Finite Group Databasebeta

← #11752870

Subgroups — #11752870

Order 960.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6780C211yesmaximal, characteristic, complemented
2C2×#6779C211yesmaximal, characteristic, complemented
3#91775C211yesmaximal, characteristic, complemented
4C5×#886C211yesmaximal, characteristic, complemented
5C3×#4027C211yesmaximal, characteristic, complemented
6#91566C211yesmaximal, characteristic, complemented
7C2×#6668C211yesmaximal, characteristic, complemented
8#91468C211yesmaximal, characteristic, complemented
9#91448C211yesmaximal, characteristic, complemented
10#91419C211yesmaximal, characteristic, complemented
11#91417C211yesmaximal, characteristic, complemented
12#91414C211yesmaximal, characteristic, complemented
13#91413C211yesmaximal, characteristic, complemented
14D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
15#91405C211yesmaximal, characteristic, complemented
16#65989—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C2×C5×#67C2211yescharacteristic
20C22×C5×Dic3C2211yescharacteristic
21C2×C3×C22⋊D5C2211yescharacteristic
22C22×C3×Dic5C2211yescharacteristic
23C2×C3×C4×D5C2211yescharacteristic
24C2×#1204C2211yescharacteristic
25C2×#1204C2211yescharacteristic
26C2×#1203C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×#1201C2211yescharacteristic
29C2×#1200C2211yescharacteristic
30C2×D3×Dic5C2211yescharacteristic
31#6780—24no—
32#6779—24no—
33C2×D5×Dic3C2211yescharacteristic
34C2×D5×Dic3C2211yescharacteristic
35C3×C5×C22⋊C4C2211yescharacteristic
36#6714C2211yescharacteristic
37#6714C2211yescharacteristic
38C4⋊Dic15C2211yescharacteristic
39C4⋊Dic15C2211yescharacteristic
40C5×(C2×D3)⋊C4C2211yescharacteristic
41C5×(C2×D3)⋊C4C2211yescharacteristic
42C5×C4⋊Dic3C2211yescharacteristic
43C5×C4⋊Dic3C2211yescharacteristic
44C3×#685C2211yescharacteristic
45C3×#683C2211yescharacteristic
46C3×C4×Dic5C2211yescharacteristic
47#6668C2211yescharacteristic
48#6668C2211yescharacteristic
49#6668C2211yescharacteristic
50#6668C2211yescharacteristic
51#6668C2211yescharacteristic
52#6667C2211yescharacteristic
53(C2×D3)⋊Dic5C2211yescharacteristic
54#5555—51nomaximal, Hall
55C2×#711—31no—
56C2×#709—31no—
57C5×#123—31no—
58#4085—31no—
59C2×#683—31no—
60#4042—31no—
61#4040—31no—
62D5×C4⋊C4—31no—
63#4034—31no—
64#4032—31no—
65#4030—31no—
66#4029—31no—
67#4027—31no—
68#4027D311yescharacteristic, complemented
69#4024—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C22×C3×D5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76#1220—22no—
77C2×Dic15—22no—
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C5×#67—22no—
82C2×C5×Dic3—22no—
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C3×C22⋊D5D414yescomplemented
87C2×C3×Dic5—22no—
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91C3×C4×D5—22no—
92#1204—22no—
93#1204—22no—
94#1203—22no—
95#1202—22no—
96#1201—22no—
97#1200—22no—
98D3×Dic5—22no—
99D5×Dic3—22no—
100D5×Dic3—22no—
101C2×#237—51no—
102C2×#237—51no—
103C3×C4×D4—51no—
104#930—51no—
105#930—51no—
106C2×C4⋊Dic3—51no—
107C2×C4⋊Dic3—51no—
108#897—51no—
109#897—51no—
110#886—51no—
111#886—51no—
112#886—51no—
113#886D511yescharacteristic, complemented
114C4×D12—51no—
115#869—51no—
116C2×C5×D4—31no—
117C22×C4×C5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5—31no—
121C2×C22⋊D5C2×D311yescharacteristic
122C22×Dic5—31no—
123C22×Dic5—31no—
124C22×Dic5C2×D311yescharacteristic
125#711—64no—
126#709—64no—
127C2×D20—31no—
128C2×C4×D5—31no—
129C2×C4×D5—31no—
130C2×C4×D5—31no—
131C2×C4×D5C2×D311yescharacteristic
132C2×Dic10—31no—
133C2×Dic10—31no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—31no—
136C5×C22⋊C4—31no—
137C5×C22⋊C4—31no—
138C5×C22⋊C4C2×D311yescharacteristic
139C22⋊Dic5—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685C2×D311yescharacteristic
144C4⋊Dic5—31no—
145C4⋊Dic5—31no—
146#683—31no—
147#683—31no—
148#683—31no—
149#683—31no—
150#683—31no—
151#683C2×D311yescharacteristic
152C4×Dic5C2×D311yescharacteristic
153#547—151noSylow
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5C2×D412yes—
157C22×C3×C5C2411yescharacteristic
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×C5×D3—21no—
162C2×C5×D3—21no—
163C2×C5×D3—21no—
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C2×C3×D5C2×D412yes—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169Dic15—21no—
170Dic15—21no—
171Dic15—21no—
172C3×Dic5—21no—
173C3×Dic5C2×D412yes—
174C3×Dic5#4112yescomplemented
175C5×Dic3—21no—
176C5×Dic3—21no—
177C5×Dic3—21no—
178C2×C3×D4—51no—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67—51no—
184C2×#67C2×D511yescharacteristic
185C22×Dic3—51no—
186C22×Dic3—51no—
187C22×Dic3—51no—
188C22×Dic3C2×D511yescharacteristic
189#237—104no—
190#237—104no—
191C2×D12—51no—
192C2×C4×D3—51no—
193C2×C4×D3—51no—
194C2×Dic6—51no—
195C2×Dic6—51no—
196C3×C4⋊C4—51no—
197C3×C22⋊C4—51no—
198C3×C22⋊C4C2×D511yescharacteristic
199C3×C42—51no—
200(C2×D3)⋊C4—51no—
201(C2×D3)⋊C4—51no—
202(C2×D3)⋊C4—51no—
203(C2×D3)⋊C4—51no—
204(C2×D3)⋊C4C2×D511yescharacteristic
205(C2×D3)⋊C4C2×D511yescharacteristic
206C4⋊Dic3—51no—
207C4⋊Dic3—51no—
208C4⋊Dic3—51no—
209C4⋊Dic3—51no—
210C4⋊Dic3—51no—
211C4⋊Dic3—51no—
212C4⋊Dic3—51no—
213C4⋊Dic3C2×D511yescharacteristic
214C4⋊Dic3C2×D511yescharacteristic
215C23×C5—31no—
216C23×C5C22×D311yescharacteristic
217C22×D5—31no—
218C22×D5C22×D311yescharacteristic
219C5×D4—62no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—62no—
224C2×C4×C5C22×D311yescharacteristic
225C2×C4×C5C22×D311yescharacteristic
226C22⋊D5—62no—
227C22⋊D5—62no—
228C22⋊D5—62no—
229C22⋊D5D1214yescomplemented
230C2×Dic5—22no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5—31no—
234C2×Dic5—62no—
235C2×Dic5—62no—
236C2×Dic5C22×D311yescharacteristic
237C2×Dic5C22×D311yescharacteristic
238C2×Dic5C22×D311yescharacteristic
239D20—62no—
240C4×D5—22no—
241C4×D5—62no—
242C4×D5—62no—
243C4×D5—62no—
244Dic10—62no—
245Dic10—62no—
246C2×#41—151no—
247C2×#41—151no—
248C4⋊Q8—151no—
249#123—31no—
250#123—151no—
251#123—151no—
252#123—151no—
253C22⋊Q8—151no—
254C22⋊Q8—151no—
255#121—151no—
256#121—151no—
257C4×D4—51no—
258C4×D4—151no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—151no—
261C2×C3×C5—22no—
262C2×C3×C5C22×D411yescharacteristic
263C2×C3×C5C2×#4111yescharacteristic
264C2×C3×C52−1+411yescharacteristic
265D15—41no—
266C3×D5—22no—
267C5×D3—41no—
268C23×C3—51no—
269C23×C3C22×D511yescharacteristic
270C22×D3—51no—
271C22×D3C22×D511yescharacteristic
272C3×D4—54no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—102no—
277C2×C3×C4—102no—
278C2×C3×C4C22×D511yescharacteristic
279C2×C3×C4C22×D511yescharacteristic
280#67—22no—
281#67—102no—
282#67—102no—
283#67—102no—
284C2×Dic3—22no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—102no—
289C2×Dic3—102no—
290C2×Dic3—102no—
291C2×Dic3C22×D511yescharacteristic
292C2×Dic3C22×D511yescharacteristic
293C2×Dic3C22×D511yescharacteristic
294D12—102no—
295C4×D3—102no—
296C4×D3—102no—
297Dic6—102no—
298Dic6—102no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—61no—
302C22×C5—61no—
303C22×C5—61no—
304C22×C5C2×D1212yes—
305C22×C5C23×D311yescharacteristic
306C2×D5—21no—
307C2×D5—21no—
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—61no—
311C2×D5C2×D1212yes—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317Dic5—21no—
318Dic5—61no—
319Dic5—61no—
320Dic5—61no—
321Dic5C2×D1212yes—
322Dic5#23712yescomplemented
323#41—304no—
324#41—304no—
325C2×Q8—151no—
326C2×Q8—151no—
327C2×D4—31no—
328C2×D4—51no—
329C2×D4—151no—
330C2×D4—151no—
331C2×D4—151no—
332C2×D4—151no—
333C22×C4—31no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—151no—
337C22×C4—151no—
338C22×C4—151no—
339C22×C4—151no—
340C22×C4—151no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—51no—
344C4⋊C4—151no—
345C4⋊C4—151no—
346C4⋊C4—151no—
347C4⋊C4—151no—
348C4⋊C4—151no—
349C4⋊C4—151no—
350C4⋊C4—151no—
351C22⋊C4—31no—
352C22⋊C4—31no—
353C22⋊C4—51no—
354C22⋊C4—151no—
355C22⋊C4—151no—
356C22⋊C4—151no—
357C22⋊C4—151no—
358C22⋊C4D3×D511yescharacteristic
359C42—51no—
360C3×C5#54711yescharacteristic, complemented, Hall
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—52no—
364C22×C3—101no—
365C22×C3—101no—
366C22×C3D4×D512yes—
367C22×C3C23×D511yescharacteristic
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—101no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—52no—
377C3×C4—52no—
378C3×C4—101no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—101no—
383Dic3—101no—
384Dic3—101no—
385C2×C5—22no—
386C2×C5—121no—
387C2×C5C22×D1211yescharacteristic
388C2×C5C2×#23711yescharacteristic
389C2×C5#101011yescharacteristic
390D5—22no—
391D5—121no—
392C23—31no—
393C23—51no—
394C23—151no—
395C23C2×D3×D511yescharacteristic
396Q8—302no—
397Q8—302no—
398D4—54no—
399D4—62no—
400D4—302no—
401D4—302no—
402D4—302no—
403D4—302no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—51no—
408C2×C4—51no—
409C2×C4—51no—
410C2×C4—62no—
411C2×C4—102no—
412C2×C4—102no—
413C2×C4—151no—
414C2×C4—151no—
415C2×C4—151no—
416C2×C4—302no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4—302no—
420C2×C4—302no—
421C2×C4C2×D3×D511yescharacteristic
422C2×C4C2×D3×D511yescharacteristic
423C2×C3—22no—
424C2×C3—102no—
425C2×C3C2×D4×D511yescharacteristic
426C2×C3D5×#4111yescharacteristic
427C2×C3#415011yescharacteristic
428D3—41no—
429D3—201no—
430C5#555511yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—52no—
434C22—61no—
435C22—61no—
436C22—61no—
437C22—101no—
438C22—101no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22D5×D1212yes—
443C22C22×D3×D511yescharacteristic
444C4—21no—
445C4—21no—
446C4—52no—
447C4—52no—
448C4—61no—
449C4—61no—
450C4—61no—
451C4—101no—
452C4—301no—
453C4—301no—
454C4—301no—
455C3#6598911yescharacteristic, complemented, Sylow
456C2—22no—
457C2—102no—
458C2—121no—
459C2—601no—
460C2C2×D5×D1211yescharacteristic
461C2#9202011yescharacteristic
462C2D5×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#547
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×#6779C2semidirect
3. #91775C2semidirect
4. C5×#886C2semidirect
5. C3×#4027C2semidirect
6. #91566C2semidirect
7. C2×#6668C2semidirect
8. #91468C2semidirect
9. #91448C2semidirect
10. #91419C2semidirect
11. #91417C2semidirect
12. #91414C2semidirect
13. #91413C2semidirect
14. D5×C4⋊Dic3C2semidirect
15. #91405C2semidirect
68. #4027D3semidirect
86. C3×C22⋊D5D4semidirect
113. #886D5semidirect
174. C3×Dic5#41semidirect
229. C22⋊D5D12semidirect
322. Dic5#237semidirect
360. C3×C5#547semidirect
430. C5#5555semidirect
455. C3#65989semidirect

Maximal subgroups

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

subgroupindex
C2×#67802
C2×#67792
#917752
C5×#8862
C3×#40272
#915662
C2×#66682
#914682
#914482
#914192
#914172
#914142
#914132
D5×C4⋊Dic32
#914052
#659893
#55555