Subgroups — C₅×D₃×#518 #14478948

Order 1920.

3840 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5798	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5545	C₂	1	8	yes	maximal, complemented
5	C₄×C₅×D₃×D₄	C₂	1	8	yes	maximal, complemented
6	C₅×#5521	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#117	C₂	1	2	yes	maximal, complemented
8	C₅×#5486	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
10	C₂×C₅×#518	—	3	1	no	maximal, Hall
11	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₅×#67	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	C₄	1	16	yes	complemented
15	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
16	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	8	yes	complemented
20	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
21	C₃×C₅×#117	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
23	C₂×C₅×#217	C₂²	1	4	yes	complemented
24	C₅×D₄×Dic₃	C₂²	1	8	yes	complemented
25	C₄×C₅×#67	C₂²	1	16	yes	complemented
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
27	C₅×#926	C₂²	1	2	yes	complemented
28	C₅×#893	C₂²	1	8	yes	complemented
29	C₅×#892	C₂²	1	4	yes	complemented
30	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
31	C₅×#67⋊C₄	C₂²	1	16	yes	complemented
32	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
33	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
34	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
35	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
36	C₅×#877	C₂²	1	4	yes	complemented
37	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
38	C₅×#872	C₂²	1	4	yes	complemented
39	C₄²×C₅×D₃	C₂²	1	4	yes	complemented
40	D₃×#518	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂³×C₅×D₄	—	3	1	no	—
42	C₅×#518	—	3	1	no	—
43	C₅×#518	—	3	8	no	—
44	C₅×#518	—	3	2	no	—
45	C₅×#518	—	3	4	no	—
46	C₅×#518	D₃	1	1	yes	characteristic, direct product factor
47	C₂×C₄×C₅×D₄	—	3	8	no	—
48	C₂×C₅×#117	—	3	2	no	—
49	C₂²×C₅×C₂²⋊C₄	—	3	4	no	—
50	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
51	C₂³×C₅×D₃	—	4	8	no	—
52	C₂³×C₅×D₃	C₂×C₄	1	16	yes	complemented
53	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₂³×C₅×D₃	C₂³	1	4	yes	—
55	C₂³×C₅×D₃	C₂³	1	2	yes	—
56	C₂³×C₅×D₃	C₂³	1	4	yes	—
57	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
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	8	yes	complemented
61	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
62	C₂×C₅×#67	C₂³	1	8	yes	—
63	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Dic₃	C₂³	1	8	yes	complemented
65	C₅×D₃×D₄	C₂×C₄	1	32	yes	complemented
66	C₅×D₃×D₄	C₂×C₄	1	32	yes	complemented
67	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
68	C₂×C₅×D₁₂	C₂³	1	4	yes	—
69	C₂×C₄×C₅×D₃	—	4	16	no	—
70	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
71	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
72	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
73	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
74	C₂×C₄×C₅×D₃	C₂³	1	16	yes	complemented
75	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
76	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
77	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
78	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
79	C₅×#217	C₂³	1	4	yes	—
80	C₅×#217	C₂³	1	8	yes	complemented
81	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
82	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
83	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
84	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
85	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
86	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
87	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic
88	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
89	#5798	C₂×C₅	1	1	yes	characteristic, complemented
90	#5545	C₂×C₅	1	8	yes	complemented
91	C₄×D₃×D₄	C₂×C₅	1	8	yes	complemented
92	#5521	C₂×C₅	1	2	yes	complemented
93	D₃×#117	C₂×C₅	1	2	yes	complemented
94	#5486	C₂×C₅	1	4	yes	complemented
95	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
96	C₂⁵×C₅	—	3	2	no	—
97	C₂²×C₅×D₄	—	3	2	no	—
98	C₂²×C₅×D₄	—	3	16	no	—
99	C₂²×C₅×D₄	—	3	4	no	—
100	C₂²×C₅×D₄	—	3	4	no	—
101	C₂²×C₅×D₄	—	3	1	no	—
102	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
103	C₂³×C₄×C₅	—	3	1	no	—
104	C₂³×C₄×C₅	—	3	8	no	—
105	C₄×C₅×D₄	—	3	8	no	—
106	C₄×C₅×D₄	—	3	16	no	—
107	C₄×C₅×D₄	—	3	8	no	—
108	C₄×C₅×D₄	—	3	16	no	—
109	C₄×C₅×D₄	—	3	8	no	—
110	C₄×C₅×D₄	C₂×D₃	1	8	yes	complemented
111	C₅×#117	—	3	2	no	—
112	C₅×#117	—	3	4	no	—
113	C₅×#117	—	3	4	no	—
114	C₅×#117	—	3	4	no	—
115	C₅×#117	C₂×D₃	1	2	yes	complemented
116	C₂×C₅×C₄⋊C₄	—	3	4	no	—
117	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
118	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
119	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
120	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
121	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
122	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
123	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
124	C₂×C₄²×C₅	—	3	4	no	—
125	C₂×#518	—	3	1	no	Sylow
126	C₂³×C₃×C₅	—	4	4	no	—
127	C₂³×C₃×C₅	C₂²×C₄	1	8	yes	complemented
128	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
129	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
130	C₂²×C₅×D₃	—	2	16	no	—
131	C₂²×C₅×D₃	—	2	4	no	—
132	C₂²×C₅×D₃	—	4	32	no	—
133	C₂²×C₅×D₃	—	4	4	no	—
134	C₂²×C₅×D₃	—	4	8	no	—
135	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
136	C₂²×C₅×D₃	C₂²×C₄	1	16	yes	—
137	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	complemented
138	C₂²×C₅×D₃	C₂²×C₄	1	16	yes	complemented
139	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
140	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
141	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
142	C₃×C₅×D₄	C₂²×C₄	1	16	yes	complemented
143	C₂×C₃×C₄×C₅	—	4	8	no	—
144	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	complemented
145	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
147	C₅×#67	C₂²×C₄	1	32	yes	complemented
148	C₂×C₅×Dic₃	—	4	8	no	—
149	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	complemented
150	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
151	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
152	C₅×D₁₂	C₂²×C₄	1	16	yes	complemented
153	C₄×C₅×D₃	—	2	16	no	—
154	C₄×C₅×D₃	—	4	16	no	—
155	C₄×C₅×D₃	C₂²×C₄	1	8	yes	—
156	C₄×C₅×D₃	C₂²×C₄	1	8	yes	complemented
157	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
158	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
159	C₂²×#67	C₂²×C₅	1	2	yes	—
160	C₂×D₃×D₄	C₄×C₅	1	16	yes	complemented
161	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
162	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
163	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₄×D₃	C₂²×C₅	1	8	yes	complemented
166	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
167	C₃×#117	C₂²×C₅	1	2	yes	complemented
168	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
169	C₂×#217	C₂²×C₅	1	4	yes	complemented
170	D₄×Dic₃	C₂²×C₅	1	8	yes	complemented
171	C₄×#67	C₂²×C₅	1	16	yes	complemented
172	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
173	#926	C₂²×C₅	1	2	yes	complemented
174	#893	C₂²×C₅	1	8	yes	complemented
175	#892	C₂²×C₅	1	4	yes	complemented
176	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
177	#67⋊C₄	C₂²×C₅	1	16	yes	complemented
178	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
179	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
180	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
181	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
182	#877	C₂²×C₅	1	4	yes	complemented
183	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
184	#872	C₂²×C₅	1	4	yes	complemented
185	C₄²×D₃	C₂²×C₅	1	4	yes	complemented
186	C₂⁴×C₅	—	3	1	no	—
187	C₂⁴×C₅	—	3	4	no	—
188	C₂⁴×C₅	—	3	16	no	—
189	C₂⁴×C₅	—	3	4	no	—
190	C₂⁴×C₅	—	3	2	no	—
191	C₂⁴×C₅	—	12	8	no	—
192	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
193	C₂×C₅×D₄	—	3	16	no	—
194	C₂×C₅×D₄	—	3	8	no	—
195	C₂×C₅×D₄	—	3	32	no	—
196	C₂×C₅×D₄	—	3	32	no	—
197	C₂×C₅×D₄	—	3	8	no	—
198	C₂×C₅×D₄	—	3	4	no	—
199	C₂×C₅×D₄	C₄×D₃	1	8	yes	complemented
200	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
201	C₂²×C₄×C₅	—	3	1	no	—
202	C₂²×C₄×C₅	—	3	8	no	—
203	C₂²×C₄×C₅	—	3	2	no	—
204	C₂²×C₄×C₅	—	3	2	no	—
205	C₂²×C₄×C₅	—	3	8	no	—
206	C₂²×C₄×C₅	—	3	8	no	—
207	C₂²×C₄×C₅	—	3	16	no	—
208	C₂²×C₄×C₅	—	12	16	no	—
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	complemented
211	C₅×C₄⋊C₄	—	3	8	no	—
212	C₅×C₄⋊C₄	—	3	4	no	—
213	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
214	C₅×C₂²⋊C₄	—	3	4	no	—
215	C₅×C₂²⋊C₄	—	3	8	no	—
216	C₅×C₂²⋊C₄	—	3	8	no	—
217	C₅×C₂²⋊C₄	—	3	16	no	—
218	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
219	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
220	C₄²×C₅	—	3	8	no	—
221	C₄²×C₅	—	3	4	no	—
222	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
223	C₂³×D₄	—	3	1	no	—
224	#518	—	3	1	no	—
225	#518	—	3	8	no	—
226	#518	—	3	2	no	—
227	#518	—	3	4	no	—
228	#518	C₅×D₃	1	1	yes	characteristic, direct product factor
229	C₂×C₄×D₄	—	3	8	no	—
230	C₂×#117	—	3	2	no	—
231	C₂²×C₂²⋊C₄	—	3	4	no	—
232	C₂²×C₃×C₅	—	2	8	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	—	4	8	no	—
235	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
236	C₂²×C₃×C₅	C₂³×C₄	1	8	yes	—
237	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
238	C₂×C₅×D₃	—	2	8	no	—
239	C₂×C₅×D₃	—	2	2	no	—
240	C₂×C₅×D₃	—	2	8	no	—
241	C₂×C₅×D₃	—	2	32	no	—
242	C₂×C₅×D₃	—	4	16	no	—
243	C₂×C₅×D₃	—	4	8	no	—
244	C₂×C₅×D₃	C₂³×C₄	1	2	yes	—
245	C₂×C₅×D₃	C₂³×C₄	1	8	yes	—
246	C₂×C₅×D₃	C₂³×C₄	1	2	yes	—
247	C₂×C₅×D₃	H(5,𝔽₂)	1	4	yes	—
248	C₃×C₄×C₅	—	2	8	no	—
249	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
250	C₅×Dic₃	—	2	8	no	—
251	C₅×Dic₃	C₂³×C₄	1	4	yes	—
252	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
253	C₂³×D₃	—	4	8	no	—
254	C₂³×D₃	C₂×C₄×C₅	1	16	yes	complemented
255	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
256	C₂³×D₃	C₂³×C₅	1	4	yes	—
257	C₂³×D₃	C₂³×C₅	1	2	yes	—
258	C₂³×D₃	C₂³×C₅	1	4	yes	—
259	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
260	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
261	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	complemented
263	C₂×#67	C₂×C₄×C₅	1	16	yes	complemented
264	C₂×#67	C₂³×C₅	1	8	yes	—
265	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
266	C₂²×Dic₃	C₂³×C₅	1	8	yes	complemented
267	D₃×D₄	C₂×C₄×C₅	1	32	yes	complemented
268	D₃×D₄	C₂×C₄×C₅	1	32	yes	complemented
269	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
270	C₂×D₁₂	C₂³×C₅	1	4	yes	—
271	C₂×C₄×D₃	—	4	16	no	—
272	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
273	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
274	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
275	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
276	C₂×C₄×D₃	C₂³×C₅	1	16	yes	complemented
277	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
278	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
279	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
280	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
281	#217	C₂³×C₅	1	4	yes	—
282	#217	C₂³×C₅	1	8	yes	complemented
283	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
284	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
285	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
286	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
287	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
288	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
289	C₂³×C₅	—	3	1	no	—
290	C₂³×C₅	—	3	4	no	—
291	C₂³×C₅	—	3	16	no	—
292	C₂³×C₅	—	3	1	no	—
293	C₂³×C₅	—	3	4	no	—
294	C₂³×C₅	—	3	16	no	—
295	C₂³×C₅	—	3	8	no	—
296	C₂³×C₅	—	4	4	no	—
297	C₂³×C₅	—	6	16	no	—
298	C₂³×C₅	—	6	4	no	—
299	C₂³×C₅	—	12	8	no	—
300	C₂³×C₅	—	12	4	no	—
301	C₂³×C₅	—	12	32	no	—
302	C₂³×C₅	C₂×C₄×D₃	1	8	yes	complemented
303	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₂³×C₅	C₂³×D₃	1	4	yes	—
305	C₅×D₄	—	3	32	no	—
306	C₅×D₄	—	3	16	no	—
307	C₅×D₄	C₂×C₄×D₃	1	16	yes	complemented
308	C₂×C₄×C₅	—	3	4	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	3	8	no	—
311	C₂×C₄×C₅	—	3	8	no	—
312	C₂×C₄×C₅	—	3	8	no	—
313	C₂×C₄×C₅	—	4	8	no	—
314	C₂×C₄×C₅	—	6	16	no	—
315	C₂×C₄×C₅	—	12	16	no	—
316	C₂×C₄×C₅	—	12	8	no	—
317	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	complemented
318	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
319	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
320	C₂⁵	—	3	2	no	—
321	C₂²×D₄	—	3	2	no	—
322	C₂²×D₄	—	3	16	no	—
323	C₂²×D₄	—	3	4	no	—
324	C₂²×D₄	—	3	4	no	—
325	C₂²×D₄	—	3	1	no	—
326	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
327	C₂³×C₄	—	3	1	no	—
328	C₂³×C₄	—	3	8	no	—
329	C₄×D₄	—	3	8	no	—
330	C₄×D₄	—	3	16	no	—
331	C₄×D₄	—	3	8	no	—
332	C₄×D₄	—	3	16	no	—
333	C₄×D₄	—	3	8	no	—
334	C₄×D₄	C₂×C₅×D₃	1	8	yes	complemented
335	#117	—	3	2	no	—
336	#117	—	3	4	no	—
337	#117	—	3	4	no	—
338	#117	—	3	4	no	—
339	#117	C₂×C₅×D₃	1	2	yes	complemented
340	C₂×C₄⋊C₄	—	3	4	no	—
341	C₂×C₂²⋊C₄	—	3	4	no	—
342	C₂×C₂²⋊C₄	—	3	8	no	—
343	C₂×C₂²⋊C₄	—	3	4	no	—
344	C₂×C₂²⋊C₄	—	3	8	no	—
345	C₂×C₂²⋊C₄	—	3	8	no	—
346	C₂×C₂²⋊C₄	—	3	8	no	—
347	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
348	C₂×C₄²	—	3	4	no	—
349	C₂×C₃×C₅	—	2	2	no	—
350	C₂×C₃×C₅	—	2	8	no	—
351	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
352	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
353	C₅×D₃	—	2	2	no	—
354	C₅×D₃	—	2	8	no	—
355	C₅×D₃	#518	1	4	yes	direct product factor
356	C₂³×C₃	—	4	4	no	—
357	C₂³×C₃	C₂²×C₄×C₅	1	8	yes	complemented
358	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
359	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
360	C₂²×D₃	—	2	16	no	—
361	C₂²×D₃	—	2	4	no	—
362	C₂²×D₃	—	4	32	no	—
363	C₂²×D₃	—	4	4	no	—
364	C₂²×D₃	—	4	8	no	—
365	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
366	C₂²×D₃	C₂²×C₄×C₅	1	16	yes	—
367	C₂²×D₃	C₂²×C₄×C₅	1	8	yes	complemented
368	C₂²×D₃	C₂²×C₄×C₅	1	16	yes	complemented
369	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
370	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
371	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
372	C₃×D₄	C₂²×C₄×C₅	1	16	yes	complemented
373	C₂×C₃×C₄	—	4	8	no	—
374	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	complemented
375	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
376	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
377	#67	C₂²×C₄×C₅	1	32	yes	complemented
378	C₂×Dic₃	—	4	8	no	—
379	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	complemented
380	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
381	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
382	D₁₂	C₂²×C₄×C₅	1	16	yes	complemented
383	C₄×D₃	—	2	16	no	—
384	C₄×D₃	—	4	16	no	—
385	C₄×D₃	C₂²×C₄×C₅	1	8	yes	—
386	C₄×D₃	C₂²×C₄×C₅	1	8	yes	complemented
387	C₂²×C₅	—	2	8	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	3	2	no	—
390	C₂²×C₅	—	3	4	no	—
391	C₂²×C₅	—	3	2	no	—
392	C₂²×C₅	—	3	8	no	—
393	C₂²×C₅	—	4	8	no	—
394	C₂²×C₅	—	6	32	no	—
395	C₂²×C₅	—	6	8	no	—
396	C₂²×C₅	—	6	8	no	—
397	C₂²×C₅	—	6	2	no	—
398	C₂²×C₅	—	12	8	no	—
399	C₂²×C₅	—	12	16	no	—
400	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
401	C₂²×C₅	C₂²×C₄×D₃	1	8	yes	—
402	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
403	C₄×C₅	—	2	8	no	—
404	C₄×C₅	—	3	4	no	—
405	C₄×C₅	—	6	8	no	—
406	C₄×C₅	C₂²×C₄×D₃	1	4	yes	—
407	C₂⁴	—	3	1	no	—
408	C₂⁴	—	3	4	no	—
409	C₂⁴	—	3	16	no	—
410	C₂⁴	—	3	4	no	—
411	C₂⁴	—	3	2	no	—
412	C₂⁴	—	12	8	no	—
413	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
414	C₂×D₄	—	3	16	no	—
415	C₂×D₄	—	3	8	no	—
416	C₂×D₄	—	3	32	no	—
417	C₂×D₄	—	3	32	no	—
418	C₂×D₄	—	3	8	no	—
419	C₂×D₄	—	3	4	no	—
420	C₂×D₄	C₄×C₅×D₃	1	8	yes	complemented
421	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
422	C₂²×C₄	—	3	1	no	—
423	C₂²×C₄	—	3	8	no	—
424	C₂²×C₄	—	3	2	no	—
425	C₂²×C₄	—	3	2	no	—
426	C₂²×C₄	—	3	8	no	—
427	C₂²×C₄	—	3	8	no	—
428	C₂²×C₄	—	3	16	no	—
429	C₂²×C₄	—	12	16	no	—
430	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	complemented
432	C₄⋊C₄	—	3	8	no	—
433	C₄⋊C₄	—	3	4	no	—
434	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
435	C₂²⋊C₄	—	3	4	no	—
436	C₂²⋊C₄	—	3	8	no	—
437	C₂²⋊C₄	—	3	8	no	—
438	C₂²⋊C₄	—	3	16	no	—
439	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
440	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
441	C₄²	—	3	8	no	—
442	C₄²	—	3	4	no	—
443	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
444	C₃×C₅	C₂×#518	1	1	yes	characteristic, complemented, Hall
445	C₂²×C₃	—	2	8	no	—
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	4	8	no	—
448	C₂²×C₃	C₂³×C₄×C₅	1	2	yes	—
449	C₂²×C₃	C₂³×C₄×C₅	1	8	yes	—
450	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
451	C₂×D₃	—	2	8	no	—
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	2	8	no	—
454	C₂×D₃	—	2	32	no	—
455	C₂×D₃	—	4	16	no	—
456	C₂×D₃	—	4	8	no	—
457	C₂×D₃	C₂³×C₄×C₅	1	2	yes	—
458	C₂×D₃	C₂³×C₄×C₅	1	8	yes	—
459	C₂×D₃	C₂³×C₄×C₅	1	2	yes	—
460	C₂×D₃	C₅×H(5,𝔽₂)	1	4	yes	—
461	C₃×C₄	—	2	8	no	—
462	C₃×C₄	C₂³×C₄×C₅	1	4	yes	—
463	Dic₃	—	2	8	no	—
464	Dic₃	C₂³×C₄×C₅	1	4	yes	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	2	8	no	—
467	C₂×C₅	—	3	4	no	—
468	C₂×C₅	—	6	2	no	—
469	C₂×C₅	—	6	8	no	—
470	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
471	C₂×C₅	D₃×H(5,𝔽₂)	1	2	yes	—
472	C₂³	—	3	1	no	—
473	C₂³	—	3	4	no	—
474	C₂³	—	3	16	no	—
475	C₂³	—	3	1	no	—
476	C₂³	—	3	4	no	—
477	C₂³	—	3	16	no	—
478	C₂³	—	3	8	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	6	16	no	—
481	C₂³	—	6	4	no	—
482	C₂³	—	12	8	no	—
483	C₂³	—	12	4	no	—
484	C₂³	—	12	32	no	—
485	C₂³	C₂×C₄×C₅×D₃	1	8	yes	complemented
486	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
487	C₂³	C₂³×C₅×D₃	1	4	yes	—
488	D₄	—	3	32	no	—
489	D₄	—	3	16	no	—
490	D₄	C₂×C₄×C₅×D₃	1	16	yes	complemented
491	C₂×C₄	—	3	4	no	—
492	C₂×C₄	—	3	2	no	—
493	C₂×C₄	—	3	8	no	—
494	C₂×C₄	—	3	8	no	—
495	C₂×C₄	—	3	8	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	6	16	no	—
498	C₂×C₄	—	12	16	no	—
499	C₂×C₄	—	12	8	no	—
500	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	complemented
501	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
502	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
503	C₂×C₃	—	2	2	no	—
504	C₂×C₃	—	2	8	no	—
505	C₂×C₃	C₂⁴×C₄×C₅	1	1	yes	characteristic
506	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
507	D₃	—	2	2	no	—
508	D₃	—	2	8	no	—
509	D₃	C₅×#518	1	4	yes	direct product factor
510	C₅	D₃×#518	1	1	yes	characteristic, direct product factor, Sylow
511	C₂²	—	2	8	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	3	2	no	—
514	C₂²	—	3	4	no	—
515	C₂²	—	3	2	no	—
516	C₂²	—	3	8	no	—
517	C₂²	—	4	8	no	—
518	C₂²	—	6	8	no	—
519	C₂²	—	6	32	no	—
520	C₂²	—	6	8	no	—
521	C₂²	—	6	2	no	—
522	C₂²	—	12	8	no	—
523	C₂²	—	12	16	no	—
524	C₂²	C₂²×C₄×C₅×D₃	1	2	yes	—
525	C₂²	C₂²×C₄×C₅×D₃	1	8	yes	—
526	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
527	C₄	—	2	8	no	—
528	C₄	—	3	4	no	—
529	C₄	—	6	8	no	—
530	C₄	C₂²×C₄×C₅×D₃	1	4	yes	—
531	C₃	C₂×C₅×#518	1	1	yes	characteristic, complemented, Sylow
532	C₂	—	2	2	no	—
533	C₂	—	2	8	no	—
534	C₂	—	3	4	no	—
535	C₂	—	6	2	no	—
536	C₂	—	6	8	no	—
537	C₂	C₂³×C₄×C₅×D₃	1	1	yes	characteristic
538	C₂	C₅×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator	C₂×C₃	C₂⁴×C₄×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#518	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂²×C₅×D₃×D₄	C₂
cosocle	C₂²×C₃	C₂⁵×C₅
hypercenter	C₅×#518	D₃
hypocenter	C₃	C₂×C₅×#518
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#518

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#518	C₂	semidirect
3. C₅×#5798	C₂	semidirect
4. C₅×#5545	C₂	semidirect
5. C₄×C₅×D₃×D₄	C₂	semidirect
6. C₅×#5521	C₂	semidirect
7. C₅×D₃×#117	C₂	semidirect
8. C₅×#5486	C₂	semidirect
9. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂×C₅×D₃×D₄	C₄	semidirect
19. C₂²×C₄×C₅×D₃	C₂²	semidirect
20. C₃×C₄×C₅×D₄	C₂²	semidirect
21. C₃×C₅×#117	C₂²	semidirect
22. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
23. C₂×C₅×#217	C₂²	semidirect
24. C₅×D₄×Dic₃	C₂²	semidirect
25. C₄×C₅×#67	C₂²	semidirect
26. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
27. C₅×#926	C₂²	semidirect
28. C₅×#893	C₂²	semidirect
29. C₅×#892	C₂²	semidirect
30. C₅×D₃×C₄⋊C₄	C₂²	semidirect
31. C₅×#67⋊C₄	C₂²	semidirect
33. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
34. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
35. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
36. C₅×#877	C₂²	semidirect
37. C₄×C₅×D₁₂	C₂²	semidirect
38. C₅×#872	C₂²	semidirect
39. C₄²×C₅×D₃	C₂²	semidirect
40. D₃×#518	C₅	direct (N × H)
46. C₅×#518	D₃	direct (N × H)
52. C₂³×C₅×D₃	C₂×C₄	semidirect
57. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
60. C₂²×C₃×C₄×C₅	C₂³	semidirect
61. C₂×C₅×#67	C₂×C₄	semidirect
64. C₂²×C₅×Dic₃	C₂³	semidirect
65. C₅×D₃×D₄	C₂×C₄	semidirect
66. C₅×D₃×D₄	C₂×C₄	semidirect
67. C₂×C₅×D₁₂	C₂×C₄	semidirect
70. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
74. C₂×C₄×C₅×D₃	C₂³	semidirect
75. C₃×C₅×C₄⋊C₄	C₂³	semidirect
77. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
78. C₃×C₄²×C₅	C₂³	semidirect
80. C₅×#217	C₂³	semidirect
82. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
83. C₅×C₄⋊Dic₃	C₂³	semidirect
84. C₅×Dic₃⋊C₄	C₂³	semidirect
85. C₄×C₅×Dic₃	C₂³	semidirect
86. C₄×C₅×Dic₃	C₂³	semidirect
88. C₃×#518	C₂×C₅	semidirect
89. #5798	C₂×C₅	semidirect
90. #5545	C₂×C₅	semidirect
91. C₄×D₃×D₄	C₂×C₅	semidirect
92. #5521	C₂×C₅	semidirect
93. D₃×#117	C₂×C₅	semidirect
94. #5486	C₂×C₅	semidirect
95. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
110. C₄×C₅×D₄	C₂×D₃	semidirect
115. C₅×#117	C₂×D₃	semidirect
123. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
127. C₂³×C₃×C₅	C₂²×C₄	semidirect
137. C₂²×C₅×D₃	C₂²×C₄	semidirect
138. C₂²×C₅×D₃	C₂²×C₄	semidirect
142. C₃×C₅×D₄	C₂²×C₄	semidirect
144. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
147. C₅×#67	C₂²×C₄	semidirect
149. C₂×C₅×Dic₃	C₂²×C₄	semidirect
152. C₅×D₁₂	C₂²×C₄	semidirect
156. C₄×C₅×D₃	C₂²×C₄	semidirect
160. C₂×D₃×D₄	C₄×C₅	semidirect
165. C₂²×C₄×D₃	C₂²×C₅	semidirect
166. C₃×C₄×D₄	C₂²×C₅	semidirect
167. C₃×#117	C₂²×C₅	semidirect
168. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
169. C₂×#217	C₂²×C₅	semidirect
170. D₄×Dic₃	C₂²×C₅	semidirect
171. C₄×#67	C₂²×C₅	semidirect
172. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
173. #926	C₂²×C₅	semidirect
174. #893	C₂²×C₅	semidirect
175. #892	C₂²×C₅	semidirect
176. D₃×C₄⋊C₄	C₂²×C₅	semidirect
177. #67⋊C₄	C₂²×C₅	semidirect
179. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
180. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
181. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
182. #877	C₂²×C₅	semidirect
183. C₄×D₁₂	C₂²×C₅	semidirect
184. #872	C₂²×C₅	semidirect
185. C₄²×D₃	C₂²×C₅	semidirect
199. C₂×C₅×D₄	C₄×D₃	semidirect
210. C₂²×C₄×C₅	C₂²×D₃	semidirect
213. C₅×C₄⋊C₄	C₂²×D₃	semidirect
219. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
222. C₄²×C₅	C₂²×D₃	semidirect
228. #518	C₅×D₃	direct (N × H)
254. C₂³×D₃	C₂×C₄×C₅	semidirect
259. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
262. C₂²×C₃×C₄	C₂³×C₅	semidirect
263. C₂×#67	C₂×C₄×C₅	semidirect
266. C₂²×Dic₃	C₂³×C₅	semidirect
267. D₃×D₄	C₂×C₄×C₅	semidirect
268. D₃×D₄	C₂×C₄×C₅	semidirect
269. C₂×D₁₂	C₂×C₄×C₅	semidirect
272. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
276. C₂×C₄×D₃	C₂³×C₅	semidirect
277. C₃×C₄⋊C₄	C₂³×C₅	semidirect
279. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
280. C₃×C₄²	C₂³×C₅	semidirect
282. #217	C₂³×C₅	semidirect
284. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
285. C₄⋊Dic₃	C₂³×C₅	semidirect
286. Dic₃⋊C₄	C₂³×C₅	semidirect
287. C₄×Dic₃	C₂³×C₅	semidirect
288. C₄×Dic₃	C₂³×C₅	semidirect
302. C₂³×C₅	C₂×C₄×D₃	semidirect
307. C₅×D₄	C₂×C₄×D₃	semidirect
317. C₂×C₄×C₅	C₂×C₄×D₃	semidirect
334. C₄×D₄	C₂×C₅×D₃	semidirect
339. #117	C₂×C₅×D₃	semidirect
347. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
355. C₅×D₃	#518	direct (N × H)
357. C₂³×C₃	C₂²×C₄×C₅	semidirect
367. C₂²×D₃	C₂²×C₄×C₅	semidirect
368. C₂²×D₃	C₂²×C₄×C₅	semidirect
372. C₃×D₄	C₂²×C₄×C₅	semidirect
374. C₂×C₃×C₄	C₂²×C₄×C₅	semidirect
377. #67	C₂²×C₄×C₅	semidirect
379. C₂×Dic₃	C₂²×C₄×C₅	semidirect
382. D₁₂	C₂²×C₄×C₅	semidirect
386. C₄×D₃	C₂²×C₄×C₅	semidirect
420. C₂×D₄	C₄×C₅×D₃	semidirect
431. C₂²×C₄	C₂²×C₅×D₃	semidirect
434. C₄⋊C₄	C₂²×C₅×D₃	semidirect
440. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
443. C₄²	C₂²×C₅×D₃	semidirect
444. C₃×C₅	C₂×#518	semidirect
485. C₂³	C₂×C₄×C₅×D₃	semidirect
490. D₄	C₂×C₄×C₅×D₃	semidirect
500. C₂×C₄	C₂×C₄×C₅×D₃	semidirect
509. D₃	C₅×#518	direct (N × H)
510. C₅	D₃×#518	direct (N × H)
531. C₃	C₂×C₅×#518	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×D₃×D₄	2
C₃×C₅×#518	2
C₅×#5798	2
C₅×#5545	2
C₄×C₅×D₃×D₄	2
C₅×#5521	2
C₅×D₃×#117	2
C₅×#5486	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#518	3
D₃×#518	5

Subgroups — C5×D3×#518 #14478948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#518 #14478948