Finite Group Databasebeta

← C2×#11750996 #14417838

Subgroups — C2×#11750996 #14417838

Order 1920.

944 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
1C2×#91796C212yesmaximal, complemented
2C2×#91793C211yesmaximal, characteristic
3C2×C3×C5×#108C211yesmaximal, characteristic, complemented
4C2×#91109C212yesmaximal, complemented
5C2×C8×Dic15C211yesmaximal, characteristic, complemented
6#11750996C218yesmaximal, direct product factor
7C2×#65184—31nomaximal, Hall
8C2×#6817C2212yes—
9C2×C3×C5×M16C2212yes—
10C22×C3×C5×C8C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13#91796—24no—
14#91796C2218yescomplemented
15C2×Dic60C411yescharacteristic, complemented
16#91793C414yescomplemented
17#91793C2214yes—
18C2×D120C411yescharacteristic, complemented
19C2×#6706C412yescomplemented
20C2×#6705—22no—
21C2×C8×D15—22no—
22C3×C5×#108C2214yescomplemented
23#91109C2218yescomplemented
24C8×Dic15C2214yescomplemented
25C2×#4895—51nomaximal, Hall
26C2×#4053—32no—
27C2×#4050—31no—
28C2×C5×#108D311yescharacteristic, complemented
29C2×#3957—32no—
30C2×C8×Dic5—31no—
31#65184—38no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220—22no—
34C22×Dic15—21no—
35#6817—22no—
36#6817—22no—
37#6817C2×C414yes—
38#6817C2314yes—
39C2×D60C2×C412yes—
40C2×C4×D15—22no—
41C2×Dic30C2×C412yes—
42C3×C5×M16—22no—
43C3×C5×M16C2314yes—
44C2×C3×C5×C8—22no—
45C2×C3×C5×C8C2×C411yescharacteristic
46C2×C3×C5×C8C2×C411yescharacteristic
47C2×C3×C5×C8C2×C412yes—
48C2×C3×C5×C8C2312yes—
49C4×Dic15—21no—
50C4×Dic15C2312yes—
51C2×C3⋊#168D411yescharacteristic
52C2×C3⋊#168D411yescharacteristic
53C2×C3⋊#168D412yes—
54C2×C3⋊#168C2312yes—
55Dic60C2×C414yescomplemented
56D120C2×C414yescomplemented
57#6706C2×C418yescomplemented
58#6705—28no—
59C8×D15—28no—
60C2×#907—52no—
61C2×#904—51no—
62C2×C3×#108D511yescharacteristic, complemented
63C2×#825—52no—
64C2×C8×Dic3—51no—
65#4895—58no—
66C2×#709—32no—
67C2×C5×M16C2×D312yes—
68C22×C5×C8C2×D311yescharacteristic
69C2×C4×Dic5—31no—
70C22×#168—31no—
71#4053—38no—
72#4053—64no—
73C2×Dic20—31no—
74#4050—34no—
75#4050—34no—
76C2×D40—31no—
77C2×#677—32no—
78C2×#676—62no—
79C2×C8×D5—62no—
80C5×#108C2×D314yescomplemented
81#3957—38no—
82C8×Dic5—34no—
83C2×#443—151noSylow
84C23×C3×C5#4111yescharacteristic
85C22×D15—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5C2411yescharacteristic
92#1220—24no—
93#1220—24no—
94C2×Dic15—24no—
95C2×Dic15—22no—
96C2×Dic15—22no—
97D60—22no—
98D60C22×C414yes—
99C4×D15—24no—
100C4×D15—24no—
101Dic30—22no—
102Dic30C22×C414yes—
103C3×C5×C8—24no—
104C3×C5×C8C22×C412yes—
105C3×C5×C8C22×C412yes—
106C3⋊#168C2×D412yes—
107C3⋊#168C2×D412yes—
108C2×#235—52no—
109C2×C3×M16C2×D512yes—
110C22×C3×C8C2×D511yescharacteristic
111C2×C4×Dic3—51no—
112C22×C3⋊C8—51no—
113#907—58no—
114#907—104no—
115C2×Dic12—51no—
116#904—54no—
117#904—54no—
118C2×D24—51no—
119C2×#204—52no—
120C2×ΓL(1,𝔽25)—102no—
121C2×D3×C8—102no—
122C3×#108C2×D514yescomplemented
123#825—58no—
124C8×Dic3—54no—
125C22×C4×C5C22×D311yescharacteristic
126C2×C22⋊D5—62no—
127C22×Dic5—61no—
128#709—34no—
129#709—34no—
130#709—62no—
131#709—62no—
132C2×D20—32no—
133C2×C4×D5—62no—
134C2×Dic10—32no—
135C5×M16—22no—
136C5×M16C22×D314yes—
137C2×C5×C8—22no—
138C2×C5×C8C4×D311yescharacteristic
139C2×C5×C8C4×D311yescharacteristic
140C2×C5×C8C4×D312yes—
141C2×C5×C8C22×D312yes—
142C4×Dic5—32no—
143C4×Dic5—61no—
144C2×#168—31no—
145C2×#168—31no—
146C2×#168—32no—
147C2×#168—32no—
148Dic20—34no—
149D40—34no—
150#677—38no—
151#676—68no—
152C8×D5—68no—
153C2×#135—151no—
154C2×#131—152no—
155#443—158no—
156C2×#108D1511yescharacteristic, complemented
157C2×#104—152no—
158C2×C4×C8—151no—
159C22×C3×C5—22no—
160C22×C3×C5C4×D411yescharacteristic
161C22×C3×C5C4×D411yescharacteristic
162C22×C3×C5C2×#4111yescharacteristic
163C2×D15—24no—
164C2×D15—44no—
165C3×C4×C5C4×D411yescharacteristic
166C3×C4×C5C4×D411yescharacteristic
167C3×C4×C5C23×C411yescharacteristic
168C3×C4×C5C22×D411yescharacteristic
169Dic15—24no—
170Dic15—24no—
171C22×C3×C4C22×D511yescharacteristic
172C2×#67—102no—
173C22×Dic3—101no—
174#235—54no—
175#235—54no—
176#235—102no—
177#235—102no—
178C2×D12—52no—
179C2×C4×D3—102no—
180C2×Dic6—52no—
181C3×M16—22no—
182C3×M16C22×D514yes—
183C2×C3×C8—22no—
184C2×C3×C8C4×D511yescharacteristic
185C2×C3×C8C4×D511yescharacteristic
186C2×C3×C8C4×D512yes—
187C2×C3×C8C22×D512yes—
188C4×Dic3—52no—
189C4×Dic3—101no—
190C2×C3⋊C8—51no—
191C2×C3⋊C8—51no—
192C2×C3⋊C8—52no—
193C2×C3⋊C8—52no—
194Dic12—54no—
195D24—54no—
196#204—58no—
197ΓL(1,𝔽25)—108no—
198D3×C8—108no—
199C23×C5#23911yescharacteristic
200C22×D5—62no—
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5C2×C4×D311yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5#23911yescharacteristic
206C2×C4×C5C23×D311yescharacteristic
207C22⋊D5—64no—
208C22⋊D5—64no—
209C2×Dic5—64no—
210C2×Dic5—62no—
211C2×Dic5—62no—
212D20—34no—
213D20—62no—
214C4×D5—64no—
215C4×D5—64no—
216Dic10—34no—
217Dic10—62no—
218C5×C8—24no—
219C5×C8C2×C4×D312yes—
220C5×C8C2×C4×D312yes—
221#168—32no—
222#168—32no—
223C2×#41—152no—
224#135—154no—
225#135—154no—
226C2×Q16—151no—
227C2×SD16—152no—
228C2×D8—151no—
229#131—158no—
230#131—304no—
231C2×M16—302no—
232C2×M16C2×D1512yes—
233C22×C8—151no—
234C22×C8—302no—
235C22×C8C2×D1511yescharacteristic
236C2×C42—151no—
237#108C2×D1514yescomplemented
238#104—158no—
239C4×C8—154no—
240C2×C3×C5—21no—
241C2×C3×C5—21no—
242C2×C3×C5#44312yescomplemented
243C2×C3×C5C2×C4×D411yescharacteristic
244D15—44no—
245C23×C3#71311yescharacteristic
246C22×D3—102no—
247C2×C3×C4C2×C4×D511yescharacteristic
248C2×C3×C4C2×C4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4#71311yescharacteristic
252C2×C3×C4C23×D511yescharacteristic
253#67—104no—
254#67—104no—
255C2×Dic3—104no—
256C2×Dic3—102no—
257C2×Dic3—102no—
258D12—54no—
259D12—102no—
260C4×D3—104no—
261C4×D3—104no—
262Dic6—54no—
263Dic6—102no—
264C3×C8—24no—
265C3×C8C2×C4×D512yes—
266C3×C8C2×C4×D512yes—
267C3⋊C8—52no—
268C3⋊C8—52no—
269C22×C5—22no—
270C22×C5#89311yescharacteristic
271C22×C5#89311yescharacteristic
272C22×C5C2×#23911yescharacteristic
273C2×D5—64no—
274C2×D5—124no—
275C4×C5#89311yescharacteristic
276C4×C5#89311yescharacteristic
277C4×C5C22×C4×D311yescharacteristic
278C4×C5C2×D3×D411yescharacteristic
279Dic5—64no—
280Dic5—64no—
281#41—154no—
282#41—154no—
283#41—302no—
284#41—302no—
285C2×Q8—152no—
286C2×D4—152no—
287C2×D4—302no—
288C22×C4—301no—
289C22×C4—302no—
290C22×C4C22×D1511yescharacteristic
291Q16—154no—
292SD16—158no—
293D8—154no—
294M16—22no—
295M16—308no—
296M16C22×D1514yes—
297C2×C8—22no—
298C2×C8—152no—
299C2×C8—151no—
300C2×C8—151no—
301C2×C8—152no—
302C2×C8—308no—
303C2×C8C4×D1511yescharacteristic
304C2×C8C4×D1511yescharacteristic
305C2×C8C4×D1512yes—
306C2×C8C22×D1512yes—
307C42—152no—
308C42—301no—
309C3×C5C2×#44311yescharacteristic, complemented, Hall
310C22×C3—22no—
311C22×C3#403911yescharacteristic
312C22×C3#403911yescharacteristic
313C22×C3C2×#71311yescharacteristic
314C2×D3—104no—
315C2×D3—204no—
316C3×C4#403911yescharacteristic
317C3×C4#403911yescharacteristic
318C3×C4C22×C4×D511yescharacteristic
319C3×C4C2×D4×D511yescharacteristic
320Dic3—104no—
321Dic3—104no—
322C2×C5—21no—
323C2×C5—21no—
324C2×C5#489512yescomplemented
325C2×C5C2×#89311yescharacteristic
326D5—124no—
327C23—302no—
328C23#682111yescharacteristic
329Q8—154no—
330Q8—302no—
331D4—154no—
332D4—304no—
333D4—304no—
334D4—302no—
335C2×C4—304no—
336C2×C4—302no—
337C2×C4—302no—
338C2×C4—304no—
339C2×C4—304no—
340C2×C4C2×C4×D1511yescharacteristic
341C2×C4C2×C4×D1511yescharacteristic
342C2×C4D4×D1511yescharacteristic
343C2×C4D4×D1511yescharacteristic
344C2×C4#682111yescharacteristic
345C2×C4C23×D1511yescharacteristic
346C8—24no—
347C8—152no—
348C8—152no—
349C8C2×C4×D1512yes—
350C8C2×C4×D1512yes—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3#6518412yescomplemented
354C2×C3C2×#403911yescharacteristic
355D3—204no—
356C5C2×#489511yescharacteristic, complemented, Sylow
357C22—22no—
358C22—304no—
359C22—604no—
360C22#9178211yescharacteristic
361C22#9178211yescharacteristic
362C22C2×#682111yescharacteristic
363C4—304no—
364C4—304no—
365C4#9178211yescharacteristic
366C4#9178211yescharacteristic
367C4C22×C4×D1511yescharacteristic
368C4C2×D4×D1511yescharacteristic
369C3C2×#6518411yescharacteristic, complemented, Sylow
370C2—21no—
371C2—21no—
372C2—604no—
373C2#1175099612yesdirect product factor
374C2C2×#9178211yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#108C2
socleC22×C3×C5C4×D4
prime radicalC2×#91793C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#108D15
hypocenterC3×C5C2×#443
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
1. C2×#91796C2semidirect
3. C2×C3×C5×#108C2semidirect
4. C2×#91109C2semidirect
5. C2×C8×Dic15C2semidirect
6. #11750996C2direct (N × H)
14. #91796C22semidirect
15. C2×Dic60C4semidirect
16. #91793C4semidirect
18. C2×D120C4semidirect
19. C2×#6706C4semidirect
22. C3×C5×#108C22semidirect
23. #91109C22semidirect
24. C8×Dic15C22semidirect
28. C2×C5×#108D3semidirect
55. Dic60C2×C4semidirect
56. D120C2×C4semidirect
57. #6706C2×C4semidirect
62. C2×C3×#108D5semidirect
80. C5×#108C2×D3semidirect
122. C3×#108C2×D5semidirect
156. C2×#108D15semidirect
237. #108C2×D15semidirect
242. C2×C3×C5#443semidirect
309. C3×C5C2×#443semidirect
324. C2×C5#4895semidirect
353. C2×C3#65184semidirect
356. C5C2×#4895semidirect
369. C3C2×#65184semidirect
373. C2#11750996direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917962
C2×#917932
C2×C3×C5×#1082
C2×#911092
C2×C8×Dic152
#117509962
C2×#651843
C2×#48955