Finite Group Databasebeta

← C3×#10599218 #14285073

Subgroups — C3×#10599218 #14285073

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66062C211yesmaximal, characteristic
2C3×#65124C211yesmaximal, characteristic
3C3×D5×C4⋊C8C211yesmaximal, characteristic
4C3×C5×#332C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64702C211yesmaximal, characteristic, complemented
8#10599218C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×#4092—21no—
11C3×Q8×Dic5—21no—
12C2×C3×C8×D5—21no—
13C3×#4043—21no—
14C3×#4038C412yes—
15C3×#4036C412yes—
16C3×#4033—21no—
17C3×C42×D5C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×#3952—21no—
22C3×#3947—21no—
23C3×#3946—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4⋊#168C2211yescharacteristic
26C3×#1552—51nomaximal, Hall
27#66062C2×C311yescharacteristic
28#65124C2×C311yescharacteristic
29D5×C4⋊C8C2×C311yescharacteristic
30C5×#332C2×C311yescharacteristic, complemented
31#64767C2×C311yescharacteristic, complemented
32#64706C2×C311yescharacteristic, complemented
33#64702C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C4×D5C2×C411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4C2×C412yes—
43C3×C42×C5C2311yescharacteristic
44C3×#685—22no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—22no—
47C3×C4⋊Dic5C2×C412yes—
48C3×#683—22no—
49C3×C4×Dic5—22no—
50C3×C4×Dic5C2×C411yescharacteristic
51C3×C4×Dic5D411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55C3×C8×D5—42no—
56C3×#533—51no—
57C3×#432—51no—
58C2×C3×C4⋊C8—51no—
59C3×#332—51no—
60C3×#332—51no—
61C3×#332—51no—
62C3×#332D511yescharacteristic, complemented
63C5×C4⋊Q8C22×C311yescharacteristic
64#4092—21no—
65Q8×Dic5—21no—
66C2×C8×D5—21no—
67#4043—21no—
68#4038C3×C412yes—
69#4036C3×C412yes—
70#4033—21no—
71C42×D5C22×C311yescharacteristic
72#4015C22×C311yescharacteristic
73C5×C4⋊C8C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75#3952—21no—
76#3947—21no—
77#3946—21no—
78C4⋊#168C22×C311yescharacteristic
79C4⋊#168C22×C311yescharacteristic
80#1552—51noSylow
81C22×C3×D5C22⋊C411yescharacteristic
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×Dic5—22no—
89C2×C3×Dic5C22⋊C411yescharacteristic
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C3×C4×D5—22no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C3×#168—41no—
102C3×#168—41no—
103C22×C3×C8—101no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×#125—52no—
107C3×C22⋊Q8—101no—
108C3×C22⋊Q8—101no—
109C3×C4×Q8—101no—
110C3×C4×Q8—101no—
111C3×#117—52no—
112C2×C3×C42—51no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8—51no—
115C3×C4⋊C8—101no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C22⋊C8—101no—
119C3×#97—101no—
120C2×C5×Q8—21no—
121C2×C4×D5C2×C3×C411yescharacteristic
122C2×C4×D5C3×D411yescharacteristic
123C2×C4×D5C3×D411yescharacteristic
124C2×Dic10—21no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C2×C3×C412yes—
129C42×C5C23×C311yescharacteristic
130#685—22no—
131C4⋊Dic5—21no—
132C4⋊Dic5—22no—
133C4⋊Dic5C2×C3×C412yes—
134#683—22no—
135C4×Dic5—22no—
136C4×Dic5C2×C3×C411yescharacteristic
137C4×Dic5C3×D411yescharacteristic
138C4×Dic5C3×D411yescharacteristic
139C2×#168—21no—
140C2×#168—21no—
141C8×D5—42no—
142#533—51no—
143#432—51no—
144C2×C4⋊C8—51no—
145#332—51no—
146#332—51no—
147#332—51no—
148#332C3×D511yescharacteristic, complemented
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#10112yes—
153C3×C4×C5—21no—
154C3×C4×C5—42no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C3×Dic5—42no—
163C2×C3×Q8—21no—
164C2×C3×Q8—101no—
165C22×C3×C4—51no—
166C22×C3×C4—51no—
167C22×C3×C4—51no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—101no—
171C2×C3×C8—101no—
172C2×C3×C8—202no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—52no—
175C3×C4⋊C4—102no—
176C3×C4⋊C4—102no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4C4×D512yes—
179C3×C22⋊C4—102no—
180C3×C42—51no—
181C3×C42—51no—
182C3×C42—51no—
183C3×C42—102no—
184C3×C42C22×D511yescharacteristic
185C22×D5C3×C22⋊C411yescharacteristic
186C5×Q8—41no—
187C5×Q8—41no—
188C2×C4×C5—22no—
189C2×C4×C5C22×C3×C411yescharacteristic
190C2×C4×C5C2×C3×D411yescharacteristic
191C2×C4×C5C2×C3×D411yescharacteristic
192C2×Dic5—22no—
193C2×Dic5C3×C22⋊C411yescharacteristic
194C2×Dic5C3×C22⋊C411yescharacteristic
195C2×Dic5C3×C22⋊C411yescharacteristic
196C4×D5—22no—
197C4×D5—21no—
198C4×D5—21no—
199C4×D5—21no—
200C4×D5—21no—
201Dic10—41no—
202Dic10—41no—
203C5×C8—41no—
204C5×C8—41no—
205#168—41no—
206#168—41no—
207C22×C8—101no—
208C4⋊Q8—51no—
209C4⋊Q8C2×C3×D511yescharacteristic
210#125—52no—
211C22⋊Q8—101no—
212C22⋊Q8—101no—
213C4×Q8—101no—
214C4×Q8—101no—
215#117—52no—
216C2×C42—51no—
217C4⋊C8—51no—
218C4⋊C8—51no—
219C4⋊C8—101no—
220C4⋊C8C2×C3×D511yescharacteristic
221C4⋊C8C2×C3×D511yescharacteristic
222C22⋊C8—101no—
223#97—101no—
224C2×C3×C5C2×#10111yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#41711yescharacteristic
227C3×D5—22no—
228C23×C3—51no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—201no—
232C3×Q8—201no—
233C2×C3×C4—22no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—51no—
237C2×C3×C4—102no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4—101no—
242C2×C3×C4—102no—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C3×C8—41no—
247C3×C8—41no—
248C3×C8—201no—
249C3×C8—201no—
250C22×C5C2×C3×C22⋊C411yescharacteristic
251C2×D5—21no—
252C2×D5—21no—
253C2×D5C3×#10112yes—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5C3×#13511yescharacteristic
257C4×C5C3×#13511yescharacteristic
258C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
259C4×C5C3×#13711yescharacteristic
260Dic5—21no—
261Dic5—21no—
262Dic5—21no—
263Dic5—42no—
264C2×Q8—21no—
265C2×Q8—101no—
266C22×C4—51no—
267C22×C4—51no—
268C22×C4—51no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—101no—
272C2×C8—101no—
273C2×C8—202no—
274C4⋊C4—21no—
275C4⋊C4—52no—
276C4⋊C4—102no—
277C4⋊C4—102no—
278C4⋊C4—101no—
279C4⋊C4C3×C4×D512yes—
280C22⋊C4—102no—
281C42—51no—
282C42—51no—
283C42—51no—
284C42—102no—
285C42C22×C3×D511yescharacteristic
286C3×C5#155211yescharacteristic, complemented, Hall
287C22×C3—52no—
288C22×C3—101no—
289C22×C3—101no—
290C22×C3D5×C22⋊C411yescharacteristic
291C3×C4—21no—
292C3×C4—42no—
293C3×C4—101no—
294C3×C4—101no—
295C3×C4—101no—
296C3×C4—202no—
297C3×C4#405711yescharacteristic
298C3×C4#406111yescharacteristic
299C3×C4#406211yescharacteristic
300C3×C4#406511yescharacteristic
301C2×C5C2×C3×#10111yescharacteristic
302C2×C5C3×#41611yescharacteristic
303C2×C5C3×#41711yescharacteristic
304D5—22no—
305C23—51no—
306Q8—41no—
307Q8—41no—
308Q8—201no—
309Q8—201no—
310C2×C4—22no—
311C2×C4—51no—
312C2×C4—51no—
313C2×C4—51no—
314C2×C4—102no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—101no—
319C2×C4—102no—
320C2×C4C2×C3×C4×D511yescharacteristic
321C2×C4C3×D4×D511yescharacteristic
322C2×C4C3×D4×D511yescharacteristic
323C8—41no—
324C8—41no—
325C8—201no—
326C8—201no—
327C2×C3—102no—
328C2×C3D5×#10111yescharacteristic
329C2×C3#6506011yescharacteristic
330C2×C3#6509311yescharacteristic
331C5C3×#155211yescharacteristic, complemented, Sylow
332C22—52no—
333C22—101no—
334C22—101no—
335C22C3×D5×C22⋊C411yescharacteristic
336C4—21no—
337C4—42no—
338C4—101no—
339C4—101no—
340C4—101no—
341C4—202no—
342C4C3×#405711yescharacteristic
343C4C3×#406111yescharacteristic
344C4C3×#406211yescharacteristic
345C4C3×#406511yescharacteristic
346C3#1059921811yescharacteristic, direct product factor, Sylow
347C2—102no—
348C2C3×D5×#10111yescharacteristic
349C2C3×#6506011yescharacteristic
350C2C3×#6509311yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#332C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC3×#332D5
hypocenterC5C3×#1552
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
4. C3×C5×#332C2semidirect
5. C3×#64767C2semidirect
6. C3×#64706C2semidirect
7. C3×#64702C2semidirect
8. #10599218C3direct (N × H)
30. C5×#332C2×C3semidirect
31. #64767C2×C3semidirect
32. #64706C2×C3semidirect
33. #64702C2×C3semidirect
62. C3×#332D5semidirect
148. #332C3×D5semidirect
286. C3×C5#1552semidirect
331. C5C3×#1552semidirect
346. C3#10599218direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660622
C3×#651242
C3×D5×C4⋊C82
C3×C5×#3322
C3×#647672
C3×#647062
C3×#647022
#105992183
C3×#15525