Finite Group Databasebeta

← #13087487

Subgroups — #13087487

Order 1440.

554 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D15C211yesmaximal, characteristic, complemented
2C2×C3×D60C211yesmaximal, characteristic, complemented
3C2×#67151C211yesmaximal, characteristic, complemented
4C2×#67150C211yesmaximal, characteristic, complemented
5#10623908C211yesmaximal, characteristic, complemented
6C3×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10623811C211yesmaximal, characteristic, complemented
8#91771—31nomaximal
9#91474—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C22×C3×D15C2211yescharacteristic, complemented
13C22×C3×C5×D3C2211yescharacteristic
14C2×D3×D15—22no—
15C2×D3×D15—22no—
16C2×D3×D15—22no—
17C2×C32×C4×C5C2211yescharacteristic, complemented
18C2×C3⋊Dic15C2211yescharacteristic, complemented
19C3×D60—22no—
20C2×C3×C5×Dic3C2211yescharacteristic, complemented
21#67151—22no—
22#67150—22no—
23#63922—51nomaximal, Hall
24C23×D15—31no—
25C22×D3×D5—31no—
26C2×#1220—31no—
27C2×D60—31no—
28C2×D60D311yescharacteristic, complemented
29C2×C3×D20—31no—
30C2×#1202—31no—
31C2×#1201—31no—
32C3×C5×C22⋊C4—31no—
33#6714—31no—
34#6714—31no—
35#6714—31no—
36#6714—61no—
37C5×(C2×D3)⋊C4D311yescharacteristic, complemented
38#6665—31no—
39C22×C32×C5C2311yescharacteristic
40C2×C3⋊D15—21no—
41C2×C3⋊D15—21no—
42C2×C3⋊D15D412yescomplemented
43C2×C3×D15—21no—
44C2×C3×D15—21no—
45C2×C3×D15—21no—
46C2×C3×D15—21no—
47C2×C3×D15—21no—
48C2×C3×D15D412yescomplemented
49C2×C3×C5×D3—21no—
50C2×C3×C5×D3—21no—
51C2×C3×C5×D3D412yescomplemented
52D3×D15—28no—
53C32×C4×C5—21no—
54C3⋊Dic15—21no—
55C3×C5×Dic3—21no—
56#4028—91noHall
57C22×D32—51no—
58C2×C3×D12—51no—
59C2×#626—51no—
60C2×#625—51no—
61#3752—51no—
62C3×(C2×D3)⋊C4D511yescharacteristic, complemented
63(C2×D3)⋊Dic3—51no—
64C23×C3×C5—31no—
65C22×D15—31no—
66C22×D15—31no—
67C22×D15—62no—
68C22×D15—62no—
69C22×D15—62no—
70C22×D15—61no—
71C22×D15C2×D311yescharacteristic
72C22×D15C2×D311yescharacteristic, complemented
73C22×C5×D3C2×D311yescharacteristic
74C22×C3×D5—31no—
75C22×C3×D5—31no—
76C2×D3×D5—62no—
77C2×D3×D5—62no—
78C2×D3×D5—62no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—31no—
81C2×C3×C4×C5C2×D311yescharacteristic, complemented
82C2×C3×C4×C5C2×D311yescharacteristic, complemented
83#1220—62no—
84C2×Dic15—31no—
85C2×Dic15—31no—
86C2×Dic15—61no—
87D60—22no—
88D60—62no—
89C2×C5×Dic3C2×D311yescharacteristic, complemented
90C3×D20—62no—
91#1202—62no—
92#1201—62no—
93#937—151no—
94#882—151no—
95C2×C32×C5C2×D411yescharacteristic
96C2×C32×C5C2×D411yescharacteristic
97C2×C32×C5C2×D411yescharacteristic
98C3⋊D15—22no—
99C3×D15—22no—
100C3×D15—41no—
101C3×C5×D3—22no—
102C23×D5—91no—
103C2×C22⋊D5—91no—
104C2×D20—31no—
105C2×D20—91no—
106C5×C22⋊C4—31no—
107#685—91no—
108#685—91no—
109C22×C3⋊D3—51no—
110C22×C3×D3—51no—
111C22×C3×D3—51no—
112C22×C3×D3C2×D511yescharacteristic
113C2×D32—102no—
114C2×D32—102no—
115C2×D32—102no—
116C2×C32×C4C2×D511yescharacteristic, complemented
117C2×C3⋊Dic3—51no—
118C2×C3×Dic3C2×D511yescharacteristic, complemented
119C3×D12—102no—
120#626—102no—
121#625—102no—
122C22×C3×C5—21no—
123C22×C3×C5—32no—
124C22×C3×C5—61no—
125C22×C3×C5—61no—
126C22×C3×C5C22×D311yescharacteristic
127C22×C3×C5C22×D311yescharacteristic
128C2×D15—21no—
129C2×D15—21no—
130C2×D15—21no—
131C2×D15—21no—
132C2×D15—21no—
133C2×D15—32no—
134C2×D15—32no—
135C2×D15—62no—
136C2×D15—68no—
137C2×D15—61no—
138C2×D15—61no—
139C2×D15—61no—
140C2×D15—61no—
141C2×D15—121no—
142C2×D15—121no—
143C2×D15#6712yescomplemented
144C2×C5×D3—21no—
145C2×C5×D3—21no—
146C2×C5×D3D1212yescomplemented
147C2×C3×D5—32no—
148C2×C3×D5—61no—
149C2×C3×D5—61no—
150C2×C3×D5—61no—
151C2×C3×D5—61no—
152C2×C3×D5—61no—
153D3×D5—68no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—61no—
158Dic15—61no—
159Dic15—61no—
160Dic15—121no—
161C5×Dic3—21no—
162C23×D3—151no—
163C23×D3—151no—
164C2×C3×D4—151no—
165C2×#67—151no—
166C2×#67—151no—
167C2×#67—151no—
168C2×D12—51no—
169C2×D12—151no—
170C3×C22⋊C4—31no—
171#217—151no—
172(C2×D3)⋊C4—151no—
173(C2×D3)⋊C4—151no—
174(C2×D3)⋊C4—151no—
175(C2×D3)⋊C4—301no—
176(C2×D3)⋊C4D1511yescharacteristic, complemented
177C32×C5#12011yescharacteristic, complemented, Hall
178C23×C5—31no—
179C22×D5—31no—
180C22×D5—31no—
181C22×D5—91no—
182C22×D5—182no—
183C22×D5—182no—
184C22×D5—182no—
185C2×C4×C5—31no—
186C2×C4×C5D3211yescharacteristic, complemented
187C22⋊D5—182no—
188C2×Dic5—91no—
189D20—62no—
190D20—182no—
191C22×C32C22×D511yescharacteristic
192C2×C3⋊D3—52no—
193C2×C3⋊D3—101no—
194C2×C3⋊D3—101no—
195C2×C3×D3—21no—
196C2×C3×D3—21no—
197C2×C3×D3—52no—
198C2×C3×D3—101no—
199C2×C3×D3—101no—
200C2×C3×D3—101no—
201C2×C3×D3—101no—
202C2×C3×D3—101no—
203C2×C3×D3D2012yescomplemented
204D32—108no—
205C32×C4—21no—
206C3⋊Dic3—101no—
207C3×Dic3—21no—
208#120—451noSylow
209C2×C3×C5—21no—
210C2×C3×C5—21no—
211C2×C3×C5—21no—
212C2×C3×C5—62no—
213C2×C3×C5C2×D1211yescharacteristic
214C2×C3×C5D3×D411yescharacteristic
215C2×C3×C5D3×D411yescharacteristic
216C2×C3×C5D3×D411yescharacteristic
217C2×C3×C5D3×D411yescharacteristic
218C2×C3×C5C2×#6711yescharacteristic
219D15—22no—
220D15—41no—
221D15—62no—
222D15—62no—
223D15—122no—
224C3×D5—62no—
225C3×D5—121no—
226C5×D3—22no—
227C23×C3—31no—
228C23×C3—151no—
229C23×C3—151no—
230C22×D3—51no—
231C22×D3—51no—
232C22×D3—151no—
233C22×D3—151no—
234C22×D3—301no—
235C22×D3—302no—
236C22×D3—302no—
237C22×D3—302no—
238C22×D3—302no—
239C22×D3—302no—
240C22×D3—302no—
241C22×D3C2×D1511yescharacteristic
242C3×D4—302no—
243C2×C3×C4—21no—
244C2×C3×C4—31no—
245C2×C3×C4D3×D511yescharacteristic, complemented
246C2×C3×C4C2×D1511yescharacteristic, complemented
247#67—302no—
248#67—302no—
249#67—302no—
250C2×Dic3—151no—
251C2×Dic3—151no—
252C2×Dic3—301no—
253C2×Dic3C2×D1511yescharacteristic, complemented
254D12—102no—
255D12—302no—
256C22×C5—32no—
257C22×C5—61no—
258C22×C5—61no—
259C22×C5C2×D3211yescharacteristic
260C2×D5—32no—
261C2×D5—61no—
262C2×D5—61no—
263C2×D5—61no—
264C2×D5—61no—
265C2×D5—61no—
266C2×D5—92no—
267C2×D5—188no—
268C2×D5—181no—
269C2×D5—181no—
270C4×C5—21no—
271C4×C5—61no—
272Dic5—181no—
273C2×C32C2×D2011yescharacteristic
274C2×C32D4×D511yescharacteristic
275C2×C32D4×D511yescharacteristic
276C3⋊D3—102no—
277C3×D3—22no—
278C3×D3—102no—
279C3×D3—201no—
280C24—451no—
281C2×D4—151no—
282C2×D4—451no—
283C2×D4—451no—
284C22⋊C4—31no—
285C22⋊C4—451no—
286C22⋊C4—451no—
287C3×C5—21no—
288C3×C5#88211yescharacteristic, complemented
289C3×C5#93711yescharacteristic, complemented
290C22×C3—21no—
291C22×C3—32no—
292C22×C3—61no—
293C22×C3—61no—
294C22×C3—152no—
295C22×C3—301no—
296C22×C3—301no—
297C22×C3—301no—
298C22×C3—301no—
299C22×C3—301no—
300C22×C3C2×D3×D511yescharacteristic
301C22×C3C22×D1511yescharacteristic
302C2×D3—21no—
303C2×D3—21no—
304C2×D3—52no—
305C2×D3—101no—
306C2×D3—101no—
307C2×D3—101no—
308C2×D3—101no—
309C2×D3—101no—
310C2×D3—152no—
311C2×D3—152no—
312C2×D3—302no—
313C2×D3—308no—
314C2×D3—308no—
315C2×D3—301no—
316C2×D3—301no—
317C2×D3—301no—
318C2×D3—301no—
319C2×D3—601no—
320C2×D3—601no—
321C2×D3D6012yescomplemented
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—61no—
326Dic3—21no—
327Dic3—301no—
328Dic3—301no—
329Dic3—601no—
330C2×C5—62no—
331C2×C5D3×D1211yescharacteristic
332C2×C5#380211yescharacteristic
333C2×C5D3×#6711yescharacteristic
334D5—62no—
335D5—121no—
336D5—182no—
337C32#402811yescharacteristic, complemented, Sylow
338C23—31no—
339C23—151no—
340C23—151no—
341C23—451no—
342C23—902no—
343C23—902no—
344C23—902no—
345D4—302no—
346D4—902no—
347D4—902no—
348C2×C4—31no—
349C2×C4—451no—
350C2×C4D3×D1511yescharacteristic, complemented
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—62no—
355C2×C3—302no—
356C2×C3—601no—
357C2×C3D3×D2011yescharacteristic
358C2×C3#677711yescharacteristic
359C2×C3D5×#6711yescharacteristic
360C2×C3C2×D6011yescharacteristic
361C2×C3D4×D1511yescharacteristic
362C2×C3D4×D1511yescharacteristic
363D3—22no—
364D3—102no—
365D3—201no—
366D3—302no—
367D3—302no—
368D3—602no—
369C5#6392211yescharacteristic, complemented, Sylow
370C22—32no—
371C22—61no—
372C22—61no—
373C22—152no—
374C22—301no—
375C22—301no—
376C22—301no—
377C22—301no—
378C22—301no—
379C22—452no—
380C22—908no—
381C22—901no—
382C22—901no—
383C22C2×D3×D1511yescharacteristic
384C4—21no—
385C4—61no—
386C4—901no—
387C3—21no—
388C3#9147411yescharacteristic, complemented
389C3#9177111yescharacteristic, complemented
390C2—62no—
391C2—302no—
392C2—601no—
393C2—902no—
394C2D3×D6011yescharacteristic
395C2#1062420511yescharacteristic
396C2#67×D1511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D3×D15
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D15C2semidirect
2. C2×C3×D60C2semidirect
3. C2×#67151C2semidirect
4. C2×#67150C2semidirect
5. #10623908C2semidirect
6. C3×C5×(C2×D3)⋊C4C2semidirect
7. #10623811C2semidirect
12. C22×C3×D15C22semidirect
17. C2×C32×C4×C5C22semidirect
18. C2×C3⋊Dic15C22semidirect
20. C2×C3×C5×Dic3C22semidirect
28. C2×D60D3semidirect
37. C5×(C2×D3)⋊C4D3semidirect
42. C2×C3⋊D15D4semidirect
48. C2×C3×D15D4semidirect
51. C2×C3×C5×D3D4semidirect
62. C3×(C2×D3)⋊C4D5semidirect
72. C22×D15C2×D3semidirect
81. C2×C3×C4×C5C2×D3semidirect
82. C2×C3×C4×C5C2×D3semidirect
89. C2×C5×Dic3C2×D3semidirect
116. C2×C32×C4C2×D5semidirect
118. C2×C3×Dic3C2×D5semidirect
143. C2×D15#67semidirect
146. C2×C5×D3D12semidirect
176. (C2×D3)⋊C4D15semidirect
177. C32×C5#120semidirect
186. C2×C4×C5D32semidirect
203. C2×C3×D3D20semidirect
245. C2×C3×C4D3×D5semidirect
246. C2×C3×C4C2×D15semidirect
253. C2×Dic3C2×D15semidirect
288. C3×C5#882semidirect
289. C3×C5#937semidirect
321. C2×D3D60semidirect
337. C32#4028semidirect
350. C2×C4D3×D15semidirect
369. C5#63922semidirect
388. C3#91474semidirect
389. C3#91771semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D152
C2×C3×D602
C2×#671512
C2×#671502
#106239082
C3×C5×(C2×D3)⋊C42
#106238112
#917713
#914743
#639225