Finite Group Databasebeta

← C3×#10598128 #14279046

Subgroups — C3×#10598128 #14279046

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
1C3×C5×#386C211yesmaximal, characteristic
2C2×C3×#3966C211yesmaximal, characteristic
3C2×C3×#3965C211yesmaximal, characteristic
4#10598128C311yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C5×D4C2211yescharacteristic
6C23×C3×C4×C5C411yescharacteristic, complemented
7C2×C3×C5×C22⋊C4—21no—
8C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
9C2×C3×C22⋊Dic5—21no—
10C2×C3×#681—21no—
11C3×C5×#95—21no—
12C3×#3966—21no—
13C3×#3966C412yescomplemented
14C3×#3965—21no—
15C3×#3965C412yescomplemented
16C3×#1390—51nomaximal, Hall
17C5×#386C2×C311yescharacteristic
18C2×#3966C2×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—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5—42no—
31C22×C3×C4×C5—41no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×Dic5—41no—
34C3×C5×C22⋊C4—42no—
35C3×C5×C22⋊C4—41no—
36C3×C22⋊Dic5—22no—
37C3×C22⋊Dic5—41no—
38C3×#681—22no—
39C3×#681—41no—
40C2×C3×#168—41no—
41C2×C3×#100—51no—
42C2×C3×#99—51no—
43C3×#386D511yescharacteristic
44C22×C5×D4C22×C311yescharacteristic
45C23×C4×C5C3×C411yescharacteristic, complemented
46C2×C5×C22⋊C4—21no—
47C2×C5×C22⋊C4C3×C411yescharacteristic, complemented
48C2×C22⋊Dic5—21no—
49C2×#681—21no—
50C5×#95—21no—
51#3966—21no—
52#3966C3×C412yescomplemented
53#3965—21no—
54#3965C3×C412yescomplemented
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—22no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5—42no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C4⋊C411yescharacteristic
85C2×C3×Dic5—42no—
86C2×C3×Dic5—81no—
87C2×C3×Dic5—81no—
88C3×#168—42no—
89C22×C3×D4C2×D511yescharacteristic
90C23×C3×C4Dic511yescharacteristic, complemented
91C2×C3×M16—101no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—101no—
94C2×C3×C22⋊C4Dic511yescharacteristic, complemented
95C3×#100—52no—
96C3×#100—101no—
97C3×#99—52no—
98C3×#99—101no—
99C3×#95—21no—
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—21no—
109C22×C4×C5—21no—
110C22×C4×C5—42no—
111C22×C4×C5—41no—
112C22×C4×C5C3×D411yescharacteristic
113C22×Dic5—41no—
114C5×C22⋊C4—42no—
115C5×C22⋊C4—41no—
116C22⋊Dic5—22no—
117C22⋊Dic5—41no—
118#681—22no—
119#681—41no—
120C2×#168—41no—
121C2×#100—51no—
122C2×#99—51no—
123#386C3×D511yescharacteristic
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—42no—
146C3×C4×C5—81no—
147C3×Dic5—82no—
148C24×C3C2×Dic511yescharacteristic
149C24×C3C22⋊D511yescharacteristic
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4Dic1011yescharacteristic
153C2×C3×D4C4×D511yescharacteristic
154C2×C3×D4C4×D511yescharacteristic
155C2×C3×D4D2011yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—42no—
159C22×C3×C4—41no—
160C22×C3×C4—201no—
161C22×C3×C4C22⋊D511yescharacteristic
162C3×M16—102no—
163C3×M16—201no—
164C2×C3×C8—201no—
165C3×C22⋊C4—42no—
166C3×C22⋊C4—41no—
167C3×C22⋊C4—102no—
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—22no—
189C2×C4×C5—41no—
190C2×C4×C5—42no—
191C2×C4×C5—41no—
192C2×C4×C5—42no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—41no—
196C2×C4×C5C3×C22⋊C411yescharacteristic
197C2×C4×C5C3×C4⋊C411yescharacteristic
198C2×Dic5—42no—
199C2×Dic5—81no—
200C2×Dic5—81no—
201#168—42no—
202C22×D4C2×C3×D511yescharacteristic
203C23×C4C3×Dic511yescharacteristic, complemented
204C2×M16—101no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—101no—
207C2×C22⋊C4C3×Dic511yescharacteristic, complemented
208#100—52no—
209#100—101no—
210#99—52no—
211#99—101no—
212#95—21no—
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×C3C4⋊Dic511yescharacteristic
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—22no—
242C2×C3×C4—41no—
243C2×C3×C4—42no—
244C2×C3×C4—41no—
245C2×C3×C4—42no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—202no—
250C2×C3×C4—401no—
251C2×C3×C4—401no—
252C2×C3×C4#68311yescharacteristic
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—42no—
277C4×C5—81no—
278Dic5—82no—
279C24C2×C3×Dic511yescharacteristic
280C24C3×C22⋊D511yescharacteristic
281C2×D4—41no—
282C2×D4—41no—
283C2×D4C3×Dic1011yescharacteristic
284C2×D4C3×C4×D511yescharacteristic
285C2×D4C3×C4×D511yescharacteristic
286C2×D4C3×D2011yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—201no—
292C22×C4C3×C22⋊D511yescharacteristic
293M16—102no—
294M16—201no—
295C2×C8—201no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—102no—
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#396311yescharacteristic
318C22×C3#396611yescharacteristic
319C22×C3#396611yescharacteristic
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—42no—
323C3×C4—81no—
324C3×C4—402no—
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×C4⋊Dic511yescharacteristic
345C23C3×#68511yescharacteristic
346C23C3×C22⋊Dic511yescharacteristic
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—202no—
362C2×C4—401no—
363C2×C4—401no—
364C2×C4C3×#68311yescharacteristic
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#6474611yescharacteristic
374C2×C3#6475611yescharacteristic
375C2×C3#6475911yescharacteristic
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×#396311yescharacteristic
394C22C3×#396611yescharacteristic
395C22C3×#396611yescharacteristic
396C4—21no—
397C4—21no—
398C4—42no—
399C4—81no—
400C4—402no—
401C3#1059812811yescharacteristic, direct product factor, Sylow
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—41no—
407C2—41no—
408C2C3×#6474611yescharacteristic
409C2C3×#6475611yescharacteristic
410C2C3×#6475911yescharacteristic
subgroupG/H
centerC22×C3#3966
commutatorC23×C5C3×C42
FrattiniC22×D4C2×C3×D5
FittingC3×C5×#386C2
socleC22×C3×C5#99
prime radicalC22×C3×C5×D4C22
cosocleC22×C5×D4C22×C3
hypercenterC3×#386D5
hypocenterC5C3×#1390
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
4. #10598128C3direct (N × H)
6. C23×C3×C4×C5C4semidirect
8. C2×C3×C5×C22⋊C4C4semidirect
13. C3×#3966C4semidirect
15. C3×#3965C4semidirect
45. C23×C4×C5C3×C4semidirect
47. C2×C5×C22⋊C4C3×C4semidirect
52. #3966C3×C4semidirect
54. #3965C3×C4semidirect
90. C23×C3×C4Dic5semidirect
94. C2×C3×C22⋊C4Dic5semidirect
203. C23×C4C3×Dic5semidirect
207. C2×C22⋊C4C3×Dic5semidirect
300. C3×C5#1390semidirect
376. C5C3×#1390semidirect
401. C3#10598128direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#3862
C2×C3×#39662
C2×C3×#39652
#105981283
C3×#13905