Finite Group Databasebeta

← C3×#10598185 #14279043

Subgroups — C3×#10598185 #14279043

Order 1920.

468 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
1C2×C3×C5×#99C211yesmaximal, characteristic
2C3×#65509C211yesmaximal, characteristic
3C2×C3×#3965C211yesmaximal, characteristic
4#10598185C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×D4C2211yescharacteristic
6C23×C3×Dic5C411yescharacteristic, complemented
7C2×C3×C5×C22⋊C4—21no—
8C2×C3×C22⋊Dic5—21no—
9C2×C3×C22⋊Dic5C411yescharacteristic, complemented
10C2×C3×#681—21no—
11C3×C5×#99—21no—
12C3×C5×#99C412yescomplemented
13C3×#3965—21no—
14C3×#3965C412yescomplemented
15C3×#3963—21no—
16C3×#1390—51nomaximal, Hall
17C2×C5×#99C2×C311yescharacteristic
18#65509C2×C311yescharacteristic
19C2×#3965C2×C311yescharacteristic
20C24×C3×C5C2×C411yescharacteristic
21C24×C3×C5D411yescharacteristic
22C2×C3×C5×D4—41no—
23C2×C3×C5×D4—41no—
24C2×C3×C5×D4C2×C411yescharacteristic
25C2×C3×C5×D4C2×C411yescharacteristic
26C2×C3×C5×D4D411yescharacteristic
27C2×C3×C5×D4Q811yescharacteristic
28C22×C3×C4×C5—41no—
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×Dic5—21no—
31C22×C3×Dic5—21no—
32C22×C3×Dic5—42no—
33C22×C3×Dic5—41no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—41no—
36C3×C22⋊Dic5—42no—
37C3×C22⋊Dic5—41no—
38C3×#681—22no—
39C3×#681—41no—
40C2×C3×#168—41no—
41C2×C3×#100—51no—
42C2×C3×#99D511yescharacteristic
43C3×#386—51no—
44C22×C5×D4C22×C311yescharacteristic
45C23×Dic5C3×C411yescharacteristic, complemented
46C2×C5×C22⋊C4—21no—
47C2×C22⋊Dic5—21no—
48C2×C22⋊Dic5C3×C411yescharacteristic, complemented
49C2×#681—21no—
50C5×#99—21no—
51C5×#99C3×C412yescomplemented
52#3965—21no—
53#3965C3×C412yescomplemented
54#3963—21no—
55#1390—51noSylow
56C23×C3×C5—21no—
57C23×C3×C5—21no—
58C23×C3×C5—21no—
59C23×C3×C5—21no—
60C23×C3×C5—41no—
61C23×C3×C5—41no—
62C23×C3×C5—41no—
63C23×C3×C5—41no—
64C23×C3×C5C4211yescharacteristic
65C23×C3×C5C22⋊C411yescharacteristic
66C23×C3×C5C22⋊C411yescharacteristic
67C23×C3×C5C4⋊C411yescharacteristic
68C23×C3×C5C4⋊C411yescharacteristic
69C3×C5×D4—41no—
70C3×C5×D4—41no—
71C3×C5×D4—41no—
72C3×C5×D4—41no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—21no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5—81no—
77C2×C3×C4×C5—81no—
78C2×C3×C4×C5C22⋊C411yescharacteristic
79C2×C3×C4×C5C4⋊C411yescharacteristic
80C2×C3×Dic5—22no—
81C2×C3×Dic5—41no—
82C2×C3×Dic5—42no—
83C2×C3×Dic5—41no—
84C2×C3×Dic5—42no—
85C2×C3×Dic5—41no—
86C2×C3×Dic5—41no—
87C2×C3×Dic5—41no—
88C3×#168—42no—
89C22×C3×D4C2×D511yescharacteristic
90C23×C3×C4—51no—
91C2×C3×M16—101no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—51no—
94C2×C3×C22⋊C4—101no—
95C3×#100—52no—
96C3×#100—101no—
97C3×#99—21no—
98C3×#99Dic512yescomplemented
99C3×#95—101no—
100C24×C5C2×C3×C411yescharacteristic
101C24×C5C3×D411yescharacteristic
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4C2×C3×C411yescharacteristic
105C2×C5×D4C2×C3×C411yescharacteristic
106C2×C5×D4C3×D411yescharacteristic
107C2×C5×D4C3×Q811yescharacteristic
108C22×C4×C5—41no—
109C22×C4×C5C3×D411yescharacteristic
110C22×Dic5—21no—
111C22×Dic5—21no—
112C22×Dic5—42no—
113C22×Dic5—41no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—41no—
116C22⋊Dic5—42no—
117C22⋊Dic5—41no—
118#681—22no—
119#681—41no—
120C2×#168—41no—
121C2×#100—51no—
122C2×#99C3×D511yescharacteristic
123#386—51no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5—21no—
130C22×C3×C5—41no—
131C22×C3×C5—41no—
132C22×C3×C5—41no—
133C22×C3×C5—41no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5—41no—
138C22×C3×C5—41no—
139C22×C3×C5—81no—
140C22×C3×C5#9511yescharacteristic
141C22×C3×C5#9911yescharacteristic
142C22×C3×C5#9911yescharacteristic
143C3×C4×C5—21no—
144C3×C4×C5—21no—
145C3×C4×C5—82no—
146C3×Dic5—42no—
147C3×Dic5—81no—
148C24×C3C4×D511yescharacteristic
149C24×C3C22⋊D511yescharacteristic
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4Dic1011yescharacteristic
153C2×C3×D4C4×D511yescharacteristic
154C2×C3×D4C2×Dic511yescharacteristic
155C2×C3×D4C22⋊D511yescharacteristic
156C22×C3×C4—41no—
157C22×C3×C4—101no—
158C22×C3×C4—101no—
159C22×C3×C4—202no—
160C22×C3×C4—201no—
161C22×C3×C4D2011yescharacteristic
162C3×M16—102no—
163C3×M16—201no—
164C2×C3×C8—201no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—41no—
167C3×C22⋊C4—202no—
168C3×C22⋊C4—201no—
169C23×C5—21no—
170C23×C5—21no—
171C23×C5—21no—
172C23×C5—21no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5C3×C4211yescharacteristic
178C23×C5C3×C22⋊C411yescharacteristic
179C23×C5C3×C22⋊C411yescharacteristic
180C23×C5C3×C4⋊C411yescharacteristic
181C23×C5C3×C4⋊C411yescharacteristic
182C5×D4—41no—
183C5×D4—41no—
184C5×D4—41no—
185C5×D4—41no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—42no—
189C2×C4×C5—81no—
190C2×C4×C5—81no—
191C2×C4×C5C3×C22⋊C411yescharacteristic
192C2×C4×C5C3×C4⋊C411yescharacteristic
193C2×Dic5—22no—
194C2×Dic5—41no—
195C2×Dic5—42no—
196C2×Dic5—41no—
197C2×Dic5—42no—
198C2×Dic5—41no—
199C2×Dic5—41no—
200C2×Dic5—41no—
201#168—42no—
202C22×D4C2×C3×D511yescharacteristic
203C23×C4—51no—
204C2×M16—101no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—51no—
207C2×C22⋊C4—101no—
208#100—52no—
209#100—101no—
210#99—21no—
211#99C3×Dic512yescomplemented
212#95—101no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—41no—
216C2×C3×C5—41no—
217C2×C3×C5—41no—
218C2×C3×C5—41no—
219C2×C3×C5#34211yescharacteristic
220C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
221C2×C3×C5#35211yescharacteristic
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—41no—
227C23×C3—41no—
228C23×C3—41no—
229C23×C3—41no—
230C23×C3C4×Dic511yescharacteristic
231C23×C3#68311yescharacteristic
232C23×C3#68311yescharacteristic
233C23×C3#68511yescharacteristic
234C23×C3C22⋊Dic511yescharacteristic
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—42no—
242C2×C3×C4—81no—
243C2×C3×C4—81no—
244C2×C3×C4—102no—
245C2×C3×C4—201no—
246C2×C3×C4—202no—
247C2×C3×C4—201no—
248C2×C3×C4—202no—
249C2×C3×C4—201no—
250C2×C3×C4—201no—
251C2×C3×C4—201no—
252C2×C3×C4C4⋊Dic511yescharacteristic
253C2×C3×C4#68511yescharacteristic
254C3×C8—202no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—42no—
266C22×C5—41no—
267C22×C5—41no—
268C22×C5—41no—
269C22×C5—41no—
270C22×C5—81no—
271C22×C5C3×#9511yescharacteristic
272C22×C5C3×#9911yescharacteristic
273C22×C5C3×#9911yescharacteristic
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—82no—
277Dic5—42no—
278Dic5—81no—
279C24C3×C4×D511yescharacteristic
280C24C3×C22⋊D511yescharacteristic
281C2×D4—41no—
282C2×D4—41no—
283C2×D4C3×Dic1011yescharacteristic
284C2×D4C3×C4×D511yescharacteristic
285C2×D4C2×C3×Dic511yescharacteristic
286C2×D4C3×C22⋊D511yescharacteristic
287C22×C4—41no—
288C22×C4—101no—
289C22×C4—101no—
290C22×C4—202no—
291C22×C4—201no—
292C22×C4C3×D2011yescharacteristic
293M16—102no—
294M16—201no—
295C2×C8—201no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—202no—
299C22⋊C4—201no—
300C3×C5#139011yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—42no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—81no—
317C22×C3#393811yescharacteristic
318C22×C3#393811yescharacteristic
319C22×C3#396311yescharacteristic
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—82no—
323C3×C4—202no—
324C3×C4—401no—
325C2×C5—21no—
326C2×C5—21no—
327C2×C5—41no—
328C2×C5—41no—
329C2×C5—41no—
330C2×C5—41no—
331C2×C5C3×#34211yescharacteristic
332C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
333C2×C5C3×#35211yescharacteristic
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23C3×C4×Dic511yescharacteristic
343C23C3×#68311yescharacteristic
344C23C3×#68311yescharacteristic
345C23C3×#68511yescharacteristic
346C23C3×C22⋊Dic511yescharacteristic
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—102no—
357C2×C4—201no—
358C2×C4—202no—
359C2×C4—201no—
360C2×C4—202no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4C3×C4⋊Dic511yescharacteristic
365C2×C4C3×#68511yescharacteristic
366C8—202no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3#6469111yescharacteristic
374C2×C3#6469211yescharacteristic
375C2×C3#6474711yescharacteristic
376C5C3×#139011yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22C3×#393811yescharacteristic
394C22C3×#393811yescharacteristic
395C22C3×#396311yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—202no—
400C4—401no—
401C3#1059818511yescharacteristic, direct product factor, Sylow
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—41no—
407C2—41no—
408C2C3×#6469111yescharacteristic
409C2C3×#6469211yescharacteristic
410C2C3×#6474711yescharacteristic
subgroupG/H
centerC22×C3#3938
commutatorC23×C5C3×C42
FrattiniC22×D4C2×C3×D5
FittingC2×C3×C5×#99C2
socleC22×C3×C5#99
prime radicalC22×C3×C5×D4C22
cosocleC22×C5×D4C22×C3
hypercenterC2×C3×#99D5
hypocenterC5C3×#1390
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
4. #10598185C3direct (N × H)
6. C23×C3×Dic5C4semidirect
9. C2×C3×C22⋊Dic5C4semidirect
12. C3×C5×#99C4semidirect
14. C3×#3965C4semidirect
45. C23×Dic5C3×C4semidirect
48. C2×C22⋊Dic5C3×C4semidirect
51. C5×#99C3×C4semidirect
53. #3965C3×C4semidirect
98. C3×#99Dic5semidirect
211. #99C3×Dic5semidirect
300. C3×C5#1390semidirect
376. C5C3×#1390semidirect
401. C3#10598185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#992
C3×#655092
C2×C3×#39652
#105981853
C3×#13905