Subgroups — C₅×#70160 #14305952

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 488 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×#815	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1961	—	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×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#102	—	2	2	no	—
20	C₅×#832	—	2	2	no	—
21	C₅×C₃⋊#95	—	2	2	no	—
22	C₅×#821	—	2	2	no	—
23	C₅×#815	—	2	2	no	—
24	C₅×#809	—	2	2	no	—
25	#70160	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×C₅×#97	—	3	1	no	—
32	C₅×#382	—	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	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
62	C₄×C₅×Dic₃	D₄	1	2	yes	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	complemented
66	C₂×#940	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#821	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
71	#4977	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×C₅×D₄	—	3	1	no	—
74	C₂²×C₅×D₄	—	6	2	no	—
75	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
76	C₂²×C₅×C₈	—	3	1	no	—
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₅×#127	—	3	4	no	—
79	C₅×#127	—	6	2	no	—
80	C₂×C₅×C₄⋊C₄	—	3	1	no	—
81	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₂×C₄²×C₅	—	3	1	no	—
83	C₅×#102	—	2	2	no	—
84	C₅×#102	—	6	2	no	—
85	C₅×#102	—	6	2	no	—
86	C₅×#102	—	6	2	no	—
87	C₅×#97	—	6	2	no	—
88	C₅×#95	—	6	2	no	—
89	#1961	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	4	1	no	—
92	C₂³×C₃×C₅	—	4	1	no	—
93	C₂³×C₃×C₅	—	4	2	no	—
94	C₂³×C₃×C₅	—	4	2	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	2	no	—
97	C₂²×C₅×D₃	—	4	1	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₅×D₃	—	4	2	no	—
100	C₂²×C₅×D₃	—	4	2	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	—	4	1	no	—
104	C₃×C₅×D₄	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	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	#41	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
113	C₅×#67	—	4	16	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	2	no	—
118	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	—	2	2	no	—
121	C₅×D₁₂	—	4	1	no	—
122	C₅×D₁₂	—	4	1	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₅×C₃⋊C₈	—	2	2	no	—
125	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
126	C₂²×#67	—	2	2	no	—
127	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
128	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	#940	—	2	2	no	—
131	#940	C₄×C₅	1	4	yes	complemented
132	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	C₃×#102	—	2	2	no	—
136	#832	—	2	2	no	—
137	C₃⋊#95	—	2	2	no	—
138	#821	—	2	2	no	—
139	#815	—	2	2	no	—
140	#809	—	2	2	no	—
141	C₂⁴×C₅	—	2	1	no	—
142	C₂⁴×C₅	—	6	1	no	—
143	C₂×C₅×D₄	—	2	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	—	3	2	no	—
149	C₂×C₅×D₄	—	6	8	no	—
150	C₂×C₅×D₄	—	6	1	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	—	12	4	no	—
156	C₂×C₅×D₄	—	12	4	no	—
157	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	3	2	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₂×C₅×C₈	—	6	1	no	—
167	C₂×C₅×C₈	#67	1	2	yes	complemented
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	6	1	no	—
171	C₅×C₄⋊C₄	—	6	1	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₄²×C₅	—	3	2	no	—
174	C₂×#127	—	3	1	no	—
175	C₂×#102	—	3	1	no	—
176	C₂×#102	—	3	1	no	—
177	C₂×#102	—	3	1	no	—
178	C₂×#102	C₅×D₃	1	1	yes	characteristic, complemented
179	C₂×#97	—	3	1	no	—
180	#382	—	3	1	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	4	no	—
183	C₂²×C₃×C₅	—	8	2	no	—
184	C₂²×C₃×C₅	—	8	1	no	—
185	C₂²×C₃×C₅	—	8	1	no	—
186	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	#124	1	1	yes	characteristic
188	C₂²×C₃×C₅	#127	1	1	yes	characteristic
189	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
190	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₅×D₃	—	4	2	no	—
192	C₂×C₅×D₃	—	4	4	no	—
193	C₂×C₅×D₃	—	8	2	no	—
194	C₂×C₅×D₃	—	8	1	no	—
195	C₂×C₅×D₃	—	8	1	no	—
196	C₃×C₄×C₅	—	8	1	no	—
197	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
198	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	#121	1	1	yes	characteristic
201	C₅×Dic₃	—	2	4	no	—
202	C₅×Dic₃	—	8	1	no	—
203	C₂⁴×C₃	—	2	1	no	—
204	C₂³×D₃	—	2	1	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	—	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	C₂×C₄×C₅	1	2	yes	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂×#67	—	2	8	no	—
214	C₂×#67	—	4	4	no	—
215	C₂×#67	—	4	4	no	—
216	C₂²×Dic₃	—	2	1	no	—
217	C₂²×Dic₃	C₅×D₄	1	2	yes	—
218	C₂×D₁₂	—	2	1	no	—
219	C₂×D₁₂	—	2	1	no	—
220	C₂×D₁₂	—	2	1	no	—
221	C₂×D₁₂	—	2	1	no	—
222	C₂×D₁₂	—	2	1	no	—
223	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	C₅×D₄	1	2	yes	complemented
227	C₃×C₄⋊C₄	—	2	1	no	—
228	C₃×C₄⋊C₄	—	2	1	no	—
229	C₄⋊Dic₃	—	2	1	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
232	C₄×Dic₃	C₅×D₄	1	2	yes	—
233	C₂×C₃⋊C₈	—	2	1	no	—
234	C₂×C₃⋊C₈	—	2	1	no	—
235	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	complemented
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	4	1	no	—
238	C₂³×C₅	—	4	2	no	—
239	C₂³×C₅	—	4	2	no	—
240	C₂³×C₅	—	4	1	no	—
241	C₂³×C₅	—	6	2	no	—
242	C₂³×C₅	—	12	1	no	—
243	C₂³×C₅	—	12	2	no	—
244	C₂³×C₅	—	12	2	no	—
245	C₂³×C₅	—	12	1	no	—
246	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	2	2	no	—
249	C₅×D₄	—	4	1	no	—
250	C₅×D₄	—	4	1	no	—
251	C₅×D₄	—	6	2	no	—
252	C₅×D₄	—	6	2	no	—
253	C₅×D₄	—	12	16	no	—
254	C₅×D₄	—	12	1	no	—
255	C₅×D₄	—	12	1	no	—
256	C₂×C₄×C₅	—	3	4	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	1	no	—
259	C₂×C₄×C₅	—	6	2	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	12	2	no	—
262	C₂×C₄×C₅	—	12	1	no	—
263	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂×C₄×C₅	#235	1	1	yes	characteristic
265	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅	#237	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
269	C₅×C₈	—	2	2	no	—
270	C₅×C₈	—	6	2	no	—
271	C₂²×D₄	—	3	1	no	—
272	C₂²×D₄	—	6	2	no	—
273	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
274	C₂²×C₈	—	3	1	no	—
275	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
276	#127	—	3	4	no	—
277	#127	—	6	2	no	—
278	C₂×C₄⋊C₄	—	3	1	no	—
279	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂×C₄²	—	3	1	no	—
281	#102	—	2	2	no	—
282	#102	—	6	2	no	—
283	#102	—	6	2	no	—
284	#102	—	6	2	no	—
285	#97	—	6	2	no	—
286	#95	—	6	2	no	—
287	C₂×C₃×C₅	—	8	2	no	—
288	C₂×C₃×C₅	#390	1	1	yes	characteristic
289	C₂×C₃×C₅	#418	1	2	yes	—
290	C₂×C₃×C₅	#490	1	2	yes	—
291	C₂×C₃×C₅	#496	1	1	yes	characteristic
292	C₂×C₃×C₅	#496	1	1	yes	characteristic
293	C₅×D₃	—	8	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	4	1	no	—
296	C₂³×C₃	—	4	1	no	—
297	C₂³×C₃	—	4	2	no	—
298	C₂³×C₃	—	4	2	no	—
299	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂²×D₃	—	2	2	no	—
301	C₂²×D₃	—	4	1	no	—
302	C₂²×D₃	—	4	1	no	—
303	C₂²×D₃	—	4	2	no	—
304	C₂²×D₃	—	4	2	no	—
305	C₃×D₄	—	2	2	no	—
306	C₃×D₄	—	2	2	no	—
307	C₃×D₄	—	4	1	no	—
308	C₃×D₄	—	4	1	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	—	4	2	no	—
311	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
316	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
317	#67	—	4	16	no	—
318	C₂×Dic₃	—	2	2	no	—
319	C₂×Dic₃	—	2	2	no	—
320	C₂×Dic₃	—	4	1	no	—
321	C₂×Dic₃	—	4	2	no	—
322	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
323	D₁₂	—	2	2	no	—
324	D₁₂	—	2	2	no	—
325	D₁₂	—	4	1	no	—
326	D₁₂	—	4	1	no	—
327	C₃×C₈	—	2	2	no	—
328	C₃⋊C₈	—	2	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	4	4	no	—
331	C₂²×C₅	—	8	1	no	—
332	C₂²×C₅	—	8	1	no	—
333	C₂²×C₅	—	8	2	no	—
334	C₂²×C₅	—	12	2	no	—
335	C₂²×C₅	—	12	4	no	—
336	C₂²×C₅	—	24	1	no	—
337	C₂²×C₅	—	24	1	no	—
338	C₂²×C₅	—	24	2	no	—
339	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₅	#885	1	1	yes	characteristic
341	C₂²×C₅	#911	1	2	yes	—
342	C₂²×C₅	#914	1	2	yes	—
343	C₂²×C₅	#940	1	1	yes	characteristic
344	C₄×C₅	—	6	4	no	—
345	C₄×C₅	—	8	1	no	—
346	C₄×C₅	—	24	1	no	—
347	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
348	C₄×C₅	#884	1	1	yes	characteristic
349	C₄×C₅	C₄×#67	1	1	yes	characteristic
350	C₄×C₅	#939	1	1	yes	characteristic
351	C₂⁴	—	2	1	no	—
352	C₂⁴	—	6	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	3	2	no	—
359	C₂×D₄	—	6	8	no	—
360	C₂×D₄	—	6	1	no	—
361	C₂×D₄	—	6	1	no	—
362	C₂×D₄	—	6	1	no	—
363	C₂×D₄	—	6	1	no	—
364	C₂×D₄	—	6	1	no	—
365	C₂×D₄	—	12	4	no	—
366	C₂×D₄	—	12	4	no	—
367	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	3	2	no	—
370	C₂²×C₄	—	6	1	no	—
371	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	6	1	no	—
376	C₂×C₈	—	6	1	no	—
377	C₂×C₈	C₅×#67	1	2	yes	complemented
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	6	1	no	—
381	C₄⋊C₄	—	6	1	no	—
382	C₄²	—	3	2	no	—
383	C₄²	—	3	2	no	—
384	C₃×C₅	#1961	1	1	yes	characteristic, complemented, Hall
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	8	2	no	—
388	C₂²×C₃	—	8	1	no	—
389	C₂²×C₃	—	8	1	no	—
390	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×C₃	C₅×#124	1	1	yes	characteristic
392	C₂²×C₃	C₅×#127	1	1	yes	characteristic
393	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
394	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
395	C₂×D₃	—	4	2	no	—
396	C₂×D₃	—	4	4	no	—
397	C₂×D₃	—	8	2	no	—
398	C₂×D₃	—	8	1	no	—
399	C₂×D₃	—	8	1	no	—
400	C₃×C₄	—	8	1	no	—
401	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
402	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
403	C₃×C₄	C₅×#121	1	1	yes	characteristic
404	C₃×C₄	C₅×#121	1	1	yes	characteristic
405	Dic₃	—	2	4	no	—
406	Dic₃	—	8	1	no	—
407	C₂×C₅	—	8	2	no	—
408	C₂×C₅	—	24	2	no	—
409	C₂×C₅	#4764	1	2	yes	—
410	C₂×C₅	#4770	1	2	yes	—
411	C₂×C₅	#4957	1	1	yes	characteristic
412	C₂×C₅	#5154	1	1	yes	characteristic
413	C₂×C₅	#5176	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	6	2	no	—
420	C₂³	—	12	1	no	—
421	C₂³	—	12	2	no	—
422	C₂³	—	12	2	no	—
423	C₂³	—	12	1	no	—
424	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	1	no	—
428	D₄	—	4	1	no	—
429	D₄	—	6	2	no	—
430	D₄	—	6	2	no	—
431	D₄	—	12	16	no	—
432	D₄	—	12	1	no	—
433	D₄	—	12	1	no	—
434	C₂×C₄	—	3	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	6	2	no	—
438	C₂×C₄	—	6	2	no	—
439	C₂×C₄	—	12	2	no	—
440	C₂×C₄	—	12	1	no	—
441	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
442	C₂×C₄	C₅×#235	1	1	yes	characteristic
443	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
444	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
445	C₂×C₄	C₅×#237	1	1	yes	characteristic
446	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	6	2	no	—
449	C₂×C₃	—	8	2	no	—
450	C₂×C₃	C₅×#390	1	1	yes	characteristic
451	C₂×C₃	C₅×#418	1	2	yes	—
452	C₂×C₃	C₅×#490	1	2	yes	—
453	C₂×C₃	C₅×#496	1	1	yes	characteristic
454	C₂×C₃	C₅×#496	1	1	yes	characteristic
455	D₃	—	8	2	no	—
456	C₅	#70160	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²	—	4	2	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	12	2	no	—
463	C₂²	—	12	4	no	—
464	C₂²	—	24	1	no	—
465	C₂²	—	24	2	no	—
466	C₂²	—	24	1	no	—
467	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²	C₅×#885	1	1	yes	characteristic
469	C₂²	C₅×#911	1	2	yes	—
470	C₂²	C₅×#914	1	2	yes	—
471	C₂²	C₅×#940	1	1	yes	characteristic
472	C₄	—	6	4	no	—
473	C₄	—	8	1	no	—
474	C₄	—	24	1	no	—
475	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
476	C₄	C₅×#884	1	1	yes	characteristic
477	C₄	C₄×C₅×#67	1	1	yes	characteristic
478	C₄	C₅×#939	1	1	yes	characteristic
479	C₃	C₅×#1961	1	1	yes	characteristic, complemented, Sylow
480	C₂	—	8	2	no	—
481	C₂	—	24	2	no	—
482	C₂	C₅×#4764	1	2	yes	—
483	C₂	C₅×#4770	1	2	yes	—
484	C₂	C₅×#4957	1	1	yes	characteristic
485	C₂	C₅×#5154	1	1	yes	characteristic
486	C₂	C₅×#5176	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×#1961
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×#815	C₂	semidirect
6. C₅×#4977	C₂	semidirect
7. C₂×C₅×#809	C₂	semidirect
15. C₅×#940	C₄	semidirect
25. #70160	C₅	direct (N × H)
30. C₂×C₅×#102	D₃	semidirect
56. C₂×C₃×C₅×C₈	D₄	semidirect
65. C₂×C₅×C₃⋊C₈	D₄	semidirect
67. C₂×C₃×#102	C₂×C₅	semidirect
68. C₂×#832	C₂×C₅	semidirect
69. C₂×#821	C₂×C₅	semidirect
70. C₂×#815	C₂×C₅	semidirect
71. #4977	C₂×C₅	semidirect
72. C₂×#809	C₂×C₅	semidirect
131. #940	C₄×C₅	semidirect
167. C₂×C₅×C₈	#67	semidirect
178. C₂×#102	C₅×D₃	semidirect
226. C₂×C₃×C₈	C₅×D₄	semidirect
235. C₂×C₃⋊C₈	C₅×D₄	semidirect
377. C₂×C₈	C₅×#67	semidirect
384. C₃×C₅	#1961	semidirect
456. C₅	#70160	direct (N × H)
479. C₃	C₅×#1961	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×#815	2
C₅×#4977	2
C₂×C₅×#809	2
C₅×#1961	3
#70160	5

Subgroups — C5×#70160 #14305952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70160 #14305952