Finite Group Databasebeta

← C22×C5×D3×C4⋊C4 #14478700

Subgroups — C22×C5×D3×C4⋊C4 #14478700

Order 1920.

4976 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C5×D3C212yesmaximal
2C23×C4×C5×D3C211yesmaximal, characteristic
3C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C22×C5×Dic3⋊C4C212yesmaximal, complemented
6C2×C5×D3×C4⋊C4C2124yesmaximal, direct product factor
7C23×C5×C4⋊C4—31nomaximal, Hall
8C24×C5×D3C2211yescharacteristic
9C23×C3×C4×C5C2212yes—
10C23×C3×C4×C5C2211yescharacteristic
11C23×C5×Dic3C2212yes—
12C23×C5×Dic3C2211yescharacteristic
13C22×C4×C5×D3—216no—
14C22×C4×C5×D3C4116yescomplemented
15C22×C4×C5×D3C22124yes—
16C22×C4×C5×D3C22112yes—
17C2×C3×C5×C4⋊C4C22112yescomplemented
18C2×C5×C4⋊Dic3C22112yescomplemented
19C2×C5×Dic3⋊C4C22124yescomplemented
20C5×D3×C4⋊C4C22164yesdirect product factor
21C22×D3×C4⋊C4C511yesmaximal, characteristic, direct product factor, Hall
22C24×C4×C5—31no—
23C24×C4×C5—32no—
24C22×C5×C4⋊C4—32no—
25C22×C5×C4⋊C4—31no—
26C22×C5×C4⋊C4—324no—
27C22×C5×C4⋊C4D311yescharacteristic, direct product factor
28C24×C3×C5C2311yescharacteristic
29C23×C5×D3C2×C418yes—
30C23×C5×D3D418yes—
31C23×C5×D3Q818yes—
32C23×C5×D3C2316yes—
33C22×C3×C4×C5—28no—
34C22×C3×C4×C5C2×C418yescomplemented
35C22×C3×C4×C5C23112yes—
36C22×C3×C4×C5C2316yes—
37C22×C5×Dic3—28no—
38C22×C5×Dic3C2×C418yescomplemented
39C22×C5×Dic3C23112yes—
40C22×C5×Dic3C2316yes—
41C2×C4×C5×D3—296no—
42C2×C4×C5×D3C2×C4196yescomplemented
43C2×C4×C5×D3C23132yes—
44C2×C4×C5×D3C23116yes—
45C3×C5×C4⋊C4C23116yescomplemented
46C5×C4⋊Dic3C23116yescomplemented
47C5×Dic3⋊C4C23132yescomplemented
48C23×C4×D3C2×C512yes—
49C23×C4×D3C2×C511yescharacteristic
50C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
51C22×C4⋊Dic3C2×C511yescharacteristic, complemented
52C22×Dic3⋊C4C2×C512yescomplemented
53C2×D3×C4⋊C4C2×C5124yesdirect product factor
54C25×C5—31no—
55C23×C4×C5—31no—
56C23×C4×C5—316no—
57C23×C4×C5—312no—
58C23×C4×C5—32no—
59C23×C4×C5—324no—
60C23×C4×C5—616no—
61C23×C4×C5C2×D312yes—
62C23×C4×C5C2×D311yescharacteristic
63C2×C5×C4⋊C4—324no—
64C2×C5×C4⋊C4—312no—
65C2×C5×C4⋊C4—364no—
66C2×C5×C4⋊C4C2×D3112yesdirect product factor
67C23×C4⋊C4—31noSylow
68C23×C3×C5C22×C414yes—
69C23×C3×C5C2×D414yes—
70C23×C3×C5C2×Q814yes—
71C23×C3×C5C2413yes—
72C22×C5×D3C4⋊C4164yesdirect product factor
73C22×C5×D3C22×C4124yes—
74C22×C5×D3C2×D4124yes—
75C22×C5×D3C2×Q8124yes—
76C22×C5×D3C2414yes—
77C2×C3×C4×C5—224no—
78C2×C3×C4×C5C22×C4124yescomplemented
79C2×C3×C4×C5C2418yes—
80C2×C3×C4×C5C2414yes—
81C2×C5×Dic3—224no—
82C2×C5×Dic3C22×C4124yescomplemented
83C2×C5×Dic3C2418yes—
84C2×C5×Dic3C2414yes—
85C4×C5×D3—264no—
86C4×C5×D3C22×C4164yescomplemented
87C24×D3C22×C511yescharacteristic
88C23×C3×C4C22×C512yes—
89C23×C3×C4C22×C511yescharacteristic
90C23×Dic3C22×C512yes—
91C23×Dic3C22×C511yescharacteristic
92C22×C4×D3—216no—
93C22×C4×D3C4×C5116yescomplemented
94C22×C4×D3C22×C5124yes—
95C22×C4×D3C22×C5112yes—
96C2×C3×C4⋊C4C22×C5112yescomplemented
97C2×C4⋊Dic3C22×C5112yescomplemented
98C2×Dic3⋊C4C22×C5124yescomplemented
99D3×C4⋊C4C22×C5164yesdirect product factor
100C24×C5—38no—
101C24×C5—38no—
102C24×C5—38no—
103C24×C5—36no—
104C24×C5C22×D311yescharacteristic
105C22×C4×C5—28no—
106C22×C4×C5—38no—
107C22×C4×C5—36no—
108C22×C4×C5—396no—
109C22×C4×C5—316no—
110C22×C4×C5—312no—
111C22×C4×C5—332no—
112C22×C4×C5—696no—
113C22×C4×C5—68no—
114C22×C4×C5C4×D318yescomplemented
115C22×C4×C5C22×D3112yes—
116C22×C4×C5C22×D316yes—
117C5×C4⋊C4—332no—
118C5×C4⋊C4—316no—
119C5×C4⋊C4C22×D3116yesdirect product factor
120C24×C4—31no—
121C24×C4—32no—
122C22×C4⋊C4—32no—
123C22×C4⋊C4—31no—
124C22×C4⋊C4—324no—
125C22×C4⋊C4C5×D311yescharacteristic, direct product factor
126C22×C3×C5C2×C4⋊C4116yescomplemented
127C22×C3×C5C23×C416yes—
128C22×C3×C5C22×D416yes—
129C22×C3×C5C22×Q816yes—
130C22×C3×C5C2511yescharacteristic
131C2×C5×D3C2×C4⋊C4196yesdirect product factor
132C2×C5×D3C23×C418yes—
133C2×C5×D3C22×D418yes—
134C2×C5×D3C22×Q818yes—
135C3×C4×C5—28no—
136C3×C4×C5C23×C418yescomplemented
137C5×Dic3—28no—
138C5×Dic3C23×C418yescomplemented
139C24×C3C23×C511yescharacteristic
140C23×D3C2×C4×C518yes—
141C23×D3C5×D418yes—
142C23×D3C5×Q818yes—
143C23×D3C23×C516yes—
144C22×C3×C4—28no—
145C22×C3×C4C2×C4×C518yescomplemented
146C22×C3×C4C23×C5112yes—
147C22×C3×C4C23×C516yes—
148C22×Dic3—28no—
149C22×Dic3C2×C4×C518yescomplemented
150C22×Dic3C23×C5112yes—
151C22×Dic3C23×C516yes—
152C2×C4×D3—296no—
153C2×C4×D3C2×C4×C5196yescomplemented
154C2×C4×D3C23×C5132yes—
155C2×C4×D3C23×C5116yes—
156C3×C4⋊C4C23×C5116yescomplemented
157C4⋊Dic3C23×C5116yescomplemented
158Dic3⋊C4C23×C5132yescomplemented
159C23×C5—364no—
160C23×C5—324no—
161C23×C5—324no—
162C23×C5—324no—
163C23×C5—34no—
164C23×C5C2×C4×D314yes—
165C23×C5D3×D414yes—
166C23×C5D3×Q814yes—
167C23×C5C23×D313yes—
168C2×C4×C5—224no—
169C2×C4×C5—324no—
170C2×C4×C5—34no—
171C2×C4×C5—364no—
172C2×C4×C5—38no—
173C2×C4×C5—664no—
174C2×C4×C5—624no—
175C2×C4×C5C2×C4×D3124yescomplemented
176C2×C4×C5C23×D318yes—
177C2×C4×C5C23×D314yes—
178C25—31no—
179C23×C4—31no—
180C23×C4—316no—
181C23×C4—312no—
182C23×C4—32no—
183C23×C4—324no—
184C23×C4—616no—
185C23×C4C2×C5×D312yes—
186C23×C4C2×C5×D311yescharacteristic
187C2×C4⋊C4—324no—
188C2×C4⋊C4—312no—
189C2×C4⋊C4—364no—
190C2×C4⋊C4C2×C5×D3112yesdirect product factor
191C2×C3×C5C22×C4⋊C4112yescomplemented
192C2×C3×C5C24×C411yescharacteristic
193C2×C3×C5C23×D411yescharacteristic
194C2×C3×C5C23×Q811yescharacteristic
195C5×D3C22×C4⋊C4116yesdirect product factor
196C23×C3C22×C4×C514yes—
197C23×C3C2×C5×D414yes—
198C23×C3C2×C5×Q814yes—
199C23×C3C24×C513yes—
200C22×D3C5×C4⋊C4164yesdirect product factor
201C22×D3C22×C4×C5124yes—
202C22×D3C2×C5×D4124yes—
203C22×D3C2×C5×Q8124yes—
204C22×D3C24×C514yes—
205C2×C3×C4—224no—
206C2×C3×C4C22×C4×C5124yescomplemented
207C2×C3×C4C24×C518yes—
208C2×C3×C4C24×C514yes—
209C2×Dic3—224no—
210C2×Dic3C22×C4×C5124yescomplemented
211C2×Dic3C24×C518yes—
212C2×Dic3C24×C514yes—
213C4×D3—264no—
214C4×D3C22×C4×C5164yescomplemented
215C22×C5—38no—
216C22×C5—38no—
217C22×C5—38no—
218C22×C5—396no—
219C22×C5D3×C4⋊C4116yesdirect product factor
220C22×C5C22×C4×D316yes—
221C22×C5C2×D3×D416yes—
222C22×C5C2×D3×Q816yes—
223C22×C5C24×D311yescharacteristic
224C4×C5—28no—
225C4×C5—38no—
226C4×C5—68no—
227C4×C5C22×C4×D318yescomplemented
228C24—38no—
229C24—38no—
230C24—38no—
231C24—36no—
232C24C22×C5×D311yescharacteristic
233C22×C4—28no—
234C22×C4—38no—
235C22×C4—36no—
236C22×C4—396no—
237C22×C4—316no—
238C22×C4—312no—
239C22×C4—332no—
240C22×C4—696no—
241C22×C4—68no—
242C22×C4C4×C5×D318yescomplemented
243C22×C4C22×C5×D3112yes—
244C22×C4C22×C5×D316yes—
245C4⋊C4—332no—
246C4⋊C4—316no—
247C4⋊C4C22×C5×D3116yesdirect product factor
248C3×C5C23×C4⋊C411yescharacteristic, complemented, Hall
249C22×C3C2×C5×C4⋊C4116yescomplemented
250C22×C3C23×C4×C516yes—
251C22×C3C22×C5×D416yes—
252C22×C3C22×C5×Q816yes—
253C22×C3C25×C511yescharacteristic
254C2×D3C2×C5×C4⋊C4196yesdirect product factor
255C2×D3C23×C4×C518yes—
256C2×D3C22×C5×D418yes—
257C2×D3C22×C5×Q818yes—
258C3×C4—28no—
259C3×C4C23×C4×C518yescomplemented
260Dic3—28no—
261Dic3C23×C4×C518yescomplemented
262C2×C5—316no—
263C2×C5C2×D3×C4⋊C4112yesdirect product factor
264C2×C5C23×C4×D311yescharacteristic
265C2×C5C22×D3×D411yescharacteristic
266C2×C5C22×D3×Q811yescharacteristic
267C23—364no—
268C23—324no—
269C23—324no—
270C23—324no—
271C23—34no—
272C23C2×C4×C5×D314yes—
273C23C5×D3×D414yes—
274C23C5×D3×Q814yes—
275C23C23×C5×D313yes—
276C2×C4—224no—
277C2×C4—324no—
278C2×C4—34no—
279C2×C4—364no—
280C2×C4—38no—
281C2×C4—664no—
282C2×C4—624no—
283C2×C4C2×C4×C5×D3124yescomplemented
284C2×C4C23×C5×D318yes—
285C2×C4C23×C5×D314yes—
286C2×C3C22×C5×C4⋊C4112yescomplemented
287C2×C3C24×C4×C511yescharacteristic
288C2×C3C23×C5×D411yescharacteristic
289C2×C3C23×C5×Q811yescharacteristic
290D3C22×C5×C4⋊C4116yesdirect product factor
291C5C22×D3×C4⋊C411yescharacteristic, direct product factor, Sylow
292C22—38no—
293C22—38no—
294C22—38no—
295C22—396no—
296C22C5×D3×C4⋊C4116yesdirect product factor
297C22C22×C4×C5×D316yes—
298C22C2×C5×D3×D416yes—
299C22C2×C5×D3×Q816yes—
300C22C24×C5×D311yescharacteristic
301C4—28no—
302C4—38no—
303C4—68no—
304C4C22×C4×C5×D318yescomplemented
305C3C23×C5×C4⋊C411yescharacteristic, complemented, Sylow
306C2—316no—
307C2C2×C5×D3×C4⋊C4112yesdirect product factor
308C2C23×C4×C5×D311yescharacteristic
309C2C22×C5×D3×D411yescharacteristic
310C2C22×C5×D3×Q811yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC2×C3C24×C4×C5
FrattiniC22C24×C5×D3
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5C23
prime radicalC24×C5×D3C22
cosocleC22×C3C25×C5
hypercenterC22×C5×C4⋊C4D3
hypocenterC3C23×C5×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C3×C5×C4⋊C4C2semidirect
4. C22×C5×C4⋊Dic3C2semidirect
5. C22×C5×Dic3⋊C4C2semidirect
6. C2×C5×D3×C4⋊C4C2direct (N × H)
14. C22×C4×C5×D3C4semidirect
17. C2×C3×C5×C4⋊C4C22semidirect
18. C2×C5×C4⋊Dic3C22semidirect
19. C2×C5×Dic3⋊C4C22semidirect
20. C5×D3×C4⋊C4C22direct (N × H)
21. C22×D3×C4⋊C4C5direct (N × H)
27. C22×C5×C4⋊C4D3direct (N × H)
34. C22×C3×C4×C5C2×C4semidirect
38. C22×C5×Dic3C2×C4semidirect
42. C2×C4×C5×D3C2×C4semidirect
45. C3×C5×C4⋊C4C23semidirect
46. C5×C4⋊Dic3C23semidirect
47. C5×Dic3⋊C4C23semidirect
50. C22×C3×C4⋊C4C2×C5semidirect
51. C22×C4⋊Dic3C2×C5semidirect
52. C22×Dic3⋊C4C2×C5semidirect
53. C2×D3×C4⋊C4C2×C5direct (N × H)
66. C2×C5×C4⋊C4C2×D3direct (N × H)
72. C22×C5×D3C4⋊C4direct (N × H)
78. C2×C3×C4×C5C22×C4semidirect
82. C2×C5×Dic3C22×C4semidirect
86. C4×C5×D3C22×C4semidirect
93. C22×C4×D3C4×C5semidirect
96. C2×C3×C4⋊C4C22×C5semidirect
97. C2×C4⋊Dic3C22×C5semidirect
98. C2×Dic3⋊C4C22×C5semidirect
99. D3×C4⋊C4C22×C5direct (N × H)
114. C22×C4×C5C4×D3semidirect
119. C5×C4⋊C4C22×D3direct (N × H)
125. C22×C4⋊C4C5×D3direct (N × H)
126. C22×C3×C5C2×C4⋊C4semidirect
131. C2×C5×D3C2×C4⋊C4direct (N × H)
136. C3×C4×C5C23×C4semidirect
138. C5×Dic3C23×C4semidirect
145. C22×C3×C4C2×C4×C5semidirect
149. C22×Dic3C2×C4×C5semidirect
153. C2×C4×D3C2×C4×C5semidirect
156. C3×C4⋊C4C23×C5semidirect
157. C4⋊Dic3C23×C5semidirect
158. Dic3⋊C4C23×C5semidirect
175. C2×C4×C5C2×C4×D3semidirect
190. C2×C4⋊C4C2×C5×D3direct (N × H)
191. C2×C3×C5C22×C4⋊C4semidirect
195. C5×D3C22×C4⋊C4direct (N × H)
200. C22×D3C5×C4⋊C4direct (N × H)
206. C2×C3×C4C22×C4×C5semidirect
210. C2×Dic3C22×C4×C5semidirect
214. C4×D3C22×C4×C5semidirect
219. C22×C5D3×C4⋊C4direct (N × H)
227. C4×C5C22×C4×D3semidirect
242. C22×C4C4×C5×D3semidirect
247. C4⋊C4C22×C5×D3direct (N × H)
248. C3×C5C23×C4⋊C4semidirect
249. C22×C3C2×C5×C4⋊C4semidirect
254. C2×D3C2×C5×C4⋊C4direct (N × H)
259. C3×C4C23×C4×C5semidirect
261. Dic3C23×C4×C5semidirect
263. C2×C5C2×D3×C4⋊C4direct (N × H)
283. C2×C4C2×C4×C5×D3semidirect
286. C2×C3C22×C5×C4⋊C4semidirect
290. D3C22×C5×C4⋊C4direct (N × H)
291. C5C22×D3×C4⋊C4direct (N × H)
296. C22C5×D3×C4⋊C4direct (N × H)
304. C4C22×C4×C5×D3semidirect
305. C3C23×C5×C4⋊C4semidirect
307. C2C2×C5×D3×C4⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C5×D32
C22×C3×C5×C4⋊C42
C22×C5×C4⋊Dic32
C22×C5×Dic3⋊C42
C2×C5×D3×C4⋊C42
C23×C5×C4⋊C43
C22×D3×C4⋊C45