Finite Group Databasebeta

← C2×#11755217 #14479107

Subgroups — C2×#11755217 #14479107

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×C3×#713C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
4#11755217C2116yesmaximal, direct product factor
5C2×#91434C213yesmaximal, complemented
6C2×Dic3×D20C213yesmaximal, complemented
7C2×D5×C4⋊Dic3C213yesmaximal, complemented
8C2×#91357C213yesmaximal, complemented
9C2×#65908—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C3×#713C4116yescomplemented
12C2×C3×#713C2218yes—
13C22×C3×D20C2213yes—
14C22×C3×C4×D5C2213yes—
15C22×D5×Dic3C2216yes—
16Q8×Dic15C2218yescomplemented
17C2×C4⋊Dic15C2213yes—
18C2×C4×Dic15C2213yes—
19C5×Q8×Dic3C2218yescomplemented
20C2×C5×C4⋊Dic3C2213yes—
21C2×C4×C5×Dic3C2213yes—
22C2×#6668C2213yes—
23C2×#6668C2211yescharacteristic
24C2×#6665C2213yes—
25C2×#6665C2213yes—
26#91434C22124yescomplemented
27Dic3×D20C22124yescomplemented
28D5×C4⋊Dic3C22124yescomplemented
29#91357C22124yescomplemented
30C2×#5827—51nomaximal, Hall
31C22×#713D311yescharacteristic
32C2×C4×C5×Q8—31no—
33C2×Q8×Dic5—31no—
34#65908—316no—
35C2×#4039—33no—
36C2×D5×C4⋊C4—33no—
37C2×C4×D20—33no—
38C2×#4018—33no—
39C23×C3×D5C2313yes—
40C2×C3×C5×Q8C2×C418yescomplemented
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44C22×Dic15C2311yescharacteristic
45C22×C5×Dic3C2311yescharacteristic
46C22×C5×Dic3C2313yes—
47C22×C3×Dic5C2311yescharacteristic
48C3×#713C2×C4164yescomplemented
49C2×C3×D20C2×C4124yescomplemented
50C2×C3×D20C23112yes—
51C2×C3×C4×D5C2×C4124yescomplemented
52C2×C3×C4×D5C23112yes—
53C2×D5×Dic3—412no—
54C2×D5×Dic3C23124yes—
55C4⋊Dic15C23112yes—
56C4×Dic15C23112yes—
57C5×C4⋊Dic3C23112yes—
58C4×C5×Dic3C23112yes—
59#6668C23112yes—
60#6668C2314yes—
61#6665C23112yes—
62#6665C23112yes—
63C22×C3×#41—51no—
64#5827—516no—
65C2×Q8×Dic3—51no—
66C2×Q8×Dic3D511yescharacteristic, complemented
67C2×D4×Dic3—53no—
68C2×D4×Dic3—53no—
69C2×#926—53no—
70C22×C4⋊Dic3—53no—
71C22×C5×Q8C2×D311yescharacteristic
72C2×#713Dic3116yescomplemented
73C2×#713C2×D318yes—
74C22×D20C2×D313yes—
75C22×C4×D5—36no—
76C22×C4×D5C2×D313yes—
77C4×C5×Q8—38no—
78C2×C5×C4⋊C4—33no—
79C2×C42×C5—33no—
80Q8×Dic5—38no—
81C2×#685—33no—
82C2×#685—33no—
83C2×C4⋊Dic5—33no—
84C2×#683—31no—
85C2×#683—33no—
86C2×C4×Dic5—33no—
87#4039—324no—
88D5×C4⋊C4—324no—
89C4×D20—324no—
90#4018—324no—
91C2×#520—151noSylow
92C23×C3×C5C2411yescharacteristic
93C22×C3×D5—26no—
94C22×C3×D5—26no—
95C22×C3×D5C22×C4112yes—
96C22×C3×D5C2416yes—
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×Dic3—26no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3C2412yes—
107C2×C5×Dic3C2416yes—
108C2×C3×Dic5C22×C414yes—
109C2×C3×Dic5C2412yes—
110C3×D20C22×C4148yescomplemented
111C3×C4×D5C22×C4148yescomplemented
112D5×Dic3—424no—
113C2×C3×#41—516no—
114C2×C3×#41—58no—
115C22×C3×Q8C2×D511yescharacteristic
116C22×C3×D4—53no—
117C23×C3×C4—53no—
118C23×Dic3—56no—
119C2×#217—53no—
120C2×#217—53no—
121Q8×Dic3—58no—
122Q8×Dic3C2×D518yescomplemented
123D4×Dic3—524no—
124D4×Dic3—524no—
125#926—524no—
126C2×C4⋊Dic3—53no—
127C2×C4⋊Dic3—53no—
128C2×C4⋊Dic3—51no—
129C2×C4⋊Dic3—524no—
130C2×C4⋊Dic3C2×D513yes—
131C2×C4×Dic3—53no—
132C2×C4×Dic3C2×D513yes—
133C23×D5C22×D313yes—
134C2×C5×Q8C2×Dic318yescomplemented
135C2×C5×Q8C22×D314yes—
136C22×C4×C5—31no—
137C22×C4×C5—33no—
138C22×C4×C5C22×D313yes—
139C22×Dic5—33no—
140C22×Dic5—31no—
141C22×Dic5C22×D311yescharacteristic
142#713C2×Dic3164yescomplemented
143C2×D20C2×Dic3124yescomplemented
144C2×D20C22×D3112yes—
145C2×C4×D5—324no—
146C2×C4×D5—1212no—
147C2×C4×D5C2×Dic3124yescomplemented
148C2×C4×D5C22×D3112yes—
149C5×C4⋊C4—312no—
150C42×C5—312no—
151#685—312no—
152#685—312no—
153C4⋊Dic5—312no—
154#683—34no—
155#683—312no—
156C4×Dic5—312no—
157C22×#41—51no—
158#520—1516no—
159C2×C4×Q8—31no—
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×C3×D5—224no—
170C2×C3×D5—26no—
171C2×C3×D5—26no—
172C2×C3×D5C23×C4112yes—
173C3×C4×C5C23×C4112yes—
174Dic15—26no—
175Dic15—22no—
176C3×Dic5C23×C414yes—
177C5×Dic3—26no—
178C5×Dic3—22no—
179C24×C3—53no—
180C3×#41—564no—
181C2×C3×Q8C4×D518yescomplemented
182C2×C3×Q8C22×D514yes—
183C2×C3×D4—524no—
184C2×C3×D4—512no—
185C22×C3×C4—51no—
186C22×C3×C4—524no—
187C22×C3×C4—512no—
188C22×C3×C4C22×D513yes—
189C22×Dic3—51no—
190C22×Dic3—53no—
191C22×Dic3—524no—
192C22×Dic3—2012no—
193C22×Dic3C22×D511yescharacteristic
194C22×Dic3C22×D513yes—
195#217—512no—
196#217—512no—
197C4⋊Dic3—512no—
198C4⋊Dic3—512no—
199C4⋊Dic3—54no—
200C4⋊Dic3C22×D5112yes—
201C4×Dic3—512no—
202C4×Dic3C22×D5112yes—
203C23×C5C23×D311yescharacteristic
204C22×D5—26no—
205C22×D5—26no—
206C22×D5C22×Dic3112yes—
207C22×D5C23×D316yes—
208C5×Q8C22×Dic3116yescomplemented
209C2×C4×C5—32no—
210C2×C4×C5—36no—
211C2×C4×C5—66no—
212C2×C4×C5—62no—
213C2×C4×C5C22×Dic3112yes—
214C2×C4×C5C23×D316yes—
215C2×Dic5—32no—
216C2×Dic5—36no—
217C2×Dic5—66no—
218C2×Dic5—62no—
219C2×Dic5C22×Dic314yes—
220C2×Dic5C23×D312yes—
221D20C22×Dic3148yescomplemented
222C4×D5—1224no—
223C4×D5C22×Dic3148yescomplemented
224C2×#41—516no—
225C2×#41—58no—
226C22×Q8D3×D511yescharacteristic
227C22×D4—53no—
228C23×C4—53no—
229C23×C4—156no—
230C4×Q8—38no—
231C4×Q8—158no—
232C4×D4—1524no—
233C4×D4—1524no—
234#117—1524no—
235C2×C4⋊C4—33no—
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—33no—
243C2×C42—153no—
244C2×C3×C5#52014yescomplemented
245C2×C3×C5C24×C411yescharacteristic
246C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
247C2×C3×C5C2×2−1+411yescharacteristic
248C3×D5—212no—
249C23×C3—512no—
250C23×C3—56no—
251C23×C3—106no—
252C23×C3—106no—
253C23×C3C23×D511yescharacteristic
254C3×Q8C2×C4×D5116yescomplemented
255C3×D4—548no—
256C2×C3×C4—54no—
257C2×C3×C4—52no—
258C2×C3×C4—548no—
259C2×C3×C4C2×C4×D5112yes—
260C2×C3×C4C23×D516yes—
261C2×Dic3—22no—
262C2×Dic3—26no—
263C2×Dic3—52no—
264C2×Dic3—56no—
265C2×Dic3—102no—
266C2×Dic3—106no—
267C2×Dic3—2024no—
268C2×Dic3C23×D512yes—
269C2×Dic3C23×D516yes—
270C22×C5#100912yes—
271C22×C5#101012yes—
272C22×C5C23×Dic312yes—
273C22×C5C24×D311yescharacteristic
274C2×D5—26no—
275C2×D5—26no—
276C2×D5—224no—
277C2×D5C23×Dic3112yes—
278C4×C5—66no—
279C4×C5—62no—
280C4×C5C23×Dic3112yes—
281Dic5—66no—
282Dic5—62no—
283Dic5C23×Dic314yes—
284C24—53no—
285#41—564no—
286C2×Q8D5×Dic318yescomplemented
287C2×Q8C2×D3×D514yes—
288C2×D4—524no—
289C2×D4—512no—
290C22×C4—31no—
291C22×C4—33no—
292C22×C4—51no—
293C22×C4—524no—
294C22×C4—512no—
295C22×C4—1524no—
296C22×C4—151no—
297C22×C4—153no—
298C22×C4—6012no—
299C22×C4C2×D3×D513yes—
300C4⋊C4—312no—
301C4⋊C4—1512no—
302C4⋊C4—154no—
303C4⋊C4—1512no—
304C22⋊C4—1512no—
305C22⋊C4—1512no—
306C42—312no—
307C42—1512no—
308C3×C5C2×#52011yescharacteristic, complemented, Hall
309C22×C3—512no—
310C22×C3—1024no—
311C22×C3—106no—
312C22×C3—106no—
313C22×C3C22×C4×D512yes—
314C22×C3#414712yes—
315C22×C3#414912yes—
316C22×C3C24×D511yescharacteristic
317C3×C4—54no—
318C3×C4C22×C4×D5112yes—
319Dic3—22no—
320Dic3—26no—
321Dic3—102no—
322Dic3—106no—
323C2×C5#582714yescomplemented
324C2×C5C2×#100911yescharacteristic
325C2×C5C2×#101011yescharacteristic
326C2×C5C24×Dic311yescharacteristic
327D5—212no—
328C23—512no—
329C23—56no—
330C23—106no—
331C23—106no—
332C23C22×D3×D511yescharacteristic
333Q8C2×D5×Dic3116yescomplemented
334D4—548no—
335C2×C4—32no—
336C2×C4—36no—
337C2×C4—54no—
338C2×C4—52no—
339C2×C4—548no—
340C2×C4—62no—
341C2×C4—66no—
342C2×C4—152no—
343C2×C4—156no—
344C2×C4—302no—
345C2×C4—306no—
346C2×C4—6024no—
347C2×C4C2×D5×Dic3112yes—
348C2×C4C22×D3×D516yes—
349C2×C3—1012no—
350C2×C3#6590814yescomplemented
351C2×C3C23×C4×D511yescharacteristic
352C2×C3C2×#414711yescharacteristic
353C2×C3C2×#414911yescharacteristic
354C5C2×#582711yescharacteristic, complemented, Sylow
355C22—512no—
356C22—1024no—
357C22—106no—
358C22—106no—
359C22#9202812yes—
360C22#9203512yes—
361C22C22×D5×Dic312yes—
362C22C23×D3×D511yescharacteristic
363C4—54no—
364C4—62no—
365C4—66no—
366C4—302no—
367C4—306no—
368C4C22×D5×Dic3112yes—
369C3C2×#6590811yescharacteristic, complemented, Sylow
370C2—1012no—
371C2#1175521714yesdirect product factor
372C2C2×#9202811yescharacteristic
373C2C2×#9203511yescharacteristic
374C2C23×D5×Dic311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC22×C3×#713C2
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×C5×Q8×Dic3C2semidirect
4. #11755217C2direct (N × H)
5. C2×#91434C2semidirect
6. C2×Dic3×D20C2semidirect
7. C2×D5×C4⋊Dic3C2semidirect
8. C2×#91357C2semidirect
11. C2×C3×#713C4semidirect
16. Q8×Dic15C22semidirect
19. C5×Q8×Dic3C22semidirect
26. #91434C22semidirect
27. Dic3×D20C22semidirect
28. D5×C4⋊Dic3C22semidirect
29. #91357C22semidirect
40. C2×C3×C5×Q8C2×C4semidirect
48. C3×#713C2×C4semidirect
49. C2×C3×D20C2×C4semidirect
51. C2×C3×C4×D5C2×C4semidirect
66. C2×Q8×Dic3D5semidirect
72. C2×#713Dic3semidirect
97. C3×C5×Q8C22×C4semidirect
110. C3×D20C22×C4semidirect
111. C3×C4×D5C22×C4semidirect
122. Q8×Dic3C2×D5semidirect
134. C2×C5×Q8C2×Dic3semidirect
142. #713C2×Dic3semidirect
143. C2×D20C2×Dic3semidirect
147. C2×C4×D5C2×Dic3semidirect
181. C2×C3×Q8C4×D5semidirect
208. C5×Q8C22×Dic3semidirect
221. D20C22×Dic3semidirect
223. C4×D5C22×Dic3semidirect
244. C2×C3×C5#520semidirect
254. C3×Q8C2×C4×D5semidirect
286. C2×Q8D5×Dic3semidirect
308. C3×C5C2×#520semidirect
323. C2×C5#5827semidirect
333. Q8C2×D5×Dic3semidirect
350. C2×C3#65908semidirect
354. C5C2×#5827semidirect
369. C3C2×#65908semidirect
371. C2#11755217direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C2×Q8×Dic152
C2×C5×Q8×Dic32
#117552172
C2×#914342
C2×Dic3×D202
C2×D5×C4⋊Dic32
C2×#913572
C2×#659083
C2×#58275