Finite Group Databasebeta

← #28491949

Subgroups — #28491949

Order 15104.

526 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#21424168C212yesmaximal
2#21424168C211yesmaximal, characteristic
3C59⋊#1304C211yesmaximal, characteristic
4C59⋊#1304C212yesmaximal
5C59×#2842C211yesmaximal, characteristic
6C22×C22⋊Dic59C2211yescharacteristic
7#16837258C2212yes—
8#16837258C2211yescharacteristic
9#16837168—24no—
10#16837168—22no—
11C59×#399—22no—
12C59×#396—24no—
13C59×#379C2211yescharacteristic
14C59×#379C2212yes—
15C23×Dic59Q812yes—
16C2×C22⋊Dic59—22no—
17C2×C22⋊Dic59—21no—
18C2×C22⋊Dic59—21no—
19C2×C22⋊Dic59—22no—
20C2×C22⋊Dic59—22no—
21C2×C22⋊Dic59—21no—
22C2×C22⋊Dic59—22no—
23C2×C22⋊Dic59—22no—
24C2×C22⋊Dic59—22no—
25C25×C59C2311yescharacteristic
26C2×C4⋊C4×C59—24no—
27C2×C4⋊C4×C59—22no—
28C2×C22⋊C4×C59—22no—
29C2×C22⋊C4×C59—22no—
30C2×C22⋊C4×C59—22no—
31C2×C22⋊C4×C59D414yes—
32C2×C22⋊C4×C59D412yes—
33#95×C59—22no—
34C24×C59—42no—
35C24×C59—82no—
36C24×C59C2×D412yes—
37C24×C59C2×D411yescharacteristic
38C24×C59C2×Q811yescharacteristic
39C24×C59#4112yes—
40C24×C59#4111yescharacteristic
41C22×C4×C59—22no—
42C22×C4×C59—24no—
43C22×Dic59—22no—
44C22×Dic59—22no—
45C22×Dic59—22no—
46C22×Dic59—42no—
47C22×Dic59—41no—
48C22×Dic59—82no—
49C4⋊C4×C59—84no—
50C4⋊C4×C59—82no—
51C22⋊C4×C59—44no—
52C22⋊C4×C59—42no—
53C22⋊C4×C59—82no—
54C22⋊C4×C59—82no—
55C22⋊C4×C59—82no—
56C22⋊Dic59—41no—
57C22⋊Dic59—42no—
58C22⋊Dic59—41no—
59C22⋊Dic59—44no—
60C22⋊Dic59—42no—
61C22⋊Dic59—82no—
62C22⋊Dic59—82no—
63C22⋊Dic59—82no—
64C23×C59—24no—
65C23×C59—22no—
66C23×C59—42no—
67C23×C59—41no—
68C23×C59—42no—
69C23×C59—42no—
70C23×C59—42no—
71C23×C59—42no—
72C23×C59—42no—
73C23×C59—42no—
74C23×C59—41no—
75C23×C59—42no—
76C23×C59—88no—
77C23×C59#12011yescharacteristic
78C23×C59C22⋊Q812yes—
79C23×C59C22⋊Q811yescharacteristic
80C23×C59#12412yes—
81C23×C59#12411yescharacteristic
82C2×C4×C59—44no—
83C2×C4×C59—44no—
84C2×C4×C59—44no—
85C2×C4×C59—44no—
86C2×C4×C59—42no—
87C2×Dic59—42no—
88C2×Dic59—82no—
89C2×Dic59—82no—
90C2×Dic59—82no—
91C2×Dic59—82no—
92C2×Dic59—81no—
93C2×Dic59—82no—
94C2×Dic59—82no—
95C2×Dic59—82no—
96#10393—591nomaximal, Sylow
97C22×C59—22no—
98C22×C59—22no—
99C22×C59—21no—
100C22×C59—22no—
101C22×C59—21no—
102C22×C59—22no—
103C22×C59—22no—
104C22×C59—22no—
105C22×C59—22no—
106C22×C59—22no—
107C22×C59—22no—
108C22×C59—44no—
109C22×C59—84no—
110C22×C59—82no—
111C22×C59—82no—
112C22×C59—84no—
113C22×C59#39311yescharacteristic
114C22×C59#45812yes—
115C4×C59—82no—
116C4×C59—84no—
117Dic59—82no—
118Dic59—162no—
119Dic59—161no—
120#2842D5911yescharacteristic
121#1819—592no—
122#1819—591no—
123#1304—591no—
124#1304—592no—
125C2×C59—22no—
126C2×C59—42no—
127C2×C59—41no—
128C2×C59—42no—
129C2×C59—41no—
130C2×C59#203011yescharacteristic
131C2×C59#203212yes—
132C22×C22⋊C4—591no—
133#399—22no—
134#396—24no—
135#379—592no—
136#379—591no—
137#379C2×D5911yescharacteristic
138#379C2×D5912yes—
139#342—1184no—
140#342—1182no—
141C59#1039311yescharacteristic, complemented, Sylow
142C25C22×D5911yescharacteristic
143C23×C4—592no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—1182no—
150C2×C22⋊C4—1182no—
151C2×C22⋊C4—1182no—
152C2×C22⋊C4—1181no—
153C2×C22⋊C4—1182no—
154C2×C22⋊C4—1182no—
155C2×C22⋊C4—1181no—
156C2×C22⋊C4—1182no—
157C2×C22⋊C4—1181no—
158C2×C22⋊C4C22⋊D5914yes—
159C2×C22⋊C4C22⋊D5912yes—
160#95—22no—
161C24—42no—
162C24—82no—
163C24Q8×D5911yescharacteristic
164C24#1174568912yes—
165C24#1174568911yescharacteristic
166C24C2×C22⋊D5912yes—
167C24C2×C22⋊D5911yescharacteristic
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—1182no—
171C22×C4—1182no—
172C22×C4—1182no—
173C22×C4—4722no—
174C22×C4—2362no—
175C22×C4—2361no—
176C4⋊C4—84no—
177C4⋊C4—82no—
178C22⋊C4—44no—
179C22⋊C4—42no—
180C22⋊C4—82no—
181C22⋊C4—82no—
182C22⋊C4—82no—
183C22⋊C4—4722no—
184C22⋊C4—4722no—
185C22⋊C4—4722no—
186C22⋊C4—2364no—
187C22⋊C4—2362no—
188C22⋊C4—2361no—
189C22⋊C4—2362no—
190C22⋊C4—2361no—
191C23—24no—
192C23—22no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—42no—
203C23—88no—
204C23#1427369611yescharacteristic
205C23#1427370312yes—
206C23#1427370311yescharacteristic
207C23#1427371612yes—
208C23#1427371611yescharacteristic
209C2×C4—44no—
210C2×C4—44no—
211C2×C4—44no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4—4722no—
215C2×C4—4722no—
216C2×C4—4722no—
217C2×C4—4722no—
218C2×C4—4721no—
219C2×C4—4722no—
220C2×C4—4722no—
221C2×C4—4722no—
222C2×C4—2362no—
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22#1683731311yescharacteristic
240C22#1683759212yes—
241C4—82no—
242C4—84no—
243C4—9442no—
244C4—9441no—
245C4—4722no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2#2142526211yescharacteristic
252C2#2142527212yes—
subgroupG/H
centerC22#16837313
commutator, prime radical, cosocleC25×C59C23
FrattiniC25C22×D59
FittingC59×#2842C2
socleC22×C59#393
hypercenter#2842D59
hypocenterC59#10393
LCSG ▷ C25×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C25 ◁ #2842

Complements

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

NH ≅ G/Ntype
141. C59#10393semidirect

Maximal subgroups

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

subgroupindex
#214241682
C59⋊#13042
C59×#28422
#1039359