Finite Group Databasebeta

← #14288568

Subgroups — #14288568

Order 1920.

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

normal subgroups only

This group has 472 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×#543C211yesmaximal, characteristic
2#11751145C212yesmaximal, complemented
3#11751050C211yesmaximal, characteristic
4#11746359C212yesmaximal, complemented
5#11746346C211yesmaximal, characteristic
6#10602684—31nomaximal, Hall
7C3×C5×C22⋊Q8—22no—
8C3×C5×C22⋊Q8—21no—
9C3×C5×C22⋊Q8—22no—
10C3×C5×C22⋊Q8C2212yes—
11C2×C3×C5×C22⋊C4—21no—
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×#6719—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15C2×#6712—21no—
16#91119—22no—
17#91115C2211yescharacteristic
18#91114C2212yes—
19#91091—22no—
20#71891—51nomaximal, Hall
21C5×#543D311yescharacteristic
22#65333—32no—
23#65238—31no—
24#64758—32no—
25#64745—31no—
26C24×C3×C5D411yescharacteristic
27C2×C3×C5×Q8—21no—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—21no—
34C22×Dic15—21no—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—22no—
37C3×C5×C4⋊C4—22no—
38C3×C5×C4⋊C4D412yes—
39C3×C5×C22⋊C4—22no—
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4—22no—
42#6719—42no—
43C4⋊Dic15—22no—
44#6712—42no—
45C2×C3⋊#168—22no—
46C3×#543D511yescharacteristic
47#5044—52no—
48#4949—51no—
49#4538—52no—
50#4525—51no—
51C5×C22⋊Q8—22no—
52C5×C22⋊Q8—21no—
53C5×C22⋊Q8—22no—
54C5×C22⋊Q8C2×D312yes—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4C2×D311yescharacteristic
57C2×C22⋊Dic5—61no—
58C2×C4⋊Dic5—31no—
59C2×#683—61no—
60#3967—62no—
61#3963—31no—
62C22⋊#168—32no—
63#3939—62no—
64#1614—151noSylow
65C23×C3×C5—21no—
66C23×C3×C5—21no—
67C23×C3×C5—41no—
68C23×C3×C5—41no—
69C23×C3×C5Q1612yes—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×Q8—42no—
72C3×C5×Q8—81no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—81no—
79C2×C3×C4×C5—81no—
80C2×C3×C4×C5C2×D412yes—
81C2×Dic15—22no—
82C2×Dic15—41no—
83C2×Dic15—41no—
84C2×Dic15—41no—
85C2×Dic15—41no—
86C2×Dic15—41no—
87C3⋊#168—42no—
88C3×C22⋊Q8—22no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8C2×D512yes—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4C2×D511yescharacteristic
94C2×#217—101no—
95C2×C4⋊Dic3—51no—
96C2×Dic3⋊C4—101no—
97#835—102no—
98C3⋊#95—51no—
99#830—52no—
100#807—102no—
101C24×C5#6711yescharacteristic
102C2×C5×Q8—21no—
103C2×C5×Q8#6712yes—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5#6711yescharacteristic
107C22×C4×C5C22×D311yescharacteristic
108C22×Dic5—61no—
109C22×Dic5—61no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—22no—
112C5×C4⋊C4—22no—
113C5×C4⋊C4#6712yes—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—22no—
116C5×C22⋊C4—22no—
117C22⋊Dic5—122no—
118C4⋊Dic5—62no—
119#683—122no—
120C2×#168—62no—
121#543D1511yescharacteristic
122#484—152no—
123#399—151no—
124#328—152no—
125#323—151no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—22no—
129C22×C3×C5—42no—
130C22×C3×C5—41no—
131C22×C3×C5—41no—
132C22×C3×C5—81no—
133C22×C3×C5#12011yescharacteristic
134C22×C3×C5C2×Q1611yescharacteristic
135C22×C3×C5#13711yescharacteristic
136C3×C4×C5—22no—
137C3×C4×C5—41no—
138C3×C4×C5—42no—
139C3×C4×C5—42no—
140Dic15—42no—
141Dic15—81no—
142C24×C3C22⋊D511yescharacteristic
143C2×C3×Q8—21no—
144C2×C3×Q8C22⋊D512yes—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4C22⋊D511yescharacteristic
148C22×C3×C4C22×D511yescharacteristic
149C22×Dic3—101no—
150C22×Dic3—101no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4C22⋊D512yes—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158#217—202no—
159C4⋊Dic3—102no—
160Dic3⋊C4—202no—
161C2×C3⋊C8—102no—
162C23×C5—21no—
163C23×C5—21no—
164C23×C5—41no—
165C23×C5—41no—
166C23×C5#21612yes—
167C23×C5C2×#6711yescharacteristic
168C5×Q8—42no—
169C5×Q8—81no—
170C2×C4×C5—22no—
171C2×C4×C5—21no—
172C2×C4×C5—22no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—81no—
176C2×C4×C5—81no—
177C2×C4×C5C2×#6712yes—
178C2×Dic5—62no—
179C2×Dic5—121no—
180C2×Dic5—121no—
181C2×Dic5—121no—
182C2×Dic5—121no—
183C2×Dic5—121no—
184#168—122no—
185C22⋊Q8—22no—
186C22⋊Q8—21no—
187C22⋊Q8—22no—
188C22⋊Q8C2×D1512yes—
189C2×C4⋊C4—151no—
190C2×C4⋊C4—301no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—301no—
193C2×C22⋊C4C2×D1511yescharacteristic
194#107—302no—
195#103—302no—
196C22⋊C8—152no—
197#95—151no—
198C2×C3×C5—21no—
199C2×C3×C5—21no—
200C2×C3×C5—42no—
201C2×C3×C5#45111yescharacteristic
202C2×C3×C5#45311yescharacteristic
203C2×C3×C5#45811yescharacteristic
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3#68912yes—
209C23×C3C2×C22⋊D511yescharacteristic
210C3×Q8—42no—
211C3×Q8—81no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—81no—
218C2×C3×C4—81no—
219C2×C3×C4C2×C22⋊D512yes—
220C2×Dic3—102no—
221C2×Dic3—201no—
222C2×Dic3—201no—
223C2×Dic3—201no—
224C2×Dic3—201no—
225C2×Dic3—201no—
226C3⋊C8—202no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—22no—
230C22×C5—42no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—81no—
234C22×C5#94211yescharacteristic
235C22×C5C2×#21611yescharacteristic
236C22×C5#95311yescharacteristic
237C4×C5—22no—
238C4×C5—41no—
239C4×C5—42no—
240C4×C5—42no—
241Dic5—122no—
242Dic5—241no—
243C24#122011yescharacteristic
244C2×Q8—21no—
245C2×Q8#122012yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—301no—
249C22×C4—301no—
250C22×C4#122011yescharacteristic
251C22×C4C22×D1511yescharacteristic
252C2×C8—302no—
253C4⋊C4—21no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—302no—
257C4⋊C4—602no—
258C4⋊C4#122012yes—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—602no—
263C3×C5#161411yescharacteristic, complemented, Hall
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—22no—
267C22×C3—42no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—81no—
271C22×C3#408811yescharacteristic
272C22×C3C2×#68911yescharacteristic
273C22×C3#409911yescharacteristic
274C3×C4—22no—
275C3×C4—41no—
276C3×C4—42no—
277C3×C4—42no—
278Dic3—202no—
279Dic3—401no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—42no—
283C2×C5#522811yescharacteristic
284C2×C5#524111yescharacteristic
285C2×C5#524311yescharacteristic
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23#671812yes—
291C23C2×#122011yescharacteristic
292Q8—42no—
293Q8—81no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—302no—
302C2×C4—601no—
303C2×C4—601no—
304C2×C4—601no—
305C2×C4—601no—
306C2×C4—601no—
307C2×C4C2×#122012yes—
308C8—602no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—42no—
312C2×C3#6551711yescharacteristic
313C2×C3#6553011yescharacteristic
314C2×C3#6553211yescharacteristic
315C5#7189111yescharacteristic, complemented, Sylow
316C22—21no—
317C22—21no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22#9183111yescharacteristic
324C22C2×#671811yescharacteristic
325C22#9184211yescharacteristic
326C4—22no—
327C4—41no—
328C4—42no—
329C4—42no—
330C4—602no—
331C4—1201no—
332C3#1060268411yescharacteristic, complemented, Sylow
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1175132911yescharacteristic
337C2#1175134211yescharacteristic
338C2#1175134411yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#543C2
socleC22×C3×C5#120
prime radicalC24×C3×C5D4
hypercenter#543D15
hypocenterC3×C5#1614
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
2. #11751145C2semidirect
4. #11746359C2semidirect
263. C3×C5#1614semidirect
315. C5#71891semidirect
332. C3#10602684semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5432
#117511452
#117510502
#117463592
#117463462
#106026843
#718915