Finite Group Databasebeta

← C3×#10601187 #14309019

Subgroups — C3×#10601187 #14309019

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65851C211yesmaximal, characteristic, complemented
2C3×C5×#421C211yesmaximal, characteristic
3C3×#65529C211yesmaximal, characteristic
4C2×C3×#3969C211yesmaximal, characteristic
5C3×#64776C211yesmaximal, characteristic, complemented
6C3×#64775C211yesmaximal, characteristic, complemented
7C3×#64751C211yesmaximal, characteristic, complemented
8#10601187C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C3×#4072C2211yescharacteristic
13C3×#4072C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×#4036—21no—
17C3×#4034—21no—
18C3×#4024—22no—
19C3×C4×Dic10—22no—
20C3×C5×#104—22no—
21C3×#3969—21no—
22C3×#3969—21no—
23C3×#3966—22no—
24C3×#2031—51nomaximal, Hall
25#65851C2×C311yescharacteristic, complemented
26C5×#421C2×C311yescharacteristic
27#65529C2×C311yescharacteristic
28C2×#3969C2×C311yescharacteristic
29#64776C2×C311yescharacteristic, complemented
30#64775C2×C311yescharacteristic, complemented
31#64751C2×C311yescharacteristic, complemented
32C3×C5×#41—21no—
33C3×C5×#41—21no—
34C3×C5×#41—21no—
35C3×C5×#41—21no—
36C2×C3×C5×Q8Q811yescharacteristic, complemented
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4Q811yescharacteristic, complemented
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5C2311yescharacteristic
41C22×C3×Dic5—21no—
42C2×C3×Dic10—22no—
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5D412yes—
49C3×C22⋊Dic5—21no—
50C3×C22⋊Dic5D412yes—
51C3×C4⋊Dic5—22no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×#683—22no—
55C3×#683—22no—
56C3×C4×Dic5—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5D411yescharacteristic
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64C3×#533—51no—
65C3×#421D511yescharacteristic
66C2×C3×#104—51no—
67C3×#410—51no—
68C3×#344—51no—
69C3×#339—51no—
70C3×H(3,ℤ/4)—51no—
71C2×C5×#41C22×C311yescharacteristic
72C2×C5×M16C22×C311yescharacteristic
73C5×#117C22×C311yescharacteristic
74#4072C22×C311yescharacteristic
75#4072C22×C311yescharacteristic
76C2×C4×Dic5C22×C311yescharacteristic
77C2×#681C22×C311yescharacteristic
78#4036—21no—
79#4034—21no—
80#4024—22no—
81C4×Dic10—22no—
82C5×#104—22no—
83#3969—21no—
84#3969—21no—
85#3966—22no—
86#2031—51noSylow
87C23×C3×C5—21no—
88C23×C3×C5C2×D411yescharacteristic
89C3×C5×Q8—21no—
90C3×C5×Q8—21no—
91C3×C5×D4—21no—
92C3×C5×D4—21no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—42no—
109C2×C3×Dic5—41no—
110C3×Dic10—44no—
111C3×C5×C8—41no—
112C3×#168—41no—
113C2×C3×#41C2×D511yescharacteristic
114C2×C3×M16—51no—
115C2×C3×M16C2×D511yescharacteristic
116C3×C4⋊Q8—101no—
117C3×#125—101no—
118C3×C22⋊Q8—102no—
119C3×C4×Q8—102no—
120C3×#117—51no—
121C3×#117—51no—
122C3×#117C2×D511yescharacteristic
123C2×C3×C42—51no—
124C3×#104—22no—
125C3×#104—101no—
126C3×#104—101no—
127C3×#99—102no—
128C5×#41—21no—
129C5×#41—21no—
130C5×#41—21no—
131C5×#41—21no—
132C2×C5×Q8C3×Q811yescharacteristic, complemented
133C2×C5×D4—21no—
134C2×C5×D4C3×Q811yescharacteristic, complemented
135C22×C4×C5—21no—
136C22×C4×C5C23×C311yescharacteristic
137C22×Dic5—21no—
138C2×Dic10—22no—
139C5×M16—21no—
140C5×M16—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5C3×D412yes—
145C22⋊Dic5—21no—
146C22⋊Dic5C3×D412yes—
147C4⋊Dic5—22no—
148C4⋊Dic5—21no—
149C4⋊Dic5—21no—
150#683—22no—
151#683—22no—
152C4×Dic5—21no—
153C4×Dic5—21no—
154C4×Dic5—21no—
155C4×Dic5C3×D411yescharacteristic
156C4×Dic5C3×D411yescharacteristic
157#681—21no—
158#681—21no—
159C2×#168—21no—
160#533—51no—
161#421C3×D511yescharacteristic
162C2×#104—51no—
163#410—51no—
164#344—51no—
165#339—51no—
166H(3,ℤ/4)—51no—
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—81no—
170C22×C3×C5#12011yescharacteristic
171C22×C3×C5C22⋊Q811yescharacteristic
172C22×C3×C5#12411yescharacteristic
173C3×C4×C5—42no—
174C3×C4×C5—41no—
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5C22⋊Q811yescharacteristic
177C3×C4×C5#12411yescharacteristic
178C3×C4×C5#12411yescharacteristic
179C3×Dic5—22no—
180C3×Dic5—42no—
181C3×Dic5—41no—
182C3×Dic5—81no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—21no—
187C2×C3×Q8—102no—
188C2×C3×Q8Dic1011yescharacteristic, complemented
189C2×C3×D4—21no—
190C2×C3×D4Dic1011yescharacteristic, complemented
191C22×C3×C4—21no—
192C22×C3×C4—101no—
193C22×C3×C4C22×D511yescharacteristic
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—101no—
197C3×M16—101no—
198C2×C3×C8—21no—
199C2×C3×C8—101no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—102no—
202C3×C4⋊C4—102no—
203C3×C4⋊C4—102no—
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—52no—
208C3×C22⋊C4—101no—
209C3×C42—51no—
210C3×C42—51no—
211C3×C42—101no—
212C3×C42—101no—
213C3×C42—101no—
214C3×C42C22⋊D512yes—
215C23×C5—21no—
216C23×C5C2×C3×D411yescharacteristic
217C5×Q8—21no—
218C5×Q8—21no—
219C5×D4—21no—
220C5×D4—21no—
221C5×D4—41no—
222C5×D4—41no—
223C2×C4×C5—22no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5C2×C3×D411yescharacteristic
228C2×C4×C5C2×C3×D411yescharacteristic
229C2×C4×C5C2×C3×Q811yescharacteristic
230C2×C4×C5C3×#4111yescharacteristic
231C2×C4×C5C3×#4111yescharacteristic
232C2×C4×C5C3×#4111yescharacteristic
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—22no—
236C2×Dic5—42no—
237C2×Dic5—41no—
238Dic10—44no—
239C5×C8—41no—
240#168—41no—
241C2×#41C2×C3×D511yescharacteristic
242C2×M16—51no—
243C2×M16C2×C3×D511yescharacteristic
244C4⋊Q8—101no—
245#125—101no—
246C22⋊Q8—102no—
247C4×Q8—102no—
248#117—51no—
249#117—51no—
250#117C2×C3×D511yescharacteristic
251C2×C42—51no—
252#104—22no—
253#104—101no—
254#104—101no—
255#99—102no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5—81no—
260C2×C3×C5#39311yescharacteristic
261C23×C3—21no—
262C23×C3D4×D511yescharacteristic
263C3×Q8—21no—
264C3×Q8—21no—
265C3×Q8—204no—
266C3×D4—21no—
267C3×D4—21no—
268C3×D4—41no—
269C3×D4—41no—
270C2×C3×C4—21no—
271C2×C3×C4—22no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—101no—
275C2×C3×C4—101no—
276C2×C3×C4—102no—
277C2×C3×C4—202no—
278C2×C3×C4—201no—
279C2×C3×C4C2×Dic1011yescharacteristic
280C2×C3×C4#70911yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4#71111yescharacteristic
283C2×C3×C4#71111yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285C3×C8—41no—
286C3×C8—201no—
287C22×C5—41no—
288C22×C5—41no—
289C22×C5—81no—
290C22×C5C3×#12011yescharacteristic
291C22×C5C3×C22⋊Q811yescharacteristic
292C22×C5C3×#12411yescharacteristic
293C4×C5—42no—
294C4×C5—41no—
295C4×C5C3×C22⋊Q811yescharacteristic
296C4×C5C3×C22⋊Q811yescharacteristic
297C4×C5C3×#12411yescharacteristic
298C4×C5C3×#12411yescharacteristic
299Dic5—22no—
300Dic5—42no—
301Dic5—41no—
302Dic5—81no—
303#41—21no—
304#41—21no—
305#41—21no—
306#41—21no—
307C2×Q8—102no—
308C2×Q8C3×Dic1011yescharacteristic, complemented
309C2×D4—21no—
310C2×D4C3×Dic1011yescharacteristic, complemented
311C22×C4—21no—
312C22×C4—101no—
313C22×C4C22×C3×D511yescharacteristic
314M16—21no—
315M16—21no—
316M16—101no—
317M16—101no—
318C2×C8—21no—
319C2×C8—101no—
320C4⋊C4—21no—
321C4⋊C4—102no—
322C4⋊C4—102no—
323C4⋊C4—102no—
324C4⋊C4—101no—
325C4⋊C4—101no—
326C22⋊C4—21no—
327C22⋊C4—52no—
328C22⋊C4—101no—
329C42—51no—
330C42—51no—
331C42—101no—
332C42—101no—
333C42—101no—
334C42C3×C22⋊D512yes—
335C3×C5#203111yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—81no—
339C22×C3#402411yescharacteristic
340C22×C3#403111yescharacteristic
341C22×C3#408311yescharacteristic
342C3×C4—42no—
343C3×C4—41no—
344C3×C4—102no—
345C3×C4—201no—
346C3×C4—202no—
347C3×C4—401no—
348C3×C4#402411yescharacteristic
349C3×C4#403111yescharacteristic
350C3×C4#407011yescharacteristic
351C3×C4#408211yescharacteristic
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5—81no—
356C2×C5C3×#39311yescharacteristic
357C23—21no—
358C23C3×D4×D511yescharacteristic
359Q8—21no—
360Q8—21no—
361Q8—204no—
362D4—21no—
363D4—21no—
364D4—41no—
365D4—41no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—102no—
373C2×C4—202no—
374C2×C4—201no—
375C2×C4C2×C3×Dic1011yescharacteristic
376C2×C4C3×#70911yescharacteristic
377C2×C4C3×D4×D511yescharacteristic
378C2×C4C3×#71111yescharacteristic
379C2×C4C3×#71111yescharacteristic
380C2×C4C2×C3×C22⋊D511yescharacteristic
381C8—41no—
382C8—201no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—81no—
387C2×C3#6523611yescharacteristic
388C5C3×#203111yescharacteristic, complemented, Sylow
389C22—41no—
390C22—41no—
391C22—81no—
392C22C3×#402411yescharacteristic
393C22C3×#403111yescharacteristic
394C22C3×#408311yescharacteristic
395C4—42no—
396C4—41no—
397C4—102no—
398C4—201no—
399C4—202no—
400C4—401no—
401C4C3×#402411yescharacteristic
402C4C3×#403111yescharacteristic
403C4C3×#407011yescharacteristic
404C4C3×#408211yescharacteristic
405C3#1060118711yescharacteristic, direct product factor, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—81no—
410C2C3×#6523611yescharacteristic
subgroupG/H
centerC3×C4#4082
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5#393
prime radicalC2×C3×C5×#41C22
hypercenterC3×#421D5
hypocenterC5C3×#2031
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
1. C3×#65851C2semidirect
5. C3×#64776C2semidirect
6. C3×#64775C2semidirect
7. C3×#64751C2semidirect
8. #10601187C3direct (N × H)
25. #65851C2×C3semidirect
29. #64776C2×C3semidirect
30. #64775C2×C3semidirect
31. #64751C2×C3semidirect
36. C2×C3×C5×Q8Q8semidirect
38. C2×C3×C5×D4Q8semidirect
132. C2×C5×Q8C3×Q8semidirect
134. C2×C5×D4C3×Q8semidirect
188. C2×C3×Q8Dic10semidirect
190. C2×C3×D4Dic10semidirect
308. C2×Q8C3×Dic10semidirect
310. C2×D4C3×Dic10semidirect
335. C3×C5#2031semidirect
388. C5C3×#2031semidirect
405. C3#10601187direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658512
C3×C5×#4212
C3×#655292
C2×C3×#39692
C3×#647762
C3×#647752
C3×#647512
#106011873
C3×#20315