Finite Group Databasebeta

← #14282774

Subgroups — #14282774

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#11754415C211yesmaximal, characteristic
2C3×#64937C211yesmaximal, characteristic, complemented
3#11748316C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic
5C5×#4452C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745958C211yesmaximal, characteristic
8#10599101—31nomaximal, Hall
9#91819C2211yescharacteristic
10C5×#924C2211yescharacteristic
11C2×C3×C4×Dic5—21no—
12C2×C3×C4×Dic5C2211yescharacteristic
13#91552—21no—
14#91546—21no—
15#91418C411yescharacteristic, complemented
16#91402—21no—
17#91388C411yescharacteristic, complemented
18#91387—21no—
19#91375C411yescharacteristic, complemented
20Dic5×Dic6C411yescharacteristic, complemented
21C3×C5×#95C2211yescharacteristic
22#91114C2211yescharacteristic
23C5×#830C2211yescharacteristic
24C3×#3963—21no—
25C3×#3963C2211yescharacteristic
26#90982—21no—
27Dic5×C3⋊C8—21no—
28#69431—51nomaximal, Hall
29#65958—31no—
30#65007—31no—
31#64937D311yescharacteristic, complemented
32C5×#328—31no—
33#64758—31no—
34#64690—31no—
35#64671—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×D60C2×C411yescharacteristic
40C2×C5×Dic6C2×C411yescharacteristic
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×#1200—21no—
45#6714—21no—
46C4⋊Dic15C2×C411yescharacteristic
47C2×C3⋊#168—21no—
48C5×#217—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5—24no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5C2×C411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C3×C4×Dic5D411yescharacteristic
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63Dic3×Dic5—21no—
64#5479—51no—
65C3×#376—51no—
66#4925—51no—
67#4452—51no—
68#4452D511yescharacteristic, complemented
69#4451—51no—
70#4451—51no—
71C5×C22⋊Q8—31no—
72#4093—31no—
73Q8×Dic5—31no—
74#4076—31no—
75C2×C4×Dic5—21no—
76C2×C4×Dic5C2×D311yescharacteristic
77#4044—61no—
78#4039—31no—
79#4038—61no—
80#4036—31no—
81#4032—61no—
82#4027—61no—
83C5×C22⋊C8—31no—
84C5×#95C2×D311yescharacteristic
85#3963—21no—
86#3963C2×D311yescharacteristic
87C22⋊#168—31no—
88#3946—61no—
89C8×Dic5—61no—
90#1500—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99#1220—41no—
100#1220—41no—
101C2×Dic15—21no—
102D60—41no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C5×Dic6—41no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116#1200—42no—
117C3⋊#168—41no—
118C5×C3⋊C8—41no—
119C2×C3×C42—51no—
120C2×C3×C42—101no—
121#930—51no—
122#929—101no—
123C4×#67—101no—
124#924C2×D511yescharacteristic
125#876—101no—
126#875—51no—
127C4×D12—51no—
128#872—101no—
129#870—51no—
130C4×Dic6—51no—
131C3×#95—51no—
132C3×#95—101no—
133C3×#95C2×D511yescharacteristic
134#830—51no—
135#830C2×D511yescharacteristic
136C4⋊(C3⋊C8)—101no—
137C4×C3⋊C8—101no—
138C2×C5×Q8—31no—
139C22×C4×C5—21no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—61no—
142C22×Dic5—21no—
143C22×Dic5#6711yescharacteristic
144C22×Dic5#6711yescharacteristic
145C2×D20—31no—
146C2×C4×D5—61no—
147C2×C5×C8—61no—
148C5×C4⋊C4—31no—
149C5×C4⋊C4—61no—
150C5×C22⋊C4—61no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158#683—61no—
159C4×Dic5—24no—
160C4×Dic5—61no—
161C4×Dic5C4×D311yescharacteristic
162C4×Dic5C4×D311yescharacteristic
163C4×Dic5D1211yescharacteristic
164C4×Dic5D1211yescharacteristic
165C2×#168—61no—
166#529—151no—
167#431—151no—
168#376—51no—
169#328—31no—
170#328—151no—
171#327—151no—
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×D15—41no—
179C2×D15—41no—
180C2×D15—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—42no—
184Dic15—41no—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—42no—
189C3×Dic5#10412yes—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C22×C3×C4—21no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—101no—
196C22×C3×C4C22×D511yescharacteristic
197C2×#67—101no—
198C2×D12—51no—
199C2×C4×D3—101no—
200C2×Dic6C4×D511yescharacteristic
201C3×C42—51no—
202C3×C42—51no—
203C3×C42—51no—
204C3×C42—51no—
205C3×C42—104no—
206#217—21no—
207(C2×D3)⋊C4—101no—
208(C2×D3)⋊C4—101no—
209(C2×D3)⋊C4—101no—
210(C2×D3)⋊C4—101no—
211C4⋊Dic3—51no—
212C4⋊Dic3C4×D511yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—101no—
215Dic3⋊C4—101no—
216Dic3⋊C4—101no—
217C4×Dic3—101no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—101no—
220C23×C5C2×#6711yescharacteristic
221C22×D5—61no—
222C5×Q8—121no—
223C2×C4×C5—22no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—61no—
228C2×C4×C5—61no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5C2×D1211yescharacteristic
231C22⋊D5—121no—
232C22⋊D5—121no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—22no—
236C2×Dic5—22no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5—61no—
240C2×Dic5(C2×D3)⋊C411yescharacteristic
241C2×Dic5(C2×D3)⋊C411yescharacteristic
242C2×Dic5(C2×D3)⋊C411yescharacteristic
243C2×Dic5(C2×D3)⋊C411yescharacteristic
244D20—121no—
245C4×D5—122no—
246C5×C8—121no—
247#168—121no—
248#126—301no—
249#125—151no—
250#124—151no—
251#123—301no—
252C22⋊Q8—31no—
253#121—151no—
254C4×Q8—151no—
255C4×D4—151no—
256C4×D4—301no—
257#117—301no—
258C2×C42—51no—
259C2×C42—101no—
260C4⋊C8—301no—
261C22⋊C8—31no—
262C22⋊C8—151no—
263C4×C8—301no—
264#95—51no—
265#95—101no—
266#95D3×D511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272D15—81no—
273C23×C3D4×D511yescharacteristic
274C22×D3—101no—
275C2×C3×C4—22no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—51no—
282C2×C3×C4—51no—
283C2×C3×C4—102no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—102no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
289C2×C3×C4C2×C4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291#67—201no—
292#67—201no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—101no—
296D12—201no—
297C4×D3—202no—
298Dic6—41no—
299C3⋊C8—41no—
300C3⋊C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5C2×(C2×D3)⋊C411yescharacteristic
304C22×C5#95011yescharacteristic
305C22×C5#95011yescharacteristic
306C2×D5—121no—
307C2×D5—121no—
308C2×D5—121no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—42no—
312C4×C5—121no—
313C4×C5—121no—
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—42no—
318Dic5—121no—
319Dic5#80512yes—
320C2×Q8—31no—
321C2×D4—151no—
322C2×D4—301no—
323C22×C4—21no—
324C22×C4—51no—
325C22×C4—51no—
326C22×C4—101no—
327C22×C4—301no—
328C22×C4C2×D3×D511yescharacteristic
329C2×C8—61no—
330C2×C8—301no—
331C4⋊C4—31no—
332C4⋊C4—61no—
333C4⋊C4—151no—
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—104no—
347C42—301no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#406211yescharacteristic
353C22×C3#406511yescharacteristic
354C2×D3—201no—
355C2×D3—201no—
356C2×D3—201no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—42no—
360C3×C4—52no—
361C3×C4—101no—
362C3×C4—101no—
363C3×C4—101no—
364C3×C4—202no—
365Dic3—41no—
366Dic3—41no—
367Dic3—201no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5C2×#80511yescharacteristic
371C2×C5#500211yescharacteristic
372C2×C5#500611yescharacteristic
373D5—241no—
374C23—301no—
375C23D5×#6711yescharacteristic
376Q8—121no—
377D4—601no—
378D4—601no—
379D4—601no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—102no—
391C2×C4—101no—
392C2×C4—101no—
393C2×C4—102no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4—301no—
397C2×C4—602no—
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D5×D1211yescharacteristic
400C8—121no—
401C8—601no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3#6502911yescharacteristic
405C2×C3#6509311yescharacteristic
406C2×C3D5×#10411yescharacteristic
407D3—401no—
408C5#6943111yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—601no—
412C22—601no—
413C22—601no—
414C22D5×(C2×D3)⋊C411yescharacteristic
415C22#9149211yescharacteristic
416C22#9151611yescharacteristic
417C4—21no—
418C4—21no—
419C4—42no—
420C4—52no—
421C4—101no—
422C4—101no—
423C4—101no—
424C4—121no—
425C4—121no—
426C4—202no—
427C4—601no—
428C3#1059910111yescharacteristic, complemented, Sylow
429C2—21no—
430C2—21no—
431C2—1201no—
432C2D5×#80511yescharacteristic
433C2#1174712911yescharacteristic
434C2#1174750111yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C22
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1500
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#64937C2semidirect
3. #11748316C2semidirect
5. C5×#4452C2semidirect
6. #11745962C2semidirect
15. #91418C4semidirect
17. #91388C4semidirect
19. #91375C4semidirect
20. Dic5×Dic6C4semidirect
31. #64937D3semidirect
68. #4452D5semidirect
348. C3×C5#1500semidirect
408. C5#69431semidirect
428. C3#10599101semidirect

Maximal subgroups

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

subgroupindex
#117544152
C3×#649372
#117483162
#117462722
C5×#44522
#117459622
#117459582
#105991013
#694315