Finite Group Databasebeta

← C3×#10598766 #14276857

Subgroups — C3×#10598766 #14276857

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic
3C2×C3×#3952C211yesmaximal, characteristic
4#10598766C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×C3×C22⋊AGL(1,𝔽5)C412yes—
7C2×C3×C4×AGL(1,𝔽5)—21no—
8C2×C3×D5⋊C8—21no—
9C22×C3×C5×C8C411yescharacteristic, complemented
10C22×C3×#168C411yescharacteristic, complemented
11C3×C22⋊#170C412yescomplemented
12C3×(C2×AGL(1,𝔽5))⋊C4—21no—
13C3×#4003—21no—
14C3×#3952—21no—
15C3×#3952—21no—
16C3×#1282—51nomaximal, Hall
17C4×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic
18D5⋊(C22⋊C8)C2×C311yescharacteristic
19C2×#3952C2×C311yescharacteristic
20C23×C3×D5C2×C411yescharacteristic
21C22×C3×AGL(1,𝔽5)—22no—
22C22×C3×C4×C5C2×C411yescharacteristic
23C22×C3×Dic5C2×C411yescharacteristic
24C2×C3×C4×D5—41no—
25C2×C3×C4×D5—41no—
26C2×C3×C4×D5D411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×C4×D5Q811yescharacteristic
30C3×C22⋊AGL(1,𝔽5)—22no—
31C3×C22⋊AGL(1,𝔽5)C814yescomplemented
32C2×C3×#170—22no—
33C3×C4×AGL(1,𝔽5)—41no—
34C3×C4×AGL(1,𝔽5)—41no—
35C3×D5⋊C8—41no—
36C3×D5⋊C8—41no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—41no—
39C2×C3×#168—21no—
40C2×C3×#168—41no—
41C2×C3×C22⋊C8—51no—
42C2×C3×C22⋊C8—51no—
43C3×C4×C22⋊C4—51no—
44C22×C4×D5C22×C311yescharacteristic
45C2×C22⋊AGL(1,𝔽5)C3×C412yes—
46C2×C4×AGL(1,𝔽5)—21no—
47C2×D5⋊C8—21no—
48C22×C5×C8C3×C411yescharacteristic, complemented
49C22×#168C3×C411yescharacteristic, complemented
50C22⋊#170C3×C412yescomplemented
51(C2×AGL(1,𝔽5))⋊C4—21no—
52#4003—21no—
53#3952—21no—
54#3952—21no—
55#1282—51noSylow
56C23×C3×C5C4211yescharacteristic
57C22×C3×D5—41no—
58C22×C3×D5—41no—
59C22×C3×D5C22⋊C411yescharacteristic
60C22×C3×D5C4⋊C411yescharacteristic
61C22×C3×D5C2×C812yes—
62C22×C3×D5M1612yes—
63C2×C3×AGL(1,𝔽5)—24no—
64C2×C3×AGL(1,𝔽5)—42no—
65C2×C3×AGL(1,𝔽5)—42no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C4⋊C411yescharacteristic
70C2×C3×Dic5—41no—
71C2×C3×Dic5C22⋊C411yescharacteristic
72C2×C3×Dic5C4⋊C411yescharacteristic
73C3×C4×D5—21no—
74C3×C4×D5—21no—
75C3×C4×D5—21no—
76C3×C4×D5—21no—
77C3×C4×D5—41no—
78C3×C4×D5—41no—
79C3×#170—42no—
80C3×C5×C8—41no—
81C3×#168—41no—
82C23×C3×C4—51no—
83C22×C3×C8—51no—
84C22×C3×C8—101no—
85C22×C3×C8AGL(1,𝔽5)11yescharacteristic, complemented
86C2×C3×C22⋊C4—52no—
87C2×C3×C42—101no—
88C3×C22⋊C8—52no—
89C3×C22⋊C8—101no—
90C3×C22⋊C8—101no—
91C3×C22⋊C8—101no—
92C3×#95—101no—
93C23×D5C2×C3×C411yescharacteristic
94C22×AGL(1,𝔽5)—22no—
95C22×C4×C5C2×C3×C411yescharacteristic
96C22×Dic5C2×C3×C411yescharacteristic
97C2×C4×D5—41no—
98C2×C4×D5—41no—
99C2×C4×D5C3×D411yescharacteristic
100C2×C4×D5C3×D411yescharacteristic
101C2×C4×D5C3×D411yescharacteristic
102C2×C4×D5C3×Q811yescharacteristic
103C22⋊AGL(1,𝔽5)—22no—
104C22⋊AGL(1,𝔽5)C3×C814yescomplemented
105C2×#170—22no—
106C4×AGL(1,𝔽5)—41no—
107C4×AGL(1,𝔽5)—41no—
108D5⋊C8—41no—
109D5⋊C8—41no—
110C2×C5×C8—21no—
111C2×C5×C8—41no—
112C2×#168—21no—
113C2×#168—41no—
114C2×C22⋊C8—51no—
115C2×C22⋊C8—51no—
116C4×C22⋊C4—51no—
117C22×C3×C5—21no—
118C22×C3×C5—21no—
119C22×C3×C5#9511yescharacteristic
120C22×C3×C5C4×C811yescharacteristic
121C22×C3×C5#9711yescharacteristic
122C2×C3×D5—21no—
123C2×C3×D5—21no—
124C2×C3×D5—21no—
125C2×C3×D5—21no—
126C2×C3×D5—42no—
127C2×C3×D5—42no—
128C2×C3×D5C22⋊C812yes—
129C2×C3×D5C4⋊C812yes—
130C3×AGL(1,𝔽5)—44no—
131C3×C4×C5—21no—
132C3×C4×C5#9911yescharacteristic
133C3×C4×C5#9911yescharacteristic
134C3×Dic5—21no—
135C3×Dic5—21no—
136C24×C3—51no—
137C22×C3×C4—51no—
138C22×C3×C4—51no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4—102no—
143C22×C3×C4—201no—
144C22×C3×C4—201no—
145C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
146C2×C3×C8—21no—
147C2×C3×C8—41no—
148C2×C3×C8—102no—
149C2×C3×C8—101no—
150C2×C3×C8—201no—
151C2×C3×C8—201no—
152C2×C3×C8—201no—
153C3×C22⋊C4—54no—
154C3×C22⋊C4—102no—
155C3×C42—201no—
156C3×C42—201no—
157C23×C5C3×C4211yescharacteristic
158C22×D5—41no—
159C22×D5—41no—
160C22×D5C3×C22⋊C411yescharacteristic
161C22×D5C3×C4⋊C411yescharacteristic
162C22×D5C2×C3×C812yes—
163C22×D5C3×M1612yes—
164C2×AGL(1,𝔽5)—24no—
165C2×AGL(1,𝔽5)—42no—
166C2×AGL(1,𝔽5)—42no—
167C2×C4×C5—21no—
168C2×C4×C5—21no—
169C2×C4×C5C3×C22⋊C411yescharacteristic
170C2×C4×C5C3×C4⋊C411yescharacteristic
171C2×Dic5—41no—
172C2×Dic5C3×C22⋊C411yescharacteristic
173C2×Dic5C3×C4⋊C411yescharacteristic
174C4×D5—21no—
175C4×D5—21no—
176C4×D5—21no—
177C4×D5—21no—
178C4×D5—41no—
179C4×D5—41no—
180#170—42no—
181C5×C8—41no—
182#168—41no—
183C23×C4—51no—
184C22×C8—51no—
185C22×C8—101no—
186C22×C8C3×AGL(1,𝔽5)11yescharacteristic, complemented
187C2×C22⋊C4—52no—
188C2×C42—101no—
189C22⋊C8—52no—
190C22⋊C8—101no—
191C22⋊C8—101no—
192C22⋊C8—101no—
193#95—101no—
194C2×C3×C5—21no—
195C2×C3×C5—21no—
196C2×C3×C5#33611yescharacteristic
197C2×C3×C5#34211yescharacteristic
198C2×C3×C5#34411yescharacteristic
199C3×D5—22no—
200C3×D5—22no—
201C23×C3—51no—
202C23×C3—51no—
203C23×C3—52no—
204C23×C3—52no—
205C23×C3—201no—
206C23×C3—201no—
207C23×C3C4×AGL(1,𝔽5)11yescharacteristic
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—51no—
211C2×C3×C4—51no—
212C2×C3×C4—101no—
213C2×C3×C4—101no—
214C2×C3×C4—101no—
215C2×C3×C4—101no—
216C2×C3×C4—104no—
217C2×C3×C4—201no—
218C2×C3×C4—201no—
219C2×C3×C4—201no—
220C2×C3×C4—202no—
221C2×C3×C4—202no—
222C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
223C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
224C3×C8—41no—
225C3×C8—202no—
226C3×C8—201no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5C3×#9511yescharacteristic
230C22×C5C3×C4×C811yescharacteristic
231C22×C5C3×#9711yescharacteristic
232C2×D5—21no—
233C2×D5—21no—
234C2×D5—21no—
235C2×D5—21no—
236C2×D5—42no—
237C2×D5—42no—
238C2×D5C3×C22⋊C812yes—
239C2×D5C3×C4⋊C812yes—
240AGL(1,𝔽5)—44no—
241C4×C5—21no—
242C4×C5C3×#9911yescharacteristic
243C4×C5C3×#9911yescharacteristic
244Dic5—21no—
245Dic5—21no—
246C24—51no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—51no—
250C22×C4—51no—
251C22×C4—51no—
252C22×C4—102no—
253C22×C4—201no—
254C22×C4—201no—
255C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—102no—
259C2×C8—101no—
260C2×C8—201no—
261C2×C8—201no—
262C2×C8—201no—
263C22⋊C4—54no—
264C22⋊C4—102no—
265C42—201no—
266C42—201no—
267C3×C5#128211yescharacteristic, complemented, Hall
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—52no—
271C22×C3—52no—
272C22×C3—101no—
273C22×C3—101no—
274C22×C3—101no—
275C22×C3—101no—
276C22×C3—202no—
277C22×C3—202no—
278C22×C3C8×AGL(1,𝔽5)11yescharacteristic
279C22×C3#399211yescharacteristic
280C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
281C3×C4—21no—
282C3×C4—101no—
283C3×C4—101no—
284C3×C4—204no—
285C3×C4#399911yescharacteristic
286C3×C4#401111yescharacteristic
287C2×C5—21no—
288C2×C5—21no—
289C2×C5C3×#33611yescharacteristic
290C2×C5C3×#34211yescharacteristic
291C2×C5C3×#34411yescharacteristic
292D5—22no—
293D5—22no—
294C23—51no—
295C23—51no—
296C23—52no—
297C23—52no—
298C23—201no—
299C23—201no—
300C23C3×C4×AGL(1,𝔽5)11yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—101no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—104no—
310C2×C4—201no—
311C2×C4—201no—
312C2×C4—201no—
313C2×C4—202no—
314C2×C4—202no—
315C2×C4C3×C4⋊AGL(1,𝔽5)11yescharacteristic
316C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
317C8—41no—
318C8—202no—
319C8—201no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—102no—
323C2×C3—102no—
324C2×C3(C2×AGL(1,𝔽5))⋊C811yescharacteristic
325C2×C3#6489411yescharacteristic
326C2×C3#6491711yescharacteristic
327C5C3×#128211yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—52no—
331C22—52no—
332C22—101no—
333C22—101no—
334C22—101no—
335C22—101no—
336C22—202no—
337C22—202no—
338C22C3×C8×AGL(1,𝔽5)11yescharacteristic
339C22C3×#399211yescharacteristic
340C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
341C4—21no—
342C4—101no—
343C4—101no—
344C4—204no—
345C4C3×#399911yescharacteristic
346C4C3×#401111yescharacteristic
347C3#1059876611yescharacteristic, direct product factor, Sylow
348C2—21no—
349C2—21no—
350C2—102no—
351C2—102no—
352C2C3×(C2×AGL(1,𝔽5))⋊C811yescharacteristic
353C2C3×#6489411yescharacteristic
354C2C3×#6491711yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C3×C4×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC22×C3×C5#95
prime radicalC23×C3×D5C2×C4
cosocleC22×C4×D5C22×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1282
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8

Complements

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

NH ≅ G/Ntype
4. #10598766C3direct (N × H)
9. C22×C3×C5×C8C4semidirect
10. C22×C3×#168C4semidirect
11. C3×C22⋊#170C4semidirect
31. C3×C22⋊AGL(1,𝔽5)C8semidirect
48. C22×C5×C8C3×C4semidirect
49. C22×#168C3×C4semidirect
50. C22⋊#170C3×C4semidirect
85. C22×C3×C8AGL(1,𝔽5)semidirect
104. C22⋊AGL(1,𝔽5)C3×C8semidirect
186. C22×C8C3×AGL(1,𝔽5)semidirect
267. C3×C5#1282semidirect
327. C5C3×#1282semidirect
347. C3#10598766direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C22⋊AGL(1,𝔽5)2
C3×D5⋊(C22⋊C8)2
C2×C3×#39522
#105987663
C3×#12825