Subgroups — C₂×C₅×D₅×#41 #13107865

Order 1600.

1944 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅×#41	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#713	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#711	C₂	1	3	yes	maximal, complemented
6	C₂×C₅×D₄×D₅	C₂	1	3	yes	maximal, complemented
7	C₂×C₅×#709	C₂	1	3	yes	maximal, complemented
8	C₂²×C₄×C₅×D₅	C₂	1	3	yes	maximal, complemented
9	C₂³×C₅×D₅	C₂²	1	3	yes	—
10	C₅²×#41	C₂²	1	8	yes	complemented
11	C₂×C₅²×Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₅²×D₄	C₂²	1	3	yes	complemented
13	C₂²×C₄×C₅²	C₂²	1	3	yes	complemented
14	C₂×C₅×C₂²⋊D₅	C₂²	1	6	yes	complemented
15	C₂²×C₅×Dic₅	C₂²	1	3	yes	complemented
16	C₅×#713	C₂²	1	8	yes	complemented
17	C₅×Q₈×D₅	C₂²	1	8	yes	complemented
18	C₅×#711	C₂²	1	24	yes	complemented
19	C₅×D₄×D₅	C₂²	1	24	yes	complemented
20	C₅×#709	C₂²	1	24	yes	complemented
21	C₂×C₅×D₂₀	C₂²	1	3	yes	complemented
22	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₅	C₂²	1	3	yes	—
24	C₂×C₄×C₅×D₅	C₂²	1	24	yes	complemented
25	C₂×C₄×C₅×D₅	C₂²	1	3	yes	complemented
26	C₂×C₄×C₅×D₅	C₂²	1	3	yes	complemented
27	C₂×C₅×Dic₁₀	C₂²	1	3	yes	complemented
28	C₂²×C₅×#41	—	5	1	no	maximal
29	C₂×D₅×#41	C₅	1	1	yes	maximal, characteristic, direct product factor
30	C₂³×C₅²	C₂³	1	3	yes	—
31	C₂²×C₅×D₅	—	2	12	no	—
32	C₂²×C₅×D₅	C₂³	1	3	yes	—
33	C₂²×C₅×D₅	C₂³	1	12	yes	—
34	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
35	C₅²×Q₈	C₂³	1	4	yes	complemented
36	C₅²×D₄	C₂³	1	12	yes	complemented
37	C₂×C₄×C₅²	C₂³	1	3	yes	—
38	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
39	C₂×C₄×C₅²	C₂³	1	12	yes	complemented
40	C₅×C₂²⋊D₅	C₂³	1	24	yes	complemented
41	C₂×C₅×Dic₅	C₂³	1	3	yes	—
42	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
43	C₂×C₅×Dic₅	C₂³	1	12	yes	complemented
44	C₅×D₂₀	C₂³	1	12	yes	complemented
45	C₄×C₅×D₅	C₂³	1	4	yes	—
46	C₄×C₅×D₅	C₂³	1	12	yes	—
47	C₄×C₅×D₅	C₂³	1	12	yes	complemented
48	C₄×C₅×D₅	C₂³	1	12	yes	complemented
49	C₅×Dic₁₀	C₂³	1	12	yes	complemented
50	C₂×C₅×#41	—	2	2	no	—
51	C₂×C₅×#41	—	5	16	no	—
52	C₂×C₅×#41	—	5	1	no	—
53	C₂×C₅×#41	—	5	3	no	—
54	C₂×C₅×#41	—	5	3	no	—
55	C₂×C₅×#41	D₅	1	1	yes	characteristic, direct product factor
56	C₂×C₅×#41	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂²×C₅×Q₈	—	5	1	no	—
58	C₂²×C₅×D₄	—	5	3	no	—
59	C₂³×C₄×C₅	—	5	3	no	—
60	D₅×#41	C₂×C₅	1	16	yes	direct product factor
61	C₂×#713	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×Q₈×D₅	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#711	C₂×C₅	1	3	yes	complemented
64	C₂×D₄×D₅	C₂×C₅	1	3	yes	complemented
65	C₂×#709	C₂×C₅	1	3	yes	complemented
66	C₂²×C₄×D₅	C₂×C₅	1	3	yes	complemented
67	C₂²×C₅²	—	2	6	no	—
68	C₂²×C₅²	C₂⁴	1	6	yes	—
69	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
70	C₂×C₅×D₅	—	2	24	no	—
71	C₂×C₅×D₅	—	2	6	no	—
72	C₂×C₅×D₅	#41	1	4	yes	direct product factor
73	C₂×C₅×D₅	C₂⁴	1	6	yes	—
74	C₂×C₅×D₅	C₂⁴	1	2	yes	—
75	C₄×C₅²	C₂⁴	1	6	yes	—
76	C₄×C₅²	C₂⁴	1	2	yes	—
77	C₅×Dic₅	C₂⁴	1	6	yes	—
78	C₅×Dic₅	C₂⁴	1	2	yes	—
79	C₂⁴×C₅	—	5	3	no	—
80	C₂³×D₅	C₂²×C₅	1	3	yes	—
81	C₅×#41	—	2	16	no	—
82	C₅×#41	—	5	8	no	—
83	C₅×#41	—	5	24	no	—
84	C₅×#41	—	5	24	no	—
85	C₅×#41	C₂×D₅	1	8	yes	direct product factor
86	C₅×#41	C₂²×C₅	1	8	yes	complemented
87	C₂×C₅×Q₈	—	2	2	no	—
88	C₂×C₅×Q₈	—	5	8	no	—
89	C₂×C₅×Q₈	—	5	3	no	—
90	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
91	C₂×C₅×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
92	C₂×C₅×D₄	—	2	6	no	—
93	C₂×C₅×D₄	—	5	6	no	—
94	C₂×C₅×D₄	—	5	24	no	—
95	C₂×C₅×D₄	—	5	3	no	—
96	C₂×C₅×D₄	C₂×D₅	1	3	yes	complemented
97	C₂×C₅×D₄	C₂²×C₅	1	3	yes	complemented
98	C₂²×C₄×C₅	—	2	6	no	—
99	C₂²×C₄×C₅	—	5	3	no	—
100	C₂²×C₄×C₅	—	5	3	no	—
101	C₂²×C₄×C₅	—	5	3	no	—
102	C₂²×C₄×C₅	—	5	1	no	—
103	C₂²×C₄×C₅	—	5	3	no	—
104	C₂²×C₄×C₅	—	5	24	no	—
105	C₂²×C₄×C₅	C₂×D₅	1	3	yes	complemented
106	C₂²×C₄×C₅	C₂²×C₅	1	3	yes	complemented
107	C₂×C₂²⋊D₅	C₂²×C₅	1	6	yes	complemented
108	C₂²×Dic₅	C₂²×C₅	1	3	yes	complemented
109	#713	C₂²×C₅	1	8	yes	complemented
110	Q₈×D₅	C₂²×C₅	1	8	yes	complemented
111	#711	C₂²×C₅	1	24	yes	complemented
112	D₄×D₅	C₂²×C₅	1	24	yes	complemented
113	#709	C₂²×C₅	1	24	yes	complemented
114	C₂×D₂₀	C₂²×C₅	1	3	yes	complemented
115	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂²×C₅	1	3	yes	—
117	C₂×C₄×D₅	C₂²×C₅	1	24	yes	complemented
118	C₂×C₄×D₅	C₂²×C₅	1	3	yes	complemented
119	C₂×C₄×D₅	C₂²×C₅	1	3	yes	complemented
120	C₂×Dic₁₀	C₂²×C₅	1	3	yes	complemented
121	C₂²×#41	—	5	1	no	Sylow
122	C₂×C₅²	—	2	6	no	—
123	C₂×C₅²	C₂×#41	1	2	yes	complemented
124	C₂×C₅²	C₂⁵	1	1	yes	characteristic
125	C₅×D₅	—	2	6	no	—
126	C₅×D₅	C₂×#41	1	4	yes	direct product factor
127	C₂³×C₅	—	2	6	no	—
128	C₂³×C₅	—	5	1	no	—
129	C₂³×C₅	—	5	12	no	—
130	C₂³×C₅	—	5	3	no	—
131	C₂³×C₅	—	10	12	no	—
132	C₂³×C₅	C₂²×D₅	1	3	yes	—
133	C₂³×C₅	C₂³×C₅	1	3	yes	—
134	C₂²×D₅	—	2	12	no	—
135	C₂²×D₅	C₂³×C₅	1	3	yes	—
136	C₂²×D₅	C₂³×C₅	1	12	yes	—
137	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
138	C₅×Q₈	—	2	8	no	—
139	C₅×Q₈	—	5	12	no	—
140	C₅×Q₈	C₂²×D₅	1	4	yes	complemented
141	C₅×Q₈	C₂³×C₅	1	4	yes	complemented
142	C₅×D₄	—	2	24	no	—
143	C₅×D₄	—	5	24	no	—
144	C₅×D₄	—	5	12	no	—
145	C₅×D₄	C₂²×D₅	1	12	yes	complemented
146	C₅×D₄	C₂³×C₅	1	12	yes	complemented
147	C₂×C₄×C₅	—	2	2	no	—
148	C₂×C₄×C₅	—	2	6	no	—
149	C₂×C₄×C₅	—	2	24	no	—
150	C₂×C₄×C₅	—	5	1	no	—
151	C₂×C₄×C₅	—	5	3	no	—
152	C₂×C₄×C₅	—	5	12	no	—
153	C₂×C₄×C₅	—	5	4	no	—
154	C₂×C₄×C₅	—	5	12	no	—
155	C₂×C₄×C₅	—	5	12	no	—
156	C₂×C₄×C₅	—	5	12	no	—
157	C₂×C₄×C₅	C₂²×D₅	1	3	yes	—
158	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂²×D₅	1	12	yes	complemented
160	C₂×C₄×C₅	C₂³×C₅	1	3	yes	—
161	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂³×C₅	1	12	yes	complemented
163	C₂²⋊D₅	C₂³×C₅	1	24	yes	complemented
164	C₂×Dic₅	C₂³×C₅	1	3	yes	—
165	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
166	C₂×Dic₅	C₂³×C₅	1	12	yes	complemented
167	D₂₀	C₂³×C₅	1	12	yes	complemented
168	C₄×D₅	C₂³×C₅	1	4	yes	—
169	C₄×D₅	C₂³×C₅	1	12	yes	—
170	C₄×D₅	C₂³×C₅	1	12	yes	complemented
171	C₄×D₅	C₂³×C₅	1	12	yes	complemented
172	Dic₁₀	C₂³×C₅	1	12	yes	complemented
173	C₂×#41	—	5	16	no	—
174	C₂×#41	—	5	1	no	—
175	C₂×#41	—	5	3	no	—
176	C₂×#41	—	5	3	no	—
177	C₂×#41	C₅×D₅	1	1	yes	characteristic, direct product factor
178	C₂²×Q₈	—	5	1	no	—
179	C₂²×D₄	—	5	3	no	—
180	C₂³×C₄	—	5	3	no	—
181	C₅²	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
182	C₂²×C₅	—	2	6	no	—
183	C₂²×C₅	—	2	6	no	—
184	C₂²×C₅	—	2	2	no	—
185	C₂²×C₅	—	2	12	no	—
186	C₂²×C₅	—	4	12	no	—
187	C₂²×C₅	—	5	4	no	—
188	C₂²×C₅	—	5	2	no	—
189	C₂²×C₅	—	5	6	no	—
190	C₂²×C₅	—	10	24	no	—
191	C₂²×C₅	—	10	6	no	—
192	C₂²×C₅	C₂³×D₅	1	6	yes	—
193	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
194	C₂²×C₅	C₂⁴×C₅	1	6	yes	—
195	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
196	C₂×D₅	—	2	6	no	—
197	C₂×D₅	—	2	24	no	—
198	C₂×D₅	C₅×#41	1	4	yes	direct product factor
199	C₂×D₅	C₂⁴×C₅	1	6	yes	—
200	C₂×D₅	C₂⁴×C₅	1	2	yes	—
201	C₄×C₅	—	2	4	no	—
202	C₄×C₅	—	2	12	no	—
203	C₄×C₅	—	5	2	no	—
204	C₄×C₅	—	5	6	no	—
205	C₄×C₅	C₂³×D₅	1	2	yes	—
206	C₄×C₅	C₂³×D₅	1	6	yes	—
207	C₄×C₅	C₂⁴×C₅	1	6	yes	—
208	C₄×C₅	C₂⁴×C₅	1	2	yes	—
209	Dic₅	C₂⁴×C₅	1	6	yes	—
210	Dic₅	C₂⁴×C₅	1	2	yes	—
211	C₂⁴	—	5	3	no	—
212	#41	—	5	8	no	—
213	#41	—	5	24	no	—
214	#41	—	5	24	no	—
215	#41	C₂×C₅×D₅	1	8	yes	direct product factor
216	C₂×Q₈	—	5	8	no	—
217	C₂×Q₈	—	5	3	no	—
218	C₂×Q₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
219	C₂×D₄	—	5	6	no	—
220	C₂×D₄	—	5	24	no	—
221	C₂×D₄	—	5	3	no	—
222	C₂×D₄	C₂×C₅×D₅	1	3	yes	complemented
223	C₂²×C₄	—	5	3	no	—
224	C₂²×C₄	—	5	1	no	—
225	C₂²×C₄	—	5	3	no	—
226	C₂²×C₄	—	5	3	no	—
227	C₂²×C₄	—	5	3	no	—
228	C₂²×C₄	—	5	24	no	—
229	C₂²×C₄	C₂×C₅×D₅	1	3	yes	complemented
230	C₂×C₅	—	2	6	no	—
231	C₂×C₅	—	2	6	no	—
232	C₂×C₅	—	2	4	no	—
233	C₂×C₅	—	2	2	no	—
234	C₂×C₅	—	4	12	no	—
235	C₂×C₅	—	5	4	no	—
236	C₂×C₅	—	10	6	no	—
237	C₂×C₅	D₅×#41	1	2	yes	direct product factor
238	C₂×C₅	C₂×C₅×#41	1	2	yes	complemented
239	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
240	C₂×C₅	C₂⁵×C₅	1	1	yes	characteristic
241	D₅	—	2	6	no	—
242	D₅	C₂×C₅×#41	1	4	yes	direct product factor
243	C₂³	—	5	1	no	—
244	C₂³	—	5	12	no	—
245	C₂³	—	5	3	no	—
246	C₂³	—	10	12	no	—
247	C₂³	C₂²×C₅×D₅	1	3	yes	—
248	Q₈	—	5	12	no	—
249	Q₈	C₂²×C₅×D₅	1	4	yes	complemented
250	D₄	—	5	24	no	—
251	D₄	—	5	12	no	—
252	D₄	C₂²×C₅×D₅	1	12	yes	complemented
253	C₂×C₄	—	5	1	no	—
254	C₂×C₄	—	5	3	no	—
255	C₂×C₄	—	5	12	no	—
256	C₂×C₄	—	5	4	no	—
257	C₂×C₄	—	5	12	no	—
258	C₂×C₄	—	5	12	no	—
259	C₂×C₄	—	5	12	no	—
260	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
261	C₂×C₄	C₂²×C₅×D₅	1	3	yes	—
262	C₂×C₄	C₂²×C₅×D₅	1	12	yes	complemented
263	C₅	—	2	2	no	—
264	C₅	C₂×D₅×#41	1	1	yes	characteristic, direct product factor
265	C₅	C₂²×C₅×#41	1	1	yes	characteristic, complemented
266	C₂²	—	2	6	no	—
267	C₂²	—	5	4	no	—
268	C₂²	—	5	2	no	—
269	C₂²	—	5	6	no	—
270	C₂²	—	10	24	no	—
271	C₂²	—	10	6	no	—
272	C₂²	C₂³×C₅×D₅	1	6	yes	—
273	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
274	C₄	—	5	2	no	—
275	C₄	—	5	6	no	—
276	C₄	C₂³×C₅×D₅	1	2	yes	—
277	C₄	C₂³×C₅×D₅	1	6	yes	—
278	C₂	—	2	6	no	—
279	C₂	—	5	4	no	—
280	C₂	—	10	6	no	—
281	C₂	C₅×D₅×#41	1	2	yes	direct product factor
282	C₂	C₂⁴×C₅×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₅
commutator, cosocle	C₂×C₅	C₂⁵×C₅
Frattini	C₂	C₂⁴×C₅×D₅
Fitting	C₂×C₅²×#41	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂×C₅×#41	D₅
hypocenter	C₅	C₂²×C₅×#41
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#41	C₂	semidirect
2. C₅×D₅×#41	C₂	direct (N × H)
3. C₂×C₅×#713	C₂	semidirect
4. C₂×C₅×Q₈×D₅	C₂	semidirect
5. C₂×C₅×#711	C₂	semidirect
6. C₂×C₅×D₄×D₅	C₂	semidirect
7. C₂×C₅×#709	C₂	semidirect
8. C₂²×C₄×C₅×D₅	C₂	semidirect
10. C₅²×#41	C₂²	semidirect
11. C₂×C₅²×Q₈	C₂²	semidirect
12. C₂×C₅²×D₄	C₂²	semidirect
13. C₂²×C₄×C₅²	C₂²	semidirect
14. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
15. C₂²×C₅×Dic₅	C₂²	semidirect
16. C₅×#713	C₂²	semidirect
17. C₅×Q₈×D₅	C₂²	semidirect
18. C₅×#711	C₂²	semidirect
19. C₅×D₄×D₅	C₂²	semidirect
20. C₅×#709	C₂²	semidirect
21. C₂×C₅×D₂₀	C₂²	semidirect
24. C₂×C₄×C₅×D₅	C₂²	semidirect
25. C₂×C₄×C₅×D₅	C₂²	semidirect
26. C₂×C₄×C₅×D₅	C₂²	semidirect
27. C₂×C₅×Dic₁₀	C₂²	semidirect
29. C₂×D₅×#41	C₅	direct (N × H)
35. C₅²×Q₈	C₂³	semidirect
36. C₅²×D₄	C₂³	semidirect
39. C₂×C₄×C₅²	C₂³	semidirect
40. C₅×C₂²⋊D₅	C₂³	semidirect
43. C₂×C₅×Dic₅	C₂³	semidirect
44. C₅×D₂₀	C₂³	semidirect
47. C₄×C₅×D₅	C₂³	semidirect
48. C₄×C₅×D₅	C₂³	semidirect
49. C₅×Dic₁₀	C₂³	semidirect
55. C₂×C₅×#41	D₅	direct (N × H)
56. C₂×C₅×#41	C₂×C₅	semidirect
60. D₅×#41	C₂×C₅	direct (N × H)
61. C₂×#713	C₂×C₅	semidirect
62. C₂×Q₈×D₅	C₂×C₅	semidirect
63. C₂×#711	C₂×C₅	semidirect
64. C₂×D₄×D₅	C₂×C₅	semidirect
65. C₂×#709	C₂×C₅	semidirect
66. C₂²×C₄×D₅	C₂×C₅	semidirect
72. C₂×C₅×D₅	#41	direct (N × H)
85. C₅×#41	C₂×D₅	direct (N × H)
86. C₅×#41	C₂²×C₅	semidirect
90. C₂×C₅×Q₈	C₂×D₅	semidirect
91. C₂×C₅×Q₈	C₂²×C₅	semidirect
96. C₂×C₅×D₄	C₂×D₅	semidirect
97. C₂×C₅×D₄	C₂²×C₅	semidirect
105. C₂²×C₄×C₅	C₂×D₅	semidirect
106. C₂²×C₄×C₅	C₂²×C₅	semidirect
107. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
108. C₂²×Dic₅	C₂²×C₅	semidirect
109. #713	C₂²×C₅	semidirect
110. Q₈×D₅	C₂²×C₅	semidirect
111. #711	C₂²×C₅	semidirect
112. D₄×D₅	C₂²×C₅	semidirect
113. #709	C₂²×C₅	semidirect
114. C₂×D₂₀	C₂²×C₅	semidirect
117. C₂×C₄×D₅	C₂²×C₅	semidirect
118. C₂×C₄×D₅	C₂²×C₅	semidirect
119. C₂×C₄×D₅	C₂²×C₅	semidirect
120. C₂×Dic₁₀	C₂²×C₅	semidirect
123. C₂×C₅²	C₂×#41	semidirect
126. C₅×D₅	C₂×#41	direct (N × H)
140. C₅×Q₈	C₂²×D₅	semidirect
141. C₅×Q₈	C₂³×C₅	semidirect
145. C₅×D₄	C₂²×D₅	semidirect
146. C₅×D₄	C₂³×C₅	semidirect
159. C₂×C₄×C₅	C₂²×D₅	semidirect
162. C₂×C₄×C₅	C₂³×C₅	semidirect
163. C₂²⋊D₅	C₂³×C₅	semidirect
166. C₂×Dic₅	C₂³×C₅	semidirect
167. D₂₀	C₂³×C₅	semidirect
170. C₄×D₅	C₂³×C₅	semidirect
171. C₄×D₅	C₂³×C₅	semidirect
172. Dic₁₀	C₂³×C₅	semidirect
177. C₂×#41	C₅×D₅	direct (N × H)
181. C₅²	C₂²×#41	semidirect
198. C₂×D₅	C₅×#41	direct (N × H)
215. #41	C₂×C₅×D₅	direct (N × H)
218. C₂×Q₈	C₂×C₅×D₅	semidirect
222. C₂×D₄	C₂×C₅×D₅	semidirect
229. C₂²×C₄	C₂×C₅×D₅	semidirect
237. C₂×C₅	D₅×#41	direct (N × H)
238. C₂×C₅	C₂×C₅×#41	semidirect
242. D₅	C₂×C₅×#41	direct (N × H)
249. Q₈	C₂²×C₅×D₅	semidirect
252. D₄	C₂²×C₅×D₅	semidirect
262. C₂×C₄	C₂²×C₅×D₅	semidirect
264. C₅	C₂×D₅×#41	direct (N × H)
265. C₅	C₂²×C₅×#41	semidirect
281. C₂	C₅×D₅×#41	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×C₅²×#41	2
C₅×D₅×#41	2
C₂×C₅×#713	2
C₂×C₅×Q₈×D₅	2
C₂×C₅×#711	2
C₂×C₅×D₄×D₅	2
C₂×C₅×#709	2
C₂²×C₄×C₅×D₅	2
C₂²×C₅×#41	5
C₂×D₅×#41	5

Subgroups — C2×C5×D5×#41 #13107865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₅×#41 #13107865