Subgroups — C₂×C₅×#4862 #14431467

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4862	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#483	—	3	1	no	maximal, Hall
10	C₂²×C₄×C₅×D₃	—	2	1	no	—
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₅×#897	—	2	2	no	—
22	C₅×#897	C₂²	1	4	yes	—
23	C₅×D₃×C₄⋊C₄	—	2	2	no	—
24	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
25	C₃×C₅×#106	C₂²	1	4	yes	complemented
26	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
27	C₅×#816	C₂²	1	4	yes	complemented
28	C₅×#810	C₂²	1	4	yes	complemented
29	C₅×#808	C₂²	1	4	yes	complemented
30	C₂×#4862	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
32	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
33	C₅×#483	—	3	8	no	—
34	C₂×C₅×#106	—	3	1	no	—
35	C₂×C₅×#106	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#103	—	3	1	no	—
37	C₂×C₅×#103	—	3	1	no	—
38	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
39	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	—	2	2	no	—
47	C₂×C₄×C₅×D₃	—	2	2	no	—
48	C₂×C₄×C₅×D₃	—	2	4	no	—
49	C₂×C₄×C₅×D₃	—	4	4	no	—
50	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
51	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
52	C₂×C₅×Dic₆	—	2	2	no	—
53	C₂×C₅×Dic₆	—	2	2	no	—
54	C₂×C₅×Dic₆	—	2	1	no	—
55	C₂×C₅×Dic₆	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	—	2	2	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
63	C₅×C₄⋊Dic₃	—	2	1	no	—
64	C₅×C₄⋊Dic₃	—	2	4	no	—
65	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
66	C₅×Dic₃⋊C₄	—	2	4	no	—
67	C₂×C₅×C₃⋊C₈	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₂×#897	C₂×C₅	1	1	yes	characteristic
70	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
71	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic
73	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
76	#4862	C₂×C₅	1	8	yes	direct product factor
77	C₂²×C₅×Q₈	—	3	1	no	—
78	C₂³×C₄×C₅	—	3	1	no	—
79	C₂³×C₄×C₅	—	6	1	no	—
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
82	C₅×C₂²⋊Q₈	—	3	4	no	—
83	C₅×C₂²⋊Q₈	—	6	2	no	—
84	C₂×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂×C₅×C₄⋊C₄	—	3	4	no	—
86	C₂×C₅×C₄⋊C₄	—	6	2	no	—
87	C₂×C₅×C₄⋊C₄	—	6	1	no	—
88	C₂×C₅×C₄⋊C₄	—	6	1	no	—
89	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
92	C₅×#106	—	3	4	no	—
93	C₅×#106	C₂×D₃	1	4	yes	complemented
94	C₅×#103	—	3	4	no	—
95	C₅×#103	—	3	4	no	—
96	C₅×C₂²⋊C₈	—	3	4	no	—
97	C₂×#483	—	3	1	no	Sylow
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	SD₁₆	1	4	yes	—
102	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	4	2	no	—
115	C₂×C₅×Dic₃	—	4	2	no	—
116	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
117	C₄×C₅×D₃	—	2	4	no	—
118	C₄×C₅×D₃	—	2	2	no	—
119	C₄×C₅×D₃	—	2	2	no	—
120	C₄×C₅×D₃	—	4	8	no	—
121	C₅×Dic₆	—	2	2	no	—
122	C₅×Dic₆	—	2	2	no	—
123	C₅×Dic₆	—	4	2	no	—
124	C₃×C₅×C₈	—	2	2	no	—
125	C₅×C₃⋊C₈	—	2	2	no	—
126	C₂²×C₄×D₃	—	2	1	no	—
127	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
128	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
129	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
132	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
133	C₂×C₄⋊Dic₃	—	2	1	no	—
134	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
135	C₂×Dic₃⋊C₄	—	2	1	no	—
136	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
137	#897	—	2	2	no	—
138	#897	C₂²×C₅	1	4	yes	—
139	D₃×C₄⋊C₄	—	2	2	no	—
140	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
141	C₃×#106	C₂²×C₅	1	4	yes	complemented
142	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	—
143	#816	C₂²×C₅	1	4	yes	complemented
144	#810	C₂²×C₅	1	4	yes	complemented
145	#808	C₂²×C₅	1	4	yes	complemented
146	C₂⁴×C₅	—	3	1	no	—
147	C₂×C₅×Q₈	—	3	2	no	—
148	C₂×C₅×Q₈	—	6	1	no	—
149	C₂×C₅×Q₈	—	6	2	no	—
150	C₂×C₅×Q₈	—	6	2	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	3	2	no	—
155	C₂²×C₄×C₅	—	3	2	no	—
156	C₂²×C₄×C₅	—	6	4	no	—
157	C₂²×C₄×C₅	—	6	2	no	—
158	C₂²×C₄×C₅	—	6	2	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	—	12	4	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	3	2	no	—
165	C₂×C₅×C₈	—	6	2	no	—
166	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	3	2	no	—
170	C₅×C₄⋊C₄	—	6	4	no	—
171	C₅×C₄⋊C₄	—	6	4	no	—
172	C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
174	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₂×C₂²⋊Q₈	—	3	1	no	—
177	C₂²×C₄⋊C₄	—	3	1	no	—
178	#483	—	3	8	no	—
179	C₂×#106	—	3	1	no	—
180	C₂×#106	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂×#103	—	3	1	no	—
182	C₂×#103	—	3	1	no	—
183	C₂×C₂²⋊C₈	—	3	1	no	—
184	C₂²×C₃×C₅	#123	1	2	yes	—
185	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
186	C₂²×C₃×C₅	#137	1	2	yes	—
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₅×D₃	—	2	2	no	—
189	C₂×C₅×D₃	—	2	2	no	—
190	C₂×C₅×D₃	—	2	8	no	—
191	C₂×C₅×D₃	C₂×SD₁₆	1	4	yes	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	#123	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	—	4	2	no	—
199	C₅×Dic₃	—	4	2	no	—
200	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×Dic₃	—	2	1	no	—
205	C₂²×Dic₃	—	2	1	no	—
206	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
207	C₂×C₄×D₃	—	2	2	no	—
208	C₂×C₄×D₃	—	2	2	no	—
209	C₂×C₄×D₃	—	2	4	no	—
210	C₂×C₄×D₃	—	4	4	no	—
211	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
212	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
213	C₂×Dic₆	—	2	2	no	—
214	C₂×Dic₆	—	2	2	no	—
215	C₂×Dic₆	—	2	1	no	—
216	C₂×Dic₆	C₂³×C₅	1	2	yes	—
217	C₂×C₃×C₈	—	2	2	no	—
218	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
219	C₃×C₄⋊C₄	—	2	1	no	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
222	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
223	(C₂×D₃)⋊C₄	—	2	4	no	—
224	C₄⋊Dic₃	—	2	1	no	—
225	C₄⋊Dic₃	—	2	4	no	—
226	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
227	Dic₃⋊C₄	—	2	4	no	—
228	C₂×C₃⋊C₈	—	2	2	no	—
229	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
230	C₂³×C₅	—	3	4	no	—
231	C₂³×C₅	—	3	2	no	—
232	C₂³×C₅	—	6	2	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
235	C₅×Q₈	—	6	2	no	—
236	C₅×Q₈	—	6	2	no	—
237	C₅×Q₈	—	12	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	4	no	—
245	C₂×C₄×C₅	—	6	2	no	—
246	C₂×C₄×C₅	—	6	2	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	12	8	no	—
250	C₂×C₄×C₅	—	12	2	no	—
251	C₂×C₄×C₅	—	12	2	no	—
252	C₂×C₄×C₅	#235	1	2	yes	—
253	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	#239	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	6	2	no	—
258	C₂²×Q₈	—	3	1	no	—
259	C₂³×C₄	—	3	1	no	—
260	C₂³×C₄	—	6	1	no	—
261	C₂²×C₈	—	3	1	no	—
262	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂²⋊Q₈	—	3	4	no	—
264	C₂²⋊Q₈	—	6	2	no	—
265	C₂×C₄⋊C₄	—	3	1	no	—
266	C₂×C₄⋊C₄	—	3	4	no	—
267	C₂×C₄⋊C₄	—	6	2	no	—
268	C₂×C₄⋊C₄	—	6	1	no	—
269	C₂×C₄⋊C₄	—	6	1	no	—
270	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	6	1	no	—
273	#106	—	3	4	no	—
274	#106	C₂×C₅×D₃	1	4	yes	complemented
275	#103	—	3	4	no	—
276	#103	—	3	4	no	—
277	C₂²⋊C₈	—	3	4	no	—
278	C₂×C₃×C₅	#483	1	4	yes	complemented
279	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
281	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
282	C₅×D₃	—	2	4	no	—
283	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×D₃	—	2	2	no	—
285	C₂²×D₃	—	2	2	no	—
286	C₂²×D₃	C₅×SD₁₆	1	4	yes	—
287	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	4	2	no	—
291	C₂×C₃×C₄	—	4	2	no	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₅×#41	1	2	yes	—
294	C₂×C₃×C₄	C₅×#41	1	2	yes	—
295	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	C₂×Dic₃	—	2	2	no	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	—	2	2	no	—
299	C₂×Dic₃	—	4	2	no	—
300	C₂×Dic₃	—	4	2	no	—
301	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
302	C₄×D₃	—	2	4	no	—
303	C₄×D₃	—	2	2	no	—
304	C₄×D₃	—	2	2	no	—
305	C₄×D₃	—	4	8	no	—
306	Dic₆	—	2	2	no	—
307	Dic₆	—	2	2	no	—
308	Dic₆	—	4	2	no	—
309	C₃×C₈	—	2	2	no	—
310	C₃⋊C₈	—	2	2	no	—
311	C₂²×C₅	—	3	4	no	—
312	C₂²×C₅	—	6	2	no	—
313	C₂²×C₅	—	6	2	no	—
314	C₂²×C₅	—	6	8	no	—
315	C₂²×C₅	#894	1	2	yes	—
316	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
317	C₂²×C₅	#915	1	2	yes	—
318	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	6	2	no	—
322	C₄×C₅	—	12	2	no	—
323	C₄×C₅	—	12	2	no	—
324	C₄×C₅	#894	1	2	yes	—
325	C₄×C₅	C₂×#235	1	1	yes	characteristic
326	C₄×C₅	C₂×#239	1	1	yes	characteristic
327	C₂⁴	—	3	1	no	—
328	C₂×Q₈	—	3	2	no	—
329	C₂×Q₈	—	6	1	no	—
330	C₂×Q₈	—	6	2	no	—
331	C₂×Q₈	—	6	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	2	no	—
336	C₂²×C₄	—	3	2	no	—
337	C₂²×C₄	—	6	4	no	—
338	C₂²×C₄	—	6	2	no	—
339	C₂²×C₄	—	6	2	no	—
340	C₂²×C₄	—	6	1	no	—
341	C₂²×C₄	—	6	1	no	—
342	C₂²×C₄	—	12	4	no	—
343	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	3	2	no	—
346	C₂×C₈	—	6	2	no	—
347	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	3	2	no	—
351	C₄⋊C₄	—	6	4	no	—
352	C₄⋊C₄	—	6	4	no	—
353	C₄⋊C₄	—	6	1	no	—
354	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
355	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
356	C₂²⋊C₄	—	6	4	no	—
357	C₃×C₅	C₂×#483	1	1	yes	characteristic, complemented, Hall
358	C₂²×C₃	C₅×#123	1	2	yes	—
359	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
360	C₂²×C₃	C₅×#137	1	2	yes	—
361	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
362	C₂×D₃	—	2	8	no	—
363	C₂×D₃	—	2	2	no	—
364	C₂×D₃	—	2	2	no	—
365	C₂×D₃	C₂×C₅×SD₁₆	1	4	yes	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	C₅×#123	1	2	yes	—
369	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
370	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
371	Dic₃	—	2	2	no	—
372	Dic₃	—	4	2	no	—
373	Dic₃	—	4	2	no	—
374	C₂×C₅	—	6	4	no	—
375	C₂×C₅	#4862	1	4	yes	direct product factor
376	C₂×C₅	C₂×#894	1	1	yes	characteristic
377	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
378	C₂×C₅	C₂×#915	1	1	yes	characteristic
379	C₂³	—	3	4	no	—
380	C₂³	—	3	2	no	—
381	C₂³	—	6	2	no	—
382	C₂³	—	6	2	no	—
383	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
384	Q₈	—	6	2	no	—
385	Q₈	—	6	2	no	—
386	Q₈	—	12	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	3	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	4	no	—
394	C₂×C₄	—	6	2	no	—
395	C₂×C₄	—	6	2	no	—
396	C₂×C₄	—	6	2	no	—
397	C₂×C₄	—	6	2	no	—
398	C₂×C₄	—	12	8	no	—
399	C₂×C₄	—	12	2	no	—
400	C₂×C₄	—	12	2	no	—
401	C₂×C₄	C₅×#235	1	2	yes	—
402	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
403	C₂×C₄	C₅×#239	1	2	yes	—
404	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	6	2	no	—
407	C₂×C₃	C₅×#483	1	4	yes	complemented
408	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
409	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
410	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
411	D₃	—	2	4	no	—
412	C₅	C₂×#4862	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	3	4	no	—
414	C₂²	—	6	2	no	—
415	C₂²	—	6	2	no	—
416	C₂²	—	6	8	no	—
417	C₂²	C₅×#894	1	2	yes	—
418	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
419	C₂²	C₅×#915	1	2	yes	—
420	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	6	2	no	—
424	C₄	—	12	2	no	—
425	C₄	—	12	2	no	—
426	C₄	C₅×#894	1	2	yes	—
427	C₄	C₂×C₅×#235	1	1	yes	characteristic
428	C₄	C₂×C₅×#239	1	1	yes	characteristic
429	C₃	C₂×C₅×#483	1	1	yes	characteristic, complemented, Sylow
430	C₂	—	6	4	no	—
431	C₂	C₅×#4862	1	4	yes	direct product factor
432	C₂	C₂×C₅×#894	1	1	yes	characteristic
433	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
434	C₂	C₂×C₅×#915	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	C₂³×C₅×D₃	D₄
hypercenter	C₂×C₅×#106	D₃
hypocenter	C₃	C₂×C₅×#483
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
3. C₂×C₃×C₅×#106	C₂	semidirect
5. C₂×C₅×#816	C₂	semidirect
6. C₂×C₅×#810	C₂	semidirect
7. C₂×C₅×#808	C₂	semidirect
8. C₅×#4862	C₂	direct (N × H)
25. C₃×C₅×#106	C₂²	semidirect
27. C₅×#816	C₂²	semidirect
28. C₅×#810	C₂²	semidirect
29. C₅×#808	C₂²	semidirect
30. C₂×#4862	C₅	direct (N × H)
35. C₂×C₅×#106	D₃	semidirect
71. C₂×C₃×#106	C₂×C₅	semidirect
73. C₂×#816	C₂×C₅	semidirect
74. C₂×#810	C₂×C₅	semidirect
75. C₂×#808	C₂×C₅	semidirect
76. #4862	C₂×C₅	direct (N × H)
93. C₅×#106	C₂×D₃	semidirect
141. C₃×#106	C₂²×C₅	semidirect
143. #816	C₂²×C₅	semidirect
144. #810	C₂²×C₅	semidirect
145. #808	C₂²×C₅	semidirect
180. C₂×#106	C₅×D₃	semidirect
274. #106	C₂×C₅×D₃	semidirect
278. C₂×C₃×C₅	#483	semidirect
357. C₃×C₅	C₂×#483	semidirect
375. C₂×C₅	#4862	direct (N × H)
407. C₂×C₃	C₅×#483	semidirect
412. C₅	C₂×#4862	direct (N × H)
429. C₃	C₂×C₅×#483	semidirect
431. C₂	C₅×#4862	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×#897	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₃×C₅×#106	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#816	2
C₂×C₅×#810	2
C₂×C₅×#808	2
C₅×#4862	2
C₂×C₅×#483	3
C₂×#4862	5

Subgroups — C2×C5×#4862 #14431467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4862 #14431467