Subgroups — C₅×#73653 #14329454

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#893	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4988	C₂	1	2	yes	maximal, complemented
6	C₅×#4939	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4665	C₂	1	4	yes	maximal, complemented
9	C₅×#2366	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
12	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
13	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
24	C₅×#893	—	2	8	no	—
25	C₅×#874	C₄	1	8	yes	complemented
26	C₄×C₅×D₁₂	—	2	8	no	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₅×C₃⋊#95	C₂²	1	2	yes	—
29	#73653	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×#127	—	3	1	no	—
31	C₂×C₄×C₅×D₄	—	3	2	no	—
32	C₂×C₄×C₅×D₄	—	3	2	no	—
33	C₅×#390	—	3	2	no	—
34	C₅×#390	—	3	2	no	—
35	C₅×#386	—	3	4	no	—
36	C₄×C₅×C₄⋊C₄	—	3	1	no	—
37	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₅×D₃	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
45	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
46	C₂×C₅×D₁₂	—	2	4	no	—
47	C₂×C₅×D₁₂	—	2	4	no	—
48	C₂×C₅×D₁₂	—	2	4	no	—
49	C₂×C₅×D₁₂	—	2	4	no	—
50	C₂×C₅×D₁₂	—	4	2	no	—
51	C₂×C₅×D₁₂	—	4	2	no	—
52	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
53	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
54	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
55	C₂×C₄×C₅×D₃	—	2	8	no	—
56	C₂×C₄×C₅×D₃	—	2	8	no	—
57	C₂×C₄×C₅×D₃	—	4	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
62	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
64	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
65	C₅×C₄⋊Dic₃	—	2	2	no	—
66	C₅×C₄⋊Dic₃	D₄	1	4	yes	complemented
67	C₄×C₅×Dic₃	—	2	4	no	—
68	C₂×#893	C₂×C₅	1	2	yes	complemented
69	C₂×#874	C₂×C₅	1	1	yes	characteristic
70	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	complemented
71	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
72	#4988	C₂×C₅	1	2	yes	complemented
73	#4939	C₂×C₅	1	2	yes	complemented
74	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
75	#4665	C₂×C₅	1	4	yes	complemented
76	C₂²×C₅×D₄	—	3	2	no	—
77	C₂²×C₅×D₄	—	3	2	no	—
78	C₂²×C₅×D₄	—	3	2	no	—
79	C₂³×C₄×C₅	—	3	4	no	—
80	C₅×#127	—	3	8	no	—
81	C₄×C₅×D₄	—	6	8	no	—
82	C₄×C₅×D₄	—	6	8	no	—
83	C₂×C₅×C₄⋊C₄	—	3	1	no	—
84	C₂×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
90	C₂×C₄²×C₅	—	3	2	no	—
91	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
92	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
93	C₅×#95	—	3	2	no	—
94	C₅×#95	C₂×D₃	1	2	yes	—
95	#2366	—	3	1	no	Sylow
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	4	no	—
98	C₂²×C₅×D₃	—	2	4	no	—
99	C₂²×C₅×D₃	—	2	4	no	—
100	C₂²×C₅×D₃	—	2	4	no	—
101	C₂²×C₅×D₃	—	2	4	no	—
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	2	2	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
125	C₅×D₁₂	—	2	16	no	—
126	C₅×D₁₂	—	2	16	no	—
127	C₅×D₁₂	—	4	8	no	—
128	C₄×C₅×D₃	—	4	16	no	—
129	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
130	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
131	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
132	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
138	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
139	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
140	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
143	#893	—	2	8	no	—
144	#874	C₄×C₅	1	8	yes	complemented
145	C₄×D₁₂	—	2	8	no	—
146	C₃×#95	C₂²×C₅	1	2	yes	—
147	C₃⋊#95	C₂²×C₅	1	2	yes	—
148	C₂⁴×C₅	—	3	4	no	—
149	C₂×C₅×D₄	—	3	8	no	—
150	C₂×C₅×D₄	—	3	8	no	—
151	C₂×C₅×D₄	—	3	8	no	—
152	C₂×C₅×D₄	—	6	4	no	—
153	C₂×C₅×D₄	—	6	4	no	—
154	C₂×C₅×D₄	—	6	4	no	—
155	C₂×C₅×D₄	—	6	4	no	—
156	C₂×C₅×D₄	—	12	2	no	—
157	C₂×C₅×D₄	—	12	2	no	—
158	C₂²×C₄×C₅	—	3	2	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	6	8	no	—
161	C₂²×C₄×C₅	—	6	8	no	—
162	C₂²×C₄×C₅	—	12	4	no	—
163	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	3	4	no	—
170	C₅×C₄⋊C₄	—	6	2	no	—
171	C₅×C₄⋊C₄	D₁₂	1	4	yes	complemented
172	C₅×C₂²⋊C₄	—	6	8	no	—
173	C₅×C₂²⋊C₄	—	6	8	no	—
174	C₅×C₂²⋊C₄	—	12	4	no	—
175	C₄²×C₅	—	2	4	no	—
176	C₄²×C₅	—	6	4	no	—
177	C₄²×C₅	C₄×D₃	1	4	yes	complemented
178	C₂×#127	—	3	1	no	—
179	C₂×C₄×D₄	—	3	2	no	—
180	C₂×C₄×D₄	—	3	2	no	—
181	#390	—	3	2	no	—
182	#390	—	3	2	no	—
183	#386	—	3	4	no	—
184	C₄×C₄⋊C₄	—	3	1	no	—
185	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
191	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	8	no	—
194	C₂×C₅×D₃	—	2	8	no	—
195	C₂×C₅×D₃	—	2	8	no	—
196	C₂×C₅×D₃	—	4	4	no	—
197	C₂×C₅×D₃	—	4	4	no	—
198	C₂×C₅×D₃	—	4	4	no	—
199	C₂×C₅×D₃	—	4	4	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	2	4	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
204	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
205	C₅×Dic₃	—	2	4	no	—
206	C₅×Dic₃	—	4	2	no	—
207	C₂³×D₃	C₂³×C₅	1	4	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
214	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
215	C₂×D₁₂	—	2	4	no	—
216	C₂×D₁₂	—	2	4	no	—
217	C₂×D₁₂	—	2	4	no	—
218	C₂×D₁₂	—	2	4	no	—
219	C₂×D₁₂	—	4	2	no	—
220	C₂×D₁₂	—	4	2	no	—
221	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
222	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
223	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
224	C₂×C₄×D₃	—	2	8	no	—
225	C₂×C₄×D₃	—	2	8	no	—
226	C₂×C₄×D₃	—	4	4	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
229	C₃×C₄²	—	2	4	no	—
230	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
231	(C₂×D₃)⋊C₄	—	2	8	no	—
232	(C₂×D₃)⋊C₄	—	2	8	no	—
233	(C₂×D₃)⋊C₄	—	4	4	no	—
234	C₄⋊Dic₃	—	2	2	no	—
235	C₄⋊Dic₃	C₅×D₄	1	4	yes	complemented
236	C₄×Dic₃	—	2	4	no	—
237	C₂³×C₅	—	3	8	no	—
238	C₂³×C₅	—	6	4	no	—
239	C₂³×C₅	—	6	4	no	—
240	C₂³×C₅	—	6	4	no	—
241	C₂³×C₅	—	6	4	no	—
242	C₂³×C₅	—	6	4	no	—
243	C₂³×C₅	—	6	4	no	—
244	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
245	C₅×D₄	—	6	16	no	—
246	C₅×D₄	—	6	16	no	—
247	C₅×D₄	—	12	8	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	3	4	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	—	6	2	no	—
258	C₂×C₄×C₅	—	6	2	no	—
259	C₂×C₄×C₅	—	6	2	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	12	16	no	—
262	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
263	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
264	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
265	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
266	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
267	C₂×C₄×C₅	#235	1	2	yes	—
268	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
269	C₂×C₄×C₅	#239	1	2	yes	—
270	C₂²×D₄	—	3	2	no	—
271	C₂²×D₄	—	3	2	no	—
272	C₂²×D₄	—	3	2	no	—
273	C₂³×C₄	—	3	4	no	—
274	#127	—	3	8	no	—
275	C₄×D₄	—	6	8	no	—
276	C₄×D₄	—	6	8	no	—
277	C₂×C₄⋊C₄	—	3	1	no	—
278	C₂×C₄⋊C₄	—	3	1	no	—
279	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	3	4	no	—
282	C₂×C₂²⋊C₄	—	3	4	no	—
283	C₂×C₂²⋊C₄	—	3	4	no	—
284	C₂×C₄²	—	3	2	no	—
285	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
286	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
287	#95	—	3	2	no	—
288	#95	C₂×C₅×D₃	1	2	yes	—
289	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×C₃×C₅	#518	1	1	yes	characteristic
292	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
293	C₂×C₃×C₅	#550	1	1	yes	characteristic
294	C₂×C₃×C₅	#550	1	1	yes	characteristic
295	C₂×C₃×C₅	#559	1	1	yes	characteristic
296	C₅×D₃	—	4	8	no	—
297	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
298	C₂²×D₃	—	2	4	no	—
299	C₂²×D₃	—	2	4	no	—
300	C₂²×D₃	—	2	4	no	—
301	C₂²×D₃	—	2	4	no	—
302	C₂²×D₃	—	2	4	no	—
303	C₂²×D₃	—	2	4	no	—
304	C₂²×D₃	C₂²×C₄×C₅	1	8	yes	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
313	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
314	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
315	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
316	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂×C₃×C₄	C₅×#41	1	2	yes	—
319	C₂×C₃×C₄	C₅×#41	1	2	yes	—
320	C₂×Dic₃	—	2	2	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
326	D₁₂	—	2	16	no	—
327	D₁₂	—	2	16	no	—
328	D₁₂	—	4	8	no	—
329	C₄×D₃	—	4	16	no	—
330	C₂²×C₅	—	6	8	no	—
331	C₂²×C₅	—	6	8	no	—
332	C₂²×C₅	—	6	8	no	—
333	C₂²×C₅	—	12	4	no	—
334	C₂²×C₅	—	12	4	no	—
335	C₂²×C₅	—	12	4	no	—
336	C₂²×C₅	—	12	4	no	—
337	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
338	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
339	C₂²×C₅	C₂×#235	1	1	yes	characteristic
340	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
341	C₂²×C₅	C₂×#239	1	1	yes	characteristic
342	C₂²×C₅	#1009	1	1	yes	characteristic
343	C₂²×C₅	#1009	1	1	yes	characteristic
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	2	4	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	6	4	no	—
348	C₄×C₅	—	12	2	no	—
349	C₄×C₅	C₄×D₁₂	1	4	yes	complemented
350	C₄×C₅	#893	1	4	yes	complemented
351	C₂⁴	—	3	4	no	—
352	C₂×D₄	—	3	8	no	—
353	C₂×D₄	—	3	8	no	—
354	C₂×D₄	—	3	8	no	—
355	C₂×D₄	—	6	4	no	—
356	C₂×D₄	—	6	4	no	—
357	C₂×D₄	—	6	4	no	—
358	C₂×D₄	—	6	4	no	—
359	C₂×D₄	—	12	2	no	—
360	C₂×D₄	—	12	2	no	—
361	C₂²×C₄	—	3	2	no	—
362	C₂²×C₄	—	3	2	no	—
363	C₂²×C₄	—	6	8	no	—
364	C₂²×C₄	—	6	8	no	—
365	C₂²×C₄	—	12	4	no	—
366	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
367	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
369	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	3	4	no	—
373	C₄⋊C₄	—	6	2	no	—
374	C₄⋊C₄	C₅×D₁₂	1	4	yes	complemented
375	C₂²⋊C₄	—	6	8	no	—
376	C₂²⋊C₄	—	6	8	no	—
377	C₂²⋊C₄	—	12	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	6	4	no	—
380	C₄²	C₄×C₅×D₃	1	4	yes	complemented
381	C₃×C₅	#2366	1	1	yes	characteristic, complemented, Hall
382	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
383	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
384	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
386	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
387	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×D₃	—	2	8	no	—
390	C₂×D₃	—	2	8	no	—
391	C₂×D₃	—	2	8	no	—
392	C₂×D₃	—	4	4	no	—
393	C₂×D₃	—	4	4	no	—
394	C₂×D₃	—	4	4	no	—
395	C₂×D₃	—	4	4	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	4	no	—
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
400	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
401	Dic₃	—	2	4	no	—
402	Dic₃	—	4	2	no	—
403	C₂×C₅	—	12	8	no	—
404	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
405	C₂×C₅	C₂×#893	1	1	yes	characteristic
406	C₂×C₅	#5521	1	1	yes	characteristic
407	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
408	C₂×C₅	#5553	1	1	yes	characteristic
409	C₂×C₅	#5577	1	1	yes	characteristic
410	C₂×C₅	#5585	1	1	yes	characteristic
411	C₂³	—	3	8	no	—
412	C₂³	—	6	4	no	—
413	C₂³	—	6	4	no	—
414	C₂³	—	6	4	no	—
415	C₂³	—	6	4	no	—
416	C₂³	—	6	4	no	—
417	C₂³	—	6	4	no	—
418	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
419	D₄	—	6	16	no	—
420	D₄	—	6	16	no	—
421	D₄	—	12	8	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	3	4	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	6	2	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	12	16	no	—
436	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
437	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
438	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
439	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
440	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
441	C₂×C₄	C₅×#235	1	2	yes	—
442	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
443	C₂×C₄	C₅×#239	1	2	yes	—
444	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
445	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
446	C₂×C₃	C₅×#518	1	1	yes	characteristic
447	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
448	C₂×C₃	C₅×#550	1	1	yes	characteristic
449	C₂×C₃	C₅×#550	1	1	yes	characteristic
450	C₂×C₃	C₅×#559	1	1	yes	characteristic
451	D₃	—	4	8	no	—
452	C₅	#73653	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²	—	6	8	no	—
454	C₂²	—	6	8	no	—
455	C₂²	—	6	8	no	—
456	C₂²	—	12	4	no	—
457	C₂²	—	12	4	no	—
458	C₂²	—	12	4	no	—
459	C₂²	—	12	4	no	—
460	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
461	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
462	C₂²	C₂×C₅×#235	1	1	yes	characteristic
463	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
464	C₂²	C₂×C₅×#239	1	1	yes	characteristic
465	C₂²	C₅×#1009	1	1	yes	characteristic
466	C₂²	C₅×#1009	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	6	4	no	—
471	C₄	—	12	2	no	—
472	C₄	C₄×C₅×D₁₂	1	4	yes	complemented
473	C₄	C₅×#893	1	4	yes	complemented
474	C₃	C₅×#2366	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	12	8	no	—
476	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
477	C₂	C₂×C₅×#893	1	1	yes	characteristic
478	C₂	C₅×#5521	1	1	yes	characteristic
479	C₂	C₅×D₄×D₁₂	1	1	yes	characteristic
480	C₂	C₅×#5553	1	1	yes	characteristic
481	C₂	C₅×#5577	1	1	yes	characteristic
482	C₂	C₅×#5585	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×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#874	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2366
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#893	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×#4988	C₂	semidirect
6. C₅×#4939	C₂	semidirect
7. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
8. C₅×#4665	C₂	semidirect
25. C₅×#874	C₄	semidirect
29. #73653	C₅	direct (N × H)
37. C₄×C₅×C₄⋊C₄	D₃	semidirect
52. C₂×C₅×D₁₂	C₂×C₄	semidirect
53. C₂×C₅×D₁₂	C₂×C₄	semidirect
54. C₂×C₅×D₁₂	C₂×C₄	semidirect
59. C₃×C₅×C₄⋊C₄	D₄	semidirect
61. C₃×C₄²×C₅	C₂×C₄	semidirect
66. C₅×C₄⋊Dic₃	D₄	semidirect
68. C₂×#893	C₂×C₅	semidirect
70. C₂×C₄×D₁₂	C₂×C₅	semidirect
71. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
72. #4988	C₂×C₅	semidirect
73. #4939	C₂×C₅	semidirect
74. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
75. #4665	C₂×C₅	semidirect
144. #874	C₄×C₅	semidirect
171. C₅×C₄⋊C₄	D₁₂	semidirect
177. C₄²×C₅	C₄×D₃	semidirect
185. C₄×C₄⋊C₄	C₅×D₃	semidirect
203. C₃×C₄×C₅	C₄×D₄	semidirect
204. C₃×C₄×C₅	C₄×D₄	semidirect
221. C₂×D₁₂	C₂×C₄×C₅	semidirect
222. C₂×D₁₂	C₂×C₄×C₅	semidirect
223. C₂×D₁₂	C₂×C₄×C₅	semidirect
228. C₃×C₄⋊C₄	C₅×D₄	semidirect
230. C₃×C₄²	C₂×C₄×C₅	semidirect
235. C₄⋊Dic₃	C₅×D₄	semidirect
349. C₄×C₅	C₄×D₁₂	semidirect
350. C₄×C₅	#893	semidirect
374. C₄⋊C₄	C₅×D₁₂	semidirect
380. C₄²	C₄×C₅×D₃	semidirect
381. C₃×C₅	#2366	semidirect
399. C₃×C₄	C₄×C₅×D₄	semidirect
400. C₃×C₄	C₄×C₅×D₄	semidirect
452. C₅	#73653	direct (N × H)
472. C₄	C₄×C₅×D₁₂	semidirect
473. C₄	C₅×#893	semidirect
474. C₃	C₅×#2366	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#893	2
C₂×C₅×#874	2
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4988	2
C₅×#4939	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4665	2
C₅×#2366	3
#73653	5

Subgroups — C5×#73653 #14329454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73653 #14329454