Finite Group Databasebeta

← #14289641

Subgroups — #14289641

Order 1920.

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

normal subgroups only

This group has 468 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#11752493C211yesmaximal, characteristic
2#11751185C211yesmaximal, characteristic, complemented
3C5×#5079C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11745857C211yesmaximal, characteristic, complemented
6#11745838C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10602021—31nomaximal, Hall
9C2×#6773—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C4×D60C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91465—21no—
15#91437—21no—
16#91359—21no—
17#91356—22no—
18#91093—21no—
19#91092—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#835—22no—
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71140—51nomaximal, Hall
27#66060—31no—
28C5×#487—31no—
29#65373—31no—
30#65373D311yescharacteristic, complemented
31#64767—31no—
32#64679—31no—
33#64679—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C5×Dic6—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1202—22no—
41C2×#1200—22no—
42#6773—42no—
43#6773—42no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—21no—
48C4⋊Dic15D411yescharacteristic
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D412yes—
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56#6669—22no—
57#6665—22no—
58#5551—51no—
59C3×#476—51no—
60#5084—51no—
61#5079D511yescharacteristic, complemented
62D4⋊(C3⋊C8)—51no—
63#4486—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×D20C2×D311yescharacteristic
74C5×#103—62no—
75C4×C5×C8—31no—
76#3941—21no—
77#3941—61no—
78#3940—21no—
79#3940—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1635—151noSylow
83C22×D15—21no—
84C22×C3×D5—21no—
85C3×C5×Q8—42no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91D60—21no—
92D60SD1612yes—
93C4×D15—41no—
94C4×D15—41no—
95C2×C5×Dic3—22no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C2×C3×Dic5—21no—
99C3×D20—21no—
100C3×D20—21no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103#1202—44no—
104#1200—44no—
105C3⋊#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×#235—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×C4×D4—51no—
111#938—101no—
112#924—101no—
113D3×C4⋊C4—101no—
114#883—102no—
115C4×D12—51no—
116#869C2×D511yescharacteristic
117C3×#106—101no—
118C3×C4⋊C8—51no—
119C3×#102—101no—
120#835—22no—
121#809—101no—
122#808—101no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×Q8—61no—
127#713—122no—
128#713—122no—
129C2×D20—31no—
130C2×D20—62no—
131C2×D20#6711yescharacteristic
132C2×C4×D5—21no—
133C2×C4×D5—62no—
134C2×C4×D5—61no—
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—32no—
139C5×C4⋊C4—61no—
140C42×C5C22×D311yescharacteristic
141#685—21no—
142#685—62no—
143#685—61no—
144C4⋊Dic5—31no—
145C4⋊Dic5#6711yescharacteristic
146#683—62no—
147C2×#168—21no—
148C2×#168—61no—
149#547—151no—
150#487—31no—
151#476—51no—
152#476—151no—
153#332—151no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—22no—
158C2×D15—41no—
159C2×D15—41no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5—81no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—41no—
170C3×Dic5—41no—
171C5×Dic3—42no—
172C2×C3×Q8—21no—
173C2×C3×D4—51no—
174C22×C3×C4—101no—
175C2×#67—102no—
176#235—202no—
177#235—202no—
178C2×D12—51no—
179C2×C4×D3—102no—
180C2×C4×D3—101no—
181C2×Dic6—21no—
182C2×C3×C8—101no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—51no—
186C3×C22⋊C4—101no—
187C3×C42C22×D511yescharacteristic
188#217—102no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3—21no—
191C4⋊Dic3—51no—
192C4⋊Dic3C22⋊D512yes—
193Dic3⋊C4—102no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C22×D5—21no—
197C22×D5—61no—
198C5×Q8—42no—
199C5×Q8—121no—
200C5×Q8—121no—
201C2×C4×C5—41no—
202C2×C4×C5—62no—
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—61no—
208D20—21no—
209D20—21no—
210D20—32no—
211D20—61no—
212D20—124no—
213C4×D5—41no—
214C4×D5—41no—
215C4×D5—124no—
216C4×D5—121no—
217C4×D5—121no—
218C5×C8—121no—
219#168—41no—
220#168—121no—
221C2×#41—301no—
222C4⋊Q8—31no—
223C4⋊Q8D3×D511yescharacteristic
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—51no—
228C4×D4—151no—
229C2×C4⋊C4—301no—
230#106—101no—
231#106—301no—
232C4⋊C8—51no—
233C4⋊C8—151no—
234#103—62no—
235#102—101no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—42no—
242C3×D5—81no—
243C23×C3—101no—
244C22×D3—101no—
245C3×Q8—42no—
246C3×D4—101no—
247C3×D4—101no—
248C2×C3×C4—41no—
249C2×C3×C4—101no—
250C2×C3×C4—201no—
251C2×C3×C4—201no—
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255#67—204no—
256C2×Dic3—22no—
257C2×Dic3—101no—
258D12—52no—
259D12—101no—
260C4×D3—204no—
261C4×D3—201no—
262C4×D3—201no—
263Dic6—41no—
264Dic6—41no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5#93711yescharacteristic
269C2×D5—41no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—62no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—81no—
277C4×C5—122no—
278C4×C5D3×SD1611yescharacteristic
279C4×C5#91411yescharacteristic
280C4×C5#94211yescharacteristic
281C4×C5#95011yescharacteristic
282Dic5—41no—
283Dic5—121no—
284#41—602no—
285#41—602no—
286C2×Q8—21no—
287C2×Q8—61no—
288C2×D4—51no—
289C2×D4—151no—
290C2×D4—302no—
291C22×C4—101no—
292C22×C4—302no—
293C22×C4—301no—
294C2×C8—61no—
295C2×C8—101no—
296C2×C8—301no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—32no—
300C4⋊C4—51no—
301C4⋊C4—61no—
302C4⋊C4—151no—
303C4⋊C4—302no—
304C22⋊C4—101no—
305C22⋊C4—302no—
306C22⋊C4—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—201no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3#408311yescharacteristic
313C2×D3—102no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—81no—
318C3×C4—201no—
319C3×C4D5×SD1611yescharacteristic
320C3×C4#406011yescharacteristic
321C3×C4#406411yescharacteristic
322C3×C4#406511yescharacteristic
323Dic3—42no—
324Dic3—201no—
325C2×C5#504711yescharacteristic
326C2×C5#516911yescharacteristic
327C2×C5#520111yescharacteristic
328D5—81no—
329D5—122no—
330C23—101no—
331C23—301no—
332Q8—42no—
333Q8—121no—
334Q8—121no—
335D4—101no—
336D4—101no—
337D4—152no—
338D4—301no—
339D4—604no—
340C2×C4—41no—
341C2×C4—62no—
342C2×C4—101no—
343C2×C4—201no—
344C2×C4—201no—
345C2×C4—301no—
346C2×C4—604no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4D5×#6711yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—201no—
354C8—601no—
355C2×C3—401no—
356C2×C3#6535111yescharacteristic
357C2×C3#6545811yescharacteristic
358C2×C3#6547611yescharacteristic
359D3—202no—
360C5#7114011yescharacteristic, complemented, Sylow
361C22—201no—
362C22—201no—
363C22—201no—
364C22—302no—
365C22—601no—
366C22—601no—
367C22#9157711yescharacteristic
368C4—21no—
369C4—81no—
370C4—122no—
371C4—201no—
372C4—601no—
373C4#9150511yescharacteristic
374C4#9150611yescharacteristic
375C4#9151511yescharacteristic
376C4#9151611yescharacteristic
377C3#1060202111yescharacteristic, complemented, Sylow
378C2—401no—
379C2—602no—
380C2#1174916711yescharacteristic
381C2#1174939911yescharacteristic
382C2#1174940611yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752493C2
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. #11751185C2semidirect
3. C5×#5079C2semidirect
4. C3×#65373C2semidirect
5. #11745857C2semidirect
6. #11745838C2semidirect
7. #11745835C2semidirect
30. #65373D3semidirect
61. #5079D5semidirect
308. C3×C5#1635semidirect
360. C5#71140semidirect
377. C3#10602021semidirect

Maximal subgroups

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

subgroupindex
#117524932
#117511852
C5×#50792
C3×#653732
#117458572
#117458382
#117458352
#106020213
#711405