Finite Group Databasebeta

← C3×#10602086 #14317027

Subgroups — C3×#10602086 #14317027

Order 1920.

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

normal subgroups only

This group has 372 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×C5×#493C211yesmaximal, characteristic, complemented
2C2×C3×#3958C212yesmaximal, complemented
3C3×C4×D40C211yesmaximal, characteristic, complemented
4C3×#64782C212yesmaximal, complemented
5C3×C4⋊#672C211yesmaximal, characteristic, complemented
6#10602086C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×D8—21no—
8C2×C3×C5×D8C2212yes—
9C3×C5×#127—21no—
10C2×C3×D40C2211yescharacteristic
11C3×C4×D20—21no—
12C3×C4×C5×C8C2211yescharacteristic
13C3×#3958—24no—
14C3×#3953—21no—
15C3×#3950C2211yescharacteristic
16C2×C3×#672C2212yes—
17C3×#2206—51nomaximal, Hall
18C5×#493C2×C311yescharacteristic, complemented
19C2×#3958C2×C312yescomplemented
20C4×D40C2×C311yescharacteristic, complemented
21#64782C2×C312yescomplemented
22C4⋊#672C2×C311yescharacteristic, complemented
23C2×C3×C5×D4—22no—
24C2×C3×C5×D4—41no—
25C2×C3×C5×D4—41no—
26C2×C3×D20—21no—
27C2×C3×C4×D5—41no—
28C3×C5×D8—22no—
29C3×C5×D8—22no—
30C3×C5×D8—42no—
31C2×C3×C5×C8D411yescharacteristic
32C2×C3×C5×C8C2311yescharacteristic
33C3×C42×C5D411yescharacteristic
34C3×#685—41no—
35C3×C4⋊Dic5—21no—
36C3×D40—21no—
37C3×D40D412yescomplemented
38C3×#672—22no—
39C2×C3×D16—52no—
40C3×#493D511yescharacteristic, complemented
41C3×C4×D8—51no—
42C3×C4⋊C16—51no—
43C3×#357—52no—
44C2×C5×D8—21no—
45C2×C5×D8C22×C312yes—
46C5×#127—21no—
47C2×D40C22×C311yescharacteristic
48C4×D20—21no—
49C4×C5×C8C22×C311yescharacteristic
50#3958—24no—
51#3953—21no—
52#3950C22×C311yescharacteristic
53C2×#672C22×C312yes—
54#2206—51noSylow
55C23×C3×C5—42no—
56C22×C3×D5—41no—
57C3×C5×D4—42no—
58C3×C5×D4—42no—
59C3×C5×D4—82no—
60C3×C5×D4—82no—
61C2×C3×C4×C5D811yescharacteristic
62C2×C3×C4×C5D811yescharacteristic
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×C3×Dic5—41no—
65C3×D20—22no—
66C3×D20—41no—
67C3×C4×D5—82no—
68C3×C5×C8—21no—
69C3×C5×C8C2×D411yescharacteristic
70C3×C5×C8#4111yescharacteristic
71C2×C3×D8—21no—
72C2×C3×D8—51no—
73C2×C3×D8C2×D512yes—
74C3×#127—21no—
75C3×C4×D4—101no—
76C3×D16—104no—
77C2×C3×C16—52no—
78C3×#107—51no—
79C3×#102—101no—
80C3×C4×C8C2×D511yescharacteristic
81C2×C5×D4—22no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×D20—21no—
85C2×C4×D5—41no—
86C5×D8—22no—
87C5×D8—22no—
88C5×D8—42no—
89C2×C5×C8C3×D411yescharacteristic
90C2×C5×C8C23×C311yescharacteristic
91C42×C5C3×D411yescharacteristic
92#685—41no—
93C4⋊Dic5—21no—
94D40—21no—
95D40C3×D412yescomplemented
96#672—22no—
97C2×D16—52no—
98#493C3×D511yescharacteristic, complemented
99C4×D8—51no—
100C4⋊C16—51no—
101#357—52no—
102C22×C3×C5—82no—
103C22×C3×C5—82no—
104C22×C3×C5—82no—
105C22×C3×C5C2×D811yescharacteristic
106C2×C3×D5—42no—
107C2×C3×D5—81no—
108C2×C3×D5—81no—
109C3×C4×C5—21no—
110C3×C4×C5D1612yescomplemented
111C3×C4×C5#12111yescharacteristic
112C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
113C3×Dic5—81no—
114C2×C3×D4—22no—
115C2×C3×D4—41no—
116C2×C3×D4—41no—
117C2×C3×D4—101no—
118C22×C3×C4—201no—
119C3×D8—22no—
120C3×D8—22no—
121C3×D8—42no—
122C3×D8—52no—
123C3×D8—101no—
124C2×C3×C8C22⋊D511yescharacteristic
125C2×C3×C8C22×D511yescharacteristic
126C3×C4⋊C4—101no—
127C3×C22⋊C4—201no—
128C3×C42C22⋊D511yescharacteristic
129C3×C16—102no—
130C23×C5—42no—
131C22×D5—41no—
132C5×D4—42no—
133C5×D4—42no—
134C5×D4—82no—
135C5×D4—82no—
136C2×C4×C5C3×D811yescharacteristic
137C2×C4×C5C3×D811yescharacteristic
138C2×C4×C5C2×C3×D411yescharacteristic
139C2×Dic5—41no—
140D20—22no—
141D20—41no—
142C4×D5—82no—
143C5×C8—21no—
144C5×C8C2×C3×D411yescharacteristic
145C5×C8C3×#4111yescharacteristic
146C2×D8—21no—
147C2×D8—51no—
148C2×D8C2×C3×D512yes—
149#127—21no—
150C4×D4—101no—
151D16—104no—
152C2×C16—52no—
153#107—51no—
154#102—101no—
155C4×C8C2×C3×D511yescharacteristic
156C2×C3×C5—162no—
157C2×C3×C5#45911yescharacteristic
158C2×C3×C5C2×D1611yescharacteristic
159C2×C3×C5#50911yescharacteristic
160C3×D5—82no—
161C23×C3—42no—
162C23×C3—201no—
163C3×D4—42no—
164C3×D4—42no—
165C3×D4—82no—
166C3×D4—82no—
167C3×D4—102no—
168C3×D4—201no—
169C2×C3×C4—201no—
170C2×C3×C4—402no—
171C2×C3×C4#68611yescharacteristic
172C2×C3×C4#68611yescharacteristic
173C2×C3×C4C2×C22⋊D511yescharacteristic
174C3×C8—21no—
175C3×C8D4×D511yescharacteristic
176C3×C8#71111yescharacteristic
177C22×C5—82no—
178C22×C5—82no—
179C22×C5—82no—
180C22×C5C2×C3×D811yescharacteristic
181C2×D5—42no—
182C2×D5—81no—
183C2×D5—81no—
184C4×C5—21no—
185C4×C5C3×D1612yescomplemented
186C4×C5C3×#12111yescharacteristic
187C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
188Dic5—81no—
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—101no—
193C22×C4—201no—
194D8—22no—
195D8—22no—
196D8—42no—
197D8—52no—
198D8—101no—
199C2×C8C3×C22⋊D511yescharacteristic
200C2×C8C22×C3×D511yescharacteristic
201C4⋊C4—101no—
202C22⋊C4—201no—
203C42C3×C22⋊D511yescharacteristic
204C16—102no—
205C3×C5#220611yescharacteristic, complemented, Hall
206C22×C3—82no—
207C22×C3—82no—
208C22×C3—82no—
209C22×C3—202no—
210C22×C3—401no—
211C22×C3—401no—
212C22×C3C2×#68611yescharacteristic
213C3×C4—21no—
214C3×C4—401no—
215C3×C4#395812yescomplemented
216C3×C4#407811yescharacteristic
217C3×C4#408411yescharacteristic
218C2×C5—162no—
219C2×C5C3×#45911yescharacteristic
220C2×C5C2×C3×D1611yescharacteristic
221C2×C5C3×#50911yescharacteristic
222D5—82no—
223C23—42no—
224C23—201no—
225D4—42no—
226D4—42no—
227D4—82no—
228D4—82no—
229D4—102no—
230D4—201no—
231C2×C4—201no—
232C2×C4—402no—
233C2×C4C3×#68611yescharacteristic
234C2×C4C3×#68611yescharacteristic
235C2×C4C2×C3×C22⋊D511yescharacteristic
236C8—21no—
237C8C3×D4×D511yescharacteristic
238C8C3×#71111yescharacteristic
239C2×C3—162no—
240C2×C3—402no—
241C2×C3#6536111yescharacteristic
242C2×C3C2×#395811yescharacteristic
243C2×C3#6543611yescharacteristic
244C5C3×#220611yescharacteristic, complemented, Sylow
245C22—82no—
246C22—82no—
247C22—82no—
248C22—202no—
249C22—401no—
250C22—401no—
251C22C2×C3×#68611yescharacteristic
252C4—21no—
253C4—401no—
254C4C3×#395812yescomplemented
255C4C3×#407811yescharacteristic
256C4C3×#408411yescharacteristic
257C3#1060208611yescharacteristic, direct product factor, Sylow
258C2—162no—
259C2—402no—
260C2C3×#6536111yescharacteristic
261C2C2×C3×#395811yescharacteristic
262C2C3×#6543611yescharacteristic
subgroupG/H
centerC22×C3C2×#686
commutator, cosocleC2×C5×C8C23×C3
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#493C2
socleC22×C3×C5C2×D8
hypercenterC3×#493D5
hypocenterC5C3×#2206
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×C8 ◁ C3×#493

Complements

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

NH ≅ G/Ntype
1. C3×C5×#493C2semidirect
2. C2×C3×#3958C2semidirect
3. C3×C4×D40C2semidirect
4. C3×#64782C2semidirect
5. C3×C4⋊#672C2semidirect
6. #10602086C3direct (N × H)
18. C5×#493C2×C3semidirect
19. C2×#3958C2×C3semidirect
20. C4×D40C2×C3semidirect
21. #64782C2×C3semidirect
22. C4⋊#672C2×C3semidirect
37. C3×D40D4semidirect
40. C3×#493D5semidirect
95. D40C3×D4semidirect
98. #493C3×D5semidirect
110. C3×C4×C5D16semidirect
185. C4×C5C3×D16semidirect
205. C3×C5#2206semidirect
215. C3×C4#3958semidirect
244. C5C3×#2206semidirect
254. C4C3×#3958semidirect
257. C3#10602086direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4932
C2×C3×#39582
C3×C4×D402
C3×#647822
C3×C4⋊#6722
#106020863
C3×#22065