Subgroups — C₂×C₅×#4870 #14429868

Order 1920.

960 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×C₅×#893	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4870	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#476	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	—	2	1	no	—
12	C₂²×C₅×Dic₆	—	2	1	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₅×#893	—	2	2	no	—
22	C₅×#893	C₂²	1	4	yes	—
23	C₅×#888	—	2	2	no	—
24	C₅×#888	C₂²	1	4	yes	complemented
25	C₃×C₅×#106	C₂²	1	4	yes	complemented
26	C₅×#821	C₂²	1	4	yes	—
27	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
28	C₅×#809	C₂²	1	4	yes	—
29	C₅×#808	C₂²	1	4	yes	complemented
30	C₂×#4870	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
32	C₂×C₄×C₅×D₄	—	3	1	no	—
33	C₅×#476	—	3	8	no	—
34	C₂×C₅×#106	—	3	1	no	—
35	C₂×C₅×#106	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×C₄⋊C₈	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂³×C₅×D₃	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	2	no	—
48	C₂×C₅×D₁₂	Q₈	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	C₂×C₅×Dic₆	—	2	4	no	—
53	C₂×C₅×Dic₆	—	4	4	no	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
63	C₅×Dic₃⋊C₄	—	2	4	no	—
64	C₄×C₅×Dic₃	D₄	1	2	yes	—
65	C₄×C₅×Dic₃	C₂³	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	—	2	2	no	—
67	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
68	C₂×#893	C₂×C₅	1	1	yes	characteristic
69	C₂×#888	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#821	C₂×C₅	1	1	yes	characteristic
72	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#809	C₂×C₅	1	1	yes	characteristic
74	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
75	#4870	C₂×C₅	1	8	yes	direct product factor
76	C₂²×C₅×Q₈	—	6	1	no	—
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂³×C₄×C₅	—	6	1	no	—
79	C₂²×C₅×C₈	—	3	1	no	—
80	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
81	C₅×C₄⋊Q₈	—	3	4	no	—
82	C₅×C₄⋊Q₈	—	6	2	no	—
83	C₄×C₅×D₄	—	3	4	no	—
84	C₄×C₅×D₄	—	6	2	no	—
85	C₂×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂×C₅×C₄⋊C₄	—	6	1	no	—
87	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
90	C₂×C₄²×C₅	—	3	1	no	—
91	C₅×#106	—	3	4	no	—
92	C₅×#106	C₂×D₃	1	4	yes	complemented
93	C₅×C₄⋊C₈	—	3	4	no	—
94	C₅×#102	—	3	4	no	—
95	C₅×#102	—	3	4	no	—
96	C₂×#476	—	3	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₅×D₃	—	2	4	no	—
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	4	2	no	—
101	C₂²×C₅×D₃	—	4	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	4	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	4	2	no	—
113	C₂×C₅×Dic₃	SD₁₆	1	4	yes	—
114	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
115	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
116	C₅×D₁₂	—	2	4	no	—
117	C₅×D₁₂	—	2	2	no	—
118	C₅×D₁₂	C₂×Q₈	1	4	yes	complemented
119	C₄×C₅×D₃	—	4	8	no	—
120	C₅×Dic₆	—	4	8	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
124	C₂²×C₄×D₃	—	2	1	no	—
125	C₂²×Dic₆	—	2	1	no	—
126	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
130	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×Dic₃⋊C₄	—	2	1	no	—
132	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
134	#893	—	2	2	no	—
135	#893	C₂²×C₅	1	4	yes	—
136	#888	—	2	2	no	—
137	#888	C₂²×C₅	1	4	yes	complemented
138	C₃×#106	C₂²×C₅	1	4	yes	complemented
139	#821	C₂²×C₅	1	4	yes	—
140	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
141	#809	C₂²×C₅	1	4	yes	—
142	#808	C₂²×C₅	1	4	yes	complemented
143	C₂⁴×C₅	—	6	1	no	—
144	C₂×C₅×Q₈	—	6	4	no	—
145	C₂×C₅×Q₈	—	12	4	no	—
146	C₂×C₅×D₄	—	3	4	no	—
147	C₂×C₅×D₄	—	3	2	no	—
148	C₂×C₅×D₄	—	6	2	no	—
149	C₂×C₅×D₄	—	6	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	3	1	no	—
153	C₂²×C₄×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	6	4	no	—
155	C₂²×C₄×C₅	—	6	1	no	—
156	C₂²×C₄×C₅	—	12	4	no	—
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	3	2	no	—
160	C₂×C₅×C₈	—	6	2	no	—
161	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	3	2	no	—
165	C₅×C₄⋊C₄	—	6	4	no	—
166	C₅×C₄⋊C₄	—	6	1	no	—
167	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
168	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
169	C₅×C₂²⋊C₄	—	6	4	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₄²×C₅	—	3	2	no	—
172	C₂×C₄⋊Q₈	—	3	1	no	—
173	C₂×C₄×D₄	—	3	1	no	—
174	#476	—	3	8	no	—
175	C₂×#106	—	3	1	no	—
176	C₂×#106	C₅×D₃	1	1	yes	characteristic, complemented
177	C₂×C₄⋊C₈	—	3	1	no	—
178	C₂×#102	—	3	1	no	—
179	C₂×#102	—	3	1	no	—
180	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
181	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
182	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₅×D₃	—	2	4	no	—
185	C₂×C₅×D₃	—	4	2	no	—
186	C₂×C₅×D₃	—	4	2	no	—
187	C₂×C₅×D₃	—	4	8	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
191	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
193	C₅×Dic₃	—	2	2	no	—
194	C₅×Dic₃	—	4	2	no	—
195	C₅×Dic₃	C₂×SD₁₆	1	4	yes	—
196	C₂³×D₃	—	2	1	no	—
197	C₂²×C₃×C₄	—	2	1	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂²×Dic₃	—	2	1	no	—
201	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
202	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	—	2	2	no	—
205	C₂×D₁₂	C₅×Q₈	1	4	yes	complemented
206	C₂×D₁₂	C₂³×C₅	1	2	yes	—
207	C₂×C₄×D₃	—	2	4	no	—
208	C₂×C₄×D₃	—	4	4	no	—
209	C₂×Dic₆	—	2	4	no	—
210	C₂×Dic₆	—	4	4	no	—
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	—	2	1	no	—
215	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
216	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
217	(C₂×D₃)⋊C₄	—	2	4	no	—
218	C₄⋊Dic₃	—	2	1	no	—
219	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
220	Dic₃⋊C₄	—	2	4	no	—
221	C₄×Dic₃	C₅×D₄	1	2	yes	—
222	C₄×Dic₃	C₂³×C₅	1	2	yes	—
223	C₂×C₃⋊C₈	—	2	2	no	—
224	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
225	C₂³×C₅	—	6	4	no	—
226	C₂³×C₅	—	6	2	no	—
227	C₂³×C₅	—	12	2	no	—
228	C₂³×C₅	—	12	2	no	—
229	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
230	C₅×Q₈	—	12	8	no	—
231	C₅×D₄	—	3	4	no	—
232	C₅×D₄	—	6	4	no	—
233	C₅×D₄	—	6	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	3	4	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	12	8	no	—
244	C₂×C₄×C₅	—	12	2	no	—
245	C₂×C₄×C₅	#235	1	2	yes	—
246	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
248	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	6	2	no	—
251	C₂²×Q₈	—	6	1	no	—
252	C₂²×D₄	—	3	1	no	—
253	C₂³×C₄	—	6	1	no	—
254	C₂²×C₈	—	3	1	no	—
255	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
256	C₄⋊Q₈	—	3	4	no	—
257	C₄⋊Q₈	—	6	2	no	—
258	C₄×D₄	—	3	4	no	—
259	C₄×D₄	—	6	2	no	—
260	C₂×C₄⋊C₄	—	3	1	no	—
261	C₂×C₄⋊C₄	—	6	1	no	—
262	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	6	1	no	—
265	C₂×C₄²	—	3	1	no	—
266	#106	—	3	4	no	—
267	#106	C₂×C₅×D₃	1	4	yes	complemented
268	C₄⋊C₈	—	3	4	no	—
269	#102	—	3	4	no	—
270	#102	—	3	4	no	—
271	C₂×C₃×C₅	#476	1	4	yes	complemented
272	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
275	C₅×D₃	—	4	4	no	—
276	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂²×D₃	—	2	4	no	—
278	C₂²×D₃	—	2	2	no	—
279	C₂²×D₃	—	4	2	no	—
280	C₂²×D₃	—	4	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	—	4	2	no	—
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
287	C₂×C₃×C₄	C₅×#41	1	2	yes	—
288	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
289	C₂×Dic₃	—	2	2	no	—
290	C₂×Dic₃	—	2	2	no	—
291	C₂×Dic₃	—	4	2	no	—
292	C₂×Dic₃	C₅×SD₁₆	1	4	yes	—
293	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
294	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
295	D₁₂	—	2	4	no	—
296	D₁₂	—	2	2	no	—
297	D₁₂	C₂×C₅×Q₈	1	4	yes	complemented
298	C₄×D₃	—	4	8	no	—
299	Dic₆	—	4	8	no	—
300	C₃×C₈	—	2	2	no	—
301	C₃⋊C₈	—	2	2	no	—
302	C₂²×C₅	—	6	4	no	—
303	C₂²×C₅	—	12	8	no	—
304	C₂²×C₅	—	12	2	no	—
305	C₂²×C₅	—	12	2	no	—
306	C₂²×C₅	#896	1	2	yes	—
307	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
308	C₂²×C₅	#914	1	2	yes	—
309	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
310	C₄×C₅	—	3	4	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	6	2	no	—
314	C₄×C₅	—	12	2	no	—
315	C₄×C₅	#896	1	2	yes	—
316	C₄×C₅	C₂×#235	1	1	yes	characteristic
317	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
318	C₂⁴	—	6	1	no	—
319	C₂×Q₈	—	6	4	no	—
320	C₂×Q₈	—	12	4	no	—
321	C₂×D₄	—	3	4	no	—
322	C₂×D₄	—	3	2	no	—
323	C₂×D₄	—	6	2	no	—
324	C₂×D₄	—	6	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	3	1	no	—
328	C₂²×C₄	—	3	1	no	—
329	C₂²×C₄	—	6	4	no	—
330	C₂²×C₄	—	6	1	no	—
331	C₂²×C₄	—	12	4	no	—
332	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	3	2	no	—
335	C₂×C₈	—	6	2	no	—
336	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	3	2	no	—
340	C₄⋊C₄	—	6	4	no	—
341	C₄⋊C₄	—	6	1	no	—
342	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
343	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
344	C₂²⋊C₄	—	6	4	no	—
345	C₄²	—	3	2	no	—
346	C₄²	—	3	2	no	—
347	C₃×C₅	C₂×#476	1	1	yes	characteristic, complemented, Hall
348	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
349	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
350	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
351	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
352	C₂×D₃	—	2	4	no	—
353	C₂×D₃	—	4	8	no	—
354	C₂×D₃	—	4	2	no	—
355	C₂×D₃	—	4	2	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
359	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
360	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
361	Dic₃	—	2	2	no	—
362	Dic₃	—	4	2	no	—
363	Dic₃	C₂×C₅×SD₁₆	1	4	yes	—
364	C₂×C₅	—	12	4	no	—
365	C₂×C₅	#4870	1	4	yes	direct product factor
366	C₂×C₅	C₂×#896	1	1	yes	characteristic
367	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
368	C₂×C₅	C₂×#914	1	1	yes	characteristic
369	C₂³	—	6	4	no	—
370	C₂³	—	6	2	no	—
371	C₂³	—	12	2	no	—
372	C₂³	—	12	2	no	—
373	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
374	Q₈	—	12	8	no	—
375	D₄	—	3	4	no	—
376	D₄	—	6	4	no	—
377	D₄	—	6	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	3	4	no	—
381	C₂×C₄	—	3	2	no	—
382	C₂×C₄	—	3	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	6	2	no	—
386	C₂×C₄	—	6	2	no	—
387	C₂×C₄	—	12	8	no	—
388	C₂×C₄	—	12	2	no	—
389	C₂×C₄	C₅×#235	1	2	yes	—
390	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
391	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
392	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	6	2	no	—
395	C₂×C₃	C₅×#476	1	4	yes	complemented
396	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
397	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
398	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
399	D₃	—	4	4	no	—
400	C₅	C₂×#4870	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²	—	6	4	no	—
402	C₂²	—	12	2	no	—
403	C₂²	—	12	2	no	—
404	C₂²	—	12	8	no	—
405	C₂²	C₅×#896	1	2	yes	—
406	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
407	C₂²	C₅×#914	1	2	yes	—
408	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
409	C₄	—	3	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	6	2	no	—
413	C₄	—	12	2	no	—
414	C₄	C₅×#896	1	2	yes	—
415	C₄	C₂×C₅×#235	1	1	yes	characteristic
416	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
417	C₃	C₂×C₅×#476	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	12	4	no	—
419	C₂	C₅×#4870	1	4	yes	direct product factor
420	C₂	C₂×C₅×#896	1	1	yes	characteristic
421	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
422	C₂	C₂×C₅×#914	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#106	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×#106	D₃
hypocenter	C₃	C₂×C₅×#476
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#106

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#888	C₂	semidirect
3. C₂×C₃×C₅×#106	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
7. C₂×C₅×#808	C₂	semidirect
8. C₅×#4870	C₂	direct (N × H)
24. C₅×#888	C₂²	semidirect
25. C₃×C₅×#106	C₂²	semidirect
27. C₅×Dic₃⋊C₈	C₂²	semidirect
29. C₅×#808	C₂²	semidirect
30. C₂×#4870	C₅	direct (N × H)
35. C₂×C₅×#106	D₃	semidirect
48. C₂×C₅×D₁₂	Q₈	semidirect
69. C₂×#888	C₂×C₅	semidirect
70. C₂×C₃×#106	C₂×C₅	semidirect
72. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
74. C₂×#808	C₂×C₅	semidirect
75. #4870	C₂×C₅	direct (N × H)
92. C₅×#106	C₂×D₃	semidirect
118. C₅×D₁₂	C₂×Q₈	semidirect
137. #888	C₂²×C₅	semidirect
138. C₃×#106	C₂²×C₅	semidirect
140. Dic₃⋊C₈	C₂²×C₅	semidirect
142. #808	C₂²×C₅	semidirect
176. C₂×#106	C₅×D₃	semidirect
205. C₂×D₁₂	C₅×Q₈	semidirect
267. #106	C₂×C₅×D₃	semidirect
271. C₂×C₃×C₅	#476	semidirect
297. D₁₂	C₂×C₅×Q₈	semidirect
347. C₃×C₅	C₂×#476	semidirect
365. C₂×C₅	#4870	direct (N × H)
395. C₂×C₃	C₅×#476	semidirect
400. C₅	C₂×#4870	direct (N × H)
417. C₃	C₂×C₅×#476	semidirect
419. C₂	C₅×#4870	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×C₅×#893	2
C₂×C₅×#888	2
C₂×C₃×C₅×#106	2
C₂×C₅×#821	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₅×#4870	2
C₂×C₅×#476	3
C₂×#4870	5

Subgroups — C2×C5×#4870 #14429868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4870 #14429868