Finite Group Databasebeta

← C2×#11755220 #14479109

Subgroups — C2×#11755220 #14479109

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#239C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
4#11755220C2116yesmaximal, direct product factor
5C2×#91435C213yesmaximal, complemented
6C2×D3×C4⋊Dic5C213yesmaximal, complemented
7C2×Dic5×D12C213yesmaximal, complemented
8C2×#91371C213yesmaximal, complemented
9C2×#66161—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C5×#239C4116yescomplemented
12C2×C5×#239C2218yes—
13C22×C5×D12C2213yes—
14C22×C4×C5×D3C2213yes—
15C22×D3×Dic5C2216yes—
16Q8×Dic15C2218yescomplemented
17C2×C4⋊Dic15C2213yes—
18C2×C4×Dic15C2213yes—
19C3×Q8×Dic5C2218yescomplemented
20C2×C3×C4⋊Dic5C2213yes—
21C2×C3×C4×Dic5C2213yes—
22C2×Dic3⋊Dic5C2211yescharacteristic
23C2×Dic3⋊Dic5C2213yes—
24C2×(C2×D3)⋊Dic5C2213yes—
25C2×(C2×D3)⋊Dic5C2213yes—
26#91435C22124yescomplemented
27D3×C4⋊Dic5C22124yescomplemented
28Dic5×D12C22124yescomplemented
29#91371C22124yescomplemented
30C2×#5574—51nomaximal, Hall
31C22×C5×#41—31no—
32#66161—316no—
33C2×Q8×Dic5—31no—
34C2×Q8×Dic5D311yescharacteristic, complemented
35C2×D4×Dic5—33no—
36C2×D4×Dic5—33no—
37C2×#4072—33no—
38C22×C4⋊Dic5—33no—
39C23×C5×D3C2313yes—
40C2×C3×C5×Q8C2×C418yescomplemented
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44C22×Dic15C2311yescharacteristic
45C22×C5×Dic3C2311yescharacteristic
46C5×#239C2×C4164yescomplemented
47C2×C5×D12C2×C4124yescomplemented
48C2×C5×D12C23112yes—
49C2×C4×C5×D3C2×C4124yescomplemented
50C2×C4×C5×D3C23112yes—
51C22×C3×Dic5C2313yes—
52C22×C3×Dic5C2311yescharacteristic
53C2×D3×Dic5—412no—
54C2×D3×Dic5C23124yes—
55C4⋊Dic15C23112yes—
56C4×Dic15C23112yes—
57C3×C4⋊Dic5C23112yes—
58C3×C4×Dic5C23112yes—
59Dic3⋊Dic5C23112yes—
60Dic3⋊Dic5C2314yes—
61(C2×D3)⋊Dic5C23112yes—
62(C2×D3)⋊Dic5C23112yes—
63C22×#239D511yescharacteristic
64C2×C3×C4×Q8—51no—
65C2×Q8×Dic3—51no—
66#5574—516no—
67C2×#893—53no—
68C2×D3×C4⋊C4—53no—
69C2×C4×D12—53no—
70C2×#872—53no—
71C2×C5×#41—316no—
72C2×C5×#41—38no—
73C22×C5×Q8C2×D311yescharacteristic
74C22×C5×D4—33no—
75C23×C4×C5—33no—
76C23×Dic5—36no—
77C2×C22⋊Dic5—33no—
78C2×C22⋊Dic5—33no—
79Q8×Dic5—38no—
80Q8×Dic5C2×D318yescomplemented
81D4×Dic5—324no—
82D4×Dic5—324no—
83#4072—324no—
84C2×C4⋊Dic5—33no—
85C2×C4⋊Dic5—33no—
86C2×C4⋊Dic5—31no—
87C2×C4⋊Dic5—324no—
88C2×C4⋊Dic5C2×D313yes—
89C2×C4×Dic5—33no—
90C2×C4×Dic5C2×D313yes—
91C2×#520—151noSylow
92C23×C3×C5C2411yescharacteristic
93C22×C5×D3—26no—
94C22×C5×D3—26no—
95C22×C5×D3C22×C4112yes—
96C22×C5×D3C2416yes—
97C3×C5×Q8C22×C4116yescomplemented
98C2×C3×C4×C5C22×C4112yes—
99C2×C3×C4×C5C2416yes—
100C2×Dic15—26no—
101C2×Dic15—22no—
102C2×Dic15C2412yes—
103C2×Dic15C2416yes—
104C2×C5×Dic3C22×C414yes—
105C2×C5×Dic3C2412yes—
106C5×D12C22×C4148yescomplemented
107C4×C5×D3C22×C4148yescomplemented
108C2×C3×Dic5—26no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5C2412yes—
111C2×C3×Dic5C2416yes—
112D3×Dic5—424no—
113C22×C3×Q8C2×D511yescharacteristic
114C2×#239Dic5116yescomplemented
115C2×#239C2×D518yes—
116C22×D12C2×D513yes—
117C22×C4×D3—56no—
118C22×C4×D3C2×D513yes—
119C3×C4×Q8—58no—
120C2×C3×C4⋊C4—53no—
121C2×C3×C42—53no—
122Q8×Dic3—58no—
123C2×(C2×D3)⋊C4—53no—
124C2×(C2×D3)⋊C4—53no—
125C2×C4⋊Dic3—53no—
126C2×Dic3⋊C4—51no—
127C2×Dic3⋊C4—53no—
128C2×C4×Dic3—53no—
129#893—524no—
130D3×C4⋊C4—524no—
131C4×D12—524no—
132#872—524no—
133C24×C5—33no—
134C5×#41—364no—
135C2×C5×Q8C4×D318yescomplemented
136C2×C5×Q8C22×D314yes—
137C2×C5×D4—324no—
138C2×C5×D4—312no—
139C22×C4×C5—31no—
140C22×C4×C5—324no—
141C22×C4×C5—312no—
142C22×C4×C5C22×D313yes—
143C22×Dic5—31no—
144C22×Dic5—33no—
145C22×Dic5—324no—
146C22×Dic5—1212no—
147C22×Dic5C22×D311yescharacteristic
148C22×Dic5C22×D313yes—
149C22⋊Dic5—312no—
150C22⋊Dic5—312no—
151C4⋊Dic5—312no—
152C4⋊Dic5—312no—
153C4⋊Dic5—34no—
154C4⋊Dic5C22×D3112yes—
155C4×Dic5—312no—
156C4×Dic5C22×D3112yes—
157C22×#41—31no—
158#520—1516no—
159C2×C4×Q8—51no—
160C2×C4×Q8—151no—
161C2×C4×D4—153no—
162C2×C4×D4—153no—
163C2×#117—153no—
164C22×C4⋊C4—153no—
165C22×C3×C5C23×C412yes—
166C22×C3×C5H(5,𝔽2)12yes—
167C22×C3×C52−1+412yes—
168C22×C3×C5C2511yescharacteristic
169C2×C5×D3—224no—
170C2×C5×D3—26no—
171C2×C5×D3—26no—
172C2×C5×D3C23×C4112yes—
173C3×C4×C5C23×C4112yes—
174Dic15—26no—
175Dic15—22no—
176C3×Dic5—26no—
177C3×Dic5—22no—
178C5×Dic3C23×C414yes—
179C23×D3C22×D513yes—
180C2×C3×Q8C2×Dic518yescomplemented
181C2×C3×Q8C22×D514yes—
182C22×C3×C4—51no—
183C22×C3×C4—53no—
184C22×C3×C4C22×D513yes—
185C22×Dic3—51no—
186C22×Dic3—53no—
187C22×Dic3C22×D511yescharacteristic
188#239C2×Dic5164yescomplemented
189C2×D12C2×Dic5124yescomplemented
190C2×D12C22×D5112yes—
191C2×C4×D3—524no—
192C2×C4×D3—2012no—
193C2×C4×D3C2×Dic5124yescomplemented
194C2×C4×D3C22×D5112yes—
195C3×C4⋊C4—512no—
196C3×C42—512no—
197(C2×D3)⋊C4—512no—
198(C2×D3)⋊C4—512no—
199C4⋊Dic3—512no—
200Dic3⋊C4—54no—
201Dic3⋊C4—512no—
202C4×Dic3—512no—
203C23×C5—312no—
204C23×C5—36no—
205C23×C5—66no—
206C23×C5—66no—
207C23×C5C23×D311yescharacteristic
208C5×Q8C2×C4×D3116yescomplemented
209C5×D4—348no—
210C2×C4×C5—34no—
211C2×C4×C5—32no—
212C2×C4×C5—348no—
213C2×C4×C5C2×C4×D3112yes—
214C2×C4×C5C23×D316yes—
215C2×Dic5—22no—
216C2×Dic5—26no—
217C2×Dic5—32no—
218C2×Dic5—36no—
219C2×Dic5—62no—
220C2×Dic5—66no—
221C2×Dic5—1224no—
222C2×Dic5C23×D312yes—
223C2×Dic5C23×D316yes—
224C2×#41—316no—
225C2×#41—38no—
226C22×Q8D3×D511yescharacteristic
227C22×D4—33no—
228C23×C4—33no—
229C23×C4—156no—
230C4×Q8—58no—
231C4×Q8—158no—
232C4×D4—1524no—
233C4×D4—1524no—
234#117—1524no—
235C2×C4⋊C4—53no—
236C2×C4⋊C4—1524no—
237C2×C4⋊C4—153no—
238C2×C4⋊C4—151no—
239C2×C4⋊C4—153no—
240C2×C22⋊C4—153no—
241C2×C22⋊C4—153no—
242C2×C42—53no—
243C2×C42—153no—
244C2×C3×C5#52014yescomplemented
245C2×C3×C5C24×C411yescharacteristic
246C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
247C2×C3×C5C2×2−1+411yescharacteristic
248C5×D3—212no—
249C23×C3C23×D511yescharacteristic
250C22×D3—26no—
251C22×D3—26no—
252C22×D3C22×Dic5112yes—
253C22×D3C23×D516yes—
254C3×Q8C22×Dic5116yescomplemented
255C2×C3×C4—52no—
256C2×C3×C4—56no—
257C2×C3×C4—106no—
258C2×C3×C4—102no—
259C2×C3×C4C22×Dic5112yes—
260C2×C3×C4C23×D516yes—
261C2×Dic3—52no—
262C2×Dic3—56no—
263C2×Dic3—106no—
264C2×Dic3—102no—
265C2×Dic3C22×Dic514yes—
266C2×Dic3C23×D512yes—
267D12C22×Dic5148yescomplemented
268C4×D3—2024no—
269C4×D3C22×Dic5148yescomplemented
270C22×C5—312no—
271C22×C5—66no—
272C22×C5—66no—
273C22×C5—624no—
274C22×C5C22×C4×D312yes—
275C22×C5#100712yes—
276C22×C5#100912yes—
277C22×C5C24×D311yescharacteristic
278C4×C5—34no—
279C4×C5C22×C4×D3112yes—
280Dic5—22no—
281Dic5—26no—
282Dic5—62no—
283Dic5—66no—
284C24—33no—
285#41—364no—
286C2×Q8D3×Dic518yescomplemented
287C2×Q8C2×D3×D514yes—
288C2×D4—324no—
289C2×D4—312no—
290C22×C4—31no—
291C22×C4—324no—
292C22×C4—312no—
293C22×C4—51no—
294C22×C4—53no—
295C22×C4—1524no—
296C22×C4—151no—
297C22×C4—153no—
298C22×C4—6012no—
299C22×C4C2×D3×D513yes—
300C4⋊C4—512no—
301C4⋊C4—1512no—
302C4⋊C4—154no—
303C4⋊C4—1512no—
304C22⋊C4—1512no—
305C22⋊C4—1512no—
306C42—512no—
307C42—1512no—
308C3×C5C2×#52011yescharacteristic, complemented, Hall
309C22×C3#414912yes—
310C22×C3#415012yes—
311C22×C3C23×Dic512yes—
312C22×C3C24×D511yescharacteristic
313C2×D3—224no—
314C2×D3—26no—
315C2×D3—26no—
316C2×D3C23×Dic5112yes—
317C3×C4—106no—
318C3×C4—102no—
319C3×C4C23×Dic5112yes—
320Dic3—106no—
321Dic3—102no—
322Dic3C23×Dic514yes—
323C2×C5—612no—
324C2×C5#557414yescomplemented
325C2×C5C23×C4×D311yescharacteristic
326C2×C5C2×#100711yescharacteristic
327C2×C5C2×#100911yescharacteristic
328C23—312no—
329C23—36no—
330C23—66no—
331C23—66no—
332C23C22×D3×D511yescharacteristic
333Q8C2×D3×Dic5116yescomplemented
334D4—348no—
335C2×C4—34no—
336C2×C4—32no—
337C2×C4—348no—
338C2×C4—52no—
339C2×C4—56no—
340C2×C4—102no—
341C2×C4—106no—
342C2×C4—152no—
343C2×C4—156no—
344C2×C4—302no—
345C2×C4—306no—
346C2×C4—6024no—
347C2×C4C2×D3×Dic5112yes—
348C2×C4C22×D3×D516yes—
349C2×C3#6616114yescomplemented
350C2×C3C2×#414911yescharacteristic
351C2×C3C2×#415011yescharacteristic
352C2×C3C24×Dic511yescharacteristic
353D3—212no—
354C5C2×#557411yescharacteristic, complemented, Sylow
355C22—312no—
356C22—624no—
357C22—66no—
358C22—66no—
359C22#9203012yes—
360C22#9203512yes—
361C22C22×D3×Dic512yes—
362C22C23×D3×D511yescharacteristic
363C4—34no—
364C4—102no—
365C4—106no—
366C4—302no—
367C4—306no—
368C4C22×D3×Dic5112yes—
369C3C2×#6616111yescharacteristic, complemented, Sylow
370C2—612no—
371C2#1175522014yesdirect product factor
372C2C2×#9203011yescharacteristic
373C2C2×#9203511yescharacteristic
374C2C23×D3×Dic511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C5×#239C2
cosocleC22×C3×C5C25
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×C3×Q8×Dic5C2semidirect
4. #11755220C2direct (N × H)
5. C2×#91435C2semidirect
6. C2×D3×C4⋊Dic5C2semidirect
7. C2×Dic5×D12C2semidirect
8. C2×#91371C2semidirect
11. C2×C5×#239C4semidirect
16. Q8×Dic15C22semidirect
19. C3×Q8×Dic5C22semidirect
26. #91435C22semidirect
27. D3×C4⋊Dic5C22semidirect
28. Dic5×D12C22semidirect
29. #91371C22semidirect
34. C2×Q8×Dic5D3semidirect
40. C2×C3×C5×Q8C2×C4semidirect
46. C5×#239C2×C4semidirect
47. C2×C5×D12C2×C4semidirect
49. C2×C4×C5×D3C2×C4semidirect
80. Q8×Dic5C2×D3semidirect
97. C3×C5×Q8C22×C4semidirect
106. C5×D12C22×C4semidirect
107. C4×C5×D3C22×C4semidirect
114. C2×#239Dic5semidirect
135. C2×C5×Q8C4×D3semidirect
180. C2×C3×Q8C2×Dic5semidirect
188. #239C2×Dic5semidirect
189. C2×D12C2×Dic5semidirect
193. C2×C4×D3C2×Dic5semidirect
208. C5×Q8C2×C4×D3semidirect
244. C2×C3×C5#520semidirect
254. C3×Q8C22×Dic5semidirect
267. D12C22×Dic5semidirect
269. C4×D3C22×Dic5semidirect
286. C2×Q8D3×Dic5semidirect
308. C3×C5C2×#520semidirect
324. C2×C5#5574semidirect
333. Q8C2×D3×Dic5semidirect
349. C2×C3#66161semidirect
354. C5C2×#5574semidirect
369. C3C2×#66161semidirect
371. C2#11755220direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2392
C2×Q8×Dic152
C2×C3×Q8×Dic52
#117552202
C2×#914352
C2×D3×C4⋊Dic52
C2×Dic5×D122
C2×#913712
C2×#661613
C2×#55745