Finite Group Databasebeta

← C3×C5⋊(C5⋊#64418) #36347979

Subgroups — C3×C5⋊(C5⋊#64418) #36347979

Order 22050.

256 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 50 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×C52×#3862C211yesmaximal, characteristic, complemented, Hall
2C3×C7×C5⋊D35—31nomaximal
3C5⋊(C5⋊#64418)C311yesmaximal, characteristic, direct product factor
4C3×C5⋊#64418—51nomaximal
5C3×C5⋊#64418—51nomaximal
6C3×C5⋊#64418—51nomaximal
7C3×C5⋊#64418—51nomaximal
8C3×C5⋊#64418—52nomaximal
9C52×#3862—21no—
10C52×#3862C2×C311yescharacteristic, complemented
11C3×C52×C72D311yescharacteristic, complemented
12C7×C5⋊D35—31noHall
13C3×C5×#3862D511yescharacteristic, complemented
14C3×C5×#3862D511yescharacteristic, complemented
15C3×C5×#3862D511yescharacteristic, complemented
16C3×C5×#3862D511yescharacteristic, complemented
17C3×C5×#3862D512yescomplemented
18C3×C52×ΓL(1,𝔽8)—141no—
19C3×C7×D35—151no—
20C3×C7×D35—151no—
21C3×C7×D35—151no—
22C3×C7×D35—151no—
23C3×C7×D35—152no—
24C5⋊#64418—51no—
25C5⋊#64418—51no—
26C5⋊#64418—51no—
27C5⋊#64418—51no—
28C5⋊#64418—52no—
29C52×C72C3×D311yescharacteristic, complemented, Hall
30C3×C5⋊D35—31no—
31C3×C7×C5⋊D5—211no—
32C3×#64418—251noHall
33C3×C5×C72D1511yescharacteristic, complemented
34C3×C5×C72D1511yescharacteristic, complemented
35C3×C5×C72D1511yescharacteristic, complemented
36C3×C5×C72D1511yescharacteristic, complemented
37C3×C5×C72D1512yescomplemented
38C5×#3862—21no—
39C5×#3862—21no—
40C5×#3862—21no—
41C5×#3862—21no—
42C5×#3862—22no—
43C5×#3862C3×D511yescharacteristic, complemented
44C5×#3862C3×D511yescharacteristic, complemented
45C5×#3862C3×D511yescharacteristic, complemented
46C5×#3862C3×D511yescharacteristic, complemented
47C5×#3862C3×D512yescomplemented
48C3×C52×C7—21no—
49C3×C52×C7—61no—
50C3×C52×C7—61no—
51C52×ΓL(1,𝔽8)—142no—
52C52×ΓL(1,𝔽8)—141no—
53C7×D35—151no—
54C7×D35—151no—
55C7×D35—151no—
56C7×D35—151no—
57C7×D35—152no—
58C3×C3⋊(C5⋊D5)—491nomaximal, Hall
59C3×#3862C5⋊D511yescharacteristic, complemented, Hall
60C5⋊D35—31no—
61C7×C5⋊D5—211no—
62C3×C5×ΓL(1,𝔽8)—141no—
63C3×C5×ΓL(1,𝔽8)—141no—
64C3×C5×ΓL(1,𝔽8)—141no—
65C3×C5×ΓL(1,𝔽8)—141no—
66C3×C5×ΓL(1,𝔽8)—142no—
67C3×C7×D7—751no—
68#64418—251no—
69C5×C72C3×D1511yescharacteristic, complemented
70C5×C72C3×D1511yescharacteristic, complemented
71C5×C72C3×D1511yescharacteristic, complemented
72C5×C72C3×D1511yescharacteristic, complemented
73C5×C72C3×D1512yescomplemented
74C32×C52—981noHall
75C3×D35—151no—
76C3×D35—151no—
77C3×D35—151no—
78C3×D35—151no—
79C3×D35—152no—
80C3×C7×D5—1051no—
81C3×C7×D5—1051no—
82C3×C7×D5—1051no—
83C3×C7×D5—1051no—
84C3×C7×D5—1052no—
85C52×C7—21no—
86C52×C7—61no—
87C52×C7—61no—
88C3⋊(C5⋊D5)—491no—
89C3×C5⋊D5—211no—
90C3×C72C3⋊(C5⋊D5)11yescharacteristic, complemented
91#3862—21no—
92#3862C3×C5⋊D511yescharacteristic, complemented
93C3×C5×C7—21no—
94C3×C5×C7—21no—
95C3×C5×C7—21no—
96C3×C5×C7—21no—
97C3×C5×C7—22no—
98C3×C5×C7—31no—
99C3×C5×C7—31no—
100C3×C5×C7—31no—
101C3×C5×C7—61no—
102C3×C5×C7—61no—
103C3×C5×C7—61no—
104C3×C5×C7—61no—
105C3×C5×C7—62no—
106C3×C5×C7—61no—
107C3×C5×C7—62no—
108C5×ΓL(1,𝔽8)—142no—
109C5×ΓL(1,𝔽8)—142no—
110C5×ΓL(1,𝔽8)—142no—
111C5×ΓL(1,𝔽8)—142no—
112C5×ΓL(1,𝔽8)—144no—
113C5×ΓL(1,𝔽8)—141no—
114C5×ΓL(1,𝔽8)—141no—
115C5×ΓL(1,𝔽8)—141no—
116C5×ΓL(1,𝔽8)—141no—
117C5×ΓL(1,𝔽8)—142no—
118C7×D7—751noHall
119C3×D15—2451no—
120C3×D15—2451no—
121C3×D15—2451no—
122C3×D15—2451no—
123C3×D15—2452no—
124C3×C52—981no—
125C3×C52—981no—
126C3×C52#6441811yescharacteristic, complemented
127D35—151no—
128D35—151no—
129D35—151no—
130D35—151no—
131D35—152no—
132C7×D5—1051no—
133C7×D5—1051no—
134C7×D5—1051no—
135C7×D5—1051no—
136C7×D5—1052no—
137C3×ΓL(1,𝔽8)—141no—
138C5⋊D5—211noHall
139C72C3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
140C32×C5—491no—
141C32×C5—491no—
142C32×C5—981no—
143C32×C5—981no—
144C32×C5—982no—
145C2×C3×C7—5251no—
146C3×D7—751no—
147C5×C7—21no—
148C5×C7—21no—
149C5×C7—21no—
150C5×C7—21no—
151C5×C7—22no—
152C5×C7—31no—
153C5×C7—31no—
154C5×C7—31no—
155C5×C7—61no—
156C5×C7—61no—
157C5×C7—61no—
158C5×C7—62no—
159C5×C7—61no—
160C5×C7—61no—
161C5×C7—62no—
162D15—2451no—
163D15—2451no—
164D15—2451no—
165D15—2451no—
166D15—2452no—
167C3×D5—1051no—
168C3×D5—1051no—
169C3×D5—1051no—
170C3×D5—1051no—
171C3×D5—1052no—
172C52C3×#6441811yescharacteristic, complemented, Sylow
173C3×C7—21no—
174C3×C7—31no—
175C3×C7—61no—
176ΓL(1,𝔽8)—142no—
177ΓL(1,𝔽8)—141no—
178C3×D3—12251noHall
179C3×C5—981no—
180C3×C5—981no—
181C3×C5—981no—
182C3×C5—981no—
183C3×C5—982no—
184C3×C5—981no—
185C3×C5—981no—
186C3×C5—981no—
187C3×C5—981no—
188C3×C5—982no—
189C3×C5C5⋊#6441811yescharacteristic, complemented
190C3×C5C5⋊#6441811yescharacteristic, complemented
191C3×C5C5⋊#6441811yescharacteristic, complemented
192C3×C5C5⋊#6441811yescharacteristic, complemented
193C3×C5C5⋊#6441812yescomplemented
194C2×C7—5251no—
195D7—751no—
196D5—1051no—
197D5—1051no—
198D5—1051no—
199D5—1051no—
200D5—1052no—
201C32—981noSylow
202C7—21no—
203C7—31no—
204C7—61no—
205C2×C3—5251no—
206D3—12251no—
207C5C3×C5⋊#6441811yescharacteristic, complemented
208C5C3×C5⋊#6441811yescharacteristic, complemented
209C5C3×C5⋊#6441811yescharacteristic, complemented
210C5C3×C5⋊#6441811yescharacteristic, complemented
211C5C3×C5⋊#6441812yescomplemented
212C3—981no—
213C3—981no—
214C3C5⋊(C5⋊#64418)11yescharacteristic, direct product factor
215C2—5251noSylow
subgroupG/H
center, hypercenterC3C5⋊(C5⋊#64418)
commutator, cosocle, hypocenterC52×#3862C2×C3
FrattiniC1G
Fitting, socleC3×C52×C72D3
LCSG ▷ C52×#3862
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C52×#3862C2semidirect
3. C5⋊(C5⋊#64418)C3direct (N × H)
10. C52×#3862C2×C3semidirect
11. C3×C52×C72D3semidirect
13. C3×C5×#3862D5semidirect
14. C3×C5×#3862D5semidirect
15. C3×C5×#3862D5semidirect
16. C3×C5×#3862D5semidirect
17. C3×C5×#3862D5semidirect
29. C52×C72C3×D3semidirect
33. C3×C5×C72D15semidirect
34. C3×C5×C72D15semidirect
35. C3×C5×C72D15semidirect
36. C3×C5×C72D15semidirect
37. C3×C5×C72D15semidirect
43. C5×#3862C3×D5semidirect
44. C5×#3862C3×D5semidirect
45. C5×#3862C3×D5semidirect
46. C5×#3862C3×D5semidirect
47. C5×#3862C3×D5semidirect
59. C3×#3862C5⋊D5semidirect
69. C5×C72C3×D15semidirect
70. C5×C72C3×D15semidirect
71. C5×C72C3×D15semidirect
72. C5×C72C3×D15semidirect
73. C5×C72C3×D15semidirect
90. C3×C72C3⋊(C5⋊D5)semidirect
92. #3862C3×C5⋊D5semidirect
126. C3×C52#64418semidirect
139. C72C3×C3⋊(C5⋊D5)semidirect
172. C52C3×#64418semidirect
189. C3×C5C5⋊#64418semidirect
190. C3×C5C5⋊#64418semidirect
191. C3×C5C5⋊#64418semidirect
192. C3×C5C5⋊#64418semidirect
193. C3×C5C5⋊#64418semidirect
207. C5C3×C5⋊#64418semidirect
208. C5C3×C5⋊#64418semidirect
209. C5C3×C5⋊#64418semidirect
210. C5C3×C5⋊#64418semidirect
211. C5C3×C5⋊#64418semidirect
214. C3C5⋊(C5⋊#64418)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×#38622
C3×C7×C5⋊D353
C5⋊(C5⋊#64418)3
C3×C5⋊#644185
C3×C3⋊(C5⋊D5)49