Subgroups — C₂×C₅×#5602 #14480926

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#935	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#935	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5602	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#889	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#879	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#539	—	3	1	no	maximal, Hall
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
17	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₅×#121	C₂²	1	8	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₅×#217	C₂²	1	2	yes	—
23	C₂×C₅×#217	C₂²	1	2	yes	—
24	C₂×C₅×#217	C₂²	1	2	yes	—
25	C₂×C₅×#217	C₂²	1	2	yes	—
26	C₅×#935	C₂²	1	16	yes	complemented
27	C₅×#935	C₂²	1	16	yes	complemented
28	C₅×D₄×Dic₃	C₂²	1	16	yes	complemented
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₅×#924	C₂²	1	8	yes	complemented
32	C₂×C₅×Dic₃⋊C₄	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	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	complemented
38	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
39	C₅×#889	C₂²	1	16	yes	complemented
40	C₅×#879	C₂²	1	16	yes	complemented
41	C₅×#878	C₂²	1	16	yes	complemented
42	C₂×#5602	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#539	—	3	16	no	—
44	C₂×C₅×#126	—	3	2	no	—
45	C₂×C₅×#125	—	3	2	no	—
46	C₂×C₅×#123	—	3	2	no	—
47	C₂×C₅×#123	—	3	2	no	—
48	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
49	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
50	C₂×C₅×#121	D₃	1	1	yes	characteristic
51	C₂×C₄×C₅×D₄	—	3	2	no	—
52	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
53	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
54	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	8	no	—
56	C₂×C₃×C₅×D₄	—	4	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
59	C₂²×C₃×C₄×C₅	—	4	2	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
64	C₂²×C₅×Dic₃	—	2	4	no	—
65	C₂²×C₅×Dic₃	—	4	4	no	—
66	C₂²×C₅×Dic₃	—	4	2	no	—
67	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
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	4	yes	—
72	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
73	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
74	C₂×C₅×Dic₆	—	4	2	no	—
75	C₂×C₅×Dic₆	C₂³	1	4	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
77	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
78	C₅×#217	C₂³	1	8	yes	—
79	C₅×#217	C₂³	1	8	yes	—
80	C₅×#217	C₂³	1	8	yes	—
81	C₅×#217	C₂³	1	8	yes	—
82	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
83	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
84	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
85	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
86	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
87	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
88	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
89	C₄×C₅×Dic₃	C₂³	1	8	yes	—
90	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
91	C₂×#935	C₂×C₅	1	2	yes	complemented
92	C₂×#935	C₂×C₅	1	2	yes	complemented
93	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	complemented
94	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
96	#5602	C₂×C₅	1	16	yes	direct product factor
97	C₂×#889	C₂×C₅	1	2	yes	complemented
98	C₂×#879	C₂×C₅	1	2	yes	complemented
99	C₂×#878	C₂×C₅	1	2	yes	complemented
100	C₂²×C₅×Q₈	—	3	1	no	—
101	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
102	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
103	C₂³×C₄×C₅	—	3	1	no	—
104	C₂³×C₄×C₅	—	3	1	no	—
105	C₂³×C₄×C₅	—	3	2	no	—
106	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
107	C₅×#126	—	3	16	no	—
108	C₅×#125	—	3	16	no	—
109	C₅×#123	—	3	16	no	—
110	C₅×#123	—	3	16	no	—
111	C₅×C₂²⋊Q₈	—	3	8	no	—
112	C₅×C₂²⋊Q₈	—	3	16	no	—
113	C₅×#121	C₂×D₃	1	8	yes	—
114	C₄×C₅×D₄	—	3	16	no	—
115	C₂×C₅×C₄⋊C₄	—	3	2	no	—
116	C₂×C₅×C₄⋊C₄	—	3	2	no	—
117	C₂×C₅×C₄⋊C₄	—	3	2	no	—
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₂×C₅×C₄⋊C₄	—	3	2	no	—
120	C₂×C₅×C₄⋊C₄	—	3	8	no	—
121	C₂×C₅×C₄⋊C₄	—	3	2	no	—
122	C₂×C₅×C₄⋊C₄	—	3	1	no	—
123	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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×C₄²×C₅	—	3	2	no	—
130	C₂×#539	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	—	2	4	no	—
134	C₂³×C₃×C₅	—	2	4	no	—
135	C₂³×C₃×C₅	—	2	4	no	—
136	C₂³×C₃×C₅	#41	1	4	yes	—
137	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
138	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
139	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₅×D₄	—	2	16	no	—
141	C₃×C₅×D₄	—	4	4	no	—
142	C₂×C₃×C₄×C₅	—	2	4	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	4	4	no	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
149	C₂×C₅×Dic₃	—	2	8	no	—
150	C₂×C₅×Dic₃	—	2	4	no	—
151	C₂×C₅×Dic₃	—	2	4	no	—
152	C₂×C₅×Dic₃	—	2	4	no	—
153	C₂×C₅×Dic₃	—	2	4	no	—
154	C₂×C₅×Dic₃	—	4	8	no	—
155	C₂×C₅×Dic₃	—	4	4	no	—
156	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
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×Dic₆	—	4	4	no	—
161	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
162	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
164	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
165	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
166	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
167	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
168	C₃×#121	C₂²×C₅	1	8	yes	—
169	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×#217	C₂²×C₅	1	2	yes	—
172	C₂×#217	C₂²×C₅	1	2	yes	—
173	C₂×#217	C₂²×C₅	1	2	yes	—
174	C₂×#217	C₂²×C₅	1	2	yes	—
175	#935	C₂²×C₅	1	16	yes	complemented
176	#935	C₂²×C₅	1	16	yes	complemented
177	D₄×Dic₃	C₂²×C₅	1	16	yes	complemented
178	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
179	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
180	#924	C₂²×C₅	1	8	yes	complemented
181	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
182	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
183	C₂×Dic₃⋊C₄	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	8	yes	complemented
187	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
188	#889	C₂²×C₅	1	16	yes	complemented
189	#879	C₂²×C₅	1	16	yes	complemented
190	#878	C₂²×C₅	1	16	yes	complemented
191	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
192	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×Q₈	—	3	4	no	—
194	C₂×C₅×Q₈	—	12	2	no	—
195	C₂×C₅×D₄	—	2	8	no	—
196	C₂×C₅×D₄	—	4	2	no	—
197	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
198	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
199	C₂²×C₄×C₅	—	3	4	no	—
200	C₂²×C₄×C₅	—	3	2	no	—
201	C₂²×C₄×C₅	—	3	2	no	—
202	C₂²×C₄×C₅	—	3	2	no	—
203	C₂²×C₄×C₅	—	3	2	no	—
204	C₂²×C₄×C₅	—	3	4	no	—
205	C₂²×C₄×C₅	—	3	8	no	—
206	C₂²×C₄×C₅	—	4	2	no	—
207	C₂²×C₄×C₅	—	6	4	no	—
208	C₂²×C₄×C₅	—	12	2	no	—
209	C₂²×C₄×C₅	—	12	4	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
211	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
214	C₅×C₄⋊C₄	—	3	8	no	—
215	C₅×C₄⋊C₄	—	3	8	no	—
216	C₅×C₄⋊C₄	—	3	8	no	—
217	C₅×C₄⋊C₄	—	3	8	no	—
218	C₅×C₄⋊C₄	—	3	8	no	—
219	C₅×C₄⋊C₄	—	3	4	no	—
220	C₅×C₄⋊C₄	—	3	8	no	—
221	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
222	C₅×C₂²⋊C₄	—	3	8	no	—
223	C₅×C₂²⋊C₄	—	3	8	no	—
224	C₅×C₂²⋊C₄	—	3	8	no	—
225	C₅×C₂²⋊C₄	—	3	8	no	—
226	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
227	C₄²×C₅	—	3	8	no	—
228	#539	—	3	16	no	—
229	C₂×#126	—	3	2	no	—
230	C₂×#125	—	3	2	no	—
231	C₂×#123	—	3	2	no	—
232	C₂×#123	—	3	2	no	—
233	C₂×C₂²⋊Q₈	—	3	1	no	—
234	C₂×C₂²⋊Q₈	—	3	2	no	—
235	C₂×#121	C₅×D₃	1	1	yes	characteristic
236	C₂×C₄×D₄	—	3	2	no	—
237	C₂²×C₄⋊C₄	—	3	1	no	—
238	C₂²×C₃×C₅	—	2	8	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	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	C₂×#41	1	4	yes	—
246	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
247	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
248	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
249	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	2	no	—
253	C₅×Dic₃	—	2	4	no	—
254	C₅×Dic₃	—	2	4	no	—
255	C₅×Dic₃	—	2	4	no	—
256	C₅×Dic₃	—	2	4	no	—
257	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
258	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₃×D₄	—	2	8	no	—
260	C₂×C₃×D₄	—	4	2	no	—
261	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
262	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
263	C₂²×C₃×C₄	—	4	2	no	—
264	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
265	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
268	C₂²×Dic₃	—	2	4	no	—
269	C₂²×Dic₃	—	4	4	no	—
270	C₂²×Dic₃	—	4	2	no	—
271	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
272	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
273	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
274	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
275	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
276	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
277	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
278	C₂×Dic₆	—	4	2	no	—
279	C₂×Dic₆	C₂³×C₅	1	4	yes	—
280	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
281	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
282	#217	C₂³×C₅	1	8	yes	—
283	#217	C₂³×C₅	1	8	yes	—
284	#217	C₂³×C₅	1	8	yes	—
285	#217	C₂³×C₅	1	8	yes	—
286	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
287	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
288	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
289	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
290	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
291	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
292	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
293	C₄×Dic₃	C₂³×C₅	1	8	yes	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	4	no	—
297	C₂³×C₅	—	2	4	no	—
298	C₂³×C₅	—	2	4	no	—
299	C₂³×C₅	#237	1	4	yes	—
300	C₂³×C₅	C₂³×D₃	1	4	yes	—
301	C₂³×C₅	C₂³×D₃	1	2	yes	—
302	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
303	C₅×Q₈	—	12	4	no	—
304	C₅×D₄	—	2	16	no	—
305	C₅×D₄	—	4	4	no	—
306	C₂×C₄×C₅	—	2	4	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	3	4	no	—
310	C₂×C₄×C₅	—	3	4	no	—
311	C₂×C₄×C₅	—	3	4	no	—
312	C₂×C₄×C₅	—	3	4	no	—
313	C₂×C₄×C₅	—	4	4	no	—
314	C₂×C₄×C₅	—	6	8	no	—
315	C₂×C₄×C₅	—	6	4	no	—
316	C₂×C₄×C₅	—	6	4	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	6	4	no	—
319	C₂×C₄×C₅	—	12	4	no	—
320	C₂×C₄×C₅	—	12	8	no	—
321	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
322	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
323	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
324	C₂²×Q₈	—	3	1	no	—
325	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
326	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
327	C₂³×C₄	—	3	1	no	—
328	C₂³×C₄	—	3	1	no	—
329	C₂³×C₄	—	3	2	no	—
330	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
331	#126	—	3	16	no	—
332	#125	—	3	16	no	—
333	#123	—	3	16	no	—
334	#123	—	3	16	no	—
335	C₂²⋊Q₈	—	3	8	no	—
336	C₂²⋊Q₈	—	3	16	no	—
337	#121	C₂×C₅×D₃	1	8	yes	—
338	C₄×D₄	—	3	16	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	8	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₄⋊C₄	—	3	1	no	—
346	C₂×C₄⋊C₄	—	3	2	no	—
347	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
353	C₂×C₄²	—	3	2	no	—
354	C₂×C₃×C₅	—	2	4	no	—
355	C₂×C₃×C₅	—	4	4	no	—
356	C₂×C₃×C₅	#539	1	4	yes	complemented
357	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
358	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	2	2	no	—
362	C₂³×C₃	—	2	4	no	—
363	C₂³×C₃	—	2	4	no	—
364	C₂³×C₃	—	2	4	no	—
365	C₂³×C₃	C₅×#41	1	4	yes	—
366	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
367	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
368	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
369	C₃×D₄	—	2	16	no	—
370	C₃×D₄	—	4	4	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	4	4	no	—
375	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
376	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
378	C₂×Dic₃	—	2	8	no	—
379	C₂×Dic₃	—	2	4	no	—
380	C₂×Dic₃	—	2	4	no	—
381	C₂×Dic₃	—	2	4	no	—
382	C₂×Dic₃	—	2	4	no	—
383	C₂×Dic₃	—	4	8	no	—
384	C₂×Dic₃	—	4	4	no	—
385	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
386	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
387	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
388	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
389	Dic₆	—	4	4	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	8	no	—
393	C₂²×C₅	—	2	4	no	—
394	C₂²×C₅	—	2	4	no	—
395	C₂²×C₅	—	2	4	no	—
396	C₂²×C₅	—	4	8	no	—
397	C₂²×C₅	C₂×#237	1	4	yes	—
398	C₂²×C₅	C₂×#237	1	2	yes	—
399	C₂²×C₅	#1004	1	2	yes	—
400	C₂²×C₅	#1010	1	2	yes	—
401	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
402	C₄×C₅	—	2	4	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	6	4	no	—
406	C₄×C₅	—	6	4	no	—
407	C₄×C₅	—	6	4	no	—
408	C₄×C₅	—	6	4	no	—
409	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
410	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
411	C₂×Q₈	—	3	4	no	—
412	C₂×Q₈	—	12	2	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
416	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
417	C₂²×C₄	—	3	2	no	—
418	C₂²×C₄	—	3	2	no	—
419	C₂²×C₄	—	3	2	no	—
420	C₂²×C₄	—	3	2	no	—
421	C₂²×C₄	—	3	4	no	—
422	C₂²×C₄	—	3	4	no	—
423	C₂²×C₄	—	3	8	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	6	4	no	—
426	C₂²×C₄	—	12	2	no	—
427	C₂²×C₄	—	12	4	no	—
428	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
429	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
432	C₄⋊C₄	—	3	8	no	—
433	C₄⋊C₄	—	3	8	no	—
434	C₄⋊C₄	—	3	8	no	—
435	C₄⋊C₄	—	3	8	no	—
436	C₄⋊C₄	—	3	8	no	—
437	C₄⋊C₄	—	3	4	no	—
438	C₄⋊C₄	—	3	8	no	—
439	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
440	C₂²⋊C₄	—	3	8	no	—
441	C₂²⋊C₄	—	3	8	no	—
442	C₂²⋊C₄	—	3	8	no	—
443	C₂²⋊C₄	—	3	8	no	—
444	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
445	C₄²	—	3	8	no	—
446	C₃×C₅	C₂×#539	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	8	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	2	4	no	—
451	C₂²×C₃	—	2	4	no	—
452	C₂²×C₃	—	2	4	no	—
453	C₂²×C₃	—	4	8	no	—
454	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
455	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
456	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
457	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
458	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	2	2	no	—
462	Dic₃	—	2	4	no	—
463	Dic₃	—	2	4	no	—
464	Dic₃	—	2	4	no	—
465	Dic₃	—	2	4	no	—
466	C₂×C₅	—	2	4	no	—
467	C₂×C₅	—	4	4	no	—
468	C₂×C₅	#5602	1	4	yes	direct product factor
469	C₂×C₅	C₂²×#237	1	1	yes	characteristic
470	C₂×C₅	C₂×#1004	1	1	yes	characteristic
471	C₂×C₅	C₂×#1010	1	1	yes	characteristic
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	C₅×#237	1	4	yes	—
478	C₂³	C₂³×C₅×D₃	1	4	yes	—
479	C₂³	C₂³×C₅×D₃	1	2	yes	—
480	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
481	Q₈	—	12	4	no	—
482	D₄	—	2	16	no	—
483	D₄	—	4	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	3	4	no	—
488	C₂×C₄	—	3	4	no	—
489	C₂×C₄	—	3	4	no	—
490	C₂×C₄	—	3	4	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	6	8	no	—
493	C₂×C₄	—	6	4	no	—
494	C₂×C₄	—	6	4	no	—
495	C₂×C₄	—	6	4	no	—
496	C₂×C₄	—	6	4	no	—
497	C₂×C₄	—	12	4	no	—
498	C₂×C₄	—	12	8	no	—
499	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
500	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
501	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
502	C₂×C₃	—	2	4	no	—
503	C₂×C₃	—	4	4	no	—
504	C₂×C₃	C₅×#539	1	4	yes	complemented
505	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
506	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
508	C₅	C₂×#5602	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	4	8	no	—
516	C₂²	C₂×C₅×#237	1	4	yes	—
517	C₂²	C₂×C₅×#237	1	2	yes	—
518	C₂²	C₅×#1004	1	2	yes	—
519	C₂²	C₅×#1010	1	2	yes	—
520	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	6	4	no	—
525	C₄	—	6	4	no	—
526	C₄	—	6	4	no	—
527	C₄	—	6	4	no	—
528	C₃	C₂×C₅×#539	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	2	4	no	—
530	C₂	—	4	4	no	—
531	C₂	C₅×#5602	1	4	yes	direct product factor
532	C₂	C₂²×C₅×#237	1	1	yes	characteristic
533	C₂	C₂×C₅×#1004	1	1	yes	characteristic
534	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, prime radical	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#935	C₂	semidirect
3. C₂×C₅×#935	C₂	semidirect
4. C₂×C₅×D₄×Dic₃	C₂	semidirect
5. C₂×C₅×#924	C₂	semidirect
6. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
7. C₅×#5602	C₂	direct (N × H)
8. C₂×C₅×#889	C₂	semidirect
9. C₂×C₅×#879	C₂	semidirect
10. C₂×C₅×#878	C₂	semidirect
26. C₅×#935	C₂²	semidirect
27. C₅×#935	C₂²	semidirect
28. C₅×D₄×Dic₃	C₂²	semidirect
31. C₅×#924	C₂²	semidirect
37. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
39. C₅×#889	C₂²	semidirect
40. C₅×#879	C₂²	semidirect
41. C₅×#878	C₂²	semidirect
42. C₂×#5602	C₅	direct (N × H)
91. C₂×#935	C₂×C₅	semidirect
92. C₂×#935	C₂×C₅	semidirect
93. C₂×D₄×Dic₃	C₂×C₅	semidirect
94. C₂×#924	C₂×C₅	semidirect
95. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
96. #5602	C₂×C₅	direct (N × H)
97. C₂×#889	C₂×C₅	semidirect
98. C₂×#879	C₂×C₅	semidirect
99. C₂×#878	C₂×C₅	semidirect
175. #935	C₂²×C₅	semidirect
176. #935	C₂²×C₅	semidirect
177. D₄×Dic₃	C₂²×C₅	semidirect
180. #924	C₂²×C₅	semidirect
186. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
188. #889	C₂²×C₅	semidirect
189. #879	C₂²×C₅	semidirect
190. #878	C₂²×C₅	semidirect
356. C₂×C₃×C₅	#539	semidirect
446. C₃×C₅	C₂×#539	semidirect
468. C₂×C₅	#5602	direct (N × H)
504. C₂×C₃	C₅×#539	semidirect
508. C₅	C₂×#5602	direct (N × H)
528. C₃	C₂×C₅×#539	semidirect
531. C₂	C₅×#5602	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×#121	2
C₂×C₅×#935	2
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#924	2
C₂²×C₅×Dic₃⋊C₄	2
C₅×#5602	2
C₂×C₅×#889	2
C₂×C₅×#879	2
C₂×C₅×#878	2
C₂×C₅×#539	3
C₂×#5602	5

Subgroups — C2×C5×#5602 #14480926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5602 #14480926