Finite Group Databasebeta

← #14279472

Subgroups — #14279472

Order 1920.

208 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 42 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×#65374C211yesmaximal, characteristic
2#11746369C211yesmaximal, characteristic, complemented
3C5×#4548C211yesmaximal, characteristic, complemented
4#10598043—31nomaximal, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6C2×C3×#688—21no—
7C2×C3×#688—21no—
8C3×#4020C411yescharacteristic
9#91120—21no—
10C5×#836—21no—
11C3×C4×#168C411yescharacteristic
12#67789—51nomaximal, Hall
13#65374D311yescharacteristic
14C5×#356—31no—
15#64768—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C2×C3×D20—21no—
19C2×C3×D20—41no—
20C3×C5×C4⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6710—41no—
23C5×#208—41no—
24C3×#688—42no—
25C3×#688—42no—
26C2×C3×#168—21no—
27C3×#492—51no—
28#4548—51no—
29#4548D511yescharacteristic, complemented
30C5×C4⋊Q8C2×D311yescharacteristic
31C2×#688—21no—
32C2×#688—21no—
33#4020Dic311yescharacteristic
34C5×#101—61no—
35#3968—61no—
36C4×#168Dic311yescharacteristic
37#1410—151noSylow
38C22×C3×D5—41no—
39C3×C5×Q8—41no—
40C3×C5×Q8—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C3×D20—41no—
46C3×D20—41no—
47C3×D20—82no—
48C3⋊#168—81no—
49C3×#168—22no—
50C5×C3⋊C8—81no—
51C2×C3×SD16—101no—
52C2×C3×SD16—101no—
53C3×C4⋊Q8C2×D511yescharacteristic
54C3×#127—51no—
55C3×C4×C8—51no—
56#836—21no—
57#836—101no—
58C2×C5×Q8#6711yescharacteristic
59C2×C5×Q8#6711yescharacteristic
60C2×D20—21no—
61C2×D20—41no—
62C5×M16—121no—
63C5×C4⋊C4—41no—
64C42×C5C2×Dic311yescharacteristic
65#688—42no—
66#688—42no—
67#681—121no—
68C2×#168—21no—
69#492—51no—
70#356—31no—
71#356—151no—
72C22×C3×C5#9911yescharacteristic
73C2×C3×D5—82no—
74C2×C3×D5—81no—
75C3×C4×C5—22no—
76C3×C4×C5—21no—
77C3×C4×C5—41no—
78C3×C4×C5—41no—
79C2×C3×Q8D2011yescharacteristic
80C2×C3×Q8C22⋊D511yescharacteristic
81C2×C3×D4—101no—
82C2×C3×D4—201no—
83C3×SD16—202no—
84C3×SD16—202no—
85C2×C3×C8—101no—
86C3×C4⋊C4—41no—
87C3×C42C4×D511yescharacteristic
88#208—41no—
89#208—201no—
90C22×D5—41no—
91C5×Q8—41no—
92C5×Q8—41no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5#21711yescharacteristic
97D20—41no—
98D20—41no—
99D20—82no—
100C5×C8—241no—
101#168—22no—
102#168—241no—
103C2×SD16—101no—
104C2×SD16—101no—
105C4⋊Q8D3×D511yescharacteristic
106#127—51no—
107#101—61no—
108#101—301no—
109C4×C8—51no—
110C2×C3×C5—21no—
111C2×C3×C5#35311yescharacteristic
112C3×D5—161no—
113C23×C3—201no—
114C3×Q8—41no—
115C3×Q8—41no—
116C3×D4—201no—
117C3×D4—201no—
118C3×D4—402no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4#68511yescharacteristic
123C3×C8—102no—
124C3⋊C8—81no—
125C3⋊C8—401no—
126C22×C5#83411yescharacteristic
127C2×D5—82no—
128C2×D5—81no—
129C4×C5—22no—
130C4×C5—21no—
131C4×C5—41no—
132C4×C5—41no—
133C2×Q8#120111yescharacteristic
134C2×Q8#120211yescharacteristic
135C2×D4—101no—
136C2×D4—201no—
137SD16—202no—
138SD16—202no—
139M16—121no—
140M16—601no—
141C2×C8—101no—
142C4⋊C4—41no—
143C42D5×Dic311yescharacteristic
144C3×C5#141011yescharacteristic, complemented, Hall
145C22×C3—402no—
146C22×C3—401no—
147C22×C3#393811yescharacteristic
148C3×C4—22no—
149C3×C4—21no—
150C3×C4—41no—
151C3×C4—41no—
152C2×C5—21no—
153C2×C5#454511yescharacteristic
154D5—161no—
155C23—201no—
156Q8—41no—
157Q8—41no—
158D4—201no—
159D4—201no—
160D4—402no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4#666511yescharacteristic
165C8—102no—
166C8—241no—
167C8—1201no—
168C2×C3—21no—
169C2×C3—801no—
170C2×C3#6469411yescharacteristic
171C5#6778911yescharacteristic, complemented, Sylow
172C22—402no—
173C22—401no—
174C22#9099511yescharacteristic
175C4—22no—
176C4—21no—
177C4—41no—
178C4—41no—
179C3#1059804311yescharacteristic, complemented, Sylow
180C2—21no—
181C2—801no—
182C2#1174600611yescharacteristic
subgroupG/H
centerC2#11746006
commutatorC3×C42×C5C2×C4
Frattini, hypercenterC4⋊Q8D3×D5
Fitting, cosocleC3×C5×C4⋊Q8C22
socleC2×C3×C5#353
prime radicalC3×#4020C4
hypocenterC3×C5#1410
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11746369C2semidirect
3. C5×#4548C2semidirect
29. #4548D5semidirect
144. C3×C5#1410semidirect
171. C5#67789semidirect
179. C3#10598043semidirect

Maximal subgroups

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

subgroupindex
C3×#653742
#117463692
C5×#45482
#105980433
#677895