Finite Group Databasebeta

← #14287863

Subgroups — #14287863

Order 1920.

532 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 103 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#11751147C212yesmaximal
3#11751092C211yesmaximal, characteristic
4#11746359C212yesmaximal, complemented
5#11746349C211yesmaximal, characteristic, complemented
6#10602695—31nomaximal, Hall
7C22×D60C2211yescharacteristic
8C3×C5×C4⋊Q8—22no—
9C3×C5×#125—22no—
10C3×C5×C22⋊Q8—21no—
11C3×C5×C22⋊Q8C2212yes—
12C3×C5×#117—21no—
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×#6717—22no—
15C2×#6714—21no—
16C2×#6714—21no—
17#91115C2211yescharacteristic
18#91114C2212yes—
19#91093—22no—
20#71902—51nomaximal, Hall
21C5×#544D311yescharacteristic, complemented
22#65335—32no—
23#65280—31no—
24#64758—32no—
25#64748—31no—
26C23×D15—21no—
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5C2311yescharacteristic
32C22×Dic15—21no—
33C2×D60—22no—
34C2×D60—42no—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—22no—
39C3×C5×C4⋊C4—22no—
40C3×C5×C4⋊C4—22no—
41C3×C5×C4⋊C4D412yes—
42C3×C5×C22⋊C4—22no—
43C3×C42×C5—22no—
44#6717—44no—
45#6714—42no—
46#6714—42no—
47C2×C3⋊#168—22no—
48C3×#544D511yescharacteristic, complemented
49#5046—52no—
50#4991—51no—
51#4538—52no—
52#4528—51no—
53C22×D20—31no—
54C5×C4⋊Q8—22no—
55C5×#125—22no—
56C5×C22⋊Q8—21no—
57C5×C22⋊Q8C2×D312yes—
58C5×#117—21no—
59C2×C5×C4⋊C4C2×D311yescharacteristic
60C2×#688—62no—
61C2×#685—61no—
62C2×#685—61no—
63#3963—31no—
64C22⋊#168—32no—
65#3941—62no—
66#1599—151noSylow
67C23×C3×C5C2×D411yescharacteristic
68C22×D15—22no—
69C22×D15—41no—
70C22×D15—41no—
71C22×D15—41no—
72C22×D15—41no—
73C22×D15—41no—
74C22×D15—41no—
75C3×C5×Q8—42no—
76C3×C5×Q8—81no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5SD1612yescomplemented
85C2×C3×C4×C5C2×D412yes—
86C2×Dic15—41no—
87C2×Dic15—41no—
88C2×Dic15—41no—
89D60—24no—
90D60—42no—
91C3⋊#168—42no—
92C22×D12—51no—
93C3×C4⋊Q8—22no—
94C3×#125—22no—
95C3×C22⋊Q8—21no—
96C3×C22⋊Q8C2×D512yes—
97C3×#117—21no—
98C2×C3×C4⋊C4C2×D511yescharacteristic
99C2×#215—102no—
100C2×(C2×D3)⋊C4—101no—
101C2×(C2×D3)⋊C4—101no—
102C3⋊#95—51no—
103#830—52no—
104#809—102no—
105C23×D5—61no—
106C2×C5×Q8—21no—
107C2×C5×Q8#6712yes—
108C22×C4×C5#6711yescharacteristic
109C22×C4×C5#6711yescharacteristic
110C22×C4×C5C22×D311yescharacteristic
111C22×Dic5—61no—
112C2×D20—62no—
113C2×D20—122no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—22no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4—22no—
120C5×C4⋊C4#6712yes—
121C5×C22⋊C4—22no—
122C42×C5—22no—
123#688—124no—
124#685—122no—
125#685—122no—
126C2×#168—62no—
127#544D1511yescharacteristic, complemented
128#450—152no—
129#394—151no—
130#328—152no—
131#324—151no—
132C22×C3×C5—21no—
133C22×C3×C5—21no—
134C22×C3×C5#12011yescharacteristic
135C22×C3×C5C2×SD1611yescharacteristic
136C22×C3×C5#13711yescharacteristic
137C2×D15—42no—
138C2×D15—42no—
139C2×D15—42no—
140C2×D15—81no—
141C2×D15—81no—
142C2×D15—81no—
143C2×D15—81no—
144C3×C4×C5—22no—
145C3×C4×C5—22no—
146C3×C4×C5—42no—
147C3×C4×C5—41no—
148C3×C4×C5—42no—
149Dic15—81no—
150C23×D3—101no—
151C2×C3×Q8—21no—
152C2×C3×Q8C22⋊D512yes—
153C22×C3×C4C22⋊D511yescharacteristic
154C22×C3×C4C22⋊D511yescharacteristic
155C22×C3×C4C22×D511yescharacteristic
156C22×Dic3—101no—
157C2×D12—102no—
158C2×D12—202no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4C22⋊D512yes—
166C3×C22⋊C4—22no—
167C3×C42—22no—
168#215—204no—
169(C2×D3)⋊C4—202no—
170(C2×D3)⋊C4—202no—
171C2×C3⋊C8—102no—
172C23×C5C2×#6711yescharacteristic
173C22×D5—62no—
174C22×D5—121no—
175C22×D5—121no—
176C22×D5—121no—
177C22×D5—121no—
178C22×D5—121no—
179C22×D5—121no—
180C5×Q8—42no—
181C5×Q8—81no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—21no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5#21512yescomplemented
190C2×C4×C5C2×#6712yes—
191C2×Dic5—121no—
192C2×Dic5—121no—
193C2×Dic5—121no—
194D20—64no—
195D20—122no—
196#168—122no—
197C22×D4—151no—
198C2×SD16—302no—
199C4⋊Q8—22no—
200#125—22no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D1512yes—
203#117—21no—
204C2×C4⋊C4C2×D1511yescharacteristic
205C2×C22⋊C4—301no—
206C2×C22⋊C4—301no—
207#102—302no—
208C22⋊C8—152no—
209#95—151no—
210C2×C3×C5—21no—
211C2×C3×C5—21no—
212C2×C3×C5#44811yescharacteristic
213C2×C3×C5#45411yescharacteristic
214C2×C3×C5B(4,𝔽2)11yescharacteristic
215D15—82no—
216C23×C3C2×C22⋊D511yescharacteristic
217C22×D3—102no—
218C22×D3—201no—
219C22×D3—201no—
220C22×D3—201no—
221C22×D3—201no—
222C22×D3—201no—
223C22×D3—201no—
224C3×Q8—42no—
225C3×Q8—81no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4#68812yescomplemented
234C2×C3×C4C2×C22⋊D512yes—
235C2×Dic3—201no—
236C2×Dic3—201no—
237C2×Dic3—201no—
238D12—104no—
239D12—202no—
240C3⋊C8—202no—
241C22×C5—21no—
242C22×C5—21no—
243C22×C5C2×#21511yescharacteristic
244C22×C5#94211yescharacteristic
245C22×C5#95311yescharacteristic
246C2×D5—122no—
247C2×D5—122no—
248C2×D5—122no—
249C2×D5—241no—
250C2×D5—241no—
251C2×D5—241no—
252C2×D5—241no—
253C4×C5—22no—
254C4×C5—22no—
255C4×C5—41no—
256C4×C5—42no—
257C4×C5—42no—
258Dic5—241no—
259C24—301no—
260C2×Q8—21no—
261C2×Q8#122012yes—
262C2×D4—302no—
263C2×D4—602no—
264C22×C4—301no—
265C22×C4#122011yescharacteristic
266C22×C4#122011yescharacteristic
267C22×C4C22×D1511yescharacteristic
268SD16—604no—
269C2×C8—302no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4#122012yes—
277C22⋊C4—22no—
278C22⋊C4—602no—
279C22⋊C4—602no—
280C42—22no—
281C3×C5#159911yescharacteristic, complemented, Hall
282C22×C3—21no—
283C22×C3—21no—
284C22×C3C2×#68811yescharacteristic
285C22×C3#408811yescharacteristic
286C22×C3#409911yescharacteristic
287C2×D3—202no—
288C2×D3—202no—
289C2×D3—202no—
290C2×D3—401no—
291C2×D3—401no—
292C2×D3—401no—
293C2×D3—401no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—41no—
297C3×C4—42no—
298C3×C4—42no—
299Dic3—401no—
300C2×C5—21no—
301C2×C5—21no—
302C2×C5#522711yescharacteristic
303C2×C5#524411yescharacteristic
304C2×C5#524511yescharacteristic
305D5—242no—
306C23—302no—
307C23—601no—
308C23—601no—
309C23—601no—
310C23—601no—
311C23—601no—
312C23—601no—
313C23C2×#122011yescharacteristic
314Q8—42no—
315Q8—81no—
316D4—304no—
317D4—602no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—601no—
326C2×C4—601no—
327C2×C4—601no—
328C2×C4#671712yescomplemented
329C2×C4C2×#122012yes—
330C8—602no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3#6551611yescharacteristic
334C2×C3#6553311yescharacteristic
335C2×C3#6553411yescharacteristic
336D3—402no—
337C5#7190211yescharacteristic, complemented, Sylow
338C22—21no—
339C22—21no—
340C22—602no—
341C22—602no—
342C22—602no—
343C22—1201no—
344C22—1201no—
345C22—1201no—
346C22—1201no—
347C22C2×#671711yescharacteristic
348C22#9183111yescharacteristic
349C22#9184211yescharacteristic
350C4—22no—
351C4—22no—
352C4—41no—
353C4—42no—
354C4—42no—
355C4—1201no—
356C3#1060269511yescharacteristic, complemented, Sylow
357C2—21no—
358C2—21no—
359C2—1202no—
360C2#1175132811yescharacteristic
361C2#1175134511yescharacteristic
362C2#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#1599
LCSG ▷ C22×C3×C4×C5 ▷ C22×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. #11746359C2semidirect
5. #11746349C2semidirect
21. C5×#544D3semidirect
48. C3×#544D5semidirect
84. C2×C3×C4×C5SD16semidirect
127. #544D15semidirect
189. C2×C4×C5#215semidirect
233. C2×C3×C4#688semidirect
281. C3×C5#1599semidirect
328. C2×C4#6717semidirect
337. C5#71902semidirect
356. C3#10602695semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5442
#117511472
#117510922
#117463592
#117463492
#106026953
#719025