Subgroups — #14297482

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91371	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₂×D₃)⋊#168	C₂	1	1	yes	maximal, characteristic
6	#11746371	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745968	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600702	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₂×Dic₃⋊Dic₅	C₄	1	1	yes	characteristic
17	C₂×Dic₃⋊Dic₅	C₄	1	1	yes	characteristic
18	C₂×(C₂×D₃)⋊Dic₅	C₄	1	1	yes	characteristic
19	C₂×(C₂×D₃)⋊Dic₅	C₄	1	1	yes	characteristic
20	#91371	—	2	2	no	—
21	#91371	—	2	2	no	—
22	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
23	C₃×#3946	—	2	2	no	—
24	#90982	—	2	2	no	—
25	(C₂×D₃)⋊#168	—	2	2	no	—
26	#70476	—	5	1	no	maximal, Hall
27	C₂×#4072	—	3	1	no	—
28	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
29	C₂×C₂²⋊#168	—	3	1	no	—
30	C₂×#3946	—	3	1	no	—
31	C₂×#3946	D₃	1	1	yes	characteristic, complemented
32	#64770	—	3	1	no	—
33	#64770	—	3	1	no	—
34	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₄×Dic₁₅	—	2	1	no	—
51	C₄×Dic₁₅	—	2	1	no	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₂×C₃⋊#168	—	2	1	no	—
54	C₂×C₃⋊#168	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₃×C₄×Dic₅	D₄	1	2	yes	—
59	C₃×C₄×Dic₅	D₄	1	2	yes	—
60	C₂×C₃×#168	—	2	1	no	—
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	Dic₃⋊Dic₅	—	2	2	no	—
64	Dic₃⋊Dic₅	—	2	2	no	—
65	(C₂×D₃)⋊Dic₅	—	2	2	no	—
66	(C₂×D₃)⋊Dic₅	—	2	2	no	—
67	C₂×#872	—	5	1	no	—
68	C₂×C₃×C₄⋊C₈	—	5	1	no	—
69	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
70	C₂×(C₂×D₃)⋊C₈	D₅	1	1	yes	characteristic
71	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
72	#4550	—	5	1	no	—
73	#4550	—	5	1	no	—
74	C₂³×C₄×C₅	—	3	1	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₅	—	3	1	no	—
78	C₂×C₂²⋊Dic₅	—	3	1	no	—
79	#4072	—	6	2	no	—
80	#4072	—	6	2	no	—
81	C₂×C₄⋊Dic₅	—	3	1	no	—
82	C₂×C₄⋊Dic₅	—	3	1	no	—
83	C₂×C₄×Dic₅	—	3	1	no	—
84	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
85	C₂²×#168	—	3	1	no	—
86	C₂²×#168	C₂×D₃	1	1	yes	characteristic
87	C₅×C₂²⋊C₈	—	6	2	no	—
88	C₂²⋊#168	—	6	2	no	—
89	#3946	—	2	2	no	—
90	#3946	—	6	2	no	—
91	#1798	—	15	1	no	Sylow
92	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₂²×C₅×D₃	—	2	1	no	—
95	C₂²×C₅×D₃	—	2	1	no	—
96	C₂²×C₅×D₃	—	2	1	no	—
97	C₂²×C₅×D₃	—	2	1	no	—
98	C₂²×C₅×D₃	—	2	1	no	—
99	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×Dic₁₅	—	2	1	no	—
107	C₂×Dic₁₅	—	2	1	no	—
108	C₂×Dic₁₅	—	2	1	no	—
109	C₂×Dic₁₅	—	2	1	no	—
110	C₂×Dic₁₅	—	2	1	no	—
111	C₂×Dic₁₅	—	2	1	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
115	C₄×C₅×D₃	—	2	2	no	—
116	C₄×C₅×D₃	—	2	2	no	—
117	C₄×C₅×D₃	—	2	2	no	—
118	C₄×C₅×D₃	—	2	2	no	—
119	C₂×C₃×Dic₅	—	2	1	no	—
120	C₂×C₃×Dic₅	—	2	1	no	—
121	C₂×C₃×Dic₅	—	2	1	no	—
122	C₂×C₃×Dic₅	—	2	1	no	—
123	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
124	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
125	C₃×C₅×C₈	—	4	1	no	—
126	C₃⋊#168	—	4	1	no	—
127	C₃×#168	—	4	1	no	—
128	C₅×C₃⋊C₈	—	4	1	no	—
129	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₃×C₈	—	5	1	no	—
131	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
132	C₂×C₃×C₄²	—	5	1	no	—
133	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
134	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
135	C₂×Dic₃⋊C₄	—	5	1	no	—
136	C₂×Dic₃⋊C₄	—	5	1	no	—
137	C₂×C₄×Dic₃	—	5	1	no	—
138	C₂²×C₃⋊C₈	—	5	1	no	—
139	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
140	#872	—	10	2	no	—
141	#872	—	10	2	no	—
142	C₃×C₄⋊C₈	—	10	2	no	—
143	(C₂×D₃)⋊C₈	—	2	2	no	—
144	(C₂×D₃)⋊C₈	—	10	2	no	—
145	C₄⋊(C₃⋊C₈)	—	10	2	no	—
146	C₂⁴×C₅	—	3	1	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	2	no	—
149	C₂²×C₄×C₅	—	3	2	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂²×C₄×C₅	—	6	1	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
155	C₂²×Dic₅	—	3	1	no	—
156	C₂²×Dic₅	—	3	1	no	—
157	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
158	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	6	1	no	—
163	C₂×C₅×C₈	—	6	1	no	—
164	C₂×C₅×C₈	—	6	1	no	—
165	C₂²⋊Dic₅	—	6	2	no	—
166	C₂²⋊Dic₅	—	6	2	no	—
167	C₄⋊Dic₅	—	6	2	no	—
168	C₄⋊Dic₅	—	6	2	no	—
169	C₄×Dic₅	—	6	1	no	—
170	C₄×Dic₅	—	6	1	no	—
171	C₄×Dic₅	D₁₂	1	2	yes	—
172	C₄×Dic₅	#67	1	2	yes	—
173	C₂×#168	—	2	1	no	—
174	C₂×#168	—	2	1	no	—
175	C₂×#168	—	2	1	no	—
176	C₂×#168	—	6	1	no	—
177	C₂×#168	—	6	1	no	—
178	C₂×#168	—	6	1	no	—
179	C₂×#117	—	15	1	no	—
180	C₂×C₄⋊C₈	—	5	1	no	—
181	C₂×C₄⋊C₈	—	15	1	no	—
182	C₂×C₂²⋊C₈	—	3	1	no	—
183	C₂×C₂²⋊C₈	—	15	1	no	—
184	#336	—	15	1	no	—
185	#336	—	15	1	no	—
186	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	#117	1	1	yes	characteristic
189	C₂²×C₃×C₅	#131	1	1	yes	characteristic
190	C₂²×C₃×C₅	#131	1	1	yes	characteristic
191	C₂²×C₃×C₅	#131	1	1	yes	characteristic
192	C₂²×C₃×C₅	#131	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	2	no	—
194	C₂×C₅×D₃	—	2	2	no	—
195	C₂×C₅×D₃	—	2	2	no	—
196	C₂×C₅×D₃	—	4	1	no	—
197	C₂×C₅×D₃	—	4	1	no	—
198	C₂×C₅×D₃	—	4	1	no	—
199	C₂×C₅×D₃	—	4	1	no	—
200	C₃×C₄×C₅	#121	1	1	yes	characteristic
201	C₃×C₄×C₅	#121	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
203	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
204	Dic₁₅	—	4	1	no	—
205	Dic₁₅	—	4	1	no	—
206	C₃×Dic₅	—	2	2	no	—
207	C₃×Dic₅	—	2	2	no	—
208	C₅×Dic₃	—	2	2	no	—
209	C₂³×D₃	C₄×D₅	1	1	yes	characteristic
210	C₂²×C₃×C₄	—	5	1	no	—
211	C₂²×C₃×C₄	—	5	1	no	—
212	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
213	C₂²×Dic₃	—	5	1	no	—
214	C₂²×Dic₃	—	5	1	no	—
215	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
216	C₂×C₄×D₃	—	2	1	no	—
217	C₂×C₄×D₃	—	2	1	no	—
218	C₂×C₄×D₃	—	2	1	no	—
219	C₂×C₄×D₃	—	2	1	no	—
220	C₂×C₄×D₃	Dic₁₀	1	2	yes	—
221	C₂×C₄×D₃	C₂²⋊D₅	1	2	yes	—
222	C₂×C₃×C₈	—	2	1	no	—
223	C₂×C₃×C₈	—	2	1	no	—
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	10	1	no	—
226	C₂×C₃×C₈	—	10	1	no	—
227	C₂×C₃×C₈	—	10	1	no	—
228	C₃×C₄²	—	5	2	no	—
229	C₃×C₄²	—	5	2	no	—
230	(C₂×D₃)⋊C₄	—	10	2	no	—
231	(C₂×D₃)⋊C₄	—	10	2	no	—
232	Dic₃⋊C₄	—	10	2	no	—
233	Dic₃⋊C₄	—	10	2	no	—
234	C₄×Dic₃	—	10	1	no	—
235	C₄×Dic₃	—	10	1	no	—
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂×C₃⋊C₈	—	2	1	no	—
238	C₂×C₃⋊C₈	—	2	1	no	—
239	C₂×C₃⋊C₈	—	10	1	no	—
240	C₂×C₃⋊C₈	—	10	1	no	—
241	C₂×C₃⋊C₈	—	10	1	no	—
242	C₂³×C₅	—	3	2	no	—
243	C₂³×C₅	—	6	1	no	—
244	C₂³×C₅	—	6	1	no	—
245	C₂³×C₅	—	6	1	no	—
246	C₂³×C₅	—	6	1	no	—
247	C₂³×C₅	—	6	1	no	—
248	C₂³×C₅	—	6	1	no	—
249	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
250	C₂×C₄×C₅	—	3	2	no	—
251	C₂×C₄×C₅	—	6	1	no	—
252	C₂×C₄×C₅	—	6	1	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	6	2	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
258	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	#237	1	1	yes	characteristic
260	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
261	C₂×C₄×C₅	#239	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
263	C₂×Dic₅	—	2	1	no	—
264	C₂×Dic₅	—	2	1	no	—
265	C₂×Dic₅	—	2	1	no	—
266	C₂×Dic₅	—	2	1	no	—
267	C₂×Dic₅	—	6	1	no	—
268	C₂×Dic₅	—	6	1	no	—
269	C₂×Dic₅	—	6	1	no	—
270	C₂×Dic₅	—	6	1	no	—
271	C₂×Dic₅	—	6	1	no	—
272	C₂×Dic₅	—	6	1	no	—
273	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
274	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
275	C₅×C₈	—	4	1	no	—
276	C₅×C₈	—	12	1	no	—
277	#168	—	4	1	no	—
278	#168	—	12	1	no	—
279	C₂³×C₄	—	3	1	no	—
280	C₂²×C₈	—	3	1	no	—
281	C₂²×C₈	—	5	1	no	—
282	C₂²×C₈	—	15	1	no	—
283	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
284	#117	—	30	2	no	—
285	#117	—	30	2	no	—
286	C₂×C₄⋊C₄	—	15	1	no	—
287	C₂×C₄⋊C₄	—	15	1	no	—
288	C₂×C₂²⋊C₄	—	15	1	no	—
289	C₂×C₂²⋊C₄	—	15	1	no	—
290	C₂×C₄²	—	5	1	no	—
291	C₂×C₄²	—	15	1	no	—
292	C₄⋊C₈	—	10	2	no	—
293	C₄⋊C₈	—	30	2	no	—
294	C₂²⋊C₈	—	6	2	no	—
295	C₂²⋊C₈	—	30	2	no	—
296	C₂×C₃×C₅	#380	1	1	yes	characteristic
297	C₂×C₃×C₅	#408	1	1	yes	characteristic
298	C₂×C₃×C₅	#408	1	1	yes	characteristic
299	C₂×C₃×C₅	#424	1	1	yes	characteristic
300	C₂×C₃×C₅	#424	1	1	yes	characteristic
301	C₂×C₃×C₅	#433	1	1	yes	characteristic
302	C₂×C₃×C₅	#433	1	1	yes	characteristic
303	C₅×D₃	—	4	2	no	—
304	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
305	C₂²×D₃	—	2	1	no	—
306	C₂²×D₃	—	2	1	no	—
307	C₂²×D₃	—	2	1	no	—
308	C₂²×D₃	—	2	1	no	—
309	C₂²×D₃	—	2	1	no	—
310	C₂²×D₃	—	2	1	no	—
311	C₂²×D₃	#683	1	2	yes	—
312	C₂×C₃×C₄	—	5	2	no	—
313	C₂×C₃×C₄	—	5	2	no	—
314	C₂×C₃×C₄	—	10	1	no	—
315	C₂×C₃×C₄	—	10	1	no	—
316	C₂×C₃×C₄	—	10	1	no	—
317	C₂×C₃×C₄	—	10	1	no	—
318	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
319	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
320	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
321	C₂×C₃×C₄	#711	1	1	yes	characteristic
322	C₂×C₃×C₄	#711	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
324	C₂×Dic₃	—	2	1	no	—
325	C₂×Dic₃	—	2	1	no	—
326	C₂×Dic₃	—	10	1	no	—
327	C₂×Dic₃	—	10	1	no	—
328	C₂×Dic₃	—	10	1	no	—
329	C₂×Dic₃	—	10	1	no	—
330	C₂×Dic₃	—	10	1	no	—
331	C₂×Dic₃	—	10	1	no	—
332	C₂×Dic₃	#683	1	2	yes	—
333	C₄×D₃	—	2	2	no	—
334	C₄×D₃	—	2	2	no	—
335	C₄×D₃	—	2	2	no	—
336	C₄×D₃	—	2	2	no	—
337	C₃×C₈	—	4	1	no	—
338	C₃×C₈	—	20	1	no	—
339	C₃⋊C₈	—	4	1	no	—
340	C₃⋊C₈	—	20	1	no	—
341	C₂²×C₅	—	6	2	no	—
342	C₂²×C₅	—	6	2	no	—
343	C₂²×C₅	—	6	2	no	—
344	C₂²×C₅	—	12	1	no	—
345	C₂²×C₅	—	12	1	no	—
346	C₂²×C₅	—	12	1	no	—
347	C₂²×C₅	—	12	1	no	—
348	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
349	C₂²×C₅	#892	1	1	yes	characteristic
350	C₂²×C₅	#901	1	1	yes	characteristic
351	C₂²×C₅	#901	1	1	yes	characteristic
352	C₂²×C₅	#907	1	1	yes	characteristic
353	C₂²×C₅	#907	1	1	yes	characteristic
354	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
355	C₄×C₅	—	6	2	no	—
356	C₄×C₅	#895	1	1	yes	characteristic
357	C₄×C₅	#897	1	1	yes	characteristic
358	C₄×C₅	#938	1	1	yes	characteristic
359	C₄×C₅	#946	1	1	yes	characteristic
360	Dic₅	—	2	2	no	—
361	Dic₅	—	2	2	no	—
362	Dic₅	—	12	1	no	—
363	Dic₅	—	12	1	no	—
364	C₂⁴	—	3	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	6	1	no	—
371	C₂²×C₄	—	6	1	no	—
372	C₂²×C₄	—	6	1	no	—
373	C₂²×C₄	—	6	1	no	—
374	C₂²×C₄	—	15	1	no	—
375	C₂²×C₄	—	15	1	no	—
376	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	6	1	no	—
381	C₂×C₈	—	6	1	no	—
382	C₂×C₈	—	6	1	no	—
383	C₂×C₈	—	10	1	no	—
384	C₂×C₈	—	10	1	no	—
385	C₂×C₈	—	10	1	no	—
386	C₂×C₈	—	30	1	no	—
387	C₂×C₈	—	30	1	no	—
388	C₂×C₈	—	30	1	no	—
389	C₄⋊C₄	—	30	2	no	—
390	C₄⋊C₄	—	30	2	no	—
391	C₂²⋊C₄	—	30	2	no	—
392	C₂²⋊C₄	—	30	2	no	—
393	C₄²	—	5	2	no	—
394	C₄²	—	5	2	no	—
395	C₄²	—	30	1	no	—
396	C₄²	—	30	1	no	—
397	C₃×C₅	#1798	1	1	yes	characteristic, complemented, Hall
398	C₂²×C₃	#4023	1	1	yes	characteristic
399	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
400	C₂²×C₃	#4047	1	1	yes	characteristic
401	C₂²×C₃	#4047	1	1	yes	characteristic
402	C₂²×C₃	#4053	1	1	yes	characteristic
403	C₂²×C₃	#4053	1	1	yes	characteristic
404	C₂²×C₃	C₂×#683	1	1	yes	characteristic
405	C₂×D₃	—	2	2	no	—
406	C₂×D₃	—	2	2	no	—
407	C₂×D₃	—	2	2	no	—
408	C₂×D₃	—	4	1	no	—
409	C₂×D₃	—	4	1	no	—
410	C₂×D₃	—	4	1	no	—
411	C₂×D₃	—	4	1	no	—
412	C₃×C₄	—	10	2	no	—
413	C₃×C₄	—	10	2	no	—
414	C₃×C₄	#4024	1	1	yes	characteristic
415	C₃×C₄	#4024	1	1	yes	characteristic
416	C₃×C₄	#4085	1	1	yes	characteristic
417	C₃×C₄	#4085	1	1	yes	characteristic
418	Dic₃	—	2	2	no	—
419	Dic₃	—	20	1	no	—
420	Dic₃	—	20	1	no	—
421	C₂×C₅	—	12	2	no	—
422	C₂×C₅	#4839	1	1	yes	characteristic
423	C₂×C₅	#4839	1	1	yes	characteristic
424	C₂×C₅	#4840	1	1	yes	characteristic
425	C₂×C₅	#4840	1	1	yes	characteristic
426	C₂×C₅	#4987	1	1	yes	characteristic
427	C₂×C₅	#5110	1	1	yes	characteristic
428	C₂×C₅	#5129	1	1	yes	characteristic
429	C₂³	—	3	2	no	—
430	C₂³	—	6	1	no	—
431	C₂³	—	6	1	no	—
432	C₂³	—	6	1	no	—
433	C₂³	—	6	1	no	—
434	C₂³	—	6	1	no	—
435	C₂³	—	6	1	no	—
436	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	5	2	no	—
439	C₂×C₄	—	5	2	no	—
440	C₂×C₄	—	6	1	no	—
441	C₂×C₄	—	6	1	no	—
442	C₂×C₄	—	6	2	no	—
443	C₂×C₄	—	6	2	no	—
444	C₂×C₄	—	6	2	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	—	10	1	no	—
447	C₂×C₄	—	10	1	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	1	no	—
450	C₂×C₄	—	30	1	no	—
451	C₂×C₄	—	30	1	no	—
452	C₂×C₄	—	30	1	no	—
453	C₂×C₄	—	30	1	no	—
454	C₂×C₄	—	30	1	no	—
455	C₂×C₄	—	30	1	no	—
456	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
457	C₂×C₄	#6768	1	1	yes	characteristic
458	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
459	C₂×C₄	#6780	1	1	yes	characteristic
460	C₂×C₄	D₅×#67	1	1	yes	characteristic
461	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
462	C₈	—	4	1	no	—
463	C₈	—	12	1	no	—
464	C₈	—	20	1	no	—
465	C₈	—	60	1	no	—
466	C₂×C₃	#65009	1	1	yes	characteristic
467	C₂×C₃	#65009	1	1	yes	characteristic
468	C₂×C₃	#65016	1	1	yes	characteristic
469	C₂×C₃	#65016	1	1	yes	characteristic
470	C₂×C₃	#65231	1	1	yes	characteristic
471	C₂×C₃	#65391	1	1	yes	characteristic
472	C₂×C₃	#65408	1	1	yes	characteristic
473	D₃	—	4	2	no	—
474	C₅	#70476	1	1	yes	characteristic, complemented, Sylow
475	C₂²	—	6	2	no	—
476	C₂²	—	6	2	no	—
477	C₂²	—	6	2	no	—
478	C₂²	—	12	1	no	—
479	C₂²	—	12	1	no	—
480	C₂²	—	12	1	no	—
481	C₂²	—	12	1	no	—
482	C₂²	#91265	1	1	yes	characteristic
483	C₂²	#91266	1	1	yes	characteristic
484	C₂²	#91267	1	1	yes	characteristic
485	C₂²	#91268	1	1	yes	characteristic
486	C₂²	D₃×#683	1	1	yes	characteristic
487	C₂²	#91400	1	1	yes	characteristic
488	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
489	C₄	—	6	2	no	—
490	C₄	—	10	2	no	—
491	C₄	—	10	2	no	—
492	C₄	—	60	1	no	—
493	C₄	—	60	1	no	—
494	C₄	#91410	1	1	yes	characteristic
495	C₄	#91416	1	1	yes	characteristic
496	C₄	#91417	1	1	yes	characteristic
497	C₄	#91565	1	1	yes	characteristic
498	C₃	#10600702	1	1	yes	characteristic, complemented, Sylow
499	C₂	—	12	2	no	—
500	C₂	#11747655	1	1	yes	characteristic
501	C₂	#11747656	1	1	yes	characteristic
502	C₂	#11747661	1	1	yes	characteristic
503	C₂	#11747662	1	1	yes	characteristic
504	C₂	#11748134	1	1	yes	characteristic
505	C₂	#11748136	1	1	yes	characteristic
506	C₂	#11748874	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator, socle	C₂³×C₃×C₅	C₂²×C₄
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1798
LCS	G ▷ C₂³×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#3946	C₂	semidirect
4. C₂×#90982	C₂	semidirect
6. #11746371	C₂	semidirect
7. #11745968	C₂	semidirect
31. C₂×#3946	D₃	semidirect
397. C₃×C₅	#1798	semidirect
474. C₅	#70476	semidirect
498. C₃	#10600702	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91371	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₃×#3946	2
C₂×#90982	2
C₂×(C₂×D₃)⋊#168	2
#11746371	2
#11745968	2
#10600702	3
#70476	5