Subgroups — C₂×C₅×#5684 #14495275

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#946	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
4	C₅×#5684	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#886	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#883	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#562	—	3	1	no	maximal, Hall
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#67	C₂²	1	2	yes	—
15	C₂²×C₅×#67	C₂²	1	2	yes	—
16	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×#124	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×#217	C₂²	1	2	yes	—
25	C₅×#946	C₂²	1	16	yes	complemented
26	C₅×#939	C₂²	1	16	yes	complemented
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₅×#886	C₂²	1	16	yes	complemented
37	C₅×#884	C₂²	1	16	yes	complemented
38	C₅×#883	C₂²	1	16	yes	complemented
39	C₅×#878	C₂²	1	16	yes	complemented
40	C₅×#875	C₂²	1	8	yes	complemented
41	C₅×#870	C₂²	1	8	yes	complemented
42	C₂×#5684	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#562	—	3	16	no	—
44	C₂×C₅×#125	—	3	1	no	—
45	C₂×C₅×#124	—	3	1	no	—
46	C₂×C₅×#124	D₃	1	1	yes	characteristic, complemented
47	C₂×C₅×#123	—	3	2	no	—
48	C₂×C₅×#123	—	3	2	no	—
49	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
50	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
51	C₂×C₅×#121	—	3	2	no	—
52	C₂×C₅×#121	—	3	2	no	—
53	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
54	C₂³×C₅×D₃	C₂³	1	2	yes	—
55	C₂×C₃×C₅×Q₈	—	4	2	no	—
56	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
57	C₂×C₃×C₅×D₄	—	4	2	no	—
58	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₅×#67	—	4	4	no	—
64	C₂×C₅×#67	—	4	4	no	—
65	C₂×C₅×#67	C₂³	1	8	yes	—
66	C₂×C₅×#67	C₂³	1	8	yes	—
67	C₂²×C₅×Dic₃	—	4	4	no	—
68	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
69	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
72	C₂×C₅×D₁₂	—	4	2	no	—
73	C₂×C₅×D₁₂	C₂³	1	4	yes	—
74	C₂×C₄×C₅×D₃	—	4	4	no	—
75	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
76	C₂×C₅×Dic₆	—	4	2	no	—
77	C₂×C₅×Dic₆	C₂³	1	4	yes	—
78	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₃×C₄²×C₅	C₂³	1	4	yes	—
81	C₅×#217	C₂³	1	8	yes	—
82	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
83	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
84	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
85	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
86	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
87	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
88	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
89	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
90	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
91	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#946	C₂×C₅	1	2	yes	complemented
93	C₂×#939	C₂×C₅	1	2	yes	complemented
94	#5684	C₂×C₅	1	16	yes	direct product factor
95	C₂×#886	C₂×C₅	1	2	yes	complemented
96	C₂×#884	C₂×C₅	1	2	yes	complemented
97	C₂×#883	C₂×C₅	1	2	yes	complemented
98	C₂×#878	C₂×C₅	1	2	yes	complemented
99	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×#870	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×C₅×Q₈	—	3	1	no	—
102	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₅×D₄	—	3	2	no	—
104	C₂²×C₅×D₄	—	3	2	no	—
105	C₂²×C₅×D₄	—	3	1	no	—
106	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
107	C₂³×C₄×C₅	—	3	2	no	—
108	C₂³×C₄×C₅	—	3	2	no	—
109	C₅×#125	—	3	8	no	—
110	C₅×#124	—	3	8	no	—
111	C₅×#124	C₂×D₃	1	8	yes	complemented
112	C₅×#123	—	3	16	no	—
113	C₅×#123	—	3	16	no	—
114	C₅×C₂²⋊Q₈	—	3	16	no	—
115	C₅×C₂²⋊Q₈	—	3	16	no	—
116	C₅×#121	—	3	16	no	—
117	C₅×#121	—	3	16	no	—
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₂×C₅×C₄⋊C₄	—	3	2	no	—
120	C₂×C₅×C₄⋊C₄	—	3	2	no	—
121	C₂×C₅×C₄⋊C₄	—	3	2	no	—
122	C₂×C₅×C₄⋊C₄	—	3	1	no	—
123	C₂×C₅×C₄⋊C₄	—	3	1	no	—
124	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
125	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
126	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
127	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
128	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
130	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
131	C₂×#562	—	3	1	no	Sylow
132	C₂³×C₃×C₅	—	2	4	no	—
133	C₂³×C₃×C₅	—	2	4	no	—
134	C₂³×C₃×C₅	—	2	4	no	—
135	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
136	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
137	C₂²×C₅×D₃	—	2	4	no	—
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	—	2	4	no	—
140	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
141	C₃×C₅×Q₈	—	4	4	no	—
142	C₃×C₅×D₄	—	4	4	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	4	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
151	C₅×#67	—	4	8	no	—
152	C₅×#67	—	4	8	no	—
153	C₂×C₅×Dic₃	—	2	4	no	—
154	C₂×C₅×Dic₃	—	2	4	no	—
155	C₂×C₅×Dic₃	—	2	4	no	—
156	C₂×C₅×Dic₃	—	4	8	no	—
157	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
158	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
159	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
160	C₅×D₁₂	—	4	4	no	—
161	C₄×C₅×D₃	—	4	8	no	—
162	C₅×Dic₆	—	4	4	no	—
163	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
165	C₂²×#67	C₂²×C₅	1	2	yes	—
166	C₂²×#67	C₂²×C₅	1	2	yes	—
167	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
168	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
169	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
170	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
171	C₃×#124	C₂²×C₅	1	8	yes	complemented
172	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
175	C₂×#217	C₂²×C₅	1	2	yes	—
176	#946	C₂²×C₅	1	16	yes	complemented
177	#939	C₂²×C₅	1	16	yes	complemented
178	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
180	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
181	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
184	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
186	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
187	#886	C₂²×C₅	1	16	yes	complemented
188	#884	C₂²×C₅	1	16	yes	complemented
189	#883	C₂²×C₅	1	16	yes	complemented
190	#878	C₂²×C₅	1	16	yes	complemented
191	#875	C₂²×C₅	1	8	yes	complemented
192	#870	C₂²×C₅	1	8	yes	complemented
193	C₂⁴×C₅	—	3	2	no	—
194	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
195	C₂×C₅×Q₈	—	3	4	no	—
196	C₂×C₅×Q₈	—	4	2	no	—
197	C₂×C₅×Q₈	—	12	2	no	—
198	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
199	C₂×C₅×D₄	—	3	8	no	—
200	C₂×C₅×D₄	—	3	8	no	—
201	C₂×C₅×D₄	—	3	4	no	—
202	C₂×C₅×D₄	—	4	2	no	—
203	C₂×C₅×D₄	—	12	2	no	—
204	C₂×C₅×D₄	—	12	4	no	—
205	C₂×C₅×D₄	—	12	4	no	—
206	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
207	C₂²×C₄×C₅	—	3	2	no	—
208	C₂²×C₄×C₅	—	3	2	no	—
209	C₂²×C₄×C₅	—	3	2	no	—
210	C₂²×C₄×C₅	—	3	8	no	—
211	C₂²×C₄×C₅	—	3	8	no	—
212	C₂²×C₄×C₅	—	12	4	no	—
213	C₂²×C₄×C₅	—	12	4	no	—
214	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
218	C₅×C₄⋊C₄	—	3	8	no	—
219	C₅×C₄⋊C₄	—	3	8	no	—
220	C₅×C₄⋊C₄	—	3	8	no	—
221	C₅×C₄⋊C₄	—	3	8	no	—
222	C₅×C₄⋊C₄	—	3	4	no	—
223	C₅×C₄⋊C₄	—	3	4	no	—
224	C₅×C₂²⋊C₄	—	3	8	no	—
225	C₅×C₂²⋊C₄	—	3	8	no	—
226	C₅×C₂²⋊C₄	—	3	8	no	—
227	C₅×C₂²⋊C₄	—	3	8	no	—
228	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
229	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
230	C₄²×C₅	C₂²×D₃	1	4	yes	—
231	#562	—	3	16	no	—
232	C₂×#125	—	3	1	no	—
233	C₂×#124	—	3	1	no	—
234	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
235	C₂×#123	—	3	2	no	—
236	C₂×#123	—	3	2	no	—
237	C₂×C₂²⋊Q₈	—	3	2	no	—
238	C₂×C₂²⋊Q₈	—	3	2	no	—
239	C₂×#121	—	3	2	no	—
240	C₂×#121	—	3	2	no	—
241	C₂²×C₃×C₅	—	2	4	no	—
242	C₂²×C₃×C₅	—	2	4	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	4	8	no	—
245	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
246	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
247	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
248	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
249	C₂×C₅×D₃	—	2	4	no	—
250	C₂×C₅×D₃	—	2	4	no	—
251	C₂×C₅×D₃	—	2	4	no	—
252	C₂×C₅×D₃	—	4	8	no	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	4	no	—
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₅×Dic₃	—	2	4	no	—
258	C₅×Dic₃	—	2	4	no	—
259	C₅×Dic₃	—	2	4	no	—
260	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
261	C₂³×D₃	C₂³×C₅	1	2	yes	—
262	C₂×C₃×Q₈	—	4	2	no	—
263	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
264	C₂×C₃×D₄	—	4	2	no	—
265	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
266	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×#67	—	4	4	no	—
271	C₂×#67	—	4	4	no	—
272	C₂×#67	C₂³×C₅	1	8	yes	—
273	C₂×#67	C₂³×C₅	1	8	yes	—
274	C₂²×Dic₃	—	4	4	no	—
275	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
276	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
277	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
278	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
279	C₂×D₁₂	—	4	2	no	—
280	C₂×D₁₂	C₂³×C₅	1	4	yes	—
281	C₂×C₄×D₃	—	4	4	no	—
282	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
283	C₂×Dic₆	—	4	2	no	—
284	C₂×Dic₆	C₂³×C₅	1	4	yes	—
285	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
286	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
287	C₃×C₄²	C₂³×C₅	1	4	yes	—
288	#217	C₂³×C₅	1	8	yes	—
289	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
290	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
291	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
292	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
293	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
294	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
295	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
296	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
297	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
298	C₂³×C₅	—	2	4	no	—
299	C₂³×C₅	—	2	4	no	—
300	C₂³×C₅	—	2	4	no	—
301	C₂³×C₅	—	3	4	no	—
302	C₂³×C₅	—	6	4	no	—
303	C₂³×C₅	—	6	4	no	—
304	C₂³×C₅	—	6	4	no	—
305	C₂³×C₅	C₂³×D₃	1	4	yes	—
306	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
307	C₅×Q₈	—	4	4	no	—
308	C₅×Q₈	—	12	4	no	—
309	C₅×D₄	—	4	4	no	—
310	C₅×D₄	—	12	4	no	—
311	C₅×D₄	—	12	8	no	—
312	C₅×D₄	—	12	8	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	3	4	no	—
318	C₂×C₄×C₅	—	3	4	no	—
319	C₂×C₄×C₅	—	3	4	no	—
320	C₂×C₄×C₅	—	6	4	no	—
321	C₂×C₄×C₅	—	6	4	no	—
322	C₂×C₄×C₅	—	6	4	no	—
323	C₂×C₄×C₅	—	12	8	no	—
324	C₂×C₄×C₅	—	12	8	no	—
325	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
326	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
327	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
328	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
329	C₂²×Q₈	—	3	1	no	—
330	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂²×D₄	—	3	2	no	—
332	C₂²×D₄	—	3	2	no	—
333	C₂²×D₄	—	3	1	no	—
334	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
335	C₂³×C₄	—	3	2	no	—
336	C₂³×C₄	—	3	2	no	—
337	#125	—	3	8	no	—
338	#124	—	3	8	no	—
339	#124	C₂×C₅×D₃	1	8	yes	complemented
340	#123	—	3	16	no	—
341	#123	—	3	16	no	—
342	C₂²⋊Q₈	—	3	16	no	—
343	C₂²⋊Q₈	—	3	16	no	—
344	#121	—	3	16	no	—
345	#121	—	3	16	no	—
346	C₂×C₄⋊C₄	—	3	2	no	—
347	C₂×C₄⋊C₄	—	3	2	no	—
348	C₂×C₄⋊C₄	—	3	2	no	—
349	C₂×C₄⋊C₄	—	3	2	no	—
350	C₂×C₄⋊C₄	—	3	1	no	—
351	C₂×C₄⋊C₄	—	3	1	no	—
352	C₂×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₂²⋊C₄	—	3	2	no	—
354	C₂×C₂²⋊C₄	—	3	2	no	—
355	C₂×C₂²⋊C₄	—	3	2	no	—
356	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
358	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
359	C₂×C₃×C₅	—	4	4	no	—
360	C₂×C₃×C₅	#562	1	4	yes	complemented
361	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
364	C₅×D₃	—	4	4	no	—
365	C₂³×C₃	—	2	4	no	—
366	C₂³×C₃	—	2	4	no	—
367	C₂³×C₃	—	2	4	no	—
368	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
369	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
370	C₂²×D₃	—	2	4	no	—
371	C₂²×D₃	—	2	4	no	—
372	C₂²×D₃	—	2	4	no	—
373	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
374	C₃×Q₈	—	4	4	no	—
375	C₃×D₄	—	4	4	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	4	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
381	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
382	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
383	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
384	#67	—	4	8	no	—
385	#67	—	4	8	no	—
386	C₂×Dic₃	—	2	4	no	—
387	C₂×Dic₃	—	2	4	no	—
388	C₂×Dic₃	—	2	4	no	—
389	C₂×Dic₃	—	4	8	no	—
390	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
391	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
392	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
393	D₁₂	—	4	4	no	—
394	C₄×D₃	—	4	8	no	—
395	Dic₆	—	4	4	no	—
396	C₂²×C₅	—	2	4	no	—
397	C₂²×C₅	—	2	4	no	—
398	C₂²×C₅	—	2	4	no	—
399	C₂²×C₅	—	4	8	no	—
400	C₂²×C₅	—	6	4	no	—
401	C₂²×C₅	—	6	4	no	—
402	C₂²×C₅	—	6	4	no	—
403	C₂²×C₅	—	12	8	no	—
404	C₂²×C₅	#1004	1	2	yes	—
405	C₂²×C₅	#1009	1	2	yes	—
406	C₂²×C₅	#1010	1	2	yes	—
407	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
408	C₄×C₅	—	2	4	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	2	2	no	—
411	C₄×C₅	—	2	2	no	—
412	C₄×C₅	—	6	4	no	—
413	C₄×C₅	—	6	4	no	—
414	C₄×C₅	—	6	4	no	—
415	C₂⁴	—	3	2	no	—
416	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
417	C₂×Q₈	—	3	4	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	12	2	no	—
420	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
421	C₂×D₄	—	3	8	no	—
422	C₂×D₄	—	3	8	no	—
423	C₂×D₄	—	3	4	no	—
424	C₂×D₄	—	4	2	no	—
425	C₂×D₄	—	12	2	no	—
426	C₂×D₄	—	12	4	no	—
427	C₂×D₄	—	12	4	no	—
428	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
429	C₂²×C₄	—	3	2	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	3	8	no	—
433	C₂²×C₄	—	3	8	no	—
434	C₂²×C₄	—	12	4	no	—
435	C₂²×C₄	—	12	4	no	—
436	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
440	C₄⋊C₄	—	3	8	no	—
441	C₄⋊C₄	—	3	8	no	—
442	C₄⋊C₄	—	3	8	no	—
443	C₄⋊C₄	—	3	8	no	—
444	C₄⋊C₄	—	3	4	no	—
445	C₄⋊C₄	—	3	4	no	—
446	C₂²⋊C₄	—	3	8	no	—
447	C₂²⋊C₄	—	3	8	no	—
448	C₂²⋊C₄	—	3	8	no	—
449	C₂²⋊C₄	—	3	8	no	—
450	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
451	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
452	C₄²	C₂²×C₅×D₃	1	4	yes	—
453	C₃×C₅	C₂×#562	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	2	4	no	—
455	C₂²×C₃	—	2	4	no	—
456	C₂²×C₃	—	2	4	no	—
457	C₂²×C₃	—	4	8	no	—
458	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
459	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
460	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
461	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
462	C₂×D₃	—	2	4	no	—
463	C₂×D₃	—	2	4	no	—
464	C₂×D₃	—	2	4	no	—
465	C₂×D₃	—	4	8	no	—
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	2	4	no	—
468	C₃×C₄	—	2	2	no	—
469	C₃×C₄	—	2	2	no	—
470	Dic₃	—	2	4	no	—
471	Dic₃	—	2	4	no	—
472	Dic₃	—	2	4	no	—
473	C₂×C₅	—	4	4	no	—
474	C₂×C₅	—	12	4	no	—
475	C₂×C₅	#5684	1	4	yes	direct product factor
476	C₂×C₅	C₂×#1004	1	1	yes	characteristic
477	C₂×C₅	C₂×#1009	1	1	yes	characteristic
478	C₂×C₅	C₂×#1010	1	1	yes	characteristic
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	3	4	no	—
483	C₂³	—	6	4	no	—
484	C₂³	—	6	4	no	—
485	C₂³	—	6	4	no	—
486	C₂³	C₂³×C₅×D₃	1	4	yes	—
487	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
488	Q₈	—	4	4	no	—
489	Q₈	—	12	4	no	—
490	D₄	—	4	4	no	—
491	D₄	—	12	4	no	—
492	D₄	—	12	8	no	—
493	D₄	—	12	8	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	3	4	no	—
499	C₂×C₄	—	3	4	no	—
500	C₂×C₄	—	3	4	no	—
501	C₂×C₄	—	6	4	no	—
502	C₂×C₄	—	6	4	no	—
503	C₂×C₄	—	6	4	no	—
504	C₂×C₄	—	12	8	no	—
505	C₂×C₄	—	12	8	no	—
506	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
507	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
508	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
509	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
510	C₂×C₃	—	4	4	no	—
511	C₂×C₃	C₅×#562	1	4	yes	complemented
512	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
515	D₃	—	4	4	no	—
516	C₅	C₂×#5684	1	1	yes	characteristic, direct product factor, Sylow
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	4	8	no	—
521	C₂²	—	6	4	no	—
522	C₂²	—	6	4	no	—
523	C₂²	—	6	4	no	—
524	C₂²	—	12	8	no	—
525	C₂²	C₅×#1004	1	2	yes	—
526	C₂²	C₅×#1009	1	2	yes	—
527	C₂²	C₅×#1010	1	2	yes	—
528	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
529	C₄	—	2	4	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	6	4	no	—
534	C₄	—	6	4	no	—
535	C₄	—	6	4	no	—
536	C₃	C₂×C₅×#562	1	1	yes	characteristic, complemented, Sylow
537	C₂	—	4	4	no	—
538	C₂	—	12	4	no	—
539	C₂	C₅×#5684	1	4	yes	direct product factor
540	C₂	C₂×C₅×#1004	1	1	yes	characteristic
541	C₂	C₂×C₅×#1009	1	1	yes	characteristic
542	C₂	C₂×C₅×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#562
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₅×#946	C₂	semidirect
3. C₂×C₅×#939	C₂	semidirect
4. C₅×#5684	C₂	direct (N × H)
5. C₂×C₅×#886	C₂	semidirect
6. C₂×C₅×#884	C₂	semidirect
7. C₂×C₅×#883	C₂	semidirect
8. C₂×C₅×#878	C₂	semidirect
9. C₂×C₅×#875	C₂	semidirect
10. C₂×C₅×#870	C₂	semidirect
20. C₃×C₅×#124	C₂²	semidirect
25. C₅×#946	C₂²	semidirect
26. C₅×#939	C₂²	semidirect
36. C₅×#886	C₂²	semidirect
37. C₅×#884	C₂²	semidirect
38. C₅×#883	C₂²	semidirect
39. C₅×#878	C₂²	semidirect
40. C₅×#875	C₂²	semidirect
41. C₅×#870	C₂²	semidirect
42. C₂×#5684	C₅	direct (N × H)
46. C₂×C₅×#124	D₃	semidirect
91. C₂×C₃×#124	C₂×C₅	semidirect
92. C₂×#946	C₂×C₅	semidirect
93. C₂×#939	C₂×C₅	semidirect
94. #5684	C₂×C₅	direct (N × H)
95. C₂×#886	C₂×C₅	semidirect
96. C₂×#884	C₂×C₅	semidirect
97. C₂×#883	C₂×C₅	semidirect
98. C₂×#878	C₂×C₅	semidirect
99. C₂×#875	C₂×C₅	semidirect
100. C₂×#870	C₂×C₅	semidirect
111. C₅×#124	C₂×D₃	semidirect
171. C₃×#124	C₂²×C₅	semidirect
176. #946	C₂²×C₅	semidirect
177. #939	C₂²×C₅	semidirect
187. #886	C₂²×C₅	semidirect
188. #884	C₂²×C₅	semidirect
189. #883	C₂²×C₅	semidirect
190. #878	C₂²×C₅	semidirect
191. #875	C₂²×C₅	semidirect
192. #870	C₂²×C₅	semidirect
234. C₂×#124	C₅×D₃	semidirect
339. #124	C₂×C₅×D₃	semidirect
360. C₂×C₃×C₅	#562	semidirect
453. C₃×C₅	C₂×#562	semidirect
475. C₂×C₅	#5684	direct (N × H)
511. C₂×C₃	C₅×#562	semidirect
516. C₅	C₂×#5684	direct (N × H)
536. C₃	C₂×C₅×#562	semidirect
539. C₂	C₅×#5684	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×C₃×C₅×#124	2
C₂×C₅×#946	2
C₂×C₅×#939	2
C₅×#5684	2
C₂×C₅×#886	2
C₂×C₅×#884	2
C₂×C₅×#883	2
C₂×C₅×#878	2
C₂×C₅×#875	2
C₂×C₅×#870	2
C₂×C₅×#562	3
C₂×#5684	5

Subgroups — C2×C5×#5684 #14495275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5684 #14495275