Subgroups — C₂×C₅×#5062 #14425074

Order 1920.

1456 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1007	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#932	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#836	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5062	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#805	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#454	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₅×#1007	—	2	2	no	—
11	C₅×#1007	—	2	4	no	—
12	C₅×#1007	C₂²	1	4	yes	complemented
13	C₂×C₅×#239	—	2	2	no	—
14	C₂×C₅×D₃×Q₈	—	2	2	no	—
15	C₂×C₅×#235	—	2	2	no	—
16	C₂×C₅×#235	C₂²	1	2	yes	—
17	C₃×C₅×#124	—	2	2	no	—
18	C₃×C₅×#124	C₂²	1	4	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#214	—	2	2	no	—
22	C₅×#932	—	2	4	no	—
23	C₅×#932	C₂²	1	8	yes	complemented
24	C₂×C₅×#213	—	2	2	no	—
25	C₂×C₅×#208	C₂²	1	2	yes	—
26	C₅×#836	C₂²	1	4	yes	complemented
27	C₅×#805	C₂²	1	8	yes	complemented
28	C₂×#5062	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
30	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
31	C₂×C₅×#124	D₃	1	1	yes	characteristic, complemented
32	C₅×#454	—	3	8	no	—
33	C₂×C₅×#104	—	3	2	no	—
34	C₂×C₅×#101	—	3	1	no	—
35	C₂⁴×C₃×C₅	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
39	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×#67	—	2	2	no	—
48	C₅×#239	—	2	8	no	—
49	C₅×#239	—	2	8	no	—
50	C₅×D₃×Q₈	—	2	8	no	—
51	C₅×D₃×Q₈	—	2	8	no	—
52	C₅×#235	—	2	8	no	—
53	C₅×#235	—	2	8	no	—
54	C₅×#235	—	2	2	no	—
55	C₅×#235	—	2	2	no	—
56	C₅×#235	D₄	1	4	yes	—
57	C₅×#235	C₂³	1	4	yes	—
58	C₂×C₅×D₁₂	—	2	2	no	—
59	C₂×C₅×D₁₂	D₄	1	2	yes	—
60	C₂×C₄×C₅×D₃	—	2	4	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₅×Dic₆	—	2	2	no	—
63	C₂×C₅×Dic₆	D₄	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
65	C₃×C₄²×C₅	—	2	1	no	—
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₅×#214	—	2	8	no	—
68	C₅×#213	—	2	8	no	—
69	C₅×#208	—	2	2	no	—
70	C₅×#208	C₂³	1	4	yes	—
71	C₂×C₅×C₃⋊C₈	—	2	2	no	—
72	C₂×#1007	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#932	C₂×C₅	1	2	yes	complemented
75	C₂×#836	C₂×C₅	1	1	yes	characteristic, complemented
76	#5062	C₂×C₅	1	8	yes	direct product factor
77	C₂×#805	C₂×C₅	1	2	yes	complemented
78	C₅×2₋¹⁺⁴	—	3	4	no	—
79	C₅×2₋¹⁺⁴	—	6	4	no	—
80	C₅×2₋¹⁺⁴	—	6	2	no	—
81	C₂×C₅×#41	—	3	2	no	—
82	C₂×C₅×#41	—	6	2	no	—
83	C₂×C₅×#41	—	6	2	no	—
84	C₂²×C₅×Q₈	—	6	2	no	—
85	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
87	C₅×AGL(1,ℤ/8)	—	3	8	no	—
88	C₅×AGL(1,ℤ/8)	—	6	4	no	—
89	C₂×C₅×SD₁₆	—	6	2	no	—
90	C₂×C₅×D₈	—	6	2	no	—
91	C₂×C₅×M₁₆	—	3	2	no	—
92	C₅×#124	—	2	2	no	—
93	C₅×#124	C₂×D₃	1	4	yes	complemented
94	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
96	C₅×#104	—	3	8	no	—
97	C₅×#101	—	3	4	no	—
98	C₂×#454	—	3	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	4	4	no	—
101	C₂³×C₃×C₅	—	4	1	no	—
102	C₂³×C₃×C₅	—	4	1	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	4	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×D₄	—	2	4	no	—
108	C₃×C₅×D₄	—	4	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×#67	—	2	4	no	—
119	C₅×#67	—	2	4	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₅×D₁₂	—	2	8	no	—
122	C₅×D₁₂	—	2	2	no	—
123	C₅×D₁₂	C₂×D₄	1	4	yes	—
124	C₄×C₅×D₃	—	2	16	no	—
125	C₄×C₅×D₃	—	2	4	no	—
126	C₄×C₅×D₃	—	2	4	no	—
127	C₅×Dic₆	—	2	8	no	—
128	C₅×Dic₆	—	2	2	no	—
129	C₅×Dic₆	C₂×D₄	1	4	yes	—
130	C₅×C₃⋊C₈	—	2	4	no	—
131	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
133	#1007	—	2	2	no	—
134	#1007	—	2	4	no	—
135	#1007	C₂²×C₅	1	4	yes	complemented
136	C₂×#239	—	2	2	no	—
137	C₂×D₃×Q₈	—	2	2	no	—
138	C₂×#235	—	2	2	no	—
139	C₂×#235	C₂²×C₅	1	2	yes	—
140	C₃×#124	—	2	2	no	—
141	C₃×#124	C₂²×C₅	1	4	yes	complemented
142	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×#214	—	2	2	no	—
145	#932	—	2	4	no	—
146	#932	C₂²×C₅	1	8	yes	complemented
147	C₂×#213	—	2	2	no	—
148	C₂×#208	C₂²×C₅	1	2	yes	—
149	#836	C₂²×C₅	1	4	yes	complemented
150	#805	C₂²×C₅	1	8	yes	complemented
151	C₂⁴×C₅	—	2	1	no	—
152	C₅×#41	—	3	4	no	—
153	C₅×#41	—	3	4	no	—
154	C₅×#41	—	6	8	no	—
155	C₅×#41	—	6	8	no	—
156	C₅×#41	—	6	8	no	—
157	C₅×#41	—	6	2	no	—
158	C₅×#41	—	6	2	no	—
159	C₅×#41	—	6	8	no	—
160	C₂×C₅×Q₈	—	2	2	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	3	2	no	—
163	C₂×C₅×Q₈	—	6	2	no	—
164	C₂×C₅×Q₈	—	6	8	no	—
165	C₂×C₅×Q₈	—	6	8	no	—
166	C₂×C₅×Q₈	#67	1	2	yes	—
167	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	2	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	3	2	no	—
172	C₂×C₅×D₄	—	6	2	no	—
173	C₂×C₅×D₄	—	6	2	no	—
174	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	6	4	no	—
177	C₂²×C₄×C₅	—	6	2	no	—
178	C₂²×C₄×C₅	#67	1	2	yes	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₅×SD₁₆	—	6	8	no	—
181	C₅×D₈	—	6	8	no	—
182	C₅×M₁₆	—	3	4	no	—
183	C₅×M₁₆	—	6	2	no	—
184	C₂×C₅×C₈	—	6	2	no	—
185	C₅×C₂²⋊C₄	—	2	8	no	—
186	C₄²×C₅	—	2	1	no	—
187	C₄²×C₅	C₂²×D₃	1	2	yes	—
188	C₂×2₋¹⁺⁴	—	3	1	no	—
189	C₂×AGL(1,ℤ/8)	—	3	2	no	—
190	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
191	#454	—	3	8	no	—
192	C₂×#104	—	3	2	no	—
193	C₂×#101	—	3	1	no	—
194	C₂²×C₃×C₅	—	2	2	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	8	2	no	—
198	C₂²×C₃×C₅	—	8	2	no	—
199	C₂²×C₃×C₅	#120	1	1	yes	characteristic
200	C₂²×C₃×C₅	#120	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₅×D₃	—	2	4	no	—
203	C₂×C₅×D₃	—	4	4	no	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	—	4	2	no	—
206	C₃×C₄×C₅	#120	1	2	yes	—
207	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
208	C₅×Dic₃	—	2	4	no	—
209	C₂⁴×C₃	—	2	1	no	—
210	C₂×C₃×Q₈	—	2	2	no	—
211	C₂×C₃×Q₈	—	2	2	no	—
212	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
213	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
214	C₂×C₃×D₄	—	2	2	no	—
215	C₂×C₃×D₄	—	2	2	no	—
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
218	C₂²×C₃×C₄	—	2	1	no	—
219	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂×#67	—	2	2	no	—
222	#239	—	2	8	no	—
223	#239	—	2	8	no	—
224	D₃×Q₈	—	2	8	no	—
225	D₃×Q₈	—	2	8	no	—
226	#235	—	2	8	no	—
227	#235	—	2	8	no	—
228	#235	—	2	2	no	—
229	#235	—	2	2	no	—
230	#235	C₅×D₄	1	4	yes	—
231	#235	C₂³×C₅	1	4	yes	—
232	C₂×D₁₂	—	2	2	no	—
233	C₂×D₁₂	C₅×D₄	1	2	yes	—
234	C₂×C₄×D₃	—	2	4	no	—
235	C₂×C₄×D₃	—	2	2	no	—
236	C₂×Dic₆	—	2	2	no	—
237	C₂×Dic₆	C₅×D₄	1	2	yes	—
238	C₃×C₂²⋊C₄	—	2	8	no	—
239	C₃×C₄²	—	2	1	no	—
240	C₃×C₄²	C₂³×C₅	1	2	yes	—
241	#214	—	2	8	no	—
242	#213	—	2	8	no	—
243	#208	—	2	2	no	—
244	#208	C₂³×C₅	1	4	yes	—
245	C₂×C₃⋊C₈	—	2	2	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	4	4	no	—
248	C₂³×C₅	—	4	1	no	—
249	C₂³×C₅	—	4	1	no	—
250	C₂³×C₅	—	6	2	no	—
251	C₂³×C₅	C₂×#67	1	1	yes	characteristic
252	C₅×Q₈	—	2	4	no	—
253	C₅×Q₈	—	2	4	no	—
254	C₅×Q₈	—	3	4	no	—
255	C₅×Q₈	—	6	8	no	—
256	C₅×Q₈	—	6	2	no	—
257	C₅×D₄	—	2	4	no	—
258	C₅×D₄	—	3	4	no	—
259	C₅×D₄	—	4	2	no	—
260	C₅×D₄	—	6	8	no	—
261	C₅×D₄	—	6	4	no	—
262	C₅×D₄	—	6	4	no	—
263	C₅×D₄	—	6	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	6	16	no	—
269	C₂×C₄×C₅	—	6	2	no	—
270	C₂×C₄×C₅	—	6	4	no	—
271	C₂×C₄×C₅	—	6	4	no	—
272	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
273	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
274	C₂×C₄×C₅	C₂×#67	1	4	yes	—
275	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
277	C₅×C₈	—	6	4	no	—
278	2₋¹⁺⁴	—	3	4	no	—
279	2₋¹⁺⁴	—	6	4	no	—
280	2₋¹⁺⁴	—	6	2	no	—
281	C₂×#41	—	3	2	no	—
282	C₂×#41	—	6	2	no	—
283	C₂×#41	—	6	2	no	—
284	C₂²×Q₈	—	6	2	no	—
285	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
286	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
287	AGL(1,ℤ/8)	—	3	8	no	—
288	AGL(1,ℤ/8)	—	6	4	no	—
289	C₂×SD₁₆	—	6	2	no	—
290	C₂×D₈	—	6	2	no	—
291	C₂×M₁₆	—	3	2	no	—
292	#124	—	2	2	no	—
293	#124	C₂×C₅×D₃	1	4	yes	complemented
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
296	#104	—	3	8	no	—
297	#101	—	3	4	no	—
298	C₂×C₃×C₅	—	2	1	no	—
299	C₂×C₃×C₅	—	2	1	no	—
300	C₂×C₃×C₅	—	8	2	no	—
301	C₂×C₃×C₅	#454	1	2	yes	complemented
302	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
303	C₅×D₃	—	4	4	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	4	4	no	—
306	C₂³×C₃	—	4	1	no	—
307	C₂³×C₃	—	4	1	no	—
308	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×D₃	—	2	2	no	—
310	C₃×Q₈	—	2	4	no	—
311	C₃×Q₈	—	2	4	no	—
312	C₃×D₄	—	2	4	no	—
313	C₃×D₄	—	4	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	4	2	no	—
318	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
319	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
323	#67	—	2	4	no	—
324	#67	—	2	4	no	—
325	C₂×Dic₃	—	2	2	no	—
326	D₁₂	—	2	8	no	—
327	D₁₂	—	2	2	no	—
328	D₁₂	C₂×C₅×D₄	1	4	yes	—
329	C₄×D₃	—	2	16	no	—
330	C₄×D₃	—	2	4	no	—
331	C₄×D₃	—	2	4	no	—
332	Dic₆	—	2	8	no	—
333	Dic₆	—	2	2	no	—
334	Dic₆	C₂×C₅×D₄	1	4	yes	—
335	C₃⋊C₈	—	2	4	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	4	4	no	—
338	C₂²×C₅	—	4	2	no	—
339	C₂²×C₅	—	6	4	no	—
340	C₂²×C₅	—	8	2	no	—
341	C₂²×C₅	—	8	2	no	—
342	C₂²×C₅	—	12	4	no	—
343	C₂²×C₅	#937	1	1	yes	characteristic
344	C₂²×C₅	#937	1	1	yes	characteristic
345	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	—	6	4	no	—
349	C₄×C₅	#937	1	2	yes	—
350	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
351	C₂⁴	—	2	1	no	—
352	#41	—	3	4	no	—
353	#41	—	3	4	no	—
354	#41	—	6	8	no	—
355	#41	—	6	8	no	—
356	#41	—	6	8	no	—
357	#41	—	6	2	no	—
358	#41	—	6	2	no	—
359	#41	—	6	8	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	3	2	no	—
363	C₂×Q₈	—	6	2	no	—
364	C₂×Q₈	—	6	8	no	—
365	C₂×Q₈	—	6	8	no	—
366	C₂×Q₈	C₅×#67	1	2	yes	—
367	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	3	2	no	—
372	C₂×D₄	—	6	2	no	—
373	C₂×D₄	—	6	2	no	—
374	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	6	4	no	—
377	C₂²×C₄	—	6	2	no	—
378	C₂²×C₄	C₅×#67	1	2	yes	—
379	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
380	SD₁₆	—	6	8	no	—
381	D₈	—	6	8	no	—
382	M₁₆	—	3	4	no	—
383	M₁₆	—	6	2	no	—
384	C₂×C₈	—	6	2	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₄²	—	2	1	no	—
387	C₄²	C₂²×C₅×D₃	1	2	yes	—
388	C₃×C₅	C₂×#454	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	4	4	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	8	2	no	—
393	C₂²×C₃	—	8	2	no	—
394	C₂²×C₃	C₅×#120	1	1	yes	characteristic
395	C₂²×C₃	C₅×#120	1	1	yes	characteristic
396	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
397	C₂×D₃	—	2	4	no	—
398	C₂×D₃	—	4	4	no	—
399	C₃×C₄	—	2	4	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	C₅×#120	1	2	yes	—
402	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
403	Dic₃	—	2	4	no	—
404	C₂×C₅	—	2	1	no	—
405	C₂×C₅	—	2	1	no	—
406	C₂×C₅	—	8	2	no	—
407	C₂×C₅	—	12	4	no	—
408	C₂×C₅	#5062	1	2	yes	direct product factor
409	C₂×C₅	C₂×#937	1	1	yes	characteristic
410	C₂³	—	2	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	6	2	no	—
415	C₂³	C₂×C₅×#67	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	3	4	no	—
419	Q₈	—	6	8	no	—
420	Q₈	—	6	2	no	—
421	D₄	—	2	4	no	—
422	D₄	—	3	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	6	8	no	—
425	D₄	—	6	4	no	—
426	D₄	—	6	4	no	—
427	D₄	—	6	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	6	16	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	4	no	—
435	C₂×C₄	—	6	4	no	—
436	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
437	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
438	C₂×C₄	C₂×C₅×#67	1	4	yes	—
439	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
440	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
441	C₈	—	6	4	no	—
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	8	2	no	—
445	C₂×C₃	C₅×#454	1	2	yes	complemented
446	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
447	D₃	—	4	4	no	—
448	C₅	C₂×#5062	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	6	4	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	12	4	no	—
456	C₂²	C₅×#937	1	1	yes	characteristic
457	C₂²	C₅×#937	1	1	yes	characteristic
458	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	6	4	no	—
462	C₄	C₅×#937	1	2	yes	—
463	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
464	C₃	C₂×C₅×#454	1	1	yes	characteristic, complemented, Sylow
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	8	2	no	—
468	C₂	—	12	4	no	—
469	C₂	C₅×#5062	1	2	yes	direct product factor
470	C₂	C₂×C₅×#937	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#454
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1007	C₂	semidirect
2. C₂×C₃×C₅×#124	C₂	semidirect
3. C₂×C₅×#932	C₂	semidirect
4. C₂×C₅×#836	C₂	semidirect
5. C₅×#5062	C₂	direct (N × H)
6. C₂×C₅×#805	C₂	semidirect
12. C₅×#1007	C₂²	semidirect
18. C₃×C₅×#124	C₂²	semidirect
23. C₅×#932	C₂²	semidirect
26. C₅×#836	C₂²	semidirect
27. C₅×#805	C₂²	semidirect
28. C₂×#5062	C₅	direct (N × H)
31. C₂×C₅×#124	D₃	semidirect
72. C₂×#1007	C₂×C₅	semidirect
73. C₂×C₃×#124	C₂×C₅	semidirect
74. C₂×#932	C₂×C₅	semidirect
75. C₂×#836	C₂×C₅	semidirect
76. #5062	C₂×C₅	direct (N × H)
77. C₂×#805	C₂×C₅	semidirect
93. C₅×#124	C₂×D₃	semidirect
135. #1007	C₂²×C₅	semidirect
141. C₃×#124	C₂²×C₅	semidirect
146. #932	C₂²×C₅	semidirect
149. #836	C₂²×C₅	semidirect
150. #805	C₂²×C₅	semidirect
190. C₂×#124	C₅×D₃	semidirect
293. #124	C₂×C₅×D₃	semidirect
301. C₂×C₃×C₅	#454	semidirect
388. C₃×C₅	C₂×#454	semidirect
408. C₂×C₅	#5062	direct (N × H)
445. C₂×C₃	C₅×#454	semidirect
448. C₅	C₂×#5062	direct (N × H)
464. C₃	C₂×C₅×#454	semidirect
469. C₂	C₅×#5062	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×#1007	2
C₂×C₃×C₅×#124	2
C₂×C₅×#932	2
C₂×C₅×#836	2
C₅×#5062	2
C₂×C₅×#805	2
C₂×C₅×#454	3
C₂×#5062	5

Subgroups — C2×C5×#5062 #14425074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5062 #14425074