Subgroups — #14294501

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
2	D₅×#926	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×#208	C₂	1	1	yes	maximal, characteristic
4	#11746344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745978	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745977	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599546	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	#91815	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	1	yes	characteristic
13	C₅×#926	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₃×#685	—	2	1	no	—
16	C₂×C₃×#683	—	2	1	no	—
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₃×#4018	—	2	2	no	—
19	C₃×#4018	C₄	1	4	yes	complemented
20	D₅×#217	—	2	1	no	—
21	#91528	—	2	1	no	—
22	D₅×C₄⋊Dic₃	C₄	1	2	yes	complemented
23	C₄×D₅×Dic₃	—	2	1	no	—
24	#91358	C₄	1	2	yes	complemented
25	#91357	—	2	1	no	—
26	C₂×#6649	—	2	1	no	—
27	D₅×#208	—	2	2	no	—
28	D₅×#208	C₄	1	4	yes	complemented
29	C₂×D₅×C₃⋊C₈	—	2	1	no	—
30	#71578	—	5	1	no	maximal, Hall
31	C₂×D₅×M₁₆	—	3	1	no	—
32	D₅×#117	—	3	1	no	—
33	C₂×#4018	D₃	1	1	yes	characteristic
34	C₅×#339	—	3	1	no	—
35	#64775	—	3	1	no	—
36	#64752	—	3	1	no	—
37	#64743	—	3	1	no	—
38	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	—	2	1	no	—
42	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
50	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
51	C₂×D₅×Dic₃	—	2	2	no	—
52	C₃×C₄²×C₅	—	2	1	no	—
53	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
54	#6719	—	2	1	no	—
55	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₅	—	2	1	no	—
57	#6710	—	2	1	no	—
58	#6710	C₂×C₄	1	2	yes	complemented
59	C₂×C₃⋊#168	—	2	1	no	—
60	C₅×#217	—	2	1	no	—
61	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	C₂×C₄	1	2	yes	complemented
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₃×#685	—	2	4	no	—
67	C₃×#683	—	2	4	no	—
68	C₃×C₄×Dic₅	—	2	1	no	—
69	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
70	#6668	—	2	2	no	—
71	#6665	—	2	2	no	—
72	Dic₃×Dic₅	—	2	2	no	—
73	#6649	—	2	4	no	—
74	D₅×C₃⋊C₈	—	2	4	no	—
75	C₂×C₃×#117	—	5	1	no	—
76	C₂×#926	—	5	1	no	—
77	C₂²×#208	—	5	1	no	—
78	#4523	—	5	1	no	—
79	#4523	—	5	1	no	—
80	#4523	—	5	1	no	—
81	#4523	D₅	1	1	yes	characteristic, complemented
82	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
83	C₂×C₅×M₁₆	—	3	1	no	—
84	C₅×#117	—	3	1	no	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	C₂×#685	—	2	1	no	—
87	#4072	—	3	1	no	—
88	C₂×#683	—	2	1	no	—
89	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
90	C₂×#681	—	3	1	no	—
91	D₅×M₁₆	—	3	4	no	—
92	D₅×M₁₆	—	6	2	no	—
93	C₂×#676	—	6	1	no	—
94	C₂×C₈×D₅	—	6	1	no	—
95	#4038	—	3	2	no	—
96	D₅×C₄⋊C₄	—	3	2	no	—
97	D₅×C₂²⋊C₄	—	6	1	no	—
98	#4023	—	6	1	no	—
99	#4018	—	2	2	no	—
100	#4018	—	6	1	no	—
101	#4018	Dic₃	1	4	yes	complemented
102	C₄²×D₅	—	6	1	no	—
103	#1733	—	15	1	no	Sylow
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	2	no	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
118	C₂×Dic₁₅	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	4	2	no	—
122	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
125	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
126	C₃×C₄×D₅	C₄²	1	2	yes	—
127	C₃×C₄×D₅	C₄²	1	2	yes	—
128	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
129	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
130	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
131	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
132	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
133	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
134	D₅×Dic₃	—	4	4	no	—
135	C₃⋊#168	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₂³×C₃×C₄	—	5	1	no	—
138	C₃×#117	—	5	4	no	—
139	C₃×#117	—	10	2	no	—
140	C₂×C₃×C₄⋊C₄	—	10	1	no	—
141	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
142	C₂×C₃×C₄²	—	5	1	no	—
143	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
144	C₂×#217	—	10	1	no	—
145	#926	—	5	1	no	—
146	#926	—	5	2	no	—
147	#926	—	10	1	no	—
148	#926	—	10	1	no	—
149	#926	C₂×D₅	1	1	yes	characteristic
150	C₂×C₄⋊Dic₃	—	5	2	no	—
151	C₂×C₄×Dic₃	—	10	1	no	—
152	C₂×#208	—	5	1	no	—
153	C₂×#208	—	5	4	no	—
154	C₂×#208	—	10	1	no	—
155	C₂×#208	—	10	2	no	—
156	C₂×#208	C₂×D₅	1	1	yes	characteristic
157	C₂²×C₃⋊C₈	—	10	1	no	—
158	C₂³×D₅	#67	1	1	yes	characteristic
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₂²×Dic₅	—	2	1	no	—
162	C₂²×Dic₅	#67	1	1	yes	characteristic
163	C₂×C₄×D₅	—	6	2	no	—
164	C₂×C₄×D₅	Dic₆	1	2	yes	—
165	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
166	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
167	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
168	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
169	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
171	C₂×C₄×D₅	#67	1	2	yes	—
172	C₅×M₁₆	—	3	2	no	—
173	C₅×M₁₆	—	6	1	no	—
174	C₂×C₅×C₈	—	6	1	no	—
175	C₅×C₄⋊C₄	—	3	2	no	—
176	C₅×C₂²⋊C₄	—	6	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	6	1	no	—
179	C₄²×C₅	C₂×Dic₃	1	2	yes	complemented
180	C₂²⋊Dic₅	—	6	1	no	—
181	#685	—	2	4	no	—
182	#685	—	6	2	no	—
183	C₄⋊Dic₅	—	3	2	no	—
184	#683	—	2	4	no	—
185	#683	—	6	2	no	—
186	C₄×Dic₅	—	2	1	no	—
187	C₄×Dic₅	—	6	1	no	—
188	C₄×Dic₅	—	6	2	no	—
189	C₄×Dic₅	C₂×Dic₃	1	2	yes	complemented
190	#681	—	3	2	no	—
191	#681	—	6	1	no	—
192	C₂×#168	—	6	1	no	—
193	#676	—	6	4	no	—
194	C₈×D₅	—	6	4	no	—
195	C₂²×M₁₆	—	15	1	no	—
196	C₂×#117	—	5	1	no	—
197	C₂×#117	—	15	1	no	—
198	#339	—	3	1	no	—
199	#339	—	15	1	no	—
200	#339	—	15	1	no	—
201	#339	—	15	1	no	—
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₃×D₅	—	2	2	no	—
207	C₂×C₃×D₅	—	2	2	no	—
208	C₂×C₃×D₅	—	4	2	no	—
209	C₂×C₃×D₅	—	4	2	no	—
210	C₂×C₃×D₅	#95	1	2	yes	—
211	C₂×C₃×D₅	#95	1	2	yes	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
217	Dic₁₅	—	4	2	no	—
218	C₃×Dic₅	—	4	2	no	—
219	C₃×Dic₅	#95	1	2	yes	—
220	C₃×Dic₅	#95	1	2	yes	—
221	C₅×Dic₃	—	4	2	no	—
222	C₂⁴×C₃	—	5	1	no	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	—	5	1	no	—
225	C₂²×C₃×C₄	—	5	2	no	—
226	C₂²×C₃×C₄	—	5	1	no	—
227	C₂²×C₃×C₄	—	5	1	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	—	5	1	no	—
230	C₂²×C₃×C₄	—	5	1	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	10	1	no	—
234	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
235	C₂²×Dic₃	—	10	2	no	—
236	C₃×C₄⋊C₄	—	10	4	no	—
237	C₃×C₂²⋊C₄	—	10	4	no	—
238	C₃×C₄²	—	2	1	no	—
239	C₃×C₄²	—	5	2	no	—
240	C₃×C₄²	—	10	1	no	—
241	C₃×C₄²	C₄×D₅	1	2	yes	complemented
242	#217	—	2	1	no	—
243	#217	—	10	2	no	—
244	#217	—	10	1	no	—
245	C₄⋊Dic₃	—	5	2	no	—
246	C₄⋊Dic₃	—	10	2	no	—
247	C₄⋊Dic₃	C₄×D₅	1	2	yes	—
248	C₄×Dic₃	—	2	1	no	—
249	C₄×Dic₃	—	10	2	no	—
250	C₄×Dic₃	—	10	1	no	—
251	#208	—	2	1	no	—
252	#208	—	5	2	no	—
253	#208	—	10	4	no	—
254	#208	—	10	1	no	—
255	#208	C₄×D₅	1	2	yes	complemented
256	C₂×C₃⋊C₈	—	2	1	no	—
257	C₂×C₃⋊C₈	—	10	4	no	—
258	C₂×C₃⋊C₈	—	10	1	no	—
259	C₂³×C₅	C₂×#67	1	1	yes	characteristic
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	Dic₃⋊C₄	1	2	yes	—
262	C₂²×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
263	C₂²×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
264	C₂²×D₅	#217	1	2	yes	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	4	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	4	2	no	—
276	C₂×Dic₅	—	6	2	no	—
277	C₂×Dic₅	Dic₃⋊C₄	1	2	yes	—
278	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
279	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
280	C₂×Dic₅	#217	1	2	yes	—
281	C₄×D₅	—	12	4	no	—
282	C₄×D₅	C₄×Dic₃	1	2	yes	—
283	C₄×D₅	C₄×Dic₃	1	2	yes	—
284	C₄×D₅	Dic₃⋊C₄	1	2	yes	—
285	C₄×D₅	Dic₃⋊C₄	1	2	yes	—
286	C₄×D₅	C₄⋊Dic₃	1	2	yes	—
287	C₄×D₅	C₄⋊Dic₃	1	2	yes	—
288	C₄×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
289	C₄×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
290	C₅×C₈	—	6	2	no	—
291	#168	—	6	2	no	—
292	C₂³×C₄	—	5	1	no	—
293	C₂×M₁₆	—	3	1	no	—
294	C₂×M₁₆	—	15	4	no	—
295	C₂×M₁₆	—	15	1	no	—
296	C₂×M₁₆	—	30	1	no	—
297	C₂×M₁₆	—	30	2	no	—
298	C₂²×C₈	—	30	1	no	—
299	#117	—	3	1	no	—
300	#117	—	5	4	no	—
301	#117	—	10	2	no	—
302	#117	—	15	2	no	—
303	#117	—	15	1	no	—
304	#117	—	30	1	no	—
305	#117	—	30	1	no	—
306	C₂×C₄⋊C₄	—	10	1	no	—
307	C₂×C₄⋊C₄	—	15	2	no	—
308	C₂×C₂²⋊C₄	—	10	1	no	—
309	C₂×C₂²⋊C₄	—	30	1	no	—
310	C₂×C₄²	—	5	1	no	—
311	C₂×C₄²	—	30	1	no	—
312	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
313	C₂×C₃×C₅	—	2	1	no	—
314	C₂×C₃×C₅	—	2	1	no	—
315	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
316	C₂×C₃×C₅	#421	1	2	yes	—
317	C₃×D₅	—	2	2	no	—
318	C₃×D₅	—	2	2	no	—
319	C₂³×C₃	—	5	1	no	—
320	C₂³×C₃	—	5	1	no	—
321	C₂³×C₃	—	5	2	no	—
322	C₂³×C₃	—	5	2	no	—
323	C₂³×C₃	—	20	2	no	—
324	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	4	2	no	—
327	C₂×C₃×C₄	—	5	1	no	—
328	C₂×C₃×C₄	—	5	1	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	—	5	2	no	—
332	C₂×C₃×C₄	—	5	2	no	—
333	C₂×C₃×C₄	—	5	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	5	2	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	—	5	2	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	—	20	2	no	—
341	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
345	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
346	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
347	C₂×Dic₃	—	2	2	no	—
348	C₂×Dic₃	—	10	2	no	—
349	C₂×Dic₃	—	20	4	no	—
350	C₃⋊C₈	—	2	2	no	—
351	C₃⋊C₈	—	10	2	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
354	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
355	C₂²×C₅	C₂×#217	1	1	yes	characteristic
356	C₂×D₅	—	2	2	no	—
357	C₂×D₅	—	2	2	no	—
358	C₂×D₅	—	4	2	no	—
359	C₂×D₅	—	4	2	no	—
360	C₂×D₅	C₃⋊#95	1	2	yes	—
361	C₂×D₅	C₃⋊#95	1	2	yes	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	—	12	2	no	—
364	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
365	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
366	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
367	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
368	Dic₅	—	4	2	no	—
369	Dic₅	—	12	2	no	—
370	Dic₅	C₃⋊#95	1	2	yes	—
371	Dic₅	C₃⋊#95	1	2	yes	—
372	C₂⁴	—	5	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	2	no	—
376	C₂²×C₄	—	5	1	no	—
377	C₂²×C₄	—	5	1	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	5	1	no	—
380	C₂²×C₄	—	5	1	no	—
381	C₂²×C₄	—	5	2	no	—
382	C₂²×C₄	—	5	2	no	—
383	C₂²×C₄	—	10	1	no	—
384	C₂²×C₄	—	30	2	no	—
385	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
386	M₁₆	—	3	2	no	—
387	M₁₆	—	6	1	no	—
388	M₁₆	—	15	2	no	—
389	M₁₆	—	30	4	no	—
390	M₁₆	—	30	1	no	—
391	C₂×C₈	—	6	1	no	—
392	C₂×C₈	—	30	4	no	—
393	C₂×C₈	—	30	1	no	—
394	C₄⋊C₄	—	3	2	no	—
395	C₄⋊C₄	—	10	4	no	—
396	C₄⋊C₄	—	15	2	no	—
397	C₄⋊C₄	—	30	2	no	—
398	C₂²⋊C₄	—	6	1	no	—
399	C₂²⋊C₄	—	10	4	no	—
400	C₂²⋊C₄	—	30	2	no	—
401	C₂²⋊C₄	—	30	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	5	2	no	—
404	C₄²	—	6	1	no	—
405	C₄²	—	10	1	no	—
406	C₄²	—	30	2	no	—
407	C₄²	—	30	1	no	—
408	C₄²	D₅×Dic₃	1	2	yes	complemented
409	C₃×C₅	#1733	1	1	yes	characteristic, complemented, Hall
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	5	2	no	—
412	C₂²×C₃	—	5	2	no	—
413	C₂²×C₃	—	10	2	no	—
414	C₂²×C₃	—	10	2	no	—
415	C₂²×C₃	—	20	2	no	—
416	C₂²×C₃	—	20	2	no	—
417	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
418	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	—	5	2	no	—
422	C₃×C₄	—	5	2	no	—
423	C₃×C₄	—	20	2	no	—
424	C₃×C₄	C₄²×D₅	1	1	yes	characteristic
425	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
427	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
428	Dic₃	—	4	2	no	—
429	Dic₃	—	20	2	no	—
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	#5005	1	2	yes	—
433	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
434	D₅	—	2	2	no	—
435	D₅	—	2	2	no	—
436	C₂³	—	5	1	no	—
437	C₂³	—	5	1	no	—
438	C₂³	—	5	2	no	—
439	C₂³	—	5	2	no	—
440	C₂³	—	20	2	no	—
441	C₂³	D₅×#67	1	1	yes	characteristic
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	1	no	—
447	C₂×C₄	—	5	2	no	—
448	C₂×C₄	—	5	2	no	—
449	C₂×C₄	—	5	2	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	2	no	—
454	C₂×C₄	—	5	2	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	20	2	no	—
459	C₂×C₄	—	30	2	no	—
460	C₂×C₄	—	60	4	no	—
461	C₂×C₄	D₅×Dic₆	1	1	yes	characteristic
462	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
463	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
464	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
465	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
466	C₂×C₄	D₅×#67	1	1	yes	characteristic
467	C₈	—	6	2	no	—
468	C₈	—	30	2	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	10	2	no	—
472	C₂×C₃	—	10	2	no	—
473	C₂×C₃	D₅×#95	1	1	yes	characteristic
474	C₂×C₃	#65110	1	2	yes	—
475	C₅	#71578	1	1	yes	characteristic, complemented, Sylow
476	C₂²	—	2	2	no	—
477	C₂²	—	5	2	no	—
478	C₂²	—	5	2	no	—
479	C₂²	—	10	2	no	—
480	C₂²	—	10	2	no	—
481	C₂²	—	20	2	no	—
482	C₂²	—	20	2	no	—
483	C₂²	D₅×Dic₃⋊C₄	1	1	yes	characteristic
484	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
485	C₂²	D₅×#217	1	1	yes	characteristic
486	C₄	—	4	2	no	—
487	C₄	—	5	2	no	—
488	C₄	—	5	2	no	—
489	C₄	—	12	2	no	—
490	C₄	—	20	2	no	—
491	C₄	—	60	2	no	—
492	C₄	C₄×D₅×Dic₃	1	1	yes	characteristic
493	C₄	D₅×Dic₃⋊C₄	1	1	yes	characteristic
494	C₄	D₅×C₄⋊Dic₃	1	1	yes	characteristic
495	C₄	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
496	C₃	#10599546	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	2	1	no	—
498	C₂	—	2	1	no	—
499	C₂	—	10	2	no	—
500	C₂	—	10	2	no	—
501	C₂	#11747109	1	2	yes	—
502	C₂	D₅×C₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₁₂
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1733
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #11746344	C₂	semidirect
5. C₅×#4523	C₂	semidirect
6. #11745978	C₂	semidirect
7. #11745977	C₂	semidirect
19. C₃×#4018	C₄	semidirect
22. D₅×C₄⋊Dic₃	C₄	semidirect
24. #91358	C₄	semidirect
28. D₅×#208	C₄	semidirect
53. C₃×C₄²×C₅	C₂×C₄	semidirect
58. #6710	C₂×C₄	semidirect
64. C₅×#208	C₂×C₄	semidirect
69. C₃×C₄×Dic₅	C₂×C₄	semidirect
81. #4523	D₅	semidirect
101. #4018	Dic₃	semidirect
179. C₄²×C₅	C₂×Dic₃	semidirect
189. C₄×Dic₅	C₂×Dic₃	semidirect
241. C₃×C₄²	C₄×D₅	semidirect
255. #208	C₄×D₅	semidirect
408. C₄²	D₅×Dic₃	semidirect
409. C₃×C₅	#1733	semidirect
475. C₅	#71578	semidirect
496. C₃	#10599546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#4018	2
D₅×#926	2
C₂×D₅×#208	2
#11746344	2
C₅×#4523	2
#11745978	2
#11745977	2
#10599546	3
#71578	5