Subgroups — #14327050

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×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#91435	C₂	1	2	yes	maximal
3	C₂×D₃×C₄⋊Dic₅	C₂	1	2	yes	maximal, complemented
4	C₄×C₄⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65224	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748897	C₂	1	4	yes	maximal, complemented
7	#11748868	C₂	1	2	yes	maximal, complemented
8	#11748786	C₂	1	2	yes	maximal, complemented
9	D₄×C₄⋊Dic₅	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
12	C₂²×D₃×Dic₅	C₂²	1	4	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₁₅	C₂²	1	2	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₄×C₅×D₁₂	C₄	1	8	yes	complemented
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
23	C₂×Dic₃⋊Dic₅	C₂²	1	4	yes	—
24	C₂×(C₂×D₃)⋊Dic₅	C₂²	1	4	yes	—
25	#91435	—	2	8	no	—
26	D₃×C₄⋊Dic₅	—	2	8	no	—
27	#91115	C₂²	1	2	yes	—
28	#90994	C₂²	1	4	yes	—
29	#74360	—	5	1	no	maximal, Hall
30	C₂×C₄×C₅×D₄	—	3	1	no	—
31	C₂×D₄×Dic₅	—	3	2	no	—
32	C₂²×C₄⋊Dic₅	—	3	2	no	—
33	#65501	—	3	2	no	—
34	#65274	—	3	2	no	—
35	#65239	—	3	4	no	—
36	#65224	D₃	1	1	yes	characteristic, complemented
37	C₄×C₄⋊Dic₅	—	3	1	no	—
38	C₂³×C₅×D₃	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₅	C₂³	1	2	yes	—
43	C₂²×Dic₁₅	C₂³	1	2	yes	—
44	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
45	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
46	C₂×C₅×D₁₂	D₄	1	4	yes	—
47	C₂×C₅×D₁₂	Q₈	1	4	yes	—
48	C₂×C₄×C₅×D₃	—	2	4	no	—
49	C₂×C₄×C₅×D₃	—	2	4	no	—
50	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
51	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
52	C₂×D₃×Dic₅	—	2	8	no	—
53	C₂×D₃×Dic₅	—	2	8	no	—
54	C₂×D₃×Dic₅	—	4	4	no	—
55	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
56	C₄⋊Dic₁₅	—	2	2	no	—
57	C₄⋊Dic₁₅	D₄	1	4	yes	complemented
58	C₄×Dic₁₅	—	2	4	no	—
59	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
60	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
61	C₃×C₄⋊Dic₅	—	2	4	no	—
62	C₃×C₄⋊Dic₅	—	2	4	no	—
63	C₃×C₄⋊Dic₅	—	4	2	no	—
64	Dic₃⋊Dic₅	—	2	8	no	—
65	(C₂×D₃)⋊Dic₅	—	2	8	no	—
66	C₂×#893	—	5	2	no	—
67	C₂×D₃×C₄⋊C₄	—	5	2	no	—
68	C₂×C₄×D₁₂	D₅	1	1	yes	characteristic
69	C₃×#384	—	5	1	no	—
70	#4989	—	5	4	no	—
71	#4987	—	5	2	no	—
72	#4972	—	5	2	no	—
73	C₄×C₄⋊Dic₃	—	5	1	no	—
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂³×C₄×C₅	—	3	2	no	—
76	C₂³×Dic₅	—	3	4	no	—
77	C₄×C₅×D₄	—	3	8	no	—
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂×C₂²⋊Dic₅	—	3	4	no	—
82	D₄×Dic₅	—	6	8	no	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×C₄⋊Dic₅	—	3	1	no	—
85	C₂×C₄⋊Dic₅	—	3	4	no	—
86	C₂×C₄⋊Dic₅	—	6	8	no	—
87	C₂×C₄⋊Dic₅	C₂×D₃	1	2	yes	—
88	C₂×C₄⋊Dic₅	C₂×D₃	1	2	yes	—
89	C₂×C₄⋊Dic₅	C₂×D₃	1	2	yes	—
90	C₂×C₄×Dic₅	—	3	2	no	—
91	#3963	—	3	2	no	—
92	#3963	—	3	4	no	—
93	D₄×C₄⋊C₄	—	15	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	1	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×Dic₁₅	—	2	2	no	—
112	C₂×Dic₁₅	—	2	2	no	—
113	C₂×Dic₁₅	—	2	2	no	—
114	C₂×Dic₁₅	—	2	2	no	—
115	C₂×Dic₁₅	—	2	2	no	—
116	C₂×Dic₁₅	C₂×D₄	1	4	yes	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
120	C₅×D₁₂	C₄⋊C₄	1	16	yes	complemented
121	C₄×C₅×D₃	—	2	16	no	—
122	C₂×C₃×Dic₅	—	2	4	no	—
123	C₂×C₃×Dic₅	—	2	4	no	—
124	C₂×C₃×Dic₅	—	2	4	no	—
125	D₃×Dic₅	—	4	16	no	—
126	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
127	C₂²×C₄×D₃	—	5	4	no	—
128	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	—	5	2	no	—
130	C₂×C₃×C₄⋊C₄	—	5	2	no	—
131	C₂×C₃×C₄⋊C₄	—	5	2	no	—
132	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
133	C₂×(C₂×D₃)⋊C₄	—	5	4	no	—
134	C₂×(C₂×D₃)⋊C₄	C₂×D₅	1	2	yes	—
135	C₂×C₄⋊Dic₃	—	5	1	no	—
136	C₂×C₄⋊Dic₃	—	5	1	no	—
137	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
138	C₂×Dic₃⋊C₄	—	5	4	no	—
139	C₂×C₄×Dic₃	—	5	2	no	—
140	#893	—	10	8	no	—
141	D₃×C₄⋊C₄	—	10	8	no	—
142	C₄×D₁₂	Dic₅	1	8	yes	complemented
143	C₃⋊#95	—	5	2	no	—
144	C₃⋊#95	—	5	4	no	—
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	—	6	4	no	—
152	C₂²×C₄×C₅	—	6	4	no	—
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₂²×Dic₅	—	3	2	no	—
157	C₂²×Dic₅	—	3	2	no	—
158	C₂²×Dic₅	—	6	8	no	—
159	C₂²×Dic₅	—	6	8	no	—
160	C₂²×Dic₅	—	12	4	no	—
161	C₂²×Dic₅	C₂²×D₃	1	4	yes	—
162	C₅×C₄⋊C₄	—	3	4	no	—
163	C₅×C₂²⋊C₄	—	3	8	no	—
164	C₄²×C₅	C₄×D₃	1	4	yes	complemented
165	C₂²⋊Dic₅	—	6	8	no	—
166	C₄⋊Dic₅	—	2	4	no	—
167	C₄⋊Dic₅	—	2	4	no	—
168	C₄⋊Dic₅	—	3	4	no	—
169	C₄⋊Dic₅	—	4	2	no	—
170	C₄⋊Dic₅	—	6	8	no	—
171	C₄⋊Dic₅	—	6	2	no	—
172	C₄×Dic₅	—	6	4	no	—
173	C₂×C₄×D₄	—	3	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	—	5	1	no	—
179	#380	—	15	2	no	—
180	C₄×C₄⋊C₄	—	15	1	no	—
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	C₂×C₄⋊C₄	1	4	yes	complemented
197	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
198	Dic₁₅	—	2	4	no	—
199	Dic₁₅	—	4	2	no	—
200	C₃×Dic₅	—	4	4	no	—
201	C₅×Dic₃	—	2	4	no	—
202	C₂³×D₃	C₂²×D₅	1	2	yes	—
203	C₂²×C₃×C₄	—	5	4	no	—
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂²×Dic₃	—	5	2	no	—
208	C₂²×Dic₃	—	5	2	no	—
209	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
210	C₂×D₁₂	Dic₁₀	1	4	yes	—
211	C₂×D₁₂	D₂₀	1	4	yes	—
212	C₂×D₁₂	C₂×Dic₅	1	4	yes	—
213	C₂×C₄×D₃	—	2	4	no	—
214	C₂×C₄×D₃	—	2	4	no	—
215	C₂×C₄×D₃	—	10	8	no	—
216	C₂×C₄×D₃	—	10	8	no	—
217	C₂×C₄×D₃	—	20	4	no	—
218	C₂×C₄×D₃	C₂×Dic₅	1	8	yes	complemented
219	C₃×C₄⋊C₄	—	10	4	no	—
220	C₃×C₄⋊C₄	—	10	4	no	—
221	C₃×C₄⋊C₄	—	20	2	no	—
222	C₃×C₄²	C₂×Dic₅	1	4	yes	complemented
223	(C₂×D₃)⋊C₄	—	10	8	no	—
224	(C₂×D₃)⋊C₄	C₂×Dic₅	1	8	yes	complemented
225	C₄⋊Dic₃	—	5	4	no	—
226	C₄⋊Dic₃	—	10	2	no	—
227	C₄⋊Dic₃	C₂×Dic₅	1	4	yes	complemented
228	Dic₃⋊C₄	—	10	8	no	—
229	C₄×Dic₃	—	10	4	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	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	3	4	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	16	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	D₃×D₄	1	2	yes	—
249	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
251	C₂×C₄×C₅	#239	1	2	yes	—
252	C₂×Dic₅	—	2	4	no	—
253	C₂×Dic₅	—	2	4	no	—
254	C₂×Dic₅	—	2	4	no	—
255	C₂×Dic₅	—	3	4	no	—
256	C₂×Dic₅	—	6	2	no	—
257	C₂×Dic₅	—	6	2	no	—
258	C₂×Dic₅	—	6	2	no	—
259	C₂×Dic₅	—	6	2	no	—
260	C₂×Dic₅	—	6	2	no	—
261	C₂×Dic₅	—	12	16	no	—
262	C₂²×D₄	—	3	1	no	—
263	C₂³×C₄	—	3	2	no	—
264	C₂³×C₄	—	15	4	no	—
265	C₄×D₄	—	3	8	no	—
266	C₄×D₄	—	30	8	no	—
267	C₂×C₄⋊C₄	—	3	1	no	—
268	C₂×C₄⋊C₄	—	5	2	no	—
269	C₂×C₄⋊C₄	—	5	2	no	—
270	C₂×C₄⋊C₄	—	5	2	no	—
271	C₂×C₄⋊C₄	—	15	1	no	—
272	C₂×C₄⋊C₄	—	15	4	no	—
273	C₂×C₄⋊C₄	—	15	1	no	—
274	C₂×C₄⋊C₄	—	30	8	no	—
275	C₂×C₂²⋊C₄	—	3	2	no	—
276	C₂×C₂²⋊C₄	—	15	4	no	—
277	C₂×C₄²	—	15	2	no	—
278	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
279	#95	—	15	4	no	—
280	#95	—	15	2	no	—
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	C₂³×D₅	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	C₂×Dic₁₀	1	4	yes	—
295	C₂²×D₃	C₂×D₂₀	1	4	yes	—
296	C₂²×D₃	C₂²×Dic₅	1	4	yes	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	10	4	no	—
300	C₂×C₃×C₄	—	10	4	no	—
301	C₂×C₃×C₄	—	10	4	no	—
302	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
303	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
304	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
305	C₂×C₃×C₄	#711	1	2	yes	—
306	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
307	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
308	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	5	4	no	—
312	C₂×Dic₃	—	10	2	no	—
313	C₂×Dic₃	—	10	2	no	—
314	C₂×Dic₃	—	10	2	no	—
315	C₂×Dic₃	—	10	2	no	—
316	C₂×Dic₃	—	10	2	no	—
317	C₂×Dic₃	C₂²×Dic₅	1	4	yes	—
318	D₁₂	C₄⋊Dic₅	1	16	yes	complemented
319	C₄×D₃	—	2	16	no	—
320	C₄×D₃	—	20	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	C₂×D₃×D₄	1	1	yes	characteristic
330	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
331	C₂²×C₅	#1004	1	1	yes	characteristic
332	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
333	C₂²×C₅	C₂×#239	1	1	yes	characteristic
334	C₂²×C₅	#1007	1	1	yes	characteristic
335	C₄×C₅	—	2	2	no	—
336	C₄×C₅	—	6	4	no	—
337	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	complemented
338	C₄×C₅	#893	1	4	yes	complemented
339	Dic₅	—	4	4	no	—
340	Dic₅	—	6	4	no	—
341	Dic₅	—	12	2	no	—
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	—	5	4	no	—
349	C₂²×C₄	—	6	4	no	—
350	C₂²×C₄	—	6	4	no	—
351	C₂²×C₄	—	15	2	no	—
352	C₂²×C₄	—	15	2	no	—
353	C₂²×C₄	—	30	8	no	—
354	C₂²×C₄	—	30	8	no	—
355	C₂²×C₄	—	60	4	no	—
356	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
359	C₄⋊C₄	—	3	4	no	—
360	C₄⋊C₄	—	10	4	no	—
361	C₄⋊C₄	—	10	4	no	—
362	C₄⋊C₄	—	15	4	no	—
363	C₄⋊C₄	—	20	2	no	—
364	C₄⋊C₄	—	30	8	no	—
365	C₄⋊C₄	—	30	2	no	—
366	C₂²⋊C₄	—	3	8	no	—
367	C₂²⋊C₄	—	30	8	no	—
368	C₄²	—	30	4	no	—
369	C₄²	D₃×Dic₅	1	4	yes	complemented
370	C₃×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	C₂²×Dic₁₀	1	1	yes	characteristic
372	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
373	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
374	C₂²×C₃	C₂×#711	1	1	yes	characteristic
375	C₂²×C₃	#4149	1	1	yes	characteristic
376	C₂²×C₃	#4150	1	1	yes	characteristic
377	C₂²×C₃	C₂³×Dic₅	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×C₄⋊Dic₅	1	8	yes	complemented
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	20	4	no	—
387	C₃×C₄	C₂×C₄⋊Dic₅	1	4	yes	complemented
388	C₃×C₄	D₄×Dic₅	1	4	yes	complemented
389	Dic₃	—	2	4	no	—
390	Dic₃	—	10	4	no	—
391	Dic₃	—	20	2	no	—
392	C₂×C₅	—	6	8	no	—
393	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
394	C₂×C₅	C₂×#893	1	1	yes	characteristic
395	C₂×C₅	#5504	1	1	yes	characteristic
396	C₂×C₅	#5717	1	1	yes	characteristic
397	C₂×C₅	#5726	1	1	yes	characteristic
398	C₂×C₅	#5727	1	1	yes	characteristic
399	C₂×C₅	#5730	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	C₂²×D₃×D₅	1	1	yes	characteristic
408	D₄	—	3	16	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	3	4	no	—
412	C₂×C₄	—	6	2	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	—	6	16	no	—
415	C₂×C₄	—	10	4	no	—
416	C₂×C₄	—	10	4	no	—
417	C₂×C₄	—	10	4	no	—
418	C₂×C₄	—	15	4	no	—
419	C₂×C₄	—	30	2	no	—
420	C₂×C₄	—	30	2	no	—
421	C₂×C₄	—	30	2	no	—
422	C₂×C₄	—	30	2	no	—
423	C₂×C₄	—	30	2	no	—
424	C₂×C₄	—	60	16	no	—
425	C₂×C₄	D₃×Dic₁₀	1	2	yes	—
426	C₂×C₄	#6768	1	2	yes	—
427	C₂×C₄	D₃×D₂₀	1	2	yes	—
428	C₂×C₄	#6777	1	2	yes	—
429	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
430	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
431	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
432	C₂×C₃	D₄×Dic₁₀	1	1	yes	characteristic
433	C₂×C₃	#65877	1	1	yes	characteristic
434	C₂×C₃	D₄×D₂₀	1	1	yes	characteristic
435	C₂×C₃	#65889	1	1	yes	characteristic
436	C₂×C₃	C₂²×C₄⋊Dic₅	1	1	yes	characteristic
437	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
438	C₂×C₃	#66161	1	1	yes	characteristic
439	D₃	—	2	8	no	—
440	C₅	#74360	1	1	yes	characteristic, complemented, 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	C₂×D₃×Dic₁₀	1	1	yes	characteristic
449	C₂²	C₂×#6768	1	1	yes	characteristic
450	C₂²	#92004	1	1	yes	characteristic
451	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
452	C₂²	C₂×#6777	1	1	yes	characteristic
453	C₂²	#92017	1	1	yes	characteristic
454	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	6	4	no	—
457	C₄	—	20	4	no	—
458	C₄	—	30	4	no	—
459	C₄	—	60	2	no	—
460	C₄	D₃×C₄⋊Dic₅	1	4	yes	complemented
461	C₄	#91435	1	4	yes	complemented
462	C₃	D₄×C₄⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	8	no	—
464	C₂	#11752549	1	1	yes	characteristic
465	C₂	#11752558	1	1	yes	characteristic
466	C₂	#11752641	1	1	yes	characteristic
467	C₂	#11752745	1	1	yes	characteristic
468	C₂	C₂×D₃×C₄⋊Dic₅	1	1	yes	characteristic
469	C₂	C₂×#91435	1	1	yes	characteristic
470	C₂	#11754492	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃×D₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle, cosocle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	D₄×C₄⋊C₄
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂×D₃×C₄⋊Dic₅	C₂	semidirect
4. C₄×C₄⋊Dic₁₅	C₂	semidirect
5. C₃×#65224	C₂	semidirect
6. #11748897	C₂	semidirect
7. #11748868	C₂	semidirect
8. #11748786	C₂	semidirect
19. C₄×C₅×D₁₂	C₄	semidirect
36. #65224	D₃	semidirect
50. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
55. C₃×C₄²×C₅	C₂×C₄	semidirect
57. C₄⋊Dic₁₅	D₄	semidirect
59. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
60. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
120. C₅×D₁₂	C₄⋊C₄	semidirect
142. C₄×D₁₂	Dic₅	semidirect
164. C₄²×C₅	C₄×D₃	semidirect
194. C₂×C₅×D₃	C₂×C₄⋊C₄	semidirect
196. C₃×C₄×C₅	C₂×C₄⋊C₄	semidirect
197. C₃×C₄×C₅	C₄×D₄	semidirect
218. C₂×C₄×D₃	C₂×Dic₅	semidirect
222. C₃×C₄²	C₂×Dic₅	semidirect
224. (C₂×D₃)⋊C₄	C₂×Dic₅	semidirect
227. C₄⋊Dic₃	C₂×Dic₅	semidirect
318. D₁₂	C₄⋊Dic₅	semidirect
337. C₄×C₅	D₃×C₄⋊C₄	semidirect
338. C₄×C₅	#893	semidirect
369. C₄²	D₃×Dic₅	semidirect
370. C₃×C₅	D₄×C₄⋊C₄	semidirect
384. C₂×D₃	C₂×C₄⋊Dic₅	semidirect
387. C₃×C₄	C₂×C₄⋊Dic₅	semidirect
388. C₃×C₄	D₄×Dic₅	semidirect
440. C₅	#74360	semidirect
460. C₄	D₃×C₄⋊Dic₅	semidirect
461. C₄	#91435	semidirect
462. C₃	D₄×C₄⋊Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₂×#91435	2
C₂×D₃×C₄⋊Dic₅	2
C₄×C₄⋊Dic₁₅	2
C₃×#65224	2
#11748897	2
#11748868	2
#11748786	2
D₄×C₄⋊Dic₅	3
#74360	5