Finite Group Databasebeta

← #13087460

Subgroups — #13087460

Order 1440.

430 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×C4⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
2C2×#67151C211yesmaximal, characteristic, complemented
3C2×#67151C211yesmaximal, characteristic, complemented
4C2×#67149C211yesmaximal, characteristic, complemented
5C3×#6714C211yesmaximal, characteristic, complemented
6C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10623813C211yesmaximal, characteristic, complemented
8#91784—31nomaximal
9#91459—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3⋊D15C2211yescharacteristic
12C22×C3×D15C2211yescharacteristic
13C2×C32×C4×C5C2211yescharacteristic
14C4⋊(C3⋊D15)—22no—
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67151—22no—
19#67151—22no—
20#67149—22no—
21#63910—51nomaximal, Hall
22C2×D60—31no—
23C2×D60—31no—
24C2×D60—31no—
25C2×D60—31no—
26C2×D60—61no—
27C2×C4×D15—31no—
28C2×#1202—31no—
29C2×#1202—31no—
30C2×#1200—31no—
31C3×C5×C4⋊C4—31no—
32#6714—31no—
33#6714D311yescharacteristic, complemented
34C5×Dic3⋊C4D311yescharacteristic, complemented
35C3×#685—31no—
36#6667—31no—
37C22×C32×C5C2311yescharacteristic
38C2×C3⋊D15—21no—
39C2×C3⋊D15—21no—
40C2×C3⋊D15—21no—
41C2×C3⋊D15—21no—
42C2×C3⋊D15—21no—
43C2×C3⋊D15D412yescomplemented
44C2×C3×D15—21no—
45C2×C3×D15—21no—
46C2×C3×D15—21no—
47C32×C4×C5—21no—
48C3×Dic15—21no—
49C3×C5×Dic3—21no—
50C3×C5×Dic3D412yescomplemented
51#4041—91noHall
52C2×C4⋊(C3⋊D3)—51no—
53C2×#626—51no—
54C2×#626—51no—
55C2×#624—51no—
56C3×(C2×D3)⋊C4—51no—
57C3×Dic3⋊C4D511yescharacteristic, complemented
58#3722—51no—
59C22×D15—31no—
60C22×D15—31no—
61C22×D15—31no—
62C22×D15—31no—
63C22×D15—61no—
64C22×D15—61no—
65C22×D15C2×D311yescharacteristic
66C22×C3×D5—31no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—31no—
69C2×C3×C4×C5—31no—
70C2×C3×C4×C5C2×D311yescharacteristic
71C2×C3×C4×C5C2×D311yescharacteristic
72C2×Dic15C2×D311yescharacteristic
73D60—62no—
74D60—62no—
75D60—64no—
76D60—62no—
77D60—62no—
78C4×D15—62no—
79C2×C5×Dic3C2×D311yescharacteristic
80C2×C5×Dic3C2×D311yescharacteristic
81C2×C3×Dic5—31no—
82#1202—62no—
83#1202—62no—
84#1200—62no—
85#895—151no—
86#884—151no—
87C2×C32×C5C2×D411yescharacteristic
88C2×C32×C5C2×D411yescharacteristic
89C2×C32×C5#4111yescharacteristic
90C3⋊D15—22no—
91C3⋊D15—41no—
92C3×D15—41no—
93C2×D20—91no—
94C2×D20—91no—
95C2×D20—91no—
96C2×C4×D5—91no—
97C5×C4⋊C4—31no—
98#685—31no—
99#685—91no—
100C22×C3⋊D3—51no—
101C22×C3⋊D3—51no—
102C22×C3×D3—51no—
103C2×C32×C4C2×D511yescharacteristic
104C4⋊(C3⋊D3)—102no—
105C2×C3×Dic3—51no—
106C2×C3×Dic3C2×D511yescharacteristic
107C2×C3×Dic3C2×D511yescharacteristic
108#626—102no—
109#626—102no—
110#624—102no—
111C22×C3×C5—21no—
112C22×C3×C5C22×D311yescharacteristic
113C22×C3×C5C22×D311yescharacteristic
114C2×D15—21no—
115C2×D15—21no—
116C2×D15—21no—
117C2×D15—32no—
118C2×D15—32no—
119C2×D15—62no—
120C2×D15—61no—
121C2×D15—61no—
122C2×D15—61no—
123C2×D15—61no—
124C2×D15—62no—
125C2×D15—61no—
126C2×D15—61no—
127C2×D15—61no—
128C2×D15—61no—
129C2×D15—61no—
130C2×D15—61no—
131C2×D15—121no—
132C2×D15—121no—
133C2×D15—121no—
134C2×D15—121no—
135C2×C3×D5—61no—
136C2×C3×D5—61no—
137C2×C3×D5—61no—
138C3×C4×C5—22no—
139C3×C4×C5—21no—
140C3×C4×C5—21no—
141C3×C4×C5—32no—
142C3×C4×C5—61no—
143Dic15—21no—
144C3×Dic5—61no—
145C5×Dic3—21no—
146C5×Dic3D1212yescomplemented
147C2×#67—151no—
148C2×#67—151no—
149C2×D12—151no—
150C2×D12—151no—
151C2×D12—151no—
152C2×D12—151no—
153C2×D12—301no—
154C2×C4×D3—151no—
155C2×C4×D3—151no—
156C3×C4⋊C4—31no—
157C3×C22⋊C4—151no—
158(C2×D3)⋊C4—51no—
159(C2×D3)⋊C4—151no—
160(C2×D3)⋊C4—151no—
161Dic3⋊C4D1511yescharacteristic, complemented
162C32×C5#12111yescharacteristic, complemented, Hall
163C22×D5—31no—
164C22×D5—91no—
165C22×D5—91no—
166C2×C4×C5—31no—
167C2×C4×C5—31no—
168C2×C4×C5D3211yescharacteristic
169C2×Dic5—31no—
170D20—182no—
171D20—182no—
172D20—182no—
173C4×D5—182no—
174C22×C32C22×D511yescharacteristic
175C2×C3⋊D3—52no—
176C2×C3⋊D3—101no—
177C2×C3⋊D3—101no—
178C2×C3⋊D3—101no—
179C2×C3⋊D3—101no—
180C2×C3⋊D3—101no—
181C2×C3×D3—101no—
182C2×C3×D3—101no—
183C2×C3×D3—101no—
184C32×C4—21no—
185C3×Dic3—21no—
186C3×Dic3—101no—
187C3×Dic3D2012yescomplemented
188#121—451noSylow
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5—21no—
192C2×C3×C5C2×D1211yescharacteristic
193C2×C3×C5#23511yescharacteristic
194C2×C3×C5D3×D411yescharacteristic
195C2×C3×C5D3×D411yescharacteristic
196C2×C3×C5D3×D411yescharacteristic
197C2×C3×C5#23911yescharacteristic
198D15—41no—
199D15—62no—
200D15—62no—
201D15—122no—
202D15—122no—
203D15—121no—
204D15—121no—
205C3×D5—121no—
206C23×C3—151no—
207C22×D3—51no—
208C22×D3—151no—
209C22×D3—151no—
210C22×D3—151no—
211C22×D3—151no—
212C22×D3—301no—
213C22×D3—301no—
214C2×C3×C4—21no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—151no—
218C2×C3×C4D3×D511yescharacteristic
219C2×C3×C4C2×D1511yescharacteristic
220#67—302no—
221#67—302no—
222C2×Dic3—51no—
223C2×Dic3C2×D1511yescharacteristic
224C2×Dic3C2×D1511yescharacteristic
225D12—302no—
226D12—302no—
227D12—304no—
228D12—302no—
229D12—302no—
230C4×D3—302no—
231C4×D3—302no—
232C22×C5C2×D3211yescharacteristic
233C2×D5—61no—
234C2×D5—61no—
235C2×D5—61no—
236C2×D5—92no—
237C2×D5—181no—
238C2×D5—181no—
239C2×D5—181no—
240C2×D5—181no—
241C2×D5—181no—
242C4×C5—21no—
243C4×C5—32no—
244C4×C5—61no—
245Dic5—61no—
246C2×C32C2×D2011yescharacteristic
247C2×C32D4×D511yescharacteristic
248C2×C32#71311yescharacteristic
249C3⋊D3—102no—
250C3⋊D3—201no—
251C3×D3—201no—
252C2×D4—451no—
253C2×D4—451no—
254C2×D4—451no—
255C22×C4—451no—
256C4⋊C4—31no—
257C22⋊C4—151no—
258C22⋊C4—451no—
259C3×C5—21no—
260C3×C5#88411yescharacteristic, complemented
261C3×C5#89511yescharacteristic, complemented
262C22×C3—21no—
263C22×C3—301no—
264C22×C3—301no—
265C22×C3—301no—
266C22×C3C2×D3×D511yescharacteristic
267C22×C3C22×D1511yescharacteristic
268C2×D3—101no—
269C2×D3—101no—
270C2×D3—101no—
271C2×D3—152no—
272C2×D3—152no—
273C2×D3—302no—
274C2×D3—301no—
275C2×D3—301no—
276C2×D3—301no—
277C2×D3—301no—
278C2×D3—302no—
279C2×D3—301no—
280C2×D3—301no—
281C2×D3—301no—
282C2×D3—301no—
283C2×D3—301no—
284C2×D3—301no—
285C2×D3—601no—
286C2×D3—601no—
287C2×D3—601no—
288C2×D3—601no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—32no—
293C3×C4—61no—
294C3×C4—301no—
295Dic3—21no—
296Dic3—101no—
297Dic3D6012yescomplemented
298C2×C5#379911yescharacteristic
299C2×C5D3×D1211yescharacteristic
300C2×C5#381111yescharacteristic
301D5—121no—
302D5—182no—
303D5—361no—
304C32#404111yescharacteristic, complemented, Sylow
305C23—151no—
306C23—451no—
307C23—451no—
308D4—902no—
309D4—902no—
310D4—902no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—151no—
314C2×C4—902no—
315C2×C4D3×D1511yescharacteristic
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—601no—
320C2×C3#677311yescharacteristic
321C2×C3D3×D2011yescharacteristic
322C2×C3#679011yescharacteristic
323C2×C3C2×D6011yescharacteristic
324C2×C3D4×D1511yescharacteristic
325C2×C3#682111yescharacteristic
326D3—201no—
327D3—302no—
328D3—302no—
329D3—602no—
330D3—602no—
331D3—601no—
332D3—601no—
333C5#6391011yescharacteristic, complemented, Sylow
334C22—301no—
335C22—301no—
336C22—301no—
337C22—452no—
338C22—901no—
339C22—901no—
340C22—901no—
341C22—901no—
342C22—901no—
343C22C2×D3×D1511yescharacteristic
344C4—21no—
345C4—32no—
346C4—61no—
347C4—301no—
348C3—21no—
349C3#9145911yescharacteristic, complemented
350C3#9178411yescharacteristic, complemented
351C2—601no—
352C2—902no—
353C2—1801no—
354C2#1062420111yescharacteristic
355C2D3×D6011yescharacteristic
356C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D3×D15
hypocenterC32×C5#121
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. C2×C4⋊(C3⋊D15)C2semidirect
2. C2×#67151C2semidirect
3. C2×#67151C2semidirect
4. C2×#67149C2semidirect
5. C3×#6714C2semidirect
6. C3×C5×Dic3⋊C4C2semidirect
7. #10623813C2semidirect
33. #6714D3semidirect
34. C5×Dic3⋊C4D3semidirect
43. C2×C3⋊D15D4semidirect
50. C3×C5×Dic3D4semidirect
57. C3×Dic3⋊C4D5semidirect
146. C5×Dic3D12semidirect
161. Dic3⋊C4D15semidirect
162. C32×C5#121semidirect
187. C3×Dic3D20semidirect
260. C3×C5#884semidirect
261. C3×C5#895semidirect
297. Dic3D60semidirect
304. C32#4041semidirect
333. C5#63910semidirect
349. C3#91459semidirect
350. C3#91784semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊D15)2
C2×#671512
C2×#671492
C3×#67142
C3×C5×Dic3⋊C42
#106238132
#917843
#914593
#639105