Finite Group Databasebeta

← C3×C5×#1663 #14274697

Subgroups — C3×C5×#1663 #14274697

Order 1920.

344 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 120 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×#564C211yesmaximal, characteristic
2C3×C5×#501C212yesmaximal
3C3×C5×#491C211yesmaximal, characteristic
4C3×C5×#330C211yesmaximal, characteristic
5C3×C5×#330C212yesmaximal
6C5×#1663C311yesmaximal, characteristic, direct product factor, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#125—22no—
9C3×C5×#125—22no—
10C3×C5×#125—22no—
11C3×C5×#125C2211yescharacteristic
12C3×C5×#125C2212yes—
13C3×C5×#107—22no—
14C3×C5×#106—22no—
15C3×C5×#103—22no—
16C3×C5×#97C2211yescharacteristic
17C3×C5×#97C2212yes—
18C3×#1663C511yesmaximal, characteristic, direct product factor, Hall
19C5×#564C2×C311yescharacteristic
20C5×#501C2×C312yes—
21C5×#491C2×C311yescharacteristic
22C5×#330C2×C311yescharacteristic
23C5×#330C2×C312yes—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×C8—22no—
26C2×C3×C5×C8—21no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4—22no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4D412yes—
35C3×C5×C4⋊C4D412yes—
36C3×C5×C4⋊C4D412yes—
37C3×C42×C5—22no—
38C3×C42×C5C2311yescharacteristic
39C3×#564C2×C511yescharacteristic
40C3×#501C2×C512yes—
41C3×#491C2×C511yescharacteristic
42C3×#330C2×C512yes—
43C3×#330C2×C511yescharacteristic
44C5×C4⋊Q8C22×C311yescharacteristic
45C5×#125—22no—
46C5×#125—22no—
47C5×#125—22no—
48C5×#125C22×C311yescharacteristic
49C5×#125C22×C312yes—
50C5×#107—22no—
51C5×#106—22no—
52C5×#103—22no—
53C5×#97C22×C311yescharacteristic
54C5×#97C22×C312yes—
55#1663C3×C511yescharacteristic, direct product factor, Sylow
56C3×C5×Q8—42no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5—41no—
61C2×C3×C4×C5C2×D412yes—
62C2×C3×C4×C5C2×D411yescharacteristic
63C3×C5×C8—24no—
64C3×C5×C8—41no—
65C3×C4⋊Q8C22×C511yescharacteristic
66C3×#125—22no—
67C3×#125—22no—
68C3×#125—22no—
69C3×#125C22×C511yescharacteristic
70C3×#125C22×C512yes—
71C3×#107—22no—
72C3×#106—22no—
73C3×#103—22no—
74C3×#97C22×C511yescharacteristic
75C3×#97C22×C512yes—
76C2×C5×Q8—21no—
77C2×C5×C8—22no—
78C2×C5×C8—21no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4—22no—
82C5×C4⋊C4—22no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4C3×D412yes—
87C5×C4⋊C4C3×D412yes—
88C5×C4⋊C4C3×D412yes—
89C42×C5—22no—
90C42×C5C23×C311yescharacteristic
91#564C2×C3×C511yescharacteristic
92#501C2×C3×C512yes—
93#491C2×C3×C511yescharacteristic
94#330C2×C3×C512yes—
95#330C2×C3×C511yescharacteristic
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100C3×C4×C5—42no—
101C3×C4×C5—42no—
102C3×C4×C5—81no—
103C2×C3×Q8—21no—
104C2×C3×C8—22no—
105C2×C3×C8—21no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4C5×D412yes—
114C3×C4⋊C4C5×D412yes—
115C3×C4⋊C4C5×D412yes—
116C3×C42—22no—
117C3×C42C23×C511yescharacteristic
118C5×Q8—42no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—22no—
122C2×C4×C5—41no—
123C2×C4×C5C2×C3×D412yes—
124C2×C4×C5C2×C3×D411yescharacteristic
125C5×C8—24no—
126C5×C8—41no—
127C4⋊Q8C22×C3×C511yescharacteristic
128#125—22no—
129#125—22no—
130#125—22no—
131#125C22×C3×C511yescharacteristic
132#125C22×C3×C512yes—
133#107—22no—
134#106—22no—
135#103—22no—
136#97C22×C3×C511yescharacteristic
137#97C22×C3×C512yes—
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C3×Q8—42no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—22no—
144C2×C3×C4—41no—
145C2×C3×C4C2×C5×D412yes—
146C2×C3×C4C2×C5×D411yescharacteristic
147C3×C8—24no—
148C3×C8—41no—
149C22×C5C3×#12011yescharacteristic
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—42no—
153C4×C5—42no—
154C4×C5—42no—
155C4×C5—81no—
156C2×Q8—21no—
157C2×C8—22no—
158C2×C8—21no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4C3×C5×D412yes—
167C4⋊C4C3×C5×D412yes—
168C4⋊C4C3×C5×D412yes—
169C42—22no—
170C42C23×C3×C511yescharacteristic
171C3×C5#166311yescharacteristic, direct product factor, Hall
172C22×C3C5×#12011yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—42no—
177C3×C4—42no—
178C3×C4—81no—
179C2×C5C3×#45411yescharacteristic
180C2×C5C3×#45612yes—
181Q8—42no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—41no—
186C2×C4C2×C3×C5×D412yes—
187C2×C4C2×C3×C5×D411yescharacteristic
188C8—24no—
189C8—41no—
190C2×C3C5×#45411yescharacteristic
191C2×C3C5×#45612yes—
192C5C3×#166311yescharacteristic, direct product factor, Sylow
193C22C3×C5×#12011yescharacteristic
194C4—21no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—42no—
199C4—81no—
200C3C5×#166311yescharacteristic, direct product factor, Sylow
201C2C3×C5×#45411yescharacteristic
202C2C3×C5×#45612yes—
subgroupG/H
center, socle, prime radicalC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C5×#1663C3direct (N × H)
18. C3×#1663C5direct (N × H)
55. #1663C3×C5direct (N × H)
171. C3×C5#1663direct (N × H)
192. C5C3×#1663direct (N × H)
200. C3C5×#1663direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5642
C3×C5×#5012
C3×C5×#4912
C3×C5×#3302
C5×#16633
C3×#16635