Finite Group Databasebeta

← C3×#10599959 #14313715

Subgroups — C3×#10599959 #14313715

Order 1920.

524 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 110 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×#66008C211yesmaximal, characteristic
2C3×#65040C212yesmaximal, complemented
3C3×C5×#355C211yesmaximal, characteristic, complemented
4C3×#64762C211yesmaximal, characteristic, complemented
5C3×#64697C212yesmaximal, complemented
6#10599959C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×#713C2211yescharacteristic
8C2×C3×D4×D5C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4093C2211yescharacteristic
11C3×#4086C411yescharacteristic
12C3×D5×M16—22no—
13C3×#4030—22no—
14C3×#4028—22no—
15C3×#4020C411yescharacteristic
16C3×#4018C411yescharacteristic
17C3×C5×#101C2212yescomplemented
18C3×#3968C2212yescomplemented
19C3×#3955—22no—
20C3×#2134—51nomaximal, Hall
21#66008C2×C311yescharacteristic
22#65040C2×C312yescomplemented
23C5×#355C2×C311yescharacteristic, complemented
24#64762C2×C311yescharacteristic, complemented
25#64697C2×C312yescomplemented
26C23×C3×D5—21no—
27C2×C3×C5×Q8C2311yescharacteristic
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C3×C22⋊D5—22no—
30C2×C3×C22⋊D5—21no—
31C3×#713—42no—
32C3×D4×D5—42no—
33C2×C3×D20—22no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×D20C2×C411yescharacteristic
36C2×C3×D20D412yes—
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D412yes—
39C3×C5×M16—22no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5C2×C411yescharacteristic
42C3×#685—21no—
43C3×#685—22no—
44C3×#683—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×#681—22no—
47C3×#676—42no—
48C3×C8×D5—42no—
49C3×#535—51no—
50C3×#413—52no—
51C3×#355—51no—
52C3×#355—52no—
53C3×#355D511yescharacteristic, complemented
54C2×#713C22×C311yescharacteristic
55C2×D4×D5C3×C411yescharacteristic
56C5×#124C22×C311yescharacteristic
57#4093C22×C311yescharacteristic
58#4086C3×C411yescharacteristic
59D5×M16—22no—
60#4030—22no—
61#4028—22no—
62#4020C3×C411yescharacteristic
63#4018C3×C411yescharacteristic
64C5×#101C22×C312yescomplemented
65#3968C22×C312yescomplemented
66#3955—22no—
67#2134—51noSylow
68C23×C3×C5—21no—
69C22×C3×D5—21no—
70C22×C3×D5—42no—
71C22×C3×D5—82no—
72C22×C3×D5C22⋊C411yescharacteristic
73C22×C3×D5C22⋊C412yes—
74C3×C5×Q8—41no—
75C3×C5×D4—41no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D412yes—
79C3×C22⋊D5—42no—
80C3×C22⋊D5—82no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5C22⋊C411yescharacteristic
83C3×D20—41no—
84C3×D20—42no—
85C3×D20—41no—
86C3×D20—82no—
87C3×C4×D5—22no—
88C3×C4×D5—22no—
89C3×C4×D5—22no—
90C3×C5×C8—42no—
91C3×#168—42no—
92C2×C3×#41—51no—
93C22×C3×D4—51no—
94C2×C3×M16—102no—
95C3×#127—51no—
96C3×#127—51no—
97C3×#124—51no—
98C3×#124C2×D511yescharacteristic
99C3×#121—102no—
100C3×#120—102no—
101C3×#117—51no—
102C3×#101—52no—
103C3×#101C2×D512yescomplemented
104C3×#100—102no—
105C23×D5—21no—
106C2×C5×Q8C23×C311yescharacteristic
107C2×C5×D4C2×C3×C411yescharacteristic
108C2×C22⋊D5—22no—
109C2×C22⋊D5—21no—
110#713—42no—
111D4×D5—42no—
112C2×D20—22no—
113C2×D20C2×C3×C411yescharacteristic
114C2×D20C2×C3×C411yescharacteristic
115C2×D20C3×D412yes—
116C2×C4×D5C2×C3×C411yescharacteristic
117C2×C4×D5C3×D412yes—
118C5×M16—22no—
119C5×C22⋊C4—22no—
120C42×C5C2×C3×C411yescharacteristic
121#685—21no—
122#685—22no—
123#683—21no—
124C4×Dic5C2×C3×C411yescharacteristic
125#681—22no—
126#676—42no—
127C8×D5—42no—
128#535—51no—
129#413—52no—
130#355—51no—
131#355—52no—
132#355C3×D511yescharacteristic, complemented
133C22×C3×C5—42no—
134C22×C3×C5—41no—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C2×C3×D5—21no—
137C2×C3×D5—22no—
138C2×C3×D5—42no—
139C2×C3×D5—41no—
140C2×C3×D5—42no—
141C2×C3×D5—41no—
142C2×C3×D5—84no—
143C3×C4×C5—22no—
144C3×C4×C5—21no—
145C3×C4×C5—41no—
146C3×Dic5—41no—
147C3×Dic5#9912yes—
148C24×C3—101no—
149C3×#41—202no—
150C2×C3×Q8C22×D511yescharacteristic
151C2×C3×D4—51no—
152C2×C3×D4—51no—
153C2×C3×D4—52no—
154C2×C3×D4—102no—
155C2×C3×D4—101no—
156C2×C3×D4—102no—
157C2×C3×D4—202no—
158C2×C3×D4C4×D511yescharacteristic
159C22×C3×C4—51no—
160C22×C3×C4—52no—
161C3×M16—22no—
162C3×M16—102no—
163C3×M16—202no—
164C2×C3×C8—202no—
165C3×C4⋊C4—101no—
166C3×C22⋊C4—22no—
167C3×C22⋊C4—101no—
168C3×C22⋊C4—102no—
169C3×C42—51no—
170C3×C42C4×D511yescharacteristic
171C23×C5—21no—
172C22×D5—21no—
173C22×D5—42no—
174C22×D5—82no—
175C22×D5C3×C22⋊C411yescharacteristic
176C22×D5C3×C22⋊C412yes—
177C5×Q8—41no—
178C5×D4—41no—
179C2×C4×C5—21no—
180C2×C4×C5C22×C3×C411yescharacteristic
181C2×C4×C5C2×C3×D412yes—
182C22⋊D5—42no—
183C22⋊D5—82no—
184C2×Dic5—21no—
185C2×Dic5C3×C22⋊C411yescharacteristic
186D20—41no—
187D20—42no—
188D20—41no—
189D20—82no—
190C4×D5—22no—
191C4×D5—22no—
192C4×D5—22no—
193C5×C8—42no—
194#168—42no—
195C2×#41—51no—
196C22×D4—51no—
197C2×M16—102no—
198#127—51no—
199#127—51no—
200#124—51no—
201#124C2×C3×D511yescharacteristic
202#121—102no—
203#120—102no—
204#117—51no—
205#101—52no—
206#101C2×C3×D512yescomplemented
207#100—102no—
208C2×C3×C5—21no—
209C2×C3×C5—81no—
210C2×C3×C5C2×#9911yescharacteristic
211C3×D5—42no—
212C3×D5—41no—
213C3×D5—81no—
214C23×C3—21no—
215C23×C3—51no—
216C23×C3—52no—
217C23×C3—101no—
218C23×C3—202no—
219C23×C3—402no—
220C3×Q8—41no—
221C3×D4—41no—
222C3×D4—202no—
223C3×D4—201no—
224C3×D4—201no—
225C3×D4—202no—
226C3×D4—402no—
227C3×D4—402no—
228C2×C3×C4—21no—
229C2×C3×C4—51no—
230C2×C3×C4—102no—
231C2×C3×C4—102no—
232C2×C3×C4—102no—
233C2×C3×C4—101no—
234C2×C3×C4C2×C4×D511yescharacteristic
235C2×C3×C4D4×D512yes—
236C3×C8—42no—
237C3×C8—202no—
238C22×C5—42no—
239C22×C5—41no—
240C22×C5C2×C3×C22⋊C411yescharacteristic
241C2×D5—21no—
242C2×D5—22no—
243C2×D5—42no—
244C2×D5—41no—
245C2×D5—42no—
246C2×D5—41no—
247C2×D5—84no—
248C4×C5—22no—
249C4×C5—21no—
250C4×C5—41no—
251Dic5—41no—
252Dic5C3×#9912yes—
253C24—101no—
254#41—202no—
255C2×Q8C22×C3×D511yescharacteristic
256C2×D4—51no—
257C2×D4—51no—
258C2×D4—52no—
259C2×D4—102no—
260C2×D4—101no—
261C2×D4—102no—
262C2×D4—202no—
263C2×D4C3×C4×D511yescharacteristic
264C22×C4—51no—
265C22×C4—52no—
266M16—22no—
267M16—102no—
268M16—202no—
269C2×C8—202no—
270C4⋊C4—101no—
271C22⋊C4—22no—
272C22⋊C4—101no—
273C22⋊C4—102no—
274C42—51no—
275C42C3×C4×D511yescharacteristic
276C3×C5#213411yescharacteristic, complemented, Hall
277C22×C3—42no—
278C22×C3—41no—
279C22×C3—102no—
280C22×C3—101no—
281C22×C3—202no—
282C22×C3—201no—
283C22×C3—202no—
284C22×C3—201no—
285C22×C3—404no—
286C22×C3D5×C22⋊C411yescharacteristic
287C3×C4—22no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—52no—
291C3×C4—201no—
292C2×C5—21no—
293C2×C5—81no—
294C2×C5C2×C3×#9911yescharacteristic
295D5—41no—
296D5—42no—
297D5—81no—
298C23—21no—
299C23—51no—
300C23—52no—
301C23—101no—
302C23—202no—
303C23—402no—
304Q8—41no—
305D4—41no—
306D4—202no—
307D4—201no—
308D4—201no—
309D4—202no—
310D4—402no—
311D4—402no—
312C2×C4—21no—
313C2×C4—51no—
314C2×C4—102no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—101no—
318C2×C4C2×C3×C4×D511yescharacteristic
319C2×C4C3×D4×D512yes—
320C8—42no—
321C8—202no—
322C2×C3—21no—
323C2×C3—81no—
324C2×C3—201no—
325C2×C3—202no—
326C2×C3—401no—
327C2×C3D5×#9911yescharacteristic
328C5C3×#213411yescharacteristic, complemented, Sylow
329C22—42no—
330C22—41no—
331C22—101no—
332C22—102no—
333C22—202no—
334C22—201no—
335C22—202no—
336C22—201no—
337C22—404no—
338C22C3×D5×C22⋊C411yescharacteristic
339C4—22no—
340C4—21no—
341C4—41no—
342C4—52no—
343C4—201no—
344C3#1059995911yescharacteristic, direct product factor, Sylow
345C2—21no—
346C2—81no—
347C2—201no—
348C2—202no—
349C2—401no—
350C2C3×D5×#9911yescharacteristic
subgroupG/H
centerC2×C3D5×#99
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#355C2
socleC2×C3×C5C2×#99
prime radicalC3×#66008C2
cosocleC2×C5×Q8C23×C3
hypercenterC3×#355D5
hypocenterC5C3×#2134
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×Q8 ◁ C3×#355

Complements

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

NH ≅ G/Ntype
2. C3×#65040C2semidirect
3. C3×C5×#355C2semidirect
4. C3×#64762C2semidirect
5. C3×#64697C2semidirect
6. #10599959C3direct (N × H)
17. C3×C5×#101C22semidirect
18. C3×#3968C22semidirect
22. #65040C2×C3semidirect
23. C5×#355C2×C3semidirect
24. #64762C2×C3semidirect
25. #64697C2×C3semidirect
53. C3×#355D5semidirect
64. C5×#101C22×C3semidirect
65. #3968C22×C3semidirect
103. C3×#101C2×D5semidirect
132. #355C3×D5semidirect
206. #101C2×C3×D5semidirect
276. C3×C5#2134semidirect
328. C5C3×#2134semidirect
344. C3#10599959direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660082
C3×#650402
C3×C5×#3552
C3×#647622
C3×#646972
#105999593
C3×#21345