Finite Group Databasebeta

← C3×#10598586 #14277177

Subgroups — C3×#10598586 #14277177

Order 1920.

376 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65688C211yesmaximal, characteristic
2C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic
3C3×D5×C4⋊C8C211yesmaximal, characteristic
4#10598586C311yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C4⋊AGL(1,𝔽5)—21no—
6C2×C3×C4⋊AGL(1,𝔽5)—21no—
7C2×C3×C4⋊AGL(1,𝔽5)C412yes—
8C2×C3×D5⋊C8—21no—
9C2×C3×C8×D5—21no—
10C3×C42×D5C2211yescharacteristic
11C3×#4004C412yescomplemented
12C3×C4⋊#170—21no—
13C3×C5×C4⋊C8C411yescharacteristic, complemented
14C3×#3946—21no—
15C3×C4⋊#168C411yescharacteristic, complemented
16C3×#1296—51nomaximal, Hall
17#65688C2×C311yescharacteristic
18D5⋊(C4⋊C8)C2×C311yescharacteristic
19D5×C4⋊C8C2×C311yescharacteristic
20C22×C3×AGL(1,𝔽5)—22no—
21C2×C3×C4×D5C2×C411yescharacteristic
22C2×C3×C4×D5D411yescharacteristic
23C2×C3×C4×D5D411yescharacteristic
24C2×C3×#170—22no—
25C3×C4⋊AGL(1,𝔽5)—42no—
26C3×C4⋊AGL(1,𝔽5)—41no—
27C3×C4⋊AGL(1,𝔽5)—41no—
28C3×C4⋊AGL(1,𝔽5)—41no—
29C3×C4⋊AGL(1,𝔽5)—41no—
30C3×D5⋊C8—41no—
31C3×D5⋊C8—41no—
32C2×C3×C5×C8—21no—
33C3×C42×C5C2×C411yescharacteristic
34C3×C4×Dic5C2×C411yescharacteristic
35C3×C4×Dic5D411yescharacteristic
36C3×C4×Dic5Q811yescharacteristic
37C2×C3×#168—21no—
38C3×C8×D5—41no—
39C3×C8×D5—41no—
40C2×C3×C4⋊C8—51no—
41C2×C3×C4⋊C8—51no—
42C3×#384—51no—
43C2×C4⋊AGL(1,𝔽5)—21no—
44C2×C4⋊AGL(1,𝔽5)—21no—
45C2×C4⋊AGL(1,𝔽5)C3×C412yes—
46C2×D5⋊C8—21no—
47C2×C8×D5—21no—
48C42×D5C22×C311yescharacteristic
49#4004C3×C412yescomplemented
50C4⋊#170—21no—
51C5×C4⋊C8C3×C411yescharacteristic, complemented
52#3946—21no—
53C4⋊#168C3×C411yescharacteristic, complemented
54#1296—51noSylow
55C22×C3×D5C22⋊C411yescharacteristic
56C2×C3×AGL(1,𝔽5)—42no—
57C2×C3×AGL(1,𝔽5)—42no—
58C2×C3×AGL(1,𝔽5)—42no—
59C2×C3×C4×C5C4211yescharacteristic
60C2×C3×C4×C5C22⋊C411yescharacteristic
61C2×C3×C4×C5C4⋊C411yescharacteristic
62C2×C3×Dic5C22⋊C411yescharacteristic
63C2×C3×Dic5C4⋊C411yescharacteristic
64C2×C3×Dic5C4⋊C411yescharacteristic
65C3×C4×D5—21no—
66C3×C4×D5—21no—
67C3×C4×D5D811yescharacteristic
68C3×C4×D5D811yescharacteristic
69C3×C4×D5SD1611yescharacteristic
70C3×C4×D5SD1611yescharacteristic
71C3×C4×D5SD1611yescharacteristic
72C3×C4×D5SD1611yescharacteristic
73C3×C4×D5Q1611yescharacteristic
74C3×C4×D5Q1611yescharacteristic
75C3×#170—42no—
76C3×C5×C8—41no—
77C3×#168—41no—
78C22×C3×C8—101no—
79C22×C3×C8—101no—
80C2×C3×C4⋊C4—52no—
81C2×C3×C4⋊C4—101no—
82C2×C3×C4⋊C4—101no—
83C2×C3×C42—51no—
84C3×C4⋊C8—52no—
85C3×C4⋊C8—51no—
86C3×C4⋊C8—101no—
87C3×C4⋊C8—101no—
88C3×C4⋊C8AGL(1,𝔽5)11yescharacteristic, complemented
89C22×AGL(1,𝔽5)—22no—
90C2×C4×D5C2×C3×C411yescharacteristic
91C2×C4×D5C3×D411yescharacteristic
92C2×C4×D5C3×D411yescharacteristic
93C2×#170—22no—
94C4⋊AGL(1,𝔽5)—42no—
95C4⋊AGL(1,𝔽5)—41no—
96C4⋊AGL(1,𝔽5)—41no—
97C4⋊AGL(1,𝔽5)—41no—
98C4⋊AGL(1,𝔽5)—41no—
99D5⋊C8—41no—
100D5⋊C8—41no—
101C2×C5×C8—21no—
102C42×C5C2×C3×C411yescharacteristic
103C4×Dic5C2×C3×C411yescharacteristic
104C4×Dic5C3×D411yescharacteristic
105C4×Dic5C3×Q811yescharacteristic
106C2×#168—21no—
107C8×D5—41no—
108C8×D5—41no—
109C2×C4⋊C8—51no—
110C2×C4⋊C8—51no—
111#384—51no—
112C22×C3×C5#9511yescharacteristic
113C2×C3×D5#10011yescharacteristic
114C2×C3×D5#10111yescharacteristic
115C2×C3×D5#10211yescharacteristic
116C2×C3×D5#10211yescharacteristic
117C2×C3×D5#10311yescharacteristic
118C2×C3×D5#10311yescharacteristic
119C3×AGL(1,𝔽5)—82no—
120C3×C4×C5—21no—
121C3×C4×C5#10211yescharacteristic
122C3×C4×C5#10311yescharacteristic
123C3×C4×C5#10611yescharacteristic
124C3×C4×C5#10711yescharacteristic
125C3×Dic5—21no—
126C3×Dic5#10211yescharacteristic
127C3×Dic5#10311yescharacteristic
128C3×Dic5#10611yescharacteristic
129C3×Dic5#10711yescharacteristic
130C22×C3×C4—51no—
131C22×C3×C4—51no—
132C22×C3×C4—51no—
133C22×C3×C4—102no—
134C2×C3×C8—21no—
135C2×C3×C8—102no—
136C2×C3×C8—101no—
137C2×C3×C8—201no—
138C2×C3×C8—201no—
139C2×C3×C8—201no—
140C2×C3×C8—201no—
141C3×C4⋊C4—201no—
142C3×C4⋊C4—201no—
143C3×C4⋊C4—201no—
144C3×C4⋊C4—201no—
145C3×C4⋊C4—202no—
146C3×C42—51no—
147C3×C42—51no—
148C3×C42—51no—
149C3×C42C2×AGL(1,𝔽5)11yescharacteristic
150C22×D5C3×C22⋊C411yescharacteristic
151C2×AGL(1,𝔽5)—42no—
152C2×AGL(1,𝔽5)—42no—
153C2×AGL(1,𝔽5)—42no—
154C2×C4×C5C3×C4211yescharacteristic
155C2×C4×C5C3×C22⋊C411yescharacteristic
156C2×C4×C5C3×C4⋊C411yescharacteristic
157C2×Dic5C3×C22⋊C411yescharacteristic
158C2×Dic5C3×C4⋊C411yescharacteristic
159C2×Dic5C3×C4⋊C411yescharacteristic
160C4×D5—21no—
161C4×D5—21no—
162C4×D5C3×D811yescharacteristic
163C4×D5C3×D811yescharacteristic
164C4×D5C3×SD1611yescharacteristic
165C4×D5C3×SD1611yescharacteristic
166C4×D5C3×SD1611yescharacteristic
167C4×D5C3×SD1611yescharacteristic
168C4×D5C3×Q1611yescharacteristic
169C4×D5C3×Q1611yescharacteristic
170#170—42no—
171C5×C8—41no—
172#168—41no—
173C22×C8—101no—
174C22×C8—101no—
175C2×C4⋊C4—52no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—101no—
178C2×C42—51no—
179C4⋊C8—52no—
180C4⋊C8—51no—
181C4⋊C8—101no—
182C4⋊C8—101no—
183C4⋊C8C3×AGL(1,𝔽5)11yescharacteristic, complemented
184C2×C3×C5#34011yescharacteristic
185C2×C3×C5#34011yescharacteristic
186C2×C3×C5#34311yescharacteristic
187C3×D5#33111yescharacteristic
188C3×D5#33211yescharacteristic
189C3×D5#33211yescharacteristic
190C3×D5#33311yescharacteristic
191C23×C3—51no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—51no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—51no—
201C2×C3×C4—51no—
202C2×C3×C4—51no—
203C2×C3×C4—101no—
204C2×C3×C4—101no—
205C2×C3×C4—202no—
206C2×C3×C4—202no—
207C2×C3×C4—202no—
208C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
209C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
210C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
211C3×C8—41no—
212C3×C8—202no—
213C3×C8—201no—
214C22×C5C3×#9511yescharacteristic
215C2×D5C3×#10011yescharacteristic
216C2×D5C3×#10111yescharacteristic
217C2×D5C3×#10211yescharacteristic
218C2×D5C3×#10211yescharacteristic
219C2×D5C3×#10311yescharacteristic
220C2×D5C3×#10311yescharacteristic
221AGL(1,𝔽5)—82no—
222C4×C5—21no—
223C4×C5C3×#10211yescharacteristic
224C4×C5C3×#10311yescharacteristic
225C4×C5C3×#10611yescharacteristic
226C4×C5C3×#10711yescharacteristic
227Dic5—21no—
228Dic5C3×#10211yescharacteristic
229Dic5C3×#10311yescharacteristic
230Dic5C3×#10611yescharacteristic
231Dic5C3×#10711yescharacteristic
232C22×C4—51no—
233C22×C4—51no—
234C22×C4—51no—
235C22×C4—102no—
236C2×C8—21no—
237C2×C8—102no—
238C2×C8—101no—
239C2×C8—201no—
240C2×C8—201no—
241C2×C8—201no—
242C2×C8—201no—
243C4⋊C4—201no—
244C4⋊C4—201no—
245C4⋊C4—201no—
246C4⋊C4—201no—
247C4⋊C4—202no—
248C42—51no—
249C42—51no—
250C42—51no—
251C42C2×C3×AGL(1,𝔽5)11yescharacteristic
252C3×C5#129611yescharacteristic, complemented, Hall
253C22×C3—51no—
254C22×C3—51no—
255C22×C3—51no—
256C22×C3—51no—
257C22×C3—51no—
258C22×C3—51no—
259C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
260C3×C4—21no—
261C3×C4—51no—
262C3×C4—51no—
263C3×C4—51no—
264C3×C4—51no—
265C3×C4—101no—
266C3×C4—402no—
267C3×C4#399311yescharacteristic
268C3×C4#399411yescharacteristic
269C3×C4#400711yescharacteristic
270C3×C4#400911yescharacteristic
271C2×C5C3×#34011yescharacteristic
272C2×C5C3×#34011yescharacteristic
273C2×C5C3×#34311yescharacteristic
274D5C3×#33111yescharacteristic
275D5C3×#33211yescharacteristic
276D5C3×#33211yescharacteristic
277D5C3×#33311yescharacteristic
278C23—51no—
279C2×C4—51no—
280C2×C4—51no—
281C2×C4—51no—
282C2×C4—51no—
283C2×C4—51no—
284C2×C4—51no—
285C2×C4—51no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—51no—
289C2×C4—51no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—202no—
293C2×C4—202no—
294C2×C4—202no—
295C2×C4C3×C4×AGL(1,𝔽5)11yescharacteristic
296C2×C4C3×C4⋊AGL(1,𝔽5)11yescharacteristic
297C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
298C8—41no—
299C8—202no—
300C8—201no—
301C2×C3—51no—
302C2×C3—51no—
303C2×C3—51no—
304C2×C3—51no—
305C2×C3#6487411yescharacteristic
306C2×C3#6489311yescharacteristic
307C2×C3#6489911yescharacteristic
308C5C3×#129611yescharacteristic, complemented, Sylow
309C22—51no—
310C22—51no—
311C22—51no—
312C22—51no—
313C22—51no—
314C22—51no—
315C22C3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
316C4—21no—
317C4—51no—
318C4—51no—
319C4—51no—
320C4—51no—
321C4—101no—
322C4—402no—
323C4C3×#399311yescharacteristic
324C4C3×#399411yescharacteristic
325C4C3×#400711yescharacteristic
326C4C3×#400911yescharacteristic
327C3#1059858611yescharacteristic, direct product factor, Sylow
328C2—51no—
329C2—51no—
330C2—51no—
331C2—51no—
332C2C3×#6487411yescharacteristic
333C2C3×#6489311yescharacteristic
334C2C3×#6489911yescharacteristic
subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C3×C42
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C8C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C22⋊C4
cosocleC42×D5C22×C3
hypercenterC3×C4⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1296
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10598586C3direct (N × H)
11. C3×#4004C4semidirect
13. C3×C5×C4⋊C8C4semidirect
15. C3×C4⋊#168C4semidirect
49. #4004C3×C4semidirect
51. C5×C4⋊C8C3×C4semidirect
53. C4⋊#168C3×C4semidirect
88. C3×C4⋊C8AGL(1,𝔽5)semidirect
183. C4⋊C8C3×AGL(1,𝔽5)semidirect
252. C3×C5#1296semidirect
308. C5C3×#1296semidirect
327. C3#10598586direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#656882
C3×D5⋊(C4⋊C8)2
C3×D5×C4⋊C82
#105985863
C3×#12965