Finite Group Databasebeta

← D59×#1355 #28499858

Subgroups — D59×#1355 #28499858

Order 15104.

366 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 71 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#490×D59C211yesmaximal, characteristic
2#347×D59C212yesmaximal, complemented
3#21422129C211yesmaximal, characteristic, complemented
4#21422128C212yesmaximal, complemented
5C59×#1355C211yesmaximal, characteristic, complemented
6#127×D59C411yescharacteristic
7#125×D59C411yescharacteristic
8M32×D59—22no—
9#16837768C411yescharacteristic
10#16837767C2211yescharacteristic
11#16837766C411yescharacteristic
12#16837765—22no—
13#102×D59—22no—
14#97×D59C2211yescharacteristic
15#16837180C2212yescomplemented
16#16837179—22no—
17C59×#490C2211yescharacteristic
18C59×#347C2212yescomplemented
19C2×D4×D59—21no—
20C2×D4×D59—41no—
21C2×C8×D59D412yes—
22#14273724C2×C411yescharacteristic
23#14273723—21no—
24#14273723—41no—
25#14273719C2×C411yescharacteristic
26#14273718—21no—
27#14273717—41no—
28C4⋊C4×D59—21no—
29C4⋊C4×D59—41no—
30C42×D59C2×C411yescharacteristic
31#14273667—22no—
32#14273666—24no—
33C16×D59—24no—
34#14273649—22no—
35#14273648—22no—
36#14273647—22no—
37#14273638C2×C411yescharacteristic
38#14273637D412yes—
39#127×C59C2×C411yescharacteristic
40#125×C59C2×C411yescharacteristic
41M32×C59—22no—
42#102×C59—22no—
43#97×C59C2311yescharacteristic
44C23×D59—41no—
45C2×D4×C59—21no—
46C2×D4×C59—41no—
47C2×C22⋊D59—42no—
48C2×C22⋊D59—41no—
49D4×D59—42no—
50D4×D59—42no—
51D4×D59—84no—
52C2×D236—21no—
53C2×D236—41no—
54C2×C4×D59—21no—
55C2×C4×D59—41no—
56C2×C4×D59C22⋊C411yescharacteristic
57C2×C8×C59C2×D412yes—
58C4⋊C4×C59—21no—
59C4⋊C4×C59—41no—
60C42×C59C22×C411yescharacteristic
61C4⋊Dic59—21no—
62C4⋊Dic59—41no—
63Dic59⋊C4—41no—
64Dic59⋊C4—41no—
65Dic59⋊C4—41no—
66C4×Dic59—21no—
67C4×Dic59C22⋊C411yescharacteristic
68C2×C59⋊C8C22⋊C412yes—
69C8×D59—22no—
70C8×D59—22no—
71C16×C59—24no—
72C59⋊C16—24no—
73C23×C59—41no—
74C22×D59—41no—
75C22×D59—84no—
76C22×D59—81no—
77C22×D59—81no—
78C22×D59#10011yescharacteristic
79D4×C59—42no—
80D4×C59—82no—
81C2×C4×C59—21no—
82C2×C4×C59—41no—
83C2×C4×C59C2×C22⋊C411yescharacteristic
84C22⋊D59—84no—
85C22⋊D59—82no—
86C2×Dic59—21no—
87C2×Dic59—41no—
88C2×Dic59#10011yescharacteristic
89D236—42no—
90D236—82no—
91C4×D59—42no—
92C4×D59—82no—
93C4×D59#10412yes—
94C4×D59#10412yes—
95C8×C59—22no—
96C59⋊C8—22no—
97C2×#1355—591nomaximal, Sylow
98C22×C59—82no—
99C22×C59—81no—
100C22×C59C2×#10011yescharacteristic
101C2×D59—22no—
102C2×D59—82no—
103C2×D59—81no—
104C2×D59—162no—
105C2×D59—162no—
106C2×D59#32911yescharacteristic
107C2×D59#32911yescharacteristic
108C4×C59—41no—
109C4×C59—81no—
110C4×C59C2×#10412yes—
111Dic59—41no—
112Dic59—81no—
113Dic59#32912yes—
114C2×#490—591no—
115C2×#347—592no—
116#1355—591no—
117#1355—592no—
118#1355D5911yescharacteristic, direct product factor
119C2×C59—21no—
120C2×C59—161no—
121C2×C59C2×#32911yescharacteristic
122D59—21no—
123D59—161no—
124D59#135512yesdirect product factor
125C2×#127—591no—
126C2×#125—591no—
127C2×M32—1182no—
128#490—591no—
129#490—591no—
130#490—591no—
131#490—1182no—
132#490C2×D5911yescharacteristic
133C2×#102—1182no—
134C2×#97—591no—
135#347—592no—
136#347—1182no—
137#347C2×D5912yescomplemented
138C59C2×#135511yescharacteristic, complemented, Sylow
139C22×D4—1181no—
140C22×D4—2361no—
141C22×C8—592no—
142#127—591no—
143#127—1181no—
144#127—2361no—
145#127C4×D5911yescharacteristic
146#125—591no—
147#125—1181no—
148#125—2361no—
149#125C4×D5911yescharacteristic
150C2×C4⋊C4—1181no—
151C2×C4⋊C4—2361no—
152C2×C42—591no—
153M32—22no—
154M32—1184no—
155M32—1182no—
156C2×C16—1184no—
157#102—22no—
158#102—1182no—
159#102—1182no—
160#102—1182no—
161#97—592no—
162#97—591no—
163#97C22×D5911yescharacteristic
164C24—2361no—
165C2×D4—21no—
166C2×D4—41no—
167C2×D4—1181no—
168C2×D4—4724no—
169C2×D4—2361no—
170C2×D4—2362no—
171C2×D4—2362no—
172C2×D4—2361no—
173C2×D4—2362no—
174C22×C4—591no—
175C22×C4—1181no—
176C22×C4—2361no—
177C2×C8—592no—
178C2×C8—1182no—
179C2×C8—1182no—
180C2×C8D4×D5912yes—
181C4⋊C4—21no—
182C4⋊C4—41no—
183C4⋊C4—1181no—
184C4⋊C4—2361no—
185C4⋊C4—2361no—
186C4⋊C4—2361no—
187C4⋊C4—2361no—
188C42—591no—
189C42—1181no—
190C42C2×C4×D5911yescharacteristic
191C16—24no—
192C16—1184no—
193C23—41no—
194C23—591no—
195C23—4721no—
196C23—4721no—
197C23—4724no—
198C23—2361no—
199D4—42no—
200D4—82no—
201D4—4722no—
202D4—4722no—
203D4—4724no—
204D4—2362no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—591no—
208C2×C4—592no—
209C2×C4—592no—
210C2×C4—1181no—
211C2×C4—4722no—
212C2×C4—2362no—
213C2×C4—2361no—
214C2×C4C22⋊C4×D5911yescharacteristic
215C8—22no—
216C8—1182no—
217C22—82no—
218C22—81no—
219C22—591no—
220C22—591no—
221C22—1182no—
222C22—9442no—
223C22—9442no—
224C22—4722no—
225C22—4721no—
226C22#100×D5911yescharacteristic
227C4—41no—
228C4—81no—
229C4—592no—
230C4—4721no—
231C4—2361no—
232C4#104×D5912yes—
233C2—21no—
234C2—161no—
235C2—592no—
236C2—1181no—
237C2—9441no—
238C2#329×D5911yescharacteristic
subgroupG/H
centerC2#329×D59
commutatorC42×C59C22×C4
Frattini#97C22×D59
FittingC59×#1355C2
socleC2×C59C2×#329
prime radical#127×D59C4
cosocle#97×C59C23
hypercenter#1355D59
hypocenterC59C2×#1355
LCSG ▷ C42×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #347×D59C2semidirect
3. #21422129C2semidirect
4. #21422128C2semidirect
5. C59×#1355C2semidirect
15. #16837180C22semidirect
18. C59×#347C22semidirect
118. #1355D59direct (N × H)
124. D59#1355direct (N × H)
137. #347C2×D59semidirect
138. C59C2×#1355semidirect

Maximal subgroups

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

subgroupindex
#490×D592
#347×D592
#214221292
#214221282
C59×#13552
C2×#135559