Finite Group Databasebeta

← #14281830

Subgroups — #14281830

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65912C211yesmaximal, characteristic
2D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
3#11746868C211yesmaximal, characteristic
4#11746356C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599025—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4092C411yescharacteristic
11C3×#4090C411yescharacteristic
12C3×#4043C411yescharacteristic
13C3×#4042—21no—
14C3×#4035—21no—
15C3×#4034C411yescharacteristic
16C3×#4018—21no—
17C3×C42×D5C2211yescharacteristic
18C3×C4×Dic10—21no—
19C3×C4×Dic10C2211yescharacteristic
20C2×D5×C3⋊C8—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25#90982—21no—
26#90982—21no—
27#90955—21no—
28#71824—51nomaximal, Hall
29#65912D311yescharacteristic
30D5×C4⋊C8—31no—
31#64974—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×Dic10—21no—
41C2×C3×Dic10C2×C411yescharacteristic
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5C2×C411yescharacteristic
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63D5×C3⋊C8—42no—
64C3×#533—51no—
65#4925—51no—
66C2×C4⋊(C3⋊C8)—51no—
67#4535—51no—
68#4535—51no—
69#4535—51no—
70#4535D511yescharacteristic, complemented
71C4×C5×Q8C2×D311yescharacteristic
72#4092Dic311yescharacteristic
73#4090Dic311yescharacteristic
74C2×C8×D5—61no—
75#4043Dic311yescharacteristic
76#4042—21no—
77#4035—21no—
78#4034Dic311yescharacteristic
79#4018—21no—
80C42×D5C2×D311yescharacteristic
81C4×Dic10—21no—
82C4×Dic10C2×D311yescharacteristic
83C5×C4⋊C8—31no—
84C4×C5×C8—31no—
85#3952—61no—
86#3946—61no—
87#3946—61no—
88C4⋊#168—31no—
89C4×#168—31no—
90#1481—151noSylow
91C22×C3×D5C22⋊C411yescharacteristic
92C3×C5×Q8—21no—
93C3×C5×Q8—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C3×C4×D5—21no—
105C3×C4×D5—21no—
106C3×C4×D5—41no—
107C3×C4×D5SD1612yes—
108C3×C4×D5Q1612yes—
109C3×Dic10—21no—
110C3×Dic10—21no—
111C3×Dic10—42no—
112C3⋊#168—41no—
113C3⋊#168—41no—
114C5×C3⋊C8—41no—
115C5×C3⋊C8—41no—
116C3×C4⋊Q8—51no—
117C3×C4⋊Q8—51no—
118C3×#125—101no—
119C3×C22⋊Q8—51no—
120C3×C22⋊Q8—51no—
121C3×C22⋊Q8—101no—
122C3×C4×Q8—51no—
123C3×C4×Q8—101no—
124C3×C4×Q8C2×D511yescharacteristic
125C3×#117—101no—
126C2×C3×C42—51no—
127C22×C3⋊C8—101no—
128#830—101no—
129C4⋊(C3⋊C8)—51no—
130C4⋊(C3⋊C8)—101no—
131C4⋊(C3⋊C8)—101no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic
133C4×C3⋊C8—51no—
134C4×C3⋊C8C2×D511yescharacteristic
135C2×C5×Q8C2×Dic311yescharacteristic
136C2×C4×D5C2×Dic311yescharacteristic
137C2×C4×D5#6711yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×Dic10—21no—
140C2×Dic10C2×Dic311yescharacteristic
141C2×C5×C8—61no—
142C2×C5×C8—61no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4C2×Dic311yescharacteristic
145C42×C5—21no—
146C42×C5C22×D311yescharacteristic
147#685—21no—
148#685—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5C2×Dic311yescharacteristic
151#683—21no—
152#683—21no—
153#683—21no—
154#683—21no—
155#683—21no—
156C4×Dic5—21no—
157C4×Dic5C2×Dic311yescharacteristic
158C4×Dic5#6711yescharacteristic
159C4×Dic5#6711yescharacteristic
160C2×#168—61no—
161C2×#168—61no—
162C8×D5—122no—
163#533—51no—
164#431—151no—
165C2×C4⋊C8—151no—
166Q8⋊C8—31no—
167Q8⋊C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5#10312yes—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5—41no—
177C3×C4×C5#13111yescharacteristic
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5C2×SD1611yescharacteristic
180C3×C4×C5C2×Q1611yescharacteristic
181C3×Dic5—21no—
182C3×Dic5—21no—
183C3×Dic5—41no—
184C3×Dic5—41no—
185C3×Dic5#10312yes—
186C2×C3×Q8—51no—
187C2×C3×Q8—101no—
188C2×C3×Q8C4×D511yescharacteristic
189C22×C3×C4—51no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4C4×D511yescharacteristic
201C3×C22⋊C4—101no—
202C3×C22⋊C4—101no—
203C3×C42—21no—
204C3×C42—51no—
205C3×C42—51no—
206C3×C42—51no—
207C3×C42—101no—
208C3×C42C22×D511yescharacteristic
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—101no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—202no—
214C22×D5#21711yescharacteristic
215C5×Q8—21no—
216C5×Q8—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5C22×Dic311yescharacteristic
220C2×C4×C5C2×#6711yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×Dic5—21no—
223C2×Dic5—21no—
224C2×Dic5#21711yescharacteristic
225C2×Dic5#21711yescharacteristic
226C2×Dic5#21711yescharacteristic
227C4×D5—21no—
228C4×D5—21no—
229C4×D5—41no—
230C4×D5#21512yes—
231C4×D5#21612yes—
232Dic10—21no—
233Dic10—21no—
234Dic10—42no—
235C5×C8—121no—
236C5×C8—121no—
237#168—121no—
238#168—121no—
239C22×C8—301no—
240C4⋊Q8—51no—
241C4⋊Q8—51no—
242#125—101no—
243C22⋊Q8—51no—
244C22⋊Q8—51no—
245C22⋊Q8—101no—
246C4×Q8—51no—
247C4×Q8—101no—
248C4×Q8D3×D511yescharacteristic
249#117—101no—
250C2×C42—51no—
251C4⋊C8—31no—
252C4⋊C8—151no—
253C4⋊C8—301no—
254C4⋊C8—301no—
255C22⋊C8—301no—
256C4×C8—31no—
257C4×C8—151no—
258C2×C3×C5#40811yescharacteristic
259C2×C3×C5C2×#10311yescharacteristic
260C2×C3×C5#42111yescharacteristic
261C3×D5—22no—
262C23×C3—51no—
263C3×Q8—21no—
264C3×Q8—21no—
265C3×Q8—101no—
266C3×Q8—101no—
267C3×Q8—202no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—51no—
271C2×C3×C4—52no—
272C2×C3×C4—52no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—101no—
278C2×C3×C4—101no—
279C2×C3×C4—201no—
280C2×C3×C4C2×C4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4D4×D511yescharacteristic
283C3⋊C8—41no—
284C3⋊C8—41no—
285C3⋊C8—201no—
286C3⋊C8—201no—
287C22×C5C2×#21711yescharacteristic
288C2×D5—21no—
289C2×D5—21no—
290C2×D5#83512yes—
291C4×C5—21no—
292C4×C5—41no—
293C4×C5—41no—
294C4×C5C2×#21511yescharacteristic
295C4×C5C2×#21611yescharacteristic
296C4×C5#94811yescharacteristic
297C4×C5#94811yescharacteristic
298Dic5—21no—
299Dic5—21no—
300Dic5—41no—
301Dic5—41no—
302Dic5#83512yes—
303C2×Q8—51no—
304C2×Q8—101no—
305C2×Q8D5×Dic311yescharacteristic
306C22×C4—51no—
307C22×C4—51no—
308C22×C4—51no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—301no—
312C2×C8—301no—
313C2×C8—602no—
314C4⋊C4—21no—
315C4⋊C4—51no—
316C4⋊C4—101no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C4⋊C4—101no—
320C4⋊C4—101no—
321C4⋊C4—101no—
322C4⋊C4D5×Dic311yescharacteristic
323C22⋊C4—101no—
324C22⋊C4—101no—
325C42—21no—
326C42—51no—
327C42—51no—
328C42—51no—
329C42—101no—
330C42C2×D3×D511yescharacteristic
331C3×C5#148111yescharacteristic, complemented, Hall
332C22×C3—52no—
333C22×C3—101no—
334C22×C3—101no—
335C22×C3D5×C22⋊C411yescharacteristic
336C3×C4—21no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—52no—
340C3×C4—101no—
341C3×C4—101no—
342C3×C4—201no—
343C3×C4—201no—
344C3×C4#404711yescharacteristic
345C3×C4#405311yescharacteristic
346C3×C4D5×SD1611yescharacteristic
347C3×C4D5×Q1611yescharacteristic
348C2×C5C2×#83511yescharacteristic
349C2×C5#523411yescharacteristic
350C2×C5#523611yescharacteristic
351D5—22no—
352C23—51no—
353Q8—21no—
354Q8—21no—
355Q8—101no—
356Q8—101no—
357Q8—202no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—51no—
361C2×C4—52no—
362C2×C4—52no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—101no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—101no—
369C2×C4—201no—
370C2×C4C2×D5×Dic311yescharacteristic
371C2×C4D5×#6711yescharacteristic
372C2×C4D5×#6711yescharacteristic
373C8—121no—
374C8—121no—
375C8—601no—
376C8—601no—
377C2×C3—102no—
378C2×C3#6501611yescharacteristic
379C2×C3D5×#10311yescharacteristic
380C2×C3#6511011yescharacteristic
381C5#7182411yescharacteristic, complemented, Sylow
382C22—52no—
383C22—101no—
384C22—101no—
385C22D5×#21711yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—52no—
390C4—101no—
391C4—101no—
392C4—201no—
393C4—201no—
394C4#9128311yescharacteristic
395C4#9128411yescharacteristic
396C4D5×#21511yescharacteristic
397C4D5×#21611yescharacteristic
398C3#1059902511yescharacteristic, complemented, Sylow
399C2—102no—
400C2#1174848211yescharacteristic
401C2D5×#83511yescharacteristic
402C2#1174942711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1481
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. #11746356C2semidirect
5. C5×#4535C2semidirect
6. #11745841C2semidirect
7. #11745840C2semidirect
70. #4535D5semidirect
331. C3×C5#1481semidirect
381. C5#71824semidirect
398. C3#10599025semidirect

Maximal subgroups

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

subgroupindex
C3×#659122
D5×C4⋊(C3⋊C8)2
#117468682
#117463562
C5×#45352
#117458412
#117458402
#105990253
#718245