Finite Group Databasebeta

← #14282471

Subgroups — #14282471

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
1#11752682C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic, complemented
3C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
4#11746305C211yesmaximal, characteristic, complemented
5C5×#4483C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10598970—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91449C411yescharacteristic
13#91447—21no—
14C4×#1201—21no—
15#91388C411yescharacteristic
16#91373C411yescharacteristic
17#91372—21no—
18#91371—21no—
19#91360C411yescharacteristic
20C2×D5×C3⋊C8—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3952—21no—
25C3×#3947—21no—
26C3×C4⋊#168C2211yescharacteristic
27Dic5×C3⋊C8—21no—
28#70800—51nomaximal, Hall
29#65891—31no—
30#65124D311yescharacteristic, complemented
31C4×C8×D5—31no—
32C5×D4⋊C8—31no—
33D4⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×Dic30C2×C411yescharacteristic
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×#1201—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15C2×C411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59(C2×D3)⋊Dic5—21no—
60(C2×D3)⋊Dic5—21no—
61(C2×D3)⋊Dic5—21no—
62#6665—21no—
63D5×C3⋊C8—24no—
64#5479—51no—
65C3×#432—51no—
66C2×C4×C3⋊C8—51no—
67#4484—51no—
68#4484—51no—
69#4483—51no—
70#4483D511yescharacteristic, complemented
71C4×C5×D4—31no—
72#4084—31no—
73#4082—31no—
74C4×C22⋊D5—61no—
75#4072—61no—
76C2×C8×D5—61no—
77#4043—31no—
78#4036—31no—
79#4029—61no—
80#4025—61no—
81C42×D5C2×D311yescharacteristic
82C4×Dic10—31no—
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8—31no—
85#3952—21no—
86#3947—21no—
87C8×Dic5—61no—
88C4⋊#168C2×D311yescharacteristic
89C4×#168—31no—
90#1494—151noSylow
91C22×C5×D3—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98Dic30—21no—
99Dic30—21no—
100C2×C5×Dic3—21no—
101C5×D12—21no—
102C5×D12—21no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C22⋊C411yescharacteristic
108C3×C4×D5—22no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—21no—
113#1201—42no—
114C3×C5×C8—41no—
115C3⋊#168—22no—
116C3×#168—41no—
117C5×C3⋊C8—22no—
118C2×C3×C42—51no—
119#930—51no—
120#929—101no—
121C4×#67—101no—
122#924—51no—
123C22×C3⋊C8—101no—
124#876—101no—
125#875—51no—
126C4×D12C2×D511yescharacteristic
127#872—101no—
128#870—51no—
129C4×Dic6—51no—
130C3×C4⋊C8—51no—
131C3×C4⋊C8C2×D511yescharacteristic
132C3×C22⋊C8—101no—
133C3×#97—101no—
134C4×C3⋊C8—51no—
135C4×C3⋊C8—101no—
136C4×C3⋊C8C2×D511yescharacteristic
137C2×C5×D4—31no—
138C22×C4×C5—61no—
139C2×C22⋊D5—61no—
140C2×C4×D5C4×D311yescharacteristic
141C2×C4×D5D1211yescharacteristic
142C2×C4×D5#6711yescharacteristic
143C2×Dic10—31no—
144C2×C5×C8—21no—
145C2×C5×C8—61no—
146C5×C4⋊C4—31no—
147C5×C22⋊C4—61no—
148C42×C5C22×D311yescharacteristic
149C22⋊Dic5—61no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152#685—61no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—61no—
159C4×Dic5C4×D311yescharacteristic
160C4×Dic5D1211yescharacteristic
161C4×Dic5#6711yescharacteristic
162C2×#168—21no—
163C2×#168—61no—
164C8×D5—64no—
165#529—151no—
166#432—51no—
167C2×C4×C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170D4⋊C8—31no—
171D4⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C5×D3—41no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5#10412yes—
179C3×C4×C5—21no—
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5#13511yescharacteristic
184Dic15—41no—
185Dic15—41no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C5×Dic3—41no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C2×#67—101no—
194C2×D12C4×D511yescharacteristic
195C2×C4×D3—21no—
196C2×Dic6—51no—
197C2×C3×C8—21no—
198C2×C3×C8—101no—
199C3×C42—51no—
200C3×C42—51no—
201C3×C42—51no—
202C3×C42C22×D511yescharacteristic
203#217—101no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208C4⋊Dic3—51no—
209C4⋊Dic3C4×D511yescharacteristic
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213Dic3⋊C4—101no—
214C4×Dic3—101no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—104no—
217C2×C3⋊C8—101no—
218C23×C5—61no—
219C22×D5(C2×D3)⋊C411yescharacteristic
220C5×D4—61no—
221C5×D4—61no—
222C2×C4×C5—61no—
223C2×C4×C5—121no—
224C2×C4×C5—121no—
225C2×C4×C5C2×C4×D311yescharacteristic
226C2×C4×C5C2×D1211yescharacteristic
227C2×C4×C5C2×#6711yescharacteristic
228C22⋊D5—122no—
229C2×Dic5—61no—
230C2×Dic5—61no—
231C2×Dic5(C2×D3)⋊C411yescharacteristic
232C2×Dic5(C2×D3)⋊C411yescharacteristic
233C2×Dic5(C2×D3)⋊C411yescharacteristic
234C4×D5—22no—
235C4×D5—21no—
236C4×D5—21no—
237C4×D5—21no—
238C4×D5—21no—
239Dic10—61no—
240Dic10—61no—
241C5×C8—41no—
242C5×C8—62no—
243#168—41no—
244#168—62no—
245C22×C8—301no—
246#126—301no—
247#125—151no—
248#124—151no—
249#123—301no—
250C22⋊Q8—151no—
251#121—151no—
252C4×Q8—151no—
253C4×D4—31no—
254C4×D4—301no—
255#117—301no—
256C2×C42—51no—
257C4⋊C8—51no—
258C4⋊C8D3×D511yescharacteristic
259C22⋊C8—101no—
260#97—101no—
261C4×C8—31no—
262C4×C8—151no—
263C4×C8—301no—
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267C3×D5—22no—
268C5×D3—81no—
269C23×C3—51no—
270C22×D3—21no—
271C2×C3×C4—51no—
272C2×C3×C4—51no—
273C2×C3×C4—51no—
274C2×C3×C4—102no—
275C2×C3×C4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—101no—
278C2×C3×C4—101no—
279C2×C3×C4C2×C4×D511yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282#67—202no—
283C2×Dic3—21no—
284C2×Dic3—101no—
285C2×Dic3—101no—
286D12—21no—
287D12—21no—
288C4×D3—41no—
289C4×D3—41no—
290Dic6—101no—
291Dic6—101no—
292C3×C8—41no—
293C3×C8—201no—
294C3⋊C8—22no—
295C3⋊C8—102no—
296C22×C5—121no—
297C22×C5—121no—
298C22×C5—121no—
299C22×C5C2×(C2×D3)⋊C411yescharacteristic
300C2×D5—21no—
301C2×D5—21no—
302C2×D5#82512yes—
303C4×C5—21no—
304C4×C5—121no—
305C4×C5#90711yescharacteristic
306C4×C5#90711yescharacteristic
307C4×C5#95011yescharacteristic
308C4×C5#95011yescharacteristic
309Dic5—21no—
310Dic5—21no—
311Dic5—21no—
312Dic5—121no—
313Dic5—121no—
314C2×Q8—151no—
315C2×D4—31no—
316C2×D4—301no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—61no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—101no—
324C2×C8—304no—
325C2×C8—301no—
326C4⋊C4—31no—
327C4⋊C4—151no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—301no—
332C22⋊C4—61no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—51no—
338C42—51no—
339C42—51no—
340C42—301no—
341C42C2×D3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—52no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3D5×C22⋊C411yescharacteristic
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C3×C4—21no—
351C3×C4—101no—
352C3×C4—101no—
353C3×C4—101no—
354C3×C4#404711yescharacteristic
355C3×C4#405311yescharacteristic
356C3×C4#405811yescharacteristic
357C3×C4#406211yescharacteristic
358Dic3—41no—
359Dic3—201no—
360Dic3—201no—
361C2×C5—241no—
362C2×C5#500211yescharacteristic
363C2×C5#512911yescharacteristic
364C2×C5C2×#82511yescharacteristic
365D5—22no—
366C23—51no—
367C23—61no—
368Q8—301no—
369Q8—301no—
370D4—61no—
371D4—61no—
372D4—602no—
373C2×C4—51no—
374C2×C4—51no—
375C2×C4—51no—
376C2×C4—61no—
377C2×C4—102no—
378C2×C4—101no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4D5×D1211yescharacteristic
388C2×C4D5×#6711yescharacteristic
389C8—41no—
390C8—62no—
391C8—201no—
392C8—302no—
393C2×C3—102no—
394C2×C3#6501611yescharacteristic
395C2×C3#6506111yescharacteristic
396C2×C3D5×#10411yescharacteristic
397D3—81no—
398C5#7080011yescharacteristic, complemented, Sylow
399C22—52no—
400C22—101no—
401C22—101no—
402C22—121no—
403C22—121no—
404C22—121no—
405C22D5×(C2×D3)⋊C411yescharacteristic
406C4—21no—
407C4—101no—
408C4—101no—
409C4—101no—
410C4—121no—
411C4—601no—
412C4—601no—
413C4#9126711yescharacteristic
414C4#9126811yescharacteristic
415C4#9149011yescharacteristic
416C4#9151411yescharacteristic
417C3#1059897011yescharacteristic, complemented, Sylow
418C2—102no—
419C2—241no—
420C2#1174749911yescharacteristic
421C2#1174813611yescharacteristic
422C2D5×#82511yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91449C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1494
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×#65124C2semidirect
3. C4×D5×C3⋊C8C2semidirect
4. #11746305C2semidirect
5. C5×#4483C2semidirect
6. #11745844C2semidirect
7. #11745836C2semidirect
30. #65124D3semidirect
70. #4483D5semidirect
342. C3×C5#1494semidirect
398. C5#70800semidirect
417. C3#10598970semidirect

Maximal subgroups

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

subgroupindex
#117526822
C3×#651242
C4×D5×C3⋊C82
#117463052
C5×#44832
#117458442
#117458362
#105989703
#708005