Subgroups — C₅×#73751 #14319714

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 404 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
2	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
6	C₅×#4932	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4666	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#95	C₂	1	2	yes	maximal, complemented
9	C₅×#2275	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
12	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
21	C₅×#893	C₄	1	16	yes	complemented
22	C₄×C₅×D₁₂	C₄	1	8	yes	complemented
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
25	C₅×C₃⋊#95	C₂²	1	4	yes	—
26	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
27	C₅×C₃⋊#95	C₂²	1	2	yes	—
28	#73751	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×D₄	—	3	2	no	—
30	C₂×C₄×C₅×D₄	—	3	1	no	—
31	C₄×C₅×C₄⋊C₄	—	3	2	no	—
32	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
33	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
34	C₄×C₅×C₂²⋊C₄	—	3	4	no	—
35	C₅×#376	—	3	1	no	—
36	C₂×C₅×#95	—	3	2	no	—
37	C₂³×C₅×D₃	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
43	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
44	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
45	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
46	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	—
47	C₂×C₄×C₅×D₃	—	4	4	no	—
48	C₂×C₄×C₅×D₃	—	4	4	no	—
49	C₂×C₄×C₅×D₃	—	4	4	no	—
50	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
51	C₂×C₄×C₅×D₃	C₂×C₄	1	16	yes	complemented
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
53	C₃×C₄²×C₅	—	4	2	no	—
54	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
55	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
56	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	16	yes	complemented
57	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
58	C₄×C₅×Dic₃	—	4	4	no	—
59	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
60	C₂×#893	C₂×C₅	1	2	yes	—
61	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
62	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
63	Dic₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
64	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	4	yes	complemented
65	#4932	C₂×C₅	1	1	yes	characteristic, complemented
66	#4666	C₂×C₅	1	2	yes	complemented
67	D₃×#95	C₂×C₅	1	2	yes	complemented
68	C₂²×C₅×D₄	—	3	1	no	—
69	C₂³×C₄×C₅	—	3	2	no	—
70	C₂³×C₄×C₅	—	3	4	no	—
71	C₄×C₅×D₄	—	3	16	no	—
72	C₄×C₅×D₄	—	3	8	no	—
73	C₂×C₅×C₄⋊C₄	—	3	1	no	—
74	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
75	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
76	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
77	C₂×C₄²×C₅	—	3	2	no	—
78	C₂×C₄²×C₅	—	3	4	no	—
79	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₅×#95	—	3	1	no	—
82	C₅×#95	—	3	4	no	—
83	C₅×#95	—	3	1	no	—
84	C₅×#95	—	3	2	no	—
85	C₅×#95	C₂×D₃	1	2	yes	—
86	#2275	—	3	1	no	Sylow
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₂²×C₅×D₃	—	2	2	no	—
89	C₂²×C₅×D₃	—	2	4	no	—
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	2	4	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
109	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
110	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
111	C₅×D₁₂	C₄²	1	16	yes	complemented
112	C₄×C₅×D₃	—	4	16	no	—
113	C₄×C₅×D₃	—	4	8	no	—
114	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
115	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
116	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
120	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
121	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
124	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
125	#893	C₄×C₅	1	16	yes	complemented
126	C₄×D₁₂	C₄×C₅	1	8	yes	complemented
127	C₃×#95	C₂²×C₅	1	2	yes	—
128	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
129	C₃⋊#95	C₂²×C₅	1	4	yes	—
130	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
131	C₃⋊#95	C₂²×C₅	1	2	yes	—
132	C₂⁴×C₅	—	3	2	no	—
133	C₂×C₅×D₄	—	3	8	no	—
134	C₂×C₅×D₄	—	3	4	no	—
135	C₂²×C₄×C₅	—	3	2	no	—
136	C₂²×C₄×C₅	—	3	2	no	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	—	3	16	no	—
139	C₂²×C₄×C₅	—	3	8	no	—
140	C₂²×C₄×C₅	—	12	4	no	—
141	C₂²×C₄×C₅	—	12	4	no	—
142	C₂²×C₄×C₅	—	12	4	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	3	4	no	—
148	C₅×C₄⋊C₄	C₄×D₃	1	8	yes	complemented
149	C₅×C₂²⋊C₄	—	3	16	no	—
150	C₅×C₂²⋊C₄	—	3	8	no	—
151	C₄²×C₅	—	3	8	no	—
152	C₄²×C₅	—	4	2	no	—
153	C₄²×C₅	—	12	4	no	—
154	C₄²×C₅	C₄×D₃	1	4	yes	complemented
155	C₂×C₄×D₄	—	3	2	no	—
156	C₂×C₄×D₄	—	3	1	no	—
157	C₄×C₄⋊C₄	—	3	2	no	—
158	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
159	C₄×C₂²⋊C₄	—	3	4	no	—
160	C₄×C₂²⋊C₄	—	3	2	no	—
161	#376	—	3	1	no	—
162	C₂×#95	—	3	2	no	—
163	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
165	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
167	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₅×D₃	—	2	4	no	—
169	C₂×C₅×D₃	—	2	8	no	—
170	C₂×C₅×D₃	—	2	4	no	—
171	C₂×C₅×D₃	—	2	8	no	—
172	C₂×C₅×D₃	C₂×C₄²	1	8	yes	—
173	C₃×C₄×C₅	—	2	2	no	—
174	C₃×C₄×C₅	—	2	8	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
177	C₅×Dic₃	—	2	4	no	—
178	C₅×Dic₃	—	2	4	no	—
179	C₅×Dic₃	—	2	4	no	—
180	C₂³×D₃	C₂³×C₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
186	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
187	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
188	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
189	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	—
190	C₂×C₄×D₃	—	4	4	no	—
191	C₂×C₄×D₃	—	4	4	no	—
192	C₂×C₄×D₃	—	4	4	no	—
193	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
194	C₂×C₄×D₃	C₂×C₄×C₅	1	16	yes	complemented
195	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
196	C₃×C₄²	—	4	2	no	—
197	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
198	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
199	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
200	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
201	C₄×Dic₃	—	4	4	no	—
202	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
203	C₂³×C₅	—	3	4	no	—
204	C₂³×C₅	—	3	8	no	—
205	C₂³×C₅	—	6	2	no	—
206	C₂³×C₅	—	6	2	no	—
207	C₂³×C₅	—	6	4	no	—
208	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
209	C₅×D₄	—	3	16	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	3	4	no	—
216	C₂×C₄×C₅	—	3	4	no	—
217	C₂×C₄×C₅	—	3	4	no	—
218	C₂×C₄×C₅	—	6	2	no	—
219	C₂×C₄×C₅	—	6	2	no	—
220	C₂×C₄×C₅	—	6	2	no	—
221	C₂×C₄×C₅	—	6	4	no	—
222	C₂×C₄×C₅	—	6	2	no	—
223	C₂×C₄×C₅	—	12	8	no	—
224	C₂×C₄×C₅	—	12	16	no	—
225	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
226	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
227	C₂×C₄×C₅	C₂×C₄×D₃	1	8	yes	—
228	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
230	C₂²×D₄	—	3	1	no	—
231	C₂³×C₄	—	3	4	no	—
232	C₂³×C₄	—	3	2	no	—
233	C₄×D₄	—	3	16	no	—
234	C₄×D₄	—	3	8	no	—
235	C₂×C₄⋊C₄	—	3	1	no	—
236	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
237	C₂×C₂²⋊C₄	—	3	4	no	—
238	C₂×C₂²⋊C₄	—	3	2	no	—
239	C₂×C₄²	—	3	2	no	—
240	C₂×C₄²	—	3	4	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
242	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
243	#95	—	3	1	no	—
244	#95	—	3	4	no	—
245	#95	—	3	2	no	—
246	#95	—	3	1	no	—
247	#95	C₂×C₅×D₃	1	2	yes	—
248	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
249	C₂×C₃×C₅	#518	1	1	yes	characteristic
250	C₂×C₃×C₅	#518	1	2	yes	—
251	C₂×C₃×C₅	#520	1	1	yes	characteristic
252	C₂×C₃×C₅	#520	1	2	yes	—
253	C₅×D₃	—	2	8	no	—
254	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
255	C₂²×D₃	—	2	2	no	—
256	C₂²×D₃	—	2	4	no	—
257	C₂²×D₃	—	2	2	no	—
258	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
259	C₂²×D₃	C₂²×C₄×C₅	1	8	yes	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
266	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
267	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
268	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
269	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
270	C₂×Dic₃	—	2	2	no	—
271	C₂×Dic₃	—	2	4	no	—
272	C₂×Dic₃	—	2	2	no	—
273	C₂×Dic₃	—	2	2	no	—
274	C₂×Dic₃	—	2	2	no	—
275	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
276	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
277	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
278	D₁₂	C₄²×C₅	1	16	yes	complemented
279	C₄×D₃	—	4	16	no	—
280	C₄×D₃	—	4	8	no	—
281	C₂²×C₅	—	3	8	no	—
282	C₂²×C₅	—	6	4	no	—
283	C₂²×C₅	—	6	4	no	—
284	C₂²×C₅	—	6	8	no	—
285	C₂²×C₅	—	6	8	no	—
286	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
287	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
288	C₂²×C₅	#1004	1	1	yes	characteristic
289	C₂²×C₅	#1007	1	1	yes	characteristic
290	C₂²×C₅	#1009	1	2	yes	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	8	no	—
294	C₄×C₅	—	6	4	no	—
295	C₄×C₅	—	6	4	no	—
296	C₄×C₅	—	6	4	no	—
297	C₄×C₅	C₄²×D₃	1	4	yes	—
298	C₂⁴	—	3	2	no	—
299	C₂×D₄	—	3	8	no	—
300	C₂×D₄	—	3	4	no	—
301	C₂²×C₄	—	3	2	no	—
302	C₂²×C₄	—	3	2	no	—
303	C₂²×C₄	—	3	2	no	—
304	C₂²×C₄	—	3	16	no	—
305	C₂²×C₄	—	3	8	no	—
306	C₂²×C₄	—	12	4	no	—
307	C₂²×C₄	—	12	4	no	—
308	C₂²×C₄	—	12	4	no	—
309	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
312	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
313	C₄⋊C₄	—	3	4	no	—
314	C₄⋊C₄	C₄×C₅×D₃	1	8	yes	complemented
315	C₂²⋊C₄	—	3	16	no	—
316	C₂²⋊C₄	—	3	8	no	—
317	C₄²	—	3	8	no	—
318	C₄²	—	4	2	no	—
319	C₄²	—	12	4	no	—
320	C₄²	C₄×C₅×D₃	1	4	yes	complemented
321	C₃×C₅	#2275	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
323	C₂²×C₃	C₂³×C₄×C₅	1	2	yes	—
324	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
326	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
327	C₂×D₃	—	2	4	no	—
328	C₂×D₃	—	2	8	no	—
329	C₂×D₃	—	2	4	no	—
330	C₂×D₃	—	2	8	no	—
331	C₂×D₃	C₂×C₄²×C₅	1	8	yes	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	8	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	C₂×C₄²×C₅	1	4	yes	—
336	Dic₃	—	2	4	no	—
337	Dic₃	—	2	4	no	—
338	Dic₃	—	2	4	no	—
339	C₂×C₅	—	6	8	no	—
340	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
341	C₂×C₅	#5504	1	1	yes	characteristic
342	C₂×C₅	#5521	1	1	yes	characteristic
343	C₂×C₅	#5545	1	2	yes	—
344	C₂×C₅	#5574	1	2	yes	—
345	C₂³	—	3	4	no	—
346	C₂³	—	3	8	no	—
347	C₂³	—	6	2	no	—
348	C₂³	—	6	2	no	—
349	C₂³	—	6	4	no	—
350	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
351	D₄	—	3	16	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	3	4	no	—
358	C₂×C₄	—	3	4	no	—
359	C₂×C₄	—	3	4	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	6	2	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	—	6	2	no	—
365	C₂×C₄	—	12	8	no	—
366	C₂×C₄	—	12	16	no	—
367	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
368	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
369	C₂×C₄	C₂×C₄×C₅×D₃	1	8	yes	—
370	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
371	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
372	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
373	C₂×C₃	C₅×#518	1	1	yes	characteristic
374	C₂×C₃	C₅×#518	1	2	yes	—
375	C₂×C₃	C₅×#520	1	1	yes	characteristic
376	C₂×C₃	C₅×#520	1	2	yes	—
377	D₃	—	2	8	no	—
378	C₅	#73751	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	3	8	no	—
380	C₂²	—	6	4	no	—
381	C₂²	—	6	4	no	—
382	C₂²	—	6	8	no	—
383	C₂²	—	6	8	no	—
384	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
385	C₂²	C₂²×C₄×C₅×D₃	1	2	yes	—
386	C₂²	C₅×#1004	1	1	yes	characteristic
387	C₂²	C₅×#1007	1	1	yes	characteristic
388	C₂²	C₅×#1009	1	2	yes	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	8	no	—
392	C₄	—	6	4	no	—
393	C₄	—	6	4	no	—
394	C₄	—	6	4	no	—
395	C₄	C₄²×C₅×D₃	1	4	yes	—
396	C₃	C₅×#2275	1	1	yes	characteristic, complemented, Sylow
397	C₂	—	6	8	no	—
398	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
399	C₂	C₅×#5504	1	1	yes	characteristic
400	C₂	C₅×#5521	1	1	yes	characteristic
401	C₂	C₅×#5545	1	2	yes	—
402	C₂	C₅×#5574	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2275
LCS	G ▷ C₂×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
3. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
5. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₅×#4932	C₂	semidirect
7. C₅×#4666	C₂	semidirect
8. C₅×D₃×#95	C₂	semidirect
21. C₅×#893	C₄	semidirect
22. C₄×C₅×D₁₂	C₄	semidirect
28. #73751	C₅	direct (N × H)
32. C₄×C₅×C₄⋊C₄	D₃	semidirect
50. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
51. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
52. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
54. C₃×C₄²×C₅	C₂×C₄	semidirect
55. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
56. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
57. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
59. C₄×C₅×Dic₃	C₂×C₄	semidirect
62. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
63. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
64. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
65. #4932	C₂×C₅	semidirect
66. #4666	C₂×C₅	semidirect
67. D₃×#95	C₂×C₅	semidirect
111. C₅×D₁₂	C₄²	semidirect
125. #893	C₄×C₅	semidirect
126. C₄×D₁₂	C₄×C₅	semidirect
148. C₅×C₄⋊C₄	C₄×D₃	semidirect
154. C₄²×C₅	C₄×D₃	semidirect
158. C₄×C₄⋊C₄	C₅×D₃	semidirect
193. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
194. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
195. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
197. C₃×C₄²	C₂×C₄×C₅	semidirect
198. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
199. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
200. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
202. C₄×Dic₃	C₂×C₄×C₅	semidirect
278. D₁₂	C₄²×C₅	semidirect
314. C₄⋊C₄	C₄×C₅×D₃	semidirect
320. C₄²	C₄×C₅×D₃	semidirect
321. C₃×C₅	#2275	semidirect
378. C₅	#73751	direct (N × H)
396. C₃	C₅×#2275	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×C₄×C₅×D₁₂	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×Dic₃×C₄⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4932	2
C₅×#4666	2
C₅×D₃×#95	2
C₅×#2275	3
#73751	5

Subgroups — C5×#73751 #14319714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73751 #14319714