Finite Group Databasebeta

← #14330633

Subgroups — #14330633

Order 1920.

1376 conjugacy classes of subgroups; only the 255 normal subgroups are shown.

normal subgroups only

This group has 1376 conjugacy classes of subgroups — too many to draw. Only its 255 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×#91842C211yesmaximal, characteristic
2C3×C5×#379C211yesmaximal, characteristic, complemented
3#11751348C211yesmaximal, characteristic, complemented
4#11751058C213yesmaximal, complemented
5#11751057C213yesmaximal, complemented
6#11751046C213yesmaximal, complemented
7#11751045C213yesmaximal, complemented
8#10605582—31nomaximal, Hall
9C25×C3×C5C2211yescharacteristic
10C22×#1220C2213yes—
11C22×C4×D15C2211yescharacteristic, complemented
12C2×C3×C5×C22⋊C4C2213yes—
13C2×C3×C5×C22⋊C4C2213yes—
14#91842C418yescomplemented
15C2×#6719C2213yes—
16C2×#6719C2213yes—
17C2×#6719C2213yes—
18C2×#6714C2213yescomplemented
19C2×#6712C2213yescomplemented
20C2×C4×Dic15C2213yescomplemented
21#91115C2213yescomplemented
22#91115C2213yescomplemented
23#73851—51nomaximal, Hall
24C2×#4099—31no—
25C5×#379D311yescharacteristic, complemented
26#65536—31no—
27#65246—33no—
28#65245—33no—
29#65234—33no—
30#65233—33no—
31C24×C3×C5—43no—
32C24×C3×C5—43no—
33C24×C3×C5C2×C414yescomplemented
34C24×C3×C5C2313yes—
35C23×D15C2311yescharacteristic
36C22×C3×C4×C5C2313yes—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—43no—
39C2×#1220—43no—
40C2×#1220C2×C4112yes—
41C22×Dic15C2313yes—
42C22×Dic15C2311yescharacteristic
43C22×Dic15C2313yes—
44C2×C4×D15—43no—
45C3×C5×C22⋊C4—43no—
46C3×C5×C22⋊C4—43no—
47#6719—43no—
48#6719—43no—
49#6719C2×C4112yescomplemented
50#6714—43no—
51#6712—43no—
52C4×Dic15—43no—
53C2×#953—51no—
54C3×#379D511yescharacteristic, complemented
55#5247—51no—
56#4957—53no—
57#4956—53no—
58#4945—53no—
59#4944—53no—
60C25×C5C2×D311yescharacteristic
61C22×C22⋊D5—33no—
62C22×C4×D5—31no—
63C2×C5×C22⋊C4C2×D313yes—
64C2×C5×C22⋊C4C2×D313yes—
65#4099—38no—
66C2×C22⋊Dic5—33no—
67C2×C22⋊Dic5—33no—
68C2×C22⋊Dic5—33no—
69C2×#685—33no—
70C2×#683—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×D15—23no—
87C22×D15—23no—
88C22×D15C22×C412yes—
89C2×C3×C4×C5—23no—
90C2×C3×C4×C5—23no—
91C2×C3×C4×C5—23no—
92C2×C3×C4×C5—23no—
93#1220—412no—
94C2×Dic15—23no—
95C2×Dic15—23no—
96C2×Dic15—23no—
97C2×Dic15—23no—
98C2×Dic15—23no—
99C2×Dic15—23no—
100C2×Dic15C22×C416yes—
101C4×D15—44no—
102C25×C3C2×D511yescharacteristic
103C22×#67—53no—
104C22×C4×D3—51no—
105C2×C3×C22⋊C4C2×D513yes—
106C2×C3×C22⋊C4C2×D513yes—
107#953—58no—
108C2×#217—53no—
109C2×#217—53no—
110C2×#217—53no—
111C2×(C2×D3)⋊C4—53no—
112C2×Dic3⋊C4—53no—
113C2×C4×Dic3—53no—
114C3⋊#95—53no—
115C3⋊#95—53no—
116C24×C5—43no—
117C24×C5—43no—
118C24×C5C4×D314yescomplemented
119C24×C5C22×D313yes—
120C23×D5—31no—
121C22×C4×C5C22×D311yescharacteristic
122C22×C4×C5C22×D313yes—
123C2×C22⋊D5—312no—
124C2×C22⋊D5—123no—
125C2×C22⋊D5—123no—
126C22×Dic5—33no—
127C22×Dic5—31no—
128C22×Dic5—33no—
129C2×C4×D5—123no—
130C5×C22⋊C4—43no—
131C5×C22⋊C4—43no—
132C22⋊Dic5—312no—
133C22⋊Dic5—123no—
134C22⋊Dic5—123no—
135#685—123no—
136#683—123no—
137C4×Dic5—123no—
138C2×#120—151no—
139#390—153no—
140#388—153no—
141#388—153no—
142#386—153no—
143#379—151no—
144#379D1511yescharacteristic, complemented
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×D15—26no—
157C2×D15—43no—
158C2×D15—41no—
159C3×C4×C5—43no—
160C3×C4×C5—41no—
161Dic15—26no—
162Dic15—43no—
163Dic15—41no—
164C24×C3—43no—
165C24×C3—43no—
166C24×C3C4×D514yescomplemented
167C24×C3C22×D513yes—
168C23×D3—51no—
169C22×C3×C4C22×D511yescharacteristic
170C22×C3×C4C22×D513yes—
171C2×#67—512no—
172C2×#67—203no—
173C2×#67—203no—
174C22×Dic3—53no—
175C22×Dic3—51no—
176C22×Dic3—53no—
177C2×C4×D3—203no—
178C3×C22⋊C4—43no—
179C3×C22⋊C4—43no—
180#217—512no—
181#217—203no—
182#217—203no—
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—412no—
193C23×C5—44no—
194C23×C5—412no—
195C23×C5C2×C4×D316yes—
196C23×C5C23×D311yescharacteristic
197C22×D5—32no—
198C22×D5—63no—
199C22×D5—63no—
200C2×C4×C5—23no—
201C2×C4×C5—23no—
202C2×C4×C5—23no—
203C2×C4×C5—23no—
204C22⋊D5—1212no—
205C2×Dic5—36no—
206C2×Dic5—63no—
207C2×Dic5—63no—
208C2×Dic5—63no—
209C2×Dic5—63no—
210C2×Dic5—63no—
211C2×Dic5—63no—
212C4×D5—124no—
213C25C2×D1511yescharacteristic
214C22×D4—153no—
215C23×C4—151no—
216#120—158no—
217C2×C4⋊C4—153no—
218C2×C22⋊C4—153no—
219C2×C22⋊C4—153no—
220C2×C22⋊C4—153no—
221C2×C22⋊C4—153no—
222C2×C22⋊C4C2×D1513yes—
223C2×C22⋊C4C2×D1513yes—
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
231D15—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×C3C2×C4×D516yes—
242C23×C3C23×D511yescharacteristic
243C22×D3—52no—
244C22×D3—103no—
245C22×D3—103no—
246C2×C3×C4—23no—
247C2×C3×C4—23no—
248C2×C3×C4—23no—
249C2×C3×C4—23no—
250#67—2012no—
251C2×Dic3—56no—
252C2×Dic3—103no—
253C2×Dic3—103no—
254C2×Dic3—103no—
255C2×Dic3—103no—
256C2×Dic3—103no—
257C2×Dic3—103no—
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×C5C22×C4×D311yescharacteristic
268C22×C5#100413yes—
269C22×C5#100413yes—
270C2×D5—66no—
271C2×D5—121no—
272C2×D5—123no—
273C4×C5—41no—
274C4×C5—43no—
275Dic5—66no—
276Dic5—121no—
277Dic5—123no—
278C24—43no—
279C24—43no—
280C24—151no—
281C24C4×D1514yescomplemented
282C24C22×D1513yes—
283C2×D4—1512no—
284C2×D4—603no—
285C2×D4—603no—
286C22×C4—153no—
287C22×C4—151no—
288C22×C4—153no—
289C22×C4—603no—
290C22×C4C22×D1511yescharacteristic
291C22×C4C22×D1513yes—
292C4⋊C4—603no—
293C22⋊C4—43no—
294C22⋊C4—43no—
295C22⋊C4—1512no—
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×C3C22×C4×D511yescharacteristic
310C22×C3#414413yes—
311C22×C3#414413yes—
312C2×D3—106no—
313C2×D3—201no—
314C2×D3—203no—
315C3×C4—41no—
316C3×C4—43no—
317Dic3—106no—
318Dic3—201no—
319Dic3—203no—
320C2×C5—46no—
321C2×C5#548613yes—
322C2×C5#559411yescharacteristic
323C2×C5#559513yes—
324D5—122no—
325C23—23no—
326C23—23no—
327C23—23no—
328C23—23no—
329C23—23no—
330C23—23no—
331C23—412no—
332C23—44no—
333C23—412no—
334C23—152no—
335C23—303no—
336C23—303no—
337C23C2×C4×D1516yes—
338C23C23×D1511yescharacteristic
339D4—6012no—
340C2×C4—23no—
341C2×C4—23no—
342C2×C4—23no—
343C2×C4—23no—
344C2×C4—156no—
345C2×C4—303no—
346C2×C4—303no—
347C2×C4—303no—
348C2×C4—303no—
349C2×C4—303no—
350C2×C4—303no—
351C2×C4—604no—
352C2×C3—46no—
353C2×C3#6582013yes—
354C2×C3#6592811yescharacteristic
355C2×C3#6592913yes—
356D3—202no—
357C5#7385111yescharacteristic, complemented, Sylow
358C22—26no—
359C22—26no—
360C22—26no—
361C22—416no—
362C22—43no—
363C22—43no—
364C22—43no—
365C22—43no—
366C22—306no—
367C22—601no—
368C22—603no—
369C22C22×C4×D1511yescharacteristic
370C22#9209513yes—
371C22#9209513yes—
372C4—41no—
373C4—43no—
374C4—306no—
375C4—601no—
376C4—603no—
377C3#1060558211yescharacteristic, complemented, Sylow
378C2—46no—
379C2—602no—
380C2#1175624513yes—
381C2#1175635311yescharacteristic
382C2#1175635413yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#379C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91842C2
hypercenter#379D15
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C3×C5×#379C2semidirect
3. #11751348C2semidirect
4. #11751058C2semidirect
5. #11751057C2semidirect
6. #11751046C2semidirect
7. #11751045C2semidirect
11. C22×C4×D15C22semidirect
14. #91842C4semidirect
18. C2×#6714C22semidirect
19. C2×#6712C22semidirect
20. C2×C4×Dic15C22semidirect
21. #91115C22semidirect
22. #91115C22semidirect
25. C5×#379D3semidirect
33. C24×C3×C5C2×C4semidirect
49. #6719C2×C4semidirect
54. C3×#379D5semidirect
118. C24×C5C4×D3semidirect
144. #379D15semidirect
166. C24×C3C4×D5semidirect
281. C24C4×D15semidirect
300. C3×C5#2375semidirect
357. C5#73851semidirect
377. C3#10605582semidirect

Maximal subgroups

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

subgroupindex
C2×#918422
C3×C5×#3792
#117513482
#117510582
#117510572
#117510462
#117510452
#106055823
#738515