Finite Group Databasebeta

← C2×#91474 #11754630

Subgroups — C2×#91474 #11754630

Order 960.

1324 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 200 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
1C23×D3×D5C211yesmaximal, characteristic, complemented
2C22×C3×D20C211yesmaximal, characteristic, complemented
3C22×#1202C211yesmaximal, characteristic, complemented
4C22×#1201C211yesmaximal, characteristic, complemented
5C2×#6714C211yesmaximal, characteristic, complemented
6C2×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#6665C211yesmaximal, characteristic, complemented
8#91474C218yesmaximal, direct product factor
9C2×#4028—31nomaximal, Hall
10C23×D15C2211yescharacteristic
11C23×C5×D3C2211yescharacteristic
12C23×C3×D5C2211yescharacteristic
13C23×C3×D5C2211yescharacteristic, complemented
14C22×D3×D5—24no—
15C22×D3×D5—24no—
16C22×D3×D5—24no—
17C22×D3×D5C2214yescomplemented
18C22×C3×C4×C5C2211yescharacteristic, complemented
19C22×Dic15C2211yescharacteristic, complemented
20C22×C5×Dic3C2211yescharacteristic, complemented
21C2×C3×D20—24no—
22C2×C3×D20C2214yescomplemented
23C2×#1202—24no—
24C2×#1202C2214yescomplemented
25C2×#1201—24no—
26C2×#1201C2214yescomplemented
27#6714C2214yescomplemented
28C5×(C2×D3)⋊C4C2214yescomplemented
29#6665C2214yescomplemented
30C2×#937—51nomaximal, Hall
31C24×D5—31no—
32C22×C22⋊D5—31no—
33C22×D20—31no—
34C22×D20D311yescharacteristic, complemented
35C2×C5×C22⋊C4—31no—
36C2×#685—31no—
37C2×#685—31no—
38#4028—38no—
39C23×C3×C5C2311yescharacteristic
40C22×D15—22no—
41C22×D15—22no—
42C22×D15D414yescomplemented
43C22×D15C2312yes—
44C22×C5×D3—22no—
45C22×C5×D3—22no—
46C22×C5×D3D414yescomplemented
47C22×C5×D3C2312yes—
48C22×C3×D5—22no—
49C22×C3×D5—22no—
50C22×C3×D5—22no—
51C22×C3×D5—22no—
52C22×C3×D5—22no—
53C22×C3×D5D414yescomplemented
54C22×C3×D5C2312yes—
55C22×C3×D5C2312yescomplemented
56C2×D3×D5—232no—
57C2×D3×D5—28no—
58C2×D3×D5—28no—
59C2×D3×D5—28no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2312yescomplemented
62C2×Dic15—22no—
63C2×Dic15C2312yescomplemented
64C2×C5×Dic3—22no—
65C2×C5×Dic3C2312yescomplemented
66C3×D20—28no—
67#1202—28no—
68#1201—28no—
69C24×D3—51no—
70C22×C3×D4—51no—
71C22×#67—51no—
72C22×#67—51no—
73C2×#217—51no—
74#937—58no—
75C2×(C2×D3)⋊C4—51no—
76C2×(C2×D3)⋊C4D511yescharacteristic, complemented
77C24×C5—31no—
78C23×D5—31no—
79C23×D5—34no—
80C23×D5—64no—
81C23×D5—64no—
82C23×D5—64no—
83C23×D5C2×D311yescharacteristic
84C23×D5C2×D311yescharacteristic, complemented
85C22×C4×C5—31no—
86C22×C4×C5C2×D311yescharacteristic, complemented
87C2×C22⋊D5—34no—
88C2×C22⋊D5—64no—
89C22×Dic5—31no—
90C2×D20—24no—
91C2×D20—34no—
92C2×D20—64no—
93C2×D20C2×D314yescomplemented
94C5×C22⋊C4—34no—
95#685—34no—
96#685—34no—
97C2×#120—151noSylow
98C22×C3×C5C2×D412yes—
99C22×C3×C5C2×D412yes—
100C22×C3×C5C2×D412yes—
101C22×C3×C5C2411yescharacteristic
102C2×D15—28no—
103C2×D15—22no—
104C2×D15—22no—
105C2×D15C2×D414yescomplemented
106C2×C5×D3—28no—
107C2×C5×D3—22no—
108C2×C5×D3—22no—
109C2×C5×D3C2×D414yescomplemented
110C2×C3×D5—28no—
111C2×C3×D5—22no—
112C2×C3×D5—22no—
113C2×C3×D5—22no—
114C2×C3×D5—22no—
115C2×C3×D5—22no—
116C2×C3×D5—44no—
117C2×C3×D5C2×D414yescomplemented
118D3×D5—232no—
119C3×C4×C5—22no—
120Dic15—22no—
121C5×Dic3—22no—
122C24×C3—51no—
123C24×C3—51no—
124C23×D3—51no—
125C23×D3—54no—
126C23×D3—104no—
127C23×D3—104no—
128C23×D3—104no—
129C23×D3C2×D511yescharacteristic
130C2×C3×D4—54no—
131C2×C3×D4—104no—
132C22×C3×C4C2×D511yescharacteristic, complemented
133C2×#67—54no—
134C2×#67—54no—
135C2×#67—104no—
136C2×#67—104no—
137C22×Dic3—51no—
138C22×Dic3C2×D511yescharacteristic, complemented
139#217—54no—
140(C2×D3)⋊C4—54no—
141(C2×D3)⋊C4C2×D514yescomplemented
142C23×C5—34no—
143C23×C5—32no—
144C23×C5—62no—
145C23×C5—62no—
146C23×C5C22×D311yescharacteristic
147C22×D5—22no—
148C22×D5—22no—
149C22×D5—22no—
150C22×D5—22no—
151C22×D5—22no—
152C22×D5—34no—
153C22×D5—32no—
154C22×D5—68no—
155C22×D5—68no—
156C22×D5—632no—
157C22×D5—62no—
158C22×D5—62no—
159C22×D5—68no—
160C22×D5#6714yescomplemented
161C22×D5C22×D312yes—
162C22×D5C22×D312yescomplemented
163C2×C4×C5—22no—
164C2×C4×C5—32no—
165C2×C4×C5—62no—
166C2×C4×C5C22×D312yescomplemented
167C22⋊D5—68no—
168C2×Dic5—32no—
169C2×Dic5—62no—
170D20—28no—
171D20—68no—
172C25—151no—
173C22×D4—51no—
174C22×D4—151no—
175C22×D4—151no—
176#120—158no—
177C2×C22⋊C4—31no—
178C2×C22⋊C4—151no—
179C2×C22⋊C4—151no—
180C2×C3×C5#12014yescomplemented
181C2×C3×C5C22×D411yescharacteristic
182C2×C3×C5C22×D411yescharacteristic
183C2×C3×C5C22×D411yescharacteristic
184D15—24no—
185C3×D5—24no—
186C3×D5—42no—
187C5×D3—24no—
188C23×C3—54no—
189C23×C3—52no—
190C23×C3—52no—
191C23×C3—102no—
192C23×C3—102no—
193C23×C3—102no—
194C23×C3—102no—
195C23×C3—102no—
196C23×C3C22×D511yescharacteristic
197C22×D3—22no—
198C22×D3—22no—
199C22×D3—54no—
200C22×D3—52no—
201C22×D3—108no—
202C22×D3—108no—
203C22×D3—1032no—
204C22×D3—102no—
205C22×D3—102no—
206C22×D3—108no—
207C22×D3D2014yescomplemented
208C22×D3C22×D512yes—
209C3×D4—108no—
210C2×C3×C4—22no—
211C2×C3×C4C22×D512yescomplemented
212#67—108no—
213#67—108no—
214C2×Dic3—22no—
215C2×Dic3—52no—
216C2×Dic3—102no—
217C2×Dic3C22×D512yescomplemented
218C22×C5—34no—
219C22×C5—68no—
220C22×C5—62no—
221C22×C5—62no—
222C22×C5D3×D412yes—
223C22×C5D3×D412yes—
224C22×C5C2×#6712yes—
225C22×C5C23×D311yescharacteristic
226C2×D5—28no—
227C2×D5—22no—
228C2×D5—22no—
229C2×D5—22no—
230C2×D5—22no—
231C2×D5—22no—
232C2×D5—34no—
233C2×D5—44no—
234C2×D5—632no—
235C2×D5—68no—
236C2×D5—62no—
237C2×D5—62no—
238C2×D5C2×#6714yescomplemented
239C4×C5—22no—
240C4×C5—62no—
241Dic5—62no—
242C24—31no—
243C24—51no—
244C24—51no—
245C24—154no—
246C24—151no—
247C24—304no—
248C24—304no—
249C24—304no—
250C2×D4—54no—
251C2×D4—104no—
252C2×D4—154no—
253C2×D4—154no—
254C2×D4—304no—
255C2×D4—304no—
256C22×C4—31no—
257C22×C4—151no—
258C22×C4D3×D511yescharacteristic, complemented
259C22⋊C4—34no—
260C22⋊C4—154no—
261C22⋊C4—154no—
262C3×C5C2×#12011yescharacteristic, complemented, Hall
263C22×C3—54no—
264C22×C3—102no—
265C22×C3—102no—
266C22×C3—108no—
267C22×C3—102no—
268C22×C3—102no—
269C22×C3—102no—
270C22×C3—204no—
271C22×C3C2×D2012yes—
272C22×C3D4×D512yes—
273C22×C3D4×D512yes—
274C22×C3C23×D511yescharacteristic
275C2×D3—22no—
276C2×D3—22no—
277C2×D3—28no—
278C2×D3—54no—
279C2×D3—1032no—
280C2×D3—102no—
281C2×D3—102no—
282C2×D3—108no—
283C2×D3C2×D2014yescomplemented
284C3×C4—22no—
285Dic3—22no—
286Dic3—102no—
287C2×C5—64no—
288C2×C5#93714yescomplemented
289C2×C5C2×D3×D411yescharacteristic
290C2×C5C2×D3×D411yescharacteristic
291C2×C5C22×#6711yescharacteristic
292D5—24no—
293D5—42no—
294D5—64no—
295C23—34no—
296C23—32no—
297C23—54no—
298C23—52no—
299C23—52no—
300C23—62no—
301C23—62no—
302C23—102no—
303C23—102no—
304C23—102no—
305C23—102no—
306C23—102no—
307C23—154no—
308C23—152no—
309C23—308no—
310C23—308no—
311C23—308no—
312C23—3032no—
313C23—302no—
314C23—302no—
315C23C2×D3×D511yescharacteristic
316D4—108no—
317D4—308no—
318D4—308no—
319C2×C4—22no—
320C2×C4—32no—
321C2×C4—62no—
322C2×C4—152no—
323C2×C4—302no—
324C2×C4C2×D3×D512yescomplemented
325C2×C3—104no—
326C2×C3—202no—
327C2×C3#402814yescomplemented
328C2×C3C22×D2011yescharacteristic
329C2×C3C2×D4×D511yescharacteristic
330C2×C3C2×D4×D511yescharacteristic
331D3—24no—
332D3—104no—
333C5C2×#93711yescharacteristic, complemented, Sylow
334C22—34no—
335C22—54no—
336C22—68no—
337C22—62no—
338C22—62no—
339C22—108no—
340C22—102no—
341C22—102no—
342C22—102no—
343C22—102no—
344C22—102no—
345C22—154no—
346C22—204no—
347C22—3032no—
348C22—308no—
349C22—302no—
350C22—302no—
351C22D3×D2012yes—
352C22#677712yes—
353C22D5×#6712yes—
354C22C22×D3×D511yescharacteristic
355C4—22no—
356C4—62no—
357C4—302no—
358C3C2×#402811yescharacteristic, complemented, Sylow
359C2—64no—
360C2—104no—
361C2—202no—
362C2—304no—
363C2#9147414yesdirect product factor
364C2C2×D3×D2011yescharacteristic
365C2C2×#677711yescharacteristic
366C2C2×D5×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D5
commutator, cosocleC22×C3×C5C24
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
socleC23×C3×C5C23
hypercenterC22×C4D3×D5
hypocenterC3×C5C2×#120
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×D5C2semidirect
2. C22×C3×D20C2semidirect
3. C22×#1202C2semidirect
4. C22×#1201C2semidirect
5. C2×#6714C2semidirect
6. C2×C5×(C2×D3)⋊C4C2semidirect
7. C2×#6665C2semidirect
8. #91474C2direct (N × H)
13. C23×C3×D5C22semidirect
17. C22×D3×D5C22semidirect
18. C22×C3×C4×C5C22semidirect
19. C22×Dic15C22semidirect
20. C22×C5×Dic3C22semidirect
22. C2×C3×D20C22semidirect
24. C2×#1202C22semidirect
26. C2×#1201C22semidirect
27. #6714C22semidirect
28. C5×(C2×D3)⋊C4C22semidirect
29. #6665C22semidirect
34. C22×D20D3semidirect
42. C22×D15D4semidirect
46. C22×C5×D3D4semidirect
53. C22×C3×D5D4semidirect
55. C22×C3×D5C23semidirect
61. C2×C3×C4×C5C23semidirect
63. C2×Dic15C23semidirect
65. C2×C5×Dic3C23semidirect
76. C2×(C2×D3)⋊C4D5semidirect
84. C23×D5C2×D3semidirect
86. C22×C4×C5C2×D3semidirect
93. C2×D20C2×D3semidirect
105. C2×D15C2×D4semidirect
109. C2×C5×D3C2×D4semidirect
117. C2×C3×D5C2×D4semidirect
132. C22×C3×C4C2×D5semidirect
138. C22×Dic3C2×D5semidirect
141. (C2×D3)⋊C4C2×D5semidirect
160. C22×D5#67semidirect
162. C22×D5C22×D3semidirect
166. C2×C4×C5C22×D3semidirect
180. C2×C3×C5#120semidirect
207. C22×D3D20semidirect
211. C2×C3×C4C22×D5semidirect
217. C2×Dic3C22×D5semidirect
238. C2×D5C2×#67semidirect
258. C22×C4D3×D5semidirect
262. C3×C5C2×#120semidirect
283. C2×D3C2×D20semidirect
288. C2×C5#937semidirect
324. C2×C4C2×D3×D5semidirect
327. C2×C3#4028semidirect
333. C5C2×#937semidirect
358. C3C2×#4028semidirect
363. C2#91474direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×D52
C22×C3×D202
C22×#12022
C22×#12012
C2×#67142
C2×C5×(C2×D3)⋊C42
C2×#66652
#914742
C2×#40283
C2×#9375