Finite Group Databasebeta

← #14281896

Subgroups — #14281896

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×#65914C211yesmaximal, characteristic
2#11746869C211yesmaximal, characteristic, complemented
3#11746868C211yesmaximal, characteristic, complemented
4#11746356C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745835C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599026—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic
11C3×#4092C411yescharacteristic
12C3×#4044—21no—
13C3×#4041C411yescharacteristic
14C3×#4040—21no—
15C3×#4036C411yescharacteristic
16C3×C4×D20—21no—
17C3×C4×D20C2211yescharacteristic
18C3×#4018—21no—
19C3×C42×D5C2211yescharacteristic
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#65914D311yescharacteristic
30#65122—31no—
31#64974—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4C2×C411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5C2×C411yescharacteristic
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×#529—51no—
64#4925—51no—
65#4925—51no—
66#4535—51no—
67#4535D511yescharacteristic, complemented
68D4⋊(C3⋊C8)—51no—
69D4⋊(C3⋊C8)—51no—
70C4×C5×Q8C2×D311yescharacteristic
71#4093Dic311yescharacteristic
72#4092Dic311yescharacteristic
73#4044—21no—
74#4041Dic311yescharacteristic
75#4040—21no—
76#4036Dic311yescharacteristic
77C4×D20—21no—
78C4×D20C2×D311yescharacteristic
79#4018—21no—
80C42×D5C2×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
90C22×C3×D5—21no—
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×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C3×D20—21no—
104C3×D20—21no—
105C3×D20—42no—
106C3×C4×D5—21no—
107C3×C4×D5—21no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112C3×C4×D5—41no—
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×Q8C2×D511yescharacteristic
124C3×C4×D4—51no—
125C3×C4×D4—101no—
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×Q8C2×Dic311yescharacteristic
137C2×D20—21no—
138C2×D20C2×Dic311yescharacteristic
139C2×C4×D5—21no—
140C2×C4×D5C2×Dic311yescharacteristic
141C2×C4×D5#6711yescharacteristic
142C2×C4×D5#6711yescharacteristic
143C2×C5×C8—61no—
144C2×C5×C8—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4C2×Dic311yescharacteristic
147C42×C5—21no—
148C42×C5C22×D311yescharacteristic
149#685—21no—
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5C2×Dic311yescharacteristic
156#683—21no—
157#683—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—31no—
167Q8⋊C8—151no—
168D4⋊C8—151no—
169D4⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5#13511yescharacteristic
184C3×Dic5—21no—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—41no—
188C2×C3×Q8C4×D511yescharacteristic
189C2×C3×D4—51no—
190C2×C3×D4—101no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—101no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—51no—
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×C22⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C42—21no—
207C3×C42—51no—
208C3×C42—51no—
209C3×C42—51no—
210C3×C42C22×D511yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C22×D5—21no—
216C22×D5#21711yescharacteristic
217C5×Q8—21no—
218C5×Q8—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5C22×Dic311yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×Dic5—21no—
225C2×Dic5#21711yescharacteristic
226C2×Dic5#21711yescharacteristic
227C2×Dic5#21711yescharacteristic
228D20—21no—
229D20—21no—
230D20—42no—
231C4×D5—21no—
232C4×D5—21no—
233C4×D5—21no—
234C4×D5—21no—
235C4×D5—41no—
236C4×D5—41no—
237C4×D5—41no—
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×Q8D3×D511yescharacteristic
249C4×D4—51no—
250C4×D4—101no—
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#40811yescharacteristic
262C2×C3×C5#41611yescharacteristic
263C2×C3×C5#42111yescharacteristic
264C3×D5—41no—
265C3×D5—81no—
266C23×C3—51no—
267C23×C3—101no—
268C3×Q8—21no—
269C3×Q8—21no—
270C3×D4—101no—
271C3×D4—101no—
272C3×D4—202no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—101no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
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×C5C2×#21711yescharacteristic
294C2×D5—21no—
295C2×D5—21no—
296C2×D5—21no—
297C2×D5—41no—
298C2×D5—41no—
299C2×D5—41no—
300C4×C5—21no—
301C4×C5—41no—
302C4×C5—41no—
303C4×C5#94811yescharacteristic
304C4×C5#94811yescharacteristic
305C4×C5#95011yescharacteristic
306C4×C5#95011yescharacteristic
307Dic5—21no—
308Dic5—21no—
309Dic5—21no—
310Dic5—41no—
311C2×Q8D5×Dic311yescharacteristic
312C2×D4—51no—
313C2×D4—101no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—101no—
318C2×C8—61no—
319C2×C8—61no—
320C2×C8—301no—
321C2×C8—301no—
322C4⋊C4—21no—
323C4⋊C4—51no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C4⋊C4—101no—
327C4⋊C4D5×Dic311yescharacteristic
328C22⋊C4—101no—
329C22⋊C4—101no—
330C22⋊C4—101no—
331C22⋊C4—101no—
332C22⋊C4—101no—
333C42—21no—
334C42—51no—
335C42—51no—
336C42—51no—
337C42C2×D3×D511yescharacteristic
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—101no—
340C22×C3—101no—
341C22×C3—101no—
342C22×C3—201no—
343C22×C3—201no—
344C22×C3—201no—
345C22×C3D5×C22⋊C411yescharacteristic
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—101no—
350C3×C4—101no—
351C3×C4—101no—
352C3×C4—201no—
353C3×C4#404711yescharacteristic
354C3×C4#405311yescharacteristic
355C3×C4#406211yescharacteristic
356C3×C4#406511yescharacteristic
357C2×C5#523311yescharacteristic
358C2×C5#523411yescharacteristic
359C2×C5#523611yescharacteristic
360D5—41no—
361D5—81no—
362C23—51no—
363C23—101no—
364Q8—21no—
365Q8—21no—
366D4—101no—
367D4—101no—
368D4—202no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—51no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—101no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4—201no—
382C2×C4C2×D5×Dic311yescharacteristic
383C2×C4D5×#6711yescharacteristic
384C2×C4D5×#6711yescharacteristic
385C8—121no—
386C8—121no—
387C8—601no—
388C8—601no—
389C2×C3—201no—
390C2×C3—401no—
391C2×C3#6501611yescharacteristic
392C2×C3#6509311yescharacteristic
393C2×C3#6511011yescharacteristic
394C5#7175011yescharacteristic, complemented, Sylow
395C22—101no—
396C22—101no—
397C22—101no—
398C22—201no—
399C22—201no—
400C22—201no—
401C22D5×#21711yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—101no—
406C4—101no—
407C4—101no—
408C4—201no—
409C4#9128311yescharacteristic
410C4#9128411yescharacteristic
411C4#9151411yescharacteristic
412C4#9151611yescharacteristic
413C3#1059902611yescharacteristic, complemented, Sylow
414C2—201no—
415C2—401no—
416C2#1174848211yescharacteristic
417C2#1174920711yescharacteristic
418C2#1174942711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4041C4
cosocleC3×C42×C5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1482
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
2. #11746869C2semidirect
3. #11746868C2semidirect
4. #11746356C2semidirect
5. C5×#4535C2semidirect
6. #11745835C2semidirect
7. #11745834C2semidirect
67. #4535D5semidirect
338. C3×C5#1482semidirect
394. C5#71750semidirect
413. C3#10599026semidirect

Maximal subgroups

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

subgroupindex
C3×#659142
#117468692
#117468682
#117463562
C5×#45352
#117458352
#117458342
#105990263
#717505