Subgroups — C₅×#75985 #14329033

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4990	C₂	1	2	yes	maximal, complemented
6	C₅×#4988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4988	C₂	1	2	yes	maximal, complemented
8	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4666	C₂	1	2	yes	maximal, complemented
11	C₅×#4665	C₂	1	2	yes	maximal, complemented
12	C₅×#2363	—	3	1	no	maximal, Hall
13	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
32	C₅×#895	C₄	1	8	yes	complemented
33	C₅×#892	—	2	4	no	—
34	C₄×C₅×D₁₂	—	2	4	no	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
38	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
39	#75985	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×#121	—	3	1	no	—
41	C₂×C₄×C₅×D₄	—	3	1	no	—
42	C₂×C₅×#117	—	3	1	no	—
43	C₅×#390	—	3	1	no	—
44	C₅×#390	—	3	2	no	—
45	C₅×#389	D₃	1	1	yes	characteristic, complemented
46	C₅×#388	—	3	2	no	—
47	C₅×#386	—	3	2	no	—
48	C₄×C₅×C₄⋊C₄	—	3	1	no	—
49	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
50	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
51	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
52	C₂³×C₅×D₃	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
61	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	—	2	2	no	—
64	C₂×C₅×D₁₂	—	4	2	no	—
65	C₂×C₅×D₁₂	—	4	2	no	—
66	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
67	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
68	C₂×C₄×C₅×D₃	—	2	2	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₄×C₅×D₃	—	2	4	no	—
71	C₂×C₄×C₅×D₃	—	2	4	no	—
72	C₂×C₄×C₅×D₃	—	4	2	no	—
73	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	4	2	no	—
76	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
77	C₃×C₄²×C₅	—	2	2	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
84	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
85	C₅×C₄⋊Dic₃	D₄	1	4	yes	complemented
86	C₄×C₅×Dic₃	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	4	no	—
88	C₄×C₅×Dic₃	—	4	2	no	—
89	C₂×#895	C₂×C₅	1	1	yes	characteristic
90	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
93	#4990	C₂×C₅	1	2	yes	complemented
94	#4988	C₂×C₅	1	1	yes	characteristic, complemented
95	#4988	C₂×C₅	1	2	yes	complemented
96	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
97	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
98	#4666	C₂×C₅	1	2	yes	complemented
99	#4665	C₂×C₅	1	2	yes	complemented
100	C₂²×C₅×D₄	—	3	1	no	—
101	C₂²×C₅×D₄	—	3	2	no	—
102	C₂³×C₄×C₅	—	3	1	no	—
103	C₂³×C₄×C₅	—	3	2	no	—
104	C₅×#121	—	3	8	no	—
105	C₄×C₅×D₄	—	6	4	no	—
106	C₅×#117	—	6	4	no	—
107	C₂×C₅×C₄⋊C₄	—	3	1	no	—
108	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
114	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
115	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
116	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
117	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
118	C₂×C₄²×C₅	—	3	1	no	—
119	C₂×C₄²×C₅	—	3	2	no	—
120	C₂×C₄²×C₅	—	3	2	no	—
121	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
122	C₅×#95	—	3	1	no	—
123	C₅×#95	—	3	1	no	—
124	C₅×#95	—	3	2	no	—
125	C₅×#95	C₂×D₃	1	2	yes	—
126	#2363	—	3	1	no	Sylow
127	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
128	C₂²×C₅×D₃	—	2	1	no	—
129	C₂²×C₅×D₃	—	2	2	no	—
130	C₂²×C₅×D₃	—	2	1	no	—
131	C₂²×C₅×D₃	—	2	1	no	—
132	C₂²×C₅×D₃	—	2	2	no	—
133	C₂²×C₅×D₃	—	2	1	no	—
134	C₂²×C₅×D₃	—	2	2	no	—
135	C₂²×C₅×D₃	—	2	2	no	—
136	C₂²×C₅×D₃	—	2	2	no	—
137	C₂²×C₅×D₃	—	2	2	no	—
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₂²×C₅×D₃	—	2	1	no	—
140	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
153	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	#41	1	2	yes	—
156	C₂×C₃×C₄×C₅	#41	1	2	yes	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	1	no	—
159	C₂×C₅×Dic₃	—	2	1	no	—
160	C₂×C₅×Dic₃	—	2	2	no	—
161	C₂×C₅×Dic₃	—	2	1	no	—
162	C₂×C₅×Dic₃	—	2	2	no	—
163	C₂×C₅×Dic₃	—	2	1	no	—
164	C₂×C₅×Dic₃	—	2	1	no	—
165	C₂×C₅×Dic₃	—	2	1	no	—
166	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
167	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
168	C₂×C₅×Dic₃	#41	1	2	yes	—
169	C₅×D₁₂	—	2	8	no	—
170	C₅×D₁₂	—	4	8	no	—
171	C₄×C₅×D₃	—	2	8	no	—
172	C₄×C₅×D₃	—	4	8	no	—
173	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
174	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
175	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
176	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
181	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
183	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
184	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
186	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
187	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
188	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
190	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
192	#895	C₄×C₅	1	8	yes	complemented
193	#892	—	2	4	no	—
194	C₄×D₁₂	—	2	4	no	—
195	C₃×#95	C₂²×C₅	1	2	yes	—
196	C₃⋊#95	C₂²×C₅	1	2	yes	—
197	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
198	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
199	C₂⁴×C₅	—	3	2	no	—
200	C₂⁴×C₅	—	3	1	no	—
201	C₂×C₅×D₄	—	3	4	no	—
202	C₂×C₅×D₄	—	3	8	no	—
203	C₂×C₅×D₄	—	6	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	12	2	no	—
206	C₂×C₅×D₄	—	12	2	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	3	2	no	—
209	C₂²×C₄×C₅	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	4	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	6	4	no	—
213	C₂²×C₄×C₅	—	6	2	no	—
214	C₂²×C₄×C₅	—	6	2	no	—
215	C₂²×C₄×C₅	—	6	4	no	—
216	C₂²×C₄×C₅	—	12	2	no	—
217	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₅×C₄⋊C₄	—	2	2	no	—
223	C₅×C₄⋊C₄	—	3	4	no	—
224	C₅×C₄⋊C₄	—	4	2	no	—
225	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	complemented
226	C₅×C₂²⋊C₄	—	3	8	no	—
227	C₅×C₂²⋊C₄	—	6	4	no	—
228	C₅×C₂²⋊C₄	—	6	4	no	—
229	C₅×C₂²⋊C₄	—	6	4	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	—	6	2	no	—
232	C₅×C₂²⋊C₄	—	12	2	no	—
233	C₄²×C₅	—	2	2	no	—
234	C₄²×C₅	—	6	4	no	—
235	C₄²×C₅	—	6	2	no	—
236	C₄²×C₅	—	12	2	no	—
237	C₂×#121	—	3	1	no	—
238	C₂×C₄×D₄	—	3	1	no	—
239	C₂×#117	—	3	1	no	—
240	#390	—	3	1	no	—
241	#390	—	3	2	no	—
242	#389	C₅×D₃	1	1	yes	characteristic, complemented
243	#388	—	3	2	no	—
244	#386	—	3	2	no	—
245	C₄×C₄⋊C₄	—	3	1	no	—
246	C₄×C₂²⋊C₄	—	3	1	no	—
247	C₄×C₂²⋊C₄	—	3	2	no	—
248	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
251	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
252	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
253	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₅×D₃	—	2	2	no	—
256	C₂×C₅×D₃	—	2	4	no	—
257	C₂×C₅×D₃	—	2	2	no	—
258	C₂×C₅×D₃	—	2	4	no	—
259	C₂×C₅×D₃	—	2	2	no	—
260	C₂×C₅×D₃	—	2	4	no	—
261	C₂×C₅×D₃	—	4	2	no	—
262	C₂×C₅×D₃	—	4	1	no	—
263	C₂×C₅×D₃	—	4	1	no	—
264	C₂×C₅×D₃	—	4	2	no	—
265	C₂×C₅×D₃	—	4	1	no	—
266	C₂×C₅×D₃	—	4	2	no	—
267	C₂×C₅×D₃	—	4	1	no	—
268	C₂×C₅×D₃	—	4	2	no	—
269	C₃×C₄×C₅	—	2	4	no	—
270	C₃×C₄×C₅	—	2	2	no	—
271	C₃×C₄×C₅	—	4	2	no	—
272	C₃×C₄×C₅	—	4	1	no	—
273	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
274	C₅×Dic₃	—	2	2	no	—
275	C₅×Dic₃	—	2	4	no	—
276	C₅×Dic₃	—	2	2	no	—
277	C₅×Dic₃	—	4	1	no	—
278	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
279	C₂³×D₃	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
282	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
286	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
287	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
288	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₂×D₁₂	—	2	2	no	—
290	C₂×D₁₂	—	2	2	no	—
291	C₂×D₁₂	—	4	2	no	—
292	C₂×D₁₂	—	4	2	no	—
293	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
294	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
295	C₂×C₄×D₃	—	2	2	no	—
296	C₂×C₄×D₃	—	2	2	no	—
297	C₂×C₄×D₃	—	2	4	no	—
298	C₂×C₄×D₃	—	2	4	no	—
299	C₂×C₄×D₃	—	4	2	no	—
300	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
301	C₃×C₄⋊C₄	—	2	2	no	—
302	C₃×C₄⋊C₄	—	4	2	no	—
303	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
304	C₃×C₄²	—	2	2	no	—
305	(C₂×D₃)⋊C₄	—	2	2	no	—
306	(C₂×D₃)⋊C₄	—	2	4	no	—
307	(C₂×D₃)⋊C₄	—	2	4	no	—
308	(C₂×D₃)⋊C₄	—	2	4	no	—
309	(C₂×D₃)⋊C₄	—	2	2	no	—
310	(C₂×D₃)⋊C₄	—	4	2	no	—
311	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
312	C₄⋊Dic₃	C₅×D₄	1	4	yes	complemented
313	C₄×Dic₃	—	2	2	no	—
314	C₄×Dic₃	—	2	4	no	—
315	C₄×Dic₃	—	4	2	no	—
316	C₂³×C₅	—	3	4	no	—
317	C₂³×C₅	—	3	2	no	—
318	C₂³×C₅	—	6	1	no	—
319	C₂³×C₅	—	6	2	no	—
320	C₂³×C₅	—	6	2	no	—
321	C₂³×C₅	—	6	1	no	—
322	C₂³×C₅	—	6	1	no	—
323	C₂³×C₅	—	6	1	no	—
324	C₂³×C₅	—	6	2	no	—
325	C₂³×C₅	—	6	2	no	—
326	C₂³×C₅	—	6	2	no	—
327	C₂³×C₅	—	6	1	no	—
328	C₂³×C₅	—	6	2	no	—
329	C₂³×C₅	—	6	1	no	—
330	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
331	C₅×D₄	—	6	8	no	—
332	C₅×D₄	—	12	8	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	3	2	no	—
344	C₂×C₄×C₅	—	3	4	no	—
345	C₂×C₄×C₅	—	3	2	no	—
346	C₂×C₄×C₅	—	6	1	no	—
347	C₂×C₄×C₅	—	6	1	no	—
348	C₂×C₄×C₅	—	6	1	no	—
349	C₂×C₄×C₅	—	6	2	no	—
350	C₂×C₄×C₅	—	6	1	no	—
351	C₂×C₄×C₅	—	6	2	no	—
352	C₂×C₄×C₅	—	6	8	no	—
353	C₂×C₄×C₅	—	6	1	no	—
354	C₂×C₄×C₅	—	6	1	no	—
355	C₂×C₄×C₅	—	6	1	no	—
356	C₂×C₄×C₅	—	12	8	no	—
357	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
358	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
359	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
360	C₂×C₄×C₅	#239	1	2	yes	—
361	C₂×C₄×C₅	#239	1	2	yes	—
362	C₂²×D₄	—	3	1	no	—
363	C₂²×D₄	—	3	2	no	—
364	C₂³×C₄	—	3	1	no	—
365	C₂³×C₄	—	3	2	no	—
366	#121	—	3	8	no	—
367	C₄×D₄	—	6	4	no	—
368	#117	—	6	4	no	—
369	C₂×C₄⋊C₄	—	3	1	no	—
370	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	3	2	no	—
374	C₂×C₂²⋊C₄	—	3	2	no	—
375	C₂×C₂²⋊C₄	—	3	2	no	—
376	C₂×C₂²⋊C₄	—	3	1	no	—
377	C₂×C₂²⋊C₄	—	3	1	no	—
378	C₂×C₂²⋊C₄	—	3	2	no	—
379	C₂×C₂²⋊C₄	—	3	2	no	—
380	C₂×C₄²	—	3	2	no	—
381	C₂×C₄²	—	3	1	no	—
382	C₂×C₄²	—	3	2	no	—
383	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
384	#95	—	3	1	no	—
385	#95	—	3	1	no	—
386	#95	—	3	2	no	—
387	#95	C₂×C₅×D₃	1	2	yes	—
388	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
389	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
390	C₂×C₃×C₅	#518	1	1	yes	characteristic
391	C₂×C₃×C₅	#546	1	1	yes	characteristic
392	C₂×C₃×C₅	#550	1	1	yes	characteristic
393	C₂×C₃×C₅	#553	1	1	yes	characteristic
394	C₂×C₃×C₅	#555	1	1	yes	characteristic
395	C₅×D₃	—	4	2	no	—
396	C₅×D₃	—	4	4	no	—
397	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
398	C₂²×D₃	—	2	1	no	—
399	C₂²×D₃	—	2	2	no	—
400	C₂²×D₃	—	2	1	no	—
401	C₂²×D₃	—	2	1	no	—
402	C₂²×D₃	—	2	2	no	—
403	C₂²×D₃	—	2	1	no	—
404	C₂²×D₃	—	2	2	no	—
405	C₂²×D₃	—	2	2	no	—
406	C₂²×D₃	—	2	2	no	—
407	C₂²×D₃	—	2	2	no	—
408	C₂²×D₃	—	2	1	no	—
409	C₂²×D₃	—	2	1	no	—
410	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
411	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
423	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
425	C₂×C₃×C₄	C₅×#41	1	2	yes	—
426	C₂×C₃×C₄	C₅×#41	1	2	yes	—
427	C₂×Dic₃	—	2	1	no	—
428	C₂×Dic₃	—	2	1	no	—
429	C₂×Dic₃	—	2	1	no	—
430	C₂×Dic₃	—	2	2	no	—
431	C₂×Dic₃	—	2	1	no	—
432	C₂×Dic₃	—	2	2	no	—
433	C₂×Dic₃	—	2	1	no	—
434	C₂×Dic₃	—	2	1	no	—
435	C₂×Dic₃	—	2	1	no	—
436	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
437	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
438	C₂×Dic₃	C₅×#41	1	2	yes	—
439	D₁₂	—	2	8	no	—
440	D₁₂	—	4	8	no	—
441	C₄×D₃	—	2	8	no	—
442	C₄×D₃	—	4	8	no	—
443	C₂²×C₅	—	6	2	no	—
444	C₂²×C₅	—	6	4	no	—
445	C₂²×C₅	—	6	2	no	—
446	C₂²×C₅	—	6	4	no	—
447	C₂²×C₅	—	6	4	no	—
448	C₂²×C₅	—	6	2	no	—
449	C₂²×C₅	—	12	1	no	—
450	C₂²×C₅	—	12	2	no	—
451	C₂²×C₅	—	12	2	no	—
452	C₂²×C₅	—	12	1	no	—
453	C₂²×C₅	—	12	1	no	—
454	C₂²×C₅	—	12	2	no	—
455	C₂²×C₅	—	12	2	no	—
456	C₂²×C₅	—	12	1	no	—
457	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
458	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
459	C₂²×C₅	#1004	1	1	yes	characteristic
460	C₂²×C₅	C₂×#239	1	1	yes	characteristic
461	C₂²×C₅	C₂×#239	1	1	yes	characteristic
462	C₂²×C₅	D₃×#41	1	1	yes	characteristic
463	C₂²×C₅	#1009	1	1	yes	characteristic
464	C₄×C₅	—	2	4	no	—
465	C₄×C₅	—	2	2	no	—
466	C₄×C₅	—	4	1	no	—
467	C₄×C₅	—	4	2	no	—
468	C₄×C₅	—	6	2	no	—
469	C₄×C₅	—	6	2	no	—
470	C₄×C₅	—	6	4	no	—
471	C₄×C₅	—	12	1	no	—
472	C₄×C₅	#893	1	4	yes	—
473	C₂⁴	—	3	2	no	—
474	C₂⁴	—	3	1	no	—
475	C₂×D₄	—	3	4	no	—
476	C₂×D₄	—	3	8	no	—
477	C₂×D₄	—	6	2	no	—
478	C₂×D₄	—	6	2	no	—
479	C₂×D₄	—	12	2	no	—
480	C₂×D₄	—	12	2	no	—
481	C₂²×C₄	—	3	1	no	—
482	C₂²×C₄	—	3	1	no	—
483	C₂²×C₄	—	3	2	no	—
484	C₂²×C₄	—	3	4	no	—
485	C₂²×C₄	—	3	1	no	—
486	C₂²×C₄	—	6	4	no	—
487	C₂²×C₄	—	6	2	no	—
488	C₂²×C₄	—	6	2	no	—
489	C₂²×C₄	—	6	4	no	—
490	C₂²×C₄	—	12	2	no	—
491	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
492	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
493	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
494	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
495	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	3	4	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
500	C₂²⋊C₄	—	3	8	no	—
501	C₂²⋊C₄	—	6	4	no	—
502	C₂²⋊C₄	—	6	4	no	—
503	C₂²⋊C₄	—	6	2	no	—
504	C₂²⋊C₄	—	6	4	no	—
505	C₂²⋊C₄	—	6	2	no	—
506	C₂²⋊C₄	—	12	2	no	—
507	C₄²	—	2	2	no	—
508	C₄²	—	6	4	no	—
509	C₄²	—	6	2	no	—
510	C₄²	—	12	2	no	—
511	C₃×C₅	#2363	1	1	yes	characteristic, complemented, Hall
512	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
513	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
514	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
515	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
516	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
517	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×D₃	—	2	2	no	—
520	C₂×D₃	—	2	4	no	—
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	2	4	no	—
523	C₂×D₃	—	2	2	no	—
524	C₂×D₃	—	2	4	no	—
525	C₂×D₃	—	4	2	no	—
526	C₂×D₃	—	4	1	no	—
527	C₂×D₃	—	4	1	no	—
528	C₂×D₃	—	4	2	no	—
529	C₂×D₃	—	4	1	no	—
530	C₂×D₃	—	4	2	no	—
531	C₂×D₃	—	4	1	no	—
532	C₂×D₃	—	4	2	no	—
533	C₃×C₄	—	2	4	no	—
534	C₃×C₄	—	2	2	no	—
535	C₃×C₄	—	4	2	no	—
536	C₃×C₄	—	4	1	no	—
537	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
538	Dic₃	—	2	2	no	—
539	Dic₃	—	2	4	no	—
540	Dic₃	—	2	2	no	—
541	Dic₃	—	4	1	no	—
542	C₂×C₅	—	12	2	no	—
543	C₂×C₅	—	12	4	no	—
544	C₂×C₅	C₂×#893	1	1	yes	characteristic
545	C₂×C₅	#5545	1	1	yes	characteristic
546	C₂×C₅	C₄×#239	1	1	yes	characteristic
547	C₂×C₅	#5599	1	1	yes	characteristic
548	C₂×C₅	#5630	1	1	yes	characteristic
549	C₂×C₅	#5695	1	1	yes	characteristic
550	C₂×C₅	#5734	1	1	yes	characteristic
551	C₂³	—	3	4	no	—
552	C₂³	—	3	2	no	—
553	C₂³	—	6	1	no	—
554	C₂³	—	6	2	no	—
555	C₂³	—	6	2	no	—
556	C₂³	—	6	1	no	—
557	C₂³	—	6	1	no	—
558	C₂³	—	6	1	no	—
559	C₂³	—	6	2	no	—
560	C₂³	—	6	2	no	—
561	C₂³	—	6	2	no	—
562	C₂³	—	6	1	no	—
563	C₂³	—	6	2	no	—
564	C₂³	—	6	1	no	—
565	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
566	D₄	—	6	8	no	—
567	D₄	—	12	8	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	3	2	no	—
579	C₂×C₄	—	3	4	no	—
580	C₂×C₄	—	3	2	no	—
581	C₂×C₄	—	6	1	no	—
582	C₂×C₄	—	6	1	no	—
583	C₂×C₄	—	6	1	no	—
584	C₂×C₄	—	6	2	no	—
585	C₂×C₄	—	6	1	no	—
586	C₂×C₄	—	6	2	no	—
587	C₂×C₄	—	6	8	no	—
588	C₂×C₄	—	6	1	no	—
589	C₂×C₄	—	6	1	no	—
590	C₂×C₄	—	6	1	no	—
591	C₂×C₄	—	12	8	no	—
592	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
593	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
594	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
595	C₂×C₄	C₅×#239	1	2	yes	—
596	C₂×C₄	C₅×#239	1	2	yes	—
597	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
598	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
599	C₂×C₃	C₅×#518	1	1	yes	characteristic
600	C₂×C₃	C₅×#546	1	1	yes	characteristic
601	C₂×C₃	C₅×#550	1	1	yes	characteristic
602	C₂×C₃	C₅×#553	1	1	yes	characteristic
603	C₂×C₃	C₅×#555	1	1	yes	characteristic
604	D₃	—	4	2	no	—
605	D₃	—	4	4	no	—
606	C₅	#75985	1	1	yes	characteristic, direct product factor, Sylow
607	C₂²	—	6	2	no	—
608	C₂²	—	6	4	no	—
609	C₂²	—	6	2	no	—
610	C₂²	—	6	4	no	—
611	C₂²	—	6	4	no	—
612	C₂²	—	6	2	no	—
613	C₂²	—	12	1	no	—
614	C₂²	—	12	2	no	—
615	C₂²	—	12	2	no	—
616	C₂²	—	12	1	no	—
617	C₂²	—	12	1	no	—
618	C₂²	—	12	2	no	—
619	C₂²	—	12	2	no	—
620	C₂²	—	12	1	no	—
621	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
622	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
623	C₂²	C₅×#1004	1	1	yes	characteristic
624	C₂²	C₂×C₅×#239	1	1	yes	characteristic
625	C₂²	C₂×C₅×#239	1	1	yes	characteristic
626	C₂²	C₅×D₃×#41	1	1	yes	characteristic
627	C₂²	C₅×#1009	1	1	yes	characteristic
628	C₄	—	2	4	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	6	2	no	—
633	C₄	—	6	2	no	—
634	C₄	—	6	4	no	—
635	C₄	—	12	1	no	—
636	C₄	C₅×#893	1	4	yes	—
637	C₃	C₅×#2363	1	1	yes	characteristic, complemented, Sylow
638	C₂	—	12	2	no	—
639	C₂	—	12	4	no	—
640	C₂	C₂×C₅×#893	1	1	yes	characteristic
641	C₂	C₅×#5545	1	1	yes	characteristic
642	C₂	C₄×C₅×#239	1	1	yes	characteristic
643	C₂	C₅×#5599	1	1	yes	characteristic
644	C₂	C₅×#5630	1	1	yes	characteristic
645	C₂	C₅×#5695	1	1	yes	characteristic
646	C₂	C₅×#5734	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#389	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#895	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#389	D₃
hypocenter	C₃	C₅×#2363
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#389

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#892	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₃×C₅×#389	C₂	semidirect
5. C₅×#4990	C₂	semidirect
6. C₅×#4988	C₂	semidirect
7. C₅×#4988	C₂	semidirect
8. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
9. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
10. C₅×#4666	C₂	semidirect
11. C₅×#4665	C₂	semidirect
32. C₅×#895	C₄	semidirect
39. #75985	C₅	direct (N × H)
45. C₅×#389	D₃	semidirect
67. C₂×C₅×D₁₂	C₂×C₄	semidirect
73. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
76. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
84. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
85. C₅×C₄⋊Dic₃	D₄	semidirect
90. C₂×#892	C₂×C₅	semidirect
91. C₂×C₄×D₁₂	C₂×C₅	semidirect
92. C₃×#389	C₂×C₅	semidirect
93. #4990	C₂×C₅	semidirect
94. #4988	C₂×C₅	semidirect
95. #4988	C₂×C₅	semidirect
96. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
97. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
98. #4666	C₂×C₅	semidirect
99. #4665	C₂×C₅	semidirect
192. #895	C₄×C₅	semidirect
225. C₅×C₄⋊C₄	C₄×D₃	semidirect
242. #389	C₅×D₃	semidirect
294. C₂×D₁₂	C₂×C₄×C₅	semidirect
300. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
303. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
311. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
312. C₄⋊Dic₃	C₅×D₄	semidirect
499. C₄⋊C₄	C₄×C₅×D₃	semidirect
511. C₃×C₅	#2363	semidirect
606. C₅	#75985	direct (N × H)
637. C₃	C₅×#2363	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#895	2
C₂×C₅×#892	2
C₂×C₄×C₅×D₁₂	2
C₃×C₅×#389	2
C₅×#4990	2
C₅×#4988	2
C₅×Dic₃×C₄⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4666	2
C₅×#4665	2
C₅×#2363	3
#75985	5

Subgroups — C5×#75985 #14329033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75985 #14329033