Finite Group Databasebeta

← #14302861

Subgroups — #14302861

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66139C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11751316C211yesmaximal, characteristic, complemented
4C5×#5215C211yesmaximal, characteristic, complemented
5#11748624C211yesmaximal, characteristic, complemented
6#11745970C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10601123—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4099—22no—
16C3×#4086C412yescomplemented
17C3×#4084—22no—
18C3×#4082C412yescomplemented
19C3×#4072C2211yescharacteristic
20#91284—22no—
21#91283—22no—
22D5×#208—22no—
23#91116—22no—
24C5×#832—22no—
25#90995—22no—
26#71854—51nomaximal, Hall
27#66139D311yescharacteristic
28#66079—31no—
29C5×#418—31no—
30#65504—31no—
31#65295—31no—
32#64777—31no—
33#64751—31no—
34C24×C3×C5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×C22⋊D5—24no—
43C2×C3×C22⋊D5D412yes—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20C2×C411yescharacteristic
49C2×C3×C4×D5D412yes—
50C2×C3×Dic10C2×C411yescharacteristic
51#6719—21no—
52C4⋊Dic15—21no—
53C4×Dic15—21no—
54#6710—21no—
55#6710—21no—
56C2×C3⋊#168D412yescomplemented
57C5×#217—21no—
58C5×C4⋊Dic3—21no—
59C4×C5×Dic3—21no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8D412yescomplemented
63C3×C22⋊Dic5—21no—
64C3×C22⋊Dic5—24no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5C2×C412yes—
67#6649—24no—
68D5×C3⋊C8—24no—
69C3×#535—51no—
70#5819—51no—
71#5240—51no—
72#5215—51no—
73#5215D511yescharacteristic, complemented
74#4531—51no—
75#4531—51no—
76C22×C5×D4C2×D311yescharacteristic
77C2×#709C2×D311yescharacteristic
78C2×C5×M16—31no—
79C5×#117—31no—
80#4099—22no—
81#4086Dic312yescomplemented
82#4084—22no—
83#4082Dic312yescomplemented
84#4072—31no—
85#4072C2×D311yescharacteristic
86C2×#681—31no—
87#4053—62no—
88D5×M16—62no—
89#4047—62no—
90C5×#102—62no—
91#3964—62no—
92#3938—62no—
93#1910—151noSylow
94C23×C3×C5—22no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5—82no—
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5C22⋊C412yes—
100C3×C5×D4—22no—
101C3×C5×D4—22no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—41no—
111C2×C5×Dic3—41no—
112C3×C22⋊D5—22no—
113C3×C22⋊D5—22no—
114C3×C22⋊D5—84no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5C22⋊C412yes—
117C3×D20—21no—
118C3×D20—21no—
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×Dic10—21no—
122C3×Dic10—21no—
123C3⋊#168—22no—
124C5×C3⋊C8—22no—
125C2×C3×#41—51no—
126C22×C3×D4C2×D511yescharacteristic
127C3×#127—52no—
128C3×#124—52no—
129C3×#121—102no—
130C3×#120—102no—
131C3×#117—51no—
132#948—102no—
133#948—102no—
134#926—51no—
135#926C2×D511yescharacteristic
136C2×#208—51no—
137C2×#208—102no—
138C2×#208C2×D511yescharacteristic
139#834—102no—
140#832—22no—
141#832—102no—
142C24×C5—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4C2×Dic312yes—
149C22×C4×C5C22×D311yescharacteristic
150C2×C22⋊D5—24no—
151C2×C22⋊D5#6712yes—
152#709—21no—
153#709—21no—
154#709—21no—
155#709—21no—
156C2×D20C2×Dic311yescharacteristic
157C2×C4×D5#6712yes—
158C2×Dic10C2×Dic311yescharacteristic
159C5×M16—61no—
160C5×M16—61no—
161C2×C5×C8—32no—
162C5×C4⋊C4—61no—
163C5×C22⋊C4—61no—
164C42×C5—61no—
165C22⋊Dic5—21no—
166C22⋊Dic5—24no—
167C22⋊Dic5—61no—
168C4⋊Dic5—21no—
169C4⋊Dic5—61no—
170C4×Dic5—61no—
171C4×Dic5C2×Dic312yes—
172#681—61no—
173#681—61no—
174C2×#168—32no—
175#676—64no—
176C8×D5—64no—
177#568—151no—
178#535—51no—
179#418—31no—
180#418—151no—
181#410—151no—
182H(3,ℤ/4)—151no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5—44no—
186C22×C3×C5—42no—
187C22×C3×C5—82no—
188C22×C3×C5—82no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#12111yescharacteristic
191C22×C3×C5#12111yescharacteristic
192C2×C3×D5—22no—
193C2×C3×D5—42no—
194C3×C4×C5C4×D411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5#12011yescharacteristic
197C3×C4×C5#12311yescharacteristic
198Dic15—81no—
199C3×Dic5—22no—
200C3×Dic5—42no—
201C5×Dic3—81no—
202C24×C3—21no—
203C3×#41—101no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C2×C3×Q8—51no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—52no—
214C2×C3×D4—51no—
215C2×C3×D4—104no—
216C2×C3×D4C4×D512yes—
217C22×C3×C4—52no—
218C22×C3×C4C22×D511yescharacteristic
219C3×C4⋊C4—101no—
220C3×C22⋊C4—104no—
221C3×C22⋊C4—101no—
222C3×C42—52no—
223#217—21no—
224#217—101no—
225C4⋊Dic3—21no—
226C4⋊Dic3—101no—
227C4×Dic3—21no—
228C4×Dic3—101no—
229#208—21no—
230#208—21no—
231#208—104no—
232#208—101no—
233#208—101no—
234C2×C3⋊C8—52no—
235C2×C3⋊C8—104no—
236C2×C3⋊C8C22⋊D512yescomplemented
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—82no—
241C23×C5C2×#6711yescharacteristic
242C22×D5#21712yes—
243C5×D4—22no—
244C5×D4—22no—
245C5×D4—41no—
246C5×D4—41no—
247C2×C4×C5—121no—
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5#23711yescharacteristic
252C2×C4×C5C22×Dic311yescharacteristic
253C2×C4×C5C2×#6711yescharacteristic
254C22⋊D5—22no—
255C22⋊D5—22no—
256C22⋊D5—84no—
257C2×Dic5—22no—
258C2×Dic5—121no—
259C2×Dic5#21712yes—
260D20—21no—
261D20—21no—
262C4×D5—22no—
263C4×D5—22no—
264Dic10—21no—
265Dic10—21no—
266C5×C8—62no—
267#168—62no—
268C2×#41—51no—
269C22×D4D3×D511yescharacteristic
270#131—302no—
271#131—302no—
272C2×M16—31no—
273C2×M16—151no—
274C2×M16—302no—
275#127—52no—
276#124—52no—
277#121—102no—
278#120—102no—
279#117—31no—
280#117—51no—
281#117—151no—
282#102—62no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5—82no—
289C2×C3×C5#38611yescharacteristic
290C3×D5—42no—
291C23×C3—22no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—52no—
295C23×C3—82no—
296C23×C3D4×D511yescharacteristic
297C3×Q8—101no—
298C3×Q8—101no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—102no—
304C3×D4—102no—
305C3×D4—101no—
306C3×D4—101no—
307C3×D4—404no—
308C2×C3×C4—52no—
309C2×C3×C4—102no—
310C2×C3×C4—102no—
311C2×C3×C4—102no—
312C2×C3×C4C2×C4×D511yescharacteristic
313C2×C3×C4#70911yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315C2×C3×C4D4×D511yescharacteristic
316C2×C3×C4#71111yescharacteristic
317C2×C3×C4C2×C22⋊D511yescharacteristic
318C2×Dic3—41no—
319C2×Dic3—201no—
320C3⋊C8—22no—
321C3⋊C8—102no—
322C22×C5—41no—
323C22×C5—44no—
324C22×C5—42no—
325C22×C5—82no—
326C22×C5—82no—
327C22×C5#93911yescharacteristic
328C22×C5#93911yescharacteristic
329C22×C5C2×#21711yescharacteristic
330C2×D5—22no—
331C2×D5—42no—
332C4×C5—241no—
333C4×C5D4×Dic311yescharacteristic
334C4×C5D4×Dic311yescharacteristic
335C4×C5#93511yescharacteristic
336C4×C5#93711yescharacteristic
337Dic5—22no—
338Dic5—42no—
339Dic5—241no—
340C24—21no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—52no—
352C2×D4—51no—
353C2×D4—104no—
354C2×D4D5×Dic312yes—
355C22×C4—52no—
356C22×C4C2×D3×D511yescharacteristic
357M16—61no—
358M16—61no—
359M16—304no—
360M16—301no—
361M16—301no—
362C2×C8—32no—
363C2×C8—152no—
364C2×C8—304no—
365C4⋊C4—61no—
366C4⋊C4—101no—
367C4⋊C4—301no—
368C22⋊C4—61no—
369C22⋊C4—104no—
370C22⋊C4—101no—
371C22⋊C4—301no—
372C42—52no—
373C42—61no—
374C42—301no—
375C3×C5#191011yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—44no—
378C22×C3—42no—
379C22×C3—82no—
380C22×C3—82no—
381C22×C3—102no—
382C22×C3—202no—
383C22×C3D5×C22⋊C411yescharacteristic
384C22×C3#403011yescharacteristic
385C22×C3#408411yescharacteristic
386C3×C4—102no—
387C3×C4—202no—
388C3×C4#402711yescharacteristic
389C3×C4#402911yescharacteristic
390C3×C4C4×C22⋊D511yescharacteristic
391C3×C4#408311yescharacteristic
392Dic3—81no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—82no—
398C2×C5#522011yescharacteristic
399D5—42no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23—52no—
404C23—82no—
405C23D5×#6711yescharacteristic
406Q8—101no—
407Q8—101no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412D4—102no—
413D4—102no—
414D4—101no—
415D4—101no—
416D4—404no—
417C2×C4—52no—
418C2×C4—102no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—121no—
422C2×C4—601no—
423C2×C4C2×D5×Dic311yescharacteristic
424C2×C4#677911yescharacteristic
425C2×C4#678011yescharacteristic
426C2×C4D5×#6711yescharacteristic
427C2×C4D3×C22⋊D511yescharacteristic
428C2×C4#679011yescharacteristic
429C8—62no—
430C8—302no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—82no—
435C2×C3—202no—
436C2×C3#6524511yescharacteristic
437C5#7185411yescharacteristic, complemented, Sylow
438C22—41no—
439C22—44no—
440C22—42no—
441C22—82no—
442C22—82no—
443C22—102no—
444C22—202no—
445C22D5×#21711yescharacteristic
446C22#9154911yescharacteristic
447C22#9155011yescharacteristic
448C4—102no—
449C4—202no—
450C4—241no—
451C4—1201no—
452C4#9154811yescharacteristic
453C4Dic3×C22⋊D511yescharacteristic
454C4#9155911yescharacteristic
455C4#9157711yescharacteristic
456C3#1060112311yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—82no—
461C2—202no—
462C2#1174951811yescharacteristic
subgroupG/H
centerC2#11749518
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radicalC3×#66139C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1910
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11754120C2semidirect
3. #11751316C2semidirect
4. C5×#5215C2semidirect
5. #11748624C2semidirect
6. #11745970C2semidirect
7. #11745969C2semidirect
16. C3×#4086C4semidirect
18. C3×#4082C4semidirect
56. C2×C3⋊#168D4semidirect
62. C2×C5×C3⋊C8D4semidirect
73. #5215D5semidirect
81. #4086Dic3semidirect
83. #4082Dic3semidirect
236. C2×C3⋊C8C22⋊D5semidirect
375. C3×C5#1910semidirect
437. C5#71854semidirect
456. C3#10601123semidirect

Maximal subgroups

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

subgroupindex
C3×#661392
#117541202
#117513162
C5×#52152
#117486242
#117459702
#117459692
#106011233
#718545