Finite Group Databasebeta

← C3×#10599536 #14303596

Subgroups — C3×#10599536 #14303596

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65408C211yesmaximal, characteristic
2C3×#65287C211yesmaximal, characteristic
3C3×#65286C211yesmaximal, characteristic
4C3×C5×#339C211yesmaximal, characteristic
5C3×#64778C211yesmaximal, characteristic
6C3×#64744C211yesmaximal, characteristic
7C3×#64743C211yesmaximal, characteristic
8#10599536C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×M16C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C3×#4072C2211yescharacteristic
13C2×C3×#681C2211yescharacteristic
14C22×C3×#168C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C3×#3946—21no—
17C3×#3946—21no—
18C3×#3940C411yescharacteristic, complemented
19C3×#3940C411yescharacteristic, complemented
20C3×#3939C411yescharacteristic, complemented
21C3×#3939C411yescharacteristic, complemented
22C3×#3935—21no—
23C3×C4×#168—21no—
24C3×#1922—51nomaximal, Hall
25#65408C2×C311yescharacteristic
26#65287C2×C311yescharacteristic
27#65286C2×C311yescharacteristic
28C5×#339C2×C311yescharacteristic
29#64778C2×C311yescharacteristic
30#64744C2×C311yescharacteristic
31#64743C2×C311yescharacteristic
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C3×C5×M16—21no—
35C3×C5×M16—21no—
36C2×C3×C5×C8—21no—
37C3×C5×C4⋊C4C2×C411yescharacteristic
38C3×C5×C4⋊C4C2×C411yescharacteristic
39C3×C5×C22⋊C4—21no—
40C3×C42×C5—21no—
41C3×C42×C5—21no—
42C3×C42×C5—21no—
43C3×C22⋊Dic5—21no—
44C3×C4⋊Dic5C2×C411yescharacteristic
45C3×C4⋊Dic5C2×C411yescharacteristic
46C3×C4×Dic5—21no—
47C3×#681—21no—
48C3×#681Q812yes—
49C2×C3×#168—21no—
50C2×C3×#168—21no—
51C2×C3×#168—21no—
52C2×C3×#168—21no—
53C2×C3×#168—21no—
54C2×C3×#168C2×C411yescharacteristic
55C2×C3×#168C2×C411yescharacteristic
56C2×C3×#168D411yescharacteristic
57C2×C3×#168D411yescharacteristic
58C3×#427—51no—
59C3×#424—51no—
60C3×#405—51no—
61C3×#341—51no—
62C3×#339—51no—
63C3×#339D511yescharacteristic
64C3×#336—51no—
65C2×C5×M16C22×C311yescharacteristic
66C5×#117C22×C311yescharacteristic
67C2×C42×C5C22×C311yescharacteristic
68#4072C22×C311yescharacteristic
69C2×#681C22×C311yescharacteristic
70C22×#168C22×C311yescharacteristic
71C22×#168C22×C311yescharacteristic
72#3946—21no—
73#3946—21no—
74#3940C3×C411yescharacteristic, complemented
75#3940C3×C411yescharacteristic, complemented
76#3939C3×C411yescharacteristic, complemented
77#3939C3×C411yescharacteristic, complemented
78#3935—21no—
79C4×#168—21no—
80#1922—51noSylow
81C23×C3×C5#4111yescharacteristic
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×Q811yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×C5×C8—41no—
96C3×#168—21no—
97C3×#168—21no—
98C3×#168—22no—
99C3×#168—21no—
100C3×#168—21no—
101C2×C3×M16—51no—
102C2×C3×M16C2×D511yescharacteristic
103C22×C3×C8—51no—
104C22×C3×C8—51no—
105C3×#117—51no—
106C3×#117C2×D511yescharacteristic
107C2×C3×C42C2×D511yescharacteristic
108C3×#107—51no—
109C3×#107—51no—
110C3×#106—51no—
111C3×#106—51no—
112C3×C4⋊C8—101no—
113C3×C4⋊C8—101no—
114C3×#97—101no—
115C3×C4×C8—101no—
116C22×C4×C5—21no—
117C22×C4×C5C23×C311yescharacteristic
118C5×M16—21no—
119C5×M16—21no—
120C2×C5×C8—21no—
121C5×C4⋊C4C2×C3×C411yescharacteristic
122C5×C4⋊C4C2×C3×C411yescharacteristic
123C5×C22⋊C4—21no—
124C42×C5—21no—
125C42×C5—21no—
126C42×C5—21no—
127C22⋊Dic5—21no—
128C4⋊Dic5C2×C3×C411yescharacteristic
129C4⋊Dic5C2×C3×C411yescharacteristic
130C4×Dic5—21no—
131#681—21no—
132#681C3×Q812yes—
133C2×#168—21no—
134C2×#168—21no—
135C2×#168—21no—
136C2×#168—21no—
137C2×#168—21no—
138C2×#168C2×C3×C411yescharacteristic
139C2×#168C2×C3×C411yescharacteristic
140C2×#168C3×D411yescharacteristic
141C2×#168C3×D411yescharacteristic
142#427—51no—
143#424—51no—
144#405—51no—
145#341—51no—
146#339—51no—
147#339C3×D511yescharacteristic
148#336—51no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C4×D411yescharacteristic
152C22×C3×C5#12511yescharacteristic
153C22×C3×C5#12611yescharacteristic
154C3×C4×C5—42no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5#11711yescharacteristic
158C3×C4×C5C4×Q811yescharacteristic
159C3×C4×C5C22⋊Q811yescharacteristic
160C3×C4×C5#12311yescharacteristic
161C3×Dic5—41no—
162C3×Dic5—41no—
163C22×C3×C4—21no—
164C22×C3×C4C22×D511yescharacteristic
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—52no—
168C3×M16—101no—
169C2×C3×C8—21no—
170C2×C3×C8—51no—
171C2×C3×C8—51no—
172C2×C3×C8—51no—
173C2×C3×C8—51no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4C4×D511yescharacteristic
182C3×C4⋊C4C4×D511yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—101no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—101no—
189C23×C5C3×#4111yescharacteristic
190C2×C4×C5—22no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5C22×C3×C411yescharacteristic
196C2×C4×C5C2×C3×D411yescharacteristic
197C2×C4×C5C2×C3×Q811yescharacteristic
198C2×C4×C5C3×#4111yescharacteristic
199C2×C4×C5C3×#4111yescharacteristic
200C2×C4×C5C3×#4111yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203C5×C8—41no—
204#168—21no—
205#168—21no—
206#168—22no—
207#168—21no—
208#168—21no—
209C2×M16—51no—
210C2×M16C2×C3×D511yescharacteristic
211C22×C8—51no—
212C22×C8—51no—
213#117—51no—
214#117C2×C3×D511yescharacteristic
215C2×C42C2×C3×D511yescharacteristic
216#107—51no—
217#107—51no—
218#106—51no—
219#106—51no—
220C4⋊C8—101no—
221C4⋊C8—101no—
222#97—101no—
223C4×C8—101no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5#38711yescharacteristic
227C2×C3×C5#44311yescharacteristic
228C2×C3×C5#44411yescharacteristic
229C23×C3#71111yescharacteristic
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4C2×C4×D511yescharacteristic
238C2×C3×C4#70911yescharacteristic
239C2×C3×C4#70911yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4#71111yescharacteristic
242C2×C3×C4Q8×D511yescharacteristic
243C3×C8—41no—
244C3×C8—101no—
245C3×C8—101no—
246C3×C8—101no—
247C3×C8—101no—
248C3×C8—102no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5C3×C4×D411yescharacteristic
252C22×C5C3×#12511yescharacteristic
253C22×C5C3×#12611yescharacteristic
254C4×C5—42no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5C3×#11711yescharacteristic
258C4×C5C3×C4×Q811yescharacteristic
259C4×C5C3×C22⋊Q811yescharacteristic
260C4×C5C3×#12311yescharacteristic
261Dic5—41no—
262Dic5—41no—
263C22×C4—21no—
264C22×C4C22×C3×D511yescharacteristic
265M16—21no—
266M16—21no—
267M16—52no—
268M16—101no—
269C2×C8—21no—
270C2×C8—51no—
271C2×C8—51no—
272C2×C8—51no—
273C2×C8—51no—
274C2×C8—101no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8—101no—
278C2×C8—101no—
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4C3×C4×D511yescharacteristic
282C4⋊C4C3×C4×D511yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—101no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—101no—
289C3×C5#192211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3#402511yescharacteristic
293C22×C3#402711yescharacteristic
294C22×C3#403511yescharacteristic
295C3×C4—42no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—201no—
299C3×C4—201no—
300C3×C4#401811yescharacteristic
301C3×C4#402911yescharacteristic
302C3×C4#403311yescharacteristic
303C3×C4#404211yescharacteristic
304C2×C5—21no—
305C2×C5—21no—
306C2×C5C3×#38711yescharacteristic
307C2×C5C3×#44311yescharacteristic
308C2×C5C3×#44411yescharacteristic
309C23C3×#71111yescharacteristic
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4C2×C3×C4×D511yescharacteristic
318C2×C4C3×#70911yescharacteristic
319C2×C4C3×#70911yescharacteristic
320C2×C4C3×D4×D511yescharacteristic
321C2×C4C3×#71111yescharacteristic
322C2×C4C3×Q8×D511yescharacteristic
323C8—41no—
324C8—101no—
325C8—101no—
326C8—101no—
327C8—101no—
328C8—102no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3#6494111yescharacteristic
332C2×C3#6511211yescharacteristic
333C2×C3#6511311yescharacteristic
334C5C3×#192211yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22C3×#402511yescharacteristic
338C22C3×#402711yescharacteristic
339C22C3×#403511yescharacteristic
340C4—42no—
341C4—41no—
342C4—41no—
343C4—201no—
344C4—201no—
345C4C3×#401811yescharacteristic
346C4C3×#402911yescharacteristic
347C4C3×#403311yescharacteristic
348C4C3×#404211yescharacteristic
349C3#1059953611yescharacteristic, direct product factor, Sylow
350C2—21no—
351C2—21no—
352C2C3×#6494111yescharacteristic
353C2C3×#6511211yescharacteristic
354C2C3×#6511311yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C4×C5C23×C3
hypercenterC3×#339D5
hypocenterC5C3×#1922
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
8. #10599536C3direct (N × H)
18. C3×#3940C4semidirect
19. C3×#3940C4semidirect
20. C3×#3939C4semidirect
21. C3×#3939C4semidirect
74. #3940C3×C4semidirect
75. #3940C3×C4semidirect
76. #3939C3×C4semidirect
77. #3939C3×C4semidirect
289. C3×C5#1922semidirect
334. C5C3×#1922semidirect
349. C3#10599536direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#654082
C3×#652872
C3×#652862
C3×C5×#3392
C3×#647782
C3×#647442
C3×#647432
#105995363
C3×#19225