Finite Group Databasebeta

← C139×#10513 #48005109

Subgroups — C139×#10513 #48005109

Order 35584.

388 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 94 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#3245×C139C211yesmaximal, characteristic
2#1832×C139C211yesmaximal, characteristic, complemented
3#1551×C139C212yesmaximal, complemented
4#1505×C139C212yesmaximal, complemented
5#1290×C139C211yesmaximal, characteristic, complemented
6#532×C139C2212yes—
7#474×C139—22no—
8#466×C139—22no—
9#459×C139—22no—
10#432×C139C2212yes—
11C2×C4⋊C8×C139C2211yescharacteristic
12C2×C4⋊C8×C139C2211yescharacteristic
13#376×C139C2211yescharacteristic
14#336×C139—22no—
15#333×C139—22no—
16#331×C139—22no—
17#327×C139—24no—
18C2×#41×C139—22no—
19C2×D8×C139—22no—
20C22×C8×C139—21no—
21C22×C8×C139D412yes—
22C4⋊Q8×C139D412yes—
23#127×C139D412yes—
24#124×C139—22no—
25#121×C139—22no—
26#121×C139—22no—
27C4×D4×C139—22no—
28C4×D4×C139—22no—
29C2×C42×C139—21no—
30C2×C42×C139C2311yescharacteristic
31#107×C139—22no—
32C4⋊C8×C139—22no—
33C4⋊C8×C139—22no—
34C4⋊C8×C139—22no—
35#102×C139—24no—
36C22⋊C8×C139—22no—
37#97×C139—22no—
38#95×C139—21no—
39#95×C139D412yes—
40#41×C139—84no—
41C2×Q8×C139—22no—
42C2×D4×C139—22no—
43C2×D4×C139—22no—
44C2×D4×C139—22no—
45C2×D4×C139—42no—
46C22×C4×C139—22no—
47C22×C4×C139—42no—
48C22×C4×C139C2×D411yescharacteristic
49C22×C4×C139C2×D411yescharacteristic
50C22×C4×C139#4111yescharacteristic
51D8×C139—82no—
52C2×C8×C139—22no—
53C2×C8×C139—42no—
54C2×C8×C139—42no—
55C2×C8×C139—41no—
56C2×C8×C139—42no—
57C4⋊C4×C139—22no—
58C4⋊C4×C139—22no—
59C22⋊C4×C139—42no—
60C22⋊C4×C139—42no—
61C42×C139—41no—
62C42×C139—41no—
63C42×C139C2×D412yes—
64C42×C139#4112yes—
65C23×C139—42no—
66C23×C139#12111yescharacteristic
67Q8×C139—82no—
68D4×C139—42no—
69D4×C139—42no—
70D4×C139—82no—
71D4×C139—82no—
72D4×C139—84no—
73C2×C4×C139—22no—
74C2×C4×C139—21no—
75C2×C4×C139—21no—
76C2×C4×C139—41no—
77C2×C4×C139—42no—
78C2×C4×C139—42no—
79C2×C4×C139—42no—
80C2×C4×C139—42no—
81C2×C4×C139—84no—
82C2×C4×C139#12011yescharacteristic
83C2×C4×C139#12112yes—
84C2×C4×C139#12312yes—
85C2×C4×C139#12411yescharacteristic
86C8×C139—42no—
87C8×C139—82no—
88C8×C139—81no—
89C22×C139—21no—
90C22×C139—21no—
91C22×C139—82no—
92C22×C139—82no—
93C22×C139—82no—
94C22×C139#39411yescharacteristic
95C22×C139#47212yes—
96C4×C139—22no—
97C4×C139—21no—
98C4×C139—22no—
99C4×C139—82no—
100C4×C139—82no—
101C4×C139#45411yescharacteristic
102C4×C139#45511yescharacteristic
103C2×C139—22no—
104C2×C139—162no—
105C2×C139#204011yescharacteristic
106C2×C139#204511yescharacteristic
107C2×C139#205311yescharacteristic
108#10513C13911yesmaximal, characteristic, direct product factor, Sylow
109C139#1051311yescharacteristic, direct product factor, Sylow
110#3245C2×C13911yescharacteristic
111#1832C2×C13911yescharacteristic, complemented
112#1551C2×C13912yescomplemented
113#1505C2×C13912yescomplemented
114#1290C2×C13911yescharacteristic, complemented
115#532C22×C13912yes—
116#474—22no—
117#466—22no—
118#459—22no—
119#432C22×C13912yes—
120C2×C4⋊C8C22×C13911yescharacteristic
121C2×C4⋊C8C22×C13911yescharacteristic
122#376C22×C13911yescharacteristic
123#336—22no—
124#333—22no—
125#331—22no—
126#327—24no—
127C2×#41—22no—
128C2×D8—22no—
129C22×C8—21no—
130C22×C8D4×C13912yes—
131C4⋊Q8D4×C13912yes—
132#127D4×C13912yes—
133#124—22no—
134#121—22no—
135#121—22no—
136C4×D4—22no—
137C4×D4—22no—
138C2×C42—21no—
139C2×C42C23×C13911yescharacteristic
140#107—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144#102—24no—
145C22⋊C8—22no—
146#97—22no—
147#95—21no—
148#95D4×C13912yes—
149#41—84no—
150C2×Q8—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—42no—
155C22×C4—22no—
156C22×C4—42no—
157C22×C4C2×D4×C13911yescharacteristic
158C22×C4C2×D4×C13911yescharacteristic
159C22×C4#41×C13911yescharacteristic
160D8—82no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C2×C8—42no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42—41no—
171C42—41no—
172C42C2×D4×C13912yes—
173C42#41×C13912yes—
174C23—42no—
175C23#121×C13911yescharacteristic
176Q8—82no—
177D4—42no—
178D4—42no—
179D4—82no—
180D4—82no—
181D4—84no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—84no—
191C2×C4#120×C13911yescharacteristic
192C2×C4#121×C13912yes—
193C2×C4#123×C13912yes—
194C2×C4#124×C13911yescharacteristic
195C8—42no—
196C8—82no—
197C8—81no—
198C22—21no—
199C22—21no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22#394×C13911yescharacteristic
204C22#472×C13912yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—82no—
210C4#454×C13911yescharacteristic
211C4#455×C13911yescharacteristic
212C2—22no—
213C2—162no—
214C2#2040×C13911yescharacteristic
215C2#2045×C13911yescharacteristic
216C2#2053×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#394
commutator, Frattini, cosocleC2×C42C23×C139
prime radical#3245×C139C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1832×C139C2semidirect
3. #1551×C139C2semidirect
4. #1505×C139C2semidirect
5. #1290×C139C2semidirect
108. #10513C139direct (N × H)
109. C139#10513direct (N × H)
111. #1832C2×C139semidirect
112. #1551C2×C139semidirect
113. #1505C2×C139semidirect
114. #1290C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3245×C1392
#1832×C1392
#1551×C1392
#1505×C1392
#1290×C1392
#10513139