Subgroups — C₂×C₃×D₄×Dic₁₀ #14482909

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×Dic₁₀	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₄×Dic₅	C₂	1	2	yes	maximal
4	C₂×C₃×#4070	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×Dic₁₀	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#4034	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4024	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#4015	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄×Dic₁₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂³×C₃×Dic₅	C₂²	1	4	yes	—
14	C₂²×C₃×Dic₁₀	—	2	16	no	—
15	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
16	C₂²×C₃×Dic₁₀	C₂²	1	4	yes	—
17	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
18	C₂²×C₃×Dic₁₀	C₂²	1	16	yes	complemented
19	C₃×C₄×C₅×D₄	C₂²	1	8	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
24	C₃×D₄×Dic₅	C₂²	1	16	yes	—
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
28	C₃×#4070	C₂²	1	16	yes	complemented
29	C₂×C₃×#683	C₂²	1	4	yes	—
30	C₂×C₃×#683	C₂²	1	2	yes	—
31	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
32	C₃×#4034	C₂²	1	16	yes	complemented
33	C₃×#4024	C₂²	1	32	yes	complemented
34	C₃×#4015	C₂²	1	8	yes	complemented
35	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
36	C₂×C₃×D₄×Q₈	—	5	1	no	maximal, Hall
37	C₂³×Dic₁₀	C₂×C₃	1	2	yes	complemented
38	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
39	C₂×D₄×Dic₅	C₂×C₃	1	2	yes	—
40	C₂×#4070	C₂×C₃	1	2	yes	complemented
41	D₄×Dic₁₀	C₂×C₃	1	16	yes	direct product factor
42	C₂×#4034	C₂×C₃	1	2	yes	complemented
43	C₂×#4024	C₂×C₃	1	4	yes	complemented
44	C₂×#4015	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	Q₈	1	8	yes	complemented
48	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	—	2	8	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×Dic₅	—	2	16	no	—
56	C₂²×C₃×Dic₅	C₂³	1	16	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
58	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
59	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
60	C₂×C₃×Dic₁₀	—	2	8	no	—
61	C₂×C₃×Dic₁₀	—	2	16	no	—
62	C₂×C₃×Dic₁₀	—	2	64	no	—
63	C₂×C₃×Dic₁₀	D₄	1	8	yes	direct product factor
64	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
65	C₂×C₃×Dic₁₀	C₂³	1	16	yes	—
66	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
69	C₃×C₄²×C₅	C₂³	1	4	yes	—
70	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	—
71	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
72	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
73	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
74	C₃×#683	C₂³	1	8	yes	—
75	C₃×#683	C₂³	1	16	yes	—
76	C₃×C₄×Dic₅	C₂³	1	8	yes	—
77	C₂³×C₃×Q₈	—	5	2	no	—
78	C₃×D₄×Q₈	—	5	16	no	—
79	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
80	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
81	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
82	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
83	C₂×C₃×C₄×Q₈	—	5	1	no	—
84	C₂×C₃×C₄×D₄	—	5	2	no	—
85	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
86	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
88	C₂³×Dic₅	C₂²×C₃	1	4	yes	—
89	C₂²×Dic₁₀	—	2	16	no	—
90	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
91	C₂²×Dic₁₀	C₂²×C₃	1	4	yes	—
92	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
93	C₂²×Dic₁₀	C₂²×C₃	1	16	yes	complemented
94	C₄×C₅×D₄	C₂²×C₃	1	8	yes	—
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
99	D₄×Dic₅	C₂²×C₃	1	16	yes	—
100	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
102	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
103	#4070	C₂²×C₃	1	16	yes	complemented
104	C₂×#683	C₂²×C₃	1	2	yes	—
105	C₂×#683	C₂²×C₃	1	4	yes	—
106	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
107	#4034	C₂²×C₃	1	16	yes	complemented
108	#4024	C₂²×C₃	1	32	yes	complemented
109	#4015	C₂²×C₃	1	8	yes	complemented
110	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
111	C₂×D₄×Q₈	—	5	1	no	Sylow
112	C₂³×C₃×C₅	—	2	4	no	—
113	C₂³×C₃×C₅	—	2	4	no	—
114	C₂³×C₃×C₅	C₂×Q₈	1	8	yes	complemented
115	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
116	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
117	C₃×C₅×D₄	C₂×Q₈	1	16	yes	complemented
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	16	no	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
127	C₂×C₃×Dic₅	—	2	8	no	—
128	C₂×C₃×Dic₅	—	2	4	no	—
129	C₂×C₃×Dic₅	—	2	32	no	—
130	C₂×C₃×Dic₅	C₂×D₄	1	8	yes	—
131	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
132	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
133	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
134	C₃×Dic₁₀	—	2	16	no	—
135	C₃×Dic₁₀	—	2	32	no	—
136	C₃×Dic₁₀	C₂×D₄	1	16	yes	direct product factor
137	C₂²×C₃×Q₈	—	5	1	no	—
138	C₂²×C₃×Q₈	—	5	4	no	—
139	C₂²×C₃×Q₈	—	5	2	no	—
140	C₂²×C₃×Q₈	—	5	16	no	—
141	C₂²×C₃×Q₈	—	10	16	no	—
142	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
143	C₂³×C₃×C₄	—	5	4	no	—
144	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
145	C₃×C₄⋊Q₈	—	5	16	no	—
146	C₃×C₄⋊Q₈	—	5	8	no	—
147	C₃×C₂²⋊Q₈	—	5	16	no	—
148	C₃×C₂²⋊Q₈	—	5	32	no	—
149	C₃×C₄×Q₈	—	5	8	no	—
150	C₃×C₄×D₄	—	5	16	no	—
151	C₃×C₄×D₄	C₂×D₅	1	8	yes	—
152	C₂×C₃×C₄⋊C₄	—	5	2	no	—
153	C₂×C₃×C₄⋊C₄	—	5	2	no	—
154	C₂×C₃×C₄⋊C₄	—	5	1	no	—
155	C₂×C₃×C₄⋊C₄	—	5	4	no	—
156	C₂×C₃×C₄⋊C₄	—	5	2	no	—
157	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
159	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
160	C₂×C₃×C₄²	—	5	2	no	—
161	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
162	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
163	C₂×C₅×D₄	C₃×Q₈	1	8	yes	complemented
164	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
165	C₂²×C₄×C₅	—	2	8	no	—
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×Dic₅	—	2	16	no	—
172	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
173	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
174	C₂²×Dic₅	C₂³×C₃	1	16	yes	—
175	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
176	C₂×Dic₁₀	—	2	8	no	—
177	C₂×Dic₁₀	—	2	16	no	—
178	C₂×Dic₁₀	—	2	64	no	—
179	C₂×Dic₁₀	C₃×D₄	1	8	yes	direct product factor
180	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
181	C₂×Dic₁₀	C₂³×C₃	1	16	yes	—
182	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
183	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
184	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
185	C₄²×C₅	C₂³×C₃	1	4	yes	—
186	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	—
187	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
188	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
189	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
190	#683	C₂³×C₃	1	8	yes	—
191	#683	C₂³×C₃	1	16	yes	—
192	C₄×Dic₅	C₂³×C₃	1	8	yes	—
193	C₂³×Q₈	—	5	2	no	—
194	D₄×Q₈	—	5	16	no	—
195	C₂×C₄⋊Q₈	—	5	2	no	—
196	C₂×C₄⋊Q₈	—	5	1	no	—
197	C₂×C₂²⋊Q₈	—	5	2	no	—
198	C₂×C₂²⋊Q₈	—	5	4	no	—
199	C₂×C₄×Q₈	—	5	1	no	—
200	C₂×C₄×D₄	—	5	2	no	—
201	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic
202	C₂²×C₃×C₅	—	2	16	no	—
203	C₂²×C₃×C₅	—	2	4	no	—
204	C₂²×C₃×C₅	—	2	4	no	—
205	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
206	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
207	C₂²×C₃×C₅	C₂²×Q₈	1	8	yes	complemented
208	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
209	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
210	C₃×C₄×C₅	—	2	4	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
213	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	complemented
214	C₃×Dic₅	—	2	8	no	—
215	C₃×Dic₅	—	2	4	no	—
216	C₃×Dic₅	C₂²×D₄	1	8	yes	—
217	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
218	C₂×C₃×Q₈	—	5	8	no	—
219	C₂×C₃×Q₈	—	5	4	no	—
220	C₂×C₃×Q₈	—	5	16	no	—
221	C₂×C₃×Q₈	—	5	8	no	—
222	C₂×C₃×Q₈	—	10	16	no	—
223	C₂×C₃×Q₈	—	10	64	no	—
224	C₂×C₃×Q₈	—	10	8	no	—
225	C₂×C₃×D₄	Dic₁₀	1	8	yes	direct product factor
226	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
227	C₂²×C₃×C₄	—	2	8	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	—	5	16	no	—
230	C₂²×C₃×C₄	—	5	2	no	—
231	C₂²×C₃×C₄	—	5	4	no	—
232	C₂²×C₃×C₄	—	10	16	no	—
233	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
234	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
236	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₃×C₄⋊C₄	—	5	8	no	—
239	C₃×C₄⋊C₄	—	5	16	no	—
240	C₃×C₄⋊C₄	—	5	8	no	—
241	C₃×C₄⋊C₄	—	5	4	no	—
242	C₃×C₄⋊C₄	—	5	8	no	—
243	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
244	C₃×C₂²⋊C₄	—	5	16	no	—
245	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
246	C₃×C₄²	—	5	8	no	—
247	C₃×C₄²	C₂²×D₅	1	4	yes	—
248	C₂³×C₅	—	2	4	no	—
249	C₂³×C₅	—	2	4	no	—
250	C₂³×C₅	C₂×C₃×Q₈	1	8	yes	complemented
251	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
252	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
253	C₅×D₄	C₂×C₃×Q₈	1	16	yes	complemented
254	C₂×C₄×C₅	—	2	4	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	16	no	—
257	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
258	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	complemented
259	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
260	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
261	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
262	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
263	C₂×Dic₅	—	2	8	no	—
264	C₂×Dic₅	—	2	4	no	—
265	C₂×Dic₅	—	2	32	no	—
266	C₂×Dic₅	C₂×C₃×D₄	1	8	yes	—
267	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
268	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
269	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
270	Dic₁₀	—	2	16	no	—
271	Dic₁₀	—	2	32	no	—
272	Dic₁₀	C₂×C₃×D₄	1	16	yes	direct product factor
273	C₂²×Q₈	—	5	1	no	—
274	C₂²×Q₈	—	5	4	no	—
275	C₂²×Q₈	—	5	2	no	—
276	C₂²×Q₈	—	5	16	no	—
277	C₂²×Q₈	—	10	16	no	—
278	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
279	C₂³×C₄	—	5	4	no	—
280	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
281	C₄⋊Q₈	—	5	16	no	—
282	C₄⋊Q₈	—	5	8	no	—
283	C₂²⋊Q₈	—	5	16	no	—
284	C₂²⋊Q₈	—	5	32	no	—
285	C₄×Q₈	—	5	8	no	—
286	C₄×D₄	—	5	16	no	—
287	C₄×D₄	C₂×C₃×D₅	1	8	yes	—
288	C₂×C₄⋊C₄	—	5	2	no	—
289	C₂×C₄⋊C₄	—	5	2	no	—
290	C₂×C₄⋊C₄	—	5	1	no	—
291	C₂×C₄⋊C₄	—	5	4	no	—
292	C₂×C₄⋊C₄	—	5	2	no	—
293	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	5	4	no	—
295	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
296	C₂×C₄²	—	5	2	no	—
297	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×C₃×C₅	—	2	8	no	—
299	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
300	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂³×C₃	—	2	4	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	C₂×Dic₁₀	1	8	yes	complemented
306	C₂³×C₃	C₂³×D₅	1	4	yes	—
307	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
308	C₃×Q₈	—	5	16	no	—
309	C₃×Q₈	—	10	32	no	—
310	C₃×Q₈	—	10	16	no	—
311	C₃×D₄	C₂×Dic₁₀	1	16	yes	direct product factor
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	16	no	—
315	C₂×C₃×C₄	—	5	8	no	—
316	C₂×C₃×C₄	—	5	4	no	—
317	C₂×C₃×C₄	—	5	4	no	—
318	C₂×C₃×C₄	—	5	8	no	—
319	C₂×C₃×C₄	—	10	32	no	—
320	C₂×C₃×C₄	—	10	8	no	—
321	C₂×C₃×C₄	—	10	4	no	—
322	C₂×C₃×C₄	C₂×Dic₁₀	1	4	yes	complemented
323	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
324	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
326	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
327	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
328	C₂²×C₅	—	2	4	no	—
329	C₂²×C₅	—	2	4	no	—
330	C₂²×C₅	—	2	16	no	—
331	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
332	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
333	C₂²×C₅	C₂²×C₃×Q₈	1	8	yes	complemented
334	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
335	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
336	C₄×C₅	—	2	4	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
339	C₄×C₅	C₂²×C₃×Q₈	1	4	yes	complemented
340	Dic₅	—	2	8	no	—
341	Dic₅	—	2	4	no	—
342	Dic₅	C₂²×C₃×D₄	1	8	yes	—
343	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
344	C₂×Q₈	—	5	8	no	—
345	C₂×Q₈	—	5	4	no	—
346	C₂×Q₈	—	5	16	no	—
347	C₂×Q₈	—	5	8	no	—
348	C₂×Q₈	—	10	16	no	—
349	C₂×Q₈	—	10	64	no	—
350	C₂×Q₈	—	10	8	no	—
351	C₂×D₄	C₃×Dic₁₀	1	8	yes	direct product factor
352	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	5	2	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	—	5	4	no	—
357	C₂²×C₄	—	5	16	no	—
358	C₂²×C₄	—	10	16	no	—
359	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
361	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
362	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
364	C₄⋊C₄	—	5	8	no	—
365	C₄⋊C₄	—	5	8	no	—
366	C₄⋊C₄	—	5	4	no	—
367	C₄⋊C₄	—	5	16	no	—
368	C₄⋊C₄	—	5	8	no	—
369	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
370	C₂²⋊C₄	—	5	16	no	—
371	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
372	C₄²	—	5	8	no	—
373	C₄²	C₂²×C₃×D₅	1	4	yes	—
374	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	16	no	—
376	C₂²×C₃	—	2	4	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	C₂²×Dic₁₀	1	2	yes	—
379	C₂²×C₃	C₂²×Dic₁₀	1	8	yes	complemented
380	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
381	C₂²×C₃	#4150	1	2	yes	—
382	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
383	C₃×C₄	—	2	4	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	5	8	no	—
386	C₃×C₄	—	10	8	no	—
387	C₃×C₄	—	10	4	no	—
388	C₃×C₄	C₂²×Dic₁₀	1	4	yes	complemented
389	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
390	C₂×C₅	—	2	8	no	—
391	C₂×C₅	C₃×D₄×Q₈	1	4	yes	complemented
392	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
393	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
394	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	C₂×C₃×Dic₁₀	1	8	yes	complemented
398	C₂³	C₂³×C₃×D₅	1	4	yes	—
399	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
400	Q₈	—	5	16	no	—
401	Q₈	—	10	32	no	—
402	Q₈	—	10	16	no	—
403	D₄	C₂×C₃×Dic₁₀	1	16	yes	direct product factor
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	5	8	no	—
408	C₂×C₄	—	5	4	no	—
409	C₂×C₄	—	5	4	no	—
410	C₂×C₄	—	5	8	no	—
411	C₂×C₄	—	10	32	no	—
412	C₂×C₄	—	10	8	no	—
413	C₂×C₄	—	10	4	no	—
414	C₂×C₄	C₂×C₃×Dic₁₀	1	4	yes	complemented
415	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
416	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
417	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
418	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
419	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
420	C₂×C₃	—	2	8	no	—
421	C₂×C₃	D₄×Dic₁₀	1	4	yes	direct product factor
422	C₂×C₃	C₂³×Dic₁₀	1	1	yes	characteristic
423	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
424	C₂×C₃	C₂×#4150	1	1	yes	characteristic
425	C₅	C₂×C₃×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
426	C₂²	—	2	16	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	C₂²×C₃×Dic₁₀	1	2	yes	—
430	C₂²	C₂²×C₃×Dic₁₀	1	8	yes	complemented
431	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
432	C₂²	C₃×#4150	1	2	yes	—
433	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	5	8	no	—
437	C₄	—	10	8	no	—
438	C₄	—	10	4	no	—
439	C₄	C₂²×C₃×Dic₁₀	1	4	yes	complemented
440	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
441	C₃	C₂×D₄×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	2	8	no	—
443	C₂	C₃×D₄×Dic₁₀	1	4	yes	direct product factor
444	C₂	C₂³×C₃×Dic₁₀	1	1	yes	characteristic
445	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
446	C₂	C₂×C₃×#4150	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₂×C₃×D₄×Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×Dic₁₀	C₂	semidirect
4. C₂×C₃×#4070	C₂	semidirect
5. C₃×D₄×Dic₁₀	C₂	direct (N × H)
6. C₂×C₃×#4034	C₂	semidirect
7. C₂×C₃×#4024	C₂	semidirect
8. C₂×C₃×#4015	C₂	semidirect
9. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
10. C₂×D₄×Dic₁₀	C₃	direct (N × H)
18. C₂²×C₃×Dic₁₀	C₂²	semidirect
28. C₃×#4070	C₂²	semidirect
32. C₃×#4034	C₂²	semidirect
33. C₃×#4024	C₂²	semidirect
34. C₃×#4015	C₂²	semidirect
35. C₃×C₄×Dic₁₀	C₂²	semidirect
37. C₂³×Dic₁₀	C₂×C₃	semidirect
40. C₂×#4070	C₂×C₃	semidirect
41. D₄×Dic₁₀	C₂×C₃	direct (N × H)
42. C₂×#4034	C₂×C₃	semidirect
43. C₂×#4024	C₂×C₃	semidirect
44. C₂×#4015	C₂×C₃	semidirect
45. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
47. C₂×C₃×C₅×D₄	Q₈	semidirect
63. C₂×C₃×Dic₁₀	D₄	direct (N × H)
93. C₂²×Dic₁₀	C₂²×C₃	semidirect
103. #4070	C₂²×C₃	semidirect
107. #4034	C₂²×C₃	semidirect
108. #4024	C₂²×C₃	semidirect
109. #4015	C₂²×C₃	semidirect
110. C₄×Dic₁₀	C₂²×C₃	semidirect
114. C₂³×C₃×C₅	C₂×Q₈	semidirect
117. C₃×C₅×D₄	C₂×Q₈	semidirect
122. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
136. C₃×Dic₁₀	C₂×D₄	direct (N × H)
163. C₂×C₅×D₄	C₃×Q₈	semidirect
179. C₂×Dic₁₀	C₃×D₄	direct (N × H)
207. C₂²×C₃×C₅	C₂²×Q₈	semidirect
213. C₃×C₄×C₅	C₂²×Q₈	semidirect
225. C₂×C₃×D₄	Dic₁₀	direct (N × H)
250. C₂³×C₅	C₂×C₃×Q₈	semidirect
253. C₅×D₄	C₂×C₃×Q₈	semidirect
258. C₂×C₄×C₅	C₂×C₃×Q₈	semidirect
272. Dic₁₀	C₂×C₃×D₄	direct (N × H)
299. C₂×C₃×C₅	D₄×Q₈	semidirect
305. C₂³×C₃	C₂×Dic₁₀	semidirect
311. C₃×D₄	C₂×Dic₁₀	direct (N × H)
322. C₂×C₃×C₄	C₂×Dic₁₀	semidirect
333. C₂²×C₅	C₂²×C₃×Q₈	semidirect
339. C₄×C₅	C₂²×C₃×Q₈	semidirect
351. C₂×D₄	C₃×Dic₁₀	direct (N × H)
374. C₃×C₅	C₂×D₄×Q₈	semidirect
379. C₂²×C₃	C₂²×Dic₁₀	semidirect
388. C₃×C₄	C₂²×Dic₁₀	semidirect
391. C₂×C₅	C₃×D₄×Q₈	semidirect
397. C₂³	C₂×C₃×Dic₁₀	semidirect
403. D₄	C₂×C₃×Dic₁₀	direct (N × H)
414. C₂×C₄	C₂×C₃×Dic₁₀	semidirect
421. C₂×C₃	D₄×Dic₁₀	direct (N × H)
425. C₅	C₂×C₃×D₄×Q₈	semidirect
430. C₂²	C₂²×C₃×Dic₁₀	semidirect
439. C₄	C₂²×C₃×Dic₁₀	semidirect
441. C₃	C₂×D₄×Dic₁₀	direct (N × H)
443. C₂	C₃×D₄×Dic₁₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×Dic₁₀	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₃×D₄×Dic₅	2
C₂×C₃×#4070	2
C₃×D₄×Dic₁₀	2
C₂×C₃×#4034	2
C₂×C₃×#4024	2
C₂×C₃×#4015	2
C₂×C₃×C₄×Dic₁₀	2
C₂×D₄×Dic₁₀	3
C₂×C₃×D₄×Q₈	5

Subgroups — C2×C3×D4×Dic10 #14482909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄×Dic₁₀ #14482909