Finite Group Databasebeta

← C59×#33761 #28445870

Subgroups — C59×#33761 #28445870

Order 15104.

584 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C2×C59×#467C212yesmaximal
2C59×#2235C214yesmaximal, complemented
3C59×#2219C214yesmaximal, complemented
4C59×#2188C214yesmaximal, complemented
5C59×#2112C211yesmaximal, characteristic
6C22×Q16×C59C2212yes—
7C23×C8×C59C2211yescharacteristic
8C2×C22⋊Q8×C59—22no—
9C2×Q32×C59C2214yescomplemented
10C2×M32×C59C2212yes—
11C59×#467—22no—
12C59×#467—22no—
13C59×#467C2214yes—
14C59×#467C2214yes—
15C2×#107×C59C2212yes—
16C2×#103×C59—22no—
17C59×#367C2214yescomplemented
18C59×#358C2218yescomplemented
19C59×C22⋊C16C2214yes—
20C22×Q8×C59—22no—
21C23×C4×C59D411yescharacteristic
22C2×Q16×C59—22no—
23C2×Q16×C59—44no—
24C2×Q16×C59C2314yes—
25C22×C8×C59—42no—
26C22×C8×C59D412yes—
27C22×C8×C59D411yescharacteristic
28C22×C8×C59C2312yes—
29C22×C8×C59C2311yescharacteristic
30C22⋊Q8×C59—24no—
31C22⋊Q8×C59—24no—
32C22⋊Q8×C59—42no—
33C22⋊Q8×C59—42no—
34C2×C4⋊C4×C59—22no—
35C2×C4⋊C4×C59—42no—
36C2×C22⋊C4×C59—42no—
37Q32×C59—44no—
38M32×C59—42no—
39C2×C16×C59C2314yes—
40#107×C59—22no—
41#107×C59C2314yes—
42#103×C59—24no—
43#103×C59—24no—
44C24×C59D811yescharacteristic
45C2×Q8×C59—24no—
46C2×Q8×C59—44no—
47C2×Q8×C59—44no—
48C2×Q8×C59—42no—
49C22×C4×C59—41no—
50C22×C4×C59—41no—
51C22×C4×C59—42no—
52C22×C4×C59—42no—
53C22×C4×C59D812yes—
54C22×C4×C59D811yescharacteristic
55C22×C4×C59C2×D412yes—
56C22×C4×C59C2×D411yescharacteristic
57Q16×C59—28no—
58Q16×C59—44no—
59C2×C8×C59—22no—
60C2×C8×C59—24no—
61C2×C8×C59—42no—
62C2×C8×C59—41no—
63C2×C8×C59C2×D411yescharacteristic
64C2×C8×C59C2×D412yes—
65C2×C8×C59C2411yescharacteristic
66C4⋊C4×C59—24no—
67C4⋊C4×C59—42no—
68C4⋊C4×C59—44no—
69C4⋊C4×C59—44no—
70C22⋊C4×C59—44no—
71C22⋊C4×C59—44no—
72C16×C59—24no—
73C23×C59—24no—
74C23×C59—41no—
75C23×C59C2×D811yescharacteristic
76C23×C59C2×D812yes—
77Q8×C59—44no—
78Q8×C59—44no—
79Q8×C59—84no—
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—42no—
85C2×C4×C59—41no—
86C2×C4×C59—44no—
87C2×C4×C59—44no—
88C2×C4×C59—84no—
89C2×C4×C59—84no—
90C2×C4×C59C2×D811yescharacteristic
91C2×C4×C59C2×D812yes—
92C2×C4×C59C22×D411yescharacteristic
93C8×C59—21no—
94C8×C59—22no—
95C8×C59H(5,𝔽2)12yes—
96#33761C5911yesmaximal, characteristic, direct product factor, Sylow
97C22×C59—22no—
98C22×C59—22no—
99C22×C59—22no—
100C22×C59—21no—
101C22×C59—44no—
102C22×C59#51014yes—
103C22×C59C22×D811yescharacteristic
104C4×C59—21no—
105C4×C59—22no—
106C4×C59—84no—
107C4×C59—84no—
108C4×C59#53411yescharacteristic
109C4×C59#57511yescharacteristic
110C2×#467C2×C5912yes—
111#2235C2×C5914yescomplemented
112#2219C2×C5914yescomplemented
113#2188C2×C5914yescomplemented
114#2112C2×C5911yescharacteristic
115C2×C59—24no—
116C2×C59—41no—
117C2×C59#318611yescharacteristic
118C2×C59C2×#51012yes—
119C22×Q16C22×C5912yes—
120C23×C8C22×C5911yescharacteristic
121C2×C22⋊Q8—22no—
122C2×Q32C22×C5914yescomplemented
123C2×M32C22×C5912yes—
124#467—22no—
125#467—22no—
126#467C22×C5914yes—
127#467C22×C5914yes—
128C2×#107C22×C5912yes—
129C2×#103—22no—
130#367C22×C5914yescomplemented
131#358C22×C5918yescomplemented
132C22⋊C16C22×C5914yes—
133C59#3376111yescharacteristic, direct product factor, Sylow
134C22×Q8—22no—
135C23×C4D4×C5911yescharacteristic
136C2×Q16—22no—
137C2×Q16—44no—
138C2×Q16C23×C5914yes—
139C22×C8—42no—
140C22×C8D4×C5912yes—
141C22×C8D4×C5911yescharacteristic
142C22×C8C23×C5912yes—
143C22×C8C23×C5911yescharacteristic
144C22⋊Q8—24no—
145C22⋊Q8—24no—
146C22⋊Q8—42no—
147C22⋊Q8—42no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—42no—
150C2×C22⋊C4—42no—
151Q32—44no—
152M32—42no—
153C2×C16C23×C5914yes—
154#107—22no—
155#107C23×C5914yes—
156#103—24no—
157#103—24no—
158C24D8×C5911yescharacteristic
159C2×Q8—24no—
160C2×Q8—44no—
161C2×Q8—44no—
162C2×Q8—42no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4D8×C5912yes—
168C22×C4D8×C5911yescharacteristic
169C22×C4C2×D4×C5912yes—
170C22×C4C2×D4×C5911yescharacteristic
171Q16—28no—
172Q16—44no—
173C2×C8—22no—
174C2×C8—24no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8C2×D4×C5911yescharacteristic
178C2×C8C2×D4×C5912yes—
179C2×C8C24×C5911yescharacteristic
180C4⋊C4—24no—
181C4⋊C4—42no—
182C4⋊C4—44no—
183C4⋊C4—44no—
184C22⋊C4—44no—
185C22⋊C4—44no—
186C16—24no—
187C23—24no—
188C23—41no—
189C23C2×D8×C5911yescharacteristic
190C23C2×D8×C5912yes—
191Q8—44no—
192Q8—44no—
193Q8—84no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4—84no—
203C2×C4—84no—
204C2×C4C2×D8×C5911yescharacteristic
205C2×C4C2×D8×C5912yes—
206C2×C4C22×D4×C5911yescharacteristic
207C8—21no—
208C8—22no—
209C8H(5,𝔽2)×C5912yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—21no—
214C22—44no—
215C22C59×#51014yes—
216C22C22×D8×C5911yescharacteristic
217C4—22no—
218C4—21no—
219C4—84no—
220C4—84no—
221C4C59×#53411yescharacteristic
222C4C59×#57511yescharacteristic
223C2—24no—
224C2—41no—
225C2C59×#318611yescharacteristic
226C2C2×C59×#51012yes—
subgroupG/H
center, socleC22×C59C22×D8
commutator, Frattini, cosocleC2×C8C24×C59
prime radicalC24×C59D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ C23×C8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#2235C2semidirect
3. C59×#2219C2semidirect
4. C59×#2188C2semidirect
9. C2×Q32×C59C22semidirect
17. C59×#367C22semidirect
18. C59×#358C22semidirect
96. #33761C59direct (N × H)
111. #2235C2×C59semidirect
112. #2219C2×C59semidirect
113. #2188C2×C59semidirect
122. C2×Q32C22×C59semidirect
130. #367C22×C59semidirect
131. #358C22×C59semidirect
133. C59#33761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#4672
C59×#22352
C59×#22192
C59×#21882
C59×#21122
#3376159