Finite Group Databasebeta

← C3×#10599986 #14316167

Subgroups — C3×#10599986 #14316167

Order 1920.

512 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3×D5×D8C211yesmaximal, characteristic
2C2×C3×#3959C211yesmaximal, characteristic, complemented
3C2×C3×#3932C211yesmaximal, characteristic, complemented
4C3×#65176C211yesmaximal, characteristic, complemented
5C3×C5×#357C211yesmaximal, characteristic, complemented
6C3×#64727C211yesmaximal, characteristic, complemented
7C3×#64711C211yesmaximal, characteristic, complemented
8#10599986C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×C3×#686—21no—
12C3×D5×D8—22no—
13C3×D5×D8—22no—
14C2×C3×Dic20C2211yescharacteristic, complemented
15C2×C3×D40C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17C3×#4043—21no—
18C2×C3×C5×C16C2211yescharacteristic, complemented
19C3×C5×#107C2211yescharacteristic, complemented
20C3×#3959—22no—
21C2×C3×#672C2211yescharacteristic, complemented
22C3×#3942—21no—
23C3×#3932—22no—
24C3×#2187—51nomaximal, Hall
25C2×D5×D8C2×C311yescharacteristic
26C2×#3959C2×C311yescharacteristic, complemented
27C2×#3932C2×C311yescharacteristic, complemented
28#65176C2×C311yescharacteristic, complemented
29C5×#357C2×C311yescharacteristic, complemented
30#64727C2×C311yescharacteristic, complemented
31#64711C2×C311yescharacteristic, complemented
32C23×C3×D5—41no—
33C2×C3×C5×D4—21no—
34C2×C3×C22⋊D5—41no—
35C3×D4×D5—24no—
36C3×D4×D5—42no—
37C2×C3×D20—21no—
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10—21no—
40C3×C5×D8—21no—
41C3×C5×D8D412yes—
42C2×C3×C5×C8C2311yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×#686—24no—
45C3×#685—41no—
46C3×C4⋊Dic5—41no—
47C2×C3×#168D411yescharacteristic
48C3×Dic20—21no—
49C3×Dic20—21no—
50C3×D40—21no—
51C3×D40D412yes—
52C3×C8×D5—21no—
53C3×C8×D5—21no—
54C3×C5×C16—21no—
55C3×#672—21no—
56C22×C3×D8—51no—
57C2×C3×SD32—51no—
58C2×C3×SD32—51no—
59C3×#467—51no—
60C3×#357—51no—
61C3×#357D511yescharacteristic, complemented
62C3×C22⋊C16—51no—
63C2×D4×D5—21no—
64C2×C5×D8C22×C311yescharacteristic
65C2×#686—21no—
66D5×D8—22no—
67D5×D8—22no—
68C2×Dic20C22×C311yescharacteristic, complemented
69C2×D40C22×C311yescharacteristic
70C2×C8×D5C22×C311yescharacteristic
71#4043—21no—
72C2×C5×C16C22×C311yescharacteristic, complemented
73C5×#107C22×C311yescharacteristic, complemented
74#3959—22no—
75C2×#672C22×C311yescharacteristic, complemented
76#3942—21no—
77#3932—22no—
78#2187—51noSylow
79C23×C3×C5—41no—
80C22×C3×D5—44no—
81C22×C3×D5—41no—
82C22×C3×D5—82no—
83C22×C3×D5—82no—
84C22×C3×D5D811yescharacteristic
85C3×C5×D4—22no—
86C3×C5×D4—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C3×C22⋊D5—44no—
90C2×C3×Dic5—41no—
91C2×C3×Dic5D811yescharacteristic
92C3×D20—22no—
93C3×D20—41no—
94C3×C4×D5—21no—
95C3×C4×D5—21no—
96C3×Dic10—41no—
97C3×Dic10—41no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C3×#168—21no—
101C22×C3×D4—101no—
102C2×C3×Q16—51no—
103C2×C3×D8—51no—
104C2×C3×D8—101no—
105C2×C3×D8—102no—
106C2×C3×D8—102no—
107C2×C3×D8C2×D511yescharacteristic
108C22×C3×C8—51no—
109C3×C22⋊Q8—101no—
110C3×SD32—102no—
111C3×SD32—102no—
112C2×C3×C16—51no—
113C2×C3×C16C2×D511yescharacteristic, complemented
114C3×#107C2×D511yescharacteristic, complemented
115C3×#103—101no—
116C23×D5—41no—
117C2×C5×D4—21no—
118C2×C22⋊D5—41no—
119D4×D5—24no—
120D4×D5—42no—
121C2×D20—21no—
122C2×C4×D5C3×D411yescharacteristic
123C2×Dic10—21no—
124C5×D8—21no—
125C5×D8C3×D412yes—
126C2×C5×C8C23×C311yescharacteristic
127C5×C4⋊C4—21no—
128#686—24no—
129#685—41no—
130C4⋊Dic5—41no—
131C2×#168C3×D411yescharacteristic
132Dic20—21no—
133Dic20—21no—
134D40—21no—
135D40C3×D412yes—
136C8×D5—21no—
137C8×D5—21no—
138C5×C16—21no—
139#672—21no—
140C22×D8—51no—
141C2×SD32—51no—
142C2×SD32—51no—
143#467—51no—
144#357—51no—
145#357C3×D511yescharacteristic, complemented
146C22⋊C16—51no—
147C22×C3×C5—42no—
148C22×C3×C5—81no—
149C22×C3×C5—81no—
150C22×C3×C5C2×D811yescharacteristic
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—42no—
154C2×C3×D5—88no—
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5SD3212yescomplemented
158C3×C4×C5—81no—
159C3×C4×C5#12011yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×Dic5—21no—
162C3×Dic5—81no—
163C24×C3—201no—
164C2×C3×Q8—101no—
165C2×C3×D4—21no—
166C2×C3×D4—104no—
167C2×C3×D4—101no—
168C2×C3×D4—201no—
169C2×C3×D4—202no—
170C22×C3×C4—51no—
171C3×Q16—101no—
172C3×Q16—101no—
173C3×D8—21no—
174C3×D8—52no—
175C3×D8—104no—
176C3×D8—101no—
177C3×D8D2012yes—
178C2×C3×C8—51no—
179C2×C3×C8—101no—
180C2×C3×C8—101no—
181C2×C3×C8C22×D511yescharacteristic
182C3×C4⋊C4—21no—
183C3×C4⋊C4—201no—
184C3×C22⋊C4—201no—
185C3×C16—21no—
186C3×C16—101no—
187C23×C5—41no—
188C22×D5—44no—
189C22×D5—41no—
190C22×D5—82no—
191C22×D5—82no—
192C22×D5C3×D811yescharacteristic
193C5×D4—22no—
194C5×D4—41no—
195C2×C4×C5—41no—
196C2×C4×C5C2×C3×D411yescharacteristic
197C22⋊D5—44no—
198C2×Dic5—41no—
199C2×Dic5C3×D811yescharacteristic
200D20—22no—
201D20—41no—
202C4×D5—21no—
203C4×D5—21no—
204Dic10—41no—
205Dic10—41no—
206C5×C8C2×C3×D411yescharacteristic
207C5×C8C2×C3×D411yescharacteristic
208#168—21no—
209C22×D4—101no—
210C2×Q16—51no—
211C2×D8—51no—
212C2×D8—101no—
213C2×D8—102no—
214C2×D8—102no—
215C2×D8C2×C3×D511yescharacteristic
216C22×C8—51no—
217C22⋊Q8—101no—
218SD32—102no—
219SD32—102no—
220C2×C16—51no—
221C2×C16C2×C3×D511yescharacteristic, complemented
222#107C2×C3×D511yescharacteristic, complemented
223#103—101no—
224C2×C3×C5—82no—
225C2×C3×C5#44711yescharacteristic
226C2×C3×C5C2×SD3211yescharacteristic
227C2×C3×C5#50911yescharacteristic
228C3×D5—22no—
229C3×D5—82no—
230C23×C3—41no—
231C23×C3—51no—
232C23×C3—204no—
233C23×C3—201no—
234C23×C3—402no—
235C23×C3—402no—
236C3×Q8—201no—
237C3×Q8—201no—
238C3×D4—22no—
239C3×D4—41no—
240C3×D4—102no—
241C3×D4—204no—
242C3×D4—201no—
243C2×C3×C4—41no—
244C2×C3×C4—51no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—201no—
248C2×C3×C4D4×D511yescharacteristic
249C3×C8—101no—
250C3×C8C2×D2011yescharacteristic
251C3×C8D4×D511yescharacteristic
252C22×C5—42no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5C2×C3×D811yescharacteristic
256C2×D5—21no—
257C2×D5—21no—
258C2×D5—42no—
259C2×D5—88no—
260C2×D5—81no—
261C2×D5—81no—
262C2×D5C3×SD3212yescomplemented
263C4×C5—81no—
264C4×C5C3×#12011yescharacteristic
265C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
266Dic5—21no—
267Dic5—81no—
268C24—201no—
269C2×Q8—101no—
270C2×D4—21no—
271C2×D4—104no—
272C2×D4—101no—
273C2×D4—201no—
274C2×D4—202no—
275C22×C4—51no—
276Q16—101no—
277Q16—101no—
278D8—21no—
279D8—52no—
280D8—104no—
281D8—101no—
282D8C3×D2012yes—
283C2×C8—51no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8C22×C3×D511yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—201no—
289C22⋊C4—201no—
290C16—21no—
291C16—101no—
292C3×C5#218711yescharacteristic, complemented, Hall
293C22×C3—42no—
294C22×C3—52no—
295C22×C3—81no—
296C22×C3—81no—
297C22×C3—101no—
298C22×C3—101no—
299C22×C3—202no—
300C22×C3—408no—
301C22×C3—401no—
302C22×C3—401no—
303C22×C3D5×D811yescharacteristic
304C3×C4—81no—
305C3×C4—101no—
306C3×C4—401no—
307C3×C4#402811yescharacteristic
308C3×C4#406011yescharacteristic
309C2×C5—82no—
310C2×C5C3×#44711yescharacteristic
311C2×C5C2×C3×SD3211yescharacteristic
312C2×C5C3×#50911yescharacteristic
313D5—22no—
314D5—82no—
315C23—41no—
316C23—51no—
317C23—204no—
318C23—201no—
319C23—402no—
320C23—402no—
321Q8—201no—
322Q8—201no—
323D4—22no—
324D4—41no—
325D4—102no—
326D4—204no—
327D4—201no—
328C2×C4—41no—
329C2×C4—51no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—201no—
333C2×C4C3×D4×D511yescharacteristic
334C8—101no—
335C8C2×C3×D2011yescharacteristic
336C8C3×D4×D511yescharacteristic
337C2×C3—82no—
338C2×C3—102no—
339C2×C3—402no—
340C2×C3#6506211yescharacteristic
341C2×C3#6520011yescharacteristic
342C2×C3D5×SD3211yescharacteristic
343C5C3×#218711yescharacteristic, complemented, Sylow
344C22—42no—
345C22—52no—
346C22—81no—
347C22—81no—
348C22—101no—
349C22—101no—
350C22—202no—
351C22—408no—
352C22—401no—
353C22—401no—
354C22C3×D5×D811yescharacteristic
355C4—81no—
356C4—101no—
357C4—401no—
358C4C3×#402811yescharacteristic
359C4C3×#406011yescharacteristic
360C3#1059998611yescharacteristic, direct product factor, Sylow
361C2—82no—
362C2—102no—
363C2—402no—
364C2C3×#6506211yescharacteristic
365C2C3×#6520011yescharacteristic
366C2C3×D5×SD3211yescharacteristic
subgroupG/H
centerC22×C3D5×D8
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×D5×D8C2
hypercenterC3×#357D5
hypocenterC5C3×#2187
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#357

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3959C2semidirect
3. C2×C3×#3932C2semidirect
4. C3×#65176C2semidirect
5. C3×C5×#357C2semidirect
6. C3×#64727C2semidirect
7. C3×#64711C2semidirect
8. #10599986C3direct (N × H)
14. C2×C3×Dic20C22semidirect
18. C2×C3×C5×C16C22semidirect
19. C3×C5×#107C22semidirect
21. C2×C3×#672C22semidirect
26. C2×#3959C2×C3semidirect
27. C2×#3932C2×C3semidirect
28. #65176C2×C3semidirect
29. C5×#357C2×C3semidirect
30. #64727C2×C3semidirect
31. #64711C2×C3semidirect
61. C3×#357D5semidirect
68. C2×Dic20C22×C3semidirect
72. C2×C5×C16C22×C3semidirect
73. C5×#107C22×C3semidirect
75. C2×#672C22×C3semidirect
113. C2×C3×C16C2×D5semidirect
114. C3×#107C2×D5semidirect
145. #357C3×D5semidirect
157. C2×C3×D5SD32semidirect
221. C2×C16C2×C3×D5semidirect
222. #107C2×C3×D5semidirect
262. C2×D5C3×SD32semidirect
292. C3×C5#2187semidirect
343. C5C3×#2187semidirect
360. C3#10599986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×D82
C2×C3×#39592
C2×C3×#39322
C3×#651762
C3×C5×#3572
C3×#647272
C3×#647112
#105999863
C3×#21875