Finite Group Databasebeta

← C3×#10601831 #14291983

Subgroups — C3×#10601831 #14291983

Order 1920.

332 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#461C211yesmaximal, characteristic
2C3×#65382C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic
4C3×#65296C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64700C211yesmaximal, characteristic, complemented
8#10601831C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C22×C3×#168—21no—
13C3×#4015C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×#103—21no—
16C3×#3964—21no—
17C3×C22⋊#168—21no—
18C3×#3942—21no—
19C3×#3942—21no—
20C3×#3939—21no—
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1679—51nomaximal, Hall
25C5×#461C2×C311yescharacteristic
26#65382C2×C311yescharacteristic, complemented
27D4×#168C2×C311yescharacteristic
28#65296C2×C311yescharacteristic
29#64767C2×C311yescharacteristic, complemented
30#64706C2×C311yescharacteristic, complemented
31#64700C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4D411yescharacteristic
34C22×C3×C4×C5—21no—
35C2×C3×Dic10—21no—
36C3×C5×SD16—42no—
37C2×C3×C5×C8—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C2×C3×#168—21no—
46C2×C3×#168—21no—
47C2×C3×#168—42no—
48C2×C3×#168D411yescharacteristic
49C2×C3×#168D411yescharacteristic
50C3×#487—51no—
51C3×#474—51no—
52C3×#461D511yescharacteristic
53C3×C8×D4—51no—
54C3×#334—51no—
55C3×#332—51no—
56C3×#332—51no—
57C2×C5×SD16—21no—
58C5×C4⋊Q8C22×C311yescharacteristic
59C4×C5×D4C22×C311yescharacteristic
60C22×#168—21no—
61#4015C22×C311yescharacteristic
62C5×C4⋊C8C22×C311yescharacteristic
63C5×#103—21no—
64#3964—21no—
65C22⋊#168—21no—
66#3942—21no—
67#3942—21no—
68#3939—21no—
69C4⋊#168C22×C311yescharacteristic
70C4⋊#168C22×C311yescharacteristic
71C4×#168C22×C311yescharacteristic
72#1679—51noSylow
73C23×C3×C5—21no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C3×C5×D4—21no—
77C3×C5×D4SD1612yes—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C3×Dic5—41no—
86C3×Dic10—41no—
87C3×Dic10—41no—
88C3×C5×C8—41no—
89C3×#168—21no—
90C3×#168—21no—
91C3×#168—41no—
92C3×#168—41no—
93C2×C3×SD16—21no—
94C22×C3×C8—101no—
95C3×C4⋊Q8—51no—
96C3×C4⋊Q8C2×D511yescharacteristic
97C3×C4×D4C2×D511yescharacteristic
98C3×#107—101no—
99C3×C4⋊C8—51no—
100C3×C4⋊C8—51no—
101C3×C4⋊C8C2×D511yescharacteristic
102C3×#103—21no—
103C3×#103—101no—
104C3×#103—101no—
105C3×#102—101no—
106C3×C22⋊C8—101no—
107C3×C4×C8—51no—
108C2×C5×Q8—21no—
109C2×C5×D4C3×D411yescharacteristic
110C22×C4×C5—21no—
111C2×Dic10—21no—
112C5×SD16—42no—
113C2×C5×C8—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4C3×D411yescharacteristic
117C5×C22⋊C4—21no—
118C42×C5C23×C311yescharacteristic
119C4⋊Dic5—21no—
120C4⋊Dic5—21no—
121C2×#168—21no—
122C2×#168—21no—
123C2×#168—42no—
124C2×#168C3×D411yescharacteristic
125C2×#168C3×D411yescharacteristic
126#487—51no—
127#474—51no—
128#461C3×D511yescharacteristic
129C8×D4—51no—
130#334—51no—
131#332—51no—
132#332—51no—
133C22×C3×C5—22no—
134C22×C3×C5—41no—
135C22×C3×C5—41no—
136C22×C3×C5#12111yescharacteristic
137C3×C4×C5—21no—
138C3×C4×C5—41no—
139C3×C4×C5—81no—
140C3×C4×C5C2×SD1611yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5#13511yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C3×Dic5—81no—
145C2×C3×Q8—21no—
146C2×C3×Q8—101no—
147C2×C3×D4C22⋊D511yescharacteristic
148C22×C3×C4—21no—
149C3×SD16—42no—
150C2×C3×C8—21no—
151C2×C3×C8—51no—
152C2×C3×C8—51no—
153C2×C3×C8—101no—
154C2×C3×C8—101no—
155C2×C3×C8—202no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—101no—
159C3×C4⋊C4—101no—
160C3×C4⋊C4C22⋊D511yescharacteristic
161C3×C22⋊C4—21no—
162C3×C42C22×D511yescharacteristic
163C23×C5—21no—
164C5×Q8—41no—
165C5×Q8—41no—
166C5×D4—21no—
167C5×D4C3×SD1612yes—
168C2×C4×C5—21no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5C2×C3×D411yescharacteristic
173C2×C4×C5C2×C3×D411yescharacteristic
174C2×C4×C5C3×#4111yescharacteristic
175C2×Dic5—41no—
176Dic10—41no—
177Dic10—41no—
178C5×C8—41no—
179#168—21no—
180#168—21no—
181#168—41no—
182#168—41no—
183C2×SD16—21no—
184C22×C8—101no—
185C4⋊Q8—51no—
186C4⋊Q8C2×C3×D511yescharacteristic
187C4×D4C2×C3×D511yescharacteristic
188#107—101no—
189C4⋊C8—51no—
190C4⋊C8—51no—
191C4⋊C8C2×C3×D511yescharacteristic
192#103—21no—
193#103—101no—
194#103—101no—
195#102—101no—
196C22⋊C8—101no—
197C4×C8—51no—
198C2×C3×C5—42no—
199C2×C3×C5#46311yescharacteristic
200C2×C3×C5#46511yescharacteristic
201C2×C3×C5#47311yescharacteristic
202C23×C3—21no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×Q8—201no—
206C3×Q8—201no—
207C3×D4—21no—
208C3×D4#68712yes—
209C2×C3×C4—21no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—201no—
214C2×C3×C4D4×D511yescharacteristic
215C2×C3×C4#71111yescharacteristic
216C2×C3×C4C2×C22⋊D511yescharacteristic
217C3×C8—41no—
218C3×C8—101no—
219C3×C8—101no—
220C3×C8—201no—
221C3×C8—201no—
222C22×C5—22no—
223C22×C5—41no—
224C22×C5—41no—
225C22×C5C3×#12111yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—81no—
229C4×C5C2×C3×SD1611yescharacteristic
230C4×C5C3×#13511yescharacteristic
231C4×C5C3×#13511yescharacteristic
232C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
233Dic5—81no—
234C2×Q8—21no—
235C2×Q8—101no—
236C2×D4C3×C22⋊D511yescharacteristic
237C22×C4—21no—
238SD16—42no—
239C2×C8—21no—
240C2×C8—51no—
241C2×C8—51no—
242C2×C8—101no—
243C2×C8—101no—
244C2×C8—202no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—101no—
248C4⋊C4—101no—
249C4⋊C4C3×C22⋊D511yescharacteristic
250C22⋊C4—21no—
251C42C22×C3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3—22no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3#408511yescharacteristic
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—81no—
260C3×C4—401no—
261C3×C4#406011yescharacteristic
262C3×C4#406211yescharacteristic
263C3×C4C2×#68711yescharacteristic
264C3×C4#409611yescharacteristic
265C2×C5—42no—
266C2×C5C3×#46311yescharacteristic
267C2×C5C3×#46511yescharacteristic
268C2×C5C3×#47311yescharacteristic
269C23—21no—
270Q8—41no—
271Q8—41no—
272Q8—201no—
273Q8—201no—
274D4—21no—
275D4C3×#68712yes—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—201no—
281C2×C4C3×D4×D511yescharacteristic
282C2×C4C3×#71111yescharacteristic
283C2×C4C2×C3×C22⋊D511yescharacteristic
284C8—41no—
285C8—101no—
286C8—101no—
287C8—201no—
288C8—201no—
289C2×C3—42no—
290C2×C3#6533011yescharacteristic
291C2×C3#6545411yescharacteristic
292C2×C3#6549311yescharacteristic
293C5C3×#167911yescharacteristic, complemented, Sylow
294C22—22no—
295C22—41no—
296C22—41no—
297C22C3×#408511yescharacteristic
298C4—21no—
299C4—41no—
300C4—81no—
301C4—401no—
302C4C3×#406011yescharacteristic
303C4C3×#406211yescharacteristic
304C4C2×C3×#68711yescharacteristic
305C4C3×#409611yescharacteristic
306C3#1060183111yescharacteristic, direct product factor, Sylow
307C2—42no—
308C2C3×#6533011yescharacteristic
309C2C3×#6545411yescharacteristic
310C2C3×#6549311yescharacteristic
subgroupG/H
centerC22×C3#4085
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#461C2
socleC22×C3×C5#121
prime radicalC2×C3×C5×D4D4
hypercenterC3×#461D5
hypocenterC5C3×#1679
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
2. C3×#65382C2semidirect
5. C3×#64767C2semidirect
6. C3×#64706C2semidirect
7. C3×#64700C2semidirect
8. #10601831C3direct (N × H)
26. #65382C2×C3semidirect
29. #64767C2×C3semidirect
30. #64706C2×C3semidirect
31. #64700C2×C3semidirect
252. C3×C5#1679semidirect
293. C5C3×#1679semidirect
306. C3#10601831direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4612
C3×#653822
C3×D4×#1682
C3×#652962
C3×#647672
C3×#647062
C3×#647002
#106018313
C3×#16795