Finite Group Databasebeta

← #14290566

Subgroups — #14290566

Order 1920.

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

normal subgroups only

This group has 400 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#11756491C211yesmaximal, characteristic
2C3×C5×#500C211yesmaximal, characteristic, complemented
3#11751195C211yesmaximal, characteristic, complemented
4#11751184C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic
7#11746277C211yesmaximal, characteristic, complemented
8#10602163—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91836—21no—
12Q8×Dic15—21no—
13C2×#6717—21no—
14#91787—22no—
15#91786—21no—
16#91781—21no—
17C4×D60C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×#107—22no—
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91094—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71370—51nomaximal, Hall
27#66066—31no—
28C5×#500D311yescharacteristic, 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—
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45#6717—42no—
46#6714—22no—
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—22no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D411yescharacteristic
52#6712—21no—
53C4×Dic15—22no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5732—51no—
58C3×#500D511yescharacteristic, complemented
59#5094—51no—
60#5083—51no—
61#4547—51no—
62#4459—51no—
63#4456—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C5×C4⋊Q8C2×D311yescharacteristic
66#4093—61no—
67Q8×Dic5—61no—
68C2×#688—61no—
69#4044—62no—
70#4043—61no—
71#4038—61no—
72C4×D20—31no—
73C4×Dic10—31no—
74C5×#107—22no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3942—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1650—151noSylow
82C22×D15—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95D60—21no—
96D60—21no—
97C4×D15—41no—
98C4×D15—41no—
99Dic30—21no—
100Dic30—21no—
101C3×C5×C8—22no—
102C3⋊#168—41no—
103C3⋊#168—41no—
104C3×C4⋊Q8C2×D511yescharacteristic
105C3×C4⋊Q8C2×D511yescharacteristic
106#947—101no—
107Q8×Dic3—101no—
108C2×#215—101no—
109#898—102no—
110#897—101no—
111#892—101no—
112C4×D12—51no—
113C4×Dic6—51no—
114C3×#107—22no—
115C3×C4×C8C2×D511yescharacteristic
116#835—101no—
117#810—101no—
118#808—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)—51no—
121C2×C5×Q8—21no—
122C2×C5×Q8—21no—
123C2×D20—31no—
124C2×C4×D5—61no—
125C2×Dic10—31no—
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4#6712yes—
131C42×C5C22×D311yescharacteristic
132#688—122no—
133#685—62no—
134#685—62no—
135#685—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—31no—
138C4⋊Dic5—62no—
139#683—61no—
140C4×Dic5—62no—
141C4×Dic5—61no—
142C2×#168—61no—
143C2×#168—61no—
144#556—151no—
145#500D1511yescharacteristic, complemented
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×D15—41no—
153C2×D15—41no—
154C2×D15—41no—
155C3×C4×C5—21no—
156C3×C4×C5—42no—
157C3×C4×C5—81no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—41no—
163Dic15—41no—
164Dic15—41no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×D12—51no—
168C2×C4×D3—101no—
169C2×Dic6—51no—
170C2×C3×C8—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4C22⋊D512yes—
175C3×C42C22×D511yescharacteristic
176#215—202no—
177(C2×D3)⋊C4—102no—
178(C2×D3)⋊C4—102no—
179(C2×D3)⋊C4—101no—
180C4⋊Dic3—51no—
181C4⋊Dic3—51no—
182C4⋊Dic3—102no—
183Dic3⋊C4—101no—
184C4×Dic3—102no—
185C4×Dic3—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C22×D5—61no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×Q8—41no—
192C5×Q8—41no—
193C2×C4×C5—22no—
194C2×C4×C5—41no—
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×Dic5—61no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201D20—61no—
202D20—61no—
203C4×D5—121no—
204C4×D5—121no—
205Dic10—61no—
206Dic10—61no—
207C5×C8—22no—
208#168—121no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8C2×D1511yescharacteristic
212C4⋊Q8C2×D1511yescharacteristic
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—151no—
217C4×Q8—301no—
218C4×D4—151no—
219#117—301no—
220#107—22no—
221#106—301no—
222C4⋊C8—151no—
223C4⋊C8—151no—
224#103—301no—
225#103—301no—
226C4×C8C2×D1511yescharacteristic
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230D15—81no—
231C22×D3—101no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—41no—
235C3×Q8—41no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×C3×C4C2×C22⋊D511yescharacteristic
241C2×Dic3—101no—
242C2×Dic3—101no—
243C2×Dic3—101no—
244D12—101no—
245D12—101no—
246C4×D3—201no—
247C4×D3—201no—
248Dic6—101no—
249Dic6—101no—
250C3×C8—22no—
251C3⋊C8—201no—
252C3⋊C8—201no—
253C22×C5#93711yescharacteristic
254C2×D5—121no—
255C2×D5—121no—
256C2×D5—121no—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5—81no—
260C4×C5#91111yescharacteristic
261C4×C5#91211yescharacteristic
262C4×C5#91811yescharacteristic
263C4×C5#91911yescharacteristic
264Dic5—121no—
265Dic5—121no—
266Dic5—121no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—151no—
270C2×D4—151no—
271C22×C4—301no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—301no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—151no—
280C4⋊C4—151no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C4⋊C4#122012yes—
284C22⋊C4—302no—
285C22⋊C4—302no—
286C22⋊C4—301no—
287C42—302no—
288C42—301no—
289C42C22×D1511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#408311yescharacteristic
292C2×D3—201no—
293C2×D3—201no—
294C2×D3—201no—
295C3×C4—21no—
296C3×C4—42no—
297C3×C4—81no—
298C3×C4#405711yescharacteristic
299C3×C4#405811yescharacteristic
300C3×C4#406411yescharacteristic
301C3×C4#406511yescharacteristic
302Dic3—201no—
303Dic3—201no—
304Dic3—201no—
305C2×C5#509511yescharacteristic
306C2×C5#515811yescharacteristic
307C2×C5#518711yescharacteristic
308D5—241no—
309C23—301no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313Q8—41no—
314Q8—301no—
315Q8—301no—
316D4—301no—
317D4—301no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—301no—
321C2×C4—301no—
322C2×C4—301no—
323C2×C4—601no—
324C2×C4—601no—
325C2×C4D4×D1511yescharacteristic
326C2×C4D4×D1511yescharacteristic
327C2×C4C2×#122011yescharacteristic
328C8—22no—
329C8—601no—
330C8—601no—
331C2×C3#6538411yescharacteristic
332C2×C3#6544711yescharacteristic
333C2×C3#6547611yescharacteristic
334D3—401no—
335C5#7137011yescharacteristic, complemented, Sylow
336C22—601no—
337C22—601no—
338C22—601no—
339C22#9182611yescharacteristic
340C4—21no—
341C4—42no—
342C4—81no—
343C4—601no—
344C4—601no—
345C4—601no—
346C4#9180011yescharacteristic
347C4#9180111yescharacteristic
348C4#9180711yescharacteristic
349C4#9180811yescharacteristic
350C3#1060216311yescharacteristic, complemented, Sylow
351C2—1201no—
352C2#1175119611yescharacteristic
353C2#1175125911yescharacteristic
354C2#1175128811yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#500C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#500D15
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C3×C5×#500C2semidirect
3. #11751195C2semidirect
5. #11746368C2semidirect
7. #11746277C2semidirect
28. C5×#500D3semidirect
58. C3×#500D5semidirect
145. #500D15semidirect
290. C3×C5#1650semidirect
335. C5#71370semidirect
350. C3#10602163semidirect

Maximal subgroups

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

subgroupindex
#117564912
C3×C5×#5002
#117511952
#117511842
#117463682
#117462802
#117462772
#106021633
#713705