Finite Group Databasebeta

← C59×#7491 #28419600

Subgroups — C59×#7491 #28419600

Order 15104.

276 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×C59×#356C211yesmaximal, characteristic
2C59×#1886C211yesmaximal, characteristic
3C2×C59×#333C211yesmaximal, characteristic
4C2×C4⋊Q8×C59C2211yescharacteristic
5C59×#519C411yescharacteristic
6C2×C4⋊C8×C59—21no—
7C59×#419—21no—
8C2×#101×C59—21no—
9C2×#101×C59C411yescharacteristic
10C59×#356—21no—
11C59×#356C412yescomplemented
12C59×#339—21no—
13C59×#333—21no—
14C59×#333C412yescomplemented
15C22×Q8×C59C2×C411yescharacteristic
16C22×Q8×C59D411yescharacteristic
17C2×M16×C59—21no—
18C2×M16×C59—41no—
19C22×C8×C59—41no—
20C4⋊Q8×C59—41no—
21C4⋊Q8×C59C2×C411yescharacteristic
22C4⋊Q8×C59C2×C411yescharacteristic
23C4⋊Q8×C59D411yescharacteristic
24C4⋊Q8×C59Q811yescharacteristic
25C4×Q8×C59—42no—
26#117×C59—21no—
27#117×C59—41no—
28C2×C4⋊C4×C59—41no—
29C2×C42×C59D411yescharacteristic
30C4⋊C8×C59—22no—
31C4⋊C8×C59—41no—
32#103×C59—42no—
33#101×C59—22no—
34#101×C59—41no—
35#101×C59—41no—
36C2×Q8×C59—21no—
37C2×Q8×C59—21no—
38C2×Q8×C59—41no—
39C2×Q8×C59—41no—
40C2×Q8×C59—41no—
41C2×Q8×C59—41no—
42C2×Q8×C59C4211yescharacteristic
43C2×Q8×C59C22⋊C411yescharacteristic
44C2×Q8×C59C4⋊C411yescharacteristic
45C2×Q8×C59C4⋊C411yescharacteristic
46C22×C4×C59—21no—
47C22×C4×C59—21no—
48C22×C4×C59—21no—
49C22×C4×C59C22⋊C411yescharacteristic
50M16×C59—42no—
51M16×C59—41no—
52M16×C59—41no—
53M16×C59—81no—
54C2×C8×C59—41no—
55C2×C8×C59—42no—
56C2×C8×C59—82no—
57C2×C8×C59—81no—
58C4⋊C4×C59—22no—
59C4⋊C4×C59—41no—
60C4⋊C4×C59—41no—
61C4⋊C4×C59—41no—
62C4⋊C4×C59—41no—
63C4⋊C4×C59—42no—
64C22⋊C4×C59—41no—
65C42×C59—21no—
66C42×C59—41no—
67C42×C59—42no—
68C42×C59C22⋊C411yescharacteristic
69C42×C59C4⋊C411yescharacteristic
70C23×C59#9911yescharacteristic
71Q8×C59—41no—
72Q8×C59—41no—
73Q8×C59—41no—
74Q8×C59—41no—
75Q8×C59—42no—
76Q8×C59—81no—
77C2×C4×C59—22no—
78C2×C4×C59—22no—
79C2×C4×C59—21no—
80C2×C4×C59—21no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—41no—
88C2×C4×C59—41no—
89C2×C4×C59—41no—
90C2×C4×C59—41no—
91C2×C4×C59—42no—
92C2×C4×C59#9511yescharacteristic
93C2×C4×C59#9911yescharacteristic
94C8×C59—82no—
95C8×C59—81no—
96C8×C59—82no—
97#7491C5911yesmaximal, characteristic, direct product factor, Sylow
98C22×C59—22no—
99C22×C59#34211yescharacteristic
100C22×C59AΣL(1,𝔽16)11yescharacteristic
101C22×C59#35211yescharacteristic
102C4×C59—21no—
103C4×C59—22no—
104C4×C59—21no—
105C4×C59—21no—
106C4×C59—21no—
107C4×C59—41no—
108C4×C59—41no—
109C4×C59—41no—
110C4×C59—41no—
111C4×C59—82no—
112C2×#356C2×C5911yescharacteristic
113#1886C2×C5911yescharacteristic
114C2×#333C2×C5911yescharacteristic
115C2×C59—21no—
116C2×C59—21no—
117C2×C59#139011yescharacteristic
118C2×C59#140512yes—
119C2×C4⋊Q8C22×C5911yescharacteristic
120#519C4×C5911yescharacteristic
121C2×C4⋊C8—21no—
122#419—21no—
123C2×#101—21no—
124C2×#101C4×C5911yescharacteristic
125#356—21no—
126#356C4×C5912yescomplemented
127#339—21no—
128#333—21no—
129#333C4×C5912yescomplemented
130C59#749111yescharacteristic, direct product factor, Sylow
131C22×Q8C2×C4×C5911yescharacteristic
132C22×Q8D4×C5911yescharacteristic
133C2×M16—21no—
134C2×M16—41no—
135C22×C8—41no—
136C4⋊Q8—41no—
137C4⋊Q8C2×C4×C5911yescharacteristic
138C4⋊Q8C2×C4×C5911yescharacteristic
139C4⋊Q8D4×C5911yescharacteristic
140C4⋊Q8Q8×C5911yescharacteristic
141C4×Q8—42no—
142#117—21no—
143#117—41no—
144C2×C4⋊C4—41no—
145C2×C42D4×C5911yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—41no—
148#103—42no—
149#101—22no—
150#101—41no—
151#101—41no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8C42×C5911yescharacteristic
159C2×Q8C22⋊C4×C5911yescharacteristic
160C2×Q8C4⋊C4×C5911yescharacteristic
161C2×Q8C4⋊C4×C5911yescharacteristic
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C22⋊C4×C5911yescharacteristic
166M16—42no—
167M16—41no—
168M16—41no—
169M16—81no—
170C2×C8—41no—
171C2×C8—42no—
172C2×C8—82no—
173C2×C8—81no—
174C4⋊C4—22no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C22⋊C4—41no—
181C42—21no—
182C42—41no—
183C42—42no—
184C42C22⋊C4×C5911yescharacteristic
185C42C4⋊C4×C5911yescharacteristic
186C23#99×C5911yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—42no—
192Q8—81no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4#95×C5911yescharacteristic
209C2×C4#99×C5911yescharacteristic
210C8—82no—
211C8—81no—
212C8—82no—
213C22—22no—
214C22C59×#34211yescharacteristic
215C22C59×AΣL(1,𝔽16)11yescharacteristic
216C22C59×#35211yescharacteristic
217C4—21no—
218C4—22no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—82no—
227C2—21no—
228C2—21no—
229C2C59×#139011yescharacteristic
230C2C59×#140512yes—
subgroupG/H
center, socleC22×C59AΣL(1,𝔽16)
commutatorC2×Q8C42×C59
Frattini, cosocleC2×C4⋊Q8C22×C59
prime radicalC23×C59#99
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×C4×C59 ◁ C2×C4⋊Q8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
11. C59×#356C4semidirect
14. C59×#333C4semidirect
97. #7491C59direct (N × H)
126. #356C4×C59semidirect
129. #333C4×C59semidirect
130. C59#7491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3562
C59×#18862
C2×C59×#3332
#749159