Finite Group Databasebeta

← #11754571

Subgroups — #11754571

Order 960.

480 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
1#91819C211yesmaximal, characteristic, complemented
2C5×#929C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4#91567C211yesmaximal, characteristic, complemented
5#91562C211yesmaximal, characteristic, complemented
6#91558C211yesmaximal, characteristic, complemented
7#91533C211yesmaximal, characteristic, complemented
8#91459C211yesmaximal, characteristic, complemented
9#91457C211yesmaximal, characteristic, complemented
10#91448C211yesmaximal, characteristic, complemented
11#91420C211yesmaximal, characteristic, complemented
12#91405C211yesmaximal, characteristic, complemented
13#91402C211yesmaximal, characteristic, complemented
14#91348C211yesmaximal, characteristic, complemented
15#91334C211yesmaximal, characteristic, complemented
16#65997—31nomaximal, Hall
17C22×C3×C4×C5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×D60C2211yescharacteristic
21C2×C5×#67C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C4×D5C2211yescharacteristic
24C2×#1203C2211yescharacteristic
25C2×#1203C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×#1201C2211yescharacteristic
29C2×#1200C2211yescharacteristic
30C2×#1200C2211yescharacteristic
31C2×D3×Dic5C2211yescharacteristic
32#6714C2211yescharacteristic
33#6714C2211yescharacteristic
34C4⋊Dic15C2211yescharacteristic
35C5×#217C2211yescharacteristic
36C5×(C2×D3)⋊C4C2211yescharacteristic
37C5×(C2×D3)⋊C4C2211yescharacteristic
38C5×Dic3⋊C4C2211yescharacteristic
39C5×Dic3⋊C4C2211yescharacteristic
40C3×C22⋊Dic5C2211yescharacteristic
41C3×#685C2211yescharacteristic
42C3×#683C2211yescharacteristic
43C3×C4×Dic5C2211yescharacteristic
44Dic3⋊Dic5C2211yescharacteristic
45#6669C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5562—51nomaximal, Hall
53C5×#123—31no—
54#4086—31no—
55#4085—31no—
56#4076—31no—
57C4×C22⋊D5D311yescharacteristic, complemented
58#4041—31no—
59#4040—31no—
60#4038—31no—
61#4035—31no—
62#4032—31no—
63#4030—31no—
64#4030—31no—
65#4030—31no—
66#4029—31no—
67#4027—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C5×D3C2311yescharacteristic
72C22×C3×D5C2311yescharacteristic
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76#1220—41no—
77#1220—41no—
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80D60—41no—
81C5×#67—41no—
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C3×C22⋊D5—22no—
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C3×C4×D5—41no—
90#1203—22no—
91#1203—41no—
92#1202—41no—
93#1202—41no—
94#1201—41no—
95#1200—22no—
96#1200—41no—
97D3×Dic5—41no—
98C3×C4×D4—51no—
99#940—51no—
100#938—51no—
101#930—51no—
102#930—51no—
103#929—51no—
104#929D511yescharacteristic, complemented
105#895—51no—
106#890—51no—
107#884—51no—
108#884—51no—
109#883—51no—
110#883—51no—
111C4×D12—51no—
112#872—51no—
113C2×C5×D4—31no—
114C22×C4×C5C2×D311yescharacteristic
115C2×C22⋊D5—31no—
116C2×C22⋊D5—31no—
117C2×C22⋊D5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5C2×D311yescharacteristic
121C22×Dic5—31no—
122C2×D20—31no—
123C2×D20—31no—
124C2×D20—31no—
125C2×C4×D5—31no—
126C2×C4×D5—31no—
127C2×C4×D5C2×D311yescharacteristic
128C5×C4⋊C4—31no—
129C5×C4⋊C4—31no—
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C5×C22⋊C4—31no—
133C22⋊Dic5C2×D311yescharacteristic
134#685—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685C2×D311yescharacteristic
140C4⋊Dic5—31no—
141C4⋊Dic5—31no—
142#683—31no—
143#683—31no—
144#683—31no—
145#683C2×D311yescharacteristic
146C4×Dic5—31no—
147C4×Dic5C2×D311yescharacteristic
148#540—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—21no—
159C2×C5×D3—21no—
160C2×C5×D3—21no—
161C2×C5×D3—21no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167Dic15—21no—
168Dic15—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×Dic5#4112yes—
172C5×Dic3—21no—
173C5×Dic3—21no—
174C5×Dic3—21no—
175C2×C3×D4—51no—
176C22×C3×C4—51no—
177C22×C3×C4C2×D511yescharacteristic
178C2×#67—51no—
179C2×#67—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67C2×D511yescharacteristic
184C2×D12—51no—
185C2×D12—51no—
186C2×D12—51no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C3×C4⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C22⋊C4—51no—
193C3×C42—51no—
194#217—51no—
195#217C2×D511yescharacteristic
196(C2×D3)⋊C4—51no—
197(C2×D3)⋊C4—51no—
198(C2×D3)⋊C4—51no—
199(C2×D3)⋊C4—51no—
200(C2×D3)⋊C4C2×D511yescharacteristic
201(C2×D3)⋊C4C2×D511yescharacteristic
202C4⋊Dic3—51no—
203C4⋊Dic3—51no—
204C4⋊Dic3—51no—
205Dic3⋊C4—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4C2×D511yescharacteristic
208Dic3⋊C4C2×D511yescharacteristic
209C4×Dic3—51no—
210C23×C5—31no—
211C23×C5C22×D311yescharacteristic
212C22×D5—31no—
213C22×D5—31no—
214C22×D5C22×D311yescharacteristic
215C5×D4—121no—
216C2×C4×C5—31no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—41no—
220C2×C4×C5C22×D311yescharacteristic
221C2×C4×C5C22×D311yescharacteristic
222C22⋊D5—22no—
223C22⋊D5—62no—
224C22⋊D5—121no—
225C22⋊D5—121no—
226C22⋊D5—121no—
227C22⋊D5—121no—
228C2×Dic5—31no—
229C2×Dic5—31no—
230C2×Dic5—121no—
231C2×Dic5C22×D311yescharacteristic
232C2×Dic5C22×D311yescharacteristic
233C2×Dic5C22×D311yescharacteristic
234D20—121no—
235D20—121no—
236D20—121no—
237C4×D5—41no—
238C4×D5—62no—
239C4×D5—121no—
240#127—151no—
241#125—151no—
242#123—31no—
243#123—151no—
244#123—151no—
245#123—151no—
246#121—151no—
247#121—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#121—151no—
252C4×D4—51no—
253C4×D4—151no—
254#117—151no—
255C2×C3×C5—41no—
256C2×C3×C5C2×#4111yescharacteristic
257C2×C3×C5H(5,𝔽2)11yescharacteristic
258C2×C3×C5H(5,𝔽2)11yescharacteristic
259D15—41no—
260D15—41no—
261C3×D5—41no—
262C5×D3—41no—
263C23×C3—51no—
264C23×C3C22×D511yescharacteristic
265C22×D3—51no—
266C22×D3—51no—
267C22×D3C22×D511yescharacteristic
268C3×D4—102no—
269C2×C3×C4—41no—
270C2×C3×C4—51no—
271C2×C3×C4—51no—
272C2×C3×C4—51no—
273C2×C3×C4—201no—
274C2×C3×C4C22×D511yescharacteristic
275C2×C3×C4C22×D511yescharacteristic
276#67—41no—
277#67—201no—
278#67—201no—
279#67—201no—
280#67—201no—
281#67—201no—
282C2×Dic3—51no—
283C2×Dic3—51no—
284C2×Dic3C22×D511yescharacteristic
285C2×Dic3C22×D511yescharacteristic
286C2×Dic3C22×D511yescharacteristic
287D12—102no—
288D12—201no—
289D12—201no—
290C4×D3—102no—
291C4×D3—201no—
292C4×D3—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—61no—
297C22×C5—61no—
298C22×C5—61no—
299C22×C5C23×D311yescharacteristic
300C2×D5—21no—
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—61no—
304C2×D5—61no—
305C2×D5—61no—
306C2×D5—61no—
307C2×D5—61no—
308C2×D5—61no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—61no—
312C4×C5—61no—
313C4×C5—61no—
314Dic5—21no—
315Dic5—21no—
316Dic5—61no—
317Dic5—61no—
318Dic5#23512yes—
319C2×D4—31no—
320C2×D4—51no—
321C2×D4—151no—
322C2×D4—151no—
323C2×D4—151no—
324C2×D4—151no—
325C2×D4—151no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C22×C4—51no—
330C22×C4—151no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4D3×D511yescharacteristic
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—51no—
337C4⋊C4—151no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C4⋊C4—151no—
341C4⋊C4—151no—
342C22⋊C4—31no—
343C22⋊C4—31no—
344C22⋊C4—31no—
345C22⋊C4—51no—
346C22⋊C4—51no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C42—51no—
353C42—151no—
354C3×C5#54011yescharacteristic, complemented, Hall
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—101no—
359C22×C3—101no—
360C22×C3—101no—
361C22×C3C23×D511yescharacteristic
362C2×D3—21no—
363C2×D3—21no—
364C2×D3—21no—
365C2×D3—101no—
366C2×D3—101no—
367C2×D3—101no—
368C2×D3—101no—
369C2×D3—101no—
370C2×D3—101no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—52no—
374C3×C4—101no—
375C3×C4—101no—
376Dic3—21no—
377Dic3—21no—
378Dic3—21no—
379Dic3—101no—
380Dic3—101no—
381C2×C5—41no—
382C2×C5—121no—
383C2×C5C2×#23511yescharacteristic
384C2×C5#100411yescharacteristic
385C2×C5#100911yescharacteristic
386D5—41no—
387D5—121no—
388D5—121no—
389C23—31no—
390C23—51no—
391C23—151no—
392C23—151no—
393C23C2×D3×D511yescharacteristic
394D4—102no—
395D4—121no—
396D4—302no—
397D4—601no—
398D4—601no—
399D4—601no—
400D4—601no—
401D4—601no—
402D4—601no—
403D4—601no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—41no—
408C2×C4—51no—
409C2×C4—51no—
410C2×C4—51no—
411C2×C4—151no—
412C2×C4—151no—
413C2×C4—201no—
414C2×C4—302no—
415C2×C4—601no—
416C2×C4—601no—
417C2×C4C2×D3×D511yescharacteristic
418C2×C4C2×D3×D511yescharacteristic
419C2×C3—41no—
420C2×C3—201no—
421C2×C3#414411yescharacteristic
422C2×C3D5×#4111yescharacteristic
423C2×C3#414911yescharacteristic
424D3—41no—
425D3—201no—
426D3—201no—
427C5#556211yescharacteristic, complemented, Sylow
428C22—21no—
429C22—21no—
430C22—21no—
431C22—61no—
432C22—61no—
433C22—61no—
434C22—101no—
435C22—101no—
436C22—101no—
437C22—301no—
438C22—301no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22—301no—
443C22C22×D3×D511yescharacteristic
444C4—21no—
445C4—21no—
446C4—52no—
447C4—61no—
448C4—61no—
449C4—61no—
450C4—101no—
451C4—101no—
452C4—301no—
453C4—301no—
454C3#6599711yescharacteristic, complemented, Sylow
455C2—41no—
456C2—121no—
457C2—201no—
458C2—601no—
459C2—601no—
460C2D5×#23511yescharacteristic
461C2#9201911yescharacteristic
462C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#540
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. #91819C2semidirect
2. C5×#929C2semidirect
3. C3×C4×C22⋊D5C2semidirect
4. #91567C2semidirect
5. #91562C2semidirect
6. #91558C2semidirect
7. #91533C2semidirect
8. #91459C2semidirect
9. #91457C2semidirect
10. #91448C2semidirect
11. #91420C2semidirect
12. #91405C2semidirect
13. #91402C2semidirect
14. #91348C2semidirect
15. #91334C2semidirect
57. C4×C22⋊D5D3semidirect
104. #929D5semidirect
354. C3×C5#540semidirect
427. C5#5562semidirect
454. C3#65997semidirect

Maximal subgroups

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

subgroupindex
#918192
C5×#9292
C3×C4×C22⋊D52
#915672
#915622
#915582
#915332
#914592
#914572
#914482
#914202
#914052
#914022
#913482
#913342
#659973
#55625