Subgroups — C₅×#21435 #11944155

Order 1280.

790 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₅×#1924	C₂	1	2	yes	maximal
3	C₅×#1923	C₂	1	2	yes	maximal
4	C₅×#1917	C₂	1	2	yes	maximal, complemented
5	C₅×#1916	C₂	1	2	yes	maximal, complemented
6	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1749	C₂	1	1	yes	maximal, characteristic
9	C₅×#1749	C₂	1	1	yes	maximal, characteristic
10	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#117	C₄	1	1	yes	characteristic
13	C₂×C₅×#117	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#97	C₂²	1	1	yes	characteristic
20	C₂×C₅×#97	C₂²	1	1	yes	characteristic
21	C₂×C₅×#97	C₂²	1	1	yes	characteristic
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
30	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₅×#376	C₄	1	1	yes	characteristic
34	C₅×#376	C₄	1	1	yes	characteristic
35	C₄³×C₅	C₂²	1	1	yes	characteristic
36	C₄³×C₅	C₂²	1	1	yes	characteristic
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#21435	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₅×#117	—	2	4	no	—
52	C₅×#117	—	2	4	no	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	—	2	2	no	—
62	C₂×C₄²×C₅	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	2	4	no	—
80	C₅×C₄⋊C₈	—	2	4	no	—
81	C₅×C₂²⋊C₈	—	2	4	no	—
82	C₅×C₂²⋊C₈	—	2	4	no	—
83	C₅×#97	—	2	4	no	—
84	C₅×#97	—	2	2	no	—
85	C₅×#97	—	2	2	no	—
86	C₅×#97	—	2	2	no	—
87	C₅×#97	—	2	2	no	—
88	C₄×C₅×C₈	—	2	4	no	—
89	C₅×#95	C₂×C₄	1	1	yes	characteristic
90	C₅×#95	C₂×C₄	1	1	yes	characteristic
91	C₅×#95	C₂×C₄	1	1	yes	characteristic
92	C₅×#95	C₂×C₄	1	1	yes	characteristic
93	C₅×#95	C₂×C₄	1	1	yes	characteristic
94	C₅×#95	C₂×C₄	1	1	yes	characteristic
95	C₅×#95	C₂×C₄	1	1	yes	characteristic
96	C₅×#95	C₂×C₄	1	1	yes	characteristic
97	C₄×#117	C₂×C₅	1	1	yes	characteristic
98	#1924	C₂×C₅	1	2	yes	—
99	#1923	C₂×C₅	1	2	yes	—
100	#1917	C₂×C₅	1	2	yes	complemented
101	#1916	C₂×C₅	1	2	yes	complemented
102	#1767	C₂×C₅	1	1	yes	characteristic, complemented
103	#1767	C₂×C₅	1	1	yes	characteristic, complemented
104	#1749	C₂×C₅	1	1	yes	characteristic
105	#1749	C₂×C₅	1	1	yes	characteristic
106	#1745	C₂×C₅	1	1	yes	characteristic, complemented
107	C₄×#97	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	#41	1	4	yes	—
144	C₂×C₅×C₈	#41	1	4	yes	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	2	2	no	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	M₁₆	1	4	yes	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	4	1	no	—
166	C₄²×C₅	—	4	1	no	—
167	C₄²×C₅	—	4	1	no	—
168	C₄²×C₅	—	4	1	no	—
169	C₄²×C₅	#41	1	2	yes	—
170	C₄²×C₅	#41	1	2	yes	—
171	C₂×#117	C₄×C₅	1	1	yes	characteristic
172	C₂×#117	C₄×C₅	1	1	yes	characteristic
173	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
178	C₂×#97	C₂²×C₅	1	2	yes	—
179	C₂×#97	C₂²×C₅	1	1	yes	characteristic
180	C₂×#97	C₂²×C₅	1	1	yes	characteristic
181	C₂×#97	C₂²×C₅	1	1	yes	characteristic
182	C₂×#97	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
184	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
185	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
189	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
190	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	#376	C₄×C₅	1	1	yes	characteristic
193	#376	C₄×C₅	1	1	yes	characteristic
194	C₄³	C₂²×C₅	1	1	yes	characteristic
195	C₄³	C₂²×C₅	1	1	yes	characteristic
196	#336	C₂²×C₅	1	2	yes	—
197	#336	C₂²×C₅	1	2	yes	—
198	#336	C₂²×C₅	1	2	yes	—
199	#336	C₂²×C₅	1	2	yes	—
200	#336	C₂²×C₅	1	2	yes	—
201	#336	C₂²×C₅	1	2	yes	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	—	2	1	no	—
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	—	2	1	no	—
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	—	2	1	no	—
208	C₂³×C₅	C₂×M₁₆	1	2	yes	—
209	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	—	2	8	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	4	4	no	—
244	C₂×C₄×C₅	—	4	2	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	#117	1	2	yes	—
247	C₂×C₄×C₅	#117	1	2	yes	—
248	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
249	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
250	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
251	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
252	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
253	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#41	1	2	yes	—
256	C₂×C₄×C₅	C₂×#41	1	2	yes	—
257	C₅×C₈	—	2	4	no	—
258	C₅×C₈	—	2	4	no	—
259	C₅×C₈	—	4	2	no	—
260	C₅×C₈	—	4	2	no	—
261	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
262	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₅	1	2	yes	—
265	C₂²×C₈	C₂³×C₅	1	2	yes	—
266	C₂²×C₈	C₂³×C₅	1	2	yes	—
267	C₂²×C₈	C₂³×C₅	1	2	yes	—
268	#117	—	2	4	no	—
269	#117	—	2	4	no	—
270	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
281	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
282	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
286	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
287	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
288	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
296	C₄⋊C₈	—	2	4	no	—
297	C₄⋊C₈	—	2	4	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	C₂²⋊C₈	—	2	4	no	—
300	#97	—	2	4	no	—
301	#97	—	2	2	no	—
302	#97	—	2	2	no	—
303	#97	—	2	2	no	—
304	#97	—	2	2	no	—
305	C₄×C₈	—	2	4	no	—
306	#95	C₂×C₄×C₅	1	1	yes	characteristic
307	#95	C₂×C₄×C₅	1	1	yes	characteristic
308	#95	C₂×C₄×C₅	1	1	yes	characteristic
309	#95	C₂×C₄×C₅	1	1	yes	characteristic
310	#95	C₂×C₄×C₅	1	1	yes	characteristic
311	#95	C₂×C₄×C₅	1	1	yes	characteristic
312	#95	C₂×C₄×C₅	1	1	yes	characteristic
313	#95	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	2	2	no	—
316	C₂²×C₅	—	2	2	no	—
317	C₂²×C₅	—	4	1	no	—
318	C₂²×C₅	—	4	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	C₂×#117	1	1	yes	characteristic
322	C₂²×C₅	C₄×#41	1	1	yes	characteristic
323	C₂²×C₅	C₄×#41	1	1	yes	characteristic
324	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
325	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
326	C₂²×C₅	#568	1	1	yes	characteristic
327	C₂²×C₅	#568	1	1	yes	characteristic
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	—	2	2	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	2	2	no	—
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	2	2	no	—
335	C₄×C₅	—	4	1	no	—
336	C₄×C₅	—	4	1	no	—
337	C₄×C₅	—	4	1	no	—
338	C₄×C₅	—	4	1	no	—
339	C₄×C₅	—	4	1	no	—
340	C₄×C₅	—	4	1	no	—
341	C₄×C₅	#529	1	2	yes	—
342	C₄×C₅	#529	1	2	yes	—
343	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	C₅×#41	1	4	yes	—
379	C₂×C₈	C₅×#41	1	4	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	C₅×M₁₆	1	4	yes	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	1	no	—
403	C₄²	—	4	1	no	—
404	C₄²	C₅×#41	1	2	yes	—
405	C₄²	C₅×#41	1	2	yes	—
406	C₂×C₅	—	4	2	no	—
407	C₂×C₅	#2298	1	1	yes	characteristic
408	C₂×C₅	#2920	1	1	yes	characteristic
409	C₂×C₅	#2921	1	1	yes	characteristic
410	C₂×C₅	#2970	1	1	yes	characteristic
411	C₂×C₅	#2970	1	1	yes	characteristic
412	C₂×C₅	#2970	1	1	yes	characteristic
413	C₂×C₅	#2971	1	1	yes	characteristic
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	C₂×C₅×M₁₆	1	2	yes	—
421	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	C₅×#117	1	2	yes	—
459	C₂×C₄	C₅×#117	1	2	yes	—
460	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
461	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
462	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
463	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
464	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
465	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
467	C₂×C₄	C₂×C₅×#41	1	2	yes	—
468	C₂×C₄	C₂×C₅×#41	1	2	yes	—
469	C₈	—	2	4	no	—
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₅	#21435	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	C₂×C₅×#117	1	1	yes	characteristic
482	C₂²	C₄×C₅×#41	1	1	yes	characteristic
483	C₂²	C₄×C₅×#41	1	1	yes	characteristic
484	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
485	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
486	C₂²	C₅×#568	1	1	yes	characteristic
487	C₂²	C₅×#568	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	1	no	—
501	C₄	C₅×#529	1	2	yes	—
502	C₄	C₅×#529	1	2	yes	—
503	C₂	—	4	2	no	—
504	C₂	C₅×#2298	1	1	yes	characteristic
505	C₂	C₅×#2920	1	1	yes	characteristic
506	C₂	C₅×#2921	1	1	yes	characteristic
507	C₂	C₅×#2970	1	1	yes	characteristic
508	C₂	C₅×#2970	1	1	yes	characteristic
509	C₂	C₅×#2970	1	1	yes	characteristic
510	C₂	C₅×#2971	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
4. C₅×#1917	C₂	semidirect
5. C₅×#1916	C₂	semidirect
6. C₅×#1767	C₂	semidirect
7. C₅×#1767	C₂	semidirect
10. C₅×#1745	C₂	semidirect
11. C₄×C₅×#97	C₂	semidirect
43. #21435	C₅	direct (N × H)
100. #1917	C₂×C₅	semidirect
101. #1916	C₂×C₅	semidirect
102. #1767	C₂×C₅	semidirect
103. #1767	C₂×C₅	semidirect
106. #1745	C₂×C₅	semidirect
107. C₄×#97	C₂×C₅	semidirect
473. C₅	#21435	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×#117	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1767	2
C₅×#1749	2
C₅×#1745	2
C₄×C₅×#97	2
#21435	5

Subgroups — C5×#21435 #11944155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21435 #11944155