Finite Group Databasebeta

← #14289206

Subgroups — #14289206

Order 1920.

420 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752477C211yesmaximal, characteristic, complemented
2C3×#65137C211yesmaximal, characteristic
3#11747083C211yesmaximal, characteristic
4#11746895C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic, complemented
6C5×#4486C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599249—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C2×C3×#677—21no—
12C3×#4020C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91384—21no—
15#91376—21no—
16#91335—22no—
17Dic5×Dic6—21no—
18#91331—21no—
19C2×#6657—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3953—21no—
24#90965—21no—
25#90964—22no—
26#71030—51nomaximal, Hall
27#66055—31no—
28#65377—31no—
29#65137—31no—
30#65137D311yescharacteristic
31C5×#332—31no—
32#64704—31no—
33#64704—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×Dic10D411yescharacteristic
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D412yes—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52C3×#677—42no—
53Dic3⋊Dic5—22no—
54#6668—22no—
55#6668—22no—
56Dic3×Dic5—22no—
57#6657—42no—
58#5570—51no—
59C3×#460—51no—
60#5075—51no—
61#5070—51no—
62#4535—51no—
63#4486D511yescharacteristic, complemented
64#4484—51no—
65C5×C4⋊Q8—31no—
66Q8×Dic5—61no—
67#4090—61no—
68C2×#677—21no—
69C2×#677—61no—
70#4036—61no—
71#4035—62no—
72#4033—61no—
73#4020C2×D311yescharacteristic
74C4×Dic10—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78#3953—21no—
79#3953—61no—
80#3941—62no—
81C4×#168—31no—
82#1626—151noSylow
83C22×C3×D5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89Dic30—21no—
90Dic30—21no—
91C2×C5×Dic3—22no—
92C5×Dic6—41no—
93C5×Dic6—41no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×Dic10—21no—
102C3×Dic10SD1612yescomplemented
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C2×C3×SD16—101no—
107C3×#127—51no—
108C3×C4×Q8—51no—
109Q8×Dic3—101no—
110C2×#214—101no—
111#890—101no—
112#890—102no—
113#869—101no—
114#869C2×D511yescharacteristic
115C4×Dic6—51no—
116C4×Dic6—101no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×#102—101no—
119#832—101no—
120#832—102no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8—61no—
124C2×D20—21no—
125C2×D20—21no—
126C2×D20—21no—
127C2×Dic10—31no—
128C2×Dic10#6711yescharacteristic
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⋊Dic5#6711yescharacteristic
137#683—21no—
138#683—62no—
139#683—62no—
140#683—61no—
141C4×Dic5—21no—
142C4×Dic5—62no—
143C4×Dic5—61no—
144C2×#168—61no—
145#677—42no—
146#677—122no—
147#557—151no—
148#486—151no—
149#460—51no—
150#460—151no—
151#332—31no—
152Q8⋊C8—151no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5—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—41no—
164Dic15—41no—
165C3×Dic5—22no—
166C3×Dic5—41no—
167C5×Dic3—42no—
168C2×C3×Q8—51no—
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C2×Dic6—21no—
173C2×Dic6—51no—
174C3×SD16—202no—
175C2×C3×C8—21no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—101no—
178C3×C42—101no—
179C3×C42C22×D511yescharacteristic
180#214—202no—
181C4⋊Dic3—21no—
182C4⋊Dic3—51no—
183C4⋊Dic3—102no—
184C4⋊Dic3—102no—
185C4⋊Dic3D2012yes—
186Dic3⋊C4—102no—
187Dic3⋊C4—101no—
188C4×Dic3—102no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—41no—
193C5×Q8—121no—
194C5×Q8—121no—
195C2×C4×C5—62no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—42no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—41no—
208Dic10—21no—
209Dic10—61no—
210Dic10—61no—
211Dic10#21412yescomplemented
212C5×C8—41no—
213C5×C8—121no—
214#168—121no—
215C2×SD16—101no—
216C2×SD16—301no—
217C4⋊Q8—31no—
218C4⋊Q8—301no—
219#127—51no—
220#125—302no—
221#125—301no—
222C4×Q8—51no—
223C4×Q8—151no—
224C4×Q8—301no—
225C4×Q8—301no—
226C4⋊C8—31no—
227C4⋊C8D3×D511yescharacteristic
228#102—101no—
229#102—302no—
230#102—301no—
231C4×C8—151no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—161no—
236C23×C3—201no—
237C3×Q8—52no—
238C3×Q8—101no—
239C3×D4—202no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—201no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4C2×D2011yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×Dic3—22no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252Dic6—41no—
253Dic6—41no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—41no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—81no—
261C2×D5—81no—
262C2×D5—81no—
263C4×C5—21no—
264C4×C5—122no—
265C4×C5#91411yescharacteristic
266C4×C5#91611yescharacteristic
267C4×C5C2×#21411yescharacteristic
268C4×C5#95111yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—51no—
274C2×Q8—61no—
275C2×Q8—151no—
276C2×D4—101no—
277C2×D4—101no—
278C2×D4—101no—
279SD16—202no—
280SD16—602no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—301no—
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—401no—
299C22×C3—401no—
300C22×C3—401no—
301C22×C3#402811yescharacteristic
302C3×C4—21no—
303C3×C4—102no—
304C3×C4—201no—
305C3×C4#405711yescharacteristic
306C3×C4D5×SD1611yescharacteristic
307C3×C4#406211yescharacteristic
308C3×C4#406411yescharacteristic
309Dic3—42no—
310Dic3—201no—
311Dic3—201no—
312C2×C5#504011yescharacteristic
313C2×C5#517211yescharacteristic
314C2×C5#520111yescharacteristic
315D5—161no—
316C23—201no—
317Q8—52no—
318Q8—101no—
319Q8—121no—
320Q8—121no—
321Q8—301no—
322Q8—301no—
323D4—202no—
324D4—201no—
325D4—201no—
326D4—201no—
327D4—201no—
328C2×C4—62no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—301no—
332C2×C4—301no—
333C2×C4D3×D2011yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—41no—
337C8—121no—
338C8—601no—
339C2×C3—801no—
340C2×C3#6504211yescharacteristic
341C2×C3#6507011yescharacteristic
342C2×C3#6509511yescharacteristic
343C5#7103011yescharacteristic, complemented, Sylow
344C22—401no—
345C22—401no—
346C22—401no—
347C22#9147411yescharacteristic
348C4—21no—
349C4—102no—
350C4—122no—
351C4—201no—
352C4—601no—
353C4—601no—
354C4#9125711yescharacteristic
355C4#9127611yescharacteristic
356C4D5×#21411yescharacteristic
357C4#9150811yescharacteristic
358C3#1059924911yescharacteristic, complemented, Sylow
359C2—801no—
360C2#1174749311yescharacteristic
361C2#1174788911yescharacteristic
362C2#1174825511yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
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. #11752477C2semidirect
5. #11746305C2semidirect
6. C5×#4486C2semidirect
7. #11745840C2semidirect
63. #4486D5semidirect
102. C3×Dic10SD16semidirect
211. Dic10#214semidirect
297. C3×C5#1626semidirect
343. C5#71030semidirect
358. C3#10599249semidirect

Maximal subgroups

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

subgroupindex
#117524772
C3×#651372
#117470832
#117468952
#117463052
C5×#44862
#117458402
#105992493
#710305