Finite Group Databasebeta

← C2×#11756269 #14480574

Subgroups — C2×#11756269 #14480574

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6817C212yesmaximal, complemented
2C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#91819C214yesmaximal, complemented
4#11756269C2116yesmaximal, direct product factor
5C2×#91786C214yesmaximal, complemented
6C2×#91784C214yesmaximal, complemented
7C2×#65844—31nomaximal, Hall
8C23×C3×C4×C5C2212yes—
9C23×C3×C4×C5C2211yescharacteristic
10C22×#1220C2214yes—
11C2×#6817—216no—
12C2×#6817C22116yescomplemented
13C22×D60C2212yes—
14C22×D60C2214yes—
15C22×C4×D15C2214yes—
16C22×Dic30C2212yes—
17C2×C3×C5×C4⋊C4C2214yes—
18C2×C3×C5×C4⋊C4C2218yescomplemented
19#91819C22132yescomplemented
20C2×#6714C2218yes—
21C2×C4⋊Dic15C2214yes—
22#91786C22132yescomplemented
23#91784C22132yescomplemented
24C2×#5510—51nomaximal, Hall
25C22×#709—32no—
26C22×C5×C4⋊C4D311yescharacteristic, complemented
27C2×#4076—34no—
28#65844—316no—
29C2×#4043—34no—
30C2×#4041—34no—
31C24×C3×C5C2311yescharacteristic
32C23×D15C2314yes—
33C22×C3×C4×C5—44no—
34C22×C3×C4×C5D418yescomplemented
35C22×C3×C4×C5C2314yes—
36C22×C3×C4×C5C2318yes—
37C22×C3×C4×C5C2312yes—
38C22×C3×C4×C5C2314yes—
39C2×#1220—216no—
40C2×#1220C23116yes—
41C22×Dic15C2314yes—
42#6817—264no—
43C2×D60—28no—
44C2×D60—48no—
45C2×D60C2318yes—
46C2×D60C23116yes—
47C2×C4×D15—216no—
48C2×C4×D15C23116yes—
49C2×Dic30—28no—
50C2×Dic30C2318yes—
51C3×C5×C4⋊C4C23116yes—
52#6714C23132yes—
53C4⋊Dic15C23116yes—
54C22×#235—52no—
55C22×C3×C4⋊C4D511yescharacteristic, complemented
56C2×#930—54no—
57#5510—516no—
58C2×#897—54no—
59C2×#895—54no—
60C23×C4×C5C2×D312yes—
61C23×C4×C5C2×D311yescharacteristic
62C22×C22⋊D5—34no—
63C2×#709—316no—
64C2×#709—616no—
65C22×D20—32no—
66C22×D20—34no—
67C22×C4×D5—34no—
68C22×Dic10—32no—
69C2×C5×C4⋊C4C2×D314yes—
70C2×C5×C4⋊C4C2×D318yescomplemented
71#4076—332no—
72C2×#685—38no—
73C2×C4⋊Dic5—34no—
74#4043—332no—
75#4041—332no—
76C2×#537—151noSylow
77C23×C3×C5—22no—
78C23×C3×C5—22no—
79C23×C3×C5C2×D414yes—
80C23×C3×C5C2412yes—
81C23×C3×C5C2411yescharacteristic
82C22×D15—28no—
83C22×D15—28no—
84C22×D15—28no—
85C22×D15C2418yes—
86C2×C3×C4×C5—28no—
87C2×C3×C4×C5—48no—
88C2×C3×C4×C5C2×D418yes—
89C2×C3×C4×C5C2×D4116yescomplemented
90C2×C3×C4×C5C2418yes—
91C2×C3×C4×C5C2414yes—
92#1220—232no—
93C2×Dic15—28no—
94C2×Dic15C2418yes—
95D60—216no—
96D60—416no—
97C4×D15—232no—
98Dic30—216no—
99C23×C3×C4C2×D512yes—
100C23×C3×C4C2×D511yescharacteristic
101C22×#67—54no—
102C2×#235—516no—
103C2×#235—1016no—
104C22×D12—52no—
105C22×D12—54no—
106C22×C4×D3—54no—
107C22×Dic6—52no—
108C2×C3×C4⋊C4C2×D514yes—
109C2×C3×C4⋊C4C2×D518yescomplemented
110#930—532no—
111C2×(C2×D3)⋊C4—58no—
112C2×C4⋊Dic3—54no—
113#897—532no—
114#895—532no—
115C24×C5C22×D311yescharacteristic
116C23×D5—34no—
117C22×C4×C5—44no—
118C22×C4×C5D1218yescomplemented
119C22×C4×C5C22×D314yes—
120C22×C4×C5C22×D318yes—
121C22×C4×C5C22×D312yes—
122C22×C4×C5C22×D314yes—
123C2×C22⋊D5—316no—
124C2×C22⋊D5—616no—
125C22×Dic5—34no—
126#709—664no—
127C2×D20—38no—
128C2×D20—316no—
129C2×D20—68no—
130C2×D20—128no—
131C2×C4×D5—316no—
132C2×C4×D5—616no—
133C2×Dic10—38no—
134C2×Dic10—68no—
135C5×C4⋊C4C22×D3116yes—
136#685—332no—
137C4⋊Dic5—316no—
138C22×#41—152no—
139#537—1516no—
140C2×C22⋊Q8—154no—
141C2×#121—154no—
142C2×#121—154no—
143C22×C4⋊C4D1511yescharacteristic, complemented
144C22×C3×C5—28no—
145C22×C3×C5—22no—
146C22×C3×C5—22no—
147C22×C3×C5C22×D414yes—
148C22×C3×C5C22×D412yes—
149C22×C3×C5H(5,𝔽2)12yes—
150C22×C3×C52−1+412yes—
151C22×C3×C5C2511yescharacteristic
152C2×D15—28no—
153C2×D15—28no—
154C2×D15—28no—
155C2×D15—416no—
156C3×C4×C5—28no—
157C3×C4×C5C22×D418yes—
158Dic15—28no—
159C24×C3C22×D511yescharacteristic
160C23×D3—54no—
161C22×C3×C4—44no—
162C22×C3×C4D2018yescomplemented
163C22×C3×C4C22×D514yes—
164C22×C3×C4C22×D518yes—
165C22×C3×C4C22×D512yes—
166C22×C3×C4C22×D514yes—
167C2×#67—516no—
168C2×#67—1016no—
169C22×Dic3—54no—
170#235—1064no—
171C2×D12—58no—
172C2×D12—516no—
173C2×D12—108no—
174C2×D12—208no—
175C2×C4×D3—516no—
176C2×C4×D3—1016no—
177C2×Dic6—58no—
178C2×Dic6—108no—
179C3×C4⋊C4C22×D5116yes—
180(C2×D3)⋊C4—532no—
181C4⋊Dic3—516no—
182C23×C5—22no—
183C23×C5—22no—
184C23×C5C2×D1214yes—
185C23×C5C23×D312yes—
186C23×C5C23×D311yescharacteristic
187C22×D5—38no—
188C22×D5—68no—
189C22×D5—68no—
190C22×D5—68no—
191C2×C4×C5—28no—
192C2×C4×C5—48no—
193C2×C4×C5C2×D1218yes—
194C2×C4×C5C2×D12116yescomplemented
195C2×C4×C5C23×D318yes—
196C2×C4×C5C23×D314yes—
197C22⋊D5—632no—
198C2×Dic5—38no—
199C2×Dic5—68no—
200D20—616no—
201D20—1216no—
202C4×D5—632no—
203Dic10—616no—
204C2×#41—1516no—
205C2×#41—3016no—
206C22×Q8—152no—
207C22×D4—154no—
208C22×D4—152no—
209C22×D4—154no—
210C23×C4—154no—
211C23×C4C2×D1512yes—
212C23×C4C2×D1511yescharacteristic
213C22⋊Q8—1532no—
214#121—1532no—
215#121—1532no—
216C2×C4⋊C4—154no—
217C2×C4⋊C4C2×D1514yes—
218C2×C4⋊C4C2×D1518yescomplemented
219C2×C22⋊C4—158no—
220C2×C3×C5—24no—
221C2×C3×C5#53714yescomplemented
222C2×C3×C5C23×D411yescharacteristic
223C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
224C2×C3×C5C2×2−1+411yescharacteristic
225D15—48no—
226C23×C3—22no—
227C23×C3—22no—
228C23×C3C2×D2014yes—
229C23×C3C23×D512yes—
230C23×C3C23×D511yescharacteristic
231C22×D3—58no—
232C22×D3—108no—
233C22×D3—108no—
234C22×D3—108no—
235C2×C3×C4—28no—
236C2×C3×C4—48no—
237C2×C3×C4C2×D2018yes—
238C2×C3×C4C2×D20116yescomplemented
239C2×C3×C4C23×D518yes—
240C2×C3×C4C23×D514yes—
241#67—1032no—
242C2×Dic3—58no—
243C2×Dic3—108no—
244D12—1016no—
245D12—2016no—
246C4×D3—1032no—
247Dic6—1016no—
248C22×C5—22no—
249C22×C5—22no—
250C22×C5—28no—
251C22×C5C22×D1214yes—
252C22×C5C22×D1212yes—
253C22×C5#100412yes—
254C22×C5#100712yes—
255C22×C5C24×D311yescharacteristic
256C2×D5—68no—
257C2×D5—68no—
258C2×D5—68no—
259C2×D5—1216no—
260C4×C5—28no—
261C4×C5C22×D1218yes—
262Dic5—68no—
263C24—154no—
264C24C22×D1511yescharacteristic
265#41—3064no—
266C2×Q8—158no—
267C2×Q8—308no—
268C2×D4—1516no—
269C2×D4—158no—
270C2×D4—1516no—
271C2×D4—3016no—
272C2×D4—308no—
273C2×D4—608no—
274C22×C4—44no—
275C22×C4—154no—
276C22×C4—1516no—
277C22×C4—3016no—
278C22×C4D6018yescomplemented
279C22×C4C22×D1514yes—
280C22×C4C22×D1518yes—
281C22×C4C22×D1512yes—
282C22×C4C22×D1514yes—
283C4⋊C4—1516no—
284C4⋊C4C22×D15116yes—
285C22⋊C4—1532no—
286C3×C5C2×#53711yescharacteristic, complemented, Hall
287C22×C3—28no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3C22×D2014yes—
291C22×C3C22×D2012yes—
292C22×C3#414412yes—
293C22×C3#414712yes—
294C22×C3C24×D511yescharacteristic
295C2×D3—108no—
296C2×D3—108no—
297C2×D3—108no—
298C2×D3—2016no—
299C3×C4—28no—
300C3×C4C22×D2018yes—
301Dic3—108no—
302C2×C5—24no—
303C2×C5#551014yescomplemented
304C2×C5C23×D1211yescharacteristic
305C2×C5C2×#100411yescharacteristic
306C2×C5C2×#100711yescharacteristic
307D5—128no—
308C23—22no—
309C23—22no—
310C23—158no—
311C23—308no—
312C23—308no—
313C23—308no—
314C23C2×D6014yes—
315C23C23×D1512yes—
316C23C23×D1511yescharacteristic
317Q8—3016no—
318D4—3032no—
319D4—3016no—
320D4—6016no—
321C2×C4—28no—
322C2×C4—48no—
323C2×C4—158no—
324C2×C4—308no—
325C2×C4—3032no—
326C2×C4C2×D6018yes—
327C2×C4C2×D60116yescomplemented
328C2×C4C23×D1518yes—
329C2×C4C23×D1514yes—
330C2×C3—24no—
331C2×C3#6584414yescomplemented
332C2×C3C23×D2011yescharacteristic
333C2×C3C2×#414411yescharacteristic
334C2×C3C2×#414711yescharacteristic
335D3—208no—
336C5C2×#551011yescharacteristic, complemented, Sylow
337C22—22no—
338C22—22no—
339C22—28no—
340C22—308no—
341C22—308no—
342C22—308no—
343C22—6016no—
344C22C22×D6014yes—
345C22C22×D6012yes—
346C22#9209512yes—
347C22#9209812yes—
348C22C24×D1511yescharacteristic
349C4—28no—
350C4—308no—
351C4C22×D6018yes—
352C3C2×#6584411yescharacteristic, complemented, Sylow
353C2—24no—
354C2—608no—
355C2#1175626914yesdirect product factor
356C2C23×D6011yescharacteristic
357C2C2×#9209511yescharacteristic
358C2C2×#9209811yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C24
hypercenterC22×C4⋊C4D15
hypocenterC3×C5C2×#537
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6817C2semidirect
2. C22×C3×C5×C4⋊C4C2semidirect
3. C2×#91819C2semidirect
4. #11756269C2direct (N × H)
5. C2×#91786C2semidirect
6. C2×#91784C2semidirect
12. C2×#6817C22semidirect
18. C2×C3×C5×C4⋊C4C22semidirect
19. #91819C22semidirect
22. #91786C22semidirect
23. #91784C22semidirect
26. C22×C5×C4⋊C4D3semidirect
34. C22×C3×C4×C5D4semidirect
55. C22×C3×C4⋊C4D5semidirect
70. C2×C5×C4⋊C4C2×D3semidirect
89. C2×C3×C4×C5C2×D4semidirect
109. C2×C3×C4⋊C4C2×D5semidirect
118. C22×C4×C5D12semidirect
143. C22×C4⋊C4D15semidirect
162. C22×C3×C4D20semidirect
194. C2×C4×C5C2×D12semidirect
218. C2×C4⋊C4C2×D15semidirect
221. C2×C3×C5#537semidirect
238. C2×C3×C4C2×D20semidirect
278. C22×C4D60semidirect
286. C3×C5C2×#537semidirect
303. C2×C5#5510semidirect
327. C2×C4C2×D60semidirect
331. C2×C3#65844semidirect
336. C5C2×#5510semidirect
352. C3C2×#65844semidirect
355. C2#11756269direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68172
C22×C3×C5×C4⋊C42
C2×#918192
#117562692
C2×#917862
C2×#917842
C2×#658443
C2×#55105