Finite Group Databasebeta

← #11754817

Subgroups — #11754817

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×#6819C211yesmaximal, characteristic, complemented
2C2×#6779C211yesmaximal, characteristic, complemented
3C5×#935C211yesmaximal, characteristic, complemented
4C3×#4085C211yesmaximal, characteristic, complemented
5#91576C211yesmaximal, characteristic, complemented
6#91562C211yesmaximal, characteristic, complemented
7#91559C211yesmaximal, characteristic, complemented
8#91552C211yesmaximal, characteristic, complemented
9C2×#6668C211yesmaximal, characteristic, complemented
10#91537C211yesmaximal, characteristic, complemented
11#91533C211yesmaximal, characteristic, complemented
12#91431C211yesmaximal, characteristic, complemented
13#91404C211yesmaximal, characteristic, complemented
14#91354C211yesmaximal, characteristic, complemented
15#91328C211yesmaximal, characteristic, complemented
16#65989—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C22×Dic15C2211yescharacteristic
21C22×Dic15C2211yescharacteristic
22#6819—24no—
23C2×C4×D15C2211yescharacteristic
24C2×Dic30C2211yescharacteristic
25C22×C5×Dic3C2211yescharacteristic
26C2×C3×C22⋊D5C2211yescharacteristic
27C2×C3×C22⋊D5C2211yescharacteristic
28C22×C3×Dic5C2211yescharacteristic
29C2×#1204C2211yescharacteristic
30C2×#1202C2211yescharacteristic
31C2×#1200C2211yescharacteristic
32C2×#1200C2211yescharacteristic
33#6779—24no—
34C2×D5×Dic3C2211yescharacteristic
35C5×#217C2211yescharacteristic
36C5×#217C2211yescharacteristic
37C5×#217C2211yescharacteristic
38C5×Dic3⋊C4C2211yescharacteristic
39C5×Dic3⋊C4C2211yescharacteristic
40C3×C22⋊Dic5C2211yescharacteristic
41C3×#685C2211yescharacteristic
42C3×#683C2211yescharacteristic
43Dic3⋊Dic5C2211yescharacteristic
44Dic3⋊Dic5C2211yescharacteristic
45#6669C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48#6668C2211yescharacteristic
49#6668C2211yescharacteristic
50#6667C2211yescharacteristic
51#6665C2211yescharacteristic
52#6665C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5611—51nomaximal, Hall
55C2×#711—31no—
56C2×#709—31no—
57C5×#123—31no—
58#4085D311yescharacteristic, complemented
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#4027—31no—
69#4024—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×C3×D5C2311yescharacteristic
74C3×C5×D4—22no—
75C2×C3×C4×C5C2311yescharacteristic
76#1220—22no—
77#1220D414yescomplemented
78C2×Dic15—22no—
79C2×Dic15—22no—
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83C4×D15—22no—
84Dic30—22no—
85C2×C5×Dic3—22no—
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C2×C5×Dic3C2311yescharacteristic
89C2×C5×Dic3C2311yescharacteristic
90C3×C22⋊D5—22no—
91C3×C22⋊D5—22no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5C2311yescharacteristic
94C2×C3×Dic5C2311yescharacteristic
95C2×C3×Dic5C2311yescharacteristic
96#1204—22no—
97#1202—22no—
98#1200—22no—
99#1200—22no—
100D5×Dic3—22no—
101C2×#237—51no—
102C2×#237—51no—
103C3×#121—51no—
104#938—51no—
105#935—51no—
106#935D511yescharacteristic, complemented
107D4×Dic3—51no—
108C4×#67—51no—
109C2×C4⋊Dic3—51no—
110D3×C4⋊C4—51no—
111#888—51no—
112#883—51no—
113#883—51no—
114#878—51no—
115#878—51no—
116C2×C5×D4C2×D311yescharacteristic
117C22×C4×C5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5C2×D311yescharacteristic
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×D5—31no—
132C2×Dic10—31no—
133C2×Dic10—31no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—31no—
136C5×C22⋊C4—31no—
137C5×C22⋊C4—31no—
138C5×C22⋊C4—31no—
139C22⋊Dic5C2×D311yescharacteristic
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×Dic5—31no—
153#547—151noSylow
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5C2×D412yes—
160C22×C3×C5C2411yescharacteristic
161C2×D15—21no—
162C2×D15—21no—
163C2×D15C2×D412yes—
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C2×C3×D5—21no—
167C3×C4×C5—21no—
168Dic15—21no—
169Dic15—21no—
170Dic15C2×D412yes—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5#4112yescomplemented
174C5×Dic3—21no—
175C5×Dic3—21no—
176C5×Dic3—21no—
177C5×Dic3—21no—
178C2×C3×D4—51no—
179C2×C3×D4—51no—
180C2×C3×D4C2×D511yescharacteristic
181C22×C3×C4—51no—
182C2×#67—51no—
183C2×#67—51no—
184C2×#67—51no—
185C22×Dic3—51no—
186C22×Dic3—51no—
187C22×Dic3—51no—
188C22×Dic3C2×D511yescharacteristic
189#237—104no—
190#237—104no—
191C2×C4×D3—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⋊C4—51no—
199#217—51no—
200#217—51no—
201#217C2×D511yescharacteristic
202#217C2×D511yescharacteristic
203#217C2×D511yescharacteristic
204(C2×D3)⋊C4—51no—
205C4⋊Dic3—51no—
206C4⋊Dic3—51no—
207C4⋊Dic3—51no—
208C4⋊Dic3—51no—
209Dic3⋊C4—51no—
210Dic3⋊C4—51no—
211Dic3⋊C4—51no—
212Dic3⋊C4C2×D511yescharacteristic
213Dic3⋊C4C2×D511yescharacteristic
214C4×Dic3—51no—
215C23×C5C22×D311yescharacteristic
216C23×C5C22×D311yescharacteristic
217C22×D5—31no—
218C22×D5C22×D311yescharacteristic
219C5×D4—22no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—62no—
225C2×C4×C5C22×D311yescharacteristic
226C22⋊D5—22no—
227C22⋊D5—22no—
228C22⋊D5—34no—
229C22⋊D5—62no—
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—62no—
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—51no—
256#121—151no—
257C4×D4—151no—
258C4×D4—151no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—151no—
261C2×C3×C5—22no—
262C2×C3×C5—41no—
263C2×C3×C5C22×D411yescharacteristic
264C2×C3×C5C2×#4111yescharacteristic
265C2×C3×C52−1+411yescharacteristic
266D15—22no—
267C3×D5—41no—
268C23×C3—51no—
269C23×C3C22×D511yescharacteristic
270C23×C3C22×D511yescharacteristic
271C22×D3—51no—
272C3×D4—22no—
273C3×D4—102no—
274C3×D4—102no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—102no—
279C2×C3×C4C22×D511yescharacteristic
280#67—54no—
281#67—102no—
282#67—102no—
283C2×Dic3—22no—
284C2×Dic3—51no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—102no—
288C2×Dic3—102no—
289C2×Dic3—102no—
290C2×Dic3C22×D511yescharacteristic
291C2×Dic3C22×D511yescharacteristic
292C2×Dic3C22×D511yescharacteristic
293C2×Dic3C22×D511yescharacteristic
294C4×D3—102no—
295C4×D3—102no—
296C4×D3—102no—
297Dic6—102no—
298Dic6—102no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5D3×D412yes—
305C22×C5C23×D311yescharacteristic
306C2×D5—21no—
307C2×D5—21no—
308C2×D5—21no—
309C2×D5—32no—
310C2×D5—61no—
311C2×D5—61no—
312C4×C5—21no—
313C4×C5—61no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317Dic5—21no—
318Dic5—21no—
319Dic5—32no—
320Dic5—61no—
321Dic5—61no—
322Dic5#23712yescomplemented
323#41—304no—
324#41—304no—
325C2×Q8—151no—
326C2×Q8—151no—
327C2×D4—51no—
328C2×D4—51no—
329C2×D4—151no—
330C2×D4—151no—
331C2×D4—151no—
332C2×D4D3×D511yescharacteristic
333C22×C4—31no—
334C22×C4—51no—
335C22×C4—151no—
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—31no—
354C22⋊C4—51no—
355C22⋊C4—51no—
356C22⋊C4—151no—
357C22⋊C4—151no—
358C22⋊C4—151no—
359C42—151no—
360C3×C5#54711yescharacteristic, complemented, Hall
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—101no—
367C22×C3—101no—
368C22×C3—101no—
369C22×C3D4×D512yes—
370C22×C3C23×D511yescharacteristic
371C2×D3—52no—
372C2×D3—101no—
373C2×D3—101no—
374C3×C4—21no—
375C3×C4—52no—
376C3×C4—101no—
377C3×C4—101no—
378Dic3—21no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—52no—
383Dic3—101no—
384Dic3—101no—
385C2×C5—22no—
386C2×C5—41no—
387C2×C5C2×D3×D411yescharacteristic
388C2×C5C2×#23711yescharacteristic
389C2×C5#101011yescharacteristic
390D5—41no—
391D5—62no—
392C23—51no—
393C23—151no—
394C23C2×D3×D511yescharacteristic
395C23C2×D3×D511yescharacteristic
396Q8—302no—
397Q8—302no—
398D4—22no—
399D4—102no—
400D4—102no—
401D4—154no—
402D4—302no—
403D4—302no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—51no—
409C2×C4—51no—
410C2×C4—51no—
411C2×C4—62no—
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×C4—302no—
422C2×C4C2×D3×D511yescharacteristic
423C2×C3—22no—
424C2×C3—41no—
425C2×C3—201no—
426C2×C3C2×D4×D511yescharacteristic
427C2×C3D5×#4111yescharacteristic
428C2×C3#415011yescharacteristic
429D3—102no—
430C5#561111yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—101no—
437C22—101no—
438C22—101no—
439C22—152no—
440C22—301no—
441C22—301no—
442C22#679012yes—
443C22C22×D3×D511yescharacteristic
444C4—21no—
445C4—52no—
446C4—61no—
447C4—61no—
448C4—61no—
449C4—61no—
450C4—101no—
451C4—101no—
452C4—152no—
453C4—301no—
454C4—301no—
455C3#6598911yescharacteristic, complemented, Sylow
456C2—22no—
457C2—41no—
458C2—201no—
459C2—302no—
460C2#9202011yescharacteristic
461C2D5×#23711yescharacteristic
462C2C2×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#6819C2semidirect
2. C2×#6779C2semidirect
3. C5×#935C2semidirect
4. C3×#4085C2semidirect
5. #91576C2semidirect
6. #91562C2semidirect
7. #91559C2semidirect
8. #91552C2semidirect
9. C2×#6668C2semidirect
10. #91537C2semidirect
11. #91533C2semidirect
12. #91431C2semidirect
13. #91404C2semidirect
14. #91354C2semidirect
15. #91328C2semidirect
58. #4085D3semidirect
77. #1220D4semidirect
106. #935D5semidirect
173. C3×Dic5#41semidirect
322. Dic5#237semidirect
360. C3×C5#547semidirect
430. C5#5611semidirect
455. C3#65989semidirect

Maximal subgroups

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

subgroupindex
C2×#68192
C2×#67792
C5×#9352
C3×#40852
#915762
#915622
#915592
#915522
C2×#66682
#915372
#915332
#914312
#914042
#913542
#913282
#659893
#56115