Finite Group Databasebeta

← #14290629

Subgroups — #14290629

Order 1920.

468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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#11756486C211yesmaximal, characteristic
2C3×C5×#498C211yesmaximal, characteristic, complemented
3#11751195C211yesmaximal, characteristic, complemented
4#11751184C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic
7#11746277C211yesmaximal, characteristic, complemented
8#10602135—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12#91835—21no—
13C2×#6717—21no—
14#91785—22no—
15#91782—21no—
16#91777—21no—
17C4×D60C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×#106—22no—
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91094—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71342—51nomaximal, Hall
27#66061—31no—
28C5×#498D311yescharacteristic, complemented
29#65383—31no—
30#65372—31no—
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36Q8×D15—42no—
37Q8×D15—42no—
38C2×D60D411yescharacteristic
39C2×C4×D15—22no—
40C2×C4×D15—21no—
41C2×Dic30—22no—
42C2×Dic30D411yescharacteristic
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D412yes—
48C3×C42×C5C2311yescharacteristic
49#6717—42no—
50#6714—22no—
51#6714—21no—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D411yescharacteristic
54#6712—22no—
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5727—51no—
60C3×#498D511yescharacteristic, complemented
61#5094—51no—
62#5083—51no—
63#4547—51no—
64#4459—51no—
65#4456—51no—
66C2×Q8×D5—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×C4⋊Q8C2×D311yescharacteristic
69#4092—61no—
70C2×#688—61no—
71#4042—62no—
72#4039—61no—
73#4034—61no—
74C4×D20—31no—
75C4×Dic10—31no—
76C5×#106—22no—
77C4×C5×C8C2×D311yescharacteristic
78#3967—61no—
79#3942—61no—
80#3940—61no—
81C4⋊#168—31no—
82C4⋊#168—31no—
83#1651—151noSylow
84C22×D15—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C2×C3×C4×C5—22no—
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—
97D60—21no—
98D60SD1612yes—
99C4×D15—44no—
100C4×D15—41no—
101C4×D15—41no—
102Dic30—21no—
103Dic30—44no—
104Dic30SD1612yescomplemented
105C3×C5×C8—22no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C2×D3×Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×C4⋊Q8C2×D511yescharacteristic
111#946—101no—
112C2×#215—101no—
113#896—102no—
114#893—101no—
115#888—101no—
116C4×D12—51no—
117C4×Dic6—51no—
118C3×#106—22no—
119C3×C4×C8C2×D511yescharacteristic
120#835—101no—
121#810—101no—
122#808—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)—51no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127Q8×D5—122no—
128Q8×D5—122no—
129C2×D20—31no—
130C2×C4×D5—62no—
131C2×C4×D5—61no—
132C2×Dic10—31no—
133C2×Dic10—62no—
134C2×C5×C8—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4#6712yes—
139C42×C5C22×D311yescharacteristic
140#688—122no—
141#685—62no—
142#685—61no—
143C4⋊Dic5—31no—
144C4⋊Dic5—31no—
145#683—62no—
146#683—61no—
147C4×Dic5—61no—
148C2×#168—61no—
149C2×#168—61no—
150D4×Q8—151no—
151#498D1511yescharacteristic, complemented
152#475—151no—
153#461—151no—
154#332—151no—
155Q8⋊C8—151no—
156D4⋊C8—151no—
157C22×C3×C5#12011yescharacteristic
158C2×D15—22no—
159C2×D15—41no—
160C2×D15—41no—
161C3×C4×C5—21no—
162C3×C4×C5—42no—
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—41no—
170Dic15—41no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173D3×Q8—202no—
174D3×Q8—202no—
175C2×D12—51no—
176C2×C4×D3—102no—
177C2×C4×D3—101no—
178C2×Dic6—51no—
179C2×Dic6—102no—
180C2×C3×C8—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C22⋊D512yes—
185C3×C42C22×D511yescharacteristic
186#215—202no—
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—101no—
189C4⋊Dic3—51no—
190C4⋊Dic3—51no—
191Dic3⋊C4—102no—
192Dic3⋊C4—101no—
193C4×Dic3—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C22×D5—61no—
197C5×Q8—41no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×Q8—41no—
201C2×C4×C5—22no—
202C2×C4×C5—41no—
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5—61no—
207C2×Dic5—61no—
208C2×Dic5—61no—
209D20—32no—
210D20—61no—
211C4×D5—124no—
212C4×D5—121no—
213C4×D5—121no—
214Dic10—32no—
215Dic10—61no—
216Dic10—124no—
217C5×C8—22no—
218#168—121no—
219#168—121no—
220C22×Q8—301no—
221C2×SD16—301no—
222C4⋊Q8—301no—
223C4⋊Q8C2×D1511yescharacteristic
224C4⋊Q8C2×D1511yescharacteristic
225C22⋊Q8—301no—
226C22⋊Q8—302no—
227C4×Q8—151no—
228C4×D4—151no—
229C4×D4—301no—
230#106—22no—
231#106—301no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234#103—301no—
235#103—301no—
236C4×C8C2×D1511yescharacteristic
237C2×C3×C5#44811yescharacteristic
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45611yescharacteristic
240D15—42no—
241C22×D3—101no—
242C3×Q8—41no—
243C3×Q8—41no—
244C3×Q8—41no—
245C3×Q8—41no—
246C2×C3×C4—22no—
247C2×C3×C4—41no—
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—101no—
252C2×Dic3—101no—
253C2×Dic3—101no—
254D12—52no—
255D12—101no—
256C4×D3—204no—
257C4×D3—201no—
258C4×D3—201no—
259Dic6—52no—
260Dic6—101no—
261Dic6—204no—
262C3×C8—22no—
263C3⋊C8—201no—
264C3⋊C8—201no—
265C22×C5#93711yescharacteristic
266C2×D5—62no—
267C2×D5—121no—
268C2×D5—121no—
269C4×C5—21no—
270C4×C5—42no—
271C4×C5—81no—
272C4×C5D3×SD1611yescharacteristic
273C4×C5D3×SD1611yescharacteristic
274C4×C5#91411yescharacteristic
275C4×C5#91511yescharacteristic
276Dic5—62no—
277Dic5—121no—
278Dic5—121no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—151no—
282C2×Q8—302no—
283C2×Q8—602no—
284C2×Q8—602no—
285C2×D4—151no—
286C22×C4—302no—
287C22×C4—301no—
288SD16—602no—
289C2×C8—21no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—151no—
296C4⋊C4—151no—
297C4⋊C4—302no—
298C4⋊C4—301no—
299C4⋊C4#122012yes—
300C22⋊C4—302no—
301C22⋊C4—301no—
302C42—301no—
303C42C22×D1511yescharacteristic
304C3×C5#165111yescharacteristic, complemented, Hall
305C22×C3#408311yescharacteristic
306C2×D3—102no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—42no—
311C3×C4—81no—
312C3×C4D5×SD1611yescharacteristic
313C3×C4D5×SD1611yescharacteristic
314C3×C4#406011yescharacteristic
315C3×C4#406111yescharacteristic
316Dic3—102no—
317Dic3—201no—
318Dic3—201no—
319C2×C5#509511yescharacteristic
320C2×C5#516911yescharacteristic
321C2×C5#517011yescharacteristic
322D5—122no—
323C23—301no—
324Q8—41no—
325Q8—41no—
326Q8—41no—
327Q8—41no—
328Q8—152no—
329Q8—301no—
330Q8—604no—
331D4—152no—
332D4—301no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—301no—
336C2×C4—301no—
337C2×C4—301no—
338C2×C4—604no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4D4×D1511yescharacteristic
342C2×C4D4×D1511yescharacteristic
343C2×C4C2×#122011yescharacteristic
344C8—22no—
345C8—601no—
346C8—601no—
347C2×C3#6538411yescharacteristic
348C2×C3#6545811yescharacteristic
349C2×C3#6545911yescharacteristic
350D3—202no—
351C5#7134211yescharacteristic, complemented, Sylow
352C22—302no—
353C22—601no—
354C22—601no—
355C22#9182611yescharacteristic
356C4—21no—
357C4—42no—
358C4—81no—
359C4—302no—
360C4—601no—
361C4—601no—
362C4SD16×D1511yescharacteristic
363C4SD16×D1511yescharacteristic
364C4#9180311yescharacteristic
365C4#9180411yescharacteristic
366C3#1060213511yescharacteristic, complemented, Sylow
367C2—602no—
368C2#1175119611yescharacteristic
369C2#1175127011yescharacteristic
370C2#1175127111yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#498C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#498D15
hypocenterC3×C5#1651
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C3×C5×#498C2semidirect
3. #11751195C2semidirect
5. #11746368C2semidirect
7. #11746277C2semidirect
28. C5×#498D3semidirect
60. C3×#498D5semidirect
104. Dic30SD16semidirect
151. #498D15semidirect
304. C3×C5#1651semidirect
351. C5#71342semidirect
366. C3#10602135semidirect

Maximal subgroups

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

subgroupindex
#117564862
C3×C5×#4982
#117511952
#117511842
#117463682
#117462802
#117462772
#106021353
#713425