Subgroups — C₅×C₄⋊C₄×D₁₂ #14327013

Order 1920.

1552 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4987	C₂	1	2	yes	maximal, complemented
6	C₅×#4935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4928	C₂	1	2	yes	maximal, complemented
8	C₅×#4668	C₂	1	4	yes	maximal, complemented
9	C₅×D₄×C₄⋊C₄	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
12	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
24	C₅×D₃×C₄⋊C₄	—	2	8	no	—
25	C₄×C₅×D₁₂	—	2	8	no	—
26	C₄×C₅×D₁₂	C₄	1	8	yes	complemented
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₅×C₃⋊#95	C₂²	1	4	yes	—
29	C₄⋊C₄×D₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₄×C₅×D₄	—	3	1	no	—
31	C₂×C₄×C₅×D₄	—	3	2	no	—
32	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
33	C₅×#389	—	3	2	no	—
34	C₅×#385	—	3	4	no	—
35	C₅×#384	—	3	1	no	—
36	C₅×#380	—	3	2	no	—
37	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₅×D₃	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
45	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
46	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
47	C₂×C₅×D₁₂	D₄	1	4	yes	—
48	C₂×C₅×D₁₂	Q₈	1	4	yes	—
49	C₂×C₄×C₅×D₃	—	2	4	no	—
50	C₂×C₄×C₅×D₃	—	2	4	no	—
51	C₂×C₄×C₅×D₃	—	2	8	no	—
52	C₂×C₄×C₅×D₃	—	2	8	no	—
53	C₂×C₄×C₅×D₃	—	4	4	no	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
57	C₃×C₄²×C₅	—	2	4	no	—
58	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
59	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
60	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
61	C₅×C₄⋊Dic₃	—	2	4	no	—
62	C₅×C₄⋊Dic₃	—	2	4	no	—
63	C₅×C₄⋊Dic₃	—	4	2	no	—
64	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
65	C₅×Dic₃⋊C₄	—	2	8	no	—
66	C₂×D₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
67	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	—
68	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
69	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
70	#4987	C₂×C₅	1	2	yes	complemented
71	#4935	C₂×C₅	1	1	yes	characteristic, complemented
72	#4928	C₂×C₅	1	2	yes	complemented
73	#4668	C₂×C₅	1	4	yes	complemented
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂³×C₄×C₅	—	3	2	no	—
76	C₂³×C₄×C₅	—	3	4	no	—
77	C₄×C₅×D₄	—	3	8	no	—
78	C₄×C₅×D₄	—	6	8	no	—
79	C₂×C₅×C₄⋊C₄	—	3	1	no	—
80	C₂×C₅×C₄⋊C₄	—	3	2	no	—
81	C₂×C₅×C₄⋊C₄	—	3	2	no	—
82	C₂×C₅×C₄⋊C₄	—	3	4	no	—
83	C₂×C₅×C₄⋊C₄	—	3	2	no	—
84	C₂×C₅×C₄⋊C₄	—	6	8	no	—
85	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
91	C₅×#95	—	3	4	no	—
92	C₅×#95	C₂×D₃	1	2	yes	—
93	D₄×C₄⋊C₄	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	2	2	no	—
96	C₂²×C₅×D₃	—	2	2	no	—
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
100	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
101	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	1	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
116	C₂×C₃×C₄×C₅	#41	1	2	yes	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	4	no	—
120	C₂×C₅×Dic₃	—	2	4	no	—
121	C₂×C₅×Dic₃	—	2	4	no	—
122	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
123	C₅×D₁₂	C₄⋊C₄	1	16	yes	direct product factor
124	C₄×C₅×D₃	—	2	16	no	—
125	C₄×C₅×D₃	—	4	16	no	—
126	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
127	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
128	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
134	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
135	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
136	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
137	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
138	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
139	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
140	D₃×C₄⋊C₄	—	2	8	no	—
141	C₄×D₁₂	—	2	8	no	—
142	C₄×D₁₂	C₄×C₅	1	8	yes	complemented
143	C₃×#95	C₂²×C₅	1	2	yes	—
144	C₃⋊#95	C₂²×C₅	1	4	yes	—
145	C₂⁴×C₅	—	3	2	no	—
146	C₂×C₅×D₄	—	3	4	no	—
147	C₂×C₅×D₄	—	3	4	no	—
148	C₂×C₅×D₄	—	3	4	no	—
149	C₂²×C₄×C₅	—	3	2	no	—
150	C₂²×C₄×C₅	—	3	8	no	—
151	C₂²×C₄×C₅	—	3	4	no	—
152	C₂²×C₄×C₅	—	6	8	no	—
153	C₂²×C₄×C₅	—	6	4	no	—
154	C₂²×C₄×C₅	—	6	4	no	—
155	C₂²×C₄×C₅	—	6	8	no	—
156	C₂²×C₄×C₅	—	12	4	no	—
157	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	3	4	no	—
164	C₅×C₄⋊C₄	—	6	8	no	—
165	C₅×C₄⋊C₄	—	6	4	no	—
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₅×C₄⋊C₄	—	12	2	no	—
168	C₅×C₄⋊C₄	D₁₂	1	4	yes	direct product factor
169	C₅×C₂²⋊C₄	—	3	8	no	—
170	C₅×C₂²⋊C₄	—	6	8	no	—
171	C₄²×C₅	—	2	4	no	—
172	C₄²×C₅	C₄×D₃	1	4	yes	complemented
173	C₂×C₄×D₄	—	3	1	no	—
174	C₂×C₄×D₄	—	3	2	no	—
175	C₂²×C₄⋊C₄	—	3	2	no	—
176	#389	—	3	2	no	—
177	#385	—	3	4	no	—
178	#384	—	3	1	no	—
179	#380	—	3	2	no	—
180	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
186	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×C₅×D₃	—	2	4	no	—
189	C₂×C₅×D₃	—	2	4	no	—
190	C₂×C₅×D₃	—	2	4	no	—
191	C₂×C₅×D₃	—	2	4	no	—
192	C₂×C₅×D₃	—	2	4	no	—
193	C₂×C₅×D₃	—	2	4	no	—
194	C₂×C₅×D₃	C₂×C₄⋊C₄	1	8	yes	complemented
195	C₃×C₄×C₅	—	2	2	no	—
196	C₃×C₄×C₅	—	2	4	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	complemented
199	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
200	C₅×Dic₃	—	2	4	no	—
201	C₅×Dic₃	—	4	4	no	—
202	C₂³×D₃	C₂³×C₅	1	2	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
209	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
210	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
211	C₂×D₁₂	C₅×D₄	1	4	yes	—
212	C₂×D₁₂	C₅×Q₈	1	4	yes	—
213	C₂×C₄×D₃	—	2	4	no	—
214	C₂×C₄×D₃	—	2	4	no	—
215	C₂×C₄×D₃	—	2	8	no	—
216	C₂×C₄×D₃	—	2	8	no	—
217	C₂×C₄×D₃	—	4	4	no	—
218	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
221	C₃×C₄²	—	2	4	no	—
222	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
223	(C₂×D₃)⋊C₄	—	2	8	no	—
224	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
225	C₄⋊Dic₃	—	2	4	no	—
226	C₄⋊Dic₃	—	2	4	no	—
227	C₄⋊Dic₃	—	4	2	no	—
228	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
229	Dic₃⋊C₄	—	2	8	no	—
230	C₂³×C₅	—	3	4	no	—
231	C₂³×C₅	—	3	4	no	—
232	C₂³×C₅	—	3	4	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	—	6	2	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×D₄	—	3	16	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	3	4	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	16	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	—	12	16	no	—
254	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
256	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
258	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
259	C₂×C₄×C₅	#235	1	2	yes	—
260	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
261	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
262	C₂²×D₄	—	3	1	no	—
263	C₂³×C₄	—	3	2	no	—
264	C₂³×C₄	—	3	4	no	—
265	C₄×D₄	—	3	8	no	—
266	C₄×D₄	—	6	8	no	—
267	C₂×C₄⋊C₄	—	3	1	no	—
268	C₂×C₄⋊C₄	—	3	2	no	—
269	C₂×C₄⋊C₄	—	3	4	no	—
270	C₂×C₄⋊C₄	—	3	2	no	—
271	C₂×C₄⋊C₄	—	3	2	no	—
272	C₂×C₄⋊C₄	—	6	8	no	—
273	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	3	2	no	—
276	C₂×C₂²⋊C₄	—	3	4	no	—
277	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
278	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
279	#95	—	3	4	no	—
280	#95	C₂×C₅×D₃	1	2	yes	—
281	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂×C₃×C₅	#520	1	1	yes	characteristic
284	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
285	C₂×C₃×C₅	#547	1	1	yes	characteristic
286	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
287	C₂×C₃×C₅	#554	1	1	yes	characteristic
288	C₅×D₃	—	2	8	no	—
289	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
290	C₂²×D₃	—	2	2	no	—
291	C₂²×D₃	—	2	2	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
295	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
296	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
305	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
306	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
308	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
310	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
311	C₂×C₃×C₄	C₅×#41	1	2	yes	—
312	C₂×Dic₃	—	2	2	no	—
313	C₂×Dic₃	—	2	2	no	—
314	C₂×Dic₃	—	2	4	no	—
315	C₂×Dic₃	—	2	4	no	—
316	C₂×Dic₃	—	2	4	no	—
317	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
318	D₁₂	C₅×C₄⋊C₄	1	16	yes	direct product factor
319	C₄×D₃	—	2	16	no	—
320	C₄×D₃	—	4	16	no	—
321	C₂²×C₅	—	3	8	no	—
322	C₂²×C₅	—	6	4	no	—
323	C₂²×C₅	—	6	4	no	—
324	C₂²×C₅	—	6	4	no	—
325	C₂²×C₅	—	6	4	no	—
326	C₂²×C₅	—	6	4	no	—
327	C₂²×C₅	—	6	4	no	—
328	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
329	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
330	C₂²×C₅	C₂×#235	1	1	yes	characteristic
331	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
332	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
333	C₂²×C₅	#1009	1	1	yes	characteristic
334	C₂²×C₅	#1010	1	1	yes	characteristic
335	C₄×C₅	—	2	2	no	—
336	C₄×C₅	—	2	4	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	—	6	4	no	—
339	C₄×C₅	—	12	4	no	—
340	C₄×C₅	C₄×D₁₂	1	4	yes	complemented
341	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	complemented
342	C₂⁴	—	3	2	no	—
343	C₂×D₄	—	3	4	no	—
344	C₂×D₄	—	3	4	no	—
345	C₂×D₄	—	3	4	no	—
346	C₂²×C₄	—	3	2	no	—
347	C₂²×C₄	—	3	8	no	—
348	C₂²×C₄	—	3	4	no	—
349	C₂²×C₄	—	6	8	no	—
350	C₂²×C₄	—	6	4	no	—
351	C₂²×C₄	—	6	4	no	—
352	C₂²×C₄	—	6	8	no	—
353	C₂²×C₄	—	12	4	no	—
354	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
355	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	3	4	no	—
361	C₄⋊C₄	—	6	8	no	—
362	C₄⋊C₄	—	6	4	no	—
363	C₄⋊C₄	—	6	4	no	—
364	C₄⋊C₄	—	12	2	no	—
365	C₄⋊C₄	C₅×D₁₂	1	4	yes	direct product factor
366	C₂²⋊C₄	—	3	8	no	—
367	C₂²⋊C₄	—	6	8	no	—
368	C₄²	—	2	4	no	—
369	C₄²	C₄×C₅×D₃	1	4	yes	complemented
370	C₃×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
372	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
375	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
376	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂×D₃	—	2	4	no	—
379	C₂×D₃	—	2	4	no	—
380	C₂×D₃	—	2	4	no	—
381	C₂×D₃	—	2	4	no	—
382	C₂×D₃	—	2	4	no	—
383	C₂×D₃	—	2	4	no	—
384	C₂×D₃	C₂×C₅×C₄⋊C₄	1	8	yes	complemented
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	complemented
389	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
390	Dic₃	—	2	4	no	—
391	Dic₃	—	4	4	no	—
392	C₂×C₅	—	6	8	no	—
393	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
394	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
395	C₂×C₅	#5523	1	1	yes	characteristic
396	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
397	C₂×C₅	#5551	1	1	yes	characteristic
398	C₂×C₅	Q₈×D₁₂	1	1	yes	characteristic
399	C₂×C₅	#5579	1	1	yes	characteristic
400	C₂³	—	3	4	no	—
401	C₂³	—	3	4	no	—
402	C₂³	—	3	4	no	—
403	C₂³	—	6	2	no	—
404	C₂³	—	6	2	no	—
405	C₂³	—	6	2	no	—
406	C₂³	—	6	2	no	—
407	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
408	D₄	—	3	16	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	3	4	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	6	16	no	—
420	C₂×C₄	—	6	4	no	—
421	C₂×C₄	—	6	4	no	—
422	C₂×C₄	—	6	4	no	—
423	C₂×C₄	—	12	16	no	—
424	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
425	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
426	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
427	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
428	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
429	C₂×C₄	C₅×#235	1	2	yes	—
430	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
431	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
432	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
433	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
434	C₂×C₃	C₅×#520	1	1	yes	characteristic
435	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
436	C₂×C₃	C₅×#547	1	1	yes	characteristic
437	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
438	C₂×C₃	C₅×#554	1	1	yes	characteristic
439	D₃	—	2	8	no	—
440	C₅	C₄⋊C₄×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	3	8	no	—
442	C₂²	—	6	4	no	—
443	C₂²	—	6	4	no	—
444	C₂²	—	6	4	no	—
445	C₂²	—	6	4	no	—
446	C₂²	—	6	4	no	—
447	C₂²	—	6	4	no	—
448	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
449	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
450	C₂²	C₂×C₅×#235	1	1	yes	characteristic
451	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
452	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
453	C₂²	C₅×#1009	1	1	yes	characteristic
454	C₂²	C₅×#1010	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	6	4	no	—
459	C₄	—	12	4	no	—
460	C₄	C₄×C₅×D₁₂	1	4	yes	complemented
461	C₄	C₅×D₃×C₄⋊C₄	1	4	yes	complemented
462	C₃	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	8	no	—
464	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
465	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
466	C₂	C₅×#5523	1	1	yes	characteristic
467	C₂	C₅×D₄×D₁₂	1	1	yes	characteristic
468	C₂	C₅×#5551	1	1	yes	characteristic
469	C₂	C₅×Q₈×D₁₂	1	1	yes	characteristic
470	C₂	C₅×#5579	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×#4987	C₂	semidirect
6. C₅×#4935	C₂	semidirect
7. C₅×#4928	C₂	semidirect
8. C₅×#4668	C₂	semidirect
26. C₄×C₅×D₁₂	C₄	semidirect
29. C₄⋊C₄×D₁₂	C₅	direct (N × H)
37. C₄×C₅×C₄⋊C₄	D₃	semidirect
54. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
56. C₃×C₅×C₄⋊C₄	D₄	semidirect
58. C₃×C₄²×C₅	C₂×C₄	semidirect
60. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
64. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
66. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
69. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
70. #4987	C₂×C₅	semidirect
71. #4935	C₂×C₅	semidirect
72. #4928	C₂×C₅	semidirect
73. #4668	C₂×C₅	semidirect
123. C₅×D₁₂	C₄⋊C₄	direct (N × H)
142. C₄×D₁₂	C₄×C₅	semidirect
168. C₅×C₄⋊C₄	D₁₂	direct (N × H)
172. C₄²×C₅	C₄×D₃	semidirect
180. C₄×C₄⋊C₄	C₅×D₃	semidirect
194. C₂×C₅×D₃	C₂×C₄⋊C₄	semidirect
198. C₃×C₄×C₅	C₂×C₄⋊C₄	semidirect
199. C₃×C₄×C₅	C₄×D₄	semidirect
218. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
220. C₃×C₄⋊C₄	C₅×D₄	semidirect
222. C₃×C₄²	C₂×C₄×C₅	semidirect
224. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
228. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
318. D₁₂	C₅×C₄⋊C₄	direct (N × H)
340. C₄×C₅	C₄×D₁₂	semidirect
341. C₄×C₅	D₃×C₄⋊C₄	semidirect
365. C₄⋊C₄	C₅×D₁₂	direct (N × H)
369. C₄²	C₄×C₅×D₃	semidirect
370. C₃×C₅	D₄×C₄⋊C₄	semidirect
384. C₂×D₃	C₂×C₅×C₄⋊C₄	semidirect
388. C₃×C₄	C₂×C₅×C₄⋊C₄	semidirect
389. C₃×C₄	C₄×C₅×D₄	semidirect
440. C₅	C₄⋊C₄×D₁₂	direct (N × H)
460. C₄	C₄×C₅×D₁₂	semidirect
461. C₄	C₅×D₃×C₄⋊C₄	semidirect
462. C₃	C₅×D₄×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4987	2
C₅×#4935	2
C₅×#4928	2
C₅×#4668	2
C₅×D₄×C₄⋊C₄	3
C₄⋊C₄×D₁₂	5

Subgroups — C5×C4⋊C4×D12 #14327013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊C₄×D₁₂ #14327013