Finite Group Databasebeta

← C3×#10604410 #14285132

Subgroups — C3×#10604410 #14285132

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65882C211yesmaximal, characteristic
2C3×#65684C211yesmaximal, characteristic, complemented
3C3×#65678C211yesmaximal, characteristic, complemented
4C3×#64925C212yesmaximal, complemented
5C3×#64873C212yesmaximal, complemented
6#10604410C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#709—21no—
8C3×C4×C5×D4C411yescharacteristic
9C3×#4086C2211yescharacteristic
10C3×#4084C411yescharacteristic
11C3×C4×C22⋊D5—21no—
12C3×#4041C411yescharacteristic
13C3×#4034C2211yescharacteristic
14C3×#4031—21no—
15C3×#4030—21no—
16C3×C4×D20C411yescharacteristic
17C3×C42×D5C2211yescharacteristic
18C3×#4004C2212yes—
19C3×#4004C2212yes—
20C3×#4003—21no—
21C3×#4003—21no—
22C3×#4002—21no—
23C3×C4×#170—21no—
24C3×#1553—51nomaximal, Hall
25#65882C2×C311yescharacteristic
26#65684C2×C311yescharacteristic, complemented
27#65678C2×C311yescharacteristic, complemented
28#64925C2×C312yescomplemented
29#64873C2×C312yescomplemented
30C2×C3×C5×D4C2×C411yescharacteristic
31C22×C3×C4×C5—21no—
32C2×C3×C22⋊D5—21no—
33C2×C3×C22⋊D5—21no—
34C2×C3×C22⋊D5—21no—
35C3×#709—44no—
36C2×C3×D20—21no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5C2×C411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×Dic10—21no—
43C2×C3×#170—22no—
44C2×C3×#170—22no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2×C411yescharacteristic
48C3×C22⋊Dic5—21no—
49C3×#685—21no—
50C3×#685—21no—
51C3×C4⋊Dic5C2×C411yescharacteristic
52C3×#683—21no—
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5C2311yescharacteristic
56C3×#532—51no—
57C3×#432—51no—
58C3×#431—51no—
59C3×#332—52no—
60C3×#331—52no—
61C2×#709—21no—
62C4×C5×D4C3×C411yescharacteristic
63#4086C22×C311yescharacteristic
64#4084C3×C411yescharacteristic
65C4×C22⋊D5—21no—
66#4041C3×C411yescharacteristic
67#4034C22×C311yescharacteristic
68#4031—21no—
69#4030—21no—
70C4×D20C3×C411yescharacteristic
71C42×D5C22×C311yescharacteristic
72#4004C22×C312yes—
73#4004C22×C312yes—
74#4003—21no—
75#4003—21no—
76#4002—21no—
77C4×#170—21no—
78#1553—51noSylow
79C23×C3×C5—21no—
80C22×C3×D5—21no—
81C22×C3×D5C22⋊C411yescharacteristic
82C3×C5×D4—41no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—42no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C3×C22⋊D5—42no—
89C3×C22⋊D5—42no—
90C3×C22⋊D5—42no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C3×D20—41no—
96C3×D20—42no—
97C3×C4×D5—22no—
98C3×C4×D5—22no—
99C3×C4×D5—41no—
100C3×C4×D5—42no—
101C3×Dic10—42no—
102C3×#170—42no—
103C3×#170—42no—
104C2×C3×#41—101no—
105C3×C4⋊Q8—51no—
106C3×#127—51no—
107C3×#124—101no—
108C3×#121—51no—
109C3×#121—51no—
110C3×#121—101no—
111C3×C4×D4—51no—
112C3×C4×D4—101no—
113C3×C4×D4AGL(1,𝔽5)11yescharacteristic
114C2×C3×C42—51no—
115C3×C4⋊C8—52no—
116C3×C4⋊C8—52no—
117C3×C22⋊C8—101no—
118C3×C22⋊C8—101no—
119C3×#97—101no—
120C3×C4×C8—101no—
121C2×C5×D4C2×C3×C411yescharacteristic
122C22×C4×C5—21no—
123C2×C22⋊D5—21no—
124C2×C22⋊D5—21no—
125C2×C22⋊D5—21no—
126#709—44no—
127C2×D20—21no—
128C2×D20C2×C3×C411yescharacteristic
129C2×C4×D5—21no—
130C2×C4×D5C2×C3×C411yescharacteristic
131C2×C4×D5C3×D411yescharacteristic
132C2×C4×D5C3×D411yescharacteristic
133C2×Dic10—21no—
134C2×#170—22no—
135C2×#170—22no—
136C5×C4⋊C4C2×C3×C411yescharacteristic
137C5×C22⋊C4—21no—
138C42×C5C2×C3×C411yescharacteristic
139C22⋊Dic5—21no—
140#685—21no—
141#685—21no—
142C4⋊Dic5C2×C3×C411yescharacteristic
143#683—21no—
144C4×Dic5C3×D411yescharacteristic
145C4×Dic5C3×D411yescharacteristic
146C4×Dic5C23×C311yescharacteristic
147#532—51no—
148#432—51no—
149#431—51no—
150#332—52no—
151#331—52no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—41no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165C3×C4×C5—41no—
166C3×Dic5—21no—
167C3×Dic5—41no—
168C3×Dic5#13512yes—
169C3×Dic5AGL(1,ℤ/8)12yes—
170C3×#41—204no—
171C2×C3×Q8—101no—
172C2×C3×D4—51no—
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
178C22×C3×C4—21no—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C22×C3×C4—101no—
183C2×C3×C8—102no—
184C2×C3×C8—102no—
185C3×C4⋊C4—51no—
186C3×C4⋊C4—101no—
187C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
188C3×C22⋊C4—21no—
189C3×C22⋊C4—101no—
190C3×C22⋊C4—101no—
191C3×C22⋊C4—101no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—51no—
195C3×C42C2×AGL(1,𝔽5)11yescharacteristic
196C23×C5—21no—
197C22×D5—21no—
198C22×D5C3×C22⋊C411yescharacteristic
199C5×D4—41no—
200C2×C4×C5—21no—
201C2×C4×C5—42no—
202C2×C4×C5C3×C22⋊C411yescharacteristic
203C2×C4×C5C3×C22⋊C411yescharacteristic
204C2×C4×C5C22×C3×C411yescharacteristic
205C22⋊D5—42no—
206C22⋊D5—42no—
207C22⋊D5—42no—
208C2×Dic5—21no—
209C2×Dic5C3×C22⋊C411yescharacteristic
210C2×Dic5C2×C3×D411yescharacteristic
211C2×Dic5C2×C3×D411yescharacteristic
212D20—41no—
213D20—42no—
214C4×D5—22no—
215C4×D5—22no—
216C4×D5—41no—
217C4×D5—42no—
218Dic10—42no—
219#170—42no—
220#170—42no—
221C2×#41—101no—
222C4⋊Q8—51no—
223#127—51no—
224#124—101no—
225#121—51no—
226#121—51no—
227#121—101no—
228C4×D4—51no—
229C4×D4—101no—
230C4×D4C3×AGL(1,𝔽5)11yescharacteristic
231C2×C42—51no—
232C4⋊C8—52no—
233C4⋊C8—52no—
234C22⋊C8—101no—
235C22⋊C8—101no—
236#97—101no—
237C4×C8—101no—
238C2×C3×C5—81no—
239C2×C3×C5#41311yescharacteristic
240C2×C3×C5#41611yescharacteristic
241C2×C3×C5#41811yescharacteristic
242C3×D5—41no—
243C3×D5—81no—
244C23×C3—21no—
245C23×C3—51no—
246C23×C3—101no—
247C3×Q8—202no—
248C3×D4—41no—
249C3×D4—201no—
250C3×D4—202no—
251C3×D4—202no—
252C3×D4—202no—
253C3×D4—202no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—51no—
257C2×C3×C4—51no—
258C2×C3×C4—51no—
259C2×C3×C4—102no—
260C2×C3×C4—102no—
261C2×C3×C4—101no—
262C2×C3×C4—201no—
263C2×C3×C4—202no—
264C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
265C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
266C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
267C3×C8—202no—
268C3×C8—202no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—41no—
272C22×C5C2×C3×C22⋊C411yescharacteristic
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—21no—
276C2×D5—41no—
277C2×D5—41no—
278C2×D5—41no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—41no—
283Dic5—21no—
284Dic5—41no—
285Dic5C3×#13512yes—
286Dic5C3×AGL(1,ℤ/8)12yes—
287#41—204no—
288C2×Q8—101no—
289C2×D4—51no—
290C2×D4—101no—
291C2×D4—101no—
292C2×D4—101no—
293C2×D4—101no—
294C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
295C22×C4—21no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—101no—
300C2×C8—102no—
301C2×C8—102no—
302C4⋊C4—51no—
303C4⋊C4—101no—
304C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—101no—
307C22⋊C4—101no—
308C22⋊C4—101no—
309C42—51no—
310C42—51no—
311C42—51no—
312C42C2×C3×AGL(1,𝔽5)11yescharacteristic
313C3×C5#155311yescharacteristic, complemented, Hall
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—101no—
318C22×C3—101no—
319C22×C3—101no—
320C22×C3—201no—
321C22×C3—201no—
322C22×C3—201no—
323C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—52no—
329C3×C4—52no—
330C3×C4—101no—
331C3×C4—201no—
332C2×C5—81no—
333C2×C5C3×#41311yescharacteristic
334C2×C5C3×#41611yescharacteristic
335C2×C5C3×#41811yescharacteristic
336D5—41no—
337D5—81no—
338C23—21no—
339C23—51no—
340C23—101no—
341Q8—202no—
342D4—41no—
343D4—201no—
344D4—202no—
345D4—202no—
346D4—202no—
347D4—202no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—51no—
353C2×C4—102no—
354C2×C4—102no—
355C2×C4—101no—
356C2×C4—201no—
357C2×C4—202no—
358C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
359C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
360C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
361C8—202no—
362C8—202no—
363C2×C3—81no—
364C2×C3—201no—
365C2×C3—401no—
366C2×C3#6576111yescharacteristic
367C2×C3#6576711yescharacteristic
368C2×C3#6579411yescharacteristic
369C5C3×#155311yescharacteristic, complemented, Sylow
370C22—41no—
371C22—41no—
372C22—41no—
373C22—101no—
374C22—101no—
375C22—101no—
376C22—201no—
377C22—201no—
378C22—201no—
379C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—52no—
385C4—52no—
386C4—101no—
387C4—201no—
388C3#1060441011yescharacteristic, direct product factor, Sylow
389C2—81no—
390C2—201no—
391C2—401no—
392C2C3×#6576111yescharacteristic
393C2C3×#6576711yescharacteristic
394C2C3×#6579411yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65882C2
cosocleC4×Dic5C23×C3
hypercenterC3×C4×D4AGL(1,𝔽5)
hypocenterC5C3×#1553
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65684C2semidirect
3. C3×#65678C2semidirect
4. C3×#64925C2semidirect
5. C3×#64873C2semidirect
6. #10604410C3direct (N × H)
26. #65684C2×C3semidirect
27. #65678C2×C3semidirect
28. #64925C2×C3semidirect
29. #64873C2×C3semidirect
313. C3×C5#1553semidirect
369. C5C3×#1553semidirect
388. C3#10604410direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658822
C3×#656842
C3×#656782
C3×#649252
C3×#648732
#106044103
C3×#15535