Finite Group Databasebeta

← C3×#10600849 #14313132

Subgroups — C3×#10600849 #14313132

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66162C211yesmaximal, characteristic
2C3×C5×#410C211yesmaximal, characteristic, complemented
3C3×#65526C211yesmaximal, characteristic, complemented
4C3×#64692C212yesmaximal, complemented
5C3×#64691C212yesmaximal, complemented
6#10600849C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×C3×C4×D5C411yescharacteristic, complemented
9C3×C5×#117—21no—
10C3×#4092—21no—
11C3×#4084—21no—
12C3×#4083C411yescharacteristic, complemented
13C3×#4083C2211yescharacteristic
14C3×#4081C411yescharacteristic, complemented
15C3×#4081C2211yescharacteristic
16C3×C4×C22⋊D5—21no—
17C3×C4×C22⋊D5—21no—
18C3×#4072C411yescharacteristic, complemented
19C2×C3×#681—21no—
20C3×C5×#99—21no—
21C3×C5×#99C2212yes—
22C3×#3968—21no—
23C3×#3965C2212yes—
24C3×#2120—51nomaximal, Hall
25#66162C2×C311yescharacteristic
26C5×#410C2×C311yescharacteristic, complemented
27#65526C2×C311yescharacteristic, complemented
28#64692C2×C312yescomplemented
29#64691C2×C312yescomplemented
30C23×C3×D5C2×C411yescharacteristic
31C3×C5×#41—41no—
32C3×C5×#41—41no—
33C2×C3×C5×Q8D411yescharacteristic
34C2×C3×C5×D4C2×C411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—41no—
46C2×C3×C4×D5—41no—
47C3×C5×C4⋊C4—41no—
48C3×C5×C22⋊C4—22no—
49C3×C42×C5—41no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5C2×C411yescharacteristic
53C3×C22⋊Dic5C2×C411yescharacteristic
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×C4×Dic5—21no—
60C3×#681—22no—
61C3×#681—41no—
62C2×C3×#168—41no—
63C3×#525—51no—
64C3×#413—51no—
65C3×#410D511yescharacteristic, complemented
66C3×#352—52no—
67C3×AΣL(1,𝔽16)—52no—
68C2×C5×#41C22×C311yescharacteristic
69C22×C4×D5C3×C411yescharacteristic, complemented
70C5×#117—21no—
71#4092—21no—
72#4084—21no—
73#4083C3×C411yescharacteristic, complemented
74#4083C22×C311yescharacteristic
75#4081C3×C411yescharacteristic, complemented
76#4081C22×C311yescharacteristic
77C4×C22⋊D5—21no—
78C4×C22⋊D5—21no—
79#4072C3×C411yescharacteristic, complemented
80C2×#681—21no—
81C5×#99—21no—
82C5×#99C22×C312yes—
83#3968—21no—
84#3965C22×C312yes—
85#2120—51noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22×C411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×C3×D5—21no—
90C22×C3×D5—42no—
91C22×C3×D5—41no—
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—42no—
103C2×C3×C4×C5C22⋊C411yescharacteristic
104C2×C3×C4×C5C22⋊C411yescharacteristic
105C2×C3×C4×C5C22⋊C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C3×C22⋊D5—42no—
108C3×C22⋊D5—42no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C3×C4×D5—42no—
114C3×C4×D5—41no—
115C3×C4×D5—41no—
116C3×#168—42no—
117C2×C3×#41C2×D511yescharacteristic
118C23×C3×C4—51no—
119C2×C3×M16—101no—
120C3×#123—51no—
121C3×#123—51no—
122C3×C22⋊Q8—101no—
123C3×#121—101no—
124C3×#120—51no—
125C3×#120—51no—
126C3×C4×D4—101no—
127C3×C4×D4—101no—
128C3×#117—21no—
129C3×#117—51no—
130C3×#101—101no—
131C3×#100—52no—
132C3×#99—21no—
133C3×#99C2×D512yes—
134C23×D5C2×C3×C411yescharacteristic
135C5×#41—41no—
136C5×#41—41no—
137C2×C5×Q8C3×D411yescharacteristic
138C2×C5×D4C2×C3×C411yescharacteristic
139C2×C5×D4C3×D411yescharacteristic
140C2×C5×D4C23×C311yescharacteristic
141C22×C4×C5C2×C3×C411yescharacteristic
142C22×C4×C5C3×D411yescharacteristic
143C22×C4×C5C3×D411yescharacteristic
144C2×C22⋊D5—21no—
145C2×C22⋊D5—21no—
146C22×Dic5C2×C3×C411yescharacteristic
147C2×C4×D5—21no—
148C2×C4×D5—21no—
149C2×C4×D5—41no—
150C2×C4×D5—41no—
151C5×C4⋊C4—41no—
152C5×C22⋊C4—22no—
153C42×C5—41no—
154C22⋊Dic5—21no—
155C22⋊Dic5—21no—
156C22⋊Dic5C2×C3×C411yescharacteristic
157C22⋊Dic5C2×C3×C411yescharacteristic
158#685—21no—
159#685—21no—
160C4⋊Dic5—21no—
161#683—21no—
162#683—21no—
163C4×Dic5—21no—
164#681—22no—
165#681—41no—
166C2×#168—41no—
167#525—51no—
168#413—51no—
169#410C3×D511yescharacteristic, complemented
170#352—52no—
171AΣL(1,𝔽16)—52no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C3×D5—22no—
180C2×C3×D5—41no—
181C2×C3×D5—42no—
182C2×C3×D5—41no—
183C2×C3×D5—42no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187C3×C4×C5—82no—
188C3×C4×C5#9911yescharacteristic
189C3×C4×C5#9911yescharacteristic
190C3×Dic5—41no—
191C3×Dic5—41no—
192C3×Dic5—41no—
193C24×C3—51no—
194C3×#41—41no—
195C3×#41—41no—
196C2×C3×Q8D2011yescharacteristic
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C2×C3×D4C4×D511yescharacteristic
200C2×C3×D4C22⋊D511yescharacteristic
201C2×C3×D4C22×D511yescharacteristic
202C22×C3×C4—51no—
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4—201no—
206C22×C3×C4—201no—
207C22×C3×C4C4×D511yescharacteristic
208C22×C3×C4D2011yescharacteristic
209C22×C3×C4C22⋊D511yescharacteristic
210C3×M16—102no—
211C3×M16—201no—
212C2×C3×C8—201no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—51no—
219C3×C22⋊C4—51no—
220C3×C22⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C22⋊C4—101no—
223C3×C22⋊C4—101no—
224C3×C42—41no—
225C3×C42—101no—
226C23×C5C3×C22⋊C411yescharacteristic
227C23×C5C22×C3×C411yescharacteristic
228C23×C5C2×C3×D411yescharacteristic
229C22×D5—21no—
230C22×D5—42no—
231C22×D5—41no—
232C5×Q8—41no—
233C5×D4—41no—
234C5×D4—41no—
235C5×D4—41no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—42no—
243C2×C4×C5C3×C22⋊C411yescharacteristic
244C2×C4×C5C3×C22⋊C411yescharacteristic
245C2×C4×C5C3×C22⋊C411yescharacteristic
246C2×C4×C5C2×C3×D411yescharacteristic
247C22⋊D5—42no—
248C22⋊D5—42no—
249C2×Dic5—21no—
250C2×Dic5—21no—
251C2×Dic5—21no—
252C2×Dic5—41no—
253C4×D5—42no—
254C4×D5—41no—
255C4×D5—41no—
256#168—42no—
257C2×#41C2×C3×D511yescharacteristic
258C23×C4—51no—
259C2×M16—101no—
260#123—51no—
261#123—51no—
262C22⋊Q8—101no—
263#121—101no—
264#120—51no—
265#120—51no—
266C4×D4—101no—
267C4×D4—101no—
268#117—21no—
269#117—51no—
270#101—101no—
271#100—52no—
272#99—21no—
273#99C2×C3×D512yes—
274C2×C3×C5—21no—
275C2×C3×C5—41no—
276C2×C3×C5—41no—
277C2×C3×C5—41no—
278C2×C3×C5C2×#9911yescharacteristic
279C3×D5—42no—
280C23×C3—101no—
281C23×C3—201no—
282C23×C3—202no—
283C23×C3#68511yescharacteristic
284C23×C3C2×C4×D511yescharacteristic
285C23×C3C2×C22⋊D511yescharacteristic
286C3×Q8—41no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—41no—
290C3×D4—202no—
291C3×D4—202no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—42no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—101no—
302C2×C3×C4—202no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4#68511yescharacteristic
307C2×C3×C4#68511yescharacteristic
308C2×C3×C4#68511yescharacteristic
309C2×C3×C4C2×D2011yescharacteristic
310C3×C8—202no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—41no—
317C22×C5C2×C3×C22⋊C411yescharacteristic
318C2×D5—22no—
319C2×D5—41no—
320C2×D5—42no—
321C2×D5—41no—
322C2×D5—42no—
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—21no—
326C4×C5—82no—
327C4×C5C3×#9911yescharacteristic
328C4×C5C3×#9911yescharacteristic
329Dic5—41no—
330Dic5—41no—
331Dic5—41no—
332C24—51no—
333#41—41no—
334#41—41no—
335C2×Q8C3×D2011yescharacteristic
336C2×D4—101no—
337C2×D4—101no—
338C2×D4C3×C4×D511yescharacteristic
339C2×D4C3×C22⋊D511yescharacteristic
340C2×D4C22×C3×D511yescharacteristic
341C22×C4—51no—
342C22×C4—101no—
343C22×C4—101no—
344C22×C4—201no—
345C22×C4—201no—
346C22×C4C3×C4×D511yescharacteristic
347C22×C4C3×D2011yescharacteristic
348C22×C4C3×C22⋊D511yescharacteristic
349M16—102no—
350M16—201no—
351C2×C8—201no—
352C4⋊C4—41no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C22⋊C4—22no—
357C22⋊C4—51no—
358C22⋊C4—51no—
359C22⋊C4—101no—
360C22⋊C4—101no—
361C22⋊C4—101no—
362C22⋊C4—101no—
363C42—41no—
364C42—101no—
365C3×C5#212011yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—102no—
373C22×C3—201no—
374C22×C3—202no—
375C22×C3—202no—
376C22×C3—201no—
377C22×C3C2×#68511yescharacteristic
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—82no—
382C3×C4—201no—
383C3×C4—201no—
384C3×C4—201no—
385C3×C4#393811yescharacteristic
386C3×C4#393811yescharacteristic
387C2×C5—21no—
388C2×C5—41no—
389C2×C5—41no—
390C2×C5—41no—
391C2×C5C2×C3×#9911yescharacteristic
392D5—42no—
393C23—101no—
394C23—201no—
395C23—202no—
396C23C3×#68511yescharacteristic
397C23C2×C3×C4×D511yescharacteristic
398C23C2×C3×C22⋊D511yescharacteristic
399Q8—41no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—202no—
404D4—202no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—42no—
412C2×C4—101no—
413C2×C4—101no—
414C2×C4—101no—
415C2×C4—202no—
416C2×C4—201no—
417C2×C4—201no—
418C2×C4—201no—
419C2×C4C3×#68511yescharacteristic
420C2×C4C3×#68511yescharacteristic
421C2×C4C3×#68511yescharacteristic
422C2×C4C2×C3×D2011yescharacteristic
423C8—202no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—41no—
428C2×C3—202no—
429C2×C3C2×#393811yescharacteristic
430C5C3×#212011yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—102no—
438C22—201no—
439C22—202no—
440C22—202no—
441C22—201no—
442C22C2×C3×#68511yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—82no—
447C4—201no—
448C4—201no—
449C4—201no—
450C4C3×#393811yescharacteristic
451C4C3×#393811yescharacteristic
452C3#1060084911yescharacteristic, direct product factor, Sylow
453C2—21no—
454C2—41no—
455C2—41no—
456C2—41no—
457C2—202no—
458C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC3×C4#3938
commutatorC23×C5C22×C3×C4
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#410C2
socleC2×C3×C5C2×#99
prime radicalC3×#66162C2
cosocleC2×C5×D4C23×C3
hypercenterC3×#410D5
hypocenterC5C3×#2120
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
2. C3×C5×#410C2semidirect
3. C3×#65526C2semidirect
4. C3×#64692C2semidirect
5. C3×#64691C2semidirect
6. #10600849C3direct (N × H)
8. C22×C3×C4×D5C4semidirect
12. C3×#4083C4semidirect
14. C3×#4081C4semidirect
18. C3×#4072C4semidirect
26. C5×#410C2×C3semidirect
27. #65526C2×C3semidirect
28. #64692C2×C3semidirect
29. #64691C2×C3semidirect
65. C3×#410D5semidirect
69. C22×C4×D5C3×C4semidirect
73. #4083C3×C4semidirect
75. #4081C3×C4semidirect
79. #4072C3×C4semidirect
169. #410C3×D5semidirect
365. C3×C5#2120semidirect
430. C5C3×#2120semidirect
452. C3#10600849direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661622
C3×C5×#4102
C3×#655262
C3×#646922
C3×#646912
#106008493
C3×#21205