Finite Group Databasebeta

← #14289653

Subgroups — #14289653

Order 1920.

468 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 96 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#11756314C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic, complemented
3#11746929C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10601939—31nomaximal, Hall
9C2×#6819—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91819—21no—
12C2×C4⋊Dic15—21no—
13#91786—21no—
14#91775—22no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C5×#832—21no—
19C5×#808—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23#90985—21no—
24#90973—22no—
25#90969—21no—
26#68204—51nomaximal, Hall
27#65889—31no—
28C5×#476—31no—
29#65373—31no—
30#65370—31no—
31D4⋊#168D311yescharacteristic, complemented
32#64703—31no—
33#64702—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C22×Dic15—22no—
38#6819—42no—
39#6819—42no—
40C2×D60D411yescharacteristic
41C2×C4×D15—21no—
42C2×Dic30—21no—
43C2×C5×Dic6—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—22no—
50C4⋊Dic15—21no—
51C4⋊Dic15D412yes—
52C4⋊Dic15D411yescharacteristic
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C2×C5×C3⋊C8—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58#5555—51no—
59#5008D511yescharacteristic, complemented
60#4842—51no—
61#4681—51no—
62C3×D4⋊C8—51no—
63#4486—51no—
64#4459—51no—
65C2×#711—61no—
66C5×C4⋊Q8—31no—
67C4×C5×D4C2×D311yescharacteristic
68#4076—61no—
69C2×C4⋊Dic5—61no—
70#4043—61no—
71#4032—62no—
72C4×D20—31no—
73#4015—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3967—62no—
78#3941—61no—
79#3940—61no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168C2×D311yescharacteristic
82#1635—151noSylow
83C23×C3×C5—21no—
84C22×D15—21no—
85C3×C5×D4—21no—
86C3×C5×D4SD1612yes—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93#1220—44no—
94C2×Dic15—22no—
95C2×Dic15—21no—
96C2×Dic15—44no—
97D60—21no—
98D60—21no—
99C4×D15—41no—
100C4×D15—41no—
101Dic30—41no—
102Dic30—41no—
103C2×C5×Dic3—41no—
104C5×Dic6—42no—
105C3×#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×#237—101no—
109C3×C4×D4C2×D511yescharacteristic
110#930—101no—
111C2×C4⋊Dic3—101no—
112#897—101no—
113#886—102no—
114C4×D12—51no—
115#869—51no—
116#869C2×D511yescharacteristic
117C3×C4⋊C8—51no—
118C3×C4×C8—51no—
119#832—21no—
120#821—101no—
121#817—101no—
122#816—102no—
123#808—21no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C2×C5×Q8—61no—
126C2×C5×D4D1211yescharacteristic
127C22×C4×C5—21no—
128C2×C22⋊D5—62no—
129C22×Dic5—62no—
130#711—122no—
131#711—122no—
132C2×D20—31no—
133C2×C4×D5—61no—
134C2×Dic10—61no—
135C2×C5×C8—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4D1211yescharacteristic
139C5×C22⋊C4—21no—
140C42×C5C22×D311yescharacteristic
141#685—62no—
142#685—61no—
143C4⋊Dic5—31no—
144C4⋊Dic5—32no—
145C4⋊Dic5—62no—
146C4⋊Dic5—61no—
147C2×#168—21no—
148C2×#168—21no—
149#547—151no—
150#487—151no—
151#476—31no—
152#476—151no—
153#332—151no—
154D4⋊C8—51no—
155D4⋊C8—151no—
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—42no—
170Dic15—41no—
171C5×Dic3—81no—
172C2×C3×D4C22⋊D511yescharacteristic
173C22×C3×C4—21no—
174C2×#67—102no—
175C22×Dic3—102no—
176#237—202no—
177#237—202no—
178C2×D12—51no—
179C2×C4×D3—101no—
180C2×Dic6—21no—
181C2×Dic6—101no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C22⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—101no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—52no—
192C4⋊Dic3—51no—
193C4⋊Dic3—102no—
194C4⋊Dic3—101no—
195C2×C3⋊C8—21no—
196C23×C5—21no—
197C22×D5—61no—
198C5×Q8—122no—
199C5×D4—21no—
200C5×D4#20412yes—
201C2×C4×C5—21no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—121no—
205C2×C4×C5C2×D1211yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C22⋊D5—124no—
209C2×Dic5—62no—
210C2×Dic5—61no—
211C2×Dic5—124no—
212D20—61no—
213D20—61no—
214C4×D5—121no—
215C4×D5—121no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—121no—
219#168—41no—
220#168—41no—
221C2×#41—301no—
222C4⋊Q8—31no—
223C4⋊Q8—151no—
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—151no—
228C4×D4D3×D511yescharacteristic
229C2×C4⋊C4—301no—
230#106—61no—
231#106—301no—
232C4⋊C8—31no—
233C4⋊C8—51no—
234#103—302no—
235#102—61no—
236#102—301no—
237C4×C8—51no—
238C2×C3×C5—42no—
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45211yescharacteristic
241C2×C3×C5#45411yescharacteristic
242D15—81no—
243C23×C3—21no—
244C22×D3—101no—
245C3×D4—21no—
246C3×D4#68812yes—
247C2×C3×C4—21no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4C2×C22⋊D511yescharacteristic
253#67—204no—
254C2×Dic3—41no—
255C2×Dic3—102no—
256C2×Dic3—101no—
257C2×Dic3—204no—
258D12—101no—
259D12—101no—
260C4×D3—201no—
261C4×D3—201no—
262Dic6—42no—
263Dic6—201no—
264Dic6—201no—
265C3×C8—201no—
266C3×C8—201no—
267C3⋊C8—41no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5#88211yescharacteristic
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—241no—
278C4×C5C2×#20411yescharacteristic
279C4×C5#90811yescharacteristic
280C4×C5#91211yescharacteristic
281C4×C5#91511yescharacteristic
282Dic5—122no—
283Dic5—121no—
284#41—602no—
285#41—602no—
286C2×Q8—61no—
287C2×Q8—301no—
288C2×D4—151no—
289C2×D4—302no—
290C2×D4#120311yescharacteristic
291C22×C4—21no—
292C22×C4—302no—
293C22×C4—301no—
294C2×C8—61no—
295C2×C8—101no—
296C2×C8—101no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—152no—
300C4⋊C4—151no—
301C4⋊C4—302no—
302C4⋊C4—301no—
303C4⋊C4#120311yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—302no—
306C22⋊C4—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3#408311yescharacteristic
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4#406111yescharacteristic
319C3×C4#406211yescharacteristic
320C3×C4C2×#68811yescharacteristic
321C3×C4#409511yescharacteristic
322Dic3—81no—
323Dic3—202no—
324Dic3—201no—
325C2×C5—42no—
326C2×C5#473111yescharacteristic
327C2×C5#478311yescharacteristic
328C2×C5#482711yescharacteristic
329D5—241no—
330C23—21no—
331C23—301no—
332Q8—122no—
333Q8—601no—
334Q8—601no—
335D4—21no—
336D4—301no—
337D4—301no—
338D4—604no—
339D4#666012yes—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—121no—
344C2×C4—301no—
345C2×C4—302no—
346C2×C4—604no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×#120311yescharacteristic
350C2×C4#679011yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—201no—
354C8—201no—
355C2×C3—42no—
356C2×C3#6533511yescharacteristic
357C2×C3#6546211yescharacteristic
358C2×C3#6549011yescharacteristic
359D3—401no—
360C5#6820411yescharacteristic, complemented, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9157311yescharacteristic
368C4—21no—
369C4—41no—
370C4—241no—
371C4—601no—
372C4—602no—
373C4#9130511yescharacteristic
374C4C2×#666011yescharacteristic
375C4#9148811yescharacteristic
376C4#9149711yescharacteristic
377C3#1060193911yescharacteristic, complemented, Sylow
378C2—42no—
379C2—1201no—
380C2#1174855411yescharacteristic
381C2#1174906111yescharacteristic
382C2#1174946111yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radical#11756314C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1635
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5008C2semidirect
3. #11746929C2semidirect
4. #11746885C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745859C2semidirect
7. #11745839C2semidirect
31. D4⋊#168D3semidirect
59. #5008D5semidirect
308. C3×C5#1635semidirect
360. C5#68204semidirect
377. C3#10601939semidirect

Maximal subgroups

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

subgroupindex
#117563142
C5×#50082
#117469292
#117468852
C3×D4⋊#1682
#117458592
#117458392
#106019393
#682045