Finite Group Databasebeta

← C3×#10604832 #14313974

Subgroups — C3×#10604832 #14313974

Order 1920.

440 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×Q16C211yesmaximal, characteristic
2C3×#65721C211yesmaximal, characteristic
3C3×D5⋊M32C211yesmaximal, characteristic
4C3×#64908C214yesmaximal, complemented
5#10604832C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×Q8×D5—21no—
7C3×#4130—21no—
8C2×C3×C5×Q16C411yescharacteristic, complemented
9C2×C3×#689—21no—
10C3×D5×Q16—21no—
11C3×D5×Q16—21no—
12C3×D5×Q16C412yescomplemented
13C3×D5×Q16C2212yes—
14C2×C3×Dic20C411yescharacteristic, complemented
15C2×C3×C8×D5C2211yescharacteristic
16C3×#3998—21no—
17C3×#3994C2212yes—
18C3×#3993—21no—
19C3×#3990—21no—
20C3×D5⋊C16C2212yes—
21C3×#2141—51nomaximal, Hall
22C2×D5×Q16C2×C311yescharacteristic
23#65721C2×C311yescharacteristic
24D5⋊M32C2×C311yescharacteristic
25#64908C2×C314yescomplemented
26C2×C3×C5×Q8—21no—
27C3×Q8×D5—22no—
28C3×Q8×D5—22no—
29C3×Q8×D5—41no—
30C3×Q8×D5—41no—
31C2×C3×C4×D5—41no—
32C2×C3×C4×D5D411yescharacteristic
33C2×C3×Dic10—21no—
34C2×C3×Dic10—41no—
35C3×C22⋊AGL(1,𝔽5)—41no—
36C3×C4⋊AGL(1,𝔽5)—22no—
37C3×C4×AGL(1,𝔽5)—41no—
38C3×C5×Q16—21no—
39C3×C5×Q16C2×C412yes—
40C2×C3×C5×C8C2×C411yescharacteristic
41C3×#689—22no—
42C3×#689—22no—
43C2×C3×#168D411yescharacteristic
44C3×Dic20—21no—
45C3×Dic20C2×C412yes—
46C3×C8×D5C2×C411yescharacteristic
47C3×C8×D5D411yescharacteristic
48C3×C8×D5D411yescharacteristic
49C3×C8×D5C2311yescharacteristic
50C3×#674—22no—
51C22×C3×Q16—51no—
52C2×C3×M32—51no—
53C3×#427—51no—
54C3×#358—54no—
55C2×Q8×D5—21no—
56#4130—21no—
57C2×C5×Q16C3×C411yescharacteristic, complemented
58C2×#689—21no—
59D5×Q16—21no—
60D5×Q16—21no—
61D5×Q16C3×C412yescomplemented
62D5×Q16C22×C312yes—
63C2×Dic20C3×C411yescharacteristic, complemented
64C2×C8×D5C22×C311yescharacteristic
65#3998—21no—
66#3994C22×C312yes—
67#3993—21no—
68#3990—21no—
69D5⋊C16C22×C312yes—
70#2141—51noSylow
71C22×C3×D5D811yescharacteristic
72C2×C3×AGL(1,𝔽5)—42no—
73C3×C5×Q8—22no—
74C3×C5×Q8—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×Dic5—41no—
78C2×C3×Dic5SD1611yescharacteristic
79C3×C4×D5—42no—
80C3×C4×D5—42no—
81C3×C4×D5C22⋊C411yescharacteristic
82C3×C4×D5D811yescharacteristic
83C3×C4×D5SD1611yescharacteristic
84C3×C4×D5C2×D411yescharacteristic
85C3×Dic10—22no—
86C3×Dic10—41no—
87C3×Dic10—42no—
88C3×Dic10—42no—
89C3×C5×C8C22⋊C411yescharacteristic
90C3×C5×C8C22×C411yescharacteristic
91C3×#168C22⋊C411yescharacteristic
92C3×#168C2×D411yescharacteristic
93C22×C3×Q8—101no—
94C2×C3×Q16—52no—
95C2×C3×Q16—52no—
96C2×C3×Q16—51no—
97C2×C3×Q16—101no—
98C2×C3×Q16—101no—
99C2×C3×Q16—101no—
100C2×C3×Q16AGL(1,𝔽5)11yescharacteristic, complemented
101C22×C3×C8—51no—
102C3×#117—101no—
103C3×M32—101no—
104C3×M32—101no—
105C2×C3×C16—52no—
106C3×#107—52no—
107C3×#106—101no—
108C2×C5×Q8—21no—
109Q8×D5—22no—
110Q8×D5—22no—
111Q8×D5—41no—
112Q8×D5—41no—
113C2×C4×D5—41no—
114C2×C4×D5C3×D411yescharacteristic
115C2×Dic10—21no—
116C2×Dic10—41no—
117C22⋊AGL(1,𝔽5)—41no—
118C4⋊AGL(1,𝔽5)—22no—
119C4×AGL(1,𝔽5)—41no—
120C5×Q16—21no—
121C5×Q16C2×C3×C412yes—
122C2×C5×C8C2×C3×C411yescharacteristic
123#689—22no—
124#689—22no—
125C2×#168C3×D411yescharacteristic
126Dic20—21no—
127Dic20C2×C3×C412yes—
128C8×D5C2×C3×C411yescharacteristic
129C8×D5C3×D411yescharacteristic
130C8×D5C3×D411yescharacteristic
131C8×D5C23×C311yescharacteristic
132#674—22no—
133C22×Q16—51no—
134C2×M32—51no—
135#427—51no—
136#358—54no—
137C22×C3×C5#10211yescharacteristic
138C2×C3×D5—22no—
139C2×C3×D5#10211yescharacteristic
140C2×C3×D5C2×D811yescharacteristic
141C3×AGL(1,𝔽5)—82no—
142C3×C4×C5—42no—
143C3×C4×C5#10211yescharacteristic
144C3×C4×C5C2×C22⋊C411yescharacteristic
145C3×Dic5—42no—
146C3×Dic5#10211yescharacteristic
147C3×Dic5C2×SD1611yescharacteristic
148C2×C3×Q8—21no—
149C2×C3×Q8—102no—
150C2×C3×Q8—102no—
151C2×C3×Q8—101no—
152C2×C3×Q8—201no—
153C2×C3×Q8—201no—
154C2×C3×Q8—201no—
155C22×C3×C4—51no—
156C22×C3×C4—201no—
157C3×Q16—21no—
158C3×Q16—52no—
159C3×Q16—102no—
160C3×Q16—102no—
161C3×Q16—101no—
162C3×Q16C2×AGL(1,𝔽5)12yes—
163C2×C3×C8—51no—
164C2×C3×C8—51no—
165C2×C3×C8—51no—
166C2×C3×C8—51no—
167C2×C3×C8—51no—
168C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
169C3×C4⋊C4—102no—
170C3×C22⋊C4—201no—
171C3×C42—201no—
172C3×C16—102no—
173C22×D5C3×D811yescharacteristic
174C2×AGL(1,𝔽5)—42no—
175C5×Q8—22no—
176C5×Q8—41no—
177C2×C4×C5—41no—
178C2×C4×C5C3×C22⋊C411yescharacteristic
179C2×Dic5—41no—
180C2×Dic5C3×SD1611yescharacteristic
181C4×D5—42no—
182C4×D5—42no—
183C4×D5C3×C22⋊C411yescharacteristic
184C4×D5C3×D811yescharacteristic
185C4×D5C3×SD1611yescharacteristic
186C4×D5C2×C3×D411yescharacteristic
187Dic10—22no—
188Dic10—41no—
189Dic10—42no—
190Dic10—42no—
191C5×C8C3×C22⋊C411yescharacteristic
192C5×C8C22×C3×C411yescharacteristic
193#168C3×C22⋊C411yescharacteristic
194#168C2×C3×D411yescharacteristic
195C22×Q8—101no—
196C2×Q16—52no—
197C2×Q16—52no—
198C2×Q16—51no—
199C2×Q16—101no—
200C2×Q16—101no—
201C2×Q16—101no—
202C2×Q16C3×AGL(1,𝔽5)11yescharacteristic, complemented
203C22×C8—51no—
204#117—101no—
205M32—101no—
206M32—101no—
207C2×C16—52no—
208#107—52no—
209#106—101no—
210C2×C3×C5—21no—
211C2×C3×C5C2×#10211yescharacteristic
212C3×D5—21no—
213C3×D5#51012yes—
214C23×C3—51no—
215C3×Q8—22no—
216C3×Q8—41no—
217C3×Q8—102no—
218C3×Q8—202no—
219C3×Q8—202no—
220C3×Q8—201no—
221C2×C3×C4—41no—
222C2×C3×C4—51no—
223C2×C3×C4—51no—
224C2×C3×C4—51no—
225C2×C3×C4—51no—
226C2×C3×C4—51no—
227C2×C3×C4—202no—
228C2×C3×C4—202no—
229C2×C3×C4—201no—
230C2×C3×C4—202no—
231C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
232C3×C8—51no—
233C3×C8—51no—
234C3×C8C22⋊AGL(1,𝔽5)11yescharacteristic
235C3×C8C22×AGL(1,𝔽5)11yescharacteristic
236C22×C5C3×#10211yescharacteristic
237C2×D5—22no—
238C2×D5C3×#10211yescharacteristic
239C2×D5C2×C3×D811yescharacteristic
240AGL(1,𝔽5)—82no—
241C4×C5—42no—
242C4×C5C3×#10211yescharacteristic
243C4×C5C2×C3×C22⋊C411yescharacteristic
244Dic5—42no—
245Dic5C3×#10211yescharacteristic
246Dic5C2×C3×SD1611yescharacteristic
247C2×Q8—21no—
248C2×Q8—102no—
249C2×Q8—102no—
250C2×Q8—101no—
251C2×Q8—201no—
252C2×Q8—201no—
253C2×Q8—201no—
254C22×C4—51no—
255C22×C4—201no—
256Q16—21no—
257Q16—52no—
258Q16—102no—
259Q16—102no—
260Q16—101no—
261Q16C2×C3×AGL(1,𝔽5)12yes—
262C2×C8—51no—
263C2×C8—51no—
264C2×C8—51no—
265C2×C8—51no—
266C2×C8—51no—
267C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
268C4⋊C4—102no—
269C22⋊C4—201no—
270C42—201no—
271C16—102no—
272C3×C5#214111yescharacteristic, complemented, Hall
273C22×C3—51no—
274C22×C3—51no—
275C22×C3—102no—
276C22×C3#400711yescharacteristic
277C3×C4—42no—
278C3×C4—51no—
279C3×C4—51no—
280C3×C4—202no—
281C3×C4—402no—
282C3×C4#400711yescharacteristic
283C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
284C2×C5—21no—
285C2×C5C2×C3×#10211yescharacteristic
286D5—21no—
287D5C3×#51012yes—
288C23—51no—
289Q8—22no—
290Q8—41no—
291Q8—102no—
292Q8—202no—
293Q8—202no—
294Q8—201no—
295C2×C4—41no—
296C2×C4—51no—
297C2×C4—51no—
298C2×C4—51no—
299C2×C4—51no—
300C2×C4—51no—
301C2×C4—202no—
302C2×C4—202no—
303C2×C4—201no—
304C2×C4—202no—
305C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
306C8—51no—
307C8—51no—
308C8C3×C22⋊AGL(1,𝔽5)11yescharacteristic
309C8C22×C3×AGL(1,𝔽5)11yescharacteristic
310C2×C3—21no—
311C2×C3—52no—
312C2×C3—101no—
313C2×C3C2×#400711yescharacteristic
314C5C3×#214111yescharacteristic, complemented, Sylow
315C22—51no—
316C22—51no—
317C22—102no—
318C22C3×#400711yescharacteristic
319C4—42no—
320C4—51no—
321C4—51no—
322C4—202no—
323C4—402no—
324C4C3×#400711yescharacteristic
325C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
326C3#1060483211yescharacteristic, direct product factor, Sylow
327C2—21no—
328C2—52no—
329C2—101no—
330C2C2×C3×#400711yescharacteristic
subgroupG/H
centerC2×C3C2×#4007
commutatorC5×C8C22×C3×C4
FrattiniC8C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×Q16C4
socleC2×C3×C5C2×#102
prime radicalC22×C3×D5D8
cosocleC8×D5C23×C3
hypercenterC2×C3×Q16AGL(1,𝔽5)
hypocenterC5C3×#2141
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×Q16

Complements

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

NH ≅ G/Ntype
4. C3×#64908C2semidirect
5. #10604832C3direct (N × H)
8. C2×C3×C5×Q16C4semidirect
12. C3×D5×Q16C4semidirect
14. C2×C3×Dic20C4semidirect
25. #64908C2×C3semidirect
57. C2×C5×Q16C3×C4semidirect
61. D5×Q16C3×C4semidirect
63. C2×Dic20C3×C4semidirect
100. C2×C3×Q16AGL(1,𝔽5)semidirect
202. C2×Q16C3×AGL(1,𝔽5)semidirect
272. C3×C5#2141semidirect
314. C5C3×#2141semidirect
326. C3#10604832direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
C3×#657212
C3×D5⋊M322
C3×#649082
#106048323
C3×#21415