Subgroups — D₅⋊#4717 #14418003

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊#901	C₂	1	2	yes	maximal, complemented
2	D₅×#904	C₂	1	1	yes	maximal, characteristic
3	D₅⋊#819	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3992	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅⋊#805	C₂	1	2	yes	maximal, complemented
6	#11751684	C₂	1	2	yes	maximal, complemented
7	#11751682	C₂	1	2	yes	maximal, complemented
8	#11751681	C₂	1	4	yes	maximal, complemented
9	D₅⋊#444	—	3	1	no	maximal, Hall
10	D₅×#235	C₂²	1	2	yes	—
11	D₅⋊#208	C₂²	1	2	yes	—
12	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
14	#91927	—	2	4	no	—
15	D₅⋊ΓL(1,𝔽₂₅)	—	2	2	no	—
16	#91914	C₂²	1	4	yes	complemented
17	#91911	C₂²	1	4	yes	complemented
18	D₃×D₅⋊C₈	—	2	2	no	—
19	#91793	C₄	1	1	yes	characteristic, complemented
20	C₅×#904	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	#91303	C₄	1	2	yes	complemented
23	#91271	C₂²	1	1	yes	characteristic
24	#91270	C₂²	1	1	yes	characteristic
25	#91269	C₂²	1	2	yes	—
26	D₅×Dic₁₂	C₄	1	1	yes	characteristic, complemented
27	D₅×D₂₄	C₄	1	1	yes	characteristic, complemented
28	D₅×#204	C₄	1	2	yes	complemented
29	#91225	C₂²	1	2	yes	complemented
30	#91224	C₂²	1	2	yes	complemented
31	C₃×#3992	C₂²	1	2	yes	complemented
32	C₃×#3992	C₂²	1	2	yes	complemented
33	#91158	C₂²	1	4	yes	complemented
34	#91156	C₂²	1	4	yes	complemented
35	C₂×#4717	—	5	1	no	maximal, Hall
36	D₅⋊#131	—	3	2	no	—
37	D₅×#135	—	3	1	no	—
38	D₅⋊#104	—	3	2	no	—
39	#65741	—	3	2	no	—
40	#65737	—	3	4	no	—
41	#65733	—	3	2	no	—
42	D₅⋊#108	—	3	1	no	—
43	C₂×#3992	D₃	1	1	yes	characteristic, complemented
44	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
45	#6817	C₂×C₄	1	2	yes	—
46	C₅×#235	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
48	D₅×#67	—	2	2	no	—
49	#6782	—	2	2	no	—
50	D₅×D₁₂	C₂×C₄	1	2	yes	—
51	C₄×D₃×D₅	—	2	2	no	—
52	#6773	C₂³	1	2	yes	—
53	#6772	C₂³	1	2	yes	—
54	#6771	—	2	2	no	—
55	D₅×Dic₆	C₂×C₄	1	2	yes	—
56	#6762	—	2	2	no	—
57	#6758	C₂³	1	4	yes	—
58	D₅⋊(C₃⋊C₈)	—	2	2	no	—
59	C₂×C₃×#170	D₄	1	2	yes	—
60	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
61	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
62	C₃×D₅⋊C₈	D₄	1	2	yes	—
63	C₃×D₅⋊C₈	C₂³	1	2	yes	—
64	#6740	—	2	4	no	—
65	#6739	—	2	4	no	—
66	#6738	—	2	4	no	—
67	D₃×#170	—	2	4	no	—
68	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
69	Dic₆₀	C₂×C₄	1	1	yes	characteristic, complemented
70	D₁₂₀	C₂×C₄	1	1	yes	characteristic, complemented
71	#6706	C₂×C₄	1	2	yes	complemented
72	C₅×Dic₁₂	C₂×C₄	1	1	yes	characteristic, complemented
73	C₅×D₂₄	C₂×C₄	1	1	yes	characteristic, complemented
74	C₅×#204	C₂×C₄	1	2	yes	complemented
75	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
76	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
77	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
79	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
80	#6663	C₂×C₄	1	2	yes	complemented
81	#6660	C₂×C₄	1	2	yes	complemented
82	#6659	C₂×C₄	1	2	yes	complemented
83	#6654	C₂×C₄	1	2	yes	complemented
84	C₂×#904	—	5	1	no	—
85	C₂×#901	—	5	2	no	—
86	C₂×C₃×#97	—	5	1	no	—
87	C₂×#819	—	5	1	no	—
88	C₂×#805	—	5	2	no	—
89	#4717	—	5	4	no	—
90	#4717	—	5	2	no	—
91	#4717	—	5	2	no	—
92	D₅×#41	—	3	2	no	—
93	#4133	—	3	4	no	—
94	#4131	—	3	4	no	—
95	#4131	—	6	4	no	—
96	C₂×C₄×AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
97	D₅⋊M₁₆	—	3	2	no	—
98	D₅⋊M₁₆	—	6	2	no	—
99	C₂×D₅⋊C₈	—	6	2	no	—
100	C₂×D₅⋊C₈	C₂×D₃	1	1	yes	characteristic
101	C₅×#135	—	3	1	no	—
102	#4096	—	3	2	no	—
103	#4065	—	3	1	no	—
104	D₅×Q₁₆	—	3	1	no	—
105	#4062	—	3	2	no	—
106	D₅×SD₁₆	—	3	2	no	—
107	#4058	—	3	1	no	—
108	D₅×D₈	—	3	1	no	—
109	#4050	—	3	1	no	—
110	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
111	#4010	—	3	4	no	—
112	#4008	—	3	4	no	—
113	#3996	—	3	2	no	—
114	#3995	—	3	2	no	—
115	#3992	C₂×D₃	1	2	yes	complemented
116	#3992	C₂×D₃	1	2	yes	complemented
117	C₂×#444	—	15	1	no	Sylow
118	C₂²×C₃×D₅	#41	1	1	yes	characteristic
119	C₂×D₃×D₅	—	2	2	no	—
120	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
121	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	#1220	—	2	2	no	—
124	D₆₀	C₂²×C₄	1	2	yes	—
125	C₄×D₁₅	—	2	2	no	—
126	Dic₃₀	C₂²×C₄	1	2	yes	—
127	C₅×#67	—	2	2	no	—
128	C₅×D₁₂	C₂²×C₄	1	2	yes	—
129	C₄×C₅×D₃	—	2	2	no	—
130	C₅×Dic₆	C₂²×C₄	1	2	yes	—
131	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
132	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
133	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₄×D₅	#41	1	1	yes	characteristic
135	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
136	#1204	—	2	2	no	—
137	#1203	—	2	2	no	—
138	#1202	—	2	2	no	—
139	#1201	—	2	2	no	—
140	#1200	—	2	2	no	—
141	D₃×Dic₅	—	2	2	no	—
142	D₅×Dic₃	—	2	2	no	—
143	C₃⋊#170	—	2	4	no	—
144	C₃×#170	C₂×D₄	1	4	yes	—
145	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₃×#168	C₂²×C₄	1	1	yes	characteristic
148	C₃×#168	C₂²×C₄	1	1	yes	characteristic
149	C₂×#235	—	5	2	no	—
150	C₂²×C₃×C₈	—	5	1	no	—
151	C₂²×C₃×C₈	—	5	1	no	—
152	C₂×C₃×C₄²	—	5	1	no	—
153	C₂×#208	—	5	2	no	—
154	C₂×Dic₁₂	—	5	1	no	—
155	#904	—	5	2	no	—
156	#904	—	5	1	no	—
157	#904	—	5	1	no	—
158	#904	—	5	1	no	—
159	#904	—	5	2	no	—
160	#904	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
161	C₂×D₂₄	—	5	1	no	—
162	C₂×#204	—	5	2	no	—
163	#901	—	5	4	no	—
164	#901	—	5	4	no	—
165	#901	—	10	4	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
167	C₂×D₃×C₈	—	10	2	no	—
168	C₃×#97	—	5	2	no	—
169	C₃×#97	—	5	2	no	—
170	#819	—	5	2	no	—
171	#819	—	5	2	no	—
172	#805	—	5	4	no	—
173	#805	—	5	4	no	—
174	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
175	C₅×#41	—	3	2	no	—
176	#713	—	3	2	no	—
177	Q₈×D₅	—	3	2	no	—
178	#711	—	3	2	no	—
179	#711	—	6	2	no	—
180	D₄×D₅	—	3	2	no	—
181	D₄×D₅	—	6	2	no	—
182	#709	—	3	2	no	—
183	#709	—	6	2	no	—
184	C₂×C₄×D₅	—	6	2	no	—
185	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
186	#704	—	6	2	no	—
187	#704	—	6	4	no	—
188	C₂×#170	—	6	4	no	—
189	C₂×#170	D₁₂	1	2	yes	—
190	C₄×AGL(1,𝔽₅)	—	2	1	no	—
191	C₄×AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
192	#700	—	3	4	no	—
193	#700	—	6	4	no	—
194	D₅⋊C₈	—	6	2	no	—
195	D₅⋊C₈	—	6	4	no	—
196	D₅⋊C₈	D₁₂	1	2	yes	—
197	D₅⋊C₈	C₂²×D₃	1	2	yes	—
198	C₅×Q₁₆	—	3	1	no	—
199	C₅×SD₁₆	—	3	2	no	—
200	C₅×D₈	—	3	1	no	—
201	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
202	#689	—	3	2	no	—
203	#688	—	3	2	no	—
204	#687	—	3	2	no	—
205	#686	—	3	2	no	—
206	C₂×#168	C₄×D₃	1	1	yes	characteristic
207	Dic₂₀	—	3	1	no	—
208	D₄₀	—	3	1	no	—
209	#677	—	3	2	no	—
210	C₈×D₅	C₄×D₃	1	1	yes	characteristic
211	C₈×D₅	C₄×D₃	1	1	yes	characteristic
212	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
213	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
214	C₂×#135	—	15	1	no	—
215	C₂×#131	—	15	2	no	—
216	#444	—	15	2	no	—
217	#444	—	15	4	no	—
218	#444	—	15	2	no	—
219	C₂×#108	—	15	1	no	—
220	C₂×#104	—	15	2	no	—
221	C₂×#97	—	5	1	no	—
222	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
223	C₂×D₁₅	—	2	2	no	—
224	C₂×C₅×D₃	—	2	2	no	—
225	C₂×C₃×D₅	—	2	2	no	—
226	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
228	D₃×D₅	—	4	4	no	—
229	C₃×AGL(1,𝔽₅)	—	4	2	no	—
230	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
231	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
232	Dic₁₅	—	2	2	no	—
233	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
234	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
235	C₅×Dic₃	—	2	2	no	—
236	C₂²×C₃×C₄	—	5	1	no	—
237	C₂²×C₃×C₄	—	10	1	no	—
238	C₂×#67	—	10	2	no	—
239	#235	—	5	2	no	—
240	#235	—	5	2	no	—
241	#235	—	5	2	no	—
242	#235	—	10	2	no	—
243	#235	—	10	2	no	—
244	#235	C₂×AGL(1,𝔽₅)	1	2	yes	—
245	C₂×D₁₂	—	5	2	no	—
246	C₂×C₄×D₃	—	10	2	no	—
247	C₂×Dic₆	—	5	2	no	—
248	C₂×C₃×C₈	—	5	2	no	—
249	C₂×C₃×C₈	—	5	2	no	—
250	C₂×C₃×C₈	—	5	2	no	—
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
257	C₃×C₄²	—	5	2	no	—
258	C₃×C₄²	—	10	1	no	—
259	#208	—	5	4	no	—
260	#208	—	10	2	no	—
261	C₂×C₃⋊C₈	—	10	2	no	—
262	Dic₁₂	—	5	2	no	—
263	Dic₁₂	—	5	1	no	—
264	Dic₁₂	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
265	D₂₄	—	5	2	no	—
266	D₂₄	—	5	1	no	—
267	D₂₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
268	#204	—	5	2	no	—
269	#204	—	5	2	no	—
270	#204	—	5	2	no	—
271	#204	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
272	ΓL(1,𝔽₂₅)	—	10	4	no	—
273	ΓL(1,𝔽₂₅)	—	10	4	no	—
274	D₃×C₈	—	10	4	no	—
275	D₃×C₈	—	10	4	no	—
276	C₂²×D₅	—	6	2	no	—
277	C₂²×D₅	#235	1	1	yes	characteristic
278	C₂×AGL(1,𝔽₅)	—	2	2	no	—
279	C₂×AGL(1,𝔽₅)	—	4	2	no	—
280	C₅×Q₈	—	3	2	no	—
281	C₅×D₄	—	3	2	no	—
282	C₅×D₄	—	6	2	no	—
283	C₂×C₄×C₅	—	6	2	no	—
284	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂²⋊D₅	—	6	2	no	—
286	C₂²⋊D₅	—	6	2	no	—
287	C₂²⋊D₅	—	6	2	no	—
288	C₂×Dic₅	—	6	2	no	—
289	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
290	D₂₀	—	3	2	no	—
291	D₂₀	—	6	2	no	—
292	C₄×D₅	—	6	2	no	—
293	C₄×D₅	—	6	2	no	—
294	C₄×D₅	—	6	2	no	—
295	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
296	C₄×D₅	C₂×D₁₂	1	1	yes	characteristic
297	C₄×D₅	#235	1	1	yes	characteristic
298	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
299	Dic₁₀	—	3	2	no	—
300	Dic₁₀	—	6	2	no	—
301	#170	—	6	4	no	—
302	#170	C₂×D₁₂	1	4	yes	—
303	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
304	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
305	#168	C₂×C₄×D₃	1	1	yes	characteristic
306	#168	C₂×C₄×D₃	1	1	yes	characteristic
307	C₂×#41	—	15	2	no	—
308	#135	—	3	1	no	—
309	#135	—	15	1	no	—
310	#135	—	15	2	no	—
311	#135	—	15	1	no	—
312	#135	—	15	2	no	—
313	#135	—	15	1	no	—
314	C₂×Q₁₆	—	15	1	no	—
315	C₂×SD₁₆	—	15	2	no	—
316	C₂×D₈	—	15	1	no	—
317	#131	—	15	4	no	—
318	#131	—	15	4	no	—
319	#131	—	30	4	no	—
320	C₂×M₁₆	—	15	2	no	—
321	C₂×M₁₆	—	30	2	no	—
322	C₂²×C₈	—	5	1	no	—
323	C₂²×C₈	—	5	1	no	—
324	C₂²×C₈	—	30	2	no	—
325	C₂×C₄²	—	5	1	no	—
326	#108	—	15	2	no	—
327	#108	—	15	2	no	—
328	#104	—	15	4	no	—
329	#104	—	15	4	no	—
330	#97	—	5	2	no	—
331	#97	—	5	2	no	—
332	C₂×C₃×C₅	—	2	1	no	—
333	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	D₁₅	—	4	2	no	—
335	C₃×D₅	—	2	1	no	—
336	C₃×D₅	#444	1	2	yes	complemented
337	C₅×D₃	—	4	2	no	—
338	C₂³×C₃	—	5	1	no	—
339	C₂²×D₃	—	10	2	no	—
340	C₂×C₃×C₄	—	5	1	no	—
341	C₂×C₃×C₄	—	5	1	no	—
342	C₂×C₃×C₄	—	5	1	no	—
343	C₂×C₃×C₄	—	5	1	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	10	2	no	—
346	C₂×C₃×C₄	—	20	2	no	—
347	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
348	#67	—	2	2	no	—
349	#67	—	10	2	no	—
350	#67	—	10	2	no	—
351	#67	—	10	2	no	—
352	C₂×Dic₃	—	10	2	no	—
353	D₁₂	—	5	2	no	—
354	D₁₂	—	10	2	no	—
355	D₁₂	C₂²×AGL(1,𝔽₅)	1	2	yes	—
356	C₄×D₃	—	2	2	no	—
357	C₄×D₃	—	10	2	no	—
358	C₄×D₃	—	10	2	no	—
359	C₄×D₃	—	10	2	no	—
360	Dic₆	—	5	2	no	—
361	Dic₆	—	10	2	no	—
362	Dic₆	C₂²×AGL(1,𝔽₅)	1	2	yes	—
363	C₃×C₈	—	5	4	no	—
364	C₃×C₈	—	5	1	no	—
365	C₃×C₈	—	5	1	no	—
366	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₃⋊C₈	—	10	4	no	—
369	C₂²×C₅	—	6	2	no	—
370	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
371	C₂×D₅	—	2	2	no	—
372	C₂×D₅	—	6	2	no	—
373	C₂×D₅	—	12	4	no	—
374	C₂×D₅	C₄×D₁₂	1	1	yes	characteristic
375	C₂×D₅	C₂×#235	1	1	yes	characteristic
376	AGL(1,𝔽₅)	—	4	2	no	—
377	C₄×C₅	—	6	2	no	—
378	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
379	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
380	Dic₅	—	6	2	no	—
381	Dic₅	C₄×D₁₂	1	1	yes	characteristic
382	Dic₅	C₂²×D₁₂	1	1	yes	characteristic
383	#41	—	3	2	no	—
384	#41	—	15	2	no	—
385	#41	—	15	2	no	—
386	#41	—	15	2	no	—
387	#41	—	30	2	no	—
388	#41	—	30	2	no	—
389	C₂×Q₈	—	15	2	no	—
390	C₂×D₄	—	15	2	no	—
391	C₂×D₄	—	30	2	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	10	1	no	—
394	C₂²×C₄	—	30	2	no	—
395	Q₁₆	—	3	1	no	—
396	Q₁₆	—	15	2	no	—
397	Q₁₆	—	15	1	no	—
398	SD₁₆	—	3	2	no	—
399	SD₁₆	—	15	2	no	—
400	SD₁₆	—	15	2	no	—
401	SD₁₆	—	15	2	no	—
402	D₈	—	3	1	no	—
403	D₈	—	15	2	no	—
404	D₈	—	15	1	no	—
405	M₁₆	—	15	4	no	—
406	M₁₆	—	30	4	no	—
407	M₁₆	—	30	4	no	—
408	M₁₆	—	30	2	no	—
409	C₂×C₈	—	5	2	no	—
410	C₂×C₈	—	5	2	no	—
411	C₂×C₈	—	5	2	no	—
412	C₂×C₈	—	5	1	no	—
413	C₂×C₈	—	5	1	no	—
414	C₂×C₈	—	5	1	no	—
415	C₂×C₈	—	5	1	no	—
416	C₂×C₈	—	5	1	no	—
417	C₂×C₈	—	30	4	no	—
418	C₂×C₈	—	30	4	no	—
419	C₂×C₈	—	30	2	no	—
420	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₄²	—	5	2	no	—
422	C₄²	—	10	1	no	—
423	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	5	1	no	—
425	C₂²×C₃	—	5	1	no	—
426	C₂²×C₃	—	10	2	no	—
427	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	—	10	2	no	—
430	C₂×D₃	—	20	4	no	—
431	C₃×C₄	—	5	1	no	—
432	C₃×C₄	—	5	1	no	—
433	C₃×C₄	—	20	2	no	—
434	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
435	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
436	Dic₃	—	2	2	no	—
437	Dic₃	—	10	2	no	—
438	C₂×C₅	—	2	1	no	—
439	C₂×C₅	—	12	2	no	—
440	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
441	D₅	—	2	1	no	—
442	D₅	—	12	2	no	—
443	D₅	#4717	1	2	yes	complemented
444	C₂³	—	5	1	no	—
445	C₂³	—	30	2	no	—
446	Q₈	—	3	2	no	—
447	Q₈	—	15	2	no	—
448	Q₈	—	30	2	no	—
449	D₄	—	3	2	no	—
450	D₄	—	6	2	no	—
451	D₄	—	15	2	no	—
452	D₄	—	30	2	no	—
453	D₄	—	30	2	no	—
454	D₄	—	30	2	no	—
455	D₄	—	30	2	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	6	2	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	20	2	no	—
464	C₂×C₄	—	30	2	no	—
465	C₂×C₄	—	30	2	no	—
466	C₂×C₄	—	30	2	no	—
467	C₂×C₄	—	30	2	no	—
468	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
469	C₈	—	5	4	no	—
470	C₈	—	5	1	no	—
471	C₈	—	5	1	no	—
472	C₈	—	30	4	no	—
473	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
474	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	—	5	2	no	—
477	C₂×C₃	—	10	1	no	—
478	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
479	D₃	—	4	2	no	—
480	D₃	—	20	2	no	—
481	C₅	C₂×#4717	1	1	yes	characteristic, complemented, Sylow
482	C₂²	—	5	1	no	—
483	C₂²	—	5	1	no	—
484	C₂²	—	6	2	no	—
485	C₂²	—	10	2	no	—
486	C₂²	—	30	2	no	—
487	C₂²	—	60	4	no	—
488	C₂²	AGL(1,𝔽₅)×D₁₂	1	1	yes	characteristic
489	C₄	—	5	1	no	—
490	C₄	—	5	1	no	—
491	C₄	—	6	2	no	—
492	C₄	—	20	2	no	—
493	C₄	—	30	2	no	—
494	C₄	AGL(1,𝔽₅)×D₁₂	1	1	yes	characteristic
495	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
496	C₃	D₅⋊#444	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	2	1	no	—
498	C₂	—	5	2	no	—
499	C₂	—	10	1	no	—
500	C₂	—	12	2	no	—
501	C₂	—	60	2	no	—
502	C₂	C₂×AGL(1,𝔽₅)×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	AGL(1,𝔽₅)×D₁₂
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	D₅×#904	C₂
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#444
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. D₅⋊#901	C₂	semidirect
3. D₅⋊#819	C₂	semidirect
4. C₂×C₃×#3992	C₂	semidirect
5. D₅⋊#805	C₂	semidirect
6. #11751684	C₂	semidirect
7. #11751682	C₂	semidirect
8. #11751681	C₂	semidirect
16. #91914	C₂²	semidirect
17. #91911	C₂²	semidirect
19. #91793	C₄	semidirect
20. C₅×#904	C₄	semidirect
22. #91303	C₄	semidirect
26. D₅×Dic₁₂	C₄	semidirect
27. D₅×D₂₄	C₄	semidirect
28. D₅×#204	C₄	semidirect
29. #91225	C₂²	semidirect
30. #91224	C₂²	semidirect
31. C₃×#3992	C₂²	semidirect
32. C₃×#3992	C₂²	semidirect
33. #91158	C₂²	semidirect
34. #91156	C₂²	semidirect
43. C₂×#3992	D₃	semidirect
69. Dic₆₀	C₂×C₄	semidirect
70. D₁₂₀	C₂×C₄	semidirect
71. #6706	C₂×C₄	semidirect
72. C₅×Dic₁₂	C₂×C₄	semidirect
73. C₅×D₂₄	C₂×C₄	semidirect
74. C₅×#204	C₂×C₄	semidirect
80. #6663	C₂×C₄	semidirect
81. #6660	C₂×C₄	semidirect
82. #6659	C₂×C₄	semidirect
83. #6654	C₂×C₄	semidirect
115. #3992	C₂×D₃	semidirect
116. #3992	C₂×D₃	semidirect
160. #904	AGL(1,𝔽₅)	semidirect
264. Dic₁₂	C₂×AGL(1,𝔽₅)	semidirect
267. D₂₄	C₂×AGL(1,𝔽₅)	semidirect
271. #204	C₂×AGL(1,𝔽₅)	semidirect
336. C₃×D₅	#444	semidirect
423. C₃×C₅	C₂×#444	semidirect
443. D₅	#4717	semidirect
481. C₅	C₂×#4717	semidirect
496. C₃	D₅⋊#444	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊#901	2
D₅×#904	2
D₅⋊#819	2
C₂×C₃×#3992	2
D₅⋊#805	2
#11751684	2
#11751682	2
#11751681	2
D₅⋊#444	3
C₂×#4717	5

Subgroups — D5⋊#4717 #14418003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#4717 #14418003