Subgroups — D₅⋊#4907 #14478156

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 448 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	1	yes	maximal, characteristic
2	C₂×D₅⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751742	C₂	1	2	yes	maximal, complemented
5	#11751738	C₂	1	2	yes	maximal, complemented
6	D₅⋊#798	C₂	1	2	yes	maximal, complemented
7	#11751644	C₂	1	4	yes	maximal, complemented
8	D₃×D₅⋊C₁₆	C₂	1	2	yes	maximal, complemented
9	D₅⋊#504	—	3	1	no	maximal, Hall
10	D₅×#235	C₄	1	1	yes	characteristic
11	#91790	C₄	1	1	yes	characteristic
12	C₅×#901	C₄	1	1	yes	characteristic
13	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
14	#91290	C₂²	1	1	yes	characteristic
15	#91286	C₂²	1	1	yes	characteristic
16	D₅×#208	C₄	1	1	yes	characteristic
17	#91266	C₂²	1	2	yes	—
18	#91265	C₄	1	2	yes	—
19	D₅×ΓL(1,𝔽₂₅)	C₄	1	2	yes	—
20	D₃×C₈×D₅	C₂²	1	2	yes	—
21	C₂×C₃⋊#674	C₂²	1	2	yes	complemented
22	D₅⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
23	D₅⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
24	D₅⋊(C₃⋊C₁₆)	C₂²	1	2	yes	complemented
25	C₃×#3998	C₂²	1	2	yes	complemented
26	C₃×#3990	C₂²	1	2	yes	complemented
27	C₃×D₅⋊C₁₆	C₂²	1	2	yes	—
28	#91166	C₂²	1	4	yes	complemented
29	#91165	C₂²	1	4	yes	complemented
30	#91164	C₂²	1	4	yes	complemented
31	D₃×#674	C₂²	1	4	yes	complemented
32	C₂×#4907	—	5	1	no	maximal, Hall
33	D₅×#131	—	3	1	no	—
34	#65791	—	3	2	no	—
35	#65725	—	3	2	no	—
36	#65725	—	3	4	no	—
37	D₅⋊M₃₂	—	3	2	no	—
38	D₅⋊M₃₂	D₃	1	1	yes	characteristic, complemented
39	C₂×D₅⋊C₁₆	—	3	1	no	—
40	C₂×D₅⋊C₁₆	—	3	2	no	—
41	#6817	C₂×C₄	1	1	yes	characteristic
42	C₅×#235	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
44	D₅×#67	C₈	1	2	yes	—
45	#6782	C₈	1	2	yes	—
46	D₅×D₁₂	C₈	1	1	yes	characteristic
47	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
48	#6773	C₈	1	1	yes	characteristic
49	#6772	C₈	1	1	yes	characteristic
50	#6771	C₂×C₄	1	2	yes	—
51	D₅×Dic₆	C₈	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	#6710	C₂×C₄	1	1	yes	characteristic
54	#6705	C₂×C₄	1	2	yes	—
55	C₈×D₁₅	C₂×C₄	1	2	yes	—
56	C₅×#208	C₂×C₄	1	1	yes	characteristic
57	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
58	C₅×D₃×C₈	C₂×C₄	1	2	yes	—
59	C₂×C₃×#168	C₂³	1	1	yes	characteristic
60	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
63	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
64	#6651	C₂×C₄	1	2	yes	—
65	#6650	C₂×C₄	1	2	yes	—
66	#6649	C₂×C₄	1	2	yes	—
67	#6648	C₂³	1	2	yes	—
68	D₃×#168	C₂³	1	2	yes	—
69	D₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
70	C₃⋊#674	C₂³	1	2	yes	—
71	C₃⋊#674	C₂³	1	2	yes	—
72	C₃×#674	C₂³	1	4	yes	—
73	C₂×#901	—	5	1	no	—
74	C₂×C₃×M₃₂	—	5	1	no	—
75	C₂²×C₃⋊C₁₆	—	5	1	no	—
76	#4907	—	5	2	no	—
77	#4907	—	5	2	no	—
78	#4907	—	5	4	no	—
79	C₂×#798	—	5	2	no	—
80	C₂×D₃×C₁₆	—	5	2	no	—
81	D₅×#41	—	3	1	no	—
82	C₅×#131	—	3	1	no	—
83	#4094	—	3	1	no	—
84	#4053	—	3	1	no	—
85	#4053	—	3	2	no	—
86	D₅×M₁₆	—	3	1	no	—
87	D₅×M₁₆	—	3	2	no	—
88	#4047	—	3	1	no	—
89	#4047	—	3	2	no	—
90	C₂×C₈×D₅	—	3	2	no	—
91	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
92	#3998	—	3	4	no	—
93	#3998	C₂×D₃	1	2	yes	complemented
94	C₂×#674	—	3	2	no	—
95	C₂×#674	—	3	4	no	—
96	#3990	—	3	4	no	—
97	#3990	C₂×D₃	1	2	yes	complemented
98	D₅⋊C₁₆	—	3	1	no	—
99	D₅⋊C₁₆	—	3	1	no	—
100	D₅⋊C₁₆	—	3	2	no	—
101	D₅⋊C₁₆	—	3	4	no	—
102	D₅⋊C₁₆	C₂×D₃	1	2	yes	—
103	C₂×#504	—	15	1	no	Sylow
104	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
105	C₂×D₃×D₅	C₂×C₈	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	#1220	C₂×C₈	1	2	yes	—
108	D₆₀	C₂×C₈	1	1	yes	characteristic
109	C₄×D₁₅	C₂²×C₄	1	2	yes	—
110	Dic₃₀	C₂×C₈	1	1	yes	characteristic
111	C₅×#67	C₂×C₈	1	2	yes	—
112	C₅×D₁₂	C₂×C₈	1	1	yes	characteristic
113	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
114	C₅×Dic₆	C₂×C₈	1	1	yes	characteristic
115	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
116	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
117	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
118	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
119	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
120	#1204	C₂×C₈	1	2	yes	—
121	#1203	C₂×C₈	1	2	yes	—
122	#1202	C₂×C₈	1	2	yes	—
123	#1201	C₂×C₈	1	2	yes	—
124	#1200	C₂×C₈	1	2	yes	—
125	D₃×Dic₅	C₂×C₈	1	2	yes	—
126	D₅×Dic₃	C₂×C₈	1	2	yes	—
127	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₃⋊#168	C₂²×C₄	1	2	yes	—
130	C₃×#168	C₂²×C₄	1	1	yes	characteristic
131	C₃×#168	C₂⁴	1	1	yes	characteristic
132	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×#235	—	5	1	no	—
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₂×#208	—	5	1	no	—
136	#901	—	5	1	no	—
137	#901	—	5	1	no	—
138	#901	—	5	1	no	—
139	#901	—	5	2	no	—
140	#901	—	5	2	no	—
141	#901	AGL(1,𝔽₅)	1	1	yes	characteristic
142	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
143	C₂×D₃×C₈	—	5	2	no	—
144	C₃×M₃₂	—	5	2	no	—
145	C₃×M₃₂	—	5	2	no	—
146	C₂×C₃×C₁₆	—	5	2	no	—
147	C₂×C₃⋊C₁₆	—	5	1	no	—
148	C₂×C₃⋊C₁₆	—	5	1	no	—
149	C₂×C₃⋊C₁₆	—	5	2	no	—
150	C₂×C₃⋊C₁₆	—	5	2	no	—
151	#798	—	5	4	no	—
152	#798	—	5	4	no	—
153	D₃×C₁₆	—	5	4	no	—
154	D₃×C₁₆	—	5	4	no	—
155	C₅×#41	—	3	1	no	—
156	#713	—	3	1	no	—
157	Q₈×D₅	—	3	1	no	—
158	#711	—	3	2	no	—
159	#711	—	3	1	no	—
160	D₄×D₅	—	3	2	no	—
161	D₄×D₅	—	3	1	no	—
162	#709	—	3	1	no	—
163	#709	—	3	2	no	—
164	C₂×C₄×D₅	—	3	2	no	—
165	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
166	C₅×M₁₆	—	3	1	no	—
167	C₅×M₁₆	—	3	2	no	—
168	C₂×C₅×C₈	—	3	2	no	—
169	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
170	#681	—	3	1	no	—
171	#681	—	3	2	no	—
172	C₂×#168	—	3	2	no	—
173	C₂×#168	C₂²×D₃	1	1	yes	characteristic
174	#676	—	3	2	no	—
175	#676	—	3	2	no	—
176	#676	—	3	2	no	—
177	C₈×D₅	—	3	2	no	—
178	C₈×D₅	—	3	2	no	—
179	C₈×D₅	—	3	2	no	—
180	C₈×D₅	C₄×D₃	1	1	yes	characteristic
181	C₈×D₅	C₄×D₃	1	1	yes	characteristic
182	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
183	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
184	#674	—	3	2	no	—
185	#674	—	3	2	no	—
186	#674	C₂²×D₃	1	4	yes	—
187	C₂×#131	—	15	1	no	—
188	#504	—	15	2	no	—
189	#504	—	15	4	no	—
190	#504	—	15	2	no	—
191	C₂×M₃₂	—	5	1	no	—
192	C₂×M₃₂	—	15	2	no	—
193	C₂²×C₁₆	—	15	2	no	—
194	C₂²×C₁₆	—	15	1	no	—
195	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
196	C₂×D₁₅	C₂²×C₈	1	2	yes	—
197	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
198	C₂×C₃×D₅	—	2	2	no	—
199	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
200	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
201	D₃×D₅	—	2	4	no	—
202	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
203	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
204	Dic₁₅	C₂²×C₈	1	2	yes	—
205	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
206	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
207	C₅×Dic₃	C₂²×C₈	1	2	yes	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂×#67	—	5	2	no	—
210	#235	—	5	1	no	—
211	#235	—	5	2	no	—
212	#235	—	5	1	no	—
213	#235	—	5	2	no	—
214	#235	—	5	1	no	—
215	#235	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₂×D₁₂	—	5	1	no	—
217	C₂×C₄×D₃	—	5	2	no	—
218	C₂×Dic₆	—	5	1	no	—
219	C₂×C₃×C₈	—	5	1	no	—
220	C₂×C₃×C₈	—	5	1	no	—
221	C₂×C₃×C₈	—	5	1	no	—
222	C₂×C₃×C₈	—	5	1	no	—
223	C₂×C₃×C₈	—	5	1	no	—
224	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
225	#208	—	5	1	no	—
226	#208	—	5	2	no	—
227	#208	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
228	C₂×C₃⋊C₈	—	5	2	no	—
229	ΓL(1,𝔽₂₅)	—	5	2	no	—
230	ΓL(1,𝔽₂₅)	—	5	2	no	—
231	ΓL(1,𝔽₂₅)	—	5	2	no	—
232	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	2	yes	—
233	D₃×C₈	—	5	2	no	—
234	D₃×C₈	—	5	2	no	—
235	D₃×C₈	—	5	2	no	—
236	D₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
237	C₃×C₁₆	—	5	4	no	—
238	C₃⋊C₁₆	—	5	2	no	—
239	C₃⋊C₁₆	—	5	2	no	—
240	C₂²×D₅	—	3	2	no	—
241	C₂²×D₅	D₃×C₈	1	1	yes	characteristic
242	C₅×Q₈	—	3	1	no	—
243	C₅×D₄	—	3	2	no	—
244	C₅×D₄	—	3	1	no	—
245	C₂×C₄×C₅	—	3	2	no	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂²⋊D₅	—	3	2	no	—
248	C₂²⋊D₅	—	3	2	no	—
249	C₂²⋊D₅	—	3	2	no	—
250	C₂×Dic₅	—	3	2	no	—
251	C₂×Dic₅	D₃×C₈	1	1	yes	characteristic
252	D₂₀	—	3	2	no	—
253	D₂₀	—	3	1	no	—
254	C₄×D₅	—	3	2	no	—
255	C₄×D₅	—	3	2	no	—
256	C₄×D₅	—	3	2	no	—
257	C₄×D₅	D₃×C₈	1	1	yes	characteristic
258	C₄×D₅	D₃×C₈	1	1	yes	characteristic
259	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
260	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
261	Dic₁₀	—	3	1	no	—
262	Dic₁₀	—	3	2	no	—
263	C₅×C₈	—	3	2	no	—
264	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
265	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
266	#168	—	3	2	no	—
267	#168	C₂×C₄×D₃	1	1	yes	characteristic
268	#168	C₂³×D₃	1	1	yes	characteristic
269	C₂×#41	—	15	1	no	—
270	#131	—	3	1	no	—
271	#131	—	15	2	no	—
272	#131	—	15	1	no	—
273	#131	—	15	2	no	—
274	#131	—	15	1	no	—
275	#131	—	15	1	no	—
276	C₂×M₁₆	—	15	2	no	—
277	C₂×M₁₆	—	15	1	no	—
278	C₂²×C₈	—	5	1	no	—
279	C₂²×C₈	—	15	2	no	—
280	M₃₂	—	5	2	no	—
281	M₃₂	—	5	2	no	—
282	M₃₂	—	15	4	no	—
283	M₃₂	—	15	4	no	—
284	C₂×C₁₆	—	5	2	no	—
285	C₂×C₁₆	—	15	4	no	—
286	C₂×C₁₆	—	15	4	no	—
287	C₂×C₁₆	—	15	1	no	—
288	C₂×C₁₆	—	15	1	no	—
289	C₂×C₁₆	—	15	2	no	—
290	C₂×C₁₆	—	15	2	no	—
291	C₂×C₃×C₅	—	2	1	no	—
292	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
293	D₁₅	—	2	2	no	—
294	C₃×D₅	—	2	1	no	—
295	C₃×D₅	#504	1	2	yes	complemented
296	C₅×D₃	—	2	2	no	—
297	C₂³×C₃	—	5	1	no	—
298	C₂²×D₃	—	5	2	no	—
299	C₂×C₃×C₄	—	5	1	no	—
300	C₂×C₃×C₄	—	5	1	no	—
301	C₂×C₃×C₄	—	5	1	no	—
302	C₂×C₃×C₄	—	5	1	no	—
303	C₂×C₃×C₄	—	5	1	no	—
304	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
305	#67	—	5	2	no	—
306	#67	—	5	2	no	—
307	#67	—	5	2	no	—
308	#67	D₅⋊C₈	1	2	yes	—
309	C₂×Dic₃	—	5	2	no	—
310	D₁₂	—	5	2	no	—
311	D₁₂	—	5	1	no	—
312	D₁₂	D₅⋊C₈	1	1	yes	characteristic
313	C₄×D₃	—	5	2	no	—
314	C₄×D₃	—	5	2	no	—
315	C₄×D₃	—	5	2	no	—
316	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
317	Dic₆	—	5	1	no	—
318	Dic₆	—	5	2	no	—
319	Dic₆	D₅⋊C₈	1	1	yes	characteristic
320	C₃×C₈	—	5	1	no	—
321	C₃×C₈	—	5	1	no	—
322	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
323	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₃⋊C₈	—	5	2	no	—
325	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
326	C₂²×C₅	—	3	2	no	—
327	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
328	C₂×D₅	—	2	2	no	—
329	C₂×D₅	—	3	2	no	—
330	C₂×D₅	—	6	4	no	—
331	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
332	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
333	C₄×C₅	—	3	2	no	—
334	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
335	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
336	Dic₅	—	3	2	no	—
337	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
338	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
339	#41	—	3	1	no	—
340	#41	—	15	2	no	—
341	#41	—	15	2	no	—
342	#41	—	15	1	no	—
343	#41	—	15	1	no	—
344	#41	—	15	1	no	—
345	C₂×Q₈	—	15	1	no	—
346	C₂×D₄	—	15	1	no	—
347	C₂×D₄	—	15	2	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	15	2	no	—
350	M₁₆	—	3	1	no	—
351	M₁₆	—	3	2	no	—
352	M₁₆	—	15	2	no	—
353	M₁₆	—	15	2	no	—
354	M₁₆	—	15	2	no	—
355	M₁₆	—	15	1	no	—
356	M₁₆	—	15	2	no	—
357	C₂×C₈	—	3	2	no	—
358	C₂×C₈	—	5	1	no	—
359	C₂×C₈	—	5	1	no	—
360	C₂×C₈	—	5	1	no	—
361	C₂×C₈	—	5	1	no	—
362	C₂×C₈	—	5	1	no	—
363	C₂×C₈	—	15	2	no	—
364	C₂×C₈	—	15	2	no	—
365	C₂×C₈	—	15	2	no	—
366	C₂×C₈	—	15	2	no	—
367	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₁₆	—	5	4	no	—
369	C₁₆	—	15	2	no	—
370	C₁₆	—	15	2	no	—
371	C₃×C₅	C₂×#504	1	1	yes	characteristic, complemented, Hall
372	C₂²×C₃	—	5	1	no	—
373	C₂²×C₃	—	5	1	no	—
374	C₂²×C₃	—	10	2	no	—
375	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
376	C₂×D₃	—	5	2	no	—
377	C₂×D₃	—	10	4	no	—
378	C₂×D₃	C₂×D₅⋊C₈	1	2	yes	—
379	C₃×C₄	—	5	1	no	—
380	C₃×C₄	—	5	1	no	—
381	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
382	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
383	Dic₃	—	5	2	no	—
384	Dic₃	C₂×D₅⋊C₈	1	2	yes	—
385	C₂×C₅	—	2	1	no	—
386	C₂×C₅	—	6	2	no	—
387	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
388	D₅	—	2	1	no	—
389	D₅	—	6	2	no	—
390	D₅	#4907	1	2	yes	complemented
391	C₂³	—	5	1	no	—
392	C₂³	—	15	2	no	—
393	Q₈	—	3	1	no	—
394	Q₈	—	15	2	no	—
395	Q₈	—	15	1	no	—
396	D₄	—	3	2	no	—
397	D₄	—	3	1	no	—
398	D₄	—	15	2	no	—
399	D₄	—	15	2	no	—
400	D₄	—	15	2	no	—
401	D₄	—	15	2	no	—
402	D₄	—	15	1	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	15	2	no	—
410	C₂×C₄	—	15	2	no	—
411	C₂×C₄	—	15	2	no	—
412	C₂×C₄	—	15	2	no	—
413	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₈	—	3	2	no	—
415	C₈	—	5	1	no	—
416	C₈	—	5	1	no	—
417	C₈	—	15	2	no	—
418	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	5	2	no	—
422	C₂×C₃	—	10	1	no	—
423	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
424	D₃	—	2	2	no	—
425	D₃	—	10	2	no	—
426	C₅	C₂×#4907	1	1	yes	characteristic, complemented, Sylow
427	C₂²	—	3	2	no	—
428	C₂²	—	5	1	no	—
429	C₂²	—	5	1	no	—
430	C₂²	—	10	2	no	—
431	C₂²	—	15	2	no	—
432	C₂²	—	30	4	no	—
433	C₂²	D₃×D₅⋊C₈	1	1	yes	characteristic
434	C₄	—	3	2	no	—
435	C₄	—	5	1	no	—
436	C₄	—	5	1	no	—
437	C₄	—	15	2	no	—
438	C₄	D₃×D₅⋊C₈	1	1	yes	characteristic
439	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₃	D₅⋊#504	1	1	yes	characteristic, complemented, Sylow
441	C₂	—	2	1	no	—
442	C₂	—	5	2	no	—
443	C₂	—	6	2	no	—
444	C₂	—	10	1	no	—
445	C₂	—	30	2	no	—
446	C₂	C₂×D₃×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
prime radical	D₅×#235	C₄
cosocle	C₃×#168	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#504
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×D₅⋊(C₃⋊C₁₆)	C₂	semidirect
3. C₃×D₅⋊M₃₂	C₂	semidirect
4. #11751742	C₂	semidirect
5. #11751738	C₂	semidirect
6. D₅⋊#798	C₂	semidirect
7. #11751644	C₂	semidirect
8. D₃×D₅⋊C₁₆	C₂	semidirect
21. C₂×C₃⋊#674	C₂²	semidirect
24. D₅⋊(C₃⋊C₁₆)	C₂²	semidirect
25. C₃×#3998	C₂²	semidirect
26. C₃×#3990	C₂²	semidirect
28. #91166	C₂²	semidirect
29. #91165	C₂²	semidirect
30. #91164	C₂²	semidirect
31. D₃×#674	C₂²	semidirect
38. D₅⋊M₃₂	D₃	semidirect
93. #3998	C₂×D₃	semidirect
97. #3990	C₂×D₃	semidirect
295. C₃×D₅	#504	semidirect
371. C₃×C₅	C₂×#504	semidirect
390. D₅	#4907	semidirect
426. C₅	C₂×#4907	semidirect
440. C₃	D₅⋊#504	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
C₂×D₅⋊(C₃⋊C₁₆)	2
C₃×D₅⋊M₃₂	2
#11751742	2
#11751738	2
D₅⋊#798	2
#11751644	2
D₃×D₅⋊C₁₆	2
D₅⋊#504	3
C₂×#4907	5

Subgroups — D5⋊#4907 #14478156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#4907 #14478156