Finite Group Databasebeta

← #14301186

Subgroups — #14301186

Order 1920.

620 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756578C211yesmaximal, characteristic, complemented
2C5×#5822C211yesmaximal, characteristic
3C3×#65522C211yesmaximal, characteristic, complemented
4#11748425C211yesmaximal, characteristic, complemented
5#11748345C211yesmaximal, characteristic, complemented
6#11745993C211yesmaximal, characteristic, complemented
7#11745984C211yesmaximal, characteristic, complemented
8#10602909—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11#91837—22no—
12#91837—22no—
13C2×#6710—22no—
14C2×#6710C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C5×#951C412yescomplemented
17C5×#950—22no—
18C5×#949C412yescomplemented
19C5×#942—21no—
20C5×#932—21no—
21C2×C5×#208C2211yescharacteristic
22C3×#4072C2211yescharacteristic
23C22×C3×#168C2211yescharacteristic
24C3×#3967—21no—
25C3×#3964—21no—
26#90979—22no—
27(C2×D3)⋊#168—22no—
28#70293—51nomaximal, Hall
29C5×#575—31no—
30#66153—31no—
31#65525—31no—
32#65523—31no—
33#65522D311yescharacteristic, complemented
34#64779—31no—
35#64778—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41C2×C412yes—
39C3×C5×#41D412yes—
40C2×C3×C5×Q8D411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4D411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C5×#67—21no—
46C5×#235—21no—
47C5×#235—21no—
48C5×#235—21no—
49C5×#235—21no—
50C2×C5×D12C2×C411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C5×Dic6C2×C411yescharacteristic
53#6710—24no—
54#6710—21no—
55#6710—21no—
56#6710—21no—
57#6710D412yes—
58C2×C3⋊#168—24no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168D412yes—
61C5×#216—22no—
62C5×#215—22no—
63C5×#214—22no—
64C5×#213—22no—
65C5×#208—21no—
66C5×#208C2×C412yes—
67C2×C5×C3⋊C8—21no—
68C3×C22⋊Dic5—21no—
69C3×C4⋊Dic5—21no—
70C3×C4×Dic5—21no—
71C2×C3×#168—21no—
72C2×C3×#168—21no—
73C2×C3×#168—21no—
74#5822D511yescharacteristic
75#5819—51no—
76C3×#416—51no—
77#5110—51no—
78#5005—51no—
79#4552—51no—
80#4533—51no—
81C2×C5×#41—31no—
82C2×C5×#41C2×D311yescharacteristic
83C5×#137—32no—
84C5×#137—61no—
85C5×AGL(1,ℤ/8)—32no—
86C5×AGL(1,ℤ/8)—61no—
87C5×#135—62no—
88C2×C5×M16—31no—
89#4094—62no—
90#4094—62no—
91#4072C2×D311yescharacteristic
92C2×#681—31no—
93C2×#681—31no—
94C2×#681—62no—
95C22×#168C2×D311yescharacteristic
96#3969—62no—
97#3967—21no—
98#3964—21no—
99C22⋊#168—62no—
100#1881—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5#4111yescharacteristic
103C22×C5×D3—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8C22⋊C412yes—
106C3×C5×D4—22no—
107C3×C5×D4—22no—
108C3×C5×D4—21no—
109C3×C5×D4C22⋊C412yes—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C5×#67—41no—
120C5×#67—41no—
121C2×C5×Dic3—21no—
122C5×D12—21no—
123C5×D12—21no—
124C4×C5×D3—41no—
125C4×C5×D3—41no—
126C5×Dic6—21no—
127C5×Dic6—21no—
128C2×C3×Dic5—41no—
129C3⋊#168—22no—
130C3⋊#168—22no—
131C3×#168—41no—
132C5×C3⋊C8—22no—
133C2×C3×#41C2×D511yescharacteristic
134C2×#235C2×D511yescharacteristic
135C22×C3×C8—51no—
136C3×#117—51no—
137#951Dic512yescomplemented
138#950—22no—
139#949Dic512yescomplemented
140#948—102no—
141#948—102no—
142#942—21no—
143#932—21no—
144C2×#208—51no—
145C2×#208—51no—
146C2×#208—102no—
147C2×#208C2×D511yescharacteristic
148C3×#103—101no—
149C3×#102—101no—
150(C2×D3)⋊C8—102no—
151#805—102no—
152C5×#41—21no—
153C5×#41—21no—
154C5×#41—61no—
155C5×#41—61no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41C4×D312yes—
159C5×#41D1212yes—
160C2×C5×Q8—31no—
161C2×C5×Q8#6711yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4—31no—
164C2×C5×D4—61no—
165C2×C5×D4#6711yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—61no—
168C22×C4×C5C22×D311yescharacteristic
169C5×Q16—62no—
170C5×SD16—62no—
171C5×SD16—62no—
172C5×D8—62no—
173C5×M16—32no—
174C5×M16—61no—
175C2×C5×C8—61no—
176C22⋊Dic5—21no—
177C4⋊Dic5—21no—
178C4×Dic5—21no—
179#681—32no—
180#681—64no—
181#681—61no—
182#681—61no—
183#681—61no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168—21no—
187C2×#168—32no—
188C2×#168—64no—
189C2×#168—61no—
190#575—31no—
191#568—151no—
192#421—151no—
193#416—51no—
194#408—151no—
195#344—151no—
196#341—151no—
197C22×C3×C5—22no—
198C22×C3×C5—41no—
199C22×C3×C5—81no—
200C22×C3×C5C4×D411yescharacteristic
201C22×C3×C5#12111yescharacteristic
202C22×C3×C5#12311yescharacteristic
203C2×C5×D3—42no—
204C2×C5×D3—41no—
205C3×C4×C5—22no—
206C3×C4×C5C2×C22⋊C411yescharacteristic
207C3×C4×C5C4×D411yescharacteristic
208C3×C4×C5#12011yescharacteristic
209C3×C4×C5#12111yescharacteristic
210C3×Dic5—81no—
211C5×Dic3—41no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41C2×Dic512yes—
215C3×#41C22⋊D512yes—
216C2×C3×Q8C22⋊D511yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4C22⋊D511yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4C22×D511yescharacteristic
221C2×#67—21no—
222#235—21no—
223#235—21no—
224#235—21no—
225#235—21no—
226C2×D12C2×Dic511yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6C2×Dic511yescharacteristic
229C2×C3×C8—101no—
230C2×C3×C8—101no—
231C2×C3×C8—101no—
232C3×C4⋊C4—101no—
233C3×C22⋊C4—101no—
234C3×C42—101no—
235#216—22no—
236#215—22no—
237#214—22no—
238#213—22no—
239#208—21no—
240#208—52no—
241#208—104no—
242#208—101no—
243#208—101no—
244#208—101no—
245#208C2×Dic512yes—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—52no—
248C2×C3⋊C8—104no—
249C2×C3⋊C8—101no—
250C23×C5—21no—
251C23×C5—61no—
252C23×C5#23711yescharacteristic
253C5×Q8—21no—
254C5×Q8—61no—
255C5×Q8—61no—
256C5×Q8(C2×D3)⋊C412yes—
257C5×D4—22no—
258C5×D4—22no—
259C5×D4—21no—
260C5×D4—61no—
261C5×D4—61no—
262C5×D4—121no—
263C5×D4—121no—
264C5×D4(C2×D3)⋊C412yes—
265C2×C4×C5—21no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—61no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5C2×D1211yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×Dic5—41no—
278C5×C8—62no—
279#168—41no—
280#168—62no—
281#168—62no—
282C2×#41—31no—
283C2×#41D3×D511yescharacteristic
284#137—32no—
285#137—61no—
286AGL(1,ℤ/8)—32no—
287AGL(1,ℤ/8)—61no—
288#135—62no—
289#131—302no—
290#131—302no—
291C2×M16—31no—
292C2×M16—151no—
293C2×M16—151no—
294C2×M16—302no—
295C22×C8—51no—
296#117—51no—
297#104—302no—
298#103—101no—
299#102—101no—
300C22⋊C8—302no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5—42no—
305C2×C3×C5#38611yescharacteristic
306C5×D3—81no—
307C23×C3—21no—
308C23×C3#71111yescharacteristic
309C22×D3—21no—
310C3×Q8—21no—
311C3×Q8C22⋊Dic512yes—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—21no—
315C3×D4C22⋊Dic512yes—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—201no—
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4D4×D511yescharacteristic
322C2×C3×C4#71111yescharacteristic
323C2×C3×C4C22×Dic511yescharacteristic
324C2×C3×C4C2×C22⋊D511yescharacteristic
325C2×C3×C4C2×C22⋊D511yescharacteristic
326#67—41no—
327#67—41no—
328C2×Dic3—21no—
329D12—21no—
330D12—21no—
331C4×D3—41no—
332C4×D3—41no—
333Dic6—21no—
334Dic6—21no—
335C3×C8—201no—
336C3⋊C8—22no—
337C3⋊C8—102no—
338C3⋊C8—102no—
339C22×C5—22no—
340C22×C5—41no—
341C22×C5—81no—
342C22×C5—122no—
343C22×C5—121no—
344C22×C5#67⋊C411yescharacteristic
345C22×C5#88611yescharacteristic
346C22×C5#93911yescharacteristic
347C4×C5—22no—
348C4×C5—121no—
349C4×C5#67⋊C411yescharacteristic
350C4×C5#88211yescharacteristic
351C4×C5C2×(C2×D3)⋊C411yescharacteristic
352C4×C5#93911yescharacteristic
353Dic5—81no—
354#41—21no—
355#41—21no—
356#41—61no—
357#41—61no—
358#41—61no—
359#41—61no—
360#41D3×Dic512yes—
361#41#120312yes—
362C2×Q8—31no—
363C2×Q8#120111yescharacteristic
364C2×D4—21no—
365C2×D4—31no—
366C2×D4—61no—
367C2×D4#120111yescharacteristic
368C22×C4—21no—
369C22×C4—61no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—62no—
372SD16—62no—
373SD16—62no—
374D8—62no—
375M16—32no—
376M16—61no—
377M16—152no—
378M16—304no—
379M16—301no—
380M16—301no—
381M16—301no—
382C2×C8—61no—
383C2×C8—101no—
384C2×C8—101no—
385C2×C8—101no—
386C2×C8—152no—
387C2×C8—304no—
388C2×C8—301no—
389C4⋊C4—101no—
390C22⋊C4—101no—
391C42—101no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—22no—
394C22×C3—41no—
395C22×C3—81no—
396C22×C3D4×Dic511yescharacteristic
397C22×C3#408111yescharacteristic
398C22×C3#408511yescharacteristic
399C2×D3—42no—
400C2×D3—41no—
401C3×C4—22no—
402C3×C4—401no—
403C3×C4D4×Dic511yescharacteristic
404C3×C4#408311yescharacteristic
405C3×C4#408511yescharacteristic
406C3×C4C2×C22⋊Dic511yescharacteristic
407Dic3—41no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—42no—
412C2×C5—241no—
413C2×C5#495811yescharacteristic
414C23—21no—
415C23—61no—
416C23#678011yescharacteristic
417Q8—21no—
418Q8—61no—
419Q8—61no—
420Q8(C2×D3)⋊Dic512yes—
421D4—22no—
422D4—22no—
423D4—21no—
424D4—61no—
425D4—61no—
426D4—121no—
427D4—121no—
428D4(C2×D3)⋊Dic512yes—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—61no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—201no—
436C2×C4#678011yescharacteristic
437C2×C4C2×D3×Dic511yescharacteristic
438C2×C4C2×#120111yescharacteristic
439C2×C4C2×#120311yescharacteristic
440C2×C4#679011yescharacteristic
441C2×C4#679011yescharacteristic
442C8—62no—
443C8—201no—
444C8—302no—
445C8—302no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—42no—
450C2×C3#6550911yescharacteristic
451D3—81no—
452C5#7029311yescharacteristic, complemented, Sylow
453C22—22no—
454C22—41no—
455C22—81no—
456C22—122no—
457C22—121no—
458C22#9154311yescharacteristic
459C22#67⋊Dic511yescharacteristic
460C22#9157111yescharacteristic
461C4—22no—
462C4—121no—
463C4—401no—
464C4C2×(C2×D3)⋊Dic511yescharacteristic
465C4#67⋊Dic511yescharacteristic
466C4#9157111yescharacteristic
467C4#9157311yescharacteristic
468C3#1060290911yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—241no—
474C2#1174950111yescharacteristic
subgroupG/H
centerC4#91573
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radicalC5×#5822C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1881
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756578C2semidirect
3. C3×#65522C2semidirect
4. #11748425C2semidirect
5. #11748345C2semidirect
6. #11745993C2semidirect
7. #11745984C2semidirect
16. C5×#951C4semidirect
18. C5×#949C4semidirect
33. #65522D3semidirect
137. #951Dic5semidirect
139. #949Dic5semidirect
392. C3×C5#1881semidirect
452. C5#70293semidirect
468. C3#10602909semidirect

Maximal subgroups

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

subgroupindex
#117565782
C5×#58222
C3×#655222
#117484252
#117483452
#117459932
#117459842
#106029093
#702935