Finite Group Databasebeta

← #14290377

Subgroups — #14290377

Order 1920.

480 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756485C211yesmaximal, characteristic
2C3×C5×#500C211yesmaximal, characteristic, complemented
3#11751188C211yesmaximal, characteristic, complemented
4#11751184C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10602162—31nomaximal, Hall
9C2×#6821—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12#91835—21no—
13C2×#6717—21no—
14#91784—21no—
15#91783—22no—
16C4⋊C4×D15—21no—
17C4×D60C2211yescharacteristic
18C4×D60C2211yescharacteristic
19C3×C5×#107—22no—
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91093—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71369—51nomaximal, Hall
27#66060—31no—
28C5×#500D311yescharacteristic, complemented
29#65376—31no—
30#65372—31no—
31#64767—31no—
32#64679—31no—
33#64679—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36#6821—42no—
37#6821—42no—
38C2×D60—22no—
39C2×D60D411yescharacteristic
40C2×D60D411yescharacteristic
41C2×C4×D15—22no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5C2311yescharacteristic
50#6717—42no—
51#6714—22no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15D411yescharacteristic
55C4⋊Dic15D411yescharacteristic
56#6712—22no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5726—51no—
60C3×#500D511yescharacteristic, complemented
61#5087—51no—
62#5083—51no—
63#4547—51no—
64#4459—51no—
65#4459—51no—
66C2×#713—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×C4⋊Q8C2×D311yescharacteristic
69#4092—61no—
70C2×#688—61no—
71#4041—61no—
72#4040—62no—
73D5×C4⋊C4—61no—
74C4×D20—31no—
75C4×D20—31no—
76C5×#107—22no—
77C4×C5×C8C2×D311yescharacteristic
78#3967—61no—
79#3941—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4⋊#168—31no—
83#1647—151noSylow
84C22×D15—21no—
85C22×D15—21no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97D60—21no—
98D60—21no—
99D60—21no—
100D60—44no—
101D60D812yes—
102C4×D15—44no—
103C4×D15—41no—
104C4×D15—41no—
105C4×D15—41no—
106C4×D15—41no—
107C3×C5×C8—22no—
108C3⋊#168—41no—
109C3⋊#168—41no—
110C2×#239—101no—
111C3×C4⋊Q8C2×D511yescharacteristic
112C3×C4⋊Q8C2×D511yescharacteristic
113#946—101no—
114C2×#215—101no—
115#895—101no—
116#894—102no—
117D3×C4⋊C4—101no—
118C4×D12—51no—
119C4×D12—51no—
120C3×#107—22no—
121C3×C4×C8C2×D511yescharacteristic
122#835—101no—
123#809—101no—
124#807—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)—51no—
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129#713—122no—
130#713—122no—
131C2×D20—31no—
132C2×D20—31no—
133C2×D20—62no—
134C2×C4×D5—62no—
135C2×C4×D5—61no—
136C2×C4×D5—61no—
137C2×C5×C8—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4#6712yes—
142C42×C5C22×D311yescharacteristic
143#688—122no—
144#685—62no—
145#685—61no—
146#685—61no—
147C4⋊Dic5—31no—
148C4⋊Dic5—31no—
149#683—62no—
150C2×#168—61no—
151C2×#168—61no—
152#547—151no—
153#500D1511yescharacteristic, complemented
154#474—151no—
155#461—151no—
156#332—151no—
157D4⋊C8—151no—
158D4⋊C8—151no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—22no—
161C2×D15—41no—
162C2×D15—41no—
163C2×D15—41no—
164C2×D15—41no—
165C2×D15—41no—
166C3×C4×C5—21no—
167C3×C4×C5—42no—
168C3×C4×C5—81no—
169C3×C4×C5C2×D811yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—41no—
174Dic15—41no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177#239—202no—
178#239—202no—
179C2×D12—51no—
180C2×D12—51no—
181C2×D12—102no—
182C2×C4×D3—102no—
183C2×C4×D3—101no—
184C2×C4×D3—101no—
185C2×C3×C8—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4C22⋊D512yes—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192(C2×D3)⋊C4—102no—
193(C2×D3)⋊C4—101no—
194(C2×D3)⋊C4—101no—
195C4⋊Dic3—51no—
196C4⋊Dic3—51no—
197Dic3⋊C4—102no—
198C2×C3⋊C8—101no—
199C2×C3⋊C8—101no—
200C22×D5—61no—
201C22×D5—61no—
202C5×Q8—41no—
203C5×Q8—41no—
204C5×Q8—41no—
205C5×Q8—41no—
206C2×C4×C5—22no—
207C2×C4×C5—41no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×Dic5—61no—
212C2×Dic5—61no—
213D20—32no—
214D20—61no—
215D20—61no—
216D20—61no—
217D20—124no—
218C4×D5—124no—
219C4×D5—121no—
220C4×D5—121no—
221C4×D5—121no—
222C4×D5—121no—
223C5×C8—22no—
224#168—121no—
225#168—121no—
226C2×#41—301no—
227C2×SD16—301no—
228C4⋊Q8C2×D1511yescharacteristic
229C4⋊Q8C2×D1511yescharacteristic
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—151no—
234C4×D4—151no—
235C2×C4⋊C4—301no—
236#107—22no—
237#107—301no—
238C4⋊C8—151no—
239C4⋊C8—151no—
240#103—301no—
241#102—301no—
242C4×C8C2×D1511yescharacteristic
243C2×C3×C5#44711yescharacteristic
244C2×C3×C5#45211yescharacteristic
245C2×C3×C5#45611yescharacteristic
246D15—42no—
247D15—81no—
248C22×D3—101no—
249C22×D3—101no—
250C3×Q8—41no—
251C3×Q8—41no—
252C3×Q8—41no—
253C3×Q8—41no—
254C2×C3×C4—22no—
255C2×C3×C4—41no—
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×Dic3—101no—
260C2×Dic3—101no—
261D12—52no—
262D12—101no—
263D12—101no—
264D12—101no—
265D12—204no—
266C4×D3—204no—
267C4×D3—201no—
268C4×D3—201no—
269C4×D3—201no—
270C4×D3—201no—
271C3×C8—22no—
272C3⋊C8—201no—
273C3⋊C8—201no—
274C22×C5#93711yescharacteristic
275C2×D5—62no—
276C2×D5—121no—
277C2×D5—121no—
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—121no—
281C4×C5—21no—
282C4×C5—42no—
283C4×C5—81no—
284C4×C5D3×D811yescharacteristic
285C4×C5#91111yescharacteristic
286C4×C5#91811yescharacteristic
287C4×C5#91911yescharacteristic
288Dic5—121no—
289Dic5—121no—
290#41—602no—
291#41—602no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—151no—
295C2×D4—151no—
296C2×D4—302no—
297C22×C4—302no—
298C22×C4—301no—
299C22×C4—301no—
300SD16—602no—
301C2×C8—21no—
302C2×C8—301no—
303C2×C8—301no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—302no—
310C4⋊C4#122012yes—
311C22⋊C4—302no—
312C22⋊C4—301no—
313C22⋊C4—301no—
314C42C22×D1511yescharacteristic
315C3×C5#164711yescharacteristic, complemented, Hall
316C22×C3#408311yescharacteristic
317C2×D3—102no—
318C2×D3—201no—
319C2×D3—201no—
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—42no—
325C3×C4—81no—
326C3×C4D5×D811yescharacteristic
327C3×C4#405711yescharacteristic
328C3×C4#406411yescharacteristic
329C3×C4#406511yescharacteristic
330Dic3—201no—
331Dic3—201no—
332C2×C5#509511yescharacteristic
333C2×C5#515611yescharacteristic
334C2×C5#518711yescharacteristic
335D5—122no—
336D5—241no—
337C23—301no—
338C23—301no—
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343D4—152no—
344D4—301no—
345D4—301no—
346D4—301no—
347D4—604no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—604no—
353C2×C4—601no—
354C2×C4—601no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4D4×D1511yescharacteristic
358C2×C4D4×D1511yescharacteristic
359C2×C4C2×#122011yescharacteristic
360C8—22no—
361C8—601no—
362C8—601no—
363C2×C3#6538411yescharacteristic
364C2×C3#6544511yescharacteristic
365C2×C3#6547611yescharacteristic
366D3—202no—
367D3—401no—
368C5#7136911yescharacteristic, complemented, Sylow
369C22—302no—
370C22—601no—
371C22—601no—
372C22—601no—
373C22—601no—
374C22—601no—
375C22#9182611yescharacteristic
376C4—21no—
377C4—42no—
378C4—81no—
379C4—601no—
380C4—601no—
381C4D8×D1511yescharacteristic
382C4#9180011yescharacteristic
383C4#9180711yescharacteristic
384C4#9180811yescharacteristic
385C3#1060216211yescharacteristic, complemented, Sylow
386C2—602no—
387C2—1201no—
388C2#1175119611yescharacteristic
389C2#1175125711yescharacteristic
390C2#1175128811yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#500C2
socleC22×C3×C5#120
prime radical#11756485C2
hypercenter#500D15
hypocenterC3×C5#1647
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C3×C5×#500C2semidirect
3. #11751188C2semidirect
4. #11751184C2semidirect
5. #11746368C2semidirect
6. #11746280C2semidirect
7. #11746280C2semidirect
28. C5×#500D3semidirect
60. C3×#500D5semidirect
153. #500D15semidirect
315. C3×C5#1647semidirect
368. C5#71369semidirect
385. C3#10602162semidirect

Maximal subgroups

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

subgroupindex
#117564852
C3×C5×#5002
#117511882
#117511842
#117463682
#117462802
#106021623
#713695