Finite Group Databasebeta

← #14308901

Subgroups — #14308901

Order 1920.

564 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C3×C5×#544C211yesmaximal, characteristic, complemented
2#11751102C212yesmaximal
3#11751089C211yesmaximal, characteristic
4#11746353C212yesmaximal, complemented
5#11746351C211yesmaximal, characteristic, complemented
6#10602696—31nomaximal, Hall
7C22×D60C2211yescharacteristic
8C3×C5×C4⋊Q8—22no—
9C3×C5×#125—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#117C2212yes—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×#6714—22no—
14C2×C4×Dic15C2211yescharacteristic
15C2×#6710C2212yes—
16#91093—22no—
17#91093—22no—
18#71903—51nomaximal, Hall
19C5×#544D311yescharacteristic, complemented
20#65290—32no—
21#65277—31no—
22#64752—32no—
23#64750—31no—
24C23×D15—21no—
25C2×C3×C5×Q8—22no—
26C22×C3×C4×C5D412yes—
27C22×C3×C4×C5C2311yescharacteristic
28C22×Dic15—21no—
29C2×D60—22no—
30C2×D60—22no—
31C2×D60—21no—
32C2×D60Q812yescomplemented
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—24no—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4D412yes—
37C3×C5×C4⋊C4D412yes—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5—22no—
40#6714—44no—
41C4×Dic15—22no—
42#6710—22no—
43#6710—22no—
44C2×C3⋊#168—22no—
45C3×#544D511yescharacteristic, complemented
46#5001—52no—
47#4988—51no—
48#4532—52no—
49#4530—51no—
50C22×D20—31no—
51C5×C4⋊Q8—22no—
52C5×#125—22no—
53C5×C22⋊Q8—22no—
54C5×#117C2×D312yes—
55C2×C5×C4⋊C4C2×D311yescharacteristic
56C2×#685—62no—
57C2×C4×Dic5—31no—
58C2×#681—32no—
59#3941—62no—
60#3941—62no—
61#2027—151noSylow
62C23×C3×C5C2×D411yescharacteristic
63C22×D15—22no—
64C22×D15—42no—
65C22×D15—42no—
66C22×D15—41no—
67C22×D15—41no—
68C3×C5×Q8—82no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—42no—
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×Q811yescharacteristic
75C2×C3×C4×C5#4112yes—
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—22no—
78C2×Dic15—41no—
79C2×Dic15—41no—
80D60—24no—
81D60—42no—
82C3⋊#168—42no—
83C22×D12—51no—
84C3×C4⋊Q8—22no—
85C3×#125—22no—
86C3×C22⋊Q8—22no—
87C3×#117C2×D512yes—
88C2×C3×C4⋊C4C2×D511yescharacteristic
89C2×(C2×D3)⋊C4—102no—
90C2×C4×Dic3—51no—
91C2×#208—52no—
92#809—102no—
93#809—102no—
94C23×D5—61no—
95C2×C5×Q8—22no—
96C22×C4×C5#6712yes—
97C22×C4×C5C22×D311yescharacteristic
98C22×Dic5—61no—
99C2×D20—32no—
100C2×D20—62no—
101C2×D20—62no—
102C2×D20—61no—
103C5×C4⋊C4—22no—
104C5×C4⋊C4—24no—
105C5×C4⋊C4—22no—
106C5×C4⋊C4#6712yes—
107C5×C4⋊C4#6712yes—
108C5×C22⋊C4—22no—
109C42×C5—22no—
110#685—124no—
111C4×Dic5—62no—
112#681—62no—
113#681—62no—
114C2×#168—62no—
115#544D1511yescharacteristic, complemented
116#418—152no—
117#390—151no—
118#343—151no—
119#339—152no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C22⋊Q811yescharacteristic
124C22×C3×C5#12411yescharacteristic
125C2×D15—44no—
126C2×D15—42no—
127C2×D15—82no—
128C2×D15—81no—
129C2×D15—81no—
130C3×C4×C5—42no—
131C3×C4×C5—42no—
132C3×C4×C5—42no—
133C3×C4×C5C22⋊Q812yes—
134C3×C4×C5#12412yes—
135Dic15—42no—
136C23×D3—101no—
137C2×C3×Q8—22no—
138C22×C3×C4C22⋊D512yes—
139C22×C3×C4C22×D511yescharacteristic
140C22×Dic3—101no—
141C2×D12—52no—
142C2×D12—102no—
143C2×D12—102no—
144C2×D12—101no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—24no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4C22⋊D512yes—
149C3×C4⋊C4C22⋊D512yes—
150C3×C22⋊C4—22no—
151C3×C42—22no—
152(C2×D3)⋊C4—204no—
153C4×Dic3—102no—
154#208—102no—
155#208—102no—
156C2×C3⋊C8—102no—
157C23×C5C2×#6711yescharacteristic
158C22×D5—62no—
159C22×D5—122no—
160C22×D5—122no—
161C22×D5—121no—
162C22×D5—121no—
163C5×Q8—82no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—22no—
167C2×C4×C5—42no—
168C2×C4×C5D3×Q811yescharacteristic
169C2×C4×C5#23912yes—
170C2×C4×C5#23911yescharacteristic
171C2×C4×C5C2×#6712yes—
172C2×Dic5—62no—
173C2×Dic5—121no—
174C2×Dic5—121no—
175D20—64no—
176D20—122no—
177#168—122no—
178C22×D4—151no—
179C2×M16—152no—
180C4⋊Q8—22no—
181#125—22no—
182C22⋊Q8—22no—
183#117C2×D1512yes—
184C2×C4⋊C4C2×D1511yescharacteristic
185C2×C22⋊C4—302no—
186C2×C42—151no—
187#102—302no—
188#102—302no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#39311yescharacteristic
192C2×C3×C5#45311yescharacteristic
193C2×C3×C5#45411yescharacteristic
194D15—82no—
195C23×C3C2×C22⋊D511yescharacteristic
196C22×D3—102no—
197C22×D3—202no—
198C22×D3—202no—
199C22×D3—201no—
200C22×D3—201no—
201C3×Q8—82no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—42no—
206C2×C3×C4Q8×D511yescharacteristic
207C2×C3×C4#71312yes—
208C2×C3×C4#71311yescharacteristic
209C2×C3×C4C2×C22⋊D512yes—
210C2×Dic3—102no—
211C2×Dic3—201no—
212C2×Dic3—201no—
213D12—104no—
214D12—202no—
215C3⋊C8—202no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5#94611yescharacteristic
219C22×C5#94711yescharacteristic
220C22×C5#95311yescharacteristic
221C2×D5—124no—
222C2×D5—122no—
223C2×D5—242no—
224C2×D5—241no—
225C2×D5—241no—
226C4×C5—42no—
227C4×C5—42no—
228C4×C5—42no—
229C4×C5#94612yes—
230C4×C5#94712yes—
231Dic5—122no—
232C24—301no—
233C2×Q8—22no—
234C2×D4—152no—
235C2×D4—302no—
236C2×D4—301no—
237C2×D4—302no—
238C22×C4—301no—
239C22×C4#122012yes—
240C22×C4C22×D1511yescharacteristic
241M16—302no—
242M16—302no—
243C2×C8—302no—
244C4⋊C4—22no—
245C4⋊C4—24no—
246C4⋊C4—22no—
247C4⋊C4#122012yes—
248C4⋊C4#122012yes—
249C22⋊C4—22no—
250C22⋊C4—604no—
251C42—22no—
252C42—302no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3#409211yescharacteristic
257C22×C3#409311yescharacteristic
258C22×C3#409911yescharacteristic
259C2×D3—204no—
260C2×D3—202no—
261C2×D3—402no—
262C2×D3—401no—
263C2×D3—401no—
264C3×C4—42no—
265C3×C4—42no—
266C3×C4—42no—
267C3×C4#409212yes—
268C3×C4#409312yes—
269Dic3—202no—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5#523111yescharacteristic
273C2×C5#524111yescharacteristic
274C2×C5#524511yescharacteristic
275D5—242no—
276C23—302no—
277C23—602no—
278C23—602no—
279C23—601no—
280C23—601no—
281C23C2×#122011yescharacteristic
282Q8—82no—
283D4—304no—
284D4—602no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—302no—
290C2×C4—601no—
291C2×C4—601no—
292C2×C4Q8×D1511yescharacteristic
293C2×C4#682112yes—
294C2×C4#682111yescharacteristic
295C2×C4C2×#122012yes—
296C8—602no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#6552011yescharacteristic
300C2×C3#6553011yescharacteristic
301C2×C3#6553411yescharacteristic
302D3—402no—
303C5#7190311yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—604no—
307C22—602no—
308C22—1202no—
309C22—1201no—
310C22—1201no—
311C22#9183511yescharacteristic
312C22#9183611yescharacteristic
313C22#9184211yescharacteristic
314C4—42no—
315C4—42no—
316C4—42no—
317C4—602no—
318C4#9183512yes—
319C4#9183612yes—
320C3#1060269611yescharacteristic, complemented, Sylow
321C2—21no—
322C2—21no—
323C2—1202no—
324C2#1175133211yescharacteristic
325C2#1175134211yescharacteristic
326C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#544C2
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenter#544D15
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C3×C5×#544C2semidirect
4. #11746353C2semidirect
5. #11746351C2semidirect
19. C5×#544D3semidirect
32. C2×D60Q8semidirect
45. C3×#544D5semidirect
115. #544D15semidirect
253. C3×C5#2027semidirect
303. C5#71903semidirect
320. C3#10602696semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5442
#117511022
#117510892
#117463532
#117463512
#106026963
#719035