Finite Group Databasebeta

← #72243103

Subgroups — #72243103

Order 2800.

280 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C2×D5×D35C211yesmaximal, characteristic, complemented
2C2×D7×C5⋊D5C211yesmaximal, characteristic, complemented
3#13063794C211yesmaximal, characteristic, complemented
4#13063787C211yesmaximal, characteristic, complemented
5C7×#6038C211yesmaximal, characteristic, complemented
6C5×#63306C211yesmaximal, characteristic, complemented
7C5×#63305C211yesmaximal, characteristic, complemented
8C2×C5⋊D35C2211yescharacteristic
9C2×C7×C5⋊D5C2211yescharacteristic, complemented
10C2×C5×D35C2211yescharacteristic, complemented
11C2×C5×C7×D5C2211yescharacteristic, complemented
12C2×C52×D7C2211yescharacteristic, complemented
13D5×D35—22no—
14D7×C5⋊D5—22no—
15C5×Dic35C2211yescharacteristic, complemented
16C5×C7×Dic5C2211yescharacteristic, complemented
17#10587963—51nomaximal
18#10587950—51nomaximal
19#87886—71nomaximal, Hall
20C2×C52×C7C2311yescharacteristic
21C5⋊D35D412yescomplemented
22C7×C5⋊D5—21no—
23C5×D35—21no—
24C5×C7×D5—21no—
25C52×D7—21no—
26C22×D35—51no—
27C2×D5×D7—51no—
28C2×D5×D7—51no—
29C2×D5×D7—51no—
30C2×D5×D7—102no—
31C4×D35—51no—
32C7×C22⋊D5—51no—
33C7×D20—51no—
34C5×C22⋊D7—51no—
35C5×D28—51no—
36#63307—51no—
37#63306D511yescharacteristic, complemented
38#63305—51no—
39#63305D511yescharacteristic, complemented
40#63304—51no—
41C22×C5⋊D5—71no—
42C2×D52—71no—
43C5×C22⋊D5—71no—
44C5×C22⋊D5—71no—
45#6038—71no—
46#6038D711yescharacteristic, complemented
47#6036—71no—
48C52×C7C2×D411yescharacteristic, complemented, Hall
49C22×C5×C7—51no—
50C2×D35—51no—
51C2×D35—51no—
52C2×D35—102no—
53C2×D35—102no—
54C2×D35C2×D511yescharacteristic, complemented
55C2×C7×D5—51no—
56C2×C7×D5—51no—
57C2×C7×D5—102no—
58C2×C7×D5C2×D511yescharacteristic, complemented
59C2×C5×D7—22no—
60C2×C5×D7—51no—
61C2×C5×D7C2×D511yescharacteristic, complemented
62C2×C5×D7C2×D511yescharacteristic, complemented
63D5×D7—102no—
64D5×D7—102no—
65D5×D7—102no—
66D5×D7—104no—
67D5×D7—104no—
68C4×C5×C7—51no—
69Dic35C2×D511yescharacteristic, complemented
70C5×Dic7—51no—
71C7×Dic5C2×D511yescharacteristic, complemented
72D4×D7—251noHall
73C22×C52—71no—
74C2×C5⋊D5—71no—
75C2×C5⋊D5—142no—
76C2×C5⋊D5C2×D711yescharacteristic, complemented
77C2×C5×D5—71no—
78C2×C5×D5C2×D711yescharacteristic, complemented
79D52—142no—
80C5×Dic5—71no—
81C5×Dic5C2×D711yescharacteristic, complemented
82D4×D5—351no—
83D4×D5—351no—
84C2×C5×C7—22no—
85C2×C5×C7—101no—
86C2×C5×C7C22×D511yescharacteristic
87C2×C5×C7C22×D511yescharacteristic
88D35—21no—
89D35—52no—
90D35—52no—
91D35—104no—
92C5×D7—22no—
93C5×D7—22no—
94C5×D7—21no—
95C5×D7—21no—
96C5×D7—101no—
97C7×D5—21no—
98C7×D5—102no—
99C7×D5—102no—
100C7×D5—101no—
101C7×D5—101no—
102C22×D7—251no—
103C22×D7—251no—
104C7×D4—251no—
105C22⋊D7—51no—
106C22⋊D7—251no—
107D28—51no—
108C4×D7—251no—
109C2×C52—141no—
110C2×C52C22×D711yescharacteristic
111C5⋊D5—21no—
112C5⋊D5—72no—
113C5×D5—21no—
114C5×D5—141no—
115C22×D5—351no—
116C22×D5—351no—
117C22×D5—351no—
118C22×D5—351no—
119C22×D5—702no—
120C5×D4—351no—
121C5×D4—351no—
122C22⋊D5—51no—
123C22⋊D5—71no—
124C22⋊D5—71no—
125C22⋊D5—351no—
126D20—51no—
127D20—351no—
128C4×D5—351no—
129C4×D5—351no—
130C5×C7—22no—
131C5×C7D4×D511yescharacteristic, complemented
132C5×C7D4×D511yescharacteristic, complemented
133C22×C7—51no—
134C22×C7—251no—
135C2×D7—51no—
136C2×D7—251no—
137C2×D7—502no—
138C2×D7—502no—
139C2×D7D5211yescharacteristic, complemented
140C4×C7—51no—
141Dic7—51no—
142C52D4×D711yescharacteristic, complemented, Sylow
143C22×C5—51no—
144C22×C5—71no—
145C22×C5—71no—
146C22×C5—142no—
147C22×C5—351no—
148C2×D5—51no—
149C2×D5—51no—
150C2×D5—71no—
151C2×D5—102no—
152C2×D5—351no—
153C2×D5—351no—
154C2×D5—702no—
155C2×D5—702no—
156C2×D5—702no—
157C2×D5—704no—
158C2×D5—704no—
159C2×D5—702no—
160C2×D5—702no—
161C2×D5D5×D711yescharacteristic, complemented
162C4×C5—51no—
163C4×C5—351no—
164Dic5—71no—
165Dic5D5×D711yescharacteristic, complemented
166C2×D4—1751noSylow
167C2×C7—101no—
168C2×C7—501no—
169C2×C7C2×D5211yescharacteristic
170D7—21no—
171D7—101no—
172D7—252no—
173C2×C5—22no—
174C2×C5—101no—
175C2×C5—142no—
176C2×C5—142no—
177C2×C5—141no—
178C2×C5—141no—
179C2×C5—701no—
180C2×C5C2×D5×D711yescharacteristic
181C2×C5C2×D5×D711yescharacteristic
182D5—21no—
183D5—102no—
184D5—102no—
185D5—101no—
186D5—101no—
187D5—141no—
188D5—352no—
189D5—352no—
190D5—704no—
191C23—1751no—
192C23—1751no—
193D4—251no—
194D4—351no—
195D4—351no—
196D4—1751no—
197C2×C4—1751no—
198C7#8788611yescharacteristic, complemented, Sylow
199C5—22no—
200C5#1058795011yescharacteristic, complemented
201C5#1058796311yescharacteristic, complemented
202C22—51no—
203C22—71no—
204C22—251no—
205C22—351no—
206C22—3502no—
207C22—3502no—
208C22—1751no—
209C4—51no—
210C4—351no—
211C2—101no—
212C2—141no—
213C2—501no—
214C2—701no—
215C2—1752no—
216C2D52×D711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D52×D7
commutator, Fitting, socle, cosocleC2×C52×C7C23
hypocenterC52×C7C2×D4
LCSG ▷ C2×C52×C7 ▷ C52×C7
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D5×D35C2semidirect
2. C2×D7×C5⋊D5C2semidirect
3. #13063794C2semidirect
4. #13063787C2semidirect
5. C7×#6038C2semidirect
6. C5×#63306C2semidirect
7. C5×#63305C2semidirect
9. C2×C7×C5⋊D5C22semidirect
10. C2×C5×D35C22semidirect
11. C2×C5×C7×D5C22semidirect
12. C2×C52×D7C22semidirect
15. C5×Dic35C22semidirect
16. C5×C7×Dic5C22semidirect
21. C5⋊D35D4semidirect
37. #63306D5semidirect
39. #63305D5semidirect
46. #6038D7semidirect
48. C52×C7C2×D4semidirect
54. C2×D35C2×D5semidirect
58. C2×C7×D5C2×D5semidirect
61. C2×C5×D7C2×D5semidirect
62. C2×C5×D7C2×D5semidirect
69. Dic35C2×D5semidirect
71. C7×Dic5C2×D5semidirect
76. C2×C5⋊D5C2×D7semidirect
78. C2×C5×D5C2×D7semidirect
81. C5×Dic5C2×D7semidirect
131. C5×C7D4×D5semidirect
132. C5×C7D4×D5semidirect
139. C2×D7D52semidirect
142. C52D4×D7semidirect
161. C2×D5D5×D7semidirect
165. Dic5D5×D7semidirect
198. C7#87886semidirect
200. C5#10587950semidirect
201. C5#10587963semidirect

Maximal subgroups

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

subgroupindex
C2×D5×D352
C2×D7×C5⋊D52
#130637942
#130637872
C7×#60382
C5×#633062
C5×#633052
#105879635
#105879505
#878867