Finite Group Databasebeta

← #14302799

Subgroups — #14302799

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756504C211yesmaximal, characteristic
2#11754270C211yesmaximal, characteristic
3C5×#5120C211yesmaximal, characteristic, complemented
4#11748626C211yesmaximal, characteristic
5#11748407C211yesmaximal, characteristic, complemented
6C3×#64777C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10601143—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13#91796—22no—
14M16×D15—22no—
15#91790—22no—
16C5×#926C2211yescharacteristic
17C3×#4072C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19#91542—22no—
20#91383—22no—
21#91376C412yescomplemented
22#91375C412yescomplemented
23C5×#816—22no—
24#90997—22no—
25#90972—22no—
26#68712—51nomaximal, Hall
27#66150—31no—
28#66079—31no—
29C5×#419—31no—
30#65514—31no—
31#65295—31no—
32#64777D311yescharacteristic, complemented
33#64751—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220D412yes—
36#6817—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40C2×D60C2×C411yescharacteristic
41C2×C4×D15D412yes—
42C2×Dic30C2×C411yescharacteristic
43C22×C5×Dic3—21no—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6C2×C412yes—
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8D412yes—
53#6710—21no—
54#6710—21no—
55C2×C3⋊#168D412yes—
56#6705—24no—
57C8×D15—24no—
58C5×#217—21no—
59C5×C4⋊Dic3—21no—
60C4×C5×Dic3—21no—
61C3×C22⋊Dic5—21no—
62C3×C22⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5—21no—
65C3×C4×Dic5—21no—
66C3×C4×Dic5C2×C412yes—
67#6668—24no—
68#6667—24no—
69#5745—51no—
70#5526—51no—
71#5120D511yescharacteristic, complemented
72#5006—51no—
73#5004—51no—
74C3×H(3,ℤ/4)—51no—
75#4531—51no—
76C22×C5×Q8—31no—
77C2×#709—31no—
78C2×C5×M16C2×D311yescharacteristic
79C5×#117—31no—
80#4093—32no—
81#4092—62no—
82#4090—32no—
83#4075—62no—
84#4072C2×D311yescharacteristic
85#4072C2×D311yescharacteristic
86C2×#681—31no—
87#4053—62no—
88D5×M16—62no—
89#4047—62no—
90C5×#103—62no—
91#3967—62no—
92#3938—62no—
93#1909—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15C22⋊C412yes—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102#1220—22no—
103#1220—22no—
104C2×Dic15C22⋊C412yes—
105D60—21no—
106D60—21no—
107C4×D15—22no—
108C4×D15—22no—
109Dic30—21no—
110Dic30—21no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3—41no—
114C2×C5×Dic3—41no—
115C5×Dic6—22no—
116C5×Dic6—22no—
117C5×Dic6—41no—
118C5×Dic6—41no—
119C2×C3×Dic5—22no—
120C2×C3×Dic5—41no—
121C3×C5×C8—22no—
122C3⋊#168—22no—
123C2×#235—51no—
124C22×Dic6C2×D511yescharacteristic
125C2×C3×M16C2×D511yescharacteristic
126C3×#117—51no—
127C3×#117—51no—
128#926C2×D511yescharacteristic
129C2×#208—51no—
130#907—102no—
131D3×M16—102no—
132#901—102no—
133#897—102no—
134#886—102no—
135#875—52no—
136#869—52no—
137#816—22no—
138#810—102no—
139#806—102no—
140C2×C5×Q8—32no—
141C2×C5×Q8—61no—
142C2×C5×Q8—61no—
143C2×C5×Q8—61no—
144C2×C5×Q8—61no—
145C2×C5×Q8—61no—
146C22×C4×C5—61no—
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—32no—
149#709—61no—
150#709—61no—
151#709—61no—
152#709—61no—
153C2×D20—31no—
154C2×C4×D5—32no—
155C2×Dic10—31no—
156C5×M16—21no—
157C5×M16—21no—
158C2×C5×C8D1212yes—
159C5×C4⋊C4—61no—
160C5×C22⋊C4—61no—
161C42×C5—61no—
162C22⋊Dic5—21no—
163C22⋊Dic5—21no—
164#685—64no—
165C4⋊Dic5—21no—
166C4⋊Dic5—21no—
167#683—64no—
168C4×Dic5—21no—
169C4×Dic5C4×D312yes—
170#681—61no—
171#681—61no—
172C2×#168—32no—
173#676—64no—
174C8×D5—64no—
175#568—151no—
176#536—151no—
177#419—31no—
178#419—151no—
179#410—151no—
180H(3,ℤ/4)—51no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12111yescharacteristic
185C22×C3×C5#12111yescharacteristic
186C2×D15—22no—
187C2×D15—42no—
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5#12011yescharacteristic
191C3×C4×C5#12311yescharacteristic
192Dic15—22no—
193C3×Dic5—42no—
194C3×Dic5—81no—
195C5×Dic3—42no—
196C5×Dic3—81no—
197C22×C3×C4C22×D511yescharacteristic
198C2×#67—52no—
199C22×Dic3—21no—
200#235—101no—
201#235—101no—
202#235—101no—
203#235—101no—
204C2×D12—51no—
205C2×C4×D3—52no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—51no—
212C2×Dic6C4×D512yes—
213C3×M16—21no—
214C3×M16—21no—
215C2×C3×C8C22⋊D512yes—
216C3×C4⋊C4—101no—
217C3×C4⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C42—52no—
221C3×C42—101no—
222#217—21no—
223(C2×D3)⋊C4—104no—
224C4⋊Dic3—21no—
225C4⋊Dic3—104no—
226C4×Dic3—21no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—52no—
230ΓL(1,𝔽25)—104no—
231D3×C8—104no—
232C23×C5D3×D411yescharacteristic
233C22×D5—32no—
234C5×Q8—62no—
235C5×Q8—62no—
236C5×Q8—121no—
237C5×Q8—121no—
238C2×C4×C5—62no—
239C2×C4×C5—121no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5C2×D1211yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23911yescharacteristic
248C22⋊D5—62no—
249C22⋊D5—62no—
250C2×Dic5—22no—
251C2×Dic5—32no—
252C2×Dic5—41no—
253D20—61no—
254D20—61no—
255C4×D5—62no—
256C4×D5—62no—
257Dic10—61no—
258Dic10—61no—
259C5×C8—22no—
260#168—62no—
261C2×#41—151no—
262C22×Q8—31no—
263#131—302no—
264#131—302no—
265C2×M16—151no—
266C2×M16—302no—
267C2×M16D3×D511yescharacteristic
268C4⋊Q8—152no—
269#124—152no—
270#123—302no—
271C22⋊Q8—302no—
272#117—31no—
273#117—51no—
274#117—51no—
275#103—62no—
276#103—302no—
277#99—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282D15—42no—
283C23×C3D4×D511yescharacteristic
284C22×D3—52no—
285C2×C3×C4—102no—
286C2×C3×C4—201no—
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4#70911yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293#67—102no—
294#67—102no—
295C2×Dic3—22no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—52no—
300D12—101no—
301D12—101no—
302C4×D3—102no—
303C4×D3—102no—
304Dic6—22no—
305Dic6—22no—
306Dic6—41no—
307Dic6—41no—
308Dic6—101no—
309Dic6—101no—
310C3×C8—22no—
311C3⋊C8—102no—
312C22×C5—41no—
313C22×C5D3×C22⋊C411yescharacteristic
314C22×C5#88411yescharacteristic
315C22×C5#89511yescharacteristic
316C2×D5—62no—
317C2×D5—122no—
318C4×C5—122no—
319C4×C5—241no—
320C4×C5C4×D1211yescharacteristic
321C4×C5#88211yescharacteristic
322C4×C5#89311yescharacteristic
323C4×C5#89411yescharacteristic
324Dic5—42no—
325Dic5—62no—
326Dic5—81no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—32no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×Q8—151no—
338C2×D4—152no—
339C2×D4—151no—
340C22×C4—61no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—21no—
345M16—304no—
346M16—301no—
347M16—301no—
348C2×C8—152no—
349C2×C8—304no—
350C2×C8#120312yes—
351C4⋊C4—61no—
352C4⋊C4—101no—
353C4⋊C4—101no—
354C4⋊C4—304no—
355C22⋊C4—61no—
356C22⋊C4—101no—
357C22⋊C4—101no—
358C22⋊C4—304no—
359C42—52no—
360C42—61no—
361C42—101no—
362C3×C5#190911yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3D5×C22⋊C411yescharacteristic
365C22×C3#403011yescharacteristic
366C22×C3#408411yescharacteristic
367C2×D3—102no—
368C2×D3—202no—
369C3×C4—202no—
370C3×C4—401no—
371C3×C4#402711yescharacteristic
372C3×C4#402911yescharacteristic
373C3×C4C4×C22⋊D511yescharacteristic
374C3×C4#408311yescharacteristic
375Dic3—42no—
376Dic3—81no—
377Dic3—102no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#466511yescharacteristic
382D5—122no—
383C23—152no—
384C23#677711yescharacteristic
385Q8—62no—
386Q8—62no—
387Q8—121no—
388Q8—121no—
389Q8—301no—
390Q8—301no—
391D4—302no—
392D4—302no—
393D4—301no—
394D4—301no—
395C2×C4—62no—
396C2×C4—102no—
397C2×C4—121no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—152no—
401C2×C4—201no—
402C2×C4—302no—
403C2×C4—302no—
404C2×C4#676811yescharacteristic
405C2×C4#677111yescharacteristic
406C2×C4C4×D3×D511yescharacteristic
407C2×C4C2×#120311yescharacteristic
408C2×C4#679011yescharacteristic
409C2×C4#679011yescharacteristic
410C8—22no—
411C8—302no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3#6524511yescharacteristic
416D3—202no—
417C5#6871211yescharacteristic, complemented, Sylow
418C22—41no—
419C22—302no—
420C22—602no—
421C22#9146111yescharacteristic
422C22#9146611yescharacteristic
423C22#9147311yescharacteristic
424C4—122no—
425C4—202no—
426C4—241no—
427C4—302no—
428C4—401no—
429C4#9135511yescharacteristic
430C4#9140611yescharacteristic
431C4C4×#120311yescharacteristic
432C4#9157311yescharacteristic
433C3#1060114311yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—602no—
438C2#1174891811yescharacteristic
subgroupG/H
centerC2#11748918
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1909
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C5×#5120C2semidirect
5. #11748407C2semidirect
6. C3×#64777C2semidirect
7. #11745969C2semidirect
21. #91376C4semidirect
22. #91375C4semidirect
32. #64777D3semidirect
71. #5120D5semidirect
362. C3×C5#1909semidirect
417. C5#68712semidirect
433. C3#10601143semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117542702
C5×#51202
#117486262
#117484072
C3×#647772
#117459692
#106011433
#687125