Finite Group Databasebeta

← C3×#10602916 #14316512

Subgroups — C3×#10602916 #14316512

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#576C211yesmaximal, characteristic
2C3×#65484C211yesmaximal, characteristic, complemented
3C2×C3×#3959C211yesmaximal, characteristic, complemented
4C3×#65432C211yesmaximal, characteristic, complemented
5C3×#64787C211yesmaximal, characteristic, complemented
6C3×#64783C211yesmaximal, characteristic, complemented
7C3×#64781C211yesmaximal, characteristic, complemented
8#10602916C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×H(5,𝔽2)—21no—
10C3×C5×AGL(1,ℤ/8)—22no—
11C3×C5×AGL(1,ℤ/8)—21no—
12C3×C5×#135—21no—
13C3×C5×#135C2211yescharacteristic
14C2×C3×C5×D8—21no—
15C2×C3×C5×D8C2211yescharacteristic
16C3×C5×#131C2211yescharacteristic
17C3×#4097—21no—
18C2×C3×Dic20C2211yescharacteristic, complemented
19C3×#3961—21no—
20C3×#3959—22no—
21C3×#3959—21no—
22C3×#3956—21no—
23C3×#3951C2211yescharacteristic, complemented
24C3×#3944C2211yescharacteristic, complemented
25C2×C3×#672C2211yescharacteristic, complemented
26C3×#2194—51nomaximal, Hall
27C5×#576C2×C311yescharacteristic
28#65484C2×C311yescharacteristic, complemented
29C2×#3959C2×C311yescharacteristic, complemented
30#65432C2×C311yescharacteristic, complemented
31#64787C2×C311yescharacteristic, complemented
32#64783C2×C311yescharacteristic, complemented
33#64781C2×C311yescharacteristic, complemented
34C3×C5×#41—22no—
35C3×C5×#41—21no—
36C3×C5×#41—41no—
37C3×C5×#41D411yescharacteristic
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—42no—
41C2×C3×C5×D4—41no—
42C2×C3×Dic10—21no—
43C3×C5×Q16D411yescharacteristic
44C3×C5×SD16—22no—
45C3×C5×SD16—21no—
46C3×C5×D8—22no—
47C3×C5×D8—21no—
48C3×C5×D8D411yescharacteristic
49C3×C5×D8D412yes—
50C3×C5×M16—21no—
51C3×C5×M16D411yescharacteristic
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8C2311yescharacteristic
54C3×#689—41no—
55C3×#687—41no—
56C3×#681—21no—
57C3×Dic20—21no—
58C3×Dic20—21no—
59C3×#672—21no—
60C3×#672—21no—
61C3×#576D511yescharacteristic
62C3×#510—51no—
63C2×C3×SD32—51no—
64C3×#473—51no—
65C3×#361—51no—
66C3×#359—51no—
67C3×#350—51no—
68C5×H(5,𝔽2)—21no—
69C5×AGL(1,ℤ/8)—22no—
70C5×AGL(1,ℤ/8)—21no—
71C5×#135—21no—
72C5×#135C22×C311yescharacteristic
73C2×C5×D8—21no—
74C2×C5×D8C22×C311yescharacteristic
75C5×#131C22×C311yescharacteristic
76#4097—21no—
77C2×Dic20C22×C311yescharacteristic, complemented
78#3961—21no—
79#3959—22no—
80#3959—21no—
81#3956—21no—
82#3951C22×C311yescharacteristic, complemented
83#3944C22×C311yescharacteristic, complemented
84C2×#672C22×C311yescharacteristic, complemented
85#2194—51noSylow
86C23×C3×C5—42no—
87C23×C3×C5—41no—
88C3×C5×Q8—21no—
89C3×C5×Q8D811yescharacteristic
90C3×C5×D4—21no—
91C3×C5×D4—21no—
92C3×C5×D4—22no—
93C3×C5×D4—42no—
94C3×C5×D4—42no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C3×C5×D4D811yescharacteristic
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×Dic5—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3×C5×C8—21no—
106C3×C5×C8C2×D411yescharacteristic
107C3×C5×C8C2×D411yescharacteristic
108C3×#168—41no—
109C3×H(5,𝔽2)—21no—
110C3×#137—101no—
111C3×AGL(1,ℤ/8)—22no—
112C3×AGL(1,ℤ/8)—21no—
113C3×#135—21no—
114C3×#135C2×D511yescharacteristic
115C2×C3×Q16—51no—
116C2×C3×D8—21no—
117C2×C3×D8C2×D511yescharacteristic
118C3×#131C2×D511yescharacteristic
119C3×Q32—101no—
120C3×SD32—102no—
121C3×SD32—101no—
122C3×M32—51no—
123C2×C3×C16—51no—
124C3×#108—51no—
125C3×#101—101no—
126C5×#41—22no—
127C5×#41—21no—
128C5×#41—41no—
129C5×#41C3×D411yescharacteristic
130C2×C5×D4—22no—
131C2×C5×D4—21no—
132C2×C5×D4—42no—
133C2×C5×D4—41no—
134C2×Dic10—21no—
135C5×Q16C3×D411yescharacteristic
136C5×SD16—22no—
137C5×SD16—21no—
138C5×D8—22no—
139C5×D8—21no—
140C5×D8C3×D411yescharacteristic
141C5×D8C3×D412yes—
142C5×M16—21no—
143C5×M16C3×D411yescharacteristic
144C2×C5×C8—21no—
145C2×C5×C8C23×C311yescharacteristic
146#689—41no—
147#687—41no—
148#681—21no—
149Dic20—21no—
150Dic20—21no—
151#672—21no—
152#672—21no—
153#576C3×D511yescharacteristic
154#510—51no—
155C2×SD32—51no—
156#473—51no—
157#361—51no—
158#359—51no—
159#350—51no—
160C22×C3×C5—21no—
161C22×C3×C5—42no—
162C22×C3×C5—41no—
163C22×C3×C5—161no—
164C22×C3×C5—162no—
165C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
166C3×C4×C5—21no—
167C3×C4×C5—41no—
168C3×C4×C5#12011yescharacteristic
169C3×C4×C5C2×D811yescharacteristic
170C3×Dic5—81no—
171C3×#41—22no—
172C3×#41—21no—
173C3×#41—41no—
174C3×#41C22⋊D511yescharacteristic
175C2×C3×Q8—101no—
176C2×C3×D4—22no—
177C2×C3×D4—21no—
178C2×C3×D4—42no—
179C2×C3×D4—41no—
180C3×Q16—101no—
181C3×Q16—101no—
182C3×Q16—201no—
183C3×Q16C22⋊D511yescharacteristic
184C3×SD16—22no—
185C3×SD16—21no—
186C3×SD16—201no—
187C3×D8—22no—
188C3×D8—21no—
189C3×D8C22⋊D511yescharacteristic
190C3×D8C22⋊D512yes—
191C3×M16—21no—
192C3×M16—101no—
193C3×M16C22⋊D511yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8C22×D511yescharacteristic
196C3×C16—101no—
197C3×C16—101no—
198C23×C5—42no—
199C23×C5—41no—
200C5×Q8—21no—
201C5×Q8C3×D811yescharacteristic
202C5×D4—21no—
203C5×D4—21no—
204C5×D4—22no—
205C5×D4—42no—
206C5×D4—42no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4C3×D811yescharacteristic
210C2×C4×C5—21no—
211C2×C4×C5—42no—
212C2×C4×C5—41no—
213C2×C4×C5C2×C3×D411yescharacteristic
214C2×Dic5—41no—
215Dic10—41no—
216Dic10—41no—
217C5×C8—21no—
218C5×C8C2×C3×D411yescharacteristic
219C5×C8C2×C3×D411yescharacteristic
220#168—41no—
221H(5,𝔽2)—21no—
222#137—101no—
223AGL(1,ℤ/8)—22no—
224AGL(1,ℤ/8)—21no—
225#135—21no—
226#135C2×C3×D511yescharacteristic
227C2×Q16—51no—
228C2×D8—21no—
229C2×D8C2×C3×D511yescharacteristic
230#131C2×C3×D511yescharacteristic
231Q32—101no—
232SD32—102no—
233SD32—101no—
234M32—51no—
235C2×C16—51no—
236#108—51no—
237#101—101no—
238C2×C3×C5—21no—
239C2×C3×C5—41no—
240C2×C3×C5—82no—
241C2×C3×C5—81no—
242C2×C3×C5#44711yescharacteristic
243C23×C3—42no—
244C23×C3—41no—
245C3×Q8—21no—
246C3×Q8—201no—
247C3×Q8—201no—
248C3×Q8#68611yescharacteristic
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—22no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4#68611yescharacteristic
257C2×C3×C4—21no—
258C2×C3×C4—42no—
259C2×C3×C4—41no—
260C2×C3×C4—201no—
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C3×C8—21no—
263C3×C8—201no—
264C3×C8C2×C22⋊D511yescharacteristic
265C3×C8C2×C22⋊D511yescharacteristic
266C22×C5—21no—
267C22×C5—42no—
268C22×C5—41no—
269C22×C5—161no—
270C22×C5—162no—
271C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
272C4×C5—21no—
273C4×C5—41no—
274C4×C5C3×#12011yescharacteristic
275C4×C5C2×C3×D811yescharacteristic
276Dic5—81no—
277#41—22no—
278#41—21no—
279#41—41no—
280#41C3×C22⋊D511yescharacteristic
281C2×Q8—101no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—42no—
285C2×D4—41no—
286Q16—101no—
287Q16—101no—
288Q16—201no—
289Q16C3×C22⋊D511yescharacteristic
290SD16—22no—
291SD16—21no—
292SD16—201no—
293D8—22no—
294D8—21no—
295D8C3×C22⋊D511yescharacteristic
296D8C3×C22⋊D512yes—
297M16—21no—
298M16—101no—
299M16C3×C22⋊D511yescharacteristic
300C2×C8—21no—
301C2×C8C22×C3×D511yescharacteristic
302C16—101no—
303C16—101no—
304C3×C5#219411yescharacteristic, complemented, Hall
305C22×C3—21no—
306C22×C3—42no—
307C22×C3—41no—
308C22×C3—161no—
309C22×C3—162no—
310C22×C3#407811yescharacteristic
311C3×C4—21no—
312C3×C4—41no—
313C3×C4—401no—
314C3×C4C2×#68611yescharacteristic
315C3×C4#409911yescharacteristic
316C2×C5—21no—
317C2×C5—41no—
318C2×C5—82no—
319C2×C5—81no—
320C2×C5C3×#44711yescharacteristic
321C23—42no—
322C23—41no—
323Q8—21no—
324Q8—201no—
325Q8—201no—
326Q8C3×#68611yescharacteristic
327D4—21no—
328D4—21no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4C3×#68611yescharacteristic
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—201no—
339C2×C4C2×C3×C22⋊D511yescharacteristic
340C8—21no—
341C8—201no—
342C8C2×C3×C22⋊D511yescharacteristic
343C8C2×C3×C22⋊D511yescharacteristic
344C2×C3—21no—
345C2×C3—41no—
346C2×C3—82no—
347C2×C3—81no—
348C2×C3#6550611yescharacteristic
349C5C3×#219411yescharacteristic, complemented, Sylow
350C22—21no—
351C22—42no—
352C22—41no—
353C22—161no—
354C22—162no—
355C22C3×#407811yescharacteristic
356C4—21no—
357C4—41no—
358C4—401no—
359C4C2×C3×#68611yescharacteristic
360C4C3×#409911yescharacteristic
361C3#1060291611yescharacteristic, direct product factor, Sylow
362C2—21no—
363C2—41no—
364C2—82no—
365C2—81no—
366C2C3×#6550611yescharacteristic
subgroupG/H
centerC2×C3#65506
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
Fitting, prime radicalC3×C5×#576C2
socleC2×C3×C5#447
hypercenterC3×#576D5
hypocenterC5C3×#2194
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#131 ◁ C3×#576

Complements

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

NH ≅ G/Ntype
2. C3×#65484C2semidirect
3. C2×C3×#3959C2semidirect
4. C3×#65432C2semidirect
5. C3×#64787C2semidirect
6. C3×#64783C2semidirect
7. C3×#64781C2semidirect
8. #10602916C3direct (N × H)
18. C2×C3×Dic20C22semidirect
23. C3×#3951C22semidirect
24. C3×#3944C22semidirect
25. C2×C3×#672C22semidirect
28. #65484C2×C3semidirect
29. C2×#3959C2×C3semidirect
30. #65432C2×C3semidirect
31. #64787C2×C3semidirect
32. #64783C2×C3semidirect
33. #64781C2×C3semidirect
77. C2×Dic20C22×C3semidirect
82. #3951C22×C3semidirect
83. #3944C22×C3semidirect
84. C2×#672C22×C3semidirect
304. C3×C5#2194semidirect
349. C5C3×#2194semidirect
361. C3#10602916direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5762
C3×#654842
C2×C3×#39592
C3×#654322
C3×#647872
C3×#647832
C3×#647812
#106029163
C3×#21945