Finite Group Databasebeta

← #14290371

Subgroups — #14290371

Order 1920.

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752710C211yesmaximal, characteristic
2#11750947C211yesmaximal, characteristic, complemented
3#11747077C211yesmaximal, characteristic, complemented
4#11746920C211yesmaximal, characteristic, complemented
5C5×#4483C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10599000—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10#91758C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91466—21no—
14#91460—21no—
15#91347—21no—
16#91338—21no—
17#91326—22no—
18C2×#6659—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91105—21no—
21#91102—21no—
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90975—21no—
25#90971—22no—
26#68495—51nomaximal, Hall
27#65897—31no—
28#65308—31no—
29#65135—31no—
30#64970—31no—
31C5×D4⋊C8—31no—
32#64701D311yescharacteristic, complemented
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30—21no—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C3×Dic10D412yes—
40C2×#1203—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C2×C3×#168—21no—
53#6667—22no—
54(C2×D3)⋊Dic5—22no—
55Dic3×Dic5—22no—
56#6659—42no—
57#5734—51no—
58#5079—51no—
59#4846—51no—
60#4841—51no—
61C3×#333—51no—
62#4483—51no—
63#4483D511yescharacteristic, complemented
64C4×C5×D4—31no—
65#4084—61no—
66C2×#687—61no—
67#4076—61no—
68#4072—61no—
69#4038—61no—
70#4031—62no—
71C4×D20—31no—
72#4015—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3953—61no—
77#3950—61no—
78#3948—62no—
79#3942—61no—
80C4⋊#168C2×D311yescharacteristic
81#1646—151noSylow
82C22×D15—21no—
83C22×C5×D3—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—41no—
89D60—21no—
90D60—21no—
91C4×D15—41no—
92C4×D15—41no—
93Dic30—41no—
94Dic30—41no—
95C2×C5×Dic3—21no—
96C5×D12—21no—
97C5×D12—21no—
98C4×C5×D3—41no—
99C4×C5×D3—41no—
100C2×C3×Dic5—22no—
101C3×Dic10—42no—
102#1203—82no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—51no—
107#947—102no—
108C2×#204—101no—
109#895—101no—
110#895—101no—
111#892—101no—
112#892—101no—
113C4×D12—51no—
114C4×D12C2×D511yescharacteristic
115#869—51no—
116C3×C4⋊C8—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118#835—102no—
119#821—101no—
120#818—101no—
121#816—101no—
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×D4—31no—
124C22×C4×C5—61no—
125C2×C22⋊D5—62no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×Dic10—61no—
129C2×Dic10D1212yes—
130C2×C5×C8—21no—
131C2×C5×C8—61no—
132C5×C4⋊C4—31no—
133C5×C22⋊C4—61no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—62no—
136#687—122no—
137#685—62no—
138#685—61no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4⋊Dic5—61no—
143C4⋊Dic5—61no—
144C4×Dic5—62no—
145C2×#168—21no—
146#555—151no—
147#487—151no—
148#474—151no—
149#461—151no—
150#333—51no—
151D4⋊C8—31no—
152D4⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×D15—41no—
155C2×D15—41no—
156C2×D15—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C3×C4×C5—21no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—81no—
167C3×Dic5—42no—
168C5×Dic3—41no—
169C2×C3×Q8—52no—
170C2×D12—51no—
171C2×D12—102no—
172C2×D12D2011yescharacteristic
173C2×C4×D3—21no—
174C2×C4×D3—101no—
175C2×Dic6—101no—
176C2×C3×C8—21no—
177C2×C3×C8—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C42C22×D511yescharacteristic
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—102no—
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—51no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4⋊Dic3D2011yescharacteristic
189C4×Dic3—102no—
190C2×C3⋊C8—21no—
191#204—202no—
192C23×C5—61no—
193C22×D5—61no—
194C5×D4—61no—
195C5×D4—61no—
196C2×C4×C5—61no—
197C2×C4×C5—121no—
198C2×C4×C5—121no—
199C2×C4×C5C2×D1211yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C22⋊D5—242no—
203C2×Dic5—22no—
204C2×Dic5—61no—
205C2×Dic5—121no—
206D20—61no—
207D20—61no—
208C4×D5—121no—
209C4×D5—121no—
210Dic10—42no—
211Dic10—121no—
212Dic10—121no—
213C5×C8—41no—
214C5×C8—121no—
215#168—41no—
216C2×SD16—301no—
217C4⋊Q8—51no—
218C4⋊Q8—151no—
219#124—302no—
220#121—301no—
221#121—301no—
222C4×D4—31no—
223C4×D4—151no—
224#117—301no—
225#117—301no—
226#107—301no—
227C4⋊C8—51no—
228C4⋊C8D3×D511yescharacteristic
229#103—301no—
230#103—302no—
231#102—301no—
232C4×C8—31no—
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45211yescharacteristic
235C2×C3×C5#45511yescharacteristic
236D15—81no—
237C5×D3—81no—
238C22×D3—21no—
239C22×D3—101no—
240C3×Q8—202no—
241C2×C3×C4—102no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—101no—
247C2×Dic3—201no—
248D12—21no—
249D12—21no—
250D12—101no—
251D12—101no—
252D12—402no—
253C4×D3—41no—
254C4×D3—41no—
255C4×D3—201no—
256C4×D3—201no—
257Dic6—201no—
258Dic6—201no—
259C3×C8—41no—
260C3×C8—201no—
261C3⋊C8—41no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5#88211yescharacteristic
266C2×D5—121no—
267C2×D5—121no—
268C2×D5—121no—
269C4×C5—21no—
270C4×C5—121no—
271C4×C5#91411yescharacteristic
272C4×C5#91611yescharacteristic
273C4×C5#91811yescharacteristic
274C4×C5#91911yescharacteristic
275Dic5—42no—
276Dic5—121no—
277Dic5—241no—
278C2×Q8—52no—
279C2×Q8—301no—
280C2×D4—31no—
281C2×D4—151no—
282C2×D4—302no—
283C22×C4—61no—
284C22×C4—301no—
285SD16—602no—
286C2×C8—21no—
287C2×C8—61no—
288C2×C8—101no—
289C4⋊C4—31no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4—151no—
293C4⋊C4—301no—
294C4⋊C4—301no—
295C22⋊C4—61no—
296C22⋊C4—302no—
297C22⋊C4—302no—
298C22⋊C4—301no—
299C42—302no—
300C42C2×D3×D511yescharacteristic
301C3×C5#164611yescharacteristic, complemented, Hall
302C22×C3#402811yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—201no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—202no—
311C3×C4#405011yescharacteristic
312C3×C4#405411yescharacteristic
313C3×C4#405811yescharacteristic
314C3×C4#406111yescharacteristic
315Dic3—41no—
316Dic3—201no—
317Dic3—401no—
318C2×C5—241no—
319C2×C5#474611yescharacteristic
320C2×C5#480811yescharacteristic
321C2×C5#481011yescharacteristic
322D5—241no—
323C23—61no—
324C23—301no—
325Q8—202no—
326Q8—601no—
327Q8—601no—
328D4—61no—
329D4—61no—
330D4—301no—
331D4—301no—
332D4—1202no—
333C2×C4—61no—
334C2×C4—102no—
335C2×C4—121no—
336C2×C4—121no—
337C2×C4—301no—
338C2×C4—601no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4D5×D1211yescharacteristic
342C2×C4D3×D2011yescharacteristic
343C2×C4#679011yescharacteristic
344C8—41no—
345C8—121no—
346C8—201no—
347C2×C3#6502311yescharacteristic
348C2×C3#6507211yescharacteristic
349C2×C3#6511411yescharacteristic
350D3—81no—
351D3—401no—
352C5#6849511yescharacteristic, complemented, Sylow
353C22—121no—
354C22—121no—
355C22—121no—
356C22—601no—
357C22—601no—
358C22—601no—
359C22#9147611yescharacteristic
360C4—21no—
361C4—121no—
362C4—202no—
363C4—601no—
364C4—1201no—
365C4#9125311yescharacteristic
366C4#9127511yescharacteristic
367C4#9149911yescharacteristic
368C4#9152411yescharacteristic
369C3#1059900011yescharacteristic, complemented, Sylow
370C2—241no—
371C2—1201no—
372C2#1174752111yescharacteristic
373C2#1174816711yescharacteristic
374C2#1174825011yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752710C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1646
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. #11750947C2semidirect
3. #11747077C2semidirect
4. #11746920C2semidirect
5. C5×#4483C2semidirect
6. C3×#64701C2semidirect
7. #11745838C2semidirect
32. #64701D3semidirect
63. #4483D5semidirect
301. C3×C5#1646semidirect
352. C5#68495semidirect
369. C3#10599000semidirect

Maximal subgroups

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

subgroupindex
#117527102
#117509472
#117470772
#117469202
C5×#44832
C3×#647012
#117458382
#105990003
#684955