Finite Group Databasebeta

← #14289936

Subgroups — #14289936

Order 1920.

424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756472C211yesmaximal, characteristic
2C3×C5×#486C211yesmaximal, characteristic
3#11751195C211yesmaximal, characteristic, complemented
4#11751191C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic
6#11746277C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10601999—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×#6718—21no—
12#91825—21no—
13#91825—21no—
14#91824—22no—
15D4×Dic15—21no—
16D4×Dic15—21no—
17C4×Dic30C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×#102—22no—
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91094—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71206—51nomaximal, Hall
27#66047—31no—
28C5×#486D311yescharacteristic
29#65383—31no—
30#65379—31no—
31#64764—31no—
32#64676—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D412yes—
38C22×Dic15—22no—
39C2×Dic30D411yescharacteristic
40C2×Dic30D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6719—22no—
46#6719—22no—
47#6719—22no—
48#6718—42no—
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52#6712—21no—
53C4×Dic15—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5713—51no—
58C3×#486D511yescharacteristic
59#5094—51no—
60#5090—51no—
61#4544—51no—
62#4456—51no—
63#4456—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C5×#127C2×D311yescharacteristic
66C2×#689—61no—
67#4082—61no—
68#4082—61no—
69#4081—62no—
70D4×Dic5—61no—
71D4×Dic5—61no—
72C4×Dic10—31no—
73C4×Dic10—31no—
74C5×#102—22no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3942—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1640—151noSylow
82C23×C3×C5—22no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C3×C5×D4—42no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—82no—
99Dic30—21no—
100Dic30—21no—
101Dic30—21no—
102Dic30—21no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3⋊#168—41no—
106C3×C4⋊Q8C2×D511yescharacteristic
107C3×#127C2×D511yescharacteristic
108C2×#216—101no—
109#936—101no—
110#936—101no—
111#935—102no—
112D4×Dic3—101no—
113D4×Dic3—101no—
114C4×Dic6—51no—
115C4×Dic6—51no—
116C3×#102—22no—
117C3×C4×C8C2×D511yescharacteristic
118#835—101no—
119#810—101no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—21no—
124C2×C5×D4—21no—
125C2×C5×D4—21no—
126C2×C5×D4#6712yes—
127C22×Dic5—62no—
128C2×Dic10—31no—
129C2×Dic10—31no—
130C2×C5×C8—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C42×C5C22×D311yescharacteristic
134C22⋊Dic5—62no—
135C22⋊Dic5—62no—
136C22⋊Dic5—62no—
137#689—122no—
138C4⋊Dic5—31no—
139C4⋊Dic5—31no—
140#683—61no—
141#683—61no—
142C4×Dic5—61no—
143C4×Dic5—61no—
144C2×#168—61no—
145C2×#168—61no—
146#559—151no—
147#486D1511yescharacteristic
148#475—151no—
149#462—151no—
150#331—151no—
151Q8⋊C8—151no—
152Q8⋊C8—151no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—42no—
156C22×C3×C5#12011yescharacteristic
157C3×C4×C5—21no—
158C3×C4×C5—81no—
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—41no—
164Dic15—41no—
165Dic15—41no—
166Dic15—41no—
167C2×C3×Q8—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4C22⋊D512yes—
171C22×Dic3—102no—
172C2×Dic6—51no—
173C2×Dic6—51no—
174C2×C3×C8—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C42C22×D511yescharacteristic
178#217—102no—
179#217—102no—
180#217—102no—
181#216—202no—
182C4⋊Dic3—51no—
183C4⋊Dic3—51no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186C4×Dic3—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—101no—
189C2×C3⋊C8—101no—
190C23×C5—22no—
191C5×Q8—41no—
192C5×Q8—41no—
193C5×D4—42no—
194C5×D4—41no—
195C5×D4—41no—
196C5×D4—41no—
197C5×D4—41no—
198C2×C4×C5—41no—
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—242no—
207Dic10—61no—
208Dic10—61no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—41no—
212#168—121no—
213#168—121no—
214C2×Q16—301no—
215C4⋊Q8C2×D1511yescharacteristic
216#127C2×D1511yescharacteristic
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—151no—
221C4×Q8—151no—
222C4×D4—301no—
223C4×D4—301no—
224#106—301no—
225C4⋊C8—151no—
226C4⋊C8—151no—
227#103—301no—
228#103—301no—
229#102—22no—
230C4×C8C2×D1511yescharacteristic
231C2×C3×C5—82no—
232C2×C3×C5#44911yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45511yescharacteristic
235C23×C3—22no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×D4—42no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C2×C3×C4—41no—
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×Dic3—101no—
248C2×Dic3—101no—
249C2×Dic3—101no—
250C2×Dic3—101no—
251C2×Dic3—402no—
252Dic6—101no—
253Dic6—101no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—41no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—42no—
260C22×C5—42no—
261C22×C5—42no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—81no—
265C4×C5#91111yescharacteristic
266C4×C5#91211yescharacteristic
267C4×C5#91511yescharacteristic
268C4×C5#91611yescharacteristic
269Dic5—121no—
270Dic5—121no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—151no—
275C2×Q8—151no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4#122012yes—
279C22×C4—302no—
280Q16—602no—
281C2×C8—21no—
282C2×C8—301no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—151no—
287C4⋊C4—151no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—301no—
294C42—301no—
295C42C22×D1511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3#408311yescharacteristic
301C3×C4—21no—
302C3×C4—81no—
303C3×C4#405711yescharacteristic
304C3×C4#405811yescharacteristic
305C3×C4#406111yescharacteristic
306C3×C4#406211yescharacteristic
307Dic3—201no—
308Dic3—201no—
309Dic3—201no—
310Dic3—201no—
311C2×C5—82no—
312C2×C5#506111yescharacteristic
313C2×C5#515811yescharacteristic
314C2×C5#517311yescharacteristic
315C23—22no—
316Q8—41no—
317Q8—41no—
318Q8—301no—
319Q8—301no—
320Q8—301no—
321Q8—301no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—41no—
327C2×C4—41no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4D4×D1511yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4C2×#122011yescharacteristic
336C8—41no—
337C8—601no—
338C8—601no—
339C2×C3—82no—
340C2×C3#6535011yescharacteristic
341C2×C3#6544711yescharacteristic
342C2×C3#6546211yescharacteristic
343C5#7120611yescharacteristic, complemented, Sylow
344C22—42no—
345C22—42no—
346C22—42no—
347C22#9182611yescharacteristic
348C4—21no—
349C4—81no—
350C4—601no—
351C4—601no—
352C4—601no—
353C4—601no—
354C4#9180011yescharacteristic
355C4#9180111yescharacteristic
356C4#9180411yescharacteristic
357C4#9180511yescharacteristic
358C3#1060199911yescharacteristic, complemented, Sylow
359C2—82no—
360C2#1175116211yescharacteristic
361C2#1175125911yescharacteristic
362C2#1175127411yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenter#486D15
hypocenterC3×C5#1640
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
3. #11751195C2semidirect
4. #11751191C2semidirect
6. #11746277C2semidirect
7. #11746277C2semidirect
296. C3×C5#1640semidirect
343. C5#71206semidirect
358. C3#10601999semidirect

Maximal subgroups

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

subgroupindex
#117564722
C3×C5×#4862
#117511952
#117511912
#117463652
#117462772
#106019993
#712065