Finite Group Databasebeta

← #14289643

Subgroups — #14289643

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#11752676C211yesmaximal, characteristic
2#11751180C211yesmaximal, characteristic, complemented
3C5×#5084C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11745859C211yesmaximal, characteristic, complemented
6#11745836C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601939—31nomaximal, Hall
9C2×#6772—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91457—22no—
15#91456—21no—
16D3×C4⋊Dic5—21no—
17#91360—21no—
18#91119—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#809—21no—
21C5×#808—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71140—51nomaximal, Hall
27#65889—31no—
28C5×#476—31no—
29#65373D311yescharacteristic, complemented
30#65370—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—22no—
41C2×D3×Dic5—22no—
42#6772—42no—
43#6772—42no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15—21no—
48C4⋊Dic15D412yes—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—22no—
57#6665—22no—
58#5551—51no—
59C3×#476—51no—
60#5084D511yescharacteristic, complemented
61#5079—51no—
62D4⋊(C3⋊C8)—51no—
63#4486—51no—
64#4483—51no—
65C2×#711—61no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C4×C5×D4—31no—
68#4076—61no—
69C2×C4⋊Dic5—61no—
70#4043—61no—
71#4032—62no—
72C4×D20C2×D311yescharacteristic
73#4015—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3967—62no—
78#3941—21no—
79#3940—21no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1635—151noSylow
83C22×C5×D3—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—22no—
91Dic30—41no—
92Dic30—41no—
93C2×C5×Dic3—21no—
94C5×D12—21no—
95C5×D12SD1612yes—
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C2×C3×Dic5—21no—
99C3×D20—21no—
100C3×D20—21no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103#1201—44no—
104D3×Dic5—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×D12C2×D511yescharacteristic
116#869—51no—
117C3×#106—101no—
118C3×C4⋊C8—51no—
119C3×#102—101no—
120#835—102no—
121#809—21no—
122#808—21no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C4×C3⋊C8—51no—
125C2×C5×Q8—21no—
126C2×C5×D4—31no—
127C22×C4×C5—61no—
128C2×C22⋊D5—62no—
129C22×Dic5—62no—
130#711—122no—
131#711—122no—
132C2×D20#6711yescharacteristic
133C2×C4×D5—21no—
134C2×Dic10—61no—
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—31no—
139C5×C22⋊C4—61no—
140C42×C5C22×D311yescharacteristic
141#685—21no—
142#685—62no—
143C4⋊Dic5—32no—
144C4⋊Dic5—62no—
145C4⋊Dic5—61no—
146C4⋊Dic5#6711yescharacteristic
147C2×#168—21no—
148C2×#168—61no—
149#547—151no—
150#487—151no—
151#476—31no—
152#476—51no—
153#332—151no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—22no—
158C2×C5×D3—41no—
159C2×C5×D3—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—42no—
170C3×Dic5—41no—
171C5×Dic3—41no—
172C2×C3×Q8—21no—
173C2×C3×D4—51no—
174C22×C3×C4—101no—
175C2×#67—102no—
176#235—202no—
177#235—202no—
178C2×D12C22⋊D511yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—102no—
181C2×Dic6—101no—
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—21no—
190C4⋊Dic3—52no—
191C4⋊Dic3—101no—
192C4⋊Dic3C22⋊D511yescharacteristic
193Dic3⋊C4—102no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C23×C5—61no—
197C22×D5—21no—
198C5×Q8—42no—
199C5×D4—32no—
200C5×D4—61no—
201C2×C4×C5—41no—
202C2×C4×C5—61no—
203C2×C4×C5—121no—
204C2×C4×C5—121no—
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C22⋊D5—124no—
209C2×Dic5—21no—
210C2×Dic5—62no—
211C2×Dic5—124no—
212D20—21no—
213D20—21no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—121no—
219#168—41no—
220#168—121no—
221C2×#41—301no—
222C4⋊Q8—151no—
223C4⋊Q8D3×D511yescharacteristic
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—31no—
228C4×D4—51no—
229C2×C4⋊C4—301no—
230#106—61no—
231#106—101no—
232C4⋊C8—31no—
233C4⋊C8—51no—
234#103—302no—
235#102—61no—
236#102—101no—
237C4×C8—151no—
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—81no—
242C5×D3—42no—
243C23×C3—101no—
244C22×D3—21no—
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—21no—
257C2×Dic3—102no—
258D12—21no—
259D12#68812yes—
260C4×D3—41no—
261C4×D3—41no—
262C4×D3—204no—
263Dic6—201no—
264Dic6—201no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5—62no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5#93711yescharacteristic
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—81no—
277C4×C5—121no—
278C4×C5D3×SD1611yescharacteristic
279C4×C5#91411yescharacteristic
280C4×C5#94211yescharacteristic
281C4×C5#95011yescharacteristic
282Dic5—41no—
283Dic5—122no—
284#41—602no—
285#41—602no—
286C2×Q8—21no—
287C2×Q8—301no—
288C2×D4—31no—
289C2×D4—51no—
290C2×D4—302no—
291C22×C4—61no—
292C22×C4—101no—
293C22×C4—302no—
294C2×C8—61no—
295C2×C8—101no—
296C2×C8—301no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—31no—
300C4⋊C4—51no—
301C4⋊C4—152no—
302C4⋊C4—302no—
303C4⋊C4—301no—
304C22⋊C4—61no—
305C22⋊C4—101no—
306C22⋊C4—302no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—201no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3#408311yescharacteristic
313C2×D3—22no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—81no—
318C3×C4—201no—
319C3×C4#406111yescharacteristic
320C3×C4#406211yescharacteristic
321C3×C4C2×#68811yescharacteristic
322C3×C4#409511yescharacteristic
323Dic3—41no—
324Dic3—202no—
325C2×C5—122no—
326C2×C5#504711yescharacteristic
327C2×C5#516911yescharacteristic
328C2×C5#520111yescharacteristic
329D5—81no—
330C23—61no—
331C23—101no—
332Q8—42no—
333Q8—601no—
334Q8—601no—
335D4—32no—
336D4—61no—
337D4—101no—
338D4—101no—
339D4—604no—
340C2×C4—41no—
341C2×C4—61no—
342C2×C4—101no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4—201no—
346C2×C4—201no—
347C2×C4—302no—
348C2×C4—604no—
349C2×C4D5×#6711yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—201no—
354C8—601no—
355C2×C3—401no—
356C2×C3#6533511yescharacteristic
357C2×C3#6546211yescharacteristic
358C2×C3#6549011yescharacteristic
359D3—42no—
360C5#7114011yescharacteristic, complemented, Sylow
361C22—62no—
362C22—121no—
363C22—121no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22#9157711yescharacteristic
368C4—21no—
369C4—81no—
370C4—121no—
371C4—201no—
372C4—602no—
373C4D3×#68811yescharacteristic
374C4#9150411yescharacteristic
375C4#9151311yescharacteristic
376C4#9151411yescharacteristic
377C3#1060193911yescharacteristic, complemented, Sylow
378C2—122no—
379C2—401no—
380C2#1174916611yescharacteristic
381C2#1174939811yescharacteristic
382C2#1174940511yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752676C2
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. #11751180C2semidirect
3. C5×#5084C2semidirect
4. C3×#65373C2semidirect
5. #11745859C2semidirect
6. #11745836C2semidirect
7. #11745834C2semidirect
29. #65373D3semidirect
60. #5084D5semidirect
308. C3×C5#1635semidirect
360. C5#71140semidirect
377. C3#10601939semidirect

Maximal subgroups

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

subgroupindex
#117526762
#117511802
C5×#50842
C3×#653732
#117458592
#117458362
#117458342
#106019393
#711405