Finite Group Databasebeta

← C3×#10598881 #14287170

Subgroups — C3×#10598881 #14287170

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×C4×#677C211yesmaximal, characteristic
2C3×#64977C211yesmaximal, characteristic
3C3×C8×Dic10C211yesmaximal, characteristic, complemented
4C3×C5×#322C211yesmaximal, characteristic, complemented
5C3×#64679C211yesmaximal, characteristic
6C3×#64678C211yesmaximal, characteristic, complemented
7C3×#64676C211yesmaximal, characteristic, complemented
8#10598881C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#677C411yescharacteristic
10C2×C3×#676—21no—
11C3×C4×D20C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13C3×C4×C5×C8C2211yescharacteristic
14C3×C4×C5×C8C2211yescharacteristic
15C3×C4×C5×C8C2211yescharacteristic
16C3×#3953C411yescharacteristic
17C3×#3952—21no—
18C3×#3949C411yescharacteristic
19C3×#3948C411yescharacteristic
20C3×#3946—21no—
21C3×C8×Dic5—21no—
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24C3×#1588—51nomaximal, Hall
25C4×#677C2×C311yescharacteristic
26#64977C2×C311yescharacteristic
27C8×Dic10C2×C311yescharacteristic, complemented
28C5×#322C2×C311yescharacteristic, complemented
29#64679C2×C311yescharacteristic
30#64678C2×C311yescharacteristic, complemented
31#64676C2×C311yescharacteristic, complemented
32C2×C3×D20C2×C411yescharacteristic
33C2×C3×C4×D5—21no—
34C2×C3×Dic10C2×C411yescharacteristic
35C2×C3×C5×C8—21no—
36C2×C3×C5×C8C2×C411yescharacteristic
37C2×C3×C5×C8C2×C411yescharacteristic
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8D411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41C3×#685—21no—
42C3×C4⋊Dic5C2×C411yescharacteristic
43C3×C4⋊Dic5C2×C411yescharacteristic
44C3×#683—21no—
45C3×C4×Dic5—21no—
46C2×C3×#168—21no—
47C2×C3×#168—21no—
48C3×#677—22no—
49C3×#676—42no—
50C3×C8×Q8—51no—
51C3×C4×SD16—51no—
52C3×#436—51no—
53C3×#335—51no—
54C3×Q8⋊C8—51no—
55C3×D4⋊C8—51no—
56C3×#322D511yescharacteristic, complemented
57C2×#677C3×C411yescharacteristic
58C2×#676—21no—
59C4×D20C22×C311yescharacteristic
60C4×Dic10C22×C311yescharacteristic
61C4×C5×C8C22×C311yescharacteristic
62C4×C5×C8C22×C311yescharacteristic
63C4×C5×C8C22×C311yescharacteristic
64#3953C3×C411yescharacteristic
65#3952—21no—
66#3949C3×C411yescharacteristic
67#3948C3×C411yescharacteristic
68#3946—21no—
69C8×Dic5—21no—
70C4⋊#168C22×C311yescharacteristic
71C4⋊#168C22×C311yescharacteristic
72#1588—51noSylow
73C22×C3×D5—21no—
74C2×C3×C4×C5C22×C411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×C3×Dic5—21no—
78C2×C3×Dic5—21no—
79C2×C3×Dic5—21no—
80C3×D20—21no—
81C3×D20—21no—
82C3×C4×D5—41no—
83C3×C4×D5—41no—
84C3×Dic10—21no—
85C3×Dic10M1612yescomplemented
86C3×C5×C8—22no—
87C3×C5×C8—21no—
88C3×C5×C8—21no—
89C3×C5×C8—21no—
90C3×C5×C8—21no—
91C3×#168—41no—
92C3×#168—41no—
93C2×C3×SD16—51no—
94C2×C3×M16—101no—
95C3×C4×Q8—51no—
96C3×C4×D4—51no—
97C3×#106—51no—
98C3×C4⋊C8—51no—
99C3×C4⋊C8—51no—
100C3×C4⋊C8—101no—
101C3×#103—51no—
102C3×#102—51no—
103C3×C22⋊C8—101no—
104C3×C4×C8—101no—
105C3×C4×C8C2×D511yescharacteristic
106C3×C4×C8C2×D511yescharacteristic
107C3×C4×C8C2×D511yescharacteristic
108C2×D20C2×C3×C411yescharacteristic
109C2×C4×D5—21no—
110C2×Dic10C2×C3×C411yescharacteristic
111C2×C5×C8—21no—
112C2×C5×C8C2×C3×C411yescharacteristic
113C2×C5×C8C2×C3×C411yescharacteristic
114C2×C5×C8C3×D411yescharacteristic
115C2×C5×C8C3×D411yescharacteristic
116C42×C5C23×C311yescharacteristic
117#685—21no—
118C4⋊Dic5C2×C3×C411yescharacteristic
119C4⋊Dic5C2×C3×C411yescharacteristic
120#683—21no—
121C4×Dic5—21no—
122C2×#168—21no—
123C2×#168—21no—
124#677—22no—
125#676—42no—
126C8×Q8—51no—
127C4×SD16—51no—
128#436—51no—
129#335—51no—
130Q8⋊C8—51no—
131D4⋊C8—51no—
132#322C3×D511yescharacteristic, complemented
133C22×C3×C5C4×D411yescharacteristic
134C2×C3×D5—41no—
135C2×C3×D5—41no—
136C2×C3×D5—41no—
137C3×C4×C5—21no—
138C3×C4×C5C2×M1611yescharacteristic
139C3×C4×C5#13111yescharacteristic
140C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
141C3×C4×C5#13711yescharacteristic
142C3×Dic5—22no—
143C3×Dic5—41no—
144C3×Dic5—41no—
145C2×C3×Q8—51no—
146C2×C3×D4—51no—
147C22×C3×C4—101no—
148C3×SD16—102no—
149C3×M16—202no—
150C2×C3×C8—21no—
151C2×C3×C8—101no—
152C2×C3×C8—101no—
153C2×C3×C8C4×D511yescharacteristic
154C2×C3×C8C4×D511yescharacteristic
155C2×C3×C8D2011yescharacteristic
156C2×C3×C8D2011yescharacteristic
157C3×C4⋊C4—51no—
158C3×C4⋊C4—51no—
159C3×C4⋊C4—101no—
160C3×C22⋊C4—101no—
161C3×C42—101no—
162C3×C42C22×D511yescharacteristic
163C22×D5—21no—
164C2×C4×C5C22×C3×C411yescharacteristic
165C2×C4×C5C2×C3×D411yescharacteristic
166C2×C4×C5C3×#4111yescharacteristic
167C2×Dic5—21no—
168C2×Dic5—21no—
169C2×Dic5—21no—
170D20—21no—
171D20—21no—
172C4×D5—41no—
173C4×D5—41no—
174Dic10—21no—
175Dic10C3×M1612yescomplemented
176C5×C8—22no—
177C5×C8—21no—
178C5×C8—21no—
179C5×C8—21no—
180C5×C8—21no—
181#168—41no—
182#168—41no—
183C2×SD16—51no—
184C2×M16—101no—
185C4×Q8—51no—
186C4×D4—51no—
187#106—51no—
188C4⋊C8—51no—
189C4⋊C8—51no—
190C4⋊C8—101no—
191#103—51no—
192#102—51no—
193C22⋊C8—101no—
194C4×C8—101no—
195C4×C8C2×C3×D511yescharacteristic
196C4×C8C2×C3×D511yescharacteristic
197C4×C8C2×C3×D511yescharacteristic
198C2×C3×C5#43511yescharacteristic
199C2×C3×C5#44011yescharacteristic
200C2×C3×C5#44311yescharacteristic
201C3×D5—81no—
202C23×C3—101no—
203C3×Q8—52no—
204C3×Q8—101no—
205C3×D4—101no—
206C3×D4—101no—
207C2×C3×C4—101no—
208C2×C3×C4—101no—
209C2×C3×C4—101no—
210C2×C3×C4—201no—
211C2×C3×C4—201no—
212C2×C3×C4C2×C4×D511yescharacteristic
213C2×C3×C4C2×D2011yescharacteristic
214C2×C3×C4#70911yescharacteristic
215C3×C8—22no—
216C3×C8—21no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—21no—
220C3×C8—201no—
221C3×C8—201no—
222C22×C5C3×C4×D411yescharacteristic
223C2×D5—41no—
224C2×D5—41no—
225C2×D5—41no—
226C4×C5—21no—
227C4×C5C2×C3×M1611yescharacteristic
228C4×C5C3×#13111yescharacteristic
229C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
230C4×C5C3×#13711yescharacteristic
231Dic5—22no—
232Dic5—41no—
233Dic5—41no—
234C2×Q8—51no—
235C2×D4—51no—
236C22×C4—101no—
237SD16—102no—
238M16—202no—
239C2×C8—21no—
240C2×C8—101no—
241C2×C8—101no—
242C2×C8C3×C4×D511yescharacteristic
243C2×C8C3×C4×D511yescharacteristic
244C2×C8C3×D2011yescharacteristic
245C2×C8C3×D2011yescharacteristic
246C4⋊C4—51no—
247C4⋊C4—51no—
248C4⋊C4—101no—
249C22⋊C4—101no—
250C42—101no—
251C42C22×C3×D511yescharacteristic
252C3×C5#158811yescharacteristic, complemented, Hall
253C22×C3—201no—
254C22×C3—201no—
255C22×C3—201no—
256C22×C3C4×D2011yescharacteristic
257C3×C4—21no—
258C3×C4—102no—
259C3×C4—201no—
260C3×C4—201no—
261C3×C4D5×M1611yescharacteristic
262C3×C4#405311yescharacteristic
263C3×C4#405411yescharacteristic
264C3×C4#405511yescharacteristic
265C2×C5C3×#43511yescharacteristic
266C2×C5C3×#44011yescharacteristic
267C2×C5C3×#44311yescharacteristic
268D5—81no—
269C23—101no—
270Q8—52no—
271Q8—101no—
272D4—101no—
273D4—101no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—201no—
278C2×C4—201no—
279C2×C4C2×C3×C4×D511yescharacteristic
280C2×C4C2×C3×D2011yescharacteristic
281C2×C4C3×#70911yescharacteristic
282C8—22no—
283C8—21no—
284C8—21no—
285C8—21no—
286C8—21no—
287C8—201no—
288C8—201no—
289C2×C3—401no—
290C2×C3#6498911yescharacteristic
291C2×C3#6499511yescharacteristic
292C2×C3#6499911yescharacteristic
293C5C3×#158811yescharacteristic, complemented, Sylow
294C22—201no—
295C22—201no—
296C22—201no—
297C22C3×C4×D2011yescharacteristic
298C4—21no—
299C4—102no—
300C4—201no—
301C4—201no—
302C4C3×D5×M1611yescharacteristic
303C4C3×#405311yescharacteristic
304C4C3×#405411yescharacteristic
305C4C3×#405511yescharacteristic
306C3#1059888111yescharacteristic, direct product factor, Sylow
307C2—401no—
308C2C3×#6498911yescharacteristic
309C2C3×#6499511yescharacteristic
310C2C3×#6499911yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#322C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×D20C2×C4
cosocleC42×C5C23×C3
hypercenterC3×#322D5
hypocenterC5C3×#1588
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ C3×#322

Complements

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

NH ≅ G/Ntype
3. C3×C8×Dic10C2semidirect
4. C3×C5×#322C2semidirect
6. C3×#64678C2semidirect
7. C3×#64676C2semidirect
8. #10598881C3direct (N × H)
27. C8×Dic10C2×C3semidirect
28. C5×#322C2×C3semidirect
30. #64678C2×C3semidirect
31. #64676C2×C3semidirect
56. C3×#322D5semidirect
85. C3×Dic10M16semidirect
132. #322C3×D5semidirect
175. Dic10C3×M16semidirect
252. C3×C5#1588semidirect
293. C5C3×#1588semidirect
306. C3#10598881direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×#6772
C3×#649772
C3×C8×Dic102
C3×C5×#3222
C3×#646792
C3×#646782
C3×#646762
#105988813
C3×#15885