Finite Group Databasebeta

← C59×#10584 #28422693

Subgroups — C59×#10584 #28422693

Order 15104.

374 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2844C211yesmaximal, characteristic
2C59×#1847C211yesmaximal, characteristic
3C59×#1836C212yesmaximal
4C59×#1295C212yesmaximal
5C59×#1295C211yesmaximal, characteristic
6C2×#107×C59—21no—
7C2×#106×C59—21no—
8C2×#97×C59C2212yes—
9C2×#97×C59C2211yescharacteristic
10C59×#400—22no—
11C59×#400—21no—
12C59×#395—22no—
13C59×#395—21no—
14C59×#384C2211yescharacteristic
15C59×#382C2212yes—
16C59×#382C2211yescharacteristic
17C59×#340—22no—
18C59×#340—22no—
19C22×Q8×C59—21no—
20C22×C8×C59—21no—
21C22×C8×C59—22no—
22C2×C4⋊C4×C59—22no—
23C2×C4⋊C4×C59—21no—
24C2×C4⋊C4×C59—21no—
25C2×C4⋊C4×C59—22no—
26C2×C4⋊C4×C59D412yes—
27C2×C4⋊C4×C59D412yes—
28C2×C4⋊C4×C59D411yescharacteristic
29C2×C4⋊C4×C59D411yescharacteristic
30C2×C42×C59C2311yescharacteristic
31#107×C59—42no—
32#106×C59—42no—
33#97×C59—21no—
34#97×C59—22no—
35#97×C59Q812yescomplemented
36#97×C59Q814yescomplemented
37#95×C59—22no—
38#95×C59—21no—
39#95×C59—21no—
40#95×C59—22no—
41#95×C59—22no—
42#95×C59—22no—
43C2×Q8×C59—81no—
44C2×Q8×C59—82no—
45C22×C4×C59—21no—
46C22×C4×C59—22no—
47C22×C4×C59—21no—
48C22×C4×C59—22no—
49C22×C4×C59—41no—
50C22×C4×C59C2×D411yescharacteristic
51C22×C4×C59C2×D412yes—
52C2×C8×C59—22no—
53C2×C8×C59—22no—
54C2×C8×C59—22no—
55C2×C8×C59—24no—
56C2×C8×C59—42no—
57C2×C8×C59—42no—
58C4⋊C4×C59—41no—
59C4⋊C4×C59—41no—
60C4⋊C4×C59—42no—
61C4⋊C4×C59—42no—
62C4⋊C4×C59—41no—
63C4⋊C4×C59—41no—
64C4⋊C4×C59—44no—
65C4⋊C4×C59—81no—
66C4⋊C4×C59—82no—
67C42×C59C2×Q811yescharacteristic
68C42×C59C2×Q812yes—
69C42×C59#4111yescharacteristic
70C23×C59#12011yescharacteristic
71Q8×C59—84no—
72C2×C4×C59—21no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59—42no—
79C2×C4×C59—42no—
80C2×C4×C59—42no—
81C2×C4×C59—42no—
82C2×C4×C59—42no—
83C2×C4×C59—42no—
84C2×C4×C59—42no—
85C2×C4×C59—42no—
86C2×C4×C59—81no—
87C2×C4×C59—82no—
88C2×C4×C59C22⋊Q811yescharacteristic
89C2×C4×C59C22⋊Q812yes—
90C2×C4×C59C4⋊Q811yescharacteristic
91C2×C4×C59C4⋊Q812yes—
92C8×C59—24no—
93C8×C59—44no—
94#10584C5911yesmaximal, characteristic, direct product factor, Sylow
95C22×C59#39511yescharacteristic
96C22×C59#45311yescharacteristic
97C22×C59#45412yes—
98C22×C59#45512yes—
99C22×C59#45611yescharacteristic
100C4×C59—21no—
101C4×C59—21no—
102C4×C59—22no—
103C4×C59—22no—
104C4×C59—81no—
105C4×C59—81no—
106C4×C59—82no—
107C4×C59—82no—
108C4×C59—161no—
109#2844C2×C5911yescharacteristic
110#1847C2×C5911yescharacteristic
111#1836C2×C5912yes—
112#1295C2×C5912yes—
113#1295C2×C5911yescharacteristic
114C2×C59#165711yescharacteristic
115C2×C59#165911yescharacteristic
116C2×C59#166412yes—
117C2×C59#206011yescharacteristic
118C2×C59#206112yes—
119C2×#107—21no—
120C2×#106—21no—
121C2×#97C22×C5912yes—
122C2×#97C22×C5911yescharacteristic
123#400—22no—
124#400—21no—
125#395—22no—
126#395—21no—
127#384C22×C5911yescharacteristic
128#382C22×C5912yes—
129#382C22×C5911yescharacteristic
130#340—22no—
131#340—22no—
132C59#1058411yescharacteristic, direct product factor, Sylow
133C22×Q8—21no—
134C22×C8—21no—
135C22×C8—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4D4×C5912yes—
141C2×C4⋊C4D4×C5912yes—
142C2×C4⋊C4D4×C5911yescharacteristic
143C2×C4⋊C4D4×C5911yescharacteristic
144C2×C42C23×C5911yescharacteristic
145#107—42no—
146#106—42no—
147#97—21no—
148#97—22no—
149#97Q8×C5912yescomplemented
150#97Q8×C5914yescomplemented
151#95—22no—
152#95—21no—
153#95—21no—
154#95—22no—
155#95—22no—
156#95—22no—
157C2×Q8—81no—
158C2×Q8—82no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—41no—
164C22×C4C2×D4×C5911yescharacteristic
165C22×C4C2×D4×C5912yes—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—24no—
170C2×C8—42no—
171C2×C8—42no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—44no—
179C4⋊C4—81no—
180C4⋊C4—82no—
181C42C2×Q8×C5911yescharacteristic
182C42C2×Q8×C5912yes—
183C42#41×C5911yescharacteristic
184C23#120×C5911yescharacteristic
185Q8—84no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—81no—
201C2×C4—82no—
202C2×C4C22⋊Q8×C5911yescharacteristic
203C2×C4C22⋊Q8×C5912yes—
204C2×C4C4⋊Q8×C5911yescharacteristic
205C2×C4C4⋊Q8×C5912yes—
206C8—24no—
207C8—44no—
208C22C59×#39511yescharacteristic
209C22C59×#45311yescharacteristic
210C22C59×#45412yes—
211C22C59×#45512yes—
212C22C59×#45611yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—82no—
220C4—82no—
221C4—161no—
222C2C59×#165711yescharacteristic
223C2C59×#165911yescharacteristic
224C2C59×#166412yes—
225C2C59×#206011yescharacteristic
226C2C59×#206112yes—
subgroupG/H
center, socle, prime radicalC23×C59#120
commutator, Frattini, cosocleC2×C42C23×C59
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
35. #97×C59Q8semidirect
36. #97×C59Q8semidirect
94. #10584C59direct (N × H)
132. C59#10584direct (N × H)
149. #97Q8×C59semidirect
150. #97Q8×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#28442
C59×#18472
C59×#18362
C59×#12952
#1058459