Finite Group Databasebeta

← #14290632

Subgroups — #14290632

Order 1920.

468 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 101 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
1D4×Dic30C211yesmaximal, characteristic
2C3×C5×#461C211yesmaximal, characteristic
3#11751195C211yesmaximal, characteristic, complemented
4#11751181C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11746307C211yesmaximal, characteristic, complemented
7#11746305C211yesmaximal, characteristic, complemented
8#10601843—31nomaximal, Hall
9C22×Dic30—21no—
10C2×C3×C5×SD16—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C4×C5×D4C2211yescharacteristic
13D4×Dic15—21no—
14#91813—21no—
15#91777—21no—
16#91767—22no—
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21#91094—21no—
22#91092—22no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71050—51nomaximal, Hall
27D4×Dic10—31no—
28C5×#461D311yescharacteristic
29#65383—31no—
30#65368—31no—
31D4⋊#168—31no—
32#64706—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×Dic15—22no—
38C2×Dic30—22no—
39C2×Dic30—21no—
40C2×Dic30—42no—
41C2×Dic30—42no—
42C2×Dic30D411yescharacteristic
43C3×C5×SD16—42no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5C2311yescharacteristic
50#6719—22no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D412yes—
54#6712—22no—
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59D4×Dic6—51no—
60C3×#461D511yescharacteristic
61#5094—51no—
62#5080—51no—
63D4⋊(C3⋊C8)—51no—
64#4486—51no—
65#4484—51no—
66C22×Dic10—61no—
67C2×C5×SD16—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C4×C5×D4C2×D311yescharacteristic
70D4×Dic5—61no—
71#4070—61no—
72#4034—61no—
73#4024—62no—
74#4015—31no—
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#103—21no—
78#3942—61no—
79#3940—62no—
80#3940—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1651—151noSylow
84C23×C3×C5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×D4—21no—
88C3×C5×D4SD1612yes—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—22no—
99C2×Dic15—44no—
100Dic30—21no—
101Dic30—44no—
102Dic30—41no—
103Dic30—41no—
104Dic30SD1612yescomplemented
105C3×C5×C8—41no—
106C3⋊#168—22no—
107C3⋊#168—41no—
108C22×Dic6—101no—
109C2×C3×SD16—21no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×C4×D4C2×D511yescharacteristic
112D4×Dic3—101no—
113#924—101no—
114#888—101no—
115#878—102no—
116#869—51no—
117C4×Dic6—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#103—21no—
120#810—101no—
121#808—102no—
122#808—101no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C2×C5×Q8—21no—
126C2×C5×D4#6711yescharacteristic
127C22×C4×C5—21no—
128C22×Dic5—62no—
129C2×Dic10—31no—
130C2×Dic10—62no—
131C2×Dic10—61no—
132C2×Dic10—122no—
133C2×Dic10—122no—
134C5×SD16—42no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4#6711yescharacteristic
139C5×C22⋊C4—21no—
140C42×C5C22×D311yescharacteristic
141C22⋊Dic5—62no—
142C4⋊Dic5—31no—
143C4⋊Dic5—32no—
144C4⋊Dic5—61no—
145#683—62no—
146#683—61no—
147C4×Dic5—61no—
148C2×#168—61no—
149C2×#168—61no—
150D4×Q8—151no—
151#498—151no—
152#475—151no—
153#461D1511yescharacteristic
154#332—151no—
155Q8⋊C8—151no—
156D4⋊C8—151no—
157C22×C3×C5—22no—
158C22×C3×C5—41no—
159C22×C3×C5—41no—
160C22×C3×C5#12011yescharacteristic
161C3×C4×C5—21no—
162C3×C4×C5—41no—
163C3×C4×C5—81no—
164C3×C4×C5C2×SD1611yescharacteristic
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168Dic15—22no—
169Dic15—42no—
170Dic15—41no—
171C2×C3×Q8—21no—
172C2×C3×D4C22⋊D511yescharacteristic
173C22×C3×C4—21no—
174C22×Dic3—102no—
175C2×Dic6—51no—
176C2×Dic6—102no—
177C2×Dic6—101no—
178C2×Dic6—202no—
179C2×Dic6—202no—
180C3×SD16—42no—
181C2×C3×C8—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C22⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187#217—102no—
188C4⋊Dic3—51no—
189C4⋊Dic3—52no—
190C4⋊Dic3—101no—
191Dic3⋊C4—102no—
192Dic3⋊C4—101no—
193C4×Dic3—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C5×Q8—41no—
198C5×Q8—41no—
199C5×D4—21no—
200C5×D4#21412yes—
201C2×C4×C5—21no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—61no—
209C2×Dic5—61no—
210C2×Dic5—62no—
211C2×Dic5—124no—
212Dic10—32no—
213Dic10—61no—
214Dic10—124no—
215Dic10—121no—
216Dic10—121no—
217C5×C8—41no—
218#168—62no—
219#168—121no—
220C22×Q8—301no—
221C2×SD16—21no—
222C4⋊Q8—151no—
223C4⋊Q8—301no—
224C4⋊Q8C2×D1511yescharacteristic
225C22⋊Q8—302no—
226C22⋊Q8—301no—
227C4×Q8—151no—
228C4×D4—301no—
229C4×D4C2×D1511yescharacteristic
230#106—301no—
231#106—302no—
232C4⋊C8—151no—
233C4⋊C8C2×D1511yescharacteristic
234#103—21no—
235#103—301no—
236C4×C8—151no—
237C2×C3×C5—42no—
238C2×C3×C5#44811yescharacteristic
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45611yescharacteristic
241C23×C3—21no—
242C3×Q8—41no—
243C3×Q8—41no—
244C3×D4—21no—
245C3×D4#68712yes—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4C2×C22⋊D511yescharacteristic
253C2×Dic3—101no—
254C2×Dic3—101no—
255C2×Dic3—102no—
256C2×Dic3—204no—
257Dic6—52no—
258Dic6—101no—
259Dic6—204no—
260Dic6—201no—
261Dic6—201no—
262C3×C8—41no—
263C3⋊C8—102no—
264C3⋊C8—201no—
265C22×C5—22no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5#93711yescharacteristic
269C4×C5—21no—
270C4×C5—41no—
271C4×C5—81no—
272C4×C5D3×SD1611yescharacteristic
273C4×C5#91411yescharacteristic
274C4×C5C2×#21411yescharacteristic
275C4×C5#95111yescharacteristic
276Dic5—62no—
277Dic5—122no—
278Dic5—121no—
279C2×Q8—21no—
280C2×Q8—151no—
281C2×Q8—302no—
282C2×Q8—301no—
283C2×Q8—602no—
284C2×Q8—602no—
285C2×D4#122011yescharacteristic
286C22×C4—21no—
287C22×C4—302no—
288SD16—42no—
289C2×C8—21no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—151no—
295C4⋊C4—152no—
296C4⋊C4—302no—
297C4⋊C4—301no—
298C4⋊C4—301no—
299C4⋊C4#122011yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—302no—
302C42—301no—
303C42C22×D1511yescharacteristic
304C3×C5#165111yescharacteristic, complemented, Hall
305C22×C3—22no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3#408311yescharacteristic
309C3×C4—21no—
310C3×C4—41no—
311C3×C4—81no—
312C3×C4D5×SD1611yescharacteristic
313C3×C4#406011yescharacteristic
314C3×C4C2×#68711yescharacteristic
315C3×C4#409711yescharacteristic
316Dic3—102no—
317Dic3—202no—
318Dic3—201no—
319C2×C5—42no—
320C2×C5#504011yescharacteristic
321C2×C5#516911yescharacteristic
322C2×C5#520511yescharacteristic
323C23—21no—
324Q8—41no—
325Q8—41no—
326Q8—152no—
327Q8—301no—
328Q8—604no—
329Q8—601no—
330Q8—601no—
331D4—21no—
332D4#671612yes—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—301no—
338C2×C4—301no—
339C2×C4—302no—
340C2×C4—604no—
341C2×C4D4×D1511yescharacteristic
342C2×C4D4×D1511yescharacteristic
343C2×C4C2×#122011yescharacteristic
344C8—41no—
345C8—302no—
346C8—601no—
347C2×C3—42no—
348C2×C3#6532911yescharacteristic
349C2×C3#6545811yescharacteristic
350C2×C3#6549411yescharacteristic
351C5#7105011yescharacteristic, complemented, Sylow
352C22—22no—
353C22—41no—
354C22—41no—
355C22#9182611yescharacteristic
356C4—21no—
357C4—41no—
358C4—81no—
359C4—302no—
360C4—602no—
361C4—601no—
362C4SD16×D1511yescharacteristic
363C4#9180311yescharacteristic
364C4C2×#671611yescharacteristic
365C4#9184011yescharacteristic
366C3#1060184311yescharacteristic, complemented, Sylow
367C2—42no—
368C2#1175114111yescharacteristic
369C2#1175127011yescharacteristic
370C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#461C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#461D15
hypocenterC3×C5#1651
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
3. #11751195C2semidirect
4. #11751181C2semidirect
6. #11746307C2semidirect
7. #11746305C2semidirect
104. Dic30SD16semidirect
304. C3×C5#1651semidirect
351. C5#71050semidirect
366. C3#10601843semidirect

Maximal subgroups

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

subgroupindex
D4×Dic302
C3×C5×#4612
#117511952
#117511812
D4⋊(C3⋊#168)2
#117463072
#117463052
#106018433
#710505