Finite Group Databasebeta

← #13087444

Subgroups — #13087444

Order 1440.

410 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 86 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×C3×D60C211yesmaximal, characteristic, complemented
2C2×#67151C211yesmaximal, characteristic, complemented
3C2×#67151C211yesmaximal, characteristic, complemented
4C2×Dic3×D15C211yesmaximal, characteristic, complemented
5#10623908C211yesmaximal, characteristic, complemented
6C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10623811C211yesmaximal, characteristic, complemented
8#91784—31nomaximal
9#91409—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C22×C3×D15C2211yescharacteristic
13C2×C32×C4×C5C2211yescharacteristic
14C2×C3⋊Dic15C2211yescharacteristic
15C3×D60—22no—
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67151—22no—
19#67151—22no—
20Dic3×D15—22no—
21#63886—51nomaximal, Hall
22C2×D60—31no—
23C2×D60—31no—
24C2×D60D311yescharacteristic, complemented
25C2×C4×D15—31no—
26C2×C3×D20—31no—
27C2×#1202—31no—
28C2×#1202—31no—
29C2×D5×Dic3—31no—
30C3×C5×C4⋊C4—31no—
31#6714—31no—
32#6714—31no—
33#6714—31no—
34#6714—61no—
35C5×Dic3⋊C4D311yescharacteristic, complemented
36#6665—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×D15—21no—
44C2×C3×D15—21no—
45C2×C3×D15—21no—
46C2×C3×D15D412yescomplemented
47C32×C4×C5—21no—
48C3⋊Dic15—21no—
49C3×C5×Dic3—21no—
50C3×C5×Dic3D412yescomplemented
51#4041—91noHall
52C2×C3×D12—51no—
53C2×#626—51no—
54C2×#626—51no—
55C2×D3×Dic3—51no—
56#3752—51no—
57C3×Dic3⋊C4D511yescharacteristic, complemented
58(C2×D3)⋊Dic3—51no—
59C22×D15—31no—
60C22×D15—31no—
61C22×D15—61no—
62C22×D15C2×D311yescharacteristic
63C22×D15C2×D311yescharacteristic
64C22×C3×D5—31no—
65C22×C3×D5—31no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5—31no—
68C2×C3×C4×C5—31no—
69C2×C3×C4×C5C2×D311yescharacteristic
70C2×C3×C4×C5C2×D311yescharacteristic
71C2×Dic15—31no—
72C2×Dic15—31no—
73C2×Dic15—61no—
74D60—22no—
75D60—62no—
76D60—62no—
77C4×D15—62no—
78C2×C5×Dic3C2×D311yescharacteristic
79C2×C5×Dic3C2×D311yescharacteristic
80C3×D20—62no—
81#1202—62no—
82#1202—62no—
83D5×Dic3—62no—
84#939—151no—
85#895—151no—
86C2×C32×C5C2×D411yescharacteristic
87C2×C32×C5C2×D411yescharacteristic
88C2×C32×C5#4111yescharacteristic
89C3⋊D15—41no—
90C3×D15—22no—
91C3×D15—41no—
92C2×D20—31no—
93C2×D20—91no—
94C2×D20—91no—
95C2×C4×D5—91no—
96C5×C4⋊C4—31no—
97#685—91no—
98#685—91no—
99C22×C3⋊D3—51no—
100C22×C3×D3—51no—
101C22×C3×D3—51no—
102C2×C32×C4C2×D511yescharacteristic
103C2×C3⋊Dic3—51no—
104C2×C3×Dic3C2×D511yescharacteristic
105C2×C3×Dic3C2×D511yescharacteristic
106C3×D12—102no—
107#626—102no—
108#626—102no—
109D3×Dic3—102no—
110C22×C3×C5—21no—
111C22×C3×C5C22×D311yescharacteristic
112C22×C3×C5C22×D311yescharacteristic
113C2×D15—21no—
114C2×D15—21no—
115C2×D15—21no—
116C2×D15—21no—
117C2×D15—21no—
118C2×D15—62no—
119C2×D15—61no—
120C2×D15—61no—
121C2×D15—61no—
122C2×D15—61no—
123C2×D15—61no—
124C2×D15—61no—
125C2×D15—121no—
126C2×D15—121no—
127C2×D15#6712yescomplemented
128C2×C3×D5—32no—
129C2×C3×D5—61no—
130C2×C3×D5—61no—
131C2×C3×D5—61no—
132C2×C3×D5—61no—
133C2×C3×D5—61no—
134C3×C4×C5—21no—
135C3×C4×C5—21no—
136C3×C4×C5—32no—
137C3×C4×C5—41no—
138C3×C4×C5—61no—
139Dic15—61no—
140Dic15—61no—
141Dic15—121no—
142C5×Dic3—21no—
143C5×Dic3D1212yescomplemented
144C2×C3×D4—151no—
145C2×#67—151no—
146C2×#67—151no—
147C22×Dic3—151no—
148C2×D12—51no—
149C2×D12—151no—
150C2×D12—151no—
151C2×C4×D3—151no—
152C3×C4⋊C4—31no—
153#217—151no—
154(C2×D3)⋊C4—151no—
155(C2×D3)⋊C4—151no—
156(C2×D3)⋊C4—151no—
157(C2×D3)⋊C4—301no—
158Dic3⋊C4D1511yescharacteristic, complemented
159C32×C5#12111yescharacteristic, complemented, Hall
160C22×D5—31no—
161C22×D5—31no—
162C22×D5—91no—
163C2×C4×C5—31no—
164C2×C4×C5—31no—
165C2×C4×C5D3211yescharacteristic
166C2×Dic5—91no—
167D20—62no—
168D20—182no—
169D20—182no—
170C4×D5—182no—
171C22×C32C22×D511yescharacteristic
172C2×C3⋊D3—101no—
173C2×C3⋊D3—101no—
174C2×C3⋊D3—101no—
175C2×C3×D3—52no—
176C2×C3×D3—101no—
177C2×C3×D3—101no—
178C2×C3×D3—101no—
179C2×C3×D3—101no—
180C2×C3×D3—101no—
181C32×C4—21no—
182C3⋊Dic3—101no—
183C3×Dic3—21no—
184C3×Dic3D2012yescomplemented
185#121—451noSylow
186C2×C3×C5—21no—
187C2×C3×C5—21no—
188C2×C3×C5—21no—
189C2×C3×C5C2×D1211yescharacteristic
190C2×C3×C5D3×D411yescharacteristic
191C2×C3×C5D3×D411yescharacteristic
192C2×C3×C5#23711yescharacteristic
193C2×C3×C5#23911yescharacteristic
194C2×C3×C5C2×#6711yescharacteristic
195D15—22no—
196D15—41no—
197D15—122no—
198D15—121no—
199D15—121no—
200C3×D5—62no—
201C3×D5—121no—
202C23×C3—151no—
203C23×C3—151no—
204C22×D3—51no—
205C22×D3—51no—
206C22×D3—151no—
207C22×D3—151no—
208C22×D3—301no—
209C3×D4—302no—
210C2×C3×C4—21no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4D3×D511yescharacteristic
214C2×C3×C4C2×D1511yescharacteristic
215#67—302no—
216#67—302no—
217C2×Dic3—151no—
218C2×Dic3—151no—
219C2×Dic3—301no—
220C2×Dic3—302no—
221C2×Dic3C2×D1511yescharacteristic
222C2×Dic3C2×D1511yescharacteristic
223D12—102no—
224D12—302no—
225D12—302no—
226C4×D3—302no—
227C22×C5C2×D3211yescharacteristic
228C2×D5—32no—
229C2×D5—61no—
230C2×D5—61no—
231C2×D5—61no—
232C2×D5—61no—
233C2×D5—61no—
234C2×D5—181no—
235C2×D5—181no—
236C2×D5—181no—
237C4×C5—21no—
238C4×C5—32no—
239C4×C5—61no—
240Dic5—181no—
241C2×C32C2×D2011yescharacteristic
242C2×C32D4×D511yescharacteristic
243C2×C32#71311yescharacteristic
244C3⋊D3—201no—
245C3×D3—102no—
246C3×D3—201no—
247C2×D4—151no—
248C2×D4—451no—
249C2×D4—451no—
250C22×C4—451no—
251C4⋊C4—31no—
252C22⋊C4—451no—
253C22⋊C4—451no—
254C3×C5—21no—
255C3×C5#89511yescharacteristic, complemented
256C3×C5#93911yescharacteristic, complemented
257C22×C3—21no—
258C22×C3—152no—
259C22×C3—301no—
260C22×C3—301no—
261C22×C3—301no—
262C22×C3—301no—
263C22×C3—301no—
264C22×C3C2×D3×D511yescharacteristic
265C22×C3C22×D1511yescharacteristic
266C2×D3—52no—
267C2×D3—101no—
268C2×D3—101no—
269C2×D3—101no—
270C2×D3—101no—
271C2×D3—101no—
272C2×D3—302no—
273C2×D3—301no—
274C2×D3—301no—
275C2×D3—301no—
276C2×D3—301no—
277C2×D3—301no—
278C2×D3—301no—
279C2×D3—601no—
280C2×D3—601no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—32no—
284C3×C4—41no—
285C3×C4—61no—
286Dic3—21no—
287Dic3—301no—
288Dic3—301no—
289Dic3—601no—
290Dic3D6012yescomplemented
291C2×C5#379611yescharacteristic
292C2×C5D3×D1211yescharacteristic
293C2×C5D3×#6711yescharacteristic
294D5—62no—
295D5—121no—
296D5—361no—
297C32#404111yescharacteristic, complemented, Sylow
298C23—151no—
299C23—151no—
300C23—451no—
301D4—302no—
302D4—902no—
303D4—902no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—451no—
307C2×C4—902no—
308C2×C4D3×D1511yescharacteristic
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—302no—
313C2×C3—601no—
314C2×C3#676611yescharacteristic
315C2×C3D3×D2011yescharacteristic
316C2×C3D5×#6711yescharacteristic
317C2×C3C2×D6011yescharacteristic
318C2×C3D4×D1511yescharacteristic
319C2×C3#682111yescharacteristic
320D3—102no—
321D3—201no—
322D3—602no—
323D3—601no—
324D3—601no—
325C5#6388611yescharacteristic, complemented, Sylow
326C22—152no—
327C22—301no—
328C22—301no—
329C22—301no—
330C22—301no—
331C22—301no—
332C22—901no—
333C22—901no—
334C22—901no—
335C22C2×D3×D1511yescharacteristic
336C4—21no—
337C4—32no—
338C4—61no—
339C4—901no—
340C3—21no—
341C3#9140911yescharacteristic, complemented
342C3#9178411yescharacteristic, complemented
343C2—302no—
344C2—601no—
345C2—1801no—
346C2#1062419411yescharacteristic
347C2D3×D6011yescharacteristic
348C2#67×D1511yescharacteristic
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×C3×D60C2semidirect
2. C2×#67151C2semidirect
3. C2×#67151C2semidirect
4. C2×Dic3×D15C2semidirect
5. #10623908C2semidirect
6. C3×C5×Dic3⋊C4C2semidirect
7. #10623811C2semidirect
24. C2×D60D3semidirect
35. C5×Dic3⋊C4D3semidirect
46. C2×C3×D15D4semidirect
50. C3×C5×Dic3D4semidirect
57. C3×Dic3⋊C4D5semidirect
127. C2×D15#67semidirect
143. C5×Dic3D12semidirect
158. Dic3⋊C4D15semidirect
159. C32×C5#121semidirect
184. C3×Dic3D20semidirect
255. C3×C5#895semidirect
256. C3×C5#939semidirect
290. Dic3D60semidirect
297. C32#4041semidirect
325. C5#63886semidirect
341. C3#91409semidirect
342. C3#91784semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D602
C2×#671512
C2×Dic3×D152
#106239082
C3×C5×Dic3⋊C42
#106238112
#917843
#914093
#638865