Finite Group Databasebeta

← #14291141

Subgroups — #14291141

Order 1920.

392 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 75 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#11756443C211yesmaximal, characteristic
2C3×C5×#489C211yesmaximal, characteristic, complemented
3#11751190C211yesmaximal, characteristic, complemented
4#11751183C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#11746286C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic, complemented
8#10602039—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#124C2211yescharacteristic
11#91835—21no—
12#91828—21no—
13#91775—21no—
14#91773—21no—
15#91772—21no—
16#91767—21no—
17#91764C2211yescharacteristic
18#91759C2211yescharacteristic
19C3×C5×#103—21no—
20C3×C5×#102—21no—
21C3×C5×#97C2211yescharacteristic
22#91119—21no—
23#91119—21no—
24#91094—21no—
25#91093—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#71246—51nomaximal, Hall
29#66018—31no—
30C5×#489D311yescharacteristic, complemented
31#65378—31no—
32#65371—31no—
33#64760—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4D411yescharacteristic
39C2×#1220—21no—
40C2×#1220—21no—
41C22×Dic15—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C22⋊C4—21no—
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51#6719—21no—
52#6714—21no—
53#6714—21no—
54#6714—21no—
55C4⋊Dic15—21no—
56C4⋊Dic15D411yescharacteristic
57C4⋊Dic15D411yescharacteristic
58#6712—21no—
59#6712—21no—
60#6712—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63#5684—51no—
64C3×#489D511yescharacteristic, complemented
65#5089—51no—
66#5082—51no—
67#4540—51no—
68#4465—51no—
69#4464—51no—
70C5×C4⋊Q8C2×D311yescharacteristic
71C5×#124C2×D311yescharacteristic
72#4092—61no—
73#4085—61no—
74#4032—61no—
75#4030—61no—
76#4029—61no—
77#4024—61no—
78#4021—31no—
79#4016—31no—
80C5×#103—21no—
81C5×#102—21no—
82C5×#97C2×D311yescharacteristic
83#3967—61no—
84#3967—61no—
85#3942—61no—
86#3941—61no—
87#3935—31no—
88#3935—31no—
89#1662—151noSylow
90C23×C3×C5—21no—
91C22×D15—21no—
92C3×C5×Q8—41no—
93C3×C5×Q8—42no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100#1220—81no—
101#1220—81no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—81no—
106D60—41no—
107C4×D15—81no—
108Dic30—41no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3⋊#168—41no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×#124C2×D511yescharacteristic
114#946—101no—
115#939—101no—
116#886—101no—
117#884—101no—
118#883—101no—
119#878—101no—
120#875—51no—
121#870—51no—
122C3×#103—21no—
123C3×#102—21no—
124C3×#97C2×D511yescharacteristic
125#835—101no—
126#835—101no—
127#810—101no—
128#809—101no—
129#803—51no—
130#803—51no—
131C2×C5×Q8—21no—
132C2×C5×Q8#6711yescharacteristic
133C2×C5×D4#6711yescharacteristic
134C2×C22⋊D5—61no—
135C2×C22⋊D5—61no—
136C22×Dic5—61no—
137C2×D20—31no—
138C2×C4×D5—61no—
139C2×Dic10—31no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C22⋊C4—21no—
144C5×C22⋊C4—21no—
145C42×C5C22×D311yescharacteristic
146C22⋊Dic5—61no—
147#685—61no—
148#685—61no—
149#685—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—31no—
152C4⋊Dic5—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C2×#168—61no—
157C2×#168—61no—
158#562—151no—
159#491—151no—
160#489—151no—
161#489D1511yescharacteristic, complemented
162#330—151no—
163#329—151no—
164#329—151no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5#12011yescharacteristic
169C2×D15—41no—
170C2×D15—41no—
171C2×D15—41no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5—81no—
177Dic15—41no—
178Dic15—41no—
179Dic15—41no—
180C2×C3×Q8—21no—
181C2×C3×Q8C22⋊D511yescharacteristic
182C2×C3×D4C22⋊D511yescharacteristic
183C2×#67—101no—
184C2×#67—101no—
185C22×Dic3—101no—
186C2×D12—51no—
187C2×C4×D3—101no—
188C2×Dic6—51no—
189C2×C3×C8—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C42C22×D511yescharacteristic
195#217—101no—
196(C2×D3)⋊C4—101no—
197(C2×D3)⋊C4—101no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—51no—
200C4⋊Dic3—51no—
201C4⋊Dic3—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205C2×C3⋊C8—101no—
206C2×C3⋊C8—101no—
207C23×C5—21no—
208C22×D5—61no—
209C5×Q8—41no—
210C5×Q8—42no—
211C5×D4—41no—
212C2×C4×C5—21no—
213C2×C4×C5—41no—
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C22⋊D5—241no—
218C22⋊D5—241no—
219C2×Dic5—61no—
220C2×Dic5—61no—
221C2×Dic5—61no—
222C2×Dic5—241no—
223D20—121no—
224C4×D5—241no—
225Dic10—121no—
226C5×C8—41no—
227#168—121no—
228#168—121no—
229C4⋊Q8C2×D1511yescharacteristic
230#125—151no—
231#124—151no—
232#124C2×D1511yescharacteristic
233#123—301no—
234#123—301no—
235C22⋊Q8—301no—
236C22⋊Q8—301no—
237#121—301no—
238#121—301no—
239#103—21no—
240#103—301no—
241#103—301no—
242#103—301no—
243#102—21no—
244#102—301no—
245#97—151no—
246#97—151no—
247#97C2×D1511yescharacteristic
248C2×C3×C5—81no—
249C2×C3×C5#45411yescharacteristic
250C2×C3×C5#45511yescharacteristic
251C2×C3×C5#45511yescharacteristic
252D15—81no—
253C23×C3—21no—
254C22×D3—101no—
255C3×Q8—41no—
256C3×Q8—42no—
257C3×D4—41no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263#67—401no—
264#67—401no—
265C2×Dic3—101no—
266C2×Dic3—101no—
267C2×Dic3—101no—
268C2×Dic3—401no—
269D12—201no—
270C4×D3—401no—
271Dic6—201no—
272C3×C8—41no—
273C3⋊C8—201no—
274C3⋊C8—201no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5—41no—
278C22×C5#93711yescharacteristic
279C2×D5—121no—
280C2×D5—121no—
281C2×D5—121no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—81no—
287Dic5—121no—
288Dic5—121no—
289Dic5—121no—
290C2×Q8—21no—
291C2×Q8—151no—
292C2×Q8#122011yescharacteristic
293C2×D4—151no—
294C2×D4—301no—
295C2×D4—301no—
296C2×D4#122011yescharacteristic
297C22×C4—301no—
298C22×C4—301no—
299C2×C8—21no—
300C2×C8—301no—
301C2×C8—301no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—151no—
305C4⋊C4—151no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C4⋊C4—301no—
309C4⋊C4—301no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—301no—
313C22⋊C4—301no—
314C22⋊C4—301no—
315C22⋊C4—301no—
316C42C22×D1511yescharacteristic
317C3×C5#166211yescharacteristic, complemented, Hall
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3#408311yescharacteristic
322C2×D3—201no—
323C2×D3—201no—
324C2×D3—201no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—81no—
330Dic3—201no—
331Dic3—201no—
332Dic3—201no—
333C2×C5—81no—
334C2×C5#506111yescharacteristic
335C2×C5#520111yescharacteristic
336C2×C5#520211yescharacteristic
337D5—241no—
338C23—21no—
339C23—301no—
340Q8—41no—
341Q8—42no—
342Q8—601no—
343D4—41no—
344D4—601no—
345D4—1201no—
346D4—1201no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—301no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—1201no—
353C2×C4—1201no—
354C2×C4D4×D1511yescharacteristic
355C2×C4D4×D1511yescharacteristic
356C2×C4C2×#122011yescharacteristic
357C8—41no—
358C8—601no—
359C8—601no—
360C2×C3—81no—
361C2×C3#6535011yescharacteristic
362C2×C3#6549011yescharacteristic
363C2×C3#6549111yescharacteristic
364D3—401no—
365C5#7124611yescharacteristic, complemented, Sylow
366C22—41no—
367C22—41no—
368C22—41no—
369C22—601no—
370C22—601no—
371C22—601no—
372C22#9182611yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—81no—
378C4—601no—
379C4—601no—
380C4—601no—
381C3#1060203911yescharacteristic, complemented, Sylow
382C2—81no—
383C2—1201no—
384C2#1175116211yescharacteristic
385C2#1175130211yescharacteristic
386C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#489C2
socleC22×C3×C5#120
prime radical#11756443C2
hypercenter#489D15
hypocenterC3×C5#1662
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. C3×C5×#489C2semidirect
3. #11751190C2semidirect
4. #11751183C2semidirect
5. #11746361C2semidirect
6. #11746286C2semidirect
7. #11746285C2semidirect
30. C5×#489D3semidirect
64. C3×#489D5semidirect
161. #489D15semidirect
317. C3×C5#1662semidirect
365. C5#71246semidirect
381. C3#10602039semidirect

Maximal subgroups

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

subgroupindex
#117564432
C3×C5×#4892
#117511902
#117511832
#117463612
#117462862
#117462852
#106020393
#712465