Finite Group Databasebeta

← #14316078

Subgroups — #14316078

Order 1920.

452 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 92 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×C3×D5×Q16C211yesmaximal, characteristic, complemented
2C2×#91112C211yesmaximal, characteristic, complemented
3#11747899C211yesmaximal, characteristic
4C2×#90943C211yesmaximal, characteristic, complemented
5C5×#4564C211yesmaximal, characteristic, complemented
6#11745897C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10600016—31nomaximal, Hall
9C2×C3×Q8×D5—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×D120C2211yescharacteristic
12C2×C3×#689—21no—
13C3×D5×Q16—22no—
14C3×D5×Q16—22no—
15C2×C3×Dic20C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17#91450—21no—
18#91112—22no—
19C2×C3⋊#672C2211yescharacteristic
20C5×#818C2211yescharacteristic
21C2×C5×C3⋊C16C2211yescharacteristic
22#90969—21no—
23#90943—22no—
24#72063—51nomaximal, Hall
25C2×D5×Q16D311yescharacteristic, complemented
26C2×#3960—31no—
27C2×#3932—31no—
28#65172—31no—
29C5×#358—31no—
30#64727—31no—
31#64712—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C3×Q8×D5—24no—
35C3×Q8×D5—42no—
36C2×C3×C4×D5—41no—
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×Dic10—41no—
40C2×#1202—41no—
41C3×C5×Q16—21no—
42C3×C5×Q16D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44D120—21no—
45D120—21no—
46C5×C4⋊Dic3—21no—
47C3×#689—24no—
48C2×C3×#168D411yescharacteristic
49C3×Dic20—21no—
50C3×Dic20D412yescomplemented
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6667—41no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C22×C3×Q16—51no—
57C2×#828—51no—
58C2×#828—51no—
59#5115—51no—
60#4564—51no—
61#4564D511yescharacteristic, complemented
62#4549—51no—
63C2×Q8×D5—21no—
64C2×C5×Q16C2×D311yescharacteristic
65C2×#689—21no—
66D5×Q16—22no—
67D5×Q16—22no—
68C2×Dic20C2×D311yescharacteristic
69C2×D40—31no—
70C2×C8×D5C2×D311yescharacteristic
71#4041—61no—
72C2×C5×C16—31no—
73C5×#107—31no—
74#3960—62no—
75C2×#672—31no—
76#3941—61no—
77#3932—62no—
78#2185—151noSylow
79C22×D15—41no—
80C22×C3×D5D811yescharacteristic
81C3×C5×Q8—22no—
82C3×C5×Q8—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85D60—41no—
86D60—41no—
87C2×C5×Dic3—41no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5D811yescharacteristic
90C3×C4×D5—21no—
91C3×C4×D5—21no—
92C3×C4×D5—44no—
93C3×Dic10—22no—
94C3×Dic10—44no—
95C3×Dic10—41no—
96#1202—82no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C22×C3×Q8—101no—
101C2×C3×Q16—51no—
102C2×C3×Q16—101no—
103C2×C3×Q16—102no—
104C2×C3×Q16—102no—
105C2×C3×Q16C2×D511yescharacteristic
106C22×C3×C8—51no—
107#930—101no—
108C2×D24—51no—
109#828—102no—
110#828—102no—
111#821—101no—
112#818C2×D511yescharacteristic
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×Q8—21no—
116Q8×D5—24no—
117Q8×D5—42no—
118C2×D20—61no—
119C2×D20—121no—
120C2×C4×D5—41no—
121C2×C4×D5#6711yescharacteristic
122C2×Dic10—21no—
123C2×Dic10—41no—
124C5×Q16—21no—
125C5×Q16#6712yescomplemented
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—61no—
128#689—24no—
129#685—121no—
130C2×#168#6711yescharacteristic
131Dic20—21no—
132Dic20#6712yescomplemented
133D40—61no—
134D40—61no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C22×Q16—51no—
140C2×SD32—151no—
141C2×SD32—151no—
142#466—151no—
143#358—31no—
144#358—151no—
145C22⋊C16—151no—
146C22×C3×C5C2×D811yescharacteristic
147C2×D15—81no—
148C2×D15—81no—
149C2×D15—81no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5SD3212yescomplemented
153C3×C4×C5—42no—
154C3×C4×C5#12011yescharacteristic
155C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
156C3×Dic5—21no—
157C3×Dic5—42no—
158C5×Dic3—81no—
159C2×C3×Q8—21no—
160C2×C3×Q8—104no—
161C2×C3×Q8—101no—
162C2×C3×Q8—201no—
163C2×C3×Q8—202no—
164C22×C3×C4—51no—
165C22×C3×C4—201no—
166C2×#67—201no—
167C2×D12—101no—
168C3×Q16—21no—
169C3×Q16—52no—
170C3×Q16—104no—
171C3×Q16—101no—
172C3×Q16D2012yescomplemented
173C2×C3×C8—51no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C2×C3×C8C22×D511yescharacteristic
177(C2×D3)⋊C4—201no—
178C4⋊Dic3—21no—
179D24—101no—
180D24—101no—
181C3⋊C16—21no—
182C3⋊C16—101no—
183C22×D5—121no—
184C22×D5#21311yescharacteristic
185C5×Q8—22no—
186C5×Q8—41no—
187C2×C4×C5—41no—
188C2×C4×C5—121no—
189C2×C4×C5C2×#6711yescharacteristic
190C2×Dic5—41no—
191C2×Dic5#21311yescharacteristic
192D20—121no—
193D20—121no—
194D20—242no—
195C4×D5—21no—
196C4×D5—21no—
197C4×D5—44no—
198Dic10—22no—
199Dic10—44no—
200Dic10—41no—
201C5×C8C2×#6711yescharacteristic
202C5×C8C2×#6711yescharacteristic
203#168—21no—
204C22×Q8—101no—
205C2×Q16—51no—
206C2×Q16—101no—
207C2×Q16—102no—
208C2×Q16—102no—
209C2×Q16D3×D511yescharacteristic
210C2×D8—151no—
211C22×C8—51no—
212#121—301no—
213SD32—302no—
214SD32—302no—
215C2×C16—31no—
216C2×C16—151no—
217#107—31no—
218#102—301no—
219C2×C3×C5#44711yescharacteristic
220C2×C3×C5C2×SD3211yescharacteristic
221C2×C3×C5#51011yescharacteristic
222D15—161no—
223C3×D5—22no—
224C23×C3—51no—
225C22×D3—201no—
226C3×Q8—22no—
227C3×Q8—41no—
228C3×Q8—102no—
229C3×Q8—204no—
230C3×Q8—201no—
231C2×C3×C4—41no—
232C2×C3×C4—51no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—204no—
236C2×C3×C4—201no—
237C2×C3×C4D4×D511yescharacteristic
238#67—402no—
239C2×Dic3—41no—
240D12—201no—
241D12—201no—
242C3×C8—101no—
243C3×C8C2×D2011yescharacteristic
244C3×C8D4×D511yescharacteristic
245C22×C5C2×#21311yescharacteristic
246C2×D5—21no—
247C2×D5—21no—
248C2×D5—241no—
249C2×D5—241no—
250C2×D5—241no—
251C2×D5#82812yescomplemented
252C4×C5—42no—
253C4×C5—241no—
254C4×C5#93211yescharacteristic
255C4×C5#95311yescharacteristic
256Dic5—21no—
257Dic5—42no—
258C2×Q8—21no—
259C2×Q8—104no—
260C2×Q8—101no—
261C2×Q8—201no—
262C2×Q8—202no—
263C2×D4—301no—
264C2×D4—601no—
265C22×C4—51no—
266C22×C4—201no—
267Q16—21no—
268Q16—52no—
269Q16—104no—
270Q16—101no—
271Q16#120212yescomplemented
272D8—301no—
273D8—301no—
274C2×C8—51no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8C2×D3×D511yescharacteristic
278C4⋊C4—61no—
279C22⋊C4—601no—
280C16—61no—
281C16—301no—
282C3×C5#218511yescharacteristic, complemented, Hall
283C22×C3—52no—
284C22×C3—101no—
285C22×C3—101no—
286C22×C3D5×D811yescharacteristic
287C2×D3—401no—
288C2×D3—401no—
289C2×D3—401no—
290C3×C4—42no—
291C3×C4—101no—
292C3×C4—202no—
293C3×C4#402811yescharacteristic
294C3×C4#406011yescharacteristic
295Dic3—81no—
296C2×C5C2×#82811yescharacteristic
297C2×C5#517911yescharacteristic
298C2×C5#521711yescharacteristic
299D5—22no—
300D5—481no—
301C23—51no—
302C23—601no—
303Q8—22no—
304Q8—41no—
305Q8—102no—
306Q8—204no—
307Q8—201no—
308D4—601no—
309D4—601no—
310D4—1202no—
311C2×C4—41no—
312C2×C4—51no—
313C2×C4—101no—
314C2×C4—101no—
315C2×C4—121no—
316C2×C4—204no—
317C2×C4—201no—
318C2×C4D5×#6711yescharacteristic
319C8—101no—
320C8C2×#120211yescharacteristic
321C8D5×#6711yescharacteristic
322C2×C3—102no—
323C2×C3#6506211yescharacteristic
324C2×C3D5×SD3211yescharacteristic
325C2×C3#6520711yescharacteristic
326D3—801no—
327C5#7206311yescharacteristic, complemented, Sylow
328C22—52no—
329C22—101no—
330C22—101no—
331C22—1201no—
332C22—1201no—
333C22—1201no—
334C22D5×#21311yescharacteristic
335C4—42no—
336C4—101no—
337C4—202no—
338C4—241no—
339C4#9149111yescharacteristic
340C4#9156411yescharacteristic
341C3#1060001611yescharacteristic, complemented, Sylow
342C2—102no—
343C2—2401no—
344C2D5×#82811yescharacteristic
345C2#1174830211yescharacteristic
346C2#1174902211yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radical#11747899C2
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2185
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×Q16C2semidirect
2. C2×#91112C2semidirect
4. C2×#90943C2semidirect
5. C5×#4564C2semidirect
6. #11745897C2semidirect
7. #11745879C2semidirect
25. C2×D5×Q16D3semidirect
42. C3×C5×Q16D4semidirect
50. C3×Dic20D4semidirect
61. #4564D5semidirect
125. C5×Q16#67semidirect
132. Dic20#67semidirect
152. C2×C3×D5SD32semidirect
172. C3×Q16D20semidirect
251. C2×D5#828semidirect
271. Q16#1202semidirect
282. C3×C5#2185semidirect
327. C5#72063semidirect
341. C3#10600016semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
C2×#911122
#117478992
C2×#909432
C5×#45642
#117458972
#117458792
#106000163
#720635