Finite Group Databasebeta

← #14279513

Subgroups — #14279513

Order 1920.

156 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#11751183C211yesmaximal, characteristic
2C3×C5×#356C211yesmaximal, characteristic
3#11746369C211yesmaximal, characteristic
4#10598042—31nomaximal, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6#91759C411yescharacteristic
7C3×C5×#101—21no—
8#91120—21no—
9#91119—21no—
10#91119—21no—
11#91087C411yescharacteristic
12#67551—51nomaximal, Hall
13#65371—31no—
14C5×#356D311yescharacteristic
15#64768—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C3×C5×M16—41no—
19C3×C5×C4⋊C4—41no—
20C3×C42×C5C2×C411yescharacteristic
21C4⋊Dic15—21no—
22#6712—41no—
23#6710—41no—
24C2×C3⋊#168—21no—
25#5082—51no—
26C3×#356D511yescharacteristic
27#4548—51no—
28C5×C4⋊Q8C2×D311yescharacteristic
29#4016—31no—
30C5×#101—21no—
31#3968—61no—
32#3967—61no—
33#3967—61no—
34#3935—31no—
35#1413—151noSylow
36C3×C5×Q8—41no—
37C3×C5×Q8—41no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5—21no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5C22⋊C411yescharacteristic
42C2×Dic15—41no—
43C3×C5×C8—81no—
44C3⋊#168—41no—
45C3⋊#168—81no—
46C3×C4⋊Q8C2×D511yescharacteristic
47#870—51no—
48C3×#101—21no—
49#836—101no—
50#835—101no—
51#835—101no—
52#803—51no—
53C2×C5×Q8D1211yescharacteristic
54C2×C5×Q8#6711yescharacteristic
55C5×M16—41no—
56C5×C4⋊C4—41no—
57C42×C5C4×D311yescharacteristic
58C4⋊Dic5—61no—
59#683—121no—
60#681—121no—
61C2×#168—61no—
62#491—151no—
63#356—151no—
64#356D1511yescharacteristic
65C22×C3×C5#9911yescharacteristic
66C3×C4×C5—21no—
67C3×C4×C5—41no—
68C3×C4×C5—41no—
69C3×C4×C5—41no—
70Dic15—81no—
71C2×C3×Q8D2011yescharacteristic
72C2×C3×Q8C22⋊D511yescharacteristic
73C3×M16—41no—
74C3×C4⋊C4—41no—
75C3×C42C4×D511yescharacteristic
76C4⋊Dic3—101no—
77Dic3⋊C4—201no—
78#208—201no—
79C2×C3⋊C8—101no—
80C5×Q8—41no—
81C5×Q8—41no—
82C2×C4×C5—21no—
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5(C2×D3)⋊C411yescharacteristic
86C2×Dic5—121no—
87C5×C8—81no—
88#168—121no—
89#168—241no—
90C4⋊Q8C2×D1511yescharacteristic
91#125—151no—
92#103—301no—
93#103—301no—
94#101—21no—
95#101—301no—
96#97—151no—
97C2×C3×C5—21no—
98C2×C3×C5#35411yescharacteristic
99C3×Q8—41no—
100C3×Q8—41no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4#68511yescharacteristic
105C2×Dic3—201no—
106C3×C8—81no—
107C3⋊C8—201no—
108C3⋊C8—401no—
109C22×C5#80611yescharacteristic
110C4×C5—21no—
111C4×C5—41no—
112C4×C5—41no—
113C4×C5—41no—
114Dic5—241no—
115C2×Q8D6011yescharacteristic
116C2×Q8#122011yescharacteristic
117M16—41no—
118M16—601no—
119C2×C8—301no—
120C4⋊C4—41no—
121C4⋊C4—301no—
122C4⋊C4—601no—
123C42C4×D1511yescharacteristic
124C3×C5#141311yescharacteristic, complemented, Hall
125C22×C3#393811yescharacteristic
126C3×C4—21no—
127C3×C4—41no—
128C3×C4—41no—
129C3×C4—41no—
130Dic3—401no—
131C2×C5—21no—
132C2×C5#447311yescharacteristic
133Q8—41no—
134Q8—41no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—601no—
139C2×C4#671411yescharacteristic
140C8—81no—
141C8—601no—
142C8—1201no—
143C2×C3—21no—
144C2×C3#6469311yescharacteristic
145C5#6755111yescharacteristic, complemented, Sylow
146C22#9109011yescharacteristic
147C4—21no—
148C4—41no—
149C4—41no—
150C4—41no—
151C4—1201no—
152C3#1059804211yescharacteristic, complemented, Sylow
153C2—21no—
154C2#1174629411yescharacteristic
subgroupG/H
centerC2#11746294
commutatorC3×C42×C5C2×C4
FrattiniC4⋊Q8C2×D15
FittingC3×C5×#356C2
socleC2×C3×C5#354
prime radicalC22×C3×C5#99
cosocleC3×C5×C4⋊Q8C22
hypercenter#356D15
hypocenterC3×C5#1413
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
124. C3×C5#1413semidirect
145. C5#67551semidirect
152. C3#10598042semidirect

Maximal subgroups

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

subgroupindex
#117511832
C3×C5×#3562
#117463692
#105980423
#675515