Finite Group Databasebeta

← C3×C5⋊#5934 #72277551

Subgroups — C3×C5⋊#5934 #72277551

Order 2880.

414 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 30 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×#997C211yesmaximal, characteristic, complemented
2C5⋊#5934C311yesmaximal, characteristic, direct product factor
3C3×#65533—31nomaximal
4C2×C3×C5⋊S4—43nomaximal
5C3×#5934—51nomaximal, Hall
6C3×C5×H(5,𝔽2)D311yescharacteristic, complemented
7C5×#997—21no—
8C5×#997C2×C311yescharacteristic, complemented
9C3×#4083—33no—
10C3×#3966—33no—
11C2×C3×C5×A4—43no—
12C3×C5⋊S4—46no—
13C3×C5×SL(2,𝔽3)—81no—
14#65533—31noHall
15C3×#997D511yescharacteristic, complemented
16C23×C3×D5—31no—
17C2×C5⋊S4—43no—
18C3×C5×#41—61no—
19C2×C3×C5×D4—33no—
20C2×C3×C22⋊D5—63no—
21C3×C22⋊Dic5—33no—
22C3×#685—63no—
23#5934—51no—
24C3×B(4,𝔽2)—151no—
25C2×C3×D15—161no—
26C3×C5×A4—43no—
27C5×H(5,𝔽2)C3×D311yescharacteristic, complemented
28#4083—33no—
29#3966—33no—
30C2×C3×S4—203no—
31C23×C3×C5—31no—
32C23×C3×C5S413yescomplemented
33C22×C3×D5—63no—
34C22×C3×D5—122no—
35C2×C5×A4—43no—
36C2×C5×A4—83no—
37C5⋊S4—46no—
38C3×C5×Q8—21no—
39C3×C5×D4—63no—
40C2×C3×C4×C5—33no—
41C3×C22⋊D5—126no—
42C2×C3×Dic5—63no—
43C5×SL(2,𝔽3)—81no—
44C5×SL(2,𝔽3)—82no—
45C3×H(5,𝔽2)D1511yescharacteristic, complemented
46#997—21no—
47#997C3×D511yescharacteristic, complemented
48C3×#120—153no—
49C3×#99—153no—
50C2×C32×C5—161no—
51C3×D15—162no—
52C23×D5—31no—
53C5×#41—61no—
54C2×C5×D4—33no—
55C2×C22⋊D5—63no—
56C22⋊Dic5—33no—
57#685—63no—
58C2×C3×A4—43no—
59C3×S4—206no—
60C3×SL(2,𝔽3)—81no—
61B(4,𝔽2)—151noSylow
62C22×C3×C5—33no—
63C22×C3×C5—43no—
64C22×C3×C5—121no—
65C2×D15—161no—
66C2×C3×D5—66no—
67C2×C3×D5—123no—
68C2×C3×D5—121no—
69C5×A4—43no—
70C5×A4—83no—
71C3×C4×C5—61no—
72C3×Dic5—123no—
73C24×C3—151no—
74C2×S4—203no—
75C3×#41—61no—
76C2×C3×D4—33no—
77C2×C3×D4—303no—
78C3×C22⋊C4—153no—
79C3×C22⋊C4—303no—
80C32×C5—161noHall
81C23×C5—31no—
82C23×C5C3×S413yescomplemented
83C22×D5—63no—
84C22×D5—122no—
85C5×Q8—21no—
86C5×D4—63no—
87C2×C4×C5—33no—
88C22⋊D5—126no—
89C2×Dic5—63no—
90C2×C3×D3—801no—
91C3×A4—43no—
92H(5,𝔽2)C3×D1511yescharacteristic, complemented
93#120—153no—
94#99—153no—
95C2×C3×C5—63no—
96C2×C3×C5—161no—
97C2×C3×C5—321no—
98C2×C3×C5#102011yescharacteristic
99D15—162no—
100C3×D5—122no—
101C23×C3—31no—
102C23×C3—303no—
103C23×C3—602no—
104C23×C3C5⋊S413yescomplemented
105C2×A4—43no—
106C2×A4—83no—
107S4—206no—
108C3×Q8—21no—
109C3×D4—63no—
110C3×D4—606no—
111C2×C3×C4—33no—
112C2×C3×C4—303no—
113SL(2,𝔽3)—81no—
114SL(2,𝔽3)—82no—
115C22×C5—33no—
116C22×C5—43no—
117C22×C5—121no—
118C2×D5—66no—
119C2×D5—123no—
120C2×D5—121no—
121C4×C5—61no—
122Dic5—123no—
123C2×C32—161no—
124C3×D3—802no—
125C24—151no—
126#41—61no—
127C2×D4—33no—
128C2×D4—303no—
129C22⋊C4—153no—
130C22⋊C4—303no—
131C3×C5—161no—
132C3×C5—321no—
133C3×C5#593411yescharacteristic, complemented
134C22×C3—33no—
135C22×C3—43no—
136C22×C3—121no—
137C22×C3—306no—
138C22×C3—603no—
139C22×C3—601no—
140C2×D3—801no—
141A4—43no—
142A4—83no—
143C3×C4—61no—
144C3×C4—603no—
145C2×C5—63no—
146C2×C5C3×#102011yescharacteristic
147D5—122no—
148C32—161noSylow
149C23—31no—
150C23—303no—
151C23—602no—
152C23C3×C5⋊S413yescomplemented
153Q8—21no—
154D4—63no—
155D4—606no—
156C2×C4—33no—
157C2×C4—303no—
158C2×C3—63no—
159C2×C3—161no—
160C2×C3—321no—
161C2×C3—602no—
162C2×C3C5⋊#102011yescharacteristic
163D3—802no—
164C5C3×#593411yescharacteristic, complemented, Sylow
165C22—33no—
166C22—43no—
167C22—121no—
168C22—306no—
169C22—603no—
170C22—601no—
171C4—61no—
172C4—603no—
173C3—161no—
174C3—321no—
175C3C5⋊#593411yescharacteristic, direct product factor
176C2—63no—
177C2—602no—
178C2C3×C5⋊#102011yescharacteristic
subgroupG/H
center, hypercenterC2×C3C5⋊#1020
commutator, cosocle, hypocenterC5×#997C2×C3
FrattiniC2C3×C5⋊#1020
FittingC3×C5×H(5,𝔽2)D3
socleC2×C3×C5#1020
LCSG ▷ C5×#997
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×#997C2semidirect
2. C5⋊#5934C3direct (N × H)
6. C3×C5×H(5,𝔽2)D3semidirect
8. C5×#997C2×C3semidirect
15. C3×#997D5semidirect
27. C5×H(5,𝔽2)C3×D3semidirect
32. C23×C3×C5S4semidirect
45. C3×H(5,𝔽2)D15semidirect
47. #997C3×D5semidirect
82. C23×C5C3×S4semidirect
92. H(5,𝔽2)C3×D15semidirect
104. C23×C3C5⋊S4semidirect
133. C3×C5#5934semidirect
152. C23C3×C5⋊S4semidirect
164. C5C3×#5934semidirect
175. C3C5⋊#5934direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#9972
C5⋊#59343
C3×#655333
C2×C3×C5⋊S44
C3×#59345