Finite Group Databasebeta

← C3×#10602673 #14288105

Subgroups — C3×#10602673 #14288105

Order 1920.

564 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 114 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×C5×#537C211yesmaximal, characteristic
2C3×#65329C212yesmaximal, complemented
3C3×#65268C211yesmaximal, characteristic, complemented
4C3×#64757C212yesmaximal, complemented
5C3×#64748C211yesmaximal, characteristic, complemented
6#10602673C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41—21no—
8C22×C3×Dic10C2211yescharacteristic
9C3×C5×C22⋊Q8—22no—
10C3×C5×#121—22no—
11C3×C5×#121—21no—
12C3×C5×#121C2212yes—
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×#687—22no—
15C2×C3×#683—21no—
16C3×#3963—21no—
17C3×#3963C2211yescharacteristic
18C3×C22⋊#168C2212yes—
19C3×#3942—22no—
20C3×#1604—51nomaximal, Hall
21C5×#537C2×C311yescharacteristic
22#65329C2×C312yescomplemented
23#65268C2×C311yescharacteristic, complemented
24#64757C2×C312yescomplemented
25#64748C2×C311yescharacteristic, complemented
26C3×C5×#41—42no—
27C3×C5×#41—42no—
28C2×C3×C5×Q8—21no—
29C2×C3×C5×D4—21no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5—22no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5—21no—
38C22×C3×Dic5—21no—
39C2×C3×Dic10—22no—
40C2×C3×Dic10—42no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4D412yes—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×#687—44no—
47C3×#683—42no—
48C2×C3×#168—22no—
49C3×#537D511yescharacteristic
50C3×#448—52no—
51C3×#395—51no—
52C3×#327—52no—
53C3×#324—51no—
54C2×C5×#41—21no—
55C22×Dic10C22×C311yescharacteristic
56C5×C22⋊Q8—22no—
57C5×#121—22no—
58C5×#121—21no—
59C5×#121C22×C312yes—
60C2×C5×C4⋊C4C22×C311yescharacteristic
61C2×#687—22no—
62C2×#683—21no—
63#3963—21no—
64#3963C22×C311yescharacteristic
65C22⋊#168C22×C312yes—
66#3942—22no—
67#1604—51noSylow
68C23×C3×C5—22no—
69C23×C3×C5C2×D411yescharacteristic
70C3×C5×Q8—42no—
71C3×C5×D4—42no—
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C3×C5×D4—42no—
75C3×C5×D4—81no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—44no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5SD1612yescomplemented
84C2×C3×C4×C5C2×D412yes—
85C2×C3×Dic5—22no—
86C2×C3×Dic5—22no—
87C2×C3×Dic5—41no—
88C2×C3×Dic5—41no—
89C2×C3×Dic5—41no—
90C2×C3×Dic5—41no—
91C3×Dic10—24no—
92C3×Dic10—42no—
93C3×#168—42no—
94C2×C3×#41—21no—
95C22×C3×Q8—51no—
96C2×C3×SD16—102no—
97C3×C22⋊Q8—22no—
98C3×#121—22no—
99C3×#121—21no—
100C3×#121C2×D512yes—
101C2×C3×C4⋊C4—101no—
102C2×C3×C4⋊C4C2×D511yescharacteristic
103C3×#103—102no—
104C3×C22⋊C8—52no—
105C3×#95—51no—
106C3×#95—101no—
107C5×#41—42no—
108C5×#41—42no—
109C2×C5×Q8—21no—
110C2×C5×D4—21no—
111C2×C5×D4—22no—
112C2×C5×D4—21no—
113C2×C5×D4C3×D412yes—
114C22×C4×C5—22no—
115C22×C4×C5C3×D411yescharacteristic
116C22×C4×C5C3×D411yescharacteristic
117C22×C4×C5C23×C311yescharacteristic
118C22×Dic5—21no—
119C22×Dic5—21no—
120C2×Dic10—22no—
121C2×Dic10—42no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—22no—
124C5×C4⋊C4C3×D412yes—
125C5×C22⋊C4—22no—
126C5×C22⋊C4—22no—
127#687—44no—
128#683—42no—
129C2×#168—22no—
130#537C3×D511yescharacteristic
131#448—52no—
132#395—51no—
133#327—52no—
134#324—51no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5—42no—
138C22×C3×C5—42no—
139C22×C3×C5—42no—
140C22×C3×C5#12011yescharacteristic
141C22×C3×C5C2×SD1611yescharacteristic
142C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
143C3×C4×C5—22no—
144C3×C4×C5—22no—
145C3×C4×C5—42no—
146C3×C4×C5—41no—
147C3×Dic5—42no—
148C3×Dic5—42no—
149C3×#41—42no—
150C3×#41—42no—
151C2×C3×Q8—21no—
152C2×C3×Q8—102no—
153C2×C3×Q8—202no—
154C2×C3×D4—21no—
155C2×C3×D4—22no—
156C2×C3×D4—21no—
157C2×C3×D4C22⋊D512yes—
158C22×C3×C4—22no—
159C22×C3×C4—101no—
160C22×C3×C4—101no—
161C22×C3×C4C22⋊D511yescharacteristic
162C22×C3×C4C22⋊D511yescharacteristic
163C22×C3×C4C22×D511yescharacteristic
164C3×SD16—204no—
165C2×C3×C8—102no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—202no—
169C3×C4⋊C4C22⋊D512yes—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172C23×C5—22no—
173C23×C5C2×C3×D411yescharacteristic
174C5×Q8—42no—
175C5×D4—42no—
176C5×D4—42no—
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—81no—
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—22no—
184C2×C4×C5—41no—
185C2×C4×C5—44no—
186C2×C4×C5—41no—
187C2×C4×C5C3×SD1612yescomplemented
188C2×C4×C5C2×C3×D412yes—
189C2×Dic5—22no—
190C2×Dic5—22no—
191C2×Dic5—41no—
192C2×Dic5—41no—
193C2×Dic5—41no—
194C2×Dic5—41no—
195Dic10—24no—
196Dic10—42no—
197#168—42no—
198C2×#41—21no—
199C22×Q8—51no—
200C2×SD16—102no—
201C22⋊Q8—22no—
202#121—22no—
203#121—21no—
204#121C2×C3×D512yes—
205C2×C4⋊C4—101no—
206C2×C4⋊C4C2×C3×D511yescharacteristic
207#103—102no—
208C22⋊C8—52no—
209#95—51no—
210#95—101no—
211C2×C3×C5—21no—
212C2×C3×C5—21no—
213C2×C3×C5—82no—
214C2×C3×C5#45011yescharacteristic
215C2×C3×C5#45611yescharacteristic
216C2×C3×C5B(4,𝔽2)11yescharacteristic
217C23×C3—22no—
218C23×C3C2×C22⋊D511yescharacteristic
219C3×Q8—42no—
220C3×Q8—104no—
221C3×Q8—202no—
222C3×D4—42no—
223C3×D4—42no—
224C3×D4—42no—
225C3×D4—42no—
226C3×D4—81no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—41no—
232C2×C3×C4—44no—
233C2×C3×C4—41no—
234C2×C3×C4—102no—
235C2×C3×C4—102no—
236C2×C3×C4—201no—
237C2×C3×C4—201no—
238C2×C3×C4—201no—
239C2×C3×C4—201no—
240C2×C3×C4#68712yescomplemented
241C2×C3×C4C2×C22⋊D512yes—
242C3×C8—202no—
243C22×C5—21no—
244C22×C5—21no—
245C22×C5—42no—
246C22×C5—42no—
247C22×C5—42no—
248C22×C5C3×#12011yescharacteristic
249C22×C5C2×C3×SD1611yescharacteristic
250C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
251C4×C5—22no—
252C4×C5—22no—
253C4×C5—42no—
254C4×C5—41no—
255Dic5—42no—
256Dic5—42no—
257#41—42no—
258#41—42no—
259C2×Q8—21no—
260C2×Q8—102no—
261C2×Q8—202no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4C3×C22⋊D512yes—
266C22×C4—22no—
267C22×C4—101no—
268C22×C4—101no—
269C22×C4C3×C22⋊D511yescharacteristic
270C22×C4C3×C22⋊D511yescharacteristic
271C22×C4C22×C3×D511yescharacteristic
272SD16—204no—
273C2×C8—102no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—202no—
277C4⋊C4C3×C22⋊D512yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C3×C5#160411yescharacteristic, complemented, Hall
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—42no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3#407811yescharacteristic
287C22×C3C2×#68711yescharacteristic
288C22×C3#409911yescharacteristic
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—202no—
294C3×C4—202no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5—82no—
298C2×C5C3×#45011yescharacteristic
299C2×C5C3×#45611yescharacteristic
300C2×C5C3×B(4,𝔽2)11yescharacteristic
301C23—22no—
302C23C2×C3×C22⋊D511yescharacteristic
303Q8—42no—
304Q8—104no—
305Q8—202no—
306D4—42no—
307D4—42no—
308D4—42no—
309D4—42no—
310D4—81no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—102no—
319C2×C4—102no—
320C2×C4—201no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4C3×#68712yescomplemented
325C2×C4C2×C3×C22⋊D512yes—
326C8—202no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—82no—
330C2×C3#6550711yescharacteristic
331C2×C3#6553311yescharacteristic
332C2×C3#6553511yescharacteristic
333C5C3×#160411yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22C3×#407811yescharacteristic
340C22C2×C3×#68711yescharacteristic
341C22C3×#409911yescharacteristic
342C4—22no—
343C4—22no—
344C4—42no—
345C4—41no—
346C4—202no—
347C4—202no—
348C3#1060267311yescharacteristic, direct product factor, Sylow
349C2—21no—
350C2—21no—
351C2—82no—
352C2C3×#6550711yescharacteristic
353C2C3×#6553311yescharacteristic
354C2C3×#6553511yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC3×C5×#537C2
socleC22×C3×C5#120
hypercenterC3×#537D5
hypocenterC5C3×#1604
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
2. C3×#65329C2semidirect
3. C3×#65268C2semidirect
4. C3×#64757C2semidirect
5. C3×#64748C2semidirect
6. #10602673C3direct (N × H)
22. #65329C2×C3semidirect
23. #65268C2×C3semidirect
24. #64757C2×C3semidirect
25. #64748C2×C3semidirect
83. C2×C3×C4×C5SD16semidirect
187. C2×C4×C5C3×SD16semidirect
240. C2×C3×C4#687semidirect
280. C3×C5#1604semidirect
324. C2×C4C3×#687semidirect
333. C5C3×#1604semidirect
348. C3#10602673direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5372
C3×#653292
C3×#652682
C3×#647572
C3×#647482
#106026733
C3×#16045