Finite Group Databasebeta

← #14316151

Subgroups — #14316151

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×#91270C211yesmaximal, characteristic, complemented
2C2×#91084C211yesmaximal, characteristic, complemented
3#11747899C211yesmaximal, characteristic, complemented
4C2×#90939C211yesmaximal, characteristic, complemented
5C5×#4509C211yesmaximal, characteristic, complemented
6C3×#64727C211yesmaximal, characteristic, complemented
7#11745902C211yesmaximal, characteristic, complemented
8#10599985—31nomaximal, Hall
9C2×#6772—21no—
10C2×Dic60C2211yescharacteristic
11C2×D120C2211yescharacteristic
12C2×C5×D24C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14#91450—21no—
15C2×#6659—21no—
16#91270—22no—
17#91270—22no—
18C2×C3×C5×C16C2211yescharacteristic
19#91084—22no—
20C5×#818C2211yescharacteristic
21C2×C3×#672C2211yescharacteristic
22#90969—21no—
23#90939—22no—
24#69109—51nomaximal, Hall
25C2×#4058—31no—
26C2×#3958—31no—
27C2×#3932—31no—
28#65172—31no—
29C5×#357—31no—
30#64727D311yescharacteristic, complemented
31#64712—31no—
32C2×D60—21no—
33C2×Dic30—21no—
34C2×C5×D12—21no—
35C2×C3×C4×D5D411yescharacteristic
36C2×#1202—41no—
37C2×#1201—41no—
38C2×D3×Dic5—41no—
39#6772—24no—
40#6772—42no—
41C2×C3×C5×C8C2311yescharacteristic
42Dic60—21no—
43Dic60D412yescomplemented
44D120—21no—
45D120—21no—
46C5×C4⋊Dic3—21no—
47C5×D24—21no—
48C5×D24D412yescomplemented
49C2×C3×#168D411yescharacteristic
50C3×C8×D5—21no—
51C3×C8×D5—21no—
52#6667—41no—
53#6659—24no—
54C3×C5×C16—21no—
55C3×#672—21no—
56C2×#904—51no—
57#5115—51no—
58C2×#800—51no—
59C2×D48—51no—
60C3×C22⋊C16—51no—
61#4509D511yescharacteristic, complemented
62#4503—51no—
63C2×#711—61no—
64C2×C5×D8—31no—
65C2×#687—61no—
66#4058—62no—
67#4058—62no—
68C2×Dic20—31no—
69C2×D40—31no—
70C2×C8×D5C2×D311yescharacteristic
71#4041—61no—
72C2×C5×C16C2×D311yescharacteristic
73C5×#107—31no—
74#3958—62no—
75C2×#672C2×D311yescharacteristic
76#3941—61no—
77#3932—62no—
78#2186—151noSylow
79C22×D15—41no—
80C22×C5×D3—41no—
81C22×C3×D5D811yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×Dic15—41no—
84D60—41no—
85D60—41no—
86Dic30—22no—
87Dic30—41no—
88C2×C5×Dic3—41no—
89C5×D12—22no—
90C5×D12—41no—
91C2×C3×Dic5D811yescharacteristic
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94#1202—82no—
95#1201—44no—
96D3×Dic5—44no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C2×#235—101no—
101C22×C3×C8—51no—
102#930—101no—
103C2×Dic12—51no—
104#904—102no—
105#904—102no—
106C2×D24—51no—
107C2×D24C2×D511yescharacteristic
108C2×#204—101no—
109C2×C3×C16—51no—
110C2×C3×C16C2×D511yescharacteristic
111#821—101no—
112#818C2×D511yescharacteristic
113#800—102no—
114D48—102no—
115C2×C5×D4—61no—
116C2×C22⋊D5—121no—
117C22×Dic5—121no—
118#711—64no—
119#711—122no—
120C2×D20—61no—
121C2×D20—121no—
122C2×C4×D5D1211yescharacteristic
123C2×Dic10—61no—
124C5×D8—32no—
125C5×D8—61no—
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—61no—
128#687—64no—
129#685—121no—
130C2×#168D1211yescharacteristic
131Dic20—32no—
132Dic20—61no—
133D40—61no—
134D40—61no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—21no—
138#672—21no—
139C2×#135—151no—
140C2×SD32—151no—
141C2×D16—151no—
142#466—151no—
143#358—151no—
144#357—31no—
145C22⋊C16—51no—
146C22×C3×C5C2×D811yescharacteristic
147C2×D15—81no—
148C2×D15—81no—
149C2×D15—81no—
150C2×C5×D3—42no—
151C2×C5×D3—81no—
152C2×C5×D3—81no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C3×C4×C5#12011yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158Dic15—42no—
159C3×Dic5—21no—
160C5×Dic3—81no—
161C22×C3×C4—51no—
162C2×#67—201no—
163C2×#67—201no—
164#235—104no—
165#235—202no—
166C2×D12—21no—
167C2×D12—101no—
168C2×C4×D3—201no—
169C2×Dic6—101no—
170C2×C3×C8—51no—
171C2×C3×C8—101no—
172C2×C3×C8—101no—
173C2×C3×C8C22×D511yescharacteristic
174(C2×D3)⋊C4—201no—
175C4⋊Dic3—21no—
176Dic12—52no—
177Dic12—101no—
178D24—21no—
179D24—101no—
180D24—101no—
181D24D2012yescomplemented
182#204—104no—
183C3×C16—21no—
184C3×C16—101no—
185C23×C5—121no—
186C22×D5—121no—
187C22×D5D2411yescharacteristic
188C5×D4—62no—
189C5×D4—121no—
190C2×C4×C5—121no—
191C2×C4×C5C2×D1211yescharacteristic
192C22⋊D5—124no—
193C2×Dic5—124no—
194C2×Dic5—121no—
195C2×Dic5D2411yescharacteristic
196D20—121no—
197D20—121no—
198D20—242no—
199C4×D5—21no—
200C4×D5—21no—
201Dic10—62no—
202Dic10—121no—
203C5×C8D3×D411yescharacteristic
204C5×C8D3×D411yescharacteristic
205#168—21no—
206C2×#41—301no—
207#135—302no—
208#135—302no—
209C2×Q16—151no—
210C2×SD16—301no—
211C2×D8—31no—
212C2×D8—151no—
213C22×C8—51no—
214#121—301no—
215SD32—302no—
216D16—302no—
217C2×C16—51no—
218C2×C16D3×D511yescharacteristic
219#107—31no—
220#102—301no—
221C2×C3×C5#44711yescharacteristic
222C2×C3×C5#50811yescharacteristic
223C2×C3×C5#50911yescharacteristic
224D15—161no—
225C3×D5—41no—
226C5×D3—82no—
227C23×C3—51no—
228C22×D3—41no—
229C22×D3—201no—
230C2×C3×C4—51no—
231C2×C3×C4—101no—
232C2×C3×C4—101no—
233C2×C3×C4D4×D511yescharacteristic
234#67—204no—
235#67—402no—
236C2×Dic3—41no—
237C2×Dic3—201no—
238D12—22no—
239D12—41no—
240D12—201no—
241D12—201no—
242C4×D3—204no—
243Dic6—102no—
244Dic6—201no—
245C3×C8—101no—
246C3×C8C2×D2011yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5—122no—
249C22×C5—241no—
250C22×C5—241no—
251C22×C5C2×D2411yescharacteristic
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—21no—
255C2×D5—241no—
256C2×D5—241no—
257C2×D5—241no—
258C4×C5—241no—
259C4×C5#88211yescharacteristic
260C4×C5#90811yescharacteristic
261Dic5—21no—
262Dic5—122no—
263#41—304no—
264#41—602no—
265C2×Q8—301no—
266C2×D4—61no—
267C2×D4—301no—
268C2×D4—601no—
269C2×D4—601no—
270C22×C4—51no—
271C22×C4—601no—
272Q16—152no—
273Q16—301no—
274SD16—304no—
275D8—32no—
276D8—61no—
277D8—301no—
278D8—301no—
279C2×C8—51no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—61no—
284C22⋊C4—601no—
285C16—21no—
286C16—101no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—101no—
289C22×C3—101no—
290C22×C3—101no—
291C22×C3D5×D811yescharacteristic
292C2×D3—42no—
293C2×D3—81no—
294C2×D3—81no—
295C2×D3—401no—
296C2×D3—401no—
297C2×D3—401no—
298C3×C4—101no—
299C3×C4#402811yescharacteristic
300C3×C4#406011yescharacteristic
301Dic3—81no—
302Dic3—202no—
303C2×C5—242no—
304C2×C5#473211yescharacteristic
305C2×C5#490411yescharacteristic
306C2×C5#490811yescharacteristic
307D5—41no—
308D5—481no—
309C23—51no—
310C23—121no—
311C23—601no—
312Q8—302no—
313Q8—601no—
314D4—62no—
315D4—121no—
316D4—604no—
317D4—601no—
318D4—601no—
319D4—1202no—
320C2×C4—51no—
321C2×C4—101no—
322C2×C4—101no—
323C2×C4—121no—
324C2×C4—604no—
325C2×C4—601no—
326C2×C4D5×D1211yescharacteristic
327C8—101no—
328C8D3×D2011yescharacteristic
329C8#679011yescharacteristic
330C2×C3—201no—
331C2×C3#6506211yescharacteristic
332C2×C3#6520011yescharacteristic
333C2×C3#6520511yescharacteristic
334D3—82no—
335D3—801no—
336C5#6910911yescharacteristic, complemented, Sylow
337C22—101no—
338C22—101no—
339C22—101no—
340C22—122no—
341C22—241no—
342C22—241no—
343C22—1201no—
344C22—1201no—
345C22—1201no—
346C22D5×D2411yescharacteristic
347C4—101no—
348C4—241no—
349C4—602no—
350C4#9124911yescharacteristic
351C4#9147611yescharacteristic
352C3#1059998511yescharacteristic, complemented, Sylow
353C2—201no—
354C2—242no—
355C2—2401no—
356C2#1174681611yescharacteristic
357C2#1174683311yescharacteristic
358C2#1174811711yescharacteristic
subgroupG/H
centerC22D5×D24
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#91270C2semidirect
2. C2×#91084C2semidirect
3. #11747899C2semidirect
4. C2×#90939C2semidirect
5. C5×#4509C2semidirect
6. C3×#64727C2semidirect
7. #11745902C2semidirect
30. #64727D3semidirect
43. Dic60D4semidirect
48. C5×D24D4semidirect
61. #4509D5semidirect
181. D24D20semidirect
287. C3×C5#2186semidirect
336. C5#69109semidirect
352. C3#10599985semidirect

Maximal subgroups

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

subgroupindex
C2×#912702
C2×#910842
#117478992
C2×#909392
C5×#45092
C3×#647272
#117459022
#105999853
#691095