Finite Group Databasebeta

← C3×C5×#1633 #14274667

Subgroups — C3×C5×#1633 #14274667

Order 1920.

412 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 152 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×Q82C211yesmaximal, characteristic
2C3×C5×#494C211yesmaximal, characteristic
3C3×C5×#477C212yesmaximal
4C3×C5×#333C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C212yesmaximal
6C5×#1633C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8—22no—
9C3×C5×C4⋊Q8—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C4×C5×Q8—22no—
13C3×C4×C5×Q8C2212yes—
14C3×C5×#107—22no—
15C3×C5×C4⋊C8C2212yes—
16C3×C5×#103—22no—
17C3×C4×C5×C8C2211yescharacteristic
18C3×#1633C511yesmaximal, characteristic, direct product factor, Hall
19C5×Q82C2×C311yescharacteristic
20C5×#494C2×C311yescharacteristic
21C5×#477C2×C312yes—
22C5×#333C2×C311yescharacteristic
23C5×Q8⋊C8C2×C312yes—
24C2×C3×C5×Q8—22no—
25C2×C3×C5×Q8—21no—
26C2×C3×C5×Q8D412yes—
27C2×C3×C5×Q8D412yes—
28C3×C5×Q16—44no—
29C2×C3×C5×C8—21no—
30C2×C3×C5×C8—22no—
31C3×C5×C4⋊C4—24no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C4⋊C4D412yes—
36C3×C42×C5—22no—
37C3×C42×C5—22no—
38C3×C42×C5C2311yescharacteristic
39C3×Q82C2×C511yescharacteristic
40C3×#494C2×C511yescharacteristic
41C3×#477C2×C512yes—
42C3×#333C2×C511yescharacteristic
43C3×Q8⋊C8C2×C512yes—
44C2×C5×Q16—22no—
45C5×C4⋊Q8—22no—
46C5×C4⋊Q8—22no—
47C5×C4⋊Q8C22×C311yescharacteristic
48C5×C4⋊Q8C22×C311yescharacteristic
49C4×C5×Q8—22no—
50C4×C5×Q8C22×C312yes—
51C5×#107—22no—
52C5×C4⋊C8C22×C312yes—
53C5×#103—22no—
54C4×C5×C8C22×C311yescharacteristic
55#1633C3×C511yescharacteristic, direct product factor, Sylow
56C3×C5×Q8—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—42no—
59C3×C5×Q8—82no—
60C3×C5×Q8Q1614yescomplemented
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—41no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C3×C5×C8—22no—
68C3×C5×C8—42no—
69C2×C3×Q16—22no—
70C3×C4⋊Q8—22no—
71C3×C4⋊Q8—22no—
72C3×C4⋊Q8C22×C511yescharacteristic
73C3×C4⋊Q8C22×C511yescharacteristic
74C3×C4×Q8—22no—
75C3×C4×Q8C22×C512yes—
76C3×#107—22no—
77C3×C4⋊C8C22×C512yes—
78C3×#103—22no—
79C3×C4×C8C22×C511yescharacteristic
80C2×C5×Q8—22no—
81C2×C5×Q8—21no—
82C2×C5×Q8C3×D412yes—
83C2×C5×Q8C3×D412yes—
84C5×Q16—44no—
85C2×C5×C8—21no—
86C2×C5×C8—22no—
87C5×C4⋊C4—24no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4C3×D412yes—
92C42×C5—22no—
93C42×C5—22no—
94C42×C5C23×C311yescharacteristic
95Q82C2×C3×C511yescharacteristic
96#494C2×C3×C511yescharacteristic
97#477C2×C3×C512yes—
98#333C2×C3×C511yescharacteristic
99Q8⋊C8C2×C3×C512yes—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—24no—
102C3×C4×C5—21no—
103C3×C4×C5—42no—
104C3×C4×C5—42no—
105C3×C4×C5—81no—
106C3×C4×C5C2×Q1612yes—
107C3×C4×C5#13712yes—
108C2×C3×Q8—22no—
109C2×C3×Q8—21no—
110C2×C3×Q8C5×D412yes—
111C2×C3×Q8C5×D412yes—
112C3×Q16—44no—
113C2×C3×C8—21no—
114C2×C3×C8—22no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4C5×D412yes—
120C3×C42—22no—
121C3×C42—22no—
122C3×C42C23×C511yescharacteristic
123C5×Q8—22no—
124C5×Q8—42no—
125C5×Q8—42no—
126C5×Q8—82no—
127C5×Q8C3×Q1614yescomplemented
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—41no—
132C2×C4×C5C2×C3×D411yescharacteristic
133C2×C4×C5C2×C3×D412yes—
134C5×C8—22no—
135C5×C8—42no—
136C2×Q16—22no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8C22×C3×C511yescharacteristic
140C4⋊Q8C22×C3×C511yescharacteristic
141C4×Q8—22no—
142C4×Q8C22×C3×C512yes—
143#107—22no—
144C4⋊C8C22×C3×C512yes—
145#103—22no—
146C4×C8C22×C3×C511yescharacteristic
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—22no—
150C3×Q8—42no—
151C3×Q8—42no—
152C3×Q8—82no—
153C3×Q8C5×Q1614yescomplemented
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—41no—
158C2×C3×C4C2×C5×D411yescharacteristic
159C2×C3×C4C2×C5×D412yes—
160C3×C8—22no—
161C3×C8—42no—
162C22×C5C3×#12011yescharacteristic
163C4×C5—24no—
164C4×C5—21no—
165C4×C5—42no—
166C4×C5—42no—
167C4×C5—81no—
168C4×C5C2×C3×Q1612yes—
169C4×C5C3×#13712yes—
170C2×Q8—22no—
171C2×Q8—21no—
172C2×Q8C3×C5×D412yes—
173C2×Q8C3×C5×D412yes—
174Q16—44no—
175C2×C8—21no—
176C2×C8—22no—
177C4⋊C4—24no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4C3×C5×D412yes—
182C42—22no—
183C42—22no—
184C42C23×C3×C511yescharacteristic
185C3×C5#163311yescharacteristic, direct product factor, Hall
186C22×C3C5×#12011yescharacteristic
187C3×C4—24no—
188C3×C4—21no—
189C3×C4—42no—
190C3×C4—42no—
191C3×C4—81no—
192C3×C4C2×C5×Q1612yes—
193C3×C4C5×#13712yes—
194C2×C5C3×#45112yes—
195C2×C5C3×#45311yescharacteristic
196Q8—22no—
197Q8—42no—
198Q8—42no—
199Q8—82no—
200Q8C3×C5×Q1614yescomplemented
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4C2×C3×C5×D411yescharacteristic
206C2×C4C2×C3×C5×D412yes—
207C8—22no—
208C8—42no—
209C2×C3C5×#45112yes—
210C2×C3C5×#45311yescharacteristic
211C5C3×#163311yescharacteristic, direct product factor, Sylow
212C22C3×C5×#12011yescharacteristic
213C4—24no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—81no—
218C4C2×C3×C5×Q1612yes—
219C4C3×C5×#13712yes—
220C3C5×#163311yescharacteristic, direct product factor, Sylow
221C2C3×C5×#45112yes—
222C2C3×C5×#45311yescharacteristic
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×#1633C3direct (N × H)
18. C3×#1633C5direct (N × H)
55. #1633C3×C5direct (N × H)
60. C3×C5×Q8Q16semidirect
127. C5×Q8C3×Q16semidirect
153. C3×Q8C5×Q16semidirect
185. C3×C5#1633direct (N × H)
200. Q8C3×C5×Q16semidirect
211. C5C3×#1633direct (N × H)
220. C3C5×#1633direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×Q822
C3×C5×#4942
C3×C5×#4772
C3×C5×#3332
C3×C5×Q8⋊C82
C5×#16333
C3×#16335