Finite Group Databasebeta

← C59×#10030 #28422139

Subgroups — C59×#10030 #28422139

Order 15104.

520 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3249C211yesmaximal, characteristic, complemented
2C59×#3110C212yesmaximal
3C59×#1955C211yesmaximal, characteristic
4C59×#1531C212yesmaximal, complemented
5C59×#1290C211yesmaximal, characteristic, complemented
6C59×#533C2212yes—
7C2×C4×D4×C59C2211yescharacteristic
8C59×#484—22no—
9C59×#477—22no—
10C59×#474—22no—
11C59×#467—22no—
12C59×#462—22no—
13C59×#461—22no—
14C59×#450—22no—
15C59×#440—24no—
16C59×#432C2212yes—
17C2×C4⋊C8×C59C2211yescharacteristic
18C2×C22⋊C8×C59—22no—
19C2×#97×C59C2211yescharacteristic
20C59×#330—24no—
21C22×D4×C59D411yescharacteristic
22C23×C4×C59—21no—
23C2×Q16×C59—22no—
24C2×SD16×C59—24no—
25C22×C8×C59—21no—
26C22×C8×C59D412yes—
27C4⋊Q8×C59D412yes—
28C4⋊Q8×C59D412yes—
29#125×C59—22no—
30C22⋊Q8×C59—22no—
31C22⋊Q8×C59—22no—
32C4×Q8×C59—22no—
33C4×Q8×C59—22no—
34C4×D4×C59—22no—
35C4×D4×C59—22no—
36#117×C59—22no—
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C22⋊C4×C59—21no—
39C2×C42×C59C2311yescharacteristic
40#107×C59—24no—
41#107×C59—22no—
42C4⋊C8×C59—22no—
43C4⋊C8×C59—22no—
44#103×C59—24no—
45#103×C59—24no—
46#102×C59—24no—
47C22⋊C8×C59—22no—
48C22⋊C8×C59—44no—
49#97×C59—22no—
50#97×C59D414yes—
51C24×C59—21no—
52C2×Q8×C59—22no—
53C2×Q8×C59—22no—
54C2×D4×C59—22no—
55C2×D4×C59—42no—
56C22×C4×C59—21no—
57C22×C4×C59—42no—
58C22×C4×C59—42no—
59C22×C4×C59—41no—
60C22×C4×C59—41no—
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59#4111yescharacteristic
64Q16×C59—82no—
65SD16×C59—48no—
66C2×C8×C59—22no—
67C2×C8×C59—24no—
68C2×C8×C59—22no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—42no—
72C4⋊C4×C59—22no—
73C4⋊C4×C59—22no—
74C4⋊C4×C59—22no—
75C4⋊C4×C59—22no—
76C4⋊C4×C59—22no—
77C4⋊C4×C59—42no—
78C4⋊C4×C59—42no—
79C22⋊C4×C59—42no—
80C22⋊C4×C59—42no—
81C42×C59—42no—
82C42×C59C2×D412yes—
83C42×C59C2×D412yes—
84C23×C59—22no—
85C23×C59—42no—
86C23×C59—41no—
87C23×C59—41no—
88C23×C59—42no—
89C23×C59#12111yescharacteristic
90Q8×C59—44no—
91Q8×C59—42no—
92Q8×C59—42no—
93D4×C59—24no—
94D4×C59—42no—
95C2×C4×C59—22no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—41no—
99C2×C4×C59—42no—
100C2×C4×C59—42no—
101C2×C4×C59—42no—
102C2×C4×C59—41no—
103C2×C4×C59—82no—
104C2×C4×C59—81no—
105C2×C4×C59—81no—
106C2×C4×C59#12012yes—
107C2×C4×C59#12011yescharacteristic
108C2×C4×C59#12112yes—
109C2×C4×C59#12711yescharacteristic
110C8×C59—42no—
111C8×C59—44no—
112C8×C59—42no—
113#10030C5911yesmaximal, characteristic, direct product factor, Sylow
114C22×C59—21no—
115C22×C59—21no—
116C22×C59—44no—
117C22×C59—42no—
118C22×C59—82no—
119C22×C59—81no—
120C22×C59—81no—
121C22×C59#39211yescharacteristic
122C22×C59#47312yes—
123C4×C59—21no—
124C4×C59—22no—
125C4×C59—22no—
126C4×C59—81no—
127C4×C59—82no—
128C4×C59—82no—
129C4×C59#45311yescharacteristic
130C4×C59#45411yescharacteristic
131#3249C2×C5911yescharacteristic, complemented
132#3110C2×C5912yes—
133#1955C2×C5911yescharacteristic
134#1531C2×C5912yescomplemented
135#1290C2×C5911yescharacteristic, complemented
136C2×C59—22no—
137C2×C59—82no—
138C2×C59#200611yescharacteristic
139C2×C59#201011yescharacteristic
140C2×C59#202011yescharacteristic
141#533C22×C5912yes—
142C2×C4×D4C22×C5911yescharacteristic
143#484—22no—
144#477—22no—
145#474—22no—
146#467—22no—
147#462—22no—
148#461—22no—
149#450—22no—
150#440—24no—
151#432C22×C5912yes—
152C2×C4⋊C8C22×C5911yescharacteristic
153C2×C22⋊C8—22no—
154C2×#97C22×C5911yescharacteristic
155#330—24no—
156C59#1003011yescharacteristic, direct product factor, Sylow
157C22×D4D4×C5911yescharacteristic
158C23×C4—21no—
159C2×Q16—22no—
160C2×SD16—24no—
161C22×C8—21no—
162C22×C8D4×C5912yes—
163C4⋊Q8D4×C5912yes—
164C4⋊Q8D4×C5912yes—
165#125—22no—
166C22⋊Q8—22no—
167C22⋊Q8—22no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×D4—22no—
171C4×D4—22no—
172#117—22no—
173C2×C4⋊C4D4×C5911yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42C23×C5911yescharacteristic
176#107—24no—
177#107—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180#103—24no—
181#103—24no—
182#102—24no—
183C22⋊C8—22no—
184C22⋊C8—44no—
185#97—22no—
186#97D4×C5914yes—
187C24—21no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D4×C5911yescharacteristic
198C22×C4C2×D4×C5911yescharacteristic
199C22×C4#41×C5911yescharacteristic
200Q16—82no—
201SD16—48no—
202C2×C8—22no—
203C2×C8—24no—
204C2×C8—22no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—42no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C42—42no—
218C42C2×D4×C5912yes—
219C42C2×D4×C5912yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—41no—
224C23—42no—
225C23#121×C5911yescharacteristic
226Q8—44no—
227Q8—42no—
228Q8—42no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4#120×C5912yes—
243C2×C4#120×C5911yescharacteristic
244C2×C4#121×C5912yes—
245C2×C4#127×C5911yescharacteristic
246C8—42no—
247C8—44no—
248C8—42no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22C59×#39211yescharacteristic
257C22C59×#47312yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—81no—
262C4—82no—
263C4—82no—
264C4C59×#45311yescharacteristic
265C4C59×#45411yescharacteristic
266C2—22no—
267C2—82no—
268C2C59×#200611yescharacteristic
269C2C59×#201011yescharacteristic
270C2C59×#202011yescharacteristic
subgroupG/H
center, socleC22×C59#392
commutator, Frattini, cosocleC2×C42C23×C59
prime radicalC22×D4×C59D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3249C2semidirect
4. C59×#1531C2semidirect
5. C59×#1290C2semidirect
113. #10030C59direct (N × H)
131. #3249C2×C59semidirect
134. #1531C2×C59semidirect
135. #1290C2×C59semidirect
156. C59#10030direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32492
C59×#31102
C59×#19552
C59×#15312
C59×#12902
#1003059