Finite Group Databasebeta

← #14283940

Subgroups — #14283940

Order 1920.

468 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756439C211yesmaximal, characteristic
2#11746983C211yesmaximal, characteristic, complemented
3#11746844C211yesmaximal, characteristic, complemented
4C5×#4540C211yesmaximal, characteristic, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745851C211yesmaximal, characteristic, complemented
8#10599134—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10#91835C411yescharacteristic
11Q8×Dic15C411yescharacteristic
12#91827C411yescharacteristic
13D4×Dic15C411yescharacteristic
14#91772—21no—
15#91770—21no—
16#91768—21no—
17#91766—21no—
18C42×D15C2211yescharacteristic
19#91759C2211yescharacteristic
20C2×#6651—21no—
21C2×#6648—21no—
22C5×#803C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25C3×#3935C2211yescharacteristic
26#90954—21no—
27#90951—21no—
28#68341—51nomaximal, Hall
29#66014—31no—
30#64996—31no—
31D5×#97—31no—
32C5×#329—31no—
33#64760D311yescharacteristic, complemented
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×#1220—21no—
39C22×Dic15—21no—
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×C4×D15D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46#6719—21no—
47#6719—21no—
48#6714—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C4⋊Dic15C2×C411yescharacteristic
52#6712—21no—
53#6712—21no—
54#6712—21no—
55C4×Dic15—21no—
56C4×Dic15C2×C411yescharacteristic
57C4×Dic15D411yescharacteristic
58C4×Dic15D411yescharacteristic
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63#6651—24no—
64#6648—24no—
65#5680—51no—
66#4707—51no—
67D3×#97—51no—
68C3×#329—51no—
69#4540D511yescharacteristic, complemented
70#4465—51no—
71#4465—51no—
72C5×#124C2×D311yescharacteristic
73#4092—31no—
74Q8×Dic5—31no—
75#4084—31no—
76D4×Dic5—31no—
77C2×#676—61no—
78C2×C8×D5—61no—
79#4029—61no—
80#4027—61no—
81#4025—61no—
82#4023—61no—
83C42×D5—31no—
84#4016—31no—
85C5×#97—31no—
86C5×#97—31no—
87#3947—61no—
88C8×Dic5—61no—
89#3935C2×D311yescharacteristic
90#3935C2×D311yescharacteristic
91#1524—151noSylow
92C23×C3×C5—21no—
93C22×D15C22⋊C411yescharacteristic
94C3×C5×Q8—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100#1220—42no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—42no—
104C2×Dic15C22⋊C411yescharacteristic
105C2×Dic15C22⋊C411yescharacteristic
106C2×Dic15C22⋊C411yescharacteristic
107C4×D15—22no—
108C4×D15—22no—
109C4×D15—41no—
110C3×#168—22no—
111C3×#168—22no—
112C5×C3⋊C8—22no—
113C5×C3⋊C8—22no—
114C3×#124C2×D511yescharacteristic
115#946—51no—
116Q8×Dic3—51no—
117#938—51no—
118D4×Dic3—51no—
119C2×ΓL(1,𝔽25)—101no—
120C2×D3×C8—101no—
121#883—101no—
122#67⋊C4—101no—
123#879—101no—
124#877—101no—
125C42×D3—51no—
126#870—51no—
127C3×#97—51no—
128C3×#97—51no—
129#815—101no—
130C8×Dic3—101no—
131#803C2×D511yescharacteristic
132#803C2×D511yescharacteristic
133C2×C5×Q8C4×D311yescharacteristic
134C2×C5×D4C4×D311yescharacteristic
135C2×C22⋊D5—61no—
136C22×Dic5—61no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—61no—
146C22⋊Dic5—61no—
147#685—61no—
148C4⋊Dic5—31no—
149C4⋊Dic5—31no—
150C4⋊Dic5—61no—
151#683—61no—
152#683—61no—
153#683—61no—
154C4×Dic5—31no—
155C4×Dic5—31no—
156C4×Dic5—31no—
157C4×Dic5—61no—
158C2×#168—21no—
159C2×#168—21no—
160#676—64no—
161C8×D5—64no—
162#529—151no—
163C4×M16—151no—
164C2×#97—151no—
165#330—151no—
166#330—151no—
167#329—31no—
168#329—51no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×D15—21no—
174C2×D15—21no—
175C2×D15#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180Dic15—21no—
181Dic15—21no—
182Dic15—41no—
183Dic15—41no—
184Dic15#10412yes—
185C2×C3×Q8C4×D511yescharacteristic
186C2×C3×D4C4×D511yescharacteristic
187C2×#67—101no—
188C22×Dic3—101no—
189C2×C4×D3—51no—
190C2×C4×D3—51no—
191C2×C4×D3—51no—
192C2×C3×C8—101no—
193C2×C3×C8—101no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C42C22×D511yescharacteristic
197#217—101no—
198#217—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—51no—
201C4⋊Dic3—51no—
202C4⋊Dic3—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206C4×Dic3—51no—
207C4×Dic3—51no—
208C4×Dic3—51no—
209C4×Dic3—101no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212ΓL(1,𝔽25)—104no—
213D3×C8—104no—
214C23×C5—21no—
215C22×D5—31no—
216C5×Q8—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5C2×C4×D311yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C22⋊D5—122no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—61no—
227C2×Dic5—61no—
228C2×Dic5—122no—
229C4×D5—62no—
230C4×D5—62no—
231C4×D5—121no—
232C5×C8—62no—
233C5×C8—62no—
234#168—22no—
235#168—22no—
236C2×M16—301no—
237C22×C8—301no—
238#126—301no—
239#125—151no—
240#124D3×D511yescharacteristic
241#123—301no—
242C22⋊Q8—151no—
243#121—151no—
244C4×Q8—151no—
245C4×D4—151no—
246C4×D4—301no—
247#117—301no—
248C2×C42—151no—
249#97—31no—
250#97—31no—
251#97—51no—
252#97—51no—
253#97—301no—
254C4×C8—301no—
255C2×C3×C5—81no—
256C2×C3×C5#41311yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258C2×C3×C5C2×#10411yescharacteristic
259D15—22no—
260C23×C3—21no—
261C22×D3—51no—
262C3×Q8—41no—
263C3×D4—41no—
264C2×C3×C4—21no—
265C2×C3×C4C2×C4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268#67—202no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—101no—
273C2×Dic3—101no—
274C2×Dic3—202no—
275C4×D3—102no—
276C4×D3—102no—
277C4×D3—201no—
278C3×C8—102no—
279C3×C8—102no—
280C3⋊C8—22no—
281C3⋊C8—22no—
282C22×C5—41no—
283C22×C5—41no—
284C22×C5—41no—
285C22×C5D3×C22⋊C411yescharacteristic
286C2×D5—32no—
287C2×D5—61no—
288C2×D5—61no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—41no—
293Dic5—32no—
294Dic5—61no—
295Dic5—61no—
296Dic5—121no—
297Dic5—121no—
298C2×Q8#120011yescharacteristic
299C2×D4—301no—
300C2×D4#120011yescharacteristic
301C22×C4—151no—
302C22×C4—151no—
303C22×C4—151no—
304C22×C4—301no—
305M16—304no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—101no—
309C2×C8—101no—
310C2×C8—304no—
311C4⋊C4—151no—
312C4⋊C4—151no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—301no—
320C22⋊C4—301no—
321C22⋊C4—301no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—301no—
326C42C2×D3×D511yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3D5×C22⋊C411yescharacteristic
332C2×D3—52no—
333C2×D3—101no—
334C2×D3—101no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339Dic3—52no—
340Dic3—101no—
341Dic3—101no—
342Dic3—201no—
343Dic3—201no—
344C2×C5—81no—
345C2×C5#474511yescharacteristic
346C2×C5D3×#10411yescharacteristic
347C2×C5D3×#10411yescharacteristic
348D5—62no—
349C23—21no—
350C23—151no—
351Q8—41no—
352D4—41no—
353D4—602no—
354C2×C4—21no—
355C2×C4—151no—
356C2×C4—151no—
357C2×C4—151no—
358C2×C4—302no—
359C2×C4—302no—
360C2×C4—301no—
361C2×C4—301no—
362C2×C4—601no—
363C2×C4—602no—
364C2×C4C2×#120011yescharacteristic
365C2×C4#679011yescharacteristic
366C2×C4#679011yescharacteristic
367C8—62no—
368C8—62no—
369C8—102no—
370C8—102no—
371C2×C3—81no—
372C2×C3#6503411yescharacteristic
373C2×C3D5×#10411yescharacteristic
374C2×C3D5×#10411yescharacteristic
375D3—102no—
376C5#6834111yescharacteristic, complemented, Sylow
377C22—41no—
378C22—41no—
379C22—41no—
380C22—152no—
381C22—301no—
382C22—301no—
383C22#9156111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—152no—
389C4—301no—
390C4—301no—
391C4—601no—
392C4—601no—
393C3#1059913411yescharacteristic, complemented, Sylow
394C2—81no—
395C2—302no—
396C2#1174912811yescharacteristic
397C2#1174943011yescharacteristic
398C2#1174943011yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1524
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11746983C2semidirect
3. #11746844C2semidirect
4. C5×#4540C2semidirect
5. C3×#64760C2semidirect
6. #11745851C2semidirect
7. #11745851C2semidirect
33. #64760D3semidirect
69. #4540D5semidirect
327. C3×C5#1524semidirect
376. C5#68341semidirect
393. C3#10599134semidirect

Maximal subgroups

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

subgroupindex
#117564392
#117469832
#117468442
C5×#45402
C3×#647602
#117458512
#105991343
#683415