Finite Group Databasebeta

← C3×#10599055 #14289950

Subgroups — C3×#10599055 #14289950

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×#65320C211yesmaximal, characteristic, complemented
3C3×#65140C211yesmaximal, characteristic, complemented
4C3×#64983C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic
7C3×#64676C211yesmaximal, characteristic, complemented
8#10599055C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4093—21no—
11C2×C3×#689—21no—
12C3×#4040—22no—
13C3×#4039—21no—
14C3×#4021—21no—
15C3×#4020C2211yescharacteristic
16C3×C4×D20—21no—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3953—22no—
22C3×#3949—21no—
23C3×#3948—21no—
24C3×#3942—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1640—51nomaximal, Hall
27#65919C2×C311yescharacteristic
28#65320C2×C311yescharacteristic, complemented
29#65140C2×C311yescharacteristic, complemented
30#64983C2×C311yescharacteristic
31C5×Q8⋊C8C2×C311yescharacteristic, complemented
32#64705C2×C311yescharacteristic
33#64676C2×C311yescharacteristic, complemented
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20D412yes—
38C2×C3×C4×D5—22no—
39C2×C3×Dic10—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47C3×#689—42no—
48C3×#685—22no—
49C3×#685—22no—
50C3×#685—22no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—21no—
55C3×C4×Dic5—21no—
56C2×C3×#168—21no—
57C3×#559—51no—
58C3×#486—51no—
59C3×#475—51no—
60C3×#462—51no—
61C3×#331—51no—
62C3×Q8⋊C8—51no—
63C3×Q8⋊C8D511yescharacteristic, complemented
64C4×C5×Q8C22×C311yescharacteristic
65#4093—21no—
66C2×#689—21no—
67#4040—22no—
68#4039—21no—
69#4021—21no—
70#4020C22×C311yescharacteristic
71C4×D20—21no—
72#4015C22×C311yescharacteristic
73C4×Dic10C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C4×C5×C8C22×C311yescharacteristic
76#3953—22no—
77#3949—21no—
78#3948—21no—
79#3942—21no—
80C4⋊#168C22×C311yescharacteristic
81#1640—51noSylow
82C22×C3×D5—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—41no—
93C3×D20—42no—
94C3×D20—41no—
95C3×D20—41no—
96C3×D20—41no—
97C3×D20—41no—
98C3×C4×D5—82no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3×#168—41no—
106C2×C3×Q16—101no—
107C3×C4⋊Q8—51no—
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—101no—
120C3×#103—101no—
121C3×#102—102no—
122C3×C4×C8C2×D511yescharacteristic
123C2×C5×Q8C3×D411yescharacteristic
124C2×D20—21no—
125C2×D20—21no—
126C2×D20C3×D412yes—
127C2×C4×D5—22no—
128C2×Dic10—21no—
129C2×Dic10C3×D411yescharacteristic
130C2×C5×C8—21no—
131C2×C5×C8—21no—
132C5×C4⋊C4—21no—
133C5×C4⋊C4C3×D411yescharacteristic
134C42×C5—21no—
135C42×C5C23×C311yescharacteristic
136#689—42no—
137#685—22no—
138#685—22no—
139#685—22no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C4⋊Dic5C3×D411yescharacteristic
143#683—21no—
144C4×Dic5—21no—
145C2×#168—21no—
146#559—51no—
147#486—51no—
148#475—51no—
149#462—51no—
150#331—51no—
151Q8⋊C8—51no—
152Q8⋊C8C3×D511yescharacteristic, complemented
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#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—41no—
165C3×Dic5—41no—
166C3×Dic5—81no—
167C2×C3×Q8—51no—
168C2×C3×Q8—101no—
169C2×C3×Q8D2011yescharacteristic
170C2×C3×D4—52no—
171C2×C3×D4—101no—
172C2×C3×D4—101no—
173C22×C3×C4—102no—
174C3×Q16—202no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4D2011yescharacteristic
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—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5C2×C3×D411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×C4×C5C2×C3×D411yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—41no—
201D20—42no—
202D20—41no—
203D20—41no—
204D20—41no—
205D20—41no—
206C4×D5—82no—
207Dic10—21no—
208Dic10—21no—
209Dic10—41no—
210Dic10—41no—
211C5×C8—41no—
212C5×C8—41no—
213#168—41no—
214C2×Q16—101no—
215C4⋊Q8—51no—
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—101no—
228#103—101no—
229#102—102no—
230C4×C8C2×C3×D511yescharacteristic
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—101no—
239C3×Q8—101no—
240C3×Q8—201no—
241C3×Q8—201no—
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—101no—
250C2×C3×C4—101no—
251C2×C3×C4—201no—
252C2×C3×C4—402no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C3×C8—41no—
257C3×C8—41no—
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×C5C3×#13511yescharacteristic
267C4×C5C3×#13511yescharacteristic
268C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
269C4×C5C3×#13711yescharacteristic
270Dic5—41no—
271Dic5—41no—
272Dic5—81no—
273C2×Q8—51no—
274C2×Q8—101no—
275C2×Q8C3×D2011yescharacteristic
276C2×D4—52no—
277C2×D4—101no—
278C2×D4—101no—
279C22×C4—102no—
280Q16—202no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4C3×D2011yescharacteristic
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#402811yescharacteristic
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—201no—
305C3×C4—201no—
306C3×C4—401no—
307C3×C4#405011yescharacteristic
308C3×C4#405411yescharacteristic
309C3×C4#406211yescharacteristic
310C3×C4#406411yescharacteristic
311C2×C5C3×#44911yescharacteristic
312C2×C5C3×#45211yescharacteristic
313C2×C5C3×#45511yescharacteristic
314D5—82no—
315C23—102no—
316Q8—21no—
317Q8—21no—
318Q8—101no—
319Q8—101no—
320Q8—201no—
321Q8—201no—
322D4—202no—
323D4—201no—
324D4—201no—
325D4—201no—
326D4—201no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—201no—
332C2×C4—402no—
333C2×C4C2×C3×D2011yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C3×D4×D511yescharacteristic
336C8—41no—
337C8—41no—
338C8—201no—
339C2×C3—402no—
340C2×C3#6502311yescharacteristic
341C2×C3#6509911yescharacteristic
342C2×C3#6511411yescharacteristic
343C5C3×#164011yescharacteristic, complemented, Sylow
344C22—202no—
345C22—202no—
346C22—202no—
347C22C3×#402811yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—201no—
352C4—201no—
353C4—401no—
354C4C3×#405011yescharacteristic
355C4C3×#405411yescharacteristic
356C4C3×#406211yescharacteristic
357C4C3×#406411yescharacteristic
358C3#1059905511yescharacteristic, direct product factor, Sylow
359C2—402no—
360C2C3×#6502311yescharacteristic
361C2C3×#6509911yescharacteristic
362C2C3×#6511411yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC3×Q8⋊C8D5
hypocenterC5C3×#1640
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65320C2semidirect
3. C3×#65140C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
7. C3×#64676C2semidirect
8. #10599055C3direct (N × H)
28. #65320C2×C3semidirect
29. #65140C2×C3semidirect
31. C5×Q8⋊C8C2×C3semidirect
33. #64676C2×C3semidirect
63. C3×Q8⋊C8D5semidirect
152. Q8⋊C8C3×D5semidirect
296. C3×C5#1640semidirect
343. C5C3×#1640semidirect
358. C3#10599055direct (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×#653202
C3×#651402
C3×#649832
C3×C5×Q8⋊C82
C3×#647052
C3×#646762
#105990553
C3×#16405