Subgroups — #14327048

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×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×#91434	C₂	1	2	yes	maximal
3	C₂×D₅×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
4	C₄×C₄⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4935	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748899	C₂	1	4	yes	maximal, complemented
7	#11748865	C₂	1	2	yes	maximal, complemented
8	#11748759	C₂	1	2	yes	maximal, complemented
9	#10606091	—	3	1	no	maximal, Hall
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂²×D₅×Dic₃	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×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
20	C₂×C₃×#685	C₂²	1	2	yes	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
22	C₃×C₄×D₂₀	C₄	1	8	yes	complemented
23	C₂×#6668	C₂²	1	4	yes	—
24	C₂×#6665	C₂²	1	4	yes	—
25	#91434	—	2	8	no	—
26	D₅×C₄⋊Dic₃	—	2	8	no	—
27	#91115	C₂²	1	2	yes	—
28	#90994	C₂²	1	4	yes	—
29	D₄×C₄⋊Dic₃	—	5	1	no	maximal, Hall
30	C₂×#4039	—	3	2	no	—
31	C₂×D₅×C₄⋊C₄	—	3	2	no	—
32	C₂×C₄×D₂₀	D₃	1	1	yes	characteristic
33	C₅×#384	—	3	1	no	—
34	#65278	—	3	4	no	—
35	#65276	—	3	2	no	—
36	#65262	—	3	2	no	—
37	C₄×C₄⋊Dic₅	—	3	1	no	—
38	C₂³×C₃×D₅	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	4	yes	—
45	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
46	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
47	C₂×C₃×D₂₀	D₄	1	4	yes	—
48	C₂×C₃×D₂₀	Q₈	1	4	yes	—
49	C₂×C₃×C₄×D₅	—	2	4	no	—
50	C₂×C₃×C₄×D₅	—	2	4	no	—
51	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	complemented
52	C₂×D₅×Dic₃	—	2	8	no	—
53	C₂×D₅×Dic₃	—	2	8	no	—
54	C₂×D₅×Dic₃	—	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×C₄⋊Dic₃	—	2	4	no	—
60	C₅×C₄⋊Dic₃	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	4	2	no	—
62	C₃×#685	C₂×C₄	1	8	yes	complemented
63	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	complemented
64	#6668	—	2	8	no	—
65	#6665	—	2	8	no	—
66	C₂×C₃×C₄×D₄	—	5	1	no	—
67	C₂×D₄×Dic₃	—	5	2	no	—
68	C₂²×C₄⋊Dic₃	—	5	2	no	—
69	#5212	—	5	2	no	—
70	#4984	—	5	2	no	—
71	#4950	—	5	4	no	—
72	#4935	D₅	1	1	yes	characteristic, complemented
73	C₄×C₄⋊Dic₃	—	5	1	no	—
74	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₄×D₅	—	3	4	no	—
76	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	—	3	2	no	—
78	C₂×C₅×C₄⋊C₄	—	3	2	no	—
79	C₂×C₅×C₄⋊C₄	—	3	2	no	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂×#685	—	3	4	no	—
82	C₂×#685	C₂×D₃	1	2	yes	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×C₄⋊Dic₅	—	3	1	no	—
85	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
86	C₂×#683	—	3	4	no	—
87	C₂×C₄×Dic₅	—	3	2	no	—
88	#4039	—	6	8	no	—
89	D₅×C₄⋊C₄	—	6	8	no	—
90	C₄×D₂₀	Dic₃	1	8	yes	complemented
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×C₃×D₅	—	2	2	no	—
96	C₂²×C₃×D₅	—	2	2	no	—
97	C₂²×C₃×D₅	—	2	2	no	—
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
100	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
101	C₂²×C₃×D₅	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	4	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	—	2	4	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
123	C₃×D₂₀	C₄⋊C₄	1	16	yes	complemented
124	C₃×C₄×D₅	—	2	16	no	—
125	D₅×Dic₃	—	4	16	no	—
126	C₂²×C₃×D₄	—	5	1	no	—
127	C₂³×C₃×C₄	—	5	2	no	—
128	C₂³×Dic₃	—	5	4	no	—
129	C₃×C₄×D₄	—	5	8	no	—
130	C₂×C₃×C₄⋊C₄	—	5	1	no	—
131	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
132	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
133	C₂×#217	—	5	4	no	—
134	D₄×Dic₃	—	10	8	no	—
135	C₂×C₄⋊Dic₃	—	5	1	no	—
136	C₂×C₄⋊Dic₃	—	5	1	no	—
137	C₂×C₄⋊Dic₃	—	5	4	no	—
138	C₂×C₄⋊Dic₃	—	10	8	no	—
139	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	—
140	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	—
141	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	—
142	C₂×C₄×Dic₃	—	5	2	no	—
143	C₃⋊#95	—	5	2	no	—
144	C₃⋊#95	—	5	4	no	—
145	C₂³×D₅	C₂²×D₃	1	2	yes	—
146	C₂²×C₄×C₅	—	3	4	no	—
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₂²×Dic₅	—	3	2	no	—
151	C₂²×Dic₅	—	3	2	no	—
152	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
153	C₂×D₂₀	Dic₆	1	4	yes	—
154	C₂×D₂₀	D₁₂	1	4	yes	—
155	C₂×D₂₀	C₂×Dic₃	1	4	yes	—
156	C₂×C₄×D₅	—	2	4	no	—
157	C₂×C₄×D₅	—	2	4	no	—
158	C₂×C₄×D₅	—	6	8	no	—
159	C₂×C₄×D₅	—	6	8	no	—
160	C₂×C₄×D₅	—	12	4	no	—
161	C₂×C₄×D₅	C₂×Dic₃	1	8	yes	complemented
162	C₅×C₄⋊C₄	—	6	4	no	—
163	C₅×C₄⋊C₄	—	6	4	no	—
164	C₅×C₄⋊C₄	—	12	2	no	—
165	C₄²×C₅	C₂×Dic₃	1	4	yes	complemented
166	#685	—	6	8	no	—
167	#685	C₂×Dic₃	1	8	yes	complemented
168	C₄⋊Dic₅	—	3	4	no	—
169	C₄⋊Dic₅	—	6	2	no	—
170	C₄⋊Dic₅	C₂×Dic₃	1	4	yes	complemented
171	#683	—	6	8	no	—
172	C₄×Dic₅	—	6	4	no	—
173	C₂×C₄×D₄	—	5	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	—	3	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×C₃×D₅	—	2	4	no	—
189	C₂×C₃×D₅	—	2	4	no	—
190	C₂×C₃×D₅	—	2	4	no	—
191	C₂×C₃×D₅	—	2	4	no	—
192	C₂×C₃×D₅	—	2	4	no	—
193	C₂×C₃×D₅	—	2	4	no	—
194	C₂×C₃×D₅	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	—	2	4	no	—
201	C₅×Dic₃	—	4	4	no	—
202	C₂⁴×C₃	—	5	2	no	—
203	C₂×C₃×D₄	—	5	4	no	—
204	C₂×C₃×D₄	—	5	4	no	—
205	C₂×C₃×D₄	—	5	4	no	—
206	C₂²×C₃×C₄	—	5	2	no	—
207	C₂²×C₃×C₄	—	5	8	no	—
208	C₂²×C₃×C₄	—	10	4	no	—
209	C₂²×C₃×C₄	—	10	4	no	—
210	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
213	C₂²×Dic₃	—	5	2	no	—
214	C₂²×Dic₃	—	5	2	no	—
215	C₂²×Dic₃	—	10	8	no	—
216	C₂²×Dic₃	—	10	8	no	—
217	C₂²×Dic₃	—	20	4	no	—
218	C₂²×Dic₃	C₂²×D₅	1	4	yes	—
219	C₃×C₄⋊C₄	—	5	4	no	—
220	C₃×C₂²⋊C₄	—	5	8	no	—
221	C₃×C₄²	C₄×D₅	1	4	yes	complemented
222	#217	—	10	8	no	—
223	C₄⋊Dic₃	—	2	4	no	—
224	C₄⋊Dic₃	—	2	4	no	—
225	C₄⋊Dic₃	—	4	2	no	—
226	C₄⋊Dic₃	—	5	4	no	—
227	C₄⋊Dic₃	—	10	8	no	—
228	C₄⋊Dic₃	—	10	2	no	—
229	C₄×Dic₃	—	10	4	no	—
230	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
231	C₂²×D₅	—	2	2	no	—
232	C₂²×D₅	—	2	2	no	—
233	C₂²×D₅	—	2	2	no	—
234	C₂²×D₅	—	2	2	no	—
235	C₂²×D₅	C₂×Dic₆	1	4	yes	—
236	C₂²×D₅	C₂×D₁₂	1	4	yes	—
237	C₂²×D₅	C₂²×Dic₃	1	4	yes	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	6	4	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	—	6	4	no	—
243	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
244	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
245	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
246	C₂×C₄×C₅	#237	1	2	yes	—
247	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
248	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
249	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
250	C₂×Dic₅	—	2	2	no	—
251	C₂×Dic₅	—	2	2	no	—
252	C₂×Dic₅	—	3	4	no	—
253	C₂×Dic₅	—	6	2	no	—
254	C₂×Dic₅	—	6	2	no	—
255	C₂×Dic₅	—	6	2	no	—
256	C₂×Dic₅	—	6	2	no	—
257	C₂×Dic₅	—	6	2	no	—
258	C₂×Dic₅	C₂²×Dic₃	1	4	yes	—
259	D₂₀	C₄⋊Dic₃	1	16	yes	complemented
260	C₄×D₅	—	2	16	no	—
261	C₄×D₅	—	12	16	no	—
262	C₂²×D₄	—	5	1	no	—
263	C₂³×C₄	—	5	2	no	—
264	C₂³×C₄	—	15	4	no	—
265	C₄×D₄	—	5	8	no	—
266	C₄×D₄	—	30	8	no	—
267	C₂×C₄⋊C₄	—	3	2	no	—
268	C₂×C₄⋊C₄	—	3	2	no	—
269	C₂×C₄⋊C₄	—	3	2	no	—
270	C₂×C₄⋊C₄	—	5	1	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	—	5	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	C₃×D₅	—	2	8	no	—
289	C₂³×C₃	—	5	4	no	—
290	C₂³×C₃	—	5	4	no	—
291	C₂³×C₃	—	5	4	no	—
292	C₂³×C₃	—	10	2	no	—
293	C₂³×C₃	—	10	2	no	—
294	C₂³×C₃	—	10	2	no	—
295	C₂³×C₃	—	10	2	no	—
296	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
297	C₃×D₄	—	5	16	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	5	4	no	—
301	C₂×C₃×C₄	—	10	2	no	—
302	C₂×C₃×C₄	—	10	2	no	—
303	C₂×C₃×C₄	—	10	16	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	D₄×D₅	1	2	yes	—
308	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
309	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
310	C₂×C₃×C₄	#713	1	2	yes	—
311	C₂×Dic₃	—	2	4	no	—
312	C₂×Dic₃	—	2	4	no	—
313	C₂×Dic₃	—	2	4	no	—
314	C₂×Dic₃	—	5	4	no	—
315	C₂×Dic₃	—	10	2	no	—
316	C₂×Dic₃	—	10	2	no	—
317	C₂×Dic₃	—	10	2	no	—
318	C₂×Dic₃	—	10	2	no	—
319	C₂×Dic₃	—	10	2	no	—
320	C₂×Dic₃	—	20	16	no	—
321	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
322	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
323	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
324	C₂²×C₅	C₂×#237	1	1	yes	characteristic
325	C₂²×C₅	#1009	1	1	yes	characteristic
326	C₂²×C₅	#1010	1	1	yes	characteristic
327	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
328	C₂×D₅	—	2	4	no	—
329	C₂×D₅	—	2	4	no	—
330	C₂×D₅	—	2	4	no	—
331	C₂×D₅	—	2	4	no	—
332	C₂×D₅	—	2	4	no	—
333	C₂×D₅	—	2	4	no	—
334	C₂×D₅	C₂×C₄⋊Dic₃	1	8	yes	complemented
335	C₄×C₅	—	2	2	no	—
336	C₄×C₅	—	12	4	no	—
337	C₄×C₅	C₂×C₄⋊Dic₃	1	4	yes	complemented
338	C₄×C₅	D₄×Dic₃	1	4	yes	complemented
339	Dic₅	—	2	4	no	—
340	Dic₅	—	6	4	no	—
341	Dic₅	—	12	2	no	—
342	C₂⁴	—	5	2	no	—
343	C₂×D₄	—	5	4	no	—
344	C₂×D₄	—	5	4	no	—
345	C₂×D₄	—	5	4	no	—
346	C₂²×C₄	—	3	4	no	—
347	C₂²×C₄	—	5	2	no	—
348	C₂²×C₄	—	5	8	no	—
349	C₂²×C₄	—	10	4	no	—
350	C₂²×C₄	—	10	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	—	5	4	no	—
360	C₄⋊C₄	—	6	4	no	—
361	C₄⋊C₄	—	6	4	no	—
362	C₄⋊C₄	—	12	2	no	—
363	C₄⋊C₄	—	15	4	no	—
364	C₄⋊C₄	—	30	8	no	—
365	C₄⋊C₄	—	30	2	no	—
366	C₂²⋊C₄	—	5	8	no	—
367	C₂²⋊C₄	—	30	8	no	—
368	C₄²	—	30	4	no	—
369	C₄²	D₅×Dic₃	1	4	yes	complemented
370	C₃×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	—	5	8	no	—
372	C₂²×C₃	—	10	4	no	—
373	C₂²×C₃	—	10	4	no	—
374	C₂²×C₃	—	10	4	no	—
375	C₂²×C₃	—	10	4	no	—
376	C₂²×C₃	—	10	4	no	—
377	C₂²×C₃	—	10	4	no	—
378	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
379	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
380	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
381	C₂²×C₃	#4144	1	1	yes	characteristic
382	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
383	C₂²×C₃	C₂×#713	1	1	yes	characteristic
384	C₂²×C₃	#4147	1	1	yes	characteristic
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	10	4	no	—
387	C₃×C₄	D₅×C₄⋊C₄	1	4	yes	complemented
388	C₃×C₄	#4039	1	4	yes	complemented
389	Dic₃	—	4	4	no	—
390	Dic₃	—	10	4	no	—
391	Dic₃	—	20	2	no	—
392	C₂×C₅	D₄×Dic₆	1	1	yes	characteristic
393	C₂×C₅	#5543	1	1	yes	characteristic
394	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
395	C₂×C₅	#5555	1	1	yes	characteristic
396	C₂×C₅	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
397	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
398	C₂×C₅	#5827	1	1	yes	characteristic
399	D₅	—	2	8	no	—
400	C₂³	—	5	4	no	—
401	C₂³	—	5	4	no	—
402	C₂³	—	5	4	no	—
403	C₂³	—	10	2	no	—
404	C₂³	—	10	2	no	—
405	C₂³	—	10	2	no	—
406	C₂³	—	10	2	no	—
407	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
408	D₄	—	5	16	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	5	4	no	—
412	C₂×C₄	—	6	4	no	—
413	C₂×C₄	—	6	4	no	—
414	C₂×C₄	—	6	4	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	16	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	D₅×Dic₆	1	2	yes	—
426	C₂×C₄	#6766	1	2	yes	—
427	C₂×C₄	D₅×D₁₂	1	2	yes	—
428	C₂×C₄	#6777	1	2	yes	—
429	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
430	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
431	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
432	C₂×C₃	—	10	8	no	—
433	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
434	C₂×C₃	C₂×#4039	1	1	yes	characteristic
435	C₂×C₃	#65838	1	1	yes	characteristic
436	C₂×C₃	#66051	1	1	yes	characteristic
437	C₂×C₃	#66060	1	1	yes	characteristic
438	C₂×C₃	#66061	1	1	yes	characteristic
439	C₂×C₃	#66064	1	1	yes	characteristic
440	C₅	D₄×C₄⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	5	8	no	—
442	C₂²	—	10	4	no	—
443	C₂²	—	10	4	no	—
444	C₂²	—	10	4	no	—
445	C₂²	—	10	4	no	—
446	C₂²	—	10	4	no	—
447	C₂²	—	10	4	no	—
448	C₂²	C₂×D₅×Dic₆	1	1	yes	characteristic
449	C₂²	C₂×#6766	1	1	yes	characteristic
450	C₂²	#92000	1	1	yes	characteristic
451	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
452	C₂²	C₂×#6777	1	1	yes	characteristic
453	C₂²	#92018	1	1	yes	characteristic
454	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	10	4	no	—
457	C₄	—	12	4	no	—
458	C₄	—	30	4	no	—
459	C₄	—	60	2	no	—
460	C₄	D₅×C₄⋊Dic₃	1	4	yes	complemented
461	C₄	#91434	1	4	yes	complemented
462	C₃	#10606091	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	10	8	no	—
464	C₂	#11752533	1	1	yes	characteristic
465	C₂	#11752552	1	1	yes	characteristic
466	C₂	#11752648	1	1	yes	characteristic
467	C₂	#11752737	1	1	yes	characteristic
468	C₂	C₂×D₅×C₄⋊Dic₃	1	1	yes	characteristic
469	C₂	C₂×#91434	1	1	yes	characteristic
470	C₂	#11754499	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×C₃×D₂₀	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×D₅×C₄⋊Dic₃	C₂	semidirect
4. C₄×C₄⋊Dic₁₅	C₂	semidirect
5. C₅×#4935	C₂	semidirect
6. #11748899	C₂	semidirect
7. #11748865	C₂	semidirect
8. #11748759	C₂	semidirect
22. C₃×C₄×D₂₀	C₄	semidirect
51. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
55. C₃×C₄²×C₅	C₂×C₄	semidirect
57. C₄⋊Dic₁₅	D₄	semidirect
62. C₃×#685	C₂×C₄	semidirect
63. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
72. #4935	D₅	semidirect
90. C₄×D₂₀	Dic₃	semidirect
123. C₃×D₂₀	C₄⋊C₄	semidirect
161. C₂×C₄×D₅	C₂×Dic₃	semidirect
165. C₄²×C₅	C₂×Dic₃	semidirect
167. #685	C₂×Dic₃	semidirect
170. C₄⋊Dic₅	C₂×Dic₃	semidirect
194. C₂×C₃×D₅	C₂×C₄⋊C₄	semidirect
196. C₃×C₄×C₅	C₂×C₄⋊C₄	semidirect
197. C₃×C₄×C₅	C₄×D₄	semidirect
221. C₃×C₄²	C₄×D₅	semidirect
259. D₂₀	C₄⋊Dic₃	semidirect
334. C₂×D₅	C₂×C₄⋊Dic₃	semidirect
337. C₄×C₅	C₂×C₄⋊Dic₃	semidirect
338. C₄×C₅	D₄×Dic₃	semidirect
369. C₄²	D₅×Dic₃	semidirect
370. C₃×C₅	D₄×C₄⋊C₄	semidirect
387. C₃×C₄	D₅×C₄⋊C₄	semidirect
388. C₃×C₄	#4039	semidirect
440. C₅	D₄×C₄⋊Dic₃	semidirect
460. C₄	D₅×C₄⋊Dic₃	semidirect
461. C₄	#91434	semidirect
462. C₃	#10606091	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₂₀	2
C₂×#91434	2
C₂×D₅×C₄⋊Dic₃	2
C₄×C₄⋊Dic₁₅	2
C₅×#4935	2
#11748899	2
#11748865	2
#11748759	2
#10606091	3
D₄×C₄⋊Dic₃	5