Subgroups — #14415774

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×#208	C₂	1	2	yes	maximal, complemented
3	#11751113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5012	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748499	C₂	1	2	yes	maximal, complemented
6	#11748494	C₂	1	2	yes	maximal, complemented
7	#11748488	C₂	1	2	yes	maximal, complemented
8	#11747007	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#6649	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746996	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611271	—	3	1	no	maximal, Hall
13	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×#6710	C₂²	1	2	yes	complemented
17	C₂×C₅×#208	C₂²	1	2	yes	complemented
18	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
19	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
20	C₃×#4039	C₄	1	1	yes	characteristic
21	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₃×#4027	C₄	1	2	yes	—
23	C₃×D₅×C₂²⋊C₄	C₄	1	2	yes	—
24	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
26	C₂×#6649	C₂²	1	2	yes	—
27	C₂×#6649	C₂²	1	1	yes	characteristic
28	C₂×#6649	C₂²	1	1	yes	characteristic
29	D₅×#208	—	2	8	no	—
30	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	complemented
31	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	complemented
32	#91114	C₂²	1	2	yes	complemented
33	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
35	C₅×#830	C₂²	1	2	yes	complemented
36	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	#90982	C₂²	1	2	yes	complemented
39	#90955	C₂²	1	2	yes	complemented
40	#90955	C₂²	1	2	yes	complemented
41	#90952	C₂²	1	1	yes	characteristic, complemented
42	#90952	C₂²	1	1	yes	characteristic, complemented
43	D₄×#208	—	5	1	no	maximal, Hall
44	C₂×D₅×M₁₆	—	3	2	no	—
45	C₄×D₄×D₅	D₃	1	1	yes	characteristic
46	C₅×#436	—	3	1	no	—
47	#65416	—	3	2	no	—
48	#65301	—	3	1	no	—
49	#65126	—	3	1	no	—
50	#65123	—	3	1	no	—
51	#65017	—	3	2	no	—
52	#65015	—	3	2	no	—
53	C₄×#676	—	3	1	no	—
54	C₈×D₂₀	—	3	1	no	—
55	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
60	C₃×D₄×D₅	—	2	4	no	—
61	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	4	no	—
63	C₂×C₃×C₄×D₅	—	2	4	no	—
64	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
66	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
69	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	#6710	—	2	4	no	—
74	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
77	C₅×#208	—	2	4	no	—
78	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
82	C₃×#685	C₂×C₄	1	2	yes	—
83	C₃×#685	C₂×C₄	1	2	yes	—
84	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₃×#683	C₂×C₄	1	2	yes	—
86	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	#6649	—	2	4	no	—
90	#6649	—	2	2	no	—
91	#6649	D₄	1	4	yes	complemented
92	D₅×C₃⋊C₈	—	2	4	no	—
93	D₅×C₃⋊C₈	—	2	4	no	—
94	C₂×C₃×C₄×D₄	—	5	1	no	—
95	C₂²×#208	—	5	2	no	—
96	#5207	—	5	2	no	—
97	#5012	—	5	1	no	—
98	#5012	D₅	1	1	yes	characteristic, complemented
99	#5011	—	5	2	no	—
100	#5011	—	5	2	no	—
101	D₄×C₃⋊C₈	—	5	1	no	—
102	D₄×C₃⋊C₈	—	5	1	no	—
103	#4924	—	5	1	no	—
104	C₄×#208	—	5	1	no	—
105	C₂×D₄×D₅	Dic₃	1	1	yes	characteristic
106	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
107	C₂×C₅×M₁₆	—	3	2	no	—
108	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
109	D₄×Dic₅	Dic₃	1	1	yes	characteristic
110	C₄×C₂²⋊D₅	C₂×D₃	1	2	yes	—
111	C₂×#681	—	3	2	no	—
112	D₅×M₁₆	—	6	8	no	—
113	C₂×#676	—	3	1	no	—
114	C₂×#676	—	3	2	no	—
115	C₂×#676	—	3	1	no	—
116	C₂×C₈×D₅	—	3	2	no	—
117	C₂×C₈×D₅	—	3	2	no	—
118	#4039	Dic₃	1	1	yes	characteristic
119	D₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
120	#4027	Dic₃	1	2	yes	—
121	D₅×C₂²⋊C₄	Dic₃	1	2	yes	—
122	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
123	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
124	C₅×C₄⋊C₈	—	3	1	no	—
125	C₅×C₂²⋊C₈	—	3	2	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	C₂²⋊#168	—	3	2	no	—
128	#3952	—	3	2	no	—
129	#3952	—	3	2	no	—
130	#3947	—	3	1	no	—
131	#3947	—	3	1	no	—
132	#3946	—	3	2	no	—
133	C₄⋊#168	—	3	1	no	—
134	C₄×#168	—	3	1	no	—
135	D₄×M₁₆	—	15	1	no	Sylow
136	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₃×D₅	—	2	4	no	—
138	C₂²×C₃×D₅	—	2	4	no	—
139	C₂²×C₃×D₅	—	4	2	no	—
140	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₂²⋊D₅	—	2	4	no	—
150	C₂×C₃×Dic₅	—	2	4	no	—
151	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
154	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₃×D₂₀	M₁₆	1	4	yes	complemented
156	C₃×C₄×D₅	—	2	4	no	—
157	C₃×C₄×D₅	—	2	2	no	—
158	C₃×C₄×D₅	—	2	2	no	—
159	C₃×C₄×D₅	—	2	2	no	—
160	C₃×C₄×D₅	—	2	4	no	—
161	C₃×C₄×D₅	—	4	1	no	—
162	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
163	C₃×C₄×D₅	#41	1	2	yes	—
164	C₃⋊#168	—	2	2	no	—
165	C₃⋊#168	—	2	1	no	—
166	C₃⋊#168	C₂×D₄	1	2	yes	complemented
167	C₅×C₃⋊C₈	—	2	2	no	—
168	C₅×C₃⋊C₈	—	2	1	no	—
169	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
170	C₂²×C₃×D₄	—	5	1	no	—
171	C₂³×C₃×C₄	—	5	2	no	—
172	C₃×C₄×D₄	—	5	1	no	—
173	C₃×C₄×D₄	—	5	2	no	—
174	C₃×C₄×D₄	—	5	1	no	—
175	C₃×C₄×D₄	—	5	2	no	—
176	C₃×C₄×D₄	—	5	1	no	—
177	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	—	5	1	no	—
179	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
180	C₂×C₃×C₄²	—	5	1	no	—
181	C₂×#208	—	5	2	no	—
182	C₂×#208	—	5	1	no	—
183	C₂×#208	—	5	1	no	—
184	C₂×#208	—	5	2	no	—
185	C₂×#208	—	10	8	no	—
186	C₂×#208	C₂×D₅	1	2	yes	complemented
187	C₂²×C₃⋊C₈	—	5	2	no	—
188	C₂²×C₃⋊C₈	—	5	2	no	—
189	#830	—	5	2	no	—
190	#830	—	5	2	no	—
191	#830	—	5	2	no	—
192	#830	C₂×D₅	1	2	yes	complemented
193	C₄⋊(C₃⋊C₈)	—	5	1	no	—
194	C₄⋊(C₃⋊C₈)	—	5	2	no	—
195	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
196	#803	—	5	1	no	—
197	#803	—	5	1	no	—
198	C₄×C₃⋊C₈	—	5	1	no	—
199	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
200	C₂³×D₅	C₂×Dic₃	1	2	yes	—
201	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
203	C₂×C₂²⋊D₅	C₂×Dic₃	1	2	yes	—
204	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
205	D₄×D₅	—	2	4	no	—
206	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
207	C₂×C₄×D₅	—	2	4	no	—
208	C₂×C₄×D₅	—	2	4	no	—
209	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
210	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
211	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
212	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
213	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
214	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
215	C₅×M₁₆	—	6	4	no	—
216	C₂×C₅×C₈	—	3	1	no	—
217	C₂×C₅×C₈	—	3	2	no	—
218	C₂×C₅×C₈	—	3	1	no	—
219	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
220	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
221	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	—
223	#685	C₂×Dic₃	1	2	yes	—
224	#685	C₂×Dic₃	1	2	yes	—
225	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
226	#683	C₂×Dic₃	1	2	yes	—
227	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
228	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
229	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
230	#681	—	6	4	no	—
231	C₂×#168	—	3	1	no	—
232	C₂×#168	—	3	1	no	—
233	C₂×#168	—	3	2	no	—
234	#676	—	3	4	no	—
235	#676	—	6	4	no	—
236	#676	—	6	2	no	—
237	C₈×D₅	—	6	4	no	—
238	C₈×D₅	—	6	4	no	—
239	C₂²×M₁₆	—	15	2	no	—
240	C₂×C₄×D₄	—	5	1	no	—
241	#436	—	3	1	no	—
242	#436	—	15	1	no	—
243	#435	—	15	2	no	—
244	#435	—	15	2	no	—
245	C₈×D₄	—	15	1	no	—
246	C₈×D₄	—	15	1	no	—
247	#423	—	15	1	no	—
248	#407	—	15	2	no	—
249	C₄×M₁₆	—	15	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₃×D₅	—	2	2	no	—
255	C₂×C₃×D₅	—	2	1	no	—
256	C₂×C₃×D₅	—	2	1	no	—
257	C₂×C₃×D₅	—	2	2	no	—
258	C₂×C₃×D₅	—	4	8	no	—
259	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
260	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	complemented
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₃×Dic₅	—	2	2	no	—
267	C₃×Dic₅	—	2	1	no	—
268	C₃×Dic₅	—	2	1	no	—
269	C₃×Dic₅	C₄×D₄	1	2	yes	—
270	C₂⁴×C₃	—	5	2	no	—
271	C₂×C₃×D₄	—	5	2	no	—
272	C₂×C₃×D₄	—	5	1	no	—
273	C₂×C₃×D₄	—	10	4	no	—
274	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	5	2	no	—
277	C₂²×C₃×C₄	—	5	1	no	—
278	C₂²×C₃×C₄	—	5	2	no	—
279	C₂²×C₃×C₄	—	5	2	no	—
280	C₂²×C₃×C₄	—	5	2	no	—
281	C₂²×C₃×C₄	—	5	1	no	—
282	C₂²×C₃×C₄	—	10	4	no	—
283	C₂²×C₃×C₄	—	10	4	no	—
284	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
285	C₃×C₄⋊C₄	—	5	2	no	—
286	C₃×C₄⋊C₄	—	5	1	no	—
287	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	—	5	2	no	—
289	C₃×C₂²⋊C₄	—	5	2	no	—
290	C₃×C₂²⋊C₄	—	5	2	no	—
291	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
292	C₃×C₄²	—	5	1	no	—
293	C₃×C₄²	—	5	1	no	—
294	C₃×C₄²	—	5	1	no	—
295	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
296	#208	—	2	4	no	—
297	#208	—	5	4	no	—
298	#208	—	10	4	no	—
299	#208	—	10	2	no	—
300	#208	—	10	4	no	—
301	C₂×C₃⋊C₈	—	5	1	no	—
302	C₂×C₃⋊C₈	—	5	1	no	—
303	C₂×C₃⋊C₈	—	5	2	no	—
304	C₂×C₃⋊C₈	—	10	4	no	—
305	C₂×C₃⋊C₈	—	10	4	no	—
306	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
307	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
308	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
309	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
310	C₂²×D₅	—	2	4	no	—
311	C₂²×D₅	—	2	4	no	—
312	C₂²×D₅	—	4	2	no	—
313	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
314	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
315	C₅×D₄	—	2	2	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
320	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
322	C₂²⋊D₅	—	2	4	no	—
323	C₂×Dic₅	—	2	4	no	—
324	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
325	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
326	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
327	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
328	D₂₀	#208	1	4	yes	complemented
329	C₄×D₅	—	2	4	no	—
330	C₄×D₅	—	2	2	no	—
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	—	2	4	no	—
334	C₄×D₅	—	4	1	no	—
335	C₄×D₅	D₃×D₄	1	2	yes	—
336	C₄×D₅	#237	1	2	yes	—
337	C₅×C₈	—	3	2	no	—
338	C₅×C₈	—	6	2	no	—
339	C₅×C₈	—	6	1	no	—
340	#168	—	3	2	no	—
341	#168	—	6	2	no	—
342	#168	—	6	1	no	—
343	C₂²×D₄	—	5	1	no	—
344	C₂³×C₄	—	5	2	no	—
345	C₂×M₁₆	—	3	2	no	—
346	C₂×M₁₆	—	15	1	no	—
347	C₂×M₁₆	—	15	2	no	—
348	C₂×M₁₆	—	15	1	no	—
349	C₂×M₁₆	—	15	2	no	—
350	C₂×M₁₆	—	30	8	no	—
351	C₂²×C₈	—	15	2	no	—
352	C₂²×C₈	—	15	2	no	—
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	—	5	2	no	—
355	C₄×D₄	—	5	1	no	—
356	C₄×D₄	—	5	2	no	—
357	C₄×D₄	—	5	1	no	—
358	C₄×D₄	D₃×D₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	5	1	no	—
360	C₂×C₂²⋊C₄	—	5	2	no	—
361	C₂×C₄²	—	5	1	no	—
362	C₄⋊C₈	—	3	1	no	—
363	C₄⋊C₈	—	15	2	no	—
364	C₄⋊C₈	—	15	1	no	—
365	C₂²⋊C₈	—	3	2	no	—
366	C₂²⋊C₈	—	15	2	no	—
367	C₂²⋊C₈	—	15	2	no	—
368	C₂²⋊C₈	—	15	2	no	—
369	#97	—	15	1	no	—
370	#97	—	15	1	no	—
371	C₄×C₈	—	3	1	no	—
372	C₄×C₈	—	15	1	no	—
373	C₂×C₃×C₅	—	4	2	no	—
374	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
376	C₂×C₃×C₅	#568	1	1	yes	characteristic
377	C₃×D₅	—	2	2	no	—
378	C₃×D₅	—	2	4	no	—
379	C₂³×C₃	—	5	2	no	—
380	C₂³×C₃	—	5	1	no	—
381	C₂³×C₃	—	10	4	no	—
382	C₂³×C₃	—	10	4	no	—
383	C₂³×C₃	—	20	2	no	—
384	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
385	C₃×D₄	—	2	2	no	—
386	C₃×D₄	—	5	4	no	—
387	C₃×D₄	—	10	4	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	5	1	no	—
391	C₂×C₃×C₄	—	5	2	no	—
392	C₂×C₃×C₄	—	5	2	no	—
393	C₂×C₃×C₄	—	5	1	no	—
394	C₂×C₃×C₄	—	5	1	no	—
395	C₂×C₃×C₄	—	5	2	no	—
396	C₂×C₃×C₄	—	10	4	no	—
397	C₂×C₃×C₄	—	10	4	no	—
398	C₂×C₃×C₄	—	10	4	no	—
399	C₂×C₃×C₄	—	10	2	no	—
400	C₂×C₃×C₄	—	10	2	no	—
401	C₂×C₃×C₄	—	10	2	no	—
402	C₂×C₃×C₄	—	20	1	no	—
403	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
405	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
407	C₃⋊C₈	—	2	2	no	—
408	C₃⋊C₈	—	2	1	no	—
409	C₃⋊C₈	—	5	2	no	—
410	C₃⋊C₈	—	10	2	no	—
411	C₃⋊C₈	—	10	1	no	—
412	C₃⋊C₈	D₄×D₅	1	2	yes	complemented
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	2	no	—
419	C₂×D₅	—	2	1	no	—
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	4	8	no	—
422	C₂×D₅	C₂×#208	1	4	yes	complemented
423	C₂×D₅	D₄×Dic₃	1	2	yes	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	C₂×#208	1	2	yes	complemented
427	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
428	C₄×C₅	C₂×#237	1	1	yes	characteristic
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	2	no	—
431	Dic₅	—	2	1	no	—
432	Dic₅	D₄×Dic₃	1	2	yes	—
433	C₂⁴	—	5	2	no	—
434	C₂×D₄	—	5	2	no	—
435	C₂×D₄	—	5	1	no	—
436	C₂×D₄	—	10	4	no	—
437	C₂×D₄	D₅×Dic₃	1	1	yes	characteristic
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	2	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	2	no	—
442	C₂²×C₄	—	5	2	no	—
443	C₂²×C₄	—	5	2	no	—
444	C₂²×C₄	—	5	1	no	—
445	C₂²×C₄	—	10	4	no	—
446	C₂²×C₄	—	10	4	no	—
447	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
448	M₁₆	—	6	4	no	—
449	M₁₆	—	15	4	no	—
450	M₁₆	—	30	4	no	—
451	M₁₆	—	30	2	no	—
452	M₁₆	—	30	4	no	—
453	C₂×C₈	—	3	1	no	—
454	C₂×C₈	—	3	1	no	—
455	C₂×C₈	—	3	2	no	—
456	C₂×C₈	—	15	1	no	—
457	C₂×C₈	—	15	1	no	—
458	C₂×C₈	—	15	2	no	—
459	C₂×C₈	—	30	4	no	—
460	C₂×C₈	—	30	4	no	—
461	C₄⋊C₄	—	5	2	no	—
462	C₄⋊C₄	—	5	1	no	—
463	C₄⋊C₄	D₅×Dic₃	1	1	yes	characteristic
464	C₂²⋊C₄	—	5	2	no	—
465	C₂²⋊C₄	—	5	2	no	—
466	C₂²⋊C₄	—	5	2	no	—
467	C₂²⋊C₄	D₅×Dic₃	1	2	yes	—
468	C₄²	—	5	1	no	—
469	C₄²	—	5	1	no	—
470	C₄²	—	5	1	no	—
471	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
472	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	5	4	no	—
477	C₂²×C₃	—	5	2	no	—
478	C₂²×C₃	—	10	1	no	—
479	C₂²×C₃	—	10	1	no	—
480	C₂²×C₃	—	10	2	no	—
481	C₂²×C₃	—	10	2	no	—
482	C₂²×C₃	—	20	8	no	—
483	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	2	no	—
486	C₃×C₄	—	5	2	no	—
487	C₃×C₄	—	10	1	no	—
488	C₃×C₄	—	10	1	no	—
489	C₃×C₄	—	10	2	no	—
490	C₃×C₄	D₅×M₁₆	1	2	yes	complemented
491	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
492	C₃×C₄	D₅×#41	1	1	yes	characteristic
493	C₂×C₅	—	4	2	no	—
494	C₂×C₅	C₂²×#208	1	1	yes	characteristic
495	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
496	C₂×C₅	#5819	1	1	yes	characteristic
497	D₅	—	2	2	no	—
498	D₅	—	2	4	no	—
499	C₂³	—	5	2	no	—
500	C₂³	—	5	1	no	—
501	C₂³	—	10	4	no	—
502	C₂³	—	10	4	no	—
503	C₂³	—	20	2	no	—
504	C₂³	C₂×D₅×Dic₃	1	2	yes	—
505	D₄	—	2	2	no	—
506	D₄	—	5	4	no	—
507	D₄	—	10	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	5	2	no	—
512	C₂×C₄	—	5	2	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	2	no	—
516	C₂×C₄	—	10	4	no	—
517	C₂×C₄	—	10	4	no	—
518	C₂×C₄	—	10	4	no	—
519	C₂×C₄	—	10	2	no	—
520	C₂×C₄	—	10	2	no	—
521	C₂×C₄	—	10	2	no	—
522	C₂×C₄	—	20	1	no	—
523	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
524	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
525	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
527	C₈	—	3	2	no	—
528	C₈	—	6	2	no	—
529	C₈	—	6	1	no	—
530	C₈	—	15	2	no	—
531	C₈	—	30	2	no	—
532	C₈	—	30	1	no	—
533	C₂×C₃	—	4	2	no	—
534	C₂×C₃	—	10	2	no	—
535	C₂×C₃	—	10	4	no	—
536	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
537	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
538	C₂×C₃	#66084	1	1	yes	characteristic
539	C₅	D₄×#208	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	5	2	no	—
544	C₂²	—	5	4	no	—
545	C₂²	—	10	2	no	—
546	C₂²	—	10	1	no	—
547	C₂²	—	10	2	no	—
548	C₂²	—	10	1	no	—
549	C₂²	—	20	8	no	—
550	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	5	2	no	—
554	C₄	—	10	2	no	—
555	C₄	—	10	1	no	—
556	C₄	—	10	1	no	—
557	C₄	D₅×#208	1	2	yes	complemented
558	C₄	D₃×D₄×D₅	1	1	yes	characteristic
559	C₄	D₅×#237	1	1	yes	characteristic
560	C₃	#10611271	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	4	2	no	—
562	C₂	—	10	2	no	—
563	C₂	—	10	4	no	—
564	C₂	C₂×D₅×#208	1	1	yes	characteristic
565	C₂	D₄×D₅×Dic₃	1	1	yes	characteristic
566	C₂	#11755296	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×D₄	C₂²
prime radical	C₂×C₃×D₄×D₅	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×D₅×#208	C₂	semidirect
3. #11751113	C₂	semidirect
4. C₅×#5012	C₂	semidirect
5. #11748499	C₂	semidirect
6. #11748494	C₂	semidirect
7. #11748488	C₂	semidirect
8. #11747007	C₂	semidirect
9. C₄×#6649	C₂	semidirect
10. #11746996	C₂	semidirect
11. C₃⋊C₈×D₂₀	C₂	semidirect
16. C₂×#6710	C₂²	semidirect
17. C₂×C₅×#208	C₂²	semidirect
30. C₂×D₅×C₃⋊C₈	C₂²	semidirect
31. C₂×D₅×C₃⋊C₈	C₂²	semidirect
32. #91114	C₂²	semidirect
33. C₄⋊(C₃⋊#168)	C₂²	semidirect
34. C₄×C₃⋊#168	C₂²	semidirect
35. C₅×#830	C₂²	semidirect
36. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
37. C₄×C₅×C₃⋊C₈	C₂²	semidirect
38. #90982	C₂²	semidirect
39. #90955	C₂²	semidirect
40. #90955	C₂²	semidirect
41. #90952	C₂²	semidirect
42. #90952	C₂²	semidirect
91. #6649	D₄	semidirect
98. #5012	D₅	semidirect
155. C₃×D₂₀	M₁₆	semidirect
166. C₃⋊#168	C₂×D₄	semidirect
169. C₅×C₃⋊C₈	C₂×D₄	semidirect
186. C₂×#208	C₂×D₅	semidirect
192. #830	C₂×D₅	semidirect
195. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
199. C₄×C₃⋊C₈	C₂×D₅	semidirect
260. C₂×C₃×D₅	C₂×M₁₆	semidirect
263. C₃×C₄×C₅	C₂×M₁₆	semidirect
328. D₂₀	#208	semidirect
412. C₃⋊C₈	D₄×D₅	semidirect
422. C₂×D₅	C₂×#208	semidirect
426. C₄×C₅	C₂×#208	semidirect
472. C₃×C₅	D₄×M₁₆	semidirect
490. C₃×C₄	D₅×M₁₆	semidirect
539. C₅	D₄×#208	semidirect
557. C₄	D₅×#208	semidirect
560. C₃	#10611271	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₄×D₅	2
C₂×D₅×#208	2
#11751113	2
C₅×#5012	2
#11748499	2
#11748494	2
#11748488	2
#11747007	2
C₄×#6649	2
#11746996	2
C₃⋊C₈×D₂₀	2
#10611271	3
D₄×#208	5