Finite Group Databasebeta

← C3×#10601853 #14289938

Subgroups — C3×#10601853 #14289938

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65919C211yesmaximal, characteristic
2C3×C5×#462C211yesmaximal, characteristic, complemented
3C3×#65383C211yesmaximal, characteristic, complemented
4C3×#65377C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic
7C3×#64704C211yesmaximal, characteristic, complemented
8#10601853C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q16—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C3×#4093—21no—
13C3×#4040—22no—
14C3×#4039—21no—
15C3×#4021—21no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20—21no—
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21C3×#3942—21no—
22C3×#3941—22no—
23C3×#3940—21no—
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1640—51nomaximal, Hall
27#65919C2×C311yescharacteristic
28C5×#462C2×C311yescharacteristic, complemented
29#65383C2×C311yescharacteristic, complemented
30#65377C2×C311yescharacteristic
31Q8⋊#168C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic
33#64704C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D412yes—
39C2×C3×C4×D5—22no—
40C2×C3×Dic10D411yescharacteristic
41C3×C5×Q16—42no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49C3×#685—22no—
50C3×#685—22no—
51C3×#685—22no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C3×#559—51no—
58C3×#486—51no—
59C3×#475—51no—
60C3×#462D511yescharacteristic, complemented
61C3×#331—51no—
62C3×Q8⋊C8—51no—
63C3×Q8⋊C8—51no—
64C2×C5×Q16—21no—
65C5×C4⋊Q8C22×C311yescharacteristic
66C4×C5×Q8C22×C311yescharacteristic
67#4093—21no—
68#4040—22no—
69#4039—21no—
70#4021—21no—
71#4020C22×C311yescharacteristic
72C4×D20—21no—
73C4×Dic10C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C5×#103—21no—
76#3942—21no—
77#3941—22no—
78#3940—21no—
79C4⋊#168C22×C311yescharacteristic
80C4×#168C22×C311yescharacteristic
81#1640—51noSylow
82C22×C3×D5—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—42no—
96C3×D20—41no—
97C3×D20—41no—
98C3×D20—41no—
99C3×D20—41no—
100C3×C4×D5—82no—
101C3×Dic10—21no—
102C3×Dic10—21no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C3×#168—41no—
106C2×C3×Q16—21no—
107C3×C4⋊Q8C2×D511yescharacteristic
108C3×#127—51no—
109C3×#124—101no—
110C3×#124—101no—
111C3×#123—102no—
112C3×C4×Q8—51no—
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4—101no—
115C3×C4×D4—101no—
116C3×#106—101no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#103—21no—
120C3×#103—101no—
121C3×#102—102no—
122C3×C4×C8—51no—
123C2×C5×Q8—21no—
124C2×C5×Q8C3×D411yescharacteristic
125C2×D20—21no—
126C2×D20—21no—
127C2×D20C3×D412yes—
128C2×C4×D5—22no—
129C2×Dic10C3×D411yescharacteristic
130C5×Q16—42no—
131C2×C5×C8—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4C3×D411yescharacteristic
136C42×C5—21no—
137C42×C5C23×C311yescharacteristic
138#685—22no—
139#685—22no—
140#685—22no—
141C4⋊Dic5C3×D411yescharacteristic
142#683—21no—
143C4×Dic5—21no—
144C2×#168—21no—
145C2×#168—21no—
146#559—51no—
147#486—51no—
148#475—51no—
149#462C3×D511yescharacteristic, complemented
150#331—51no—
151Q8⋊C8—51no—
152Q8⋊C8—51no—
153C22×C3×C5#12011yescharacteristic
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5—81no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—41no—
166C3×Dic5—41no—
167C2×C3×Q8—21no—
168C2×C3×Q8—51no—
169C2×C3×Q8C22⋊D511yescharacteristic
170C2×C3×D4—52no—
171C2×C3×D4—101no—
172C2×C3×D4—101no—
173C22×C3×C4—102no—
174C3×Q16—42no—
175C2×C3×C8—21no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4C22⋊D511yescharacteristic
184C3×C22⋊C4—102no—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187C3×C42—21no—
188C3×C42—101no—
189C3×C42C22×D511yescharacteristic
190C22×D5—22no—
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×C4×C5C2×C3×D411yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203D20—42no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—41no—
208C4×D5—82no—
209Dic10—21no—
210Dic10—21no—
211C5×C8—41no—
212#168—41no—
213#168—41no—
214C2×Q16—21no—
215C4⋊Q8C2×C3×D511yescharacteristic
216#127—51no—
217#124—101no—
218#124—101no—
219#123—102no—
220C4×Q8—51no—
221C4×Q8C2×C3×D511yescharacteristic
222C4×D4—101no—
223C4×D4—101no—
224#106—101no—
225C4⋊C8—51no—
226C4⋊C8C2×C3×D511yescharacteristic
227#103—21no—
228#103—101no—
229#102—102no—
230C4×C8—51no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234C3×D5—82no—
235C23×C3—102no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—101no—
241C3×Q8—101no—
242C3×D4—202no—
243C3×D4—201no—
244C3×D4—201no—
245C3×D4—201no—
246C3×D4—201no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—41no—
250C2×C3×C4—101no—
251C2×C3×C4—101no—
252C2×C3×C4—402no—
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C3×C8—41no—
257C3×C8—201no—
258C3×C8—201no—
259C22×C5C3×#12011yescharacteristic
260C2×D5—42no—
261C2×D5—42no—
262C2×D5—42no—
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—81no—
267C4×C5C3×#13511yescharacteristic
268C4×C5C3×#13511yescharacteristic
269C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
270C4×C5C3×#13711yescharacteristic
271Dic5—41no—
272Dic5—41no—
273C2×Q8—21no—
274C2×Q8—51no—
275C2×Q8C3×C22⋊D511yescharacteristic
276C2×D4—52no—
277C2×D4—101no—
278C2×D4—101no—
279C22×C4—102no—
280Q16—42no—
281C2×C8—21no—
282C2×C8—101no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—51no—
288C4⋊C4—101no—
289C4⋊C4C3×C22⋊D511yescharacteristic
290C22⋊C4—102no—
291C22⋊C4—102no—
292C22⋊C4—102no—
293C42—21no—
294C42—101no—
295C42C22×C3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—202no—
298C22×C3—202no—
299C22×C3—202no—
300C22×C3#408311yescharacteristic
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—81no—
305C3×C4—201no—
306C3×C4—201no—
307C3×C4#406411yescharacteristic
308C3×C4#406511yescharacteristic
309C3×C4#407811yescharacteristic
310C3×C4#409611yescharacteristic
311C2×C5C3×#44911yescharacteristic
312C2×C5C3×#45211yescharacteristic
313C2×C5C3×#45511yescharacteristic
314D5—82no—
315C23—102no—
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—41no—
320Q8—101no—
321Q8—101no—
322D4—202no—
323D4—201no—
324D4—201no—
325D4—201no—
326D4—201no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—402no—
333C2×C4C3×D4×D511yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C2×C3×C22⋊D511yescharacteristic
336C8—41no—
337C8—201no—
338C8—201no—
339C2×C3—402no—
340C2×C3#6532611yescharacteristic
341C2×C3#6547611yescharacteristic
342C2×C3#6549111yescharacteristic
343C5C3×#164011yescharacteristic, complemented, Sylow
344C22—202no—
345C22—202no—
346C22—202no—
347C22C3×#408311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—201no—
353C4—201no—
354C4C3×#406411yescharacteristic
355C4C3×#406511yescharacteristic
356C4C3×#407811yescharacteristic
357C4C3×#409611yescharacteristic
358C3#1060185311yescharacteristic, direct product factor, Sylow
359C2—402no—
360C2C3×#6532611yescharacteristic
361C2C3×#6547611yescharacteristic
362C2C3×#6549111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#462C2
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC3×#462D5
hypocenterC5C3×#1640
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
2. C3×C5×#462C2semidirect
3. C3×#65383C2semidirect
5. C3×Q8⋊#168C2semidirect
7. C3×#64704C2semidirect
8. #10601853C3direct (N × H)
28. C5×#462C2×C3semidirect
29. #65383C2×C3semidirect
31. Q8⋊#168C2×C3semidirect
33. #64704C2×C3semidirect
60. C3×#462D5semidirect
149. #462C3×D5semidirect
296. C3×C5#1640semidirect
343. C5C3×#1640semidirect
358. C3#10601853direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659192
C3×C5×#4622
C3×#653832
C3×#653772
C3×Q8⋊#1682
C3×#647052
C3×#647042
#106018533
C3×#16405