Finite Group Databasebeta

← #14289205

Subgroups — #14289205

Order 1920.

420 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752487C211yesmaximal, characteristic, complemented
2#11750949C211yesmaximal, characteristic
3#11747064C211yesmaximal, characteristic
4#11746912C211yesmaximal, characteristic
5C5×#4486C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7#11745845C211yesmaximal, characteristic, complemented
8#10599249—31nomaximal, Hall
9C2×#6706—21no—
10#91763C2211yescharacteristic
11C4×Dic30C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91388—21no—
15#91385—21no—
16#91344—21no—
17#91336—22no—
18#91333—21no—
19C2×#6658—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21#91105—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90969—22no—
25#90968—21no—
26#68265—51nomaximal, Hall
27#66055—31no—
28#65377—31no—
29#65137—31no—
30#65137—31no—
31C5×#332—31no—
32#64704—31no—
33#64704D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×Dic6—21no—
39C2×C3×Dic10D411yescharacteristic
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45#6706—42no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D412yes—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52C2×C3×#168—21no—
53Dic3⋊Dic5—22no—
54#6669—22no—
55#6669—22no—
56Dic3×Dic5—22no—
57#6658—42no—
58#5567—51no—
59#5027—51no—
60#4848—51no—
61#4694—51no—
62C3×Q8⋊C8—51no—
63#4486D511yescharacteristic, complemented
64#4456—51no—
65C5×C4⋊Q8—31no—
66Q8×Dic5—61no—
67#4090—61no—
68C2×#677—61no—
69C2×#677—61no—
70#4036—61no—
71#4035—62no—
72#4033—61no—
73#4020—31no—
74C4×Dic10—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78#3953—61no—
79#3953—61no—
80#3941—62no—
81C4×#168C2×D311yescharacteristic
82#1626—151noSylow
83C22×D15—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89D60—42no—
90D60—41no—
91D60—41no—
92D60—41no—
93D60—41no—
94Dic30—21no—
95Dic30SD1612yescomplemented
96C2×C5×Dic3—22no—
97C5×Dic6—41no—
98C5×Dic6—41no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×Dic10—21no—
102C3×Dic10—21no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×C4×Q8—51no—
107#944—101no—
108C2×#215—101no—
109C2×#204—101no—
110#889—102no—
111#887—101no—
112#874—51no—
113#870—101no—
114#869C2×D511yescharacteristic
115C4×Dic6—51no—
116C4×Dic6—101no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C4×C8—51no—
119#821—101no—
120#821—102no—
121#809—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—61no—
124C2×D20—61no—
125C2×D20—61no—
126C2×D20—61no—
127C2×Dic10—31no—
128C2×Dic10D1211yescharacteristic
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—32no—
132C5×C4⋊C4—61no—
133C42×C5C22×D311yescharacteristic
134C4⋊Dic5—31no—
135C4⋊Dic5—62no—
136C4⋊Dic5D1211yescharacteristic
137#683—21no—
138#683—62no—
139#683—62no—
140#683—61no—
141C4×Dic5—21no—
142C4×Dic5—62no—
143C4×Dic5—61no—
144C2×#168—21no—
145#677—122no—
146#677—122no—
147#557—151no—
148#486—151no—
149#460—151no—
150#460—151no—
151#332—31no—
152Q8⋊C8—51no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—81no—
156C2×D15—81no—
157C2×D15—81no—
158C3×C4×C5—21no—
159C3×C4×C5C2×SD1611yescharacteristic
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—22no—
164Dic15—41no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C5×Dic3—42no—
168C2×C3×Q8—51no—
169C2×D12—101no—
170C2×D12—101no—
171C2×D12—101no—
172C2×Dic6—21no—
173C2×Dic6—51no—
174C2×C3×C8—21no—
175C2×C3×C8—101no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C42—101no—
179C3×C42C22×D511yescharacteristic
180#215—202no—
181C4⋊Dic3—21no—
182C4⋊Dic3—51no—
183C4⋊Dic3D2012yes—
184Dic3⋊C4—102no—
185Dic3⋊C4—102no—
186Dic3⋊C4—102no—
187Dic3⋊C4—101no—
188C4×Dic3—102no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191#204—202no—
192C22×D5—121no—
193C5×Q8—121no—
194C5×Q8—121no—
195C2×C4×C5—62no—
196C2×C4×C5C2×D1211yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—122no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—121no—
208Dic10—21no—
209Dic10—21no—
210Dic10—32no—
211Dic10—61no—
212C5×C8—41no—
213C5×C8—121no—
214#168—41no—
215C2×SD16—301no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—301no—
219#127—151no—
220#125—301no—
221#125—302no—
222C4×Q8—51no—
223C4×Q8—151no—
224C4×Q8—301no—
225C4×Q8—301no—
226C4⋊C8—31no—
227C4⋊C8D3×D511yescharacteristic
228#102—302no—
229#102—301no—
230#102—301no—
231C4×C8—51no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—161no—
236C22×D3—201no—
237C3×Q8—101no—
238C3×Q8—101no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×Dic3—22no—
245C2×Dic3—101no—
246C2×Dic3—101no—
247D12—202no—
248D12—201no—
249D12—201no—
250D12—201no—
251D12—201no—
252Dic6—41no—
253Dic6—41no—
254Dic6—52no—
255Dic6—101no—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—241no—
261C2×D5—241no—
262C2×D5—241no—
263C4×C5—21no—
264C4×C5—122no—
265C4×C5#90411yescharacteristic
266C4×C5#90811yescharacteristic
267C4×C5D3×SD1611yescharacteristic
268C4×C5#91811yescharacteristic
269Dic5—41no—
270Dic5—41no—
271Dic5—62no—
272Dic5—121no—
273C2×Q8—51no—
274C2×Q8—61no—
275C2×Q8—151no—
276C2×D4—301no—
277C2×D4—301no—
278C2×D4—301no—
279SD16—602no—
280SD16—602no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—101no—
284C4⋊C4—32no—
285C4⋊C4—51no—
286C4⋊C4—61no—
287C4⋊C4—101no—
288C4⋊C4—151no—
289C4⋊C4—302no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C42—101no—
294C42—302no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3#402811yescharacteristic
299C2×D3—401no—
300C2×D3—401no—
301C2×D3—401no—
302C3×C4—21no—
303C3×C4—201no—
304C3×C4—201no—
305C3×C4#405711yescharacteristic
306C3×C4D5×SD1611yescharacteristic
307C3×C4#406211yescharacteristic
308C3×C4#406411yescharacteristic
309Dic3—42no—
310Dic3—102no—
311Dic3—201no—
312C2×C5#473411yescharacteristic
313C2×C5#480611yescharacteristic
314C2×C5#482711yescharacteristic
315D5—481no—
316C23—601no—
317Q8—101no—
318Q8—101no—
319Q8—121no—
320Q8—121no—
321Q8—152no—
322Q8—301no—
323D4—602no—
324D4—601no—
325D4—601no—
326D4—601no—
327D4—601no—
328C2×C4—62no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—301no—
332C2×C4—301no—
333C2×C4D5×D1211yescharacteristic
334C2×C4D3×D2011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—41no—
337C8—121no—
338C8—201no—
339C2×C3#6504211yescharacteristic
340C2×C3#6507011yescharacteristic
341C2×C3#6509511yescharacteristic
342D3—801no—
343C5#6826511yescharacteristic, complemented, Sylow
344C22—1201no—
345C22—1201no—
346C22—1201no—
347C22#9147611yescharacteristic
348C4—21no—
349C4—122no—
350C4—201no—
351C4—201no—
352C4—302no—
353C4—601no—
354C4#9125011yescharacteristic
355C4#9126911yescharacteristic
356C4#9148711yescharacteristic
357C4#9151211yescharacteristic
358C3#1059924911yescharacteristic, complemented, Sylow
359C2—2401no—
360C2#1174749711yescharacteristic
361C2#1174816311yescharacteristic
362C2#1174826111yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1626
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752487C2semidirect
5. C5×#4486C2semidirect
6. C3×#64704C2semidirect
7. #11745845C2semidirect
33. #64704D3semidirect
63. #4486D5semidirect
95. Dic30SD16semidirect
297. C3×C5#1626semidirect
343. C5#68265semidirect
358. C3#10599249semidirect

Maximal subgroups

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

subgroupindex
#117524872
#117509492
#117470642
#117469122
C5×#44862
C3×#647042
#117458452
#105992493
#682655