Finite Group Databasebeta

← #13100711

Subgroups — #13100711

Order 1600.

238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C5×#4034C211yesmaximal, characteristic
2#11716983C211yesmaximal, characteristic
3#11716677C211yesmaximal, characteristic
4C5×#3942C211yesmaximal, characteristic
5#11716608C211yesmaximal, characteristic
6#11716606C211yesmaximal, characteristic
7Dic5×#168C211yesmaximal, characteristic
8C2×#6045C2211yescharacteristic
9C2×C5×Dic10—21no—
10C2×C5×Dic10C2211yescharacteristic
11C52×C4⋊C4C2211yescharacteristic
12C2×#6029C2211yescharacteristic
13C5×C4⋊Dic5C2211yescharacteristic
14C5×#683—21no—
15C4×C5×Dic5C2211yescharacteristic
16C2×C5×#168C2211yescharacteristic
17#87780—21no—
18#87780—21no—
19#65382—51nomaximal
20#65081—51nomaximal
21C2×C4×C52—21no—
22C2×C4×C52C2311yescharacteristic
23C2×#1039—21no—
24#6045—21no—
25#6045—21no—
26C2×C5×Dic5—21no—
27C2×C5×Dic5—21no—
28C2×C5×Dic5D411yescharacteristic
29C2×C5×Dic5D411yescharacteristic
30C5×Dic10—21no—
31C5×Dic10—21no—
32C5×Dic10—42no—
33#6029—21no—
34C5×#168—21no—
35C5×C4⋊Q8—51no—
36#4090—51no—
37#4034D511yescharacteristic
38#4015—51no—
39C5×#103—51no—
40#3967—51no—
41#3948—51no—
42C8×Dic5—51no—
43#3942—51no—
44#3942—51no—
45#3942—51no—
46#3942—51no—
47#3942—102no—
48#3942D511yescharacteristic
49C4×#168—51no—
50C22×C52C2×D411yescharacteristic
51C4×C52—41no—
52C4×C52#4111yescharacteristic
53C4×C52#4111yescharacteristic
54#1039—41no—
55C5×Dic5—41no—
56C5×Dic5—41no—
57C5×Dic5SD1612yes—
58C5×Dic5Q1612yes—
59C2×C5×Q8—51no—
60C2×C5×Q8—101no—
61C2×Dic10—21no—
62C2×Dic10—51no—
63C2×Dic10—51no—
64C2×Dic10—102no—
65C2×Dic10C2×D511yescharacteristic
66C2×C5×C8—51no—
67C5×C4⋊C4—22no—
68C5×C4⋊C4—51no—
69C5×C4⋊C4—101no—
70C5×C4⋊C4C2×D511yescharacteristic
71C5×C4⋊C4C2×D511yescharacteristic
72C42×C5—51no—
73C4⋊Dic5—101no—
74C4⋊Dic5—101no—
75C4⋊Dic5C2×D511yescharacteristic
76#683—21no—
77#683—101no—
78#683—101no—
79C4×Dic5C2×D511yescharacteristic
80C2×#168—51no—
81C2×#168—51no—
82C2×#168—102no—
83C2×#168C2×D511yescharacteristic
84#487—251noSylow
85C2×C52#12411yescharacteristic
86C2×C52C2×SD1611yescharacteristic
87C2×C52C2×Q1611yescharacteristic
88C5×Q8—101no—
89C5×Q8—101no—
90C5×Q8—202no—
91C2×C4×C5—21no—
92C2×C4×C5—21no—
93C2×C4×C5—22no—
94C2×C4×C5—42no—
95C2×C4×C5—51no—
96C2×C4×C5—51no—
97C2×C4×C5—101no—
98C2×C4×C5—101no—
99C2×C4×C5C22×D511yescharacteristic
100C2×C4×C5C22×D511yescharacteristic
101C2×Dic5—21no—
102C2×Dic5—21no—
103C2×Dic5—101no—
104C2×Dic5—101no—
105C2×Dic5—202no—
106C2×Dic5C22⋊D511yescharacteristic
107C2×Dic5C22⋊D511yescharacteristic
108Dic10—21no—
109Dic10—21no—
110Dic10—42no—
111Dic10—104no—
112Dic10—101no—
113Dic10—101no—
114Dic10—101no—
115Dic10—101no—
116Dic10—202no—
117C5×C8—101no—
118#168—21no—
119#168—101no—
120#168—101no—
121#168—202no—
122C4⋊Q8—51no—
123C4⋊Q8—251no—
124#103—51no—
125#103—251no—
126#103—251no—
127#103—251no—
128C4×C8—251no—
129C52#48711yescharacteristic, complemented, Sylow
130C22×C5—22no—
131C22×C5D4×D511yescharacteristic
132C22×C5C2×C22⋊D511yescharacteristic
133C4×C5—22no—
134C4×C5—22no—
135C4×C5—41no—
136C4×C5—41no—
137C4×C5—52no—
138C4×C5—52no—
139C4×C5—82no—
140C4×C5—201no—
141C4×C5—201no—
142C4×C5#70911yescharacteristic
143C4×C5#71111yescharacteristic
144C4×C5#71311yescharacteristic
145C4×C5#71311yescharacteristic
146Dic5—41no—
147Dic5—41no—
148Dic5—204no—
149Dic5—201no—
150Dic5—201no—
151Dic5#68712yes—
152Dic5#68912yes—
153C2×Q8—51no—
154C2×Q8—101no—
155C2×Q8—251no—
156C2×C8—51no—
157C2×C8—251no—
158C4⋊C4—51no—
159C4⋊C4—101no—
160C4⋊C4—501no—
161C4⋊C4—501no—
162C4⋊C4D5211yescharacteristic
163C42—51no—
164C2×C5—22no—
165C2×C5—22no—
166C2×C5—22no—
167C2×C5#403111yescharacteristic
168C2×C5D5×SD1611yescharacteristic
169C2×C5D5×Q1611yescharacteristic
170C2×C5C2×#68711yescharacteristic
171C2×C5C2×#68911yescharacteristic
172C2×C5#409311yescharacteristic
173Q8—101no—
174Q8—101no—
175Q8—202no—
176Q8—501no—
177Q8—501no—
178C2×C4—21no—
179C2×C4—51no—
180C2×C4—51no—
181C2×C4—101no—
182C2×C4—101no—
183C2×C4—501no—
184C2×C4C2×D5211yescharacteristic
185C8—101no—
186C8—501no—
187C5—22no—
188C5#6508111yescharacteristic, complemented
189C5#6538211yescharacteristic, complemented
190C22D5×C22⋊D511yescharacteristic
191C4—41no—
192C4—52no—
193C4—52no—
194C4—201no—
195C4—201no—
196C4—1001no—
197C4#8787111yescharacteristic
198C4#8787411yescharacteristic
199C2#1171702511yescharacteristic
200C2D5×#68711yescharacteristic
201C2D5×#68911yescharacteristic
subgroupG/H
centerC22D5×C22⋊D5
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC52×C4⋊C4C22
socle, prime radicalC22×C52C2×D4
hypercenterC4⋊C4D52
hypocenterC52#487
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
129. C52#487semidirect
188. C5#65081semidirect
189. C5#65382semidirect

Maximal subgroups

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

subgroupindex
C5×#40342
#117169832
#117166772
C5×#39422
#117166082
#117166062
Dic5×#1682
#653825
#650815