Finite Group Databasebeta

← #14301205

Subgroups — #14301205

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
1C3×#66079C211yesmaximal, characteristic, complemented
2#11754138C211yesmaximal, characteristic
3C5×#5129C211yesmaximal, characteristic, complemented
4#11748424C211yesmaximal, characteristic, complemented
5#11748365C211yesmaximal, characteristic, complemented
6#11746377C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10600805—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4053—22no—
17C3×D5×M16—22no—
18C3×#4047—22no—
19#91309—21no—
20#91307C412yescomplemented
21#91299C412yescomplemented
22#91298—21no—
23#91297—22no—
24C5×(C2×D3)⋊C8—22no—
25#90978—22no—
26#90971—21no—
27#90965—21no—
28#72020—51nomaximal, Hall
29#66156—31no—
30#66079D311yescharacteristic, complemented
31C5×#408—31no—
32#65525—31no—
33#65402—31no—
34#64776—31no—
35#64772—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C5×#67—21no—
38C5×#235—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C2×C5×D12C2×C411yescharacteristic
43C2×C4×C5×D3—21no—
44C2×C5×Dic6C2×C411yescharacteristic
45C2×C3×C22⋊D5—21no—
46C3×#709—21no—
47C3×#709—21no—
48C3×#709C2×C412yes—
49C3×#709D412yes—
50C2×C3×D20D411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×Dic10D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8D412yes—
56#6719—21no—
57C4⋊Dic15—21no—
58C4×Dic15—21no—
59#6710—21no—
60#6710C2×C412yes—
61C2×C3⋊#168—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8—21no—
64C2×C5×C3⋊C8—21no—
65C3×#681—21no—
66C3×#681D412yes—
67C2×C3×#168—21no—
68C3×#676—24no—
69C3×C8×D5—24no—
70#6661—22no—
71#6656—22no—
72#6655—22no—
73#6652—22no—
74C3×#568—51no—
75#5822—51no—
76#5233—51no—
77#5139—51no—
78#5129D511yescharacteristic, complemented
79#4558—51no—
80#4556—51no—
81C2×C5×#41—31no—
82C2×#709C2×D311yescharacteristic
83C2×C5×M16C2×D311yescharacteristic
84C22×C5×C8—31no—
85#4097—61no—
86#4096—62no—
87#4095—61no—
88#4088—32no—
89#4078—32no—
90#4072—31no—
91C2×#681—31no—
92C2×#681C2×D311yescharacteristic
93#4053—22no—
94D5×M16—22no—
95#4047—22no—
96C5×C22⋊C8—62no—
97#3969—62no—
98#3953—61no—
99#3948—61no—
100#1881—151noSylow
101C23×C3×C5#4111yescharacteristic
102C22×C5×D3—21no—
103C22×C3×D5—21no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—41no—
111C5×#67—41no—
112C5×#67—41no—
113C2×C5×Dic3—21no—
114C5×D12—21no—
115C5×D12—21no—
116C4×C5×D3—41no—
117C4×C5×D3—41no—
118C5×Dic6—21no—
119C5×Dic6—21no—
120C3×C22⋊D5—22no—
121C3×C22⋊D5—22no—
122C2×C3×Dic5—21no—
123C3×D20—21no—
124C3×D20C22⋊C412yes—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×Dic10—21no—
128C3×Dic10C22⋊C412yes—
129C3×C5×C8—22no—
130C3⋊#168—22no—
131C3×#168—22no—
132C5×C3⋊C8—41no—
133C2×C3×#41—51no—
134C2×#235C2×D511yescharacteristic
135C3×#131—102no—
136C3×#131—102no—
137C2×C3×M16—51no—
138C2×C3×M16—102no—
139C2×C3×M16C2×D511yescharacteristic
140#951—52no—
141#950—102no—
142#949—52no—
143#942—101no—
144#932—101no—
145#926—51no—
146C2×#208—51no—
147C22×C3⋊C8C2×D511yescharacteristic
148#835—101no—
149#832—101no—
150#825—102no—
151(C2×D3)⋊C8—22no—
152C5×#41—61no—
153C5×#41—61no—
154C5×#41—61no—
155C5×#41—61no—
156C2×C5×Q8—31no—
157C2×C5×D4—31no—
158C2×C5×D4—61no—
159C22×C4×C5—61no—
160C22×C4×C5C22×D311yescharacteristic
161C2×C22⋊D5—21no—
162#709—21no—
163#709—21no—
164#709C4×D312yes—
165#709#6712yes—
166C2×D20D1211yescharacteristic
167C2×C4×D5—21no—
168C2×Dic10D1211yescharacteristic
169C5×M16—21no—
170C5×M16—21no—
171C2×C5×C8—61no—
172C2×C5×C8—61no—
173C2×C5×C8—61no—
174C2×C5×C8#6712yes—
175C22⋊Dic5—61no—
176#689—62no—
177#688—62no—
178#687—62no—
179#686—62no—
180C4⋊Dic5—61no—
181C4×Dic5—61no—
182#681—21no—
183#681—32no—
184#681—61no—
185#681#6712yes—
186C2×#168—21no—
187C2×#168—61no—
188#676—24no—
189C8×D5—24no—
190#575—151no—
191#568—51no—
192#421—151no—
193#416—151no—
194#408—31no—
195#344—151no—
196#341—151no—
197C22×C3×C5—41no—
198C22×C3×C5C4×D411yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5#12311yescharacteristic
201C2×C5×D3—42no—
202C2×C5×D3—41no—
203C2×C3×D5—22no—
204C2×C3×D5—81no—
205C3×C4×C5C2×C22⋊C411yescharacteristic
206C3×C4×C5C4×D411yescharacteristic
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12111yescharacteristic
209Dic15—81no—
210C3×Dic5—22no—
211C5×Dic3—41no—
212C3×#41—52no—
213C3×#41—52no—
214C3×#41—101no—
215C3×#41—101no—
216C2×C3×Q8—51no—
217C2×C3×D4—51no—
218C2×C3×D4—101no—
219C22×C3×C4—101no—
220C22×C3×C4C22×D511yescharacteristic
221C2×#67—21no—
222#235—21no—
223#235—21no—
224#235—21no—
225#235—21no—
226C2×D12C4×D511yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6C4×D511yescharacteristic
229C3×M16—21no—
230C3×M16—21no—
231C3×M16—52no—
232C3×M16—104no—
233C3×M16—101no—
234C2×C3×C8—104no—
235C2×C3×C8—101no—
236C2×C3×C8C22⋊D512yes—
237#217—101no—
238#216—102no—
239#215—102no—
240#214—102no—
241#213—102no—
242C4⋊Dic3—101no—
243C4×Dic3—101no—
244#208—52no—
245#208—101no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—101no—
250C23×C5—61no—
251C23×C5#23511yescharacteristic
252C22×D5—21no—
253C5×Q8—61no—
254C5×Q8—61no—
255C5×D4—61no—
256C5×D4—61no—
257C5×D4—121no—
258C5×D4—121no—
259C2×C4×C5—61no—
260C2×C4×C5—121no—
261C2×C4×C5—121no—
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×C4×C5C2×D1211yescharacteristic
264C2×C4×C5#23511yescharacteristic
265C2×C4×C5C2×#6711yescharacteristic
266C2×C4×C5C2×#6711yescharacteristic
267C2×C4×C5C2×#6711yescharacteristic
268C22⋊D5—22no—
269C22⋊D5—22no—
270C2×Dic5—21no—
271C2×Dic5—121no—
272D20—21no—
273D20(C2×D3)⋊C412yes—
274C4×D5—22no—
275C4×D5—22no—
276Dic10—21no—
277Dic10(C2×D3)⋊C412yes—
278C5×C8—22no—
279C5×C8—121no—
280#168—22no—
281#168—62no—
282C2×#41—31no—
283C2×#41—51no—
284#137—152no—
285#137—301no—
286AGL(1,ℤ/8)—152no—
287AGL(1,ℤ/8)—301no—
288#135—302no—
289#131—102no—
290#131—102no—
291C2×M16—51no—
292C2×M16—102no—
293C2×M16—151no—
294C2×M16D3×D511yescharacteristic
295C22×C8—31no—
296#117—151no—
297#104—302no—
298#103—301no—
299#102—301no—
300C22⋊C8—62no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5#38611yescharacteristic
305C3×D5—42no—
306C5×D3—81no—
307C23×C3—101no—
308C23×C3#70911yescharacteristic
309C22×D3—21no—
310C3×Q8—52no—
311C3×Q8—101no—
312C3×D4—52no—
313C3×D4—102no—
314C3×D4—102no—
315C3×D4—101no—
316C2×C3×C4—101no—
317C2×C3×C4—102no—
318C2×C3×C4—102no—
319C2×C3×C4C2×C4×D511yescharacteristic
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4D4×D511yescharacteristic
322C2×C3×C4D4×D511yescharacteristic
323C2×C3×C4#71111yescharacteristic
324C2×C3×C4C2×C22⋊D511yescharacteristic
325#67—41no—
326#67—41no—
327C2×Dic3—21no—
328C2×Dic3—201no—
329D12—21no—
330D12—21no—
331C4×D3—41no—
332C4×D3—41no—
333Dic6—21no—
334Dic6—21no—
335C3×C8—22no—
336C3×C8—102no—
337C3⋊C8—41no—
338C3⋊C8—102no—
339C22×C5—41no—
340C22×C5—122no—
341C22×C5—121no—
342C22×C5C4×#6711yescharacteristic
343C22×C5#92911yescharacteristic
344C22×C5#93011yescharacteristic
345C2×D5—22no—
346C2×D5—81no—
347C4×C5—121no—
348C4×C5C2×(C2×D3)⋊C411yescharacteristic
349C4×C5C4×#6711yescharacteristic
350C4×C5#93011yescharacteristic
351C4×C5#95311yescharacteristic
352Dic5—22no—
353Dic5—241no—
354#41—52no—
355#41—52no—
356#41—61no—
357#41—61no—
358#41—61no—
359#41—61no—
360#41—101no—
361#41—101no—
362C2×Q8—31no—
363C2×Q8—51no—
364C2×D4—31no—
365C2×D4—51no—
366C2×D4—61no—
367C2×D4—101no—
368C22×C4—61no—
369C22×C4—101no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—302no—
372SD16—302no—
373SD16—302no—
374D8—302no—
375M16—21no—
376M16—21no—
377M16—52no—
378M16—104no—
379M16—101no—
380M16—152no—
381M16—301no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—104no—
386C2×C8—101no—
387C2×C8—301no—
388C2×C8#120112yes—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3—102no—
395C22×C3—401no—
396C22×C3#402911yescharacteristic
397C22×C3#403011yescharacteristic
398C22×C3C4×C22⋊D511yescharacteristic
399C2×D3—42no—
400C2×D3—41no—
401C3×C4—102no—
402C3×C4D5×C22⋊C411yescharacteristic
403C3×C4#402711yescharacteristic
404C3×C4#408311yescharacteristic
405C3×C4#408411yescharacteristic
406Dic3—41no—
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—241no—
412C2×C5#521311yescharacteristic
413D5—42no—
414C23—61no—
415C23—101no—
416C23#677111yescharacteristic
417Q8—52no—
418Q8—61no—
419Q8—61no—
420Q8—101no—
421D4—52no—
422D4—61no—
423D4—61no—
424D4—102no—
425D4—102no—
426D4—101no—
427D4—121no—
428D4—121no—
429C2×C4—61no—
430C2×C4—101no—
431C2×C4—102no—
432C2×C4—102no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—601no—
436C2×C4#677211yescharacteristic
437C2×C4C4×D3×D511yescharacteristic
438C2×C4D5×D1211yescharacteristic
439C2×C4C2×#120111yescharacteristic
440C2×C4D5×#6711yescharacteristic
441C2×C4D5×#6711yescharacteristic
442C8—22no—
443C8—102no—
444C8—121no—
445C8—302no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—202no—
450C2×C3#6524511yescharacteristic
451D3—81no—
452C5#7202011yescharacteristic, complemented, Sylow
453C22—41no—
454C22—102no—
455C22—122no—
456C22—121no—
457C22—401no—
458C22C4×#120111yescharacteristic
459C22#9144711yescharacteristic
460C22#9144811yescharacteristic
461C4—102no—
462C4—121no—
463C4—1201no—
464C4#9144011yescharacteristic
465C4#9144911yescharacteristic
466C4D5×(C2×D3)⋊C411yescharacteristic
467C4#9156311yescharacteristic
468C3#1060080511yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—202no—
473C2—241no—
474C2#1174890511yescharacteristic
subgroupG/H
centerC4#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754138C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1881
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#66079C2semidirect
3. C5×#5129C2semidirect
4. #11748424C2semidirect
5. #11748365C2semidirect
6. #11746377C2semidirect
7. #11745983C2semidirect
20. #91307C4semidirect
21. #91299C4semidirect
30. #66079D3semidirect
78. #5129D5semidirect
392. C3×C5#1881semidirect
452. C5#72020semidirect
468. C3#10600805semidirect

Maximal subgroups

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

subgroupindex
C3×#660792
#117541382
C5×#51292
#117484242
#117483652
#117463772
#117459832
#106008053
#720205