Finite Group Databasebeta

← #11752815

Subgroups — #11752815

Order 960.

392 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91775C211yesmaximal, characteristic
2C5×#879C211yesmaximal, characteristic, complemented
3C3×#4025C211yesmaximal, characteristic, complemented
4#91576C211yesmaximal, characteristic, complemented
5#91576C211yesmaximal, characteristic, complemented
6#91562C211yesmaximal, characteristic
7#91526C211yesmaximal, characteristic
8#91469C211yesmaximal, characteristic, complemented
9#91468C211yesmaximal, characteristic, complemented
10#91429C211yesmaximal, characteristic, complemented
11#91419C211yesmaximal, characteristic, complemented
12#91387C211yesmaximal, characteristic, complemented
13#91380C211yesmaximal, characteristic, complemented
14#91343C211yesmaximal, characteristic, complemented
15#91334C211yesmaximal, characteristic, complemented
16#66046—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C2×#1204C2211yescharacteristic
20C2×#1204C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×#1200C2211yescharacteristic
23C3×C5×C22⋊C4C2211yescharacteristic
24#6714C2211yescharacteristic
25#6714C2211yescharacteristic
26C4⋊Dic15C2211yescharacteristic
27C4⋊Dic15C2211yescharacteristic
28C5×#217C2211yescharacteristic
29C5×#217C2211yescharacteristic
30C5×C4⋊Dic3C2211yescharacteristic
31C5×Dic3⋊C4C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C4×C5×Dic3C2211yescharacteristic
34C3×C22⋊Dic5C2211yescharacteristic
35C3×C22⋊Dic5C2211yescharacteristic
36C3×C4⋊Dic5C2211yescharacteristic
37C3×#683C2211yescharacteristic
38C3×#683C2211yescharacteristic
39C3×C4×Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42Dic3⋊Dic5C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46#6668C2211yescharacteristic
47#6668C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50#6667C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5712—51nomaximal, Hall
53C5×#126—31no—
54#4044—31no—
55#4043—31no—
56#4042—31no—
57#4036—31no—
58#4035—31no—
59#4034—31no—
60#4032—31no—
61#4031—31no—
62#4029—31no—
63#4025D311yescharacteristic, complemented
64#4024—31no—
65#4024—31no—
66#4022—31no—
67#4015—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C2×C3×C4×C5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72#1220—41no—
73C2×Dic15—41no—
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×C5×Dic3C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C3×Dic5C2311yescharacteristic
82C2×C3×Dic5C2311yescharacteristic
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85#1204—41no—
86#1204—41no—
87#1204—41no—
88#1200—41no—
89C3×#126—51no—
90#898—51no—
91#897—51no—
92#896—51no—
93#890—51no—
94#889—51no—
95#888—51no—
96#886—51no—
97#885—51no—
98#883—51no—
99#879D511yescharacteristic, complemented
100#878—51no—
101#878—51no—
102#876—51no—
103#869—51no—
104C2×C22⋊D5—31no—
105C22×Dic5—31no—
106C2×C4×D5—31no—
107C2×Dic10—31no—
108C2×Dic10—31no—
109C2×Dic10—31no—
110C5×C4⋊C4—31no—
111C5×C4⋊C4—31no—
112C5×C4⋊C4—31no—
113C5×C22⋊C4—31no—
114C5×C22⋊C4—31no—
115C5×C22⋊C4C2×D311yescharacteristic
116C42×C5—31no—
117C22⋊Dic5C2×D311yescharacteristic
118C22⋊Dic5C2×D311yescharacteristic
119#685—31no—
120#685—31no—
121#685—31no—
122#685—31no—
123#685—31no—
124C4⋊Dic5—31no—
125C4⋊Dic5—31no—
126C4⋊Dic5—31no—
127C4⋊Dic5—31no—
128C4⋊Dic5—31no—
129C4⋊Dic5C2×D311yescharacteristic
130#683—31no—
131#683—31no—
132#683—31no—
133#683—31no—
134#683—31no—
135#683C2×D311yescharacteristic
136#683C2×D311yescharacteristic
137C4×Dic5—31no—
138C4×Dic5C2×D311yescharacteristic
139#563—151noSylow
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5C2411yescharacteristic
144C2×D15—21no—
145C2×D15—21no—
146C2×D15—21no—
147C3×C4×C5—21no—
148C3×C4×C5—21no—
149Dic15—21no—
150Dic15—21no—
151Dic15—21no—
152C3×Dic5—21no—
153C3×Dic5—21no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C5×Dic3—21no—
157C5×Dic3—21no—
158C5×Dic3—21no—
159C5×Dic3—21no—
160C2×#67—51no—
161C22×Dic3—51no—
162C2×C4×D3—51no—
163C2×Dic6—51no—
164C2×Dic6—51no—
165C2×Dic6—51no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4—51no—
169C3×C22⋊C4—51no—
170C3×C22⋊C4—51no—
171C3×C22⋊C4C2×D511yescharacteristic
172C3×C42—51no—
173#217C2×D511yescharacteristic
174#217C2×D511yescharacteristic
175(C2×D3)⋊C4—51no—
176(C2×D3)⋊C4—51no—
177(C2×D3)⋊C4—51no—
178(C2×D3)⋊C4—51no—
179(C2×D3)⋊C4—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—51no—
182C4⋊Dic3—51no—
183C4⋊Dic3—51no—
184C4⋊Dic3—51no—
185C4⋊Dic3C2×D511yescharacteristic
186Dic3⋊C4—51no—
187Dic3⋊C4—51no—
188Dic3⋊C4—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4C2×D511yescharacteristic
192Dic3⋊C4C2×D511yescharacteristic
193C4×Dic3—51no—
194C4×Dic3C2×D511yescharacteristic
195C23×C5C22×D311yescharacteristic
196C22×D5—31no—
197C2×C4×C5—31no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5C22×D311yescharacteristic
202C2×C4×C5C22×D311yescharacteristic
203C22⋊D5—121no—
204C2×Dic5—31no—
205C2×Dic5—31no—
206C2×Dic5—31no—
207C2×Dic5—121no—
208C2×Dic5C22×D311yescharacteristic
209C2×Dic5C22×D311yescharacteristic
210C2×Dic5C22×D311yescharacteristic
211C2×Dic5C22×D311yescharacteristic
212C4×D5—121no—
213Dic10—121no—
214Dic10—121no—
215Dic10—121no—
216C4⋊Q8—151no—
217C4⋊Q8—151no—
218#126—31no—
219#126—51no—
220#126—151no—
221#126—151no—
222#125—151no—
223#125—151no—
224#124—151no—
225#123—151no—
226#123—151no—
227C22⋊Q8—151no—
228C22⋊Q8—151no—
229C22⋊Q8—151no—
230C22⋊Q8—151no—
231C2×C3×C5—41no—
232C2×C3×C5H(5,𝔽2)11yescharacteristic
233C2×C3×C52−1+411yescharacteristic
234C2×C3×C52−1+411yescharacteristic
235D15—41no—
236C23×C3C22×D511yescharacteristic
237C22×D3—51no—
238C2×C3×C4—51no—
239C2×C3×C4—51no—
240C2×C3×C4—51no—
241C2×C3×C4—51no—
242C2×C3×C4C22×D511yescharacteristic
243C2×C3×C4C22×D511yescharacteristic
244#67—201no—
245C2×Dic3—51no—
246C2×Dic3—51no—
247C2×Dic3—51no—
248C2×Dic3—201no—
249C2×Dic3C22×D511yescharacteristic
250C2×Dic3C22×D511yescharacteristic
251C2×Dic3C22×D511yescharacteristic
252C2×Dic3C22×D511yescharacteristic
253C4×D3—201no—
254Dic6—201no—
255Dic6—201no—
256Dic6—201no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5C23×D311yescharacteristic
261C2×D5—61no—
262C2×D5—61no—
263C2×D5—61no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—61no—
267C4×C5—61no—
268C4×C5—61no—
269C4×C5—61no—
270Dic5—21no—
271Dic5—21no—
272Dic5—21no—
273Dic5—21no—
274Dic5—61no—
275Dic5—61no—
276Dic5—61no—
277C2×Q8—151no—
278C2×Q8—151no—
279C2×Q8—151no—
280C2×D4—151no—
281C22×C4—151no—
282C22×C4—151no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—51no—
287C4⋊C4—51no—
288C4⋊C4—51no—
289C4⋊C4—151no—
290C4⋊C4—151no—
291C4⋊C4—151no—
292C4⋊C4—151no—
293C4⋊C4—151no—
294C4⋊C4—151no—
295C4⋊C4—151no—
296C4⋊C4—151no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C22⋊C4—31no—
300C22⋊C4—31no—
301C22⋊C4—51no—
302C22⋊C4—51no—
303C22⋊C4—151no—
304C22⋊C4—151no—
305C22⋊C4—151no—
306C22⋊C4—151no—
307C22⋊C4—151no—
308C22⋊C4D3×D511yescharacteristic
309C42—31no—
310C42—51no—
311C42—151no—
312C3×C5#56311yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3C23×D511yescharacteristic
317C2×D3—101no—
318C2×D3—101no—
319C2×D3—101no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—101no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—101no—
326Dic3—21no—
327Dic3—21no—
328Dic3—21no—
329Dic3—21no—
330Dic3—101no—
331Dic3—101no—
332Dic3—101no—
333C2×C5—41no—
334C2×C5#100911yescharacteristic
335C2×C5#101011yescharacteristic
336C2×C5#101011yescharacteristic
337D5—121no—
338C23—151no—
339C23C2×D3×D511yescharacteristic
340Q8—601no—
341Q8—601no—
342Q8—601no—
343D4—601no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—51no—
351C2×C4—51no—
352C2×C4—151no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4C2×D3×D511yescharacteristic
358C2×C4C2×D3×D511yescharacteristic
359C2×C3—41no—
360C2×C3#414911yescharacteristic
361C2×C3#415011yescharacteristic
362C2×C3#415011yescharacteristic
363D3—201no—
364C5#571211yescharacteristic, complemented, Sylow
365C22—21no—
366C22—21no—
367C22—21no—
368C22—301no—
369C22—301no—
370C22—301no—
371C22C22×D3×D511yescharacteristic
372C4—21no—
373C4—21no—
374C4—61no—
375C4—61no—
376C4—61no—
377C4—61no—
378C4—101no—
379C4—101no—
380C4—101no—
381C4—101no—
382C4—301no—
383C4—301no—
384C4—301no—
385C3#6604611yescharacteristic, complemented, Sylow
386C2—41no—
387C2—601no—
388C2#9201911yescharacteristic
389C2#9202011yescharacteristic
390C2#9202011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC2×#1220C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#563
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#879C2semidirect
3. C3×#4025C2semidirect
4. #91576C2semidirect
5. #91576C2semidirect
8. #91469C2semidirect
9. #91468C2semidirect
10. #91429C2semidirect
11. #91419C2semidirect
12. #91387C2semidirect
13. #91380C2semidirect
14. #91343C2semidirect
15. #91334C2semidirect
63. #4025D3semidirect
99. #879D5semidirect
312. C3×C5#563semidirect
364. C5#5712semidirect
385. C3#66046semidirect

Maximal subgroups

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

subgroupindex
#917752
C5×#8792
C3×#40252
#915762
#915622
#915262
#914692
#914682
#914292
#914192
#913872
#913802
#913432
#913342
#660463
#57125