Subgroups — C₅×#78522 #14415846

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#907	C₂	1	2	yes	maximal, complemented
2	C₅×#5477	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5129	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4706	C₂	1	4	yes	maximal, complemented
7	C₅×#4688	C₂	1	2	yes	maximal, complemented
8	C₅×C₈×D₁₂	C₂	1	2	yes	maximal, complemented
9	C₅×#2935	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#930	C₄	1	2	yes	—
15	C₅×#930	C₄	1	2	yes	—
16	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
17	C₅×#907	—	2	8	no	—
18	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
19	C₂×C₅×D₃×C₈	C₂²	1	4	yes	—
20	C₅×#875	C₄	1	2	yes	—
21	C₅×#874	C₄	1	1	yes	characteristic
22	C₄×C₅×D₁₂	C₂²	1	2	yes	—
23	C₄×C₅×D₁₂	C₂²	1	2	yes	—
24	C₅×#869	C₄	1	1	yes	characteristic
25	C₃×C₅×#97	C₂²	1	2	yes	—
26	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
28	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
29	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
31	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
32	#78522	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₅×#131	—	3	2	no	—
34	C₅×#532	—	3	1	no	—
35	C₅×#436	—	3	2	no	—
36	C₅×#435	—	3	4	no	—
37	C₅×C₈×D₄	—	3	2	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₅×#408	—	3	2	no	—
40	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×#67	C₂×C₄	1	4	yes	—
45	C₅×#235	—	2	4	no	—
46	C₅×#235	—	2	4	no	—
47	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
48	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
50	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
51	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
52	C₃×C₅×M₁₆	—	2	2	no	—
53	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
61	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
62	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
63	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
64	C₂×C₅×C₃⋊C₈	—	2	4	no	—
65	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
68	C₅×D₃×C₈	—	2	8	no	—
69	C₂×#907	C₂×C₅	1	2	yes	complemented
70	#5477	C₂×C₅	1	1	yes	characteristic
71	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
72	#5129	C₂×C₅	1	2	yes	complemented
73	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
74	#4706	C₂×C₅	1	4	yes	complemented
75	#4688	C₂×C₅	1	2	yes	complemented
76	C₈×D₁₂	C₂×C₅	1	2	yes	complemented
77	C₂×C₅×#41	—	3	2	no	—
78	C₅×#131	—	6	8	no	—
79	C₂×C₅×M₁₆	—	3	4	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₅×C₈	—	3	2	no	—
83	C₂²×C₅×C₈	—	3	4	no	—
84	C₅×C₄⋊Q₈	—	3	1	no	—
85	C₅×#127	—	3	1	no	—
86	C₅×#124	—	3	2	no	—
87	C₅×#121	—	3	2	no	—
88	C₅×#121	—	3	2	no	—
89	C₄×C₅×D₄	—	3	2	no	—
90	C₄×C₅×D₄	—	3	2	no	—
91	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
92	C₅×C₄⋊C₈	—	3	1	no	—
93	C₅×C₄⋊C₈	—	3	2	no	—
94	C₅×C₄⋊C₈	—	3	1	no	—
95	C₅×C₂²⋊C₈	—	3	4	no	—
96	C₅×C₂²⋊C₈	—	3	4	no	—
97	C₅×#97	C₂×D₃	1	2	yes	—
98	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
99	#2935	—	3	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	—	2	8	no	—
113	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
114	C₅×D₁₂	—	2	4	no	—
115	C₅×D₁₂	—	2	4	no	—
116	C₅×D₁₂	—	4	2	no	—
117	C₄×C₅×D₃	—	2	4	no	—
118	C₄×C₅×D₃	—	2	4	no	—
119	C₅×Dic₆	—	2	4	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₂×#235	C₂²×C₅	1	2	yes	—
125	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
128	#930	C₄×C₅	1	2	yes	—
129	#930	C₄×C₅	1	2	yes	—
130	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
131	#907	—	2	8	no	—
132	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
133	C₂×D₃×C₈	C₂²×C₅	1	4	yes	—
134	#875	C₄×C₅	1	2	yes	—
135	#874	C₄×C₅	1	1	yes	characteristic
136	C₄×D₁₂	C₂²×C₅	1	2	yes	—
137	C₄×D₁₂	C₂²×C₅	1	2	yes	—
138	#869	C₄×C₅	1	1	yes	characteristic
139	C₃×#97	C₂²×C₅	1	2	yes	—
140	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
141	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
142	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
143	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
144	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
145	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
146	C₅×#41	—	6	4	no	—
147	C₅×#41	—	6	4	no	—
148	C₂×C₅×Q₈	—	3	2	no	—
149	C₂×C₅×D₄	—	3	4	no	—
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	3	2	no	—
152	C₂×C₅×D₄	—	3	2	no	—
153	C₂²×C₄×C₅	—	3	4	no	—
154	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	—	6	8	no	—
159	C₅×M₁₆	D₁₂	1	4	yes	complemented
160	C₂×C₅×C₈	—	3	2	no	—
161	C₂×C₅×C₈	—	3	2	no	—
162	C₂×C₅×C₈	—	6	4	no	—
163	C₂×C₅×C₈	—	6	8	no	—
164	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
165	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
166	C₅×C₄⋊C₄	—	3	2	no	—
167	C₅×C₄⋊C₄	—	3	2	no	—
168	C₅×C₂²⋊C₄	—	3	4	no	—
169	C₅×C₂²⋊C₄	—	3	4	no	—
170	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
171	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
172	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₂×#131	—	3	2	no	—
175	#532	—	3	1	no	—
176	#436	—	3	2	no	—
177	#435	—	3	4	no	—
178	C₈×D₄	—	3	2	no	—
179	C₂×C₄⋊C₈	—	3	1	no	—
180	#408	—	3	2	no	—
181	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	4	no	—
187	C₂×C₅×D₃	—	2	4	no	—
188	C₂×C₅×D₃	—	2	4	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
193	C₃×C₄×C₅	#131	1	2	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	C₅×Dic₃	—	2	4	no	—
197	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂×#67	C₂×C₄×C₅	1	4	yes	—
201	#235	—	2	4	no	—
202	#235	—	2	4	no	—
203	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
204	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
205	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
207	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
208	C₃×M₁₆	—	2	2	no	—
209	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
210	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
211	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
212	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
213	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
214	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
215	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
217	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
218	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
219	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
220	C₂×C₃⋊C₈	—	2	4	no	—
221	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
222	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
223	ΓL(1,𝔽₂₅)	—	2	8	no	—
224	D₃×C₈	—	2	8	no	—
225	C₂³×C₅	—	3	4	no	—
226	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₅×Q₈	—	6	4	no	—
228	C₅×D₄	—	6	8	no	—
229	C₅×D₄	—	6	4	no	—
230	C₅×D₄	—	6	4	no	—
231	C₅×D₄	—	12	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	3	4	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	6	4	no	—
236	C₂×C₄×C₅	—	6	4	no	—
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
243	C₂×C₄×C₅	#235	1	2	yes	—
244	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	6	2	no	—
247	C₅×C₈	—	6	2	no	—
248	C₅×C₈	C₂×D₁₂	1	4	yes	—
249	C₂×#41	—	3	2	no	—
250	#131	—	6	8	no	—
251	C₂×M₁₆	—	3	4	no	—
252	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
253	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
254	C₂²×C₈	—	3	2	no	—
255	C₂²×C₈	—	3	4	no	—
256	C₄⋊Q₈	—	3	1	no	—
257	#127	—	3	1	no	—
258	#124	—	3	2	no	—
259	#121	—	3	2	no	—
260	#121	—	3	2	no	—
261	C₄×D₄	—	3	2	no	—
262	C₄×D₄	—	3	2	no	—
263	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
264	C₄⋊C₈	—	3	1	no	—
265	C₄⋊C₈	—	3	2	no	—
266	C₄⋊C₈	—	3	1	no	—
267	C₂²⋊C₈	—	3	4	no	—
268	C₂²⋊C₈	—	3	4	no	—
269	#97	C₂×C₅×D₃	1	2	yes	—
270	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
274	C₂×C₃×C₅	#568	1	1	yes	characteristic
275	C₅×D₃	—	4	4	no	—
276	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
286	C₂×C₃×C₄	C₅×#41	1	2	yes	—
287	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	#67	—	2	8	no	—
289	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
290	D₁₂	—	2	4	no	—
291	D₁₂	—	2	4	no	—
292	D₁₂	—	4	2	no	—
293	C₄×D₃	—	2	4	no	—
294	C₄×D₃	—	2	4	no	—
295	Dic₆	—	2	4	no	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
298	C₃⋊C₈	—	2	2	no	—
299	C₃⋊C₈	—	2	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	6	4	no	—
303	C₂²×C₅	—	6	4	no	—
304	C₂²×C₅	—	6	4	no	—
305	C₂²×C₅	C₄×D₁₂	1	2	yes	—
306	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	6	4	no	—
311	C₄×C₅	C₄×D₁₂	1	2	yes	—
312	C₄×C₅	#907	1	2	yes	complemented
313	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
314	C₄×C₅	C₂×#235	1	1	yes	characteristic
315	#41	—	6	4	no	—
316	#41	—	6	4	no	—
317	C₂×Q₈	—	3	2	no	—
318	C₂×D₄	—	3	4	no	—
319	C₂×D₄	—	3	2	no	—
320	C₂×D₄	—	3	2	no	—
321	C₂×D₄	—	3	2	no	—
322	C₂²×C₄	—	3	4	no	—
323	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
324	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	M₁₆	—	2	2	no	—
327	M₁₆	—	6	8	no	—
328	M₁₆	C₅×D₁₂	1	4	yes	complemented
329	C₂×C₈	—	3	2	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	6	4	no	—
332	C₂×C₈	—	6	8	no	—
333	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
334	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
335	C₄⋊C₄	—	3	2	no	—
336	C₄⋊C₄	—	3	2	no	—
337	C₂²⋊C₄	—	3	4	no	—
338	C₂²⋊C₄	—	3	4	no	—
339	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
340	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
341	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
342	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
347	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
348	C₂×D₃	—	2	4	no	—
349	C₂×D₃	—	2	4	no	—
350	C₂×D₃	—	2	4	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
355	C₃×C₄	C₅×#131	1	2	yes	complemented
356	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
357	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
358	Dic₃	—	2	4	no	—
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	—	12	4	no	—
361	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
362	C₂×C₅	C₂×#907	1	1	yes	characteristic
363	C₂×C₅	#5745	1	1	yes	characteristic
364	C₂³	—	3	4	no	—
365	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
366	Q₈	—	6	4	no	—
367	D₄	—	6	8	no	—
368	D₄	—	6	4	no	—
369	D₄	—	6	4	no	—
370	D₄	—	12	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	3	4	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	6	4	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
381	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
382	C₂×C₄	C₅×#235	1	2	yes	—
383	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	6	2	no	—
386	C₈	—	6	2	no	—
387	C₈	C₂×C₅×D₁₂	1	4	yes	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
390	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
391	C₂×C₃	C₅×#568	1	1	yes	characteristic
392	D₃	—	4	4	no	—
393	C₅	#78522	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	6	4	no	—
397	C₂²	—	6	4	no	—
398	C₂²	—	6	4	no	—
399	C₂²	C₄×C₅×D₁₂	1	2	yes	—
400	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	6	4	no	—
405	C₄	C₄×C₅×D₁₂	1	2	yes	—
406	C₄	C₅×#907	1	2	yes	complemented
407	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
408	C₄	C₂×C₅×#235	1	1	yes	characteristic
409	C₃	C₅×#2935	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	12	4	no	—
412	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
413	C₂	C₂×C₅×#907	1	1	yes	characteristic
414	C₂	C₅×#5745	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×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₅×#5477	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#2935
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#907	C₂	semidirect
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₅×#5129	C₂	semidirect
5. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4706	C₂	semidirect
7. C₅×#4688	C₂	semidirect
8. C₅×C₈×D₁₂	C₂	semidirect
32. #78522	C₅	direct (N × H)
40. C₄×C₅×M₁₆	D₃	semidirect
53. C₃×C₅×M₁₆	D₄	semidirect
69. C₂×#907	C₂×C₅	semidirect
71. C₃×C₄×M₁₆	C₂×C₅	semidirect
72. #5129	C₂×C₅	semidirect
73. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
74. #4706	C₂×C₅	semidirect
75. #4688	C₂×C₅	semidirect
76. C₈×D₁₂	C₂×C₅	semidirect
159. C₅×M₁₆	D₁₂	semidirect
181. C₄×M₁₆	C₅×D₃	semidirect
193. C₃×C₄×C₅	#131	semidirect
209. C₃×M₁₆	C₅×D₄	semidirect
312. C₄×C₅	#907	semidirect
328. M₁₆	C₅×D₁₂	semidirect
343. C₃×C₅	#2935	semidirect
355. C₃×C₄	C₅×#131	semidirect
393. C₅	#78522	direct (N × H)
406. C₄	C₅×#907	semidirect
409. C₃	C₅×#2935	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#907	2
C₅×#5477	2
C₃×C₄×C₅×M₁₆	2
C₅×#5129	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4706	2
C₅×#4688	2
C₅×C₈×D₁₂	2
C₅×#2935	3
#78522	5

Subgroups — C5×#78522 #14415846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78522 #14415846