Finite Group Databasebeta

← #72231332

Subgroups — #72231332

Order 3600.

634 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 78 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×#11744719C211yesmaximal, characteristic, complemented
2C2×C3×D3×C5⋊D5C211yesmaximal, characteristic, complemented
3#14268310C212yesmaximal, complemented
4C5×#67152C212yesmaximal, complemented
5C3×#10597126C211yesmaximal, characteristic, complemented
6#11925664—31nomaximal
7#11925429—31nomaximal
8C2×C5×C3⋊D15C2212yescomplemented
9C2×C3×C3⋊(C5⋊D5)C2211yescharacteristic, complemented
10C2×C3×C52×D3C2211yescharacteristic, complemented
11C2×C32×C5⋊D5C2211yescharacteristic
12#11744719—22no—
13C3×D3×C5⋊D5—22no—
14C3×C5×Dic15C2212yescomplemented
15D5×#626—52nomaximal
16C22×C3×C5⋊D5—31no—
17C2×D15⋊D5—31no—
18C2×D15⋊D5—31no—
19C2×D15⋊D5—61no—
20C2×D3×C5⋊D5D311yescharacteristic, complemented
21C5×#1220—32no—
22#10597127—32no—
23#10597126D311yescharacteristic, complemented
24#10597122—32no—
25C5×#1203—32no—
26C3×#6036—31no—
27C2×C32×C52C2311yescharacteristic
28C5×C3⋊D15—22no—
29C3×C3⋊(C5⋊D5)—21no—
30C3×C52×D3—21no—
31C32×C5⋊D5D412yescomplemented
32#87886—91noHall
33C2×D5×C3⋊D3—52no—
34C2×C3×D3×D5—52no—
35C2×C3×D3×D5—102no—
36#67156—52no—
37#67152D512yescomplemented
38#67151—52no—
39C5×#626—52no—
40C3×D5×Dic3—52no—
41C22×C3×C52—31no—
42C2×C3⋊(C5⋊D5)C2×D311yescharacteristic, complemented
43C2×C5×D15—32no—
44C2×C5×D15—32no—
45C2×C5×D15—62no—
46C2×C52×D3C2×D311yescharacteristic, complemented
47C2×C3×C5⋊D5—21no—
48C2×C3×C5⋊D5—31no—
49C2×C3×C5⋊D5—62no—
50C2×C3×C5⋊D5C2×D311yescharacteristic
51C2×C3×C5⋊D5C2×D311yescharacteristic
52D15⋊D5—62no—
53D15⋊D5—62no—
54D15⋊D5—62no—
55D15⋊D5—62no—
56D3×C5⋊D5—22no—
57C5×Dic15C2×D312yescomplemented
58C3×C5×Dic5—32no—
59D5×#67—152no—
60D5×D12—152no—
61C32×C52C2×D411yescharacteristic, complemented, Hall
62C22×C5⋊D5—31no—
63C2×D52—91no—
64C5×C22⋊D5—92no—
65#6038—92no—
66#6036—31no—
67C2×C3⋊D15C2×D512yescomplemented
68C2×C5×C3⋊D3—52no—
69C2×C3×D15—52no—
70C2×C3×D15—102no—
71C2×C3×C5×D3—22no—
72C2×C3×C5×D3C2×D512yescomplemented
73C2×C32×D5—52no—
74C2×C32×D5—102no—
75D5×C3⋊D3—104no—
76C3×D3×D5—104no—
77C3×D3×D5—104no—
78C3×D3×D5—104no—
79C3×Dic15C2×D512yescomplemented
80C3×C5×Dic3—52no—
81C2×C3×C52—21no—
82C2×C3×C52—61no—
83C2×C3×C52C22×D311yescharacteristic
84C2×C3×C52C22×D311yescharacteristic
85C3⋊(C5⋊D5)—21no—
86C5×D15—62no—
87C5×D15—62no—
88C5×D15—62no—
89C5×D15—62no—
90C52×D3—21no—
91C3×C5⋊D5—22no—
92C3×C5⋊D5—61no—
93C3×C5⋊D5D1212yescomplemented
94C3×C5⋊D5#6712yescomplemented
95C2×#626—251noHall
96C22×C3×D5—152no—
97C22×C3×D5—302no—
98C2×D3×D5—52no—
99C2×D3×D5—102no—
100C2×D3×D5—152no—
101C2×D3×D5—152no—
102C2×D3×D5—302no—
103#1220—32no—
104D60—152no—
105C5×#67—152no—
106C5×D12—152no—
107C3×C4×D5—152no—
108#1203—32no—
109#1203—152no—
110#1202—152no—
111#1201—152no—
112D5×Dic3—52no—
113C22×C52—31no—
114C2×C5⋊D5—31no—
115C2×C5⋊D5—62no—
116C2×C5⋊D5D3211yescharacteristic
117C2×C5×D5—92no—
118D52—182no—
119C5×Dic5—32no—
120C2×C32×C5—22no—
121C2×C32×C5C22×D512yes—
122C3⋊D15—22no—
123C5×C3⋊D3—102no—
124C3×D15—102no—
125C3×D15—102no—
126C3×D15—102no—
127C3×C5×D3—22no—
128C3×C5×D3—22no—
129C3×C5×D3—22no—
130C32×D5—54no—
131C32×D5—104no—
132D4×D5—452no—
133C3×C52—21no—
134C3×C52C2×D1211yescharacteristic, complemented
135C3×C52C2×#6711yescharacteristic, complemented
136C22×C3⋊D3—251no—
137C22×C3×D3—251no—
138C2×C3×Dic3—251no—
139#626—52no—
140#626—252no—
141C22×C3×C5—32no—
142C22×C3×C5—62no—
143C2×D15—32no—
144C2×D15—32no—
145C2×D15—52no—
146C2×D15—62no—
147C2×D15—102no—
148C2×C5×D3—22no—
149C2×C5×D3—152no—
150C2×C5×D3—152no—
151C2×C5×D3—302no—
152C2×C5×D3D3×D512yescomplemented
153C2×C3×D5—52no—
154C2×C3×D5—52no—
155C2×C3×D5—102no—
156C2×C3×D5—102no—
157C2×C3×D5—102no—
158C2×C3×D5—152no—
159C2×C3×D5—202no—
160C2×C3×D5—302no—
161C2×C3×D5—304no—
162C2×C3×D5—304no—
163C2×C3×D5—304no—
164D3×D5—104no—
165D3×D5—104no—
166D3×D5—104no—
167D3×D5—304no—
168D3×D5—304no—
169D3×D5—304no—
170D3×D5—304no—
171C3×C4×C5—152no—
172Dic15D3×D512yescomplemented
173C3×Dic5—32no—
174C5×Dic3—52no—
175C2×C52—61no—
176C2×C52C2×D3211yescharacteristic
177C5⋊D5—61no—
178C5⋊D5#62612yescomplemented
179C5×D5—182no—
180C2×#67—751no—
181C2×D12—751no—
182C32×C5—22no—
183C32×C5D4×D512yescomplemented
184C22×D5—152no—
185C22×D5—302no—
186C22×D5—452no—
187C5×D4—452no—
188C22⋊D5—92no—
189C22⋊D5—452no—
190D20—452no—
191C4×D5—152no—
192C22×C32—251no—
193C2×C3⋊D3—52no—
194C2×C3⋊D3—502no—
195C2×C3×D3—251no—
196C2×C3×D3—502no—
197C2×C3×D3D5211yescharacteristic, complemented
198C3×Dic3—52no—
199C2×C3×C5—22no—
200C2×C3×C5—22no—
201C2×C3×C5—22no—
202C2×C3×C5—42no—
203C2×C3×C5—62no—
204C2×C3×C5—62no—
205C2×C3×C5—62no—
206C2×C3×C5C2×D3×D512yes—
207C2×C3×C5C2×D3×D512yes—
208D15—62no—
209D15—62no—
210D15—62no—
211D15—62no—
212D15—102no—
213D15—102no—
214D15—102no—
215C3×D5—54no—
216C3×D5—54no—
217C3×D5—104no—
218C3×D5—104no—
219C3×D5—104no—
220C3×D5—204no—
221C3×D5—302no—
222C3×D5—302no—
223C3×D5—302no—
224C5×D3—22no—
225C5×D3—22no—
226C5×D3—22no—
227C5×D3—302no—
228C5×D3—302no—
229C5×D3—302no—
230C5×D3—302no—
231C52C2×#62611yescharacteristic, complemented, Sylow
232C23×C3—751no—
233C22×D3—251no—
234C22×D3—751no—
235C22×D3—751no—
236C22×D3—1501no—
237C2×C3×C4—751no—
238#67—152no—
239#67—752no—
240C2×Dic3—251no—
241D12—152no—
242D12—752no—
243C22×C5—32no—
244C22×C5—62no—
245C22×C5—452no—
246C2×D5—52no—
247C2×D5—92no—
248C2×D5—102no—
249C2×D5—152no—
250C2×D5—302no—
251C2×D5—304no—
252C2×D5—304no—
253C2×D5—304no—
254C2×D5—904no—
255C4×C5—152no—
256Dic5—32no—
257C2×C32—252no—
258C2×C32C2×D5211yescharacteristic
259C3⋊D3—102no—
260C3×D3—21no—
261C3×D3—501no—
262C2×D4—2251noSylow
263C3×C5—22no—
264C3×C5—22no—
265C3×C5—22no—
266C3×C5—42no—
267C3×C5D5×D1212yescomplemented
268C3×C5D5×#6712yescomplemented
269C22×C3—31no—
270C22×C3—251no—
271C22×C3—251no—
272C22×C3—501no—
273C22×C3—751no—
274C22×C3—1502no—
275C2×D3—152no—
276C2×D3—152no—
277C2×D3—251no—
278C2×D3—302no—
279C2×D3—502no—
280C2×D3—1502no—
281C2×D3—1502no—
282C2×D3—1502no—
283C2×D3—1502no—
284C2×D3D15⋊D511yescharacteristic, complemented
285C3×C4—152no—
286Dic3—52no—
287C2×C5—22no—
288C2×C5—62no—
289C2×C5—62no—
290C2×C5—62no—
291C2×C5—902no—
292C2×C5D32×D512yes—
293D5—54no—
294D5—104no—
295D5—182no—
296D5—302no—
297D5—302no—
298D5—302no—
299C32#8788611yescharacteristic, complemented, Sylow
300C23—751no—
301C23—2251no—
302D4—452no—
303D4—2252no—
304C2×C4—751no—
305C2×C3—21no—
306C2×C3—61no—
307C2×C3—252no—
308C2×C3—252no—
309C2×C3—502no—
310C2×C3—1501no—
311C2×C3D3×D5211yescharacteristic
312C2×C3C2×D15⋊D511yescharacteristic
313D3—21no—
314D3—302no—
315D3—302no—
316D3—302no—
317D3—302no—
318D3—501no—
319C5—22no—
320C5D5×#62612yescomplemented
321C22—31no—
322C22—251no—
323C22—452no—
324C22—751no—
325C22—1502no—
326C22—4502no—
327C4—152no—
328C3—21no—
329C3#1192542911yescharacteristic, complemented
330C3#1192566411yescharacteristic, complemented
331C2—61no—
332C2—252no—
333C2—902no—
334C2—1501no—
335C2D3×D15⋊D511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×D15⋊D5
commutator, Fitting, socle, cosocleC2×C32×C52C23
hypocenterC32×C52C2×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#11744719C2semidirect
2. C2×C3×D3×C5⋊D5C2semidirect
3. #14268310C2semidirect
4. C5×#67152C2semidirect
5. C3×#10597126C2semidirect
8. C2×C5×C3⋊D15C22semidirect
9. C2×C3×C3⋊(C5⋊D5)C22semidirect
10. C2×C3×C52×D3C22semidirect
14. C3×C5×Dic15C22semidirect
20. C2×D3×C5⋊D5D3semidirect
23. #10597126D3semidirect
31. C32×C5⋊D5D4semidirect
37. #67152D5semidirect
42. C2×C3⋊(C5⋊D5)C2×D3semidirect
46. C2×C52×D3C2×D3semidirect
57. C5×Dic15C2×D3semidirect
61. C32×C52C2×D4semidirect
67. C2×C3⋊D15C2×D5semidirect
72. C2×C3×C5×D3C2×D5semidirect
79. C3×Dic15C2×D5semidirect
93. C3×C5⋊D5D12semidirect
94. C3×C5⋊D5#67semidirect
134. C3×C52C2×D12semidirect
135. C3×C52C2×#67semidirect
152. C2×C5×D3D3×D5semidirect
172. Dic15D3×D5semidirect
178. C5⋊D5#626semidirect
183. C32×C5D4×D5semidirect
197. C2×C3×D3D52semidirect
231. C52C2×#626semidirect
267. C3×C5D5×D12semidirect
268. C3×C5D5×#67semidirect
284. C2×D3D15⋊D5semidirect
299. C32#87886semidirect
320. C5D5×#626semidirect
329. C3#11925429semidirect
330. C3#11925664semidirect

Maximal subgroups

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

subgroupindex
C2×#117447192
C2×C3×D3×C5⋊D52
#142683102
C5×#671522
C3×#105971262
#119256643
#119254293
D5×#6265