Subgroups — C₂×C₅×#5587 #14483256

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#217	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#935	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
7	C₅×#5587	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#879	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#878	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#877	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#551	—	3	1	no	maximal, Hall
12	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
16	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
17	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#120	C₂²	1	8	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	C₂×C₅×#217	C₂²	1	16	yes	complemented
27	C₂×C₅×#217	C₂²	1	2	yes	complemented
28	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
29	C₅×#936	C₂²	1	8	yes	complemented
30	C₅×#935	C₂²	1	8	yes	complemented
31	C₅×#935	C₂²	1	16	yes	complemented
32	C₅×D₄×Dic₃	C₂²	1	16	yes	complemented
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
39	C₅×#879	C₂²	1	16	yes	complemented
40	C₅×#878	C₂²	1	16	yes	complemented
41	C₅×#877	C₂²	1	16	yes	complemented
42	C₂×#5587	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#551	—	3	16	no	—
44	C₂×C₅×#126	—	3	2	no	—
45	C₂×C₅×#124	—	3	1	no	—
46	C₂×C₅×#123	—	3	2	no	—
47	C₂×C₅×#123	—	3	1	no	—
48	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
49	C₂×C₅×#120	D₃	1	1	yes	characteristic
50	C₂×C₄×C₅×D₄	—	3	2	no	—
51	C₂×C₅×#117	—	3	2	no	—
52	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
53	C₂⁴×C₃×C₅	—	2	8	no	—
54	C₂⁴×C₃×C₅	—	4	2	no	—
55	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
56	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
57	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
58	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	—	2	8	no	—
60	C₂×C₃×C₅×D₄	—	4	2	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
62	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₅×Dic₃	—	2	8	no	—
66	C₂²×C₅×Dic₃	—	4	4	no	—
67	C₂²×C₅×Dic₃	—	4	2	no	—
68	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
69	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
72	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
75	C₂×C₅×Dic₆	—	4	2	no	—
76	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
77	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
78	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
79	C₅×#217	C₂³	1	8	yes	—
80	C₅×#217	C₂³	1	8	yes	—
81	C₅×#217	C₂³	1	8	yes	—
82	C₅×#217	C₂³	1	8	yes	—
83	C₅×#217	C₂³	1	8	yes	complemented
84	C₅×#217	C₂³	1	4	yes	complemented
85	C₅×C₄⋊Dic₃	C₂³	1	8	yes	complemented
86	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
87	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
88	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
89	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
90	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
91	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
92	C₂²×#217	C₂×C₅	1	2	yes	complemented
93	C₂×#936	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#935	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#935	C₂×C₅	1	2	yes	complemented
96	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	complemented
97	#5587	C₂×C₅	1	16	yes	direct product factor
98	C₂×#879	C₂×C₅	1	2	yes	complemented
99	C₂×#878	C₂×C₅	1	2	yes	complemented
100	C₂×#877	C₂×C₅	1	2	yes	complemented
101	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
102	C₂²×C₅×Q₈	—	3	1	no	—
103	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
104	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
105	C₂³×C₄×C₅	—	3	2	no	—
106	C₂³×C₄×C₅	—	3	2	no	—
107	C₂³×C₄×C₅	—	3	1	no	—
108	C₅×#126	—	3	16	no	—
109	C₅×#124	—	3	8	no	—
110	C₅×#123	—	3	16	no	—
111	C₅×#123	—	3	8	no	—
112	C₅×C₂²⋊Q₈	—	3	16	no	—
113	C₅×#120	C₂×D₃	1	8	yes	—
114	C₄×C₅×D₄	—	3	16	no	—
115	C₅×#117	—	3	16	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×C₂²⋊C₄	—	3	2	no	—
121	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
122	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
123	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
124	C₂×C₅×C₂²⋊C₄	—	3	16	no	—
125	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
126	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
127	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₂×C₄²×C₅	—	3	1	no	—
130	C₂×C₄²×C₅	—	3	2	no	—
131	C₂×#551	—	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	—	2	16	no	—
136	C₂³×C₃×C₅	—	2	4	no	—
137	C₂³×C₃×C₅	—	2	2	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	—	4	4	no	—
140	C₂³×C₃×C₅	—	4	16	no	—
141	C₂³×C₃×C₅	#41	1	8	yes	—
142	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
143	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
144	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
145	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×C₅×D₄	—	2	16	no	—
147	C₃×C₅×D₄	—	4	4	no	—
148	C₂×C₃×C₄×C₅	—	2	4	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
152	C₂×C₅×Dic₃	—	2	16	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	—	2	4	no	—
157	C₂×C₅×Dic₃	—	4	8	no	—
158	C₂×C₅×Dic₃	—	4	4	no	—
159	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
160	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
161	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
162	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
163	C₅×Dic₆	—	4	4	no	—
164	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
166	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
167	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
168	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
169	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₃×#120	C₂²×C₅	1	8	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×#217	C₂²×C₅	1	2	yes	—
175	C₂×#217	C₂²×C₅	1	2	yes	—
176	C₂×#217	C₂²×C₅	1	2	yes	—
177	C₂×#217	C₂²×C₅	1	2	yes	—
178	C₂×#217	C₂²×C₅	1	16	yes	complemented
179	C₂×#217	C₂²×C₅	1	2	yes	complemented
180	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
181	#936	C₂²×C₅	1	8	yes	complemented
182	#935	C₂²×C₅	1	8	yes	complemented
183	#935	C₂²×C₅	1	16	yes	complemented
184	D₄×Dic₃	C₂²×C₅	1	16	yes	complemented
185	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
186	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
187	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
188	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
189	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
191	#879	C₂²×C₅	1	16	yes	complemented
192	#878	C₂²×C₅	1	16	yes	complemented
193	#877	C₂²×C₅	1	16	yes	complemented
194	C₂⁴×C₅	—	2	8	no	—
195	C₂⁴×C₅	—	4	2	no	—
196	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
199	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
200	C₂×C₅×Q₈	—	3	4	no	—
201	C₂×C₅×Q₈	—	12	2	no	—
202	C₂×C₅×D₄	—	2	8	no	—
203	C₂×C₅×D₄	—	4	2	no	—
204	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
205	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
206	C₂²×C₄×C₅	—	3	8	no	—
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	2	no	—
211	C₂²×C₄×C₅	—	3	8	no	—
212	C₂²×C₄×C₅	—	3	4	no	—
213	C₂²×C₄×C₅	—	6	8	no	—
214	C₂²×C₄×C₅	—	12	2	no	—
215	C₂²×C₄×C₅	—	12	4	no	—
216	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
217	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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×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	—	3	8	no	—
227	C₅×C₂²⋊C₄	—	3	4	no	—
228	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
229	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
230	C₄²×C₅	—	3	4	no	—
231	C₄²×C₅	—	3	8	no	—
232	#551	—	3	16	no	—
233	C₂×#126	—	3	2	no	—
234	C₂×#124	—	3	1	no	—
235	C₂×#123	—	3	2	no	—
236	C₂×#123	—	3	1	no	—
237	C₂×C₂²⋊Q₈	—	3	2	no	—
238	C₂×#120	C₅×D₃	1	1	yes	characteristic
239	C₂×C₄×D₄	—	3	2	no	—
240	C₂×#117	—	3	2	no	—
241	C₂²×C₂²⋊C₄	—	3	2	no	—
242	C₂²×C₃×C₅	—	2	16	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	2	4	no	—
245	C₂²×C₃×C₅	—	2	4	no	—
246	C₂²×C₃×C₅	—	2	4	no	—
247	C₂²×C₃×C₅	—	2	2	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	4	16	no	—
250	C₂²×C₃×C₅	—	4	4	no	—
251	C₂²×C₃×C₅	—	4	4	no	—
252	C₂²×C₃×C₅	C₂×#41	1	8	yes	—
253	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
254	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
255	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
256	C₃×C₄×C₅	—	2	4	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₅×Dic₃	—	2	4	no	—
259	C₅×Dic₃	—	2	4	no	—
260	C₅×Dic₃	—	2	4	no	—
261	C₅×Dic₃	—	2	4	no	—
262	C₂⁴×C₃	—	2	8	no	—
263	C₂⁴×C₃	—	4	2	no	—
264	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
265	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
266	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
267	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
268	C₂×C₃×D₄	—	2	8	no	—
269	C₂×C₃×D₄	—	4	2	no	—
270	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
271	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂²×Dic₃	—	2	8	no	—
275	C₂²×Dic₃	—	4	4	no	—
276	C₂²×Dic₃	—	4	2	no	—
277	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
278	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
279	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
280	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
281	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
282	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
283	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
284	C₂×Dic₆	—	4	2	no	—
285	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
286	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
287	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
288	#217	C₂³×C₅	1	8	yes	—
289	#217	C₂³×C₅	1	8	yes	—
290	#217	C₂³×C₅	1	8	yes	—
291	#217	C₂³×C₅	1	8	yes	—
292	#217	C₂³×C₅	1	8	yes	complemented
293	#217	C₂³×C₅	1	4	yes	complemented
294	C₄⋊Dic₃	C₂³×C₅	1	8	yes	complemented
295	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
296	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
297	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
298	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
299	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
300	C₂³×C₅	—	2	4	no	—
301	C₂³×C₅	—	2	4	no	—
302	C₂³×C₅	—	2	4	no	—
303	C₂³×C₅	—	2	16	no	—
304	C₂³×C₅	—	2	4	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	4	4	no	—
308	C₂³×C₅	—	4	16	no	—
309	C₂³×C₅	#237	1	8	yes	—
310	C₂³×C₅	C₂³×D₃	1	2	yes	—
311	C₂³×C₅	C₂³×D₃	1	2	yes	—
312	C₂³×C₅	C₂³×D₃	1	4	yes	—
313	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
314	C₅×Q₈	—	12	4	no	—
315	C₅×D₄	—	2	16	no	—
316	C₅×D₄	—	4	4	no	—
317	C₂×C₄×C₅	—	2	4	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	3	4	no	—
320	C₂×C₄×C₅	—	3	4	no	—
321	C₂×C₄×C₅	—	3	4	no	—
322	C₂×C₄×C₅	—	3	4	no	—
323	C₂×C₄×C₅	—	6	16	no	—
324	C₂×C₄×C₅	—	6	4	no	—
325	C₂×C₄×C₅	—	6	4	no	—
326	C₂×C₄×C₅	—	6	4	no	—
327	C₂×C₄×C₅	—	6	4	no	—
328	C₂×C₄×C₅	—	12	4	no	—
329	C₂×C₄×C₅	—	12	8	no	—
330	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
331	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
332	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂²×Q₈	—	3	1	no	—
334	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
335	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
336	C₂³×C₄	—	3	2	no	—
337	C₂³×C₄	—	3	2	no	—
338	C₂³×C₄	—	3	1	no	—
339	#126	—	3	16	no	—
340	#124	—	3	8	no	—
341	#123	—	3	16	no	—
342	#123	—	3	8	no	—
343	C₂²⋊Q₈	—	3	16	no	—
344	#120	C₂×C₅×D₃	1	8	yes	—
345	C₄×D₄	—	3	16	no	—
346	#117	—	3	16	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	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	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	16	no	—
356	C₂×C₂²⋊C₄	—	3	2	no	—
357	C₂×C₂²⋊C₄	—	3	1	no	—
358	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
360	C₂×C₄²	—	3	1	no	—
361	C₂×C₄²	—	3	2	no	—
362	C₂×C₃×C₅	—	2	8	no	—
363	C₂×C₃×C₅	—	4	2	no	—
364	C₂×C₃×C₅	—	4	2	no	—
365	C₂×C₃×C₅	#551	1	4	yes	complemented
366	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
367	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂³×C₃	—	2	4	no	—
369	C₂³×C₃	—	2	4	no	—
370	C₂³×C₃	—	2	4	no	—
371	C₂³×C₃	—	2	16	no	—
372	C₂³×C₃	—	2	4	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	4	4	no	—
376	C₂³×C₃	—	4	16	no	—
377	C₂³×C₃	C₅×#41	1	8	yes	—
378	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
379	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
380	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
381	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
382	C₃×D₄	—	2	16	no	—
383	C₃×D₄	—	4	4	no	—
384	C₂×C₃×C₄	—	2	4	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
387	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
388	C₂×Dic₃	—	2	16	no	—
389	C₂×Dic₃	—	2	4	no	—
390	C₂×Dic₃	—	2	4	no	—
391	C₂×Dic₃	—	2	4	no	—
392	C₂×Dic₃	—	2	4	no	—
393	C₂×Dic₃	—	4	8	no	—
394	C₂×Dic₃	—	4	4	no	—
395	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
396	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
397	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
398	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
399	Dic₆	—	4	4	no	—
400	C₂²×C₅	—	2	4	no	—
401	C₂²×C₅	—	2	4	no	—
402	C₂²×C₅	—	2	16	no	—
403	C₂²×C₅	—	2	4	no	—
404	C₂²×C₅	—	2	4	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	4	16	no	—
408	C₂²×C₅	—	4	4	no	—
409	C₂²×C₅	—	4	4	no	—
410	C₂²×C₅	C₂×#237	1	8	yes	—
411	C₂²×C₅	C₂×#237	1	4	yes	—
412	C₂²×C₅	#1004	1	2	yes	—
413	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
414	C₄×C₅	—	2	4	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	6	4	no	—
417	C₄×C₅	—	6	4	no	—
418	C₄×C₅	—	6	4	no	—
419	C₄×C₅	—	6	4	no	—
420	C₂⁴	—	2	8	no	—
421	C₂⁴	—	4	2	no	—
422	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
424	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
425	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
426	C₂×Q₈	—	3	4	no	—
427	C₂×Q₈	—	12	2	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
431	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	—	3	8	no	—
437	C₂²×C₄	—	3	8	no	—
438	C₂²×C₄	—	3	4	no	—
439	C₂²×C₄	—	6	8	no	—
440	C₂²×C₄	—	12	2	no	—
441	C₂²×C₄	—	12	4	no	—
442	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
443	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
444	C₄⋊C₄	—	3	8	no	—
445	C₄⋊C₄	—	3	8	no	—
446	C₄⋊C₄	—	3	8	no	—
447	C₄⋊C₄	—	3	8	no	—
448	C₂²⋊C₄	—	3	8	no	—
449	C₂²⋊C₄	—	3	8	no	—
450	C₂²⋊C₄	—	3	8	no	—
451	C₂²⋊C₄	—	3	8	no	—
452	C₂²⋊C₄	—	3	8	no	—
453	C₂²⋊C₄	—	3	4	no	—
454	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
455	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
456	C₄²	—	3	4	no	—
457	C₄²	—	3	8	no	—
458	C₃×C₅	C₂×#551	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	16	no	—
460	C₂²×C₃	—	2	4	no	—
461	C₂²×C₃	—	2	4	no	—
462	C₂²×C₃	—	2	4	no	—
463	C₂²×C₃	—	2	4	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	4	16	no	—
467	C₂²×C₃	—	4	4	no	—
468	C₂²×C₃	—	4	4	no	—
469	C₂²×C₃	C₂×C₅×#41	1	8	yes	—
470	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
471	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
472	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	—	2	2	no	—
475	Dic₃	—	2	4	no	—
476	Dic₃	—	2	4	no	—
477	Dic₃	—	2	4	no	—
478	Dic₃	—	2	4	no	—
479	C₂×C₅	—	2	8	no	—
480	C₂×C₅	—	4	2	no	—
481	C₂×C₅	—	4	2	no	—
482	C₂×C₅	#5587	1	4	yes	direct product factor
483	C₂×C₅	C₂²×#237	1	2	yes	—
484	C₂×C₅	C₂×#1004	1	1	yes	characteristic
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	16	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	16	no	—
494	C₂³	C₅×#237	1	8	yes	—
495	C₂³	C₂³×C₅×D₃	1	2	yes	—
496	C₂³	C₂³×C₅×D₃	1	2	yes	—
497	C₂³	C₂³×C₅×D₃	1	4	yes	—
498	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
499	Q₈	—	12	4	no	—
500	D₄	—	2	16	no	—
501	D₄	—	4	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	3	4	no	—
505	C₂×C₄	—	3	4	no	—
506	C₂×C₄	—	3	4	no	—
507	C₂×C₄	—	3	4	no	—
508	C₂×C₄	—	6	16	no	—
509	C₂×C₄	—	6	4	no	—
510	C₂×C₄	—	6	4	no	—
511	C₂×C₄	—	6	4	no	—
512	C₂×C₄	—	6	4	no	—
513	C₂×C₄	—	12	4	no	—
514	C₂×C₄	—	12	8	no	—
515	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
516	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
517	C₂×C₃	—	2	8	no	—
518	C₂×C₃	—	4	2	no	—
519	C₂×C₃	—	4	2	no	—
520	C₂×C₃	C₅×#551	1	4	yes	complemented
521	C₂×C₃	C₂²×C₅×#41	1	2	yes	—
522	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
523	C₅	C₂×#5587	1	1	yes	characteristic, direct product factor, Sylow
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	16	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	16	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	4	no	—
534	C₂²	C₂×C₅×#237	1	8	yes	—
535	C₂²	C₂×C₅×#237	1	4	yes	—
536	C₂²	C₅×#1004	1	2	yes	—
537	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
538	C₄	—	2	4	no	—
539	C₄	—	2	2	no	—
540	C₄	—	6	4	no	—
541	C₄	—	6	4	no	—
542	C₄	—	6	4	no	—
543	C₄	—	6	4	no	—
544	C₃	C₂×C₅×#551	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	2	8	no	—
546	C₂	—	4	2	no	—
547	C₂	—	4	2	no	—
548	C₂	C₅×#5587	1	4	yes	direct product factor
549	C₂	C₂²×C₅×#237	1	2	yes	—
550	C₂	C₂×C₅×#1004	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×#120	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#120	D₃
hypocenter	C₃	C₂×C₅×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#120

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#217	C₂	semidirect
3. C₂×C₅×#936	C₂	semidirect
4. C₂×C₅×#935	C₂	semidirect
5. C₂×C₅×#935	C₂	semidirect
6. C₂×C₅×D₄×Dic₃	C₂	semidirect
7. C₅×#5587	C₂	direct (N × H)
8. C₂×C₅×#879	C₂	semidirect
9. C₂×C₅×#878	C₂	semidirect
10. C₂×C₅×#877	C₂	semidirect
17. C₂³×C₅×Dic₃	C₂²	semidirect
18. C₂²×C₅×Dic₆	C₂²	semidirect
26. C₂×C₅×#217	C₂²	semidirect
27. C₂×C₅×#217	C₂²	semidirect
28. C₂×C₅×#217	C₂²	semidirect
29. C₅×#936	C₂²	semidirect
30. C₅×#935	C₂²	semidirect
31. C₅×#935	C₂²	semidirect
32. C₅×D₄×Dic₃	C₂²	semidirect
33. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
34. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
35. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
36. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₂×C₄×C₅×Dic₃	C₂²	semidirect
38. C₂×C₄×C₅×Dic₃	C₂²	semidirect
39. C₅×#879	C₂²	semidirect
40. C₅×#878	C₂²	semidirect
41. C₅×#877	C₂²	semidirect
42. C₂×#5587	C₅	direct (N × H)
74. C₂²×C₅×Dic₃	C₂³	semidirect
76. C₂×C₅×Dic₆	C₂³	semidirect
83. C₅×#217	C₂³	semidirect
84. C₅×#217	C₂³	semidirect
85. C₅×C₄⋊Dic₃	C₂³	semidirect
86. C₅×Dic₃⋊C₄	C₂³	semidirect
87. C₅×Dic₃⋊C₄	C₂³	semidirect
88. C₅×Dic₃⋊C₄	C₂³	semidirect
89. C₄×C₅×Dic₃	C₂³	semidirect
90. C₄×C₅×Dic₃	C₂³	semidirect
92. C₂²×#217	C₂×C₅	semidirect
93. C₂×#936	C₂×C₅	semidirect
94. C₂×#935	C₂×C₅	semidirect
95. C₂×#935	C₂×C₅	semidirect
96. C₂×D₄×Dic₃	C₂×C₅	semidirect
97. #5587	C₂×C₅	direct (N × H)
98. C₂×#879	C₂×C₅	semidirect
99. C₂×#878	C₂×C₅	semidirect
100. C₂×#877	C₂×C₅	semidirect
169. C₂³×Dic₃	C₂²×C₅	semidirect
170. C₂²×Dic₆	C₂²×C₅	semidirect
178. C₂×#217	C₂²×C₅	semidirect
179. C₂×#217	C₂²×C₅	semidirect
180. C₂×#217	C₂²×C₅	semidirect
181. #936	C₂²×C₅	semidirect
182. #935	C₂²×C₅	semidirect
183. #935	C₂²×C₅	semidirect
184. D₄×Dic₃	C₂²×C₅	semidirect
185. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
186. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
187. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
188. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
189. C₂×C₄×Dic₃	C₂²×C₅	semidirect
190. C₂×C₄×Dic₃	C₂²×C₅	semidirect
191. #879	C₂²×C₅	semidirect
192. #878	C₂²×C₅	semidirect
193. #877	C₂²×C₅	semidirect
283. C₂²×Dic₃	C₂³×C₅	semidirect
285. C₂×Dic₆	C₂³×C₅	semidirect
292. #217	C₂³×C₅	semidirect
293. #217	C₂³×C₅	semidirect
294. C₄⋊Dic₃	C₂³×C₅	semidirect
295. Dic₃⋊C₄	C₂³×C₅	semidirect
296. Dic₃⋊C₄	C₂³×C₅	semidirect
297. Dic₃⋊C₄	C₂³×C₅	semidirect
298. C₄×Dic₃	C₂³×C₅	semidirect
299. C₄×Dic₃	C₂³×C₅	semidirect
365. C₂×C₃×C₅	#551	semidirect
458. C₃×C₅	C₂×#551	semidirect
482. C₂×C₅	#5587	direct (N × H)
520. C₂×C₃	C₅×#551	semidirect
523. C₅	C₂×#5587	direct (N × H)
544. C₃	C₂×C₅×#551	semidirect
548. C₂	C₅×#5587	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×#120	2
C₂²×C₅×#217	2
C₂×C₅×#936	2
C₂×C₅×#935	2
C₂×C₅×D₄×Dic₃	2
C₅×#5587	2
C₂×C₅×#879	2
C₂×C₅×#878	2
C₂×C₅×#877	2
C₂×C₅×#551	3
C₂×#5587	5

Subgroups — C2×C5×#5587 #14483256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5587 #14483256