Subgroups — C₅×#10612596 #72242548

Order 3200.

1178 conjugacy classes of subgroups.

The subgroup lattice has 631 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#4053	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#65941	C₂	1	2	yes	maximal, complemented
4	C₅²×#469	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#65448	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#65424	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#65327	C₂	1	2	yes	maximal, complemented
8	C₅×#65154	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#65149	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#65064	C₂	1	2	yes	maximal, complemented
11	C₅×#65059	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×D₄×D₅	C₂²	1	2	yes	—
13	C₂×C₅×#709	C₂²	1	1	yes	characteristic
14	C₂×C₅²×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₅²×M₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₅²×#121	C₂²	1	2	yes	complemented
17	C₅×#4086	—	2	2	no	—
18	C₅×#4084	C₂²	1	2	yes	complemented
19	C₅×#4083	—	2	2	no	—
20	C₂×C₅×#686	C₂²	1	2	yes	—
21	C₅×#4076	C₂²	1	2	yes	complemented
22	C₂²×C₅×#168	C₂²	1	1	yes	characteristic, complemented
23	C₅×D₅×D₈	—	2	4	no	—
24	C₅×#4053	—	2	4	no	—
25	C₂×C₅×D₄₀	C₂²	1	1	yes	characteristic
26	C₂×C₅×#676	C₂²	1	1	yes	characteristic
27	C₂×C₅×#676	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
30	C₅×#4041	C₂²	1	2	yes	complemented
31	C₅×#4038	C₂²	1	2	yes	—
32	C₅×#4031	—	2	2	no	—
33	C₅×#4028	—	2	2	no	—
34	C₅²×#106	C₂²	1	1	yes	characteristic, complemented
35	C₅²×#102	C₂²	1	2	yes	complemented
36	C₅×#3964	C₂²	1	2	yes	complemented
37	C₅×#3953	C₂²	1	2	yes	complemented
38	C₅×#3949	C₂²	1	1	yes	characteristic, complemented
39	C₅×#3941	C₂²	1	2	yes	complemented
40	C₅×#3939	C₂²	1	2	yes	complemented
41	C₅×#3058	—	5	1	no	maximal
42	#10612596	C₅	1	1	yes	maximal, characteristic, direct product factor
43	C₂³×C₅×D₅	—	2	2	no	—
44	C₂×C₅²×D₄	—	2	2	no	—
45	C₂×C₅²×D₄	C₂³	1	2	yes	—
46	C₂²×C₄×C₅²	C₂³	1	1	yes	characteristic
47	C₂×C₅×C₂²⋊D₅	—	2	2	no	—
48	C₂×C₅×C₂²⋊D₅	—	2	2	no	—
49	C₂×C₅×C₂²⋊D₅	—	2	2	no	—
50	C₂×C₅×C₂²⋊D₅	D₄	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊D₅	D₄	1	1	yes	characteristic
52	C₅×D₄×D₅	—	2	4	no	—
53	C₅×D₄×D₅	—	2	4	no	—
54	C₅×#709	—	2	2	no	—
55	C₅×#709	—	2	2	no	—
56	C₂×C₅×D₂₀	—	2	2	no	—
57	C₂×C₅×D₂₀	D₄	1	1	yes	characteristic
58	C₂×C₅×D₂₀	C₂³	1	2	yes	—
59	C₂×C₄×C₅×D₅	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₅	C₂³	1	1	yes	characteristic
61	C₂×C₅×Dic₁₀	D₄	1	1	yes	characteristic
62	C₅²×D₈	—	2	2	no	—
63	C₅²×M₁₆	—	2	2	no	—
64	C₂×C₅²×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₅²×C₈	C₂³	1	1	yes	characteristic
66	C₅²×C₄⋊C₄	C₂³	1	2	yes	—
67	C₅²×C₂²⋊C₄	—	2	2	no	—
68	C₅×C₂²⋊Dic₅	—	2	2	no	—
69	C₅×#686	—	2	4	no	—
70	C₅×#685	—	2	2	no	—
71	C₅×#685	—	2	2	no	—
72	C₅×#685	—	2	2	no	—
73	C₅×C₄⋊Dic₅	C₂³	1	2	yes	—
74	C₄×C₅×Dic₅	—	2	2	no	—
75	C₂×C₅×#168	—	2	2	no	—
76	C₂×C₅×#168	C₂³	1	1	yes	characteristic
77	C₂×C₅×#168	C₂³	1	1	yes	characteristic
78	C₅×D₄₀	—	2	2	no	—
79	C₅×#676	—	2	2	no	—
80	C₅×#676	—	2	2	no	—
81	C₅×C₈×D₅	—	2	2	no	—
82	C₅×C₈×D₅	D₄	1	4	yes	complemented
83	C₂²×C₅×D₈	—	5	1	no	—
84	C₂×C₅×#131	—	5	1	no	—
85	C₅×#535	—	5	2	no	—
86	C₂×D₅×D₈	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#4053	C₂×C₅	1	1	yes	characteristic, complemented
88	#65941	C₂×C₅	1	2	yes	complemented
89	C₅×#469	—	2	2	no	—
90	C₅×#469	—	5	1	no	—
91	C₅×#469	—	5	1	no	—
92	C₅×#469	—	5	1	no	—
93	C₅×#469	D₅	1	1	yes	characteristic, complemented
94	C₅×#469	C₂×C₅	1	1	yes	characteristic, complemented
95	C₅×#466	—	5	2	no	—
96	C₅×#466	—	5	2	no	—
97	C₅×#427	—	5	1	no	—
98	C₅×#418	—	5	2	no	—
99	#65448	C₂×C₅	1	1	yes	characteristic, complemented
100	#65424	C₂×C₅	1	1	yes	characteristic, complemented
101	#65327	C₂×C₅	1	2	yes	complemented
102	#65154	C₂×C₅	1	1	yes	characteristic, complemented
103	#65149	C₂×C₅	1	1	yes	characteristic, complemented
104	#65064	C₂×C₅	1	2	yes	complemented
105	#65059	C₂×C₅	1	2	yes	complemented
106	C₂³×C₅²	—	2	2	no	—
107	C₂³×C₅²	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₅×D₅	—	2	2	no	—
109	C₂²×C₅×D₅	—	4	4	no	—
110	C₂²×C₅×D₅	—	8	2	no	—
111	C₂²×C₅×D₅	—	8	2	no	—
112	C₂²×C₅×D₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₅×D₅	C₂×D₄	1	1	yes	characteristic
114	C₅²×D₄	—	2	2	no	—
115	C₅²×D₄	—	2	2	no	—
116	C₅²×D₄	—	8	2	no	—
117	C₂×C₄×C₅²	—	2	1	no	—
118	C₂×C₄×C₅²	—	2	1	no	—
119	C₂×C₄×C₅²	—	2	2	no	—
120	C₂×C₄×C₅²	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×C₅²	C₂⁴	1	1	yes	characteristic
122	C₅×C₂²⋊D₅	—	2	2	no	—
123	C₅×C₂²⋊D₅	—	2	2	no	—
124	C₅×C₂²⋊D₅	—	4	4	no	—
125	C₅×C₂²⋊D₅	—	8	2	no	—
126	C₅×C₂²⋊D₅	—	8	2	no	—
127	C₂×C₅×Dic₅	—	2	2	no	—
128	C₂×C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
130	C₅×D₂₀	—	2	2	no	—
131	C₅×D₂₀	—	2	2	no	—
132	C₅×D₂₀	—	2	2	no	—
133	C₅×D₂₀	—	8	2	no	—
134	C₄×C₅×D₅	—	2	1	no	—
135	C₄×C₅×D₅	—	2	1	no	—
136	C₄×C₅×D₅	C₂×D₄	1	2	yes	—
137	C₄×C₅×D₅	#41	1	2	yes	—
138	C₅×Dic₁₀	—	2	2	no	—
139	C₅²×C₈	—	2	1	no	—
140	C₅²×C₈	C₂×D₄	1	2	yes	—
141	C₅×#168	—	2	1	no	—
142	C₅×#168	C₂×D₄	1	2	yes	—
143	C₂×C₅×#41	—	5	1	no	—
144	C₂²×C₅×D₄	—	5	2	no	—
145	C₂×D₄×D₅	C₂²×C₅	1	2	yes	—
146	C₂×#709	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₅×D₈	—	2	2	no	—
148	C₂×C₅×D₈	—	5	2	no	—
149	C₂×C₅×D₈	—	5	1	no	—
150	C₂×C₅×D₈	—	10	4	no	—
151	C₂×C₅×D₈	C₂×D₅	1	1	yes	characteristic
152	C₂×C₅×D₈	C₂²×C₅	1	1	yes	characteristic
153	C₅×#131	—	10	4	no	—
154	C₂×C₅×M₁₆	—	2	2	no	—
155	C₂×C₅×M₁₆	—	5	1	no	—
156	C₂×C₅×M₁₆	—	5	1	no	—
157	C₂×C₅×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
158	C₂×C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₂²×C₅×C₈	—	5	1	no	—
160	C₂²×C₅×C₈	—	5	1	no	—
161	C₂²×C₅×C₈	—	5	1	no	—
162	C₅×#127	—	10	2	no	—
163	C₅×#124	—	10	2	no	—
164	C₅×#121	—	2	4	no	—
165	C₅×#121	—	5	2	no	—
166	C₅×#121	—	5	2	no	—
167	C₅×#121	—	5	2	no	—
168	C₅×#121	C₂×D₅	1	2	yes	complemented
169	C₅×#121	C₂²×C₅	1	2	yes	complemented
170	C₅×#120	—	10	2	no	—
171	C₅×#120	—	10	2	no	—
172	C₅×#117	—	5	2	no	—
173	#4086	—	2	2	no	—
174	#4084	C₂²×C₅	1	2	yes	complemented
175	#4083	—	2	2	no	—
176	C₂×#686	C₂²×C₅	1	2	yes	—
177	#4076	C₂²×C₅	1	2	yes	complemented
178	C₂²×#168	C₂²×C₅	1	1	yes	characteristic, complemented
179	D₅×D₈	—	2	4	no	—
180	#4053	—	2	4	no	—
181	C₂×D₄₀	C₂²×C₅	1	1	yes	characteristic
182	C₂×#676	C₂²×C₅	1	1	yes	characteristic
183	C₂×#676	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₂×C₈×D₅	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₈×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
186	#4041	C₂²×C₅	1	2	yes	complemented
187	#4038	C₂²×C₅	1	2	yes	—
188	#4031	—	2	2	no	—
189	#4028	—	2	2	no	—
190	C₅×#107	—	5	2	no	—
191	C₅×#106	—	2	2	no	—
192	C₅×#106	—	5	1	no	—
193	C₅×#106	C₂×D₅	1	1	yes	characteristic, complemented
194	C₅×#106	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₅×#102	—	2	4	no	—
196	C₅×#102	—	5	2	no	—
197	C₅×#102	—	5	2	no	—
198	C₅×#102	—	5	2	no	—
199	C₅×#102	C₂×D₅	1	2	yes	complemented
200	C₅×#102	C₂²×C₅	1	2	yes	complemented
201	#3964	C₂²×C₅	1	2	yes	complemented
202	#3953	C₂²×C₅	1	2	yes	complemented
203	#3949	C₂²×C₅	1	1	yes	characteristic, complemented
204	#3941	C₂²×C₅	1	2	yes	complemented
205	#3939	C₂²×C₅	1	2	yes	complemented
206	#3058	—	5	1	no	Sylow
207	C₂²×C₅²	—	2	1	no	—
208	C₂²×C₅²	—	2	2	no	—
209	C₂²×C₅²	—	4	2	no	—
210	C₂²×C₅²	—	4	2	no	—
211	C₂²×C₅²	—	4	2	no	—
212	C₂²×C₅²	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₅×D₅	—	2	1	no	—
214	C₂×C₅×D₅	—	2	2	no	—
215	C₂×C₅×D₅	—	2	2	no	—
216	C₂×C₅×D₅	—	4	2	no	—
217	C₂×C₅×D₅	—	4	2	no	—
218	C₂×C₅×D₅	—	4	2	no	—
219	C₂×C₅×D₅	—	8	8	no	—
220	C₂×C₅×D₅	#121	1	2	yes	—
221	C₄×C₅²	—	2	1	no	—
222	C₄×C₅²	—	4	2	no	—
223	C₄×C₅²	C₂²×D₄	1	1	yes	characteristic
224	C₄×C₅²	C₂×#41	1	1	yes	characteristic
225	C₅×Dic₅	—	2	1	no	—
226	C₅×Dic₅	—	4	2	no	—
227	C₅×Dic₅	#121	1	2	yes	—
228	C₂⁴×C₅	—	10	2	no	—
229	C₂³×D₅	—	2	2	no	—
230	C₅×#41	—	10	2	no	—
231	C₅×#41	—	10	2	no	—
232	C₂×C₅×Q₈	—	5	1	no	—
233	C₂×C₅×D₄	—	2	2	no	—
234	C₂×C₅×D₄	—	2	2	no	—
235	C₂×C₅×D₄	—	2	4	no	—
236	C₂×C₅×D₄	—	4	4	no	—
237	C₂×C₅×D₄	—	5	1	no	—
238	C₂×C₅×D₄	—	5	1	no	—
239	C₂×C₅×D₄	—	5	1	no	—
240	C₂×C₅×D₄	—	5	2	no	—
241	C₂×C₅×D₄	—	10	2	no	—
242	C₂×C₅×D₄	—	10	4	no	—
243	C₂×C₅×D₄	—	10	4	no	—
244	C₂×C₅×D₄	—	10	2	no	—
245	C₂×C₅×D₄	—	10	2	no	—
246	C₂×C₅×D₄	—	10	2	no	—
247	C₂×C₅×D₄	C₂²×D₅	1	2	yes	—
248	C₂×C₅×D₄	C₂³×C₅	1	2	yes	—
249	C₂²×C₄×C₅	—	2	2	no	—
250	C₂²×C₄×C₅	—	5	1	no	—
251	C₂²×C₄×C₅	—	5	1	no	—
252	C₂²×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₂²⋊D₅	—	2	2	no	—
255	C₂×C₂²⋊D₅	—	2	2	no	—
256	C₂×C₂²⋊D₅	—	2	2	no	—
257	C₂×C₂²⋊D₅	C₅×D₄	1	1	yes	characteristic
258	C₂×C₂²⋊D₅	C₅×D₄	1	1	yes	characteristic
259	D₄×D₅	—	2	4	no	—
260	D₄×D₅	—	2	4	no	—
261	#709	—	2	2	no	—
262	#709	—	2	2	no	—
263	C₂×D₂₀	—	2	2	no	—
264	C₂×D₂₀	C₅×D₄	1	1	yes	characteristic
265	C₂×D₂₀	C₂³×C₅	1	2	yes	—
266	C₂×C₄×D₅	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₄×D₅	C₂³×C₅	1	1	yes	characteristic
268	C₂×Dic₁₀	C₅×D₄	1	1	yes	characteristic
269	C₅×D₈	—	2	2	no	—
270	C₅×D₈	—	2	2	no	—
271	C₅×D₈	—	4	4	no	—
272	C₅×D₈	—	10	4	no	—
273	C₅×D₈	—	10	2	no	—
274	C₅×M₁₆	—	2	2	no	—
275	C₅×M₁₆	—	2	2	no	—
276	C₅×M₁₆	—	4	4	no	—
277	C₅×M₁₆	—	10	2	no	—
278	C₅×M₁₆	—	10	2	no	—
279	C₂×C₅×C₈	—	2	2	no	—
280	C₂×C₅×C₈	—	2	2	no	—
281	C₂×C₅×C₈	—	5	1	no	—
282	C₂×C₅×C₈	—	5	4	no	—
283	C₂×C₅×C₈	—	5	1	no	—
284	C₂×C₅×C₈	—	10	2	no	—
285	C₂×C₅×C₈	—	10	2	no	—
286	C₂×C₅×C₈	C₂²×D₅	1	1	yes	characteristic
287	C₂×C₅×C₈	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₅×C₈	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₅×C₈	C₂³×C₅	1	1	yes	characteristic
290	C₅×C₄⋊C₄	—	2	4	no	—
291	C₅×C₄⋊C₄	—	5	2	no	—
292	C₅×C₄⋊C₄	C₂²×D₅	1	2	yes	—
293	C₅×C₄⋊C₄	C₂³×C₅	1	2	yes	—
294	C₅×C₂²⋊C₄	—	2	2	no	—
295	C₅×C₂²⋊C₄	—	2	2	no	—
296	C₅×C₂²⋊C₄	—	4	4	no	—
297	C₅×C₂²⋊C₄	—	10	2	no	—
298	C₅×C₂²⋊C₄	—	10	2	no	—
299	C₅×C₂²⋊C₄	—	10	2	no	—
300	C₅×C₂²⋊C₄	—	10	2	no	—
301	C₄²×C₅	—	10	2	no	—
302	C₂²⋊Dic₅	—	2	2	no	—
303	#686	—	2	4	no	—
304	#685	—	2	2	no	—
305	#685	—	2	2	no	—
306	#685	—	2	2	no	—
307	C₄⋊Dic₅	C₂³×C₅	1	2	yes	—
308	C₄×Dic₅	—	2	2	no	—
309	C₂×#168	—	2	2	no	—
310	C₂×#168	C₂³×C₅	1	1	yes	characteristic
311	C₂×#168	C₂³×C₅	1	1	yes	characteristic
312	D₄₀	—	2	2	no	—
313	#676	—	2	2	no	—
314	#676	—	2	2	no	—
315	C₈×D₅	—	2	2	no	—
316	C₈×D₅	C₅×D₄	1	4	yes	complemented
317	C₂²×D₈	—	5	1	no	—
318	C₂×#131	—	5	1	no	—
319	#535	—	5	2	no	—
320	#469	—	5	1	no	—
321	#469	—	5	1	no	—
322	#469	—	5	1	no	—
323	#469	C₅×D₅	1	1	yes	characteristic, complemented
324	#466	—	5	2	no	—
325	#466	—	5	2	no	—
326	#427	—	5	1	no	—
327	#418	—	5	2	no	—
328	C₂×C₅²	—	4	1	no	—
329	C₂×C₅²	—	8	2	no	—
330	C₂×C₅²	C₂×#121	1	1	yes	characteristic
331	C₂×C₅²	#576	1	2	yes	—
332	C₅×D₅	—	2	2	no	—
333	C₅×D₅	—	4	1	no	—
334	C₅×D₅	—	8	2	no	—
335	C₂³×C₅	—	2	2	no	—
336	C₂³×C₅	—	2	2	no	—
337	C₂³×C₅	—	2	2	no	—
338	C₂³×C₅	—	4	4	no	—
339	C₂³×C₅	—	5	1	no	—
340	C₂³×C₅	—	5	1	no	—
341	C₂³×C₅	—	10	2	no	—
342	C₂³×C₅	—	20	4	no	—
343	C₂³×C₅	—	40	2	no	—
344	C₂³×C₅	—	40	2	no	—
345	C₂³×C₅	D₄×D₅	1	1	yes	characteristic
346	C₂³×C₅	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂²×D₅	—	2	2	no	—
348	C₂²×D₅	—	4	4	no	—
349	C₂²×D₅	—	8	2	no	—
350	C₂²×D₅	—	8	2	no	—
351	C₂²×D₅	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂²×D₅	C₂×C₅×D₄	1	1	yes	characteristic
353	C₅×Q₈	—	10	2	no	—
354	C₅×D₄	—	2	2	no	—
355	C₅×D₄	—	2	2	no	—
356	C₅×D₄	—	2	2	no	—
357	C₅×D₄	—	2	2	no	—
358	C₅×D₄	—	4	4	no	—
359	C₅×D₄	—	4	4	no	—
360	C₅×D₄	—	8	2	no	—
361	C₅×D₄	—	8	2	no	—
362	C₅×D₄	—	8	4	no	—
363	C₅×D₄	—	8	4	no	—
364	C₅×D₄	—	10	2	no	—
365	C₅×D₄	—	10	2	no	—
366	C₅×D₄	—	10	2	no	—
367	C₅×D₄	—	10	2	no	—
368	C₅×D₄	—	10	2	no	—
369	C₅×D₄	—	20	4	no	—
370	C₅×D₄	—	40	2	no	—
371	C₅×D₄	—	40	2	no	—
372	C₅×D₄	—	40	2	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	4	2	no	—
382	C₂×C₄×C₅	—	4	2	no	—
383	C₂×C₄×C₅	—	4	4	no	—
384	C₂×C₄×C₅	—	5	1	no	—
385	C₂×C₄×C₅	—	5	2	no	—
386	C₂×C₄×C₅	—	5	2	no	—
387	C₂×C₄×C₅	—	5	1	no	—
388	C₂×C₄×C₅	—	10	1	no	—
389	C₂×C₄×C₅	—	10	1	no	—
390	C₂×C₄×C₅	—	10	2	no	—
391	C₂×C₄×C₅	D₄×D₅	1	1	yes	characteristic
392	C₂×C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅	C₂³×D₅	1	1	yes	characteristic
394	C₂×C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
395	C₂²⋊D₅	—	2	2	no	—
396	C₂²⋊D₅	—	2	2	no	—
397	C₂²⋊D₅	—	4	4	no	—
398	C₂²⋊D₅	—	8	2	no	—
399	C₂²⋊D₅	—	8	2	no	—
400	C₂×Dic₅	—	2	2	no	—
401	C₂×Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂×Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
403	D₂₀	—	2	2	no	—
404	D₂₀	—	2	2	no	—
405	D₂₀	—	2	2	no	—
406	D₂₀	—	8	2	no	—
407	C₄×D₅	—	2	1	no	—
408	C₄×D₅	—	2	1	no	—
409	C₄×D₅	C₂×C₅×D₄	1	2	yes	—
410	C₄×D₅	C₅×#41	1	2	yes	—
411	Dic₁₀	—	2	2	no	—
412	C₅×C₈	—	2	1	no	—
413	C₅×C₈	—	2	1	no	—
414	C₅×C₈	—	2	4	no	—
415	C₅×C₈	—	4	2	no	—
416	C₅×C₈	—	5	2	no	—
417	C₅×C₈	—	10	1	no	—
418	C₅×C₈	D₄×D₅	1	2	yes	—
419	C₅×C₈	C₂×C₅×D₄	1	2	yes	—
420	#168	—	2	1	no	—
421	#168	C₂×C₅×D₄	1	2	yes	—
422	C₂×#41	—	5	1	no	—
423	C₂²×D₄	—	5	2	no	—
424	C₂×D₈	—	5	2	no	—
425	C₂×D₈	—	5	1	no	—
426	C₂×D₈	—	10	4	no	—
427	C₂×D₈	C₂×C₅×D₅	1	1	yes	characteristic
428	#131	—	10	4	no	—
429	C₂×M₁₆	—	5	1	no	—
430	C₂×M₁₆	—	5	1	no	—
431	C₂×M₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
432	C₂²×C₈	—	5	1	no	—
433	C₂²×C₈	—	5	1	no	—
434	C₂²×C₈	—	5	1	no	—
435	#127	—	10	2	no	—
436	#124	—	10	2	no	—
437	#121	—	5	2	no	—
438	#121	—	5	2	no	—
439	#121	—	5	2	no	—
440	#121	C₂×C₅×D₅	1	2	yes	complemented
441	#120	—	10	2	no	—
442	#120	—	10	2	no	—
443	#117	—	5	2	no	—
444	#107	—	5	2	no	—
445	#106	—	5	1	no	—
446	#106	C₂×C₅×D₅	1	1	yes	characteristic, complemented
447	#102	—	5	2	no	—
448	#102	—	5	2	no	—
449	#102	—	5	2	no	—
450	#102	C₂×C₅×D₅	1	2	yes	complemented
451	C₅²	#3058	1	1	yes	characteristic, complemented, Sylow
452	C₂²×C₅	—	2	2	no	—
453	C₂²×C₅	—	2	1	no	—
454	C₂²×C₅	—	2	1	no	—
455	C₂²×C₅	—	2	2	no	—
456	C₂²×C₅	—	2	2	no	—
457	C₂²×C₅	—	4	2	no	—
458	C₂²×C₅	—	4	4	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	—	4	2	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	2	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	5	2	no	—
466	C₂²×C₅	—	8	4	no	—
467	C₂²×C₅	—	8	4	no	—
468	C₂²×C₅	—	8	4	no	—
469	C₂²×C₅	—	10	2	no	—
470	C₂²×C₅	—	10	2	no	—
471	C₂²×C₅	—	10	1	no	—
472	C₂²×C₅	—	20	2	no	—
473	C₂²×C₅	—	20	2	no	—
474	C₂²×C₅	—	20	2	no	—
475	C₂²×C₅	—	40	8	no	—
476	C₂²×C₅	C₂×D₄×D₅	1	1	yes	characteristic
477	C₂²×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
478	C₂×D₅	—	2	2	no	—
479	C₂×D₅	—	2	1	no	—
480	C₂×D₅	—	2	2	no	—
481	C₂×D₅	—	4	2	no	—
482	C₂×D₅	—	4	2	no	—
483	C₂×D₅	—	4	2	no	—
484	C₂×D₅	—	8	8	no	—
485	C₂×D₅	C₅×#121	1	2	yes	—
486	C₄×C₅	—	2	1	no	—
487	C₄×C₅	—	2	1	no	—
488	C₄×C₅	—	2	2	no	—
489	C₄×C₅	—	2	2	no	—
490	C₄×C₅	—	4	2	no	—
491	C₄×C₅	—	4	2	no	—
492	C₄×C₅	—	4	2	no	—
493	C₄×C₅	—	5	2	no	—
494	C₄×C₅	—	8	4	no	—
495	C₄×C₅	—	10	1	no	—
496	C₄×C₅	—	20	2	no	—
497	C₄×C₅	C₂×D₄×D₅	1	1	yes	characteristic
498	C₄×C₅	D₅×#41	1	1	yes	characteristic
499	C₄×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
500	C₄×C₅	C₂×C₅×#41	1	1	yes	characteristic
501	Dic₅	—	2	1	no	—
502	Dic₅	—	4	2	no	—
503	Dic₅	C₅×#121	1	2	yes	—
504	C₂⁴	—	10	2	no	—
505	#41	—	10	2	no	—
506	#41	—	10	2	no	—
507	C₂×Q₈	—	5	1	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	5	1	no	—
510	C₂×D₄	—	5	1	no	—
511	C₂×D₄	—	5	1	no	—
512	C₂×D₄	—	5	2	no	—
513	C₂×D₄	—	10	2	no	—
514	C₂×D₄	—	10	4	no	—
515	C₂×D₄	—	10	4	no	—
516	C₂×D₄	—	10	2	no	—
517	C₂×D₄	—	10	2	no	—
518	C₂×D₄	—	10	2	no	—
519	C₂×D₄	C₂²×C₅×D₅	1	2	yes	—
520	C₂²×C₄	—	5	1	no	—
521	C₂²×C₄	—	5	1	no	—
522	C₂²×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
523	D₈	—	2	2	no	—
524	D₈	—	10	4	no	—
525	D₈	—	10	2	no	—
526	M₁₆	—	2	2	no	—
527	M₁₆	—	10	2	no	—
528	M₁₆	—	10	2	no	—
529	C₂×C₈	—	5	1	no	—
530	C₂×C₈	—	5	4	no	—
531	C₂×C₈	—	5	1	no	—
532	C₂×C₈	—	10	2	no	—
533	C₂×C₈	—	10	2	no	—
534	C₂×C₈	C₂²×C₅×D₅	1	1	yes	characteristic
535	C₂×C₈	C₂²×C₅×D₅	1	1	yes	characteristic
536	C₄⋊C₄	—	5	2	no	—
537	C₄⋊C₄	C₂²×C₅×D₅	1	2	yes	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	10	2	no	—
540	C₂²⋊C₄	—	10	2	no	—
541	C₂²⋊C₄	—	10	2	no	—
542	C₂²⋊C₄	—	10	2	no	—
543	C₄²	—	10	2	no	—
544	C₂×C₅	—	2	2	no	—
545	C₂×C₅	—	2	4	no	—
546	C₂×C₅	—	4	1	no	—
547	C₂×C₅	—	4	1	no	—
548	C₂×C₅	—	8	2	no	—
549	C₂×C₅	—	8	2	no	—
550	C₂×C₅	—	8	2	no	—
551	C₂×C₅	—	10	2	no	—
552	C₂×C₅	—	16	4	no	—
553	C₂×C₅	—	20	1	no	—
554	C₂×C₅	—	40	2	no	—
555	C₂×C₅	D₅×#121	1	1	yes	characteristic
556	C₂×C₅	#66108	1	2	yes	—
557	C₂×C₅	C₂×C₅×#121	1	1	yes	characteristic
558	C₂×C₅	C₅×#576	1	2	yes	—
559	D₅	—	2	2	no	—
560	D₅	—	4	1	no	—
561	D₅	—	8	2	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	5	1	no	—
564	C₂³	—	5	1	no	—
565	C₂³	—	10	2	no	—
566	C₂³	—	20	4	no	—
567	C₂³	—	40	2	no	—
568	C₂³	—	40	2	no	—
569	C₂³	C₅×D₄×D₅	1	1	yes	characteristic
570	Q₈	—	10	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	10	2	no	—
575	D₄	—	10	2	no	—
576	D₄	—	10	2	no	—
577	D₄	—	10	2	no	—
578	D₄	—	10	2	no	—
579	D₄	—	20	4	no	—
580	D₄	—	40	2	no	—
581	D₄	—	40	2	no	—
582	D₄	—	40	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	5	1	no	—
587	C₂×C₄	—	5	2	no	—
588	C₂×C₄	—	5	2	no	—
589	C₂×C₄	—	5	1	no	—
590	C₂×C₄	—	10	1	no	—
591	C₂×C₄	—	10	1	no	—
592	C₂×C₄	—	10	2	no	—
593	C₂×C₄	C₅×D₄×D₅	1	1	yes	characteristic
594	C₂×C₄	C₂³×C₅×D₅	1	1	yes	characteristic
595	C₈	—	2	1	no	—
596	C₈	—	5	2	no	—
597	C₈	—	10	1	no	—
598	C₈	C₅×D₄×D₅	1	2	yes	—
599	C₅	—	2	2	no	—
600	C₅	#10612596	1	1	yes	characteristic, direct product factor
601	C₅	C₅×#3058	1	1	yes	characteristic, complemented
602	C₂²	—	2	1	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	5	2	no	—
608	C₂²	—	10	2	no	—
609	C₂²	—	10	1	no	—
610	C₂²	—	10	2	no	—
611	C₂²	—	20	2	no	—
612	C₂²	—	20	2	no	—
613	C₂²	—	20	2	no	—
614	C₂²	—	40	8	no	—
615	C₂²	C₂×C₅×D₄×D₅	1	1	yes	characteristic
616	C₄	—	2	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	5	2	no	—
619	C₄	—	10	1	no	—
620	C₄	—	20	2	no	—
621	C₄	C₂×C₅×D₄×D₅	1	1	yes	characteristic
622	C₄	C₅×D₅×#41	1	1	yes	characteristic
623	C₂	—	4	1	no	—
624	C₂	—	8	2	no	—
625	C₂	—	10	2	no	—
626	C₂	—	20	1	no	—
627	C₂	—	40	2	no	—
628	C₂	C₅×D₅×#121	1	1	yes	characteristic
629	C₂	C₅×#66108	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₅
Fitting	C₅²×#469	C₂
socle	C₂²×C₅²	C₂²×D₄
hypercenter	C₅×#469	D₅
hypocenter	C₅	C₅×#3058
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#469

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₅×D₈	C₂	semidirect
2. C₂×C₅×#4053	C₂	semidirect
3. C₅×#65941	C₂	semidirect
4. C₅²×#469	C₂	semidirect
5. C₅×#65448	C₂	semidirect
6. C₅×#65424	C₂	semidirect
7. C₅×#65327	C₂	semidirect
8. C₅×#65154	C₂	semidirect
9. C₅×#65149	C₂	semidirect
10. C₅×#65064	C₂	semidirect
11. C₅×#65059	C₂	semidirect
15. C₂×C₅²×M₁₆	C₂²	semidirect
16. C₅²×#121	C₂²	semidirect
18. C₅×#4084	C₂²	semidirect
21. C₅×#4076	C₂²	semidirect
22. C₂²×C₅×#168	C₂²	semidirect
27. C₂×C₅×#676	C₂²	semidirect
29. C₂×C₅×C₈×D₅	C₂²	semidirect
30. C₅×#4041	C₂²	semidirect
34. C₅²×#106	C₂²	semidirect
35. C₅²×#102	C₂²	semidirect
36. C₅×#3964	C₂²	semidirect
37. C₅×#3953	C₂²	semidirect
38. C₅×#3949	C₂²	semidirect
39. C₅×#3941	C₂²	semidirect
40. C₅×#3939	C₂²	semidirect
42. #10612596	C₅	direct (N × H)
82. C₅×C₈×D₅	D₄	semidirect
86. C₂×D₅×D₈	C₂×C₅	semidirect
87. C₂×#4053	C₂×C₅	semidirect
88. #65941	C₂×C₅	semidirect
93. C₅×#469	D₅	semidirect
94. C₅×#469	C₂×C₅	semidirect
99. #65448	C₂×C₅	semidirect
100. #65424	C₂×C₅	semidirect
101. #65327	C₂×C₅	semidirect
102. #65154	C₂×C₅	semidirect
103. #65149	C₂×C₅	semidirect
104. #65064	C₂×C₅	semidirect
105. #65059	C₂×C₅	semidirect
157. C₂×C₅×M₁₆	C₂×D₅	semidirect
158. C₂×C₅×M₁₆	C₂²×C₅	semidirect
168. C₅×#121	C₂×D₅	semidirect
169. C₅×#121	C₂²×C₅	semidirect
174. #4084	C₂²×C₅	semidirect
177. #4076	C₂²×C₅	semidirect
178. C₂²×#168	C₂²×C₅	semidirect
183. C₂×#676	C₂²×C₅	semidirect
185. C₂×C₈×D₅	C₂²×C₅	semidirect
186. #4041	C₂²×C₅	semidirect
193. C₅×#106	C₂×D₅	semidirect
194. C₅×#106	C₂²×C₅	semidirect
199. C₅×#102	C₂×D₅	semidirect
200. C₅×#102	C₂²×C₅	semidirect
201. #3964	C₂²×C₅	semidirect
202. #3953	C₂²×C₅	semidirect
203. #3949	C₂²×C₅	semidirect
204. #3941	C₂²×C₅	semidirect
205. #3939	C₂²×C₅	semidirect
316. C₈×D₅	C₅×D₄	semidirect
323. #469	C₅×D₅	semidirect
431. C₂×M₁₆	C₂×C₅×D₅	semidirect
440. #121	C₂×C₅×D₅	semidirect
446. #106	C₂×C₅×D₅	semidirect
450. #102	C₂×C₅×D₅	semidirect
451. C₅²	#3058	semidirect
600. C₅	#10612596	direct (N × H)
601. C₅	C₅×#3058	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₅×D₈	2
C₂×C₅×#4053	2
C₅×#65941	2
C₅²×#469	2
C₅×#65448	2
C₅×#65424	2
C₅×#65327	2
C₅×#65154	2
C₅×#65149	2
C₅×#65064	2
C₅×#65059	2
C₅×#3058	5
#10612596	5

Subgroups — C5×#10612596 #72242548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10612596 #72242548