Finite Group Databasebeta

← C3×#10599192 #14292478

Subgroups — C3×#10599192 #14292478

Order 1920.

396 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65362C211yesmaximal, characteristic, complemented
2C3×#65361C211yesmaximal, characteristic, complemented
3C3×#65132C211yesmaximal, characteristic, complemented
4C3×#65127C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7C3×#64700C211yesmaximal, characteristic, complemented
8#10599192C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#127C2211yescharacteristic
10C2×C3×#686—21no—
11C2×C3×#686—21no—
12C2×C3×#686—21no—
13C2×C3×D40—21no—
14C2×C3×#676—21no—
15C3×#4020C2211yescharacteristic
16C3×C4×D20C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×#3964—21no—
20C3×#3953—21no—
21C3×#3952—21no—
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1687—51nomaximal, Hall
25#65362C2×C311yescharacteristic, complemented
26#65361C2×C311yescharacteristic, complemented
27#65132C2×C311yescharacteristic, complemented
28#65127C2×C311yescharacteristic, complemented
29C5×#331C2×C311yescharacteristic, complemented
30#64705C2×C311yescharacteristic, complemented
31#64700C2×C311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C3×#686—42no—
44C3×#686—42no—
45C3×#686—42no—
46C3×#685—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C2×C3×#168—21no—
49C2×C3×#168D411yescharacteristic
50C2×C3×#168D411yescharacteristic
51C3×D40—42no—
52C3×#676—42no—
53C3×#493—51no—
54C3×#459—51no—
55C3×#459—51no—
56C3×#436—51no—
57C3×#334—51no—
58C3×#331—51no—
59C3×#331D511yescharacteristic, complemented
60C5×#127C22×C311yescharacteristic
61C2×#686—21no—
62C2×#686—21no—
63C2×#686—21no—
64C2×D40—21no—
65C2×#676—21no—
66#4020C22×C311yescharacteristic
67C4×D20C22×C311yescharacteristic
68C5×C4⋊C8C22×C311yescharacteristic
69C5×C4⋊C8C22×C311yescharacteristic
70#3964—21no—
71#3953—21no—
72#3952—21no—
73C4⋊#168C22×C311yescharacteristic
74C4×#168C22×C311yescharacteristic
75#1687—51noSylow
76C23×C3×C5—41no—
77C22×C3×D5—21no—
78C22×C3×D5—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×C3×Dic5—21no—
88C3×D20—21no—
89C3×D20—21no—
90C3×D20—41no—
91C3×D20—41no—
92C3×D20—41no—
93C3×D20—41no—
94C3×D20—81no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×C5×C8—41no—
98C3×C5×C8—41no—
99C3×#168—21no—
100C3×#168—41no—
101C3×#168D812yescomplemented
102C2×C3×D8—101no—
103C2×C3×D8—101no—
104C2×C3×D8—101no—
105C2×C3×D8—101no—
106C2×C3×M16—101no—
107C3×#127—51no—
108C3×#127C2×D511yescharacteristic
109C3×C4×D4—51no—
110C3×C4⋊C8—51no—
111C3×C4⋊C8C2×D511yescharacteristic
112C3×C4⋊C8C2×D511yescharacteristic
113C3×#102—101no—
114C3×#102—101no—
115C3×C22⋊C8—101no—
116C3×C4×C8—51no—
117C2×C5×D4—21no—
118C2×C5×D4—21no—
119C2×C5×D4—21no—
120C2×D20—21no—
121C2×D20—21no—
122C2×D20—21no—
123C2×D20C3×D411yescharacteristic
124C2×C4×D5—21no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C42×C5C23×C311yescharacteristic
128#686—42no—
129#686—42no—
130#686—42no—
131#685—21no—
132C4⋊Dic5C3×D411yescharacteristic
133C2×#168—21no—
134C2×#168C3×D411yescharacteristic
135C2×#168C3×D411yescharacteristic
136D40—42no—
137#676—42no—
138#493—51no—
139#459—51no—
140#459—51no—
141#436—51no—
142#334—51no—
143#331—51no—
144#331C3×D511yescharacteristic, complemented
145C22×C3×C5—81no—
146C22×C3×C5—81no—
147C22×C3×C5—81no—
148C22×C3×C5#12111yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C2×C3×D5—81no—
153C2×C3×D5—81no—
154C2×C3×D5—81no—
155C3×C4×C5—21no—
156C3×C4×C5C2×D811yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×Dic5—41no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—51no—
165C2×C3×D4—101no—
166C2×C3×D4—101no—
167C2×C3×D4—101no—
168C22×C3×C4—101no—
169C3×D8—202no—
170C3×D8—202no—
171C3×D8—202no—
172C3×D8—202no—
173C3×M16—202no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—51no—
177C2×C3×C8—51no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C22⋊C4—101no—
181C3×C42C22×D511yescharacteristic
182C23×C5—41no—
183C22×D5—21no—
184C22×D5—41no—
185C5×D4—41no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—41no—
189C5×D4—81no—
190C2×C4×C5C2×C3×D411yescharacteristic
191C2×C4×C5C2×C3×D411yescharacteristic
192C2×C4×C5C3×#4111yescharacteristic
193C2×Dic5—21no—
194D20—21no—
195D20—21no—
196D20—41no—
197D20—41no—
198D20—41no—
199D20—41no—
200D20—81no—
201C4×D5—41no—
202C4×D5—41no—
203C5×C8—41no—
204C5×C8—41no—
205#168—21no—
206#168—41no—
207#168C3×D812yescomplemented
208C2×D8—101no—
209C2×D8—101no—
210C2×D8—101no—
211C2×D8—101no—
212C2×M16—101no—
213#127—51no—
214#127C2×C3×D511yescharacteristic
215C4×D4—51no—
216C4⋊C8—51no—
217C4⋊C8C2×C3×D511yescharacteristic
218C4⋊C8C2×C3×D511yescharacteristic
219#102—101no—
220#102—101no—
221C22⋊C8—101no—
222C4×C8—51no—
223C2×C3×C5—161no—
224C2×C3×C5#45911yescharacteristic
225C2×C3×C5#46911yescharacteristic
226C2×C3×C5#47211yescharacteristic
227C3×D5—81no—
228C3×D5—161no—
229C23×C3—41no—
230C23×C3—101no—
231C23×C3—201no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—81no—
237C3×D4—101no—
238C3×D4—101no—
239C3×D4—201no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—401no—
244C2×C3×C4—101no—
245C2×C3×C4—201no—
246C2×C3×C4—201no—
247C2×C3×C4#70911yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C3×C8—41no—
251C3×C8—41no—
252C3×C8—52no—
253C3×C8—101no—
254C3×C8—201no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5C3×#12111yescharacteristic
259C2×D5—41no—
260C2×D5—41no—
261C2×D5—41no—
262C2×D5—81no—
263C2×D5—81no—
264C2×D5—81no—
265C4×C5—21no—
266C4×C5C2×C3×D811yescharacteristic
267C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
268C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
269C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
270Dic5—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—51no—
275C2×D4—101no—
276C2×D4—101no—
277C2×D4—101no—
278C22×C4—101no—
279D8—202no—
280D8—202no—
281D8—202no—
282D8—202no—
283M16—202no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—51no—
287C2×C8—51no—
288C2×C8—101no—
289C4⋊C4—51no—
290C22⋊C4—101no—
291C42C22×C3×D511yescharacteristic
292C3×C5#168711yescharacteristic, complemented, Hall
293C22×C3—81no—
294C22×C3—81no—
295C22×C3—81no—
296C22×C3—201no—
297C22×C3—201no—
298C22×C3—201no—
299C22×C3—401no—
300C22×C3—401no—
301C22×C3—401no—
302C22×C3#403011yescharacteristic
303C3×C4—21no—
304C3×C4—201no—
305C3×C4D5×D811yescharacteristic
306C3×C4#405711yescharacteristic
307C3×C4#406011yescharacteristic
308C3×C4#406011yescharacteristic
309C2×C5—161no—
310C2×C5C3×#45911yescharacteristic
311C2×C5C3×#46911yescharacteristic
312C2×C5C3×#47211yescharacteristic
313D5—81no—
314D5—161no—
315C23—41no—
316C23—101no—
317C23—201no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—101no—
324D4—101no—
325D4—201no—
326D4—201no—
327D4—201no—
328D4—201no—
329D4—401no—
330C2×C4—101no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4C3×#70911yescharacteristic
334C2×C4C3×D4×D511yescharacteristic
335C2×C4C3×D4×D511yescharacteristic
336C8—41no—
337C8—41no—
338C8—52no—
339C8—101no—
340C8—201no—
341C2×C3—161no—
342C2×C3—401no—
343C2×C3—801no—
344C2×C3#6503811yescharacteristic
345C2×C3#6507111yescharacteristic
346C2×C3#6507511yescharacteristic
347C5C3×#168711yescharacteristic, complemented, Sylow
348C22—81no—
349C22—81no—
350C22—81no—
351C22—201no—
352C22—201no—
353C22—201no—
354C22—401no—
355C22—401no—
356C22—401no—
357C22C3×#403011yescharacteristic
358C4—21no—
359C4—201no—
360C4C3×D5×D811yescharacteristic
361C4C3×#405711yescharacteristic
362C4C3×#406011yescharacteristic
363C4C3×#406011yescharacteristic
364C3#1059919211yescharacteristic, direct product factor, Sylow
365C2—161no—
366C2—401no—
367C2—801no—
368C2C3×#6503811yescharacteristic
369C2C3×#6507111yescharacteristic
370C2C3×#6507511yescharacteristic
subgroupG/H
centerC22×C3#4030
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#331C2
socleC22×C3×C5#121
hypercenterC3×#331D5
hypocenterC5C3×#1687
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
1. C3×#65362C2semidirect
2. C3×#65361C2semidirect
3. C3×#65132C2semidirect
4. C3×#65127C2semidirect
5. C3×C5×#331C2semidirect
6. C3×#64705C2semidirect
7. C3×#64700C2semidirect
8. #10599192C3direct (N × H)
25. #65362C2×C3semidirect
26. #65361C2×C3semidirect
27. #65132C2×C3semidirect
28. #65127C2×C3semidirect
29. C5×#331C2×C3semidirect
30. #64705C2×C3semidirect
31. #64700C2×C3semidirect
59. C3×#331D5semidirect
101. C3×#168D8semidirect
144. #331C3×D5semidirect
207. #168C3×D8semidirect
292. C3×C5#1687semidirect
347. C5C3×#1687semidirect
364. C3#10599192direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653622
C3×#653612
C3×#651322
C3×#651272
C3×C5×#3312
C3×#647052
C3×#647002
#105991923
C3×#16875