Finite Group Databasebeta

← C59×#10559 #28422668

Subgroups — C59×#10559 #28422668

Order 15104.

448 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3189C211yesmaximal, characteristic
2C59×#1901C212yesmaximal
3C59×#1851C211yesmaximal, characteristic
4C59×#1508C212yesmaximal
5C59×#1293C211yesmaximal, characteristic
6C22×M16×C59C2211yescharacteristic
7C2×C22⋊Q8×C59C2212yes—
8C59×#484—22no—
9C59×#467—21no—
10C59×#467—21no—
11C59×#451—22no—
12C2×C4⋊C8×C59—21no—
13C2×#101×C59—22no—
14C59×#407C2212yes—
15C2×C22⋊C8×C59C2211yescharacteristic
16C4×C22⋊C4×C59C2211yescharacteristic
17C59×#343—22no—
18C59×#336—21no—
19C59×#328—22no—
20C59×#328—22no—
21C22×Q8×C59D412yes—
22C23×C4×C59C2311yescharacteristic
23C2×Q16×C59—21no—
24C2×Q16×C59—21no—
25C2×M16×C59—22no—
26C2×M16×C59—22no—
27C2×M16×C59—42no—
28C22×C8×C59—21no—
29C22×C8×C59D411yescharacteristic
30C22×C8×C59D411yescharacteristic
31C22⋊Q8×C59—22no—
32C22⋊Q8×C59—22no—
33C22⋊Q8×C59—22no—
34C22⋊Q8×C59—22no—
35C2×C4⋊C4×C59—22no—
36C2×C4⋊C4×C59D412yes—
37C2×C22⋊C4×C59—21no—
38C2×C22⋊C4×C59—22no—
39C2×C42×C59—21no—
40#107×C59—21no—
41#107×C59—21no—
42C4⋊C8×C59—42no—
43#103×C59—22no—
44#103×C59—22no—
45#101×C59—44no—
46C22⋊C8×C59—22no—
47C22⋊C8×C59—22no—
48C22⋊C8×C59—22no—
49#95×C59D411yescharacteristic
50#95×C59D411yescharacteristic
51C24×C59#4111yescharacteristic
52C2×Q8×C59—22no—
53C2×Q8×C59—22no—
54C2×Q8×C59—42no—
55C2×Q8×C59—42no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—22no—
59C22×C4×C59—22no—
60C22×C4×C59—41no—
61C22×C4×C59—41no—
62C22×C4×C59C2×D412yes—
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59#4112yes—
66Q16×C59—81no—
67Q16×C59—81no—
68M16×C59—24no—
69M16×C59—42no—
70M16×C59—42no—
71M16×C59—42no—
72C2×C8×C59—22no—
73C2×C8×C59—21no—
74C2×C8×C59—21no—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C2×C8×C59—42no—
80C4⋊C4×C59—22no—
81C4⋊C4×C59—22no—
82C4⋊C4×C59—42no—
83C4⋊C4×C59—42no—
84C22⋊C4×C59—42no—
85C22⋊C4×C59—42no—
86C22⋊C4×C59—42no—
87C42×C59—41no—
88C42×C59—41no—
89C23×C59—21no—
90C23×C59—21no—
91C23×C59—41no—
92C23×C59—41no—
93C23×C59#12111yescharacteristic
94C23×C59#12312yes—
95Q8×C59—42no—
96Q8×C59—42no—
97Q8×C59—82no—
98C2×C4×C59—21no—
99C2×C4×C59—22no—
100C2×C4×C59—21no—
101C2×C4×C59—22no—
102C2×C4×C59—22no—
103C2×C4×C59—41no—
104C2×C4×C59—42no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—44no—
110C2×C4×C59—42no—
111C2×C4×C59—42no—
112C2×C4×C59—41no—
113C2×C4×C59—82no—
114C2×C4×C59#12011yescharacteristic
115C2×C4×C59#12112yes—
116C2×C4×C59#12411yescharacteristic
117C8×C59—42no—
118C8×C59—41no—
119C8×C59—41no—
120C8×C59—82no—
121#10559C5911yesmaximal, characteristic, direct product factor, Sylow
122C22×C59—21no—
123C22×C59—21no—
124C22×C59—22no—
125C22×C59—22no—
126C22×C59—22no—
127C22×C59—81no—
128C22×C59—81no—
129C22×C59#39411yescharacteristic
130C22×C59#47311yescharacteristic
131C22×C59#47311yescharacteristic
132C4×C59—22no—
133C4×C59—21no—
134C4×C59—42no—
135C4×C59—81no—
136C4×C59—82no—
137C4×C59—82no—
138C4×C59B(4,𝔽2)11yescharacteristic
139C4×C59#45811yescharacteristic
140#3189C2×C5911yescharacteristic
141#1901C2×C5912yes—
142#1851C2×C5911yescharacteristic
143#1508C2×C5912yes—
144#1293C2×C5911yescharacteristic
145C2×C59—21no—
146C2×C59—21no—
147C2×C59—42no—
148C2×C59#204411yescharacteristic
149C2×C59#204711yescharacteristic
150C2×C59#205011yescharacteristic
151C22×M16C22×C5911yescharacteristic
152C2×C22⋊Q8C22×C5912yes—
153#484—22no—
154#467—21no—
155#467—21no—
156#451—22no—
157C2×C4⋊C8—21no—
158C2×#101—22no—
159#407C22×C5912yes—
160C2×C22⋊C8C22×C5911yescharacteristic
161C4×C22⋊C4C22×C5911yescharacteristic
162#343—22no—
163#336—21no—
164#328—22no—
165#328—22no—
166C59#1055911yescharacteristic, direct product factor, Sylow
167C22×Q8D4×C5912yes—
168C23×C4C23×C5911yescharacteristic
169C2×Q16—21no—
170C2×Q16—21no—
171C2×M16—22no—
172C2×M16—22no—
173C2×M16—42no—
174C22×C8—21no—
175C22×C8D4×C5911yescharacteristic
176C22×C8D4×C5911yescharacteristic
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4D4×C5912yes—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—21no—
185C2×C42—21no—
186#107—21no—
187#107—21no—
188C4⋊C8—42no—
189#103—22no—
190#103—22no—
191#101—44no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#95D4×C5911yescharacteristic
196#95D4×C5911yescharacteristic
197C24#41×C5911yescharacteristic
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—42no—
201C2×Q8—42no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4C2×D4×C5912yes—
209C22×C4C2×D4×C5911yescharacteristic
210C22×C4C2×D4×C5911yescharacteristic
211C22×C4#41×C5912yes—
212Q16—81no—
213Q16—81no—
214M16—24no—
215M16—42no—
216M16—42no—
217M16—42no—
218C2×C8—22no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—42no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C42—41no—
234C42—41no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#121×C5911yescharacteristic
240C23#123×C5912yes—
241Q8—42no—
242Q8—42no—
243Q8—82no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—82no—
260C2×C4#120×C5911yescharacteristic
261C2×C4#121×C5912yes—
262C2×C4#124×C5911yescharacteristic
263C8—42no—
264C8—41no—
265C8—41no—
266C8—82no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22C59×#39411yescharacteristic
275C22C59×#47311yescharacteristic
276C22C59×#47311yescharacteristic
277C4—22no—
278C4—21no—
279C4—42no—
280C4—81no—
281C4—82no—
282C4—82no—
283C4C59×B(4,𝔽2)11yescharacteristic
284C4C59×#45811yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2C59×#204411yescharacteristic
289C2C59×#204711yescharacteristic
290C2C59×#205011yescharacteristic
subgroupG/H
center, socleC22×C59#394
commutator, Frattini, cosocleC23×C4C23×C59
prime radicalC24×C59#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
121. #10559C59direct (N × H)
166. C59#10559direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31892
C59×#19012
C59×#18512
C59×#15082
C59×#12932
#1055959