Subgroups — #14413188

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
2	Dic₃×#709	C₂	1	1	yes	maximal, characteristic
3	C₂×#91283	C₂	1	1	yes	maximal, characteristic
4	#11751203	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748440	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748436	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747648	C₂	1	2	yes	maximal, complemented
9	#11747647	C₂	1	2	yes	maximal, complemented
10	#11747596	C₂	1	2	yes	maximal, complemented
11	D₅×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
12	#10610743	—	3	1	no	maximal, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	#91815	C₂²	1	1	yes	characteristic
16	C₂×#6710	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×#681	C₂²	1	1	yes	characteristic
20	C₃×#4047	—	2	4	no	—
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	Dic₃×C₂²⋊D₅	C₄	1	2	yes	—
24	Dic₃×C₂²⋊D₅	C₄	1	2	yes	—
25	Dic₃×D₂₀	C₄	1	1	yes	characteristic
26	Dic₃×D₂₀	C₄	1	1	yes	characteristic
27	C₄×D₅×Dic₃	C₂²	1	2	yes	—
28	#91357	C₂²	1	2	yes	—
29	Dic₃×Dic₁₀	C₄	1	1	yes	characteristic
30	Dic₃×Dic₁₀	C₄	1	1	yes	characteristic
31	C₂×#6649	C₂²	1	2	yes	—
32	#91283	—	2	4	no	—
33	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
34	#91098	C₂²	1	2	yes	—
35	#91098	C₂²	1	2	yes	—
36	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
40	Dic₃⋊#168	C₂²	1	2	yes	—
41	Dic₃⋊#168	C₂²	1	2	yes	—
42	#90983	C₂²	1	2	yes	—
43	#90983	C₂²	1	2	yes	—
44	#83783	—	5	1	no	maximal, Hall
45	C₂×#4047	—	3	1	no	—
46	C₂×#4047	D₃	1	1	yes	characteristic
47	C₄×#709	—	3	1	no	—
48	C₂×C₅×C₄⋊C₈	—	3	1	no	—
49	#65391	—	3	1	no	—
50	#65391	—	3	1	no	—
51	#65213	—	3	1	no	—
52	#65128	—	3	2	no	—
53	#65128	—	3	2	no	—
54	#65126	—	3	2	no	—
55	D₅×C₄⋊C₈	—	3	2	no	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
60	C₃×#709	D₄	1	4	yes	—
61	C₃×#709	Q₈	1	4	yes	—
62	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
64	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
65	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
66	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
67	C₂×C₃×C₅×C₈	—	2	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	#6719	C₂×C₄	1	2	yes	—
71	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
72	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₁₅	C₂³	1	2	yes	—
74	#6710	—	2	2	no	—
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	—	2	2	no	—
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₃×#681	—	2	2	no	—
84	C₂×C₃×#168	C₂³	1	2	yes	—
85	C₃×#676	—	2	4	no	—
86	C₃×C₈×D₅	—	2	4	no	—
87	#6668	C₂×C₄	1	2	yes	—
88	#6668	C₂×C₄	1	2	yes	—
89	#6665	C₂×C₄	1	2	yes	—
90	#6665	C₂×C₄	1	2	yes	—
91	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
92	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
93	#6649	—	2	4	no	—
94	D₅×C₃⋊C₈	—	2	4	no	—
95	C₂×C₃×#131	—	5	1	no	—
96	Dic₃×#41	—	5	1	no	—
97	C₂×#948	—	5	1	no	—
98	#5119	—	5	1	no	—
99	#5119	—	5	2	no	—
100	#5118	—	5	1	no	—
101	#5118	—	5	2	no	—
102	#5102	—	5	1	no	—
103	#5102	—	5	2	no	—
104	C₂×Dic₃⋊C₈	—	5	2	no	—
105	C₂×Dic₃⋊C₈	D₅	1	1	yes	characteristic, complemented
106	C₂×#709	C₂×D₃	1	1	yes	characteristic
107	C₂²×C₅×C₈	—	3	1	no	—
108	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
109	C₂×C₄²×C₅	—	3	1	no	—
110	C₄×C₂²⋊D₅	—	3	2	no	—
111	C₄×C₂²⋊D₅	—	3	2	no	—
112	#4072	—	3	1	no	—
113	C₂×#681	—	3	1	no	—
114	C₂×#681	C₂×D₃	1	1	yes	characteristic
115	#4047	—	2	4	no	—
116	#4047	—	6	4	no	—
117	C₂×#676	—	3	2	no	—
118	C₂×#676	C₂×D₃	1	2	yes	—
119	C₂×C₈×D₅	—	3	2	no	—
120	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
121	C₄×D₂₀	—	3	1	no	—
122	C₄×D₂₀	—	3	1	no	—
123	#4018	—	3	2	no	—
124	C₄²×D₅	—	3	2	no	—
125	C₄×Dic₁₀	—	3	1	no	—
126	C₄×Dic₁₀	—	3	1	no	—
127	C₅×C₄⋊C₈	—	3	1	no	—
128	C₅×C₄⋊C₈	—	3	1	no	—
129	C₅×C₄⋊C₈	—	3	1	no	—
130	C₅×C₄⋊C₈	—	3	1	no	—
131	#3946	—	3	2	no	—
132	#3946	—	3	2	no	—
133	#3946	—	3	2	no	—
134	#3946	—	3	2	no	—
135	C₄⋊#168	—	3	2	no	—
136	C₄⋊#168	—	3	2	no	—
137	#2906	—	15	1	no	Sylow
138	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
145	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₂×C₅×Dic₃	—	4	1	no	—
148	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
152	C₃×C₂²⋊D₅	C₄⋊C₄	1	8	yes	—
153	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
154	C₃×D₂₀	C₄⋊C₄	1	4	yes	—
155	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
156	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
157	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	—
158	D₅×Dic₃	—	2	4	no	—
159	D₅×Dic₃	—	4	2	no	—
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃⋊#168	—	2	2	no	—
163	C₃×#168	—	2	2	no	—
164	C₅×C₃⋊C₈	—	2	1	no	—
165	C₅×C₃⋊C₈	—	2	1	no	—
166	C₂×C₃×#41	—	5	1	no	—
167	C₃×#131	—	10	4	no	—
168	C₂×C₃×M₁₆	—	5	1	no	—
169	C₂×C₃×M₁₆	—	5	2	no	—
170	C₂²×C₃×C₈	—	5	2	no	—
171	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
172	#948	—	10	4	no	—
173	Q₈×Dic₃	—	5	1	no	—
174	Q₈×Dic₃	—	5	1	no	—
175	D₄×Dic₃	—	5	2	no	—
176	D₄×Dic₃	—	5	2	no	—
177	D₄×Dic₃	—	5	1	no	—
178	D₄×Dic₃	—	5	1	no	—
179	#926	—	5	1	no	—
180	#926	—	5	2	no	—
181	C₂×C₄×Dic₃	—	5	2	no	—
182	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
183	C₂×#208	—	5	1	no	—
184	C₂×#208	—	5	2	no	—
185	C₂²×C₃⋊C₈	—	5	2	no	—
186	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
187	Dic₃⋊C₈	—	5	2	no	—
188	Dic₃⋊C₈	—	5	2	no	—
189	Dic₃⋊C₈	—	5	2	no	—
190	Dic₃⋊C₈	—	5	2	no	—
191	Dic₃⋊C₈	—	5	2	no	—
192	Dic₃⋊C₈	—	5	2	no	—
193	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
194	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
195	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
196	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic
197	C₂²×C₄×C₅	—	3	1	no	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	C₄×D₃	1	2	yes	—
201	#709	Dic₆	1	4	yes	—
202	#709	#67	1	4	yes	—
203	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
204	C₂×C₄×D₅	—	3	2	no	—
205	C₂×C₄×D₅	—	3	2	no	—
206	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
207	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
208	C₂×C₅×C₈	—	2	2	no	—
209	C₂×C₅×C₈	—	3	1	no	—
210	C₂×C₅×C₈	—	3	1	no	—
211	C₂×C₅×C₈	—	6	2	no	—
212	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
214	C₄²×C₅	—	3	1	no	—
215	C₄²×C₅	—	3	1	no	—
216	C₄²×C₅	—	3	1	no	—
217	C₄²×C₅	—	3	1	no	—
218	C₂²⋊Dic₅	—	3	2	no	—
219	#685	—	3	2	no	—
220	#685	—	3	2	no	—
221	C₄⋊Dic₅	—	3	1	no	—
222	C₄⋊Dic₅	—	3	1	no	—
223	#683	—	3	2	no	—
224	#683	—	3	2	no	—
225	C₄×Dic₅	—	3	2	no	—
226	C₄×Dic₅	—	3	2	no	—
227	C₄×Dic₅	—	3	2	no	—
228	#681	—	2	2	no	—
229	#681	—	6	2	no	—
230	C₂×#168	—	3	2	no	—
231	C₂×#168	C₂²×D₃	1	2	yes	—
232	#676	—	2	4	no	—
233	#676	—	6	4	no	—
234	C₈×D₅	—	2	4	no	—
235	C₈×D₅	—	6	4	no	—
236	C₂×#131	—	5	1	no	—
237	C₂×#131	—	15	1	no	—
238	C₄×#41	—	15	1	no	—
239	#424	—	15	2	no	—
240	#424	—	15	2	no	—
241	#424	—	15	1	no	—
242	#424	—	15	1	no	—
243	#423	—	15	2	no	—
244	#423	—	15	1	no	—
245	C₂×C₄⋊C₈	—	3	1	no	—
246	C₂×C₄⋊C₈	—	15	2	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
250	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₃×D₅	—	2	2	no	—
252	C₂×C₃×D₅	—	2	2	no	—
253	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
254	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
255	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
257	Dic₁₅	—	2	2	no	—
258	Dic₁₅	—	2	2	no	—
259	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
260	C₅×Dic₃	—	2	1	no	—
261	C₅×Dic₃	—	2	1	no	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	#131	1	2	yes	complemented
264	C₃×#41	—	5	4	no	—
265	C₃×#41	—	5	4	no	—
266	C₂×C₃×Q₈	—	5	1	no	—
267	C₂×C₃×D₄	—	5	2	no	—
268	C₂×C₃×D₄	—	5	1	no	—
269	C₂²×C₃×C₄	—	5	2	no	—
270	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
271	C₂²×Dic₃	—	5	2	no	—
272	C₂²×Dic₃	—	5	2	no	—
273	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
274	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
275	C₃×M₁₆	—	10	4	no	—
276	C₃×M₁₆	—	10	2	no	—
277	C₂×C₃×C₈	—	2	2	no	—
278	C₂×C₃×C₈	—	5	2	no	—
279	C₂×C₃×C₈	—	10	4	no	—
280	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
282	#217	—	5	2	no	—
283	#217	—	5	2	no	—
284	#217	—	5	2	no	—
285	C₄⋊Dic₃	—	5	1	no	—
286	C₄⋊Dic₃	—	5	1	no	—
287	C₄⋊Dic₃	—	5	2	no	—
288	C₄⋊Dic₃	—	5	2	no	—
289	C₄×Dic₃	—	5	2	no	—
290	C₄×Dic₃	—	5	2	no	—
291	C₄×Dic₃	—	5	2	no	—
292	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
293	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
294	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
295	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
296	#208	—	10	4	no	—
297	#208	—	10	2	no	—
298	C₂×C₃⋊C₈	—	2	2	no	—
299	C₂×C₃⋊C₈	—	5	2	no	—
300	C₂×C₃⋊C₈	—	10	4	no	—
301	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
302	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
303	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
304	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
305	C₂×C₄×C₅	—	3	1	no	—
306	C₂×C₄×C₅	—	3	1	no	—
307	C₂×C₄×C₅	—	3	1	no	—
308	C₂×C₄×C₅	—	3	1	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	—	12	1	no	—
311	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
312	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×#67	1	2	yes	—
314	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
315	C₂²⋊D₅	Dic₃⋊C₄	1	8	yes	—
316	C₂×Dic₅	—	3	2	no	—
317	C₂×Dic₅	—	3	2	no	—
318	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
319	D₂₀	Dic₃⋊C₄	1	4	yes	—
320	C₄×D₅	—	6	4	no	—
321	C₄×D₅	—	12	2	no	—
322	C₄×D₅	C₂×Dic₆	1	4	yes	—
323	C₄×D₅	C₂×#67	1	4	yes	—
324	Dic₁₀	Dic₃⋊C₄	1	4	yes	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	6	1	no	—
328	C₅×C₈	—	6	1	no	—
329	#168	—	2	2	no	—
330	#168	—	6	2	no	—
331	C₂×#41	—	5	1	no	—
332	#131	—	10	4	no	—
333	#131	—	30	4	no	—
334	C₂×M₁₆	—	5	1	no	—
335	C₂×M₁₆	—	5	2	no	—
336	C₂×M₁₆	—	15	2	no	—
337	C₂×M₁₆	—	15	1	no	—
338	C₂²×C₈	—	3	1	no	—
339	C₂²×C₈	—	5	2	no	—
340	C₂²×C₈	—	15	2	no	—
341	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
342	C₄×Q₈	—	15	1	no	—
343	C₄×Q₈	—	15	1	no	—
344	C₄×D₄	—	15	1	no	—
345	C₄×D₄	—	15	1	no	—
346	C₄×D₄	—	15	2	no	—
347	C₄×D₄	—	15	2	no	—
348	#117	—	15	2	no	—
349	#117	—	15	1	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	—	15	2	no	—
352	C₄⋊C₈	—	3	1	no	—
353	C₄⋊C₈	—	3	1	no	—
354	C₄⋊C₈	—	3	1	no	—
355	C₄⋊C₈	—	3	1	no	—
356	C₄⋊C₈	—	15	2	no	—
357	C₄⋊C₈	—	15	2	no	—
358	C₄⋊C₈	—	15	2	no	—
359	C₄⋊C₈	—	15	2	no	—
360	C₄⋊C₈	—	15	2	no	—
361	C₄⋊C₈	—	15	2	no	—
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
364	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
365	C₂×C₃×C₅	#568	1	1	yes	characteristic
366	C₃×D₅	—	2	4	no	—
367	C₂³×C₃	—	5	2	no	—
368	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
369	C₃×Q₈	—	5	4	no	—
370	C₃×D₄	—	5	8	no	—
371	C₃×D₄	—	5	4	no	—
372	C₂×C₃×C₄	—	5	2	no	—
373	C₂×C₃×C₄	—	5	4	no	—
374	C₂×C₃×C₄	—	5	4	no	—
375	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
376	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
377	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
378	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
379	C₂×Dic₃	—	2	2	no	—
380	C₂×Dic₃	—	4	1	no	—
381	C₂×Dic₃	—	5	2	no	—
382	C₂×Dic₃	—	5	2	no	—
383	C₂×Dic₃	—	10	4	no	—
384	C₂×Dic₃	—	20	2	no	—
385	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
386	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
387	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
388	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
389	C₃×C₈	—	2	1	no	—
390	C₃×C₈	—	2	1	no	—
391	C₃×C₈	—	10	2	no	—
392	C₃⋊C₈	—	2	1	no	—
393	C₃⋊C₈	—	2	1	no	—
394	C₃⋊C₈	—	10	2	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	C₂×Dic₃⋊C₄	1	2	yes	—
398	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
399	C₂×D₅	—	2	2	no	—
400	C₂×D₅	—	2	2	no	—
401	C₂×D₅	C₂×Dic₃⋊C₄	1	4	yes	—
402	C₄×C₅	—	3	2	no	—
403	C₄×C₅	—	6	1	no	—
404	C₄×C₅	—	6	1	no	—
405	C₄×C₅	—	6	1	no	—
406	C₄×C₅	C₂×Dic₃⋊C₄	1	2	yes	—
407	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
408	C₄×C₅	C₂²×#67	1	1	yes	characteristic
409	Dic₅	—	6	2	no	—
410	Dic₅	—	6	2	no	—
411	Dic₅	C₂×Dic₃⋊C₄	1	4	yes	—
412	#41	—	5	4	no	—
413	#41	—	5	4	no	—
414	C₂×Q₈	—	5	1	no	—
415	C₂×D₄	—	5	2	no	—
416	C₂×D₄	—	5	1	no	—
417	C₂²×C₄	—	3	1	no	—
418	C₂²×C₄	—	3	1	no	—
419	C₂²×C₄	—	5	2	no	—
420	C₂²×C₄	—	15	2	no	—
421	C₂²×C₄	—	15	2	no	—
422	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
423	M₁₆	—	10	4	no	—
424	M₁₆	—	10	2	no	—
425	M₁₆	—	30	4	no	—
426	M₁₆	—	30	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	3	1	no	—
429	C₂×C₈	—	3	1	no	—
430	C₂×C₈	—	5	2	no	—
431	C₂×C₈	—	6	2	no	—
432	C₂×C₈	—	10	4	no	—
433	C₂×C₈	—	15	2	no	—
434	C₂×C₈	—	30	4	no	—
435	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
436	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
437	C₄⋊C₄	—	15	2	no	—
438	C₄⋊C₄	—	15	2	no	—
439	C₄⋊C₄	—	15	1	no	—
440	C₄⋊C₄	—	15	1	no	—
441	C₂²⋊C₄	—	15	2	no	—
442	C₂²⋊C₄	—	15	2	no	—
443	C₂²⋊C₄	—	15	2	no	—
444	C₄²	—	3	1	no	—
445	C₄²	—	3	1	no	—
446	C₄²	—	3	1	no	—
447	C₄²	—	3	1	no	—
448	C₄²	—	15	2	no	—
449	C₄²	—	15	2	no	—
450	C₄²	—	15	2	no	—
451	C₃×C₅	#2906	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	2	1	no	—
454	C₂²×C₃	—	5	4	no	—
455	C₂²×C₃	—	10	2	no	—
456	C₂²×C₃	—	10	2	no	—
457	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
458	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
459	C₃×C₄	—	5	4	no	—
460	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
461	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
462	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
463	Dic₃	—	2	1	no	—
464	Dic₃	—	2	1	no	—
465	Dic₃	—	2	1	no	—
466	Dic₃	—	10	2	no	—
467	Dic₃	—	10	2	no	—
468	Dic₃	#4047	1	2	yes	complemented
469	C₂×C₅	—	2	2	no	—
470	C₂×C₅	D₃×#131	1	1	yes	characteristic
471	C₂×C₅	#5750	1	1	yes	characteristic
472	C₂×C₅	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
473	D₅	—	2	4	no	—
474	C₂³	—	5	2	no	—
475	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
476	Q₈	—	5	4	no	—
477	D₄	—	5	8	no	—
478	D₄	—	5	4	no	—
479	C₂×C₄	—	3	1	no	—
480	C₂×C₄	—	3	1	no	—
481	C₂×C₄	—	3	1	no	—
482	C₂×C₄	—	3	1	no	—
483	C₂×C₄	—	5	2	no	—
484	C₂×C₄	—	5	4	no	—
485	C₂×C₄	—	5	4	no	—
486	C₂×C₄	—	6	2	no	—
487	C₂×C₄	—	12	1	no	—
488	C₂×C₄	—	15	2	no	—
489	C₂×C₄	—	15	2	no	—
490	C₂×C₄	—	30	4	no	—
491	C₂×C₄	—	60	2	no	—
492	C₂×C₄	D₅×Dic₆	1	2	yes	—
493	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
494	C₂×C₄	D₅×#67	1	2	yes	—
495	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
496	C₈	—	2	1	no	—
497	C₈	—	2	1	no	—
498	C₈	—	6	1	no	—
499	C₈	—	6	1	no	—
500	C₈	—	10	2	no	—
501	C₈	—	30	2	no	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	—	10	4	no	—
504	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
505	C₂×C₃	C₂×#4047	1	1	yes	characteristic
506	C₂×C₃	#66079	1	1	yes	characteristic
507	C₅	#83783	1	1	yes	characteristic, complemented, Sylow
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	5	4	no	—
511	C₂²	—	10	2	no	—
512	C₂²	—	10	2	no	—
513	C₂²	D₅×Dic₃⋊C₄	1	2	yes	—
514	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
515	C₄	—	3	2	no	—
516	C₄	—	5	4	no	—
517	C₄	—	6	1	no	—
518	C₄	—	6	1	no	—
519	C₄	—	6	1	no	—
520	C₄	—	30	2	no	—
521	C₄	—	30	2	no	—
522	C₄	D₅×Dic₃⋊C₄	1	2	yes	—
523	C₄	C₂×D₅×Dic₆	1	1	yes	characteristic
524	C₄	C₂×D₅×#67	1	1	yes	characteristic
525	C₃	#10610743	1	1	yes	characteristic, complemented, Sylow
526	C₂	—	2	2	no	—
527	C₂	—	10	4	no	—
528	C₂	D₃×#4047	1	1	yes	characteristic
529	C₂	#11753951	1	1	yes	characteristic
530	C₂	C₂×D₅×Dic₃⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#2906
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11751203	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
6. #11748440	C₂	semidirect
7. #11748436	C₂	semidirect
8. #11747648	C₂	semidirect
9. #11747647	C₂	semidirect
10. #11747596	C₂	semidirect
11. D₅×Dic₃⋊C₈	C₂	semidirect
105. C₂×Dic₃⋊C₈	D₅	semidirect
263. C₅×Dic₃	#131	semidirect
451. C₃×C₅	#2906	semidirect
468. Dic₃	#4047	semidirect
507. C₅	#83783	semidirect
525. C₃	#10610743	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#4047	2
Dic₃×#709	2
C₂×#91283	2
#11751203	2
C₂×C₅×Dic₃⋊C₈	2
#11748440	2
#11748436	2
#11747648	2
#11747647	2
#11747596	2
D₅×Dic₃⋊C₈	2
#10610743	3
#83783	5