Subgroups — #14418057

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66156	C₂	1	1	yes	maximal, characteristic
3	C₂×#91283	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751337	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749437	C₂	1	4	yes	maximal, complemented
6	#11749436	C₂	1	4	yes	maximal, complemented
7	#11748476	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748420	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748326	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615523	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	C₂²	1	1	yes	characteristic
13	#91815	C₂²	1	1	yes	characteristic
14	C₂×#6710	C₂²	1	1	yes	characteristic
15	C₅×#948	—	2	1	no	—
16	C₅×#948	—	2	1	no	—
17	C₅×#948	C₂²	1	2	yes	complemented
18	C₅×#948	C₂²	1	2	yes	complemented
19	C₂×C₅×#208	—	2	1	no	—
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×#4097	C₄	1	2	yes	complemented
24	C₃×#4096	C₂²	1	4	yes	—
25	C₃×#4095	C₄	1	2	yes	complemented
26	C₃×#4088	C₄	1	2	yes	complemented
27	C₃×#4078	C₄	1	2	yes	complemented
28	C₂×C₃×#681	C₂²	1	1	yes	characteristic
29	C₂×#6649	—	2	1	no	—
30	#91283	—	2	1	no	—
31	#91283	—	2	1	no	—
32	#91283	C₂²	1	2	yes	complemented
33	#91283	C₂²	1	2	yes	complemented
34	C₂×D₅×C₃⋊C₈	—	2	1	no	—
35	#91121	C₂²	1	4	yes	complemented
36	#90991	C₂²	1	4	yes	complemented
37	#90976	C₂²	1	4	yes	complemented
38	#90954	C₂²	1	2	yes	complemented
39	#90951	C₂²	1	2	yes	complemented
40	#83999	—	5	1	no	maximal, Hall
41	C₂×C₅×#131	—	3	1	no	—
42	#66156	D₃	1	1	yes	characteristic
43	C₂×#4047	—	3	1	no	—
44	#65525	—	3	1	no	—
45	#65434	—	3	4	no	—
46	#65433	—	3	4	no	—
47	#65428	—	3	1	no	—
48	#65413	—	3	1	no	—
49	#65390	—	3	1	no	—
50	C₃×C₅×#41	—	2	1	no	—
51	C₃×C₅×#41	—	2	1	no	—
52	C₃×C₅×#41	C₂×C₄	1	2	yes	—
53	C₃×C₅×#41	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₃×#709	—	2	1	no	—
61	C₃×#709	—	2	1	no	—
62	C₃×#709	C₂×C₄	1	2	yes	—
63	C₃×#709	C₂³	1	2	yes	—
64	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	—	2	1	no	—
66	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
67	#6719	—	2	1	no	—
68	C₄⋊Dic₁₅	—	2	1	no	—
69	C₄×Dic₁₅	C₂³	1	2	yes	—
70	#6710	—	2	1	no	—
71	#6710	C₂³	1	2	yes	—
72	C₂×C₃⋊#168	—	2	1	no	—
73	C₅×#208	—	2	1	no	—
74	C₅×#208	—	2	2	no	—
75	C₅×#208	—	2	2	no	—
76	C₅×#208	C₂³	1	2	yes	—
77	C₂×C₅×C₃⋊C₈	—	2	1	no	—
78	C₂×C₅×C₃⋊C₈	—	2	2	no	—
79	C₂×C₅×C₃⋊C₈	—	2	2	no	—
80	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₃×#689	C₂×C₄	1	4	yes	—
87	C₃×#688	C₂×C₄	1	4	yes	—
88	C₃×#687	C₂×C₄	1	4	yes	—
89	C₃×#686	C₂×C₄	1	4	yes	—
90	C₃×#681	C₂×C₄	1	2	yes	—
91	C₃×#681	C₂×C₄	1	2	yes	—
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	#6649	—	2	2	no	—
94	#6649	—	2	2	no	—
95	D₅×C₃⋊C₈	—	2	2	no	—
96	D₅×C₃⋊C₈	—	2	2	no	—
97	C₃×#575	—	5	1	no	—
98	C₂×#948	—	5	1	no	—
99	C₂×#948	D₅	1	1	yes	characteristic, complemented
100	#5236	—	5	1	no	—
101	#5236	—	5	1	no	—
102	#5197	—	5	4	no	—
103	#5196	—	5	4	no	—
104	#5125	—	5	1	no	—
105	#5122	—	5	1	no	—
106	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
107	C₂×#709	C₂×D₃	1	1	yes	characteristic
108	C₅×#131	—	3	2	no	—
109	C₅×#131	—	3	2	no	—
110	C₅×#131	—	6	1	no	—
111	C₅×#131	—	6	1	no	—
112	C₂×C₅×M₁₆	—	3	1	no	—
113	C₂×C₅×M₁₆	—	6	1	no	—
114	C₂²×C₅×C₈	—	3	1	no	—
115	C₂²×C₅×C₈	—	6	1	no	—
116	#4097	Dic₃	1	2	yes	complemented
117	#4096	C₂×D₃	1	4	yes	—
118	#4095	Dic₃	1	2	yes	complemented
119	#4088	Dic₃	1	2	yes	complemented
120	#4078	Dic₃	1	2	yes	complemented
121	#4072	—	3	1	no	—
122	C₂×#681	—	3	1	no	—
123	C₂×#681	C₂×D₃	1	1	yes	characteristic
124	#4047	—	3	2	no	—
125	#4047	—	3	2	no	—
126	#4047	—	6	1	no	—
127	#4047	—	6	1	no	—
128	C₂×#676	—	6	1	no	—
129	C₂×C₈×D₅	—	6	1	no	—
130	#3969	—	3	4	no	—
131	#3957	—	3	4	no	—
132	#3954	—	3	4	no	—
133	#3947	—	3	2	no	—
134	C₈×Dic₅	—	3	2	no	—
135	#2955	—	15	1	no	Sylow
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	#41	1	1	yes	characteristic
138	C₂²×C₃×D₅	—	2	1	no	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×Dic₁₅	—	2	2	no	—
155	C₃×C₂²⋊D₅	—	2	2	no	—
156	C₃×C₂²⋊D₅	—	2	2	no	—
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₃×D₂₀	—	2	1	no	—
159	C₃×D₂₀	C₂²×C₄	1	2	yes	—
160	C₃×C₄×D₅	—	2	2	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×Dic₁₀	—	2	1	no	—
163	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
164	C₃⋊#168	—	2	2	no	—
165	C₃×#168	C₂²×C₄	1	4	yes	—
166	C₅×C₃⋊C₈	—	2	2	no	—
167	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×#41	—	5	1	no	—
172	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
173	C₃×#137	—	5	2	no	—
174	C₃×#137	—	5	2	no	—
175	C₃×AGL(1,ℤ/8)	—	5	2	no	—
176	C₃×AGL(1,ℤ/8)	—	5	2	no	—
177	C₃×#135	—	5	4	no	—
178	C₂×C₃×M₁₆	—	5	1	no	—
179	#948	—	2	1	no	—
180	#948	—	2	1	no	—
181	#948	—	5	2	no	—
182	#948	—	5	2	no	—
183	#948	—	10	1	no	—
184	#948	—	10	1	no	—
185	#948	C₂×D₅	1	2	yes	complemented
186	#948	C₂×D₅	1	2	yes	complemented
187	#926	—	5	1	no	—
188	C₂×#208	—	2	1	no	—
189	C₂×#208	—	5	1	no	—
190	C₂×#208	—	10	1	no	—
191	C₂×#208	C₂×D₅	1	1	yes	characteristic
192	C₂²×C₃⋊C₈	—	2	1	no	—
193	C₂²×C₃⋊C₈	—	10	1	no	—
194	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
195	#837	—	5	4	no	—
196	#837	—	5	4	no	—
197	#819	—	5	4	no	—
198	#815	—	5	2	no	—
199	C₈×Dic₃	—	5	2	no	—
200	C₅×#41	—	2	1	no	—
201	C₅×#41	—	2	1	no	—
202	C₅×#41	C₂×Dic₃	1	2	yes	—
203	C₅×#41	C₂²×D₃	1	2	yes	—
204	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	—	2	1	no	—
210	#709	—	2	1	no	—
211	#709	—	2	1	no	—
212	#709	C₂×Dic₃	1	2	yes	—
213	#709	C₂²×D₃	1	2	yes	—
214	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
215	C₂×C₄×D₅	—	2	1	no	—
216	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
217	C₅×M₁₆	—	3	2	no	—
218	C₅×M₁₆	—	6	2	no	—
219	C₅×M₁₆	—	6	2	no	—
220	C₅×M₁₆	—	6	1	no	—
221	C₂×C₅×C₈	—	3	1	no	—
222	C₂×C₅×C₈	—	3	1	no	—
223	C₂×C₅×C₈	—	3	1	no	—
224	C₂×C₅×C₈	—	3	1	no	—
225	C₂×C₅×C₈	—	3	1	no	—
226	C₂×C₅×C₈	—	3	1	no	—
227	C₂×C₅×C₈	—	6	2	no	—
228	C₂×C₅×C₈	—	6	2	no	—
229	C₂×C₅×C₈	—	6	1	no	—
230	C₂²⋊Dic₅	—	6	1	no	—
231	#689	C₂×Dic₃	1	4	yes	—
232	#688	C₂×Dic₃	1	4	yes	—
233	#687	C₂×Dic₃	1	4	yes	—
234	#686	C₂×Dic₃	1	4	yes	—
235	C₄⋊Dic₅	—	6	1	no	—
236	C₄×Dic₅	—	3	2	no	—
237	#681	—	3	2	no	—
238	#681	—	6	1	no	—
239	#681	C₂×Dic₃	1	2	yes	—
240	#681	C₂×Dic₃	1	2	yes	—
241	C₂×#168	—	6	1	no	—
242	C₂×#168	C₂²×D₃	1	2	yes	—
243	#676	—	6	2	no	—
244	#676	—	6	2	no	—
245	C₈×D₅	—	6	2	no	—
246	C₈×D₅	—	6	2	no	—
247	#575	—	5	1	no	—
248	C₂×#131	—	3	1	no	—
249	C₂×#131	—	15	1	no	—
250	#444	—	15	4	no	—
251	#443	—	15	4	no	—
252	#430	—	15	1	no	—
253	#421	—	15	1	no	—
254	#421	—	15	1	no	—
255	#405	—	15	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
260	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₃×D₅	—	2	2	no	—
263	C₂×C₃×D₅	—	4	2	no	—
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
266	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
268	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	Dic₁₅	—	4	2	no	—
270	C₃×Dic₅	—	2	2	no	—
271	C₃×#41	—	2	1	no	—
272	C₃×#41	—	2	1	no	—
273	C₃×#41	—	5	2	no	—
274	C₃×#41	—	5	2	no	—
275	C₃×#41	—	10	1	no	—
276	C₃×#41	—	10	1	no	—
277	C₃×#41	C₄×D₅	1	2	yes	—
278	C₃×#41	C₂²×D₅	1	2	yes	—
279	C₂×C₃×Q₈	—	5	1	no	—
280	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×D₄	—	2	1	no	—
282	C₂×C₃×D₄	—	5	1	no	—
283	C₂×C₃×D₄	—	10	1	no	—
284	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	—	10	1	no	—
287	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
288	C₃×Q₁₆	—	5	4	no	—
289	C₃×SD₁₆	—	5	4	no	—
290	C₃×SD₁₆	—	5	4	no	—
291	C₃×D₈	—	5	4	no	—
292	C₃×M₁₆	—	5	2	no	—
293	C₃×M₁₆	—	5	2	no	—
294	C₂×C₃×C₈	—	5	2	no	—
295	#217	—	10	1	no	—
296	C₄⋊Dic₃	—	10	1	no	—
297	C₄×Dic₃	—	5	2	no	—
298	#208	—	2	1	no	—
299	#208	—	2	2	no	—
300	#208	—	2	2	no	—
301	#208	—	5	2	no	—
302	#208	—	10	1	no	—
303	#208	—	10	2	no	—
304	#208	—	10	2	no	—
305	#208	C₂²×D₅	1	2	yes	—
306	C₂×C₃⋊C₈	—	2	1	no	—
307	C₂×C₃⋊C₈	—	2	2	no	—
308	C₂×C₃⋊C₈	—	2	2	no	—
309	C₂×C₃⋊C₈	—	10	1	no	—
310	C₂×C₃⋊C₈	—	10	2	no	—
311	C₂×C₃⋊C₈	—	10	2	no	—
312	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
313	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
314	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
315	C₂×C₃⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
316	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
317	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
318	C₂³×C₅	—	2	1	no	—
319	C₂³×C₅	#237	1	1	yes	characteristic
320	C₂²×D₅	—	2	1	no	—
321	C₅×Q₈	—	2	1	no	—
322	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	1	no	—
326	C₅×D₄	C₂²×Dic₃	1	2	yes	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	#237	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	2	2	no	—
337	C₂²⋊D₅	—	2	2	no	—
338	C₂×Dic₅	—	2	1	no	—
339	C₂×Dic₅	—	6	2	no	—
340	D₂₀	—	2	1	no	—
341	D₂₀	C₂²×Dic₃	1	2	yes	—
342	C₄×D₅	—	2	2	no	—
343	C₄×D₅	—	2	2	no	—
344	Dic₁₀	—	2	1	no	—
345	Dic₁₀	C₂²×Dic₃	1	2	yes	—
346	C₅×C₈	—	3	1	no	—
347	C₅×C₈	—	3	1	no	—
348	C₅×C₈	—	3	1	no	—
349	C₅×C₈	—	3	1	no	—
350	C₅×C₈	—	6	2	no	—
351	#168	—	6	2	no	—
352	#168	C₂²×Dic₃	1	4	yes	—
353	C₂×#41	—	5	1	no	—
354	C₂×#41	D₃×D₅	1	1	yes	characteristic
355	#137	—	5	2	no	—
356	#137	—	5	2	no	—
357	AGL(1,ℤ/8)	—	5	2	no	—
358	AGL(1,ℤ/8)	—	5	2	no	—
359	#135	—	5	4	no	—
360	#131	—	3	2	no	—
361	#131	—	3	2	no	—
362	#131	—	6	1	no	—
363	#131	—	6	1	no	—
364	#131	—	15	2	no	—
365	#131	—	15	2	no	—
366	#131	—	30	1	no	—
367	#131	—	30	1	no	—
368	C₂×M₁₆	—	3	1	no	—
369	C₂×M₁₆	—	5	1	no	—
370	C₂×M₁₆	—	6	1	no	—
371	C₂×M₁₆	—	15	1	no	—
372	C₂×M₁₆	—	30	1	no	—
373	C₂²×C₈	—	3	1	no	—
374	C₂²×C₈	—	6	1	no	—
375	C₂²×C₈	—	30	1	no	—
376	#117	—	15	1	no	—
377	#108	—	15	4	no	—
378	#104	—	15	4	no	—
379	#104	—	15	4	no	—
380	#97	—	15	2	no	—
381	C₄×C₈	—	15	2	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	2	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	4	2	no	—
386	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
387	C₃×D₅	—	4	2	no	—
388	C₂³×C₃	—	2	1	no	—
389	C₂³×C₃	—	10	1	no	—
390	C₂³×C₃	#709	1	1	yes	characteristic
391	C₃×Q₈	—	2	1	no	—
392	C₃×Q₈	—	5	2	no	—
393	C₃×Q₈	—	10	1	no	—
394	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
395	C₃×D₄	—	2	2	no	—
396	C₃×D₄	—	2	2	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	—	5	2	no	—
399	C₃×D₄	—	10	2	no	—
400	C₃×D₄	—	10	2	no	—
401	C₃×D₄	—	10	1	no	—
402	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	10	1	no	—
407	C₂×C₃×C₄	—	10	2	no	—
408	C₂×C₃×C₄	—	10	2	no	—
409	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
411	C₂×C₃×C₄	#709	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
415	C₂×Dic₃	—	10	2	no	—
416	C₃×C₈	—	5	4	no	—
417	C₃⋊C₈	—	2	2	no	—
418	C₃⋊C₈	—	10	2	no	—
419	C₃⋊C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
420	C₃⋊C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
421	C₃⋊C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
422	C₃⋊C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
427	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
428	C₂²×C₅	C₂×#237	1	1	yes	characteristic
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	4	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
433	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
434	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
435	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
436	Dic₅	—	2	2	no	—
437	Dic₅	—	12	2	no	—
438	#41	—	2	1	no	—
439	#41	—	2	1	no	—
440	#41	—	5	2	no	—
441	#41	—	5	2	no	—
442	#41	—	10	1	no	—
443	#41	—	10	1	no	—
444	#41	D₅×Dic₃	1	2	yes	—
445	#41	C₂×D₃×D₅	1	2	yes	—
446	C₂×Q₈	—	5	1	no	—
447	C₂×Q₈	D₅×Dic₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	10	1	no	—
451	C₂×D₄	D₅×Dic₃	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
455	Q₁₆	—	5	4	no	—
456	SD₁₆	—	5	4	no	—
457	SD₁₆	—	5	4	no	—
458	D₈	—	5	4	no	—
459	M₁₆	—	3	2	no	—
460	M₁₆	—	5	2	no	—
461	M₁₆	—	5	2	no	—
462	M₁₆	—	6	2	no	—
463	M₁₆	—	6	2	no	—
464	M₁₆	—	6	1	no	—
465	M₁₆	—	15	2	no	—
466	M₁₆	—	30	2	no	—
467	M₁₆	—	30	2	no	—
468	M₁₆	—	30	1	no	—
469	C₂×C₈	—	3	1	no	—
470	C₂×C₈	—	3	1	no	—
471	C₂×C₈	—	3	1	no	—
472	C₂×C₈	—	3	1	no	—
473	C₂×C₈	—	3	1	no	—
474	C₂×C₈	—	3	1	no	—
475	C₂×C₈	—	5	2	no	—
476	C₂×C₈	—	6	2	no	—
477	C₂×C₈	—	6	2	no	—
478	C₂×C₈	—	6	1	no	—
479	C₂×C₈	—	30	2	no	—
480	C₂×C₈	—	30	2	no	—
481	C₂×C₈	—	30	1	no	—
482	C₄⋊C₄	—	30	1	no	—
483	C₂²⋊C₄	—	30	1	no	—
484	C₄²	—	15	2	no	—
485	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	10	2	no	—
490	C₂²×C₃	—	20	2	no	—
491	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
492	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
493	C₂²×C₃	C₂×#709	1	1	yes	characteristic
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	10	2	no	—
496	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
497	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
498	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
499	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
500	Dic₃	—	20	2	no	—
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	2	1	no	—
503	C₂×C₅	—	2	1	no	—
504	C₂×C₅	—	4	2	no	—
505	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
506	D₅	—	4	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	10	1	no	—
509	C₂³	#6779	1	1	yes	characteristic
510	Q₈	—	2	1	no	—
511	Q₈	—	5	2	no	—
512	Q₈	—	10	1	no	—
513	Q₈	C₂×D₅×Dic₃	1	2	yes	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	1	no	—
517	D₄	—	5	2	no	—
518	D₄	—	10	2	no	—
519	D₄	—	10	2	no	—
520	D₄	—	10	1	no	—
521	D₄	C₂×D₅×Dic₃	1	2	yes	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	10	2	no	—
527	C₂×C₄	—	10	2	no	—
528	C₂×C₄	—	30	2	no	—
529	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
530	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
531	C₂×C₄	#6779	1	1	yes	characteristic
532	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
533	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
535	C₈	—	3	1	no	—
536	C₈	—	3	1	no	—
537	C₈	—	3	1	no	—
538	C₈	—	3	1	no	—
539	C₈	—	5	4	no	—
540	C₈	—	6	2	no	—
541	C₈	—	30	2	no	—
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	—	20	2	no	—
547	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
548	C₅	#83999	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	10	2	no	—
553	C₂²	—	20	2	no	—
554	C₂²	Dic₃×C₂²⋊D₅	1	1	yes	characteristic
555	C₂²	Dic₃×C₂²⋊D₅	1	1	yes	characteristic
556	C₂²	C₂×#6779	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	10	2	no	—
559	C₄	—	60	2	no	—
560	C₄	Dic₃×C₂²⋊D₅	1	1	yes	characteristic
561	C₄	Dic₃×C₂²⋊D₅	1	1	yes	characteristic
562	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
563	C₄	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
564	C₃	#10615523	1	1	yes	characteristic, complemented, Sylow
565	C₂	—	2	1	no	—
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	4	2	no	—
569	C₂	—	20	2	no	—
570	C₂	C₂×Dic₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₃×C₂²⋊D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₅×#41	C₂²
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66156	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×#41	D₃×D₅
hypocenter	C₃×C₅	#2955
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#948	C₂	semidirect
3. C₂×#91283	C₂	semidirect
4. #11751337	C₂	semidirect
5. #11749437	C₂	semidirect
6. #11749436	C₂	semidirect
7. #11748476	C₂	semidirect
8. #11748420	C₂	semidirect
9. #11748326	C₂	semidirect
17. C₅×#948	C₂²	semidirect
18. C₅×#948	C₂²	semidirect
23. C₃×#4097	C₄	semidirect
25. C₃×#4095	C₄	semidirect
26. C₃×#4088	C₄	semidirect
27. C₃×#4078	C₄	semidirect
32. #91283	C₂²	semidirect
33. #91283	C₂²	semidirect
35. #91121	C₂²	semidirect
36. #90991	C₂²	semidirect
37. #90976	C₂²	semidirect
38. #90954	C₂²	semidirect
39. #90951	C₂²	semidirect
99. C₂×#948	D₅	semidirect
116. #4097	Dic₃	semidirect
118. #4095	Dic₃	semidirect
119. #4088	Dic₃	semidirect
120. #4078	Dic₃	semidirect
185. #948	C₂×D₅	semidirect
186. #948	C₂×D₅	semidirect
485. C₃×C₅	#2955	semidirect
548. C₅	#83999	semidirect
564. C₃	#10615523	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#948	2
C₃×#66156	2
C₂×#91283	2
#11751337	2
#11749437	2
#11749436	2
#11748476	2
#11748420	2
#11748326	2
#10615523	3
#83999	5