Subgroups — D₅×#4924 #14413020

Order 1920.

1152 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	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×#208	C₂	1	2	yes	maximal
3	#11751025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748431	C₂	1	2	yes	maximal, complemented
6	#11747007	C₂	1	4	yes	maximal, complemented
7	D₅×C₄⋊(C₃⋊C₈)	C₂	1	4	yes	maximal, complemented
8	D₅×#423	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	2	yes	—
13	C₂×C₅×#208	C₂²	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
17	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
18	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
19	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
20	C₃×C₄²×D₅	C₂²	1	2	yes	—
21	C₃×C₄²×D₅	C₂²	1	2	yes	—
22	C₂×#6649	C₂²	1	4	yes	—
23	D₅×#208	—	2	8	no	—
24	C₂×D₅×C₃⋊C₈	C₂²	1	4	yes	—
25	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
27	#90982	C₂²	1	8	yes	complemented
28	C₂×#4924	—	5	1	no	maximal, Hall
29	C₂×D₅×M₁₆	—	3	2	no	—
30	C₂×C₄²×D₅	D₃	1	1	yes	characteristic
31	C₅×#423	—	3	1	no	—
32	#65407	—	3	2	no	—
33	#65213	—	3	1	no	—
34	#65126	—	3	4	no	—
35	D₅×C₄⋊C₈	—	3	4	no	—
36	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	—	2	8	no	—
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
49	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	2	yes	—
55	#6710	—	2	4	no	—
56	C₂×C₃⋊#168	C₂³	1	4	yes	—
57	C₅×#208	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
59	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
62	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
63	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
64	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂³	1	2	yes	—
66	#6649	—	2	8	no	—
67	D₅×C₃⋊C₈	—	2	8	no	—
68	C₂²×C₃×C₄²	—	5	1	no	—
69	C₂²×#208	—	5	2	no	—
70	#4924	—	5	1	no	—
71	#4924	—	5	2	no	—
72	#4924	—	5	4	no	—
73	#4924	D₅	1	1	yes	characteristic, direct product factor
74	C₂×C₄⋊(C₃⋊C₈)	—	5	4	no	—
75	C₂²×C₄×D₅	Dic₃	1	2	yes	—
76	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
77	C₂×C₅×M₁₆	—	3	2	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₂×C₄×Dic₅	Dic₃	1	2	yes	—
80	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
81	C₂×#681	—	3	2	no	—
82	D₅×M₁₆	—	6	8	no	—
83	C₂×#676	—	3	4	no	—
84	C₂×C₈×D₅	—	3	4	no	—
85	C₄²×D₅	Dic₃	1	1	yes	characteristic
86	C₄²×D₅	Dic₃	1	1	yes	characteristic
87	C₄²×D₅	Dic₃	1	1	yes	characteristic
88	C₄²×D₅	Dic₃	1	1	yes	characteristic
89	C₄²×D₅	C₂×D₃	1	2	yes	—
90	C₄²×D₅	C₂×D₃	1	2	yes	—
91	C₅×C₄⋊C₈	—	3	4	no	—
92	#3946	—	3	8	no	—
93	C₄⋊#168	—	3	4	no	—
94	C₂×#423	—	15	1	no	Sylow
95	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₃×D₅	—	2	4	no	—
97	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
98	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×Dic₅	—	2	4	no	—
108	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
109	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
113	C₃×C₄×D₅	—	2	4	no	—
114	C₃×C₄×D₅	—	2	4	no	—
115	C₃×C₄×D₅	—	2	4	no	—
116	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
117	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
118	C₃×C₄×D₅	M₁₆	1	8	yes	complemented
119	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
120	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
121	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
122	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
123	C₃⋊#168	—	2	4	no	—
124	C₅×C₃⋊C₈	—	2	4	no	—
125	C₂³×C₃×C₄	—	5	1	no	—
126	C₂³×C₃×C₄	—	5	2	no	—
127	C₂×C₃×C₄²	—	5	2	no	—
128	C₂×C₃×C₄²	—	5	1	no	—
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₂×C₃×C₄²	—	5	1	no	—
131	C₂×C₃×C₄²	—	5	1	no	—
132	C₂×C₃×C₄²	—	5	1	no	—
133	C₂×C₃×C₄²	—	5	2	no	—
134	C₂×C₃×C₄²	—	5	2	no	—
135	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
136	C₂×#208	—	5	2	no	—
137	C₂×#208	—	5	4	no	—
138	C₂×#208	—	10	8	no	—
139	C₂×#208	C₂×D₅	1	2	yes	—
140	C₂²×C₃⋊C₈	—	5	4	no	—
141	C₄⋊(C₃⋊C₈)	—	5	4	no	—
142	C₄⋊(C₃⋊C₈)	—	5	8	no	—
143	C₄⋊(C₃⋊C₈)	C₂×D₅	1	4	yes	complemented
144	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
148	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
149	C₂×C₄×D₅	—	2	8	no	—
150	C₂×C₄×D₅	Dic₆	1	4	yes	—
151	C₂×C₄×D₅	D₁₂	1	4	yes	—
152	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
153	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
154	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
155	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
156	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
157	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
160	C₅×M₁₆	—	6	4	no	—
161	C₂×C₅×C₈	—	3	4	no	—
162	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
163	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
164	C₄²×C₅	C₂²×D₃	1	2	yes	—
165	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
166	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
167	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
168	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
169	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
170	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
171	C₄×Dic₅	C₂²×D₃	1	2	yes	—
172	#681	—	6	4	no	—
173	C₂×#168	—	3	4	no	—
174	#676	—	6	8	no	—
175	C₈×D₅	—	6	8	no	—
176	C₂²×M₁₆	—	15	2	no	—
177	C₂²×C₄²	—	5	1	no	—
178	#423	—	3	1	no	—
179	#423	—	15	4	no	—
180	#423	—	15	2	no	—
181	#423	—	15	1	no	—
182	C₂×C₄⋊C₈	—	15	4	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₃×D₅	—	2	2	no	—
187	C₂×C₃×D₅	—	2	8	no	—
188	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
193	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
198	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
199	C₃×Dic₅	C₂×M₁₆	1	4	yes	complemented
200	C₂⁴×C₃	—	5	1	no	—
201	C₂²×C₃×C₄	—	5	1	no	—
202	C₂²×C₃×C₄	—	5	1	no	—
203	C₂²×C₃×C₄	—	5	1	no	—
204	C₂²×C₃×C₄	—	5	2	no	—
205	C₂²×C₃×C₄	—	5	4	no	—
206	C₂²×C₃×C₄	—	5	4	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	—	5	2	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	5	2	no	—
212	C₂²×C₃×C₄	—	5	2	no	—
213	C₂²×C₃×C₄	—	10	8	no	—
214	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
215	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
216	C₃×C₄²	—	5	2	no	—
217	C₃×C₄²	—	5	1	no	—
218	C₃×C₄²	—	5	2	no	—
219	C₃×C₄²	—	5	2	no	—
220	C₃×C₄²	—	5	2	no	—
221	C₃×C₄²	—	5	1	no	—
222	C₃×C₄²	—	5	2	no	—
223	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
224	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
225	C₃×C₄²	C₂²×D₅	1	2	yes	—
226	#208	—	2	4	no	—
227	#208	—	10	8	no	—
228	#208	—	10	4	no	—
229	C₂×C₃⋊C₈	—	5	4	no	—
230	C₂×C₃⋊C₈	—	10	8	no	—
231	C₂×C₃⋊C₈	C₂²×D₅	1	4	yes	—
232	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	C₄⋊Dic₃	1	4	yes	—
235	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
236	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
239	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
240	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
241	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
242	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
244	C₂×Dic₅	—	2	4	no	—
245	C₂×Dic₅	C₄⋊Dic₃	1	4	yes	—
246	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
247	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
248	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
249	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
250	C₄×D₅	—	2	4	no	—
251	C₄×D₅	—	2	4	no	—
252	C₄×D₅	—	2	4	no	—
253	C₄×D₅	#208	1	8	yes	complemented
254	C₄×D₅	C₄⋊Dic₃	1	4	yes	—
255	C₄×D₅	C₄⋊Dic₃	1	4	yes	—
256	C₄×D₅	C₂×Dic₆	1	2	yes	—
257	C₄×D₅	C₂×Dic₆	1	2	yes	—
258	C₄×D₅	C₂×D₁₂	1	2	yes	—
259	C₄×D₅	C₂×D₁₂	1	2	yes	—
260	C₅×C₈	—	6	4	no	—
261	#168	—	6	4	no	—
262	C₂³×C₄	—	5	1	no	—
263	C₂³×C₄	—	5	2	no	—
264	C₂×M₁₆	—	3	2	no	—
265	C₂×M₁₆	—	15	4	no	—
266	C₂×M₁₆	—	15	2	no	—
267	C₂×M₁₆	—	30	8	no	—
268	C₂²×C₈	—	15	4	no	—
269	C₂×C₄²	—	5	2	no	—
270	C₂×C₄²	—	5	1	no	—
271	C₂×C₄²	—	5	1	no	—
272	C₂×C₄²	—	5	1	no	—
273	C₂×C₄²	—	5	1	no	—
274	C₂×C₄²	—	5	1	no	—
275	C₂×C₄²	—	5	2	no	—
276	C₂×C₄²	—	5	2	no	—
277	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
278	C₄⋊C₈	—	3	4	no	—
279	C₄⋊C₈	—	15	8	no	—
280	C₄⋊C₈	—	15	4	no	—
281	C₂×C₃×C₅	—	2	2	no	—
282	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
284	C₃×D₅	—	2	2	no	—
285	C₃×D₅	#423	1	4	yes	complemented
286	C₂³×C₃	—	5	1	no	—
287	C₂³×C₃	—	5	1	no	—
288	C₂³×C₃	—	5	4	no	—
289	C₂³×C₃	—	10	4	no	—
290	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	5	2	no	—
293	C₂×C₃×C₄	—	5	1	no	—
294	C₂×C₃×C₄	—	5	1	no	—
295	C₂×C₃×C₄	—	5	4	no	—
296	C₂×C₃×C₄	—	5	2	no	—
297	C₂×C₃×C₄	—	5	2	no	—
298	C₂×C₃×C₄	—	5	2	no	—
299	C₂×C₃×C₄	—	5	2	no	—
300	C₂×C₃×C₄	—	5	4	no	—
301	C₂×C₃×C₄	—	5	4	no	—
302	C₂×C₃×C₄	—	5	8	no	—
303	C₂×C₃×C₄	—	5	2	no	—
304	C₂×C₃×C₄	—	10	4	no	—
305	C₂×C₃×C₄	—	10	4	no	—
306	C₂×C₃×C₄	—	10	4	no	—
307	C₂×C₃×C₄	—	10	4	no	—
308	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
309	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
311	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
312	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
313	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
314	C₃⋊C₈	—	2	4	no	—
315	C₃⋊C₈	—	10	4	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	C₂×C₄⋊Dic₃	1	2	yes	—
318	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
319	C₂×D₅	—	2	2	no	—
320	C₂×D₅	—	2	8	no	—
321	C₂×D₅	C₂×#208	1	4	yes	—
322	C₂×D₅	C₂×C₄⋊Dic₃	1	2	yes	—
323	C₂×D₅	C₂×C₄⋊Dic₃	1	2	yes	—
324	C₄×C₅	—	2	2	no	—
325	C₄×C₅	C₂×#208	1	4	yes	complemented
326	C₄×C₅	C₂×C₄⋊Dic₃	1	2	yes	—
327	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
328	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
329	Dic₅	—	2	2	no	—
330	Dic₅	C₂×#208	1	4	yes	complemented
331	Dic₅	C₂×C₄⋊Dic₃	1	2	yes	—
332	Dic₅	C₂×C₄⋊Dic₃	1	2	yes	—
333	C₂⁴	—	5	1	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	4	no	—
336	C₂²×C₄	—	5	4	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	1	no	—
339	C₂²×C₄	—	5	2	no	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	2	no	—
343	C₂²×C₄	—	5	2	no	—
344	C₂²×C₄	—	5	2	no	—
345	C₂²×C₄	—	5	2	no	—
346	C₂²×C₄	—	10	8	no	—
347	C₂²×C₄	D₅×Dic₃	1	2	yes	—
348	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
349	M₁₆	—	6	4	no	—
350	M₁₆	—	30	8	no	—
351	M₁₆	—	30	4	no	—
352	C₂×C₈	—	3	4	no	—
353	C₂×C₈	—	15	4	no	—
354	C₂×C₈	—	30	8	no	—
355	C₄²	—	5	2	no	—
356	C₄²	—	5	1	no	—
357	C₄²	—	5	2	no	—
358	C₄²	—	5	2	no	—
359	C₄²	—	5	2	no	—
360	C₄²	—	5	1	no	—
361	C₄²	—	5	2	no	—
362	C₄²	D₅×Dic₃	1	1	yes	characteristic
363	C₄²	D₅×Dic₃	1	1	yes	characteristic
364	C₄²	C₂×D₃×D₅	1	2	yes	—
365	C₃×C₅	C₂×#423	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	5	4	no	—
368	C₂²×C₃	—	5	2	no	—
369	C₂²×C₃	—	5	2	no	—
370	C₂²×C₃	—	10	8	no	—
371	C₂²×C₃	—	10	2	no	—
372	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
373	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	5	4	no	—
376	C₃×C₄	—	5	2	no	—
377	C₃×C₄	—	5	2	no	—
378	C₃×C₄	—	10	2	no	—
379	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
380	C₃×C₄	D₅×M₁₆	1	4	yes	complemented
381	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
382	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
383	C₂×C₅	—	2	2	no	—
384	C₂×C₅	C₂²×#208	1	2	yes	—
385	C₂×C₅	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
386	D₅	—	2	2	no	—
387	D₅	#4924	1	4	yes	direct product factor
388	C₂³	—	5	1	no	—
389	C₂³	—	5	4	no	—
390	C₂³	—	5	1	no	—
391	C₂³	—	10	4	no	—
392	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	5	4	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	2	no	—
398	C₂×C₄	—	5	4	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	5	2	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	5	2	no	—
403	C₂×C₄	—	5	2	no	—
404	C₂×C₄	—	5	8	no	—
405	C₂×C₄	—	5	2	no	—
406	C₂×C₄	—	10	4	no	—
407	C₂×C₄	—	10	4	no	—
408	C₂×C₄	—	10	4	no	—
409	C₂×C₄	—	10	4	no	—
410	C₂×C₄	D₅×Dic₆	1	2	yes	—
411	C₂×C₄	D₅×D₁₂	1	2	yes	—
412	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
413	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
415	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
416	C₈	—	6	4	no	—
417	C₈	—	30	4	no	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	—	5	4	no	—
420	C₂×C₃	—	10	2	no	—
421	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
422	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
423	C₅	C₂×#4924	1	1	yes	characteristic, complemented, Sylow
424	C₂²	—	2	2	no	—
425	C₂²	—	5	2	no	—
426	C₂²	—	5	4	no	—
427	C₂²	—	5	2	no	—
428	C₂²	—	10	8	no	—
429	C₂²	—	10	2	no	—
430	C₂²	D₅×C₄⋊Dic₃	1	2	yes	—
431	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	5	2	no	—
434	C₄	—	5	2	no	—
435	C₄	—	5	4	no	—
436	C₄	—	10	2	no	—
437	C₄	D₅×#208	1	4	yes	complemented
438	C₄	D₅×C₄⋊Dic₃	1	2	yes	—
439	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
440	C₄	C₂×D₅×D₁₂	1	1	yes	characteristic
441	C₃	D₅×#423	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	5	4	no	—
444	C₂	—	10	2	no	—
445	C₂	C₂×D₅×#208	1	2	yes	—
446	C₂	C₂×D₅×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×#423
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #11751025	C₂	semidirect
4. C₅×#4924	C₂	semidirect
5. #11748431	C₂	semidirect
6. #11747007	C₂	semidirect
7. D₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
25. C₄⋊(C₃⋊#168)	C₂²	semidirect
26. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
27. #90982	C₂²	semidirect
73. #4924	D₅	direct (N × H)
118. C₃×C₄×D₅	M₁₆	semidirect
143. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
193. C₃×C₄×C₅	C₂×M₁₆	semidirect
199. C₃×Dic₅	C₂×M₁₆	semidirect
253. C₄×D₅	#208	semidirect
285. C₃×D₅	#423	semidirect
325. C₄×C₅	C₂×#208	semidirect
330. Dic₅	C₂×#208	semidirect
365. C₃×C₅	C₂×#423	semidirect
380. C₃×C₄	D₅×M₁₆	semidirect
387. D₅	#4924	direct (N × H)
423. C₅	C₂×#4924	semidirect
437. C₄	D₅×#208	semidirect
441. C₃	D₅×#423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₅	2
C₂×D₅×#208	2
#11751025	2
C₅×#4924	2
#11748431	2
#11747007	2
D₅×C₄⋊(C₃⋊C₈)	2
D₅×#423	3
C₂×#4924	5

Subgroups — D5×#4924 #14413020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#4924 #14413020