Finite Group Databasebeta

← C3×#10601777 #14316632

Subgroups — C3×#10601777 #14316632

Order 1920.

708 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C3×#66051C211yesmaximal, characteristic, complemented
2C3×C5×#453C211yesmaximal, characteristic, complemented
3C3×#65533C212yesmaximal, complemented
4C3×#64765C211yesmaximal, characteristic, complemented
5C3×#64695C212yesmaximal, complemented
6#10601777C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
8C2×C3×D4×D5—22no—
9C3×C5×AGL(1,ℤ/8)—21no—
10C3×C5×#127C2211yescharacteristic
11C3×#4084—22no—
12C3×#4083—21no—
13C3×#4083—22no—
14C3×#4083C2212yes—
15C3×C4×D20—21no—
16C3×C5×#104—21no—
17C3×C5×#100C2211yescharacteristic, complemented
18C3×#3966—22no—
19C3×#3966C2212yescomplemented
20C3×#2196—51nomaximal, Hall
21#66051C2×C311yescharacteristic, complemented
22C5×#453C2×C311yescharacteristic, complemented
23#65533C2×C312yescomplemented
24#64765C2×C311yescharacteristic, complemented
25#64695C2×C312yescomplemented
26C23×C3×D5—21no—
27C23×C3×D5D412yescomplemented
28C3×C5×#41—21no—
29C3×C5×#41—41no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—22no—
32C2×C3×C5×D4—41no—
33C2×C3×C5×D4D411yescharacteristic, complemented
34C2×C3×C5×D4C2311yescharacteristic
35C2×C3×C22⋊D5—22no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—42no—
38C3×D4×D5—48no—
39C2×C3×D20—21no—
40C2×C3×C4×D5—22no—
41C3×C5×SD16—41no—
42C3×C5×D8—41no—
43C3×C5×M16—21no—
44C3×C42×C5D411yescharacteristic, complemented
45C3×C22⋊Dic5—21no—
46C3×C22⋊Dic5—22no—
47C3×C22⋊Dic5D412yescomplemented
48C3×#685—22no—
49C3×#685—42no—
50C3×C4⋊Dic5—21no—
51C3×D42—51no—
52C3×B(4,𝔽2)—52no—
53C3×#453D511yescharacteristic, complemented
54C3×#353—51no—
55C3×AΣL(1,𝔽16)—52no—
56C5×H(5,𝔽2)C22×C311yescharacteristic, complemented
57C2×D4×D5—22no—
58C5×AGL(1,ℤ/8)—21no—
59C5×#127C22×C311yescharacteristic
60#4084—22no—
61#4083—21no—
62#4083—22no—
63#4083C22×C312yes—
64C4×D20—21no—
65C5×#104—21no—
66C5×#100C22×C311yescharacteristic, complemented
67#3966—22no—
68#3966C22×C312yescomplemented
69#2196—51noSylow
70C23×C3×C5—22no—
71C23×C3×C5—21no—
72C23×C3×C5C2×D412yes—
73C22×C3×D5—22no—
74C22×C3×D5—44no—
75C22×C3×D5—44no—
76C22×C3×D5—42no—
77C22×C3×D5—81no—
78C3×C5×Q8—21no—
79C3×C5×D4—21no—
80C3×C5×D4—41no—
81C3×C5×D4—44no—
82C3×C5×D4—41no—
83C3×C5×D4—42no—
84C3×C5×D4—41no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C3×C22⋊D5—44no—
90C3×C22⋊D5—44no—
91C3×C22⋊D5—84no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—42no—
94C3×D20—24no—
95C3×C4×D5—44no—
96C3×C5×C8—41no—
97C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
98C22×C3×D4—102no—
99C3×AGL(1,ℤ/8)—21no—
100C3×#127C2×D511yescharacteristic
101C3×#121—102no—
102C3×#120—52no—
103C3×#120—101no—
104C3×#120—102no—
105C3×C4×D4—101no—
106C3×#104—21no—
107C3×#100C2×D511yescharacteristic, complemented
108C3×#99—52no—
109C3×#99—102no—
110C23×D5—21no—
111C23×D5C3×D412yescomplemented
112C5×#41—21no—
113C5×#41—41no—
114C2×C5×D4—22no—
115C2×C5×D4—22no—
116C2×C5×D4—41no—
117C2×C5×D4C3×D411yescharacteristic, complemented
118C2×C5×D4C23×C311yescharacteristic
119C2×C22⋊D5—22no—
120C2×C22⋊D5—22no—
121C2×C22⋊D5—42no—
122D4×D5—48no—
123C2×D20—21no—
124C2×C4×D5—22no—
125C5×SD16—41no—
126C5×D8—41no—
127C5×M16—21no—
128C42×C5C3×D411yescharacteristic, complemented
129C22⋊Dic5—21no—
130C22⋊Dic5—22no—
131C22⋊Dic5C3×D412yescomplemented
132#685—22no—
133#685—42no—
134C4⋊Dic5—21no—
135D42—51no—
136B(4,𝔽2)—52no—
137#453C3×D511yescharacteristic, complemented
138#353—51no—
139AΣL(1,𝔽16)—52no—
140C22×C3×C5—22no—
141C22×C3×C5—42no—
142C22×C3×C5—42no—
143C22×C3×C5—41no—
144C22×C3×C5—41no—
145C22×C3×C5—82no—
146C22×C3×C5#12011yescharacteristic
147C2×C3×D5—24no—
148C2×C3×D5—42no—
149C2×C3×D5—42no—
150C2×C3×D5—44no—
151C2×C3×D5—82no—
152C2×C3×D5—84no—
153C3×C4×C5—22no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×Dic5—42no—
157C3×Dic5—82no—
158C24×C3—52no—
159C24×C3—101no—
160C3×#41—21no—
161C3×#41—41no—
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—41no—
165C2×C3×D4—101no—
166C2×C3×D4—102no—
167C2×C3×D4—102no—
168C2×C3×D4—208no—
169C2×C3×D4—202no—
170C2×C3×D4C22⋊D511yescharacteristic, complemented
171C2×C3×D4C22×D511yescharacteristic
172C22×C3×C4—102no—
173C3×SD16—41no—
174C3×D8—41no—
175C3×M16—21no—
176C3×C4⋊C4—101no—
177C3×C22⋊C4—52no—
178C3×C22⋊C4—101no—
179C3×C22⋊C4—102no—
180C3×C22⋊C4—102no—
181C3×C22⋊C4—202no—
182C3×C42C22⋊D511yescharacteristic, complemented
183C23×C5—22no—
184C23×C5—21no—
185C23×C5C2×C3×D412yes—
186C22×D5—22no—
187C22×D5—44no—
188C22×D5—44no—
189C22×D5—42no—
190C22×D5—81no—
191C5×Q8—21no—
192C5×D4—21no—
193C5×D4—41no—
194C5×D4—41no—
195C5×D4—44no—
196C5×D4—42no—
197C5×D4—41no—
198C2×C4×C5—21no—
199C2×C4×C5—22no—
200C2×C4×C5—41no—
201C2×C4×C5C2×C3×D411yescharacteristic
202C22⋊D5—44no—
203C22⋊D5—44no—
204C22⋊D5—84no—
205C2×Dic5—22no—
206C2×Dic5—42no—
207D20—24no—
208C4×D5—44no—
209C5×C8—41no—
210H(5,𝔽2)C2×C3×D511yescharacteristic, complemented
211C22×D4—102no—
212AGL(1,ℤ/8)—21no—
213#127C2×C3×D511yescharacteristic
214#121—102no—
215#120—52no—
216#120—101no—
217#120—102no—
218C4×D4—101no—
219#104—21no—
220#100C2×C3×D511yescharacteristic, complemented
221#99—52no—
222#99—102no—
223C2×C3×C5—21no—
224C2×C3×C5—42no—
225C2×C3×C5—81no—
226C2×C3×C5—81no—
227C2×C3×C5B(4,𝔽2)11yescharacteristic
228C3×D5—44no—
229C23×C3—22no—
230C23×C3—21no—
231C23×C3—102no—
232C23×C3—202no—
233C23×C3—204no—
234C23×C3—204no—
235C23×C3—401no—
236C23×C3D4×D512yes—
237C3×Q8—21no—
238C3×D4—21no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—44no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—104no—
245C3×D4—204no—
246C3×D4—204no—
247C3×D4—404no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—41no—
251C2×C3×C4—102no—
252C2×C3×C4—204no—
253C2×C3×C4—202no—
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C3×C8—41no—
256C22×C5—22no—
257C22×C5—42no—
258C22×C5—42no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—82no—
262C22×C5C3×#12011yescharacteristic
263C2×D5—24no—
264C2×D5—42no—
265C2×D5—42no—
266C2×D5—44no—
267C2×D5—82no—
268C2×D5—84no—
269C4×C5—22no—
270C4×C5—21no—
271C4×C5—41no—
272Dic5—42no—
273Dic5—82no—
274C24—52no—
275C24—101no—
276#41—21no—
277#41—41no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—101no—
282C2×D4—102no—
283C2×D4—102no—
284C2×D4—208no—
285C2×D4—202no—
286C2×D4C3×C22⋊D511yescharacteristic, complemented
287C2×D4C22×C3×D511yescharacteristic
288C22×C4—102no—
289SD16—41no—
290D8—41no—
291M16—21no—
292C4⋊C4—101no—
293C22⋊C4—52no—
294C22⋊C4—101no—
295C22⋊C4—102no—
296C22⋊C4—102no—
297C22⋊C4—202no—
298C42C3×C22⋊D511yescharacteristic, complemented
299C3×C5#219611yescharacteristic, complemented, Hall
300C22×C3—22no—
301C22×C3—42no—
302C22×C3—42no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—82no—
306C22×C3—104no—
307C22×C3—202no—
308C22×C3—204no—
309C22×C3—202no—
310C22×C3—402no—
311C22×C3—404no—
312C22×C3#408311yescharacteristic
313C3×C4—22no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—202no—
317C3×C4—402no—
318C2×C5—21no—
319C2×C5—42no—
320C2×C5—81no—
321C2×C5—81no—
322C2×C5C3×B(4,𝔽2)11yescharacteristic
323D5—44no—
324C23—22no—
325C23—21no—
326C23—102no—
327C23—202no—
328C23—204no—
329C23—204no—
330C23—401no—
331C23C3×D4×D512yes—
332Q8—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—44no—
337D4—42no—
338D4—41no—
339D4—104no—
340D4—204no—
341D4—204no—
342D4—404no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—102no—
347C2×C4—204no—
348C2×C4—202no—
349C2×C4C2×C3×C22⋊D511yescharacteristic
350C8—41no—
351C2×C3—21no—
352C2×C3—42no—
353C2×C3—81no—
354C2×C3—81no—
355C2×C3—204no—
356C2×C3#6532111yescharacteristic
357C5C3×#219611yescharacteristic, complemented, Sylow
358C22—22no—
359C22—42no—
360C22—42no—
361C22—41no—
362C22—41no—
363C22—82no—
364C22—104no—
365C22—202no—
366C22—204no—
367C22—202no—
368C22—402no—
369C22—404no—
370C22C3×#408311yescharacteristic
371C4—22no—
372C4—21no—
373C4—41no—
374C4—202no—
375C4—402no—
376C3#1060177711yescharacteristic, direct product factor, Sylow
377C2—21no—
378C2—42no—
379C2—81no—
380C2—81no—
381C2—204no—
382C2C3×#6532111yescharacteristic
subgroupG/H
centerC2×C3#65321
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#453C2
socleC2×C3×C5B(4,𝔽2)
hypercenterC3×#453D5
hypocenterC5C3×#2196
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#453

Complements

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

NH ≅ G/Ntype
1. C3×#66051C2semidirect
2. C3×C5×#453C2semidirect
3. C3×#65533C2semidirect
4. C3×#64765C2semidirect
5. C3×#64695C2semidirect
6. #10601777C3direct (N × H)
7. C3×C5×H(5,𝔽2)C22semidirect
17. C3×C5×#100C22semidirect
19. C3×#3966C22semidirect
21. #66051C2×C3semidirect
22. C5×#453C2×C3semidirect
23. #65533C2×C3semidirect
24. #64765C2×C3semidirect
25. #64695C2×C3semidirect
27. C23×C3×D5D4semidirect
33. C2×C3×C5×D4D4semidirect
44. C3×C42×C5D4semidirect
47. C3×C22⋊Dic5D4semidirect
53. C3×#453D5semidirect
56. C5×H(5,𝔽2)C22×C3semidirect
66. C5×#100C22×C3semidirect
68. #3966C22×C3semidirect
97. C3×H(5,𝔽2)C2×D5semidirect
107. C3×#100C2×D5semidirect
111. C23×D5C3×D4semidirect
117. C2×C5×D4C3×D4semidirect
128. C42×C5C3×D4semidirect
131. C22⋊Dic5C3×D4semidirect
137. #453C3×D5semidirect
170. C2×C3×D4C22⋊D5semidirect
182. C3×C42C22⋊D5semidirect
210. H(5,𝔽2)C2×C3×D5semidirect
220. #100C2×C3×D5semidirect
286. C2×D4C3×C22⋊D5semidirect
298. C42C3×C22⋊D5semidirect
299. C3×C5#2196semidirect
357. C5C3×#2196semidirect
376. C3#10601777direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660512
C3×C5×#4532
C3×#655332
C3×#647652
C3×#646952
#106017773
C3×#21965