Finite Group Databasebeta

← #14289663

Subgroups — #14289663

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#11752532C211yesmaximal, characteristic
2#11750782C211yesmaximal, characteristic, complemented
3#11746883C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic, complemented
5C5×#4459C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10598974—31nomaximal, Hall
9C2×#6765—21no—
10#91758C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91449—21no—
15#91414—22no—
16D5×C4⋊Dic3—21no—
17#91365—21no—
18C3×C4×C5×C8C2211yescharacteristic
19#91100—22no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90987—21no—
23#90985—21no—
24#90967—21no—
25#90965—21no—
26#68204—51nomaximal, Hall
27#65885—31no—
28#65297—31no—
29#65131—31no—
30#64970—31no—
31C5×D4⋊C8—31no—
32#64702—31no—
33#64679D311yescharacteristic, complemented
34C2×Dic30—21no—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—22no—
41C2×D5×Dic3—22no—
42#6765—42no—
43#6765—42no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D412yes—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56#6668—22no—
57(C2×D3)⋊Dic5—22no—
58#5555—51no—
59#5008—51no—
60#4842—51no—
61#4681—51no—
62C3×D4⋊C8—51no—
63#4486—51no—
64#4459D511yescharacteristic, complemented
65C2×#709—61no—
66C4×C5×D4—31no—
67#4084—61no—
68#4070—61no—
69D5×C4⋊C4—61no—
70#4029—62no—
71C4×D20C2×D311yescharacteristic
72#4015—31no—
73#4015—31no—
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3953—61no—
78#3949—61no—
79#3948—62no—
80#3940—61no—
81C4⋊#168C2×D311yescharacteristic
82#1635—151noSylow
83C22×C5×D3—21no—
84C22×C3×D5—21no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—22no—
89C2×Dic15—41no—
90Dic30—41no—
91Dic30—41no—
92Dic30—42no—
93C2×C5×Dic3—21no—
94C5×D12—21no—
95C5×D12—21no—
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C2×C3×Dic5—21no—
99C3×D20—21no—
100C3×D20SD1612yes—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103#1201—44no—
104D5×Dic3—44no—
105C3×C5×C8—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×#237—101no—
109C3×C4×D4—51no—
110#930—101no—
111C2×C4⋊Dic3—101no—
112#897—101no—
113#886—102no—
114C4×D12C2×D511yescharacteristic
115#869—51no—
116#869—51no—
117C3×C4⋊C8—51no—
118C3×C4×C8C2×D511yescharacteristic
119#832—101no—
120#821—101no—
121#817—101no—
122#816—102no—
123#808—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C2×C5×D4—31no—
126C22×C4×C5—61no—
127C2×C22⋊D5—62no—
128#709—122no—
129#709—122no—
130C2×D20D1211yescharacteristic
131C2×C4×D5—21no—
132C2×C4×D5—62no—
133C2×Dic10—61no—
134C2×Dic10—61no—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C5×C4⋊C4—31no—
138C5×C22⋊C4—61no—
139C42×C5C22×D311yescharacteristic
140C22⋊Dic5—62no—
141#685—21no—
142C4⋊Dic5—32no—
143C4⋊Dic5—61no—
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146C4⋊Dic5D1211yescharacteristic
147#683—62no—
148C2×#168—21no—
149#547—151no—
150#487—151no—
151#476—151no—
152#476—151no—
153#332—151no—
154D4⋊C8—31no—
155D4⋊C8—51no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C2×C3×D5—22no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5C2×SD1611yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168Dic15—42no—
169Dic15—81no—
170C3×Dic5—41no—
171C5×Dic3—41no—
172C2×C3×D4—51no—
173C22×C3×C4—101no—
174C2×#67—102no—
175C22×Dic3—102no—
176#237—202no—
177#237—202no—
178C2×D12D2011yescharacteristic
179C2×C4×D3—21no—
180C2×Dic6—101no—
181C2×Dic6—101no—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C3×C4⋊C4—51no—
185C3×C22⋊C4—101no—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—102no—
189C4⋊Dic3—52no—
190C4⋊Dic3—102no—
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C4⋊Dic3—101no—
194C4⋊Dic3D2011yescharacteristic
195C2×C3⋊C8—21no—
196C23×C5—61no—
197C22×D5—21no—
198C5×D4—61no—
199C5×D4—61no—
200C2×C4×C5—61no—
201C2×C4×C5—121no—
202C2×C4×C5—121no—
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C22⋊D5—124no—
207C2×Dic5—21no—
208C2×Dic5—62no—
209C2×Dic5—121no—
210D20—21no—
211D20#20412yes—
212C4×D5—41no—
213C4×D5—41no—
214C4×D5—124no—
215Dic10—121no—
216Dic10—121no—
217Dic10—122no—
218C5×C8—41no—
219C5×C8—121no—
220#168—41no—
221C2×#41—301no—
222C4⋊Q8—151no—
223C4⋊Q8—151no—
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—31no—
228C4×D4—51no—
229C2×C4⋊C4—301no—
230#106—301no—
231#106—301no—
232C4⋊C8—31no—
233C4⋊C8—51no—
234#103—302no—
235#102—301no—
236#102—301no—
237C4×C8D3×D511yescharacteristic
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—42no—
242C5×D3—81no—
243C23×C3—101no—
244C22×D3—21no—
245C3×D4—52no—
246C3×D4—101no—
247C2×C3×C4—101no—
248C2×C3×C4—201no—
249C2×C3×C4—201no—
250C2×C3×C4C2×D2011yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253#67—204no—
254C2×Dic3—21no—
255C2×Dic3—102no—
256C2×Dic3—204no—
257C2×Dic3—201no—
258D12—21no—
259D12—21no—
260C4×D3—41no—
261C4×D3—41no—
262Dic6—201no—
263Dic6—201no—
264Dic6—202no—
265C3×C8—41no—
266C3×C8—201no—
267C3⋊C8—41no—
268C22×C5—121no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5#88211yescharacteristic
272C2×D5—22no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—121no—
277C4×C5C2×#20411yescharacteristic
278C4×C5#90811yescharacteristic
279C4×C5#91211yescharacteristic
280C4×C5#91511yescharacteristic
281Dic5—41no—
282Dic5—122no—
283Dic5—241no—
284#41—602no—
285#41—602no—
286C2×Q8—301no—
287C2×Q8—301no—
288C2×D4—31no—
289C2×D4—51no—
290C2×D4—302no—
291C22×C4—61no—
292C22×C4—101no—
293C22×C4—302no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—101no—
297C4⋊C4—31no—
298C4⋊C4—51no—
299C4⋊C4—152no—
300C4⋊C4—302no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4—301no—
304C22⋊C4—61no—
305C22⋊C4—101no—
306C22⋊C4—302no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—102no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3#402811yescharacteristic
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—201no—
318C3×C4#405011yescharacteristic
319C3×C4#405511yescharacteristic
320C3×C4#405711yescharacteristic
321C3×C4D5×SD1611yescharacteristic
322Dic3—41no—
323Dic3—202no—
324Dic3—401no—
325C2×C5—241no—
326C2×C5#473111yescharacteristic
327C2×C5#478311yescharacteristic
328C2×C5#482711yescharacteristic
329D5—42no—
330C23—61no—
331C23—101no—
332Q8—602no—
333Q8—601no—
334Q8—601no—
335D4—52no—
336D4—61no—
337D4—61no—
338D4—101no—
339D4—604no—
340C2×C4—61no—
341C2×C4—101no—
342C2×C4—121no—
343C2×C4—121no—
344C2×C4—201no—
345C2×C4—201no—
346C2×C4—302no—
347C2×C4—604no—
348C2×C4—601no—
349C2×C4D5×D1211yescharacteristic
350C2×C4D3×D2011yescharacteristic
351C2×C4#679011yescharacteristic
352C8—41no—
353C8—121no—
354C8—201no—
355C2×C3—202no—
356C2×C3#6502211yescharacteristic
357C2×C3#6506511yescharacteristic
358C2×C3#6511611yescharacteristic
359D3—81no—
360C5#6820411yescharacteristic, complemented, Sylow
361C22—102no—
362C22—121no—
363C22—121no—
364C22—121no—
365C22—201no—
366C22—201no—
367C22#9147611yescharacteristic
368C4—21no—
369C4—121no—
370C4—201no—
371C4—602no—
372C4—1201no—
373C4D5×#20411yescharacteristic
374C4#9125011yescharacteristic
375C4#9127311yescharacteristic
376C4#9127411yescharacteristic
377C3#1059897411yescharacteristic, complemented, Sylow
378C2—202no—
379C2—241no—
380C2#1174712511yescharacteristic
381C2#1174811511yescharacteristic
382C2#1174816211yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11752532C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1635
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
2. #11750782C2semidirect
3. #11746883C2semidirect
4. #11746881C2semidirect
5. C5×#4459C2semidirect
6. C3×#64679C2semidirect
7. #11745859C2semidirect
33. #64679D3semidirect
64. #4459D5semidirect
308. C3×C5#1635semidirect
360. C5#68204semidirect
377. C3#10598974semidirect

Maximal subgroups

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

subgroupindex
#117525322
#117507822
#117468832
#117468812
C5×#44592
C3×#646792
#117458592
#105989743
#682045