Finite Group Databasebeta

← #14316142

Subgroups — #14316142

Order 1920.

460 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C2×#91275C211yesmaximal, characteristic, complemented
2C5×#4883C211yesmaximal, characteristic, complemented
3C2×#90941C211yesmaximal, characteristic, complemented
4C2×#90939C211yesmaximal, characteristic, complemented
5#11746312C211yesmaximal, characteristic, complemented
6C3×#64712C211yesmaximal, characteristic, complemented
7(C2×D3)⋊#672C211yesmaximal, characteristic, complemented
8#10601869—31nomaximal, Hall
9C2×#6769—21no—
10C2×D120C2211yescharacteristic
11C2×C5×D24C2211yescharacteristic
12C2×C5×D3×C8C2211yescharacteristic
13C5×#895—21no—
14C2×C3×Dic20C2211yescharacteristic
15C2×#6658—21no—
16#91275—22no—
17#91275—22no—
18C3×C5×#107C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20C5×#809—21no—
21C2×C3×#672C2211yescharacteristic
22#90941—22no—
23#90939—22no—
24#69224—51nomaximal, Hall
25C2×#4050—31no—
26C5×#466—31no—
27C2×#3959—31no—
28C2×#3958—31no—
29C22⋊#672—31no—
30#64712D311yescharacteristic, complemented
31#64711—31no—
32C2×D60—21no—
33C2×C5×D12—21no—
34C2×C5×D12—41no—
35C2×C4×C5×D3D411yescharacteristic
36C2×C3×Dic10—21no—
37C2×#1203—41no—
38C2×#1200—41no—
39#6769—24no—
40#6769—42no—
41C2×C3×C5×C8C2311yescharacteristic
42C3×C5×C4⋊C4—21no—
43D120—21no—
44D120D412yescomplemented
45C5×(C2×D3)⋊C4—41no—
46C2×C5×C3⋊C8D411yescharacteristic
47C5×D24—21no—
48C5×D24—21no—
49C5×D3×C8—21no—
50C5×D3×C8—21no—
51C3×Dic20—21no—
52C3×Dic20D412yescomplemented
53#6658—24no—
54C3⋊#672—21no—
55C3×#672—21no—
56C2×#919—51no—
57C2×#828—51no—
58C2×D48—51no—
59#4883D511yescharacteristic, complemented
60C3×#358—51no—
61(C2×D3)⋊C16—51no—
62#4491—51no—
63C2×#709—61no—
64C2×C5×D8—31no—
65C22×C5×C8—31no—
66C5×#121—61no—
67C2×Dic20C2×D311yescharacteristic
68#4050—62no—
69#4050—62no—
70C2×D40—31no—
71C2×#677—61no—
72C5×#107C2×D311yescharacteristic
73C5×#102—61no—
74#3959—62no—
75#3958—62no—
76C2×#672—31no—
77C2×#672C2×D311yescharacteristic
78#2186—151noSylow
79C22×D15—41no—
80C22×C5×D3—41no—
81C22×C5×D3D811yescharacteristic
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84D60—22no—
85D60—41no—
86C2×C5×Dic3D811yescharacteristic
87C5×D12—41no—
88C5×D12—41no—
89C5×D12—82no—
90C4×C5×D3—21no—
91C4×C5×D3—21no—
92C2×C3×Dic5—41no—
93C3×Dic10—22no—
94C3×Dic10—41no—
95#1203—44no—
96#1200—44no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C5×C3⋊C8—21no—
100C2×#239—101no—
101C2×C3×Q16—51no—
102C2×#215—101no—
103#919—102no—
104#919—102no—
105C2×D24—51no—
106C2×D24C2×D511yescharacteristic
107C2×D3×C8C2×D511yescharacteristic
108#895—21no—
109C2×C3×C16—51no—
110C3×#107C2×D511yescharacteristic
111#828—102no—
112C2×C3⋊C16—51no—
113#809—21no—
114D48—102no—
115C2×C5×D4—61no—
116C2×C5×D4—121no—
117C22×C4×C5—31no—
118C2×C22⋊D5—121no—
119#709—64no—
120#709—122no—
121C2×D20—61no—
122C2×C4×D5—121no—
123C2×Dic10—21no—
124C5×D8—61no—
125C5×D8—61no—
126C2×C5×C8—31no—
127C2×C5×C8—61no—
128C2×C5×C8—61no—
129C2×C5×C8C22×D311yescharacteristic
130C5×C4⋊C4—21no—
131C5×C22⋊C4—121no—
132Dic20—21no—
133Dic20D1212yescomplemented
134D40—32no—
135D40—61no—
136#677—64no—
137#672—21no—
138#672—61no—
139C2×#135—151no—
140C2×SD32—151no—
141C2×D16—151no—
142#466—31no—
143#358—51no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5C2×D811yescharacteristic
147C2×D15—42no—
148C2×D15—81no—
149C2×D15—81no—
150C2×C5×D3—21no—
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C2×C5×D3—81no—
154C2×C5×D3—81no—
155C2×C5×D3—81no—
156C3×C4×C5—81no—
157C3×C4×C5#12011yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5—42no—
160C5×Dic3—21no—
161C2×C3×Q8—101no—
162#239—104no—
163#239—202no—
164C2×D12—21no—
165C2×D12—41no—
166C2×D12—101no—
167C2×D12—201no—
168C2×C4×D3—201no—
169C2×C4×D3C22⋊D511yescharacteristic
170C3×Q16—52no—
171C3×Q16—101no—
172C2×C3×C8C22×D511yescharacteristic
173C3×C4⋊C4—21no—
174#215—104no—
175(C2×D3)⋊C4—41no—
176C2×C3⋊C8C22⋊D511yescharacteristic
177D24—21no—
178D24—21no—
179D24—52no—
180D24—101no—
181D3×C8—21no—
182D3×C8—21no—
183C3×C16—101no—
184C3⋊C16—101no—
185C23×C5—31no—
186C23×C5—121no—
187C22×D5—121no—
188C5×D4—121no—
189C5×D4—121no—
190C5×D4—242no—
191C2×C4×C5—31no—
192C2×C4×C5—41no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5D3×D411yescharacteristic
196C22⋊D5—124no—
197C2×Dic5—41no—
198D20—62no—
199D20—121no—
200C4×D5—124no—
201Dic10—22no—
202Dic10—41no—
203C5×C8—61no—
204C5×C8C2×D1211yescharacteristic
205C5×C8D3×D411yescharacteristic
206C2×#41—301no—
207#135—302no—
208#135—302no—
209C2×Q16—51no—
210C2×SD16—301no—
211C2×D8—31no—
212C2×D8—151no—
213C22×C8—31no—
214#121—61no—
215SD32—302no—
216D16—302no—
217C2×C16—51no—
218C2×C16—151no—
219#107D3×D511yescharacteristic
220#102—61no—
221C2×C3×C5#44711yescharacteristic
222C2×C3×C5#50811yescharacteristic
223C2×C3×C5#50911yescharacteristic
224D15—82no—
225C5×D3—41no—
226C5×D3—161no—
227C22×D3—41no—
228C22×D3—201no—
229C22×D3#68611yescharacteristic
230C3×Q8—102no—
231C3×Q8—201no—
232C2×C3×C4—41no—
233C2×C3×C4—201no—
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3#68611yescharacteristic
236D12—41no—
237D12—41no—
238D12—82no—
239D12—102no—
240D12—204no—
241D12—201no—
242C4×D3—21no—
243C4×D3—21no—
244C4×D3—204no—
245C3×C8D4×D511yescharacteristic
246C3×C8D4×D511yescharacteristic
247C3⋊C8—21no—
248C22×C5—61no—
249C22×C5—61no—
250C22×C5—61no—
251C22×C5—241no—
252C22×C5—241no—
253C22×C5—241no—
254C22×C5D3×D811yescharacteristic
255C2×D5—122no—
256C2×D5—241no—
257C2×D5—241no—
258C4×C5—61no—
259C4×C5—81no—
260C4×C5#88211yescharacteristic
261C4×C5#91411yescharacteristic
262Dic5—42no—
263#41—304no—
264#41—602no—
265C2×Q8—101no—
266C2×D4—61no—
267C2×D4—121no—
268C2×D4—301no—
269C2×D4—601no—
270C22×C4—31no—
271C22×C4—601no—
272Q16—52no—
273Q16—101no—
274SD16—304no—
275D8—61no—
276D8—61no—
277D8—152no—
278D8—301no—
279C2×C8—31no—
280C2×C8—61no—
281C2×C8—61no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—21no—
284C22⋊C4—121no—
285C16—101no—
286C16—301no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3C2×#68611yescharacteristic
289C2×D3—21no—
290C2×D3—21no—
291C2×D3—21no—
292C2×D3—81no—
293C2×D3—81no—
294C2×D3—81no—
295C2×D3—202no—
296C2×D3—401no—
297C2×D3—401no—
298C3×C4—81no—
299C3×C4—202no—
300C3×C4#408311yescharacteristic
301C3×C4#409511yescharacteristic
302Dic3—21no—
303C2×C5—121no—
304C2×C5—481no—
305C2×C5#477311yescharacteristic
306C2×C5#491411yescharacteristic
307C2×C5#491911yescharacteristic
308D5—242no—
309C23—31no—
310C23—121no—
311C23—601no—
312Q8—102no—
313Q8—201no—
314D4—121no—
315D4—121no—
316D4—242no—
317D4—302no—
318D4—604no—
319D4—601no—
320C2×C4—31no—
321C2×C4—41no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—201no—
325C2×C4—604no—
326C2×C4D3×C22⋊D511yescharacteristic
327C8—61no—
328C8D5×D1211yescharacteristic
329C8#677711yescharacteristic
330C2×C3#6532511yescharacteristic
331C2×C3#6543611yescharacteristic
332C2×C3#6548311yescharacteristic
333D3—41no—
334D3—161no—
335D3—402no—
336C5#6922411yescharacteristic, complemented, Sylow
337C22—61no—
338C22—61no—
339C22—61no—
340C22—241no—
341C22—241no—
342C22—241no—
343C22—602no—
344C22—1201no—
345C22—1201no—
346C22D3×#68611yescharacteristic
347C4—61no—
348C4—81no—
349C4—202no—
350C4#9147511yescharacteristic
351C4#9150411yescharacteristic
352C3#1060186911yescharacteristic, complemented, Sylow
353C2—121no—
354C2—481no—
355C2—1202no—
356C2#1174748211yescharacteristic
357C2#1174828311yescharacteristic
358C2#1174830611yescharacteristic
subgroupG/H
centerC22D3×#686
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
hypercenter#107D3×D5
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#91275C2semidirect
2. C5×#4883C2semidirect
3. C2×#90941C2semidirect
4. C2×#90939C2semidirect
5. #11746312C2semidirect
6. C3×#64712C2semidirect
7. (C2×D3)⋊#672C2semidirect
30. #64712D3semidirect
44. D120D4semidirect
52. C3×Dic20D4semidirect
59. #4883D5semidirect
133. Dic20D12semidirect
287. C3×C5#2186semidirect
336. C5#69224semidirect
352. C3#10601869semidirect

Maximal subgroups

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

subgroupindex
C2×#912752
C5×#48832
C2×#909412
C2×#909392
#117463122
C3×#647122
(C2×D3)⋊#6722
#106018693
#692245