Finite Group Databasebeta

← C2×D5×#131⋊C3 #14514141

Subgroups — C2×D5×#131⋊C3 #14514141

Order 1920.

718 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×D5×#41⋊C3C211yesmaximal, characteristic
2C2×C5×#131⋊C3C211yesmaximal, characteristic, complemented
3C2×#4094⋊C3C211yesmaximal, characteristic, complemented
4D5×#131⋊C3C214yesmaximal, direct product factor
5C2×D5×#131C311yesmaximal, characteristic, complemented, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7D5×#41⋊C3C412yes—
8D5×#41⋊C3C2212yes—
9C2×D5×SL(2,𝔽3)C411yescharacteristic
10C2×C5⋊(#41⋊C3)C411yescharacteristic
11C2×C3×C8×D5—41nomaximal
12C5×#131⋊C3C2212yescomplemented
13#4094⋊C3C2212yescomplemented
14C22×#131⋊C3—51nomaximal, Hall
15C2×D5×#41C2×C311yescharacteristic
16C2×C5×#131C2×C311yescharacteristic, complemented
17C2×#4094C2×C311yescharacteristic, complemented
18D5×#131—34no—
19D5×#131C2×C314yescomplemented
20C2×#4053—31no—
21C2×D5×M16—31no—
22C2×#4047—31no—
23C22×C8×D5—31no—
24C2×C3×C4×D5—41no—
25C5×#41⋊C3C2×C411yescharacteristic
26C5×#41⋊C3C2311yescharacteristic
27C2×C5×SL(2,𝔽3)C2×C411yescharacteristic
28D5×SL(2,𝔽3)C2×C412yes—
29C5⋊(#41⋊C3)C2×C412yes—
30C2×C3×C5×C8—41no—
31C2×C3×#168—41no—
32C3×C8×D5—44no—
33C22×#41⋊C3—51no—
34C2×#131⋊C3—51no—
35C2×#131⋊C3—54no—
36C2×#131⋊C3D511yescharacteristic, direct product factor
37C2×C5×#41C22×C311yescharacteristic
38D5×#41—32no—
39D5×#41—32no—
40D5×#41C3×C412yes—
41D5×#41C22×C312yes—
42C2×#713C3×C411yescharacteristic
43C2×Q8×D5C3×C411yescharacteristic
44C2×#711—31no—
45C2×D4×D5—31no—
46C2×#709—31no—
47C22×C4×D5—31no—
48C5×#131—32no—
49C5×#131C22×C312yescomplemented
50C2×C5×M16—31no—
51C22×C5×C8—31no—
52#4094—32no—
53#4094C22×C312yescomplemented
54C2×#681—31no—
55C22×#168—31no—
56#4053—34no—
57#4053—34no—
58D5×M16—34no—
59D5×M16—34no—
60#4047—34no—
61#4047—34no—
62C2×#676—32no—
63C2×C8×D5—31no—
64C2×C8×D5—31no—
65C2×C8×D5—31no—
66C2×C8×D5—34no—
67C2×C8×D5—34no—
68C2×C8×D5A411yescharacteristic
69C22×#131—51noSylow
70C22×C3×D5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×Dic5—41no—
73C3×C4×D5—42no—
74C3×C4×D5—42no—
75C5×SL(2,𝔽3)C22×C411yescharacteristic
76C3×C5×C8—42no—
77C3×#168—42no—
78C2×#41⋊C3—52no—
79C2×#41⋊C3—52no—
80C2×#41⋊C3—51no—
81C2×#41⋊C3C2×D511yescharacteristic
82C22×SL(2,𝔽3)—51no—
83C22×C3×C8—201no—
84#131⋊C3—52no—
85#131⋊C3C2×D512yesdirect product factor
86C23×D5—31no—
87C5×#41—31no—
88C5×#41—31no—
89C5×#41C2×C3×C411yescharacteristic
90C5×#41C23×C311yescharacteristic
91C2×C5×Q8C2×C3×C411yescharacteristic
92C2×C5×D4—31no—
93C22×C4×C5—31no—
94C2×C22⋊D5—32no—
95C22×Dic5—31no—
96#713—32no—
97#713C2×C3×C412yes—
98Q8×D5—32no—
99Q8×D5C2×C3×C412yes—
100#711—34no—
101#711—32no—
102#711—32no—
103D4×D5—32no—
104D4×D5—32no—
105D4×D5—34no—
106#709—32no—
107#709—32no—
108#709—32no—
109#709—32no—
110C2×D20—31no—
111C2×C4×D5—31no—
112C2×C4×D5—31no—
113C2×C4×D5—31no—
114C2×C4×D5—32no—
115C2×C4×D5—32no—
116C2×C4×D5—32no—
117C2×C4×D5—32no—
118C2×C4×D5C2×A411yescharacteristic
119C2×Dic10—31no—
120C5×M16—32no—
121C5×M16—32no—
122C2×C5×C8—31no—
123C2×C5×C8—32no—
124C2×C5×C8—32no—
125C2×C5×C8C2×A411yescharacteristic
126#681—32no—
127#681—32no—
128C2×#168—31no—
129C2×#168—32no—
130C2×#168—32no—
131C2×#168C2×A411yescharacteristic
132#676—38no—
133C8×D5—34no—
134C8×D5—34no—
135C8×D5—34no—
136C8×D5C2×A414yes—
137C22×#41—51no—
138C2×#131—51no—
139C2×#131—54no—
140C2×#131—151no—
141C2×#131—151no—
142C2×#131—154no—
143C2×#131C3×D511yescharacteristic, complemented
144C22×M16—151no—
145C23×C8—151no—
146C22×C3×C5—41no—
147C2×C3×D5—44no—
148C2×C3×D5—42no—
149C3×C4×C5—41no—
150C3×C4×C5—41no—
151C3×Dic5—42no—
152C22×C3×C4—201no—
153#41⋊C3—52no—
154#41⋊C3C4×D511yescharacteristic
155#41⋊C3C22×D511yescharacteristic
156C2×SL(2,𝔽3)—52no—
157C2×SL(2,𝔽3)C4×D511yescharacteristic
158C2×C3×C8—41no—
159C2×C3×C8—204no—
160C2×C3×C8—201no—
161C23×C5—31no—
162C22×D5—31no—
163C22×D5—32no—
164C22×D5—32no—
165C22×D5—64no—
166C22×D5C4×A411yescharacteristic
167C5×Q8—31no—
168C5×Q8C22×C3×C411yescharacteristic
169C5×D4—31no—
170C5×D4—31no—
171C5×D4—32no—
172C2×C4×C5—31no—
173C2×C4×C5—31no—
174C2×C4×C5—31no—
175C2×C4×C5—31no—
176C2×C4×C5—31no—
177C2×C4×C5C22×A411yescharacteristic
178C22⋊D5—34no—
179C22⋊D5—34no—
180C2×Dic5—31no—
181C2×Dic5—32no—
182C2×Dic5—32no—
183C2×Dic5C4×A411yescharacteristic
184D20—32no—
185D20—32no—
186C4×D5—32no—
187C4×D5—32no—
188C4×D5—32no—
189C4×D5—32no—
190C4×D5—32no—
191C4×D5—32no—
192C4×D5C4×A412yes—
193C4×D5C22×A412yes—
194Dic10—32no—
195Dic10—32no—
196C5×C8—32no—
197C5×C8C22×A412yes—
198#168—32no—
199#168C22×A412yes—
200C2×#41—52no—
201C2×#41—52no—
202C2×#41—51no—
203C2×#41—151no—
204C2×#41—151no—
205C2×#41—152no—
206C2×#41—152no—
207C2×#41C2×C3×D511yescharacteristic
208C22×Q8—51no—
209C22×D4—151no—
210C23×C4—151no—
211#131—32no—
212#131—52no—
213#131—154no—
214#131—154no—
215#131—154no—
216#131—154no—
217#131—152no—
218#131C2×C3×D512yescomplemented
219C2×M16—31no—
220C2×M16—152no—
221C2×M16—154no—
222C2×M16—154no—
223C2×M16—151no—
224C22×C8—31no—
225C22×C8—51no—
226C22×C8—154no—
227C22×C8—151no—
228C22×C8—154no—
229C22×C8—151no—
230C22×C8—151no—
231C22×C8—151no—
232C2×C3×C5—41no—
233C2×C3×C5—42no—
234C3×D5—44no—
235C23×C3—201no—
236C2×C3×C4—41no—
237C2×C3×C4—202no—
238C2×C3×C4—202no—
239C2×C3×C4—201no—
240SL(2,𝔽3)C2×C4×D511yescharacteristic
241C3×C8—42no—
242C3×C8—202no—
243C22×C5—31no—
244C22×C5—31no—
245C22×C5—62no—
246C22×C5C2×C4×A411yescharacteristic
247C2×D5—32no—
248C2×D5—62no—
249C2×D5—64no—
250C2×D5—64no—
251C2×D5#131⋊C314yesdirect product factor
252C2×D5C2×C4×A412yes—
253C4×C5—31no—
254C4×C5—31no—
255C4×C5C2×C4×A411yescharacteristic
256C4×C5C23×A411yescharacteristic
257Dic5—32no—
258Dic5C2×C4×A412yes—
259C24—151no—
260#41—31no—
261#41—31no—
262#41—52no—
263#41—152no—
264#41—152no—
265#41—152no—
266#41—152no—
267#41—154no—
268#41—152no—
269#41—152no—
270#41—152no—
271#41C3×C4×D511yescharacteristic
272#41C22×C3×D511yescharacteristic
273C2×Q8—52no—
274C2×Q8—151no—
275C2×Q8—152no—
276C2×Q8C3×C4×D511yescharacteristic
277C2×D4—31no—
278C2×D4—151no—
279C2×D4—152no—
280C2×D4—152no—
281C2×D4—154no—
282C2×D4—152no—
283C22×C4—31no—
284C22×C4—51no—
285C22×C4—152no—
286C22×C4—152no—
287C22×C4—151no—
288C22×C4—152no—
289C22×C4—152no—
290C22×C4—151no—
291C22×C4—151no—
292C22×C4—151no—
293M16—32no—
294M16—32no—
295M16—158no—
296M16—152no—
297M16—152no—
298C2×C8—31no—
299C2×C8—32no—
300C2×C8—32no—
301C2×C8—51no—
302C2×C8—54no—
303C2×C8—154no—
304C2×C8—154no—
305C2×C8—152no—
306C2×C8—152no—
307C2×C8—151no—
308C2×C8—154no—
309C2×C8D5×A411yescharacteristic
310C3×C5—41noHall
311C22×C3—41no—
312C22×C3—202no—
313C22×C3—204no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—202no—
317C2×C5—61no—
318C2×C5—61no—
319C2×C5C2×#131⋊C312yescomplemented
320C2×C5C22×C4×A411yescharacteristic
321D5—62no—
322D5C2×#131⋊C314yesdirect product factor
323C23—31no—
324C23—51no—
325C23—152no—
326C23—152no—
327C23—151no—
328C23—304no—
329Q8—31no—
330Q8—152no—
331Q8—152no—
332Q8C2×C3×C4×D511yescharacteristic
333D4—31no—
334D4—31no—
335D4—32no—
336D4—152no—
337D4—152no—
338D4—154no—
339D4—154no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—51no—
346C2×C4—52no—
347C2×C4—52no—
348C2×C4—152no—
349C2×C4—152no—
350C2×C4—152no—
351C2×C4—152no—
352C2×C4—152no—
353C2×C4—152no—
354C2×C4—151no—
355C2×C4—152no—
356C2×C4—152no—
357C2×C4C2×D5×A411yescharacteristic
358C8—32no—
359C8—52no—
360C8—152no—
361C8C2×D5×A412yes—
362C2×C3—41no—
363C2×C3—42no—
364C2×C3—204no—
365C5C22×#131⋊C311yescharacteristic, complemented, Sylow
366C22—31no—
367C22—31no—
368C22—52no—
369C22—54no—
370C22—62no—
371C22—152no—
372C22—304no—
373C22—304no—
374C22—302no—
375C22C4×D5×A411yescharacteristic
376C4—31no—
377C4—31no—
378C4—52no—
379C4—152no—
380C4C4×D5×A411yescharacteristic
381C4C22×D5×A411yescharacteristic
382C3—41noSylow
383C2—54no—
384C2—61no—
385C2—61no—
386C2—302no—
387C2D5×#131⋊C312yesdirect product factor
388C2C2×C4×D5×A411yescharacteristic
subgroupG/H
center, hypercenterC2×C8D5×A4
commutator, hypocenterC5×Q8C22×C3×C4
FrattiniC4C22×D5×A4
FittingC2×C5×#131C2×C3
socleC22×C5C2×C4×A4
prime radicalC2×D5×#41⋊C3C2
cosocleC5×#41C23×C3
LCSG ▷ C5×Q8
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C5×#131⋊C3C2semidirect
3. C2×#4094⋊C3C2semidirect
4. D5×#131⋊C3C2direct (N × H)
5. C2×D5×#131C3semidirect
12. C5×#131⋊C3C22semidirect
13. #4094⋊C3C22semidirect
16. C2×C5×#131C2×C3semidirect
17. C2×#4094C2×C3semidirect
19. D5×#131C2×C3semidirect
36. C2×#131⋊C3D5direct (N × H)
49. C5×#131C22×C3semidirect
53. #4094C22×C3semidirect
85. #131⋊C3C2×D5direct (N × H)
143. C2×#131C3×D5semidirect
218. #131C2×C3×D5semidirect
251. C2×D5#131⋊C3direct (N × H)
319. C2×C5C2×#131⋊C3semidirect
322. D5C2×#131⋊C3direct (N × H)
365. C5C22×#131⋊C3semidirect
387. C2D5×#131⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#41⋊C32
C2×C5×#131⋊C32
C2×#4094⋊C32
D5×#131⋊C32
C2×D5×#1313
C2×C3×C8×D54
C22×#131⋊C35