Subgroups — C₄⋊C₄×D₆₀ #14327015

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×C₄⋊C₄×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₆₀	C₂	1	2	yes	maximal
3	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751088	C₂	1	2	yes	maximal, complemented
6	#11751036	C₂	1	1	yes	maximal, characteristic, complemented
7	#11751029	C₂	1	2	yes	maximal, complemented
8	#11750769	C₂	1	4	yes	maximal, complemented
9	C₄⋊C₄×D₂₀	—	3	1	no	maximal, Hall
10	C₂²×D₆₀	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₁₅	C₂²	1	4	yes	—
12	C₂²×C₄×D₁₅	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×#6714	C₂²	1	4	yes	—
18	C₂×#6714	C₂²	1	2	yes	—
19	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
20	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
21	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
22	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂×#6712	C₂²	1	4	yes	—
24	C₄⋊C₄×D₁₅	—	2	8	no	—
25	C₄×D₆₀	—	2	8	no	—
26	C₄×D₆₀	C₄	1	8	yes	complemented
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	#91115	C₂²	1	4	yes	—
29	C₄⋊C₄×D₁₂	—	5	1	no	maximal, Hall
30	C₂×D₅×C₄⋊C₄	—	3	2	no	—
31	C₂×C₄×D₂₀	—	3	1	no	—
32	C₂×C₄×D₂₀	—	3	2	no	—
33	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
34	#65276	—	3	2	no	—
35	#65224	—	3	1	no	—
36	#65217	—	3	2	no	—
37	#64957	—	3	4	no	—
38	C₂³×D₁₅	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×Dic₁₅	C₂³	1	4	yes	—
45	C₂²×Dic₁₅	C₂³	1	2	yes	—
46	C₂×D₆₀	C₂×C₄	1	4	yes	—
47	C₂×D₆₀	D₄	1	4	yes	—
48	C₂×D₆₀	Q₈	1	4	yes	—
49	C₂×C₄×D₁₅	—	2	4	no	—
50	C₂×C₄×D₁₅	—	2	4	no	—
51	C₂×C₄×D₁₅	—	2	8	no	—
52	C₂×C₄×D₁₅	—	2	8	no	—
53	C₂×C₄×D₁₅	—	4	4	no	—
54	C₂×C₄×D₁₅	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	#6714	—	2	8	no	—
60	#6714	C₂×C₄	1	8	yes	complemented
61	C₄⋊Dic₁₅	—	2	4	no	—
62	C₄⋊Dic₁₅	—	2	4	no	—
63	C₄⋊Dic₁₅	—	4	2	no	—
64	C₄⋊Dic₁₅	C₂×C₄	1	4	yes	complemented
65	#6712	—	2	8	no	—
66	C₂×D₃×C₄⋊C₄	—	5	2	no	—
67	C₂×C₄×D₁₂	—	5	1	no	—
68	C₂×C₄×D₁₂	—	5	2	no	—
69	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
70	#4987	—	5	2	no	—
71	#4935	—	5	1	no	—
72	#4928	—	5	2	no	—
73	#4668	—	5	4	no	—
74	C₂²×D₂₀	—	3	1	no	—
75	C₂²×C₄×D₅	—	3	2	no	—
76	C₂²×C₄×D₅	—	3	4	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂×#685	—	3	2	no	—
82	C₂×#685	—	3	4	no	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×C₄⋊Dic₅	—	3	2	no	—
85	C₂×C₄⋊Dic₅	—	3	2	no	—
86	C₂×C₄⋊Dic₅	—	3	2	no	—
87	C₂×#683	—	3	4	no	—
88	D₅×C₄⋊C₄	—	6	8	no	—
89	C₄×D₂₀	—	3	8	no	—
90	C₄×D₂₀	—	6	8	no	—
91	C₅×#95	C₂×D₃	1	2	yes	—
92	#3963	—	3	4	no	—
93	D₄×C₄⋊C₄	—	15	1	no	Sylow
94	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
95	C₂²×D₁₅	—	2	2	no	—
96	C₂²×D₁₅	—	2	2	no	—
97	C₂²×D₁₅	—	2	2	no	—
98	C₂²×D₁₅	—	2	2	no	—
99	C₂²×D₁₅	C₂²×C₄	1	4	yes	—
100	C₂²×D₁₅	C₂×D₄	1	4	yes	—
101	C₂²×D₁₅	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×Dic₁₅	—	2	2	no	—
118	C₂×Dic₁₅	—	2	2	no	—
119	C₂×Dic₁₅	—	2	4	no	—
120	C₂×Dic₁₅	—	2	4	no	—
121	C₂×Dic₁₅	—	2	4	no	—
122	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
123	D₆₀	C₄⋊C₄	1	16	yes	direct product factor
124	C₄×D₁₅	—	2	16	no	—
125	C₄×D₁₅	—	4	16	no	—
126	C₂²×D₁₂	—	5	1	no	—
127	C₂²×C₄×D₃	—	5	2	no	—
128	C₂²×C₄×D₃	—	5	4	no	—
129	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
131	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
133	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
134	C₂×(C₂×D₃)⋊C₄	—	5	4	no	—
135	C₂×C₄⋊Dic₃	—	5	1	no	—
136	C₂×C₄⋊Dic₃	—	5	2	no	—
137	C₂×C₄⋊Dic₃	—	5	2	no	—
138	C₂×C₄⋊Dic₃	—	5	2	no	—
139	C₂×Dic₃⋊C₄	—	5	4	no	—
140	D₃×C₄⋊C₄	—	10	8	no	—
141	C₄×D₁₂	—	5	8	no	—
142	C₄×D₁₂	—	10	8	no	—
143	C₃×#95	C₂×D₅	1	2	yes	—
144	C₃⋊#95	—	5	4	no	—
145	C₂³×D₅	—	3	2	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₂²×Dic₅	—	3	2	no	—
152	C₂²×Dic₅	—	3	4	no	—
153	C₂×D₂₀	—	3	4	no	—
154	C₂×D₂₀	—	3	4	no	—
155	C₂×D₂₀	—	3	4	no	—
156	C₂×C₄×D₅	—	3	8	no	—
157	C₂×C₄×D₅	—	6	4	no	—
158	C₂×C₄×D₅	—	6	4	no	—
159	C₂×C₄×D₅	—	6	8	no	—
160	C₂×C₄×D₅	—	6	8	no	—
161	C₂×C₄×D₅	—	12	4	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	D₁₂	1	4	yes	complemented
164	C₄²×C₅	—	2	4	no	—
165	C₄²×C₅	C₄×D₃	1	4	yes	complemented
166	#685	—	3	8	no	—
167	#685	—	6	8	no	—
168	C₄⋊Dic₅	—	3	4	no	—
169	C₄⋊Dic₅	—	6	4	no	—
170	C₄⋊Dic₅	—	6	4	no	—
171	C₄⋊Dic₅	—	12	2	no	—
172	#683	—	6	8	no	—
173	C₂×C₄×D₄	—	15	1	no	—
174	C₂×C₄×D₄	—	15	2	no	—
175	C₂²×C₄⋊C₄	—	15	2	no	—
176	#389	—	15	2	no	—
177	#385	—	15	4	no	—
178	#384	—	15	1	no	—
179	#380	—	15	2	no	—
180	C₄×C₄⋊C₄	D₁₅	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×D₁₅	—	2	4	no	—
189	C₂×D₁₅	—	2	4	no	—
190	C₂×D₁₅	—	2	4	no	—
191	C₂×D₁₅	—	2	4	no	—
192	C₂×D₁₅	—	2	4	no	—
193	C₂×D₁₅	—	2	4	no	—
194	C₂×D₁₅	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	Dic₁₅	—	2	4	no	—
201	Dic₁₅	—	4	4	no	—
202	C₂³×D₃	—	5	2	no	—
203	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₂²×Dic₃	—	5	2	no	—
209	C₂²×Dic₃	—	5	4	no	—
210	C₂×D₁₂	—	5	4	no	—
211	C₂×D₁₂	—	5	4	no	—
212	C₂×D₁₂	—	5	4	no	—
213	C₂×C₄×D₃	—	5	8	no	—
214	C₂×C₄×D₃	—	10	4	no	—
215	C₂×C₄×D₃	—	10	4	no	—
216	C₂×C₄×D₃	—	10	8	no	—
217	C₂×C₄×D₃	—	10	8	no	—
218	C₂×C₄×D₃	—	20	4	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	D₂₀	1	4	yes	complemented
221	C₃×C₄²	—	2	4	no	—
222	C₃×C₄²	C₄×D₅	1	4	yes	complemented
223	(C₂×D₃)⋊C₄	—	5	8	no	—
224	(C₂×D₃)⋊C₄	—	10	8	no	—
225	C₄⋊Dic₃	—	5	4	no	—
226	C₄⋊Dic₃	—	10	4	no	—
227	C₄⋊Dic₃	—	10	4	no	—
228	C₄⋊Dic₃	—	20	2	no	—
229	Dic₃⋊C₄	—	10	8	no	—
230	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
231	C₂²×D₅	—	3	4	no	—
232	C₂²×D₅	—	3	4	no	—
233	C₂²×D₅	—	3	4	no	—
234	C₂²×D₅	—	6	2	no	—
235	C₂²×D₅	—	6	2	no	—
236	C₂²×D₅	—	6	2	no	—
237	C₂²×D₅	—	6	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
247	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
248	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
249	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
250	C₂×C₄×C₅	#235	1	2	yes	—
251	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
252	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
253	C₂×Dic₅	—	3	4	no	—
254	C₂×Dic₅	—	6	2	no	—
255	C₂×Dic₅	—	6	2	no	—
256	C₂×Dic₅	—	6	4	no	—
257	C₂×Dic₅	—	6	4	no	—
258	C₂×Dic₅	—	6	4	no	—
259	D₂₀	—	3	16	no	—
260	C₄×D₅	—	6	16	no	—
261	C₄×D₅	—	12	16	no	—
262	C₂²×D₄	—	15	1	no	—
263	C₂³×C₄	—	15	2	no	—
264	C₂³×C₄	—	15	4	no	—
265	C₄×D₄	—	15	8	no	—
266	C₄×D₄	—	30	8	no	—
267	C₂×C₄⋊C₄	—	15	1	no	—
268	C₂×C₄⋊C₄	—	15	2	no	—
269	C₂×C₄⋊C₄	—	15	4	no	—
270	C₂×C₄⋊C₄	—	15	2	no	—
271	C₂×C₄⋊C₄	—	15	2	no	—
272	C₂×C₄⋊C₄	—	30	8	no	—
273	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	15	2	no	—
276	C₂×C₂²⋊C₄	—	15	4	no	—
277	C₂×C₄²	C₂×D₁₅	1	2	yes	—
278	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
279	#95	—	15	4	no	—
280	#95	C₂×D₁₅	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	D₁₅	—	2	8	no	—
289	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
290	C₂²×D₃	—	5	4	no	—
291	C₂²×D₃	—	5	4	no	—
292	C₂²×D₃	—	5	4	no	—
293	C₂²×D₃	—	10	2	no	—
294	C₂²×D₃	—	10	2	no	—
295	C₂²×D₃	—	10	2	no	—
296	C₂²×D₃	—	10	2	no	—
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	C₂×C₄×D₅	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
307	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
308	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
309	C₂×C₃×C₄	#709	1	2	yes	—
310	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
311	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
312	C₂×Dic₃	—	5	4	no	—
313	C₂×Dic₃	—	10	2	no	—
314	C₂×Dic₃	—	10	2	no	—
315	C₂×Dic₃	—	10	4	no	—
316	C₂×Dic₃	—	10	4	no	—
317	C₂×Dic₃	—	10	4	no	—
318	D₁₂	—	5	16	no	—
319	C₄×D₃	—	10	16	no	—
320	C₄×D₃	—	20	16	no	—
321	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
322	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
323	C₂²×C₅	C₂×#235	1	1	yes	characteristic
324	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
325	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
326	C₂²×C₅	#1009	1	1	yes	characteristic
327	C₂²×C₅	#1010	1	1	yes	characteristic
328	C₂×D₅	—	3	8	no	—
329	C₂×D₅	—	6	4	no	—
330	C₂×D₅	—	6	4	no	—
331	C₂×D₅	—	6	4	no	—
332	C₂×D₅	—	6	4	no	—
333	C₂×D₅	—	6	4	no	—
334	C₂×D₅	—	6	4	no	—
335	C₄×C₅	—	2	2	no	—
336	C₄×C₅	—	2	4	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	C₄×D₁₂	1	4	yes	complemented
339	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	complemented
340	Dic₅	—	6	4	no	—
341	Dic₅	—	12	4	no	—
342	C₂⁴	—	15	2	no	—
343	C₂×D₄	—	15	4	no	—
344	C₂×D₄	—	15	4	no	—
345	C₂×D₄	—	15	4	no	—
346	C₂²×C₄	—	15	2	no	—
347	C₂²×C₄	—	15	8	no	—
348	C₂²×C₄	—	15	4	no	—
349	C₂²×C₄	—	30	8	no	—
350	C₂²×C₄	—	30	4	no	—
351	C₂²×C₄	—	30	4	no	—
352	C₂²×C₄	—	30	8	no	—
353	C₂²×C₄	—	60	4	no	—
354	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
355	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
356	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
357	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	15	4	no	—
361	C₄⋊C₄	—	30	8	no	—
362	C₄⋊C₄	—	30	4	no	—
363	C₄⋊C₄	—	30	4	no	—
364	C₄⋊C₄	—	60	2	no	—
365	C₄⋊C₄	D₆₀	1	4	yes	direct product factor
366	C₂²⋊C₄	—	15	8	no	—
367	C₂²⋊C₄	—	30	8	no	—
368	C₄²	—	2	4	no	—
369	C₄²	C₄×D₁₅	1	4	yes	complemented
370	C₃×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
372	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
373	C₂²×C₃	C₂×#709	1	1	yes	characteristic
374	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
375	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
376	C₂²×C₃	#4149	1	1	yes	characteristic
377	C₂²×C₃	#4150	1	1	yes	characteristic
378	C₂×D₃	—	5	8	no	—
379	C₂×D₃	—	10	4	no	—
380	C₂×D₃	—	10	4	no	—
381	C₂×D₃	—	10	4	no	—
382	C₂×D₃	—	10	4	no	—
383	C₂×D₃	—	10	4	no	—
384	C₂×D₃	—	10	4	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	C₄×D₂₀	1	4	yes	complemented
389	C₃×C₄	D₅×C₄⋊C₄	1	4	yes	complemented
390	Dic₃	—	10	4	no	—
391	Dic₃	—	20	4	no	—
392	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
393	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
394	C₂×C₅	#5523	1	1	yes	characteristic
395	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
396	C₂×C₅	#5551	1	1	yes	characteristic
397	C₂×C₅	Q₈×D₁₂	1	1	yes	characteristic
398	C₂×C₅	#5579	1	1	yes	characteristic
399	D₅	—	6	8	no	—
400	C₂³	—	15	4	no	—
401	C₂³	—	15	4	no	—
402	C₂³	—	15	4	no	—
403	C₂³	—	30	2	no	—
404	C₂³	—	30	2	no	—
405	C₂³	—	30	2	no	—
406	C₂³	—	30	2	no	—
407	C₂³	C₂³×D₁₅	1	1	yes	characteristic
408	D₄	—	15	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	—	15	4	no	—
417	C₂×C₄	—	30	2	no	—
418	C₂×C₄	—	30	2	no	—
419	C₂×C₄	—	30	16	no	—
420	C₂×C₄	—	30	4	no	—
421	C₂×C₄	—	30	4	no	—
422	C₂×C₄	—	30	4	no	—
423	C₂×C₄	—	60	16	no	—
424	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
425	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
426	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
427	C₂×C₄	C₂×D₆₀	1	4	yes	—
428	C₂×C₄	C₂×D₆₀	1	2	yes	—
429	C₂×C₄	#6817	1	2	yes	—
430	C₂×C₄	D₄×D₁₅	1	2	yes	—
431	C₂×C₄	Q₈×D₁₅	1	2	yes	—
432	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
433	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
434	C₂×C₃	#65857	1	1	yes	characteristic
435	C₂×C₃	D₄×D₂₀	1	1	yes	characteristic
436	C₂×C₃	#65885	1	1	yes	characteristic
437	C₂×C₃	Q₈×D₂₀	1	1	yes	characteristic
438	C₂×C₃	#65913	1	1	yes	characteristic
439	D₃	—	10	8	no	—
440	C₅	C₄⋊C₄×D₁₂	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	15	8	no	—
442	C₂²	—	30	4	no	—
443	C₂²	—	30	4	no	—
444	C₂²	—	30	4	no	—
445	C₂²	—	30	4	no	—
446	C₂²	—	30	4	no	—
447	C₂²	—	30	4	no	—
448	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
449	C₂²	C₂²×D₆₀	1	1	yes	characteristic
450	C₂²	C₂×#6817	1	1	yes	characteristic
451	C₂²	C₂×D₄×D₁₅	1	1	yes	characteristic
452	C₂²	C₂×Q₈×D₁₅	1	1	yes	characteristic
453	C₂²	#92100	1	1	yes	characteristic
454	C₂²	#92101	1	1	yes	characteristic
455	C₄	—	2	4	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	30	4	no	—
459	C₄	—	60	4	no	—
460	C₄	C₄×D₆₀	1	4	yes	complemented
461	C₄	C₄⋊C₄×D₁₅	1	4	yes	complemented
462	C₃	C₄⋊C₄×D₂₀	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	30	8	no	—
464	C₂	C₂×C₄×D₆₀	1	1	yes	characteristic
465	C₂	C₂×C₄⋊C₄×D₁₅	1	1	yes	characteristic
466	C₂	#11756282	1	1	yes	characteristic
467	C₂	D₄×D₆₀	1	1	yes	characteristic
468	C₂	#11756310	1	1	yes	characteristic
469	C₂	Q₈×D₆₀	1	1	yes	characteristic
470	C₂	#11756338	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, cosocle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×D₆₀	C₂²
hypercenter	C₄×C₄⋊C₄	D₁₅
hypocenter	C₃×C₅	D₄×C₄⋊C₄
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊C₄×D₁₅	C₂	semidirect
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. #11751088	C₂	semidirect
6. #11751036	C₂	semidirect
7. #11751029	C₂	semidirect
8. #11750769	C₂	semidirect
26. C₄×D₆₀	C₄	semidirect
33. C₄×C₅×C₄⋊C₄	D₃	semidirect
54. C₂×C₄×D₁₅	C₂×C₄	semidirect
56. C₃×C₅×C₄⋊C₄	D₄	semidirect
58. C₃×C₄²×C₅	C₂×C₄	semidirect
60. #6714	C₂×C₄	semidirect
64. C₄⋊Dic₁₅	C₂×C₄	semidirect
69. C₃×C₄×C₄⋊C₄	D₅	semidirect
123. D₆₀	C₄⋊C₄	direct (N × H)
163. C₅×C₄⋊C₄	D₁₂	semidirect
165. C₄²×C₅	C₄×D₃	semidirect
180. C₄×C₄⋊C₄	D₁₅	semidirect
194. C₂×D₁₅	C₂×C₄⋊C₄	semidirect
198. C₃×C₄×C₅	C₂×C₄⋊C₄	semidirect
199. C₃×C₄×C₅	C₄×D₄	semidirect
220. C₃×C₄⋊C₄	D₂₀	semidirect
222. C₃×C₄²	C₄×D₅	semidirect
338. C₄×C₅	C₄×D₁₂	semidirect
339. C₄×C₅	D₃×C₄⋊C₄	semidirect
365. C₄⋊C₄	D₆₀	direct (N × H)
369. C₄²	C₄×D₁₅	semidirect
370. C₃×C₅	D₄×C₄⋊C₄	semidirect
388. C₃×C₄	C₄×D₂₀	semidirect
389. C₃×C₄	D₅×C₄⋊C₄	semidirect
440. C₅	C₄⋊C₄×D₁₂	semidirect
460. C₄	C₄×D₆₀	semidirect
461. C₄	C₄⋊C₄×D₁₅	semidirect
462. C₃	C₄⋊C₄×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×D₁₅	2
C₂×C₄×D₆₀	2
C₃×C₄×C₅×C₄⋊C₄	2
#11751088	2
#11751036	2
#11751029	2
#11750769	2
C₄⋊C₄×D₂₀	3
C₄⋊C₄×D₁₂	5

Subgroups — C4⋊C4×D60 #14327015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×D₆₀ #14327015