Subgroups — C₂×C₅×#5771 #14510124

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1010	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#951	C₂	1	2	yes	maximal, complemented
4	C₅×#5771	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#915	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#912	C₂	1	2	yes	maximal, complemented
8	C₂²×C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#578	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₅×#1010	—	2	8	no	—
13	C₅×#1010	C₂²	1	16	yes	complemented
14	C₂×C₅×D₃×Q₈	C₂²	1	4	yes	—
15	C₂×C₅×#237	—	2	4	no	—
16	C₂×C₅×#237	C₂²	1	4	yes	—
17	C₂×C₅×#235	—	2	2	no	—
18	C₂×C₅×#235	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₆	—	2	2	no	—
20	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
21	C₃×C₅×#135	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×#951	C₂²	1	16	yes	complemented
27	C₂×C₅×#216	C₂²	1	4	yes	—
28	C₂×C₅×#214	C₂²	1	4	yes	—
29	C₂×C₅×#208	C₂²	1	1	yes	characteristic
30	C₅×D₃×Q₁₆	C₂²	1	16	yes	complemented
31	C₅×#915	C₂²	1	32	yes	complemented
32	C₅×#912	C₂²	1	16	yes	complemented
33	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
34	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
35	C₂×C₅×Dic₁₂	C₂²	1	8	yes	complemented
36	C₅×#901	C₂²	1	8	yes	complemented
37	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
38	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
39	C₂×#5771	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×2₋¹⁺⁴	—	3	2	no	—
41	C₅×#578	—	3	16	no	—
42	C₂×C₅×#137	—	3	2	no	—
43	C₂×C₅×#137	—	3	4	no	—
44	C₂×C₅×#135	—	3	2	no	—
45	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
46	C₂²×C₅×Q₁₆	—	3	2	no	—
47	C₂²×C₅×Q₁₆	—	3	1	no	—
48	C₂×C₅×#131	—	3	1	no	—
49	C₃×C₅×#41	—	2	4	no	—
50	C₃×C₅×#41	C₂³	1	8	yes	—
51	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×#67	—	2	4	no	—
57	C₂×C₅×#67	D₄	1	2	yes	—
58	C₂²×C₅×Dic₃	—	2	2	no	—
59	C₂²×C₅×Dic₃	—	2	4	no	—
60	C₅×D₃×Q₈	—	2	8	no	—
61	C₅×D₃×Q₈	C₂³	1	16	yes	—
62	C₅×#237	—	2	32	no	—
63	C₅×#237	—	2	8	no	—
64	C₅×#237	C₂³	1	16	yes	—
65	C₅×#235	—	2	16	no	—
66	C₅×#235	D₄	1	4	yes	—
67	C₅×#235	C₂³	1	4	yes	—
68	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
69	C₂×C₄×C₅×D₃	—	2	4	no	—
70	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
71	C₂×C₅×Dic₆	—	2	2	no	—
72	C₂×C₅×Dic₆	—	2	4	no	—
73	C₂×C₅×Dic₆	—	2	4	no	—
74	C₂×C₅×Dic₆	—	2	16	no	—
75	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
76	C₂×C₅×Dic₆	C₂³	1	4	yes	—
77	C₂×C₅×Dic₆	C₂³	1	8	yes	—
78	C₃×C₅×Q₁₆	C₂³	1	4	yes	—
79	C₃×C₅×SD₁₆	C₂³	1	8	yes	—
80	C₃×C₅×D₈	C₂³	1	4	yes	—
81	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
84	C₅×#216	C₂³	1	16	yes	—
85	C₅×#214	C₂³	1	16	yes	—
86	C₅×#208	C₂³	1	4	yes	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₅×Dic₁₂	C₂³	1	8	yes	—
89	C₅×Dic₁₂	C₂³	1	8	yes	—
90	C₅×ΓL(1,𝔽₂₅)	C₂³	1	8	yes	—
91	C₅×D₃×C₈	C₂³	1	8	yes	—
92	C₂×#1010	C₂×C₅	1	2	yes	complemented
93	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#951	C₂×C₅	1	2	yes	complemented
95	#5771	C₂×C₅	1	16	yes	direct product factor
96	C₂×D₃×Q₁₆	C₂×C₅	1	2	yes	complemented
97	C₂×#915	C₂×C₅	1	4	yes	complemented
98	C₂×#912	C₂×C₅	1	2	yes	complemented
99	C₂²×Dic₁₂	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×#901	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×2₋¹⁺⁴	—	3	16	no	—
102	C₅×2₋¹⁺⁴	—	6	8	no	—
103	C₂×C₅×#41	—	3	1	no	—
104	C₂×C₅×#41	—	3	4	no	—
105	C₂×C₅×#41	—	6	2	no	—
106	C₂×C₅×#41	—	6	4	no	—
107	C₂×C₅×#41	C₂×D₃	1	2	yes	—
108	C₂²×C₅×Q₈	—	3	4	no	—
109	C₂²×C₅×Q₈	—	3	2	no	—
110	C₂²×C₅×Q₈	—	6	2	no	—
111	C₅×#137	—	3	16	no	—
112	C₅×#137	—	3	32	no	—
113	C₅×#135	—	3	16	no	—
114	C₅×#135	C₂×D₃	1	8	yes	complemented
115	C₂×C₅×Q₁₆	—	3	4	no	—
116	C₂×C₅×Q₁₆	—	3	16	no	—
117	C₂×C₅×Q₁₆	—	3	2	no	—
118	C₂×C₅×Q₁₆	—	3	2	no	—
119	C₂×C₅×Q₁₆	—	3	8	no	—
120	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
121	C₂×C₅×SD₁₆	—	3	4	no	—
122	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
123	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
124	C₅×#131	—	3	8	no	—
125	C₂×C₅×M₁₆	—	3	1	no	—
126	C₂×C₅×M₁₆	—	3	2	no	—
127	C₂²×C₅×C₈	—	3	2	no	—
128	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
129	C₂×#578	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
135	C₃×C₅×D₄	—	2	8	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	C₂⁴	1	4	yes	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	8	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
144	C₅×#67	—	2	16	no	—
145	C₅×#67	C₂×D₄	1	8	yes	—
146	C₂×C₅×Dic₃	—	2	4	no	—
147	C₂×C₅×Dic₃	—	2	8	no	—
148	C₂×C₅×Dic₃	—	2	16	no	—
149	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
150	C₅×D₁₂	C₂×D₄	1	4	yes	—
151	C₄×C₅×D₃	—	2	16	no	—
152	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
153	C₄×C₅×D₃	C₂⁴	1	4	yes	—
154	C₅×Dic₆	—	2	8	no	—
155	C₅×Dic₆	—	2	4	no	—
156	C₅×Dic₆	—	2	16	no	—
157	C₅×Dic₆	C₂×D₄	1	4	yes	—
158	C₅×Dic₆	C₂⁴	1	8	yes	—
159	C₃×C₅×C₈	C₂⁴	1	2	yes	—
160	C₃×C₅×C₈	C₂⁴	1	2	yes	—
161	C₅×C₃⋊C₈	C₂⁴	1	4	yes	—
162	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
163	#1010	—	2	8	no	—
164	#1010	C₂²×C₅	1	16	yes	complemented
165	C₂×D₃×Q₈	C₂²×C₅	1	4	yes	—
166	C₂×#237	—	2	4	no	—
167	C₂×#237	C₂²×C₅	1	4	yes	—
168	C₂×#235	—	2	2	no	—
169	C₂×#235	C₂²×C₅	1	1	yes	characteristic
170	C₂²×Dic₆	—	2	2	no	—
171	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
172	C₃×#135	C₂²×C₅	1	8	yes	complemented
173	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
175	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
177	#951	C₂²×C₅	1	16	yes	complemented
178	C₂×#216	C₂²×C₅	1	4	yes	—
179	C₂×#214	C₂²×C₅	1	4	yes	—
180	C₂×#208	C₂²×C₅	1	1	yes	characteristic
181	D₃×Q₁₆	C₂²×C₅	1	16	yes	complemented
182	#915	C₂²×C₅	1	32	yes	complemented
183	#912	C₂²×C₅	1	16	yes	complemented
184	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
185	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
186	C₂×Dic₁₂	C₂²×C₅	1	8	yes	complemented
187	#901	C₂²×C₅	1	8	yes	complemented
188	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
189	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
190	C₅×#41	—	2	4	no	—
191	C₅×#41	—	3	4	no	—
192	C₅×#41	—	3	4	no	—
193	C₅×#41	—	3	16	no	—
194	C₅×#41	—	6	16	no	—
195	C₅×#41	—	6	8	no	—
196	C₅×#41	—	6	32	no	—
197	C₅×#41	C₂²×D₃	1	8	yes	—
198	C₂×C₅×Q₈	—	3	1	no	—
199	C₂×C₅×Q₈	—	3	16	no	—
200	C₂×C₅×Q₈	—	3	4	no	—
201	C₂×C₅×Q₈	—	3	8	no	—
202	C₂×C₅×Q₈	—	6	4	no	—
203	C₂×C₅×Q₈	—	6	16	no	—
204	C₂×C₅×Q₈	—	6	8	no	—
205	C₂×C₅×Q₈	—	6	2	no	—
206	C₂×C₅×Q₈	—	6	4	no	—
207	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
208	C₂×C₅×D₄	—	2	2	no	—
209	C₂×C₅×D₄	—	3	2	no	—
210	C₂×C₅×D₄	—	3	1	no	—
211	C₂×C₅×D₄	—	6	4	no	—
212	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
213	C₂²×C₄×C₅	—	2	2	no	—
214	C₂²×C₄×C₅	—	3	2	no	—
215	C₂²×C₄×C₅	—	6	4	no	—
216	C₂²×C₄×C₅	—	6	4	no	—
217	C₂²×C₄×C₅	—	6	2	no	—
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₅×Q₁₆	—	3	16	no	—
220	C₅×Q₁₆	—	3	8	no	—
221	C₅×Q₁₆	—	3	8	no	—
222	C₅×Q₁₆	C₂²×D₃	1	4	yes	—
223	C₅×SD₁₆	—	3	16	no	—
224	C₅×SD₁₆	C₂²×D₃	1	8	yes	—
225	C₅×D₈	C₂²×D₃	1	4	yes	—
226	C₅×M₁₆	—	3	4	no	—
227	C₅×M₁₆	—	3	8	no	—
228	C₂×C₅×C₈	—	3	2	no	—
229	C₂×C₅×C₈	—	3	8	no	—
230	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
233	C₂×2₋¹⁺⁴	—	3	2	no	—
234	#578	—	3	16	no	—
235	C₂×#137	—	3	2	no	—
236	C₂×#137	—	3	4	no	—
237	C₂×#135	—	3	2	no	—
238	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
239	C₂²×Q₁₆	—	3	2	no	—
240	C₂²×Q₁₆	—	3	1	no	—
241	C₂×#131	—	3	1	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	4	4	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
246	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₅×D₃	—	2	4	no	—
248	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
249	C₃×C₄×C₅	—	2	4	no	—
250	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
251	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
253	C₅×Dic₃	—	2	8	no	—
254	C₅×Dic₃	C₂²×D₄	1	4	yes	—
255	C₃×#41	—	2	4	no	—
256	C₃×#41	C₂³×C₅	1	8	yes	—
257	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
258	C₂×C₃×D₄	—	2	2	no	—
259	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂×#67	—	2	4	no	—
263	C₂×#67	C₅×D₄	1	2	yes	—
264	C₂²×Dic₃	—	2	2	no	—
265	C₂²×Dic₃	—	2	4	no	—
266	D₃×Q₈	—	2	8	no	—
267	D₃×Q₈	C₂³×C₅	1	16	yes	—
268	#237	—	2	32	no	—
269	#237	—	2	8	no	—
270	#237	C₂³×C₅	1	16	yes	—
271	#235	—	2	16	no	—
272	#235	C₅×D₄	1	4	yes	—
273	#235	C₂³×C₅	1	4	yes	—
274	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
275	C₂×C₄×D₃	—	2	4	no	—
276	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
277	C₂×Dic₆	—	2	2	no	—
278	C₂×Dic₆	—	2	4	no	—
279	C₂×Dic₆	—	2	4	no	—
280	C₂×Dic₆	—	2	16	no	—
281	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
282	C₂×Dic₆	C₂³×C₅	1	4	yes	—
283	C₂×Dic₆	C₂³×C₅	1	8	yes	—
284	C₃×Q₁₆	C₂³×C₅	1	4	yes	—
285	C₃×SD₁₆	C₂³×C₅	1	8	yes	—
286	C₃×D₈	C₂³×C₅	1	4	yes	—
287	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
290	#216	C₂³×C₅	1	16	yes	—
291	#214	C₂³×C₅	1	16	yes	—
292	#208	C₂³×C₅	1	4	yes	—
293	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
294	Dic₁₂	C₂³×C₅	1	8	yes	—
295	Dic₁₂	C₂³×C₅	1	8	yes	—
296	ΓL(1,𝔽₂₅)	C₂³×C₅	1	8	yes	—
297	D₃×C₈	C₂³×C₅	1	8	yes	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	3	2	no	—
300	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
301	C₅×Q₈	—	2	2	no	—
302	C₅×Q₈	—	3	4	no	—
303	C₅×Q₈	—	3	8	no	—
304	C₅×Q₈	—	6	16	no	—
305	C₅×Q₈	—	6	8	no	—
306	C₅×Q₈	—	6	4	no	—
307	C₅×Q₈	C₂³×D₃	1	4	yes	—
308	C₅×D₄	—	2	8	no	—
309	C₅×D₄	—	2	2	no	—
310	C₅×D₄	—	3	8	no	—
311	C₅×D₄	—	3	4	no	—
312	C₅×D₄	—	6	16	no	—
313	C₅×D₄	C₂³×D₃	1	4	yes	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	8	no	—
316	C₂×C₄×C₅	—	3	2	no	—
317	C₂×C₄×C₅	—	3	4	no	—
318	C₂×C₄×C₅	—	3	4	no	—
319	C₂×C₄×C₅	—	6	16	no	—
320	C₂×C₄×C₅	—	6	16	no	—
321	C₂×C₄×C₅	—	6	8	no	—
322	C₂×C₄×C₅	—	6	4	no	—
323	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
324	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
326	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
327	C₅×C₈	—	3	4	no	—
328	C₅×C₈	C₂³×D₃	1	2	yes	—
329	C₅×C₈	C₂³×D₃	1	2	yes	—
330	2₋¹⁺⁴	—	3	16	no	—
331	2₋¹⁺⁴	—	6	8	no	—
332	C₂×#41	—	3	1	no	—
333	C₂×#41	—	3	4	no	—
334	C₂×#41	—	6	2	no	—
335	C₂×#41	—	6	4	no	—
336	C₂×#41	C₂×C₅×D₃	1	2	yes	—
337	C₂²×Q₈	—	3	4	no	—
338	C₂²×Q₈	—	3	2	no	—
339	C₂²×Q₈	—	6	2	no	—
340	#137	—	3	16	no	—
341	#137	—	3	32	no	—
342	#135	—	3	16	no	—
343	#135	C₂×C₅×D₃	1	8	yes	complemented
344	C₂×Q₁₆	—	3	4	no	—
345	C₂×Q₁₆	—	3	16	no	—
346	C₂×Q₁₆	—	3	2	no	—
347	C₂×Q₁₆	—	3	2	no	—
348	C₂×Q₁₆	—	3	8	no	—
349	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
350	C₂×SD₁₆	—	3	4	no	—
351	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
352	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
353	#131	—	3	8	no	—
354	C₂×M₁₆	—	3	1	no	—
355	C₂×M₁₆	—	3	2	no	—
356	C₂²×C₈	—	3	2	no	—
357	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
358	C₂×C₃×C₅	—	2	2	no	—
359	C₂×C₃×C₅	—	4	4	no	—
360	C₂×C₃×C₅	#578	1	2	yes	complemented
361	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
362	C₅×D₃	—	2	4	no	—
363	C₂³×C₃	—	2	2	no	—
364	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	C₂⁴×C₅	1	4	yes	—
368	C₃×D₄	—	2	8	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	C₂⁴×C₅	1	4	yes	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	8	no	—
373	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
377	#67	—	2	16	no	—
378	#67	C₂×C₅×D₄	1	8	yes	—
379	C₂×Dic₃	—	2	4	no	—
380	C₂×Dic₃	—	2	8	no	—
381	C₂×Dic₃	—	2	16	no	—
382	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
383	D₁₂	C₂×C₅×D₄	1	4	yes	—
384	C₄×D₃	—	2	16	no	—
385	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
386	C₄×D₃	C₂⁴×C₅	1	4	yes	—
387	Dic₆	—	2	8	no	—
388	Dic₆	—	2	4	no	—
389	Dic₆	—	2	16	no	—
390	Dic₆	C₂×C₅×D₄	1	4	yes	—
391	Dic₆	C₂⁴×C₅	1	8	yes	—
392	C₃×C₈	C₂⁴×C₅	1	2	yes	—
393	C₃×C₈	C₂⁴×C₅	1	2	yes	—
394	C₃⋊C₈	C₂⁴×C₅	1	4	yes	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	2	4	no	—
397	C₂²×C₅	—	3	4	no	—
398	C₂²×C₅	—	4	4	no	—
399	C₂²×C₅	—	6	4	no	—
400	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
401	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
402	C₄×C₅	—	2	4	no	—
403	C₄×C₅	—	3	4	no	—
404	C₄×C₅	—	6	8	no	—
405	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
406	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
408	#41	—	2	4	no	—
409	#41	—	3	4	no	—
410	#41	—	3	4	no	—
411	#41	—	3	16	no	—
412	#41	—	6	16	no	—
413	#41	—	6	8	no	—
414	#41	—	6	32	no	—
415	#41	C₂²×C₅×D₃	1	8	yes	—
416	C₂×Q₈	—	3	1	no	—
417	C₂×Q₈	—	3	16	no	—
418	C₂×Q₈	—	3	4	no	—
419	C₂×Q₈	—	3	8	no	—
420	C₂×Q₈	—	6	4	no	—
421	C₂×Q₈	—	6	16	no	—
422	C₂×Q₈	—	6	8	no	—
423	C₂×Q₈	—	6	2	no	—
424	C₂×Q₈	—	6	4	no	—
425	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	6	4	no	—
430	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	6	4	no	—
434	C₂²×C₄	—	6	4	no	—
435	C₂²×C₄	—	6	2	no	—
436	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
437	Q₁₆	—	3	16	no	—
438	Q₁₆	—	3	8	no	—
439	Q₁₆	—	3	8	no	—
440	Q₁₆	C₂²×C₅×D₃	1	4	yes	—
441	SD₁₆	—	3	16	no	—
442	SD₁₆	C₂²×C₅×D₃	1	8	yes	—
443	D₈	C₂²×C₅×D₃	1	4	yes	—
444	M₁₆	—	3	4	no	—
445	M₁₆	—	3	8	no	—
446	C₂×C₈	—	3	2	no	—
447	C₂×C₈	—	3	8	no	—
448	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
449	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
450	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
451	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	—	2	4	no	—
454	C₂²×C₃	—	4	4	no	—
455	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
456	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
457	C₂×D₃	—	2	4	no	—
458	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
461	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
463	Dic₃	—	2	8	no	—
464	Dic₃	C₂²×C₅×D₄	1	4	yes	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	4	4	no	—
467	C₂×C₅	—	6	4	no	—
468	C₂×C₅	#5771	1	2	yes	direct product factor
469	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
470	C₂³	—	2	2	no	—
471	C₂³	—	3	2	no	—
472	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
473	Q₈	—	2	2	no	—
474	Q₈	—	3	4	no	—
475	Q₈	—	3	8	no	—
476	Q₈	—	6	16	no	—
477	Q₈	—	6	8	no	—
478	Q₈	—	6	4	no	—
479	Q₈	C₂³×C₅×D₃	1	4	yes	—
480	D₄	—	2	8	no	—
481	D₄	—	2	2	no	—
482	D₄	—	3	8	no	—
483	D₄	—	3	4	no	—
484	D₄	—	6	16	no	—
485	D₄	C₂³×C₅×D₃	1	4	yes	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	3	2	no	—
489	C₂×C₄	—	3	4	no	—
490	C₂×C₄	—	3	4	no	—
491	C₂×C₄	—	6	16	no	—
492	C₂×C₄	—	6	16	no	—
493	C₂×C₄	—	6	4	no	—
494	C₂×C₄	—	6	8	no	—
495	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
496	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
497	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
498	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
499	C₈	—	3	4	no	—
500	C₈	C₂³×C₅×D₃	1	2	yes	—
501	C₈	C₂³×C₅×D₃	1	2	yes	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	—	4	4	no	—
504	C₂×C₃	C₅×#578	1	2	yes	complemented
505	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
506	D₃	—	2	4	no	—
507	C₅	C₂×#5771	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	3	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	6	4	no	—
513	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
514	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
515	C₄	—	2	4	no	—
516	C₄	—	3	4	no	—
517	C₄	—	6	8	no	—
518	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
519	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
520	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
521	C₃	C₂×C₅×#578	1	1	yes	characteristic, complemented, Sylow
522	C₂	—	2	2	no	—
523	C₂	—	4	4	no	—
524	C₂	—	6	4	no	—
525	C₂	C₅×#5771	1	2	yes	direct product factor
526	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₂×C₅×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1010	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₂×C₅×#951	C₂	semidirect
4. C₅×#5771	C₂	direct (N × H)
5. C₂×C₅×D₃×Q₁₆	C₂	semidirect
6. C₂×C₅×#915	C₂	semidirect
7. C₂×C₅×#912	C₂	semidirect
8. C₂²×C₅×Dic₁₂	C₂	semidirect
9. C₂×C₅×#901	C₂	semidirect
13. C₅×#1010	C₂²	semidirect
21. C₃×C₅×#135	C₂²	semidirect
26. C₅×#951	C₂²	semidirect
30. C₅×D₃×Q₁₆	C₂²	semidirect
31. C₅×#915	C₂²	semidirect
32. C₅×#912	C₂²	semidirect
35. C₂×C₅×Dic₁₂	C₂²	semidirect
36. C₅×#901	C₂²	semidirect
39. C₂×#5771	C₅	direct (N × H)
45. C₂×C₅×#135	D₃	semidirect
92. C₂×#1010	C₂×C₅	semidirect
93. C₂×C₃×#135	C₂×C₅	semidirect
94. C₂×#951	C₂×C₅	semidirect
95. #5771	C₂×C₅	direct (N × H)
96. C₂×D₃×Q₁₆	C₂×C₅	semidirect
97. C₂×#915	C₂×C₅	semidirect
98. C₂×#912	C₂×C₅	semidirect
99. C₂²×Dic₁₂	C₂×C₅	semidirect
100. C₂×#901	C₂×C₅	semidirect
114. C₅×#135	C₂×D₃	semidirect
164. #1010	C₂²×C₅	semidirect
172. C₃×#135	C₂²×C₅	semidirect
177. #951	C₂²×C₅	semidirect
181. D₃×Q₁₆	C₂²×C₅	semidirect
182. #915	C₂²×C₅	semidirect
183. #912	C₂²×C₅	semidirect
186. C₂×Dic₁₂	C₂²×C₅	semidirect
187. #901	C₂²×C₅	semidirect
238. C₂×#135	C₅×D₃	semidirect
343. #135	C₂×C₅×D₃	semidirect
360. C₂×C₃×C₅	#578	semidirect
451. C₃×C₅	C₂×#578	semidirect
468. C₂×C₅	#5771	direct (N × H)
504. C₂×C₃	C₅×#578	semidirect
507. C₅	C₂×#5771	direct (N × H)
521. C₃	C₂×C₅×#578	semidirect
525. C₂	C₅×#5771	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×#1010	2
C₂×C₃×C₅×#135	2
C₂×C₅×#951	2
C₅×#5771	2
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×#915	2
C₂×C₅×#912	2
C₂²×C₅×Dic₁₂	2
C₂×C₅×#901	2
C₂×C₅×#578	3
C₂×#5771	5

Subgroups — C2×C5×#5771 #14510124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5771 #14510124