Finite Group Databasebeta

← C59×#10259 #28422368

Subgroups — C59×#10259 #28422368

Order 15104.

474 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C59×#3249C211yesmaximal, characteristic
2C59×#3078C212yesmaximal
3C59×#1984C211yesmaximal, characteristic
4C59×#1493C212yesmaximal
5C59×#1292C211yesmaximal, characteristic
6C59×#533C2212yes—
7C2×C4×Q8×C59C2211yescharacteristic
8C59×#479—24no—
9C59×#477—22no—
10C59×#477—22no—
11C59×#475—22no—
12C59×#467—22no—
13C59×#462—22no—
14C59×#428—22no—
15C59×#423C2212yes—
16C2×C4⋊C8×C59C2211yescharacteristic
17C59×#419—22no—
18C2×C4×C8×C59C2211yescharacteristic
19C59×#336—22no—
20C59×Q8⋊C8—24no—
21C22×Q8×C59D411yescharacteristic
22C2×Q16×C59—22no—
23C2×M16×C59—22no—
24C22×C8×C59—21no—
25C22×C8×C59D412yes—
26C4⋊Q8×C59D412yes—
27C4⋊Q8×C59D412yes—
28#125×C59—22no—
29C22⋊Q8×C59—22no—
30C22⋊Q8×C59—22no—
31C4×Q8×C59—22no—
32C4×Q8×C59—22no—
33C4×Q8×C59—22no—
34C4×Q8×C59—22no—
35#117×C59—22no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C42×C59—21no—
39C2×C42×C59C2311yescharacteristic
40#107×C59—24no—
41#107×C59—22no—
42#106×C59—24no—
43C4⋊C8×C59—22no—
44C4⋊C8×C59—22no—
45C4⋊C8×C59D414yes—
46#103×C59—24no—
47#103×C59—24no—
48#103×C59—24no—
49C4×C8×C59—22no—
50C2×Q8×C59—21no—
51C2×Q8×C59—22no—
52C2×Q8×C59—22no—
53C2×Q8×C59—22no—
54C2×Q8×C59—22no—
55C2×Q8×C59Q1612yescomplemented
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59#4111yescharacteristic
61Q16×C59—82no—
62M16×C59—42no—
63M16×C59—42no—
64C2×C8×C59—22no—
65C2×C8×C59—22no—
66C2×C8×C59—24no—
67C2×C8×C59—41no—
68C2×C8×C59—41no—
69C2×C8×C59—42no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—22no—
73C4⋊C4×C59—22no—
74C4⋊C4×C59—22no—
75C4⋊C4×C59—42no—
76C4⋊C4×C59—42no—
77C4⋊C4×C59—42no—
78C22⋊C4×C59—42no—
79C42×C59—41no—
80C42×C59—42no—
81C42×C59—41no—
82C42×C59C2×D412yes—
83C42×C59C2×D412yes—
84C23×C59#12111yescharacteristic
85Q8×C59—24no—
86Q8×C59—44no—
87Q8×C59—42no—
88Q8×C59—42no—
89Q8×C59—42no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—22no—
93C2×C4×C59—41no—
94C2×C4×C59—41no—
95C2×C4×C59—41no—
96C2×C4×C59—42no—
97C2×C4×C59—41no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59#12012yes—
101C2×C4×C59#12011yescharacteristic
102C2×C4×C59#12112yes—
103C2×C4×C59#12711yescharacteristic
104C2×C4×C59C2×Q1611yescharacteristic
105C2×C4×C59#13511yescharacteristic
106C2×C4×C59#13712yes—
107C8×C59—42no—
108C8×C59—44no—
109C8×C59—42no—
110#10259C5911yesmaximal, characteristic, direct product factor, Sylow
111C22×C59—21no—
112C22×C59—21no—
113C22×C59#39211yescharacteristic
114C22×C59#46711yescharacteristic
115C22×C59#47011yescharacteristic
116C4×C59—21no—
117C4×C59—22no—
118C4×C59—42no—
119C4×C59—82no—
120C4×C59—81no—
121C4×C59—82no—
122C4×C59#45112yes—
123C4×C59#45212yes—
124C4×C59#45511yescharacteristic
125C4×C59#45611yescharacteristic
126#3249C2×C5911yescharacteristic
127#3078C2×C5912yes—
128#1984C2×C5911yescharacteristic
129#1493C2×C5912yes—
130#1292C2×C5911yescharacteristic
131C2×C59—21no—
132C2×C59—21no—
133C2×C59#200111yescharacteristic
134C2×C59#200711yescharacteristic
135C2×C59#201711yescharacteristic
136#533C22×C5912yes—
137C2×C4×Q8C22×C5911yescharacteristic
138#479—24no—
139#477—22no—
140#477—22no—
141#475—22no—
142#467—22no—
143#462—22no—
144#428—22no—
145#423C22×C5912yes—
146C2×C4⋊C8C22×C5911yescharacteristic
147#419—22no—
148C2×C4×C8C22×C5911yescharacteristic
149#336—22no—
150Q8⋊C8—24no—
151C59#1025911yescharacteristic, direct product factor, Sylow
152C22×Q8D4×C5911yescharacteristic
153C2×Q16—22no—
154C2×M16—22no—
155C22×C8—21no—
156C22×C8D4×C5912yes—
157C4⋊Q8D4×C5912yes—
158C4⋊Q8D4×C5912yes—
159#125—22no—
160C22⋊Q8—22no—
161C22⋊Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166#117—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4D4×C5911yescharacteristic
169C2×C42—21no—
170C2×C42C23×C5911yescharacteristic
171#107—24no—
172#107—22no—
173#106—24no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8D4×C5914yes—
177#103—24no—
178#103—24no—
179#103—24no—
180C4×C8—22no—
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8Q16×C5912yescomplemented
187C22×C4—21no—
188C22×C4—21no—
189C22×C4C2×D4×C5911yescharacteristic
190C22×C4C2×D4×C5911yescharacteristic
191C22×C4#41×C5911yescharacteristic
192Q16—82no—
193M16—42no—
194M16—42no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—24no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—42no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—42no—
210C42—41no—
211C42—42no—
212C42—41no—
213C42C2×D4×C5912yes—
214C42C2×D4×C5912yes—
215C23#121×C5911yescharacteristic
216Q8—24no—
217Q8—44no—
218Q8—42no—
219Q8—42no—
220Q8—42no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#120×C5912yes—
232C2×C4#120×C5911yescharacteristic
233C2×C4#121×C5912yes—
234C2×C4#127×C5911yescharacteristic
235C2×C4C2×Q16×C5911yescharacteristic
236C2×C4#135×C5911yescharacteristic
237C2×C4#137×C5912yes—
238C8—42no—
239C8—44no—
240C8—42no—
241C22—21no—
242C22—21no—
243C22C59×#39211yescharacteristic
244C22C59×#46711yescharacteristic
245C22C59×#47011yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4C59×#45112yes—
253C4C59×#45212yes—
254C4C59×#45511yescharacteristic
255C4C59×#45611yescharacteristic
256C2—21no—
257C2—21no—
258C2C59×#200111yescharacteristic
259C2C59×#200711yescharacteristic
260C2C59×#201711yescharacteristic
subgroupG/H
center, socleC22×C59#392
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC23×C59#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
55. C2×Q8×C59Q16semidirect
110. #10259C59direct (N × H)
151. C59#10259direct (N × H)
186. C2×Q8Q16×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#32492
C59×#30782
C59×#19842
C59×#14932
C59×#12922
#1025959