Finite Group Databasebeta

← #14289301

Subgroups — #14289301

Order 1920.

432 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#66066C211yesmaximal, characteristic, complemented
2C5×#5088C211yesmaximal, characteristic, complemented
3#11747060C211yesmaximal, characteristic, complemented
4#11747026C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10601990—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C5×#874C2211yescharacteristic
11C3×#4093—21no—
12C3×Q8×Dic5—21no—
13C3×#4044—22no—
14C3×#4043—21no—
15C3×#4038—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C2×#6656—21no—
19C2×#6652—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#809—22no—
23C4×C5×C3⋊C8C2211yescharacteristic
24#90966—21no—
25#90966—21no—
26#71931—51nomaximal, Hall
27#66066D311yescharacteristic, complemented
28C5×#486—31no—
29#65364—31no—
30#65361—31no—
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×Dic10D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C2×C5×C3⋊C8—21no—
47C3×#685—22no—
48C3×#685—22no—
49C3×#685—21no—
50C3×C4⋊Dic5—22no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5—21no—
56#6656—42no—
57#6652—42no—
58C3×#556—51no—
59#5088D511yescharacteristic, complemented
60#5027—51no—
61#5015—51no—
62#4547—51no—
63#4535—51no—
64D4⋊(C3⋊C8)—51no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C5×#127—31no—
67#4093—21no—
68Q8×Dic5—21no—
69C2×#687—61no—
70C2×#686—61no—
71#4044—22no—
72#4043—21no—
73#4038—21no—
74C4×D20C2×D311yescharacteristic
75C4×Dic10C2×D311yescharacteristic
76C5×#102—62no—
77C4×C5×C8—31no—
78#3964—61no—
79#3964—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82#1628—151noSylow
83C22×C5×D3—41no—
84C22×C3×D5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C5×D12—42no—
92C5×D12—41no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×D20—21no—
100C3×D20—21no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×Dic10—21no—
104C3×Dic10—21no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C5×C3⋊C8—41no—
108C3×C4⋊Q8C2×D511yescharacteristic
109C3×#126—102no—
110C3×#124—101no—
111C3×C22⋊Q8—101no—
112C3×C4×Q8—51no—
113C3×C4×Q8—101no—
114C3×C4×D4—51no—
115C3×#117—101no—
116C2×#215—101no—
117C2×#213—101no—
118#874C2×D511yescharacteristic
119#809—22no—
120#809—101no—
121#809—101no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×Q8—21no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C2×D20#6711yescharacteristic
130C2×C4×D5—21no—
131C2×Dic10#6711yescharacteristic
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4#6712yes—
135C42×C5C22×D311yescharacteristic
136#687—122no—
137#686—122no—
138#685—22no—
139#685—22no—
140#685—21no—
141C4⋊Dic5—22no—
142C4⋊Dic5#6711yescharacteristic
143C4⋊Dic5#6711yescharacteristic
144#683—21no—
145C4×Dic5—22no—
146C4×Dic5—21no—
147C2×#168—61no—
148C2×#168—61no—
149#556—51no—
150#486—31no—
151#460—151no—
152#459—151no—
153#332—151no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—81no—
158C2×C5×D3—81no—
159C2×C5×D3—81no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×Dic5—41no—
170C3×Dic5—41no—
171C3×Dic5—41no—
172C2×C3×Q8—21no—
173C2×C3×Q8—51no—
174C2×C3×D4—51no—
175C22×C3×C4—101no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—102no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4C22⋊D512yes—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187C3×C22⋊C4—101no—
188C3×C42—102no—
189C3×C42—101no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192#213—202no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—121no—
197C22×D5—21no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×D4—122no—
201C5×D4—121no—
202C5×D4—121no—
203C5×D4—121no—
204C5×D4—121no—
205C2×C4×C5—22no—
206C2×C4×C5C2×#6711yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—21no—
210C2×Dic5—21no—
211C2×Dic5—21no—
212D20—21no—
213D20—21no—
214C4×D5—41no—
215C4×D5—41no—
216Dic10—21no—
217Dic10—21no—
218C5×C8—121no—
219#168—121no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8D3×D511yescharacteristic
224#127—31no—
225#126—102no—
226#124—101no—
227C22⋊Q8—101no—
228C4×Q8—51no—
229C4×Q8—101no—
230C4×D4—51no—
231#117—101no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234#102—62no—
235#102—301no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—81no—
242C5×D3—161no—
243C23×C3—101no—
244C22×D3—41no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—101no—
248C3×Q8—101no—
249C3×D4—101no—
250C3×D4—101no—
251C2×C3×C4—22no—
252C2×C3×C4—101no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260D12—42no—
261D12—41no—
262D12—41no—
263D12—41no—
264D12—41no—
265C3⋊C8—41no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—241no—
269C22×C5—241no—
270C22×C5—241no—
271C22×C5#95311yescharacteristic
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5#94911yescharacteristic
278C4×C5#94911yescharacteristic
279C4×C5#95011yescharacteristic
280C4×C5#95011yescharacteristic
281Dic5—41no—
282Dic5—41no—
283Dic5—41no—
284C2×Q8—21no—
285C2×Q8—51no—
286C2×D4—51no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C22×C4—101no—
291SD16—602no—
292D8—602no—
293C2×C8—61no—
294C2×C8—301no—
295C2×C8—301no—
296C4⋊C4—21no—
297C4⋊C4—51no—
298C4⋊C4—51no—
299C4⋊C4—102no—
300C4⋊C4—101no—
301C4⋊C4#120112yes—
302C22⋊C4—102no—
303C22⋊C4—102no—
304C22⋊C4—101no—
305C42—102no—
306C42—101no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—201no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3#408311yescharacteristic
313C2×D3—81no—
314C2×D3—81no—
315C2×D3—81no—
316C3×C4—21no—
317C3×C4—42no—
318C3×C4—201no—
319C3×C4—201no—
320C3×C4—201no—
321C3×C4#405711yescharacteristic
322C3×C4#405811yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406211yescharacteristic
325C2×C5—481no—
326C2×C5#523811yescharacteristic
327C2×C5#523811yescharacteristic
328C2×C5#524511yescharacteristic
329D5—81no—
330C23—101no—
331C23—121no—
332Q8—41no—
333Q8—41no—
334Q8—101no—
335Q8—101no—
336D4—101no—
337D4—101no—
338D4—122no—
339D4—121no—
340D4—121no—
341D4—121no—
342D4—121no—
343C2×C4—22no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—101no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4C2×#120111yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C2×C4D5×#6711yescharacteristic
352C8—121no—
353C8—601no—
354C8—601no—
355C2×C3—401no—
356C2×C3#6535111yescharacteristic
357C2×C3#6544711yescharacteristic
358C2×C3#6546111yescharacteristic
359D3—161no—
360C5#7193111yescharacteristic, complemented, Sylow
361C22—201no—
362C22—201no—
363C22—201no—
364C22—241no—
365C22—241no—
366C22—241no—
367C22#9156311yescharacteristic
368C4—21no—
369C4—42no—
370C4—201no—
371C4—201no—
372C4—201no—
373C4#9147811yescharacteristic
374C4#9149011yescharacteristic
375C4#9150211yescharacteristic
376C4#9151411yescharacteristic
377C3#1060199011yescharacteristic, complemented, Sylow
378C2—401no—
379C2—481no—
380C2#1174902411yescharacteristic
381C2#1174927011yescharacteristic
382C2#1174938311yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11747026C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1628
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
1. C3×#66066C2semidirect
2. C5×#5088C2semidirect
3. #11747060C2semidirect
5. #11746368C2semidirect
6. #11745841C2semidirect
7. #11745835C2semidirect
27. #66066D3semidirect
59. #5088D5semidirect
308. C3×C5#1628semidirect
360. C5#71931semidirect
377. C3#10601990semidirect

Maximal subgroups

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

subgroupindex
C3×#660662
C5×#50882
#117470602
#117470262
#117463682
#117458412
#117458352
#106019903
#719315