Subgroups — #14413192

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×#91790	C₂	1	1	yes	maximal, characteristic
2	#11754414	C₂	1	1	yes	maximal, characteristic
3	C₂×#91290	C₂	1	1	yes	maximal, characteristic
4	C₅×#5102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748439	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748431	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747664	C₂	1	2	yes	maximal, complemented
9	#11747660	C₂	1	2	yes	maximal, complemented
10	#11747594	C₂	1	2	yes	maximal, complemented
11	#11747585	C₂	1	2	yes	maximal, complemented
12	#10610812	—	3	1	no	maximal, Hall
13	C₂×#6817	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	1	yes	characteristic
16	#91790	—	2	4	no	—
17	C₂×#6705	C₂²	1	2	yes	—
18	C₂×C₈×D₁₅	C₂²	1	2	yes	—
19	C₅×#926	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	#91552	C₄	1	2	yes	—
24	#91552	C₄	1	2	yes	—
25	#91418	C₄	1	1	yes	characteristic
26	#91418	C₄	1	1	yes	characteristic
27	C₄×#1200	C₂²	1	2	yes	—
28	#91386	C₂²	1	2	yes	—
29	#91333	C₄	1	1	yes	characteristic
30	#91333	C₄	1	1	yes	characteristic
31	C₂×#6651	C₂²	1	2	yes	—
32	#91290	—	2	4	no	—
33	C₂×#6648	C₂²	1	2	yes	—
34	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
35	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
36	C₃×#3946	C₂²	1	1	yes	characteristic
37	C₃×#3946	C₂²	1	1	yes	characteristic
38	C₃×#3946	C₂²	1	1	yes	characteristic
39	C₃×#3946	C₂²	1	1	yes	characteristic
40	Dic₃⋊#168	C₂²	1	2	yes	—
41	Dic₃⋊#168	C₂²	1	2	yes	—
42	#90982	C₂²	1	2	yes	—
43	#90982	C₂²	1	2	yes	—
44	#79012	—	5	1	no	maximal, Hall
45	C₂×#4053	—	3	1	no	—
46	C₂×#4047	—	3	1	no	—
47	#65856	—	3	1	no	—
48	C₅×#424	—	3	1	no	—
49	#65407	—	3	1	no	—
50	C₂×#3946	D₃	1	1	yes	characteristic, complemented
51	#65288	—	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	C₂×#1220	C₂×C₄	1	2	yes	—
58	#6817	D₄	1	4	yes	—
59	#6817	Q₈	1	4	yes	—
60	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×D₁₅	C₂³	1	2	yes	—
62	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
65	C₂×#1200	C₂×C₄	1	2	yes	—
66	C₂×#1200	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	#6710	—	2	2	no	—
71	C₂×C₃⋊#168	C₂³	1	2	yes	—
72	#6705	—	2	4	no	—
73	C₈×D₁₅	—	2	4	no	—
74	C₅×#217	C₂×C₄	1	2	yes	—
75	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂³	1	2	yes	—
78	C₅×#208	—	2	2	no	—
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	—	2	2	no	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	#6669	C₂×C₄	1	2	yes	—
88	#6669	C₂×C₄	1	2	yes	—
89	#6667	C₂×C₄	1	2	yes	—
90	#6667	C₂×C₄	1	2	yes	—
91	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
92	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
93	#6651	—	2	4	no	—
94	#6648	—	2	4	no	—
95	C₂×#901	—	5	1	no	—
96	C₂×#901	—	5	1	no	—
97	C₄×#235	—	5	1	no	—
98	C₂×C₃×C₄⋊C₈	—	5	1	no	—
99	#5102	—	5	1	no	—
100	#5102	D₅	1	1	yes	characteristic, complemented
101	#4924	—	5	1	no	—
102	#4839	—	5	2	no	—
103	#4839	—	5	2	no	—
104	#4837	—	5	2	no	—
105	D₃×C₄⋊C₈	—	5	2	no	—
106	C₂×#709	—	3	1	no	—
107	C₂×C₅×M₁₆	—	3	1	no	—
108	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
109	C₅×#117	—	3	1	no	—
110	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
111	C₂×#681	—	3	1	no	—
112	C₂²×#168	C₂×D₃	1	1	yes	characteristic
113	#4053	—	6	4	no	—
114	#4047	—	6	4	no	—
115	C₂×#676	—	3	2	no	—
116	C₂×#676	—	3	2	no	—
117	C₂×C₈×D₅	—	3	2	no	—
118	C₂×C₈×D₅	—	3	2	no	—
119	#4039	—	3	1	no	—
120	#4039	—	3	1	no	—
121	#4033	—	3	1	no	—
122	#4033	—	3	1	no	—
123	#4027	—	3	2	no	—
124	#4027	—	3	2	no	—
125	#4018	—	3	2	no	—
126	C₄²×D₅	—	3	2	no	—
127	C₅×C₄⋊C₈	—	3	2	no	—
128	C₅×C₄⋊C₈	—	3	2	no	—
129	#3946	—	3	2	no	—
130	#3946	—	3	2	no	—
131	#3946	C₂×D₃	1	1	yes	characteristic
132	#3946	C₂×D₃	1	1	yes	characteristic
133	#3946	C₂×D₃	1	1	yes	characteristic
134	#3946	C₂×D₃	1	1	yes	characteristic
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×D₁₅	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	#1220	C₄⋊C₄	1	8	yes	—
145	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
146	D₆₀	C₄⋊C₄	1	4	yes	—
147	C₄×D₁₅	C₂×D₄	1	4	yes	—
148	C₄×D₁₅	C₂×Q₈	1	4	yes	—
149	Dic₃₀	C₄⋊C₄	1	4	yes	—
150	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
151	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
152	C₂×C₃×Dic₅	—	2	2	no	—
153	C₂×C₃×Dic₅	—	4	1	no	—
154	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	#1200	—	2	4	no	—
159	#1200	—	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	1	no	—
164	C₃×#168	—	2	1	no	—
165	C₅×C₃⋊C₈	—	2	2	no	—
166	C₂×#235	—	5	1	no	—
167	C₂²×C₃×C₈	—	5	1	no	—
168	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
169	C₂×C₃×C₄²	—	5	1	no	—
170	C₄×#67	—	5	2	no	—
171	C₄×#67	—	5	2	no	—
172	#926	C₂×D₅	1	1	yes	characteristic
173	C₂×#208	—	5	1	no	—
174	C₂×#208	C₂×D₅	1	1	yes	characteristic
175	#901	—	10	4	no	—
176	#901	—	10	4	no	—
177	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
178	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
179	C₂×D₃×C₈	—	5	2	no	—
180	C₂×D₃×C₈	—	5	2	no	—
181	C₄×D₁₂	—	5	1	no	—
182	C₄×D₁₂	—	5	1	no	—
183	#872	—	5	2	no	—
184	C₄²×D₃	—	5	2	no	—
185	C₄×Dic₆	—	5	1	no	—
186	C₄×Dic₆	—	5	1	no	—
187	C₃×C₄⋊C₈	—	5	1	no	—
188	C₃×C₄⋊C₈	—	5	1	no	—
189	C₃×C₄⋊C₈	—	5	1	no	—
190	C₃×C₄⋊C₈	—	5	1	no	—
191	Dic₃⋊C₈	—	5	2	no	—
192	Dic₃⋊C₈	—	5	2	no	—
193	Dic₃⋊C₈	C₂×D₅	1	2	yes	—
194	Dic₃⋊C₈	C₂×D₅	1	2	yes	—
195	C₄⋊(C₃⋊C₈)	—	5	2	no	—
196	C₄⋊(C₃⋊C₈)	—	5	2	no	—
197	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₂²⋊D₅	—	3	2	no	—
199	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
200	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
201	#709	—	3	4	no	—
202	#709	—	3	4	no	—
203	C₂×D₂₀	—	3	1	no	—
204	C₂×C₄×D₅	—	3	2	no	—
205	C₂×C₄×D₅	—	3	2	no	—
206	C₂×C₄×D₅	—	3	2	no	—
207	C₂×Dic₁₀	—	3	1	no	—
208	C₅×M₁₆	—	6	2	no	—
209	C₂×C₅×C₈	—	2	2	no	—
210	C₂×C₅×C₈	—	3	2	no	—
211	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
213	C₅×C₄⋊C₄	—	3	1	no	—
214	C₅×C₄⋊C₄	—	3	1	no	—
215	C₅×C₂²⋊C₄	—	3	2	no	—
216	C₄²×C₅	—	3	2	no	—
217	#685	—	3	2	no	—
218	#685	—	3	2	no	—
219	#683	—	3	2	no	—
220	#683	—	3	2	no	—
221	C₄×Dic₅	—	3	2	no	—
222	C₄×Dic₅	—	3	2	no	—
223	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
224	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
225	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
226	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
227	#681	—	6	2	no	—
228	C₂×#168	—	2	2	no	—
229	C₂×#168	—	3	2	no	—
230	C₂×#168	C₂²×D₃	1	1	yes	characteristic
231	C₂×#168	C₂²×D₃	1	1	yes	characteristic
232	#676	—	6	4	no	—
233	#676	—	6	4	no	—
234	C₈×D₅	—	6	4	no	—
235	C₈×D₅	—	6	4	no	—
236	C₂×#131	—	15	1	no	—
237	C₂×#131	—	15	1	no	—
238	C₄×#41	—	15	1	no	—
239	#424	—	3	1	no	—
240	#424	—	15	2	no	—
241	#424	—	15	2	no	—
242	#424	—	15	1	no	—
243	#423	—	15	2	no	—
244	#423	—	15	1	no	—
245	C₂×C₄⋊C₈	—	5	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×D₁₅	—	2	2	no	—
252	C₂×D₁₅	—	2	2	no	—
253	C₂×D₁₅	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	C₂×C₄⋊C₄	1	4	yes	—
258	C₃×Dic₅	—	2	1	no	—
259	C₃×Dic₅	—	2	1	no	—
260	C₃×Dic₅	—	2	1	no	—
261	C₃×Dic₅	#131	1	2	yes	complemented
262	C₅×Dic₃	—	2	2	no	—
263	C₅×Dic₃	—	2	2	no	—
264	C₂²×C₃×C₄	—	5	1	no	—
265	C₂²×C₃×C₄	—	5	1	no	—
266	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
267	C₂×#67	—	5	2	no	—
268	#235	—	5	4	no	—
269	#235	—	5	4	no	—
270	C₂×D₁₂	—	5	1	no	—
271	C₂×C₄×D₃	—	5	2	no	—
272	C₂×C₄×D₃	—	5	2	no	—
273	C₂×C₄×D₃	—	5	2	no	—
274	C₂×Dic₆	—	5	1	no	—
275	C₂×C₃×C₈	—	2	2	no	—
276	C₂×C₃×C₈	—	5	1	no	—
277	C₂×C₃×C₈	—	5	1	no	—
278	C₂×C₃×C₈	—	10	2	no	—
279	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
280	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
281	C₃×C₄²	—	5	1	no	—
282	C₃×C₄²	—	5	1	no	—
283	C₃×C₄²	—	5	1	no	—
284	C₃×C₄²	—	5	1	no	—
285	#217	C₄×D₅	1	2	yes	—
286	(C₂×D₃)⋊C₄	—	5	2	no	—
287	(C₂×D₃)⋊C₄	—	5	2	no	—
288	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
289	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
290	Dic₃⋊C₄	—	5	2	no	—
291	Dic₃⋊C₄	—	5	2	no	—
292	C₄×Dic₃	—	5	2	no	—
293	C₄×Dic₃	—	5	2	no	—
294	C₄×Dic₃	C₂²×D₅	1	2	yes	—
295	#208	—	2	2	no	—
296	#208	—	10	2	no	—
297	C₂×C₃⋊C₈	—	5	2	no	—
298	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
299	ΓL(1,𝔽₂₅)	—	10	4	no	—
300	ΓL(1,𝔽₂₅)	—	10	4	no	—
301	D₃×C₈	—	10	4	no	—
302	D₃×C₈	—	10	4	no	—
303	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
304	C₂²×D₅	—	3	2	no	—
305	C₂×C₄×C₅	—	3	2	no	—
306	C₂×C₄×C₅	—	3	2	no	—
307	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
308	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
309	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
310	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
311	C₂²⋊D₅	—	3	8	no	—
312	C₂×Dic₅	—	2	2	no	—
313	C₂×Dic₅	—	3	2	no	—
314	C₂×Dic₅	—	4	1	no	—
315	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
316	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
317	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
318	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
319	D₂₀	—	3	4	no	—
320	C₄×D₅	—	3	4	no	—
321	C₄×D₅	—	3	4	no	—
322	C₄×D₅	—	6	4	no	—
323	C₄×D₅	—	12	2	no	—
324	Dic₁₀	—	3	4	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	6	2	no	—
328	#168	—	2	1	no	—
329	#168	—	2	1	no	—
330	#168	—	6	2	no	—
331	C₂×#41	—	15	1	no	—
332	#131	—	30	4	no	—
333	#131	—	30	4	no	—
334	C₂×M₁₆	—	3	1	no	—
335	C₂×M₁₆	—	15	2	no	—
336	C₂×M₁₆	—	15	1	no	—
337	C₂×M₁₆	—	15	2	no	—
338	C₂²×C₈	—	5	1	no	—
339	C₂²×C₈	—	15	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	—	3	1	no	—
349	#117	—	15	2	no	—
350	C₂×C₄²	—	5	1	no	—
351	C₂×C₄²	—	15	2	no	—
352	C₄⋊C₈	—	3	2	no	—
353	C₄⋊C₈	—	3	2	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	5	1	no	—
356	C₄⋊C₈	—	5	1	no	—
357	C₄⋊C₈	—	5	1	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	D₁₅	—	2	4	no	—
367	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
368	C₂²×D₃	—	5	2	no	—
369	C₂×C₃×C₄	—	5	1	no	—
370	C₂×C₃×C₄	—	5	1	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	5	1	no	—
373	C₂×C₃×C₄	—	10	2	no	—
374	C₂×C₃×C₄	—	20	1	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	#67	—	5	8	no	—
380	C₂×Dic₃	—	5	2	no	—
381	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
382	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
383	D₁₂	—	5	4	no	—
384	C₄×D₃	—	5	4	no	—
385	C₄×D₃	—	5	4	no	—
386	C₄×D₃	—	10	4	no	—
387	C₄×D₃	—	20	2	no	—
388	Dic₆	—	5	4	no	—
389	C₃×C₈	—	2	1	no	—
390	C₃×C₈	—	2	1	no	—
391	C₃×C₈	—	10	1	no	—
392	C₃×C₈	—	10	1	no	—
393	C₃⋊C₈	—	2	2	no	—
394	C₃⋊C₈	—	10	2	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
398	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
399	C₂×D₅	—	3	4	no	—
400	C₂×D₅	—	6	2	no	—
401	C₂×D₅	—	6	2	no	—
402	C₄×C₅	—	6	2	no	—
403	C₄×C₅	—	6	2	no	—
404	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
405	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
406	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
407	Dic₅	—	2	1	no	—
408	Dic₅	—	2	1	no	—
409	Dic₅	—	2	1	no	—
410	Dic₅	—	3	4	no	—
411	Dic₅	#901	1	2	yes	complemented
412	#41	—	15	4	no	—
413	#41	—	15	4	no	—
414	C₂×Q₈	—	15	1	no	—
415	C₂×D₄	—	15	2	no	—
416	C₂×D₄	—	15	1	no	—
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	15	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	—	6	2	no	—
424	M₁₆	—	30	4	no	—
425	M₁₆	—	30	4	no	—
426	M₁₆	—	30	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	3	2	no	—
429	C₂×C₈	—	5	1	no	—
430	C₂×C₈	—	5	1	no	—
431	C₂×C₈	—	10	2	no	—
432	C₂×C₈	—	15	2	no	—
433	C₂×C₈	—	30	4	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	—	3	1	no	—
438	C₄⋊C₄	—	3	1	no	—
439	C₄⋊C₄	—	15	2	no	—
440	C₄⋊C₄	—	15	2	no	—
441	C₂²⋊C₄	—	3	2	no	—
442	C₂²⋊C₄	—	15	2	no	—
443	C₂²⋊C₄	—	15	2	no	—
444	C₄²	—	3	2	no	—
445	C₄²	—	5	1	no	—
446	C₄²	—	5	1	no	—
447	C₄²	—	5	1	no	—
448	C₄²	—	5	1	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	D₅×C₄⋊C₄	1	2	yes	—
455	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
456	C₂×D₃	—	5	4	no	—
457	C₂×D₃	—	10	2	no	—
458	C₂×D₃	—	10	2	no	—
459	C₃×C₄	—	5	2	no	—
460	C₃×C₄	—	10	1	no	—
461	C₃×C₄	—	10	1	no	—
462	C₃×C₄	—	10	1	no	—
463	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
464	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
465	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
466	Dic₃	—	2	2	no	—
467	Dic₃	—	2	2	no	—
468	Dic₃	—	5	4	no	—
469	C₂×C₅	—	2	2	no	—
470	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
471	C₂×C₅	C₂×#901	1	1	yes	characteristic
472	C₂×C₅	#5745	1	1	yes	characteristic
473	D₅	—	6	4	no	—
474	C₂³	—	15	2	no	—
475	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
476	Q₈	—	15	4	no	—
477	D₄	—	15	8	no	—
478	D₄	—	15	4	no	—
479	C₂×C₄	—	3	2	no	—
480	C₂×C₄	—	3	2	no	—
481	C₂×C₄	—	5	1	no	—
482	C₂×C₄	—	5	1	no	—
483	C₂×C₄	—	5	1	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	10	2	no	—
486	C₂×C₄	—	15	2	no	—
487	C₂×C₄	—	15	4	no	—
488	C₂×C₄	—	15	4	no	—
489	C₂×C₄	—	20	1	no	—
490	C₂×C₄	—	30	4	no	—
491	C₂×C₄	—	60	2	no	—
492	C₂×C₄	D₁₅⋊Q₈	1	2	yes	—
493	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
494	C₂×C₄	#6790	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	2	no	—
499	C₈	—	10	1	no	—
500	C₈	—	10	1	no	—
501	C₈	—	30	2	no	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
504	C₂×C₃	D₅×#131	1	1	yes	characteristic
505	C₂×C₃	#66084	1	1	yes	characteristic
506	D₃	—	10	4	no	—
507	C₅	#79012	1	1	yes	characteristic, complemented, Sylow
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	15	4	no	—
511	C₂²	—	30	2	no	—
512	C₂²	—	30	2	no	—
513	C₂²	#91404	1	2	yes	—
514	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
515	C₄	—	5	2	no	—
516	C₄	—	6	2	no	—
517	C₄	—	6	2	no	—
518	C₄	—	10	1	no	—
519	C₄	—	10	1	no	—
520	C₄	—	10	1	no	—
521	C₄	—	15	4	no	—
522	C₄	#91404	1	2	yes	—
523	C₄	C₂×D₁₅⋊Q₈	1	1	yes	characteristic
524	C₄	C₂×#6790	1	1	yes	characteristic
525	C₃	#10610812	1	1	yes	characteristic, complemented, Sylow
526	C₂	—	2	2	no	—
527	C₂	—	30	4	no	—
528	C₂	D₅×#901	1	1	yes	characteristic
529	C₂	#11753949	1	1	yes	characteristic
530	C₂	C₂×#91404	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×#6817	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. C₅×#5102	C₂	semidirect
5. C₂×C₃×#3946	C₂	semidirect
6. #11748439	C₂	semidirect
7. #11748431	C₂	semidirect
8. #11747664	C₂	semidirect
9. #11747660	C₂	semidirect
10. #11747594	C₂	semidirect
11. #11747585	C₂	semidirect
50. C₂×#3946	D₃	semidirect
100. #5102	D₅	semidirect
261. C₃×Dic₅	#131	semidirect
411. Dic₅	#901	semidirect
451. C₃×C₅	#2906	semidirect
507. C₅	#79012	semidirect
525. C₃	#10610812	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91790	2
#11754414	2
C₂×#91290	2
C₅×#5102	2
C₂×C₃×#3946	2
#11748439	2
#11748431	2
#11747664	2
#11747660	2
#11747594	2
#11747585	2
#10610812	3
#79012	5