Finite Group Databasebeta

← C3×#10602822 #14301709

Subgroups — C3×#10602822 #14301709

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#568C211yesmaximal, characteristic, complemented
2C3×#66162C211yesmaximal, characteristic
3C3×#65526C211yesmaximal, characteristic, complemented
4C3×#65415C212yesmaximal, complemented
5C3×#64776C212yesmaximal, complemented
6#10602822C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9C3×C5×#131—24no—
10C2×C3×C5×M16—22no—
11C2×C3×C5×M16C2212yes—
12C3×#4092—21no—
13C3×#4084—21no—
14C3×#4083C412yes—
15C3×#4081C412yes—
16C3×C4×C22⋊D5—22no—
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2212yes—
19C3×#3968—21no—
20C3×#3965—21no—
21C3×#3952—24no—
22C3×#1891—51nomaximal, Hall
23C5×#568C2×C311yescharacteristic, complemented
24#66162C2×C311yescharacteristic
25#65526C2×C311yescharacteristic, complemented
26#65415C2×C312yescomplemented
27#64776C2×C312yescomplemented
28C23×C3×D5C2×C411yescharacteristic
29C3×C5×#41—22no—
30C3×C5×#41—22no—
31C2×C3×C5×Q8D411yescharacteristic
32C2×C3×C5×D4C2×C412yes—
33C2×C3×C5×D4D411yescharacteristic
34C22×C3×C4×C5D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5—22no—
37C22×C3×Dic5C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—22no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—22no—
42C3×C5×M16—24no—
43C3×C5×M16—22no—
44C3×C5×M16—22no—
45C2×C3×C5×C8—24no—
46C2×C3×C5×C8D414yescomplemented
47C3×C22⋊Dic5—22no—
48C3×C22⋊Dic5C2×C412yes—
49C3×#685—22no—
50C3×C4⋊Dic5—21no—
51C3×#683—22no—
52C3×C4×Dic5—21no—
53C3×#681—22no—
54C3×#681—22no—
55C2×C3×#168—22no—
56C3×#568D511yescharacteristic, complemented
57C3×#525—51no—
58C3×#413—51no—
59C3×#407—52no—
60C3×#344—52no—
61C2×C5×#41C22×C311yescharacteristic
62C22×C4×D5C22×C311yescharacteristic
63C5×#131—24no—
64C2×C5×M16—22no—
65C2×C5×M16C22×C312yes—
66#4092—21no—
67#4084—21no—
68#4083C3×C412yes—
69#4081C3×C412yes—
70C4×C22⋊D5—22no—
71#4072C22×C311yescharacteristic
72C2×#681C22×C312yes—
73#3968—21no—
74#3965—21no—
75#3952—24no—
76#1891—51noSylow
77C23×C3×C5C22⋊C412yes—
78C23×C3×C5C22×C411yescharacteristic
79C22×C3×D5—21no—
80C22×C3×D5—22no—
81C22×C3×D5—42no—
82C3×C5×Q8—22no—
83C3×C5×D4—24no—
84C3×C5×D4—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C22⋊C412yes—
88C2×C3×C4×C5C2×D412yes—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4112yes—
92C3×C22⋊D5—44no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—22no—
96C3×C4×D5—41no—
97C3×C4×D5—42no—
98C3×C4×D5—41no—
99C3×C5×C8—24no—
100C3×#168—42no—
101C2×C3×#41C2×D511yescharacteristic
102C23×C3×C4—51no—
103C3×#131—24no—
104C2×C3×M16—22no—
105C2×C3×M16—52no—
106C2×C3×M16C2×D512yes—
107C3×#123—52no—
108C3×C22⋊Q8—101no—
109C3×#121—101no—
110C3×#120—52no—
111C3×C4×D4—102no—
112C3×#117—51no—
113C3×#101—101no—
114C3×#100—101no—
115C3×C22⋊C8—104no—
116C23×D5C2×C3×C411yescharacteristic
117C5×#41—22no—
118C5×#41—22no—
119C2×C5×Q8C3×D411yescharacteristic
120C2×C5×D4C2×C3×C412yes—
121C2×C5×D4C3×D411yescharacteristic
122C22×C4×C5C3×D412yes—
123C22×C4×C5C23×C311yescharacteristic
124C2×C22⋊D5—22no—
125C22×Dic5C2×C3×C411yescharacteristic
126C2×C4×D5—22no—
127C2×C4×D5—21no—
128C2×C4×D5—21no—
129C2×C4×D5—22no—
130C5×M16—24no—
131C5×M16—22no—
132C5×M16—22no—
133C2×C5×C8—24no—
134C2×C5×C8C3×D414yescomplemented
135C22⋊Dic5—22no—
136C22⋊Dic5C2×C3×C412yes—
137#685—22no—
138C4⋊Dic5—21no—
139#683—22no—
140C4×Dic5—21no—
141#681—22no—
142#681—22no—
143C2×#168—22no—
144#568C3×D511yescharacteristic, complemented
145#525—51no—
146#413—51no—
147#407—52no—
148#344—52no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—42no—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5C4×D412yes—
154C2×C3×D5—22no—
155C2×C3×D5—24no—
156C2×C3×D5—41no—
157C2×C3×D5—42no—
158C2×C3×D5—41no—
159C3×C4×C5—22no—
160C3×C4×C5#12011yescharacteristic
161C3×C4×C5#12112yes—
162C3×C4×C5#12311yescharacteristic
163C3×Dic5—42no—
164C3×Dic5—41no—
165C24×C3—51no—
166C3×#41—22no—
167C3×#41—22no—
168C2×C3×Q8D2011yescharacteristic
169C2×C3×D4—102no—
170C2×C3×D4C4×D512yes—
171C2×C3×D4D2011yescharacteristic
172C22×C3×C4—51no—
173C22×C3×C4—101no—
174C22×C3×C4—102no—
175C22×C3×C4—102no—
176C22×C3×C4—101no—
177C22×C3×C4C22⋊D512yes—
178C22×C3×C4C22×D511yescharacteristic
179C3×M16—24no—
180C3×M16—22no—
181C3×M16—22no—
182C3×M16—102no—
183C3×M16—102no—
184C2×C3×C8—24no—
185C2×C3×C8—102no—
186C2×C3×C8C22⋊D514yescomplemented
187C3×C4⋊C4—102no—
188C3×C4⋊C4—101no—
189C3×C22⋊C4—52no—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—102no—
192C3×C42—101no—
193C23×C5C3×C22⋊C412yes—
194C23×C5C22×C3×C411yescharacteristic
195C22×D5—21no—
196C22×D5—22no—
197C22×D5—42no—
198C5×Q8—22no—
199C5×D4—24no—
200C5×D4—22no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5C3×C22⋊C412yes—
204C2×C4×C5C2×C3×D411yescharacteristic
205C2×C4×C5C2×C3×D412yes—
206C2×C4×C5C2×C3×D411yescharacteristic
207C2×C4×C5C3×#4112yes—
208C22⋊D5—44no—
209C2×Dic5—22no—
210C2×Dic5—21no—
211C2×Dic5—22no—
212C4×D5—41no—
213C4×D5—42no—
214C4×D5—41no—
215C5×C8—24no—
216#168—42no—
217C2×#41C2×C3×D511yescharacteristic
218C23×C4—51no—
219#131—24no—
220C2×M16—22no—
221C2×M16—52no—
222C2×M16C2×C3×D512yes—
223#123—52no—
224C22⋊Q8—101no—
225#121—101no—
226#120—52no—
227C4×D4—102no—
228#117—51no—
229#101—101no—
230#100—101no—
231C22⋊C8—104no—
232C2×C3×C5—21no—
233C2×C3×C5—22no—
234C2×C3×C5—42no—
235C2×C3×C5#38611yescharacteristic
236C3×D5—42no—
237C23×C3—101no—
238C23×C3—102no—
239C23×C3—202no—
240C23×C3#68512yes—
241C23×C3C2×C4×D511yescharacteristic
242C3×Q8—22no—
243C3×D4—24no—
244C3×D4—22no—
245C3×D4—204no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—102no—
249C2×C3×C4—101no—
250C2×C3×C4—102no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4—202no—
254C2×C3×C4#68512yes—
255C2×C3×C4C2×D2011yescharacteristic
256C2×C3×C4#70912yes—
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D512yes—
259C3×C8—24no—
260C3×C8—202no—
261C22×C5—22no—
262C22×C5—41no—
263C22×C5—42no—
264C22×C5C2×C3×C22⋊C411yescharacteristic
265C22×C5C3×C4×D412yes—
266C2×D5—22no—
267C2×D5—24no—
268C2×D5—41no—
269C2×D5—42no—
270C2×D5—41no—
271C4×C5—22no—
272C4×C5C3×#12011yescharacteristic
273C4×C5C3×#12112yes—
274C4×C5C3×#12311yescharacteristic
275Dic5—42no—
276Dic5—41no—
277C24—51no—
278#41—22no—
279#41—22no—
280C2×Q8C3×D2011yescharacteristic
281C2×D4—102no—
282C2×D4C3×C4×D512yes—
283C2×D4C3×D2011yescharacteristic
284C22×C4—51no—
285C22×C4—101no—
286C22×C4—102no—
287C22×C4—102no—
288C22×C4—101no—
289C22×C4C3×C22⋊D512yes—
290C22×C4C22×C3×D511yescharacteristic
291M16—24no—
292M16—22no—
293M16—22no—
294M16—102no—
295M16—102no—
296C2×C8—24no—
297C2×C8—102no—
298C2×C8C3×C22⋊D514yescomplemented
299C4⋊C4—102no—
300C4⋊C4—101no—
301C22⋊C4—52no—
302C22⋊C4—102no—
303C22⋊C4—102no—
304C42—101no—
305C3×C5#189111yescharacteristic, complemented, Hall
306C22×C3—22no—
307C22×C3—41no—
308C22×C3—42no—
309C22×C3—102no—
310C22×C3—104no—
311C22×C3—201no—
312C22×C3—202no—
313C22×C3—201no—
314C22×C3C2×#68511yescharacteristic
315C22×C3C4×C22⋊D512yes—
316C3×C4—22no—
317C3×C4—202no—
318C3×C4—201no—
319C3×C4#407511yescharacteristic
320C3×C4#407612yes—
321C3×C4#409911yescharacteristic
322C2×C5—21no—
323C2×C5—22no—
324C2×C5—42no—
325C2×C5C3×#38611yescharacteristic
326D5—42no—
327C23—101no—
328C23—102no—
329C23—202no—
330C23C3×#68512yes—
331C23C2×C3×C4×D511yescharacteristic
332Q8—22no—
333D4—24no—
334D4—22no—
335D4—204no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—102no—
339C2×C4—101no—
340C2×C4—102no—
341C2×C4—201no—
342C2×C4—201no—
343C2×C4—202no—
344C2×C4C3×#68512yes—
345C2×C4C2×C3×D2011yescharacteristic
346C2×C4C3×#70912yes—
347C2×C4C2×C3×C22⋊D511yescharacteristic
348C2×C4C2×C3×C22⋊D512yes—
349C8—24no—
350C8—202no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—42no—
354C2×C3—202no—
355C2×C3#6550211yescharacteristic
356C5C3×#189111yescharacteristic, complemented, Sylow
357C22—22no—
358C22—41no—
359C22—42no—
360C22—102no—
361C22—104no—
362C22—201no—
363C22—202no—
364C22—201no—
365C22C2×C3×#68511yescharacteristic
366C22C3×C4×C22⋊D512yes—
367C4—22no—
368C4—202no—
369C4—201no—
370C4C3×#407511yescharacteristic
371C4C3×#407612yes—
372C4C3×#409911yescharacteristic
373C3#1060282211yescharacteristic, direct product factor, Sylow
374C2—21no—
375C2—22no—
376C2—42no—
377C2—202no—
378C2C3×#6550211yescharacteristic
subgroupG/H
centerC3×C4#4099
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#568C2
socleC2×C3×C5#386
prime radicalC3×#66162C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#568D5
hypocenterC5C3×#1891
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#568

Complements

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

NH ≅ G/Ntype
1. C3×C5×#568C2semidirect
3. C3×#65526C2semidirect
4. C3×#65415C2semidirect
5. C3×#64776C2semidirect
6. #10602822C3direct (N × H)
23. C5×#568C2×C3semidirect
25. #65526C2×C3semidirect
26. #65415C2×C3semidirect
27. #64776C2×C3semidirect
46. C2×C3×C5×C8D4semidirect
56. C3×#568D5semidirect
134. C2×C5×C8C3×D4semidirect
144. #568C3×D5semidirect
186. C2×C3×C8C22⋊D5semidirect
298. C2×C8C3×C22⋊D5semidirect
305. C3×C5#1891semidirect
356. C5C3×#1891semidirect
373. C3#10602822direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5682
C3×#661622
C3×#655262
C3×#654152
C3×#647762
#106028223
C3×#18915