Finite Group Databasebeta

← C3×#10598912 #14280844

Subgroups — C3×#10598912 #14280844

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4027C211yesmaximal, characteristic
2C3×D5×C22⋊C8C212yesmaximal, complemented
3C3×C5×#323C211yesmaximal, characteristic, complemented
4C3×#64745C211yesmaximal, characteristic, complemented
5C3×#64689C212yesmaximal, complemented
6#10598912C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C22⋊D5C411yescharacteristic
8C23×C3×Dic5C411yescharacteristic
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×#685C411yescharacteristic
12C2×C3×#683C2211yescharacteristic
13C2×C3×C4×Dic5C411yescharacteristic
14C2×C3×C8×D5—22no—
15C3×#4027—22no—
16C3×#4027—22no—
17C3×C5×C22⋊C8C2212yes—
18C3×C22⋊#168C2212yes—
19C3×#3952—22no—
20C3×#1459—51nomaximal, Hall
21C2×#4027C2×C311yescharacteristic
22D5×C22⋊C8C2×C312yescomplemented
23C5×#323C2×C311yescharacteristic, complemented
24#64745C2×C311yescharacteristic, complemented
25#64689C2×C312yescomplemented
26C24×C3×C5C2×C411yescharacteristic
27C23×C3×D5C2×C411yescharacteristic
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C2×C3×C22⋊D5—22no—
31C2×C3×C22⋊D5—22no—
32C2×C3×C22⋊D5C814yescomplemented
33C22×C3×Dic5—21no—
34C22×C3×Dic5—21no—
35C22×C3×Dic5—42no—
36C22×C3×Dic5C2×C411yescharacteristic
37C22×C3×Dic5C2×C411yescharacteristic
38C22×C3×Dic5C2×C411yescharacteristic
39C2×C3×C4×D5—42no—
40C2×C3×C4×D5D412yes—
41C2×C3×C4×D5D412yes—
42C2×C3×C5×C8—22no—
43C3×C5×C22⋊C4—22no—
44C3×#685—22no—
45C3×#683—22no—
46C3×C4×Dic5—21no—
47C3×C4×Dic5—21no—
48C2×C3×#168—22no—
49C3×C8×D5—44no—
50C2×C3×C4×D4—51no—
51C2×C3×C22⋊C8—52no—
52C3×#324—52no—
53C3×#323—51no—
54C3×#323D511yescharacteristic, complemented
55C22×C22⋊D5C3×C411yescharacteristic
56C23×Dic5C3×C411yescharacteristic
57C22×C4×D5C22×C311yescharacteristic
58C2×C5×C22⋊C4C22×C311yescharacteristic
59C2×#685C3×C411yescharacteristic
60C2×#683C22×C311yescharacteristic
61C2×C4×Dic5C3×C411yescharacteristic
62C2×C8×D5—22no—
63#4027—22no—
64#4027—22no—
65C5×C22⋊C8C22×C312yes—
66C22⋊#168C22×C312yes—
67#3952—22no—
68#1459—51noSylow
69C23×C3×C5—21no—
70C23×C3×C5—21no—
71C23×C3×C5—41no—
72C23×C3×C5—41no—
73C23×C3×C5C2×C812yescomplemented
74C23×C3×C5C22×C411yescharacteristic
75C22×C3×D5—41no—
76C22×C3×D5—41no—
77C22×C3×D5C22⋊C412yes—
78C22×C3×D5C2×C812yes—
79C22×C3×D5M1612yes—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D412yes—
84C3×C22⋊D5—28no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—21no—
87C2×C3×Dic5—22no—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—42no—
90C2×C3×Dic5—42no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×C812yescomplemented
95C3×C4×D5—24no—
96C3×C4×D5—42no—
97C3×C5×C8—42no—
98C3×#168—42no—
99C22×C3×D4—51no—
100C23×C3×C4—51no—
101C23×C3×C4—51no—
102C22×C3×C8—102no—
103C3×C4×D4—102no—
104C3×C4×D4—102no—
105C2×C3×C4⋊C4—51no—
106C2×C3×C22⋊C4—51no—
107C2×C3×C22⋊C4C2×D511yescharacteristic
108C2×C3×C42—51no—
109C3×C22⋊C8—52no—
110C3×C22⋊C8—102no—
111C3×C22⋊C8C2×D512yes—
112C24×C5C2×C3×C411yescharacteristic
113C23×D5C2×C3×C411yescharacteristic
114C22×C4×C5C2×C3×C411yescharacteristic
115C22×C4×C5C23×C311yescharacteristic
116C2×C22⋊D5—22no—
117C2×C22⋊D5—22no—
118C2×C22⋊D5C3×C814yescomplemented
119C22×Dic5—21no—
120C22×Dic5—21no—
121C22×Dic5—42no—
122C22×Dic5C2×C3×C411yescharacteristic
123C22×Dic5C2×C3×C411yescharacteristic
124C22×Dic5C2×C3×C411yescharacteristic
125C2×C4×D5—42no—
126C2×C4×D5C3×D412yes—
127C2×C4×D5C3×D412yes—
128C2×C5×C8—22no—
129C5×C22⋊C4—22no—
130#685—22no—
131#683—22no—
132C4×Dic5—21no—
133C4×Dic5—21no—
134C2×#168—22no—
135C8×D5—44no—
136C2×C4×D4—51no—
137C2×C22⋊C8—52no—
138#324—52no—
139#323—51no—
140#323C3×D511yescharacteristic, complemented
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—22no—
144C22×C3×C5—42no—
145C22×C3×C5—42no—
146C22×C3×C5—41no—
147C22×C3×C5—41no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C22×C3×C5C22×C811yescharacteristic
150C22×C3×C5C2×M1611yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—22no—
153C2×C3×D5—42no—
154C2×C3×D5—42no—
155C2×C3×D5C22⋊C814yes—
156C3×C4×C5—22no—
157C3×C4×C5—41no—
158C3×Dic5—22no—
159C3×Dic5—21no—
160C3×Dic5—41no—
161C3×Dic5#9912yes—
162C24×C3—51no—
163C24×C3C4×D511yescharacteristic
164C2×C3×D4—54no—
165C2×C3×D4—102no—
166C2×C3×D4—102no—
167C22×C3×C4—51no—
168C22×C3×C4—51no—
169C22×C3×C4—52no—
170C22×C3×C4—52no—
171C22×C3×C4—51no—
172C22×C3×C4—101no—
173C22×C3×C4—101no—
174C22×C3×C4—202no—
175C22×C3×C4—202no—
176C22×C3×C4C4×D511yescharacteristic
177C22×C3×C4C22×D511yescharacteristic
178C2×C3×C8—22no—
179C2×C3×C8—102no—
180C2×C3×C8—204no—
181C3×C4⋊C4—102no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—102no—
184C3×C42—101no—
185C3×C42—101no—
186C23×C5—21no—
187C23×C5—21no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5C2×C3×C812yescomplemented
191C23×C5C22×C3×C411yescharacteristic
192C22×D5—41no—
193C22×D5—41no—
194C22×D5C3×C22⋊C412yes—
195C22×D5C2×C3×C812yes—
196C22×D5C3×M1612yes—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5C2×C3×D412yes—
201C22⋊D5—28no—
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—22no—
205C2×Dic5—21no—
206C2×Dic5—42no—
207C2×Dic5—42no—
208C2×Dic5—41no—
209C2×Dic5C3×C22⋊C411yescharacteristic
210C2×Dic5C3×C22⋊C411yescharacteristic
211C2×Dic5C2×C3×C812yescomplemented
212C4×D5—24no—
213C4×D5—42no—
214C5×C8—42no—
215#168—42no—
216C22×D4—51no—
217C23×C4—51no—
218C23×C4—51no—
219C22×C8—102no—
220C4×D4—102no—
221C4×D4—102no—
222C2×C4⋊C4—51no—
223C2×C22⋊C4—51no—
224C2×C22⋊C4C2×C3×D511yescharacteristic
225C2×C42—51no—
226C22⋊C8—52no—
227C22⋊C8—102no—
228C22⋊C8C2×C3×D512yes—
229C2×C3×C5—21no—
230C2×C3×C5—21no—
231C2×C3×C5—42no—
232C2×C3×C5C2×C22⋊C811yescharacteristic
233C2×C3×C5C2×#9911yescharacteristic
234C2×C3×C5#41311yescharacteristic
235C3×D5—24no—
236C23×C3—21no—
237C23×C3—21no—
238C23×C3—41no—
239C23×C3—41no—
240C23×C3—52no—
241C23×C3—52no—
242C23×C3—52no—
243C23×C3—201no—
244C23×C3—201no—
245C23×C3C8×D512yescomplemented
246C23×C3C2×C4×D511yescharacteristic
247C3×D4—108no—
248C2×C3×C4—21no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—52no—
254C2×C3×C4—104no—
255C2×C3×C4—102no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—202no—
260C2×C3×C4—202no—
261C2×C3×C4—202no—
262C2×C3×C4—201no—
263C2×C3×C4D4×D512yes—
264C3×C8—42no—
265C3×C8—202no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—22no—
269C22×C5—42no—
270C22×C5—42no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5C2×C3×C22⋊C411yescharacteristic
274C22×C5C22×C3×C811yescharacteristic
275C22×C5C2×C3×M1611yescharacteristic
276C2×D5—22no—
277C2×D5—22no—
278C2×D5—42no—
279C2×D5—42no—
280C2×D5C3×C22⋊C814yes—
281C4×C5—22no—
282C4×C5—41no—
283Dic5—22no—
284Dic5—21no—
285Dic5—41no—
286Dic5C3×#9912yes—
287C24—51no—
288C24C3×C4×D511yescharacteristic
289C2×D4—54no—
290C2×D4—102no—
291C2×D4—102no—
292C22×C4—51no—
293C22×C4—51no—
294C22×C4—52no—
295C22×C4—52no—
296C22×C4—51no—
297C22×C4—101no—
298C22×C4—101no—
299C22×C4—202no—
300C22×C4—202no—
301C22×C4C3×C4×D511yescharacteristic
302C22×C4C22×C3×D511yescharacteristic
303C2×C8—22no—
304C2×C8—102no—
305C2×C8—204no—
306C4⋊C4—102no—
307C22⋊C4—22no—
308C22⋊C4—102no—
309C42—101no—
310C42—101no—
311C3×C5#145911yescharacteristic, complemented, Hall
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—22no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—54no—
320C22×C3—102no—
321C22×C3—102no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3D5×C22⋊C411yescharacteristic
325C22×C3C2×C8×D511yescharacteristic
326C22×C3D5×M1611yescharacteristic
327C3×C4—22no—
328C3×C4—41no—
329C3×C4—52no—
330C3×C4—101no—
331C3×C4—102no—
332C3×C4—201no—
333C2×C5—21no—
334C2×C5—21no—
335C2×C5—42no—
336C2×C5C2×C3×C22⋊C811yescharacteristic
337C2×C5C2×C3×#9911yescharacteristic
338C2×C5C3×#41311yescharacteristic
339D5—24no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—52no—
345C23—52no—
346C23—52no—
347C23—201no—
348C23—201no—
349C23C3×C8×D512yescomplemented
350C23C2×C3×C4×D511yescharacteristic
351D4—108no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—52no—
358C2×C4—104no—
359C2×C4—102no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—202no—
364C2×C4—202no—
365C2×C4—202no—
366C2×C4—201no—
367C2×C4C3×D4×D512yes—
368C8—42no—
369C8—202no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—42no—
373C2×C3—104no—
374C2×C3D5×C22⋊C811yescharacteristic
375C2×C3D5×#9911yescharacteristic
376C2×C3#6503411yescharacteristic
377C5C3×#145911yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—54no—
386C22—102no—
387C22—102no—
388C22—202no—
389C22—202no—
390C22C3×D5×C22⋊C411yescharacteristic
391C22C2×C3×C8×D511yescharacteristic
392C22C3×D5×M1611yescharacteristic
393C4—22no—
394C4—41no—
395C4—52no—
396C4—101no—
397C4—102no—
398C4—201no—
399C3#1059891211yescharacteristic, direct product factor, Sylow
400C2—21no—
401C2—21no—
402C2—42no—
403C2—104no—
404C2C3×D5×C22⋊C811yescharacteristic
405C2C3×D5×#9911yescharacteristic
406C2C3×#6503411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC22×C5C22×C3×C8
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#323C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#323D5
hypocenterC5C3×#1459
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
2. C3×D5×C22⋊C8C2semidirect
3. C3×C5×#323C2semidirect
4. C3×#64745C2semidirect
5. C3×#64689C2semidirect
6. #10598912C3direct (N × H)
22. D5×C22⋊C8C2×C3semidirect
23. C5×#323C2×C3semidirect
24. #64745C2×C3semidirect
25. #64689C2×C3semidirect
32. C2×C3×C22⋊D5C8semidirect
54. C3×#323D5semidirect
73. C23×C3×C5C2×C8semidirect
94. C2×C3×Dic5C2×C8semidirect
118. C2×C22⋊D5C3×C8semidirect
140. #323C3×D5semidirect
190. C23×C5C2×C3×C8semidirect
211. C2×Dic5C2×C3×C8semidirect
245. C23×C3C8×D5semidirect
311. C3×C5#1459semidirect
349. C23C3×C8×D5semidirect
377. C5C3×#1459semidirect
399. C3#10598912direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40272
C3×D5×C22⋊C82
C3×C5×#3232
C3×#647452
C3×#646892
#105989123
C3×#14595