Finite Group Databasebeta

← #14301191

Subgroups — #14301191

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
1C5×#5822C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic, complemented
4C3×#65523C211yesmaximal, characteristic, complemented
5#11748388C211yesmaximal, characteristic, complemented
6#11745991C211yesmaximal, characteristic, complemented
7#11745984C211yesmaximal, characteristic, complemented
8#10602909—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#951—21no—
14C5×#950—22no—
15C5×#949—21no—
16C5×#942C412yescomplemented
17C5×#932C412yescomplemented
18C2×C5×#208C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21#91288—22no—
22D3×#681—22no—
23#91286—22no—
24#91121—22no—
25C3×C22⋊#168—22no—
26#90973—21no—
27#90967—21no—
28#70012—51nomaximal, Hall
29C5×#575—31no—
30#66153—31no—
31#65525—31no—
32#65523D311yescharacteristic, complemented
33#65522—31no—
34#64779—31no—
35#64778—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C5×#67—21no—
46C5×#235—21no—
47C5×#235—21no—
48C5×#235C2×C412yes—
49C5×#235D412yes—
50C2×C5×D12D411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C5×Dic6D411yescharacteristic
53#6719—21no—
54C4⋊Dic15—21no—
55C4×Dic15—21no—
56#6710—21no—
57#6710D412yes—
58C2×C3⋊#168—21no—
59C5×#216—22no—
60C5×#215—22no—
61C5×#214—22no—
62C5×#213—22no—
63C5×#208—21no—
64C5×#208C2×C412yes—
65C2×C5×C3⋊C8—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168—21no—
69C2×C3×#168—21no—
70C2×C3×#168—21no—
71C2×C3×#168D412yes—
72#6650—24no—
73D3×#168—24no—
74#5822D511yescharacteristic
75#5745—51no—
76C3×#408—51no—
77#5236—51no—
78#5113—51no—
79#4556—51no—
80#4552—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#4072—31no—
92C2×#681—31no—
93C2×#681—62no—
94C2×#681C2×D311yescharacteristic
95C22×#168C2×D311yescharacteristic
96#3969—62no—
97#3967—61no—
98#3964—61no—
99C22⋊#168—22no—
100#1881—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5#4111yescharacteristic
103C22×C5×D3—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8—21no—
106C3×C5×D4—21no—
107C3×C5×D4—21no—
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
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
119C2×Dic15—41no—
120C5×#67—22no—
121C5×#67—22no—
122C2×C5×Dic3—21no—
123C5×D12—21no—
124C5×D12C22⋊C412yes—
125C4×C5×D3—22no—
126C4×C5×D3—22no—
127C5×Dic6—21no—
128C5×Dic6C22⋊C412yes—
129C3⋊#168—22no—
130C3×#168—22no—
131C3×#168—41no—
132C5×C3⋊C8—22no—
133C2×C3×#41C2×D511yescharacteristic
134C2×#235C2×D511yescharacteristic
135C2×C3×M16—51no—
136C22×C3×C8—51no—
137#951—21no—
138#950—22no—
139#949—21no—
140#942Dic512yescomplemented
141#932Dic512yescomplemented
142#926—51no—
143C2×#208—51no—
144C2×#208C2×D511yescharacteristic
145#907—102no—
146D3×M16—102no—
147#901—102no—
148C3×C22⋊C8—102no—
149#837—102no—
150#821—101no—
151#816—101no—
152C5×#41—21no—
153C5×#41—21no—
154C5×#41—21no—
155C5×#41—21no—
156C5×#41—32no—
157C5×#41—32no—
158C5×#41—61no—
159C5×#41—61no—
160C2×C5×Q8—31no—
161C2×C5×Q8C4×D311yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4—31no—
164C2×C5×D4—61no—
165C2×C5×D4C4×D311yescharacteristic
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—61no—
177C4⋊Dic5—61no—
178C4×Dic5—61no—
179#681—21no—
180#681—21no—
181#681—32no—
182#681—64no—
183#681—61no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168—21no—
187C2×#168—64no—
188C2×#168—61no—
189C2×#168#6712yes—
190#575—31no—
191#568—151no—
192#421—151no—
193#416—151no—
194#408—51no—
195#344—151no—
196#341—151no—
197C22×C3×C5—41no—
198C22×C3×C5—42no—
199C22×C3×C5—41no—
200C22×C3×C5C4×D411yescharacteristic
201C22×C3×C5#12111yescharacteristic
202C22×C3×C5#12311yescharacteristic
203C2×C5×D3—22no—
204C2×C5×D3—81no—
205C3×C4×C5—41no—
206C3×C4×C5C2×C22⋊C411yescharacteristic
207C3×C4×C5C4×D411yescharacteristic
208C3×C4×C5#12011yescharacteristic
209C3×C4×C5#12111yescharacteristic
210Dic15—81no—
211C5×Dic3—22no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C2×C3×Q8C2×Dic511yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4C2×Dic511yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4C22×D511yescharacteristic
221C2×#67—21no—
222#235—21no—
223#235—21no—
224#235C2×Dic512yes—
225#235C22⋊D512yes—
226C2×D12C22⋊D511yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6C22⋊D511yescharacteristic
229C3×M16—101no—
230C3×M16—101no—
231C2×C3×C8—52no—
232C2×C3×C8—101no—
233C2×C3×C8—101no—
234C2×C3×C8—101no—
235#217—101no—
236#216—22no—
237#215—22no—
238#214—22no—
239#213—22no—
240C4⋊Dic3—101no—
241C4×Dic3—101no—
242#208—21no—
243#208—52no—
244#208—101no—
245#208C2×Dic512yes—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—101no—
248ΓL(1,𝔽25)—104no—
249D3×C8—104no—
250C23×C5—21no—
251C23×C5—61no—
252C23×C5#23511yescharacteristic
253C5×Q8—21no—
254C5×Q8—21no—
255C5×Q8—32no—
256C5×Q8—61no—
257C5×D4—21no—
258C5×D4—21no—
259C5×D4—32no—
260C5×D4—41no—
261C5×D4—41no—
262C5×D4—62no—
263C5×D4—62no—
264C5×D4—61no—
265C2×C4×C5—21no—
266C2×C4×C5—41no—
267C2×C4×C5—41no—
268C2×C4×C5—61no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×Dic5—121no—
278C5×C8—62no—
279#168—22no—
280#168—41no—
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—51no—
293C2×M16—151no—
294C2×M16—302no—
295C22×C8—51no—
296#117—151no—
297#104—302no—
298#103—301no—
299#102—301no—
300C22⋊C8—102no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5—81no—
305C2×C3×C5#38611yescharacteristic
306C5×D3—42no—
307C23×C3—21no—
308C23×C3#71111yescharacteristic
309C22×D3—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×D4—21no—
313C3×D4—21no—
314C3×D4—41no—
315C3×D4—41no—
316C2×C3×C4—21no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4D4×D511yescharacteristic
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4#71111yescharacteristic
322C2×C3×C4C22×Dic511yescharacteristic
323C2×C3×C4C2×C22⋊D511yescharacteristic
324C2×C3×C4C2×C22⋊D511yescharacteristic
325#67—22no—
326#67—22no—
327C2×Dic3—21no—
328C2×Dic3—201no—
329D12—21no—
330D12C22⋊Dic512yes—
331C4×D3—22no—
332C4×D3—22no—
333Dic6—21no—
334Dic6C22⋊Dic512yes—
335C3×C8—102no—
336C3×C8—201no—
337C3⋊C8—22no—
338C3⋊C8—102no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5—62no—
343C22×C5—241no—
344C22×C5#88311yescharacteristic
345C22×C5#88411yescharacteristic
346C22×C5C4×#6711yescharacteristic
347C4×C5—41no—
348C4×C5—62no—
349C4×C5D3×C22⋊C411yescharacteristic
350C4×C5#67⋊C411yescharacteristic
351C4×C5#93711yescharacteristic
352C4×C5#93811yescharacteristic
353Dic5—241no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—32no—
359#41—32no—
360#41—61no—
361#41—61no—
362C2×Q8—31no—
363C2×Q8D3×Dic511yescharacteristic
364C2×D4—21no—
365C2×D4—31no—
366C2×D4—61no—
367C2×D4D3×Dic511yescharacteristic
368C22×C4—21no—
369C22×C4—61no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—62no—
372SD16—62no—
373SD16—62no—
374D8—62no—
375M16—32no—
376M16—61no—
377M16—101no—
378M16—101no—
379M16—152no—
380M16—304no—
381M16—301no—
382C2×C8—52no—
383C2×C8—61no—
384C2×C8—101no—
385C2×C8—101no—
386C2×C8—101no—
387C2×C8—304no—
388C2×C8—301no—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3D4×Dic511yescharacteristic
397C22×C3#408111yescharacteristic
398C22×C3#408511yescharacteristic
399C2×D3—22no—
400C2×D3—81no—
401C3×C4—41no—
402C3×C4D4×Dic511yescharacteristic
403C3×C4#408311yescharacteristic
404C3×C4#408511yescharacteristic
405C3×C4C2×C22⋊Dic511yescharacteristic
406Dic3—22no—
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—81no—
412C2×C5—122no—
413C2×C5#495611yescharacteristic
414C23—21no—
415C23—61no—
416C23#678211yescharacteristic
417Q8—21no—
418Q8—21no—
419Q8—32no—
420Q8—61no—
421D4—21no—
422D4—21no—
423D4—32no—
424D4—41no—
425D4—41no—
426D4—62no—
427D4—62no—
428D4—61no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—61no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—601no—
436C2×C4#678011yescharacteristic
437C2×C4C2×D3×Dic511yescharacteristic
438C2×C4D5×#6711yescharacteristic
439C2×C4D3×C22⋊D511yescharacteristic
440C2×C4D3×C22⋊D511yescharacteristic
441C2×C4#679011yescharacteristic
442C8—62no—
443C8—102no—
444C8—201no—
445C8—302no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—81no—
450C2×C3#6550911yescharacteristic
451D3—42no—
452C5#7001211yescharacteristic, complemented, Sylow
453C22—41no—
454C22—42no—
455C22—41no—
456C22—62no—
457C22—241no—
458C22Dic5×#6711yescharacteristic
459C22#9155511yescharacteristic
460C22#9155811yescharacteristic
461C4—41no—
462C4—62no—
463C4—1201no—
464C4D3×C22⋊Dic511yescharacteristic
465C4#67⋊Dic511yescharacteristic
466C4#9156511yescharacteristic
467C4#9157711yescharacteristic
468C3#1060290911yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—81no—
473C2—122no—
474C2#1174951911yescharacteristic
subgroupG/H
centerC4#91577
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
2. #11754125C2semidirect
3. #11751337C2semidirect
4. C3×#65523C2semidirect
5. #11748388C2semidirect
6. #11745991C2semidirect
7. #11745984C2semidirect
16. C5×#942C4semidirect
17. C5×#932C4semidirect
32. #65523D3semidirect
140. #942Dic5semidirect
141. #932Dic5semidirect
392. C3×C5#1881semidirect
452. C5#70012semidirect
468. C3#10602909semidirect

Maximal subgroups

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

subgroupindex
C5×#58222
#117541252
#117513372
C3×#655232
#117483882
#117459912
#117459842
#106029093
#700125