Finite Group Databasebeta

← C2×C3×#64905 #14314006

Subgroups — C2×C3×#64905 #14314006

Order 1920.

448 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
1C2×C3×#4058C211yesmaximal, characteristic
2C2×C3×#3996C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊C16C211yesmaximal, characteristic, complemented
4C3×#64905C214yesmaximal, direct product factor
5C2×#64905C311yesmaximal, characteristic, direct product factor, Hall
6C2×C3×#711—21no—
7C2×C3×#700—21no—
8C2×C3×C5×D8C411yescharacteristic
9C2×C3×#687—21no—
10C3×#4058—21no—
11C3×#4058—21no—
12C3×#4058C412yes—
13C3×#4058C2212yes—
14C2×C3×Dic20C411yescharacteristic
15C2×C3×C8×D5C2211yescharacteristic
16C2×C3×#674—21no—
17C3×#3996—21no—
18C3×#3996C2212yescomplemented
19C3×D5⋊C16—21no—
20C3×D5⋊C16C2212yescomplemented
21C2×C3×#359—51nomaximal, Hall
22C2×#4058C2×C311yescharacteristic
23C2×#3996C2×C311yescharacteristic, complemented
24C2×D5⋊C16C2×C311yescharacteristic, complemented
25#64905C2×C314yesdirect product factor
26C2×C3×C5×D4—21no—
27C2×C3×C22⋊D5—41no—
28C22×C3×Dic5—41no—
29C3×#711—22no—
30C3×#711—22no—
31C3×#711—41no—
32C3×#711—41no—
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×Dic10—21no—
35C2×C3×#170—41no—
36C3×#700—22no—
37C3×#700—41no—
38C3×C5×D8—21no—
39C3×C5×D8C2×C412yes—
40C2×C3×C5×C8C2×C411yescharacteristic
41C3×#687—22no—
42C3×#687—22no—
43C2×C3×#168D411yescharacteristic
44C3×Dic20—21no—
45C3×Dic20C2×C412yes—
46C3×C8×D5C2×C411yescharacteristic
47C3×C8×D5D411yescharacteristic
48C3×C8×D5D411yescharacteristic
49C3×C8×D5C2311yescharacteristic
50C3×#674—22no—
51C2×C3×#135—51no—
52C22×C3×C16—51no—
53C2×C3×#108—51no—
54C3×#359—54no—
55C2×#711—21no—
56C2×#700—21no—
57C2×C5×D8C3×C411yescharacteristic
58C2×#687—21no—
59#4058—21no—
60#4058—21no—
61#4058C3×C412yes—
62#4058C22×C312yes—
63C2×Dic20C3×C411yescharacteristic
64C2×C8×D5C22×C311yescharacteristic
65C2×#674—21no—
66#3996—21no—
67#3996C22×C312yescomplemented
68D5⋊C16—21no—
69D5⋊C16C22×C312yescomplemented
70C2×#359—51noSylow
71C23×C3×C5—41no—
72C22×C3×D5SD1611yescharacteristic
73C3×C5×D4—22no—
74C3×C5×D4—41no—
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C3×C22⋊D5—42no—
77C3×C22⋊D5—42no—
78C2×C3×Dic5—41no—
79C2×C3×Dic5—42no—
80C2×C3×Dic5—42no—
81C2×C3×Dic5D811yescharacteristic
82C3×C4×D5C22⋊C411yescharacteristic
83C3×C4×D5D811yescharacteristic
84C3×C4×D5SD1611yescharacteristic
85C3×C4×D5C2×D411yescharacteristic
86C3×Dic10—22no—
87C3×Dic10—41no—
88C3×#170—42no—
89C3×C5×C8C22⋊C411yescharacteristic
90C3×C5×C8C22×C411yescharacteristic
91C3×#168C22⋊C411yescharacteristic
92C3×#168C2×D411yescharacteristic
93C2×C3×#41—101no—
94C3×#135—52no—
95C3×#135—52no—
96C3×#135—101no—
97C3×#135—101no—
98C2×C3×Q16—51no—
99C2×C3×SD16—101no—
100C2×C3×D8AGL(1,𝔽5)11yescharacteristic
101C2×C3×M16—101no—
102C22×C3×C8—51no—
103C2×C3×C16—52no—
104C2×C3×C16—101no—
105C2×C3×C16—101no—
106C3×#108—52no—
107C3×#108—101no—
108C2×C5×D4—21no—
109C2×C22⋊D5—41no—
110C22×Dic5—41no—
111#711—22no—
112#711—22no—
113#711—41no—
114#711—41no—
115C2×C4×D5C3×D411yescharacteristic
116C2×Dic10—21no—
117C2×#170—41no—
118#700—22no—
119#700—41no—
120C5×D8—21no—
121C5×D8C2×C3×C412yes—
122C2×C5×C8C2×C3×C411yescharacteristic
123#687—22no—
124#687—22no—
125C2×#168C3×D411yescharacteristic
126Dic20—21no—
127Dic20C2×C3×C412yes—
128C8×D5C2×C3×C411yescharacteristic
129C8×D5C3×D411yescharacteristic
130C8×D5C3×D411yescharacteristic
131C8×D5C23×C311yescharacteristic
132#674—22no—
133C2×#135—51no—
134C22×C16—51no—
135C2×#108—51no—
136#359—54no—
137C22×C3×C5—42no—
138C22×C3×C5—82no—
139C22×C3×C5#10211yescharacteristic
140C2×C3×D5—22no—
141C2×C3×D5#10211yescharacteristic
142C2×C3×D5C2×SD1611yescharacteristic
143C3×C4×C5#10211yescharacteristic
144C3×C4×C5C2×C22⋊C411yescharacteristic
145C3×Dic5—42no—
146C3×Dic5#10211yescharacteristic
147C3×Dic5C2×D811yescharacteristic
148C3×#41—102no—
149C3×#41—102no—
150C3×#41—201no—
151C3×#41—201no—
152C2×C3×Q8—101no—
153C2×C3×D4—21no—
154C2×C3×D4—201no—
155C22×C3×C4—51no—
156C22×C3×C4—201no—
157C3×Q16—52no—
158C3×Q16—101no—
159C3×SD16—102no—
160C3×SD16—102no—
161C3×D8—21no—
162C3×D8C2×AGL(1,𝔽5)12yes—
163C3×M16—102no—
164C3×M16—201no—
165C2×C3×C8—51no—
166C2×C3×C8—51no—
167C2×C3×C8—51no—
168C2×C3×C8—51no—
169C2×C3×C8—51no—
170C2×C3×C8—201no—
171C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
172C3×C16—102no—
173C23×C5—41no—
174C22×D5C3×SD1611yescharacteristic
175C5×D4—22no—
176C5×D4—41no—
177C2×C4×C5C3×C22⋊C411yescharacteristic
178C22⋊D5—42no—
179C22⋊D5—42no—
180C2×Dic5—41no—
181C2×Dic5—42no—
182C2×Dic5—42no—
183C2×Dic5C3×D811yescharacteristic
184C4×D5C3×C22⋊C411yescharacteristic
185C4×D5C3×D811yescharacteristic
186C4×D5C3×SD1611yescharacteristic
187C4×D5C2×C3×D411yescharacteristic
188Dic10—22no—
189Dic10—41no—
190#170—42no—
191C5×C8C3×C22⋊C411yescharacteristic
192C5×C8C22×C3×C411yescharacteristic
193#168C3×C22⋊C411yescharacteristic
194#168C2×C3×D411yescharacteristic
195C2×#41—101no—
196#135—52no—
197#135—52no—
198#135—101no—
199#135—101no—
200C2×Q16—51no—
201C2×SD16—101no—
202C2×D8C3×AGL(1,𝔽5)11yescharacteristic
203C2×M16—101no—
204C22×C8—51no—
205C2×C16—52no—
206C2×C16—101no—
207C2×C16—101no—
208#108—52no—
209#108—101no—
210C2×C3×C5—82no—
211C2×C3×C5#35912yescomplemented
212C2×C3×C5C2×#10211yescharacteristic
213C3×D5—21no—
214C3×D5—21no—
215C23×C3—41no—
216C23×C3—51no—
217C3×Q8—102no—
218C3×Q8—201no—
219C3×D4—22no—
220C3×D4—41no—
221C3×D4—202no—
222C3×D4—202no—
223C2×C3×C4—51no—
224C2×C3×C4—51no—
225C2×C3×C4—51no—
226C2×C3×C4—51no—
227C2×C3×C4—51no—
228C2×C3×C4—202no—
229C2×C3×C4—202no—
230C2×C3×C4—201no—
231C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
232C3×C8—51no—
233C3×C8—51no—
234C3×C8—202no—
235C3×C8C22⋊AGL(1,𝔽5)11yescharacteristic
236C3×C8C22×AGL(1,𝔽5)11yescharacteristic
237C22×C5—42no—
238C22×C5—82no—
239C22×C5C3×#10211yescharacteristic
240C2×D5—22no—
241C2×D5C3×#10211yescharacteristic
242C2×D5C2×C3×SD1611yescharacteristic
243C4×C5C3×#10211yescharacteristic
244C4×C5C2×C3×C22⋊C411yescharacteristic
245Dic5—42no—
246Dic5C3×#10211yescharacteristic
247Dic5C2×C3×D811yescharacteristic
248#41—102no—
249#41—102no—
250#41—201no—
251#41—201no—
252C2×Q8—101no—
253C2×D4—21no—
254C2×D4—201no—
255C22×C4—51no—
256C22×C4—201no—
257Q16—52no—
258Q16—101no—
259SD16—102no—
260SD16—102no—
261D8—21no—
262D8C2×C3×AGL(1,𝔽5)12yes—
263M16—102no—
264M16—201no—
265C2×C8—51no—
266C2×C8—51no—
267C2×C8—51no—
268C2×C8—51no—
269C2×C8—51no—
270C2×C8—201no—
271C2×C8C2×C3×AGL(1,𝔽5)11yescharacteristic
272C16—102no—
273C3×C5C2×#35911yescharacteristic, complemented, Hall
274C22×C3—42no—
275C22×C3—51no—
276C22×C3—51no—
277C22×C3—82no—
278C22×C3—102no—
279C22×C3#400711yescharacteristic
280C3×C4—51no—
281C3×C4—51no—
282C3×C4—202no—
283C3×C4#400711yescharacteristic
284C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
285C2×C5—82no—
286C2×C5C3×#35912yescomplemented
287C2×C5C2×C3×#10211yescharacteristic
288D5—21no—
289D5—21no—
290C23—41no—
291C23—51no—
292Q8—102no—
293Q8—201no—
294D4—22no—
295D4—41no—
296D4—202no—
297D4—202no—
298C2×C4—51no—
299C2×C4—51no—
300C2×C4—51no—
301C2×C4—51no—
302C2×C4—51no—
303C2×C4—202no—
304C2×C4—202no—
305C2×C4—201no—
306C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
307C8—51no—
308C8—51no—
309C8—202no—
310C8C3×C22⋊AGL(1,𝔽5)11yescharacteristic
311C8C22×C3×AGL(1,𝔽5)11yescharacteristic
312C2×C3—82no—
313C2×C3—101no—
314C2×C3—101no—
315C2×C3#6490512yesdirect product factor
316C2×C3C2×#400711yescharacteristic
317C5C2×C3×#35911yescharacteristic, complemented, Sylow
318C22—42no—
319C22—51no—
320C22—51no—
321C22—82no—
322C22—102no—
323C22C3×#400711yescharacteristic
324C4—51no—
325C4—51no—
326C4—202no—
327C4C3×#400711yescharacteristic
328C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
329C3C2×#6490511yescharacteristic, direct product factor, Sylow
330C2—82no—
331C2—101no—
332C2—101no—
333C2C3×#6490512yesdirect product factor
334C2C2×C3×#400711yescharacteristic
subgroupG/H
centerC22×C3#4007
commutatorC5×C8C22×C3×C4
FrattiniC8C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×D8C4
socleC22×C3×C5#102
prime radicalC2×C3×#4058C2
cosocleC8×D5C23×C3
hypercenterC2×C3×D8AGL(1,𝔽5)
hypocenterC5C2×C3×#359
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×D8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3996C2semidirect
3. C2×C3×D5⋊C16C2semidirect
4. C3×#64905C2direct (N × H)
5. C2×#64905C3direct (N × H)
18. C3×#3996C22semidirect
20. C3×D5⋊C16C22semidirect
23. C2×#3996C2×C3semidirect
24. C2×D5⋊C16C2×C3semidirect
25. #64905C2×C3direct (N × H)
67. #3996C22×C3semidirect
69. D5⋊C16C22×C3semidirect
211. C2×C3×C5#359semidirect
273. C3×C5C2×#359semidirect
286. C2×C5C3×#359semidirect
315. C2×C3#64905direct (N × H)
317. C5C2×C3×#359semidirect
329. C3C2×#64905direct (N × H)
333. C2C3×#64905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40582
C2×C3×#39962
C2×C3×D5⋊C162
C3×#649052
C2×#649053
C2×C3×#3595