Finite Group Databasebeta

← C3×C5×#1405 #14274439

Subgroups — C3×C5×#1405 #14274439

Order 1920.

212 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 56 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×#456C211yesmaximal, characteristic
2C3×C5×#356C211yesmaximal, characteristic, complemented
3C3×C5×#333C211yesmaximal, characteristic, complemented
4C5×#1405C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×2−1+4C411yescharacteristic
6C3×C5×#137—21no—
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×C4⋊C8—21no—
9C3×C5×#104—21no—
10C3×C5×#101—21no—
11C3×C5×#101C411yescharacteristic
12C3×#1405C511yesmaximal, characteristic, direct product factor, Hall
13C5×#456C2×C311yescharacteristic
14C5×#356C2×C311yescharacteristic, complemented
15C5×#333C2×C311yescharacteristic, complemented
16C3×C5×#41—21no—
17C3×C5×#41—41no—
18C3×C5×#41—41no—
19C2×C3×C5×Q8—41no—
20C2×C3×C5×Q8C2×C411yescharacteristic
21C2×C3×C5×Q8D411yescharacteristic
22C3×C5×Q16—41no—
23C3×C5×SD16—41no—
24C3×C5×M16—21no—
25C3×C5×M16—41no—
26C2×C3×C5×C8—41no—
27C3×C5×C4⋊C4—41no—
28C3×C42×C5D411yescharacteristic
29C3×#456C2×C511yescharacteristic
30C3×#356C2×C511yescharacteristic, complemented
31C3×#333C2×C511yescharacteristic, complemented
32C5×2−1+4C3×C411yescharacteristic
33C5×#137—21no—
34C5×C4⋊Q8C22×C311yescharacteristic
35C5×C4⋊C8—21no—
36C5×#104—21no—
37C5×#101—21no—
38C5×#101C3×C411yescharacteristic
39#1405C3×C511yescharacteristic, direct product factor, Sylow
40C3×C5×Q8—21no—
41C3×C5×Q8—41no—
42C3×C5×Q8—41no—
43C3×C5×Q8—41no—
44C3×C5×D4—21no—
45C3×C5×D4—41no—
46C3×C5×D4—41no—
47C2×C3×C4×C5—21no—
48C2×C3×C4×C5—21no—
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5—42no—
52C2×C3×C4×C5C22⋊C411yescharacteristic
53C3×C5×C8—41no—
54C3×C5×C8—81no—
55C3×C5×C8—81no—
56C3×2−1+4C4×C511yescharacteristic
57C3×#137—21no—
58C3×C4⋊Q8C22×C511yescharacteristic
59C3×C4⋊C8—21no—
60C3×#104—21no—
61C3×#101—21no—
62C3×#101C4×C511yescharacteristic
63C5×#41—21no—
64C5×#41—41no—
65C5×#41—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8C2×C3×C411yescharacteristic
68C2×C5×Q8C3×D411yescharacteristic
69C5×Q16—41no—
70C5×SD16—41no—
71C5×M16—21no—
72C5×M16—41no—
73C2×C5×C8—41no—
74C5×C4⋊C4—41no—
75C42×C5C3×D411yescharacteristic
76#456C2×C3×C511yescharacteristic
77#356C2×C3×C511yescharacteristic, complemented
78#333C2×C3×C511yescharacteristic, complemented
79C22×C3×C5—41no—
80C22×C3×C5#9911yescharacteristic
81C3×C4×C5—21no—
82C3×C4×C5—21no—
83C3×C4×C5—21no—
84C3×C4×C5—41no—
85C3×C4×C5—41no—
86C3×C4×C5—41no—
87C3×#41—21no—
88C3×#41—41no—
89C3×#41—41no—
90C2×C3×Q8—41no—
91C2×C3×Q8C2×C4×C511yescharacteristic
92C2×C3×Q8C5×D411yescharacteristic
93C3×Q16—41no—
94C3×SD16—41no—
95C3×M16—21no—
96C3×M16—41no—
97C2×C3×C8—41no—
98C3×C4⋊C4—41no—
99C3×C42C5×D411yescharacteristic
100C5×Q8—21no—
101C5×Q8—41no—
102C5×Q8—41no—
103C5×Q8—41no—
104C5×D4—21no—
105C5×D4—41no—
106C5×D4—41no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—41no—
111C2×C4×C5—42no—
112C2×C4×C5C3×C22⋊C411yescharacteristic
113C5×C8—41no—
114C5×C8—81no—
115C5×C8—81no—
1162−1+4C3×C4×C511yescharacteristic
117#137—21no—
118C4⋊Q8C22×C3×C511yescharacteristic
119C4⋊C8—21no—
120#104—21no—
121#101—21no—
122#101C3×C4×C511yescharacteristic
123C2×C3×C5—21no—
124C2×C3×C5—81no—
125C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
126C3×Q8—21no—
127C3×Q8—41no—
128C3×Q8—41no—
129C3×Q8—41no—
130C3×D4—21no—
131C3×D4—41no—
132C3×D4—41no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—41no—
137C2×C3×C4—42no—
138C2×C3×C4C5×C22⋊C411yescharacteristic
139C3×C8—41no—
140C3×C8—81no—
141C3×C8—81no—
142C22×C5—41no—
143C22×C5C3×#9911yescharacteristic
144C4×C5—21no—
145C4×C5—21no—
146C4×C5—21no—
147C4×C5—41no—
148C4×C5—41no—
149C4×C5—41no—
150#41—21no—
151#41—41no—
152#41—41no—
153C2×Q8—41no—
154C2×Q8C2×C3×C4×C511yescharacteristic
155C2×Q8C3×C5×D411yescharacteristic
156Q16—41no—
157SD16—41no—
158M16—21no—
159M16—41no—
160C2×C8—41no—
161C4⋊C4—41no—
162C42C3×C5×D411yescharacteristic
163C3×C5#140511yescharacteristic, direct product factor, Hall
164C22×C3—41no—
165C22×C3C5×#9911yescharacteristic
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—41no—
170C3×C4—41no—
171C3×C4—41no—
172C2×C5—21no—
173C2×C5—81no—
174C2×C5C3×AΣL(1,𝔽16)11yescharacteristic
175Q8—21no—
176Q8—41no—
177Q8—41no—
178Q8—41no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4C3×C5×C22⋊C411yescharacteristic
188C8—41no—
189C8—81no—
190C8—81no—
191C2×C3—21no—
192C2×C3—81no—
193C2×C3C5×AΣL(1,𝔽16)11yescharacteristic
194C5C3×#140511yescharacteristic, direct product factor, Sylow
195C22—41no—
196C22C3×C5×#9911yescharacteristic
197C4—21no—
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—41no—
203C3C5×#140511yescharacteristic, direct product factor, Sylow
204C2—21no—
205C2—81no—
206C2C3×C5×AΣL(1,𝔽16)11yescharacteristic
subgroupG/H
center, socleC2×C3×C5AΣL(1,𝔽16)
commutatorC2×Q8C2×C3×C4×C5
Frattini, cosocleC4⋊Q8C22×C3×C5
prime radicalC3×C5×2−1+4C4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C5 ◁ C22×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#356C2semidirect
3. C3×C5×#333C2semidirect
4. C5×#1405C3direct (N × H)
12. C3×#1405C5direct (N × H)
14. C5×#356C2×C3semidirect
15. C5×#333C2×C3semidirect
30. C3×#356C2×C5semidirect
31. C3×#333C2×C5semidirect
39. #1405C3×C5direct (N × H)
77. #356C2×C3×C5semidirect
78. #333C2×C3×C5semidirect
163. C3×C5#1405direct (N × H)
194. C5C3×#1405direct (N × H)
203. C3C5×#1405direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4562
C3×C5×#3562
C3×C5×#3332
C5×#14053
C3×#14055