Finite Group Databasebeta

← #14289696

Subgroups — #14289696

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#11756480C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic
3#11750951C211yesmaximal, characteristic
4#11750951C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic
6#11746305C211yesmaximal, characteristic
7#11746305C211yesmaximal, characteristic
8#10599251—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10Q8×Dic15—21no—
11#91833—21no—
12#91779—21no—
13#91778—22no—
14#91776—21no—
15#91758C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20#91102—21no—
21#91102—21no—
22#91100—21no—
23#91100—21no—
24#91094—22no—
25C4×C3⋊#168C2211yescharacteristic
26#68458—51nomaximal, Hall
27#66055—31no—
28#65382—31no—
29#65139—31no—
30#65139—31no—
31C5×#332D311yescharacteristic
32#64704—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×Dic30D411yescharacteristic
37C2×Dic30D411yescharacteristic
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D412yes—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—22no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C4⋊Dic15D411yescharacteristic
48#6712—22no—
49#6712—22no—
50#6712—21no—
51#6712—21no—
52C4×Dic15—22no—
53C4×Dic15—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56#5721—51no—
57#5093—51no—
58#4850—51no—
59#4850—51no—
60C3×#332D511yescharacteristic
61#4484—51no—
62#4484—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64Q8×Dic5—61no—
65#4090—61no—
66#4036—61no—
67#4035—62no—
68#4033—61no—
69#4015—31no—
70C4×Dic10—31no—
71C4×Dic10—31no—
72C5×C4⋊C8C2×D311yescharacteristic
73C5×C4⋊C8C2×D311yescharacteristic
74#3950—61no—
75#3950—61no—
76#3948—61no—
77#3948—61no—
78#3942—62no—
79C4×#168—31no—
80#1636—151noSylow
81C3×C5×Q8—41no—
82C3×C5×Q8—41no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—41no—
92Dic30—21no—
93Dic30—21no—
94Dic30—21no—
95Dic30—42no—
96Dic30Q1612yes—
97C3×C5×C8—41no—
98C3×C5×C8—41no—
99C3⋊#168—41no—
100C3×C4⋊Q8C2×D511yescharacteristic
101Q8×Dic3—101no—
102#944—101no—
103#890—101no—
104#889—102no—
105#887—101no—
106#869—51no—
107C4×Dic6—51no—
108C4×Dic6—51no—
109C3×C4⋊C8C2×D511yescharacteristic
110C3×C4⋊C8C2×D511yescharacteristic
111#818—101no—
112#818—101no—
113#816—101no—
114#816—101no—
115#810—102no—
116C4×C3⋊C8—51no—
117C2×C5×Q8—21no—
118C2×Dic10—31no—
119C2×Dic10—31no—
120C2×Dic10—61no—
121C2×C5×C8—21no—
122C2×C5×C8—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4D1212yes—
125C42×C5C22×D311yescharacteristic
126C4⋊Dic5—31no—
127C4⋊Dic5—31no—
128C4⋊Dic5—62no—
129C4⋊Dic5—61no—
130C4⋊Dic5—61no—
131#683—62no—
132#683—62no—
133#683—61no—
134#683—61no—
135C4×Dic5—62no—
136C4×Dic5—61no—
137C4×Dic5—61no—
138C2×#168—61no—
139#557—151no—
140#487—151no—
141#477—151no—
142#477—151no—
143#332D1511yescharacteristic
144Q8⋊C8—151no—
145Q8⋊C8—151no—
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—21no—
148C3×C4×C5—42no—
149C3×C4×C5C2×Q1611yescharacteristic
150C3×C4×C5#13511yescharacteristic
151C3×C4×C5#13711yescharacteristic
152C3×C4×C5#13711yescharacteristic
153Dic15—22no—
154Dic15—41no—
155Dic15—41no—
156Dic15—41no—
157Dic15—81no—
158C2×C3×Q8—21no—
159C2×Dic6—51no—
160C2×Dic6—51no—
161C2×Dic6—101no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4D2012yes—
166C3×C42C22×D511yescharacteristic
167C4⋊Dic3—51no—
168C4⋊Dic3—51no—
169C4⋊Dic3—102no—
170C4⋊Dic3—101no—
171C4⋊Dic3—101no—
172Dic3⋊C4—102no—
173Dic3⋊C4—102no—
174Dic3⋊C4—101no—
175Dic3⋊C4—101no—
176C4×Dic3—102no—
177C4×Dic3—101no—
178C4×Dic3—101no—
179C2×C3⋊C8—101no—
180C5×Q8—41no—
181C5×Q8—41no—
182C2×C4×C5—22no—
183C2×C4×C5C2×D1211yescharacteristic
184C2×C4×C5D3×D411yescharacteristic
185C2×C4×C5D3×D411yescharacteristic
186C2×Dic5—61no—
187C2×Dic5—61no—
188C2×Dic5—61no—
189C2×Dic5—61no—
190C2×Dic5—121no—
191Dic10—32no—
192Dic10—61no—
193Dic10—61no—
194Dic10—61no—
195Dic10—122no—
196C5×C8—41no—
197C5×C8—41no—
198#168—121no—
199C4⋊Q8—151no—
200C4⋊Q8—301no—
201C4⋊Q8C2×D1511yescharacteristic
202#125—301no—
203#125—302no—
204C4×Q8—151no—
205C4×Q8—151no—
206C4×Q8—301no—
207C4×Q8—301no—
208#107—301no—
209#107—301no—
210C4⋊C8C2×D1511yescharacteristic
211C4⋊C8C2×D1511yescharacteristic
212#103—301no—
213#103—301no—
214#103—302no—
215C4×C8—151no—
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—41no—
220C3×Q8—41no—
221C2×C3×C4—22no—
222C2×C3×C4C2×D2011yescharacteristic
223C2×C3×C4D4×D511yescharacteristic
224C2×C3×C4D4×D511yescharacteristic
225C2×Dic3—101no—
226C2×Dic3—101no—
227C2×Dic3—101no—
228C2×Dic3—101no—
229C2×Dic3—201no—
230Dic6—52no—
231Dic6—101no—
232Dic6—101no—
233Dic6—101no—
234Dic6—202no—
235C3×C8—41no—
236C3×C8—41no—
237C3⋊C8—201no—
238C22×C5#88211yescharacteristic
239C4×C5—21no—
240C4×C5—42no—
241C4×C5#91211yescharacteristic
242C4×C5#91511yescharacteristic
243C4×C5#91511yescharacteristic
244C4×C5D3×Q1611yescharacteristic
245Dic5—62no—
246Dic5—121no—
247Dic5—121no—
248Dic5—121no—
249Dic5—241no—
250C2×Q8—21no—
251C2×Q8—151no—
252C2×Q8—151no—
253C2×Q8—301no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—301no—
257C4⋊C4—21no—
258C4⋊C4—151no—
259C4⋊C4—151no—
260C4⋊C4—302no—
261C4⋊C4—302no—
262C4⋊C4—302no—
263C4⋊C4—301no—
264C4⋊C4—301no—
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4D6012yes—
268C42—302no—
269C42—301no—
270C42—301no—
271C42C22×D1511yescharacteristic
272C3×C5#163611yescharacteristic, complemented, Hall
273C22×C3#402811yescharacteristic
274C3×C4—21no—
275C3×C4—42no—
276C3×C4#405811yescharacteristic
277C3×C4#406111yescharacteristic
278C3×C4#406111yescharacteristic
279C3×C4D5×Q1611yescharacteristic
280Dic3—102no—
281Dic3—201no—
282Dic3—201no—
283Dic3—201no—
284Dic3—401no—
285C2×C5#475311yescharacteristic
286C2×C5#478311yescharacteristic
287C2×C5#480911yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—152no—
291Q8—301no—
292Q8—301no—
293Q8—301no—
294Q8—602no—
295C2×C4—22no—
296C2×C4—301no—
297C2×C4—301no—
298C2×C4—301no—
299C2×C4—301no—
300C2×C4—601no—
301C2×C4C2×D6011yescharacteristic
302C2×C4D4×D1511yescharacteristic
303C2×C4D4×D1511yescharacteristic
304C8—41no—
305C8—41no—
306C8—601no—
307C2×C3#6504211yescharacteristic
308C2×C3#6507211yescharacteristic
309C2×C3#6509711yescharacteristic
310C5#6845811yescharacteristic, complemented, Sylow
311C22#9177111yescharacteristic
312C4—21no—
313C4—42no—
314C4—302no—
315C4—601no—
316C4—601no—
317C4—601no—
318C4—1201no—
319C4#9180111yescharacteristic
320C4#9180411yescharacteristic
321C4#9180411yescharacteristic
322C4Q16×D1511yescharacteristic
323C3#1059925111yescharacteristic, complemented, Sylow
324C2#1175085411yescharacteristic
325C2#1175088411yescharacteristic
326C2#1175091011yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socle, prime radicalC22×C3×C5#120
hypercenter#332D15
hypocenterC3×C5#1636
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
272. C3×C5#1636semidirect
310. C5#68458semidirect
323. C3#10599251semidirect

Maximal subgroups

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

subgroupindex
#117564802
#117511942
#117509512
C3×C5×#3322
#117463052
#105992513
#684585