Finite Group Databasebeta

← #14282784

Subgroups — #14282784

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754410C211yesmaximal, characteristic
2C3×#65007C211yesmaximal, characteristic, complemented
3#11748635C211yesmaximal, characteristic, complemented
4#11746288C211yesmaximal, characteristic, complemented
5C5×#4470C211yesmaximal, characteristic
6#11745965C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic
8#10599069—31nomaximal, Hall
9#91813C2211yescharacteristic
10C5×#930C2211yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12Dic5×#67—21no—
13#91539—21no—
14C2×Dic3×Dic5—21no—
15Dic5×D12C411yescharacteristic, complemented
16#91398—21no—
17#91388C411yescharacteristic, complemented
18#91373C411yescharacteristic, complemented
19#91372—21no—
20#91333C411yescharacteristic, complemented
21C3×C5×C22⋊C8C2211yescharacteristic
22#91115C2211yescharacteristic
23C5×C3⋊#95C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×#3946—21no—
26C3×C8×Dic5—21no—
27#90994—21no—
28#70788—51nomaximal, Hall
29#65934—31no—
30#65007D311yescharacteristic, complemented
31#64937—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×Dic30C2×C411yescharacteristic
39C2×C5×#67—21no—
40C22×C5×Dic3—21no—
41C2×C5×D12C2×C411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×D3×Dic5—21no—
45C2×C3×C5×C8—21no—
46#6719—21no—
47C4⋊Dic15C2×C411yescharacteristic
48#6712—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C3×C4×Dic5C2×C411yescharacteristic
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6669—21no—
59(C2×D3)⋊Dic5—21no—
60(C2×D3)⋊Dic5—21no—
61(C2×D3)⋊Dic5—21no—
62Dic3×Dic5—24no—
63Dic3×Dic5—21no—
64#5479—51no—
65C3×#431—51no—
66#4932—51no—
67#4470—51no—
68#4470D511yescharacteristic
69#4467—51no—
70#4467—51no—
71C5×#121—31no—
72#4082—31no—
73#4081—61no—
74D4×Dic5—31no—
75D4×Dic5—61no—
76#4070—31no—
77C2×C4×Dic5—61no—
78C2×C4×Dic5C2×D311yescharacteristic
79#4036—31no—
80#4033—31no—
81#4025—61no—
82#4023—61no—
83C5×C22⋊C8C2×D311yescharacteristic
84C5×#95—31no—
85#3963—31no—
86#3963—61no—
87C22⋊#168C2×D311yescharacteristic
88#3946—21no—
89C8×Dic5—21no—
90#1500—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C5×D3—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—22no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101Dic30—41no—
102C5×#67—41no—
103C5×#67—41no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—41no—
108C5×D12—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116D3×Dic5—42no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C2×C3×C42—51no—
120#930C2×D511yescharacteristic
121#929—101no—
122C4×#67—101no—
123#924—51no—
124C2×C4×Dic3—101no—
125#876—101no—
126#875—51no—
127C4×D12—51no—
128#872—101no—
129#870—51no—
130C4×Dic6—51no—
131C3×C4⋊C8—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×C4×C8—101no—
135C3⋊#95—51no—
136C3⋊#95—101no—
137C3⋊#95C2×D511yescharacteristic
138C2×C5×D4—31no—
139C2×C5×D4—61no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—61no—
143C22×Dic5—61no—
144C22×Dic5D1211yescharacteristic
145C22×Dic5D1211yescharacteristic
146C2×Dic10—31no—
147C2×C5×C8—21no—
148C5×C4⋊C4—31no—
149C5×C22⋊C4—61no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152C22⋊Dic5—61no—
153C22⋊Dic5—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158#683—61no—
159C4×Dic5—64no—
160C4×Dic5—61no—
161C4×Dic5C4×D311yescharacteristic
162C4×Dic5C4×D311yescharacteristic
163C4×Dic5#6711yescharacteristic
164C4×Dic5#6711yescharacteristic
165C2×#168—21no—
166#529—151no—
167#431—51no—
168#376—151no—
169#328—151no—
170#328—151no—
171#327—31no—
172#327—151no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#13511yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C2×C5×D3—41no—
179C2×C5×D3—41no—
180C2×C5×D3—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183Dic15—42no—
184Dic15—41no—
185Dic15—41no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5#10412yes—
190C5×Dic3—42no—
191C5×Dic3—41no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4C22×D511yescharacteristic
195C2×#67—21no—
196C22×Dic3—21no—
197C22×Dic3—101no—
198C2×D12C4×D511yescharacteristic
199C2×C4×D3—101no—
200C2×Dic6—51no—
201C2×C3×C8—21no—
202C2×C3×C8—101no—
203C3×C42—51no—
204C3×C42—51no—
205C3×C42—51no—
206C3×C42—51no—
207#217—101no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211(C2×D3)⋊C4—101no—
212C4⋊Dic3—51no—
213C4⋊Dic3C4×D511yescharacteristic
214Dic3⋊C4—101no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217Dic3⋊C4—101no—
218C4×Dic3—101no—
219C4×Dic3—104no—
220C23×C5—61no—
221C23×C5C2×D1211yescharacteristic
222C5×D4—121no—
223C5×D4—121no—
224C5×D4—121no—
225C2×C4×C5—41no—
226C2×C4×C5—62no—
227C2×C4×C5—61no—
228C2×C4×C5—121no—
229C2×C4×C5—121no—
230C2×C4×C5C2×C4×D311yescharacteristic
231C2×C4×C5C2×#6711yescharacteristic
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—22no—
235C2×Dic5—62no—
236C2×Dic5—61no—
237C2×Dic5—61no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240C2×Dic5—122no—
241C2×Dic5(C2×D3)⋊C411yescharacteristic
242C2×Dic5(C2×D3)⋊C411yescharacteristic
243C2×Dic5(C2×D3)⋊C411yescharacteristic
244C2×Dic5(C2×D3)⋊C411yescharacteristic
245Dic10—121no—
246C5×C8—41no—
247#168—41no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—151no—
253#121—31no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C42—51no—
259C2×C42—301no—
260C4⋊C8—101no—
261C22⋊C8—51no—
262C22⋊C8D3×D511yescharacteristic
263C4×C8—101no—
264#95—31no—
265#95—151no—
266#95—301no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272C5×D3—81no—
273C23×C3D4×D511yescharacteristic
274C22×D3—21no—
275C2×C3×C4—41no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—102no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4C2×C4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285#67—41no—
286#67—41no—
287C2×Dic3—22no—
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—102no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296D12—41no—
297C4×D3—202no—
298Dic6—201no—
299C3×C8—41no—
300C3×C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—121no—
304C22×C5—121no—
305C22×C5—121no—
306C22×C5#90411yescharacteristic
307C22×C5#90411yescharacteristic
308C22×C5C2×(C2×D3)⋊C411yescharacteristic
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—122no—
312C4×C5—121no—
313Dic5—21no—
314Dic5—21no—
315Dic5—21no—
316Dic5—122no—
317Dic5—121no—
318Dic5—121no—
319Dic5#82512yes—
320C2×Q8—151no—
321C2×D4—31no—
322C2×D4—61no—
323C22×C4—51no—
324C22×C4—51no—
325C22×C4—61no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—21no—
330C2×C8—101no—
331C4⋊C4—31no—
332C4⋊C4—151no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C22⋊C4—61no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C22⋊C4—301no—
342C42—51no—
343C42—51no—
344C42—51no—
345C42—51no—
346C42—301no—
347C42—304no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#405811yescharacteristic
353C22×C3#406211yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—52no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—101no—
363Dic3—42no—
364Dic3—41no—
365Dic3—202no—
366Dic3—201no—
367Dic3—201no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5—241no—
371C2×C5#500611yescharacteristic
372C2×C5#511311yescharacteristic
373C2×C5C2×#82511yescharacteristic
374C23—61no—
375C23D5×D1211yescharacteristic
376Q8—601no—
377D4—121no—
378D4—121no—
379D4—121no—
380C2×C4—41no—
381C2×C4—51no—
382C2×C4—51no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—62no—
386C2×C4—61no—
387C2×C4—102no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—302no—
393C2×C4—301no—
394C2×C4—301no—
395C2×C4—602no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D5×#6711yescharacteristic
400C8—41no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6502911yescharacteristic
405C2×C3#6506111yescharacteristic
406C2×C3D5×#10411yescharacteristic
407D3—81no—
408C5#7078811yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22#9126911yescharacteristic
415C22#9127011yescharacteristic
416C22D5×(C2×D3)⋊C411yescharacteristic
417C4—21no—
418C4—21no—
419C4—52no—
420C4—101no—
421C4—101no—
422C4—101no—
423C4—122no—
424C4—121no—
425C4—602no—
426C4—601no—
427C4—601no—
428C3#1059906911yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—241no—
432C2#1174712911yescharacteristic
433C2#1174813511yescharacteristic
434C2D5×#82511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65007C2semidirect
3. #11748635C2semidirect
4. #11746288C2semidirect
6. #11745965C2semidirect
15. Dic5×D12C4semidirect
17. #91388C4semidirect
18. #91373C4semidirect
20. #91333C4semidirect
30. #65007D3semidirect
348. C3×C5#1500semidirect
408. C5#70788semidirect
428. C3#10599069semidirect

Maximal subgroups

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

subgroupindex
#117544102
C3×#650072
#117486352
#117462882
C5×#44702
#117459652
#117459572
#105990693
#707885