Finite Group Databasebeta

← #14281895

Subgroups — #14281895

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752494C211yesmaximal, characteristic
2C3×#64974C211yesmaximal, characteristic, complemented
3#11746869C211yesmaximal, characteristic, complemented
4#11746280C211yesmaximal, characteristic, complemented
5C5×#4456C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10599026—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91450C411yescharacteristic
13C4×#1202—21no—
14#91388C411yescharacteristic
15#91387—21no—
16#91386—21no—
17#91375C411yescharacteristic
18#91359C411yescharacteristic
19#91348—21no—
20C3×C4×C5×C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3952—21no—
24C3×#3946—21no—
25C3×C4×#168C2211yescharacteristic
26#90955—21no—
27Dic5×C3⋊C8—21no—
28#70760—51nomaximal, Hall
29#65914—31no—
30#65122—31no—
31#64974D311yescharacteristic, complemented
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×D60C2×C411yescharacteristic
37C2×C4×D15—21no—
38C2×C5×Dic6C2×C411yescharacteristic
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×#1202—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—21no—
46C4⋊Dic15C2×C411yescharacteristic
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6669—21no—
59#6667—21no—
60#6667—21no—
61#6667—21no—
62#6665—21no—
63#5479—51no—
64C3×#431—51no—
65#4925—51no—
66#4459—51no—
67#4459—51no—
68#4456—51no—
69#4456D511yescharacteristic, complemented
70C4×C5×Q8—31no—
71#4093—31no—
72#4092—31no—
73#4044—61no—
74#4041—31no—
75#4040—61no—
76#4036—31no—
77C4×D20—31no—
78C4×D20—61no—
79#4018—61no—
80C42×D5C2×D311yescharacteristic
81C5×C4⋊C8—31no—
82C4×C5×C8C2×D311yescharacteristic
83#3952—21no—
84#3952—61no—
85#3946—21no—
86C8×Dic5—61no—
87C4⋊#168—31no—
88C4×#168C2×D311yescharacteristic
89#1482—151noSylow
90C22×D15—21no—
91C22×C3×D5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96D60—21no—
97D60—21no—
98C4×D15—41no—
99C4×D15—41no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—21no—
102C5×Dic6—21no—
103C5×Dic6—21no—
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C3×C4×D5—21no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—41no—
112#1202—42no—
113C3×C5×C8—41no—
114C3⋊#168—41no—
115C3×#168—41no—
116C5×C3⋊C8—41no—
117C2×C3×C42—51no—
118#930—51no—
119#929—101no—
120C4×#67—101no—
121#924—51no—
122#876—101no—
123#875—51no—
124C4×D12—51no—
125#872—101no—
126#870—51no—
127C4×Dic6C2×D511yescharacteristic
128C3×C4⋊C8—101no—
129C3×C22⋊C8—101no—
130C3×C4×C8—51no—
131C3×C4×C8C2×D511yescharacteristic
132#830—101no—
133C4⋊(C3⋊C8)—51no—
134C4⋊(C3⋊C8)C2×D511yescharacteristic
135C4×C3⋊C8—101no—
136C2×C5×Q8—31no—
137C2×D20—31no—
138C2×D20—61no—
139C2×C4×D5—61no—
140C2×C4×D5C4×D311yescharacteristic
141C2×C4×D5D1211yescharacteristic
142C2×C4×D5#6711yescharacteristic
143C2×C5×C8—21no—
144C2×C5×C8—61no—
145C5×C4⋊C4—31no—
146C5×C4⋊C4—61no—
147C42×C5—61no—
148C42×C5C22×D311yescharacteristic
149#685—61no—
150#685—61no—
151#685—61no—
152#685—61no—
153#685—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158C4×Dic5C4×D311yescharacteristic
159C4×Dic5D1211yescharacteristic
160C4×Dic5#6711yescharacteristic
161C2×#168—21no—
162C2×#168—61no—
163#529—151no—
164#431—51no—
165#431—151no—
166Q8⋊C8—31no—
167Q8⋊C8—151no—
168D4⋊C8—151no—
169D4⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—41no—
172C2×D15—41no—
173C2×D15—41no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C3×C4×C5—21no—
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5#13111yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5#13511yescharacteristic
182Dic15—41no—
183C3×Dic5—21no—
184C3×Dic5—21no—
185C3×Dic5—21no—
186C5×Dic3—41no—
187C5×Dic3—41no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4—51no—
191C2×#67—101no—
192C2×D12—51no—
193C2×C4×D3—101no—
194C2×Dic6C4×D511yescharacteristic
195C2×C3×C8—21no—
196C2×C3×C8—101no—
197C3×C42—51no—
198C3×C42—51no—
199C3×C42—51no—
200C3×C42C22×D511yescharacteristic
201#217—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206C4⋊Dic3—51no—
207C4⋊Dic3C4×D511yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212C4×Dic3—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—101no—
215C22×D5—61no—
216C22×D5(C2×D3)⋊C411yescharacteristic
217C5×Q8—61no—
218C5×Q8—61no—
219C2×C4×C5—61no—
220C2×C4×C5—61no—
221C2×C4×C5C2×C4×D311yescharacteristic
222C2×C4×C5C2×D1211yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×Dic5—61no—
225C2×Dic5(C2×D3)⋊C411yescharacteristic
226C2×Dic5(C2×D3)⋊C411yescharacteristic
227C2×Dic5(C2×D3)⋊C411yescharacteristic
228D20—61no—
229D20—61no—
230D20—122no—
231C4×D5—21no—
232C4×D5—21no—
233C4×D5—21no—
234C4×D5—21no—
235C4×D5—41no—
236C4×D5—121no—
237C4×D5—121no—
238C5×C8—41no—
239C5×C8—121no—
240#168—41no—
241#168—121no—
242#126—301no—
243#125—151no—
244#124—151no—
245#123—301no—
246C22⋊Q8—151no—
247#121—151no—
248C4×Q8—31no—
249C4×D4—151no—
250C4×D4—301no—
251#117—301no—
252C2×C42—51no—
253C4⋊C8—31no—
254C4⋊C8—101no—
255C4⋊C8—151no—
256C22⋊C8—101no—
257C22⋊C8—301no—
258C4×C8—51no—
259C4×C8—301no—
260C4×C8D3×D511yescharacteristic
261C2×C3×C5#40811yescharacteristic
262C2×C3×C5#41611yescharacteristic
263C2×C3×C5#42111yescharacteristic
264D15—81no—
265C3×D5—41no—
266C23×C3—51no—
267C22×D3—101no—
268C2×C3×C4—51no—
269C2×C3×C4—51no—
270C2×C3×C4—51no—
271C2×C3×C4—101no—
272C2×C3×C4—101no—
273C2×C3×C4—101no—
274C2×C3×C4—101no—
275C2×C3×C4—201no—
276C2×C3×C4C2×C4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278C2×C3×C4D4×D511yescharacteristic
279#67—202no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—101no—
283D12—101no—
284D12—101no—
285C4×D3—201no—
286C4×D3—201no—
287Dic6—21no—
288Dic6—21no—
289C3×C8—41no—
290C3×C8—201no—
291C3⋊C8—41no—
292C3⋊C8—201no—
293C22×C5C2×(C2×D3)⋊C411yescharacteristic
294C2×D5—21no—
295C2×D5—21no—
296C2×D5—21no—
297C2×D5—121no—
298C2×D5—121no—
299C2×D5—121no—
300C4×C5—21no—
301C4×C5—121no—
302C4×C5—121no—
303C4×C5#90411yescharacteristic
304C4×C5#90411yescharacteristic
305C4×C5#90711yescharacteristic
306C4×C5#90711yescharacteristic
307Dic5—21no—
308Dic5—21no—
309Dic5—21no—
310Dic5—121no—
311C2×Q8—31no—
312C2×D4—151no—
313C2×D4—301no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—301no—
318C2×C8—21no—
319C2×C8—61no—
320C2×C8—101no—
321C2×C8—301no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—151no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C22⋊C4—301no—
329C22⋊C4—301no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C22⋊C4—301no—
333C42—51no—
334C42—51no—
335C42—51no—
336C42—61no—
337C42C2×D3×D511yescharacteristic
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—101no—
340C22×C3—101no—
341C22×C3—101no—
342C22×C3D5×C22⋊C411yescharacteristic
343C2×D3—201no—
344C2×D3—201no—
345C2×D3—201no—
346C3×C4—21no—
347C3×C4—101no—
348C3×C4—101no—
349C3×C4—101no—
350C3×C4#404711yescharacteristic
351C3×C4#405311yescharacteristic
352C3×C4#406211yescharacteristic
353C3×C4#406511yescharacteristic
354Dic3—41no—
355Dic3—41no—
356Dic3—201no—
357C2×C5#500511yescharacteristic
358C2×C5#511311yescharacteristic
359C2×C5#512911yescharacteristic
360D5—41no—
361D5—241no—
362C23—51no—
363C23—301no—
364Q8—61no—
365Q8—61no—
366D4—301no—
367D4—301no—
368D4—602no—
369C2×C4—51no—
370C2×C4—51no—
371C2×C4—51no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—201no—
379C2×C4—301no—
380C2×C4—601no—
381C2×C4—601no—
382C2×C4C4×D3×D511yescharacteristic
383C2×C4D5×D1211yescharacteristic
384C2×C4D5×#6711yescharacteristic
385C8—41no—
386C8—121no—
387C8—201no—
388C8—601no—
389C2×C3—201no—
390C2×C3#6501611yescharacteristic
391C2×C3#6509311yescharacteristic
392C2×C3#6511011yescharacteristic
393D3—401no—
394C5#7076011yescharacteristic, complemented, Sylow
395C22—101no—
396C22—101no—
397C22—101no—
398C22—601no—
399C22—601no—
400C22—601no—
401C22D5×(C2×D3)⋊C411yescharacteristic
402C4—21no—
403C4—101no—
404C4—101no—
405C4—101no—
406C4—121no—
407C4—121no—
408C4—601no—
409C4#9126711yescharacteristic
410C4#9126811yescharacteristic
411C4#9126911yescharacteristic
412C4#9127111yescharacteristic
413C3#1059902611yescharacteristic, complemented, Sylow
414C2—201no—
415C2—1201no—
416C2#1174710911yescharacteristic
417C2#1174764211yescharacteristic
418C2#1174813611yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91450C4
cosocleC3×C42×C5C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#64974C2semidirect
3. #11746869C2semidirect
4. #11746280C2semidirect
5. C5×#4456C2semidirect
6. #11745843C2semidirect
7. #11745839C2semidirect
31. #64974D3semidirect
69. #4456D5semidirect
338. C3×C5#1482semidirect
394. C5#70760semidirect
413. C3#10599026semidirect

Maximal subgroups

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

subgroupindex
#117524942
C3×#649742
#117468692
#117462802
C5×#44562
#117458432
#117458392
#105990263
#707605