Finite Group Databasebeta

← #14282492

Subgroups — #14282492

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×#65914C211yesmaximal, characteristic
2C4×D5×C3⋊C8C211yesmaximal, characteristic, complemented
3#11746871C211yesmaximal, characteristic, complemented
4#11746356C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745835C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599034—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
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#65914D311yescharacteristic
30#65124—31no—
31C4×C8×D5—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
63D5×C3⋊C8—24no—
64C3×#529—51no—
65#4926—51no—
66C2×C4×C3⋊C8—51no—
67#4535—51no—
68#4535D511yescharacteristic, complemented
69D4⋊(C3⋊C8)—51no—
70D4⋊(C3⋊C8)—51no—
71C4×C5×Q8C2×D311yescharacteristic
72#4093Dic311yescharacteristic
73#4092Dic311yescharacteristic
74C2×C8×D5—61no—
75#4044—21no—
76#4041Dic311yescharacteristic
77#4040—21no—
78#4036Dic311yescharacteristic
79C4×D20—21no—
80C4×D20C2×D311yescharacteristic
81#4018—21no—
82C42×D5C2×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
91C22×C3×D5—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C3×C5×Q8—21no—
94C3×C5×Q8—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×Dic5—21no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C22⋊C411yescharacteristic
104C3×D20—21no—
105C3×D20—21no—
106C3×D20—42no—
107C3×C4×D5—22no—
108C3×C4×D5—21no—
109C3×C4×D5—21no—
110C3×C4×D5—21no—
111C3×C4×D5—21no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
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×Q8C2×D511yescharacteristic
125C3×C4×D4—51no—
126C3×C4×D4—101no—
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×Q8C2×Dic311yescharacteristic
138C2×D20—21no—
139C2×D20C2×Dic311yescharacteristic
140C2×C4×D5—21no—
141C2×C4×D5C2×Dic311yescharacteristic
142C2×C4×D5#6711yescharacteristic
143C2×C4×D5#6711yescharacteristic
144C2×C5×C8—61no—
145C2×C5×C8—61no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4C2×Dic311yescharacteristic
148C42×C5—21no—
149C42×C5C22×D311yescharacteristic
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5C2×Dic311yescharacteristic
157#683—21no—
158#683—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—31no—
169Q8⋊C8—151no—
170D4⋊C8—151no—
171D4⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5#10412yes—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5#13111yescharacteristic
183C3×C4×C5#13111yescharacteristic
184C3×C4×C5#13511yescharacteristic
185C3×C4×C5#13511yescharacteristic
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—41no—
190C2×C3×Q8C4×D511yescharacteristic
191C2×C3×D4—51no—
192C2×C3×D4—101no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—101no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—51no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4C4×D511yescharacteristic
203C3×C22⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C42—21no—
209C3×C42—51no—
210C3×C42—51no—
211C3×C42—51no—
212C3×C42C22×D511yescharacteristic
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—104no—
216C2×C3⋊C8—101no—
217C2×C3⋊C8—101no—
218C22×D5—21no—
219C22×D5#21711yescharacteristic
220C5×Q8—21no—
221C5×Q8—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5C22×Dic311yescharacteristic
225C2×C4×C5C2×#6711yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C2×Dic5—21no—
228C2×Dic5#21711yescharacteristic
229C2×Dic5#21711yescharacteristic
230C2×Dic5#21711yescharacteristic
231D20—21no—
232D20—21no—
233D20—42no—
234C4×D5—22no—
235C4×D5—21no—
236C4×D5—21no—
237C4×D5—21no—
238C4×D5—21no—
239C4×D5—41no—
240C4×D5—41no—
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×Q8D3×D511yescharacteristic
253C4×D4—51no—
254C4×D4—101no—
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#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267C3×D5—22no—
268C3×D5—81no—
269C23×C3—51no—
270C23×C3—101no—
271C3×Q8—21no—
272C3×Q8—21no—
273C3×D4—101no—
274C3×D4—101no—
275C3×D4—202no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—51no—
279C2×C3×C4—51no—
280C2×C3×C4—51no—
281C2×C3×C4—102no—
282C2×C3×C4—101no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—101no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
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×C5C2×#21711yescharacteristic
297C2×D5—21no—
298C2×D5—21no—
299C2×D5—41no—
300C2×D5—41no—
301C2×D5—41no—
302C2×D5#83712yes—
303C4×C5—21no—
304C4×C5—41no—
305C4×C5—41no—
306C4×C5#94811yescharacteristic
307C4×C5#94811yescharacteristic
308C4×C5#95011yescharacteristic
309C4×C5#95011yescharacteristic
310Dic5—21no—
311Dic5—21no—
312Dic5—21no—
313Dic5—41no—
314C2×Q8D5×Dic311yescharacteristic
315C2×D4—51no—
316C2×D4—101no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—101no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—304no—
324C2×C8—301no—
325C2×C8—301no—
326C4⋊C4—21no—
327C4⋊C4—51no—
328C4⋊C4—101no—
329C4⋊C4—101no—
330C4⋊C4—101no—
331C4⋊C4D5×Dic311yescharacteristic
332C22⋊C4—101no—
333C22⋊C4—101no—
334C22⋊C4—101no—
335C22⋊C4—101no—
336C22⋊C4—101no—
337C42—21no—
338C42—51no—
339C42—51no—
340C42—51no—
341C42C2×D3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—52no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3—201no—
347C22×C3—201no—
348C22×C3—201no—
349C22×C3D5×C22⋊C411yescharacteristic
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—101no—
354C3×C4—101no—
355C3×C4—101no—
356C3×C4—201no—
357C3×C4#404711yescharacteristic
358C3×C4#405311yescharacteristic
359C3×C4#406211yescharacteristic
360C3×C4#406511yescharacteristic
361C2×C5#523311yescharacteristic
362C2×C5#523411yescharacteristic
363C2×C5C2×#83711yescharacteristic
364D5—22no—
365D5—81no—
366C23—51no—
367C23—101no—
368Q8—21no—
369Q8—21no—
370D4—101no—
371D4—101no—
372D4—202no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—51no—
378C2×C4—102no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—201no—
385C2×C4—201no—
386C2×C4C2×D5×Dic311yescharacteristic
387C2×C4D5×#6711yescharacteristic
388C2×C4D5×#6711yescharacteristic
389C8—62no—
390C8—121no—
391C8—302no—
392C8—601no—
393C2×C3—102no—
394C2×C3—401no—
395C2×C3#6501611yescharacteristic
396C2×C3#6509311yescharacteristic
397C2×C3D5×#10411yescharacteristic
398C5#7175211yescharacteristic, complemented, Sylow
399C22—52no—
400C22—101no—
401C22—101no—
402C22—201no—
403C22—201no—
404C22—201no—
405C22D5×#21711yescharacteristic
406C4—21no—
407C4—41no—
408C4—41no—
409C4—101no—
410C4—101no—
411C4—101no—
412C4—201no—
413C4#9128311yescharacteristic
414C4#9128411yescharacteristic
415C4#9151411yescharacteristic
416C4#9151611yescharacteristic
417C3#1059903411yescharacteristic, complemented, Sylow
418C2—102no—
419C2—401no—
420C2#1174848211yescharacteristic
421C2#1174920711yescharacteristic
422C2D5×#83711yescharacteristic
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#1494
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. C4×D5×C3⋊C8C2semidirect
3. #11746871C2semidirect
4. #11746356C2semidirect
5. C5×#4535C2semidirect
6. #11745835C2semidirect
7. #11745834C2semidirect
68. #4535D5semidirect
342. C3×C5#1494semidirect
398. C5#71752semidirect
417. C3#10599034semidirect

Maximal subgroups

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

subgroupindex
C3×#659142
C4×D5×C3⋊C82
#117468712
#117463562
C5×#45352
#117458352
#117458342
#105990343
#717525