Finite Group Databasebeta

← #14297136

Subgroups — #14297136

Order 1920.

1340 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 239 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×C3×C5×H(5,𝔽2)C211yesmaximal, characteristic
2#11751321C213yesmaximal, complemented
3C2×#91118C213yesmaximal, complemented
4#10602935—31nomaximal, Hall
5C3×C5×H(5,𝔽2)—26no—
6C3×C5×H(5,𝔽2)C414yescomplemented
7C2×C3×C5×#41—23no—
8C22×C3×C5×D4—23no—
9C22×C3×C5×D4C2213yes—
10C23×Dic15C2211yescharacteristic, complemented
11C2×#6719—23no—
12C2×#6719C2213yescomplemented
13#91118—26no—
14#91115—23no—
15#72142—51nomaximal, Hall
16C2×C5×H(5,𝔽2)D311yescharacteristic
17#65509—33no—
18C2×#3966—33no—
19C24×C3×C5—21no—
20C24×C3×C5D413yes—
21C24×C3×C5C2311yescharacteristic
22C3×C5×#41—212no—
23C3×C5×#41—212no—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×D4—23no—
26C2×C3×C5×D4—212no—
27C2×C3×C5×D4—212no—
28C2×C3×C5×D4—26no—
29C2×C3×C5×D4—26no—
30C2×C3×C5×D4C2×C416yes—
31C2×C3×C5×D4D416yes—
32C22×C3×C4×C5—23no—
33C22×C3×C4×C5D413yes—
34C22×Dic15—23no—
35C22×Dic15—23no—
36C22×Dic15—42no—
37#6719—26no—
38#6719—46no—
39C2×C3×H(5,𝔽2)D511yescharacteristic
40#5220—53no—
41C2×#834—53no—
42C5×H(5,𝔽2)—26no—
43C5×H(5,𝔽2)Dic314yescomplemented
44C2×C5×#41—23no—
45C22×C5×D4—23no—
46C22×C5×D4C2×D313yes—
47C23×Dic5—31no—
48C2×C22⋊Dic5—33no—
49C2×C22⋊Dic5—63no—
50#3966—66no—
51#3963—63no—
52#1790—151noSylow
53C23×C3×C5—24no—
54C23×C3×C5—23no—
55C23×C3×C5—23no—
56C23×C3×C5—41no—
57C23×C3×C5—41no—
58C23×C3×C5—43no—
59C23×C3×C5—43no—
60C23×C3×C5—81no—
61C23×C3×C5—81no—
62C23×C3×C5C22⋊C416yescomplemented
63C23×C3×C5C22×C411yescharacteristic
64C23×C3×C5C2×D413yes—
65C23×C3×C5C2×D413yes—
66C3×C5×Q8—24no—
67C3×C5×D4—212no—
68C3×C5×D4—212no—
69C3×C5×D4—212no—
70C2×C3×C4×C5—212no—
71C2×C3×C4×C5—23no—
72C2×C3×C4×C5—23no—
73C2×C3×C4×C5C22⋊C416yescomplemented
74C2×Dic15—26no—
75C2×Dic15—43no—
76C2×Dic15—41no—
77C2×Dic15—43no—
78C2×Dic15—43no—
79C2×Dic15—43no—
80C3×H(5,𝔽2)—26no—
81C3×H(5,𝔽2)Dic514yescomplemented
82C2×C3×#41—23no—
83C22×C3×D4—23no—
84C22×C3×D4C2×D513yes—
85C23×Dic3—51no—
86C2×#217—53no—
87C2×#217—103no—
88#834—106no—
89C3⋊#95—103no—
90C24×C5—21no—
91C24×C5#6713yes—
92C24×C5C22×D311yescharacteristic
93C5×#41—212no—
94C5×#41—212no—
95C2×C5×Q8—21no—
96C2×C5×D4—23no—
97C2×C5×D4—212no—
98C2×C5×D4—212no—
99C2×C5×D4—26no—
100C2×C5×D4—26no—
101C2×C5×D4C2×Dic316yes—
102C2×C5×D4#6716yes—
103C22×C4×C5—23no—
104C22×C4×C5#6713yes—
105C22×Dic5—63no—
106C22×Dic5—63no—
107C22×Dic5—122no—
108C22⋊Dic5—66no—
109C22⋊Dic5—126no—
110C2×H(5,𝔽2)D1511yescharacteristic
111C2×#99—153no—
112#386—153no—
113C22×C3×C5—23no—
114C22×C3×C5—23no—
115C22×C3×C5—26no—
116C22×C3×C5—41no—
117C22×C3×C5—43no—
118C22×C3×C5—46no—
119C22×C3×C5—43no—
120C22×C3×C5—43no—
121C22×C3×C5—83no—
122C22×C3×C5—84no—
123C22×C3×C5C2×C22⋊C413yes—
124C22×C3×C5#12013yes—
125C22×C3×C5#12011yescharacteristic
126C3×C4×C5—26no—
127Dic15—42no—
128Dic15—83no—
129C24×C3—21no—
130C24×C3C22⋊D513yes—
131C24×C3C22×D511yescharacteristic
132C3×#41—212no—
133C3×#41—212no—
134C2×C3×Q8—21no—
135C2×C3×D4—23no—
136C2×C3×D4—212no—
137C2×C3×D4—212no—
138C2×C3×D4—26no—
139C2×C3×D4—26no—
140C2×C3×D4C2×Dic516yes—
141C2×C3×D4C22⋊D516yes—
142C22×C3×C4—23no—
143C22×C3×C4C22⋊D513yes—
144C22×Dic3—103no—
145C22×Dic3—103no—
146C22×Dic3—202no—
147#217—106no—
148#217—206no—
149C23×C5—24no—
150C23×C5—23no—
151C23×C5—23no—
152C23×C5—41no—
153C23×C5—41no—
154C23×C5—43no—
155C23×C5—43no—
156C23×C5—81no—
157C23×C5—81no—
158C23×C5#21716yescomplemented
159C23×C5C22×Dic311yescharacteristic
160C23×C5C2×#6713yes—
161C23×C5C2×#6713yes—
162C5×Q8—24no—
163C5×D4—212no—
164C5×D4—212no—
165C5×D4—212no—
166C2×C4×C5—212no—
167C2×C4×C5—23no—
168C2×C4×C5—23no—
169C2×C4×C5#21716yescomplemented
170C2×Dic5—66no—
171C2×Dic5—123no—
172C2×Dic5—121no—
173C2×Dic5—123no—
174C2×Dic5—123no—
175C2×Dic5—123no—
176H(5,𝔽2)—26no—
177H(5,𝔽2)Dic1514yescomplemented
178C2×#41—23no—
179C22×D4—23no—
180C22×D4C2×D1513yes—
181C23×C4—151no—
182C2×C22⋊C4—153no—
183C2×C22⋊C4—303no—
184#99—306no—
185#95—303no—
186C2×C3×C5—23no—
187C2×C3×C5—23no—
188C2×C3×C5—46no—
189C2×C3×C5#37911yescharacteristic
190C2×C3×C5B(4,𝔽2)11yescharacteristic
191C2×C3×C5#45811yescharacteristic
192C23×C3—24no—
193C23×C3—23no—
194C23×C3—23no—
195C23×C3—41no—
196C23×C3—41no—
197C23×C3—43no—
198C23×C3—43no—
199C23×C3—81no—
200C23×C3—81no—
201C23×C3C22⋊Dic516yescomplemented
202C23×C3C22×Dic511yescharacteristic
203C23×C3C2×C22⋊D513yes—
204C23×C3C2×C22⋊D513yes—
205C3×Q8—24no—
206C3×D4—212no—
207C3×D4—212no—
208C3×D4—212no—
209C2×C3×C4—212no—
210C2×C3×C4—23no—
211C2×C3×C4—23no—
212C2×C3×C4C22⋊Dic516yescomplemented
213C2×Dic3—106no—
214C2×Dic3—203no—
215C2×Dic3—201no—
216C2×Dic3—203no—
217C2×Dic3—203no—
218C2×Dic3—203no—
219C22×C5—23no—
220C22×C5—23no—
221C22×C5—26no—
222C22×C5—41no—
223C22×C5—43no—
224C22×C5—46no—
225C22×C5—43no—
226C22×C5—43no—
227C22×C5—83no—
228C22×C5—84no—
229C22×C5C2×#21713yes—
230C22×C5#95313yes—
231C22×C5#95311yescharacteristic
232C4×C5—26no—
233Dic5—122no—
234Dic5—243no—
235C24—21no—
236C24#122013yes—
237C24C22×D1511yescharacteristic
238#41—212no—
239#41—212no—
240C2×Q8—21no—
241C2×D4—23no—
242C2×D4—212no—
243C2×D4—212no—
244C2×D4—26no—
245C2×D4—26no—
246C2×D4C2×Dic1516yes—
247C2×D4#122016yes—
248C22×C4—23no—
249C22×C4—303no—
250C22×C4—303no—
251C22×C4—602no—
252C22×C4#122013yes—
253C22⋊C4—306no—
254C22⋊C4—606no—
255C3×C5#179011yescharacteristic, complemented, Hall
256C22×C3—23no—
257C22×C3—23no—
258C22×C3—26no—
259C22×C3—41no—
260C22×C3—43no—
261C22×C3—46no—
262C22×C3—43no—
263C22×C3—43no—
264C22×C3—83no—
265C22×C3—84no—
266C22×C3C2×C22⋊Dic513yes—
267C22×C3#409913yes—
268C22×C3#409911yescharacteristic
269C3×C4—26no—
270Dic3—202no—
271Dic3—403no—
272C2×C5—23no—
273C2×C5—23no—
274C2×C5—46no—
275C2×C5#524311yescharacteristic
276C2×C5#524411yescharacteristic
277C2×C5#524711yescharacteristic
278C23—24no—
279C23—23no—
280C23—23no—
281C23—41no—
282C23—41no—
283C23—43no—
284C23—43no—
285C23—81no—
286C23—81no—
287C23#671916yescomplemented
288C23C22×Dic1511yescharacteristic
289C23C2×#122013yes—
290C23C2×#122013yes—
291Q8—24no—
292D4—212no—
293D4—212no—
294D4—212no—
295C2×C4—212no—
296C2×C4—23no—
297C2×C4—23no—
298C2×C4—306no—
299C2×C4—603no—
300C2×C4—601no—
301C2×C4—603no—
302C2×C4—603no—
303C2×C4—603no—
304C2×C4#671916yescomplemented
305C2×C3—23no—
306C2×C3—23no—
307C2×C3—46no—
308C2×C3#6553211yescharacteristic
309C2×C3#6553311yescharacteristic
310C2×C3#6553611yescharacteristic
311C5#7214211yescharacteristic, complemented, Sylow
312C22—23no—
313C22—23no—
314C22—26no—
315C22—41no—
316C22—43no—
317C22—46no—
318C22—43no—
319C22—43no—
320C22—83no—
321C22—84no—
322C22C2×#671913yes—
323C22#9184213yes—
324C22#9184211yescharacteristic
325C4—26no—
326C4—602no—
327C4—1203no—
328C3#1060293511yescharacteristic, complemented, Sylow
329C2—23no—
330C2—23no—
331C2—46no—
332C2#1175134411yescharacteristic
333C2#1175134511yescharacteristic
334C2#1175134811yescharacteristic
subgroupG/H
centerC22#91842
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
Fitting, prime radicalC2×C3×C5×H(5,𝔽2)C2
socleC22×C3×C5#120
cosocleC24×C3×C5C23
hypercenterC2×H(5,𝔽2)D15
hypocenterC3×C5#1790
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. #11751321C2semidirect
3. C2×#91118C2semidirect
6. C3×C5×H(5,𝔽2)C4semidirect
10. C23×Dic15C22semidirect
12. C2×#6719C22semidirect
43. C5×H(5,𝔽2)Dic3semidirect
62. C23×C3×C5C22⋊C4semidirect
73. C2×C3×C4×C5C22⋊C4semidirect
81. C3×H(5,𝔽2)Dic5semidirect
158. C23×C5#217semidirect
169. C2×C4×C5#217semidirect
177. H(5,𝔽2)Dic15semidirect
201. C23×C3C22⋊Dic5semidirect
212. C2×C3×C4C22⋊Dic5semidirect
255. C3×C5#1790semidirect
287. C23#6719semidirect
304. C2×C4#6719semidirect
311. C5#72142semidirect
328. C3#10602935semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×H(5,𝔽2)2
#117513212
C2×#911182
#106029353
#721425