Finite Group Databasebeta

← C3×#10600921 #14313671

Subgroups — C3×#10600921 #14313671

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66150C211yesmaximal, characteristic
2C2×C3×C5×#101C211yesmaximal, characteristic, complemented
3C2×C3×#3968C211yesmaximal, characteristic, complemented
4C3×#64698C212yesmaximal, complemented
5C3×#64697C212yesmaximal, complemented
6#10600921C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×#709C411yescharacteristic
9C2×C3×C5×M16—21no—
10C3×#4093C411yescharacteristic
11C3×#4093C2211yescharacteristic
12C3×#4092—21no—
13C3×#4092—21no—
14C3×#4090C411yescharacteristic
15C3×#4090C2211yescharacteristic
16C3×#4075—21no—
17C3×#4075—21no—
18C3×#4072C411yescharacteristic
19C2×C3×#681—21no—
20C3×C5×#101—21no—
21C3×C5×#101C2212yes—
22C3×#3968—21no—
23C3×#3968C2212yes—
24C3×#2133—51nomaximal, Hall
25#66150C2×C311yescharacteristic
26C2×C5×#101C2×C311yescharacteristic, complemented
27C2×#3968C2×C311yescharacteristic, complemented
28#64698C2×C312yescomplemented
29#64697C2×C312yescomplemented
30C2×C3×C5×Q8—41no—
31C2×C3×C5×Q8—41no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C2×C3×C5×Q8D411yescharacteristic
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×Q8C2311yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C3×#709—41no—
41C3×#709—41no—
42C2×C3×D20C2×C411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×Dic10C2×C411yescharacteristic
45C3×C5×M16—22no—
46C3×C5×M16—41no—
47C2×C3×C5×C8—41no—
48C3×C22⋊Dic5—21no—
49C3×#685—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×#683—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5C2×C411yescharacteristic
60C3×#681—22no—
61C3×#681—41no—
62C2×C3×#168—41no—
63C3×#536—51no—
64C2×C3×#101—51no—
65C2×C3×#101D511yescharacteristic, complemented
66C3×#356—52no—
67C3×#355—52no—
68C22×C5×Q8C22×C311yescharacteristic
69C2×#709C3×C411yescharacteristic
70C2×C5×M16—21no—
71#4093C3×C411yescharacteristic
72#4093C22×C311yescharacteristic
73#4092—21no—
74#4092—21no—
75#4090C3×C411yescharacteristic
76#4090C22×C311yescharacteristic
77#4075—21no—
78#4075—21no—
79#4072C3×C411yescharacteristic
80C2×#681—21no—
81C5×#101—21no—
82C5×#101C22×C312yes—
83#3968—21no—
84#3968C22×C312yes—
85#2133—51noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C22×C3×D5—21no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×Q8—41no—
91C3×C5×Q8—41no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—41no—
105C3×C22⋊D5—41no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C3×D20—41no—
110C3×C4×D5—42no—
111C3×Dic10—41no—
112C3×C5×C8—42no—
113C3×#168—42no—
114C2×C3×#41—51no—
115C22×C3×Q8C2×D511yescharacteristic
116C2×C3×M16—21no—
117C2×C3×M16—101no—
118C3×C4⋊Q8—51no—
119C3×C4⋊Q8—51no—
120C3×#124—51no—
121C3×#124—51no—
122C3×#123—101no—
123C3×#123—101no—
124C3×C22⋊Q8—101no—
125C3×C22⋊Q8—101no—
126C3×#117—51no—
127C3×#101—21no—
128C3×#101—52no—
129C3×#101—101no—
130C3×#101C2×D512yes—
131C2×C5×Q8—41no—
132C2×C5×Q8—41no—
133C2×C5×Q8C2×C3×C411yescharacteristic
134C2×C5×Q8C3×D411yescharacteristic
135C2×C5×Q8C3×D411yescharacteristic
136C2×C5×Q8C23×C311yescharacteristic
137C22×C4×C5C2×C3×C411yescharacteristic
138C22×C4×C5C3×D411yescharacteristic
139C22×C4×C5C3×D411yescharacteristic
140C2×C22⋊D5—21no—
141#709—41no—
142#709—41no—
143C2×D20C2×C3×C411yescharacteristic
144C2×C4×D5—21no—
145C2×Dic10C2×C3×C411yescharacteristic
146C5×M16—22no—
147C5×M16—41no—
148C2×C5×C8—41no—
149C22⋊Dic5—21no—
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154C4⋊Dic5—21no—
155#683—21no—
156#683—21no—
157#683—21no—
158#683—21no—
159C4×Dic5C2×C3×C411yescharacteristic
160C4×Dic5C2×C3×C411yescharacteristic
161#681—22no—
162#681—41no—
163C2×#168—41no—
164#536—51no—
165C2×#101—51no—
166C2×#101C3×D511yescharacteristic, complemented
167#356—52no—
168#355—52no—
169C22×C3×C5—41no—
170C22×C3×C5#9911yescharacteristic
171C22×C3×C5#9911yescharacteristic
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C3×D5—42no—
174C2×C3×D5—41no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×Dic5—41no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C3×#41—201no—
185C3×#41—201no—
186C2×C3×Q8—41no—
187C2×C3×Q8—41no—
188C2×C3×Q8—51no—
189C2×C3×Q8C4×D511yescharacteristic
190C2×C3×Q8D2011yescharacteristic
191C2×C3×Q8C22⋊D511yescharacteristic
192C2×C3×Q8C22×D511yescharacteristic
193C2×C3×D4—51no—
194C2×C3×D4—101no—
195C22×C3×C4—101no—
196C22×C3×C4C4×D511yescharacteristic
197C22×C3×C4D2011yescharacteristic
198C22×C3×C4C22⋊D511yescharacteristic
199C3×M16—22no—
200C3×M16—41no—
201C3×M16—102no—
202C3×M16—201no—
203C2×C3×C8—41no—
204C2×C3×C8—201no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C42—51no—
216C3×C42—51no—
217C23×C5C3×C22⋊C411yescharacteristic
218C22×D5—21no—
219C5×Q8—41no—
220C5×Q8—41no—
221C5×Q8—41no—
222C5×Q8—41no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5C3×C22⋊C411yescharacteristic
230C2×C4×C5C3×C22⋊C411yescharacteristic
231C2×C4×C5C3×C22⋊C411yescharacteristic
232C2×C4×C5C22×C3×C411yescharacteristic
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C22⋊D5—41no—
236C22⋊D5—41no—
237C2×Dic5—21no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240D20—41no—
241C4×D5—42no—
242Dic10—41no—
243C5×C8—42no—
244#168—42no—
245C2×#41—51no—
246C22×Q8C2×C3×D511yescharacteristic
247C2×M16—21no—
248C2×M16—101no—
249C4⋊Q8—51no—
250C4⋊Q8—51no—
251#124—51no—
252#124—51no—
253#123—101no—
254#123—101no—
255C22⋊Q8—101no—
256C22⋊Q8—101no—
257#117—51no—
258#101—21no—
259#101—52no—
260#101—101no—
261#101C2×C3×D512yes—
262C2×C3×C5—21no—
263C2×C3×C5—21no—
264C2×C3×C5—21no—
265C2×C3×C5C2×#9911yescharacteristic
266C3×D5—81no—
267C23×C3—101no—
268C23×C3#68511yescharacteristic
269C3×Q8—41no—
270C3×Q8—41no—
271C3×Q8—41no—
272C3×Q8—41no—
273C3×Q8—201no—
274C3×D4—201no—
275C3×D4—201no—
276C3×D4—201no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—202no—
287C2×C3×C4#68511yescharacteristic
288C2×C3×C4#68511yescharacteristic
289C2×C3×C4#68511yescharacteristic
290C2×C3×C4C2×C4×D511yescharacteristic
291C2×C3×C4C2×D2011yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293C3×C8—42no—
294C3×C8—202no—
295C22×C5—41no—
296C22×C5C3×#9911yescharacteristic
297C22×C5C3×#9911yescharacteristic
298C22×C5C2×C3×C22⋊C411yescharacteristic
299C2×D5—42no—
300C2×D5—41no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—21no—
304C4×C5—21no—
305C4×C5—21no—
306C4×C5—21no—
307Dic5—41no—
308Dic5—41no—
309Dic5—41no—
310#41—201no—
311#41—201no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—51no—
315C2×Q8C3×C4×D511yescharacteristic
316C2×Q8C3×D2011yescharacteristic
317C2×Q8C3×C22⋊D511yescharacteristic
318C2×Q8C22×C3×D511yescharacteristic
319C2×D4—51no—
320C2×D4—101no—
321C22×C4—101no—
322C22×C4C3×C4×D511yescharacteristic
323C22×C4C3×D2011yescharacteristic
324C22×C4C3×C22⋊D511yescharacteristic
325M16—22no—
326M16—41no—
327M16—102no—
328M16—201no—
329C2×C8—41no—
330C2×C8—201no—
331C4⋊C4—101no—
332C4⋊C4—101no—
333C4⋊C4—101no—
334C4⋊C4—101no—
335C4⋊C4—101no—
336C22⋊C4—101no—
337C22⋊C4—101no—
338C22⋊C4—101no—
339C22⋊C4—101no—
340C22⋊C4—101no—
341C42—51no—
342C42—51no—
343C3×C5#213311yescharacteristic, complemented, Hall
344C22×C3—41no—
345C22×C3—202no—
346C22×C3—201no—
347C22×C3#393811yescharacteristic
348C22×C3#393811yescharacteristic
349C22×C3C2×#68511yescharacteristic
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—201no—
357C3×C4—201no—
358C3×C4—201no—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5—21no—
362C2×C5C2×C3×#9911yescharacteristic
363D5—81no—
364C23—101no—
365C23C3×#68511yescharacteristic
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—201no—
371D4—201no—
372D4—201no—
373D4—201no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—202no—
384C2×C4C3×#68511yescharacteristic
385C2×C4C3×#68511yescharacteristic
386C2×C4C3×#68511yescharacteristic
387C2×C4C2×C3×C4×D511yescharacteristic
388C2×C4C2×C3×D2011yescharacteristic
389C2×C4C2×C3×C22⋊D511yescharacteristic
390C8—42no—
391C8—202no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—401no—
396C2×C3C2×#393811yescharacteristic
397C5C3×#213311yescharacteristic, complemented, Sylow
398C22—41no—
399C22—202no—
400C22—201no—
401C22C3×#393811yescharacteristic
402C22C3×#393811yescharacteristic
403C22C2×C3×#68511yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—201no—
411C4—201no—
412C4—201no—
413C3#1060092111yescharacteristic, direct product factor, Sylow
414C2—21no—
415C2—21no—
416C2—21no—
417C2—401no—
418C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC2×C3C2×#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC2×C3×C5×#101C2
socleC2×C3×C5C2×#99
prime radicalC2×C3×#709C4
cosocleC2×C5×Q8C23×C3
hypercenterC2×C3×#101D5
hypocenterC5C3×#2133
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C22×C3×Q8 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#101C2semidirect
3. C2×C3×#3968C2semidirect
4. C3×#64698C2semidirect
5. C3×#64697C2semidirect
6. #10600921C3direct (N × H)
26. C2×C5×#101C2×C3semidirect
27. C2×#3968C2×C3semidirect
28. #64698C2×C3semidirect
29. #64697C2×C3semidirect
65. C2×C3×#101D5semidirect
166. C2×#101C3×D5semidirect
343. C3×C5#2133semidirect
397. C5C3×#2133semidirect
413. C3#10600921direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661502
C2×C3×C5×#1012
C2×C3×#39682
C3×#646982
C3×#646972
#106009213
C3×#21335