Subgroups — C₂×C₅×#4710 #14416326

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#821	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4710	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#440	—	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	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
20	C₂×C₄×C₅×Dic₃	—	2	1	no	—
21	C₂×C₅×#204	C₄	1	8	yes	complemented
22	C₂×C₅×#204	C₂²	1	4	yes	—
23	C₄×C₅×D₁₂	—	2	2	no	—
24	C₄×C₅×D₁₂	C₂²	1	4	yes	—
25	C₄×C₅×Dic₆	—	2	2	no	—
26	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
27	C₃×C₅×#97	C₂²	1	4	yes	complemented
28	C₅×#821	C₂²	1	4	yes	—
29	C₅×#818	C₂²	1	4	yes	complemented
30	C₅×#816	C₂²	1	4	yes	complemented
31	C₂×#4710	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×SD₁₆	—	3	1	no	—
33	C₂×C₄×C₅×Q₈	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₅×#440	—	3	8	no	—
36	C₂×C₅×#107	—	3	1	no	—
37	C₂×C₅×#103	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂×C₅×#97	D₃	1	1	yes	characteristic, complemented
40	C₂³×C₅×D₃	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₂²×C₅×Dic₃	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	2	no	—
49	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
50	C₂×C₅×D₁₂	C₂³	1	2	yes	—
51	C₂×C₄×C₅×D₃	—	2	4	no	—
52	C₂×C₄×C₅×D₃	—	4	4	no	—
53	C₂×C₅×Dic₆	—	2	1	no	—
54	C₂×C₅×Dic₆	—	2	2	no	—
55	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
56	C₂×C₅×Dic₆	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	—	2	2	no	—
58	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	D₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₅×C₄⋊Dic₃	—	2	1	no	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
68	C₅×Dic₃⋊C₄	—	2	4	no	—
69	C₄×C₅×Dic₃	—	2	4	no	—
70	C₅×#204	C₂×C₄	1	16	yes	complemented
71	C₂²×#204	C₂×C₅	1	1	yes	characteristic
72	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
73	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#821	C₂×C₅	1	1	yes	characteristic
76	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
78	#4710	C₂×C₅	1	8	yes	direct product factor
79	C₂²×C₅×Q₈	—	3	1	no	—
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	6	1	no	—
82	C₂×C₅×SD₁₆	—	3	8	no	—
83	C₂×C₅×SD₁₆	—	3	4	no	—
84	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
86	C₄×C₅×Q₈	—	3	4	no	—
87	C₄×C₅×Q₈	—	6	2	no	—
88	C₄×C₅×D₄	—	3	4	no	—
89	C₄×C₅×D₄	—	6	2	no	—
90	C₂×C₅×C₄⋊C₄	—	3	1	no	—
91	C₂×C₅×C₄⋊C₄	—	3	1	no	—
92	C₂×C₅×C₄⋊C₄	—	6	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
94	C₂×C₄²×C₅	—	6	1	no	—
95	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
96	C₅×#107	—	3	4	no	—
97	C₅×#103	—	3	4	no	—
98	C₅×#102	—	3	4	no	—
99	C₅×#97	C₂×D₃	1	4	yes	complemented
100	C₂×#440	—	3	1	no	Sylow
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	4	2	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₅×Dic₃	—	2	4	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	4	2	no	—
119	C₂×C₅×Dic₃	—	4	2	no	—
120	C₅×D₁₂	—	2	4	no	—
121	C₅×D₁₂	—	2	2	no	—
122	C₅×D₁₂	C₂²×C₄	1	4	yes	—
123	C₄×C₅×D₃	—	4	8	no	—
124	C₅×Dic₆	—	2	4	no	—
125	C₅×Dic₆	—	2	2	no	—
126	C₅×Dic₆	C₂²×C₄	1	4	yes	complemented
127	C₃×C₅×C₈	—	2	2	no	—
128	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄×D₃	—	2	1	no	—
131	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
133	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
135	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
136	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
138	C₂×Dic₃⋊C₄	—	2	1	no	—
139	C₂×C₄×Dic₃	—	2	1	no	—
140	C₂×#204	C₄×C₅	1	8	yes	complemented
141	C₂×#204	C₂²×C₅	1	4	yes	—
142	C₄×D₁₂	—	2	2	no	—
143	C₄×D₁₂	C₂²×C₅	1	4	yes	—
144	C₄×Dic₆	—	2	2	no	—
145	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
146	C₃×#97	C₂²×C₅	1	4	yes	complemented
147	#821	C₂²×C₅	1	4	yes	—
148	#818	C₂²×C₅	1	4	yes	complemented
149	#816	C₂²×C₅	1	4	yes	complemented
150	C₂⁴×C₅	—	6	1	no	—
151	C₂×C₅×Q₈	—	3	4	no	—
152	C₂×C₅×Q₈	—	3	2	no	—
153	C₂×C₅×Q₈	—	6	1	no	—
154	C₂×C₅×Q₈	—	6	2	no	—
155	C₂×C₅×D₄	—	3	4	no	—
156	C₂×C₅×D₄	—	3	2	no	—
157	C₂×C₅×D₄	—	6	1	no	—
158	C₂×C₅×D₄	—	6	2	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	4	no	—
163	C₂²×C₄×C₅	—	12	4	no	—
164	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
165	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₅×SD₁₆	—	3	16	no	—
168	C₂×C₅×C₈	—	2	2	no	—
169	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
170	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
171	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
172	C₅×C₄⋊C₄	—	3	2	no	—
173	C₅×C₄⋊C₄	—	3	2	no	—
174	C₅×C₄⋊C₄	—	6	1	no	—
175	C₅×C₄⋊C₄	—	6	1	no	—
176	C₅×C₄⋊C₄	—	6	4	no	—
177	C₅×C₂²⋊C₄	—	6	4	no	—
178	C₄²×C₅	—	6	4	no	—
179	C₄²×C₅	D₁₂	1	2	yes	—
180	C₄²×C₅	C₂²×D₃	1	2	yes	—
181	C₂²×SD₁₆	—	3	1	no	—
182	C₂×C₄×Q₈	—	3	1	no	—
183	C₂×C₄×D₄	—	3	1	no	—
184	#440	—	3	8	no	—
185	C₂×#107	—	3	1	no	—
186	C₂×#103	—	3	1	no	—
187	C₂×#102	—	3	1	no	—
188	C₂×#97	C₅×D₃	1	1	yes	characteristic, complemented
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
191	C₂²×C₃×C₅	#137	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	4	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	4	8	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
200	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
202	C₅×Dic₃	—	2	4	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂³×D₃	—	2	1	no	—
206	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×Dic₃	—	2	1	no	—
210	C₂²×Dic₃	—	2	1	no	—
211	C₂²×Dic₃	—	2	1	no	—
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	—	2	2	no	—
214	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
215	C₂×D₁₂	C₂³×C₅	1	2	yes	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₂×C₄×D₃	—	4	4	no	—
218	C₂×Dic₆	—	2	1	no	—
219	C₂×Dic₆	—	2	2	no	—
220	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
221	C₂×Dic₆	C₂³×C₅	1	2	yes	—
222	C₂×C₃×C₈	—	2	2	no	—
223	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
226	C₃×C₄²	C₅×D₄	1	2	yes	—
227	C₃×C₄²	C₂³×C₅	1	2	yes	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	C₄⋊Dic₃	—	2	1	no	—
230	C₄⋊Dic₃	—	2	1	no	—
231	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
232	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
233	Dic₃⋊C₄	—	2	4	no	—
234	C₄×Dic₃	—	2	4	no	—
235	#204	C₂×C₄×C₅	1	16	yes	complemented
236	C₂³×C₅	—	6	4	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	12	2	no	—
239	C₂³×C₅	—	12	2	no	—
240	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
241	C₅×Q₈	—	3	4	no	—
242	C₅×Q₈	—	6	4	no	—
243	C₅×Q₈	—	6	2	no	—
244	C₅×D₄	—	3	4	no	—
245	C₅×D₄	—	6	4	no	—
246	C₅×D₄	—	6	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	6	4	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	6	2	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	12	8	no	—
254	C₂×C₄×C₅	—	12	2	no	—
255	C₂×C₄×C₅	—	12	2	no	—
256	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
258	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
259	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
260	C₂×C₄×C₅	#235	1	2	yes	—
261	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
262	C₅×C₈	—	2	2	no	—
263	C₅×C₈	C₂×C₄×D₃	1	4	yes	complemented
264	C₂²×Q₈	—	3	1	no	—
265	C₂²×D₄	—	3	1	no	—
266	C₂³×C₄	—	6	1	no	—
267	C₂×SD₁₆	—	3	8	no	—
268	C₂×SD₁₆	—	3	4	no	—
269	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
270	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
271	C₄×Q₈	—	3	4	no	—
272	C₄×Q₈	—	6	2	no	—
273	C₄×D₄	—	3	4	no	—
274	C₄×D₄	—	6	2	no	—
275	C₂×C₄⋊C₄	—	3	1	no	—
276	C₂×C₄⋊C₄	—	3	1	no	—
277	C₂×C₄⋊C₄	—	6	1	no	—
278	C₂×C₂²⋊C₄	—	6	1	no	—
279	C₂×C₄²	—	6	1	no	—
280	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
281	#107	—	3	4	no	—
282	#103	—	3	4	no	—
283	#102	—	3	4	no	—
284	#97	C₂×C₅×D₃	1	4	yes	complemented
285	C₂×C₃×C₅	#440	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
289	C₅×D₃	—	4	4	no	—
290	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	4	2	no	—
294	C₂²×D₃	—	4	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₅×#41	1	2	yes	—
302	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
303	C₂×Dic₃	—	2	4	no	—
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	—	2	2	no	—
306	C₂×Dic₃	—	2	2	no	—
307	C₂×Dic₃	—	4	2	no	—
308	C₂×Dic₃	—	4	2	no	—
309	D₁₂	—	2	4	no	—
310	D₁₂	—	2	2	no	—
311	D₁₂	C₂²×C₄×C₅	1	4	yes	—
312	C₄×D₃	—	4	8	no	—
313	Dic₆	—	2	4	no	—
314	Dic₆	—	2	2	no	—
315	Dic₆	C₂²×C₄×C₅	1	4	yes	complemented
316	C₃×C₈	—	2	2	no	—
317	C₃×C₈	C₂²×C₄×C₅	1	4	yes	complemented
318	C₂²×C₅	—	6	4	no	—
319	C₂²×C₅	—	12	8	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	C₄×D₁₂	1	2	yes	—
323	C₂²×C₅	#908	1	2	yes	—
324	C₂²×C₅	#909	1	2	yes	—
325	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
326	C₄×C₅	—	2	2	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	6	4	no	—
329	C₄×C₅	—	12	2	no	—
330	C₄×C₅	—	12	2	no	—
331	C₄×C₅	C₄×D₁₂	1	2	yes	—
332	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
333	C₄×C₅	C₂×#235	1	1	yes	characteristic
334	C₂⁴	—	6	1	no	—
335	C₂×Q₈	—	3	4	no	—
336	C₂×Q₈	—	3	2	no	—
337	C₂×Q₈	—	6	1	no	—
338	C₂×Q₈	—	6	2	no	—
339	C₂×D₄	—	3	4	no	—
340	C₂×D₄	—	3	2	no	—
341	C₂×D₄	—	6	1	no	—
342	C₂×D₄	—	6	2	no	—
343	C₂²×C₄	—	6	1	no	—
344	C₂²×C₄	—	6	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	6	4	no	—
347	C₂²×C₄	—	12	4	no	—
348	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
349	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	SD₁₆	—	3	16	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
354	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
355	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	6	1	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	6	4	no	—
361	C₂²⋊C₄	—	6	4	no	—
362	C₄²	—	6	4	no	—
363	C₄²	C₅×D₁₂	1	2	yes	—
364	C₄²	C₂²×C₅×D₃	1	2	yes	—
365	C₃×C₅	C₂×#440	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
367	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
368	C₂²×C₃	C₅×#137	1	2	yes	—
369	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₂×D₃	—	2	4	no	—
371	C₂×D₃	—	4	8	no	—
372	C₂×D₃	—	4	2	no	—
373	C₂×D₃	—	4	2	no	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	2	2	no	—
376	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
377	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
378	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
379	Dic₃	—	2	4	no	—
380	Dic₃	—	4	2	no	—
381	Dic₃	—	4	2	no	—
382	C₂×C₅	—	12	4	no	—
383	C₂×C₅	#4710	1	4	yes	direct product factor
384	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
385	C₂×C₅	C₂×#908	1	1	yes	characteristic
386	C₂×C₅	C₂×#909	1	1	yes	characteristic
387	C₂³	—	6	4	no	—
388	C₂³	—	6	2	no	—
389	C₂³	—	12	2	no	—
390	C₂³	—	12	2	no	—
391	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
392	Q₈	—	3	4	no	—
393	Q₈	—	6	4	no	—
394	Q₈	—	6	2	no	—
395	D₄	—	3	4	no	—
396	D₄	—	6	4	no	—
397	D₄	—	6	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	6	4	no	—
401	C₂×C₄	—	6	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	2	no	—
404	C₂×C₄	—	12	8	no	—
405	C₂×C₄	—	12	2	no	—
406	C₂×C₄	—	12	2	no	—
407	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
408	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
409	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
410	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
411	C₂×C₄	C₅×#235	1	2	yes	—
412	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	C₂×C₄×C₅×D₃	1	4	yes	complemented
415	C₂×C₃	C₅×#440	1	4	yes	complemented
416	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
417	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
419	D₃	—	4	4	no	—
420	C₅	C₂×#4710	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	6	4	no	—
422	C₂²	—	12	8	no	—
423	C₂²	—	12	2	no	—
424	C₂²	—	12	2	no	—
425	C₂²	C₄×C₅×D₁₂	1	2	yes	—
426	C₂²	C₅×#908	1	2	yes	—
427	C₂²	C₅×#909	1	2	yes	—
428	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	6	4	no	—
432	C₄	—	12	2	no	—
433	C₄	—	12	2	no	—
434	C₄	C₄×C₅×D₁₂	1	2	yes	—
435	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
436	C₄	C₂×C₅×#235	1	1	yes	characteristic
437	C₃	C₂×C₅×#440	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	12	4	no	—
439	C₂	C₅×#4710	1	4	yes	direct product factor
440	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
441	C₂	C₂×C₅×#908	1	1	yes	characteristic
442	C₂	C₂×C₅×#909	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#97	D₃
hypocenter	C₃	C₂×C₅×#440
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#97

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₅×Dic₆	C₂	semidirect
4. C₂×C₃×C₅×#97	C₂	semidirect
6. C₂×C₅×#818	C₂	semidirect
7. C₂×C₅×#816	C₂	semidirect
8. C₅×#4710	C₂	direct (N × H)
21. C₂×C₅×#204	C₄	semidirect
26. C₄×C₅×Dic₆	C₂²	semidirect
27. C₃×C₅×#97	C₂²	semidirect
29. C₅×#818	C₂²	semidirect
30. C₅×#816	C₂²	semidirect
31. C₂×#4710	C₅	direct (N × H)
39. C₂×C₅×#97	D₃	semidirect
55. C₂×C₅×Dic₆	C₂×C₄	semidirect
58. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
70. C₅×#204	C₂×C₄	semidirect
73. C₂×C₄×Dic₆	C₂×C₅	semidirect
74. C₂×C₃×#97	C₂×C₅	semidirect
76. C₂×#818	C₂×C₅	semidirect
77. C₂×#816	C₂×C₅	semidirect
78. #4710	C₂×C₅	direct (N × H)
99. C₅×#97	C₂×D₃	semidirect
126. C₅×Dic₆	C₂²×C₄	semidirect
128. C₃×C₅×C₈	C₂²×C₄	semidirect
140. C₂×#204	C₄×C₅	semidirect
145. C₄×Dic₆	C₂²×C₅	semidirect
146. C₃×#97	C₂²×C₅	semidirect
148. #818	C₂²×C₅	semidirect
149. #816	C₂²×C₅	semidirect
169. C₂×C₅×C₈	C₄×D₃	semidirect
188. C₂×#97	C₅×D₃	semidirect
220. C₂×Dic₆	C₂×C₄×C₅	semidirect
223. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
235. #204	C₂×C₄×C₅	semidirect
263. C₅×C₈	C₂×C₄×D₃	semidirect
284. #97	C₂×C₅×D₃	semidirect
285. C₂×C₃×C₅	#440	semidirect
315. Dic₆	C₂²×C₄×C₅	semidirect
317. C₃×C₈	C₂²×C₄×C₅	semidirect
353. C₂×C₈	C₄×C₅×D₃	semidirect
365. C₃×C₅	C₂×#440	semidirect
383. C₂×C₅	#4710	direct (N × H)
414. C₈	C₂×C₄×C₅×D₃	semidirect
415. C₂×C₃	C₅×#440	semidirect
420. C₅	C₂×#4710	direct (N × H)
437. C₃	C₂×C₅×#440	semidirect
439. C₂	C₅×#4710	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#204	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄×C₅×Dic₆	2
C₂×C₃×C₅×#97	2
C₂×C₅×#821	2
C₂×C₅×#818	2
C₂×C₅×#816	2
C₅×#4710	2
C₂×C₅×#440	3
C₂×#4710	5

Subgroups — C2×C5×#4710 #14416326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4710 #14416326