Finite Group Databasebeta

← #14282456

Subgroups — #14282456

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#11756339C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3C4×C8×D15C211yesmaximal, characteristic, complemented
4C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10599034—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91836C411yescharacteristic
11#91835C411yescharacteristic
12C2×C8×D15—21no—
13#91787—21no—
14#91784C411yescharacteristic
15#91783—21no—
16#91779C411yescharacteristic
17C4×D60—21no—
18C4×D60C2211yescharacteristic
19#91761—21no—
20C42×D15C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23#91104—21no—
24#91099—21no—
25C8×Dic15—21no—
26C4⋊(C3⋊#168)C2211yescharacteristic
27C4×C3⋊#168C2211yescharacteristic
28#68241—51nomaximal, Hall
29#65914—31no—
30#65124—31no—
31C4×C8×D5—31no—
32C5×Q8⋊C8D311yescharacteristic, complemented
33Q8⋊#168—31no—
34#64703—31no—
35#64679—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×D60—21no—
38C2×D60C2×C411yescharacteristic
39C2×C4×D15—21no—
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×C4×D15D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15C2×C411yescharacteristic
56#6712—21no—
57#6712—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C8×D15—24no—
64#5580—51no—
65#4835—51no—
66C4×D3×C8—51no—
67C3×Q8⋊C8D511yescharacteristic, complemented
68#4535—51no—
69#4483—51no—
70#4459—51no—
71C4×C5×Q8C2×D311yescharacteristic
72#4093—31no—
73#4092—31no—
74C2×C8×D5—61no—
75#4044—61no—
76#4041—31no—
77#4040—61no—
78#4036—31no—
79C4×D20—31no—
80C4×D20—61no—
81#4018—61no—
82C42×D5—31no—
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8C2×D311yescharacteristic
85#3952—61no—
86#3947—61no—
87C8×Dic5—61no—
88C4⋊#168—31no—
89C4×#168—31no—
90#1494—151noSylow
91C22×D15—21no—
92C22×D15C22⋊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×Dic15—21no—
101C2×Dic15C22⋊C411yescharacteristic
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104D60—21no—
105D60—21no—
106D60—42no—
107C4×D15—22no—
108C4×D15—21no—
109C4×D15—21no—
110C4×D15—21no—
111C4×D15—21no—
112C4×D15—41no—
113C4×D15—41no—
114C3×C5×C8—22no—
115C3×C5×C8—41no—
116C3⋊#168—22no—
117C3⋊#168—41no—
118C3×C4×Q8C2×D511yescharacteristic
119#947—51no—
120#946—51no—
121C2×D3×C8—101no—
122#898—101no—
123#895—51no—
124#894—101no—
125#890—51no—
126C4×D12—51no—
127C4×D12—101no—
128#872—101no—
129C42×D3—51no—
130C3×C4⋊C8C2×D511yescharacteristic
131C3×C4×C8C2×D511yescharacteristic
132(C2×D3)⋊C8—101no—
133#815—101no—
134C8×Dic3—101no—
135C4⋊(C3⋊C8)—51no—
136C4×C3⋊C8—51no—
137C2×C5×Q8C4×D311yescharacteristic
138C2×D20—31no—
139C2×D20—61no—
140C2×C4×D5—31no—
141C2×C4×D5—31no—
142C2×C4×D5—31no—
143C2×C4×D5—61no—
144C2×C5×C8—21no—
145C2×C5×C8—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4C4×D311yescharacteristic
148C42×C5—21no—
149C42×C5C22×D311yescharacteristic
150#685—61no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157#683—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C2×#168—61no—
163C2×#168—61no—
164C8×D5—64no—
165#529—151no—
166#432—151no—
167C2×C4×C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8D1511yescharacteristic, complemented
170D4⋊C8—151no—
171D4⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×D15—21no—
174C2×D15—21no—
175C2×D15—41no—
176C2×D15—41no—
177C2×D15—41no—
178C2×D15#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
186Dic15—21no—
187Dic15—21no—
188Dic15—21no—
189Dic15—41no—
190C2×C3×Q8C4×D511yescharacteristic
191C2×D12—51no—
192C2×D12—101no—
193C2×C4×D3—51no—
194C2×C4×D3—51no—
195C2×C4×D3—51no—
196C2×C4×D3—101no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4C4×D511yescharacteristic
201C3×C42—21no—
202C3×C42C22×D511yescharacteristic
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207(C2×D3)⋊C4—101no—
208C4⋊Dic3—51no—
209C4⋊Dic3—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212C4×Dic3—51no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C2×C3⋊C8—101no—
216C2×C3⋊C8—101no—
217D3×C8—104no—
218C22×D5—31no—
219C22×D5—61no—
220C5×Q8—21no—
221C5×Q8—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5C2×C4×D311yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C2×Dic5—31no—
228C2×Dic5—31no—
229C2×Dic5—31no—
230C2×Dic5—61no—
231D20—61no—
232D20—61no—
233D20—122no—
234C4×D5—62no—
235C4×D5—61no—
236C4×D5—61no—
237C4×D5—61no—
238C4×D5—61no—
239C4×D5—121no—
240C4×D5—121no—
241C5×C8—22no—
242C5×C8—41no—
243#168—62no—
244#168—121no—
245C22×C8—301no—
246#126—301no—
247#125—151no—
248#124—151no—
249#123—301no—
250C22⋊Q8—151no—
251#121—151no—
252C4×Q8C2×D1511yescharacteristic
253C4×D4—151no—
254C4×D4—301no—
255#117—301no—
256C2×C42—151no—
257C4⋊C8—151no—
258C4⋊C8C2×D1511yescharacteristic
259C22⋊C8—301no—
260#97—301no—
261C4×C8—151no—
262C4×C8—301no—
263C4×C8C2×D1511yescharacteristic
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267D15—22no—
268D15—81no—
269C22×D3—51no—
270C22×D3—101no—
271C3×Q8—21no—
272C3×Q8—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4C2×C4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278C2×Dic3—51no—
279C2×Dic3—51no—
280C2×Dic3—51no—
281C2×Dic3—101no—
282D12—101no—
283D12—101no—
284D12—202no—
285C4×D3—102no—
286C4×D3—101no—
287C4×D3—101no—
288C4×D3—101no—
289C4×D3—101no—
290C4×D3—201no—
291C4×D3—201no—
292C3×C8—22no—
293C3×C8—41no—
294C3⋊C8—102no—
295C3⋊C8—201no—
296C22×C5D3×C22⋊C411yescharacteristic
297C2×D5—32no—
298C2×D5—61no—
299C2×D5—61no—
300C2×D5—121no—
301C2×D5—121no—
302C2×D5—121no—
303C4×C5—21no—
304C4×C5—41no—
305C4×C5—41no—
306C4×C5#90111yescharacteristic
307C4×C5#90711yescharacteristic
308C4×C5#91611yescharacteristic
309C4×C5#91911yescharacteristic
310Dic5—61no—
311Dic5—61no—
312Dic5—61no—
313Dic5—121no—
314C2×Q8C4×D1511yescharacteristic
315C2×D4—151no—
316C2×D4—301no—
317C22×C4—151no—
318C22×C4—151no—
319C22×C4—151no—
320C22×C4—301no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—304no—
324C2×C8—301no—
325C2×C8—301no—
326C4⋊C4—21no—
327C4⋊C4—151no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4C4×D1511yescharacteristic
332C22⋊C4—301no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—21no—
338C42—151no—
339C42—151no—
340C42—151no—
341C42C22×D1511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3D5×C22⋊C411yescharacteristic
344C2×D3—52no—
345C2×D3—101no—
346C2×D3—101no—
347C2×D3—201no—
348C2×D3—201no—
349C2×D3—201no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4#404711yescharacteristic
354C3×C4#405311yescharacteristic
355C3×C4#406211yescharacteristic
356C3×C4#406511yescharacteristic
357Dic3—101no—
358Dic3—101no—
359Dic3—101no—
360Dic3—201no—
361C2×C5#472711yescharacteristic
362C2×C5#480411yescharacteristic
363C2×C5D3×#10411yescharacteristic
364D5—62no—
365D5—241no—
366C23—151no—
367C23—301no—
368Q8—21no—
369Q8—21no—
370D4—301no—
371D4—301no—
372D4—602no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—151no—
376C2×C4—151no—
377C2×C4—151no—
378C2×C4—302no—
379C2×C4—301no—
380C2×C4—301no—
381C2×C4—301no—
382C2×C4—301no—
383C2×C4—301no—
384C2×C4—601no—
385C2×C4—601no—
386C2×C4C2×C4×D1511yescharacteristic
387C2×C4D4×D1511yescharacteristic
388C2×C4D4×D1511yescharacteristic
389C8—22no—
390C8—41no—
391C8—302no—
392C8—601no—
393C2×C3#6501611yescharacteristic
394C2×C3#6509311yescharacteristic
395C2×C3D5×#10411yescharacteristic
396D3—102no—
397D3—401no—
398C5#6824111yescharacteristic, complemented, Sylow
399C22—152no—
400C22—301no—
401C22—301no—
402C22—601no—
403C22—601no—
404C22—601no—
405C22C22⋊C4×D1511yescharacteristic
406C4—21no—
407C4—41no—
408C4—41no—
409C4—301no—
410C4—301no—
411C4—301no—
412C4—601no—
413C4#9179011yescharacteristic
414C4#9179611yescharacteristic
415C4#9180511yescharacteristic
416C4#9180811yescharacteristic
417C3#1059903411yescharacteristic, complemented, Sylow
418C2—302no—
419C2—1201no—
420C2#1175082811yescharacteristic
421C2#1175090511yescharacteristic
422C2D15×#10411yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91784C4
cosocleC3×C42×C5C23
hypercenterQ8⋊C8D15
hypocenterC3×C5#1494
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. C4×C8×D15C2semidirect
4. C3×C5×Q8⋊C8C2semidirect
5. #11746356C2semidirect
6. #11746304C2semidirect
7. #11746280C2semidirect
32. C5×Q8⋊C8D3semidirect
67. C3×Q8⋊C8D5semidirect
169. Q8⋊C8D15semidirect
342. C3×C5#1494semidirect
398. C5#68241semidirect
417. C3#10599034semidirect

Maximal subgroups

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

subgroupindex
#117563392
#117509362
C4×C8×D152
C3×C5×Q8⋊C82
#117463562
#117463042
#117462802
#105990343
#682415