×C3—26no—
303C22×C3—26no—
304C22×C3—416no—
305C22×C3—43no—
306C22×C3—43no—
307C22×C3—43no—
308C22×C3—43no—
309C22×C3#414413yes—
310C22×C3#414413yes—
311C22×C3C23×Dic511yescharacteristic
312C2×D3—26no—
313C2×D3—41no—
314C2×D3—43no—
315C3×C4—201no—
316C3×C4—203no—
317Dic3—26no—
318Dic3—201no—
319Dic3—203no—
320C2×C5—46no—
321C2×C5—122no—
322C2×C5#548613yes—
323C2×C5#559411yescharacteristic
324C2×C5#559513yes—
325C23—23no—
326C23—23no—
327C23—23no—
328C23—23no—
329C23—23no—
330C23—23no—
331C23—32no—
332C23—412no—
333C23—412no—
334C23—44no—
335C23—63no—
336C23—63no—
337C23C2×D3×Dic516yes—
338C23C22×D3×D511yescharacteristic
339D4—1212no—
340C2×C4—36no—
341C2×C4—63no—
342C2×C4—63no—
343C2×C4—103no—
344C2×C4—103no—
345C2×C4—103no—
346C2×C4—103no—
347C2×C4—303no—
348C2×C4—303no—
349C2×C4—303no—
350C2×C4—303no—
351C2×C4—604no—
352C2×C3—46no—
353C2×C3#6592811yescharacteristic
354C2×C3#6592913yes—
355C2×C3#6613213yes—
356D3—42no—
357C5#7385111yescharacteristic, complemented, Sylow
358C22—26no—
359C22—26no—
360C22—26no—
361C22—416no—
362C22—43no—
363C22—43no—
364C22—43no—
365C22—43no—
366C22—66no—
367C22—123no—
368C22—121no—
369C22C22×D3×Dic511yescharacteristic
370C22#9204913yes—
371C22#9204913yes—
372C4—66no—
373C4—203no—
374C4—201no—
375C4—603no—
376C4—601no—
377C3#1061431111yescharacteristic, complemented, Sylow
378C2—46no—
379C2—122no—
380C2#1175540513yes—
381C2#1175541013yes—
382C2#1175544311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC25×C3×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#953C2
hypercenterC25D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. #11751348C2semidirect
3. C3×#65536C2semidirect
4. #11749519C2semidirect
5. #11749482C2semidirect
6. #11749479C2semidirect
7. #11749478C2semidirect
11. C22×D3×Dic5C22semidirect
14. C5×#953C4semidirect
18. C2×Dic3⋊Dic5C22semidirect
19. C2×(C2×D3)⋊Dic5C22semidirect
20. C2×Dic3×Dic5C22semidirect
21. #90994C22semidirect
22. #90994C22semidirect
26. #65536D3semidirect
33. C24×C3×C5C2×C4semidirect
47. C5×#217C2×C4semidirect
107. #953Dic5semidirect
119. C24×C5C4×D3semidirect
166. C24×C3C2×Dic5semidirect
182. #217C2×Dic5semidirect
281. C24D3×Dic5semidirect
300. C3×C5#2375semidirect
357. C5#73851semidirect
377. C3#10614311semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9532
#117513482
C3×#655362
#117495192
#117494822
#117494792
#117494782
#106143113
#738515