Finite Group Databasebeta

← #14302966

Subgroups — #14302966

Order 1920.

628 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
1C3×#65860C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3#11748421C211yesmaximal, characteristic
4#11748420C211yesmaximal, characteristic
5C2×#90961C211yesmaximal, characteristic, complemented
6#11746352C211yesmaximal, characteristic, complemented
7C5×#4531C211yesmaximal, characteristic, complemented
8#10599501—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4043—22no—
17C3×#4032—22no—
18C3×#4021C412yescomplemented
19C3×#4015C412yescomplemented
20#91528—22no—
21#91331—22no—
22Dic3×Dic10—22no—
23#90977—22no—
24#90976—22no—
25#90961—22no—
26#71864—51nomaximal, Hall
27#65860D311yescharacteristic
28#65850—31no—
29#65428—31no—
30C2×#3956—31no—
31#65294—31no—
32C5×H(3,ℤ/4)—31no—
33#64751—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—21no—
36C22×C3×Dic5D412yes—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709—21no—
40C3×#709—21no—
41C2×C3×D20C2×C411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×Dic10—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10C2×C411yescharacteristic
48C2×C3×Dic10C2×C412yes—
49C2×C3×Dic10D412yes—
50C3×C5×C4⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2×C412yes—
53#6719—21no—
54C4⋊Dic15—21no—
55C4×Dic15D412yes—
56#6710—21no—
57#6710—21no—
58C2×C3⋊#168—21no—
59C5×#217—21no—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3D412yes—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×#685—24no—
66C3×C4⋊Dic5—24no—
67#6668—24no—
68Dic3×Dic5—24no—
69C3×#536—51no—
70#5812—51no—
71#5236—51no—
72#5236—51no—
73C2×#836—51no—
74#4531—51no—
75#4531D511yescharacteristic, complemented
76C2×#709C2×D311yescharacteristic
77C22×Dic10C2×D311yescharacteristic
78C2×C5×M16—31no—
79C5×#117—31no—
80C5×#117C2×D311yescharacteristic
81#4072—31no—
82C2×#681—31no—
83#4043—22no—
84#4033—62no—
85#4032—22no—
86#4023—62no—
87#4021Dic312yescomplemented
88#4015Dic312yescomplemented
89C4×Dic10—62no—
90#3957—62no—
91#3956—62no—
92#3937—62no—
93#1912—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×C5×Dic3—22no—
105C3×C22⋊D5—41no—
106C3×C22⋊D5—41no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5C22⋊C414yes—
111C3×D20—21no—
112C3×D20—21no—
113C3×C4×D5—41no—
114C3×C4×D5—41no—
115C3×Dic10—22no—
116C3×Dic10—22no—
117C3×Dic10—22no—
118C3×Dic10—22no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3⋊#168—41no—
122C5×C3⋊C8—41no—
123C2×C3×#41—51no—
124C22×C3×Q8—51no—
125C3×C4⋊Q8—52no—
126C3×#124—52no—
127C3×#123—102no—
128C3×C22⋊Q8—102no—
129C3×#117C2×D511yescharacteristic
130Q8×Dic3—102no—
131Q8×Dic3—102no—
132#926—51no—
133#926—102no—
134#926C2×D511yescharacteristic
135C2×#208—51no—
136C2×#208C2×D511yescharacteristic
137#837—102no—
138#837—102no—
139#836—102no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—21no—
142C22×Dic5#6712yes—
143#709—21no—
144#709—21no—
145#709—21no—
146#709—21no—
147C2×D20C2×Dic311yescharacteristic
148C2×C4×D5—21no—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10C2×Dic311yescharacteristic
154C2×Dic10C2×Dic312yes—
155C2×Dic10#6712yes—
156C5×M16—61no—
157C5×M16—61no—
158C2×C5×C8—61no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—21no—
162C5×C22⋊C4—61no—
163C42×C5—32no—
164C42×C5C2×Dic312yes—
165C22⋊Dic5—61no—
166#685—24no—
167C4⋊Dic5—24no—
168C4⋊Dic5—61no—
169#683—64no—
170C4×Dic5—32no—
171C4×Dic5—64no—
172#681—61no—
173#681—61no—
174C2×#168—61no—
175#536—51no—
176#519—151no—
177#421—151no—
178#421—151no—
179C2×#101—151no—
180H(3,ℤ/4)—31no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C3×D5—42no—
187C2×C3×D5—41no—
188C3×C4×C5—42no—
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12111yescharacteristic
192C3×C4×C5#12111yescharacteristic
193Dic15—42no—
194C3×Dic5—24no—
195C3×Dic5—41no—
196C5×Dic3—42no—
197C3×#41—101no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—52no—
202C2×C3×Q8—52no—
203C2×C3×Q8—51no—
204C2×C3×Q8—101no—
205C2×C3×Q8—101no—
206C2×C3×Q8—101no—
207C2×C3×Q8—101no—
208C2×C3×D4—51no—
209C2×C3×D4—101no—
210C22×C3×C4—52no—
211C22×C3×C4—101no—
212C22×C3×C4C22×D511yescharacteristic
213C3×C4⋊C4—21no—
214C3×C4⋊C4—104no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—104no—
217C3×C42C4×D512yes—
218#217—21no—
219#217—101no—
220C4⋊Dic3—21no—
221C4⋊Dic3—104no—
222C4⋊Dic3—101no—
223C4×Dic3—52no—
224C4×Dic3—104no—
225C4×Dic3D2012yes—
226#208—21no—
227#208—21no—
228#208—101no—
229#208—101no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—101no—
232C23×C5C2×#6711yescharacteristic
233C22×D5—21no—
234C2×C4×C5—22no—
235C2×C4×C5—62no—
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×C4×C5#23711yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5C22×Dic311yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C22⋊D5—41no—
243C22⋊D5—41no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—21no—
247C2×Dic5—62no—
248C2×Dic5#21714yes—
249D20—21no—
250D20—21no—
251C4×D5—41no—
252C4×D5—41no—
253Dic10—22no—
254Dic10—22no—
255Dic10—22no—
256Dic10—22no—
257Dic10—21no—
258Dic10—21no—
259C5×C8—121no—
260#168—121no—
261C2×#41—51no—
262C22×Q8—51no—
263C2×M16—31no—
264C2×M16—151no—
265C4⋊Q8—52no—
266#124—52no—
267#123—102no—
268C22⋊Q8—102no—
269C4×Q8—302no—
270C4×Q8—302no—
271#117—31no—
272#117—151no—
273#117—302no—
274#117D3×D511yescharacteristic
275#104—302no—
276#104—302no—
277#101—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282C3×D5—81no—
283C23×C3—101no—
284C23×C3D4×D511yescharacteristic
285C3×Q8—102no—
286C3×Q8—102no—
287C3×Q8—102no—
288C3×Q8—102no—
289C3×Q8—101no—
290C3×Q8—101no—
291C3×D4—101no—
292C3×D4—101no—
293C3×D4—201no—
294C3×D4—201no—
295C2×C3×C4—22no—
296C2×C3×C4—54no—
297C2×C3×C4—102no—
298C2×C3×C4—102no—
299C2×C3×C4—101no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4C2×C4×D511yescharacteristic
303C2×C3×C4C2×D2011yescharacteristic
304C2×C3×C4#70911yescharacteristic
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4#71311yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—102no—
310C3⋊C8—41no—
311C3⋊C8—201no—
312C22×C5—41no—
313C22×C5#93511yescharacteristic
314C22×C5#93711yescharacteristic
315C22×C5C2×#21711yescharacteristic
316C2×D5—42no—
317C2×D5—41no—
318C4×C5—42no—
319C4×C5—122no—
320C4×C5D4×Dic311yescharacteristic
321C4×C5D4×Dic311yescharacteristic
322C4×C5#93911yescharacteristic
323C4×C5#93911yescharacteristic
324Dic5—24no—
325Dic5—41no—
326Dic5—122no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—52no—
332C2×Q8—52no—
333C2×Q8—51no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×Q8—101no—
338C2×D4—51no—
339C2×D4—101no—
340C22×C4—52no—
341C22×C4—101no—
342C22×C4C2×D3×D511yescharacteristic
343M16—61no—
344M16—61no—
345M16—301no—
346M16—301no—
347C2×C8—61no—
348C2×C8—301no—
349C4⋊C4—21no—
350C4⋊C4—61no—
351C4⋊C4—104no—
352C4⋊C4—304no—
353C4⋊C4—301no—
354C22⋊C4—21no—
355C22⋊C4—61no—
356C22⋊C4—104no—
357C22⋊C4—301no—
358C42—32no—
359C42—152no—
360C42—304no—
361C42D5×Dic312yes—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—202no—
365C22×C3—201no—
366C22×C3D5×C22⋊C411yescharacteristic
367C22×C3#402811yescharacteristic
368C22×C3#404011yescharacteristic
369C3×C4—42no—
370C3×C4—104no—
371C3×C4—201no—
372C3×C4C4×D2011yescharacteristic
373C3×C4#403011yescharacteristic
374C3×C4#403911yescharacteristic
375C3×C4#404111yescharacteristic
376Dic3—42no—
377Dic3—202no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#522011yescharacteristic
382D5—81no—
383C23—101no—
384C23D5×#6711yescharacteristic
385Q8—102no—
386Q8—102no—
387Q8—102no—
388Q8—102no—
389Q8—101no—
390Q8—101no—
391D4—101no—
392D4—101no—
393D4—201no—
394D4—201no—
395C2×C4—22no—
396C2×C4—54no—
397C2×C4—62no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—101no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4—302no—
404C2×C4#676511yescharacteristic
405C2×C4#676611yescharacteristic
406C2×C4D3×D2011yescharacteristic
407C2×C4#677711yescharacteristic
408C2×C4C2×D5×Dic311yescharacteristic
409C2×C4D5×#6711yescharacteristic
410C8—121no—
411C8—601no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—401no—
416C2×C3#6495411yescharacteristic
417C5#7186411yescharacteristic, complemented, Sylow
418C22—41no—
419C22—202no—
420C22—201no—
421C22#9140711yescharacteristic
422C22#9147411yescharacteristic
423C22D5×#21711yescharacteristic
424C4—42no—
425C4—104no—
426C4—122no—
427C4—201no—
428C4—602no—
429C4#9140811yescharacteristic
430C4#9140911yescharacteristic
431C4Dic3×D2011yescharacteristic
432C4#9143411yescharacteristic
433C3#1059950111yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—401no—
438C2#1174889611yescharacteristic
subgroupG/H
centerC2#11748896
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
5. C2×#90961C2semidirect
6. #11746352C2semidirect
7. C5×#4531C2semidirect
18. C3×#4021C4semidirect
19. C3×#4015C4semidirect
75. #4531D5semidirect
87. #4021Dic3semidirect
88. #4015Dic3semidirect
362. C3×C5#1912semidirect
417. C5#71864semidirect
433. C3#10599501semidirect

Maximal subgroups

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

subgroupindex
C3×#658602
#117541882
#117484212
#117484202
C2×#909612
#117463522
C5×#45312
#105995013
#718645