Subgroups — C₂×C₅×#5072 #14425806

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#213	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
5	C₅×#5072	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#459	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	1	no	—
13	C₃×C₅×#127	—	2	2	no	—
14	C₃×C₅×#127	C₂²	1	4	yes	complemented
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×#213	—	2	8	no	—
17	C₂×C₅×#213	C₂²	1	8	yes	complemented
18	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₄×C₅×D₁₂	—	2	2	no	—
22	C₄×C₅×D₁₂	C₂²	1	4	yes	complemented
23	C₅×#832	C₂²	1	8	yes	complemented
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
25	C₂×#5072	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×D₈	—	3	2	no	—
27	C₂×C₅×#127	D₃	1	1	yes	characteristic, complemented
28	C₂×C₄×C₅×D₄	—	3	1	no	—
29	C₅×#459	—	3	8	no	—
30	C₂×C₅×C₄⋊C₈	—	3	1	no	—
31	C₂×C₅×#102	—	3	2	no	—
32	C₂⁴×C₃×C₅	—	2	2	no	—
33	C₂³×C₅×D₃	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	4	4	no	—
40	C₂×C₃×C₅×D₄	—	4	4	no	—
41	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	2	no	—
48	C₂×C₅×D₁₂	D₄	1	4	yes	complemented
49	C₂×C₅×D₁₂	C₂³	1	2	yes	—
50	C₂×C₄×C₅×D₃	—	2	4	no	—
51	C₂×C₄×C₅×D₃	—	4	4	no	—
52	C₃×C₄²×C₅	D₄	1	2	yes	—
53	C₃×C₄²×C₅	C₂³	1	2	yes	—
54	C₅×#213	—	2	16	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
60	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×#213	C₂×C₅	1	2	yes	complemented
62	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#832	C₂×C₅	1	2	yes	complemented
64	#5072	C₂×C₅	1	8	yes	direct product factor
65	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂²×C₅×D₄	—	2	1	no	—
67	C₂²×C₅×D₄	—	2	1	no	—
68	C₂²×C₅×D₄	—	3	1	no	—
69	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
70	C₂³×C₄×C₅	—	6	1	no	—
71	C₂×C₅×D₈	—	3	8	no	—
72	C₂×C₅×D₈	—	6	8	no	—
73	C₂²×C₅×C₈	—	3	2	no	—
74	C₅×#127	—	2	2	no	—
75	C₅×#127	C₂×D₃	1	4	yes	complemented
76	C₄×C₅×D₄	—	3	4	no	—
77	C₄×C₅×D₄	—	6	2	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₅×C₄⋊C₈	—	3	4	no	—
82	C₅×#102	—	3	8	no	—
83	C₂×#459	—	3	1	no	Sylow
84	C₂³×C₃×C₅	—	2	4	no	—
85	C₂³×C₃×C₅	—	4	4	no	—
86	C₂³×C₃×C₅	—	4	4	no	—
87	C₂³×C₃×C₅	—	4	4	no	—
88	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₅×D₃	—	2	4	no	—
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂²×C₅×D₃	—	4	2	no	—
92	C₂²×C₅×D₃	—	4	2	no	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	2	4	no	—
95	C₃×C₅×D₄	—	4	8	no	—
96	C₃×C₅×D₄	—	4	4	no	—
97	C₃×C₅×D₄	—	4	8	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	4	2	no	—
108	C₅×D₁₂	—	2	4	no	—
109	C₅×D₁₂	—	2	2	no	—
110	C₅×D₁₂	C₂×D₄	1	4	yes	complemented
111	C₄×C₅×D₃	—	4	8	no	—
112	C₅×C₃⋊C₈	—	2	4	no	—
113	C₂²×C₃×D₄	—	2	1	no	—
114	C₂²×C₃×D₄	—	2	1	no	—
115	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
116	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₄×D₃	—	2	1	no	—
118	C₃×#127	—	2	2	no	—
119	C₃×#127	C₂²×C₅	1	4	yes	complemented
120	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
121	C₂×#213	—	2	8	no	—
122	C₂×#213	C₂²×C₅	1	8	yes	complemented
123	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
126	C₄×D₁₂	—	2	2	no	—
127	C₄×D₁₂	C₂²×C₅	1	4	yes	complemented
128	#832	C₂²×C₅	1	8	yes	complemented
129	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
130	C₂⁴×C₅	—	2	2	no	—
131	C₂⁴×C₅	—	6	1	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	4	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	—	2	4	no	—
137	C₂×C₅×D₄	—	3	4	no	—
138	C₂×C₅×D₄	—	3	2	no	—
139	C₂×C₅×D₄	—	4	4	no	—
140	C₂×C₅×D₄	—	4	4	no	—
141	C₂×C₅×D₄	—	6	2	no	—
142	C₂×C₅×D₄	—	6	1	no	—
143	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	—	6	4	no	—
146	C₂²×C₄×C₅	—	12	4	no	—
147	C₂²×C₄×C₅	#67	1	1	yes	characteristic
148	C₂²×C₄×C₅	#67	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₅×D₈	—	6	16	no	—
151	C₂×C₅×C₈	—	3	4	no	—
152	C₂×C₅×C₈	—	6	4	no	—
153	C₅×C₄⋊C₄	—	3	2	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₂²⋊C₄	—	6	4	no	—
156	C₄²×C₅	#67	1	2	yes	—
157	C₄²×C₅	C₂²×D₃	1	2	yes	—
158	C₂²×D₈	—	3	2	no	—
159	C₂×#127	C₅×D₃	1	1	yes	characteristic, complemented
160	C₂×C₄×D₄	—	3	1	no	—
161	#459	—	3	8	no	—
162	C₂×C₄⋊C₈	—	3	1	no	—
163	C₂×#102	—	3	2	no	—
164	C₂²×C₃×C₅	—	4	4	no	—
165	C₂²×C₃×C₅	—	4	4	no	—
166	C₂²×C₃×C₅	—	4	4	no	—
167	C₂²×C₃×C₅	—	8	8	no	—
168	C₂²×C₃×C₅	#121	1	2	yes	—
169	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
170	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	4	no	—
173	C₂×C₅×D₃	—	4	2	no	—
174	C₂×C₅×D₃	—	4	2	no	—
175	C₂×C₅×D₃	—	4	8	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	#121	1	2	yes	—
178	C₃×C₄×C₅	C₂×D₈	1	4	yes	complemented
179	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
181	C₅×Dic₃	—	4	2	no	—
182	C₂⁴×C₃	—	2	2	no	—
183	C₂³×D₃	—	2	1	no	—
184	C₂×C₃×D₄	—	2	4	no	—
185	C₂×C₃×D₄	—	2	2	no	—
186	C₂×C₃×D₄	—	2	4	no	—
187	C₂×C₃×D₄	—	2	4	no	—
188	C₂×C₃×D₄	—	2	4	no	—
189	C₂×C₃×D₄	—	4	4	no	—
190	C₂×C₃×D₄	—	4	4	no	—
191	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
192	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
195	C₂²×Dic₃	—	2	1	no	—
196	C₂×D₁₂	—	2	1	no	—
197	C₂×D₁₂	—	2	2	no	—
198	C₂×D₁₂	C₅×D₄	1	4	yes	complemented
199	C₂×D₁₂	C₂³×C₅	1	2	yes	—
200	C₂×C₄×D₃	—	2	4	no	—
201	C₂×C₄×D₃	—	4	4	no	—
202	C₃×C₄²	C₅×D₄	1	2	yes	—
203	C₃×C₄²	C₂³×C₅	1	2	yes	—
204	#213	—	2	16	no	—
205	(C₂×D₃)⋊C₄	—	2	4	no	—
206	C₄⋊Dic₃	—	2	1	no	—
207	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
208	C₂×C₃⋊C₈	—	2	4	no	—
209	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
210	C₂³×C₅	—	2	4	no	—
211	C₂³×C₅	—	4	4	no	—
212	C₂³×C₅	—	4	4	no	—
213	C₂³×C₅	—	4	4	no	—
214	C₂³×C₅	—	6	4	no	—
215	C₂³×C₅	—	6	2	no	—
216	C₂³×C₅	—	12	2	no	—
217	C₂³×C₅	—	12	2	no	—
218	C₂³×C₅	C₂×#67	1	1	yes	characteristic
219	C₅×D₄	—	2	4	no	—
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	3	4	no	—
222	C₅×D₄	—	4	8	no	—
223	C₅×D₄	—	4	8	no	—
224	C₅×D₄	—	4	4	no	—
225	C₅×D₄	—	6	4	no	—
226	C₅×D₄	—	6	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	6	2	no	—
229	C₂×C₄×C₅	—	12	2	no	—
230	C₂×C₄×C₅	—	12	8	no	—
231	C₂×C₄×C₅	#213	1	4	yes	complemented
232	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
233	C₂×C₄×C₅	#237	1	2	yes	—
234	C₂×C₄×C₅	C₂×#67	1	2	yes	—
235	C₂×C₄×C₅	C₂×#67	1	2	yes	—
236	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×C₈	—	6	4	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	3	1	no	—
242	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
243	C₂³×C₄	—	6	1	no	—
244	C₂×D₈	—	3	8	no	—
245	C₂×D₈	—	6	8	no	—
246	C₂²×C₈	—	3	2	no	—
247	#127	—	2	2	no	—
248	#127	C₂×C₅×D₃	1	4	yes	complemented
249	C₄×D₄	—	3	4	no	—
250	C₄×D₄	—	6	2	no	—
251	C₂×C₄⋊C₄	—	3	1	no	—
252	C₂×C₂²⋊C₄	—	6	1	no	—
253	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
254	C₄⋊C₈	—	3	4	no	—
255	#102	—	3	8	no	—
256	C₂×C₃×C₅	—	8	4	no	—
257	C₂×C₃×C₅	#459	1	4	yes	complemented
258	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
260	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₅×D₃	—	4	4	no	—
262	C₂³×C₃	—	2	4	no	—
263	C₂³×C₃	—	4	4	no	—
264	C₂³×C₃	—	4	4	no	—
265	C₂³×C₃	—	4	4	no	—
266	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂²×D₃	—	2	4	no	—
268	C₂²×D₃	—	2	2	no	—
269	C₂²×D₃	—	4	2	no	—
270	C₂²×D₃	—	4	2	no	—
271	C₃×D₄	—	2	4	no	—
272	C₃×D₄	—	2	4	no	—
273	C₃×D₄	—	4	8	no	—
274	C₃×D₄	—	4	4	no	—
275	C₃×D₄	—	4	8	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	C₅×D₈	1	4	yes	complemented
278	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
279	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
280	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
282	C₂×C₃×C₄	C₅×#41	1	2	yes	—
283	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	—	4	2	no	—
286	D₁₂	—	2	4	no	—
287	D₁₂	—	2	2	no	—
288	D₁₂	C₂×C₅×D₄	1	4	yes	complemented
289	C₄×D₃	—	4	8	no	—
290	C₃⋊C₈	—	2	4	no	—
291	C₂²×C₅	—	4	4	no	—
292	C₂²×C₅	—	4	4	no	—
293	C₂²×C₅	—	4	4	no	—
294	C₂²×C₅	—	6	4	no	—
295	C₂²×C₅	—	8	8	no	—
296	C₂²×C₅	—	12	2	no	—
297	C₂²×C₅	—	12	2	no	—
298	C₂²×C₅	—	12	8	no	—
299	C₂²×C₅	C₂×#213	1	2	yes	—
300	C₂²×C₅	#932	1	2	yes	—
301	C₂²×C₅	#938	1	2	yes	—
302	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	12	2	no	—
305	C₄×C₅	C₂×#213	1	4	yes	complemented
306	C₄×C₅	#938	1	2	yes	—
307	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
308	C₄×C₅	C₂×#237	1	1	yes	characteristic
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	6	1	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	3	4	no	—
317	C₂×D₄	—	3	2	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	—	6	2	no	—
321	C₂×D₄	—	6	1	no	—
322	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
323	C₂²×C₄	—	6	1	no	—
324	C₂²×C₄	—	6	4	no	—
325	C₂²×C₄	—	12	4	no	—
326	C₂²×C₄	C₅×#67	1	1	yes	characteristic
327	C₂²×C₄	C₅×#67	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
329	D₈	—	6	16	no	—
330	C₂×C₈	—	3	4	no	—
331	C₂×C₈	—	6	4	no	—
332	C₄⋊C₄	—	3	2	no	—
333	C₄⋊C₄	—	6	1	no	—
334	C₂²⋊C₄	—	6	4	no	—
335	C₄²	C₅×#67	1	2	yes	—
336	C₄²	C₂²×C₅×D₃	1	2	yes	—
337	C₃×C₅	C₂×#459	1	1	yes	characteristic, complemented, Hall
338	C₂²×C₃	—	4	4	no	—
339	C₂²×C₃	—	4	4	no	—
340	C₂²×C₃	—	4	4	no	—
341	C₂²×C₃	—	8	8	no	—
342	C₂²×C₃	C₅×#121	1	2	yes	—
343	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
344	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
345	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
346	C₂×D₃	—	2	4	no	—
347	C₂×D₃	—	4	8	no	—
348	C₂×D₃	—	4	2	no	—
349	C₂×D₃	—	4	2	no	—
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	C₅×#121	1	2	yes	—
352	C₃×C₄	C₂×C₅×D₈	1	4	yes	complemented
353	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
355	Dic₃	—	4	2	no	—
356	C₂×C₅	—	8	4	no	—
357	C₂×C₅	—	12	4	no	—
358	C₂×C₅	#5072	1	4	yes	direct product factor
359	C₂×C₅	C₂²×#213	1	1	yes	characteristic
360	C₂×C₅	C₂×#932	1	1	yes	characteristic
361	C₂×C₅	C₂×#938	1	1	yes	characteristic
362	C₂³	—	2	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	6	4	no	—
367	C₂³	—	6	2	no	—
368	C₂³	—	12	2	no	—
369	C₂³	—	12	2	no	—
370	C₂³	C₂×C₅×#67	1	1	yes	characteristic
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	3	4	no	—
374	D₄	—	4	8	no	—
375	D₄	—	4	8	no	—
376	D₄	—	4	4	no	—
377	D₄	—	6	4	no	—
378	D₄	—	6	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	12	2	no	—
382	C₂×C₄	—	12	8	no	—
383	C₂×C₄	C₅×#213	1	4	yes	complemented
384	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
385	C₂×C₄	C₅×#237	1	2	yes	—
386	C₂×C₄	C₂×C₅×#67	1	2	yes	—
387	C₂×C₄	C₂×C₅×#67	1	2	yes	—
388	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
389	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
390	C₈	—	6	4	no	—
391	C₂×C₃	—	8	4	no	—
392	C₂×C₃	C₅×#459	1	4	yes	complemented
393	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
394	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
395	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
396	D₃	—	4	4	no	—
397	C₅	C₂×#5072	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	6	4	no	—
402	C₂²	—	8	8	no	—
403	C₂²	—	12	2	no	—
404	C₂²	—	12	2	no	—
405	C₂²	—	12	8	no	—
406	C₂²	C₂×C₅×#213	1	2	yes	—
407	C₂²	C₅×#932	1	2	yes	—
408	C₂²	C₅×#938	1	2	yes	—
409	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	12	2	no	—
412	C₄	C₂×C₅×#213	1	4	yes	complemented
413	C₄	C₅×#938	1	2	yes	—
414	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
415	C₄	C₂×C₅×#237	1	1	yes	characteristic
416	C₃	C₂×C₅×#459	1	1	yes	characteristic, complemented, Sylow
417	C₂	—	8	4	no	—
418	C₂	—	12	4	no	—
419	C₂	C₅×#5072	1	4	yes	direct product factor
420	C₂	C₂²×C₅×#213	1	1	yes	characteristic
421	C₂	C₂×C₅×#932	1	1	yes	characteristic
422	C₂	C₂×C₅×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#127	D₃
hypocenter	C₃	C₂×C₅×#459
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#127	C₂	semidirect
2. C₂²×C₅×#213	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5072	C₂	direct (N × H)
6. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
14. C₃×C₅×#127	C₂²	semidirect
17. C₂×C₅×#213	C₂²	semidirect
22. C₄×C₅×D₁₂	C₂²	semidirect
23. C₅×#832	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₂×#5072	C₅	direct (N × H)
27. C₂×C₅×#127	D₃	semidirect
48. C₂×C₅×D₁₂	D₄	semidirect
60. C₂×C₃×#127	C₂×C₅	semidirect
61. C₂²×#213	C₂×C₅	semidirect
62. C₂×C₄×D₁₂	C₂×C₅	semidirect
63. C₂×#832	C₂×C₅	semidirect
64. #5072	C₂×C₅	direct (N × H)
65. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
75. C₅×#127	C₂×D₃	semidirect
99. C₂×C₃×C₄×C₅	D₈	semidirect
110. C₅×D₁₂	C₂×D₄	semidirect
119. C₃×#127	C₂²×C₅	semidirect
122. C₂×#213	C₂²×C₅	semidirect
127. C₄×D₁₂	C₂²×C₅	semidirect
128. #832	C₂²×C₅	semidirect
129. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
159. C₂×#127	C₅×D₃	semidirect
178. C₃×C₄×C₅	C₂×D₈	semidirect
198. C₂×D₁₂	C₅×D₄	semidirect
231. C₂×C₄×C₅	#213	semidirect
248. #127	C₂×C₅×D₃	semidirect
257. C₂×C₃×C₅	#459	semidirect
277. C₂×C₃×C₄	C₅×D₈	semidirect
288. D₁₂	C₂×C₅×D₄	semidirect
305. C₄×C₅	C₂×#213	semidirect
337. C₃×C₅	C₂×#459	semidirect
352. C₃×C₄	C₂×C₅×D₈	semidirect
358. C₂×C₅	#5072	direct (N × H)
383. C₂×C₄	C₅×#213	semidirect
392. C₂×C₃	C₅×#459	semidirect
397. C₅	C₂×#5072	direct (N × H)
412. C₄	C₂×C₅×#213	semidirect
416. C₃	C₂×C₅×#459	semidirect
419. C₂	C₅×#5072	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#127	2
C₂²×C₅×#213	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#832	2
C₅×#5072	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#459	3
C₂×#5072	5

Subgroups — C2×C5×#5072 #14425806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5072 #14425806