Subgroups — #14297841

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×#91121	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₃⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748440	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745977	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745975	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602439	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
11	C₂×#6710	C₂²	1	1	yes	characteristic
12	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic, complemented
13	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic, complemented
14	C₅×D₄×Dic₃	—	2	1	no	—
15	C₅×D₄×Dic₃	—	2	1	no	—
16	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic, complemented
17	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic, complemented
18	C₅×#926	—	2	1	no	—
19	C₅×#926	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	—	2	1	no	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₂×Dic₃⋊Dic₅	—	2	1	no	—
25	#91121	—	2	2	no	—
26	C₃×#3969	—	2	2	no	—
27	#90994	—	2	1	no	—
28	Dic₃⋊#168	—	2	1	no	—
29	Dic₃⋊#168	—	2	1	no	—
30	#70355	—	5	1	no	maximal, Hall
31	C₄×C₅×#41	—	3	1	no	—
32	C₂×#3969	—	3	1	no	—
33	C₂×#3969	D₃	1	1	yes	characteristic
34	C₄×C₄⋊Dic₅	—	3	1	no	—
35	#65213	—	3	1	no	—
36	#64752	—	3	1	no	—
37	#64752	—	3	1	no	—
38	C₃×C₅×#41	—	2	1	no	—
39	C₃×C₅×#41	—	2	1	no	—
40	C₃×C₅×#41	D₄	1	2	yes	—
41	C₃×C₅×#41	Q₈	1	2	yes	—
42	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₅	—	2	1	no	—
48	C₂²×C₅×Dic₃	—	2	1	no	—
49	C₂²×C₅×Dic₃	—	2	1	no	—
50	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
52	C₂²×C₃×Dic₅	—	2	1	no	—
53	C₄×Dic₁₅	—	2	1	no	—
54	C₄×Dic₁₅	—	2	1	no	—
55	#6710	—	2	1	no	—
56	#6710	—	2	1	no	—
57	C₂×C₃⋊#168	—	2	1	no	—
58	C₅×#217	—	2	1	no	—
59	C₅×#217	—	2	1	no	—
60	C₅×#217	—	2	1	no	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₅×C₄⋊Dic₃	—	2	1	no	—
63	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
64	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₅×Dic₃	—	2	1	no	—
66	C₄×C₅×Dic₃	—	2	1	no	—
67	C₄×C₅×Dic₃	—	2	1	no	—
68	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
71	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
72	C₃×C₄×Dic₅	—	2	1	no	—
73	C₃×C₄×Dic₅	—	2	1	no	—
74	C₃×#681	—	2	1	no	—
75	C₃×#681	—	2	1	no	—
76	C₂×C₃×#168	—	2	1	no	—
77	Dic₃⋊Dic₅	—	2	4	no	—
78	Dic₃×#41	D₅	1	1	yes	characteristic
79	C₂×C₃×#104	—	5	1	no	—
80	C₂×#837	—	5	1	no	—
81	#5118	—	5	1	no	—
82	C₄×Dic₃⋊C₄	—	5	1	no	—
83	#4555	—	5	1	no	—
84	#4523	—	5	1	no	—
85	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
86	C₄×C₅×Q₈	—	3	1	no	—
87	C₄×C₅×Q₈	—	3	1	no	—
88	C₄×C₅×D₄	—	3	1	no	—
89	C₄×C₅×D₄	—	3	1	no	—
90	C₄×C₅×D₄	—	6	1	no	—
91	C₄×C₅×D₄	—	6	1	no	—
92	C₅×#117	—	3	1	no	—
93	C₅×#117	—	6	1	no	—
94	C₂×C₄²×C₅	—	3	1	no	—
95	C₂×C₄²×C₅	—	6	1	no	—
96	C₂×C₄⋊Dic₅	—	6	1	no	—
97	C₂×C₄×Dic₅	—	3	1	no	—
98	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
99	C₂×#681	—	3	1	no	—
100	C₂×#681	C₂×D₃	1	1	yes	characteristic
101	#3969	—	2	2	no	—
102	#3969	—	6	2	no	—
103	#3963	—	6	1	no	—
104	C₄⋊#168	—	6	1	no	—
105	C₄⋊#168	—	6	1	no	—
106	#1806	—	15	1	no	Sylow
107	C₂³×C₃×C₅	—	2	1	no	—
108	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
109	C₃×C₅×Q₈	—	2	1	no	—
110	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	complemented
111	C₃×C₅×D₄	—	2	2	no	—
112	C₃×C₅×D₄	—	2	2	no	—
113	C₃×C₅×D₄	—	2	1	no	—
114	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	complemented
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
124	C₂×Dic₁₅	—	2	2	no	—
125	C₂×Dic₁₅	—	4	1	no	—
126	C₂×Dic₁₅	—	4	1	no	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	2	1	no	—
129	C₂×C₅×Dic₃	—	2	1	no	—
130	C₂×C₅×Dic₃	—	4	1	no	—
131	C₂×C₅×Dic₃	—	4	2	no	—
132	C₂×C₅×Dic₃	—	4	2	no	—
133	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₂×C₃×Dic₅	—	4	1	no	—
139	C₂×C₃×Dic₅	—	4	1	no	—
140	C₃⋊#168	—	4	1	no	—
141	C₃×#168	—	4	1	no	—
142	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
143	C₂×C₃×M₁₆	—	5	1	no	—
144	C₂×C₃×C₄²	—	5	1	no	—
145	Q₈×Dic₃	Dic₅	1	1	yes	characteristic, complemented
146	Q₈×Dic₃	Dic₅	1	1	yes	characteristic, complemented
147	D₄×Dic₃	—	2	1	no	—
148	D₄×Dic₃	—	2	1	no	—
149	D₄×Dic₃	Dic₅	1	1	yes	characteristic, complemented
150	D₄×Dic₃	Dic₅	1	1	yes	characteristic, complemented
151	#926	—	2	1	no	—
152	#926	C₂×D₅	1	1	yes	characteristic
153	C₂×Dic₃⋊C₄	—	10	1	no	—
154	C₂×C₄×Dic₃	—	2	1	no	—
155	C₂×C₄×Dic₃	—	5	1	no	—
156	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
157	C₂×#208	—	5	1	no	—
158	C₃×#104	—	10	2	no	—
159	#837	—	10	2	no	—
160	C₃⋊#95	—	10	1	no	—
161	Dic₃⋊C₈	—	10	1	no	—
162	Dic₃⋊C₈	—	10	1	no	—
163	C₅×#41	—	2	1	no	—
164	C₅×#41	—	2	1	no	—
165	C₅×#41	Dic₆	1	2	yes	—
166	C₅×#41	#67	1	2	yes	—
167	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	3	1	no	—
172	C₂²×C₄×C₅	—	3	1	no	—
173	C₂²×C₄×C₅	—	6	1	no	—
174	C₂²×C₄×C₅	—	6	1	no	—
175	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₂²×Dic₅	—	2	1	no	—
177	C₂²×Dic₅	—	6	1	no	—
178	C₅×C₄⋊C₄	—	3	1	no	—
179	C₅×C₄⋊C₄	—	3	1	no	—
180	C₅×C₄⋊C₄	—	6	1	no	—
181	C₅×C₄⋊C₄	—	6	1	no	—
182	C₅×C₂²⋊C₄	—	6	1	no	—
183	C₅×C₂²⋊C₄	—	6	1	no	—
184	C₅×C₂²⋊C₄	—	6	1	no	—
185	C₄²×C₅	—	3	1	no	—
186	C₄²×C₅	—	3	1	no	—
187	C₄²×C₅	—	3	1	no	—
188	C₄²×C₅	—	3	1	no	—
189	C₄²×C₅	—	6	1	no	—
190	C₄²×C₅	—	6	1	no	—
191	C₄²×C₅	—	6	1	no	—
192	C₄⋊Dic₅	—	6	4	no	—
193	C₄×Dic₅	—	2	1	no	—
194	C₄×Dic₅	—	2	1	no	—
195	C₄×Dic₅	—	6	1	no	—
196	C₄×Dic₅	—	6	1	no	—
197	#681	—	2	1	no	—
198	#681	—	2	1	no	—
199	#681	—	6	1	no	—
200	#681	—	6	1	no	—
201	C₂×#168	—	2	1	no	—
202	C₂×#168	—	6	1	no	—
203	C₄×#41	—	3	1	no	—
204	#423	—	15	1	no	—
205	C₂×#104	—	5	1	no	—
206	C₂×#104	—	15	1	no	—
207	C₄×C₄⋊C₄	—	15	1	no	—
208	#339	—	15	1	no	—
209	#339	—	15	1	no	—
210	C₂²×C₃×C₅	—	2	1	no	—
211	C₂²×C₃×C₅	—	2	1	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	4	1	no	—
214	C₂²×C₃×C₅	—	4	1	no	—
215	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₃×C₅	#121	1	1	yes	characteristic
217	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₃×C₄×C₅	#117	1	1	yes	characteristic
221	C₃×C₄×C₅	#121	1	1	yes	characteristic
222	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
223	Dic₁₅	—	4	2	no	—
224	C₃×Dic₅	—	4	2	no	—
225	C₅×Dic₃	—	2	1	no	—
226	C₅×Dic₃	—	2	1	no	—
227	C₅×Dic₃	—	2	1	no	—
228	C₅×Dic₃	—	4	1	no	—
229	C₅×Dic₃	—	4	1	no	—
230	C₅×Dic₃	#104	1	2	yes	complemented
231	C₃×#41	—	2	1	no	—
232	C₃×#41	—	2	1	no	—
233	C₃×#41	Dic₁₀	1	2	yes	—
234	C₃×#41	D₂₀	1	2	yes	—
235	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
236	C₂×C₃×D₄	—	2	1	no	—
237	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
238	C₂²×C₃×C₄	—	2	1	no	—
239	C₂²×C₃×C₄	—	10	1	no	—
240	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
241	C₂²×Dic₃	—	2	1	no	—
242	C₂²×Dic₃	—	2	1	no	—
243	C₂²×Dic₃	—	10	1	no	—
244	C₂²×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
245	C₂²×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
246	C₃×M₁₆	—	10	1	no	—
247	C₃×M₁₆	—	10	1	no	—
248	C₂×C₃×C₈	—	10	1	no	—
249	C₃×C₄²	—	10	1	no	—
250	C₃×C₄²	—	10	1	no	—
251	#217	—	2	1	no	—
252	#217	—	2	1	no	—
253	#217	—	2	1	no	—
254	C₄⋊Dic₃	—	2	1	no	—
255	C₄⋊Dic₃	—	2	1	no	—
256	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
257	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
258	Dic₃⋊C₄	—	10	4	no	—
259	C₄×Dic₃	—	2	1	no	—
260	C₄×Dic₃	—	2	1	no	—
261	C₄×Dic₃	—	2	1	no	—
262	C₄×Dic₃	—	10	1	no	—
263	C₄×Dic₃	—	10	1	no	—
264	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
265	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
266	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
267	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
268	#208	—	10	1	no	—
269	#208	—	10	1	no	—
270	C₂×C₃⋊C₈	—	10	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
273	C₅×Q₈	—	2	1	no	—
274	C₅×Q₈	Dic₃⋊C₄	1	2	yes	complemented
275	C₅×D₄	—	2	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	2	1	no	—
278	C₅×D₄	Dic₃⋊C₄	1	2	yes	complemented
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	3	1	no	—
283	C₂×C₄×C₅	—	3	1	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	3	1	no	—
286	C₂×C₄×C₅	—	6	2	no	—
287	C₂×C₄×C₅	—	6	1	no	—
288	C₂×C₄×C₅	—	6	1	no	—
289	C₂×C₄×C₅	—	12	2	no	—
290	C₂×C₄×C₅	—	12	1	no	—
291	C₂×C₄×C₅	—	12	2	no	—
292	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
294	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	#237	1	1	yes	characteristic
296	C₂×C₄×C₅	#237	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
298	C₂×Dic₅	—	2	2	no	—
299	C₂×Dic₅	—	4	1	no	—
300	C₂×Dic₅	—	4	1	no	—
301	C₂×Dic₅	—	6	2	no	—
302	C₂×Dic₅	—	12	1	no	—
303	C₂×Dic₅	—	12	1	no	—
304	#168	—	4	1	no	—
305	#168	—	12	1	no	—
306	C₂×#41	D₃×D₅	1	1	yes	characteristic
307	C₂×M₁₆	—	5	1	no	—
308	C₂×M₁₆	—	15	1	no	—
309	C₄×Q₈	—	3	1	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×D₄	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	6	1	no	—
314	C₄×D₄	—	6	1	no	—
315	#117	—	3	1	no	—
316	#117	—	6	1	no	—
317	C₂×C₄⋊C₄	—	30	1	no	—
318	C₂×C₄²	—	3	1	no	—
319	C₂×C₄²	—	5	1	no	—
320	C₂×C₄²	—	6	1	no	—
321	C₂×C₄²	—	15	1	no	—
322	C₄⋊C₈	—	30	1	no	—
323	C₄⋊C₈	—	30	1	no	—
324	#104	—	10	2	no	—
325	#104	—	30	2	no	—
326	#95	—	30	1	no	—
327	C₂×C₃×C₅	—	2	1	no	—
328	C₂×C₃×C₅	—	2	1	no	—
329	C₂×C₃×C₅	—	4	2	no	—
330	C₂×C₃×C₅	#380	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
332	C₂×C₃×C₅	#421	1	1	yes	characteristic
333	C₂³×C₃	—	2	1	no	—
334	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
335	C₃×Q₈	—	2	1	no	—
336	C₃×Q₈	C₄⋊Dic₅	1	2	yes	complemented
337	C₃×D₄	—	2	2	no	—
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	2	1	no	—
340	C₃×D₄	C₄⋊Dic₅	1	2	yes	complemented
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	10	2	no	—
345	C₂×C₃×C₄	—	20	1	no	—
346	C₂×C₃×C₄	—	20	1	no	—
347	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
349	C₂×C₃×C₄	#709	1	1	yes	characteristic
350	C₂×C₃×C₄	#709	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
353	C₂×Dic₃	—	2	2	no	—
354	C₂×Dic₃	—	2	1	no	—
355	C₂×Dic₃	—	2	1	no	—
356	C₂×Dic₃	—	4	1	no	—
357	C₂×Dic₃	—	4	2	no	—
358	C₂×Dic₃	—	4	2	no	—
359	C₂×Dic₃	—	10	2	no	—
360	C₂×Dic₃	—	20	1	no	—
361	C₂×Dic₃	—	20	1	no	—
362	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
363	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
364	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
365	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
366	C₃×C₈	—	20	1	no	—
367	C₃⋊C₈	—	20	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	2	1	no	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	4	1	no	—
372	C₂²×C₅	—	4	1	no	—
373	C₂²×C₅	#878	1	1	yes	characteristic
374	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
375	C₂²×C₅	#939	1	1	yes	characteristic
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	3	2	no	—
378	C₄×C₅	—	6	1	no	—
379	C₄×C₅	—	6	1	no	—
380	C₄×C₅	—	6	1	no	—
381	C₄×C₅	—	12	1	no	—
382	C₄×C₅	—	12	1	no	—
383	C₄×C₅	#877	1	1	yes	characteristic
384	C₄×C₅	#878	1	1	yes	characteristic
385	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
386	C₄×C₅	#939	1	1	yes	characteristic
387	Dic₅	—	4	2	no	—
388	Dic₅	—	12	2	no	—
389	#41	—	2	1	no	—
390	#41	—	2	1	no	—
391	#41	#1202	1	2	yes	—
392	#41	#1204	1	2	yes	—
393	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	3	1	no	—
399	C₂²×C₄	—	6	1	no	—
400	C₂²×C₄	—	6	1	no	—
401	C₂²×C₄	—	10	1	no	—
402	C₂²×C₄	—	30	1	no	—
403	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
404	M₁₆	—	10	1	no	—
405	M₁₆	—	10	1	no	—
406	M₁₆	—	30	1	no	—
407	M₁₆	—	30	1	no	—
408	C₂×C₈	—	10	1	no	—
409	C₂×C₈	—	30	1	no	—
410	C₄⋊C₄	—	3	1	no	—
411	C₄⋊C₄	—	3	1	no	—
412	C₄⋊C₄	—	6	1	no	—
413	C₄⋊C₄	—	6	1	no	—
414	C₄⋊C₄	—	30	4	no	—
415	C₂²⋊C₄	—	6	1	no	—
416	C₂²⋊C₄	—	6	1	no	—
417	C₂²⋊C₄	—	6	1	no	—
418	C₄²	—	3	1	no	—
419	C₄²	—	3	1	no	—
420	C₄²	—	3	1	no	—
421	C₄²	—	3	1	no	—
422	C₄²	—	6	1	no	—
423	C₄²	—	6	1	no	—
424	C₄²	—	6	1	no	—
425	C₄²	—	10	1	no	—
426	C₄²	—	10	1	no	—
427	C₄²	—	30	1	no	—
428	C₄²	—	30	1	no	—
429	C₃×C₅	#1806	1	1	yes	characteristic, complemented, Hall
430	C₂²×C₃	—	2	1	no	—
431	C₂²×C₃	—	2	1	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	4	1	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	#4070	1	1	yes	characteristic
436	C₂²×C₃	#4076	1	1	yes	characteristic
437	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	20	2	no	—
440	C₃×C₄	#4070	1	1	yes	characteristic
441	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
442	C₃×C₄	#4072	1	1	yes	characteristic
443	C₃×C₄	#4076	1	1	yes	characteristic
444	Dic₃	—	2	1	no	—
445	Dic₃	—	2	1	no	—
446	Dic₃	—	2	1	no	—
447	Dic₃	—	4	1	no	—
448	Dic₃	—	4	1	no	—
449	Dic₃	—	20	2	no	—
450	Dic₃	#3969	1	2	yes	complemented
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	4	2	no	—
454	C₂×C₅	D₃×#104	1	1	yes	characteristic
455	C₂×C₅	#4821	1	1	yes	characteristic
456	C₂×C₅	#4942	1	1	yes	characteristic
457	C₂³	—	2	1	no	—
458	C₂³	D₃×C₂²⋊D₅	1	1	yes	characteristic
459	Q₈	—	2	1	no	—
460	Q₈	Dic₃⋊Dic₅	1	2	yes	complemented
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	1	no	—
464	D₄	Dic₃⋊Dic₅	1	2	yes	complemented
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	3	1	no	—
469	C₂×C₄	—	3	1	no	—
470	C₂×C₄	—	3	1	no	—
471	C₂×C₄	—	3	1	no	—
472	C₂×C₄	—	6	2	no	—
473	C₂×C₄	—	6	1	no	—
474	C₂×C₄	—	6	1	no	—
475	C₂×C₄	—	10	2	no	—
476	C₂×C₄	—	12	2	no	—
477	C₂×C₄	—	12	1	no	—
478	C₂×C₄	—	12	2	no	—
479	C₂×C₄	—	20	1	no	—
480	C₂×C₄	—	20	1	no	—
481	C₂×C₄	—	30	2	no	—
482	C₂×C₄	—	60	1	no	—
483	C₂×C₄	—	60	1	no	—
484	C₂×C₄	#6779	1	1	yes	characteristic
485	C₂×C₄	#6779	1	1	yes	characteristic
486	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
487	C₂×C₄	C₂×#1202	1	1	yes	characteristic
488	C₂×C₄	C₂×#1204	1	1	yes	characteristic
489	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
490	C₈	—	20	1	no	—
491	C₈	—	60	1	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	#65501	1	1	yes	characteristic
496	C₂×C₃	C₂×#3969	1	1	yes	characteristic
497	C₂×C₃	#65525	1	1	yes	characteristic
498	C₅	#70355	1	1	yes	characteristic, complemented, Sylow
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
505	C₂²	#91569	1	1	yes	characteristic
506	C₂²	#91575	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	3	2	no	—
509	C₄	—	6	1	no	—
510	C₄	—	6	1	no	—
511	C₄	—	6	1	no	—
512	C₄	—	12	1	no	—
513	C₄	—	12	1	no	—
514	C₄	—	20	2	no	—
515	C₄	—	60	2	no	—
516	C₄	#91529	1	1	yes	characteristic
517	C₄	C₂×Dic₃⋊Dic₅	1	1	yes	characteristic
518	C₄	#91569	1	1	yes	characteristic
519	C₄	#91575	1	1	yes	characteristic
520	C₃	#10602439	1	1	yes	characteristic, complemented, Sylow
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	2	no	—
524	C₂	D₃×#3969	1	1	yes	characteristic
525	C₂	#11749429	1	1	yes	characteristic
526	C₂	#11749513	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting, prime radical	C₂×C₃×C₅×#41	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×#41	D₃×D₅
hypocenter	C₃×C₅	#1806
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
4. C₄×Dic₃⋊Dic₅	C₂	semidirect
5. #11748440	C₂	semidirect
6. #11745977	C₂	semidirect
7. #11745975	C₂	semidirect
12. C₅×Q₈×Dic₃	C₄	semidirect
13. C₅×Q₈×Dic₃	C₄	semidirect
16. C₅×D₄×Dic₃	C₄	semidirect
17. C₅×D₄×Dic₃	C₄	semidirect
110. C₃×C₅×Q₈	C₄⋊C₄	semidirect
114. C₃×C₅×D₄	C₄⋊C₄	semidirect
145. Q₈×Dic₃	Dic₅	semidirect
146. Q₈×Dic₃	Dic₅	semidirect
149. D₄×Dic₃	Dic₅	semidirect
150. D₄×Dic₃	Dic₅	semidirect
230. C₅×Dic₃	#104	semidirect
274. C₅×Q₈	Dic₃⋊C₄	semidirect
278. C₅×D₄	Dic₃⋊C₄	semidirect
336. C₃×Q₈	C₄⋊Dic₅	semidirect
340. C₃×D₄	C₄⋊Dic₅	semidirect
429. C₃×C₅	#1806	semidirect
450. Dic₃	#3969	semidirect
460. Q₈	Dic₃⋊Dic₅	semidirect
464. D₄	Dic₃⋊Dic₅	semidirect
498. C₅	#70355	semidirect
520. C₃	#10602439	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₃×#41	2
C₂×#91121	2
C₂×C₃×#3969	2
C₄×Dic₃⋊Dic₅	2
#11748440	2
#11745977	2
#11745975	2
#10602439	3
#70355	5