Finite Group Databasebeta

← C3×#10601898 #14292553

Subgroups — C3×#10601898 #14292553

Order 1920.

332 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#474C211yesmaximal, characteristic
2C3×#65381C211yesmaximal, characteristic, complemented
3C3×#65301C211yesmaximal, characteristic
4C3×#65296C211yesmaximal, characteristic
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64700C211yesmaximal, characteristic, complemented
8#10601898C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C2×C3×#689—21no—
12C2×C3×#689—21no—
13C2×C3×#681—21no—
14C3×#4015C2211yescharacteristic
15C3×C5×#107—21no—
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×#102—21no—
18C3×#3964—21no—
19C3×C22⋊#168—21no—
20C3×#3939—21no—
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1689—51nomaximal, Hall
25C5×#474C2×C311yescharacteristic
26#65381C2×C311yescharacteristic, complemented
27#65301C2×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—
36C2×C3×C5×C8—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C22⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C3×#689—42no—
43C3×#689—42no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46C3×#681—42no—
47C2×C3×#168—21no—
48C2×C3×#168—21no—
49C2×C3×#168D411yescharacteristic
50C2×C3×#168D411yescharacteristic
51C3×#494—51no—
52C3×#474—51no—
53C3×#474D511yescharacteristic
54C3×#436—51no—
55C3×#334—51no—
56C3×#332—51no—
57C3×#332—51no—
58C5×C4⋊Q8C22×C311yescharacteristic
59C4×C5×D4C22×C311yescharacteristic
60C2×#689—21no—
61C2×#689—21no—
62C2×#681—21no—
63#4015C22×C311yescharacteristic
64C5×#107—21no—
65C5×C4⋊C8C22×C311yescharacteristic
66C5×#102—21no—
67#3964—21no—
68C22⋊#168—21no—
69#3939—21no—
70C4⋊#168C22×C311yescharacteristic
71C4⋊#168C22×C311yescharacteristic
72C4×#168C22×C311yescharacteristic
73#1689—51noSylow
74C23×C3×C5—21no—
75C3×C5×Q8—41no—
76C3×C5×Q8—41no—
77C3×C5×D4—21no—
78C3×C5×D4—21no—
79C2×C3×C4×C5—21no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×C3×Dic5—41no—
87C3×Dic10—41no—
88C3×Dic10—41no—
89C3×C5×C8—41no—
90C3×#168—21no—
91C3×#168—41no—
92C3×#168—41no—
93C3×#168D812yes—
94C2×C3×Q16—101no—
95C2×C3×Q16—101no—
96C2×C3×M16—101no—
97C3×C4⋊Q8—51no—
98C3×C4⋊Q8C2×D511yescharacteristic
99C3×C4×D4C2×D511yescharacteristic
100C3×#107—21no—
101C3×#107—101no—
102C3×C4⋊C8—51no—
103C3×C4⋊C8—51no—
104C3×C4⋊C8C2×D511yescharacteristic
105C3×#102—21no—
106C3×#102—101no—
107C3×C22⋊C8—101no—
108C3×C4×C8—51no—
109C2×C5×Q8—21no—
110C2×C5×D4C3×D411yescharacteristic
111C22×C4×C5—21no—
112C2×Dic10—21no—
113C2×C5×C8—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4C3×D411yescharacteristic
117C5×C22⋊C4—21no—
118C42×C5C23×C311yescharacteristic
119#689—42no—
120#689—42no—
121C4⋊Dic5—21no—
122C4⋊Dic5—21no—
123#681—42no—
124C2×#168—21no—
125C2×#168—21no—
126C2×#168C3×D411yescharacteristic
127C2×#168C3×D411yescharacteristic
128#494—51no—
129#474—51no—
130#474C3×D511yescharacteristic
131#436—51no—
132#334—51no—
133#332—51no—
134#332—51no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5—41no—
138C22×C3×C5#12111yescharacteristic
139C3×C4×C5—21no—
140C3×C4×C5—41no—
141C3×C4×C5—81no—
142C3×C4×C5C2×D811yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C3×C4×C5#13711yescharacteristic
145C3×C4×C5#13711yescharacteristic
146C3×Dic5—81no—
147C2×C3×Q8—21no—
148C2×C3×Q8—101no—
149C2×C3×D4C22⋊D511yescharacteristic
150C22×C3×C4—21no—
151C3×Q16—202no—
152C3×Q16—202no—
153C3×M16—202no—
154C2×C3×C8—21no—
155C2×C3×C8—51no—
156C2×C3×C8—51no—
157C2×C3×C8—101no—
158C2×C3×C8—101no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—101no—
162C3×C4⋊C4—101no—
163C3×C4⋊C4C22⋊D511yescharacteristic
164C3×C22⋊C4—21no—
165C3×C42C22×D511yescharacteristic
166C23×C5—21no—
167C5×Q8—41no—
168C5×Q8—41no—
169C5×D4—21no—
170C5×D4—21no—
171C2×C4×C5—21no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5C2×C3×D411yescharacteristic
176C2×C4×C5C2×C3×D411yescharacteristic
177C2×C4×C5C3×#4111yescharacteristic
178C2×Dic5—41no—
179Dic10—41no—
180Dic10—41no—
181C5×C8—41no—
182#168—21no—
183#168—41no—
184#168—41no—
185#168C3×D812yes—
186C2×Q16—101no—
187C2×Q16—101no—
188C2×M16—101no—
189C4⋊Q8—51no—
190C4⋊Q8C2×C3×D511yescharacteristic
191C4×D4C2×C3×D511yescharacteristic
192#107—21no—
193#107—101no—
194C4⋊C8—51no—
195C4⋊C8—51no—
196C4⋊C8C2×C3×D511yescharacteristic
197#102—21no—
198#102—101no—
199C22⋊C8—101no—
200C4×C8—51no—
201C2×C3×C5—81no—
202C2×C3×C5#45911yescharacteristic
203C2×C3×C5#47011yescharacteristic
204C2×C3×C5#47311yescharacteristic
205C23×C3—21no—
206C3×Q8—41no—
207C3×Q8—41no—
208C3×Q8—201no—
209C3×Q8—201no—
210C3×D4—21no—
211C3×D4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—201no—
217C2×C3×C4D4×D511yescharacteristic
218C2×C3×C4#71111yescharacteristic
219C2×C3×C4C2×C22⋊D511yescharacteristic
220C3×C8—41no—
221C3×C8—52no—
222C3×C8—101no—
223C3×C8—201no—
224C3×C8—201no—
225C22×C5—41no—
226C22×C5—41no—
227C22×C5—41no—
228C22×C5C3×#12111yescharacteristic
229C4×C5—21no—
230C4×C5—41no—
231C4×C5—81no—
232C4×C5C2×C3×D811yescharacteristic
233C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
234C4×C5C3×#13711yescharacteristic
235C4×C5C3×#13711yescharacteristic
236Dic5—81no—
237C2×Q8—21no—
238C2×Q8—101no—
239C2×D4C3×C22⋊D511yescharacteristic
240C22×C4—21no—
241Q16—202no—
242Q16—202no—
243M16—202no—
244C2×C8—21no—
245C2×C8—51no—
246C2×C8—51no—
247C2×C8—101no—
248C2×C8—101no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—101no—
252C4⋊C4—101no—
253C4⋊C4C3×C22⋊D511yescharacteristic
254C22⋊C4—21no—
255C42C22×C3×D511yescharacteristic
256C3×C5#168911yescharacteristic, complemented, Hall
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3#408511yescharacteristic
261C3×C4—21no—
262C3×C4—41no—
263C3×C4—81no—
264C3×C4—401no—
265C3×C4D5×D811yescharacteristic
266C3×C4#405711yescharacteristic
267C3×C4#408811yescharacteristic
268C3×C4#409711yescharacteristic
269C2×C5—81no—
270C2×C5C3×#45911yescharacteristic
271C2×C5C3×#47011yescharacteristic
272C2×C5C3×#47311yescharacteristic
273C23—21no—
274Q8—41no—
275Q8—41no—
276Q8—201no—
277Q8—201no—
278D4—21no—
279D4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—201no—
285C2×C4C3×D4×D511yescharacteristic
286C2×C4C3×#71111yescharacteristic
287C2×C4C2×C3×C22⋊D511yescharacteristic
288C8—41no—
289C8—52no—
290C8—101no—
291C8—201no—
292C8—201no—
293C2×C3—81no—
294C2×C3#6534111yescharacteristic
295C2×C3#6543911yescharacteristic
296C2×C3#6549311yescharacteristic
297C5C3×#168911yescharacteristic, complemented, Sylow
298C22—41no—
299C22—41no—
300C22—41no—
301C22C3×#408511yescharacteristic
302C4—21no—
303C4—41no—
304C4—81no—
305C4—401no—
306C4C3×D5×D811yescharacteristic
307C4C3×#405711yescharacteristic
308C4C3×#408811yescharacteristic
309C4C3×#409711yescharacteristic
310C3#1060189811yescharacteristic, direct product factor, Sylow
311C2—81no—
312C2C3×#6534111yescharacteristic
313C2C3×#6543911yescharacteristic
314C2C3×#6549311yescharacteristic
subgroupG/H
centerC22×C3#4085
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#474C2
socleC22×C3×C5#121
prime radicalC2×C3×C5×D4D4
hypercenterC3×#474D5
hypocenterC5C3×#1689
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
2. C3×#65381C2semidirect
5. C3×#64767C2semidirect
6. C3×#64706C2semidirect
7. C3×#64700C2semidirect
8. #10601898C3direct (N × H)
26. #65381C2×C3semidirect
29. #64767C2×C3semidirect
30. #64706C2×C3semidirect
31. #64700C2×C3semidirect
256. C3×C5#1689semidirect
297. C5C3×#1689semidirect
310. C3#10601898direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4742
C3×#653812
C3×#653012
C3×#652962
C3×#647672
C3×#647062
C3×#647002
#106018983
C3×#16895