Finite Group Databasebeta

← #11754856

Subgroups — #11754856

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91828C211yesmaximal, characteristic, complemented
2C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C3×#4085C211yesmaximal, characteristic, complemented
4#91569C211yesmaximal, characteristic, complemented
5#91559C211yesmaximal, characteristic, complemented
6Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
7#91552C211yesmaximal, characteristic, complemented
8#91542C211yesmaximal, characteristic, complemented
9C2×#6668C211yesmaximal, characteristic, complemented
10#91533C211yesmaximal, characteristic, complemented
11#91530C211yesmaximal, characteristic, complemented
12#91413C211yesmaximal, characteristic, complemented
13#91403C211yesmaximal, characteristic, complemented
14#91363C211yesmaximal, characteristic, complemented
15#91335C211yesmaximal, characteristic, complemented
16#65874—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C22×Dic15C2211yescharacteristic
21C22×C5×Dic3C2211yescharacteristic
22C22×C5×Dic3C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C2×C3×C22⋊D5C2211yescharacteristic
25C22×C3×Dic5C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1200C2211yescharacteristic
28C2×D5×Dic3C2211yescharacteristic
29#6719C2211yescharacteristic
30#6714C2211yescharacteristic
31#6712C2211yescharacteristic
32C5×#217C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×C4⋊Dic3C2211yescharacteristic
35C4×C5×Dic3C2211yescharacteristic
36C3×C22⋊Dic5C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×#683C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40#6669C2211yescharacteristic
41#6668C2211yescharacteristic
42#6668C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6665C2211yescharacteristic
49#6665C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5618—51nomaximal, Hall
53C4×C5×D4—31no—
54#4085—31no—
55#4085D311yescharacteristic, complemented
56#4076—31no—
57#4075—31no—
58C4×C22⋊D5—31no—
59C2×#683—31no—
60#4040—31no—
61#4035—31no—
62#4030—31no—
63#4027—31no—
64#4027—31no—
65#4025—31no—
66#4022—31no—
67#4018—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C3×C5×D4—22no—
73C2×C3×C4×C5C2311yescharacteristic
74#1220—22no—
75#1220—41no—
76C2×Dic15—41no—
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C2×C5×Dic3—41no—
81C2×C5×Dic3—41no—
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C3×C22⋊D5—22no—
87C3×C22⋊D5—22no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92#1202—41no—
93#1200—22no—
94D5×Dic3—41no—
95C3×#121—51no—
96#939—51no—
97#939—51no—
98#938—51no—
99D4×Dic3—51no—
100D4×Dic3—51no—
101D4×Dic3D511yescharacteristic, complemented
102C4×#67—51no—
103C2×C4⋊Dic3—51no—
104#892—51no—
105#890—51no—
106#886—51no—
107#886—51no—
108#879—51no—
109#879—51no—
110C2×C5×D4C2×D311yescharacteristic
111C22×C4×C5—31no—
112C22×C4×C5—31no—
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5C2×D311yescharacteristic
116C2×C22⋊D5C2×D311yescharacteristic
117C22×Dic5—31no—
118C22×Dic5C2×D311yescharacteristic
119C2×D20—31no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C5×C4⋊C4—31no—
123C5×C22⋊C4—31no—
124C5×C22⋊C4—31no—
125C42×C5—31no—
126C22⋊Dic5—31no—
127C22⋊Dic5C2×D311yescharacteristic
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685C2×D311yescharacteristic
134C4⋊Dic5—31no—
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683—31no—
142#683C2×D311yescharacteristic
143C4×Dic5—31no—
144C4×Dic5—31no—
145#553—151noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#4112yes—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160Dic15—21no—
161Dic15—21no—
162Dic15—21no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5#4112yes—
166C5×Dic3—21no—
167C5×Dic3—21no—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C2×C3×D4—51no—
171C2×C3×D4—51no—
172C2×C3×D4C2×D511yescharacteristic
173C22×C3×C4—51no—
174C2×#67—51no—
175C2×#67—51no—
176C2×#67—51no—
177C22×Dic3—51no—
178C22×Dic3—51no—
179C22×Dic3C2×D511yescharacteristic
180C22×Dic3C2×D511yescharacteristic
181C2×C4×D3—51no—
182C3×C4⋊C4—51no—
183C3×C22⋊C4—51no—
184C3×C22⋊C4—51no—
185#217—51no—
186#217—51no—
187#217—51no—
188#217C2×D511yescharacteristic
189#217C2×D511yescharacteristic
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193C4⋊Dic3—51no—
194C4⋊Dic3—51no—
195C4⋊Dic3—51no—
196C4⋊Dic3—51no—
197C4⋊Dic3—51no—
198C4⋊Dic3C2×D511yescharacteristic
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C4×Dic3C2×D511yescharacteristic
205C23×C5C22×D311yescharacteristic
206C23×C5C22×D311yescharacteristic
207C22×D5—31no—
208C22×D5C22×D311yescharacteristic
209C5×D4—22no—
210C2×C4×C5—31no—
211C2×C4×C5—31no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5C22×D311yescharacteristic
217C22⋊D5—22no—
218C22⋊D5—22no—
219C22⋊D5—62no—
220C22⋊D5—121no—
221C2×Dic5—22no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—121no—
226C2×Dic5C22×D311yescharacteristic
227C2×Dic5C22×D311yescharacteristic
228C2×Dic5C22×D311yescharacteristic
229D20—121no—
230C4×D5—62no—
231C4×D5—121no—
232#126—151no—
233#126—151no—
234#125—151no—
235#123—151no—
236#123—151no—
237#121—51no—
238#121—151no—
239#121—151no—
240#121—151no—
241C4×D4—31no—
242C4×D4—151no—
243C4×D4—151no—
244C4×D4—151no—
245#117—151no—
246C2×C4⋊C4—151no—
247C2×C3×C5—22no—
248C2×C3×C5—41no—
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5C2×#4111yescharacteristic
251C2×C3×C5H(5,𝔽2)11yescharacteristic
252D15—41no—
253C3×D5—41no—
254C23×C3—51no—
255C23×C3C22×D511yescharacteristic
256C23×C3C22×D511yescharacteristic
257C22×D3—51no—
258C3×D4—22no—
259C3×D4—102no—
260C3×D4—102no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—102no—
265C2×C3×C4C22×D511yescharacteristic
266#67—102no—
267#67—201no—
268#67—201no—
269C2×Dic3—41no—
270C2×Dic3—41no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—201no—
275C2×Dic3—201no—
276C2×Dic3C22×D511yescharacteristic
277C2×Dic3C22×D511yescharacteristic
278C2×Dic3C22×D511yescharacteristic
279C2×Dic3C22×D511yescharacteristic
280C4×D3—102no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5#23712yes—
287C22×C5C23×D311yescharacteristic
288C2×D5—21no—
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C4×C5—21no—
295C4×C5—61no—
296C4×C5—61no—
297C4×C5—61no—
298C4×C5—61no—
299Dic5—21no—
300Dic5—21no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5#23712yes—
305C2×D4—51no—
306C2×D4—51no—
307C2×D4—151no—
308C2×D4—151no—
309C2×D4—151no—
310C2×D4D3×D511yescharacteristic
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—51no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—51no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C4⋊C4—151no—
326C4⋊C4—151no—
327C22⋊C4—31no—
328C22⋊C4—31no—
329C22⋊C4—51no—
330C22⋊C4—51no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C42—31no—
338C42—151no—
339C42—151no—
340C3×C5#55311yescharacteristic, complemented, Hall
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—101no—
347C22×C3—101no—
348C22×C3—101no—
349C22×C3#70912yes—
350C22×C3C23×D511yescharacteristic
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—52no—
356C3×C4—101no—
357C3×C4—101no—
358Dic3—21no—
359Dic3—21no—
360Dic3—21no—
361Dic3—21no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5—22no—
366C2×C5—41no—
367C2×C5C2×#23711yescharacteristic
368C2×C5C2×#23711yescharacteristic
369C2×C5#100911yescharacteristic
370D5—41no—
371D5—121no—
372C23—51no—
373C23—151no—
374C23C2×D3×D511yescharacteristic
375C23C2×D3×D511yescharacteristic
376D4—22no—
377D4—102no—
378D4—102no—
379D4—302no—
380D4—601no—
381D4—601no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—102no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—22no—
400C2×C3—41no—
401C2×C3—201no—
402C2×C3C2×#70911yescharacteristic
403C2×C3#414411yescharacteristic
404C2×C3D5×#4111yescharacteristic
405D3—201no—
406C5#561811yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—101no—
413C22—101no—
414C22—101no—
415C22—301no—
416C22—301no—
417C22—301no—
418C22#677912yes—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—52no—
422C4—61no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—101no—
427C4—101no—
428C4—301no—
429C4—301no—
430C4—301no—
431C3#6587411yescharacteristic, complemented, Sylow
432C2—22no—
433C2—41no—
434C2—201no—
435C2—601no—
436C2D5×#23711yescharacteristic
437C2#9202711yescharacteristic
438C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#553
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. #91828C2semidirect
2. C5×D4×Dic3C2semidirect
3. C3×#4085C2semidirect
4. #91569C2semidirect
5. #91559C2semidirect
6. Dic3×C22⋊D5C2semidirect
7. #91552C2semidirect
8. #91542C2semidirect
9. C2×#6668C2semidirect
10. #91533C2semidirect
11. #91530C2semidirect
12. #91413C2semidirect
13. #91403C2semidirect
14. #91363C2semidirect
15. #91335C2semidirect
55. #4085D3semidirect
101. D4×Dic3D5semidirect
340. C3×C5#553semidirect
406. C5#5618semidirect
431. C3#65874semidirect

Maximal subgroups

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

subgroupindex
#918282
C5×D4×Dic32
C3×#40852
#915692
#915592
Dic3×C22⋊D52
#915522
#915422
C2×#66682
#915332
#915302
#914132
#914032
#913632
#913352
#658743
#56185