Finite Group Databasebeta

← #14285155

Subgroups — #14285155

Order 1920.

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

normal subgroups only

This group has 484 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
1#11752556C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3#11746859C211yesmaximal, characteristic, complemented
4C5×#4486C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6#11745858C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599219—31nomaximal, Hall
9C2×#6766—21no—
10C42×D15C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13#91465—21no—
14#91465C412yes—
15#91434—21no—
16#91434C412yes—
17#91368—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19#91104—21no—
20#91099—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90957—21no—
25#90951—21no—
26#68386—51nomaximal, Hall
27#66059—31no—
28#65124—31no—
29#65122—31no—
30C5×#332—31no—
31#64767—31no—
32#64705—31no—
33#64705D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×#1202—22no—
42C2×D5×Dic3—22no—
43#6766—42no—
44#6766—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15D411yescharacteristic
49C4×Dic15D411yescharacteristic
50C2×C3⋊#168—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3C2×C412yes—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55#6665—22no—
56#6665—22no—
57#5716—51no—
58#4835—51no—
59#4833—51no—
60C3×#331—51no—
61#4544—51no—
62#4486D511yescharacteristic, complemented
63#4482—51no—
64C2×#713—61no—
65C5×C4⋊Q8—31no—
66#4093—61no—
67#4041—32no—
68#4041—61no—
69#4039—32no—
70#4039—61no—
71#4020C2×D311yescharacteristic
72C42×D5—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—61no—
76#3952—61no—
77#3947—61no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1553—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C22×C3×D5—22no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C4×D15—21no—
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—41no—
95C2×C5×Dic3—22no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103#1202—44no—
104D5×Dic3—44no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3×#168—41no—
108C5×C3⋊C8—41no—
109C2×#237—101no—
110C3×#127—51no—
111#938—52no—
112#938—101no—
113#936—101no—
114D4×Dic3—52no—
115D4×Dic3—101no—
116C42×D3—51no—
117#869C2×D511yescharacteristic
118C3×C4⋊C8—51no—
119C3×C4⋊C8C2×D511yescharacteristic
120(C2×D3)⋊C8—101no—
121(C2×D3)⋊C8—101no—
122#815—101no—
123C8×Dic3—101no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×Q8—61no—
127#713—122no—
128#713—122no—
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—62no—
132C2×D20C4×D312yes—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—62no—
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C5×C4⋊C4—32no—
140C5×C4⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142#685—62no—
143#685—62no—
144C4×Dic5—31no—
145C4×Dic5—31no—
146C4×Dic5—31no—
147C2×#168—21no—
148C2×#168—61no—
149#532—151no—
150#432—151no—
151#431—151no—
152#332—31no—
153#332—151no—
154#331—51no—
155#331—151no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C2×D15—21no—
158C2×D15—21no—
159C2×D15—21no—
160C2×C3×D5—42no—
161C2×C3×D5—42no—
162C2×C3×D5—42no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168Dic15—21no—
169Dic15—21no—
170Dic15—21no—
171C5×Dic3—42no—
172C2×C3×D4—52no—
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×#67—102no—
176C22×Dic3—102no—
177#237—202no—
178#237—202no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×Dic6—21no—
183C2×C3×C8—21no—
184C2×C3×C8—101no—
185C3×C42C22×D511yescharacteristic
186#217—102no—
187#217—102no—
188C4⋊Dic3—21no—
189C4⋊Dic3C4×D512yes—
190C4×Dic3—51no—
191C4×Dic3—51no—
192C4×Dic3—51no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C22×D5—22no—
196C22×D5—31no—
197C5×Q8—121no—
198C5×Q8—121no—
199C2×C4×C5—62no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×Dic5—31no—
204C2×Dic5—31no—
205C2×Dic5—31no—
206D20—42no—
207D20—41no—
208D20—41no—
209D20—41no—
210D20—41no—
211D20—124no—
212C4×D5—61no—
213C4×D5—61no—
214C4×D5—61no—
215C4×D5—61no—
216C4×D5—121no—
217C4×D5—124no—
218C5×C8—41no—
219C5×C8—121no—
220#168—41no—
221#168—121no—
222C2×#41—301no—
223C4⋊Q8—31no—
224#127—51no—
225#124—301no—
226#121—152no—
227#121—301no—
228C4×D4—152no—
229C4×D4—301no—
230C2×C42—151no—
231C4⋊C8—31no—
232C4⋊C8—51no—
233C4⋊C8—151no—
234C4⋊C8D3×D511yescharacteristic
235C22⋊C8—301no—
236C22⋊C8—301no—
237#97—301no—
238C4×C8—301no—
239C2×C3×C5#41311yescharacteristic
240C2×C3×C5#41611yescharacteristic
241C2×C3×C5#41811yescharacteristic
242D15—41no—
243C3×D5—82no—
244C23×C3—102no—
245C22×D3—51no—
246C3×D4—202no—
247C3×D4—201no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C2×C3×C4C2×C4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254#67—204no—
255C2×Dic3—22no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—204no—
260C4×D3—101no—
261C4×D3—101no—
262C4×D3—101no—
263C4×D3—101no—
264C4×D3—201no—
265Dic6—41no—
266Dic6—41no—
267C3×C8—41no—
268C3×C8—201no—
269C3⋊C8—41no—
270C3⋊C8—201no—
271C22×C5D3×C22⋊C411yescharacteristic
272C2×D5—42no—
273C2×D5—42no—
274C2×D5—42no—
275C2×D5—61no—
276C2×D5—61no—
277C2×D5—61no—
278C4×C5—21no—
279C4×C5—122no—
280C4×C5#91111yescharacteristic
281C4×C5#91211yescharacteristic
282C4×C5#91411yescharacteristic
283C4×C5#91611yescharacteristic
284Dic5—61no—
285Dic5—61no—
286Dic5—61no—
287#41—602no—
288#41—602no—
289C2×Q8—61no—
290C2×D4—52no—
291C2×D4—101no—
292C2×D4—101no—
293C2×D4—302no—
294C22×C4—151no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—302no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—101no—
301C2×C8—301no—
302C4⋊C4—32no—
303C4⋊C4—61no—
304C22⋊C4—302no—
305C22⋊C4—302no—
306C42—151no—
307C42—151no—
308C42—151no—
309C42C2×D3×D511yescharacteristic
310C3×C5#155311yescharacteristic, complemented, Hall
311C22×C3—202no—
312C22×C3—202no—
313C22×C3—202no—
314C22×C3D5×C22⋊C411yescharacteristic
315C2×D3—101no—
316C2×D3—101no—
317C2×D3—101no—
318C3×C4—21no—
319C3×C4#405711yescharacteristic
320C3×C4#406011yescharacteristic
321C3×C4#406211yescharacteristic
322C3×C4#406511yescharacteristic
323Dic3—42no—
324Dic3—101no—
325Dic3—101no—
326Dic3—101no—
327C2×C5#474511yescharacteristic
328C2×C5#477011yescharacteristic
329C2×C5#477211yescharacteristic
330D5—82no—
331D5—121no—
332C23—102no—
333C23—151no—
334Q8—121no—
335Q8—121no—
336D4—202no—
337D4—201no—
338D4—201no—
339D4—201no—
340D4—201no—
341D4—604no—
342C2×C4—62no—
343C2×C4—151no—
344C2×C4—151no—
345C2×C4—151no—
346C2×C4—301no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4—301no—
350C2×C4—601no—
351C2×C4—604no—
352C2×C4C4×D3×D511yescharacteristic
353C2×C4#677711yescharacteristic
354C2×C4#679011yescharacteristic
355C8—41no—
356C8—121no—
357C8—201no—
358C8—601no—
359C2×C3—402no—
360C2×C3#6504011yescharacteristic
361C2×C3#6505911yescharacteristic
362C2×C3#6509311yescharacteristic
363D3—201no—
364C5#6838611yescharacteristic, complemented, Sylow
365C22—202no—
366C22—202no—
367C22—202no—
368C22—301no—
369C22—301no—
370C22—301no—
371C22#9147311yescharacteristic
372C4—21no—
373C4—122no—
374C4—301no—
375C4—301no—
376C4—301no—
377C4#9125711yescharacteristic
378C4#9125811yescharacteristic
379C4#9149711yescharacteristic
380C4#9152111yescharacteristic
381C3#1059921911yescharacteristic, complemented, Sylow
382C2—402no—
383C2—601no—
384C2#1174750611yescharacteristic
385C2#1174810911yescharacteristic
386C2#1174823811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11752556C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1553
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. #11746859C2semidirect
4. C5×#4486C2semidirect
5. C3×#64705C2semidirect
6. #11745858C2semidirect
7. #11745852C2semidirect
33. #64705D3semidirect
62. #4486D5semidirect
310. C3×C5#1553semidirect
364. C5#68386semidirect
381. C3#10599219semidirect

Maximal subgroups

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

subgroupindex
#117525562
#117509362
#117468592
C5×#44862
C3×#647052
#117458582
#117458522
#105992193
#683865