Finite Group Databasebeta

← #72230988

Subgroups — #72230988

Order 2400.

380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C3×D4×C5⋊D5C211yesmaximal, characteristic, complemented
2#11925648C211yesmaximal, characteristic, complemented
3C5×#6716C211yesmaximal, characteristic, complemented
4C5×#6715C211yesmaximal, characteristic, complemented
5#11925156C211yesmaximal, characteristic, complemented
6#11925153C211yesmaximal, characteristic, complemented
7#11925152C211yesmaximal, characteristic, complemented
8#11717055—31nomaximal, Hall
9C22×C3×C5⋊D5—21no—
10C3×C52×D4C2211yescharacteristic
11C5×D60C2211yescharacteristic, complemented
12C5×Dic30C2211yescharacteristic, complemented
13C3×C22⋊(C5⋊D5)—21no—
14C3×C4⋊(C5⋊D5)C2211yescharacteristic
15C3×C4×C5⋊D5C2211yescharacteristic
16#10597127—21no—
17#10597125—21no—
18C5×C3⋊#168C2211yescharacteristic, complemented
19C5×C3⋊#168C2211yescharacteristic, complemented
20#91491—51nomaximal
21#91489—51nomaximal
22D4×C5⋊D5D311yescharacteristic, complemented
23#87871—31no—
24C5×#687—31no—
25C5×#686—31no—
26#87774—31no—
27#87771—31no—
28#87769—31no—
29C22×C3×C52—21no—
30C2×C5×D15—21no—
31C2×C3×C5⋊D5—21no—
32C2×C3×C5⋊D5—42no—
33C2×C3×C5⋊D5D411yescharacteristic
34C3×C4×C52C2311yescharacteristic
35C5×Dic15—21no—
36C3×#1039D411yescharacteristic
37C3×D4×D5—51no—
38C3×D4×D5—51no—
39C3×D4×D5—102no—
40#6773—51no—
41#6772—51no—
42#6716D511yescharacteristic, complemented
43#6715D511yescharacteristic, complemented
44C5×#214—51no—
45C5×#213—51no—
46#6657—51no—
47#6655—51no—
48#6653—51no—
49#6652—51no—
50#6649—51no—
51#6649—51no—
52C22×C5⋊D5—21no—
53C52×D4C2×D311yescharacteristic
54C22⋊(C5⋊D5)—21no—
55C4⋊(C5⋊D5)C2×D311yescharacteristic
56C4×C5⋊D5C2×D311yescharacteristic
57C5×D20—31no—
58C5×Dic10—31no—
59#6038—61no—
60D5×Dic5—61no—
61C5×#168—31no—
62C5×#168—31no—
63#4060—151no—
64#4057—151no—
65C2×C3×C52—41no—
66C2×C3×C52C2×D411yescharacteristic
67C5×D15—41no—
68C3×C5⋊D5—21no—
69C3×C5⋊D5—41no—
70C22×C3×D5—101no—
71C22×C3×D5—101no—
72C22×C3×D5—102no—
73C22×C3×D5—102no—
74C3×C5×D4—22no—
75C3×C5×D4C2×D511yescharacteristic
76C3×C5×D4C2×D511yescharacteristic
77D60C2×D511yescharacteristic, complemented
78Dic30C2×D511yescharacteristic, complemented
79C5×D12—51no—
80C5×Dic6—51no—
81C3×C22⋊D5—101no—
82C3×C22⋊D5—101no—
83C3×C22⋊D5—102no—
84C3×C22⋊D5—102no—
85C3×D20—51no—
86C3×D20—51no—
87C3×D20—102no—
88C3×C4×D5—51no—
89C3×C4×D5—51no—
90C3×C4×D5—102no—
91#1202—101no—
92#1201—101no—
93#1200—101no—
94D3×Dic5—101no—
95C3⋊#168C2×D511yescharacteristic, complemented
96C3⋊#168C2×D511yescharacteristic, complemented
97C5×C3⋊C8—51no—
98C5×C3⋊C8—51no—
99C22×C52—21no—
100C2×C5⋊D5—21no—
101C2×C5⋊D5—42no—
102C2×C5⋊D5#6711yescharacteristic
103C2×C5×D5—61no—
104C4×C52C22×D311yescharacteristic
105#1039#6711yescharacteristic
106C5×Dic5—61no—
107#932—251noHall
108#713—151no—
109#711—151no—
110D4×D5—51no—
111D4×D5—51no—
112D4×D5—102no—
113C5×SD16—151no—
114C5×D8—151no—
115#688—151no—
116#687—31no—
117#686—31no—
118#686—151no—
119D40—151no—
120#677—151no—
121#676—151no—
122#676—151no—
123C3×C52AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
124C22×C3×C5—22no—
125C22×C3×C5—22no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C2×D15—21no—
129C2×C5×D3—101no—
130C2×C3×D5—51no—
131C2×C3×D5—51no—
132C2×C3×D5—102no—
133C2×C3×D5—102no—
134C2×C3×D5—102no—
135C2×C3×D5—101no—
136C2×C3×D5—101no—
137C2×C3×D5—204no—
138C2×C3×D5—204no—
139C2×C3×D5—202no—
140C2×C3×D5—202no—
141C3×C4×C5—22no—
142C3×C4×C5C22×D511yescharacteristic
143C3×C4×C5C22×D511yescharacteristic
144Dic15—21no—
145C3×Dic5—51no—
146C3×Dic5—51no—
147C3×Dic5—102no—
148C5×Dic3—101no—
149C2×C52—41no—
150C2×C52C2×#6711yescharacteristic
151C5⋊D5—21no—
152C5⋊D5—41no—
153C5×D5—121no—
154C2×C3×D4—251no—
155#235—251no—
156#214—51no—
157#214—251no—
158#213—51no—
159#213—251no—
160#208—251no—
161C22×D5—101no—
162C22×D5—101no—
163C22×D5—102no—
164C22×D5—102no—
165C5×Q8—151no—
166C5×D4—22no—
167C5×D4—151no—
168C5×D4D3×D511yescharacteristic
169C5×D4D3×D511yescharacteristic
170C22⋊D5—101no—
171C22⋊D5—101no—
172C22⋊D5—102no—
173C22⋊D5—102no—
174C22⋊D5—301no—
175C2×Dic5—301no—
176D20—31no—
177D20—51no—
178D20—51no—
179D20—102no—
180D20—301no—
181C4×D5—51no—
182C4×D5—51no—
183C4×D5—102no—
184C4×D5—301no—
185Dic10—31no—
186C5×C8—151no—
187C5×C8—151no—
188#168—31no—
189#168—31no—
190AGL(1,ℤ/8)—751noSylow
191C2×C3×C5—22no—
192C2×C3×C5—42no—
193C2×C3×C5—42no—
194C2×C3×C5—41no—
195C2×C3×C5—41no—
196C2×C3×C5D4×D511yescharacteristic
197C2×C3×C5D4×D511yescharacteristic
198D15—41no—
199C3×D5—102no—
200C3×D5—102no—
201C3×D5—101no—
202C3×D5—101no—
203C3×D5—202no—
204C3×D5—202no—
205C3×D5—201no—
206C3×D5—201no—
207C5×D3—201no—
208C52#93211yescharacteristic, complemented, Sylow
209C23×C3—501no—
210C3×D4—251no—
211C3×D4—501no—
212C3×D4D5211yescharacteristic
213C2×C3×C4—251no—
214#67—501no—
215D12—51no—
216C4×D3—501no—
217Dic6—51no—
218C3⋊C8—51no—
219C3⋊C8—51no—
220C22×C5—22no—
221C22×C5—22no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—301no—
225C2×D5—51no—
226C2×D5—51no—
227C2×D5—61no—
228C2×D5—102no—
229C2×D5—102no—
230C2×D5—102no—
231C2×D5—101no—
232C2×D5—101no—
233C2×D5—204no—
234C2×D5—204no—
235C2×D5—202no—
236C2×D5—202no—
237C4×C5—22no—
238C4×C5—301no—
239C4×C5C2×D3×D511yescharacteristic
240C4×C5C2×D3×D511yescharacteristic
241Dic5—51no—
242Dic5—51no—
243Dic5—61no—
244Dic5—102no—
245#41—751no—
246C2×D4—251no—
247SD16—151no—
248SD16—751no—
249D8—151no—
250D8—751no—
251M16—751no—
252C3×C5—22no—
253C3×C5#405711yescharacteristic, complemented
254C3×C5#406011yescharacteristic, complemented
255C22×C3—21no—
256C22×C3—251no—
257C22×C3—501no—
258C22×C3—1002no—
259C2×D3—101no—
260C3×C4—251no—
261C3×C4C2×D5211yescharacteristic
262Dic3—101no—
263C2×C5—22no—
264C2×C5—42no—
265C2×C5—42no—
266C2×C5—41no—
267C2×C5—41no—
268C2×C5—601no—
269C2×C5D5×#6711yescharacteristic
270C2×C5D5×#6711yescharacteristic
271D5—102no—
272D5—102no—
273D5—101no—
274D5—101no—
275D5—121no—
276D5—202no—
277D5—202no—
278D5—201no—
279D5—201no—
280C23—501no—
281Q8—151no—
282D4—151no—
283D4—251no—
284D4—501no—
285D4—1501no—
286D4D15⋊D511yescharacteristic
287C2×C4—251no—
288C2×C4—1501no—
289C8—151no—
290C8—151no—
291C2×C3—41no—
292C2×C3—501no—
293C2×C3—1001no—
294C2×C3#8788611yescharacteristic
295D3—201no—
296C5—22no—
297C5#9148911yescharacteristic, complemented
298C5#9149111yescharacteristic, complemented
299C22—21no—
300C22—251no—
301C22—301no—
302C22—501no—
303C22—1002no—
304C4—251no—
305C4—301no—
306C4C2×D15⋊D511yescharacteristic
307C3#1171705511yescharacteristic, complemented, Sylow
308C2—41no—
309C2—501no—
310C2—601no—
311C2—1001no—
312C2#1192566411yescharacteristic
subgroupG/H
centerC2#11925664
commutator, cosocleC3×C4×C52C23
FrattiniC4C2×D15⋊D5
FittingC3×C52×D4C22
socleC2×C3×C52C2×D4
hypercenterD4D15⋊D5
hypocenterC3×C52AGL(1,ℤ/8)
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×C5⋊D5C2semidirect
2. #11925648C2semidirect
3. C5×#6716C2semidirect
4. C5×#6715C2semidirect
5. #11925156C2semidirect
6. #11925153C2semidirect
7. #11925152C2semidirect
11. C5×D60C22semidirect
12. C5×Dic30C22semidirect
18. C5×C3⋊#168C22semidirect
19. C5×C3⋊#168C22semidirect
22. D4×C5⋊D5D3semidirect
42. #6716D5semidirect
43. #6715D5semidirect
77. D60C2×D5semidirect
78. Dic30C2×D5semidirect
95. C3⋊#168C2×D5semidirect
96. C3⋊#168C2×D5semidirect
123. C3×C52AGL(1,ℤ/8)semidirect
208. C52#932semidirect
253. C3×C5#4057semidirect
254. C3×C5#4060semidirect
297. C5#91489semidirect
298. C5#91491semidirect
307. C3#11717055semidirect

Maximal subgroups

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

subgroupindex
C3×D4×C5⋊D52
#119256482
C5×#67162
C5×#67152
#119251562
#119251532
#119251522
#117170553
#914915
#914895