Finite Group Databasebeta

← #14282477

Subgroups — #14282477

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65891C211yesmaximal, characteristic
2C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
3#11746871C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10598970—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
20C2×D5×C3⋊C8—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25#90955—21no—
26#90952—21no—
27Dic5×C3⋊C8—21no—
28#71752—51nomaximal, Hall
29#65891D311yescharacteristic
30#65124—31no—
31C4×C8×D5—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
63D5×C3⋊C8—24no—
64C3×#529—51no—
65#4926—51no—
66C2×C4×C3⋊C8—51no—
67#4535—51no—
68#4535—51no—
69D4⋊(C3⋊C8)—51no—
70D4⋊(C3⋊C8)D511yescharacteristic, complemented
71C4×C5×D4C2×D311yescharacteristic
72#4084Dic311yescharacteristic
73#4082Dic311yescharacteristic
74C4×C22⋊D5—21no—
75#4072—21no—
76C2×C8×D5—61no—
77#4043Dic311yescharacteristic
78#4036Dic311yescharacteristic
79#4029—21no—
80#4025—21no—
81C42×D5C2×D311yescharacteristic
82C4×Dic10C2×D311yescharacteristic
83C5×C4⋊C8—31no—
84C4×C5×C8—31no—
85#3952—61no—
86#3947—61no—
87C8×Dic5—61no—
88C4⋊#168—31no—
89C4×#168—31no—
90#1494—151noSylow
91C23×C3×C5—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C3×C5×D4—21no—
94C3×C5×D4—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C3×C22⋊D5—42no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C3×C4×D5—22no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×Dic10—21no—
113C3×Dic10—21no—
114C3⋊#168—22no—
115C3⋊#168—41no—
116C5×C3⋊C8—22no—
117C5×C3⋊C8—41no—
118C3×#126—101no—
119C3×#125—51no—
120C3×#124—51no—
121C3×#123—101no—
122C3×C22⋊Q8—51no—
123C3×#121—51no—
124C3×C4×Q8—51no—
125C3×C4×D4—101no—
126C3×C4×D4C2×D511yescharacteristic
127C3×#117—101no—
128C2×C3×C42—51no—
129C22×C3⋊C8—101no—
130#830—101no—
131C4⋊(C3⋊C8)—51no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic
133#803—101no—
134C4×C3⋊C8—51no—
135C4×C3⋊C8—101no—
136C4×C3⋊C8C2×D511yescharacteristic
137C2×C5×D4C2×Dic311yescharacteristic
138C22×C4×C5—21no—
139C2×C22⋊D5—21no—
140C2×C4×D5C2×Dic311yescharacteristic
141C2×C4×D5#6711yescharacteristic
142C2×C4×D5#6711yescharacteristic
143C2×Dic10C2×Dic311yescharacteristic
144C2×C5×C8—61no—
145C2×C5×C8—61no—
146C5×C4⋊C4C2×Dic311yescharacteristic
147C5×C22⋊C4—21no—
148C42×C5C22×D311yescharacteristic
149C22⋊Dic5—21no—
150C22⋊Dic5—21no—
151C22⋊Dic5—21no—
152#685—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5C2×Dic311yescharacteristic
156#683—21no—
157#683—21no—
158C4×Dic5—21no—
159C4×Dic5C2×Dic311yescharacteristic
160C4×Dic5#6711yescharacteristic
161C4×Dic5#6711yescharacteristic
162C2×#168—61no—
163C2×#168—61no—
164C8×D5—64no—
165#529—51no—
166#432—151no—
167C2×C4×C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170D4⋊C8—31no—
171D4⋊C8—151no—
172C22×C3×C5—41no—
173C22×C3×C5—41no—
174C22×C3×C5—41no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5#10412yes—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13111yescharacteristic
183C3×C4×C5#13511yescharacteristic
184C3×C4×C5#13511yescharacteristic
185C3×Dic5—21no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C2×C3×Q8—51no—
191C2×C3×D4—101no—
192C2×C3×D4C4×D511yescharacteristic
193C22×C3×C4—21no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—51no—
197C3×C4⋊C4—51no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4C4×D511yescharacteristic
203C3×C22⋊C4—21no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C42—51no—
209C3×C42—51no—
210C3×C42—51no—
211C3×C42—101no—
212C3×C42C22×D511yescharacteristic
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—104no—
216C2×C3⋊C8—101no—
217C2×C3⋊C8—101no—
218C23×C5—21no—
219C22×D5#21711yescharacteristic
220C5×D4—21no—
221C5×D4—21no—
222C2×C4×C5—21no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5C22×Dic311yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C2×C4×C5C2×#6711yescharacteristic
228C22⋊D5—42no—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5#21711yescharacteristic
232C2×Dic5#21711yescharacteristic
233C2×Dic5#21711yescharacteristic
234C4×D5—22no—
235C4×D5—21no—
236C4×D5—21no—
237C4×D5—21no—
238C4×D5—21no—
239Dic10—21no—
240Dic10—21no—
241C5×C8—62no—
242C5×C8—121no—
243#168—62no—
244#168—121no—
245C22×C8—301no—
246#126—101no—
247#125—51no—
248#124—51no—
249#123—101no—
250C22⋊Q8—51no—
251#121—51no—
252C4×Q8—51no—
253C4×D4—101no—
254C4×D4D3×D511yescharacteristic
255#117—101no—
256C2×C42—51no—
257C4⋊C8—31no—
258C4⋊C8—151no—
259C22⋊C8—301no—
260#97—301no—
261C4×C8—31no—
262C4×C8—151no—
263C4×C8—301no—
264C2×C3×C5—81no—
265C2×C3×C5#40811yescharacteristic
266C2×C3×C5#41611yescharacteristic
267C2×C3×C5C2×#10411yescharacteristic
268C3×D5—22no—
269C23×C3—21no—
270C23×C3—51no—
271C3×Q8—101no—
272C3×Q8—101no—
273C3×D4—21no—
274C3×D4—21no—
275C3×D4—202no—
276C2×C3×C4—21no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—51no—
282C2×C3×C4—102no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—101no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4C2×C4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4D4×D511yescharacteristic
292C3⋊C8—22no—
293C3⋊C8—41no—
294C3⋊C8—102no—
295C3⋊C8—201no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5—41no—
299C22×C5C2×#21711yescharacteristic
300C2×D5—21no—
301C2×D5—21no—
302C2×D5#83712yes—
303C4×C5—21no—
304C4×C5—41no—
305C4×C5#94811yescharacteristic
306C4×C5#94811yescharacteristic
307C4×C5#95011yescharacteristic
308C4×C5#95011yescharacteristic
309Dic5—21no—
310Dic5—21no—
311Dic5—21no—
312Dic5—41no—
313Dic5—41no—
314C2×Q8—51no—
315C2×D4—101no—
316C2×D4D5×Dic311yescharacteristic
317C22×C4—21no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—51no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—304no—
324C2×C8—301no—
325C2×C8—301no—
326C4⋊C4—51no—
327C4⋊C4—101no—
328C4⋊C4—101no—
329C4⋊C4—101no—
330C4⋊C4—101no—
331C4⋊C4D5×Dic311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—101no—
334C22⋊C4—101no—
335C22⋊C4—101no—
336C22⋊C4—101no—
337C42—51no—
338C42—51no—
339C42—51no—
340C42—101no—
341C42C2×D3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—52no—
347C22×C3—101no—
348C22×C3—101no—
349C22×C3D5×C22⋊C411yescharacteristic
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—101no—
353C3×C4—101no—
354C3×C4—101no—
355C3×C4—201no—
356C3×C4—201no—
357C3×C4#404711yescharacteristic
358C3×C4#405311yescharacteristic
359C3×C4#405811yescharacteristic
360C3×C4#406211yescharacteristic
361C2×C5—81no—
362C2×C5#523311yescharacteristic
363C2×C5#523411yescharacteristic
364C2×C5C2×#83711yescharacteristic
365D5—22no—
366C23—21no—
367C23—51no—
368Q8—101no—
369Q8—101no—
370D4—21no—
371D4—21no—
372D4—202no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—51no—
377C2×C4—51no—
378C2×C4—51no—
379C2×C4—102no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4C2×D5×Dic311yescharacteristic
387C2×C4D5×#6711yescharacteristic
388C2×C4D5×#6711yescharacteristic
389C8—62no—
390C8—121no—
391C8—302no—
392C8—601no—
393C2×C3—81no—
394C2×C3—102no—
395C2×C3#6501611yescharacteristic
396C2×C3#6506111yescharacteristic
397C2×C3D5×#10411yescharacteristic
398C5#7175211yescharacteristic, complemented, Sylow
399C22—41no—
400C22—41no—
401C22—41no—
402C22—52no—
403C22—101no—
404C22—101no—
405C22D5×#21711yescharacteristic
406C4—21no—
407C4—41no—
408C4—101no—
409C4—101no—
410C4—101no—
411C4—201no—
412C4—201no—
413C4#9128311yescharacteristic
414C4#9128411yescharacteristic
415C4#9149011yescharacteristic
416C4#9149211yescharacteristic
417C3#1059897011yescharacteristic, complemented, Sylow
418C2—81no—
419C2—102no—
420C2#1174848211yescharacteristic
421C2#1174896111yescharacteristic
422C2D5×#83711yescharacteristic
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#1494
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. C4×D5×C3⋊C8C2semidirect
3. #11746871C2semidirect
4. D4⋊(C3⋊#168)C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745841C2semidirect
7. #11745840C2semidirect
70. D4⋊(C3⋊C8)D5semidirect
342. C3×C5#1494semidirect
398. C5#71752semidirect
417. C3#10598970semidirect

Maximal subgroups

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

subgroupindex
C3×#658912
C4×D5×C3⋊C82
#117468712
D4⋊(C3⋊#168)2
C5×D4⋊(C3⋊C8)2
#117458412
#117458402
#105989703
#717525