Finite Group Databasebeta

← #14318516

Subgroups — #14318516

Order 1920.

268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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×#469C211yesmaximal, characteristic
2#11751226C211yesmaximal, characteristic, complemented
3#11746384C212yesmaximal, complemented
4#11746374C211yesmaximal, characteristic, complemented
5#11746308C212yesmaximal, complemented
6#10601881—31nomaximal, Hall
7C2×C3×C5×D8C2211yescharacteristic
8C2×C3×C5×M16C2211yescharacteristic
9C3×C5×#121—21no—
10C2×#6710—21no—
11C3×C5×#106C2211yescharacteristic
12C3×C5×#102—21no—
13#91103—21no—
14#91103C2212yes—
15#91096C2212yes—
16#71088—51nomaximal, Hall
17C5×#469D311yescharacteristic
18#65414—31no—
19#64783—32no—
20#64773—31no—
21#64707—32no—
22C2×C3×C5×D4—21no—
23C2×C3×C5×D4—41no—
24C22×C3×C4×C5D411yescharacteristic
25C3×C5×D8—22no—
26C3×C5×M16—22no—
27C2×C3×C5×C8D411yescharacteristic
28C2×C3×C5×C8C2311yescharacteristic
29C3×C5×C4⋊C4—21no—
30C3×C5×C22⋊C4—41no—
31#6710—22no—
32#6710—41no—
33C2×C3⋊#168—41no—
34C3⋊#672—22no—
35C3×#469D511yescharacteristic
36#5125—51no—
37#4563—52no—
38#4553—51no—
39#4487—52no—
40C2×C5×D8C2×D311yescharacteristic
41C2×C5×M16C2×D311yescharacteristic
42C5×#121—21no—
43C2×#681—61no—
44C5×#106C2×D311yescharacteristic
45C5×#102—21no—
46#3951—32no—
47#3951—61no—
48#3944—32no—
49#2238—151noSylow
50C23×C3×C5—41no—
51C23×C3×C5SD1611yescharacteristic
52C3×C5×D4—41no—
53C3×C5×D4—41no—
54C3×C5×D4—82no—
55C2×C3×C4×C5—21no—
56C2×C3×C4×C5—21no—
57C2×C3×C4×C5—41no—
58C2×C3×C4×C5SD1611yescharacteristic
59C2×C3×C4×C5C2×D411yescharacteristic
60C3×C5×C8—21no—
61C3×C5×C8#4112yes—
62C3⋊#168—42no—
63C2×C3×D8C2×D511yescharacteristic
64C2×C3×M16C2×D511yescharacteristic
65C3×#121—21no—
66C2×#208—101no—
67C3×#106C2×D511yescharacteristic
68C3×#102—21no—
69#819—52no—
70#819—101no—
71#812—52no—
72C2×C5×D4—21no—
73C2×C5×D4—41no—
74C22×C4×C5#6711yescharacteristic
75C5×D8—22no—
76C5×M16—22no—
77C2×C5×C8#6711yescharacteristic
78C2×C5×C8C22×D311yescharacteristic
79C5×C4⋊C4—21no—
80C5×C22⋊C4—41no—
81#681—62no—
82#681—121no—
83C2×#168—121no—
84#672—62no—
85#469D1511yescharacteristic
86#430—151no—
87#365—152no—
88#361—152no—
89#349—151no—
90C22×C3×C5—21no—
91C22×C3×C5—41no—
92C22×C3×C5—81no—
93C22×C3×C5—81no—
94C22×C3×C5—81no—
95C22×C3×C5C2×SD1611yescharacteristic
96C3×C4×C5—21no—
97C3×C4×C5—81no—
98C3×C4×C5#12311yescharacteristic
99C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
100C2×C3×D4—21no—
101C2×C3×D4—41no—
102C22×C3×C4C22⋊D511yescharacteristic
103C3×D8—22no—
104C3×M16—22no—
105C2×C3×C8C22⋊D511yescharacteristic
106C2×C3×C8C22×D511yescharacteristic
107C3×C4⋊C4—21no—
108C3×C22⋊C4—41no—
109#208—102no—
110#208—201no—
111C2×C3⋊C8—201no—
112C3⋊C16—102no—
113C23×C5—41no—
114C23×C5#21411yescharacteristic
115C5×D4—41no—
116C5×D4—41no—
117C5×D4—82no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—41no—
121C2×C4×C5#21411yescharacteristic
122C2×C4×C5C2×#6711yescharacteristic
123C5×C8—21no—
124C5×C8#23712yes—
125#168—122no—
126C2×D8C2×D1511yescharacteristic
127C2×M16—301no—
128C2×M16C2×D1511yescharacteristic
129#121—21no—
130M32—152no—
131#108—152no—
132#108—301no—
133#106C2×D1511yescharacteristic
134#102—21no—
135C2×C3×C5—21no—
136C2×C3×C5—41no—
137C2×C3×C5—161no—
138C2×C3×C5#48111yescharacteristic
139C23×C3—41no—
140C23×C3#68711yescharacteristic
141C3×D4—41no—
142C3×D4—41no—
143C3×D4—82no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—41no—
147C2×C3×C4#68711yescharacteristic
148C2×C3×C4C2×C22⋊D511yescharacteristic
149C3×C8—21no—
150C3×C8#71112yes—
151C3⋊C8—202no—
152C22×C5—21no—
153C22×C5—41no—
154C22×C5—81no—
155C22×C5—81no—
156C22×C5—81no—
157C22×C5C2×#21411yescharacteristic
158C4×C5—21no—
159C4×C5—81no—
160C4×C5#93511yescharacteristic
161C4×C5#94911yescharacteristic
162C2×D4—21no—
163C2×D4—41no—
164C22×C4#122011yescharacteristic
165D8—22no—
166M16—22no—
167M16—302no—
168M16—601no—
169C2×C8—601no—
170C2×C8#122011yescharacteristic
171C2×C8C22×D1511yescharacteristic
172C4⋊C4—21no—
173C22⋊C4—41no—
174C16—302no—
175C3×C5#223811yescharacteristic, complemented, Hall
176C22×C3—21no—
177C22×C3—41no—
178C22×C3—81no—
179C22×C3—81no—
180C22×C3—81no—
181C22×C3C2×#68711yescharacteristic
182C3×C4—21no—
183C3×C4—81no—
184C3×C4#408111yescharacteristic
185C3×C4#409511yescharacteristic
186C2×C5—21no—
187C2×C5—41no—
188C2×C5—161no—
189C2×C5#503411yescharacteristic
190C23—41no—
191C23#671611yescharacteristic
192D4—41no—
193D4—41no—
194D4—82no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4#671611yescharacteristic
199C2×C4C2×#122011yescharacteristic
200C8—21no—
201C8—602no—
202C8#681912yes—
203C2×C3—21no—
204C2×C3—41no—
205C2×C3—161no—
206C2×C3#6532311yescharacteristic
207C5#7108811yescharacteristic, complemented, Sylow
208C22—21no—
209C22—41no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22C2×#671611yescharacteristic
214C4—21no—
215C4—81no—
216C4#9182411yescharacteristic
217C4#9183811yescharacteristic
218C3#1060188111yescharacteristic, complemented, Sylow
219C2—21no—
220C2—41no—
221C2—161no—
222C2#1175113511yescharacteristic
subgroupG/H
centerC2#11751135
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
Fitting, prime radicalC3×C5×#469C2
socleC2×C3×C5#481
hypercenter#469D15
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
2. #11751226C2semidirect
3. #11746384C2semidirect
4. #11746374C2semidirect
5. #11746308C2semidirect
175. C3×C5#2238semidirect
207. C5#71088semidirect
218. C3#10601881semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4692
#117512262
#117463842
#117463742
#117463082
#106018813
#710885