Finite Group Databasebeta

← #11753080

Subgroups — #11753080

Order 960.

624 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6780C211yesmaximal, characteristic, complemented
2C2×#6771C211yesmaximal, characteristic, complemented
3#91770C211yesmaximal, characteristic, complemented
4C5×#884C211yesmaximal, characteristic, complemented
5C3×#4030C211yesmaximal, characteristic, complemented
6#91571C211yesmaximal, characteristic, complemented
7#91567C211yesmaximal, characteristic, complemented
8#91567C211yesmaximal, characteristic, complemented
9#91463C211yesmaximal, characteristic, complemented
10#91461C211yesmaximal, characteristic, complemented
11#91441C211yesmaximal, characteristic, complemented
12#91440C211yesmaximal, characteristic, complemented
13#91416C211yesmaximal, characteristic, complemented
14#91409C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#65933—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×C22⋊D5C2211yescharacteristic
26C2×C3×D20C2211yescharacteristic
27C2×C3×C4×D5C2211yescharacteristic
28C2×#1204C2211yescharacteristic
29C2×#1203C2211yescharacteristic
30C2×#1203C2211yescharacteristic
31C2×#1202C2211yescharacteristic
32C2×#1202C2211yescharacteristic
33C2×#1201C2211yescharacteristic
34C2×#1201C2211yescharacteristic
35C2×#1201C2211yescharacteristic
36C2×#1201C2211yescharacteristic
37C2×D3×Dic5C2211yescharacteristic
38#6780—24no—
39C2×D5×Dic3C2211yescharacteristic
40#6771—24no—
41C3×C5×C22⋊C4C2211yescharacteristic
42#6714C2211yescharacteristic
43#6712C2211yescharacteristic
44C4×Dic15C2211yescharacteristic
45C5×(C2×D3)⋊C4C2211yescharacteristic
46C5×Dic3⋊C4C2211yescharacteristic
47C3×#685C2211yescharacteristic
48C3×#683C2211yescharacteristic
49#6669C2211yescharacteristic
50(C2×D3)⋊Dic5C2211yescharacteristic
51#6665C2211yescharacteristic
52Dic3×Dic5C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5599—51nomaximal, Hall
55C2×#711—31no—
56C2×#709—31no—
57C5×#121—31no—
58#4086—31no—
59#4086—31no—
60#4086—31no—
61#4085—31no—
62#4085—31no—
63C4×C22⋊D5—31no—
64#4041—31no—
65#4033—31no—
66#4030—31no—
67#4030D311yescharacteristic, complemented
68#4027—31no—
69#4027—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C22×C5×D3C2311yescharacteristic
74C22×C3×D5C2311yescharacteristic
75C22×C3×D5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78#1220—22no—
79C2×Dic15—22no—
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83C4×D15—22no—
84C5×#67—22no—
85C5×#67—41no—
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C5×D12—41no—
89C4×C5×D3—22no—
90C3×C22⋊D5—22no—
91C3×C22⋊D5—41no—
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94C3×D20—41no—
95C3×C4×D5—22no—
96#1204D414yescomplemented
97#1203—22no—
98#1203—41no—
99#1202—22no—
100#1202—41no—
101#1201—22no—
102#1201—22no—
103#1201—22no—
104#1201—22no—
105D3×Dic5—22no—
106D5×Dic3—22no—
107C2×#237—51no—
108C2×#235—51no—
109C3×#121—51no—
110#940—51no—
111#940—51no—
112#940—51no—
113#939—51no—
114#939—51no—
115C4×#67—51no—
116#895—51no—
117#887—51no—
118#884—51no—
119#884D511yescharacteristic, complemented
120#67⋊C4—51no—
121#67⋊C4—51no—
122C2×C5×D4—31no—
123C2×C5×D4—31no—
124C2×C5×D4—31no—
125C22×C4×C5—31no—
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C2×C22⋊D5—31no—
129C2×C22⋊D5—31no—
130C2×C22⋊D5—31no—
131C2×C22⋊D5—31no—
132C2×C22⋊D5—31no—
133C2×C22⋊D5C2×D311yescharacteristic
134C2×C22⋊D5C2×D311yescharacteristic
135C22×Dic5—31no—
136C22×Dic5—31no—
137#711—64no—
138#709—64no—
139C2×D20—31no—
140C2×D20—31no—
141C2×D20C2×D311yescharacteristic
142C2×C4×D5—31no—
143C2×C4×D5—31no—
144C2×C4×D5C2×D311yescharacteristic
145C2×Dic10—31no—
146C5×C4⋊C4—31no—
147C5×C22⋊C4—31no—
148C5×C22⋊C4C2×D311yescharacteristic
149C22⋊Dic5—31no—
150#685—31no—
151#685—31no—
152#685C2×D311yescharacteristic
153#683—31no—
154#683—31no—
155#683C2×D311yescharacteristic
156C4×Dic5—31no—
157C4×Dic5—31no—
158C4×Dic5—31no—
159#550—151noSylow
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5C2411yescharacteristic
164C2×D15—21no—
165C2×D15—21no—
166C2×D15—21no—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C5×D3—21no—
170C2×C5×D3—21no—
171C2×C5×D3—21no—
172C2×C5×D3—21no—
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181Dic15—21no—
182Dic15C2×D412yes—
183Dic15#4112yescomplemented
184C3×Dic5—21no—
185C3×Dic5C2×D412yes—
186C5×Dic3—21no—
187C5×Dic3C2×D412yes—
188C2×C3×D4—51no—
189C2×C3×D4—51no—
190C2×C3×D4—51no—
191C22×C3×C4—51no—
192C2×#67—51no—
193C2×#67—51no—
194C2×#67—51no—
195C2×#67—51no—
196C2×#67—51no—
197C2×#67—51no—
198C2×#67—51no—
199C2×#67C2×D511yescharacteristic
200C2×#67C2×D511yescharacteristic
201C22×Dic3—51no—
202C22×Dic3—51no—
203#237—104no—
204#235—104no—
205C2×D12—51no—
206C2×D12—51no—
207C2×D12C2×D511yescharacteristic
208C2×C4×D3—51no—
209C2×C4×D3—51no—
210C2×C4×D3C2×D511yescharacteristic
211C2×Dic6—51no—
212C3×C4⋊C4—51no—
213C3×C22⋊C4—51no—
214C3×C22⋊C4C2×D511yescharacteristic
215#217—51no—
216(C2×D3)⋊C4—51no—
217(C2×D3)⋊C4—51no—
218(C2×D3)⋊C4C2×D511yescharacteristic
219Dic3⋊C4—51no—
220Dic3⋊C4—51no—
221Dic3⋊C4C2×D511yescharacteristic
222C4×Dic3—51no—
223C4×Dic3—51no—
224C4×Dic3—51no—
225C23×C5—31no—
226C23×C5—31no—
227C23×C5C22×D311yescharacteristic
228C22×D5—31no—
229C22×D5C22×D311yescharacteristic
230C22×D5C22×D311yescharacteristic
231C5×D4—62no—
232C5×D4—121no—
233C5×D4—121no—
234C2×C4×C5—31no—
235C2×C4×C5—31no—
236C2×C4×C5—62no—
237C2×C4×C5C22×D311yescharacteristic
238C2×C4×C5C22×D311yescharacteristic
239C22⋊D5—22no—
240C22⋊D5—41no—
241C22⋊D5—62no—
242C22⋊D5—62no—
243C22⋊D5—62no—
244C22⋊D5—62no—
245C22⋊D5—62no—
246C22⋊D5—62no—
247C22⋊D5—121no—
248C2×Dic5—31no—
249C2×Dic5—31no—
250C2×Dic5—31no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253C2×Dic5C22×D311yescharacteristic
254C2×Dic5C22×D311yescharacteristic
255D20—41no—
256D20—62no—
257D20—121no—
258C4×D5—22no—
259C4×D5—62no—
260C4×D5—62no—
261Dic10—34no—
262C2×#41—151no—
263C2×#41—151no—
264#127—151no—
265#127—151no—
266#127—151no—
267#121—31no—
268#121—51no—
269#121—151no—
270#121—151no—
271#121—151no—
272#121—151no—
273C4×Q8—151no—
274C4×D4—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C3×C5—41no—
278C2×C3×C5C22×D411yescharacteristic
279C2×C3×C5C2×#4111yescharacteristic
280C2×C3×C5H(5,𝔽2)11yescharacteristic
281D15—41no—
282C3×D5—41no—
283C3×D5—41no—
284C5×D3—41no—
285C5×D3—41no—
286C23×C3—51no—
287C23×C3—51no—
288C23×C3C22×D511yescharacteristic
289C22×D3—51no—
290C22×D3C22×D511yescharacteristic
291C22×D3C22×D511yescharacteristic
292C3×D4—102no—
293C3×D4—201no—
294C3×D4—201no—
295C2×C3×C4—51no—
296C2×C3×C4—51no—
297C2×C3×C4—102no—
298C2×C3×C4C22×D511yescharacteristic
299C2×C3×C4C22×D511yescharacteristic
300#67—22no—
301#67—41no—
302#67—102no—
303#67—102no—
304#67—102no—
305#67—102no—
306#67—102no—
307#67—102no—
308#67—201no—
309C2×Dic3—51no—
310C2×Dic3—51no—
311C2×Dic3—51no—
312C2×Dic3—102no—
313C2×Dic3—102no—
314C2×Dic3C22×D511yescharacteristic
315C2×Dic3C22×D511yescharacteristic
316D12—41no—
317D12—102no—
318D12—201no—
319C4×D3—22no—
320C4×D3—102no—
321C4×D3—102no—
322Dic6—54no—
323C22×C5—21no—
324C22×C5—21no—
325C22×C5—21no—
326C22×C5—61no—
327C22×C5—61no—
328C22×C5—61no—
329C22×C5—61no—
330C22×C5—61no—
331C22×C5—61no—
332C22×C5C23×D311yescharacteristic
333C2×D5—21no—
334C2×D5—21no—
335C2×D5—21no—
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—21no—
339C2×D5—61no—
340C2×D5—61no—
341C2×D5—61no—
342C4×C5—21no—
343C4×C5—21no—
344C4×C5—32no—
345C4×C5—61no—
346Dic5—21no—
347Dic5—32no—
348Dic5—32no—
349Dic5—61no—
350Dic5D3×D412yes—
351#41—304no—
352#41—304no—
353C2×Q8—151no—
354C2×D4—31no—
355C2×D4—31no—
356C2×D4—31no—
357C2×D4—51no—
358C2×D4—51no—
359C2×D4—51no—
360C2×D4—151no—
361C2×D4—151no—
362C2×D4—151no—
363C2×D4—151no—
364C2×D4—151no—
365C2×D4—151no—
366C2×D4—151no—
367C2×D4—151no—
368C2×D4—151no—
369C22×C4—31no—
370C22×C4—51no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4—151no—
375C4⋊C4—31no—
376C4⋊C4—51no—
377C4⋊C4—151no—
378C4⋊C4—151no—
379C22⋊C4—31no—
380C22⋊C4—51no—
381C22⋊C4—151no—
382C22⋊C4—151no—
383C22⋊C4—151no—
384C22⋊C4D3×D511yescharacteristic
385C42—151no—
386C42—151no—
387C42—151no—
388C3×C5#55011yescharacteristic, complemented, Hall
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—101no—
393C22×C3—101no—
394C22×C3—101no—
395C22×C3—101no—
396C22×C3—101no—
397C22×C3—101no—
398C22×C3C23×D511yescharacteristic
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—21no—
402C2×D3—21no—
403C2×D3—21no—
404C2×D3—21no—
405C2×D3—101no—
406C2×D3—101no—
407C2×D3—101no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—52no—
411C3×C4—101no—
412Dic3—21no—
413Dic3—52no—
414Dic3—52no—
415Dic3—101no—
416Dic3D4×D512yes—
417C2×C5—41no—
418C2×C5—121no—
419C2×C5—121no—
420C2×C5C2×D3×D411yescharacteristic
421C2×C5#100411yescharacteristic
422C2×C5D3×#4111yescharacteristic
423D5—41no—
424D5—41no—
425D5—121no—
426C23—31no—
427C23—31no—
428C23—51no—
429C23—51no—
430C23—151no—
431C23C2×D3×D511yescharacteristic
432Q8—154no—
433D4—62no—
434D4—102no—
435D4—121no—
436D4—121no—
437D4—201no—
438D4—201no—
439D4—302no—
440D4—302no—
441D4—302no—
442D4—302no—
443D4—302no—
444D4—302no—
445D4—302no—
446D4—601no—
447D4—601no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—51no—
451C2×C4—51no—
452C2×C4—62no—
453C2×C4—102no—
454C2×C4—151no—
455C2×C4—151no—
456C2×C4—151no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4—302no—
460C2×C4—302no—
461C2×C4C2×D3×D511yescharacteristic
462C2×C4C2×D3×D511yescharacteristic
463C2×C3—41no—
464C2×C3—201no—
465C2×C3—201no—
466C2×C3C2×D4×D511yescharacteristic
467C2×C3#414411yescharacteristic
468C2×C3D5×#4111yescharacteristic
469D3—41no—
470D3—41no—
471D3—201no—
472C5#559911yescharacteristic, complemented, Sylow
473C22—21no—
474C22—21no—
475C22—21no—
476C22—61no—
477C22—61no—
478C22—61no—
479C22—61no—
480C22—61no—
481C22—61no—
482C22—101no—
483C22—101no—
484C22—101no—
485C22—101no—
486C22—101no—
487C22—101no—
488C22—301no—
489C22—301no—
490C22—301no—
491C22C22×D3×D511yescharacteristic
492C4—21no—
493C4—21no—
494C4—32no—
495C4—52no—
496C4—61no—
497C4—101no—
498C4—152no—
499C4—152no—
500C4—301no—
501C3#6593311yescharacteristic, complemented, Sylow
502C2—41no—
503C2—121no—
504C2—121no—
505C2—201no—
506C2—201no—
507C2—601no—
508C2#9201611yescharacteristic
509C2D3×D4×D511yescharacteristic
510C2#9202511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#550
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×#6771C2semidirect
3. #91770C2semidirect
4. C5×#884C2semidirect
5. C3×#4030C2semidirect
6. #91571C2semidirect
7. #91567C2semidirect
8. #91567C2semidirect
9. #91463C2semidirect
10. #91461C2semidirect
11. #91441C2semidirect
12. #91440C2semidirect
13. #91416C2semidirect
14. #91409C2semidirect
15. #91325C2semidirect
67. #4030D3semidirect
96. #1204D4semidirect
119. #884D5semidirect
183. Dic15#41semidirect
388. C3×C5#550semidirect
472. C5#5599semidirect
501. C3#65933semidirect

Maximal subgroups

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

subgroupindex
C2×#67802
C2×#67712
#917702
C5×#8842
C3×#40302
#915712
#915672
#914632
#914612
#914412
#914402
#914162
#914092
#913252
#659333
#55995