Subgroups — C₂×C₅×D₄×D₁₂ #14482415

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₂³×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
5	C₅×D₄×D₁₂	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#895	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#882	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×D₄²	—	3	1	no	maximal, Hall
11	C₂⁴×C₅×D₃	C₂²	1	4	yes	complemented
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
14	C₂²×C₅×#67	C₂²	1	4	yes	complemented
15	C₂×C₅×D₃×D₄	—	2	16	no	—
16	C₂×C₅×D₃×D₄	C₂²	1	16	yes	complemented
17	C₂²×C₅×D₁₂	—	2	16	no	—
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	16	yes	complemented
20	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
21	C₂²×C₅×D₁₂	C₂²	1	4	yes	complemented
22	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
23	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
24	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
25	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₅×#930	C₂²	1	16	yes	complemented
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₅×#895	C₂²	1	16	yes	complemented
34	C₅×#882	C₂²	1	32	yes	complemented
35	C₅×#874	C₂²	1	8	yes	complemented
36	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
37	C₂×D₄×D₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂³×C₅×D₄	—	3	2	no	—
39	C₂³×C₅×D₄	—	3	2	no	—
40	C₅×D₄²	—	3	16	no	—
41	C₂×C₅×#127	—	3	1	no	—
42	C₂×C₅×#121	—	3	2	no	—
43	C₂×C₅×#121	—	3	2	no	—
44	C₂×C₅×#120	—	3	4	no	—
45	C₂×C₄×C₅×D₄	—	3	1	no	—
46	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
47	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
48	C₂³×C₅×D₃	—	2	16	no	—
49	C₂³×C₅×D₃	—	2	16	no	—
50	C₂³×C₅×D₃	—	4	8	no	—
51	C₂³×C₅×D₃	C₂³	1	4	yes	—
52	C₂³×C₅×D₃	C₂³	1	2	yes	—
53	C₂³×C₅×D₃	C₂³	1	16	yes	complemented
54	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
55	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
56	C₂²×C₃×C₄×C₅	—	2	8	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	complemented
62	C₂×C₅×#67	—	2	16	no	—
63	C₂×C₅×#67	C₂³	1	16	yes	complemented
64	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
65	C₅×D₃×D₄	—	2	64	no	—
66	C₂×C₅×D₁₂	—	2	16	no	—
67	C₂×C₅×D₁₂	—	2	8	no	—
68	C₂×C₅×D₁₂	—	2	8	no	—
69	C₂×C₅×D₁₂	—	2	64	no	—
70	C₂×C₅×D₁₂	—	4	4	no	—
71	C₂×C₅×D₁₂	D₄	1	8	yes	direct product factor
72	C₂×C₅×D₁₂	C₂³	1	4	yes	—
73	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
74	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
75	C₂×C₅×D₁₂	C₂³	1	16	yes	complemented
76	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
77	C₂×C₄×C₅×D₃	—	2	8	no	—
78	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
79	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
80	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
81	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
82	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
83	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
84	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
85	C₂²×D₃×D₄	C₂×C₅	1	2	yes	complemented
86	C₂³×D₁₂	C₂×C₅	1	2	yes	complemented
87	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#930	C₂×C₅	1	2	yes	complemented
89	D₄×D₁₂	C₂×C₅	1	16	yes	direct product factor
90	C₂×#895	C₂×C₅	1	2	yes	complemented
91	C₂×#882	C₂×C₅	1	4	yes	complemented
92	C₂×#874	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂⁵×C₅	—	3	4	no	—
95	C₂²×C₅×D₄	—	3	4	no	—
96	C₂²×C₅×D₄	—	3	16	no	—
97	C₂²×C₅×D₄	—	3	1	no	—
98	C₂²×C₅×D₄	—	3	4	no	—
99	C₂²×C₅×D₄	—	3	2	no	—
100	C₂²×C₅×D₄	—	3	2	no	—
101	C₂²×C₅×D₄	—	3	2	no	—
102	C₂²×C₅×D₄	—	3	16	no	—
103	C₂²×C₅×D₄	—	6	16	no	—
104	C₂²×C₅×D₄	—	6	16	no	—
105	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
106	C₂³×C₄×C₅	—	3	2	no	—
107	C₂³×C₄×C₅	C₂×D₃	1	2	yes	complemented
108	C₅×#127	—	3	8	no	—
109	C₅×#121	—	3	16	no	—
110	C₅×#121	—	3	16	no	—
111	C₅×#120	—	3	32	no	—
112	C₄×C₅×D₄	—	3	8	no	—
113	C₄×C₅×D₄	C₂×D₃	1	8	yes	complemented
114	C₂×C₅×C₄⋊C₄	—	3	1	no	—
115	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
116	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
117	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
118	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
119	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
120	C₂×D₄²	—	3	1	no	Sylow
121	C₂³×C₃×C₅	—	2	4	no	—
122	C₂³×C₃×C₅	—	2	4	no	—
123	C₂³×C₃×C₅	C₂×D₄	1	8	yes	complemented
124	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
125	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
126	C₂²×C₅×D₃	—	2	4	no	—
127	C₂²×C₅×D₃	—	2	4	no	—
128	C₂²×C₅×D₃	—	2	8	no	—
129	C₂²×C₅×D₃	—	2	8	no	—
130	C₂²×C₅×D₃	—	2	32	no	—
131	C₂²×C₅×D₃	—	2	8	no	—
132	C₂²×C₅×D₃	—	2	32	no	—
133	C₂²×C₅×D₃	—	4	16	no	—
134	C₂²×C₅×D₃	—	4	64	no	—
135	C₂²×C₅×D₃	C₂×D₄	1	8	yes	complemented
136	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
137	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
138	C₃×C₅×D₄	C₂×D₄	1	16	yes	complemented
139	C₂×C₃×C₄×C₅	—	2	4	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	16	no	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
143	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
144	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
148	C₅×#67	—	2	32	no	—
149	C₂×C₅×Dic₃	—	2	4	no	—
150	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
151	C₅×D₁₂	—	2	32	no	—
152	C₅×D₁₂	—	2	16	no	—
153	C₅×D₁₂	—	2	16	no	—
154	C₅×D₁₂	—	4	8	no	—
155	C₅×D₁₂	C₂×D₄	1	16	yes	direct product factor
156	C₄×C₅×D₃	—	2	16	no	—
157	C₂⁴×D₃	C₂²×C₅	1	4	yes	complemented
158	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
160	C₂²×#67	C₂²×C₅	1	4	yes	complemented
161	C₂×D₃×D₄	—	2	16	no	—
162	C₂×D₃×D₄	C₂²×C₅	1	16	yes	complemented
163	C₂²×D₁₂	—	2	16	no	—
164	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
165	C₂²×D₁₂	C₂²×C₅	1	16	yes	complemented
166	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
167	C₂²×D₁₂	C₂²×C₅	1	4	yes	complemented
168	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
169	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
170	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
171	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
172	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
174	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
175	#930	C₂²×C₅	1	16	yes	complemented
176	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
177	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
178	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
179	#895	C₂²×C₅	1	16	yes	complemented
180	#882	C₂²×C₅	1	32	yes	complemented
181	#874	C₂²×C₅	1	8	yes	complemented
182	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
183	C₂⁴×C₅	—	3	2	no	—
184	C₂⁴×C₅	—	3	4	no	—
185	C₂⁴×C₅	—	3	16	no	—
186	C₂⁴×C₅	—	6	16	no	—
187	C₂⁴×C₅	—	6	16	no	—
188	C₂⁴×C₅	—	12	8	no	—
189	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
190	C₂×C₅×D₄	—	3	16	no	—
191	C₂×C₅×D₄	—	3	8	no	—
192	C₂×C₅×D₄	—	3	4	no	—
193	C₂×C₅×D₄	—	3	16	no	—
194	C₂×C₅×D₄	—	3	8	no	—
195	C₂×C₅×D₄	—	3	8	no	—
196	C₂×C₅×D₄	—	3	8	no	—
197	C₂×C₅×D₄	—	6	64	no	—
198	C₂×C₅×D₄	—	6	16	no	—
199	C₂×C₅×D₄	—	6	16	no	—
200	C₂×C₅×D₄	—	6	64	no	—
201	C₂×C₅×D₄	—	6	8	no	—
202	C₂×C₅×D₄	—	6	8	no	—
203	C₂×C₅×D₄	—	12	4	no	—
204	C₂×C₅×D₄	D₁₂	1	8	yes	direct product factor
205	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
206	C₂²×C₄×C₅	—	2	8	no	—
207	C₂²×C₄×C₅	—	3	2	no	—
208	C₂²×C₄×C₅	—	3	8	no	—
209	C₂²×C₄×C₅	—	6	8	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	complemented
215	C₅×C₄⋊C₄	—	3	4	no	—
216	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
217	C₅×C₂²⋊C₄	—	3	8	no	—
218	C₅×C₂²⋊C₄	—	3	16	no	—
219	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
220	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
221	C₂³×D₄	—	3	2	no	—
222	C₂³×D₄	—	3	2	no	—
223	D₄²	—	3	16	no	—
224	C₂×#127	—	3	1	no	—
225	C₂×#121	—	3	2	no	—
226	C₂×#121	—	3	2	no	—
227	C₂×#120	—	3	4	no	—
228	C₂×C₄×D₄	—	3	1	no	—
229	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
230	C₂²×C₃×C₅	—	2	16	no	—
231	C₂²×C₃×C₅	—	2	4	no	—
232	C₂²×C₃×C₅	—	2	4	no	—
233	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
234	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
235	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	complemented
236	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
237	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
238	C₂×C₅×D₃	—	2	16	no	—
239	C₂×C₅×D₃	—	2	4	no	—
240	C₂×C₅×D₃	—	2	4	no	—
241	C₂×C₅×D₃	—	2	8	no	—
242	C₂×C₅×D₃	—	2	8	no	—
243	C₂×C₅×D₃	—	2	8	no	—
244	C₂×C₅×D₃	—	4	64	no	—
245	C₂×C₅×D₃	—	4	16	no	—
246	C₂×C₅×D₃	C₂²×D₄	1	8	yes	complemented
247	C₃×C₄×C₅	—	2	4	no	—
248	C₃×C₄×C₅	—	2	2	no	—
249	C₃×C₄×C₅	C₂²×D₄	1	4	yes	complemented
250	C₃×C₄×C₅	C₂²×D₄	1	4	yes	complemented
251	C₅×Dic₃	—	2	4	no	—
252	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
253	C₂³×D₃	—	2	16	no	—
254	C₂³×D₃	—	2	16	no	—
255	C₂³×D₃	—	4	8	no	—
256	C₂³×D₃	C₂³×C₅	1	4	yes	—
257	C₂³×D₃	C₂³×C₅	1	2	yes	—
258	C₂³×D₃	C₂³×C₅	1	16	yes	complemented
259	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
260	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
261	C₂²×C₃×C₄	—	2	8	no	—
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
264	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	complemented
267	C₂×#67	—	2	16	no	—
268	C₂×#67	C₂³×C₅	1	16	yes	complemented
269	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
270	D₃×D₄	—	2	64	no	—
271	C₂×D₁₂	—	2	16	no	—
272	C₂×D₁₂	—	2	8	no	—
273	C₂×D₁₂	—	2	8	no	—
274	C₂×D₁₂	—	2	64	no	—
275	C₂×D₁₂	—	4	4	no	—
276	C₂×D₁₂	C₅×D₄	1	8	yes	direct product factor
277	C₂×D₁₂	C₂³×C₅	1	4	yes	—
278	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
279	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
280	C₂×D₁₂	C₂³×C₅	1	16	yes	complemented
281	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
282	C₂×C₄×D₃	—	2	8	no	—
283	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
284	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
285	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
286	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
287	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
288	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
289	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
290	C₂³×C₅	—	2	4	no	—
291	C₂³×C₅	—	2	4	no	—
292	C₂³×C₅	—	3	8	no	—
293	C₂³×C₅	—	3	4	no	—
294	C₂³×C₅	—	3	8	no	—
295	C₂³×C₅	—	6	32	no	—
296	C₂³×C₅	—	6	4	no	—
297	C₂³×C₅	—	6	4	no	—
298	C₂³×C₅	—	6	8	no	—
299	C₂³×C₅	—	6	32	no	—
300	C₂³×C₅	—	6	8	no	—
301	C₂³×C₅	—	6	8	no	—
302	C₂³×C₅	—	12	16	no	—
303	C₂³×C₅	—	12	64	no	—
304	C₂³×C₅	C₂×D₁₂	1	8	yes	complemented
305	C₂³×C₅	C₂³×D₃	1	4	yes	—
306	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
307	C₅×D₄	—	3	16	no	—
308	C₅×D₄	—	6	32	no	—
309	C₅×D₄	—	6	32	no	—
310	C₅×D₄	—	6	16	no	—
311	C₅×D₄	—	6	16	no	—
312	C₅×D₄	—	12	8	no	—
313	C₅×D₄	C₂×D₁₂	1	16	yes	direct product factor
314	C₂×C₄×C₅	—	2	4	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	16	no	—
317	C₂×C₄×C₅	—	3	4	no	—
318	C₂×C₄×C₅	—	6	4	no	—
319	C₂×C₄×C₅	—	6	16	no	—
320	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	complemented
321	C₂×C₄×C₅	D₃×D₄	1	4	yes	complemented
322	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
323	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
324	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
325	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
326	C₂⁵	—	3	4	no	—
327	C₂²×D₄	—	3	4	no	—
328	C₂²×D₄	—	3	16	no	—
329	C₂²×D₄	—	3	1	no	—
330	C₂²×D₄	—	3	4	no	—
331	C₂²×D₄	—	3	2	no	—
332	C₂²×D₄	—	3	2	no	—
333	C₂²×D₄	—	3	2	no	—
334	C₂²×D₄	—	3	16	no	—
335	C₂²×D₄	—	6	16	no	—
336	C₂²×D₄	—	6	16	no	—
337	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂³×C₄	—	3	2	no	—
339	C₂³×C₄	C₂×C₅×D₃	1	2	yes	complemented
340	#127	—	3	8	no	—
341	#121	—	3	16	no	—
342	#121	—	3	16	no	—
343	#120	—	3	32	no	—
344	C₄×D₄	—	3	8	no	—
345	C₄×D₄	C₂×C₅×D₃	1	8	yes	complemented
346	C₂×C₄⋊C₄	—	3	1	no	—
347	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	4	no	—
350	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
351	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
352	C₂×C₃×C₅	—	2	8	no	—
353	C₂×C₃×C₅	D₄²	1	4	yes	complemented
354	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
355	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
356	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
357	C₅×D₃	—	2	8	no	—
358	C₅×D₃	—	4	8	no	—
359	C₂³×C₃	—	2	4	no	—
360	C₂³×C₃	—	2	4	no	—
361	C₂³×C₃	C₂×C₅×D₄	1	8	yes	complemented
362	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
363	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
364	C₂²×D₃	—	2	4	no	—
365	C₂²×D₃	—	2	4	no	—
366	C₂²×D₃	—	2	8	no	—
367	C₂²×D₃	—	2	8	no	—
368	C₂²×D₃	—	2	32	no	—
369	C₂²×D₃	—	2	8	no	—
370	C₂²×D₃	—	2	32	no	—
371	C₂²×D₃	—	4	16	no	—
372	C₂²×D₃	—	4	64	no	—
373	C₂²×D₃	C₂×C₅×D₄	1	8	yes	complemented
374	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
375	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
376	C₃×D₄	C₂×C₅×D₄	1	16	yes	complemented
377	C₂×C₃×C₄	—	2	4	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	16	no	—
380	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
381	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
382	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
384	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
385	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
386	#67	—	2	32	no	—
387	C₂×Dic₃	—	2	4	no	—
388	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
389	D₁₂	—	2	32	no	—
390	D₁₂	—	2	16	no	—
391	D₁₂	—	2	16	no	—
392	D₁₂	—	4	8	no	—
393	D₁₂	C₂×C₅×D₄	1	16	yes	direct product factor
394	C₄×D₃	—	2	16	no	—
395	C₂²×C₅	—	2	4	no	—
396	C₂²×C₅	—	2	4	no	—
397	C₂²×C₅	—	2	16	no	—
398	C₂²×C₅	—	3	8	no	—
399	C₂²×C₅	—	6	4	no	—
400	C₂²×C₅	—	6	4	no	—
401	C₂²×C₅	—	6	16	no	—
402	C₂²×C₅	—	6	8	no	—
403	C₂²×C₅	—	6	8	no	—
404	C₂²×C₅	—	6	8	no	—
405	C₂²×C₅	—	12	64	no	—
406	C₂²×C₅	—	12	16	no	—
407	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
408	C₂²×C₅	C₂²×D₁₂	1	8	yes	complemented
409	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
410	C₂²×C₅	#1009	1	2	yes	—
411	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
412	C₄×C₅	—	2	4	no	—
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	6	4	no	—
415	C₄×C₅	C₂²×D₁₂	1	4	yes	complemented
416	C₄×C₅	C₂×D₃×D₄	1	4	yes	complemented
417	C₂⁴	—	3	2	no	—
418	C₂⁴	—	3	4	no	—
419	C₂⁴	—	3	16	no	—
420	C₂⁴	—	6	16	no	—
421	C₂⁴	—	6	16	no	—
422	C₂⁴	—	12	8	no	—
423	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
424	C₂×D₄	—	3	16	no	—
425	C₂×D₄	—	3	8	no	—
426	C₂×D₄	—	3	4	no	—
427	C₂×D₄	—	3	16	no	—
428	C₂×D₄	—	3	8	no	—
429	C₂×D₄	—	3	8	no	—
430	C₂×D₄	—	3	8	no	—
431	C₂×D₄	—	6	64	no	—
432	C₂×D₄	—	6	16	no	—
433	C₂×D₄	—	6	16	no	—
434	C₂×D₄	—	6	64	no	—
435	C₂×D₄	—	6	8	no	—
436	C₂×D₄	—	6	8	no	—
437	C₂×D₄	—	12	4	no	—
438	C₂×D₄	C₅×D₁₂	1	8	yes	direct product factor
439	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	8	no	—
443	C₂²×C₄	—	6	8	no	—
444	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
446	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	complemented
449	C₄⋊C₄	—	3	4	no	—
450	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
451	C₂²⋊C₄	—	3	8	no	—
452	C₂²⋊C₄	—	3	16	no	—
453	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
454	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
455	C₃×C₅	C₂×D₄²	1	1	yes	characteristic, complemented, Hall
456	C₂²×C₃	—	2	16	no	—
457	C₂²×C₃	—	2	4	no	—
458	C₂²×C₃	—	2	4	no	—
459	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
460	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
461	C₂²×C₃	C₂²×C₅×D₄	1	8	yes	complemented
462	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
463	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
464	C₂×D₃	—	2	16	no	—
465	C₂×D₃	—	2	4	no	—
466	C₂×D₃	—	2	4	no	—
467	C₂×D₃	—	2	8	no	—
468	C₂×D₃	—	2	8	no	—
469	C₂×D₃	—	2	8	no	—
470	C₂×D₃	—	4	64	no	—
471	C₂×D₃	—	4	16	no	—
472	C₂×D₃	C₂²×C₅×D₄	1	8	yes	complemented
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	C₂²×C₅×D₄	1	4	yes	complemented
476	C₃×C₄	C₂²×C₅×D₄	1	4	yes	complemented
477	Dic₃	—	2	4	no	—
478	C₂×C₅	—	2	8	no	—
479	C₂×C₅	—	6	8	no	—
480	C₂×C₅	—	12	8	no	—
481	C₂×C₅	D₄×D₁₂	1	4	yes	direct product factor
482	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
483	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
484	C₂×C₅	C₂×#1009	1	1	yes	characteristic
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	3	8	no	—
488	C₂³	—	3	4	no	—
489	C₂³	—	3	8	no	—
490	C₂³	—	6	32	no	—
491	C₂³	—	6	4	no	—
492	C₂³	—	6	4	no	—
493	C₂³	—	6	8	no	—
494	C₂³	—	6	32	no	—
495	C₂³	—	6	8	no	—
496	C₂³	—	6	8	no	—
497	C₂³	—	12	16	no	—
498	C₂³	—	12	64	no	—
499	C₂³	C₂×C₅×D₁₂	1	8	yes	complemented
500	C₂³	C₂³×C₅×D₃	1	4	yes	—
501	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
502	D₄	—	3	16	no	—
503	D₄	—	6	32	no	—
504	D₄	—	6	32	no	—
505	D₄	—	6	16	no	—
506	D₄	—	6	16	no	—
507	D₄	—	12	8	no	—
508	D₄	C₂×C₅×D₁₂	1	16	yes	direct product factor
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	3	4	no	—
513	C₂×C₄	—	6	4	no	—
514	C₂×C₄	—	6	16	no	—
515	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	complemented
516	C₂×C₄	C₅×D₃×D₄	1	4	yes	complemented
517	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
518	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
519	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
520	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
521	C₂×C₃	—	2	8	no	—
522	C₂×C₃	C₅×D₄²	1	4	yes	complemented
523	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
524	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
525	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
526	D₃	—	2	8	no	—
527	D₃	—	4	8	no	—
528	C₅	C₂×D₄×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	16	no	—
532	C₂²	—	3	8	no	—
533	C₂²	—	6	4	no	—
534	C₂²	—	6	4	no	—
535	C₂²	—	6	16	no	—
536	C₂²	—	6	8	no	—
537	C₂²	—	6	8	no	—
538	C₂²	—	6	8	no	—
539	C₂²	—	12	64	no	—
540	C₂²	—	12	16	no	—
541	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
542	C₂²	C₂²×C₅×D₁₂	1	8	yes	complemented
543	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
544	C₂²	C₅×#1009	1	2	yes	—
545	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
546	C₄	—	2	4	no	—
547	C₄	—	2	2	no	—
548	C₄	—	6	4	no	—
549	C₄	C₂²×C₅×D₁₂	1	4	yes	complemented
550	C₄	C₂×C₅×D₃×D₄	1	4	yes	complemented
551	C₃	C₂×C₅×D₄²	1	1	yes	characteristic, complemented, Sylow
552	C₂	—	2	8	no	—
553	C₂	—	6	8	no	—
554	C₂	—	12	8	no	—
555	C₂	C₅×D₄×D₁₂	1	4	yes	direct product factor
556	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
557	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
558	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×D₄	C₂	semidirect
2. C₂³×C₅×D₁₂	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₂×C₅×#930	C₂	semidirect
5. C₅×D₄×D₁₂	C₂	direct (N × H)
6. C₂×C₅×#895	C₂	semidirect
7. C₂×C₅×#882	C₂	semidirect
8. C₂×C₅×#874	C₂	semidirect
9. C₂×C₄×C₅×D₁₂	C₂	semidirect
11. C₂⁴×C₅×D₃	C₂²	semidirect
13. C₂³×C₃×C₄×C₅	C₂²	semidirect
14. C₂²×C₅×#67	C₂²	semidirect
16. C₂×C₅×D₃×D₄	C₂²	semidirect
19. C₂²×C₅×D₁₂	C₂²	semidirect
20. C₂²×C₅×D₁₂	C₂²	semidirect
21. C₂²×C₅×D₁₂	C₂²	semidirect
22. C₂²×C₅×D₁₂	C₂²	semidirect
23. C₂²×C₅×D₁₂	C₂²	semidirect
24. C₂²×C₄×C₅×D₃	C₂²	semidirect
25. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
27. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₅×#930	C₂²	semidirect
30. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
31. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
33. C₅×#895	C₂²	semidirect
34. C₅×#882	C₂²	semidirect
35. C₅×#874	C₂²	semidirect
36. C₄×C₅×D₁₂	C₂²	semidirect
37. C₂×D₄×D₁₂	C₅	direct (N × H)
46. C₂×C₄×C₅×D₄	D₃	semidirect
53. C₂³×C₅×D₃	C₂³	semidirect
54. C₂×C₃×C₅×D₄	D₄	semidirect
61. C₂²×C₃×C₄×C₅	C₂³	semidirect
63. C₂×C₅×#67	C₂³	semidirect
71. C₂×C₅×D₁₂	D₄	direct (N × H)
73. C₂×C₅×D₁₂	C₂³	semidirect
74. C₂×C₅×D₁₂	C₂³	semidirect
75. C₂×C₅×D₁₂	C₂³	semidirect
76. C₂×C₅×D₁₂	C₂³	semidirect
78. C₂×C₄×C₅×D₃	C₂³	semidirect
79. C₃×C₅×C₄⋊C₄	C₂³	semidirect
80. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
81. C₃×C₄²×C₅	C₂³	semidirect
82. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
83. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
84. C₅×C₄⋊Dic₃	C₂³	semidirect
85. C₂²×D₃×D₄	C₂×C₅	semidirect
86. C₂³×D₁₂	C₂×C₅	semidirect
87. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
88. C₂×#930	C₂×C₅	semidirect
89. D₄×D₁₂	C₂×C₅	direct (N × H)
90. C₂×#895	C₂×C₅	semidirect
91. C₂×#882	C₂×C₅	semidirect
92. C₂×#874	C₂×C₅	semidirect
93. C₂×C₄×D₁₂	C₂×C₅	semidirect
107. C₂³×C₄×C₅	C₂×D₃	semidirect
113. C₄×C₅×D₄	C₂×D₃	semidirect
115. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
118. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
119. C₂×C₄²×C₅	C₂×D₃	semidirect
123. C₂³×C₃×C₅	C₂×D₄	semidirect
135. C₂²×C₅×D₃	C₂×D₄	semidirect
138. C₃×C₅×D₄	C₂×D₄	semidirect
142. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
143. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
155. C₅×D₁₂	C₂×D₄	direct (N × H)
157. C₂⁴×D₃	C₂²×C₅	semidirect
159. C₂³×C₃×C₄	C₂²×C₅	semidirect
160. C₂²×#67	C₂²×C₅	semidirect
162. C₂×D₃×D₄	C₂²×C₅	semidirect
165. C₂²×D₁₂	C₂²×C₅	semidirect
166. C₂²×D₁₂	C₂²×C₅	semidirect
167. C₂²×D₁₂	C₂²×C₅	semidirect
168. C₂²×D₁₂	C₂²×C₅	semidirect
169. C₂²×D₁₂	C₂²×C₅	semidirect
170. C₂²×C₄×D₃	C₂²×C₅	semidirect
171. C₃×C₄×D₄	C₂²×C₅	semidirect
172. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
173. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
174. C₂×C₃×C₄²	C₂²×C₅	semidirect
175. #930	C₂²×C₅	semidirect
176. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
177. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
178. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
179. #895	C₂²×C₅	semidirect
180. #882	C₂²×C₅	semidirect
181. #874	C₂²×C₅	semidirect
182. C₄×D₁₂	C₂²×C₅	semidirect
204. C₂×C₅×D₄	D₁₂	direct (N × H)
214. C₂²×C₄×C₅	C₂²×D₃	semidirect
216. C₅×C₄⋊C₄	C₂²×D₃	semidirect
219. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
220. C₄²×C₅	C₂²×D₃	semidirect
229. C₂×C₄×D₄	C₅×D₃	semidirect
235. C₂²×C₃×C₅	C₂²×D₄	semidirect
246. C₂×C₅×D₃	C₂²×D₄	semidirect
249. C₃×C₄×C₅	C₂²×D₄	semidirect
250. C₃×C₄×C₅	C₂²×D₄	semidirect
258. C₂³×D₃	C₂³×C₅	semidirect
259. C₂×C₃×D₄	C₅×D₄	semidirect
266. C₂²×C₃×C₄	C₂³×C₅	semidirect
268. C₂×#67	C₂³×C₅	semidirect
276. C₂×D₁₂	C₅×D₄	direct (N × H)
278. C₂×D₁₂	C₂³×C₅	semidirect
279. C₂×D₁₂	C₂³×C₅	semidirect
280. C₂×D₁₂	C₂³×C₅	semidirect
281. C₂×D₁₂	C₂³×C₅	semidirect
283. C₂×C₄×D₃	C₂³×C₅	semidirect
284. C₃×C₄⋊C₄	C₂³×C₅	semidirect
285. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
286. C₃×C₄²	C₂³×C₅	semidirect
287. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
288. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
289. C₄⋊Dic₃	C₂³×C₅	semidirect
304. C₂³×C₅	C₂×D₁₂	semidirect
313. C₅×D₄	C₂×D₁₂	direct (N × H)
320. C₂×C₄×C₅	C₂×D₁₂	semidirect
321. C₂×C₄×C₅	D₃×D₄	semidirect
339. C₂³×C₄	C₂×C₅×D₃	semidirect
345. C₄×D₄	C₂×C₅×D₃	semidirect
347. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
350. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
351. C₂×C₄²	C₂×C₅×D₃	semidirect
353. C₂×C₃×C₅	D₄²	semidirect
361. C₂³×C₃	C₂×C₅×D₄	semidirect
373. C₂²×D₃	C₂×C₅×D₄	semidirect
376. C₃×D₄	C₂×C₅×D₄	semidirect
380. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
381. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
393. D₁₂	C₂×C₅×D₄	direct (N × H)
408. C₂²×C₅	C₂²×D₁₂	semidirect
415. C₄×C₅	C₂²×D₁₂	semidirect
416. C₄×C₅	C₂×D₃×D₄	semidirect
438. C₂×D₄	C₅×D₁₂	direct (N × H)
448. C₂²×C₄	C₂²×C₅×D₃	semidirect
450. C₄⋊C₄	C₂²×C₅×D₃	semidirect
453. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
454. C₄²	C₂²×C₅×D₃	semidirect
455. C₃×C₅	C₂×D₄²	semidirect
461. C₂²×C₃	C₂²×C₅×D₄	semidirect
472. C₂×D₃	C₂²×C₅×D₄	semidirect
475. C₃×C₄	C₂²×C₅×D₄	semidirect
476. C₃×C₄	C₂²×C₅×D₄	semidirect
481. C₂×C₅	D₄×D₁₂	direct (N × H)
499. C₂³	C₂×C₅×D₁₂	semidirect
508. D₄	C₂×C₅×D₁₂	direct (N × H)
515. C₂×C₄	C₂×C₅×D₁₂	semidirect
516. C₂×C₄	C₅×D₃×D₄	semidirect
522. C₂×C₃	C₅×D₄²	semidirect
528. C₅	C₂×D₄×D₁₂	direct (N × H)
542. C₂²	C₂²×C₅×D₁₂	semidirect
549. C₄	C₂²×C₅×D₁₂	semidirect
550. C₄	C₂×C₅×D₃×D₄	semidirect
551. C₃	C₂×C₅×D₄²	semidirect
555. C₂	C₅×D₄×D₁₂	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×D₃×D₄	2
C₂³×C₅×D₁₂	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#930	2
C₅×D₄×D₁₂	2
C₂×C₅×#895	2
C₂×C₅×#882	2
C₂×C₅×#874	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×D₄²	3
C₂×D₄×D₁₂	5

Subgroups — C2×C5×D4×D12 #14482415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₄×D₁₂ #14482415