Subgroups — C₅×#20562 #11943282

Order 1280.

1002 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#2293	C₂	1	1	yes	maximal, characteristic
4	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1753	C₂	1	2	yes	maximal, complemented
8	C₅×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₅×#1750	C₂	1	2	yes	maximal, complemented
10	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1729	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₅×C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	2	yes	—
16	C₅×#436	C₄	1	8	yes	complemented
17	C₅×C₈×D₄	C₄	1	8	yes	complemented
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₅×#390	C₄	1	2	yes	—
28	C₅×#389	C₄	1	2	yes	—
29	C₅×#388	C₄	1	4	yes	—
30	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	1	yes	characteristic
37	C₅×#336	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	1	yes	characteristic
39	C₅×#336	C₂²	1	1	yes	characteristic
40	#20562	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	C₂³	1	2	yes	—
43	C₂×C₅×M₁₆	—	4	2	no	—
44	C₂×C₅×M₁₆	—	4	2	no	—
45	C₂×C₅×M₁₆	C₂×C₄	1	8	yes	—
46	C₂²×C₅×C₈	—	4	2	no	—
47	C₂²×C₅×C₈	—	4	2	no	—
48	C₂²×C₅×C₈	C₂×C₄	1	8	yes	—
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
56	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
57	C₅×#117	—	4	2	no	—
58	C₅×#117	—	4	2	no	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
72	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
73	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	—
74	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	—
75	C₅×#97	—	4	2	no	—
76	C₄×C₅×C₈	—	4	2	no	—
77	C₄×C₅×C₈	—	4	2	no	—
78	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
79	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
80	C₅×#95	C₂×C₄	1	4	yes	—
81	C₅×#95	C₂×C₄	1	2	yes	—
82	C₂×#436	C₂×C₅	1	1	yes	characteristic
83	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
84	#2293	C₂×C₅	1	1	yes	characteristic
85	#1770	C₂×C₅	1	1	yes	characteristic, complemented
86	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
87	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
88	#1753	C₂×C₅	1	2	yes	complemented
89	C₈×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
90	#1750	C₂×C₅	1	2	yes	complemented
91	#1744	C₂×C₅	1	1	yes	characteristic, complemented
92	#1729	C₂×C₅	1	2	yes	complemented
93	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₅×D₄	—	2	4	no	—
95	C₂×C₅×D₄	C₄²	1	4	yes	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₅×M₁₆	—	4	8	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	1	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	4	8	no	—
123	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
125	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
128	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
129	C₅×C₄⋊C₄	—	2	4	no	—
130	C₅×C₄⋊C₄	—	4	4	no	—
131	C₅×C₄⋊C₄	C₄²	1	4	yes	—
132	C₅×C₂²⋊C₄	—	2	8	no	—
133	C₅×C₂²⋊C₄	—	4	4	no	—
134	C₅×C₂²⋊C₄	C₄²	1	8	yes	—
135	C₄²×C₅	—	2	4	no	—
136	C₄²×C₅	—	2	4	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	—	2	1	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	1	no	—
142	C₄²×C₅	—	2	1	no	—
143	C₄²×C₅	C₂²×C₄	1	2	yes	—
144	C₄²×C₅	C₂²×C₄	1	2	yes	—
145	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
146	C₂³×C₈	C₂²×C₅	1	2	yes	—
147	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
148	C₂×#117	C₂²×C₅	1	2	yes	—
149	#436	C₄×C₅	1	8	yes	complemented
150	C₈×D₄	C₄×C₅	1	8	yes	complemented
151	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
154	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
155	C₂×#97	C₂²×C₅	1	2	yes	—
156	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
157	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
158	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
160	#390	C₄×C₅	1	2	yes	—
161	#389	C₄×C₅	1	2	yes	—
162	#388	C₄×C₅	1	4	yes	—
163	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
165	C₄³	C₂²×C₅	1	1	yes	characteristic
166	#336	C₂²×C₅	1	1	yes	characteristic
167	#336	C₂²×C₅	1	2	yes	—
168	#336	C₂²×C₅	1	2	yes	—
169	#336	C₂²×C₅	1	2	yes	—
170	#336	C₂²×C₅	1	1	yes	characteristic
171	#336	C₂²×C₅	1	1	yes	characteristic
172	#336	C₂²×C₅	1	1	yes	characteristic
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	C₂×C₄²	1	4	yes	—
178	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₅×D₄	—	2	8	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
196	C₂×C₄×C₅	C₂×C₄²	1	4	yes	—
197	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
198	C₂×C₄×C₅	#131	1	4	yes	—
199	C₂×C₄×C₅	#131	1	4	yes	—
200	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
206	C₅×C₈	—	2	2	no	—
207	C₅×C₈	—	2	4	no	—
208	C₅×C₈	—	2	4	no	—
209	C₅×C₈	—	2	2	no	—
210	C₅×C₈	—	2	2	no	—
211	C₅×C₈	—	2	2	no	—
212	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₅	1	2	yes	—
214	C₂×M₁₆	—	4	2	no	—
215	C₂×M₁₆	—	4	2	no	—
216	C₂×M₁₆	C₂×C₄×C₅	1	8	yes	—
217	C₂²×C₈	—	4	2	no	—
218	C₂²×C₈	—	4	2	no	—
219	C₂²×C₈	C₂×C₄×C₅	1	8	yes	—
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	2	yes	—
222	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₅	1	2	yes	—
224	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
226	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
227	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
228	#117	—	4	2	no	—
229	#117	—	4	2	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
235	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₅	1	2	yes	—
240	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
243	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
244	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	—
245	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	—
246	#97	—	4	2	no	—
247	C₄×C₈	—	4	2	no	—
248	C₄×C₈	—	4	2	no	—
249	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
250	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
251	#95	C₂×C₄×C₅	1	4	yes	—
252	#95	C₂×C₄×C₅	1	2	yes	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	2	4	no	—
255	C₂²×C₅	—	2	4	no	—
256	C₂²×C₅	—	4	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
259	C₂²×C₅	#518	1	1	yes	characteristic
260	C₂²×C₅	#520	1	1	yes	characteristic
261	C₂²×C₅	C₂×#131	1	2	yes	—
262	C₂²×C₅	C₂×#131	1	2	yes	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	4	no	—
265	C₄×C₅	—	2	4	no	—
266	C₄×C₅	—	4	2	no	—
267	C₄×C₅	—	4	4	no	—
268	C₄×C₅	#405	1	4	yes	—
269	C₄×C₅	#518	1	1	yes	characteristic
270	C₄×C₅	#518	1	1	yes	characteristic
271	C₄×C₅	#520	1	1	yes	characteristic
272	C₄×C₅	#520	1	1	yes	characteristic
273	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	C₄²×C₅	1	4	yes	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
281	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
285	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
286	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
289	M₁₆	—	4	8	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	4	8	no	—
303	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
304	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
305	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
306	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
307	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
308	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₄⋊C₄	C₄²×C₅	1	4	yes	—
312	C₂²⋊C₄	—	2	8	no	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	C₄²×C₅	1	8	yes	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	C₂²×C₄×C₅	1	2	yes	—
324	C₄²	C₂²×C₄×C₅	1	2	yes	—
325	C₂×C₅	—	4	4	no	—
326	C₂×C₅	#2275	1	1	yes	characteristic
327	C₂×C₅	C₂×#405	1	1	yes	characteristic
328	C₂×C₅	C₄×#131	1	1	yes	characteristic
329	C₂×C₅	#2979	1	2	yes	—
330	C₂×C₅	#2994	1	2	yes	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	C₂×C₄²×C₅	1	4	yes	—
336	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
337	D₄	—	2	8	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
354	C₂×C₄	C₂×C₄²×C₅	1	4	yes	—
355	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
356	C₂×C₄	C₅×#131	1	4	yes	—
357	C₂×C₄	C₅×#131	1	4	yes	—
358	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
359	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
360	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	4	no	—
366	C₈	—	2	2	no	—
367	C₈	—	2	4	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
370	C₅	#20562	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	C₂²×C₄²×C₅	1	1	yes	characteristic
377	C₂²	C₅×#518	1	1	yes	characteristic
378	C₂²	C₅×#520	1	1	yes	characteristic
379	C₂²	C₂×C₅×#131	1	2	yes	—
380	C₂²	C₂×C₅×#131	1	2	yes	—
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	4	no	—
386	C₄	C₅×#405	1	4	yes	—
387	C₄	C₅×#518	1	1	yes	characteristic
388	C₄	C₅×#518	1	1	yes	characteristic
389	C₄	C₅×#520	1	1	yes	characteristic
390	C₄	C₅×#520	1	1	yes	characteristic
391	C₂	—	4	4	no	—
392	C₂	C₅×#2275	1	1	yes	characteristic
393	C₂	C₂×C₅×#405	1	1	yes	characteristic
394	C₂	C₄×C₅×#131	1	1	yes	characteristic
395	C₂	C₅×#2979	1	2	yes	—
396	C₂	C₅×#2994	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1770	C₂	semidirect
5. C₅×C₈×C₄⋊C₄	C₂	semidirect
6. C₄×C₅×C₄⋊C₈	C₂	semidirect
7. C₅×#1753	C₂	semidirect
8. C₅×C₈×C₂²⋊C₄	C₂	semidirect
9. C₅×#1750	C₂	semidirect
10. C₅×#1744	C₂	semidirect
11. C₅×#1729	C₂	semidirect
16. C₅×#436	C₄	semidirect
17. C₅×C₈×D₄	C₄	semidirect
40. #20562	C₅	direct (N × H)
85. #1770	C₂×C₅	semidirect
86. C₈×C₄⋊C₄	C₂×C₅	semidirect
87. C₄×C₄⋊C₈	C₂×C₅	semidirect
88. #1753	C₂×C₅	semidirect
89. C₈×C₂²⋊C₄	C₂×C₅	semidirect
90. #1750	C₂×C₅	semidirect
91. #1744	C₂×C₅	semidirect
92. #1729	C₂×C₅	semidirect
149. #436	C₄×C₅	semidirect
150. C₈×D₄	C₄×C₅	semidirect
370. C₅	#20562	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#436	2
C₂×C₅×C₈×D₄	2
C₅×#2293	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×C₄⋊C₈	2
C₅×#1753	2
C₅×C₈×C₂²⋊C₄	2
C₅×#1750	2
C₅×#1744	2
C₅×#1729	2
#20562	5

Subgroups — C5×#20562 #11943282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20562 #11943282