Subgroups — C₅×#70157 #14305798

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1957	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	—	2	2	no	—
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₅×#940	—	2	2	no	—
15	C₅×#940	C₄	1	4	yes	complemented
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#102	—	2	2	no	—
21	C₅×#832	—	2	2	no	—
22	C₅×#821	—	2	2	no	—
23	C₅×C₈×Dic₃	—	2	2	no	—
24	C₅×#809	—	2	2	no	—
25	#70157	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#127	—	3	1	no	—
27	C₂×C₅×#102	—	3	1	no	—
28	C₂×C₅×#102	—	3	1	no	—
29	C₂×C₅×#102	—	3	1	no	—
30	C₂×C₅×#102	D₃	1	1	yes	characteristic, complemented
31	C₂×C₄×C₅×C₈	—	3	1	no	—
32	C₅×#384	—	3	1	no	—
33	C₂⁴×C₃×C₅	—	2	1	no	—
34	C₂³×C₅×D₃	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	—	2	1	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₅×#67	—	2	8	no	—
44	C₂×C₅×#67	—	4	4	no	—
45	C₂×C₅×#67	—	4	4	no	—
46	C₂²×C₅×Dic₃	—	2	1	no	—
47	C₂²×C₅×Dic₃	D₄	1	2	yes	—
48	C₂×C₅×D₁₂	—	2	1	no	—
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₅×D₁₂	—	2	1	no	—
51	C₂×C₅×D₁₂	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	1	no	—
53	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	D₄	1	2	yes	complemented
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₅×C₄⋊Dic₃	—	2	1	no	—
60	C₅×C₄⋊Dic₃	—	2	1	no	—
61	C₅×Dic₃⋊C₄	—	4	4	no	—
62	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
63	C₄×C₅×Dic₃	D₄	1	2	yes	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	complemented
67	C₂×#940	C₂×C₅	1	1	yes	characteristic
68	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
72	#4975	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂²×C₅×D₄	—	6	2	no	—
76	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	—	3	1	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×#127	—	3	4	no	—
80	C₅×#127	—	6	2	no	—
81	C₂×C₅×C₄⋊C₄	—	3	1	no	—
82	C₂×C₅×C₄⋊C₄	—	6	2	no	—
83	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	6	2	no	—
87	C₅×#102	—	6	2	no	—
88	C₅×#102	—	6	2	no	—
89	C₄×C₅×C₈	—	6	2	no	—
90	#1957	—	3	1	no	Sylow
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	4	1	no	—
93	C₂³×C₃×C₅	—	4	1	no	—
94	C₂³×C₃×C₅	—	4	2	no	—
95	C₂³×C₃×C₅	—	4	2	no	—
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₅×D₃	—	4	1	no	—
100	C₂²×C₅×D₃	—	4	2	no	—
101	C₂²×C₅×D₃	—	4	2	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	—	2	2	no	—
104	C₃×C₅×D₄	—	4	1	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	—	4	2	no	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
114	C₅×#67	—	4	16	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	2	no	—
117	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
118	C₂×C₅×Dic₃	D₈	1	4	yes	—
119	C₂×C₅×Dic₃	SD₁₆	1	4	yes	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	—	2	2	no	—
122	C₅×D₁₂	—	4	1	no	—
123	C₅×D₁₂	—	4	1	no	—
124	C₃×C₅×C₈	—	2	2	no	—
125	C₅×C₃⋊C₈	—	2	2	no	—
126	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
127	C₂²×#67	—	2	2	no	—
128	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
129	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
131	#940	—	2	2	no	—
132	#940	C₄×C₅	1	4	yes	complemented
133	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×Dic₃⋊C₄	—	2	2	no	—
135	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#102	—	2	2	no	—
138	#832	—	2	2	no	—
139	#821	—	2	2	no	—
140	C₈×Dic₃	—	2	2	no	—
141	#809	—	2	2	no	—
142	C₂⁴×C₅	—	2	1	no	—
143	C₂⁴×C₅	—	6	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	3	2	no	—
150	C₂×C₅×D₄	—	6	8	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂×C₅×D₄	—	6	1	no	—
155	C₂×C₅×D₄	—	6	1	no	—
156	C₂×C₅×D₄	—	12	4	no	—
157	C₂×C₅×D₄	—	12	4	no	—
158	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	3	2	no	—
166	C₂×C₅×C₈	—	6	1	no	—
167	C₂×C₅×C₈	—	6	1	no	—
168	C₂×C₅×C₈	#67	1	2	yes	complemented
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	6	1	no	—
172	C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×C₄⋊C₄	—	12	4	no	—
174	C₄²×C₅	—	3	2	no	—
175	C₄²×C₅	—	3	2	no	—
176	C₂×#127	—	3	1	no	—
177	C₂×#102	—	3	1	no	—
178	C₂×#102	—	3	1	no	—
179	C₂×#102	—	3	1	no	—
180	C₂×#102	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂×C₄×C₈	—	3	1	no	—
182	#384	—	3	1	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	—	4	4	no	—
185	C₂²×C₃×C₅	—	8	2	no	—
186	C₂²×C₃×C₅	—	8	1	no	—
187	C₂²×C₃×C₅	—	8	1	no	—
188	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	#124	1	1	yes	characteristic
190	C₂²×C₃×C₅	#127	1	1	yes	characteristic
191	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
192	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
193	C₂×C₅×D₃	—	4	2	no	—
194	C₂×C₅×D₃	—	4	4	no	—
195	C₂×C₅×D₃	—	8	2	no	—
196	C₂×C₅×D₃	—	8	1	no	—
197	C₂×C₅×D₃	—	8	1	no	—
198	C₃×C₄×C₅	—	8	1	no	—
199	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
201	C₃×C₄×C₅	#121	1	1	yes	characteristic
202	C₃×C₄×C₅	#121	1	1	yes	characteristic
203	C₅×Dic₃	—	8	1	no	—
204	C₅×Dic₃	#102	1	8	yes	complemented
205	C₂⁴×C₃	—	2	1	no	—
206	C₂³×D₃	—	2	1	no	—
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	—	2	1	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	1	no	—
212	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
213	C₂²×C₃×C₄	—	2	1	no	—
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂×#67	—	2	8	no	—
216	C₂×#67	—	4	4	no	—
217	C₂×#67	—	4	4	no	—
218	C₂²×Dic₃	—	2	1	no	—
219	C₂²×Dic₃	C₅×D₄	1	2	yes	—
220	C₂×D₁₂	—	2	1	no	—
221	C₂×D₁₂	—	2	1	no	—
222	C₂×D₁₂	—	2	1	no	—
223	C₂×D₁₂	—	2	1	no	—
224	C₂×D₁₂	—	2	1	no	—
225	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₂×C₃×C₈	—	2	1	no	—
228	C₂×C₃×C₈	C₅×D₄	1	2	yes	complemented
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	—	2	1	no	—
231	C₄⋊Dic₃	—	2	1	no	—
232	C₄⋊Dic₃	—	2	1	no	—
233	Dic₃⋊C₄	—	4	4	no	—
234	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
235	C₄×Dic₃	C₅×D₄	1	2	yes	—
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂×C₃⋊C₈	—	2	1	no	—
238	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	complemented
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	4	1	no	—
241	C₂³×C₅	—	4	2	no	—
242	C₂³×C₅	—	4	2	no	—
243	C₂³×C₅	—	4	1	no	—
244	C₂³×C₅	—	6	2	no	—
245	C₂³×C₅	—	12	1	no	—
246	C₂³×C₅	—	12	2	no	—
247	C₂³×C₅	—	12	2	no	—
248	C₂³×C₅	—	12	1	no	—
249	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
250	C₅×D₄	—	2	2	no	—
251	C₅×D₄	—	2	2	no	—
252	C₅×D₄	—	4	1	no	—
253	C₅×D₄	—	4	1	no	—
254	C₅×D₄	—	6	2	no	—
255	C₅×D₄	—	6	2	no	—
256	C₅×D₄	—	12	16	no	—
257	C₅×D₄	—	12	1	no	—
258	C₅×D₄	—	12	1	no	—
259	C₂×C₄×C₅	—	3	4	no	—
260	C₂×C₄×C₅	—	3	4	no	—
261	C₂×C₄×C₅	—	3	4	no	—
262	C₂×C₄×C₅	—	4	2	no	—
263	C₂×C₄×C₅	—	4	1	no	—
264	C₂×C₄×C₅	—	12	2	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	#235	1	1	yes	characteristic
268	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	#237	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
272	C₅×C₈	—	2	2	no	—
273	C₅×C₈	—	6	2	no	—
274	C₂²×D₄	—	3	1	no	—
275	C₂²×D₄	—	6	2	no	—
276	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
277	C₂²×C₈	—	3	1	no	—
278	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
279	#127	—	3	4	no	—
280	#127	—	6	2	no	—
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₄⋊C₄	—	6	2	no	—
283	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂×C₄²	—	3	1	no	—
285	#102	—	2	2	no	—
286	#102	—	6	2	no	—
287	#102	—	6	2	no	—
288	#102	—	6	2	no	—
289	C₄×C₈	—	6	2	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	#390	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#102	1	2	yes	—
293	C₂×C₃×C₅	#486	1	2	yes	—
294	C₂×C₃×C₅	#492	1	1	yes	characteristic
295	C₂×C₃×C₅	#493	1	1	yes	characteristic
296	C₅×D₃	—	8	2	no	—
297	C₂³×C₃	—	2	2	no	—
298	C₂³×C₃	—	4	1	no	—
299	C₂³×C₃	—	4	1	no	—
300	C₂³×C₃	—	4	2	no	—
301	C₂³×C₃	—	4	2	no	—
302	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂²×D₃	—	2	2	no	—
304	C₂²×D₃	—	4	1	no	—
305	C₂²×D₃	—	4	1	no	—
306	C₂²×D₃	—	4	2	no	—
307	C₂²×D₃	—	4	2	no	—
308	C₃×D₄	—	2	2	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	4	1	no	—
311	C₃×D₄	—	4	1	no	—
312	C₂×C₃×C₄	—	4	1	no	—
313	C₂×C₃×C₄	—	4	2	no	—
314	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
319	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
320	#67	—	4	16	no	—
321	C₂×Dic₃	—	4	1	no	—
322	C₂×Dic₃	—	4	2	no	—
323	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
324	C₂×Dic₃	C₅×D₈	1	4	yes	—
325	C₂×Dic₃	C₅×SD₁₆	1	4	yes	—
326	D₁₂	—	2	2	no	—
327	D₁₂	—	2	2	no	—
328	D₁₂	—	4	1	no	—
329	D₁₂	—	4	1	no	—
330	C₃×C₈	—	2	2	no	—
331	C₃⋊C₈	—	2	2	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	4	no	—
334	C₂²×C₅	—	8	1	no	—
335	C₂²×C₅	—	8	1	no	—
336	C₂²×C₅	—	8	2	no	—
337	C₂²×C₅	—	12	2	no	—
338	C₂²×C₅	—	12	4	no	—
339	C₂²×C₅	—	24	1	no	—
340	C₂²×C₅	—	24	1	no	—
341	C₂²×C₅	—	24	2	no	—
342	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₅	#885	1	1	yes	characteristic
344	C₂²×C₅	D₃×D₈	1	2	yes	—
345	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
346	C₂²×C₅	#940	1	1	yes	characteristic
347	C₄×C₅	—	3	8	no	—
348	C₄×C₅	—	8	1	no	—
349	C₄×C₅	—	24	1	no	—
350	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
351	C₄×C₅	#884	1	1	yes	characteristic
352	C₄×C₅	C₄×#67	1	1	yes	characteristic
353	C₄×C₅	#939	1	1	yes	characteristic
354	C₂⁴	—	2	1	no	—
355	C₂⁴	—	6	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	3	2	no	—
362	C₂×D₄	—	6	8	no	—
363	C₂×D₄	—	6	1	no	—
364	C₂×D₄	—	6	1	no	—
365	C₂×D₄	—	6	1	no	—
366	C₂×D₄	—	6	1	no	—
367	C₂×D₄	—	6	1	no	—
368	C₂×D₄	—	12	4	no	—
369	C₂×D₄	—	12	4	no	—
370	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	3	2	no	—
373	C₂²×C₄	—	6	1	no	—
374	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	3	2	no	—
378	C₂×C₈	—	6	1	no	—
379	C₂×C₈	—	6	1	no	—
380	C₂×C₈	C₅×#67	1	2	yes	complemented
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	6	1	no	—
384	C₄⋊C₄	—	6	1	no	—
385	C₄⋊C₄	—	12	4	no	—
386	C₄²	—	3	2	no	—
387	C₄²	—	3	2	no	—
388	C₃×C₅	#1957	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	4	4	no	—
391	C₂²×C₃	—	8	2	no	—
392	C₂²×C₃	—	8	1	no	—
393	C₂²×C₃	—	8	1	no	—
394	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₃	C₅×#124	1	1	yes	characteristic
396	C₂²×C₃	C₅×#127	1	1	yes	characteristic
397	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
398	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
399	C₂×D₃	—	4	2	no	—
400	C₂×D₃	—	4	4	no	—
401	C₂×D₃	—	8	2	no	—
402	C₂×D₃	—	8	1	no	—
403	C₂×D₃	—	8	1	no	—
404	C₃×C₄	—	8	1	no	—
405	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
406	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
407	C₃×C₄	C₅×#121	1	1	yes	characteristic
408	C₃×C₄	C₅×#121	1	1	yes	characteristic
409	Dic₃	—	8	1	no	—
410	Dic₃	C₅×#102	1	8	yes	complemented
411	C₂×C₅	—	8	2	no	—
412	C₂×C₅	—	24	2	no	—
413	C₂×C₅	#4760	1	2	yes	—
414	C₂×C₅	D₃×#102	1	2	yes	—
415	C₂×C₅	#4957	1	1	yes	characteristic
416	C₂×C₅	#5151	1	1	yes	characteristic
417	C₂×C₅	#5175	1	1	yes	characteristic
418	C₂³	—	2	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	6	2	no	—
424	C₂³	—	12	1	no	—
425	C₂³	—	12	2	no	—
426	C₂³	—	12	2	no	—
427	C₂³	—	12	1	no	—
428	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	4	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	6	2	no	—
434	D₄	—	6	2	no	—
435	D₄	—	12	16	no	—
436	D₄	—	12	1	no	—
437	D₄	—	12	1	no	—
438	C₂×C₄	—	3	4	no	—
439	C₂×C₄	—	3	4	no	—
440	C₂×C₄	—	3	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	12	2	no	—
444	C₂×C₄	—	12	1	no	—
445	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
446	C₂×C₄	C₅×#235	1	1	yes	characteristic
447	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
448	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
449	C₂×C₄	C₅×#237	1	1	yes	characteristic
450	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	6	2	no	—
453	C₂×C₃	—	8	2	no	—
454	C₂×C₃	C₅×#390	1	1	yes	characteristic
455	C₂×C₃	C₂×C₅×#102	1	2	yes	—
456	C₂×C₃	C₅×#486	1	2	yes	—
457	C₂×C₃	C₅×#492	1	1	yes	characteristic
458	C₂×C₃	C₅×#493	1	1	yes	characteristic
459	D₃	—	8	2	no	—
460	C₅	#70157	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	—	4	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	12	2	no	—
467	C₂²	—	12	4	no	—
468	C₂²	—	24	1	no	—
469	C₂²	—	24	2	no	—
470	C₂²	—	24	1	no	—
471	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
472	C₂²	C₅×#885	1	1	yes	characteristic
473	C₂²	C₅×D₃×D₈	1	2	yes	—
474	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
475	C₂²	C₅×#940	1	1	yes	characteristic
476	C₄	—	3	8	no	—
477	C₄	—	8	1	no	—
478	C₄	—	24	1	no	—
479	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
480	C₄	C₅×#884	1	1	yes	characteristic
481	C₄	C₄×C₅×#67	1	1	yes	characteristic
482	C₄	C₅×#939	1	1	yes	characteristic
483	C₃	C₅×#1957	1	1	yes	characteristic, complemented, Sylow
484	C₂	—	8	2	no	—
485	C₂	—	24	2	no	—
486	C₂	C₅×#4760	1	2	yes	—
487	C₂	C₅×D₃×#102	1	2	yes	—
488	C₂	C₅×#4957	1	1	yes	characteristic
489	C₂	C₅×#5151	1	1	yes	characteristic
490	C₂	C₅×#5175	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#102	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#940	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₅×#1957
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#102	C₂	semidirect
3. C₂×C₅×#832	C₂	semidirect
4. C₂×C₅×#821	C₂	semidirect
5. C₂×C₅×C₈×Dic₃	C₂	semidirect
6. C₅×#4975	C₂	semidirect
7. C₂×C₅×#809	C₂	semidirect
15. C₅×#940	C₄	semidirect
25. #70157	C₅	direct (N × H)
30. C₂×C₅×#102	D₃	semidirect
56. C₂×C₃×C₅×C₈	D₄	semidirect
66. C₂×C₅×C₃⋊C₈	D₄	semidirect
68. C₂×C₃×#102	C₂×C₅	semidirect
69. C₂×#832	C₂×C₅	semidirect
70. C₂×#821	C₂×C₅	semidirect
71. C₂×C₈×Dic₃	C₂×C₅	semidirect
72. #4975	C₂×C₅	semidirect
73. C₂×#809	C₂×C₅	semidirect
132. #940	C₄×C₅	semidirect
168. C₂×C₅×C₈	#67	semidirect
180. C₂×#102	C₅×D₃	semidirect
204. C₅×Dic₃	#102	semidirect
228. C₂×C₃×C₈	C₅×D₄	semidirect
238. C₂×C₃⋊C₈	C₅×D₄	semidirect
380. C₂×C₈	C₅×#67	semidirect
388. C₃×C₅	#1957	semidirect
410. Dic₃	C₅×#102	semidirect
460. C₅	#70157	direct (N × H)
483. C₃	C₅×#1957	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#940	2
C₂×C₃×C₅×#102	2
C₂×C₅×#832	2
C₂×C₅×#821	2
C₂×C₅×C₈×Dic₃	2
C₅×#4975	2
C₂×C₅×#809	2
C₅×#1957	3
#70157	5

Subgroups — C5×#70157 #14305798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70157 #14305798