Subgroups — C₅×#74228 #14327112

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 408 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×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4972	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4668	C₂	1	4	yes	maximal, complemented
7	C₅×#4667	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#95	C₂	1	2	yes	maximal, complemented
9	C₅×#2349	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
12	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
21	C₅×#893	—	2	8	no	—
22	C₄×C₅×D₁₂	C₄	1	8	yes	complemented
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
26	C₅×C₃⋊#95	C₂²	1	4	yes	—
27	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
28	#74228	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	C₅×#389	—	3	2	no	—
32	C₅×#385	—	3	4	no	—
33	C₅×#382	D₃	1	1	yes	characteristic, complemented
34	C₅×#380	—	3	2	no	—
35	C₄×C₅×C₄⋊C₄	—	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	D₄	1	4	yes	—
47	C₂×C₅×D₁₂	Q₈	1	4	yes	—
48	C₂×C₄×C₅×D₃	—	2	8	no	—
49	C₂×C₄×C₅×D₃	—	2	8	no	—
50	C₂×C₄×C₅×D₃	—	4	4	no	—
51	C₂×C₄×C₅×D₃	—	4	4	no	—
52	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
55	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
56	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
57	C₅×C₄⋊Dic₃	—	2	4	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
59	C₅×Dic₃⋊C₄	—	4	4	no	—
60	C₄×C₅×Dic₃	—	2	4	no	—
61	C₂×#893	C₂×C₅	1	2	yes	—
62	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
63	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
64	#4972	C₂×C₅	1	2	yes	complemented
65	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
66	#4668	C₂×C₅	1	4	yes	complemented
67	#4667	C₂×C₅	1	2	yes	complemented
68	D₃×#95	C₂×C₅	1	2	yes	complemented
69	C₂²×C₅×D₄	—	3	1	no	—
70	C₂³×C₄×C₅	—	3	2	no	—
71	C₂³×C₄×C₅	—	3	4	no	—
72	C₄×C₅×D₄	—	3	8	no	—
73	C₄×C₅×D₄	—	6	8	no	—
74	C₂×C₅×C₄⋊C₄	—	3	1	no	—
75	C₂×C₅×C₄⋊C₄	—	3	2	no	—
76	C₂×C₅×C₄⋊C₄	—	3	4	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
78	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
79	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
80	C₂×C₄²×C₅	—	3	2	no	—
81	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
82	C₅×#95	—	3	1	no	—
83	C₅×#95	—	3	4	no	—
84	C₅×#95	—	3	1	no	—
85	C₅×#95	C₂×D₃	1	2	yes	—
86	C₅×#95	C₂×D₃	1	2	yes	—
87	#2349	—	3	1	no	Sylow
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₂²×C₅×D₃	—	2	4	no	—
90	C₂²×C₅×D₃	—	2	4	no	—
91	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
93	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	4	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
111	C₂×C₅×Dic₃	#41	1	4	yes	—
112	C₅×D₁₂	C₄⋊C₄	1	16	yes	complemented
113	C₄×C₅×D₃	—	4	8	no	—
114	C₄×C₅×D₃	—	4	16	no	—
115	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
116	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
117	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	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	2	yes	—
123	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
124	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
125	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
126	#893	—	2	8	no	—
127	C₄×D₁₂	C₄×C₅	1	8	yes	complemented
128	C₃×#95	C₂²×C₅	1	2	yes	—
129	C₃×#95	C₂²×C₅	1	2	yes	—
130	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
131	C₃⋊#95	C₂²×C₅	1	4	yes	—
132	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
133	C₂⁴×C₅	—	3	2	no	—
134	C₂×C₅×D₄	—	3	4	no	—
135	C₂×C₅×D₄	—	3	4	no	—
136	C₂×C₅×D₄	—	3	4	no	—
137	C₂²×C₄×C₅	—	3	2	no	—
138	C₂²×C₄×C₅	—	3	2	no	—
139	C₂²×C₄×C₅	—	3	8	no	—
140	C₂²×C₄×C₅	—	3	2	no	—
141	C₂²×C₄×C₅	—	6	8	no	—
142	C₂²×C₄×C₅	—	6	8	no	—
143	C₂²×C₄×C₅	—	12	4	no	—
144	C₂²×C₄×C₅	—	12	4	no	—
145	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₅×C₄⋊C₄	—	2	4	no	—
150	C₅×C₄⋊C₄	—	3	4	no	—
151	C₅×C₄⋊C₄	—	6	4	no	—
152	C₅×C₄⋊C₄	—	12	4	no	—
153	C₅×C₂²⋊C₄	—	3	8	no	—
154	C₅×C₂²⋊C₄	—	6	8	no	—
155	C₄²×C₅	—	6	4	no	—
156	C₄²×C₅	C₄×D₃	1	4	yes	complemented
157	C₂×C₄×D₄	—	3	2	no	—
158	C₂×C₄×D₄	—	3	1	no	—
159	#389	—	3	2	no	—
160	#385	—	3	4	no	—
161	#382	C₅×D₃	1	1	yes	characteristic, complemented
162	#380	—	3	2	no	—
163	C₄×C₄⋊C₄	—	3	1	no	—
164	C₂×#95	—	3	2	no	—
165	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
169	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₅×D₃	—	2	4	no	—
171	C₂×C₅×D₃	—	2	4	no	—
172	C₂×C₅×D₃	—	2	8	no	—
173	C₂×C₅×D₃	—	2	8	no	—
174	C₂×C₅×D₃	C₂×C₄⋊C₄	1	8	yes	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	4	4	no	—
178	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
179	C₅×Dic₃	—	2	4	no	—
180	C₅×Dic₃	—	2	4	no	—
181	C₅×Dic₃	—	4	2	no	—
182	C₂³×D₃	C₂³×C₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
188	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
189	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
190	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
191	C₂×D₁₂	C₅×D₄	1	4	yes	—
192	C₂×D₁₂	C₅×Q₈	1	4	yes	—
193	C₂×C₄×D₃	—	2	8	no	—
194	C₂×C₄×D₃	—	2	8	no	—
195	C₂×C₄×D₃	—	4	4	no	—
196	C₂×C₄×D₃	—	4	4	no	—
197	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
198	C₃×C₄⋊C₄	—	2	4	no	—
199	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
200	(C₂×D₃)⋊C₄	—	2	8	no	—
201	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
202	C₄⋊Dic₃	—	2	4	no	—
203	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
204	Dic₃⋊C₄	—	4	4	no	—
205	C₄×Dic₃	—	2	4	no	—
206	C₂³×C₅	—	3	4	no	—
207	C₂³×C₅	—	3	4	no	—
208	C₂³×C₅	—	3	4	no	—
209	C₂³×C₅	—	6	4	no	—
210	C₂³×C₅	—	6	4	no	—
211	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
212	C₅×D₄	—	3	16	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	4	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	3	4	no	—
219	C₂×C₄×C₅	—	3	4	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	—	6	2	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	2	no	—
226	C₂×C₄×C₅	—	12	8	no	—
227	C₂×C₄×C₅	—	12	16	no	—
228	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
231	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
232	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
233	C₂²×D₄	—	3	1	no	—
234	C₂³×C₄	—	3	2	no	—
235	C₂³×C₄	—	3	4	no	—
236	C₄×D₄	—	3	8	no	—
237	C₄×D₄	—	6	8	no	—
238	C₂×C₄⋊C₄	—	3	1	no	—
239	C₂×C₄⋊C₄	—	3	2	no	—
240	C₂×C₄⋊C₄	—	3	4	no	—
241	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
242	C₂×C₂²⋊C₄	—	3	2	no	—
243	C₂×C₂²⋊C₄	—	3	4	no	—
244	C₂×C₄²	—	3	2	no	—
245	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
246	#95	—	3	1	no	—
247	#95	—	3	4	no	—
248	#95	—	3	1	no	—
249	#95	C₂×C₅×D₃	1	2	yes	—
250	#95	C₂×C₅×D₃	1	2	yes	—
251	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
253	C₂×C₃×C₅	#518	1	1	yes	characteristic
254	C₂×C₃×C₅	#546	1	2	yes	—
255	C₂×C₃×C₅	#554	1	2	yes	—
256	C₅×D₃	—	2	8	no	—
257	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
258	C₂²×D₃	—	2	4	no	—
259	C₂²×D₃	—	2	4	no	—
260	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
261	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
262	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
269	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
270	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
271	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
272	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
273	C₂×Dic₃	—	2	2	no	—
274	C₂×Dic₃	—	2	4	no	—
275	C₂×Dic₃	—	2	2	no	—
276	C₂×Dic₃	—	2	2	no	—
277	C₂×Dic₃	—	2	2	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
280	C₂×Dic₃	C₅×#41	1	4	yes	—
281	D₁₂	C₅×C₄⋊C₄	1	16	yes	complemented
282	C₄×D₃	—	4	8	no	—
283	C₄×D₃	—	4	16	no	—
284	C₂²×C₅	—	3	8	no	—
285	C₂²×C₅	—	6	8	no	—
286	C₂²×C₅	—	6	8	no	—
287	C₂²×C₅	—	6	4	no	—
288	C₂²×C₅	—	6	4	no	—
289	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
290	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
291	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
292	C₂²×C₅	D₃×#41	1	2	yes	—
293	C₂²×C₅	#1009	1	2	yes	—
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	4	4	no	—
297	C₄×C₅	—	6	4	no	—
298	C₄×C₅	—	6	4	no	—
299	C₄×C₅	—	12	2	no	—
300	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	—
301	C₂⁴	—	3	2	no	—
302	C₂×D₄	—	3	4	no	—
303	C₂×D₄	—	3	4	no	—
304	C₂×D₄	—	3	4	no	—
305	C₂²×C₄	—	3	2	no	—
306	C₂²×C₄	—	3	2	no	—
307	C₂²×C₄	—	3	8	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	—	6	8	no	—
310	C₂²×C₄	—	6	8	no	—
311	C₂²×C₄	—	12	4	no	—
312	C₂²×C₄	—	12	4	no	—
313	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
314	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	3	4	no	—
319	C₄⋊C₄	—	6	4	no	—
320	C₄⋊C₄	—	12	4	no	—
321	C₂²⋊C₄	—	3	8	no	—
322	C₂²⋊C₄	—	6	8	no	—
323	C₄²	—	6	4	no	—
324	C₄²	C₄×C₅×D₃	1	4	yes	complemented
325	C₃×C₅	#2349	1	1	yes	characteristic, complemented, Hall
326	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
327	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
329	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
330	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
331	C₂×D₃	—	2	4	no	—
332	C₂×D₃	—	2	4	no	—
333	C₂×D₃	—	2	8	no	—
334	C₂×D₃	—	2	8	no	—
335	C₂×D₃	C₂×C₅×C₄⋊C₄	1	8	yes	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	4	4	no	—
339	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
340	Dic₃	—	2	4	no	—
341	Dic₃	—	2	4	no	—
342	Dic₃	—	4	2	no	—
343	C₂×C₅	—	6	8	no	—
344	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₅	#5521	1	1	yes	characteristic
346	C₂×C₅	#5522	1	1	yes	characteristic
347	C₂×C₅	#5676	1	2	yes	—
348	C₂×C₅	#5690	1	2	yes	—
349	C₂³	—	3	4	no	—
350	C₂³	—	3	4	no	—
351	C₂³	—	3	4	no	—
352	C₂³	—	6	4	no	—
353	C₂³	—	6	4	no	—
354	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
355	D₄	—	3	16	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	3	4	no	—
362	C₂×C₄	—	3	4	no	—
363	C₂×C₄	—	6	2	no	—
364	C₂×C₄	—	6	4	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	—	6	2	no	—
368	C₂×C₄	—	6	2	no	—
369	C₂×C₄	—	12	8	no	—
370	C₂×C₄	—	12	16	no	—
371	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
372	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
373	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
374	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
375	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
376	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
377	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
378	C₂×C₃	C₅×#518	1	1	yes	characteristic
379	C₂×C₃	C₅×#546	1	2	yes	—
380	C₂×C₃	C₅×#554	1	2	yes	—
381	D₃	—	2	8	no	—
382	C₅	#74228	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	3	8	no	—
384	C₂²	—	6	8	no	—
385	C₂²	—	6	8	no	—
386	C₂²	—	6	4	no	—
387	C₂²	—	6	4	no	—
388	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
389	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
390	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
391	C₂²	C₅×D₃×#41	1	2	yes	—
392	C₂²	C₅×#1009	1	2	yes	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	4	no	—
396	C₄	—	6	4	no	—
397	C₄	—	6	4	no	—
398	C₄	—	12	2	no	—
399	C₄	C₅×D₃×C₄⋊C₄	1	4	yes	—
400	C₃	C₅×#2349	1	1	yes	characteristic, complemented, Sylow
401	C₂	—	6	8	no	—
402	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
403	C₂	C₅×#5521	1	1	yes	characteristic
404	C₂	C₅×#5522	1	1	yes	characteristic
405	C₂	C₅×#5676	1	2	yes	—
406	C₂	C₅×#5690	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#382	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#382	D₃
hypocenter	C₃	C₅×#2349
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#382

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#382	C₂	semidirect
4. C₅×#4972	C₂	semidirect
5. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
6. C₅×#4668	C₂	semidirect
7. C₅×#4667	C₂	semidirect
8. C₅×D₃×#95	C₂	semidirect
22. C₄×C₅×D₁₂	C₄	semidirect
28. #74228	C₅	direct (N × H)
33. C₅×#382	D₃	semidirect
52. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
54. C₃×C₄²×C₅	C₂×C₄	semidirect
56. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
58. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
63. C₃×#382	C₂×C₅	semidirect
64. #4972	C₂×C₅	semidirect
65. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
66. #4668	C₂×C₅	semidirect
67. #4667	C₂×C₅	semidirect
68. D₃×#95	C₂×C₅	semidirect
112. C₅×D₁₂	C₄⋊C₄	semidirect
127. C₄×D₁₂	C₄×C₅	semidirect
156. C₄²×C₅	C₄×D₃	semidirect
161. #382	C₅×D₃	semidirect
197. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
199. C₃×C₄²	C₂×C₄×C₅	semidirect
201. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
203. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
281. D₁₂	C₅×C₄⋊C₄	semidirect
324. C₄²	C₄×C₅×D₃	semidirect
325. C₃×C₅	#2349	semidirect
382. C₅	#74228	direct (N × H)
400. C₃	C₅×#2349	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×C₅×#382	2
C₅×#4972	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4668	2
C₅×#4667	2
C₅×D₃×#95	2
C₅×#2349	3
#74228	5

Subgroups — C5×#74228 #14327112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74228 #14327112