Finite Group Databasebeta

← C53×#7831 #27215343

Subgroups — C53×#7831 #27215343

Order 13568.

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C53×#2809C211yesmaximal, characteristic
2C53×#2100C212yesmaximal
3C53×#2095C211yesmaximal, characteristic
4C53×#1272C211yesmaximal, characteristic
5C53×#1271C212yesmaximal
6C2×#107×C53—21no—
7C2×#103×C53—21no—
8C53×#400—21no—
9C53×#398—22no—
10C53×#391—21no—
11C53×#391C2211yescharacteristic
12C53×#389C2212yes—
13C53×#387—22no—
14C53×#384C2211yescharacteristic
15C53×#340—22no—
16C53×#340—22no—
17C53×#336C2211yescharacteristic
18C53×#336C2212yes—
19C22×Q8×C53D411yescharacteristic
20C22×C8×C53—21no—
21C22×C8×C53—22no—
22C2×C4⋊C4×C53—21no—
23C2×C4⋊C4×C53—21no—
24C2×C4⋊C4×C53—22no—
25C2×C4⋊C4×C53—22no—
26C2×C4⋊C4×C53—21no—
27C2×C4⋊C4×C53D412yes—
28C2×C4⋊C4×C53D412yes—
29C2×C4⋊C4×C53D411yescharacteristic
30C2×C42×C53—21no—
31C2×C42×C53C2311yescharacteristic
32#107×C53—42no—
33#103×C53—42no—
34#95×C53—21no—
35#95×C53—22no—
36#95×C53—22no—
37#95×C53—22no—
38#95×C53—22no—
39C2×Q8×C53—21no—
40C2×Q8×C53—41no—
41C2×Q8×C53—41no—
42C2×Q8×C53Q1612yes—
43C22×C4×C53—21no—
44C22×C4×C53—21no—
45C22×C4×C53—22no—
46C22×C4×C53—22no—
47C22×C4×C53—41no—
48C22×C4×C53C2×D411yescharacteristic
49C22×C4×C53C2×D412yes—
50C2×C8×C53—22no—
51C2×C8×C53—41no—
52C2×C8×C53—41no—
53C2×C8×C53—42no—
54C2×C8×C53—42no—
55C2×C8×C53—42no—
56C4⋊C4×C53—22no—
57C4⋊C4×C53—22no—
58C4⋊C4×C53—41no—
59C4⋊C4×C53—42no—
60C4⋊C4×C53—41no—
61C4⋊C4×C53—41no—
62C4⋊C4×C53—44no—
63C4⋊C4×C53—42no—
64C4⋊C4×C53—42no—
65C4⋊C4×C53—81no—
66C4⋊C4×C53—81no—
67C42×C53—41no—
68C42×C53—81no—
69C23×C53#12011yescharacteristic
70Q8×C53—42no—
71Q8×C53—81no—
72C2×C4×C53—21no—
73C2×C4×C53—22no—
74C2×C4×C53—21no—
75C2×C4×C53—22no—
76C2×C4×C53—22no—
77C2×C4×C53—41no—
78C2×C4×C53—41no—
79C2×C4×C53—42no—
80C2×C4×C53—42no—
81C2×C4×C53—42no—
82C2×C4×C53—41no—
83C2×C4×C53—42no—
84C2×C4×C53—42no—
85C2×C4×C53—42no—
86C2×C4×C53—42no—
87C2×C4×C53—81no—
88C2×C4×C53—82no—
89C2×C4×C53C2×Q1611yescharacteristic
90C2×C4×C53#13512yes—
91C2×C4×C53#13711yescharacteristic
92C2×C4×C53#13712yes—
93C8×C53—42no—
94C8×C53—82no—
95#7831C5311yesmaximal, characteristic, direct product factor, Sylow
96C22×C53#45111yescharacteristic
97C22×C53#45212yes—
98C22×C53#45311yescharacteristic
99C22×C53#45412yes—
100C22×C53#45811yescharacteristic
101C4×C53—21no—
102C4×C53—21no—
103C4×C53—22no—
104C4×C53—22no—
105C4×C53—42no—
106C4×C53—82no—
107C4×C53—82no—
108C4×C53—81no—
109C4×C53—161no—
110#2809C2×C5311yescharacteristic
111#2100C2×C5312yes—
112#2095C2×C5311yescharacteristic
113#1272C2×C5311yescharacteristic
114#1271C2×C5312yes—
115C2×C53#161411yescharacteristic
116C2×C53#161512yes—
117C2×C53#163411yescharacteristic
118C2×C53#163612yes—
119C2×C53#165711yescharacteristic
120C2×#107—21no—
121C2×#103—21no—
122#400—21no—
123#398—22no—
124#391—21no—
125#391C22×C5311yescharacteristic
126#389C22×C5312yes—
127#387—22no—
128#384C22×C5311yescharacteristic
129#340—22no—
130#340—22no—
131#336C22×C5311yescharacteristic
132#336C22×C5312yes—
133C53#783111yescharacteristic, direct product factor, Sylow
134C22×Q8D4×C5311yescharacteristic
135C22×C8—21no—
136C22×C8—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4D4×C5312yes—
143C2×C4⋊C4D4×C5312yes—
144C2×C4⋊C4D4×C5311yescharacteristic
145C2×C42—21no—
146C2×C42C23×C5311yescharacteristic
147#107—42no—
148#103—42no—
149#95—21no—
150#95—22no—
151#95—22no—
152#95—22no—
153#95—22no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Q16×C5312yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—41no—
163C22×C4C2×D4×C5311yescharacteristic
164C22×C4C2×D4×C5312yes—
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—44no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—81no—
181C4⋊C4—81no—
182C42—41no—
183C42—81no—
184C23#120×C5311yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—82no—
204C2×C4C2×Q16×C5311yescharacteristic
205C2×C4#135×C5312yes—
206C2×C4#137×C5311yescharacteristic
207C2×C4#137×C5312yes—
208C8—42no—
209C8—82no—
210C22C53×#45111yescharacteristic
211C22C53×#45212yes—
212C22C53×#45311yescharacteristic
213C22C53×#45412yes—
214C22C53×#45811yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—82no—
222C4—82no—
223C4—161no—
224C2C53×#161411yescharacteristic
225C2C53×#161512yes—
226C2C53×#163411yescharacteristic
227C2C53×#163612yes—
228C2C53×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C53#120
commutator, Frattini, cosocleC2×C42C23×C53
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
95. #7831C53direct (N × H)
133. C53#7831direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#28092
C53×#21002
C53×#20952
C53×#12722
C53×#12712
#783153