Finite Group Databasebeta

← C59×#13428 #28425537

Subgroups — C59×#13428 #28425537

Order 15104.

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2734C211yesmaximal, characteristic
2C2×C59×#356C212yesmaximal
3C59×#1886C212yesmaximal
4C59×#1857C211yesmaximal, characteristic
5C59×#1394C211yesmaximal, characteristic
6C2×C4⋊Q8×C59C2212yes—
7C59×#519C2211yescharacteristic
8C59×#428—21no—
9C59×#419—22no—
10C2×#101×C59C2212yes—
11C2×#101×C59C2211yescharacteristic
12C59×#398—21no—
13C59×#395—22no—
14C59×#391C2211yescharacteristic
15C59×#389—21no—
16C59×#387—22no—
17C59×#356—24no—
18C59×#339—21no—
19C59×#339—22no—
20C22×Q8×C59D412yes—
21C22×Q8×C59C2311yescharacteristic
22C2×M16×C59—21no—
23C2×M16×C59—22no—
24C4⋊Q8×C59—22no—
25C4⋊Q8×C59—22no—
26C4⋊Q8×C59—22no—
27C4⋊Q8×C59—22no—
28C4×Q8×C59—41no—
29C4×Q8×C59—41no—
30#117×C59—22no—
31#117×C59—21no—
32C2×C4⋊C4×C59—21no—
33C2×C4⋊C4×C59—22no—
34C2×C4⋊C4×C59—22no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C42×C59D412yes—
39C2×C42×C59D411yescharacteristic
40#107×C59—41no—
41#106×C59—41no—
42#103×C59—42no—
43#103×C59—42no—
44#101×C59—21no—
45#101×C59—22no—
46#101×C59—22no—
47#101×C59D412yes—
48#95×C59—21no—
49#95×C59—22no—
50#95×C59—22no—
51#95×C59—22no—
52C2×Q8×C59—22no—
53C2×Q8×C59—22no—
54C2×Q8×C59—41no—
55C2×Q8×C59—41no—
56C2×Q8×C59—42no—
57C2×Q8×C59—42no—
58C2×Q8×C59C2×D411yescharacteristic
59C2×Q8×C59#4111yescharacteristic
60C2×Q8×C59#4112yes—
61C22×C4×C59—21no—
62C22×C4×C59—22no—
63C22×C4×C59—21no—
64C22×C4×C59—22no—
65C22×C4×C59C2×D412yes—
66C22×C4×C59C2×D411yescharacteristic
67M16×C59—22no—
68M16×C59—41no—
69M16×C59—42no—
70M16×C59—42no—
71C2×C8×C59—41no—
72C2×C8×C59—42no—
73C4⋊C4×C59—24no—
74C4⋊C4×C59—22no—
75C4⋊C4×C59—22no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—42no—
80C4⋊C4×C59—42no—
81C4⋊C4×C59—42no—
82C4⋊C4×C59—42no—
83C4⋊C4×C59—81no—
84C4⋊C4×C59—81no—
85C22⋊C4×C59—41no—
86C42×C59—22no—
87C42×C59—22no—
88C42×C59—41no—
89C42×C59—42no—
90C42×C59—41no—
91C23×C59#12011yescharacteristic
92Q8×C59—41no—
93Q8×C59—41no—
94Q8×C59—42no—
95Q8×C59—44no—
96Q8×C59—82no—
97C2×C4×C59—21no—
98C2×C4×C59—22no—
99C2×C4×C59—21no—
100C2×C4×C59—22no—
101C2×C4×C59—22no—
102C2×C4×C59—24no—
103C2×C4×C59—41no—
104C2×C4×C59—42no—
105C2×C4×C59—42no—
106C2×C4×C59—41no—
107C2×C4×C59—42no—
108C2×C4×C59—42no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—42no—
113C2×C4×C59—42no—
114C2×C4×C59#12112yes—
115C2×C4×C59#12111yescharacteristic
116C2×C4×C59#12312yes—
117C2×C4×C59#12411yescharacteristic
118C8×C59—42no—
119C8×C59—82no—
120#13428C5911yesmaximal, characteristic, direct product factor, Sylow
121C22×C59—21no—
122C22×C59—21no—
123C22×C59#39411yescharacteristic
124C22×C59B(4,𝔽2)11yescharacteristic
125C22×C59#45811yescharacteristic
126C4×C59—21no—
127C4×C59—22no—
128C4×C59—22no—
129C4×C59—21no—
130C4×C59—44no—
131C4×C59—42no—
132C4×C59—81no—
133C4×C59—81no—
134C4×C59—81no—
135C4×C59—82no—
136#2734C2×C5911yescharacteristic
137C2×#356C2×C5912yes—
138#1886C2×C5912yes—
139#1857C2×C5911yescharacteristic
140#1394C2×C5911yescharacteristic
141C2×C59—21no—
142C2×C59—21no—
143C2×C59#204411yescharacteristic
144C2×C59#220311yescharacteristic
145C2×C59#220511yescharacteristic
146C2×C4⋊Q8C22×C5912yes—
147#519C22×C5911yescharacteristic
148#428—21no—
149#419—22no—
150C2×#101C22×C5912yes—
151C2×#101C22×C5911yescharacteristic
152#398—21no—
153#395—22no—
154#391C22×C5911yescharacteristic
155#389—21no—
156#387—22no—
157#356—24no—
158#339—21no—
159#339—22no—
160C59#1342811yescharacteristic, direct product factor, Sylow
161C22×Q8D4×C5912yes—
162C22×Q8C23×C5911yescharacteristic
163C2×M16—21no—
164C2×M16—22no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4×Q8—41no—
170C4×Q8—41no—
171#117—22no—
172#117—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4D4×C5911yescharacteristic
179C2×C42D4×C5912yes—
180C2×C42D4×C5911yescharacteristic
181#107—41no—
182#106—41no—
183#103—42no—
184#103—42no—
185#101—21no—
186#101—22no—
187#101—22no—
188#101D4×C5912yes—
189#95—21no—
190#95—22no—
191#95—22no—
192#95—22no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8C2×D4×C5911yescharacteristic
200C2×Q8#41×C5911yescharacteristic
201C2×Q8#41×C5912yes—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4C2×D4×C5912yes—
207C22×C4C2×D4×C5911yescharacteristic
208M16—22no—
209M16—41no—
210M16—42no—
211M16—42no—
212C2×C8—41no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C22⋊C4—41no—
227C42—22no—
228C42—22no—
229C42—41no—
230C42—41no—
231C42—42no—
232C23#120×C5911yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4#121×C5912yes—
256C2×C4#121×C5911yescharacteristic
257C2×C4#123×C5912yes—
258C2×C4#124×C5911yescharacteristic
259C8—42no—
260C8—82no—
261C22—21no—
262C22—21no—
263C22C59×#39411yescharacteristic
264C22C59×B(4,𝔽2)11yescharacteristic
265C22C59×#45811yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—81no—
275C4—81no—
276C2—21no—
277C2—21no—
278C2C59×#204411yescharacteristic
279C2C59×#220311yescharacteristic
280C2C59×#220511yescharacteristic
subgroupG/H
center, socleC22×C59B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C59
prime radicalC23×C59#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C59 ◁ C22×Q8×C59 ◁ G

Complements

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

NH ≅ G/Ntype
120. #13428C59direct (N × H)
160. C59#13428direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#27342
C2×C59×#3562
C59×#18862
C59×#18572
C59×#13942
#1342859