Finite Group Databasebeta

← C5×#67694 #14279042

Subgroups — C5×#67694 #14279042

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
2C5×#5220C211yesmaximal, characteristic
3C2×C5×#833C211yesmaximal, characteristic
4C5×#1390—31nomaximal, Hall
5C22×C3×C5×D4C2211yescharacteristic
6C23×C5×Dic3C411yescharacteristic, complemented
7C2×C3×C5×C22⋊C4—21no—
8C2×C5×#217—21no—
9C2×C5×#217C411yescharacteristic, complemented
10C2×C5×#208—21no—
11C3×C5×#99—21no—
12C3×C5×#99C412yescomplemented
13C5×#833—21no—
14C5×#833C412yescomplemented
15C5×C3⋊#95—21no—
16#67694C511yesmaximal, characteristic, direct product factor, Hall
17C2×C5×#100—31no—
18C2×C5×#99D311yescharacteristic
19C5×#386—31no—
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×C5×Dic3—21no—
31C22×C5×Dic3—21no—
32C22×C5×Dic3—42no—
33C22×C5×Dic3—41no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—41no—
36C5×#217—42no—
37C5×#217—41no—
38C5×#208—22no—
39C5×#208—41no—
40C2×C5×C3⋊C8—41no—
41C2×C3×#99C2×C511yescharacteristic
42#5220C2×C511yescharacteristic
43C2×#833C2×C511yescharacteristic
44C22×C5×D4C2×D311yescharacteristic
45C23×C4×C5—31no—
46C2×C5×M16—61no—
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—31no—
49C2×C5×C22⋊C4—61no—
50C5×#100—32no—
51C5×#100—61no—
52C5×#99—21no—
53C5×#99Dic312yescomplemented
54C5×#95—61no—
55#1390—31noSylow
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×C5×Dic3—22no—
81C2×C5×Dic3—41no—
82C2×C5×Dic3—42no—
83C2×C5×Dic3—41no—
84C2×C5×Dic3—42no—
85C2×C5×Dic3—41no—
86C2×C5×Dic3—41no—
87C2×C5×Dic3—41no—
88C5×C3⋊C8—42no—
89C22×C3×D4C22×C511yescharacteristic
90C23×Dic3C4×C511yescharacteristic, complemented
91C2×C3×C22⋊C4—21no—
92C2×#217—21no—
93C2×#217C4×C511yescharacteristic, complemented
94C2×#208—21no—
95C3×#99—21no—
96C3×#99C4×C512yescomplemented
97#833—21no—
98#833C4×C512yescomplemented
99C3⋊#95—21no—
100C24×C5C4×D311yescharacteristic
101C24×C5#6711yescharacteristic
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4Dic611yescharacteristic
105C2×C5×D4C4×D311yescharacteristic
106C2×C5×D4C2×Dic311yescharacteristic
107C2×C5×D4#6711yescharacteristic
108C22×C4×C5—41no—
109C22×C4×C5—61no—
110C22×C4×C5—61no—
111C22×C4×C5—122no—
112C22×C4×C5—121no—
113C22×C4×C5D1211yescharacteristic
114C5×M16—62no—
115C5×M16—121no—
116C2×C5×C8—121no—
117C5×C22⋊C4—22no—
118C5×C22⋊C4—41no—
119C5×C22⋊C4—122no—
120C5×C22⋊C4—121no—
121C2×#100—31no—
122C2×#99C5×D311yescharacteristic
123#386—31no—
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—
146C5×Dic3—42no—
147C5×Dic3—81no—
148C24×C3C2×C4×C511yescharacteristic
149C24×C3C5×D411yescharacteristic
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4C2×C4×C511yescharacteristic
153C2×C3×D4C2×C4×C511yescharacteristic
154C2×C3×D4C5×D411yescharacteristic
155C2×C3×D4C5×Q811yescharacteristic
156C22×C3×C4—41no—
157C22×C3×C4C5×D411yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—21no—
160C22×Dic3—42no—
161C22×Dic3—41no—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—41no—
164#217—42no—
165#217—41no—
166#208—22no—
167#208—41no—
168C2×C3⋊C8—41no—
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×C5C4×Dic311yescharacteristic
178C23×C5Dic3⋊C411yescharacteristic
179C23×C5Dic3⋊C411yescharacteristic
180C23×C5(C2×D3)⋊C411yescharacteristic
181C23×C5#21711yescharacteristic
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—62no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5—121no—
193C2×C4×C5—122no—
194C2×C4×C5—121no—
195C2×C4×C5—122no—
196C2×C4×C5—121no—
197C2×C4×C5—121no—
198C2×C4×C5—121no—
199C2×C4×C5C4⋊Dic311yescharacteristic
200C2×C4×C5(C2×D3)⋊C411yescharacteristic
201C5×C8—122no—
202C22×D4C2×C5×D311yescharacteristic
203C23×C4—31no—
204C2×M16—61no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—31no—
207C2×C22⋊C4—61no—
208#100—32no—
209#100—61no—
210#99—21no—
211#99C5×Dic312yescomplemented
212#95—61no—
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×C3C42×C511yescharacteristic
231C23×C3C5×C22⋊C411yescharacteristic
232C23×C3C5×C22⋊C411yescharacteristic
233C23×C3C5×C4⋊C411yescharacteristic
234C23×C3C5×C4⋊C411yescharacteristic
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×C4C5×C22⋊C411yescharacteristic
245C2×C3×C4C5×C4⋊C411yescharacteristic
246C2×Dic3—22no—
247C2×Dic3—41no—
248C2×Dic3—42no—
249C2×Dic3—41no—
250C2×Dic3—42no—
251C2×Dic3—41no—
252C2×Dic3—41no—
253C2×Dic3—41no—
254C3⋊C8—42no—
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×C5#80611yescharacteristic
272C22×C5#80611yescharacteristic
273C22×C5C3⋊#9511yescharacteristic
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—82no—
277C4×C5—122no—
278C4×C5—241no—
279C24C4×C5×D311yescharacteristic
280C24C5×#6711yescharacteristic
281C2×D4—41no—
282C2×D4—41no—
283C2×D4C5×Dic611yescharacteristic
284C2×D4C4×C5×D311yescharacteristic
285C2×D4C2×C5×Dic311yescharacteristic
286C2×D4C5×#6711yescharacteristic
287C22×C4—41no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—122no—
291C22×C4—121no—
292C22×C4C5×D1211yescharacteristic
293M16—62no—
294M16—121no—
295C2×C8—121no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—122no—
299C22⋊C4—121no—
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×C3C5×#9511yescharacteristic
318C22×C3C5×#9911yescharacteristic
319C22×C3C5×#9911yescharacteristic
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—82no—
323Dic3—42no—
324Dic3—81no—
325C2×C5—21no—
326C2×C5—21no—
327C2×C5—41no—
328C2×C5—41no—
329C2×C5—41no—
330C2×C5—41no—
331C2×C5#447111yescharacteristic
332C2×C5#447211yescharacteristic
333C2×C5#452711yescharacteristic
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23C4×C5×Dic311yescharacteristic
343C23C5×Dic3⋊C411yescharacteristic
344C23C5×Dic3⋊C411yescharacteristic
345C23C5×(C2×D3)⋊C411yescharacteristic
346C23C5×#21711yescharacteristic
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—62no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—121no—
358C2×C4—122no—
359C2×C4—121no—
360C2×C4—122no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4—121no—
364C2×C4C5×C4⋊Dic311yescharacteristic
365C2×C4C5×(C2×D3)⋊C411yescharacteristic
366C8—122no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3C5×#34211yescharacteristic
374C2×C3C5×AΣL(1,𝔽16)11yescharacteristic
375C2×C3C5×#35211yescharacteristic
376C5#6769411yescharacteristic, direct product factor, 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—
393C22C5×#80611yescharacteristic
394C22C5×#80611yescharacteristic
395C22C5×C3⋊#9511yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—122no—
400C4—241no—
401C3C5×#139011yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—41no—
405C2—41no—
406C2—41no—
407C2—41no—
408C2C5×#447111yescharacteristic
409C2C5×#447211yescharacteristic
410C2C5×#452711yescharacteristic
subgroupG/H
centerC22×C5#806
commutatorC23×C3C42×C5
FrattiniC22×D4C2×C5×D3
FittingC2×C3×C5×#99C2
socleC22×C3×C5#99
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×D4C22×C5
hypercenterC2×C5×#99D3
hypocenterC3C5×#1390
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ C2×C5×#99

Complements

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

NH ≅ G/Ntype
6. C23×C5×Dic3C4semidirect
9. C2×C5×#217C4semidirect
12. C3×C5×#99C4semidirect
14. C5×#833C4semidirect
16. #67694C5direct (N × H)
53. C5×#99Dic3semidirect
90. C23×Dic3C4×C5semidirect
93. C2×#217C4×C5semidirect
96. C3×#99C4×C5semidirect
98. #833C4×C5semidirect
211. #99C5×Dic3semidirect
300. C3×C5#1390semidirect
376. C5#67694direct (N × H)
401. C3C5×#1390semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#992
C5×#52202
C2×C5×#8332
C5×#13903
#676945