Finite Group Databasebeta

← #14289687

Subgroups — #14289687

Order 1920.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#11756326C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic
3#11751192C211yesmaximal, characteristic
4#11751180C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic
6#11746305C211yesmaximal, characteristic
7#11746303C211yesmaximal, characteristic
8#10601955—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11#91833—21no—
12#91778—22no—
13#91776—21no—
14#91759—21no—
15#91758C2211yescharacteristic
16C4×Dic30—21no—
17C4×Dic30C2211yescharacteristic
18C3×C5×#107—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21#91119—22no—
22#91094—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71162—51nomaximal, Hall
27#65901—31no—
28C5×#477D311yescharacteristic
29#65380—31no—
30#65370—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×Dic30—21no—
37C2×Dic30D411yescharacteristic
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C4⋊Dic15D412yes—
48#6712—22no—
49#6712—22no—
50#6712—22no—
51#6712—21no—
52C4×Dic15—22no—
53C4×Dic15—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56#5567—51no—
57C3×#477D511yescharacteristic
58#5091—51no—
59#5079—51no—
60#4535—51no—
61#4484—51no—
62#4482—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C4×C5×Q8C2×D311yescharacteristic
65#4090—61no—
66#4035—62no—
67#4033—61no—
68#4016—61no—
69#4015—31no—
70C4×Dic10—31no—
71C4×Dic10—61no—
72C5×#107—21no—
73C5×C4⋊C8C2×D311yescharacteristic
74C5×#103—21no—
75#3967—62no—
76#3942—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4×#168—31no—
80#1636—151noSylow
81C3×C5×Q8—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—22no—
93Dic30—21no—
94Dic30—41no—
95Dic30—41no—
96Dic30Q1612yes—
97C3×C5×C8—41no—
98C3⋊#168—41no—
99C3⋊#168—41no—
100C3×C4⋊Q8C2×D511yescharacteristic
101C3×C4×Q8C2×D511yescharacteristic
102#944—101no—
103#889—102no—
104#887—101no—
105#870—101no—
106#869—51no—
107C4×Dic6—51no—
108C4×Dic6—101no—
109C3×#107—21no—
110C3×C4⋊C8C2×D511yescharacteristic
111C3×#103—21no—
112#835—102no—
113#810—101no—
114#807—101no—
115C4⋊(C3⋊C8)—51no—
116C4×C3⋊C8—51no—
117C2×C5×Q8—21no—
118C2×C5×Q8#6711yescharacteristic
119C2×Dic10—31no—
120C2×Dic10—61no—
121C2×C5×C8—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4#6711yescharacteristic
126C42×C5—21no—
127C42×C5C22×D311yescharacteristic
128C4⋊Dic5—31no—
129C4⋊Dic5—32no—
130C4⋊Dic5—61no—
131#683—62no—
132#683—62no—
133#683—62no—
134#683—61no—
135C4×Dic5—62no—
136C4×Dic5—61no—
137C2×#168—61no—
138C2×#168—61no—
139#557—151no—
140#487—151no—
141#477—151no—
142#477D1511yescharacteristic
143#332—151no—
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×C4×C5—41no—
150C3×C4×C5—81no—
151C3×C4×C5C2×Q1611yescharacteristic
152C3×C4×C5#13511yescharacteristic
153C3×C4×C5#13711yescharacteristic
154C3×C4×C5#13711yescharacteristic
155Dic15—22no—
156Dic15—42no—
157Dic15—41no—
158C2×C3×Q8—21no—
159C2×C3×Q8C22⋊D511yescharacteristic
160C2×Dic6—51no—
161C2×Dic6—101no—
162C2×C3×C8—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4C22⋊D511yescharacteristic
167C3×C42—21no—
168C3×C42C22×D511yescharacteristic
169C4⋊Dic3—51no—
170C4⋊Dic3—52no—
171C4⋊Dic3—101no—
172Dic3⋊C4—102no—
173Dic3⋊C4—102no—
174Dic3⋊C4—102no—
175Dic3⋊C4—101no—
176C4×Dic3—102no—
177C4×Dic3—101no—
178C2×C3⋊C8—101no—
179C2×C3⋊C8—101no—
180C5×Q8—21no—
181C5×Q8—21no—
182C5×Q8—42no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—41no—
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5C2×#6711yescharacteristic
189C2×Dic5—61no—
190C2×Dic5—61no—
191C2×Dic5—62no—
192Dic10—32no—
193Dic10—61no—
194Dic10—121no—
195Dic10—121no—
196C5×C8—41no—
197#168—121no—
198#168—121no—
199C4⋊Q8—151no—
200C4⋊Q8—301no—
201C4⋊Q8C2×D1511yescharacteristic
202#125—301no—
203#125—302no—
204C4×Q8—151no—
205C4×Q8—301no—
206C4×Q8—301no—
207C4×Q8C2×D1511yescharacteristic
208#107—21no—
209#107—301no—
210C4⋊C8—151no—
211C4⋊C8C2×D1511yescharacteristic
212#103—21no—
213#103—301no—
214#103—302no—
215C4×C8—151no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—42no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4D4×D511yescharacteristic
226C2×C3×C4D4×D511yescharacteristic
227C2×C3×C4C2×C22⋊D511yescharacteristic
228C2×Dic3—101no—
229C2×Dic3—101no—
230C2×Dic3—102no—
231Dic6—52no—
232Dic6—101no—
233Dic6—201no—
234Dic6—201no—
235C3×C8—41no—
236C3⋊C8—201no—
237C3⋊C8—201no—
238C22×C5#93711yescharacteristic
239C4×C5—21no—
240C4×C5—41no—
241C4×C5—41no—
242C4×C5—81no—
243C4×C5D3×Q1611yescharacteristic
244C4×C5#91811yescharacteristic
245C4×C5#94211yescharacteristic
246C4×C5#95011yescharacteristic
247Dic5—62no—
248Dic5—121no—
249Dic5—122no—
250C2×Q8—21no—
251C2×Q8—151no—
252C2×Q8—301no—
253C2×Q8#122011yescharacteristic
254C2×C8—21no—
255C2×C8—301no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—152no—
261C4⋊C4—151no—
262C4⋊C4—302no—
263C4⋊C4—302no—
264C4⋊C4—302no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4#122011yescharacteristic
268C42—21no—
269C42—302no—
270C42—301no—
271C42C22×D1511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#408311yescharacteristic
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—81no—
278C3×C4D5×Q1611yescharacteristic
279C3×C4#406411yescharacteristic
280C3×C4#408811yescharacteristic
281C3×C4#409611yescharacteristic
282Dic3—102no—
283Dic3—202no—
284Dic3—201no—
285C2×C5#504711yescharacteristic
286C2×C5#518611yescharacteristic
287C2×C5#520111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—42no—
291Q8—152no—
292Q8—301no—
293Q8—601no—
294Q8—601no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—302no—
301C2×C4D4×D1511yescharacteristic
302C2×C4D4×D1511yescharacteristic
303C2×C4C2×#122011yescharacteristic
304C8—41no—
305C8—601no—
306C8—601no—
307C2×C3#6533611yescharacteristic
308C2×C3#6547511yescharacteristic
309C2×C3#6549011yescharacteristic
310C5#7116211yescharacteristic, complemented, Sylow
311C22#9182611yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—302no—
317C4—601no—
318C4—602no—
319C4Q16×D1511yescharacteristic
320C4#9180711yescharacteristic
321C4#9183111yescharacteristic
322C4#9183911yescharacteristic
323C3#1060195511yescharacteristic, complemented, Sylow
324C2#1175114811yescharacteristic
325C2#1175128711yescharacteristic
326C2#1175130211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#477C2
socle, prime radicalC22×C3×C5#120
hypercenter#477D15
hypocenterC3×C5#1636
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
272. C3×C5#1636semidirect
310. C5#71162semidirect
323. C3#10601955semidirect

Maximal subgroups

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

subgroupindex
#117563262
C3×C5×#4772
#117511922
#117511802
#117463562
#117463052
#117463032
#106019553
#711625