Finite Group Databasebeta

← C2×C5×#5919 #14511416

Subgroups — C2×C5×#5919 #14511416

Order 1920.

1690 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1690 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×Q8×A4C211yesmaximal, characteristic, complemented
2C5×#5919C218yesmaximal, direct product factor
3C2×C5×C4⋊S4C213yesmaximal, complemented
4C2×C4×C5×S4C213yesmaximal, complemented
5C2×C5×#548—31nomaximal, Hall
6C22×C5×S4C2213yes—
7C2×C5×#239—41nomaximal
8C5×Q8×A4C2214yescomplemented
9C2×C4×C5×A4C2213yes—
10C2×C5×SL(2,ℤ/4)C2211yescharacteristic
11C5×C4⋊S4C22112yescomplemented
12C4×C5×S4C22112yescomplemented
13C2×#5919C511yesmaximal, characteristic, direct product factor, Hall
14C22×C5×#41—31no—
15C23×C5×Q8D311yescharacteristic, complemented
16C5×#548—38no—
17C5×#548—38no—
18C2×C5×#124—33no—
19C2×C5×C22⋊Q8—33no—
20C2×C5×#121—33no—
21C2×C4×C5×Q8—31no—
22C2×C4×C5×D4—33no—
23C22×C5×A4C2311yescharacteristic
24C2×C5×S4—26no—
25C2×C5×S4C2316yes—
26C2×C3×C5×Q8—41no—
27C5×#239—48no—
28C2×C5×D12—43no—
29C2×C4×C5×D3—43no—
30C4×C5×A4C2316yes—
31C5×SL(2,ℤ/4)C2312yes—
32C2×Q8×A4C2×C511yescharacteristic, complemented
33#5919C2×C518yesdirect product factor
34C2×C4⋊S4C2×C513yescomplemented
35C2×C4×S4C2×C513yescomplemented
36C2×C5×#41—38no—
37C2×C5×#41—64no—
38C2×C5×#41—63no—
39C2×C5×#41—61no—
40C22×C5×Q8—31no—
41C22×C5×Q8—33no—
42C22×C5×Q8—34no—
43C22×C5×Q8C2×D314yescomplemented
44C22×C5×D4—33no—
45C22×C5×D4—33no—
46C23×C4×C5—33no—
47C23×C4×C5C2×D313yes—
48C5×#124—324no—
49C5×C22⋊Q8—324no—
50C5×#121—312no—
51C5×#121—312no—
52C4×C5×Q8—38no—
53C4×C5×D4—312no—
54C4×C5×D4—312no—
55C2×C5×C4⋊C4—33no—
56C2×C5×C4⋊C4—33no—
57C2×C5×C22⋊C4—33no—
58C2×C5×C22⋊C4—36no—
59C2×C5×C22⋊C4—31no—
60C2×C42×C5—33no—
61C2×#548—31noSylow
62C22×C5×D3—43no—
63C2×C5×A4#4112yescomplemented
64C2×C5×A4C2411yescharacteristic
65C5×S4—26no—
66C3×C5×Q8—44no—
67C2×C3×C4×C5—43no—
68C2×C5×Dic3—41no—
69C5×D12—412no—
70C4×C5×D3—412no—
71C22×S4C22×C513yes—
72C2×#239—41no—
73Q8×A4C22×C514yescomplemented
74C2×C4×A4C22×C513yes—
75C2×SL(2,ℤ/4)C22×C511yescharacteristic
76C4⋊S4C22×C5112yescomplemented
77C4×S4C22×C5112yescomplemented
78C24×C5—33no—
79C24×C5C22×D311yescharacteristic
80C5×#41—624no—
81C5×#41—68no—
82C2×C5×Q8—34no—
83C2×C5×Q8—34no—
84C2×C5×Q8—312no—
85C2×C5×Q8—33no—
86C2×C5×Q8—61no—
87C2×C5×Q8—66no—
88C2×C5×Q8S411yescharacteristic, complemented
89C2×C5×D4—36no—
90C2×C5×D4—312no—
91C2×C5×D4—36no—
92C2×C5×D4—63no—
93C2×C5×D4—66no—
94C2×C5×D4—66no—
95C2×C5×D4—66no—
96C2×C5×D4—63no—
97C22×C4×C5—33no—
98C22×C4×C5—33no—
99C22×C4×C5—36no—
100C22×C4×C5—31no—
101C22×C4×C5—33no—
102C22×C4×C5—31no—
103C22×C4×C5—312no—
104C22×C4×C5—63no—
105C22×C4×C5—66no—
106C22×C4×C5—63no—
107C22×C4×C5C22×D316yes—
108C5×C4⋊C4—312no—
109C5×C4⋊C4—312no—
110C5×C22⋊C4—32no—
111C5×C22⋊C4—312no—
112C5×C22⋊C4—324no—
113C5×C22⋊C4—32no—
114C42×C5—312no—
115C22×#41—31no—
116C23×Q8C5×D311yescharacteristic, complemented
117#548—38no—
118#548—38no—
119C2×#124—33no—
120C2×C22⋊Q8—33no—
121C2×#121—33no—
122C2×C4×Q8—31no—
123C2×C4×D4—33no—
124C22×C3×C5—41no—
125C2×C5×D3—46no—
126C2×C5×D3—86no—
127C5×A4C2×#4111yescharacteristic, complemented
128C3×C4×C5—46no—
129C5×Dic3—42no—
130C22×A4C23×C511yescharacteristic
131C2×S4—26no—
132C2×S4C23×C516yes—
133C2×C3×Q8—41no—
134#239—48no—
135C2×D12—43no—
136C2×C4×D3—43no—
137C4×A4C23×C516yes—
138SL(2,ℤ/4)C23×C512yes—
139C23×C5—31no—
140C23×C5—31no—
141C23×C5—32no—
142C23×C5—36no—
143C23×C5—63no—
144C23×C5—66no—
145C23×C5—66no—
146C23×C5—63no—
147C23×C5#23912yescomplemented
148C23×C5C23×D311yescharacteristic
149C5×Q8—312no—
150C5×Q8—64no—
151C5×Q8C2×S414yescomplemented
152C5×D4—612no—
153C5×D4—612no—
154C5×D4—66no—
155C5×D4—66no—
156C5×D4—612no—
157C2×C4×C5—33no—
158C2×C4×C5—36no—
159C2×C4×C5—36no—
160C2×C4×C5—36no—
161C2×C4×C5—32no—
162C2×C4×C5—36no—
163C2×C4×C5—32no—
164C2×C4×C5—63no—
165C2×C4×C5—612no—
166C2×C4×C5—62no—
167C2×C4×C5—61no—
168C2×C4×C5—66no—
169C2×C4×C5—61no—
170C2×C4×C5—612no—
171C2×C4×C5C2×S413yes—
172C2×#41—38no—
173C2×#41—64no—
174C2×#41—63no—
175C2×#41—61no—
176C22×Q8—31no—
177C22×Q8—33no—
178C22×Q8—34no—
179C22×Q8C2×C5×D314yescomplemented
180C22×D4—33no—
181C22×D4—33no—
182C23×C4—33no—
183C23×C4C2×C5×D313yes—
184#124—324no—
185C22⋊Q8—324no—
186#121—312no—
187#121—312no—
188C4×Q8—38no—
189C4×D4—312no—
190C4×D4—312no—
191C2×C4⋊C4—33no—
192C2×C4⋊C4—33no—
193C2×C22⋊C4—33no—
194C2×C22⋊C4—36no—
195C2×C22⋊C4—31no—
196C2×C42—33no—
197C2×C3×C5—42no—
198C2×C3×C5—41no—
199C5×D3—86no—
200C22×D3—43no—
201C2×A4C5×#4112yescomplemented
202C2×A4C24×C511yescharacteristic
203S4—26no—
204C3×Q8—44no—
205C2×C3×C4—43no—
206C2×Dic3—41no—
207D12—412no—
208C4×D3—412no—
209C22×C5—32no—
210C22×C5—31no—
211C22×C5—32no—
212C22×C5—32no—
213C22×C5—31no—
214C22×C5—31no—
215C22×C5—61no—
216C22×C5—66no—
217C22×C5—66no—
218C22×C5—66no—
219C22×C5—126no—
220C22×C5—126no—
221C22×C5C2×#23911yescharacteristic, complemented
222C22×C5C22×S411yescharacteristic
223C4×C5—36no—
224C4×C5—62no—
225C4×C5—66no—
226C4×C5—62no—
227C4×C5C22×S416yes—
228C24—33no—
229C24C22×C5×D311yescharacteristic
230#41—624no—
231#41—68no—
232C2×Q8—34no—
233C2×Q8—34no—
234C2×Q8—312no—
235C2×Q8—33no—
236C2×Q8—61no—
237C2×Q8—66no—
238C2×Q8C5×S411yescharacteristic, complemented
239C2×D4—36no—
240C2×D4—312no—
241C2×D4—36no—
242C2×D4—63no—
243C2×D4—66no—
244C2×D4—66no—
245C2×D4—66no—
246C2×D4—63no—
247C22×C4—33no—
248C22×C4—33no—
249C22×C4—36no—
250C22×C4—31no—
251C22×C4—33no—
252C22×C4—31no—
253C22×C4—312no—
254C22×C4—63no—
255C22×C4—66no—
256C22×C4—63no—
257C22×C4C22×C5×D316yes—
258C4⋊C4—312no—
259C4⋊C4—312no—
260C22⋊C4—32no—
261C22⋊C4—312no—
262C22⋊C4—324no—
263C22⋊C4—32no—
264C42—312no—
265C3×C5—41noHall
266C22×C3—41no—
267C2×D3—46no—
268C2×D3—86no—
269A4C2×C5×#4111yescharacteristic, complemented
270C3×C4—46no—
271Dic3—42no—
272C2×C5—31no—
273C2×C5—31no—
274C2×C5—32no—
275C2×C5—126no—
276C2×C5#591912yesdirect product factor
277C2×C5C23×S411yescharacteristic
278C23—31no—
279C23—31no—
280C23—32no—
281C23—36no—
282C23—63no—
283C23—66no—
284C23—66no—
285C23—63no—
286C23C5×#23912yescomplemented
287C23C23×C5×D311yescharacteristic
288Q8—312no—
289Q8—64no—
290Q8C2×C5×S414yescomplemented
291D4—612no—
292D4—612no—
293D4—66no—
294D4—66no—
295D4—612no—
296C2×C4—33no—
297C2×C4—36no—
298C2×C4—36no—
299C2×C4—36no—
300C2×C4—32no—
301C2×C4—36no—
302C2×C4—32no—
303C2×C4—63no—
304C2×C4—612no—
305C2×C4—61no—
306C2×C4—66no—
307C2×C4—62no—
308C2×C4—61no—
309C2×C4—612no—
310C2×C4C2×C5×S413yes—
311C2×C3—42no—
312C2×C3—41no—
313D3—86no—
314C5C2×#591911yescharacteristic, direct product factor, Sylow
315C22—32no—
316C22—31no—
317C22—32no—
318C22—32no—
319C22—31no—
320C22—31no—
321C22—61no—
322C22—66no—
323C22—66no—
324C22—66no—
325C22—126no—
326C22—126no—
327C22C2×C5×#23911yescharacteristic, complemented
328C22C22×C5×S411yescharacteristic
329C4—36no—
330C4—66no—
331C4—62no—
332C4—62no—
333C4C22×C5×S416yes—
334C3—41noSylow
335C2—31no—
336C2—31no—
337C2—32no—
338C2—126no—
339C2C5×#591912yesdirect product factor
340C2C23×C5×S411yescharacteristic
subgroupG/H
centerC22×C5C22×S4
commutator, cosocleC2×A4C24×C5
FrattiniC2C23×C5×S4
FittingC23×C5×Q8D3
socleC24×C5C22×D3
hypercenterC2×C5×Q8S4
hypocenterA4C2×C5×#41
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C2×C5×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×Q8×A4C2semidirect
2. C5×#5919C2direct (N × H)
3. C2×C5×C4⋊S4C2semidirect
4. C2×C4×C5×S4C2semidirect
8. C5×Q8×A4C22semidirect
11. C5×C4⋊S4C22semidirect
12. C4×C5×S4C22semidirect
13. C2×#5919C5direct (N × H)
15. C23×C5×Q8D3semidirect
32. C2×Q8×A4C2×C5semidirect
33. #5919C2×C5direct (N × H)
34. C2×C4⋊S4C2×C5semidirect
35. C2×C4×S4C2×C5semidirect
43. C22×C5×Q8C2×D3semidirect
63. C2×C5×A4#41semidirect
73. Q8×A4C22×C5semidirect
76. C4⋊S4C22×C5semidirect
77. C4×S4C22×C5semidirect
88. C2×C5×Q8S4semidirect
116. C23×Q8C5×D3semidirect
127. C5×A4C2×#41semidirect
147. C23×C5#239semidirect
151. C5×Q8C2×S4semidirect
179. C22×Q8C2×C5×D3semidirect
201. C2×A4C5×#41semidirect
221. C22×C5C2×#239semidirect
238. C2×Q8C5×S4semidirect
269. A4C2×C5×#41semidirect
276. C2×C5#5919direct (N × H)
286. C23C5×#239semidirect
290. Q8C2×C5×S4semidirect
314. C5C2×#5919direct (N × H)
327. C22C2×C5×#239semidirect
339. C2C5×#5919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×Q8×A42
C5×#59192
C2×C5×C4⋊S42
C2×C4×C5×S42
C2×C5×#5483
C2×C5×#2394
C2×#59195