Finite Group Databasebeta

← C3×#10599984 #14316026

Subgroups — C3×#10599984 #14316026

Order 1920.

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

normal subgroups only

This group has 532 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, complemented
2C2×C3×#3958C211yesmaximal, characteristic, complemented
3C2×C3×D80C211yesmaximal, characteristic, complemented
4C3×#65172C211yesmaximal, characteristic, complemented
5C3×C5×#357C211yesmaximal, characteristic, complemented
6C3×#64727C211yesmaximal, characteristic, complemented
7C3×#64711C211yesmaximal, characteristic, complemented
8#10599984C311yesmaximal, 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×D40C2211yescharacteristic
15C2×C3×D40C2211yescharacteristic, complemented
16C2×C3×C8×D5C2211yescharacteristic
17C3×#4041—21no—
18C2×C3×C5×C16C2211yescharacteristic, complemented
19C3×C5×#107C2211yescharacteristic, complemented
20C3×#3958—22no—
21C2×C3×#672C2211yescharacteristic, complemented
22C3×#3941—21no—
23C3×D80—22no—
24C3×#2184—51nomaximal, Hall
25C2×D5×D8C2×C311yescharacteristic, complemented
26C2×#3958C2×C311yescharacteristic, complemented
27C2×D80C2×C311yescharacteristic, complemented
28#65172C2×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×D20—21no—
39C2×C3×D20—41no—
40C2×C3×C4×D5D411yescharacteristic
41C3×C5×D8—21no—
42C3×C5×D8D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44C3×C5×C4⋊C4—21no—
45C3×#686—24no—
46C3×#685—41no—
47C2×C3×#168D411yescharacteristic
48C3×D40—21no—
49C3×D40—21no—
50C3×D40—21no—
51C3×D40D412yescomplemented
52C3×C8×D5—21no—
53C3×C8×D5—21no—
54C3×C5×C16—21no—
55C3×#672—21no—
56C22×C3×D8—51no—
57C2×C3×D16—51no—
58C2×C3×D16—51no—
59C3×#466—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×D40C22×C311yescharacteristic
69C2×D40C22×C311yescharacteristic, complemented
70C2×C8×D5C22×C311yescharacteristic
71#4041—21no—
72C2×C5×C16C22×C311yescharacteristic, complemented
73C5×#107C22×C311yescharacteristic, complemented
74#3958—22no—
75C2×#672C22×C311yescharacteristic, complemented
76#3941—21no—
77D80—22no—
78#2184—51noSylow
79C23×C3×C5—41no—
80C22×C3×D5—44no—
81C22×C3×D5—41no—
82C22×C3×D5—41no—
83C22×C3×D5—82no—
84C22×C3×D5—82no—
85C22×C3×D5D811yescharacteristic
86C3×C5×D4—22no—
87C3×C5×D4—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C3×C22⋊D5—44no—
91C2×C3×Dic5D811yescharacteristic
92C3×D20—22no—
93C3×D20—41no—
94C3×D20—41no—
95C3×D20—41no—
96C3×D20—82no—
97C3×C4×D5—21no—
98C3×C4×D5—21no—
99C3×C5×C8C2×D411yescharacteristic
100C3×C5×C8C2×D411yescharacteristic
101C3×#168—21no—
102C22×C3×D4—101no—
103C2×C3×D8—51no—
104C2×C3×D8—51no—
105C2×C3×D8—101no—
106C2×C3×D8—102no—
107C2×C3×D8—102no—
108C2×C3×D8C2×D511yescharacteristic
109C22×C3×C8—51no—
110C3×#121—101no—
111C3×D16—102no—
112C3×D16—102no—
113C2×C3×C16—51no—
114C2×C3×C16C2×D511yescharacteristic, complemented
115C3×#107C2×D511yescharacteristic, complemented
116C3×#102—101no—
117C23×D5—41no—
118C2×C5×D4—21no—
119C2×C22⋊D5—41no—
120D4×D5—24no—
121D4×D5—42no—
122C2×D20—21no—
123C2×D20—21no—
124C2×D20—41no—
125C2×C4×D5C3×D411yescharacteristic
126C5×D8—21no—
127C5×D8C3×D412yescomplemented
128C2×C5×C8C23×C311yescharacteristic
129C5×C4⋊C4—21no—
130#686—24no—
131#685—41no—
132C2×#168C3×D411yescharacteristic
133D40—21no—
134D40—21no—
135D40—21no—
136D40C3×D412yescomplemented
137C8×D5—21no—
138C8×D5—21no—
139C5×C16—21no—
140#672—21no—
141C22×D8—51no—
142C2×D16—51no—
143C2×D16—51no—
144#466—51no—
145#357—51no—
146#357C3×D511yescharacteristic, complemented
147C22⋊C16—51no—
148C22×C3×C5—42no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5C2×D811yescharacteristic
152C2×C3×D5—21no—
153C2×C3×D5—21no—
154C2×C3×D5—42no—
155C2×C3×D5—88no—
156C2×C3×D5—81no—
157C2×C3×D5—81no—
158C2×C3×D5—81no—
159C2×C3×D5—81no—
160C2×C3×D5—81no—
161C2×C3×D5D1612yescomplemented
162C3×C4×C5—81no—
163C3×C4×C5#12011yescharacteristic
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×Dic5—21no—
166C24×C3—201no—
167C2×C3×D4—21no—
168C2×C3×D4—104no—
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C2×C3×D4—201no—
172C2×C3×D4—201no—
173C2×C3×D4—202no—
174C22×C3×C4—51no—
175C3×D8—21no—
176C3×D8—52no—
177C3×D8—104no—
178C3×D8—101no—
179C3×D8—101no—
180C3×D8—101no—
181C3×D8D2012yescomplemented
182C2×C3×C8—51no—
183C2×C3×C8—101no—
184C2×C3×C8—101no—
185C2×C3×C8C22×D511yescharacteristic
186C3×C4⋊C4—21no—
187C3×C22⋊C4—201no—
188C3×C16—21no—
189C3×C16—101no—
190C23×C5—41no—
191C22×D5—44no—
192C22×D5—41no—
193C22×D5—41no—
194C22×D5—82no—
195C22×D5—82no—
196C22×D5C3×D811yescharacteristic
197C5×D4—22no—
198C5×D4—41no—
199C2×C4×C5—41no—
200C2×C4×C5C2×C3×D411yescharacteristic
201C22⋊D5—44no—
202C2×Dic5C3×D811yescharacteristic
203D20—22no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—82no—
208C4×D5—21no—
209C4×D5—21no—
210C5×C8C2×C3×D411yescharacteristic
211C5×C8C2×C3×D411yescharacteristic
212#168—21no—
213C22×D4—101no—
214C2×D8—51no—
215C2×D8—51no—
216C2×D8—101no—
217C2×D8—102no—
218C2×D8—102no—
219C2×D8C2×C3×D511yescharacteristic
220C22×C8—51no—
221#121—101no—
222D16—102no—
223D16—102no—
224C2×C16—51no—
225C2×C16C2×C3×D511yescharacteristic, complemented
226#107C2×C3×D511yescharacteristic, complemented
227#102—101no—
228C2×C3×C5—82no—
229C2×C3×C5#44711yescharacteristic
230C2×C3×C5C2×D1611yescharacteristic
231C2×C3×C5#50911yescharacteristic
232C3×D5—22no—
233C3×D5—82no—
234C3×D5—161no—
235C23×C3—41no—
236C23×C3—51no—
237C23×C3—204no—
238C23×C3—201no—
239C23×C3—201no—
240C23×C3—402no—
241C23×C3—402no—
242C3×D4—22no—
243C3×D4—41no—
244C3×D4—102no—
245C3×D4—204no—
246C3×D4—201no—
247C3×D4—201no—
248C3×D4—201no—
249C3×D4—402no—
250C2×C3×C4—41no—
251C2×C3×C4—51no—
252C2×C3×C4—101no—
253C2×C3×C4—101no—
254C2×C3×C4D4×D511yescharacteristic
255C3×C8—101no—
256C3×C8C2×D2011yescharacteristic
257C3×C8D4×D511yescharacteristic
258C22×C5—42no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5C2×C3×D811yescharacteristic
262C2×D5—21no—
263C2×D5—21no—
264C2×D5—42no—
265C2×D5—88no—
266C2×D5—81no—
267C2×D5—81no—
268C2×D5—81no—
269C2×D5—81no—
270C2×D5—81no—
271C2×D5C3×D1612yescomplemented
272C4×C5—81no—
273C4×C5C3×#12011yescharacteristic
274C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
275Dic5—21no—
276C24—201no—
277C2×D4—21no—
278C2×D4—104no—
279C2×D4—101no—
280C2×D4—101no—
281C2×D4—201no—
282C2×D4—201no—
283C2×D4—202no—
284C22×C4—51no—
285D8—21no—
286D8—52no—
287D8—104no—
288D8—101no—
289D8—101no—
290D8—101no—
291D8C3×D2012yescomplemented
292C2×C8—51no—
293C2×C8—101no—
294C2×C8—101no—
295C2×C8C22×C3×D511yescharacteristic
296C4⋊C4—21no—
297C22⋊C4—201no—
298C16—21no—
299C16—101no—
300C3×C5#218411yescharacteristic, complemented, Hall
301C22×C3—42no—
302C22×C3—52no—
303C22×C3—81no—
304C22×C3—81no—
305C22×C3—101no—
306C22×C3—101no—
307C22×C3—202no—
308C22×C3—408no—
309C22×C3—401no—
310C22×C3—401no—
311C22×C3—401no—
312C22×C3—401no—
313C22×C3—401no—
314C22×C3D5×D811yescharacteristic
315C3×C4—81no—
316C3×C4—101no—
317C3×C4#402811yescharacteristic
318C3×C4#406011yescharacteristic
319C2×C5—82no—
320C2×C5C3×#44711yescharacteristic
321C2×C5C2×C3×D1611yescharacteristic
322C2×C5C3×#50911yescharacteristic
323D5—22no—
324D5—82no—
325D5—161no—
326C23—41no—
327C23—51no—
328C23—204no—
329C23—201no—
330C23—201no—
331C23—402no—
332C23—402no—
333D4—22no—
334D4—41no—
335D4—102no—
336D4—204no—
337D4—201no—
338D4—201no—
339D4—201no—
340D4—402no—
341C2×C4—41no—
342C2×C4—51no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4C3×D4×D511yescharacteristic
346C8—101no—
347C8C2×C3×D2011yescharacteristic
348C8C3×D4×D511yescharacteristic
349C2×C3—82no—
350C2×C3—102no—
351C2×C3—402no—
352C2×C3—801no—
353C2×C3#6506211yescharacteristic
354C2×C3D5×D1611yescharacteristic
355C2×C3#6520311yescharacteristic
356C5C3×#218411yescharacteristic, complemented, Sylow
357C22—42no—
358C22—52no—
359C22—81no—
360C22—81no—
361C22—101no—
362C22—101no—
363C22—202no—
364C22—408no—
365C22—401no—
366C22—401no—
367C22—401no—
368C22—401no—
369C22—401no—
370C22C3×D5×D811yescharacteristic
371C4—81no—
372C4—101no—
373C4C3×#402811yescharacteristic
374C4C3×#406011yescharacteristic
375C3#1059998411yescharacteristic, direct product factor, Sylow
376C2—82no—
377C2—102no—
378C2—402no—
379C2—801no—
380C2C3×#6506211yescharacteristic
381C2C3×D5×D1611yescharacteristic
382C2C3×#6520311yescharacteristic
subgroupG/H
centerC22×C3D5×D8
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
hypercenterC3×#357D5
hypocenterC5C3×#2184
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
1. C2×C3×D5×D8C2semidirect
2. C2×C3×#3958C2semidirect
3. C2×C3×D80C2semidirect
4. C3×#65172C2semidirect
5. C3×C5×#357C2semidirect
6. C3×#64727C2semidirect
7. C3×#64711C2semidirect
8. #10599984C3direct (N × H)
15. C2×C3×D40C22semidirect
18. C2×C3×C5×C16C22semidirect
19. C3×C5×#107C22semidirect
21. C2×C3×#672C22semidirect
25. C2×D5×D8C2×C3semidirect
26. C2×#3958C2×C3semidirect
27. C2×D80C2×C3semidirect
28. #65172C2×C3semidirect
29. C5×#357C2×C3semidirect
30. #64727C2×C3semidirect
31. #64711C2×C3semidirect
42. C3×C5×D8D4semidirect
51. C3×D40D4semidirect
61. C3×#357D5semidirect
69. C2×D40C22×C3semidirect
72. C2×C5×C16C22×C3semidirect
73. C5×#107C22×C3semidirect
75. C2×#672C22×C3semidirect
114. C2×C3×C16C2×D5semidirect
115. C3×#107C2×D5semidirect
127. C5×D8C3×D4semidirect
136. D40C3×D4semidirect
146. #357C3×D5semidirect
161. C2×C3×D5D16semidirect
181. C3×D8D20semidirect
225. C2×C16C2×C3×D5semidirect
226. #107C2×C3×D5semidirect
271. C2×D5C3×D16semidirect
291. D8C3×D20semidirect
300. C3×C5#2184semidirect
356. C5C3×#2184semidirect
375. C3#10599984direct (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×#39582
C2×C3×D802
C3×#651722
C3×C5×#3572
C3×#647272
C3×#647112
#105999843
C3×#21845