Subgroups — C₅×#20778 #11943498

Order 1280.

1014 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#1839	C₂	1	2	yes	maximal, complemented
3	C₅×#1831	C₂	1	2	yes	maximal, complemented
4	C₅×#1817	C₂	1	2	yes	maximal
5	C₅×#1797	C₂	1	2	yes	maximal
6	C₅×#1767	C₂	1	2	yes	maximal, complemented
7	C₅×#1749	C₂	1	2	yes	maximal
8	C₅×#1745	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄²×C₅	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₅	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₅	C₄	1	1	yes	characteristic
12	C₂²×C₄²×C₅	C₄	1	1	yes	characteristic
13	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
17	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
18	C₂×C₅×#97	C₂²	1	4	yes	—
19	C₄³×C₅	C₄	1	1	yes	characteristic
20	C₄³×C₅	C₄	1	1	yes	characteristic
21	C₄³×C₅	C₄	1	1	yes	characteristic
22	C₄³×C₅	C₄	1	1	yes	characteristic
23	C₄³×C₅	C₂²	1	1	yes	characteristic
24	C₄³×C₅	C₂²	1	1	yes	characteristic
25	C₄³×C₅	C₂²	1	1	yes	characteristic
26	C₄³×C₅	C₂²	1	1	yes	characteristic
27	C₅×#336	C₂²	1	4	yes	—
28	C₅×#336	C₂²	1	4	yes	—
29	C₅×#336	C₂²	1	4	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	#20778	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×C₈	C₂³	1	8	yes	—
40	C₂×C₄²×C₅	—	2	4	no	—
41	C₂×C₄²×C₅	—	2	4	no	—
42	C₂×C₄²×C₅	—	2	4	no	—
43	C₂×C₄²×C₅	—	2	4	no	—
44	C₂×C₄²×C₅	—	2	4	no	—
45	C₂×C₄²×C₅	—	2	4	no	—
46	C₂×C₄²×C₅	—	2	4	no	—
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	2	8	no	—
76	C₅×C₂²⋊C₈	—	2	8	no	—
77	C₅×#97	—	2	8	no	—
78	C₂×C₄³	C₂×C₅	1	1	yes	characteristic
79	#1839	C₂×C₅	1	2	yes	complemented
80	#1831	C₂×C₅	1	2	yes	complemented
81	#1817	C₂×C₅	1	2	yes	—
82	#1797	C₂×C₅	1	2	yes	—
83	#1767	C₂×C₅	1	2	yes	complemented
84	#1749	C₂×C₅	1	2	yes	—
85	#1745	C₂×C₅	1	2	yes	complemented
86	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
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	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	M₁₆	1	4	yes	—
106	C₂²×C₄×C₅	M₁₆	1	4	yes	—
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	#41	1	4	yes	—
121	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×C₈	—	2	8	no	—
123	C₂×C₅×C₈	—	2	8	no	—
124	C₂×C₅×C₈	—	2	8	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	2	2	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₄²×C₅	M₁₆	1	4	yes	—
150	C₄²×C₅	M₁₆	1	4	yes	—
151	C₄²×C₅	#41	1	4	yes	—
152	C₄²×C₅	#41	1	4	yes	—
153	C₂²×C₄²	C₄×C₅	1	1	yes	characteristic
154	C₂²×C₄²	C₄×C₅	1	1	yes	characteristic
155	C₂²×C₄²	C₄×C₅	1	1	yes	characteristic
156	C₂²×C₄²	C₄×C₅	1	1	yes	characteristic
157	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
159	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
161	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
162	C₂×#97	C₂²×C₅	1	4	yes	—
163	C₄³	C₄×C₅	1	1	yes	characteristic
164	C₄³	C₄×C₅	1	1	yes	characteristic
165	C₄³	C₄×C₅	1	1	yes	characteristic
166	C₄³	C₄×C₅	1	1	yes	characteristic
167	C₄³	C₂²×C₅	1	1	yes	characteristic
168	C₄³	C₂²×C₅	1	1	yes	characteristic
169	C₄³	C₂²×C₅	1	1	yes	characteristic
170	C₄³	C₂²×C₅	1	1	yes	characteristic
171	#336	C₂²×C₅	1	4	yes	—
172	#336	C₂²×C₅	1	4	yes	—
173	#336	C₂²×C₅	1	4	yes	—
174	#336	C₂²×C₅	1	4	yes	—
175	C₂³×C₅	—	2	1	no	—
176	C₂³×C₅	—	2	1	no	—
177	C₂³×C₅	—	2	1	no	—
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	#117	1	2	yes	—
180	C₂³×C₅	C₂×M₁₆	1	2	yes	—
181	C₂³×C₅	C₂×M₁₆	1	2	yes	—
182	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	—	2	8	no	—
184	C₂×C₄×C₅	—	2	8	no	—
185	C₂×C₄×C₅	—	2	8	no	—
186	C₂×C₄×C₅	—	2	8	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	8	no	—
212	C₂×C₄×C₅	—	2	8	no	—
213	C₂×C₄×C₅	—	2	8	no	—
214	C₂×C₄×C₅	#117	1	2	yes	—
215	C₂×C₄×C₅	#117	1	2	yes	—
216	C₂×C₄×C₅	#117	1	2	yes	—
217	C₂×C₄×C₅	#117	1	2	yes	—
218	C₂×C₄×C₅	#117	1	2	yes	—
219	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
220	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
221	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
222	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
223	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
224	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
225	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
226	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
227	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
228	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₅	C₂×#41	1	2	yes	—
230	C₂×C₄×C₅	C₂×#41	1	2	yes	—
231	C₂×C₄×C₅	C₂×#41	1	2	yes	—
232	C₅×C₈	—	4	8	no	—
233	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₅	1	8	yes	—
241	C₂×C₄²	—	2	4	no	—
242	C₂×C₄²	—	2	4	no	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
269	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
276	C₄⋊C₈	—	2	8	no	—
277	C₂²⋊C₈	—	2	8	no	—
278	#97	—	2	8	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	#432	1	4	yes	—
286	C₂²×C₅	C₂×#117	1	1	yes	characteristic
287	C₂²×C₅	C₂×#117	1	1	yes	characteristic
288	C₂²×C₅	C₂×#117	1	1	yes	characteristic
289	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
290	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
291	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
292	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	#432	1	4	yes	—
306	C₄×C₅	#529	1	4	yes	—
307	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₅×M₁₆	1	4	yes	—
327	C₂²×C₄	C₅×M₁₆	1	4	yes	—
328	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
341	C₂²×C₄	C₅×#41	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
343	C₂×C₈	—	2	8	no	—
344	C₂×C₈	—	2	8	no	—
345	C₂×C₈	—	2	8	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	C₅×M₁₆	1	4	yes	—
371	C₄²	C₅×M₁₆	1	4	yes	—
372	C₄²	C₅×#41	1	4	yes	—
373	C₄²	C₅×#41	1	4	yes	—
374	C₂×C₅	—	2	4	no	—
375	C₂×C₅	#2283	1	1	yes	characteristic
376	C₂×C₅	C₂×#432	1	1	yes	characteristic
377	C₂×C₅	C₂×#432	1	1	yes	characteristic
378	C₂×C₅	#2920	1	1	yes	characteristic
379	C₂×C₅	#2920	1	1	yes	characteristic
380	C₂×C₅	#2920	1	1	yes	characteristic
381	C₂×C₅	#2920	1	1	yes	characteristic
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	C₅×#117	1	2	yes	—
387	C₂³	C₂×C₅×M₁₆	1	2	yes	—
388	C₂³	C₂×C₅×M₁₆	1	2	yes	—
389	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	C₅×#117	1	2	yes	—
422	C₂×C₄	C₅×#117	1	2	yes	—
423	C₂×C₄	C₅×#117	1	2	yes	—
424	C₂×C₄	C₅×#117	1	2	yes	—
425	C₂×C₄	C₅×#117	1	2	yes	—
426	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
427	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
428	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
429	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
430	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
431	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
432	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
433	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
434	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
435	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
436	C₂×C₄	C₂×C₅×#41	1	2	yes	—
437	C₂×C₄	C₂×C₅×#41	1	2	yes	—
438	C₂×C₄	C₂×C₅×#41	1	2	yes	—
439	C₈	—	4	8	no	—
440	C₅	#20778	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	C₅×#432	1	4	yes	—
448	C₂²	C₂×C₅×#117	1	1	yes	characteristic
449	C₂²	C₂×C₅×#117	1	1	yes	characteristic
450	C₂²	C₂×C₅×#117	1	1	yes	characteristic
451	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
452	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
453	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
454	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	C₅×#432	1	4	yes	—
468	C₄	C₅×#529	1	4	yes	—
469	C₂	—	2	4	no	—
470	C₂	C₅×#2283	1	1	yes	characteristic
471	C₂	C₂×C₅×#432	1	1	yes	characteristic
472	C₂	C₂×C₅×#432	1	1	yes	characteristic
473	C₂	C₅×#2920	1	1	yes	characteristic
474	C₂	C₅×#2920	1	1	yes	characteristic
475	C₂	C₅×#2920	1	1	yes	characteristic
476	C₂	C₅×#2920	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×#1839	C₂	semidirect
3. C₅×#1831	C₂	semidirect
6. C₅×#1767	C₂	semidirect
8. C₅×#1745	C₂	semidirect
31. #20778	C₅	direct (N × H)
79. #1839	C₂×C₅	semidirect
80. #1831	C₂×C₅	semidirect
83. #1767	C₂×C₅	semidirect
85. #1745	C₂×C₅	semidirect
440. C₅	#20778	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×C₄³×C₅	2
C₅×#1839	2
C₅×#1831	2
C₅×#1817	2
C₅×#1797	2
C₅×#1767	2
C₅×#1749	2
C₅×#1745	2
#20778	5

Subgroups — C5×#20778 #11943498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20778 #11943498