Subgroups — C₅×#79540 #14415681

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	2	yes	maximal, complemented
2	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5127	C₂	1	2	yes	maximal, complemented
5	C₅×#5012	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4837	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4728	C₂	1	2	yes	maximal, complemented
9	C₅×#4726	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₄×M₁₆	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
18	C₄×C₅×#67	C₂²	1	2	yes	—
19	C₂×C₅×#208	C₂²	1	2	yes	complemented
20	C₅×D₃×M₁₆	—	2	8	no	—
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
25	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
26	C₅×#893	C₄	1	1	yes	characteristic
27	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
28	C₅×#67⋊C₄	C₄	1	2	yes	—
29	C₅×D₃×C₂²⋊C₄	C₄	1	2	yes	—
30	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
31	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
35	C₅×#830	C₂²	1	2	yes	complemented
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
37	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
38	C₅×#815	C₂²	1	1	yes	characteristic, complemented
39	C₅×#815	C₂²	1	1	yes	characteristic, complemented
40	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	#79540	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂²×C₅×M₁₆	—	3	2	no	—
45	C₂×C₄×C₅×D₄	—	3	1	no	—
46	C₅×#436	—	3	1	no	—
47	C₅×#436	D₃	1	1	yes	characteristic, complemented
48	C₅×#435	—	3	2	no	—
49	C₅×#435	—	3	2	no	—
50	C₅×C₈×D₄	—	3	1	no	—
51	C₅×C₈×D₄	—	3	1	no	—
52	C₅×#423	—	3	1	no	—
53	C₅×#407	—	3	2	no	—
54	C₄×C₅×M₁₆	—	3	1	no	—
55	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₅×#67	C₂×C₄	1	2	yes	—
59	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
60	C₅×D₃×D₄	—	2	4	no	—
61	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	4	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
67	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
69	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#217	C₂×C₄	1	2	yes	—
78	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
79	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
80	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
81	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
82	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₅×#208	—	2	4	no	—
86	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
90	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
91	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
92	C₅×D₃×C₈	—	2	4	no	—
93	C₅×D₃×C₈	—	2	4	no	—
94	C₂×D₃×M₁₆	C₂×C₅	1	2	yes	complemented
95	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
96	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
97	#5127	C₂×C₅	1	2	yes	complemented
98	#5012	C₂×C₅	1	1	yes	characteristic, complemented
99	#4837	C₂×C₅	1	1	yes	characteristic, complemented
100	#4834	C₂×C₅	1	1	yes	characteristic, complemented
101	#4728	C₂×C₅	1	2	yes	complemented
102	#4726	C₂×C₅	1	2	yes	complemented
103	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
104	C₈×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂²×C₅×D₄	—	3	1	no	—
106	C₂³×C₄×C₅	—	3	2	no	—
107	C₂×C₅×M₁₆	—	3	2	no	—
108	C₂×C₅×M₁₆	—	3	1	no	—
109	C₂×C₅×M₁₆	—	3	1	no	—
110	C₂×C₅×M₁₆	—	3	2	no	—
111	C₂×C₅×M₁₆	—	6	8	no	—
112	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
113	C₂²×C₅×C₈	—	3	2	no	—
114	C₂²×C₅×C₈	—	3	2	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	3	2	no	—
117	C₄×C₅×D₄	—	3	1	no	—
118	C₄×C₅×D₄	—	3	2	no	—
119	C₄×C₅×D₄	—	3	1	no	—
120	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	—	3	1	no	—
122	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
123	C₂×C₄²×C₅	—	3	1	no	—
124	C₅×C₄⋊C₈	—	3	2	no	—
125	C₅×C₄⋊C₈	—	3	1	no	—
126	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
127	C₅×C₂²⋊C₈	—	3	2	no	—
128	C₅×C₂²⋊C₈	—	3	2	no	—
129	C₅×C₂²⋊C₈	—	3	2	no	—
130	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
131	C₅×#97	—	3	1	no	—
132	C₅×#97	—	3	1	no	—
133	C₄×C₅×C₈	—	3	1	no	—
134	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
135	D₄×M₁₆	—	3	1	no	Sylow
136	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₅×D₃	—	2	4	no	—
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	—	4	2	no	—
140	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×#67	—	2	4	no	—
150	C₂×C₅×Dic₃	—	2	4	no	—
151	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
154	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
155	C₅×D₁₂	M₁₆	1	4	yes	complemented
156	C₄×C₅×D₃	—	2	4	no	—
157	C₄×C₅×D₃	—	2	2	no	—
158	C₄×C₅×D₃	—	2	2	no	—
159	C₄×C₅×D₃	—	2	2	no	—
160	C₄×C₅×D₃	—	2	4	no	—
161	C₄×C₅×D₃	—	4	1	no	—
162	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
163	C₄×C₅×D₃	#41	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
167	C₅×C₃⋊C₈	—	2	2	no	—
168	C₅×C₃⋊C₈	—	2	1	no	—
169	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
170	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
171	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
172	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
173	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
174	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic
175	C₄×#67	C₂²×C₅	1	2	yes	—
176	C₂×#208	C₂²×C₅	1	2	yes	complemented
177	D₃×M₁₆	—	2	8	no	—
178	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
179	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
180	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
181	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
182	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
183	#893	C₄×C₅	1	1	yes	characteristic
184	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
185	#67⋊C₄	C₄×C₅	1	2	yes	—
186	D₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
187	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
188	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
189	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
191	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
192	#830	C₂²×C₅	1	2	yes	complemented
193	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	complemented
194	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	complemented
195	#815	C₂²×C₅	1	1	yes	characteristic, complemented
196	#815	C₂²×C₅	1	1	yes	characteristic, complemented
197	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
198	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
199	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
200	C₂⁴×C₅	—	3	2	no	—
201	C₂×C₅×D₄	—	3	2	no	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	6	4	no	—
204	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	2	no	—
207	C₂²×C₄×C₅	—	3	1	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	1	no	—
212	C₂²×C₄×C₅	—	6	4	no	—
213	C₂²×C₄×C₅	—	6	4	no	—
214	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
215	C₅×M₁₆	—	2	4	no	—
216	C₅×M₁₆	—	3	4	no	—
217	C₅×M₁₆	—	6	4	no	—
218	C₅×M₁₆	—	6	2	no	—
219	C₅×M₁₆	—	6	4	no	—
220	C₂×C₅×C₈	—	3	1	no	—
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	—	3	1	no	—
223	C₂×C₅×C₈	—	6	4	no	—
224	C₂×C₅×C₈	—	6	4	no	—
225	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
226	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
228	C₅×C₄⋊C₄	—	3	2	no	—
229	C₅×C₄⋊C₄	—	3	1	no	—
230	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
231	C₅×C₂²⋊C₄	—	3	2	no	—
232	C₅×C₂²⋊C₄	—	3	2	no	—
233	C₅×C₂²⋊C₄	—	3	2	no	—
234	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
235	C₄²×C₅	—	3	1	no	—
236	C₄²×C₅	—	3	1	no	—
237	C₄²×C₅	—	3	1	no	—
238	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
239	C₂²×M₁₆	—	3	2	no	—
240	C₂×C₄×D₄	—	3	1	no	—
241	#436	—	3	1	no	—
242	#436	C₅×D₃	1	1	yes	characteristic, complemented
243	#435	—	3	2	no	—
244	#435	—	3	2	no	—
245	C₈×D₄	—	3	1	no	—
246	C₈×D₄	—	3	1	no	—
247	#423	—	3	1	no	—
248	#407	—	3	2	no	—
249	C₄×M₁₆	—	3	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	—	2	1	no	—
256	C₂×C₅×D₃	—	2	1	no	—
257	C₂×C₅×D₃	—	2	2	no	—
258	C₂×C₅×D₃	—	4	8	no	—
259	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
260	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₅×Dic₃	—	2	2	no	—
267	C₅×Dic₃	—	2	1	no	—
268	C₅×Dic₃	—	2	1	no	—
269	C₅×Dic₃	C₄×D₄	1	2	yes	—
270	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
271	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂×#67	C₂×C₄×C₅	1	2	yes	—
274	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
275	D₃×D₄	—	2	4	no	—
276	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂×C₄×D₃	—	2	4	no	—
278	C₂×C₄×D₃	—	2	4	no	—
279	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
281	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
282	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
284	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
285	C₃×M₁₆	—	2	4	no	—
286	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
287	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
291	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
292	#217	C₂×C₄×C₅	1	2	yes	—
293	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
294	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
295	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
296	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
297	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
298	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
299	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
300	#208	—	2	4	no	—
301	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
303	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
304	ΓL(1,𝔽₂₅)	—	2	4	no	—
305	ΓL(1,𝔽₂₅)	—	2	2	no	—
306	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	complemented
307	D₃×C₈	—	2	4	no	—
308	D₃×C₈	—	2	4	no	—
309	C₂³×C₅	—	3	2	no	—
310	C₂³×C₅	—	3	1	no	—
311	C₂³×C₅	—	6	4	no	—
312	C₂³×C₅	—	6	4	no	—
313	C₂³×C₅	—	12	2	no	—
314	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
315	C₅×D₄	—	2	2	no	—
316	C₅×D₄	—	3	4	no	—
317	C₅×D₄	—	6	4	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	3	1	no	—
321	C₂×C₄×C₅	—	3	2	no	—
322	C₂×C₄×C₅	—	3	2	no	—
323	C₂×C₄×C₅	—	3	1	no	—
324	C₂×C₄×C₅	—	3	1	no	—
325	C₂×C₄×C₅	—	3	2	no	—
326	C₂×C₄×C₅	—	6	4	no	—
327	C₂×C₄×C₅	—	6	4	no	—
328	C₂×C₄×C₅	—	6	4	no	—
329	C₂×C₄×C₅	—	6	2	no	—
330	C₂×C₄×C₅	—	6	2	no	—
331	C₂×C₄×C₅	—	6	2	no	—
332	C₂×C₄×C₅	—	12	1	no	—
333	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
335	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
337	C₅×C₈	—	2	2	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	—	3	2	no	—
340	C₅×C₈	—	6	2	no	—
341	C₅×C₈	—	6	1	no	—
342	C₅×C₈	D₃×D₄	1	2	yes	complemented
343	C₂²×D₄	—	3	1	no	—
344	C₂³×C₄	—	3	2	no	—
345	C₂×M₁₆	—	3	2	no	—
346	C₂×M₁₆	—	3	1	no	—
347	C₂×M₁₆	—	3	2	no	—
348	C₂×M₁₆	—	3	1	no	—
349	C₂×M₁₆	—	6	8	no	—
350	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
351	C₂²×C₈	—	3	2	no	—
352	C₂²×C₈	—	3	2	no	—
353	C₄×D₄	—	3	1	no	—
354	C₄×D₄	—	3	2	no	—
355	C₄×D₄	—	3	1	no	—
356	C₄×D₄	—	3	2	no	—
357	C₄×D₄	—	3	1	no	—
358	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	3	1	no	—
360	C₂×C₂²⋊C₄	—	3	2	no	—
361	C₂×C₄²	—	3	1	no	—
362	C₄⋊C₈	—	3	2	no	—
363	C₄⋊C₈	—	3	1	no	—
364	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
365	C₂²⋊C₈	—	3	2	no	—
366	C₂²⋊C₈	—	3	2	no	—
367	C₂²⋊C₈	—	3	2	no	—
368	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
369	#97	—	3	1	no	—
370	#97	—	3	1	no	—
371	C₄×C₈	—	3	1	no	—
372	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
373	C₂×C₃×C₅	—	4	2	no	—
374	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
376	C₂×C₃×C₅	#568	1	1	yes	characteristic
377	C₅×D₃	—	2	2	no	—
378	C₅×D₃	—	2	4	no	—
379	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
380	C₂²×D₃	—	2	4	no	—
381	C₂²×D₃	—	2	4	no	—
382	C₂²×D₃	—	4	2	no	—
383	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
384	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
385	C₃×D₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
390	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	#67	—	2	4	no	—
393	C₂×Dic₃	—	2	4	no	—
394	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
397	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
398	D₁₂	C₅×M₁₆	1	4	yes	complemented
399	C₄×D₃	—	2	4	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	4	no	—
404	C₄×D₃	—	4	1	no	—
405	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
406	C₄×D₃	C₅×#41	1	2	yes	—
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	1	no	—
409	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
410	C₃⋊C₈	—	2	2	no	—
411	C₃⋊C₈	—	2	1	no	—
412	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	3	4	no	—
417	C₂²×C₅	—	3	2	no	—
418	C₂²×C₅	—	6	1	no	—
419	C₂²×C₅	—	6	1	no	—
420	C₂²×C₅	—	6	2	no	—
421	C₂²×C₅	—	6	2	no	—
422	C₂²×C₅	—	12	8	no	—
423	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	3	2	no	—
427	C₄×C₅	—	6	1	no	—
428	C₄×C₅	—	6	1	no	—
429	C₄×C₅	—	6	2	no	—
430	C₄×C₅	D₃×M₁₆	1	2	yes	complemented
431	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
432	C₄×C₅	D₃×#41	1	1	yes	characteristic
433	C₂⁴	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	6	4	no	—
437	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	6	4	no	—
446	C₂²×C₄	—	6	4	no	—
447	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
448	M₁₆	—	2	4	no	—
449	M₁₆	—	3	4	no	—
450	M₁₆	—	6	4	no	—
451	M₁₆	—	6	2	no	—
452	M₁₆	—	6	4	no	—
453	C₂×C₈	—	3	1	no	—
454	C₂×C₈	—	3	1	no	—
455	C₂×C₈	—	3	2	no	—
456	C₂×C₈	—	6	4	no	—
457	C₂×C₈	—	6	4	no	—
458	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
459	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
460	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	2	no	—
467	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
468	C₄²	—	3	1	no	—
469	C₄²	—	3	1	no	—
470	C₄²	—	3	1	no	—
471	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
472	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
477	C₂×D₃	—	2	2	no	—
478	C₂×D₃	—	2	1	no	—
479	C₂×D₃	—	2	1	no	—
480	C₂×D₃	—	2	2	no	—
481	C₂×D₃	—	4	8	no	—
482	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
483	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	complemented
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	complemented
487	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
489	Dic₃	—	2	2	no	—
490	Dic₃	—	2	1	no	—
491	Dic₃	—	2	1	no	—
492	Dic₃	C₄×C₅×D₄	1	2	yes	—
493	C₂×C₅	—	4	2	no	—
494	C₂×C₅	—	6	2	no	—
495	C₂×C₅	—	6	4	no	—
496	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
497	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
498	C₂×C₅	#5750	1	1	yes	characteristic
499	C₂³	—	3	2	no	—
500	C₂³	—	3	1	no	—
501	C₂³	—	6	4	no	—
502	C₂³	—	6	4	no	—
503	C₂³	—	12	2	no	—
504	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
505	D₄	—	2	2	no	—
506	D₄	—	3	4	no	—
507	D₄	—	6	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	3	1	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	3	1	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	6	4	no	—
517	C₂×C₄	—	6	4	no	—
518	C₂×C₄	—	6	4	no	—
519	C₂×C₄	—	6	2	no	—
520	C₂×C₄	—	6	2	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	12	1	no	—
523	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
525	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
526	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	1	no	—
529	C₈	—	3	2	no	—
530	C₈	—	6	2	no	—
531	C₈	—	6	1	no	—
532	C₈	C₅×D₃×D₄	1	2	yes	complemented
533	C₂×C₃	—	4	2	no	—
534	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
535	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
536	C₂×C₃	C₅×#568	1	1	yes	characteristic
537	D₃	—	2	2	no	—
538	D₃	—	2	4	no	—
539	C₅	#79540	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	3	4	no	—
544	C₂²	—	3	2	no	—
545	C₂²	—	6	1	no	—
546	C₂²	—	6	1	no	—
547	C₂²	—	6	2	no	—
548	C₂²	—	6	2	no	—
549	C₂²	—	12	8	no	—
550	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	2	no	—
553	C₄	—	3	2	no	—
554	C₄	—	6	1	no	—
555	C₄	—	6	1	no	—
556	C₄	—	6	2	no	—
557	C₄	C₅×D₃×M₁₆	1	2	yes	complemented
558	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
559	C₄	C₅×D₃×#41	1	1	yes	characteristic
560	C₃	C₅×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	4	2	no	—
562	C₂	—	6	2	no	—
563	C₂	—	6	4	no	—
564	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
565	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
566	C₂	C₅×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#436	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×D₃×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#436	D₃
hypocenter	C₃	C₅×D₄×M₁₆
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#436

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₃×C₅×#436	C₂	semidirect
4. C₅×#5127	C₂	semidirect
5. C₅×#5012	C₂	semidirect
6. C₅×#4837	C₂	semidirect
7. C₅×#4834	C₂	semidirect
8. C₅×#4728	C₂	semidirect
9. C₅×#4726	C₂	semidirect
10. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
11. C₅×C₈×D₁₂	C₂	semidirect
15. C₂×C₃×C₅×M₁₆	C₂²	semidirect
19. C₂×C₅×#208	C₂²	semidirect
24. C₂×C₅×D₃×C₈	C₂²	semidirect
25. C₂×C₅×D₃×C₈	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
33. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
34. C₃×C₄×C₅×C₈	C₂²	semidirect
35. C₅×#830	C₂²	semidirect
36. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
37. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
38. C₅×#815	C₂²	semidirect
39. C₅×#815	C₂²	semidirect
40. C₅×Dic₃⋊C₈	C₂²	semidirect
41. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
42. C₄×C₅×C₃⋊C₈	C₂²	semidirect
43. #79540	C₅	direct (N × H)
47. C₅×#436	D₃	semidirect
91. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
94. C₂×D₃×M₁₆	C₂×C₅	semidirect
96. C₃×#436	C₂×C₅	semidirect
97. #5127	C₂×C₅	semidirect
98. #5012	C₂×C₅	semidirect
99. #4837	C₂×C₅	semidirect
100. #4834	C₂×C₅	semidirect
101. #4728	C₂×C₅	semidirect
102. #4726	C₂×C₅	semidirect
103. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
104. C₈×D₁₂	C₂×C₅	semidirect
112. C₂×C₅×M₁₆	C₂×D₃	semidirect
126. C₅×C₄⋊C₈	C₂×D₃	semidirect
130. C₅×C₂²⋊C₈	C₂×D₃	semidirect
134. C₄×C₅×C₈	C₂×D₃	semidirect
155. C₅×D₁₂	M₁₆	semidirect
166. C₃×C₅×C₈	C₂×D₄	semidirect
169. C₅×C₃⋊C₈	C₂×D₄	semidirect
172. C₂×C₃×M₁₆	C₂²×C₅	semidirect
176. C₂×#208	C₂²×C₅	semidirect
181. C₂×D₃×C₈	C₂²×C₅	semidirect
182. C₂×D₃×C₈	C₂²×C₅	semidirect
189. C₃×C₄⋊C₈	C₂²×C₅	semidirect
190. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
191. C₃×C₄×C₈	C₂²×C₅	semidirect
192. #830	C₂²×C₅	semidirect
193. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
194. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
195. #815	C₂²×C₅	semidirect
196. #815	C₂²×C₅	semidirect
197. Dic₃⋊C₈	C₂²×C₅	semidirect
198. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
199. C₄×C₃⋊C₈	C₂²×C₅	semidirect
242. #436	C₅×D₃	semidirect
260. C₂×C₅×D₃	C₂×M₁₆	semidirect
263. C₃×C₄×C₅	C₂×M₁₆	semidirect
306. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
342. C₅×C₈	D₃×D₄	semidirect
350. C₂×M₁₆	C₂×C₅×D₃	semidirect
364. C₄⋊C₈	C₂×C₅×D₃	semidirect
368. C₂²⋊C₈	C₂×C₅×D₃	semidirect
372. C₄×C₈	C₂×C₅×D₃	semidirect
398. D₁₂	C₅×M₁₆	semidirect
409. C₃×C₈	C₂×C₅×D₄	semidirect
412. C₃⋊C₈	C₂×C₅×D₄	semidirect
430. C₄×C₅	D₃×M₁₆	semidirect
472. C₃×C₅	D₄×M₁₆	semidirect
483. C₂×D₃	C₂×C₅×M₁₆	semidirect
486. C₃×C₄	C₂×C₅×M₁₆	semidirect
532. C₈	C₅×D₃×D₄	semidirect
539. C₅	#79540	direct (N × H)
557. C₄	C₅×D₃×M₁₆	semidirect
560. C₃	C₅×D₄×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#436	2
C₅×#5127	2
C₅×#5012	2
C₅×#4837	2
C₅×#4834	2
C₅×#4728	2
C₅×#4726	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×C₈×D₁₂	2
C₅×D₄×M₁₆	3
#79540	5

Subgroups — C5×#79540 #14415681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79540 #14415681