Finite Group Databasebeta

← #11753075

Subgroups — #11753075

Order 960.

620 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6780C211yesmaximal, characteristic, complemented
2C2×#6768C211yesmaximal, characteristic, complemented
3#91770C211yesmaximal, characteristic, complemented
4C5×#884C211yesmaximal, characteristic, complemented
5C3×#4031C211yesmaximal, characteristic, complemented
6#91567C211yesmaximal, characteristic, complemented
7#67⋊Dic5C211yesmaximal, characteristic, complemented
8#91558C211yesmaximal, characteristic, complemented
9#91454C211yesmaximal, characteristic, complemented
10#91453C211yesmaximal, characteristic, complemented
11#91442C211yesmaximal, characteristic, complemented
12C4×D3×Dic5C211yesmaximal, characteristic, complemented
13#91396C211yesmaximal, characteristic, complemented
14#91350C211yesmaximal, characteristic, complemented
15#91327C211yesmaximal, characteristic, complemented
16#65930—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C5×#67C2211yescharacteristic
22C2×C5×D12C2211yescharacteristic
23C2×C4×C5×D3C2211yescharacteristic
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×Dic10C2211yescharacteristic
26C2×#1204C2211yescharacteristic
27C2×#1203C2211yescharacteristic
28C2×#1203C2211yescharacteristic
29C2×#1202C2211yescharacteristic
30C2×#1201C2211yescharacteristic
31C2×#1201C2211yescharacteristic
32C2×D3×Dic5C2211yescharacteristic
33C2×D3×Dic5C2211yescharacteristic
34C2×D3×Dic5C2211yescharacteristic
35#6780—24no—
36C2×D5×Dic3C2211yescharacteristic
37#6768—24no—
38C3×C5×C22⋊C4C2211yescharacteristic
39#6714C2211yescharacteristic
40#6712C2211yescharacteristic
41C4×Dic15C2211yescharacteristic
42C5×(C2×D3)⋊C4C2211yescharacteristic
43C5×Dic3⋊C4C2211yescharacteristic
44C3×C22⋊Dic5C2211yescharacteristic
45C3×#685C2211yescharacteristic
46C3×#685C2211yescharacteristic
47C3×C4×Dic5C2211yescharacteristic
48Dic3⋊Dic5C2211yescharacteristic
49#6669C2211yescharacteristic
50#6667C2211yescharacteristic
51(C2×D3)⋊Dic5C2211yescharacteristic
52Dic3×Dic5C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5668—51nomaximal, Hall
55C2×#711—31no—
56C2×#711—31no—
57C5×#121—31no—
58#4086—31no—
59#4085—31no—
60#4085—31no—
61D4×Dic5—31no—
62#4076—31no—
63C2×C4×Dic5—31no—
64#4039—31no—
65#4034—31no—
66#4031—31no—
67#4031D311yescharacteristic, complemented
68#4027—31no—
69#4027—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C22×C5×D3C2311yescharacteristic
74C22×C3×D5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77#1220—22no—
78C2×Dic15—22no—
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C4×D15—22no—
83C5×#67—22no—
84C5×#67—22no—
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C5×D12—22no—
88C4×C5×D3—22no—
89C3×C22⋊D5—22no—
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92C2×C3×Dic5C2311yescharacteristic
93C3×Dic10—22no—
94#1204—22no—
95#1203—22no—
96#1203—22no—
97#1202—22no—
98#1201—22no—
99#1201—22no—
100D3×Dic5—22no—
101D3×Dic5—22no—
102D3×Dic5D414yescomplemented
103D5×Dic3—22no—
104C2×#239—51no—
105C2×#237—51no—
106C3×#124—51no—
107#944—51no—
108#940—51no—
109#884—51no—
110#884—51no—
111#884—51no—
112#884D511yescharacteristic, complemented
113#67⋊C4—51no—
114#67⋊C4—51no—
115#67⋊C4—51no—
116#67⋊C4—51no—
117#875—51no—
118C42×D3—51no—
119C2×C5×D4—31no—
120C2×C5×D4—31no—
121C2×C5×D4—31no—
122C22×C4×C5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C2×C22⋊D5C2×D311yescharacteristic
129C22×Dic5—31no—
130C22×Dic5—31no—
131C22×Dic5—31no—
132C22×Dic5—31no—
133#711—64no—
134#711—64no—
135C2×D20—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×Dic10—31no—
139C2×Dic10C2×D311yescharacteristic
140C5×C4⋊C4—31no—
141C5×C22⋊C4—31no—
142C5×C22⋊C4C2×D311yescharacteristic
143C22⋊Dic5—31no—
144C22⋊Dic5C2×D311yescharacteristic
145#685—31no—
146#685—31no—
147#685C2×D311yescharacteristic
148#685C2×D311yescharacteristic
149C4⋊Dic5—31no—
150#683—31no—
151#683—31no—
152C4×Dic5—31no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5C2×D311yescharacteristic
156#532—151noSylow
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5—21no—
160C22×C3×C5C2411yescharacteristic
161C2×D15—21no—
162C2×D15—21no—
163C2×D15—21no—
164C2×C5×D3—21no—
165C2×C5×D3—21no—
166C2×C5×D3—21no—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C5×D3C2×D412yes—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175Dic15—21no—
176Dic15C2×D412yes—
177Dic15#4112yescomplemented
178C3×Dic5—21no—
179C3×Dic5—21no—
180C3×Dic5C2×D412yes—
181C5×Dic3—21no—
182C5×Dic3#4112yescomplemented
183C2×C3×Q8—51no—
184C2×C3×D4—51no—
185C2×#67—51no—
186C2×#67—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67C2×D511yescharacteristic
190C2×#67C2×D511yescharacteristic
191C22×Dic3—51no—
192C22×Dic3—51no—
193#239—104no—
194#237—104no—
195C2×D12—51no—
196C2×D12—51no—
197C2×D12C2×D511yescharacteristic
198C2×C4×D3—51no—
199C2×C4×D3—51no—
200C2×C4×D3—51no—
201C2×C4×D3—51no—
202C2×C4×D3C2×D511yescharacteristic
203C2×Dic6—51no—
204C3×C22⋊C4—51no—
205C3×C22⋊C4—51no—
206C3×C22⋊C4—51no—
207C3×C22⋊C4C2×D511yescharacteristic
208C3×C42—51no—
209(C2×D3)⋊C4—51no—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4—51no—
212(C2×D3)⋊C4C2×D511yescharacteristic
213Dic3⋊C4—51no—
214Dic3⋊C4—51no—
215Dic3⋊C4—51no—
216Dic3⋊C4C2×D511yescharacteristic
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3—51no—
220C23×C5—31no—
221C23×C5—31no—
222C23×C5C22×D311yescharacteristic
223C22×D5—31no—
224C22×D5C22×D311yescharacteristic
225C5×D4—62no—
226C5×D4—62no—
227C5×D4—62no—
228C2×C4×C5—31no—
229C2×C4×C5—31no—
230C2×C4×C5—62no—
231C2×C4×C5C22×D311yescharacteristic
232C2×C4×C5C22×D311yescharacteristic
233C22⋊D5—22no—
234C22⋊D5—62no—
235C22⋊D5—62no—
236C22⋊D5—62no—
237C22⋊D5—62no—
238C22⋊D5—62no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—34no—
242C2×Dic5—31no—
243C2×Dic5—62no—
244C2×Dic5—62no—
245C2×Dic5—62no—
246C2×Dic5C22×D311yescharacteristic
247C2×Dic5C22×D311yescharacteristic
248C2×Dic5C22×D311yescharacteristic
249D20—62no—
250C4×D5—62no—
251C4×D5—62no—
252Dic10—22no—
253Dic10—62no—
254C2×#41—151no—
255C2×#41—151no—
256C4⋊Q8—151no—
257#127—151no—
258#124—51no—
259#124—151no—
260#121—31no—
261#121—151no—
262#121—151no—
263#121—151no—
264C4×D4—151no—
265C4×D4—151no—
266C4×D4—151no—
267C4×D4—151no—
268C2×C42—151no—
269C2×C3×C5—41no—
270C2×C3×C5C22×D411yescharacteristic
271C2×C3×C5C2×#4111yescharacteristic
272C2×C3×C5C2×#4111yescharacteristic
273D15—41no—
274C3×D5—41no—
275C5×D3—22no—
276C5×D3—41no—
277C23×C3—51no—
278C23×C3C22×D511yescharacteristic
279C22×D3—51no—
280C22×D3C22×D511yescharacteristic
281C22×D3C22×D511yescharacteristic
282C3×Q8—102no—
283C3×D4—102no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4C22×D511yescharacteristic
288C2×C3×C4C22×D511yescharacteristic
289#67—22no—
290#67—22no—
291#67—102no—
292#67—102no—
293#67—102no—
294#67—102no—
295C2×Dic3—51no—
296C2×Dic3—51no—
297C2×Dic3—51no—
298C2×Dic3—102no—
299C2×Dic3—102no—
300C2×Dic3C22×D511yescharacteristic
301C2×Dic3C22×D511yescharacteristic
302D12—22no—
303D12—102no—
304D12—102no—
305C4×D3—22no—
306C4×D3—54no—
307C4×D3—102no—
308C4×D3—102no—
309C4×D3—102no—
310Dic6—102no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—32no—
315C22×C5—61no—
316C22×C5—61no—
317C22×C5—61no—
318C22×C5—61no—
319C22×C5—61no—
320C22×C5C23×D311yescharacteristic
321C2×D5—21no—
322C2×D5—21no—
323C2×D5—21no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5—61no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—32no—
330C4×C5—61no—
331Dic5—21no—
332Dic5—21no—
333Dic5—32no—
334Dic5—32no—
335Dic5—61no—
336Dic5D3×D412yes—
337#41—304no—
338#41—304no—
339C2×Q8—51no—
340C2×Q8—151no—
341C2×D4—31no—
342C2×D4—31no—
343C2×D4—31no—
344C2×D4—51no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4—151no—
348C2×D4—151no—
349C2×D4—151no—
350C2×D4—151no—
351C22×C4—31no—
352C22×C4—151no—
353C22×C4—151no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4—151no—
358C4⋊C4—31no—
359C4⋊C4—151no—
360C4⋊C4—151no—
361C4⋊C4—151no—
362C22⋊C4—31no—
363C22⋊C4—51no—
364C22⋊C4—51no—
365C22⋊C4—51no—
366C22⋊C4—151no—
367C22⋊C4—151no—
368C22⋊C4—151no—
369C22⋊C4D3×D511yescharacteristic
370C42—51no—
371C42—151no—
372C42—151no—
373C42—151no—
374C3×C5#53211yescharacteristic, complemented, Hall
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—101no—
379C22×C3—101no—
380C22×C3—101no—
381C22×C3C23×D511yescharacteristic
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—21no—
385C2×D3—21no—
386C2×D3—21no—
387C2×D3—101no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3D4×D512yes—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—52no—
394C3×C4—101no—
395C3×C4—101no—
396Dic3—21no—
397Dic3—52no—
398Dic3—52no—
399Dic3—101no—
400Dic3#71112yescomplemented
401C2×C5—41no—
402C2×C5—62no—
403C2×C5—121no—
404C2×C5C2×D3×D411yescharacteristic
405C2×C5D3×#4111yescharacteristic
406C2×C5D3×#4111yescharacteristic
407D5—41no—
408D5—121no—
409C23—31no—
410C23—31no—
411C23—51no—
412C23—151no—
413C23C2×D3×D511yescharacteristic
414Q8—102no—
415Q8—302no—
416D4—62no—
417D4—62no—
418D4—62no—
419D4—102no—
420D4—302no—
421D4—302no—
422D4—302no—
423D4—302no—
424D4—302no—
425D4—302no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—51no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—62no—
432C2×C4—154no—
433C2×C4—151no—
434C2×C4—151no—
435C2×C4—151no—
436C2×C4—302no—
437C2×C4—302no—
438C2×C4—302no—
439C2×C4—302no—
440C2×C4—302no—
441C2×C4C2×D3×D511yescharacteristic
442C2×C4C2×D3×D511yescharacteristic
443C2×C3—41no—
444C2×C3—201no—
445C2×C3C2×D4×D511yescharacteristic
446C2×C3C2×#71111yescharacteristic
447C2×C3D5×#4111yescharacteristic
448D3—22no—
449D3—41no—
450D3—201no—
451C5#566811yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—32no—
456C22—61no—
457C22—61no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22C22×D3×D511yescharacteristic
468C4—21no—
469C4—21no—
470C4—32no—
471C4—52no—
472C4—61no—
473C4—101no—
474C4—101no—
475C4—152no—
476C4—152no—
477C4—301no—
478C3#6593011yescharacteristic, complemented, Sylow
479C2—41no—
480C2—62no—
481C2—121no—
482C2—201no—
483C2—601no—
484C2#9201611yescharacteristic
485C2D3×D4×D511yescharacteristic
486C2D3×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#532
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#6780C2semidirect
2. C2×#6768C2semidirect
3. #91770C2semidirect
4. C5×#884C2semidirect
5. C3×#4031C2semidirect
6. #91567C2semidirect
7. #67⋊Dic5C2semidirect
8. #91558C2semidirect
9. #91454C2semidirect
10. #91453C2semidirect
11. #91442C2semidirect
12. C4×D3×Dic5C2semidirect
13. #91396C2semidirect
14. #91350C2semidirect
15. #91327C2semidirect
67. #4031D3semidirect
102. D3×Dic5D4semidirect
112. #884D5semidirect
177. Dic15#41semidirect
182. C5×Dic3#41semidirect
374. C3×C5#532semidirect
400. Dic3#711semidirect
451. C5#5668semidirect
478. C3#65930semidirect

Maximal subgroups

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

subgroupindex
C2×#67802
C2×#67682
#917702
C5×#8842
C3×#40312
#915672
#67⋊Dic52
#915582
#914542
#914532
#914422
C4×D3×Dic52
#913962
#913502
#913272
#659303
#56685