Finite Group Databasebeta

← #11754311

Subgroups — #11754311

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×C3×#709C211yesmaximal, characteristic, complemented
2C2×#6771C211yesmaximal, characteristic, complemented
3C4×#1220C211yesmaximal, characteristic, complemented
4C4×C5×#67C211yesmaximal, characteristic, complemented
5#91567C211yesmaximal, characteristic, complemented
6#91550C211yesmaximal, characteristic, complemented
7#91549C211yesmaximal, characteristic, complemented
8#91534C211yesmaximal, characteristic, complemented
9C4×#1202C211yesmaximal, characteristic, complemented
10C4×#1201C211yesmaximal, characteristic, complemented
11#91409C211yesmaximal, characteristic, complemented
12#91408C211yesmaximal, characteristic, complemented
13C4×D5×Dic3C211yesmaximal, characteristic, complemented
14#91327C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65882—31nomaximal, Hall
17C22×C3×C4×C5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C3×#709—24no—
25C2×C3×D20C2211yescharacteristic
26C2×C3×C4×D5C2211yescharacteristic
27C2×C3×C4×D5C2211yescharacteristic
28C2×C3×Dic10C2211yescharacteristic
29C2×#1204C2211yescharacteristic
30C2×#1203C2211yescharacteristic
31C2×#1202C2211yescharacteristic
32C2×#1202C2211yescharacteristic
33C2×#1201C2211yescharacteristic
34C2×#1201C2211yescharacteristic
35C2×D5×Dic3C2211yescharacteristic
36C2×D5×Dic3C2211yescharacteristic
37#6771—24no—
38#6719C2211yescharacteristic
39#6714C2211yescharacteristic
40#6712C2211yescharacteristic
41C4×Dic15C2211yescharacteristic
42C5×#217C2211yescharacteristic
43C5×(C2×D3)⋊C4C2211yescharacteristic
44C5×Dic3⋊C4C2211yescharacteristic
45C4×C5×Dic3C2211yescharacteristic
46Dic3⋊Dic5C2211yescharacteristic
47#6669C2211yescharacteristic
48#6667C2211yescharacteristic
49(C2×D3)⋊Dic5C2211yescharacteristic
50#6665C2211yescharacteristic
51#6665C2211yescharacteristic
52Dic3×Dic5C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5832—51nomaximal, Hall
55C2×#709—31no—
56C2×#709D311yescharacteristic, complemented
57C4×C5×D4—31no—
58#4086—31no—
59#4084—31no—
60C4×C22⋊D5—31no—
61C4×C22⋊D5—31no—
62#4041—31no—
63#4034—31no—
64#4031—31no—
65#4031—31no—
66#4030—31no—
67#4030—31no—
68C4×D20—31no—
69C42×D5—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C22×C3×D5C2311yescharacteristic
74C22×C3×D5C2311yescharacteristic
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78#1220—22no—
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C4×D15—22no—
83C5×#67—22no—
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C4×C5×D3—22no—
88C3×C22⋊D5—22no—
89C3×C22⋊D5—22no—
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92C3×D20—22no—
93C3×C4×D5—22no—
94C3×C4×D5D414yescomplemented
95C3×Dic10—22no—
96#1204—22no—
97#1203—22no—
98#1202—22no—
99#1202—22no—
100#1201—22no—
101#1201—22no—
102D5×Dic3—22no—
103D5×Dic3—22no—
104C2×C3×#41—51no—
105C2×#235—51no—
106#947—51no—
107#944—51no—
108#940—51no—
109#939—51no—
110#939—51no—
111#939—51no—
112#939—51no—
113#936—51no—
114C4×#67—51no—
115C4×#67—51no—
116C4×#67—51no—
117C4×#67D511yescharacteristic, complemented
118C2×C4×Dic3—51no—
119C2×C5×D4—31no—
120C22×C4×C5—31no—
121C22×C4×C5C2×D311yescharacteristic
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5C2×D311yescharacteristic
127C2×C22⋊D5C2×D311yescharacteristic
128#709—24no—
129#709—64no—
130C2×D20—31no—
131C2×D20—31no—
132C2×D20C2×D311yescharacteristic
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5C2×D311yescharacteristic
137C2×C4×D5C2×D311yescharacteristic
138C2×Dic10—31no—
139C2×Dic10C2×D311yescharacteristic
140C5×C4⋊C4—31no—
141C5×C22⋊C4—31no—
142C5×C22⋊C4—31no—
143C42×C5—31no—
144C22⋊Dic5—31no—
145C22⋊Dic5—31no—
146#685—31no—
147#685—31no—
148#685—31no—
149#685—31no—
150C4⋊Dic5—31no—
151#683—31no—
152#683—31no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—31no—
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×C3×D5—21no—
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5C2×D412yes—
173C3×C4×C5—21no—
174C3×C4×C5C2×D412yes—
175Dic15—21no—
176Dic15—21no—
177Dic15#4112yescomplemented
178C3×Dic5—21no—
179C3×Dic5C2×D412yes—
180C5×Dic3—21no—
181C5×Dic3—21no—
182C5×Dic3#4112yescomplemented
183C3×#41—104no—
184C2×C3×Q8—51no—
185C2×C3×D4—51no—
186C2×C3×D4—51no—
187C2×C3×D4—51no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4C2×D511yescharacteristic
191C2×#67—51no—
192C2×#67—51no—
193C2×#67—51no—
194C2×#67—51no—
195C2×#67—51no—
196C2×#67C2×D511yescharacteristic
197C22×Dic3—51no—
198C22×Dic3—51no—
199#235—104no—
200C2×D12—51no—
201C2×C4×D3—51no—
202C2×C4×D3C2×D511yescharacteristic
203C2×Dic6—51no—
204#217—51no—
205#217—51no—
206#217—51no—
207#217C2×D511yescharacteristic
208(C2×D3)⋊C4—51no—
209(C2×D3)⋊C4—51no—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4C2×D511yescharacteristic
212Dic3⋊C4—51no—
213Dic3⋊C4—51no—
214Dic3⋊C4—51no—
215Dic3⋊C4C2×D511yescharacteristic
216C4×Dic3—51no—
217C4×Dic3—51no—
218C4×Dic3—51no—
219C4×Dic3C2×D511yescharacteristic
220C23×C5—31no—
221C23×C5C22×D311yescharacteristic
222C22×D5—31no—
223C22×D5C22×D311yescharacteristic
224C22×D5C22×D311yescharacteristic
225C5×D4—62no—
226C2×C4×C5—22no—
227C2×C4×C5—31no—
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—22no—
235C22⋊D5—62no—
236C22⋊D5—62no—
237C22⋊D5—62no—
238C22⋊D5—62no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—31no—
242C2×Dic5C22×D311yescharacteristic
243C2×Dic5C22×D311yescharacteristic
244D20—22no—
245D20—62no—
246D20—62no—
247C4×D5—22no—
248C4×D5—62no—
249C4×D5—62no—
250C4×D5—62no—
251C4×D5#6714yescomplemented
252Dic10—22no—
253Dic10—62no—
254C2×#41—51no—
255C2×#41—151no—
256C4⋊Q8—151no—
257#127—151no—
258#124—151no—
259#124—151no—
260#121—151no—
261#121—151no—
262#121—151no—
263#121—151no—
264C4×D4—31no—
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—22no—
275C3×D5—41no—
276C5×D3—41no—
277C23×C3—51no—
278C23×C3—51no—
279C23×C3C22×D511yescharacteristic
280C22×D3—51no—
281C22×D3C22×D511yescharacteristic
282C3×Q8—102no—
283C3×D4—102no—
284C3×D4—102no—
285C3×D4—102no—
286C2×C3×C4—22no—
287C2×C3×C4—51no—
288C2×C3×C4—54no—
289C2×C3×C4—51no—
290C2×C3×C4—102no—
291C2×C3×C4C22×D511yescharacteristic
292C2×C3×C4C22×D511yescharacteristic
293#67—22no—
294#67—102no—
295#67—102no—
296#67—102no—
297#67—102no—
298#67—102no—
299C2×Dic3—51no—
300C2×Dic3—51no—
301C2×Dic3—51no—
302C2×Dic3—102no—
303C2×Dic3—102no—
304C2×Dic3C22×D511yescharacteristic
305C2×Dic3C22×D511yescharacteristic
306C2×Dic3C22×D511yescharacteristic
307D12—102no—
308C4×D3—22no—
309C4×D3—102no—
310Dic6—102no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—61no—
315C22×C5—61no—
316C22×C5—61no—
317C22×C5C23×D311yescharacteristic
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—21no—
322C2×D5—21no—
323C2×D5—61no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5C2×#6712yes—
327C4×C5—21no—
328C4×C5—32no—
329C4×C5—61no—
330C4×C5—61no—
331C4×C5C2×#6712yes—
332Dic5—21no—
333Dic5—32no—
334Dic5—61no—
335Dic5—61no—
336Dic5C2×#6712yes—
337#41—104no—
338#41—304no—
339C2×Q8—51no—
340C2×Q8—151no—
341C2×D4—31no—
342C2×D4—51no—
343C2×D4—51no—
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—51no—
353C22×C4—51no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4D3×D511yescharacteristic
358C4⋊C4—31no—
359C4⋊C4—151no—
360C4⋊C4—151no—
361C4⋊C4—151no—
362C22⋊C4—31no—
363C22⋊C4—31no—
364C22⋊C4—151no—
365C22⋊C4—151no—
366C22⋊C4—151no—
367C22⋊C4—151no—
368C22⋊C4—151no—
369C22⋊C4—151no—
370C42—31no—
371C42—151no—
372C42—151no—
373C42—151no—
374C3×C5#53211yescharacteristic, complemented, Hall
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—52no—
379C22×C3—101no—
380C22×C3—101no—
381C22×C3—101no—
382C22×C3—101no—
383C22×C3—101no—
384C22×C3C23×D511yescharacteristic
385C2×D3—21no—
386C2×D3—21no—
387C2×D3—21no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3—101no—
391C3×C4—21no—
392C3×C4—52no—
393C3×C4—101no—
394C3×C4D4×D512yes—
395Dic3—21no—
396Dic3—21no—
397Dic3—52no—
398Dic3—101no—
399Dic3—101no—
400Dic3#70912yescomplemented
401C2×C5—41no—
402C2×C5—121no—
403C2×C5D3×#4111yescharacteristic
404C2×C5D3×#4111yescharacteristic
405C2×C5C22×#6711yescharacteristic
406D5—22no—
407D5—41no—
408D5—121no—
409C23—31no—
410C23—51no—
411C23—51no—
412C23—151no—
413C23C2×D3×D511yescharacteristic
414Q8—102no—
415Q8—302no—
416D4—62no—
417D4—102no—
418D4—102no—
419D4—102no—
420D4—302no—
421D4—302no—
422D4—302no—
423D4—302no—
424D4—302no—
425D4—302no—
426C2×C4—22no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—51no—
431C2×C4—54no—
432C2×C4—51no—
433C2×C4—62no—
434C2×C4—102no—
435C2×C4—151no—
436C2×C4—151no—
437C2×C4—151no—
438C2×C4—302no—
439C2×C4—302no—
440C2×C4—302no—
441C2×C4C2×D3×D511yescharacteristic
442C2×C4C2×D3×D511yescharacteristic
443C2×C3—41no—
444C2×C3—102no—
445C2×C3—201no—
446C2×C3C2×#70911yescharacteristic
447C2×C3C2×D4×D511yescharacteristic
448C2×C3D5×#4111yescharacteristic
449D3—41no—
450D3—201no—
451C5#583211yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—52no—
456C22—61no—
457C22—61no—
458C22—61no—
459C22—101no—
460C22—101no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22C22×D3×D511yescharacteristic
468C4—21no—
469C4—32no—
470C4—52no—
471C4—61no—
472C4—61no—
473C4—101no—
474C4—152no—
475C4—301no—
476C4—301no—
477C4D5×#6712yes—
478C3#6588211yescharacteristic, complemented, Sylow
479C2—41no—
480C2—102no—
481C2—121no—
482C2—201no—
483C2—601no—
484C2D3×#70911yescharacteristic
485C2#9201611yescharacteristic
486C2C2×D5×#6711yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#532
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#709C2semidirect
2. C2×#6771C2semidirect
3. C4×#1220C2semidirect
4. C4×C5×#67C2semidirect
5. #91567C2semidirect
6. #91550C2semidirect
7. #91549C2semidirect
8. #91534C2semidirect
9. C4×#1202C2semidirect
10. C4×#1201C2semidirect
11. #91409C2semidirect
12. #91408C2semidirect
13. C4×D5×Dic3C2semidirect
14. #91327C2semidirect
15. #91326C2semidirect
56. C2×#709D3semidirect
94. C3×C4×D5D4semidirect
117. C4×#67D5semidirect
177. Dic15#41semidirect
182. C5×Dic3#41semidirect
251. C4×D5#67semidirect
374. C3×C5#532semidirect
400. Dic3#709semidirect
451. C5#5832semidirect
478. C3#65882semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#7092
C2×#67712
C4×#12202
C4×C5×#672
#915672
#915502
#915492
#915342
C4×#12022
C4×#12012
#914092
#914082
C4×D5×Dic32
#913272
#913262
#658823
#58325