Finite Group Databasebeta

← #14301454

Subgroups — #14301454

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5521C211yesmaximal, characteristic
2C2×#91370C211yesmaximal, characteristic
3C3×#65293C211yesmaximal, characteristic, complemented
4#11748399C211yesmaximal, characteristic, complemented
5C2×#90959C211yesmaximal, characteristic
6#11746353C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10602442—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C5×#893—22no—
16C5×D3×C22⋊C4—22no—
17C4×C5×D12—22no—
18C2×C3×#681C2211yescharacteristic
19C2×(C2×D3)⋊Dic5—22no—
20#91370—22no—
21#91370C414yescomplemented
22C3×#3942—22no—
23#90970—22no—
24#90959—22no—
25#70343—51nomaximal, Hall
26C5×#518—31no—
27C2×#4082—31no—
28C2×#3965—31no—
29#65293—31no—
30#65293D311yescharacteristic, complemented
31#64752—31no—
32#64752—31no—
33C23×C5×D3D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12C2×C412yes—
41C2×C5×D12D412yes—
42C2×C4×C5×D3—24no—
43C22×C3×Dic5—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10C2×C412yescomplemented
50C3×C5×C4⋊C4D412yes—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5—21no—
53C4×Dic15—21no—
54C4×Dic15C2×C412yescomplemented
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#217—21no—
59C5×(C2×D3)⋊C4—24no—
60C5×C4⋊Dic3D412yes—
61C4×C5×Dic3—21no—
62C3×#681—21no—
63C3×#681—21no—
64C2×C3×#168—21no—
65(C2×D3)⋊Dic5—28no—
66C2×#947—51no—
67#5521D511yescharacteristic
68C3×#419—51no—
69#5225—51no—
70C2×#823—51no—
71#4555—51no—
72#4532—51no—
73C22×C5×D4—31no—
74C22×Dic10C2×D311yescharacteristic
75C4×C5×D4—62no—
76C4×C5×D4—62no—
77C5×#117—31no—
78C5×#117C2×D311yescharacteristic
79C2×C5×C22⋊C4—62no—
80C2×C22⋊Dic5—62no—
81#4082—34no—
82#4082—62no—
83C2×C4×Dic5—31no—
84C2×#681—31no—
85C2×#681C2×D311yescharacteristic
86#3965—62no—
87#3942—22no—
88#3942—62no—
89#1885—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C5×D3—22no—
92C22×C5×D3—22no—
93C22×C5×D3—44no—
94C22×C5×D3C22⋊C414yes—
95C2×C3×C4×C5—22no—
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
102C2×Dic15—22no—
103C2×Dic15—42no—
104C2×C5×Dic3—22no—
105C5×D12—22no—
106C5×D12—22no—
107C5×D12—22no—
108C5×D12—22no—
109C4×C5×D3—84no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C3×Dic10—22no—
114C3×Dic10—22no—
115C3×Dic10—41no—
116C3×Dic10—41no—
117C3⋊#168—41no—
118C3×#168—41no—
119C22×C3×Q8—51no—
120C22×D12C2×D511yescharacteristic
121C2×C3×M16—51no—
122C3×#117C2×D511yescharacteristic
123#947—54no—
124#947—102no—
125C2×(C2×D3)⋊C4—102no—
126#926C2×D511yescharacteristic
127C2×C4×Dic3—51no—
128C2×#208—51no—
129#893—22no—
130D3×C22⋊C4—22no—
131C4×D12—22no—
132C3×#103—102no—
133#835—102no—
134#823—102no—
135C24×C5—32no—
136C2×C5×D4—32no—
137C2×C5×D4—32no—
138C2×C5×D4—61no—
139C2×C5×D4—61no—
140C2×C5×D4—61no—
141C2×C5×D4—61no—
142C22×C4×C5—64no—
143C22×C4×C5C22×D311yescharacteristic
144C22×Dic5—21no—
145C22×Dic5—61no—
146C2×Dic10—21no—
147C2×Dic10—21no—
148C2×Dic10—21no—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10C4×D312yescomplemented
152C5×C4⋊C4—32no—
153C5×C4⋊C4#6712yes—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—64no—
156C5×C22⋊C4—61no—
157C42×C5—21no—
158C42×C5—61no—
159C22⋊Dic5—68no—
160C4×Dic5—32no—
161C4×Dic5—61no—
162#681—21no—
163#681—21no—
164#681—61no—
165#681—61no—
166C2×#168—21no—
167C2×#168—61no—
168C2×#124—151no—
169#518—31no—
170#419—51no—
171#419—151no—
172C2×#100—151no—
173#339—151no—
174#339—151no—
175C22×C3×C5—22no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12011yescharacteristic
178C22×C3×C5#12311yescharacteristic
179C2×C5×D3—24no—
180C2×C5×D3—44no—
181C2×C5×D3—44no—
182C2×C5×D3—82no—
183C3×C4×C5—42no—
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12111yescharacteristic
187C3×C4×C5#12111yescharacteristic
188Dic15—42no—
189C3×Dic5—42no—
190C5×Dic3—42no—
191C23×D3C22⋊D512yes—
192C2×C3×Q8—52no—
193C2×C3×Q8—101no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C22×C3×C4—101no—
199C22×C3×C4C22×D511yescharacteristic
200C22×Dic3—101no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12C4×D512yes—
206C2×D12D2012yes—
207C2×C4×D3—24no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4C22⋊D512yes—
212C3×C22⋊C4—21no—
213C3×C42—21no—
214#217—21no—
215(C2×D3)⋊C4—24no—
216(C2×D3)⋊C4—108no—
217C4⋊Dic3C22⋊D512yes—
218C4×Dic3—21no—
219C4×Dic3—52no—
220C4×Dic3—101no—
221#208—101no—
222#208—101no—
223C2×C3⋊C8—101no—
224C23×C5—34no—
225C23×C5—62no—
226C23×C5—62no—
227C23×C5—124no—
228C23×C5D3×D411yescharacteristic
229C5×D4—62no—
230C5×D4—62no—
231C5×D4—62no—
232C5×D4—62no—
233C2×C4×C5—22no—
234C2×C4×C5—62no—
235C2×C4×C5—244no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C2×Dic5—22no—
243C2×Dic5—41no—
244C2×Dic5—41no—
245C2×Dic5—62no—
246C2×Dic5—122no—
247Dic10—22no—
248Dic10—22no—
249Dic10—41no—
250Dic10—41no—
251#168—41no—
252#168—121no—
253C22×Q8—51no—
254C22×D4—31no—
255C2×M16—51no—
256C2×M16—151no—
257#124—154no—
258#124—302no—
259C4×D4—62no—
260C4×D4—62no—
261#117—31no—
262#117D3×D511yescharacteristic
263C2×C22⋊C4—62no—
264C2×C22⋊C4—302no—
265C2×C42—151no—
266#103—102no—
267#103—302no—
268#100—302no—
269C2×C3×C5—21no—
270C2×C3×C5—21no—
271C2×C3×C5#38611yescharacteristic
272C2×C3×C5#45512yes—
273C5×D3—44no—
274C23×C3C2×C22⋊D511yescharacteristic
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—44no—
278C22×D3#68514yes—
279C3×Q8—102no—
280C3×Q8—102no—
281C3×Q8—201no—
282C3×Q8—201no—
283C2×C3×C4—22no—
284C2×C3×C4—102no—
285C2×C3×C4—201no—
286C2×C3×C4—201no—
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4C2×D2011yescharacteristic
289C2×C3×C4#70911yescharacteristic
290C2×C3×C4#70911yescharacteristic
291C2×C3×C4C2×C22⋊D511yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293C2×Dic3—22no—
294C2×Dic3—102no—
295C2×Dic3—202no—
296D12—22no—
297D12—22no—
298D12—22no—
299D12—22no—
300C4×D3—84no—
301C3×C8—201no—
302C3⋊C8—201no—
303C22×C5—22no—
304C22×C5—64no—
305C22×C5—124no—
306C22×C5—124no—
307C22×C5—242no—
308C22×C5D3×C22⋊C411yescharacteristic
309C22×C5#88311yescharacteristic
310C22×C5#93711yescharacteristic
311C4×C5—42no—
312C4×C5—122no—
313C4×C5#67⋊C411yescharacteristic
314C4×C5#88411yescharacteristic
315C4×C5C4×#6711yescharacteristic
316C4×C5#93811yescharacteristic
317Dic5—42no—
318Dic5—122no—
319C24—32no—
320C2×Q8—52no—
321C2×Q8—101no—
322C2×Q8—101no—
323C2×Q8—101no—
324C2×Q8—101no—
325C2×Q8—101no—
326C2×D4—32no—
327C2×D4—32no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4—61no—
331C2×D4—61no—
332C22×C4—64no—
333C22×C4—101no—
334C22×C4—301no—
335C22×C4C2×D3×D511yescharacteristic
336M16—101no—
337M16—101no—
338M16—301no—
339M16—301no—
340C2×C8—101no—
341C2×C8—301no—
342C4⋊C4—32no—
343C4⋊C4#120112yes—
344C22⋊C4—21no—
345C22⋊C4—64no—
346C22⋊C4—61no—
347C22⋊C4—308no—
348C42—21no—
349C42—61no—
350C42—152no—
351C42—301no—
352C3×C5#188511yescharacteristic, complemented, Hall
353C22×C3—22no—
354C22×C3C2×#68511yescharacteristic
355C22×C3#407511yescharacteristic
356C22×C3#409911yescharacteristic
357C2×D3—24no—
358C2×D3—44no—
359C2×D3—44no—
360C2×D3—82no—
361C3×C4—42no—
362C3×C4—202no—
363C3×C4C4×C22⋊D511yescharacteristic
364C3×C4C4×C22⋊D511yescharacteristic
365C3×C4#407611yescharacteristic
366C3×C4#407611yescharacteristic
367Dic3—42no—
368Dic3—202no—
369C2×C5—21no—
370C2×C5—21no—
371C2×C5—124no—
372C2×C5#495611yescharacteristic
373C2×C5#520212yes—
374C23—34no—
375C23—62no—
376C23—62no—
377C23—124no—
378C23D3×C22⋊D511yescharacteristic
379Q8—102no—
380Q8—102no—
381Q8—201no—
382Q8—201no—
383D4—62no—
384D4—62no—
385D4—62no—
386D4—62no—
387C2×C4—22no—
388C2×C4—62no—
389C2×C4—102no—
390C2×C4—201no—
391C2×C4—201no—
392C2×C4—244no—
393C2×C4—302no—
394C2×C4—602no—
395C2×C4#676511yescharacteristic
396C2×C4#677111yescharacteristic
397C2×C4C4×D3×D511yescharacteristic
398C2×C4D3×D2011yescharacteristic
399C2×C4C2×#120111yescharacteristic
400C2×C4D3×C22⋊D511yescharacteristic
401C8—201no—
402C8—601no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3#6550211yescharacteristic
406C2×C3#6553112yes—
407D3—44no—
408C5#7034311yescharacteristic, complemented, Sylow
409C22—22no—
410C22—64no—
411C22—124no—
412C22—124no—
413C22—242no—
414C22#9145211yescharacteristic
415C22D3×#68511yescharacteristic
416C22#9156811yescharacteristic
417C4—42no—
418C4—122no—
419C4—202no—
420C4—602no—
421C4C4×#120111yescharacteristic
422C4#9144111yescharacteristic
423C4#9145411yescharacteristic
424C4#9145611yescharacteristic
425C3#1060244211yescharacteristic, complemented, Sylow
426C2—21no—
427C2—21no—
428C2—124no—
429C2#1174891011yescharacteristic
430C2#1174941612yes—
subgroupG/H
centerC22#91568
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1885
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#65293C2semidirect
4. #11748399C2semidirect
6. #11746353C2semidirect
7. #11745975C2semidirect
21. #91370C4semidirect
30. #65293D3semidirect
49. C2×C3×Dic10C2×C4semidirect
54. C4×Dic15C2×C4semidirect
151. C2×Dic10C4×D3semidirect
352. C3×C5#1885semidirect
408. C5#70343semidirect
425. C3#10602442semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
C2×#913702
C3×#652932
#117483992
C2×#909592
#117463532
#117459752
#106024423
#703435