Subgroups — C₅×C₂²⋊C₄×D₁₂ #14325913

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4955	C₂	1	2	yes	maximal, complemented
7	C₅×#4939	C₂	1	2	yes	maximal, complemented
8	C₅×#4665	C₂	1	4	yes	maximal, complemented
9	C₅×D₄×C₂²⋊C₄	—	3	1	no	maximal, Hall
10	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₁₂	—	2	8	no	—
13	C₂²×C₅×D₁₂	C₄	1	8	yes	complemented
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
21	C₂×C₅×#217	C₂²	1	2	yes	—
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
26	C₅×D₃×C₂²⋊C₄	—	2	8	no	—
27	C₄×C₅×D₁₂	—	2	8	no	—
28	C₃×C₅×#95	C₂²	1	2	yes	complemented
29	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
30	C₂²⋊C₄×D₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂³×C₅×D₄	—	3	1	no	—
32	C₂×C₄×C₅×D₄	—	3	2	no	—
33	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
34	C₅×#390	—	3	2	no	—
35	C₅×#386	—	3	4	no	—
36	C₅×#380	—	3	1	no	—
37	C₅×#379	—	3	2	no	—
38	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
40	C₂³×C₅×D₃	—	2	4	no	—
41	C₂³×C₅×D₃	—	2	4	no	—
42	C₂³×C₅×D₃	—	2	8	no	—
43	C₂³×C₅×D₃	—	4	4	no	—
44	C₂³×C₅×D₃	C₂×C₄	1	8	yes	complemented
45	C₂³×C₅×D₃	C₂³	1	2	yes	—
46	C₂³×C₅×D₃	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
54	C₂×C₅×D₁₂	—	2	8	no	—
55	C₂×C₅×D₁₂	—	2	4	no	—
56	C₂×C₅×D₁₂	—	2	32	no	—
57	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
58	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
59	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
60	C₂×C₅×D₁₂	D₄	1	8	yes	—
61	C₂×C₄×C₅×D₃	—	2	8	no	—
62	C₂×C₄×C₅×D₃	—	2	8	no	—
63	C₂×C₄×C₅×D₃	—	4	4	no	—
64	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
66	C₃×C₄²×C₅	—	2	4	no	—
67	C₅×#217	—	2	4	no	—
68	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
69	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
70	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
71	C₅×C₄⋊Dic₃	—	2	4	no	—
72	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic
73	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
74	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	complemented
75	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
76	#5212	C₂×C₅	1	1	yes	characteristic, complemented
77	#4955	C₂×C₅	1	2	yes	complemented
78	#4939	C₂×C₅	1	2	yes	complemented
79	#4665	C₂×C₅	1	4	yes	complemented
80	C₂⁵×C₅	—	3	2	no	—
81	C₂²×C₅×D₄	—	3	8	no	—
82	C₂²×C₅×D₄	—	3	1	no	—
83	C₂²×C₅×D₄	—	3	2	no	—
84	C₂²×C₅×D₄	—	3	1	no	—
85	C₂²×C₅×D₄	—	6	8	no	—
86	C₂³×C₄×C₅	—	3	4	no	—
87	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
88	C₄×C₅×D₄	—	6	8	no	—
89	C₂×C₅×C₄⋊C₄	—	3	2	no	—
90	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
91	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
92	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
93	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
94	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
95	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
98	C₅×#95	—	3	2	no	—
99	C₅×#95	C₂×D₃	1	2	yes	complemented
100	D₄×C₂²⋊C₄	—	3	1	no	Sylow
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
104	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
105	C₂³×C₃×C₅	#41	1	2	yes	—
106	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
107	C₂²×C₅×D₃	—	2	2	no	—
108	C₂²×C₅×D₃	—	2	2	no	—
109	C₂²×C₅×D₃	—	2	4	no	—
110	C₂²×C₅×D₃	—	2	16	no	—
111	C₂²×C₅×D₃	—	2	2	no	—
112	C₂²×C₅×D₃	—	2	4	no	—
113	C₂²×C₅×D₃	—	2	2	no	—
114	C₂²×C₅×D₃	—	2	4	no	—
115	C₂²×C₅×D₃	—	2	16	no	—
116	C₂²×C₅×D₃	—	4	8	no	—
117	C₂²×C₅×D₃	—	4	16	no	—
118	C₂²×C₅×D₃	—	4	16	no	—
119	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
120	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
121	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	8	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
133	C₂×C₅×Dic₃	—	2	4	no	—
134	C₂×C₅×Dic₃	—	2	4	no	—
135	C₂×C₅×Dic₃	—	2	4	no	—
136	C₅×D₁₂	—	2	16	no	—
137	C₅×D₁₂	—	2	8	no	—
138	C₅×D₁₂	C₂²⋊C₄	1	16	yes	direct product factor
139	C₄×C₅×D₃	—	4	16	no	—
140	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
141	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂²×D₁₂	—	2	8	no	—
143	C₂²×D₁₂	C₄×C₅	1	8	yes	complemented
144	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
145	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
146	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
147	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	complemented
148	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
151	C₂×#217	C₂²×C₅	1	2	yes	—
152	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
153	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
154	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
155	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
156	D₃×C₂²⋊C₄	—	2	8	no	—
157	C₄×D₁₂	—	2	8	no	—
158	C₃×#95	C₂²×C₅	1	2	yes	complemented
159	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
160	C₂⁴×C₅	—	3	2	no	—
161	C₂⁴×C₅	—	3	2	no	—
162	C₂⁴×C₅	—	3	8	no	—
163	C₂⁴×C₅	—	6	8	no	—
164	C₂⁴×C₅	—	6	4	no	—
165	C₂⁴×C₅	—	6	4	no	—
166	C₂⁴×C₅	—	12	4	no	—
167	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₅×D₄	—	3	4	no	—
169	C₂×C₅×D₄	—	3	8	no	—
170	C₂×C₅×D₄	—	3	4	no	—
171	C₂×C₅×D₄	—	3	8	no	—
172	C₂×C₅×D₄	—	6	32	no	—
173	C₂×C₅×D₄	—	6	8	no	—
174	C₂×C₅×D₄	—	6	4	no	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	3	4	no	—
177	C₂²×C₄×C₅	—	6	8	no	—
178	C₂²×C₄×C₅	—	6	8	no	—
179	C₂²×C₄×C₅	—	12	4	no	—
180	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
181	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
184	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	6	4	no	—
186	C₅×C₂²⋊C₄	—	2	2	no	—
187	C₅×C₂²⋊C₄	—	6	8	no	—
188	C₅×C₂²⋊C₄	—	6	4	no	—
189	C₅×C₂²⋊C₄	—	6	8	no	—
190	C₅×C₂²⋊C₄	—	12	4	no	—
191	C₅×C₂²⋊C₄	D₁₂	1	4	yes	direct product factor
192	C₄²×C₅	—	2	4	no	—
193	C₂³×D₄	—	3	1	no	—
194	C₂×C₄×D₄	—	3	2	no	—
195	C₂²×C₂²⋊C₄	—	3	2	no	—
196	#390	—	3	2	no	—
197	#386	—	3	4	no	—
198	#380	—	3	1	no	—
199	#379	—	3	2	no	—
200	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
201	C₂²×C₃×C₅	—	2	2	no	—
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	—	2	4	no	—
204	C₂²×C₃×C₅	—	2	4	no	—
205	C₂²×C₃×C₅	C₄×D₄	1	4	yes	complemented
206	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
209	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
210	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
211	C₂×C₅×D₃	—	2	4	no	—
212	C₂×C₅×D₃	—	2	4	no	—
213	C₂×C₅×D₃	—	2	8	no	—
214	C₂×C₅×D₃	—	2	8	no	—
215	C₂×C₅×D₃	—	2	4	no	—
216	C₂×C₅×D₃	—	2	4	no	—
217	C₂×C₅×D₃	—	2	4	no	—
218	C₂×C₅×D₃	—	4	32	no	—
219	C₂×C₅×D₃	—	4	4	no	—
220	C₂×C₅×D₃	—	4	4	no	—
221	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	8	yes	complemented
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	2	4	no	—
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	complemented
226	C₅×Dic₃	—	4	4	no	—
227	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
228	C₂³×D₃	—	2	4	no	—
229	C₂³×D₃	—	2	4	no	—
230	C₂³×D₃	—	2	8	no	—
231	C₂³×D₃	—	4	4	no	—
232	C₂³×D₃	C₂×C₄×C₅	1	8	yes	complemented
233	C₂³×D₃	C₂³×C₅	1	2	yes	—
234	C₂³×D₃	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	—	2	4	no	—
236	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
237	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
242	C₂×D₁₂	—	2	8	no	—
243	C₂×D₁₂	—	2	4	no	—
244	C₂×D₁₂	—	2	32	no	—
245	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
246	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
247	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
248	C₂×D₁₂	C₅×D₄	1	8	yes	—
249	C₂×C₄×D₃	—	2	8	no	—
250	C₂×C₄×D₃	—	2	8	no	—
251	C₂×C₄×D₃	—	4	4	no	—
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
254	C₃×C₄²	—	2	4	no	—
255	#217	—	2	4	no	—
256	(C₂×D₃)⋊C₄	—	2	8	no	—
257	(C₂×D₃)⋊C₄	—	2	8	no	—
258	(C₂×D₃)⋊C₄	—	4	4	no	—
259	C₄⋊Dic₃	—	2	4	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	3	4	no	—
263	C₂³×C₅	—	3	8	no	—
264	C₂³×C₅	—	3	4	no	—
265	C₂³×C₅	—	6	16	no	—
266	C₂³×C₅	—	6	2	no	—
267	C₂³×C₅	—	6	2	no	—
268	C₂³×C₅	—	6	4	no	—
269	C₂³×C₅	—	6	16	no	—
270	C₂³×C₅	—	6	2	no	—
271	C₂³×C₅	—	6	2	no	—
272	C₂³×C₅	—	6	4	no	—
273	C₂³×C₅	—	6	4	no	—
274	C₂³×C₅	—	12	8	no	—
275	C₂³×C₅	—	12	16	no	—
276	C₂³×C₅	—	12	16	no	—
277	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
278	C₂³×C₅	C₂×D₁₂	1	2	yes	—
279	C₂³×C₅	#235	1	2	yes	—
280	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
281	C₅×D₄	—	3	16	no	—
282	C₅×D₄	—	6	16	no	—
283	C₅×D₄	—	6	8	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	8	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	6	4	no	—
292	C₂×C₄×C₅	—	6	4	no	—
293	C₂×C₄×C₅	—	6	4	no	—
294	C₂×C₄×C₅	—	12	16	no	—
295	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
296	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
297	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	complemented
298	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
299	C₂⁵	—	3	2	no	—
300	C₂²×D₄	—	3	8	no	—
301	C₂²×D₄	—	3	1	no	—
302	C₂²×D₄	—	3	2	no	—
303	C₂²×D₄	—	3	1	no	—
304	C₂²×D₄	—	6	8	no	—
305	C₂³×C₄	—	3	4	no	—
306	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
307	C₄×D₄	—	6	8	no	—
308	C₂×C₄⋊C₄	—	3	2	no	—
309	C₂×C₂²⋊C₄	—	3	2	no	—
310	C₂×C₂²⋊C₄	—	3	4	no	—
311	C₂×C₂²⋊C₄	—	3	4	no	—
312	C₂×C₂²⋊C₄	—	3	4	no	—
313	C₂×C₂²⋊C₄	—	6	8	no	—
314	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
316	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
317	#95	—	3	2	no	—
318	#95	C₂×C₅×D₃	1	2	yes	complemented
319	C₂×C₃×C₅	—	2	4	no	—
320	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
322	C₂×C₃×C₅	#518	1	1	yes	characteristic
323	C₂×C₃×C₅	D₄²	1	2	yes	—
324	C₂×C₃×C₅	#546	1	2	yes	—
325	C₅×D₃	—	2	8	no	—
326	C₅×D₃	—	4	4	no	—
327	C₂³×C₃	—	2	2	no	—
328	C₂³×C₃	—	2	2	no	—
329	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
330	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
331	C₂³×C₃	C₅×#41	1	2	yes	—
332	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
333	C₂²×D₃	—	2	2	no	—
334	C₂²×D₃	—	2	2	no	—
335	C₂²×D₃	—	2	4	no	—
336	C₂²×D₃	—	2	16	no	—
337	C₂²×D₃	—	2	2	no	—
338	C₂²×D₃	—	2	4	no	—
339	C₂²×D₃	—	2	2	no	—
340	C₂²×D₃	—	2	4	no	—
341	C₂²×D₃	—	2	16	no	—
342	C₂²×D₃	—	4	8	no	—
343	C₂²×D₃	—	4	16	no	—
344	C₂²×D₃	—	4	16	no	—
345	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
346	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
347	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	8	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
356	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
357	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
359	C₂×Dic₃	—	2	4	no	—
360	C₂×Dic₃	—	2	4	no	—
361	C₂×Dic₃	—	2	4	no	—
362	D₁₂	—	2	16	no	—
363	D₁₂	—	2	8	no	—
364	D₁₂	C₅×C₂²⋊C₄	1	16	yes	direct product factor
365	C₄×D₃	—	4	16	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	2	4	no	—
369	C₂²×C₅	—	2	4	no	—
370	C₂²×C₅	—	3	8	no	—
371	C₂²×C₅	—	6	4	no	—
372	C₂²×C₅	—	6	4	no	—
373	C₂²×C₅	—	6	8	no	—
374	C₂²×C₅	—	6	8	no	—
375	C₂²×C₅	—	6	4	no	—
376	C₂²×C₅	—	6	4	no	—
377	C₂²×C₅	—	6	4	no	—
378	C₂²×C₅	—	12	32	no	—
379	C₂²×C₅	—	12	4	no	—
380	C₂²×C₅	—	12	4	no	—
381	C₂²×C₅	C₄×D₁₂	1	4	yes	complemented
382	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
383	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
384	C₂²×C₅	C₂×#235	1	1	yes	characteristic
385	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
386	C₂²×C₅	#1009	1	2	yes	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	2	4	no	—
389	C₄×C₅	—	4	2	no	—
390	C₄×C₅	—	12	4	no	—
391	C₄×C₅	D₃×C₂²⋊C₄	1	4	yes	complemented
392	C₂⁴	—	3	2	no	—
393	C₂⁴	—	3	2	no	—
394	C₂⁴	—	3	8	no	—
395	C₂⁴	—	6	8	no	—
396	C₂⁴	—	6	4	no	—
397	C₂⁴	—	6	4	no	—
398	C₂⁴	—	12	4	no	—
399	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₂×D₄	—	3	4	no	—
401	C₂×D₄	—	3	8	no	—
402	C₂×D₄	—	3	4	no	—
403	C₂×D₄	—	3	8	no	—
404	C₂×D₄	—	6	32	no	—
405	C₂×D₄	—	6	8	no	—
406	C₂×D₄	—	6	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	3	4	no	—
409	C₂²×C₄	—	6	8	no	—
410	C₂²×C₄	—	6	8	no	—
411	C₂²×C₄	—	12	4	no	—
412	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
413	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
414	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
415	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
416	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
417	C₄⋊C₄	—	6	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	6	8	no	—
420	C₂²⋊C₄	—	6	4	no	—
421	C₂²⋊C₄	—	6	8	no	—
422	C₂²⋊C₄	—	12	4	no	—
423	C₂²⋊C₄	C₅×D₁₂	1	4	yes	direct product factor
424	C₄²	—	2	4	no	—
425	C₃×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	—	2	4	no	—
429	C₂²×C₃	—	2	4	no	—
430	C₂²×C₃	C₄×C₅×D₄	1	4	yes	complemented
431	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
432	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
433	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
434	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
435	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
436	C₂×D₃	—	2	4	no	—
437	C₂×D₃	—	2	4	no	—
438	C₂×D₃	—	2	8	no	—
439	C₂×D₃	—	2	8	no	—
440	C₂×D₃	—	2	4	no	—
441	C₂×D₃	—	2	4	no	—
442	C₂×D₃	—	2	4	no	—
443	C₂×D₃	—	4	32	no	—
444	C₂×D₃	—	4	4	no	—
445	C₂×D₃	—	4	4	no	—
446	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	4	no	—
449	C₃×C₄	—	4	2	no	—
450	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
451	Dic₃	—	4	4	no	—
452	C₂×C₅	—	2	4	no	—
453	C₂×C₅	—	6	8	no	—
454	C₂×C₅	—	12	4	no	—
455	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
456	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×C₅	#5521	1	1	yes	characteristic
458	C₂×C₅	D₄×D₁₂	1	2	yes	—
459	C₂×C₅	#5550	1	2	yes	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	3	4	no	—
463	C₂³	—	3	8	no	—
464	C₂³	—	3	4	no	—
465	C₂³	—	6	16	no	—
466	C₂³	—	6	2	no	—
467	C₂³	—	6	2	no	—
468	C₂³	—	6	4	no	—
469	C₂³	—	6	16	no	—
470	C₂³	—	6	2	no	—
471	C₂³	—	6	2	no	—
472	C₂³	—	6	4	no	—
473	C₂³	—	6	4	no	—
474	C₂³	—	12	8	no	—
475	C₂³	—	12	16	no	—
476	C₂³	—	12	16	no	—
477	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
478	C₂³	C₂×C₅×D₁₂	1	2	yes	—
479	C₂³	C₅×#235	1	2	yes	—
480	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
481	D₄	—	3	16	no	—
482	D₄	—	6	16	no	—
483	D₄	—	6	8	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	6	4	no	—
492	C₂×C₄	—	6	4	no	—
493	C₂×C₄	—	6	4	no	—
494	C₂×C₄	—	12	16	no	—
495	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
496	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
497	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	complemented
498	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
499	C₂×C₃	—	2	4	no	—
500	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
501	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
502	C₂×C₃	C₅×#518	1	1	yes	characteristic
503	C₂×C₃	C₅×D₄²	1	2	yes	—
504	C₂×C₃	C₅×#546	1	2	yes	—
505	D₃	—	2	8	no	—
506	D₃	—	4	4	no	—
507	C₅	C₂²⋊C₄×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	3	8	no	—
513	C₂²	—	6	4	no	—
514	C₂²	—	6	4	no	—
515	C₂²	—	6	8	no	—
516	C₂²	—	6	8	no	—
517	C₂²	—	6	4	no	—
518	C₂²	—	6	4	no	—
519	C₂²	—	6	4	no	—
520	C₂²	—	12	32	no	—
521	C₂²	—	12	4	no	—
522	C₂²	—	12	4	no	—
523	C₂²	C₄×C₅×D₁₂	1	4	yes	complemented
524	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
525	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
526	C₂²	C₂×C₅×#235	1	1	yes	characteristic
527	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
528	C₂²	C₅×#1009	1	2	yes	—
529	C₄	—	2	2	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	12	4	no	—
533	C₄	C₅×D₃×C₂²⋊C₄	1	4	yes	complemented
534	C₃	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
535	C₂	—	2	4	no	—
536	C₂	—	6	8	no	—
537	C₂	—	12	4	no	—
538	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
539	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
540	C₂	C₅×#5521	1	1	yes	characteristic
541	C₂	C₅×D₄×D₁₂	1	2	yes	—
542	C₂	C₅×#5550	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
5. C₅×#5212	C₂	semidirect
6. C₅×#4955	C₂	semidirect
7. C₅×#4939	C₂	semidirect
8. C₅×#4665	C₂	semidirect
13. C₂²×C₅×D₁₂	C₄	semidirect
17. C₂²×C₄×C₅×D₃	C₂²	semidirect
20. C₂×C₃×C₄²×C₅	C₂²	semidirect
22. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
23. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
28. C₃×C₅×#95	C₂²	semidirect
29. C₅×C₃⋊#95	C₂²	semidirect
30. C₂²⋊C₄×D₁₂	C₅	direct (N × H)
38. C₄×C₅×C₂²⋊C₄	D₃	semidirect
44. C₂³×C₅×D₃	C₂×C₄	semidirect
48. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
58. C₂×C₅×D₁₂	C₂×C₄	semidirect
59. C₂×C₅×D₁₂	C₂×C₄	semidirect
65. C₃×C₅×C₂²⋊C₄	D₄	semidirect
73. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
74. C₂×C₄×D₁₂	C₂×C₅	semidirect
75. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
76. #5212	C₂×C₅	semidirect
77. #4955	C₂×C₅	semidirect
78. #4939	C₂×C₅	semidirect
79. #4665	C₂×C₅	semidirect
97. C₂×C₄²×C₅	C₂×D₃	semidirect
99. C₅×#95	C₂×D₃	semidirect
132. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
138. C₅×D₁₂	C₂²⋊C₄	direct (N × H)
143. C₂²×D₁₂	C₄×C₅	semidirect
147. C₂²×C₄×D₃	C₂²×C₅	semidirect
150. C₂×C₃×C₄²	C₂²×C₅	semidirect
152. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
153. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
154. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
155. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
158. C₃×#95	C₂²×C₅	semidirect
159. C₃⋊#95	C₂²×C₅	semidirect
180. C₂²×C₄×C₅	C₄×D₃	semidirect
191. C₅×C₂²⋊C₄	D₁₂	direct (N × H)
200. C₄×C₂²⋊C₄	C₅×D₃	semidirect
205. C₂²×C₃×C₅	C₄×D₄	semidirect
221. C₂×C₅×D₃	C₂×C₂²⋊C₄	semidirect
225. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
232. C₂³×D₃	C₂×C₄×C₅	semidirect
236. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
246. C₂×D₁₂	C₂×C₄×C₅	semidirect
247. C₂×D₁₂	C₂×C₄×C₅	semidirect
253. C₃×C₂²⋊C₄	C₅×D₄	semidirect
297. C₂×C₄×C₅	C₂×D₁₂	semidirect
316. C₂×C₄²	C₂×C₅×D₃	semidirect
318. #95	C₂×C₅×D₃	semidirect
358. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
364. D₁₂	C₅×C₂²⋊C₄	direct (N × H)
381. C₂²×C₅	C₄×D₁₂	semidirect
391. C₄×C₅	D₃×C₂²⋊C₄	semidirect
412. C₂²×C₄	C₄×C₅×D₃	semidirect
423. C₂²⋊C₄	C₅×D₁₂	direct (N × H)
425. C₃×C₅	D₄×C₂²⋊C₄	semidirect
430. C₂²×C₃	C₄×C₅×D₄	semidirect
446. C₂×D₃	C₂×C₅×C₂²⋊C₄	semidirect
450. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
497. C₂×C₄	C₂×C₅×D₁₂	semidirect
507. C₅	C₂²⋊C₄×D₁₂	direct (N × H)
523. C₂²	C₄×C₅×D₁₂	semidirect
533. C₄	C₅×D₃×C₂²⋊C₄	semidirect
534. C₃	C₅×D₄×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×D₁₂	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#5212	2
C₅×#4955	2
C₅×#4939	2
C₅×#4665	2
C₅×D₄×C₂²⋊C₄	3
C₂²⋊C₄×D₁₂	5

Subgroups — C5×C22⋊C4×D12 #14325913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊C₄×D₁₂ #14325913