Subgroups — C₂×D₅×#560 #13006165

Order 1280.

9606 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#560	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#560	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66054	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66045	C₂	1	2	yes	maximal, complemented
6	C₂×D₅×#126	C₂	1	2	yes	maximal, complemented
7	C₂×#66000	C₂	1	3	yes	maximal, complemented
8	C₂×D₅×#123	C₂	1	3	yes	maximal, complemented
9	C₂×#65954	C₂	1	6	yes	maximal, complemented
10	C₂×D₅×#121	C₂	1	6	yes	maximal, complemented
11	C₂×#65929	C₂	1	3	yes	maximal, complemented
12	C₂×D₅×#120	C₂	1	3	yes	maximal, complemented
13	C₂⁵×D₅	C₂²	1	1	yes	characteristic
14	C₂²×D₄×D₅	C₂²	1	3	yes	—
15	C₂²×D₄×D₅	C₂²	1	6	yes	—
16	C₂²×D₄×D₅	C₂²	1	3	yes	complemented
17	C₂³×C₄×D₅	C₂²	1	3	yes	complemented
18	C₅×#560	C₂²	1	16	yes	complemented
19	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×#126	C₂²	1	2	yes	complemented
21	C₂×C₅×#123	C₂²	1	3	yes	complemented
22	C₂×C₅×#121	C₂²	1	6	yes	complemented
23	C₂×C₅×#120	C₂²	1	3	yes	complemented
24	C₂×#4099	C₂²	1	3	yes	complemented
25	C₂×#4086	C₂²	1	3	yes	complemented
26	C₂×#4086	C₂²	1	3	yes	complemented
27	C₂×#4085	C₂²	1	6	yes	complemented
28	C₂×#4085	C₂²	1	6	yes	complemented
29	C₂×#4084	C₂²	1	6	yes	complemented
30	C₂×#4083	C₂²	1	3	yes	complemented
31	C₂×#4083	C₂²	1	6	yes	complemented
32	C₂×#4081	C₂²	1	3	yes	complemented
33	C₂×#4076	C₂²	1	6	yes	complemented
34	C₂×#4075	C₂²	1	3	yes	complemented
35	#66054	C₂²	1	16	yes	complemented
36	D₅×#127	C₂²	1	16	yes	complemented
37	#66045	C₂²	1	32	yes	complemented
38	D₅×#126	C₂²	1	32	yes	complemented
39	#66000	C₂²	1	48	yes	complemented
40	D₅×#123	C₂²	1	48	yes	complemented
41	#65954	C₂²	1	96	yes	complemented
42	D₅×#121	C₂²	1	96	yes	complemented
43	#65929	C₂²	1	48	yes	complemented
44	D₅×#120	C₂²	1	48	yes	complemented
45	C₂×#4044	C₂²	1	6	yes	complemented
46	C₂×#4041	C₂²	1	6	yes	complemented
47	C₂×#4040	C₂²	1	6	yes	complemented
48	C₂×D₅×C₄⋊C₄	C₂²	1	6	yes	complemented
49	C₂×#4032	C₂²	1	3	yes	complemented
50	C₂×#4030	C₂²	1	6	yes	complemented
51	C₂×#4030	C₂²	1	6	yes	complemented
52	C₂×#4029	C₂²	1	6	yes	complemented
53	C₂×#4028	C₂²	1	3	yes	complemented
54	C₂×#4028	C₂²	1	6	yes	complemented
55	C₂×D₅×C₂²⋊C₄	C₂²	1	3	yes	—
56	C₂×D₅×C₂²⋊C₄	C₂²	1	6	yes	—
57	C₂×D₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
58	C₂×#4025	C₂²	1	6	yes	complemented
59	C₂×#4022	C₂²	1	2	yes	complemented
60	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
62	C₂²×#560	—	5	1	no	maximal, Sylow
63	C₂⁵×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×D₅	—	4	12	no	—
65	C₂⁴×D₅	C₂³	1	1	yes	characteristic
66	C₂⁴×D₅	C₂³	1	2	yes	—
67	C₂⁴×D₅	C₂³	1	3	yes	—
68	C₂⁴×D₅	C₂³	1	1	yes	characteristic
69	C₂⁴×D₅	C₂³	1	2	yes	—
70	C₂⁴×D₅	C₂³	1	8	yes	—
71	C₂²×C₅×D₄	C₂³	1	3	yes	—
72	C₂²×C₅×D₄	C₂³	1	6	yes	—
73	C₂²×C₅×D₄	C₂³	1	3	yes	complemented
74	C₂³×C₄×C₅	C₂³	1	3	yes	complemented
75	C₂²×C₂²⋊D₅	C₂³	1	3	yes	—
76	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
77	C₂²×C₂²⋊D₅	C₂³	1	6	yes	—
78	C₂²×C₂²⋊D₅	C₂³	1	3	yes	—
79	C₂²×C₂²⋊D₅	C₂³	1	6	yes	complemented
80	C₂³×Dic₅	C₂³	1	3	yes	complemented
81	C₂×D₄×D₅	—	4	24	no	—
82	C₂×D₄×D₅	—	4	12	no	—
83	C₂×D₄×D₅	—	4	12	no	—
84	C₂×D₄×D₅	C₂³	1	24	yes	—
85	C₂×D₄×D₅	C₂³	1	48	yes	—
86	C₂×D₄×D₅	C₂³	1	24	yes	complemented
87	C₂²×D₂₀	C₂³	1	3	yes	—
88	C₂²×D₂₀	C₂³	1	6	yes	—
89	C₂²×D₂₀	C₂³	1	3	yes	complemented
90	C₂²×C₄×D₅	—	4	12	no	—
91	C₂²×C₄×D₅	C₂³	1	3	yes	—
92	C₂²×C₄×D₅	C₂³	1	6	yes	—
93	C₂²×C₄×D₅	C₂³	1	24	yes	complemented
94	C₂²×C₄×D₅	C₂³	1	6	yes	complemented
95	C₅×#127	C₂³	1	8	yes	complemented
96	C₅×#126	C₂³	1	16	yes	complemented
97	C₅×#123	C₂³	1	24	yes	complemented
98	C₅×#121	C₂³	1	48	yes	complemented
99	C₅×#120	C₂³	1	24	yes	complemented
100	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	complemented
101	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₂×C₅×C₂²⋊C₄	C₂³	1	3	yes	—
103	C₂×C₅×C₂²⋊C₄	C₂³	1	3	yes	complemented
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
105	#4099	C₂³	1	24	yes	complemented
106	C₂×C₂²⋊Dic₅	C₂³	1	6	yes	—
107	C₂×C₂²⋊Dic₅	C₂³	1	3	yes	—
108	C₂×C₂²⋊Dic₅	C₂³	1	3	yes	complemented
109	#4086	C₂³	1	24	yes	complemented
110	#4086	C₂³	1	24	yes	complemented
111	#4085	C₂³	1	48	yes	complemented
112	#4085	C₂³	1	48	yes	complemented
113	#4084	C₂³	1	48	yes	complemented
114	#4083	C₂³	1	24	yes	complemented
115	#4083	C₂³	1	48	yes	complemented
116	#4081	C₂³	1	24	yes	complemented
117	#4076	C₂³	1	48	yes	complemented
118	#4075	C₂³	1	24	yes	complemented
119	C₂×#685	C₂³	1	6	yes	—
120	C₂×#685	C₂³	1	6	yes	—
121	C₂×#685	C₂³	1	6	yes	—
122	C₂×#685	C₂³	1	6	yes	complemented
123	C₂×C₄⋊Dic₅	C₂³	1	6	yes	complemented
124	C₂×#683	C₂³	1	6	yes	complemented
125	C₂×#683	C₂³	1	6	yes	complemented
126	C₂×C₄×Dic₅	C₂³	1	3	yes	complemented
127	#4044	C₂³	1	48	yes	complemented
128	#4041	C₂³	1	48	yes	complemented
129	#4040	C₂³	1	48	yes	complemented
130	D₅×C₄⋊C₄	C₂³	1	48	yes	complemented
131	#4032	C₂³	1	24	yes	complemented
132	#4030	C₂³	1	48	yes	complemented
133	#4030	C₂³	1	48	yes	complemented
134	#4029	C₂³	1	48	yes	complemented
135	#4028	C₂³	1	48	yes	complemented
136	#4028	C₂³	1	24	yes	complemented
137	D₅×C₂²⋊C₄	C₂³	1	48	yes	—
138	D₅×C₂²⋊C₄	C₂³	1	24	yes	—
139	D₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
140	#4025	C₂³	1	48	yes	complemented
141	#4022	C₂³	1	16	yes	complemented
142	#4020	C₂³	1	8	yes	complemented
143	C₄²×D₅	C₂³	1	8	yes	complemented
144	C₂×#560	—	5	32	no	—
145	C₂×#560	—	5	1	no	—
146	C₂×#560	—	5	2	no	—
147	C₂×#560	—	5	3	no	—
148	C₂×#560	—	5	6	no	—
149	C₂×#560	—	5	3	no	—
150	C₂×#560	D₅	1	1	yes	characteristic, direct product factor
151	C₂²×#127	—	5	1	no	—
152	C₂²×#126	—	5	2	no	—
153	C₂²×#123	—	5	3	no	—
154	C₂²×#121	—	5	6	no	—
155	C₂²×#120	—	5	3	no	—
156	C₂⁴×C₅	—	4	6	no	—
157	C₂⁴×C₅	C₂⁴	1	2	yes	—
158	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₅	C₂⁴	1	3	yes	—
160	C₂⁴×C₅	C₂⁴	1	4	yes	—
161	C₂³×D₅	—	2	12	no	—
162	C₂³×D₅	—	2	24	no	—
163	C₂³×D₅	—	2	24	no	—
164	C₂³×D₅	—	2	12	no	—
165	C₂³×D₅	—	4	48	no	—
166	C₂³×D₅	—	4	6	no	—
167	C₂³×D₅	—	4	12	no	—
168	C₂³×D₅	—	4	64	no	—
169	C₂³×D₅	C₂⁴	1	3	yes	—
170	C₂³×D₅	C₂⁴	1	12	yes	—
171	C₂³×D₅	C₂⁴	1	1	yes	characteristic
172	C₂³×D₅	C₂⁴	1	2	yes	—
173	C₂³×D₅	C₂⁴	1	4	yes	—
174	C₂³×D₅	C₂⁴	1	8	yes	—
175	C₂³×D₅	C₂⁴	1	8	yes	—
176	C₂³×D₅	C₂⁴	1	4	yes	—
177	C₂³×D₅	C₂⁴	1	1	yes	characteristic
178	C₂×C₅×D₄	—	4	12	no	—
179	C₂×C₅×D₄	—	4	6	no	—
180	C₂×C₅×D₄	—	4	6	no	—
181	C₂×C₅×D₄	C₂⁴	1	24	yes	—
182	C₂×C₅×D₄	C₂⁴	1	12	yes	—
183	C₂×C₅×D₄	C₂⁴	1	12	yes	complemented
184	C₂²×C₄×C₅	—	4	6	no	—
185	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
187	C₂²×C₄×C₅	C₂⁴	1	12	yes	complemented
188	C₂×C₂²⋊D₅	—	4	12	no	—
189	C₂×C₂²⋊D₅	—	4	12	no	—
190	C₂×C₂²⋊D₅	—	4	6	no	—
191	C₂×C₂²⋊D₅	—	4	6	no	—
192	C₂×C₂²⋊D₅	—	4	12	no	—
193	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
194	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
195	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
196	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
197	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	complemented
198	C₂²×Dic₅	—	4	6	no	—
199	C₂²×Dic₅	C₂⁴	1	6	yes	—
200	C₂²×Dic₅	C₂⁴	1	3	yes	—
201	C₂²×Dic₅	C₂⁴	1	12	yes	complemented
202	D₄×D₅	—	4	96	no	—
203	D₄×D₅	—	4	48	no	—
204	D₄×D₅	—	4	48	no	—
205	C₂×D₂₀	—	4	12	no	—
206	C₂×D₂₀	—	4	6	no	—
207	C₂×D₂₀	—	4	6	no	—
208	C₂×D₂₀	C₂⁴	1	12	yes	—
209	C₂×D₂₀	C₂⁴	1	24	yes	—
210	C₂×D₂₀	C₂⁴	1	12	yes	complemented
211	C₂×C₄×D₅	—	2	24	no	—
212	C₂×C₄×D₅	—	2	12	no	—
213	C₂×C₄×D₅	—	4	48	no	—
214	C₂×C₄×D₅	—	4	12	no	—
215	C₂×C₄×D₅	C₂⁴	1	24	yes	—
216	C₂×C₄×D₅	C₂⁴	1	12	yes	—
217	C₂×C₄×D₅	C₂⁴	1	24	yes	complemented
218	C₅×C₄⋊C₄	C₂⁴	1	24	yes	complemented
219	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
220	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	—
221	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	complemented
222	C₄²×C₅	C₂⁴	1	4	yes	complemented
223	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
224	C₂²⋊Dic₅	C₂⁴	1	12	yes	—
225	C₂²⋊Dic₅	C₂⁴	1	12	yes	complemented
226	#685	C₂⁴	1	24	yes	—
227	#685	C₂⁴	1	24	yes	—
228	#685	C₂⁴	1	24	yes	—
229	#685	C₂⁴	1	24	yes	complemented
230	C₄⋊Dic₅	C₂⁴	1	24	yes	complemented
231	#683	C₂⁴	1	24	yes	complemented
232	#683	C₂⁴	1	24	yes	complemented
233	C₄×Dic₅	C₂⁴	1	12	yes	complemented
234	C₂⁶	—	5	1	no	—
235	C₂³×D₄	—	5	6	no	—
236	C₂³×D₄	—	5	3	no	—
237	C₂³×D₄	—	5	3	no	—
238	C₂⁴×C₄	—	5	3	no	—
239	#560	—	5	16	no	—
240	#560	—	5	32	no	—
241	#560	—	5	48	no	—
242	#560	—	5	96	no	—
243	#560	—	5	48	no	—
244	#560	C₂×D₅	1	16	yes	direct product factor
245	C₂×#127	—	5	3	no	—
246	C₂×#127	—	5	3	no	—
247	C₂×#127	—	5	16	no	—
248	C₂×#127	—	5	1	no	—
249	C₂×#127	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂×#126	—	5	32	no	—
251	C₂×#126	—	5	6	no	—
252	C₂×#126	—	5	6	no	—
253	C₂×#126	—	5	2	no	—
254	C₂×#126	C₂×D₅	1	2	yes	complemented
255	C₂×#123	—	5	3	no	—
256	C₂×#123	—	5	3	no	—
257	C₂×#123	—	5	48	no	—
258	C₂×#123	—	5	6	no	—
259	C₂×#123	—	5	6	no	—
260	C₂×#123	—	5	3	no	—
261	C₂×#123	C₂×D₅	1	3	yes	complemented
262	C₂×#121	—	5	6	no	—
263	C₂×#121	—	5	6	no	—
264	C₂×#121	—	5	6	no	—
265	C₂×#121	—	5	6	no	—
266	C₂×#121	—	5	96	no	—
267	C₂×#121	—	5	6	no	—
268	C₂×#121	—	5	6	no	—
269	C₂×#121	—	5	6	no	—
270	C₂×#121	C₂×D₅	1	6	yes	complemented
271	C₂×#120	—	5	3	no	—
272	C₂×#120	—	5	6	no	—
273	C₂×#120	—	5	3	no	—
274	C₂×#120	—	5	48	no	—
275	C₂×#120	—	5	3	no	—
276	C₂×#120	—	5	6	no	—
277	C₂×#120	C₂×D₅	1	3	yes	complemented
278	C₂²×C₄⋊C₄	—	5	6	no	—
279	C₂²×C₂²⋊C₄	—	5	6	no	—
280	C₂²×C₂²⋊C₄	—	5	3	no	—
281	C₂²×C₂²⋊C₄	—	5	3	no	—
282	C₂²×C₄²	—	5	1	no	—
283	C₂³×C₅	—	2	6	no	—
284	C₂³×C₅	—	2	12	no	—
285	C₂³×C₅	—	2	12	no	—
286	C₂³×C₅	—	2	6	no	—
287	C₂³×C₅	—	4	12	no	—
288	C₂³×C₅	—	4	16	no	—
289	C₂³×C₅	C₂⁵	1	4	yes	—
290	C₂³×C₅	C₂⁵	1	2	yes	—
291	C₂³×C₅	C₂⁵	1	6	yes	—
292	C₂³×C₅	C₂⁵	1	1	yes	characteristic
293	C₂²×D₅	—	2	6	no	—
294	C₂²×D₅	—	2	12	no	—
295	C₂²×D₅	—	2	12	no	—
296	C₂²×D₅	—	2	6	no	—
297	C₂²×D₅	—	2	24	no	—
298	C₂²×D₅	—	2	48	no	—
299	C₂²×D₅	—	2	48	no	—
300	C₂²×D₅	—	2	24	no	—
301	C₂²×D₅	—	4	24	no	—
302	C₂²×D₅	—	4	12	no	—
303	C₂²×D₅	—	4	16	no	—
304	C₂²×D₅	—	4	32	no	—
305	C₂²×D₅	—	4	128	no	—
306	C₂²×D₅	—	4	48	no	—
307	C₂²×D₅	—	4	32	no	—
308	C₂²×D₅	—	4	16	no	—
309	C₂²×D₅	H(5,𝔽₂)	1	12	yes	—
310	C₂²×D₅	C₂⁵	1	4	yes	—
311	C₂²×D₅	C₂⁵	1	2	yes	—
312	C₂²×D₅	C₂⁵	1	6	yes	—
313	C₂²×D₅	C₂⁵	1	2	yes	—
314	C₅×D₄	—	4	24	no	—
315	C₅×D₄	—	4	12	no	—
316	C₅×D₄	—	4	12	no	—
317	C₂×C₄×C₅	—	2	12	no	—
318	C₂×C₄×C₅	—	2	6	no	—
319	C₂×C₄×C₅	—	4	12	no	—
320	C₂×C₄×C₅	C₂⁵	1	6	yes	—
321	C₂×C₄×C₅	C₂⁵	1	12	yes	—
322	C₂²⋊D₅	—	4	24	no	—
323	C₂²⋊D₅	—	4	24	no	—
324	C₂²⋊D₅	—	4	12	no	—
325	C₂²⋊D₅	—	4	12	no	—
326	C₂²⋊D₅	—	4	24	no	—
327	C₂×Dic₅	—	2	12	no	—
328	C₂×Dic₅	—	2	6	no	—
329	C₂×Dic₅	—	4	12	no	—
330	C₂×Dic₅	C₂⁵	1	6	yes	—
331	C₂×Dic₅	C₂⁵	1	12	yes	—
332	D₂₀	—	4	24	no	—
333	D₂₀	—	4	12	no	—
334	D₂₀	—	4	12	no	—
335	C₄×D₅	—	2	48	no	—
336	C₄×D₅	—	2	24	no	—
337	C₄×D₅	—	4	24	no	—
338	C₂⁵	—	5	2	no	—
339	C₂⁵	—	5	1	no	—
340	C₂⁵	—	5	3	no	—
341	C₂⁵	—	5	8	no	—
342	C₂⁵	—	5	1	no	—
343	C₂⁵	—	5	2	no	—
344	C₂⁵	—	20	12	no	—
345	C₂⁵	C₂²×D₅	1	1	yes	characteristic
346	C₂²×D₄	—	5	6	no	—
347	C₂²×D₄	—	5	6	no	—
348	C₂²×D₄	—	5	3	no	—
349	C₂²×D₄	—	5	3	no	—
350	C₂²×D₄	—	5	6	no	—
351	C₂²×D₄	—	5	48	no	—
352	C₂²×D₄	—	5	24	no	—
353	C₂²×D₄	—	5	24	no	—
354	C₂²×D₄	—	5	6	no	—
355	C₂²×D₄	—	5	3	no	—
356	C₂²×D₄	—	5	3	no	—
357	C₂²×D₄	—	20	24	no	—
358	C₂²×D₄	—	20	12	no	—
359	C₂²×D₄	—	20	12	no	—
360	C₂²×D₄	C₂²×D₅	1	6	yes	—
361	C₂²×D₄	C₂²×D₅	1	3	yes	—
362	C₂²×D₄	C₂²×D₅	1	3	yes	complemented
363	C₂³×C₄	—	5	3	no	—
364	C₂³×C₄	—	5	6	no	—
365	C₂³×C₄	—	5	3	no	—
366	C₂³×C₄	—	5	6	no	—
367	C₂³×C₄	—	5	24	no	—
368	C₂³×C₄	—	20	12	no	—
369	C₂³×C₄	C₂²×D₅	1	3	yes	complemented
370	#127	—	5	24	no	—
371	#127	—	5	24	no	—
372	#127	—	5	8	no	—
373	#127	C₂²×D₅	1	8	yes	complemented
374	#126	—	5	48	no	—
375	#126	—	5	48	no	—
376	#126	—	5	16	no	—
377	#126	C₂²×D₅	1	16	yes	complemented
378	#123	—	5	24	no	—
379	#123	—	5	24	no	—
380	#123	—	5	48	no	—
381	#123	—	5	48	no	—
382	#123	—	5	24	no	—
383	#123	C₂²×D₅	1	24	yes	complemented
384	#121	—	5	48	no	—
385	#121	—	5	48	no	—
386	#121	—	5	48	no	—
387	#121	—	5	48	no	—
388	#121	—	5	48	no	—
389	#121	—	5	48	no	—
390	#121	—	5	48	no	—
391	#121	C₂²×D₅	1	48	yes	complemented
392	#120	—	5	24	no	—
393	#120	—	5	48	no	—
394	#120	—	5	24	no	—
395	#120	—	5	24	no	—
396	#120	—	5	48	no	—
397	#120	C₂²×D₅	1	24	yes	complemented
398	C₂×C₄⋊C₄	—	5	6	no	—
399	C₂×C₄⋊C₄	—	5	6	no	—
400	C₂×C₄⋊C₄	—	5	6	no	—
401	C₂×C₄⋊C₄	—	5	48	no	—
402	C₂×C₄⋊C₄	C₂²×D₅	1	6	yes	complemented
403	C₂×C₂²⋊C₄	—	5	6	no	—
404	C₂×C₂²⋊C₄	—	5	3	no	—
405	C₂×C₂²⋊C₄	—	5	3	no	—
406	C₂×C₂²⋊C₄	—	5	6	no	—
407	C₂×C₂²⋊C₄	—	5	6	no	—
408	C₂×C₂²⋊C₄	—	5	6	no	—
409	C₂×C₂²⋊C₄	—	5	6	no	—
410	C₂×C₂²⋊C₄	—	5	48	no	—
411	C₂×C₂²⋊C₄	—	5	24	no	—
412	C₂×C₂²⋊C₄	—	5	24	no	—
413	C₂×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
414	C₂×C₂²⋊C₄	C₂²×D₅	1	3	yes	—
415	C₂×C₂²⋊C₄	C₂²×D₅	1	3	yes	complemented
416	C₂×C₄²	—	5	3	no	—
417	C₂×C₄²	—	5	8	no	—
418	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
419	C₂²×C₅	—	2	6	no	—
420	C₂²×C₅	—	2	12	no	—
421	C₂²×C₅	—	2	12	no	—
422	C₂²×C₅	—	2	6	no	—
423	C₂²×C₅	—	4	16	no	—
424	C₂²×C₅	—	4	8	no	—
425	C₂²×C₅	—	4	4	no	—
426	C₂²×C₅	—	4	12	no	—
427	C₂²×C₅	C₂×H(5,𝔽₂)	1	6	yes	—
428	C₂²×C₅	C₂⁶	1	1	yes	characteristic
429	C₂×D₅	—	2	6	no	—
430	C₂×D₅	—	2	12	no	—
431	C₂×D₅	—	2	12	no	—
432	C₂×D₅	—	2	6	no	—
433	C₂×D₅	—	4	32	no	—
434	C₂×D₅	—	4	16	no	—
435	C₂×D₅	—	4	12	no	—
436	C₂×D₅	—	4	8	no	—
437	C₂×D₅	—	4	4	no	—
438	C₂×D₅	—	4	48	no	—
439	C₂×D₅	—	4	32	no	—
440	C₂×D₅	—	4	16	no	—
441	C₂×D₅	#560	1	16	yes	direct product factor
442	C₂×D₅	C₂×H(5,𝔽₂)	1	12	yes	—
443	C₄×C₅	—	2	12	no	—
444	C₄×C₅	—	2	6	no	—
445	Dic₅	—	2	12	no	—
446	Dic₅	—	2	6	no	—
447	C₂⁴	—	4	6	no	—
448	C₂⁴	—	5	1	no	—
449	C₂⁴	—	5	8	no	—
450	C₂⁴	—	5	4	no	—
451	C₂⁴	—	5	12	no	—
452	C₂⁴	—	5	2	no	—
453	C₂⁴	—	5	1	no	—
454	C₂⁴	—	5	3	no	—
455	C₂⁴	—	5	4	no	—
456	C₂⁴	—	5	8	no	—
457	C₂⁴	—	10	12	no	—
458	C₂⁴	—	10	24	no	—
459	C₂⁴	—	10	24	no	—
460	C₂⁴	—	10	12	no	—
461	C₂⁴	—	20	12	no	—
462	C₂⁴	—	20	6	no	—
463	C₂⁴	—	20	48	no	—
464	C₂⁴	—	20	64	no	—
465	C₂⁴	C₂³×D₅	1	2	yes	—
466	C₂⁴	C₂³×D₅	1	1	yes	characteristic
467	C₂⁴	C₂³×D₅	1	3	yes	—
468	C₂⁴	C₂³×D₅	1	4	yes	—
469	C₂×D₄	—	4	12	no	—
470	C₂×D₄	—	4	6	no	—
471	C₂×D₄	—	4	6	no	—
472	C₂×D₄	—	5	24	no	—
473	C₂×D₄	—	5	24	no	—
474	C₂×D₄	—	5	12	no	—
475	C₂×D₄	—	5	12	no	—
476	C₂×D₄	—	5	24	no	—
477	C₂×D₄	—	5	24	no	—
478	C₂×D₄	—	5	12	no	—
479	C₂×D₄	—	5	12	no	—
480	C₂×D₄	—	20	12	no	—
481	C₂×D₄	—	20	6	no	—
482	C₂×D₄	—	20	6	no	—
483	C₂×D₄	—	20	96	no	—
484	C₂×D₄	—	20	48	no	—
485	C₂×D₄	—	20	48	no	—
486	C₂×D₄	—	20	12	no	—
487	C₂×D₄	—	20	12	no	—
488	C₂×D₄	—	20	6	no	—
489	C₂×D₄	—	20	12	no	—
490	C₂×D₄	—	20	6	no	—
491	C₂×D₄	C₂³×D₅	1	24	yes	—
492	C₂×D₄	C₂³×D₅	1	12	yes	—
493	C₂×D₄	C₂³×D₅	1	12	yes	complemented
494	C₂²×C₄	—	4	6	no	—
495	C₂²×C₄	—	5	3	no	—
496	C₂²×C₄	—	5	6	no	—
497	C₂²×C₄	—	5	12	no	—
498	C₂²×C₄	—	5	12	no	—
499	C₂²×C₄	—	5	24	no	—
500	C₂²×C₄	—	5	24	no	—
501	C₂²×C₄	—	10	24	no	—
502	C₂²×C₄	—	10	12	no	—
503	C₂²×C₄	—	20	12	no	—
504	C₂²×C₄	—	20	48	no	—
505	C₂²×C₄	—	20	6	no	—
506	C₂²×C₄	C₂³×D₅	1	3	yes	—
507	C₂²×C₄	C₂³×D₅	1	6	yes	—
508	C₂²×C₄	C₂³×D₅	1	12	yes	complemented
509	C₄⋊C₄	—	5	24	no	—
510	C₄⋊C₄	—	5	24	no	—
511	C₄⋊C₄	—	5	24	no	—
512	C₄⋊C₄	C₂³×D₅	1	24	yes	complemented
513	C₂²⋊C₄	—	5	24	no	—
514	C₂²⋊C₄	—	5	12	no	—
515	C₂²⋊C₄	—	5	12	no	—
516	C₂²⋊C₄	—	5	24	no	—
517	C₂²⋊C₄	—	5	24	no	—
518	C₂²⋊C₄	—	5	24	no	—
519	C₂²⋊C₄	—	5	24	no	—
520	C₂²⋊C₄	C₂³×D₅	1	24	yes	—
521	C₂²⋊C₄	C₂³×D₅	1	12	yes	—
522	C₂²⋊C₄	C₂³×D₅	1	12	yes	complemented
523	C₄²	—	5	12	no	—
524	C₄²	C₂³×D₅	1	4	yes	complemented
525	C₂×C₅	—	4	4	no	—
526	C₂×C₅	—	4	2	no	—
527	C₂×C₅	—	4	6	no	—
528	C₂×C₅	C₂×#560	1	4	yes	complemented
529	C₂×C₅	C₂²×H(5,𝔽₂)	1	3	yes	—
530	D₅	—	4	6	no	—
531	D₅	—	4	4	no	—
532	D₅	—	4	2	no	—
533	D₅	C₂×#560	1	8	yes	direct product factor
534	C₂³	—	2	6	no	—
535	C₂³	—	2	12	no	—
536	C₂³	—	2	12	no	—
537	C₂³	—	2	6	no	—
538	C₂³	—	4	12	no	—
539	C₂³	—	4	16	no	—
540	C₂³	—	5	12	no	—
541	C₂³	—	5	2	no	—
542	C₂³	—	5	4	no	—
543	C₂³	—	5	2	no	—
544	C₂³	—	5	6	no	—
545	C₂³	—	10	24	no	—
546	C₂³	—	10	48	no	—
547	C₂³	—	10	48	no	—
548	C₂³	—	10	24	no	—
549	C₂³	—	10	6	no	—
550	C₂³	—	10	12	no	—
551	C₂³	—	10	12	no	—
552	C₂³	—	10	6	no	—
553	C₂³	—	20	24	no	—
554	C₂³	—	20	12	no	—
555	C₂³	—	20	32	no	—
556	C₂³	—	20	16	no	—
557	C₂³	—	20	48	no	—
558	C₂³	—	20	128	no	—
559	C₂³	—	20	32	no	—
560	C₂³	—	20	16	no	—
561	C₂³	C₂⁴×D₅	1	4	yes	—
562	C₂³	C₂⁴×D₅	1	2	yes	—
563	C₂³	C₂⁴×D₅	1	6	yes	—
564	C₂³	C₂⁴×D₅	1	1	yes	characteristic
565	D₄	—	4	24	no	—
566	D₄	—	4	12	no	—
567	D₄	—	4	12	no	—
568	D₄	—	20	24	no	—
569	D₄	—	20	12	no	—
570	D₄	—	20	12	no	—
571	D₄	—	20	24	no	—
572	D₄	—	20	24	no	—
573	D₄	—	20	12	no	—
574	D₄	—	20	24	no	—
575	D₄	—	20	12	no	—
576	C₂×C₄	—	2	12	no	—
577	C₂×C₄	—	2	6	no	—
578	C₂×C₄	—	4	12	no	—
579	C₂×C₄	—	5	6	no	—
580	C₂×C₄	—	5	12	no	—
581	C₂×C₄	—	10	48	no	—
582	C₂×C₄	—	10	24	no	—
583	C₂×C₄	—	10	12	no	—
584	C₂×C₄	—	10	6	no	—
585	C₂×C₄	—	20	24	no	—
586	C₂×C₄	—	20	12	no	—
587	C₂×C₄	C₂⁴×D₅	1	6	yes	—
588	C₂×C₄	C₂⁴×D₅	1	12	yes	—
589	C₅	C₂²×#560	1	1	yes	characteristic, complemented, Sylow
590	C₂²	—	2	6	no	—
591	C₂²	—	2	12	no	—
592	C₂²	—	2	12	no	—
593	C₂²	—	2	6	no	—
594	C₂²	—	4	16	no	—
595	C₂²	—	4	8	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	12	no	—
598	C₂²	—	5	12	no	—
599	C₂²	—	5	16	no	—
600	C₂²	—	10	6	no	—
601	C₂²	—	10	12	no	—
602	C₂²	—	10	12	no	—
603	C₂²	—	10	6	no	—
604	C₂²	—	20	32	no	—
605	C₂²	—	20	16	no	—
606	C₂²	—	20	48	no	—
607	C₂²	—	20	32	no	—
608	C₂²	—	20	16	no	—
609	C₂²	—	20	8	no	—
610	C₂²	—	20	4	no	—
611	C₂²	—	20	12	no	—
612	C₂²	D₅×H(5,𝔽₂)	1	6	yes	—
613	C₂²	C₂⁵×D₅	1	1	yes	characteristic
614	C₄	—	2	12	no	—
615	C₄	—	2	6	no	—
616	C₄	—	10	12	no	—
617	C₄	—	10	6	no	—
618	C₂	—	4	4	no	—
619	C₂	—	4	2	no	—
620	C₂	—	4	6	no	—
621	C₂	—	5	8	no	—
622	C₂	—	20	4	no	—
623	C₂	—	20	2	no	—
624	C₂	—	20	6	no	—
625	C₂	D₅×#560	1	4	yes	direct product factor
626	C₂	C₂×D₅×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#560	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#560	D₅
hypocenter	C₅	C₂²×#560
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#560

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#560	C₂	semidirect
2. D₅×#560	C₂	direct (N × H)
3. C₂×#66054	C₂	semidirect
4. C₂×D₅×#127	C₂	semidirect
5. C₂×#66045	C₂	semidirect
6. C₂×D₅×#126	C₂	semidirect
7. C₂×#66000	C₂	semidirect
8. C₂×D₅×#123	C₂	semidirect
9. C₂×#65954	C₂	semidirect
10. C₂×D₅×#121	C₂	semidirect
11. C₂×#65929	C₂	semidirect
12. C₂×D₅×#120	C₂	semidirect
16. C₂²×D₄×D₅	C₂²	semidirect
17. C₂³×C₄×D₅	C₂²	semidirect
18. C₅×#560	C₂²	semidirect
19. C₂×C₅×#127	C₂²	semidirect
20. C₂×C₅×#126	C₂²	semidirect
21. C₂×C₅×#123	C₂²	semidirect
22. C₂×C₅×#121	C₂²	semidirect
23. C₂×C₅×#120	C₂²	semidirect
24. C₂×#4099	C₂²	semidirect
25. C₂×#4086	C₂²	semidirect
26. C₂×#4086	C₂²	semidirect
27. C₂×#4085	C₂²	semidirect
28. C₂×#4085	C₂²	semidirect
29. C₂×#4084	C₂²	semidirect
30. C₂×#4083	C₂²	semidirect
31. C₂×#4083	C₂²	semidirect
32. C₂×#4081	C₂²	semidirect
33. C₂×#4076	C₂²	semidirect
34. C₂×#4075	C₂²	semidirect
35. #66054	C₂²	semidirect
36. D₅×#127	C₂²	semidirect
37. #66045	C₂²	semidirect
38. D₅×#126	C₂²	semidirect
39. #66000	C₂²	semidirect
40. D₅×#123	C₂²	semidirect
41. #65954	C₂²	semidirect
42. D₅×#121	C₂²	semidirect
43. #65929	C₂²	semidirect
44. D₅×#120	C₂²	semidirect
45. C₂×#4044	C₂²	semidirect
46. C₂×#4041	C₂²	semidirect
47. C₂×#4040	C₂²	semidirect
48. C₂×D₅×C₄⋊C₄	C₂²	semidirect
49. C₂×#4032	C₂²	semidirect
50. C₂×#4030	C₂²	semidirect
51. C₂×#4030	C₂²	semidirect
52. C₂×#4029	C₂²	semidirect
53. C₂×#4028	C₂²	semidirect
54. C₂×#4028	C₂²	semidirect
57. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
58. C₂×#4025	C₂²	semidirect
59. C₂×#4022	C₂²	semidirect
60. C₂×#4020	C₂²	semidirect
61. C₂×C₄²×D₅	C₂²	semidirect
73. C₂²×C₅×D₄	C₂³	semidirect
74. C₂³×C₄×C₅	C₂³	semidirect
79. C₂²×C₂²⋊D₅	C₂³	semidirect
80. C₂³×Dic₅	C₂³	semidirect
86. C₂×D₄×D₅	C₂³	semidirect
89. C₂²×D₂₀	C₂³	semidirect
93. C₂²×C₄×D₅	C₂³	semidirect
94. C₂²×C₄×D₅	C₂³	semidirect
95. C₅×#127	C₂³	semidirect
96. C₅×#126	C₂³	semidirect
97. C₅×#123	C₂³	semidirect
98. C₅×#121	C₂³	semidirect
99. C₅×#120	C₂³	semidirect
100. C₂×C₅×C₄⋊C₄	C₂³	semidirect
103. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
104. C₂×C₄²×C₅	C₂³	semidirect
105. #4099	C₂³	semidirect
108. C₂×C₂²⋊Dic₅	C₂³	semidirect
109. #4086	C₂³	semidirect
110. #4086	C₂³	semidirect
111. #4085	C₂³	semidirect
112. #4085	C₂³	semidirect
113. #4084	C₂³	semidirect
114. #4083	C₂³	semidirect
115. #4083	C₂³	semidirect
116. #4081	C₂³	semidirect
117. #4076	C₂³	semidirect
118. #4075	C₂³	semidirect
122. C₂×#685	C₂³	semidirect
123. C₂×C₄⋊Dic₅	C₂³	semidirect
124. C₂×#683	C₂³	semidirect
125. C₂×#683	C₂³	semidirect
126. C₂×C₄×Dic₅	C₂³	semidirect
127. #4044	C₂³	semidirect
128. #4041	C₂³	semidirect
129. #4040	C₂³	semidirect
130. D₅×C₄⋊C₄	C₂³	semidirect
131. #4032	C₂³	semidirect
132. #4030	C₂³	semidirect
133. #4030	C₂³	semidirect
134. #4029	C₂³	semidirect
135. #4028	C₂³	semidirect
136. #4028	C₂³	semidirect
139. D₅×C₂²⋊C₄	C₂³	semidirect
140. #4025	C₂³	semidirect
141. #4022	C₂³	semidirect
142. #4020	C₂³	semidirect
143. C₄²×D₅	C₂³	semidirect
150. C₂×#560	D₅	direct (N × H)
183. C₂×C₅×D₄	C₂⁴	semidirect
187. C₂²×C₄×C₅	C₂⁴	semidirect
197. C₂×C₂²⋊D₅	C₂⁴	semidirect
201. C₂²×Dic₅	C₂⁴	semidirect
210. C₂×D₂₀	C₂⁴	semidirect
217. C₂×C₄×D₅	C₂⁴	semidirect
218. C₅×C₄⋊C₄	C₂⁴	semidirect
221. C₅×C₂²⋊C₄	C₂⁴	semidirect
222. C₄²×C₅	C₂⁴	semidirect
225. C₂²⋊Dic₅	C₂⁴	semidirect
229. #685	C₂⁴	semidirect
230. C₄⋊Dic₅	C₂⁴	semidirect
231. #683	C₂⁴	semidirect
232. #683	C₂⁴	semidirect
233. C₄×Dic₅	C₂⁴	semidirect
244. #560	C₂×D₅	direct (N × H)
249. C₂×#127	C₂×D₅	semidirect
254. C₂×#126	C₂×D₅	semidirect
261. C₂×#123	C₂×D₅	semidirect
270. C₂×#121	C₂×D₅	semidirect
277. C₂×#120	C₂×D₅	semidirect
362. C₂²×D₄	C₂²×D₅	semidirect
369. C₂³×C₄	C₂²×D₅	semidirect
373. #127	C₂²×D₅	semidirect
377. #126	C₂²×D₅	semidirect
383. #123	C₂²×D₅	semidirect
391. #121	C₂²×D₅	semidirect
397. #120	C₂²×D₅	semidirect
402. C₂×C₄⋊C₄	C₂²×D₅	semidirect
415. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
418. C₂×C₄²	C₂²×D₅	semidirect
441. C₂×D₅	#560	direct (N × H)
493. C₂×D₄	C₂³×D₅	semidirect
508. C₂²×C₄	C₂³×D₅	semidirect
512. C₄⋊C₄	C₂³×D₅	semidirect
522. C₂²⋊C₄	C₂³×D₅	semidirect
524. C₄²	C₂³×D₅	semidirect
528. C₂×C₅	C₂×#560	semidirect
533. D₅	C₂×#560	direct (N × H)
589. C₅	C₂²×#560	semidirect
625. C₂	D₅×#560	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×C₅×#560	2
D₅×#560	2
C₂×#66054	2
C₂×D₅×#127	2
C₂×#66045	2
C₂×D₅×#126	2
C₂×#66000	2
C₂×D₅×#123	2
C₂×#65954	2
C₂×D₅×#121	2
C₂×#65929	2
C₂×D₅×#120	2
C₂²×#560	5

Subgroups — C2×D5×#560 #13006165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#560 #13006165