Finite Group Databasebeta

← #14281881

Subgroups — #14281881

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
1C3×#65891C211yesmaximal, characteristic
2#11746869C211yesmaximal, characteristic, complemented
3#11746868C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10598962—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C3×#4084C411yescharacteristic
11C3×#4082C411yescharacteristic
12C3×C4×C22⋊D5—21no—
13C3×#4072—21no—
14C3×#4043C411yescharacteristic
15C3×#4036C411yescharacteristic
16C3×#4029—21no—
17C3×#4025—21no—
18C3×C42×D5C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90982—21no—
25#90955—21no—
26#90955—21no—
27Dic5×C3⋊C8—21no—
28#71750—51nomaximal, Hall
29#65891D311yescharacteristic
30#65122—31no—
31#64974—31no—
32C5×D4⋊C8—31no—
33D4⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×C3×C22⋊D5—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×Dic10C2×C411yescharacteristic
43C3×C5×C4⋊C4C2×C411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5—21no—
53C3×#685—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—21no—
58C3×#683—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×#529—51no—
64#4925—51no—
65#4925—51no—
66#4535—51no—
67#4535—51no—
68D4⋊(C3⋊C8)—51no—
69D4⋊(C3⋊C8)D511yescharacteristic, complemented
70C4×C5×D4C2×D311yescharacteristic
71#4084Dic311yescharacteristic
72#4082Dic311yescharacteristic
73C4×C22⋊D5—21no—
74#4072—21no—
75#4043Dic311yescharacteristic
76#4036Dic311yescharacteristic
77#4029—21no—
78#4025—21no—
79C42×D5C2×D311yescharacteristic
80C4×Dic10C2×D311yescharacteristic
81C5×C4⋊C8—31no—
82C4×C5×C8—31no—
83#3952—61no—
84#3952—61no—
85#3946—61no—
86C8×Dic5—61no—
87C4⋊#168—31no—
88C4×#168—31no—
89#1482—151noSylow
90C23×C3×C5—21no—
91C22×C3×D5C22⋊C411yescharacteristic
92C3×C5×D4—21no—
93C3×C5×D4—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C3×C22⋊D5—42no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C3×C4×D5—21no—
107C3×C4×D5—21no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—41no—
111C3×Dic10—21no—
112C3×Dic10—21no—
113C3⋊#168—41no—
114C3⋊#168—41no—
115C5×C3⋊C8—41no—
116C5×C3⋊C8—41no—
117C3×#126—101no—
118C3×#125—51no—
119C3×#124—51no—
120C3×#123—101no—
121C3×C22⋊Q8—51no—
122C3×#121—51no—
123C3×C4×Q8—51no—
124C3×C4×D4—101no—
125C3×C4×D4C2×D511yescharacteristic
126C3×#117—101no—
127C2×C3×C42—51no—
128#830—101no—
129#830—101no—
130C4⋊(C3⋊C8)—51no—
131C4⋊(C3⋊C8)—101no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic
133C4×C3⋊C8—51no—
134C4×C3⋊C8—101no—
135C4×C3⋊C8C2×D511yescharacteristic
136C2×C5×D4C2×Dic311yescharacteristic
137C22×C4×C5—21no—
138C2×C22⋊D5—21no—
139C2×C4×D5C2×Dic311yescharacteristic
140C2×C4×D5#6711yescharacteristic
141C2×C4×D5#6711yescharacteristic
142C2×Dic10C2×Dic311yescharacteristic
143C2×C5×C8—61no—
144C2×C5×C8—61no—
145C5×C4⋊C4C2×Dic311yescharacteristic
146C5×C22⋊C4—21no—
147C42×C5C22×D311yescharacteristic
148C22⋊Dic5—21no—
149C22⋊Dic5—21no—
150C22⋊Dic5—21no—
151#685—21no—
152C4⋊Dic5—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5C2×Dic311yescharacteristic
155#683—21no—
156#683—21no—
157C4×Dic5—21no—
158C4×Dic5C2×Dic311yescharacteristic
159C4×Dic5#6711yescharacteristic
160C4×Dic5#6711yescharacteristic
161C2×#168—61no—
162C2×#168—61no—
163#529—51no—
164#431—151no—
165#431—151no—
166Q8⋊C8—151no—
167Q8⋊C8—151no—
168D4⋊C8—31no—
169D4⋊C8—151no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5#13111yescharacteristic
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13511yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×Dic5—21no—
184C3×Dic5—21no—
185C3×Dic5—21no—
186C3×Dic5—41no—
187C3×Dic5—41no—
188C2×C3×Q8—51no—
189C2×C3×D4—101no—
190C2×C3×D4C4×D511yescharacteristic
191C22×C3×C4—21no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4C4×D511yescharacteristic
201C3×C22⋊C4—21no—
202C3×C22⋊C4—101no—
203C3×C22⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C42—51no—
207C3×C42—51no—
208C3×C42—51no—
209C3×C42—101no—
210C3×C42C22×D511yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C23×C5—21no—
216C22×D5#21711yescharacteristic
217C5×D4—21no—
218C5×D4—21no—
219C2×C4×C5—21no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5C22×Dic311yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C22⋊D5—42no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5#21711yescharacteristic
229C2×Dic5#21711yescharacteristic
230C2×Dic5#21711yescharacteristic
231C4×D5—21no—
232C4×D5—21no—
233C4×D5—21no—
234C4×D5—21no—
235C4×D5—41no—
236Dic10—21no—
237Dic10—21no—
238C5×C8—121no—
239C5×C8—121no—
240#168—121no—
241#168—121no—
242#126—101no—
243#125—51no—
244#124—51no—
245#123—101no—
246C22⋊Q8—51no—
247#121—51no—
248C4×Q8—51no—
249C4×D4—101no—
250C4×D4D3×D511yescharacteristic
251#117—101no—
252C2×C42—51no—
253C4⋊C8—31no—
254C4⋊C8—151no—
255C4⋊C8—301no—
256C22⋊C8—301no—
257C22⋊C8—301no—
258C4×C8—31no—
259C4×C8—151no—
260C4×C8—301no—
261C2×C3×C5—81no—
262C2×C3×C5#40811yescharacteristic
263C2×C3×C5#41611yescharacteristic
264C2×C3×C5#42111yescharacteristic
265C3×D5—41no—
266C23×C3—21no—
267C23×C3—51no—
268C3×Q8—101no—
269C3×Q8—101no—
270C3×D4—21no—
271C3×D4—21no—
272C3×D4—202no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—51no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—201no—
286C2×C3×C4C2×C4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C3⋊C8—41no—
290C3⋊C8—41no—
291C3⋊C8—201no—
292C3⋊C8—201no—
293C22×C5—41no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5C2×#21711yescharacteristic
297C2×D5—21no—
298C2×D5—21no—
299C2×D5—21no—
300C4×C5—21no—
301C4×C5—41no—
302C4×C5#94811yescharacteristic
303C4×C5#94811yescharacteristic
304C4×C5#95011yescharacteristic
305C4×C5#95011yescharacteristic
306Dic5—21no—
307Dic5—21no—
308Dic5—21no—
309Dic5—41no—
310Dic5—41no—
311C2×Q8—51no—
312C2×D4—101no—
313C2×D4D5×Dic311yescharacteristic
314C22×C4—21no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—51no—
318C2×C8—61no—
319C2×C8—61no—
320C2×C8—301no—
321C2×C8—301no—
322C4⋊C4—51no—
323C4⋊C4—101no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C4⋊C4—101no—
327C4⋊C4D5×Dic311yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—101no—
330C22⋊C4—101no—
331C22⋊C4—101no—
332C22⋊C4—101no—
333C42—51no—
334C42—51no—
335C42—51no—
336C42—101no—
337C42C2×D3×D511yescharacteristic
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—101no—
343C22×C3—101no—
344C22×C3—101no—
345C22×C3D5×C22⋊C411yescharacteristic
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—101no—
349C3×C4—101no—
350C3×C4—101no—
351C3×C4—201no—
352C3×C4—201no—
353C3×C4#404711yescharacteristic
354C3×C4#405311yescharacteristic
355C3×C4#405811yescharacteristic
356C3×C4#406211yescharacteristic
357C2×C5—81no—
358C2×C5#523311yescharacteristic
359C2×C5#523411yescharacteristic
360C2×C5#523611yescharacteristic
361D5—41no—
362C23—21no—
363C23—51no—
364Q8—101no—
365Q8—101no—
366D4—21no—
367D4—21no—
368D4—202no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—51no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—101no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—201no—
382C2×C4C2×D5×Dic311yescharacteristic
383C2×C4D5×#6711yescharacteristic
384C2×C4D5×#6711yescharacteristic
385C8—121no—
386C8—121no—
387C8—601no—
388C8—601no—
389C2×C3—81no—
390C2×C3—201no—
391C2×C3#6501611yescharacteristic
392C2×C3#6506111yescharacteristic
393C2×C3#6511011yescharacteristic
394C5#7175011yescharacteristic, complemented, Sylow
395C22—41no—
396C22—41no—
397C22—41no—
398C22—101no—
399C22—101no—
400C22—101no—
401C22D5×#21711yescharacteristic
402C4—21no—
403C4—41no—
404C4—101no—
405C4—101no—
406C4—101no—
407C4—201no—
408C4—201no—
409C4#9128311yescharacteristic
410C4#9128411yescharacteristic
411C4#9149011yescharacteristic
412C4#9149211yescharacteristic
413C3#1059896211yescharacteristic, complemented, Sylow
414C2—81no—
415C2—201no—
416C2#1174848211yescharacteristic
417C2#1174896111yescharacteristic
418C2#1174942711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4084C4
cosocleC3×C42×C5C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11746869C2semidirect
3. #11746868C2semidirect
4. D4⋊(C3⋊#168)C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745841C2semidirect
7. #11745840C2semidirect
69. D4⋊(C3⋊C8)D5semidirect
338. C3×C5#1482semidirect
394. C5#71750semidirect
413. C3#10598962semidirect

Maximal subgroups

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

subgroupindex
C3×#658912
#117468692
#117468682
D4⋊(C3⋊#168)2
C5×D4⋊(C3⋊C8)2
#117458412
#117458402
#105989623
#717505