Finite Group Databasebeta

← #14289647

Subgroups — #14289647

Order 1920.

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

normal subgroups only

This group has 468 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#11756485C211yesmaximal, characteristic
2C5×#5093C211yesmaximal, characteristic, complemented
3#11746885C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745838C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10602021—31nomaximal, Hall
9C2×#6821—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91835—21no—
12#91784—21no—
13#91783—22no—
14C4⋊C4×D15—21no—
15C4×D60C2211yescharacteristic
16C4×D60C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C5×#810—22no—
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90985—21no—
23#90985—21no—
24#90969—21no—
25#90969—21no—
26#68434—51nomaximal, Hall
27#66060—31no—
28C5×#487—31no—
29#65373—31no—
30#65373—31no—
31#64767D311yescharacteristic, complemented
32#64679—31no—
33#64679—31no—
34C2×C3×C5×Q8—21no—
35#6821—42no—
36#6821—42no—
37C2×D60—22no—
38C2×D60D411yescharacteristic
39C2×D60D411yescharacteristic
40C2×C4×D15—22no—
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C5×Dic6—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D412yes—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—21no—
49#6714—21no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D411yescharacteristic
52#6712—22no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58#5726—51no—
59#5093D511yescharacteristic, complemented
60#4842—51no—
61#4842—51no—
62C3×#332—51no—
63#4483—51no—
64#4483—51no—
65C2×#713—61no—
66C5×C4⋊Q8—31no—
67C5×C4⋊Q8C2×D311yescharacteristic
68#4092—61no—
69#4041—61no—
70#4040—62no—
71D5×C4⋊C4—61no—
72C4×D20—31no—
73C4×D20—31no—
74C5×#103—62no—
75C4×C5×C8—31no—
76#3941—61no—
77#3941—61no—
78#3940—61no—
79#3940—61no—
80C4⋊#168C2×D311yescharacteristic
81C4⋊#168C2×D311yescharacteristic
82#1635—151noSylow
83C22×D15—21no—
84C22×D15—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93D60—21no—
94D60—21no—
95D60—21no—
96D60—44no—
97D60SD1612yes—
98C4×D15—44no—
99C4×D15—41no—
100C4×D15—41no—
101C4×D15—41no—
102C4×D15—41no—
103C2×C5×Dic3—41no—
104C5×Dic6—42no—
105C3×#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×#239—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110#946—101no—
111#895—101no—
112#894—102no—
113D3×C4⋊C4—101no—
114C4×D12—51no—
115C4×D12—51no—
116#869C2×D511yescharacteristic
117C3×C4⋊C8—51no—
118C3×C4⋊C8—51no—
119#821—101no—
120#821—101no—
121#817—101no—
122#817—101no—
123#810—22no—
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×Q8—61no—
127#713—122no—
128#713—122no—
129C2×D20—31no—
130C2×D20—31no—
131C2×D20—62no—
132C2×C4×D5—62no—
133C2×C4×D5—61no—
134C2×C4×D5—61no—
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4D1212yes—
140C42×C5C22×D311yescharacteristic
141#685—62no—
142#685—61no—
143#685—61no—
144C4⋊Dic5—31no—
145C4⋊Dic5—31no—
146#683—62no—
147C2×#168—21no—
148C2×#168—21no—
149#547—151no—
150#487—31no—
151#476—151no—
152#476—151no—
153#332—51no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—22no—
158C2×D15—41no—
159C2×D15—41no—
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—41no—
170Dic15—41no—
171C5×Dic3—81no—
172C2×C3×Q8—21no—
173#239—202no—
174#239—202no—
175C2×D12—51no—
176C2×D12—51no—
177C2×D12—102no—
178C2×C4×D3—102no—
179C2×C4×D3—101no—
180C2×C4×D3—101no—
181C2×Dic6—21no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C22⋊D512yes—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—101no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—51no—
193C4⋊Dic3—51no—
194Dic3⋊C4—102no—
195C2×C3⋊C8—21no—
196C22×D5—61no—
197C22×D5—61no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×Q8—122no—
201C2×C4×C5—22no—
202C2×C4×C5—121no—
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×Dic5—61no—
207C2×Dic5—61no—
208D20—32no—
209D20—61no—
210D20—61no—
211D20—61no—
212D20—124no—
213C4×D5—124no—
214C4×D5—121no—
215C4×D5—121no—
216C4×D5—121no—
217C4×D5—121no—
218C5×C8—121no—
219#168—41no—
220#168—41no—
221C2×#41—301no—
222C4⋊Q8—31no—
223C4⋊Q8D3×D511yescharacteristic
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—151no—
228C4×D4—151no—
229C2×C4⋊C4—301no—
230#106—301no—
231#106—301no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#103—62no—
235#102—301no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—42no—
242D15—81no—
243C22×D3—101no—
244C22×D3—101no—
245C3×Q8—41no—
246C3×Q8—41no—
247C2×C3×C4—22no—
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—41no—
252C2×Dic3—101no—
253C2×Dic3—101no—
254D12—52no—
255D12—101no—
256D12—101no—
257D12—101no—
258D12—204no—
259C4×D3—204no—
260C4×D3—201no—
261C4×D3—201no—
262C4×D3—201no—
263C4×D3—201no—
264Dic6—42no—
265C3×C8—201no—
266C3×C8—201no—
267C3⋊C8—41no—
268C22×C5#88211yescharacteristic
269C2×D5—62no—
270C2×D5—121no—
271C2×D5—121no—
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5—241no—
278C4×C5#91111yescharacteristic
279C4×C5D3×SD1611yescharacteristic
280C4×C5#91611yescharacteristic
281C4×C5#91811yescharacteristic
282Dic5—121no—
283Dic5—121no—
284#41—602no—
285#41—602no—
286C2×Q8—21no—
287C2×Q8—61no—
288C2×D4—151no—
289C2×D4—151no—
290C2×D4—302no—
291C22×C4—302no—
292C22×C4—301no—
293C22×C4—301no—
294C2×C8—61no—
295C2×C8—101no—
296C2×C8—101no—
297C4⋊C4—21no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—151no—
301C4⋊C4—151no—
302C4⋊C4—302no—
303C4⋊C4#120312yes—
304C22⋊C4—302no—
305C22⋊C4—301no—
306C22⋊C4—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3#408311yescharacteristic
310C2×D3—102no—
311C2×D3—201no—
312C2×D3—201no—
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—42no—
318C3×C4D5×SD1611yescharacteristic
319C3×C4#406011yescharacteristic
320C3×C4#406411yescharacteristic
321C3×C4#406511yescharacteristic
322Dic3—81no—
323Dic3—201no—
324Dic3—201no—
325C2×C5#475311yescharacteristic
326C2×C5#477611yescharacteristic
327C2×C5#480811yescharacteristic
328D5—122no—
329D5—241no—
330C23—301no—
331C23—301no—
332Q8—41no—
333Q8—41no—
334Q8—122no—
335D4—152no—
336D4—301no—
337D4—301no—
338D4—301no—
339D4—604no—
340C2×C4—22no—
341C2×C4—121no—
342C2×C4—301no—
343C2×C4—301no—
344C2×C4—604no—
345C2×C4—601no—
346C2×C4—601no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×#120311yescharacteristic
350C2×C4#679011yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—201no—
354C8—201no—
355C2×C3#6535111yescharacteristic
356C2×C3#6545811yescharacteristic
357C2×C3#6547611yescharacteristic
358D3—202no—
359D3—401no—
360C5#6843411yescharacteristic, complemented, Sylow
361C22—302no—
362C22—601no—
363C22—601no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9157311yescharacteristic
368C4—21no—
369C4—42no—
370C4—241no—
371C4—601no—
372C4—601no—
373C4#9148711yescharacteristic
374C4#9149811yescharacteristic
375C4#9151211yescharacteristic
376C4#9152111yescharacteristic
377C3#1060202111yescharacteristic, complemented, Sylow
378C2—602no—
379C2—1201no—
380C2#1174906211yescharacteristic
381C2#1174930711yescharacteristic
382C2#1174938911yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11756485C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1635
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5093C2semidirect
3. #11746885C2semidirect
4. #11746885C2semidirect
5. C3×#64767C2semidirect
6. #11745838C2semidirect
7. #11745838C2semidirect
31. #64767D3semidirect
59. #5093D5semidirect
308. C3×C5#1635semidirect
360. C5#68434semidirect
377. C3#10602021semidirect

Maximal subgroups

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

subgroupindex
#117564852
C5×#50932
#117468852
C3×#647672
#117458382
#106020213
#684345