Finite Group Databasebeta

← C3×#91828 #13088029

Subgroups — C3×#91828 #13088029

Order 1440.

430 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×#1220C211yesmaximal, characteristic, complemented
3C2×C3×#1220C211yesmaximal, characteristic, complemented
4C22×C3×Dic15C211yesmaximal, characteristic, complemented
5C3×#6719C211yesmaximal, characteristic, complemented
6C3×#6714C211yesmaximal, characteristic, complemented
7C3×#6712C211yesmaximal, characteristic, complemented
8#91828C311yesmaximal, characteristic, direct product factor
9C3×#4085—31nomaximal
10C23×C32×C5C2211yescharacteristic
11C23×C32×C5C2211yescharacteristic
12C22×C3×D15C2211yescharacteristic
13C32×C5×D4—22no—
14C2×C32×C4×C5C2211yescharacteristic
15C3×#1220—22no—
16C3×#1220—22no—
17C2×C3×Dic15—22no—
18C2×C3×Dic15C2211yescharacteristic
19C2×C3×Dic15C2211yescharacteristic
20C2×C3×Dic15C2211yescharacteristic
21C3×#939—51nomaximal, Hall
22C2×C3×C5×D4—21no—
23C2×C3×C5×D4D311yescharacteristic, complemented
24C2×C3×C5×D4C2×C311yescharacteristic, complemented
25C2×#1220C2×C311yescharacteristic, complemented
26C2×#1220C2×C311yescharacteristic, complemented
27C22×Dic15C2×C311yescharacteristic, complemented
28C2×C3×C22⋊D5—31no—
29C2×C3×C22⋊D5—31no—
30C22×C3×Dic5—31no—
31#6719C2×C311yescharacteristic, complemented
32#6714C2×C311yescharacteristic, complemented
33#6712C2×C311yescharacteristic, complemented
34C3×C22⋊Dic5—31no—
35C3×#685—31no—
36C3×#683—31no—
37C22×C32×C5—21no—
38C22×C32×C5—21no—
39C22×C32×C5—21no—
40C22×C32×C5—21no—
41C22×C32×C5—21no—
42C22×C32×C5D412yescomplemented
43C22×C32×C5C2311yescharacteristic
44C2×C3×D15—21no—
45C2×C3×D15—21no—
46C2×C3×D15—21no—
47C32×C4×C5—21no—
48C3×Dic15—21no—
49C3×Dic15—21no—
50C3×Dic15D412yescomplemented
51#4085—31noHall
52C2×C32×D4D511yescharacteristic, complemented
53C2×C3×#67—51no—
54C2×C3×#67—51no—
55C22×C3×Dic3—51no—
56C3×#217—51no—
57C3×(C2×D3)⋊C4—51no—
58C3×Dic3⋊C4—51no—
59C23×C3×C5—21no—
60C23×C3×C5—21no—
61C23×C3×C5C2×D311yescharacteristic
62C23×C3×C5C2×D311yescharacteristic
63C23×C3×C5C22×C311yescharacteristic
64C23×C3×C5C22×C311yescharacteristic
65C22×D15C22×C311yescharacteristic
66C22×C3×D5—31no—
67C3×C5×D4—24no—
68C3×C5×D4—22no—
69C3×C5×D4—22no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5C2×D311yescharacteristic
72C2×C3×C4×C5C22×C311yescharacteristic
73#1220—22no—
74#1220—22no—
75C2×Dic15—22no—
76C2×Dic15C22×C311yescharacteristic
77C2×Dic15C22×C311yescharacteristic
78C2×Dic15C22×C311yescharacteristic
79C3×C22⋊D5—62no—
80C3×C22⋊D5—62no—
81C2×C3×Dic5—31no—
82C2×C3×Dic5—31no—
83C2×C3×Dic5—31no—
84C2×C3×Dic5—62no—
85C3×#121—151no—
86#939—51no—
87C2×C32×C5—22no—
88C2×C32×C5—41no—
89C2×C32×C5C2×D411yescharacteristic
90C2×C32×C5C2×D411yescharacteristic
91C2×C32×C5#4111yescharacteristic
92C3×D15—41no—
93C2×C5×D4C3×D311yescharacteristic, complemented
94C2×C22⋊D5—31no—
95C2×C22⋊D5—31no—
96C22×Dic5—31no—
97C22⋊Dic5—31no—
98#685—31no—
99#683—31no—
100C23×C32C2×D511yescharacteristic
101C23×C32C2×D511yescharacteristic
102C22×C3×D3—51no—
103C32×D4—22no—
104C2×C32×C4C2×D511yescharacteristic
105C3×#67—102no—
106C3×#67—102no—
107C2×C3×Dic3—51no—
108C2×C3×Dic3—51no—
109C2×C3×Dic3—51no—
110C2×C3×Dic3—102no—
111C22×C3×C5—21no—
112C22×C3×C5—21no—
113C22×C3×C5—21no—
114C22×C3×C5—21no—
115C22×C3×C5—22no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5—21no—
119C22×C3×C5—21no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5—22no—
123C22×C3×C5—21no—
124C22×C3×C5—41no—
125C22×C3×C5—41no—
126C22×C3×C5—41no—
127C22×C3×C5—41no—
128C22×C3×C5#6712yescomplemented
129C22×C3×C5C3×D412yescomplemented
130C22×C3×C5C22×D311yescharacteristic
131C22×C3×C5C23×C311yescharacteristic
132C2×D15—21no—
133C2×D15—21no—
134C2×D15—21no—
135C2×C3×D5—61no—
136C2×C3×D5—61no—
137C2×C3×D5—61no—
138C3×C4×C5—22no—
139C3×C4×C5—21no—
140C3×C4×C5—21no—
141Dic15—21no—
142Dic15—21no—
143Dic15C3×D412yescomplemented
144C3×Dic5—32no—
145C3×Dic5—61no—
146C3×Dic5—61no—
147C2×C3×D4—21no—
148C2×C3×D4—151no—
149C2×C3×D4—151no—
150C2×C3×D4C3×D511yescharacteristic, complemented
151C2×C3×D4D1511yescharacteristic, complemented
152C22×C3×C4—151no—
153C2×#67—51no—
154C2×#67—51no—
155C22×Dic3—51no—
156C3×C4⋊C4—151no—
157C3×C22⋊C4—151no—
158C3×C22⋊C4—151no—
159#217—51no—
160(C2×D3)⋊C4—51no—
161Dic3⋊C4—51no—
162C32×C5#12111yescharacteristic, complemented, Hall
163C23×C5C2×C3×D311yescharacteristic
164C23×C5C2×C3×D311yescharacteristic
165C22×D5—31no—
166C5×D4—22no—
167C2×C4×C5C2×C3×D311yescharacteristic
168C22⋊D5—62no—
169C22⋊D5—62no—
170C2×Dic5—31no—
171C2×Dic5—31no—
172C2×Dic5—31no—
173C2×Dic5—62no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32—21no—
179C22×C32C22⋊D512yescomplemented
180C22×C32C22×D511yescharacteristic
181C2×C3×D3—101no—
182C2×C3×D3—101no—
183C2×C3×D3—101no—
184C32×C4—21no—
185C3×Dic3—52no—
186C3×Dic3—101no—
187C3×Dic3—101no—
188#121—151noSylow
189C2×C3×C5—22no—
190C2×C3×C5—22no—
191C2×C3×C5—21no—
192C2×C3×C5—21no—
193C2×C3×C5—21no—
194C2×C3×C5—42no—
195C2×C3×C5—42no—
196C2×C3×C5—41no—
197C2×C3×C5—41no—
198C2×C3×C5D3×D411yescharacteristic
199C2×C3×C5#23711yescharacteristic
200C2×C3×C5C2×#6711yescharacteristic
201C2×C3×C5C2×C3×D411yescharacteristic
202C2×C3×C5C2×C3×D411yescharacteristic
203C2×C3×C5C3×#4111yescharacteristic
204D15—41no—
205C3×D5—121no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—151no—
209C23×C3C2×C3×D511yescharacteristic
210C23×C3C2×C3×D511yescharacteristic
211C23×C3C2×D1511yescharacteristic
212C23×C3C2×D1511yescharacteristic
213C22×D3—51no—
214C3×D4—24no—
215C3×D4—22no—
216C3×D4—22no—
217C3×D4—302no—
218C3×D4—302no—
219C2×C3×C4—21no—
220C2×C3×C4—151no—
221C2×C3×C4—151no—
222C2×C3×C4—151no—
223C2×C3×C4—302no—
224C2×C3×C4C2×C3×D511yescharacteristic
225C2×C3×C4C2×D1511yescharacteristic
226#67—102no—
227#67—102no—
228C2×Dic3—51no—
229C2×Dic3—51no—
230C2×Dic3—51no—
231C2×Dic3—102no—
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5C3×#6712yescomplemented
238C22×C5C22×C3×D311yescharacteristic
239C2×D5—61no—
240C2×D5—61no—
241C2×D5—61no—
242C4×C5—21no—
243Dic5—32no—
244Dic5—61no—
245Dic5—61no—
246C2×C32—22no—
247C2×C32—41no—
248C2×C32D4×D511yescharacteristic
249C2×C32#71111yescharacteristic
250C2×C32C2×C22⋊D511yescharacteristic
251C3×D3—201no—
252C2×D4—151no—
253C2×D4—151no—
254C2×D4C3×D1511yescharacteristic, complemented
255C22×C4—151no—
256C4⋊C4—151no—
257C22⋊C4—151no—
258C22⋊C4—151no—
259C3×C5—21no—
260C3×C5#93911yescharacteristic, complemented
261C3×C5C3×#12111yescharacteristic, complemented
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—301no—
280C22×C3—301no—
281C22×C3—301no—
282C22×C3C3×C22⋊D512yescomplemented
283C22×C3#122012yescomplemented
284C22×C3C22×C3×D511yescharacteristic
285C22×C3C22×D1511yescharacteristic
286C2×D3—101no—
287C2×D3—101no—
288C2×D3—101no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—152no—
293C3×C4—301no—
294C3×C4—301no—
295Dic3—52no—
296Dic3—101no—
297Dic3—101no—
298C2×C5—22no—
299C2×C5—41no—
300C2×C5C3×D3×D411yescharacteristic
301C2×C5C3×#23711yescharacteristic
302C2×C5C2×C3×#6711yescharacteristic
303D5—121no—
304C32#408511yescharacteristic, complemented, Sylow
305C23—151no—
306C23C2×C3×D1511yescharacteristic
307C23C2×C3×D1511yescharacteristic
308D4—22no—
309D4—302no—
310D4—302no—
311C2×C4—151no—
312C2×C4—151no—
313C2×C4—151no—
314C2×C4—302no—
315C2×C4C2×C3×D1511yescharacteristic
316C2×C3—22no—
317C2×C3—22no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—42no—
322C2×C3—42no—
323C2×C3—41no—
324C2×C3—41no—
325C2×C3—601no—
326C2×C3C3×D4×D511yescharacteristic
327C2×C3C3×#71111yescharacteristic
328C2×C3C2×C3×C22⋊D511yescharacteristic
329C2×C3D4×D1511yescharacteristic
330C2×C3#681911yescharacteristic
331C2×C3C2×#122011yescharacteristic
332D3—201no—
333C5C3×#93911yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—301no—
340C22—301no—
341C22—301no—
342C22C3×#122012yescomplemented
343C22C22×C3×D1511yescharacteristic
344C4—21no—
345C4—152no—
346C4—301no—
347C4—301no—
348C3—21no—
349C3C3×#408511yescharacteristic, complemented
350C3#9182811yescharacteristic, direct product factor
351C2—22no—
352C2—41no—
353C2—601no—
354C2C3×D4×D1511yescharacteristic
355C2C3×#681911yescharacteristic
356C2C2×C3×#122011yescharacteristic
subgroupG/H
centerC22×C3C22×D15
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C22×C3×D15
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C3×D4D15
hypocenterC3×C5C3×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×C3×#1220C2semidirect
3. C2×C3×#1220C2semidirect
4. C22×C3×Dic15C2semidirect
5. C3×#6719C2semidirect
6. C3×#6714C2semidirect
7. C3×#6712C2semidirect
8. #91828C3direct (N × H)
23. C2×C3×C5×D4D3semidirect
24. C2×C3×C5×D4C2×C3semidirect
25. C2×#1220C2×C3semidirect
26. C2×#1220C2×C3semidirect
27. C22×Dic15C2×C3semidirect
31. #6719C2×C3semidirect
32. #6714C2×C3semidirect
33. #6712C2×C3semidirect
42. C22×C32×C5D4semidirect
50. C3×Dic15D4semidirect
52. C2×C32×D4D5semidirect
93. C2×C5×D4C3×D3semidirect
128. C22×C3×C5#67semidirect
129. C22×C3×C5C3×D4semidirect
143. Dic15C3×D4semidirect
150. C2×C3×D4C3×D5semidirect
151. C2×C3×D4D15semidirect
162. C32×C5#121semidirect
179. C22×C32C22⋊D5semidirect
237. C22×C5C3×#67semidirect
254. C2×D4C3×D15semidirect
260. C3×C5#939semidirect
261. C3×C5C3×#121semidirect
282. C22×C3C3×C22⋊D5semidirect
283. C22×C3#1220semidirect
304. C32#4085semidirect
333. C5C3×#939semidirect
342. C22C3×#1220semidirect
349. C3C3×#4085semidirect
350. C3#91828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×C3×#12202
C22×C3×Dic152
C3×#67192
C3×#67142
C3×#67122
#918283
C3×#40853
C3×#9395