Finite Group Databasebeta

← C59×#12803 #28424912

Subgroups — C59×#12803 #28424912

Order 15104.

480 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2326C211yesmaximal, characteristic
2C2×C59×#355C212yesmaximal
3C59×#1801C212yesmaximal, complemented
4C59×#1394C212yesmaximal, complemented
5C2×#124×C59C2211yescharacteristic
6C2×C4×Q8×C59C2211yescharacteristic
7C2×C4×D4×C59C411yescharacteristic
8C59×#423—22no—
9C2×#101×C59C2214yes—
10C59×#391C2211yescharacteristic
11C59×#390C411yescharacteristic
12C59×#388—22no—
13C59×#385—22no—
14C59×#384C411yescharacteristic
15C59×#376C411yescharacteristic
16C59×#355—24no—
17C59×#343—22no—
18C22×Q8×C59C2311yescharacteristic
19C22×D4×C59C2×C411yescharacteristic
20C23×C4×C59—21no—
21C2×M16×C59—24no—
22#124×C59—22no—
23#124×C59D412yes—
24#124×C59Q812yes—
25C4×Q8×C59—42no—
26C4×D4×C59—42no—
27C2×C4⋊C4×C59—22no—
28C2×C4⋊C4×C59C2×C411yescharacteristic
29C2×C4⋊C4×C59C2×C411yescharacteristic
30C2×C4⋊C4×C59D412yes—
31C2×C22⋊C4×C59—22no—
32C2×C22⋊C4×C59—21no—
33C2×C22⋊C4×C59—22no—
34C2×C42×C59C2×C411yescharacteristic
35C2×C42×C59C2×C411yescharacteristic
36C2×C42×C59C2×C411yescharacteristic
37C2×C42×C59D412yes—
38C4⋊C8×C59—44no—
39#101×C59—24no—
40#101×C59—24no—
41#95×C59—21no—
42#95×C59—21no—
43#95×C59—22no—
44C24×C59—21no—
45C2×Q8×C59—41no—
46C2×Q8×C59—41no—
47C2×Q8×C59C2×D411yescharacteristic
48C2×Q8×C59C2×Q811yescharacteristic
49C2×Q8×C59#4112yes—
50C2×D4×C59—21no—
51C2×D4×C59—41no—
52C2×D4×C59—41no—
53C2×D4×C59C4⋊C412yes—
54C22×C4×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59—42no—
58C22×C4×C59—82no—
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22⋊C412yes—
61C22×C4×C59C22⋊C411yescharacteristic
62C22×C4×C59C22×C411yescharacteristic
63C22×C4×C59C2×D412yes—
64M16×C59—44no—
65M16×C59—44no—
66C2×C8×C59—44no—
67C4⋊C4×C59—41no—
68C4⋊C4×C59—42no—
69C4⋊C4×C59—41no—
70C4⋊C4×C59—82no—
71C22⋊C4×C59—24no—
72C22⋊C4×C59—24no—
73C22⋊C4×C59—42no—
74C22⋊C4×C59—82no—
75C42×C59—24no—
76C42×C59—22no—
77C42×C59—21no—
78C42×C59—41no—
79C42×C59C4⋊C412yes—
80C23×C59—22no—
81C23×C59—42no—
82C23×C59—42no—
83C23×C59—41no—
84C23×C59—41no—
85C23×C59C2×C22⋊C411yescharacteristic
86Q8×C59—41no—
87Q8×C59—41no—
88Q8×C59—42no—
89D4×C59—42no—
90D4×C59—42no—
91C2×C4×C59—21no—
92C2×C4×C59—22no—
93C2×C4×C59—21no—
94C2×C4×C59—22no—
95C2×C4×C59—22no—
96C2×C4×C59—21no—
97C2×C4×C59—22no—
98C2×C4×C59—41no—
99C2×C4×C59—41no—
100C2×C4×C59—41no—
101C2×C4×C59—42no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—42no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—84no—
109C2×C4×C59#9912yes—
110C2×C4×C59C2×C4⋊C411yescharacteristic
111C2×C4×C59#11711yescharacteristic
112C2×C4×C59#12112yes—
113C2×C4×C59C22⋊Q812yes—
114C8×C59—84no—
115#12803C5911yesmaximal, characteristic, direct product factor, Sylow
116C22×C59—21no—
117C22×C59—21no—
118C22×C59—44no—
119C22×C59—42no—
120C22×C59—82no—
121C22×C59—81no—
122C22×C59—81no—
123C22×C59#38011yescharacteristic
124C22×C59C2×#9911yescharacteristic
125C22×C59#41011yescharacteristic
126C4×C59—22no—
127C4×C59—21no—
128C4×C59—21no—
129C4×C59—22no—
130C4×C59—22no—
131C4×C59—42no—
132C4×C59—42no—
133C4×C59—41no—
134C4×C59—81no—
135C4×C59—81no—
136#2326C2×C5911yescharacteristic
137C2×#355C2×C5912yes—
138#1801C2×C5912yescomplemented
139#1394C2×C5912yescomplemented
140C2×C59—21no—
141C2×C59—21no—
142C2×C59—82no—
143C2×C59#179911yescharacteristic
144C2×C59#213311yescharacteristic
145C2×C59#213411yescharacteristic
146C2×#124C22×C5911yescharacteristic
147C2×C4×Q8C22×C5911yescharacteristic
148C2×C4×D4C4×C5911yescharacteristic
149#423—22no—
150C2×#101C22×C5914yes—
151#391C22×C5911yescharacteristic
152#390C4×C5911yescharacteristic
153#388—22no—
154#385—22no—
155#384C4×C5911yescharacteristic
156#376C4×C5911yescharacteristic
157#355—24no—
158#343—22no—
159C59#1280311yescharacteristic, direct product factor, Sylow
160C22×Q8C23×C5911yescharacteristic
161C22×D4C2×C4×C5911yescharacteristic
162C23×C4—21no—
163C2×M16—24no—
164#124—22no—
165#124D4×C5912yes—
166#124Q8×C5912yes—
167C4×Q8—42no—
168C4×D4—42no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C2×C4×C5911yescharacteristic
171C2×C4⋊C4C2×C4×C5911yescharacteristic
172C2×C4⋊C4D4×C5912yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—22no—
176C2×C42C2×C4×C5911yescharacteristic
177C2×C42C2×C4×C5911yescharacteristic
178C2×C42C2×C4×C5911yescharacteristic
179C2×C42D4×C5912yes—
180C4⋊C8—44no—
181#101—24no—
182#101—24no—
183#95—21no—
184#95—21no—
185#95—22no—
186C24—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C2×D4×C5911yescharacteristic
190C2×Q8C2×Q8×C5911yescharacteristic
191C2×Q8#41×C5912yes—
192C2×D4—21no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4C4⋊C4×C5912yes—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—82no—
201C22×C4C22⋊C4×C5911yescharacteristic
202C22×C4C22⋊C4×C5912yes—
203C22×C4C22⋊C4×C5911yescharacteristic
204C22×C4C22×C4×C5911yescharacteristic
205C22×C4C2×D4×C5912yes—
206M16—44no—
207M16—44no—
208C2×C8—44no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—24no—
218C42—22no—
219C42—21no—
220C42—41no—
221C42C4⋊C4×C5912yes—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—41no—
226C23—41no—
227C23C2×C22⋊C4×C5911yescharacteristic
228Q8—41no—
229Q8—41no—
230Q8—42no—
231D4—42no—
232D4—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4#99×C5912yes—
252C2×C4C2×C4⋊C4×C5911yescharacteristic
253C2×C4#117×C5911yescharacteristic
254C2×C4#121×C5912yes—
255C2×C4C22⋊Q8×C5912yes—
256C8—84no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—81no—
263C22—81no—
264C22C59×#38011yescharacteristic
265C22C2×#99×C5911yescharacteristic
266C22C59×#41011yescharacteristic
267C4—22no—
268C4—21no—
269C4—21no—
270C4—22no—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—81no—
276C4—81no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C59×#179911yescharacteristic
281C2C59×#213311yescharacteristic
282C2C59×#213411yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC22×Q8C23×C59
prime radicalC22×D4×C59C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×C4×Q8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1801C2semidirect
4. C59×#1394C2semidirect
115. #12803C59direct (N × H)
138. #1801C2×C59semidirect
139. #1394C2×C59semidirect
159. C59#12803direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#23262
C2×C59×#3552
C59×#18012
C59×#13942
#1280359