Subgroups — #14297664

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
2	#11748861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90967	C₂	1	1	yes	maximal, characteristic
5	C₂×#90966	C₂	1	1	yes	maximal, characteristic
6	#11746350	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64749	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602397	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	2	1	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₅×#893	—	2	2	no	—
17	C₅×#893	C₄	1	4	yes	complemented
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₂×Dic₃⋊Dic₅	—	2	1	no	—
21	C₂×Dic₃⋊Dic₅	—	2	1	no	—
22	Dic₃⋊#168	—	2	2	no	—
23	#90967	—	2	2	no	—
24	#90966	—	2	2	no	—
25	#68892	—	5	1	no	maximal, Hall
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₂×#3964	—	3	1	no	—
28	C₂×#3964	—	3	1	no	—
29	#65224	—	3	1	no	—
30	C₂×C₄⋊#168	—	3	1	no	—
31	#64749	—	3	1	no	—
32	#64749	D₃	1	1	yes	characteristic, complemented
33	C₂³×C₅×D₃	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₅	—	2	1	no	—
37	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
38	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
43	C₂×C₅×D₁₂	D₄	1	2	yes	—
44	C₂×C₅×D₁₂	Q₈	1	2	yes	—
45	C₂×C₄×C₅×D₃	—	2	4	no	—
46	C₂×C₄×C₅×D₃	—	4	2	no	—
47	C₂×C₄×C₅×D₃	—	4	2	no	—
48	C₂²×C₃×Dic₅	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₄⋊Dic₁₅	—	2	1	no	—
52	C₄⋊Dic₁₅	—	2	1	no	—
53	C₂×C₃⋊#168	—	2	1	no	—
54	C₂×C₃⋊#168	—	2	1	no	—
55	C₂×C₃⋊#168	—	2	1	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
57	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
58	C₄×C₅×Dic₃	D₄	1	2	yes	—
59	C₃×C₄⋊Dic₅	—	2	1	no	—
60	C₃×C₄⋊Dic₅	—	2	1	no	—
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	C₂×C₃×#168	—	2	1	no	—
64	Dic₃⋊Dic₅	—	4	2	no	—
65	Dic₃⋊Dic₅	—	4	2	no	—
66	C₂×#893	D₅	1	1	yes	characteristic
67	C₂×#821	—	5	1	no	—
68	C₂×Dic₃⋊C₈	—	5	1	no	—
69	#4975	—	5	1	no	—
70	C₂×#809	—	5	1	no	—
71	C₃×#340	—	5	1	no	—
72	#4529	—	5	1	no	—
73	C₂²×C₅×D₄	—	3	1	no	—
74	C₂³×C₄×C₅	—	6	1	no	—
75	C₄×C₅×D₄	—	3	4	no	—
76	C₄×C₅×D₄	—	6	2	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
79	C₂×C₄²×C₅	—	3	1	no	—
80	C₂×C₄⋊Dic₅	—	3	1	no	—
81	C₂×C₄⋊Dic₅	—	6	1	no	—
82	C₂×C₄⋊Dic₅	—	6	1	no	—
83	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
84	C₂²×#168	—	3	1	no	—
85	C₂²×#168	C₂×D₃	1	1	yes	characteristic
86	#3964	—	6	2	no	—
87	#3964	—	6	2	no	—
88	C₄⋊#168	—	6	2	no	—
89	#1802	—	15	1	no	Sylow
90	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₅×D₃	—	2	2	no	—
92	C₂²×C₅×D₃	—	2	2	no	—
93	C₂²×C₅×D₃	—	2	2	no	—
94	C₂²×C₅×D₃	—	4	1	no	—
95	C₂²×C₅×D₃	—	4	1	no	—
96	C₂²×C₅×D₃	—	4	1	no	—
97	C₂²×C₅×D₃	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×Dic₁₅	—	4	1	no	—
108	C₂×Dic₁₅	—	4	1	no	—
109	C₂×Dic₁₅	—	4	1	no	—
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₂×C₅×Dic₃	—	2	1	no	—
112	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
114	C₂×C₅×Dic₃	D₈	1	2	yes	—
115	C₂×C₅×Dic₃	SD₁₆	1	2	yes	—
116	C₅×D₁₂	—	2	2	no	—
117	C₅×D₁₂	—	2	2	no	—
118	C₅×D₁₂	—	2	2	no	—
119	C₅×D₁₂	C₄⋊C₄	1	4	yes	complemented
120	C₄×C₅×D₃	—	4	8	no	—
121	C₂×C₃×Dic₅	—	4	1	no	—
122	C₂×C₃×Dic₅	—	4	1	no	—
123	C₂×C₃×Dic₅	—	4	1	no	—
124	C₃⋊#168	—	4	1	no	—
125	C₃×#168	—	4	1	no	—
126	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
127	C₂²×C₄×D₃	—	2	1	no	—
128	C₂²×C₃×C₈	—	5	1	no	—
129	C₂×C₃×C₄⋊C₄	—	5	1	no	—
130	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
131	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
132	C₂×C₄⋊Dic₃	—	5	1	no	—
133	C₂×Dic₃⋊C₄	—	10	1	no	—
134	C₂×Dic₃⋊C₄	—	10	1	no	—
135	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
136	C₂²×C₃⋊C₈	—	5	1	no	—
137	#893	—	2	2	no	—
138	#893	Dic₅	1	4	yes	complemented
139	#821	—	10	2	no	—
140	Dic₃⋊C₈	—	10	2	no	—
141	#809	—	10	2	no	—
142	C₂⁴×C₅	—	6	1	no	—
143	C₂×C₅×D₄	—	3	2	no	—
144	C₂×C₅×D₄	—	3	2	no	—
145	C₂×C₅×D₄	—	3	2	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	3	1	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	6	4	no	—
153	C₂²×C₄×C₅	—	12	2	no	—
154	C₂²×C₄×C₅	—	12	2	no	—
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₂²×Dic₅	—	2	1	no	—
157	C₂²×Dic₅	—	6	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
160	C₅×C₂²⋊C₄	—	6	4	no	—
161	C₄²×C₅	—	3	2	no	—
162	C₄²×C₅	—	3	2	no	—
163	C₄⋊Dic₅	—	2	1	no	—
164	C₄⋊Dic₅	—	2	1	no	—
165	C₄⋊Dic₅	—	6	1	no	—
166	C₄⋊Dic₅	—	6	1	no	—
167	C₄⋊Dic₅	—	12	2	no	—
168	C₄⋊Dic₅	—	12	2	no	—
169	C₂×#168	—	2	1	no	—
170	C₂×#168	—	2	1	no	—
171	C₂×#168	—	2	1	no	—
172	C₂×#168	—	6	1	no	—
173	C₂×#168	—	6	1	no	—
174	C₂×#168	—	6	1	no	—
175	C₂×C₄×D₄	—	3	1	no	—
176	C₂×C₄⋊C₈	—	15	1	no	—
177	C₂×#102	—	15	1	no	—
178	C₂×#102	—	15	1	no	—
179	#384	—	15	1	no	—
180	#340	—	5	1	no	—
181	#340	—	15	1	no	—
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	#121	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
187	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂²×C₃×C₅	#137	1	1	yes	characteristic
189	C₂×C₅×D₃	—	2	4	no	—
190	C₂×C₅×D₃	—	4	2	no	—
191	C₂×C₅×D₃	—	4	2	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	4	2	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₃×C₄×C₅	#117	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
201	Dic₁₅	—	8	1	no	—
202	C₃×Dic₅	—	8	1	no	—
203	C₅×Dic₃	—	2	2	no	—
204	C₅×Dic₃	#102	1	4	yes	complemented
205	C₂³×D₃	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	10	1	no	—
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₂²×Dic₃	—	10	1	no	—
210	C₂²×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
211	C₂²×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	—	2	1	no	—
214	C₂×D₁₂	—	2	1	no	—
215	C₂×D₁₂	Dic₁₀	1	2	yes	—
216	C₂×D₁₂	D₂₀	1	2	yes	—
217	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
218	C₂×C₄×D₃	—	2	4	no	—
219	C₂×C₄×D₃	—	4	2	no	—
220	C₂×C₄×D₃	—	4	2	no	—
221	C₂×C₃×C₈	—	10	1	no	—
222	C₂×C₃×C₈	—	10	1	no	—
223	C₂×C₃×C₈	—	10	1	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	10	1	no	—
226	C₃×C₄⋊C₄	—	10	1	no	—
227	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	C₄⋊Dic₃	—	10	1	no	—
230	C₄⋊Dic₃	—	10	1	no	—
231	Dic₃⋊C₄	—	20	2	no	—
232	Dic₃⋊C₄	—	20	2	no	—
233	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
234	C₄×Dic₃	C₂²⋊D₅	1	2	yes	—
235	C₂×C₃⋊C₈	—	10	1	no	—
236	C₂×C₃⋊C₈	—	10	1	no	—
237	C₂×C₃⋊C₈	—	10	1	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	—	6	2	no	—
240	C₂³×C₅	—	6	2	no	—
241	C₂³×C₅	—	12	1	no	—
242	C₂³×C₅	—	12	1	no	—
243	C₂³×C₅	—	12	1	no	—
244	C₂³×C₅	—	12	1	no	—
245	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
246	C₅×D₄	—	3	4	no	—
247	C₅×D₄	—	6	2	no	—
248	C₅×D₄	—	6	2	no	—
249	C₅×D₄	—	6	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	3	2	no	—
252	C₂×C₄×C₅	—	3	2	no	—
253	C₂×C₄×C₅	—	3	2	no	—
254	C₂×C₄×C₅	—	3	2	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	6	1	no	—
258	C₂×C₄×C₅	—	6	1	no	—
259	C₂×C₄×C₅	—	12	8	no	—
260	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₄×C₅	#235	1	1	yes	characteristic
262	C₂×C₄×C₅	#235	1	1	yes	characteristic
263	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
266	C₂×Dic₅	—	4	1	no	—
267	C₂×Dic₅	—	4	1	no	—
268	C₂×Dic₅	—	4	1	no	—
269	C₂×Dic₅	—	12	1	no	—
270	C₂×Dic₅	—	12	1	no	—
271	C₂×Dic₅	—	12	1	no	—
272	#168	—	4	1	no	—
273	#168	—	12	1	no	—
274	C₂²×D₄	—	3	1	no	—
275	C₂³×C₄	—	6	1	no	—
276	C₂²×C₈	—	5	1	no	—
277	C₂²×C₈	—	15	1	no	—
278	C₄×D₄	—	3	4	no	—
279	C₄×D₄	—	6	2	no	—
280	C₂×C₄⋊C₄	—	5	1	no	—
281	C₂×C₄⋊C₄	—	15	1	no	—
282	C₂×C₄⋊C₄	—	30	1	no	—
283	C₂×C₄⋊C₄	—	30	1	no	—
284	C₂×C₄⋊C₄	D₃×D₅	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	6	1	no	—
286	C₂×C₄²	—	3	1	no	—
287	C₄⋊C₈	—	30	2	no	—
288	#102	—	30	2	no	—
289	#102	—	30	2	no	—
290	C₂×C₃×C₅	#380	1	1	yes	characteristic
291	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
292	C₂×C₃×C₅	#417	1	1	yes	characteristic
293	C₂×C₃×C₅	#459	1	1	yes	characteristic
294	C₂×C₃×C₅	#461	1	1	yes	characteristic
295	C₂×C₃×C₅	#474	1	1	yes	characteristic
296	C₂×C₃×C₅	#476	1	1	yes	characteristic
297	C₅×D₃	—	4	4	no	—
298	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
299	C₂²×D₃	—	2	2	no	—
300	C₂²×D₃	—	2	2	no	—
301	C₂²×D₃	—	2	2	no	—
302	C₂²×D₃	—	4	1	no	—
303	C₂²×D₃	—	4	1	no	—
304	C₂²×D₃	—	4	1	no	—
305	C₂²×D₃	—	4	1	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	—	20	1	no	—
310	C₂×C₃×C₄	—	20	1	no	—
311	C₂×C₃×C₄	—	20	1	no	—
312	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
314	C₂×C₃×C₄	#709	1	1	yes	characteristic
315	C₂×C₃×C₄	#709	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
318	C₂×Dic₃	—	2	1	no	—
319	C₂×Dic₃	—	2	1	no	—
320	C₂×Dic₃	—	20	1	no	—
321	C₂×Dic₃	—	20	1	no	—
322	C₂×Dic₃	—	20	1	no	—
323	C₂×Dic₃	#686	1	2	yes	—
324	C₂×Dic₃	#687	1	2	yes	—
325	C₂×Dic₃	C₂²⋊Dic₅	1	2	yes	—
326	C₂×Dic₃	C₂²⋊Dic₅	1	2	yes	—
327	D₁₂	—	2	2	no	—
328	D₁₂	—	2	2	no	—
329	D₁₂	—	2	2	no	—
330	D₁₂	C₄⋊Dic₅	1	4	yes	complemented
331	C₄×D₃	—	4	8	no	—
332	C₃×C₈	—	20	1	no	—
333	C₃⋊C₈	—	20	1	no	—
334	C₂²×C₅	—	6	4	no	—
335	C₂²×C₅	—	12	2	no	—
336	C₂²×C₅	—	12	2	no	—
337	C₂²×C₅	—	12	2	no	—
338	C₂²×C₅	—	12	2	no	—
339	C₂²×C₅	—	12	2	no	—
340	C₂²×C₅	—	12	2	no	—
341	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
342	C₂²×C₅	#884	1	1	yes	characteristic
343	C₂²×C₅	#896	1	1	yes	characteristic
344	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
345	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
346	C₂²×C₅	#914	1	1	yes	characteristic
347	C₂²×C₅	#918	1	1	yes	characteristic
348	C₄×C₅	—	3	4	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	6	2	no	—
351	C₄×C₅	#872	1	1	yes	characteristic
352	C₄×C₅	#884	1	1	yes	characteristic
353	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
354	C₄×C₅	#896	1	1	yes	characteristic
355	Dic₅	—	8	1	no	—
356	Dic₅	—	24	1	no	—
357	C₂⁴	—	6	1	no	—
358	C₂×D₄	—	3	2	no	—
359	C₂×D₄	—	3	2	no	—
360	C₂×D₄	—	3	2	no	—
361	C₂×D₄	—	6	1	no	—
362	C₂×D₄	—	6	1	no	—
363	C₂×D₄	—	6	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	6	4	no	—
368	C₂²×C₄	—	10	1	no	—
369	C₂²×C₄	—	12	2	no	—
370	C₂²×C₄	—	12	2	no	—
371	C₂²×C₄	—	30	1	no	—
372	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
373	C₂×C₈	—	10	1	no	—
374	C₂×C₈	—	10	1	no	—
375	C₂×C₈	—	10	1	no	—
376	C₂×C₈	—	30	1	no	—
377	C₂×C₈	—	30	1	no	—
378	C₂×C₈	—	30	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	10	1	no	—
381	C₄⋊C₄	—	10	1	no	—
382	C₄⋊C₄	—	30	1	no	—
383	C₄⋊C₄	—	30	1	no	—
384	C₄⋊C₄	—	60	2	no	—
385	C₄⋊C₄	—	60	2	no	—
386	C₄⋊C₄	D₃×Dic₅	1	2	yes	—
387	C₂²⋊C₄	—	6	4	no	—
388	C₄²	—	3	2	no	—
389	C₄²	—	3	2	no	—
390	C₃×C₅	#1802	1	1	yes	characteristic, complemented, Hall
391	C₂²×C₃	#4070	1	1	yes	characteristic
392	C₂²×C₃	#4076	1	1	yes	characteristic
393	C₂²×C₃	C₂×#686	1	1	yes	characteristic
394	C₂²×C₃	C₂×#687	1	1	yes	characteristic
395	C₂²×C₃	#4095	1	1	yes	characteristic
396	C₂²×C₃	#4097	1	1	yes	characteristic
397	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
398	C₂×D₃	—	2	4	no	—
399	C₂×D₃	—	4	2	no	—
400	C₂×D₃	—	4	2	no	—
401	C₂×D₃	—	4	2	no	—
402	C₂×D₃	—	4	2	no	—
403	C₂×D₃	—	4	2	no	—
404	C₂×D₃	—	4	2	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	—	40	1	no	—
407	C₃×C₄	#4070	1	1	yes	characteristic
408	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
409	C₃×C₄	#4072	1	1	yes	characteristic
410	C₃×C₄	#4076	1	1	yes	characteristic
411	Dic₃	—	2	2	no	—
412	Dic₃	—	40	1	no	—
413	Dic₃	#3964	1	4	yes	complemented
414	C₂×C₅	—	12	4	no	—
415	C₂×C₅	#4667	1	1	yes	characteristic
416	C₂×C₅	D₃×#102	1	1	yes	characteristic
417	C₂×C₅	#4786	1	1	yes	characteristic
418	C₂×C₅	#4803	1	1	yes	characteristic
419	C₂×C₅	#4818	1	1	yes	characteristic
420	C₂×C₅	#4870	1	1	yes	characteristic
421	C₂×C₅	#4890	1	1	yes	characteristic
422	C₂³	—	6	2	no	—
423	C₂³	—	6	2	no	—
424	C₂³	—	6	2	no	—
425	C₂³	—	12	1	no	—
426	C₂³	—	12	1	no	—
427	C₂³	—	12	1	no	—
428	C₂³	—	12	1	no	—
429	C₂³	D₃×C₂²⋊D₅	1	1	yes	characteristic
430	D₄	—	3	4	no	—
431	D₄	—	6	2	no	—
432	D₄	—	6	2	no	—
433	D₄	—	6	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	3	2	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	6	1	no	—
442	C₂×C₄	—	6	1	no	—
443	C₂×C₄	—	12	8	no	—
444	C₂×C₄	—	20	1	no	—
445	C₂×C₄	—	20	1	no	—
446	C₂×C₄	—	20	1	no	—
447	C₂×C₄	—	60	1	no	—
448	C₂×C₄	—	60	1	no	—
449	C₂×C₄	—	60	1	no	—
450	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
451	C₂×C₄	#6771	1	1	yes	characteristic
452	C₂×C₄	#6771	1	1	yes	characteristic
453	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
454	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
455	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
456	C₈	—	20	1	no	—
457	C₈	—	60	1	no	—
458	C₂×C₃	#65296	1	1	yes	characteristic
459	C₂×C₃	#65297	1	1	yes	characteristic
460	C₂×C₃	#65304	1	1	yes	characteristic
461	C₂×C₃	#65308	1	1	yes	characteristic
462	C₂×C₃	#65501	1	1	yes	characteristic
463	C₂×C₃	C₂×#3964	1	1	yes	characteristic
464	C₂×C₃	#65521	1	1	yes	characteristic
465	D₃	—	4	4	no	—
466	C₅	#68892	1	1	yes	characteristic, complemented, Sylow
467	C₂²	—	6	4	no	—
468	C₂²	—	12	2	no	—
469	C₂²	—	12	2	no	—
470	C₂²	—	12	2	no	—
471	C₂²	—	12	2	no	—
472	C₂²	—	12	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	#91352	1	1	yes	characteristic
475	C₂²	#91454	1	1	yes	characteristic
476	C₂²	D₃×#686	1	1	yes	characteristic
477	C₂²	D₃×#687	1	1	yes	characteristic
478	C₂²	#91504	1	1	yes	characteristic
479	C₂²	#91510	1	1	yes	characteristic
480	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
481	C₄	—	3	4	no	—
482	C₄	—	4	2	no	—
483	C₄	—	6	2	no	—
484	C₄	—	40	1	no	—
485	C₄	—	120	1	no	—
486	C₄	#91352	1	1	yes	characteristic
487	C₄	#91371	1	1	yes	characteristic
488	C₄	D₃×C₄⋊Dic₅	1	1	yes	characteristic
489	C₄	#91454	1	1	yes	characteristic
490	C₃	#10602397	1	1	yes	characteristic, complemented, Sylow
491	C₂	—	12	4	no	—
492	C₂	#11747402	1	1	yes	characteristic
493	C₂	#11747416	1	1	yes	characteristic
494	C₂	#11747419	1	1	yes	characteristic
495	C₂	#11747420	1	1	yes	characteristic
496	C₂	#11748782	1	1	yes	characteristic
497	C₂	D₃×#3964	1	1	yes	characteristic
498	C₂	#11749201	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₄	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₃×D₅
hypocenter	C₃×C₅	#1802
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #11748861	C₂	semidirect
3. C₂×Dic₃⋊#168	C₂	semidirect
6. #11746350	C₂	semidirect
7. C₃×#64749	C₂	semidirect
17. C₅×#893	C₄	semidirect
32. #64749	D₃	semidirect
119. C₅×D₁₂	C₄⋊C₄	semidirect
138. #893	Dic₅	semidirect
204. C₅×Dic₃	#102	semidirect
330. D₁₂	C₄⋊Dic₅	semidirect
390. C₃×C₅	#1802	semidirect
413. Dic₃	#3964	semidirect
466. C₅	#68892	semidirect
490. C₃	#10602397	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#893	2
#11748861	2
C₂×Dic₃⋊#168	2
C₂×#90967	2
C₂×#90966	2
#11746350	2
C₃×#64749	2
#10602397	3
#68892	5