Finite Group Databasebeta

← #14289381

Subgroups — #14289381

Order 1920.

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

normal subgroups only

This group has 436 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#11756344C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic, complemented
3#11751192C211yesmaximal, characteristic, complemented
4#11751186C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic
7#11746305C211yesmaximal, characteristic, complemented
8#10601952—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11#91836—21no—
12C2×#6717—22no—
13#91783—22no—
14#91782—21no—
15#91764—21no—
16#91763C2211yescharacteristic
17C4×D60—21no—
18C4×Dic30C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#103—21no—
22#91094—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71159—51nomaximal, Hall
27#65919—31no—
28C5×#477D311yescharacteristic, complemented
29#65380—31no—
30#65374—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D412yes—
39C2×C4×D15—22no—
40C2×Dic30D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5C2311yescharacteristic
48#6717—44no—
49#6714—22no—
50#6714—22no—
51#6714—22no—
52C4⋊Dic15D411yescharacteristic
53#6712—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5585—51no—
58C3×#477D511yescharacteristic, complemented
59#5091—51no—
60#5085—51no—
61#4535—51no—
62#4485—51no—
63#4484—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×Q8C2×D311yescharacteristic
66#4093—61no—
67C2×#688—62no—
68#4040—62no—
69#4039—61no—
70#4021—61no—
71#4020—31no—
72C4×D20—61no—
73C4×Dic10—31no—
74C5×#107—21no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—21no—
77#3942—61no—
78#3939—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1630—151noSylow
82C22×D15—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—42no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
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—
94D60—42no—
95D60—41no—
96D60—41no—
97D60—41no—
98D60—41no—
99C4×D15—82no—
100Dic30—21no—
101Dic30—21no—
102C3×C5×C8—41no—
103C3⋊#168—22no—
104C3⋊#168—41no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4×Q8C2×D511yescharacteristic
107#947—101no—
108C2×#215—102no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874—51no—
113C4×D12—101no—
114C4×Dic6—51no—
115C3×#107—21no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#103—21no—
118#810—101no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4×C3⋊C8—51no—
122C2×C5×Q8—21no—
123C2×C5×Q8#6711yescharacteristic
124C2×D20—32no—
125C2×D20—61no—
126C2×D20—61no—
127C2×C4×D5—62no—
128C2×Dic10—31no—
129C2×C5×C8—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4#6711yescharacteristic
134C42×C5—21no—
135C42×C5C22×D311yescharacteristic
136#688—124no—
137#685—62no—
138#685—62no—
139#685—62no—
140C4⋊Dic5—31no—
141#683—61no—
142C4×Dic5—61no—
143C2×#168—61no—
144C2×#168—61no—
145#559—151no—
146#492—151no—
147#477—151no—
148#477D1511yescharacteristic, complemented
149#331—151no—
150Q8⋊C8—151no—
151Q8⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×D15—42no—
154C2×D15—42no—
155C2×D15—42no—
156C3×C4×C5—21no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5—81no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—41no—
165Dic15—41no—
166C2×C3×Q8—21no—
167C2×C3×Q8C22⋊D511yescharacteristic
168C2×D12—52no—
169C2×D12—101no—
170C2×D12—101no—
171C2×C4×D3—102no—
172C2×Dic6—51no—
173C2×C3×C8—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180#215—204no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184C4⋊Dic3—51no—
185Dic3⋊C4—101no—
186C4×Dic3—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C22×D5—62no—
190C5×Q8—21no—
191C5×Q8—21no—
192C5×Q8—42no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—41no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—61no—
200C2×Dic5—61no—
201D20—122no—
202D20—121no—
203D20—121no—
204D20—121no—
205D20—121no—
206C4×D5—242no—
207Dic10—61no—
208Dic10—61no—
209C5×C8—41no—
210#168—62no—
211#168—121no—
212C2×SD16—302no—
213C4⋊Q8C2×D1511yescharacteristic
214#127—151no—
215#124—301no—
216#124—301no—
217#123—302no—
218C4×Q8—151no—
219C4×Q8C2×D1511yescharacteristic
220C4×D4—301no—
221C4×D4—301no—
222#107—21no—
223#107—301no—
224C4⋊C8—151no—
225C4⋊C8C2×D1511yescharacteristic
226#103—21no—
227#103—301no—
228C4×C8—151no—
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45211yescharacteristic
231C2×C3×C5#45311yescharacteristic
232D15—82no—
233C22×D3—102no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—42no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—41no—
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—101no—
244C2×Dic3—101no—
245D12—202no—
246D12—201no—
247D12—201no—
248D12—201no—
249D12—201no—
250C4×D3—402no—
251Dic6—101no—
252Dic6—101no—
253C3×C8—41no—
254C3⋊C8—102no—
255C3⋊C8—201no—
256C22×C5#93711yescharacteristic
257C2×D5—122no—
258C2×D5—122no—
259C2×D5—122no—
260C4×C5—21no—
261C4×C5—41no—
262C4×C5—41no—
263C4×C5—81no—
264C4×C5#91811yescharacteristic
265C4×C5#91911yescharacteristic
266C4×C5#94211yescharacteristic
267C4×C5#95011yescharacteristic
268Dic5—121no—
269Dic5—121no—
270C2×Q8—21no—
271C2×Q8—151no—
272C2×Q8#122011yescharacteristic
273C2×D4—152no—
274C2×D4—301no—
275C2×D4—301no—
276C22×C4—302no—
277SD16—604no—
278C2×C8—21no—
279C2×C8—301no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—151no—
285C4⋊C4—301no—
286C4⋊C4#122011yescharacteristic
287C22⋊C4—302no—
288C22⋊C4—302no—
289C22⋊C4—302no—
290C42—21no—
291C42—301no—
292C42C22×D1511yescharacteristic
293C3×C5#163011yescharacteristic, complemented, Hall
294C22×C3#408311yescharacteristic
295C2×D3—202no—
296C2×D3—202no—
297C2×D3—202no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—81no—
302C3×C4#406411yescharacteristic
303C3×C4#406511yescharacteristic
304C3×C4#408811yescharacteristic
305C3×C4#409611yescharacteristic
306Dic3—201no—
307Dic3—201no—
308C2×C5#504711yescharacteristic
309C2×C5#518711yescharacteristic
310C2×C5#519811yescharacteristic
311D5—242no—
312C23—302no—
313Q8—21no—
314Q8—21no—
315Q8—42no—
316Q8—301no—
317Q8—301no—
318D4—602no—
319D4—601no—
320D4—601no—
321D4—601no—
322D4—601no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—1202no—
329C2×C4D4×D1511yescharacteristic
330C2×C4D4×D1511yescharacteristic
331C2×C4C2×#122011yescharacteristic
332C8—41no—
333C8—302no—
334C8—601no—
335C2×C3#6533611yescharacteristic
336C2×C3#6547611yescharacteristic
337C2×C3#6548711yescharacteristic
338D3—402no—
339C5#7115911yescharacteristic, complemented, Sylow
340C22—602no—
341C22—602no—
342C22—602no—
343C22#9182611yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—601no—
349C4—601no—
350C4#9180711yescharacteristic
351C4#9180811yescharacteristic
352C4#9183111yescharacteristic
353C4#9183911yescharacteristic
354C3#1060195211yescharacteristic, complemented, Sylow
355C2—1202no—
356C2#1175114811yescharacteristic
357C2#1175128811yescharacteristic
358C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#477C2
socleC22×C3×C5#120
prime radical#91763C22
hypercenter#477D15
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. C3×C5×#477C2semidirect
3. #11751192C2semidirect
5. #11746356C2semidirect
7. #11746305C2semidirect
28. C5×#477D3semidirect
58. C3×#477D5semidirect
148. #477D15semidirect
293. C3×C5#1630semidirect
339. C5#71159semidirect
354. C3#10601952semidirect

Maximal subgroups

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

subgroupindex
#117563442
C3×C5×#4772
#117511922
#117511862
#117463562
#117463062
#117463052
#106019523
#711595