Finite Group Databasebeta

← C5×#3028⋊C3 #14510986

Subgroups — C5×#3028⋊C3 #14510986

Order 1920.

312 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 36 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
1C5×#5950C211yesmaximal, characteristic
2C5×#458⋊C3C212yesmaximal, complemented
3C5×#3028C311yesmaximal, characteristic, complemented, Hall
4C5×#997C2211yescharacteristic
5C5×Q8×A4—41nomaximal
6#3028⋊C3C511yesmaximal, characteristic, direct product factor, Hall
7C5×#585C2×C311yescharacteristic
8C5×#536—31no—
9C5×#458—32no—
10C5×#458C2×C312yes—
11C5×#410—31no—
12C5×#41⋊C3—81no—
13C4×C5×A4—41no—
14C4×C5×A4—42no—
15C4×C5×A4—81no—
16#5950C2×C511yescharacteristic
17#458⋊C3C2×C512yescomplemented
18C5×2−1+4—61no—
19C5×H(5,𝔽2)—31no—
20C5×H(5,𝔽2)—61no—
21C5×H(5,𝔽2)C22×C311yescharacteristic
22C2×C5×#41—31no—
23C2×C5×#41—61no—
24C2×C5×#41—61no—
25C22×C5×Q8A411yescharacteristic, complemented
26C5×C4⋊Q8—61no—
27C5×#124—61no—
28C5×#123—32no—
29C5×#123—32no—
30C5×C22⋊Q8—61no—
31C5×C22⋊Q8—61no—
32C5×#117—31no—
33C5×#99—32no—
34C5×#99—32no—
35#3028C3×C511yescharacteristic, complemented, Sylow
36C2×C5×A4—41no—
37C2×C5×A4—81no—
38C3×C5×Q8—161no—
39C5×SL(2,𝔽3)—81no—
40#997C22×C511yescharacteristic
41Q8×A4—41no—
42C5×#41—21no—
43C5×#41—62no—
44C5×#41—62no—
45C5×#41—61no—
46C5×#41—62no—
47C5×#41—61no—
48C5×#41—62no—
49C5×#41—62no—
50C5×#41—61no—
51C2×C5×Q8—31no—
52C2×C5×Q8—61no—
53C2×C5×Q8—61no—
54C2×C5×Q8—61no—
55C2×C5×Q8—61no—
56C2×C5×D4—31no—
57C2×C5×D4—31no—
58C2×C5×D4—31no—
59C2×C5×D4—61no—
60C2×C5×D4—62no—
61C2×C5×D4—61no—
62C2×C5×D4—61no—
63C2×C5×D4—61no—
64C22×C4×C5—21no—
65C22×C4×C5—31no—
66C22×C4×C5—31no—
67C22×C4×C5—61no—
68C22×C4×C5C2×A411yescharacteristic
69C22×C4×C5C2×A412yes—
70C5×C4⋊C4—61no—
71C5×C4⋊C4—62no—
72C5×C4⋊C4—62no—
73C5×C22⋊C4—32no—
74C5×C22⋊C4—62no—
75C5×C22⋊C4—62no—
76C42×C5—61no—
77#585C2×C3×C511yescharacteristic
78#536—31no—
79#458—32no—
80#458C2×C3×C512yes—
81#410—31no—
82C5×A4—41no—
83C5×A4—81no—
84C3×C4×C5—162no—
85C3×C4×C5—161no—
86#41⋊C3—81no—
87C4×A4—42no—
88C4×A4—41no—
89C4×A4—81no—
90C23×C5—21no—
91C23×C5—31no—
92C23×C5—31no—
93C23×C5—61no—
94C23×C5C22×A411yescharacteristic
95C5×Q8—21no—
96C5×Q8—41no—
97C5×Q8—62no—
98C5×Q8—61no—
99C5×Q8—121no—
100C5×D4—62no—
101C5×D4—62no—
102C5×D4—62no—
103C5×D4—61no—
104C5×D4—61no—
105C5×D4—62no—
106C2×C4×C5—31no—
107C2×C4×C5—31no—
108C2×C4×C5—31no—
109C2×C4×C5—31no—
110C2×C4×C5—61no—
111C2×C4×C5—61no—
112C2×C4×C5—62no—
113C2×C4×C5—62no—
114C2×C4×C5—61no—
115C2×C4×C5—61no—
116C2×C4×C5—61no—
117C2×C4×C5—61no—
118C2×C4×C5—62no—
1192−1+4—61no—
120H(5,𝔽2)—31no—
121H(5,𝔽2)—61no—
122H(5,𝔽2)C22×C3×C511yescharacteristic
123C2×#41—31no—
124C2×#41—61no—
125C2×#41—61no—
126C22×Q8C5×A411yescharacteristic, complemented
127C4⋊Q8—61no—
128#124—61no—
129#123—32no—
130#123—32no—
131C22⋊Q8—61no—
132C22⋊Q8—61no—
133#117—31no—
134#99—32no—
135#99—32no—
136C2×C3×C5—161no—
137C2×A4—41no—
138C2×A4—81no—
139C3×Q8—161no—
140SL(2,𝔽3)—81no—
141C22×C5—31no—
142C22×C5—41no—
143C22×C5—61no—
144C22×C5—61no—
145C22×C5—81no—
146C22×C5—121no—
147C22×C5—121no—
148C22×C5—241no—
149C4×C5—31no—
150C4×C5—42no—
151C4×C5—61no—
152C4×C5—61no—
153C4×C5—122no—
154C4×C5#120⋊C311yescharacteristic
155#41—21no—
156#41—62no—
157#41—62no—
158#41—61no—
159#41—62no—
160#41—61no—
161#41—62no—
162#41—62no—
163#41—61no—
164C2×Q8—31no—
165C2×Q8—61no—
166C2×Q8—61no—
167C2×Q8—61no—
168C2×Q8—61no—
169C2×D4—31no—
170C2×D4—31no—
171C2×D4—31no—
172C2×D4—61no—
173C2×D4—62no—
174C2×D4—61no—
175C2×D4—61no—
176C2×D4—61no—
177C22×C4—21no—
178C22×C4—31no—
179C22×C4—31no—
180C22×C4—61no—
181C22×C4C2×C5×A411yescharacteristic
182C22×C4C2×C5×A412yes—
183C4⋊C4—61no—
184C4⋊C4—62no—
185C4⋊C4—62no—
186C22⋊C4—32no—
187C22⋊C4—62no—
188C22⋊C4—62no—
189C42—61no—
190C3×C5—161noHall
191A4—41no—
192A4—81no—
193C3×C4—162no—
194C3×C4—161no—
195C2×C5—61no—
196C2×C5—121no—
197C2×C5—121no—
198C2×C5C2×#120⋊C311yescharacteristic
199C23—21no—
200C23—31no—
201C23—31no—
202C23—61no—
203C23C22×C5×A411yescharacteristic
204Q8—21no—
205Q8—41no—
206Q8—62no—
207Q8—61no—
208Q8—121no—
209D4—62no—
210D4—62no—
211D4—62no—
212D4—61no—
213D4—61no—
214D4—62no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—31no—
218C2×C4—31no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—62no—
222C2×C4—62no—
223C2×C4—61no—
224C2×C4—61no—
225C2×C4—61no—
226C2×C4—61no—
227C2×C4—62no—
228C2×C3—161no—
229C5#3028⋊C311yescharacteristic, direct product factor, Sylow
230C22—31no—
231C22—41no—
232C22—61no—
233C22—61no—
234C22—81no—
235C22—121no—
236C22—121no—
237C22—241no—
238C4—31no—
239C4—42no—
240C4—61no—
241C4—61no—
242C4—122no—
243C4C5×#120⋊C311yescharacteristic
244C3—161noSylow
245C2—61no—
246C2—121no—
247C2—121no—
248C2C2×C5×#120⋊C311yescharacteristic
subgroupG/H
center, socleC2×C5C2×#120⋊C3
commutator, cosocle, hypocenterH(5,𝔽2)C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#3028C3
prime radicalC5×#5950C2
hypercenterC4×C5#120⋊C3
LCSG ▷ H(5,𝔽2)
UCSC1 ◁ C2×C5 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
2. C5×#458⋊C3C2semidirect
3. C5×#3028C3semidirect
6. #3028⋊C3C5direct (N × H)
17. #458⋊C3C2×C5semidirect
25. C22×C5×Q8A4semidirect
35. #3028C3×C5semidirect
126. C22×Q8C5×A4semidirect
229. C5#3028⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#59502
C5×#458⋊C32
C5×#30283
C5×Q8×A44
#3028⋊C35