Finite Group Databasebeta

← C3×#10600499 #14288102

Subgroups — C3×#10600499 #14288102

Order 1920.

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

normal subgroups only

This group has 564 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
1C3×#65844C211yesmaximal, characteristic
2C3×C5×#395C211yesmaximal, characteristic, complemented
3C3×#65516C212yesmaximal, complemented
4C3×#64748C211yesmaximal, characteristic, complemented
5C3×#64671C212yesmaximal, complemented
6#10600499C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×#709—21no—
9C2×C3×C5×C4⋊C4—21no—
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×#688—22no—
12C3×#4076—21no—
13C3×#4076C2212yes—
14C3×#4043—22no—
15C3×#4041—22no—
16C3×C5×#95—21no—
17C3×C5×#95C2211yescharacteristic
18C3×#3967—22no—
19C3×C22⋊#168C2212yes—
20C3×#1604—51nomaximal, Hall
21#65844C2×C311yescharacteristic
22C5×#395C2×C311yescharacteristic, complemented
23#65516C2×C312yescomplemented
24#64748C2×C311yescharacteristic, complemented
25#64671C2×C312yescomplemented
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8—42no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×C3×C22⋊D5—22no—
34C3×#709—42no—
35C3×#709—42no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×D20D412yes—
39C2×C3×C4×D5—22no—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—42no—
43C3×#688—44no—
44C3×#685—22no—
45C3×#685—22no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D412yes—
48C2×C3×#168—22no—
49C3×#537—51no—
50C3×#448—52no—
51C3×#395D511yescharacteristic, complemented
52C3×#327—52no—
53C3×#324—51no—
54C22×C5×Q8C22×C311yescharacteristic
55C2×#709—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4C22×C311yescharacteristic
58C2×#688—22no—
59#4076—21no—
60#4076C22×C312yes—
61#4043—22no—
62#4041—22no—
63C5×#95—21no—
64C5×#95C22×C311yescharacteristic
65#3967—22no—
66C22⋊#168C22×C312yes—
67#1604—51noSylow
68C23×C3×C5C2×D411yescharacteristic
69C22×C3×D5—22no—
70C3×C5×Q8—24no—
71C3×C5×Q8—42no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5SD1612yescomplemented
84C2×C3×C4×C5C2×D412yes—
85C3×C22⋊D5—42no—
86C3×C22⋊D5—42no—
87C2×C3×Dic5—22no—
88C3×D20—42no—
89C3×D20—42no—
90C3×D20—81no—
91C3×C4×D5—44no—
92C3×Dic10—42no—
93C3×#168—42no—
94C2×C3×#41—101no—
95C22×C3×Q8C2×D511yescharacteristic
96C2×C3×SD16—102no—
97C3×C22⋊Q8—102no—
98C3×#121—52no—
99C3×#121—102no—
100C3×#121—101no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2×D511yescharacteristic
103C3×#103—102no—
104C3×C22⋊C8—52no—
105C3×#95—21no—
106C3×#95C2×D511yescharacteristic
107C2×C5×Q8—22no—
108C2×C5×Q8—42no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5C3×D411yescharacteristic
112C22×C4×C5C3×D411yescharacteristic
113C22×C4×C5C23×C311yescharacteristic
114C2×C22⋊D5—22no—
115#709—42no—
116#709—42no—
117C2×D20—21no—
118C2×D20—21no—
119C2×D20C3×D412yes—
120C2×C4×D5—22no—
121C2×Dic10—21no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4—42no—
124#688—44no—
125#685—22no—
126#685—22no—
127C4⋊Dic5—21no—
128C4⋊Dic5C3×D412yes—
129C2×#168—22no—
130#537—51no—
131#448—52no—
132#395C3×D511yescharacteristic, complemented
133#327—52no—
134#324—51no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5#12011yescharacteristic
138C22×C3×C5C2×SD1611yescharacteristic
139C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
140C2×C3×D5—42no—
141C2×C3×D5—42no—
142C2×C3×D5—42no—
143C3×C4×C5—22no—
144C3×C4×C5—22no—
145C3×C4×C5—42no—
146C3×C4×C5—41no—
147C3×C4×C5—42no—
148C3×Dic5—42no—
149C3×#41—202no—
150C3×#41—202no—
151C2×C3×Q8—22no—
152C2×C3×Q8—42no—
153C2×C3×Q8—101no—
154C2×C3×D4—52no—
155C2×C3×D4—101no—
156C2×C3×D4—101no—
157C2×C3×D4—102no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—102no—
161C22×C3×C4C22⋊D511yescharacteristic
162C22×C3×C4C22⋊D511yescharacteristic
163C22×C3×C4C22×D511yescharacteristic
164C3×SD16—204no—
165C2×C3×C8—102no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—42no—
168C3×C4⋊C4—52no—
169C3×C4⋊C4—101no—
170C3×C22⋊C4—102no—
171C3×C22⋊C4—102no—
172C23×C5C2×C3×D411yescharacteristic
173C22×D5—22no—
174C5×Q8—24no—
175C5×Q8—42no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—22no—
179C2×C4×C5—22no—
180C2×C4×C5—21no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5C3×SD1612yescomplemented
188C2×C4×C5C2×C3×D412yes—
189C22⋊D5—42no—
190C22⋊D5—42no—
191C2×Dic5—22no—
192D20—42no—
193D20—42no—
194D20—81no—
195C4×D5—44no—
196Dic10—42no—
197#168—42no—
198C2×#41—101no—
199C22×Q8C2×C3×D511yescharacteristic
200C2×SD16—102no—
201C22⋊Q8—102no—
202#121—52no—
203#121—102no—
204#121—101no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×C3×D511yescharacteristic
207#103—102no—
208C22⋊C8—52no—
209#95—21no—
210#95C2×C3×D511yescharacteristic
211C2×C3×C5—21no—
212C2×C3×C5—21no—
213C2×C3×C5#45011yescharacteristic
214C2×C3×C5#45611yescharacteristic
215C2×C3×C5B(4,𝔽2)11yescharacteristic
216C3×D5—82no—
217C23×C3—102no—
218C23×C3C2×C22⋊D511yescharacteristic
219C3×Q8—24no—
220C3×Q8—42no—
221C3×Q8—202no—
222C3×D4—202no—
223C3×D4—202no—
224C3×D4—202no—
225C3×D4—202no—
226C3×D4—401no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—21no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—102no—
239C2×C3×C4—204no—
240C2×C3×C4#68812yescomplemented
241C2×C3×C4D4×D512yes—
242C3×C8—202no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5C3×#12011yescharacteristic
246C22×C5C2×C3×SD1611yescharacteristic
247C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
248C2×D5—42no—
249C2×D5—42no—
250C2×D5—42no—
251C4×C5—22no—
252C4×C5—22no—
253C4×C5—42no—
254C4×C5—41no—
255C4×C5—42no—
256Dic5—42no—
257#41—202no—
258#41—202no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×Q8—101no—
262C2×D4—52no—
263C2×D4—101no—
264C2×D4—101no—
265C2×D4—102no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—102no—
269C22×C4C3×C22⋊D511yescharacteristic
270C22×C4C3×C22⋊D511yescharacteristic
271C22×C4C22×C3×D511yescharacteristic
272SD16—204no—
273C2×C8—102no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—52no—
277C4⋊C4—101no—
278C22⋊C4—102no—
279C22⋊C4—102no—
280C3×C5#160411yescharacteristic, complemented, Hall
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—202no—
284C22×C3—202no—
285C22×C3—202no—
286C22×C3#408311yescharacteristic
287C22×C3C2×#68811yescharacteristic
288C22×C3#409511yescharacteristic
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—42no—
292C3×C4—42no—
293C3×C4—41no—
294C3×C4—202no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5C3×#45011yescharacteristic
298C2×C5C3×#45611yescharacteristic
299C2×C5C3×B(4,𝔽2)11yescharacteristic
300D5—82no—
301C23—102no—
302C23C2×C3×C22⋊D511yescharacteristic
303Q8—24no—
304Q8—42no—
305Q8—202no—
306D4—202no—
307D4—202no—
308D4—202no—
309D4—202no—
310D4—401no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—102no—
323C2×C4—204no—
324C2×C4C3×#68812yescomplemented
325C2×C4C3×D4×D512yes—
326C8—202no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—402no—
330C2×C3#6532111yescharacteristic
331C2×C3#6533511yescharacteristic
332C2×C3#6538411yescharacteristic
333C5C3×#160411yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—202no—
337C22—202no—
338C22—202no—
339C22C3×#408311yescharacteristic
340C22C2×C3×#68811yescharacteristic
341C22C3×#409511yescharacteristic
342C4—22no—
343C4—22no—
344C4—42no—
345C4—42no—
346C4—41no—
347C4—202no—
348C3#1060049911yescharacteristic, direct product factor, Sylow
349C2—21no—
350C2—21no—
351C2—402no—
352C2C3×#6532111yescharacteristic
353C2C3×#6533511yescharacteristic
354C2C3×#6538411yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#395C2
socleC22×C3×C5#120
prime radicalC3×#65844C2
hypercenterC3×#395D5
hypocenterC5C3×#1604
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#395

Complements

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

NH ≅ G/Ntype
2. C3×C5×#395C2semidirect
3. C3×#65516C2semidirect
4. C3×#64748C2semidirect
5. C3×#64671C2semidirect
6. #10600499C3direct (N × H)
22. C5×#395C2×C3semidirect
23. #65516C2×C3semidirect
24. #64748C2×C3semidirect
25. #64671C2×C3semidirect
51. C3×#395D5semidirect
83. C2×C3×C4×C5SD16semidirect
132. #395C3×D5semidirect
187. C2×C4×C5C3×SD16semidirect
240. C2×C3×C4#688semidirect
280. C3×C5#1604semidirect
324. C2×C4C3×#688semidirect
333. C5C3×#1604semidirect
348. C3#10600499direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658442
C3×C5×#3952
C3×#655162
C3×#647482
C3×#646712
#106004993
C3×#16045