Subgroups — C₅×#68172 #14282064

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#4837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1486	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	2	1	no	—
11	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
13	C₄×C₅×#67	—	2	1	no	—
14	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
15	C₅×#893	C₄	1	1	yes	characteristic
16	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
17	C₅×#67⋊C₄	—	2	1	no	—
18	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
19	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×Dic₃⋊C₈	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	#68172	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×D₄	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₅×#423	—	3	1	no	—
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₅×D₄⋊C₈	—	3	1	no	—
35	C₅×D₄⋊C₈	D₃	1	1	yes	characteristic, complemented
36	C₂³×C₅×D₃	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂×C₅×#67	—	2	1	no	—
40	C₂²×C₅×Dic₃	—	2	1	no	—
41	C₅×D₃×D₄	—	2	2	no	—
42	C₅×D₃×D₄	—	2	2	no	—
43	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	—	2	1	no	—
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₂×C₄×C₅×D₃	—	2	1	no	—
47	C₂×C₄×C₅×D₃	—	4	2	no	—
48	C₂×C₄×C₅×D₃	—	4	2	no	—
49	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₅×#217	—	2	1	no	—
58	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
59	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
60	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₅×Dic₃⋊C₄	—	2	1	no	—
62	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
64	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	C₅×ΓL(1,𝔽₂₅)	—	4	2	no	—
68	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
69	#4837	C₂×C₅	1	1	yes	characteristic, complemented
70	#4685	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
72	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
73	#4483	C₂×C₅	1	1	yes	characteristic, complemented
74	#4459	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×C₅×D₄	—	3	1	no	—
76	C₂³×C₄×C₅	—	6	1	no	—
77	C₂×C₅×M₁₆	—	6	1	no	—
78	C₄×C₅×D₄	—	3	1	no	—
79	C₄×C₅×D₄	—	3	1	no	—
80	C₄×C₅×D₄	—	3	1	no	—
81	C₄×C₅×D₄	—	6	1	no	—
82	C₄×C₅×D₄	—	6	1	no	—
83	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
86	C₂×C₄²×C₅	—	3	1	no	—
87	C₅×C₄⋊C₈	—	3	1	no	—
88	C₅×C₄⋊C₈	—	6	1	no	—
89	C₅×C₄⋊C₈	—	6	1	no	—
90	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
91	C₅×C₂²⋊C₈	—	6	1	no	—
92	C₄×C₅×C₈	—	3	1	no	—
93	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
94	#1486	—	3	1	no	Sylow
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂²×C₅×D₃	—	2	4	no	—
97	C₂²×C₅×D₃	—	2	1	no	—
98	C₂²×C₅×D₃	—	4	2	no	—
99	C₂²×C₅×D₃	—	4	2	no	—
100	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₃×C₅×D₄	—	2	1	no	—
102	C₃×C₅×D₄	M₁₆	1	2	yes	complemented
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₅×#67	—	2	4	no	—
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₂×C₅×Dic₃	—	4	2	no	—
112	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₅×D₁₂	—	2	1	no	—
116	C₅×D₁₂	M₁₆	1	2	yes	complemented
117	C₄×C₅×D₃	—	2	1	no	—
118	C₄×C₅×D₃	—	2	1	no	—
119	C₄×C₅×D₃	—	4	1	no	—
120	C₄×C₅×D₃	—	4	2	no	—
121	C₄×C₅×D₃	—	4	1	no	—
122	C₄×C₅×D₃	—	4	1	no	—
123	C₄×C₅×D₃	—	4	2	no	—
124	C₄×C₅×D₃	D₈	1	2	yes	—
125	C₄×C₅×D₃	SD₁₆	1	2	yes	—
126	C₃×C₅×C₈	—	4	1	no	—
127	C₃×C₅×C₈	—	4	1	no	—
128	C₅×C₃⋊C₈	—	4	1	no	—
129	C₅×C₃⋊C₈	—	4	1	no	—
130	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
131	C₂²×C₄×D₃	—	2	1	no	—
132	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
133	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic
134	C₄×#67	—	2	1	no	—
135	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
136	#893	C₄×C₅	1	1	yes	characteristic
137	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
138	#67⋊C₄	—	2	1	no	—
139	D₃×C₂²⋊C₄	—	2	1	no	—
140	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
141	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
142	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
144	(C₂×D₃)⋊C₈	—	2	1	no	—
145	Dic₃⋊C₈	—	2	1	no	—
146	Dic₃⋊C₈	—	2	1	no	—
147	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₂⁴×C₅	—	6	1	no	—
150	C₂×C₅×D₄	—	3	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	2	no	—
153	C₂×C₅×D₄	—	6	2	no	—
154	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	—	6	1	no	—
163	C₂²×C₄×C₅	—	12	2	no	—
164	C₂²×C₄×C₅	—	12	2	no	—
165	C₅×M₁₆	—	12	2	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	6	1	no	—
169	C₂×C₅×C₈	—	6	1	no	—
170	C₅×C₄⋊C₄	—	3	1	no	—
171	C₅×C₄⋊C₄	—	6	1	no	—
172	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
173	C₅×C₂²⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	6	1	no	—
175	C₅×C₂²⋊C₄	—	6	1	no	—
176	C₅×C₂²⋊C₄	—	6	1	no	—
177	C₄²×C₅	—	3	1	no	—
178	C₄²×C₅	—	3	1	no	—
179	C₄²×C₅	—	3	1	no	—
180	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₄×D₄	—	3	1	no	—
182	#431	—	3	1	no	—
183	#423	—	3	1	no	—
184	D₄⋊C₈	—	3	1	no	—
185	D₄⋊C₈	—	3	1	no	—
186	D₄⋊C₈	—	3	1	no	—
187	D₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	4	1	no	—
190	C₂²×C₃×C₅	—	4	1	no	—
191	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₅×D₃	—	2	1	no	—
193	C₂×C₅×D₃	—	2	1	no	—
194	C₂×C₅×D₃	—	2	2	no	—
195	C₂×C₅×D₃	—	4	8	no	—
196	C₂×C₅×D₃	—	4	1	no	—
197	C₂×C₅×D₃	—	4	1	no	—
198	C₂×C₅×D₃	#102	1	2	yes	—
199	C₃×C₄×C₅	—	2	1	no	—
200	C₃×C₄×C₅	—	4	1	no	—
201	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
203	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
204	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
205	C₅×Dic₃	—	2	1	no	—
206	C₅×Dic₃	—	2	1	no	—
207	C₅×Dic₃	—	4	1	no	—
208	C₅×Dic₃	#102	1	2	yes	—
209	C₂³×D₃	—	2	1	no	—
210	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂×#67	—	2	1	no	—
213	C₂²×Dic₃	—	2	1	no	—
214	D₃×D₄	—	2	2	no	—
215	D₃×D₄	—	2	2	no	—
216	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄×D₃	—	2	1	no	—
218	C₂×C₄×D₃	—	2	1	no	—
219	C₂×C₄×D₃	—	2	1	no	—
220	C₂×C₄×D₃	—	4	2	no	—
221	C₂×C₄×D₃	—	4	2	no	—
222	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
224	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
228	C₃×C₂²⋊C₄	—	2	1	no	—
229	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
230	#217	—	2	1	no	—
231	(C₂×D₃)⋊C₄	—	2	1	no	—
232	(C₂×D₃)⋊C₄	—	2	1	no	—
233	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
234	Dic₃⋊C₄	—	2	1	no	—
235	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
236	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
237	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
238	C₂×C₃⋊C₈	—	2	1	no	—
239	C₂×C₃⋊C₈	—	2	1	no	—
240	ΓL(1,𝔽₂₅)	—	4	2	no	—
241	C₂³×C₅	—	2	1	no	—
242	C₂³×C₅	—	3	1	no	—
243	C₂³×C₅	—	6	4	no	—
244	C₂³×C₅	—	6	1	no	—
245	C₂³×C₅	—	12	2	no	—
246	C₂³×C₅	—	12	2	no	—
247	C₅×D₄	—	2	1	no	—
248	C₅×D₄	—	3	2	no	—
249	C₅×D₄	—	6	4	no	—
250	C₅×D₄	—	6	1	no	—
251	C₅×D₄	ΓL(1,𝔽₂₅)	1	2	yes	complemented
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	3	1	no	—
254	C₂×C₄×C₅	—	3	2	no	—
255	C₂×C₄×C₅	—	3	2	no	—
256	C₂×C₄×C₅	—	3	1	no	—
257	C₂×C₄×C₅	—	3	1	no	—
258	C₂×C₄×C₅	—	4	1	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	—	6	1	no	—
261	C₂×C₄×C₅	—	6	1	no	—
262	C₂×C₄×C₅	—	6	1	no	—
263	C₂×C₄×C₅	—	12	1	no	—
264	C₂×C₄×C₅	—	12	2	no	—
265	C₂×C₄×C₅	—	12	2	no	—
266	C₂×C₄×C₅	—	12	2	no	—
267	C₂×C₄×C₅	—	12	1	no	—
268	C₂×C₄×C₅	—	12	1	no	—
269	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
270	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
272	C₅×C₈	—	4	1	no	—
273	C₅×C₈	—	4	1	no	—
274	C₅×C₈	—	12	1	no	—
275	C₅×C₈	—	12	1	no	—
276	C₂²×D₄	—	3	1	no	—
277	C₂³×C₄	—	6	1	no	—
278	C₂×M₁₆	—	6	1	no	—
279	C₄×D₄	—	3	1	no	—
280	C₄×D₄	—	3	1	no	—
281	C₄×D₄	—	3	1	no	—
282	C₄×D₄	—	6	1	no	—
283	C₄×D₄	—	6	1	no	—
284	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	—	3	1	no	—
286	C₂×C₂²⋊C₄	—	6	1	no	—
287	C₂×C₄²	—	3	1	no	—
288	C₄⋊C₈	—	3	1	no	—
289	C₄⋊C₈	—	6	1	no	—
290	C₄⋊C₈	—	6	1	no	—
291	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
292	C₂²⋊C₈	—	6	1	no	—
293	C₄×C₈	—	3	1	no	—
294	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
295	C₂×C₃×C₅	—	4	2	no	—
296	C₂×C₃×C₅	#407	1	1	yes	characteristic
297	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
298	C₂×C₃×C₅	#421	1	1	yes	characteristic
299	C₅×D₃	—	2	2	no	—
300	C₅×D₃	—	4	2	no	—
301	C₂³×C₃	—	2	1	no	—
302	C₂²×D₃	—	2	4	no	—
303	C₂²×D₃	—	2	1	no	—
304	C₂²×D₃	—	4	2	no	—
305	C₂²×D₃	—	4	2	no	—
306	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
307	C₃×D₄	—	2	1	no	—
308	C₃×D₄	C₅×M₁₆	1	2	yes	complemented
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	4	1	no	—
311	C₂×C₃×C₄	—	4	1	no	—
312	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	#67	—	2	4	no	—
316	C₂×Dic₃	—	2	1	no	—
317	C₂×Dic₃	—	4	2	no	—
318	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
321	D₁₂	—	2	1	no	—
322	D₁₂	C₅×M₁₆	1	2	yes	complemented
323	C₄×D₃	—	2	1	no	—
324	C₄×D₃	—	2	1	no	—
325	C₄×D₃	—	4	1	no	—
326	C₄×D₃	—	4	2	no	—
327	C₄×D₃	—	4	1	no	—
328	C₄×D₃	—	4	1	no	—
329	C₄×D₃	—	4	2	no	—
330	C₄×D₃	C₅×D₈	1	2	yes	—
331	C₄×D₃	C₅×SD₁₆	1	2	yes	—
332	C₃×C₈	—	4	1	no	—
333	C₃×C₈	—	4	1	no	—
334	C₃⋊C₈	—	4	1	no	—
335	C₃⋊C₈	—	4	1	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	3	2	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	1	no	—
340	C₂²×C₅	—	6	1	no	—
341	C₂²×C₅	—	6	1	no	—
342	C₂²×C₅	—	6	2	no	—
343	C₂²×C₅	—	12	8	no	—
344	C₂²×C₅	—	12	1	no	—
345	C₂²×C₅	—	12	1	no	—
346	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	3	2	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	—	6	1	no	—
351	C₄×C₅	—	6	1	no	—
352	C₄×C₅	—	12	1	no	—
353	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
354	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
355	C₄×C₅	D₃×D₈	1	1	yes	characteristic
356	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
357	C₂⁴	—	6	1	no	—
358	C₂×D₄	—	3	1	no	—
359	C₂×D₄	—	6	1	no	—
360	C₂×D₄	—	6	2	no	—
361	C₂×D₄	—	6	2	no	—
362	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	6	1	no	—
368	C₂²×C₄	—	6	1	no	—
369	C₂²×C₄	—	6	1	no	—
370	C₂²×C₄	—	6	1	no	—
371	C₂²×C₄	—	12	2	no	—
372	C₂²×C₄	—	12	2	no	—
373	M₁₆	—	12	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	6	1	no	—
377	C₂×C₈	—	6	1	no	—
378	C₄⋊C₄	—	3	1	no	—
379	C₄⋊C₄	—	6	1	no	—
380	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	6	1	no	—
383	C₂²⋊C₄	—	6	1	no	—
384	C₂²⋊C₄	—	6	1	no	—
385	C₄²	—	3	1	no	—
386	C₄²	—	3	1	no	—
387	C₄²	—	3	1	no	—
388	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
389	C₃×C₅	#1486	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	4	1	no	—
392	C₂²×C₃	—	4	1	no	—
393	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×D₃	—	2	1	no	—
395	C₂×D₃	—	2	1	no	—
396	C₂×D₃	—	2	2	no	—
397	C₂×D₃	—	4	8	no	—
398	C₂×D₃	—	4	1	no	—
399	C₂×D₃	—	4	1	no	—
400	C₂×D₃	C₅×#102	1	2	yes	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
404	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
405	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
406	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
407	Dic₃	—	2	1	no	—
408	Dic₃	—	2	1	no	—
409	Dic₃	—	4	1	no	—
410	Dic₃	C₅×#102	1	2	yes	—
411	C₂×C₅	—	4	2	no	—
412	C₂×C₅	—	6	2	no	—
413	C₂×C₅	—	12	2	no	—
414	C₂×C₅	#4726	1	1	yes	characteristic
415	C₂×C₅	D₃×#102	1	1	yes	characteristic
416	C₂×C₅	#4821	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	3	1	no	—
419	C₂³	—	6	4	no	—
420	C₂³	—	6	1	no	—
421	C₂³	—	12	2	no	—
422	C₂³	—	12	2	no	—
423	D₄	—	2	1	no	—
424	D₄	—	3	2	no	—
425	D₄	—	6	4	no	—
426	D₄	—	6	1	no	—
427	D₄	C₅×ΓL(1,𝔽₂₅)	1	2	yes	complemented
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	3	2	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	6	1	no	—
437	C₂×C₄	—	6	1	no	—
438	C₂×C₄	—	6	1	no	—
439	C₂×C₄	—	12	1	no	—
440	C₂×C₄	—	12	2	no	—
441	C₂×C₄	—	12	2	no	—
442	C₂×C₄	—	12	2	no	—
443	C₂×C₄	—	12	1	no	—
444	C₂×C₄	—	12	1	no	—
445	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
446	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
447	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
448	C₈	—	4	1	no	—
449	C₈	—	4	1	no	—
450	C₈	—	12	1	no	—
451	C₈	—	12	1	no	—
452	C₂×C₃	—	4	2	no	—
453	C₂×C₃	C₅×#407	1	1	yes	characteristic
454	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
455	C₂×C₃	C₅×#421	1	1	yes	characteristic
456	D₃	—	2	2	no	—
457	D₃	—	4	2	no	—
458	C₅	#68172	1	1	yes	characteristic, direct product factor, Sylow
459	C₂²	—	2	2	no	—
460	C₂²	—	3	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	6	1	no	—
464	C₂²	—	6	1	no	—
465	C₂²	—	6	2	no	—
466	C₂²	—	12	8	no	—
467	C₂²	—	12	1	no	—
468	C₂²	—	12	1	no	—
469	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	3	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	6	1	no	—
474	C₄	—	6	1	no	—
475	C₄	—	12	1	no	—
476	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
477	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
478	C₄	C₅×D₃×D₈	1	1	yes	characteristic
479	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
480	C₃	C₅×#1486	1	1	yes	characteristic, complemented, Sylow
481	C₂	—	4	2	no	—
482	C₂	—	6	2	no	—
483	C₂	—	12	2	no	—
484	C₂	C₅×#4726	1	1	yes	characteristic
485	C₂	C₅×D₃×#102	1	1	yes	characteristic
486	C₂	C₅×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×D₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×D₃×D₄	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×D₄⋊C₈	D₃
hypocenter	C₃	C₅×#1486
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×D₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#4837	C₂	semidirect
3. C₅×#4685	C₂	semidirect
4. C₃×C₅×D₄⋊C₈	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4483	C₂	semidirect
7. C₅×#4459	C₂	semidirect
21. C₃×C₅×C₄⋊C₈	C₂²	semidirect
22. C₃×C₄×C₅×C₈	C₂²	semidirect
26. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
27. C₄×C₅×C₃⋊C₈	C₂²	semidirect
28. #68172	C₅	direct (N × H)
35. C₅×D₄⋊C₈	D₃	semidirect
69. #4837	C₂×C₅	semidirect
70. #4685	C₂×C₅	semidirect
71. C₃×D₄⋊C₈	C₂×C₅	semidirect
72. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
73. #4483	C₂×C₅	semidirect
74. #4459	C₂×C₅	semidirect
90. C₅×C₄⋊C₈	C₂×D₃	semidirect
93. C₄×C₅×C₈	C₂×D₃	semidirect
102. C₃×C₅×D₄	M₁₆	semidirect
116. C₅×D₁₂	M₁₆	semidirect
142. C₃×C₄⋊C₈	C₂²×C₅	semidirect
143. C₃×C₄×C₈	C₂²×C₅	semidirect
147. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
148. C₄×C₃⋊C₈	C₂²×C₅	semidirect
187. D₄⋊C₈	C₅×D₃	semidirect
251. C₅×D₄	ΓL(1,𝔽₂₅)	semidirect
291. C₄⋊C₈	C₂×C₅×D₃	semidirect
294. C₄×C₈	C₂×C₅×D₃	semidirect
308. C₃×D₄	C₅×M₁₆	semidirect
322. D₁₂	C₅×M₁₆	semidirect
389. C₃×C₅	#1486	semidirect
427. D₄	C₅×ΓL(1,𝔽₂₅)	semidirect
458. C₅	#68172	direct (N × H)
480. C₃	C₅×#1486	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₃×D₄	2
C₅×#4837	2
C₅×#4685	2
C₃×C₅×D₄⋊C₈	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#4483	2
C₅×#4459	2
C₅×#1486	3
#68172	5

Subgroups — C5×#68172 #14282064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68172 #14282064