Finite Group Databasebeta

← C2×#66168⋊C3 #14514209

Subgroups — C2×#66168⋊C3 #14514209

Order 1920.

822 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C22×C5×#41⋊C3C211yesmaximal, characteristic, complemented
2C22×C5⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
3#66168⋊C3C214yesmaximal, direct product factor
4C2×Dic5×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×#66168C311yesmaximal, characteristic, complemented, Hall
6C2×C5×#41⋊C3—22no—
7C2×C5×#41⋊C3C2212yescomplemented
8C22×C5×SL(2,𝔽3)C2211yescharacteristic
9C2×C5⋊(#41⋊C3)—22no—
10C2×C5⋊(#41⋊C3)C2212yescomplemented
11C2×C3×#683—41nomaximal
12Dic5×SL(2,𝔽3)C2212yescomplemented
13C2×C4⋊(#41⋊C3)—51nomaximal, Hall
14C22×C5×#41C2×C311yescharacteristic
15C22×#713C2×C311yescharacteristic
16#66168—34no—
17#66168C2×C314yescomplemented
18C2×Q8×Dic5C2×C311yescharacteristic
19C2×#4086—31no—
20C2×#4084—31no—
21C2×#4076—31no—
22C2×C4×C22⋊D5—31no—
23C22×C3×C4×C5—41no—
24C22×C3×Dic5—41no—
25C22×C3×Dic5—41no—
26C5×#41⋊C3—22no—
27C2×C5×SL(2,𝔽3)D412yescomplemented
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C5⋊(#41⋊C3)—22no—
30C3×#683—44no—
31C22×#41⋊C3—51no—
32C22×#41⋊C3D511yescharacteristic, complemented
33C4⋊(#41⋊C3)—54no—
34C2×C4×SL(2,𝔽3)—51no—
35C2×C5×#41—22no—
36C2×C5×#41—32no—
37C2×C5×#41—62no—
38C2×C5×#41C22×C312yes—
39C22×C5×Q8C22×C311yescharacteristic
40C22×C5×D4—31no—
41C23×C4×C5—31no—
42C22×C22⋊D5—32no—
43C22×C22⋊D5—31no—
44C2×#713—22no—
45C2×#713—32no—
46C2×#713—62no—
47C2×#713C22×C312yes—
48C22×D20—31no—
49C22×C4×D5—31no—
50C2×C22⋊Dic5—31no—
51Q8×Dic5—32no—
52Q8×Dic5C22×C312yes—
53#4086—34no—
54#4086—34no—
55#4084—34no—
56#4084—34no—
57#4076—34no—
58#4076—34no—
59C4×C22⋊D5—34no—
60C4×C22⋊D5—34no—
61C2×#685—31no—
62C2×C4⋊Dic5—31no—
63C2×#683A411yescharacteristic
64C2×C4×Dic5—31no—
65C2×#550—51noSylow
66C23×C3×C5—41no—
67C2×C3×C4×C5—42no—
68C2×C3×C4×C5—82no—
69C2×C3×Dic5—44no—
70C2×C3×Dic5—42no—
71C2×C3×Dic5—42no—
72C2×C3×Dic5—82no—
73C5×SL(2,𝔽3)C2×D411yescharacteristic, complemented
74C2×#41⋊C3—22no—
75C2×#41⋊C3—52no—
76C2×#41⋊C3—102no—
77C2×#41⋊C3C2×D512yescomplemented
78C22×SL(2,𝔽3)C2×D511yescharacteristic
79C2×C3×C4⋊C4—201no—
80C4×SL(2,𝔽3)—52no—
81C24×C5—31no—
82C23×D5—31no—
83C5×#41—22no—
84C5×#41—64no—
85C5×#41—64no—
86C5×#41—62no—
87C2×C5×Q8—31no—
88C2×C5×Q8—32no—
89C2×C5×Q8C3×D412yes—
90C2×C5×Q8C23×C311yescharacteristic
91C2×C5×D4—32no—
92C2×C5×D4—32no—
93C2×C5×D4—62no—
94C2×C5×D4—62no—
95C22×C4×C5—31no—
96C22×C4×C5—32no—
97C22×C4×C5—32no—
98C22×C4×C5—62no—
99C22×C4×C5—62no—
100C22×C4×C5C2×A411yescharacteristic
101C2×C22⋊D5—38no—
102C2×C22⋊D5—34no—
103C2×C22⋊D5—64no—
104C2×C22⋊D5—124no—
105C22×Dic5—31no—
106C22×Dic5C2×A411yescharacteristic
107C22×Dic5C2×A411yescharacteristic
108#713—22no—
109#713—64no—
110#713—64no—
111#713—62no—
112C2×D20—32no—
113C2×D20—32no—
114C2×D20—62no—
115C2×D20—62no—
116C2×C4×D5—32no—
117C2×C4×D5—32no—
118C2×C4×D5—62no—
119C2×C4×D5—62no—
120C22⋊Dic5—34no—
121#685—34no—
122C4⋊Dic5—32no—
123C4⋊Dic5—32no—
124#683C2×A414yes—
125C4×Dic5—32no—
126C4×Dic5—32no—
127C22×#41—51no—
128C22×#41C3×D511yescharacteristic
129#550—54no—
130#550—154no—
131C2×#127—151no—
132C2×#121—151no—
133C2×#121—151no—
134C2×C4×Q8—51no—
135C2×C4×D4—151no—
136C22×C3×C5—42no—
137C22×C3×C5—42no—
138C22×C3×C5—42no—
139C22×C3×C5—41no—
140C3×C4×C5—82no—
141C3×Dic5—44no—
142C3×Dic5—82no—
143C22×C3×C4—41no—
144C22×C3×C4—201no—
145C22×C3×C4—201no—
146#41⋊C3—22no—
147#41⋊C3—102no—
148C2×SL(2,𝔽3)C22⋊D512yescomplemented
149C2×SL(2,𝔽3)C22×D511yescharacteristic
150C3×C4⋊C4—204no—
151C23×C5—32no—
152C23×C5—62no—
153C23×C5—62no—
154C23×C5—62no—
155C23×C5C22×A411yescharacteristic
156C22×D5—32no—
157C22×D5—62no—
158C22×D5—62no—
159C22×D5—62no—
160C5×Q8—32no—
161C5×Q8—31no—
162C5×Q8—32no—
163C5×Q8C2×C3×D411yescharacteristic
164C5×D4—62no—
165C5×D4—62no—
166C5×D4—64no—
167C2×C4×C5—22no—
168C2×C4×C5—32no—
169C2×C4×C5—32no—
170C2×C4×C5—31no—
171C2×C4×C5—31no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5—64no—
175C2×C4×C5C22×A412yes—
176C22⋊D5—68no—
177C22⋊D5—128no—
178C2×Dic5—22no—
179C2×Dic5—32no—
180C2×Dic5—62no—
181C2×Dic5#41⋊C314yescomplemented
182C2×Dic5C22×A412yes—
183C2×Dic5C22×A412yes—
184D20—62no—
185D20—62no—
186D20—64no—
187C4×D5—62no—
188C4×D5—62no—
189C4×D5—64no—
190C2×#41—22no—
191C2×#41—32no—
192C2×#41—52no—
193C2×#41—62no—
194C2×#41—102no—
195C2×#41—152no—
196C2×#41—302no—
197C2×#41C2×C3×D512yes—
198C22×Q8C2×C3×D511yescharacteristic
199C22×D4—31no—
200C22×D4—151no—
201C22×D4—151no—
202C22×D4—152no—
203C23×C4—31no—
204C23×C4—151no—
205#127—154no—
206#127—154no—
207#121—154no—
208#121—154no—
209#121—154no—
210#121—154no—
211C4×Q8—52no—
212C4×Q8—152no—
213C4×D4—154no—
214C4×D4—154no—
215C2×C4⋊C4—51no—
216C2×C4⋊C4—151no—
217C2×C22⋊C4—151no—
218C2×C22⋊C4—151no—
219C2×C42—151no—
220C2×C3×C5—41no—
221C2×C3×C5—41no—
222C2×C3×C5—41no—
223C2×C3×C5—44no—
224C23×C3—41no—
225C2×C3×C4—42no—
226C2×C3×C4—82no—
227C2×C3×C4—202no—
228C2×C3×C4—204no—
229C2×C3×C4—202no—
230C2×C3×C4—402no—
231SL(2,𝔽3)C2×C22⋊D511yescharacteristic, complemented
232C22×C5—62no—
233C22×C5—62no—
234C22×C5—62no—
235C22×C5—124no—
236C22×C5D4×A412yes—
237C22×C5C2×#41⋊C312yes—
238C22×C5#99412yes—
239C22×C5C23×A411yescharacteristic
240C2×D5—62no—
241C2×D5—62no—
242C2×D5—62no—
243C2×D5—124no—
244C4×C5—22no—
245C4×C5—31no—
246C4×C5—32no—
247C4×C5—31no—
248Dic5—22no—
249Dic5—62no—
250Dic5C2×#41⋊C314yescomplemented
251C24—31no—
252C24—151no—
253#41—22no—
254#41—64no—
255#41—64no—
256#41—62no—
257#41—102no—
258#41—304no—
259#41—304no—
260#41—302no—
261C2×Q8—31no—
262C2×Q8—32no—
263C2×Q8C3×C22⋊D512yes—
264C2×Q8C22×C3×D511yescharacteristic
265C2×D4—32no—
266C2×D4—32no—
267C2×D4—62no—
268C2×D4—62no—
269C2×D4—152no—
270C2×D4—152no—
271C2×D4—154no—
272C2×D4—158no—
273C2×D4—302no—
274C2×D4—302no—
275C2×D4—304no—
276C2×D4—604no—
277C22×C4—31no—
278C22×C4—32no—
279C22×C4—32no—
280C22×C4—51no—
281C22×C4—51no—
282C22×C4—62no—
283C22×C4—62no—
284C22×C4—152no—
285C22×C4—152no—
286C22×C4—151no—
287C22×C4—302no—
288C22×C4—302no—
289C22×C4D5×A411yescharacteristic
290C4⋊C4—54no—
291C4⋊C4—152no—
292C4⋊C4—152no—
293C22⋊C4—154no—
294C22⋊C4—154no—
295C42—152no—
296C42—152no—
297C3×C5—41noHall
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—42no—
301C22×C3—41no—
302C3×C4—82no—
303C3×C4—204no—
304C3×C4—402no—
305C2×C5—122no—
306C2×C5C4⋊(#41⋊C3)14yescomplemented
307C2×C5C2×D4×A411yescharacteristic
308C2×C5C22×#41⋊C311yescharacteristic
309C2×C5C2×#99411yescharacteristic
310D5—122no—
311C23—32no—
312C23—62no—
313C23—62no—
314C23—62no—
315C23—152no—
316C23—302no—
317C23—302no—
318C23—302no—
319C23C2×D5×A411yescharacteristic
320Q8—32no—
321Q8—31no—
322Q8—32no—
323Q8C2×C3×C22⋊D511yescharacteristic
324D4—62no—
325D4—62no—
326D4—64no—
327D4—302no—
328D4—302no—
329D4—304no—
330D4—308no—
331D4—608no—
332C2×C4—22no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—54no—
338C2×C4—52no—
339C2×C4—52no—
340C2×C4—62no—
341C2×C4—62no—
342C2×C4—64no—
343C2×C4—102no—
344C2×C4—152no—
345C2×C4—302no—
346C2×C4—302no—
347C2×C4—304no—
348C2×C4—302no—
349C2×C4C2×D5×A412yes—
350C2×C3—44no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—41no—
354C5C2×C4⋊(#41⋊C3)11yescharacteristic, complemented, Sylow
355C22—62no—
356C22—62no—
357C22—62no—
358C22—124no—
359C22—302no—
360C22—302no—
361C22—302no—
362C22—604no—
363C22C5⋊#99412yes—
364C22D5×#41⋊C312yes—
365C22A4×C22⋊D512yes—
366C22C22×D5×A411yescharacteristic
367C4—22no—
368C4—31no—
369C4—32no—
370C4—31no—
371C4—54no—
372C4—102no—
373C4—302no—
374C3—41noSylow
375C2—122no—
376C2—602no—
377C2#66168⋊C314yesdirect product factor
378C2C2×C5⋊#99411yescharacteristic
379C2C2×D5×#41⋊C311yescharacteristic
380C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
centerC23C2×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC22C22×D5×A4
FittingC22×C5×#41C2×C3
socleC23×C5C22×A4
hypercenterC22×C4D5×A4
hypocenterC5×Q8C2×C3×D4
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#41⋊C3C2semidirect
2. C22×C5⋊(#41⋊C3)C2semidirect
3. #66168⋊C3C2direct (N × H)
4. C2×Dic5×SL(2,𝔽3)C2semidirect
5. C2×#66168C3semidirect
7. C2×C5×#41⋊C3C22semidirect
10. C2×C5⋊(#41⋊C3)C22semidirect
12. Dic5×SL(2,𝔽3)C22semidirect
17. #66168C2×C3semidirect
27. C2×C5×SL(2,𝔽3)D4semidirect
32. C22×#41⋊C3D5semidirect
73. C5×SL(2,𝔽3)C2×D4semidirect
77. C2×#41⋊C3C2×D5semidirect
148. C2×SL(2,𝔽3)C22⋊D5semidirect
181. C2×Dic5#41⋊C3semidirect
231. SL(2,𝔽3)C2×C22⋊D5semidirect
250. Dic5C2×#41⋊C3semidirect
306. C2×C5C4⋊(#41⋊C3)semidirect
354. C5C2×C4⋊(#41⋊C3)semidirect
377. C2#66168⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#41⋊C32
C22×C5⋊(#41⋊C3)2
#66168⋊C32
C2×Dic5×SL(2,𝔽3)2
C2×#661683
C2×C3×#6834
C2×C4⋊(#41⋊C3)5