Subgroups — #14415261

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91265	C₂	1	2	yes	maximal, complemented
2	#11752671	C₂	1	1	yes	maximal, characteristic
3	C₈×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748134	C₂	1	2	yes	maximal, complemented
7	#11747708	C₂	1	2	yes	maximal, complemented
8	C₈×#1203	C₂	1	2	yes	maximal, complemented
9	#11747009	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747008	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747007	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611153	—	3	1	no	maximal, Hall
13	C₂×#6771	C₂²	1	2	yes	—
14	C₂×C₈×D₁₅	C₂²	1	2	yes	—
15	C₄×D₆₀	C₂²	1	1	yes	characteristic
16	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	#91468	C₄	1	1	yes	characteristic
22	#91451	C₄	1	1	yes	characteristic
23	#91450	C₄	1	1	yes	characteristic
24	#91449	C₄	1	1	yes	characteristic
25	#91448	C₄	1	2	yes	—
26	C₄×#1203	C₂²	1	2	yes	—
27	#91350	C₄	1	2	yes	—
28	C₂×#6651	C₂²	1	2	yes	—
29	C₂×#6650	C₂²	1	2	yes	—
30	C₂×#6649	C₂²	1	2	yes	—
31	#91265	—	2	8	no	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	#91104	C₂²	1	2	yes	—
34	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
35	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
36	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
39	C₃×C₄×#168	C₂²	1	1	yes	characteristic
40	#90982	C₂²	1	2	yes	—
41	#90957	C₂²	1	2	yes	—
42	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
43	#78458	—	5	1	no	maximal, Hall
44	C₂×#4047	—	3	2	no	—
45	#65882	—	3	1	no	—
46	C₅×C₈×D₄	—	3	1	no	—
47	C₈×C₂²⋊D₅	—	3	2	no	—
48	#65301	—	3	1	no	—
49	#65127	—	3	1	no	—
50	#65126	—	3	1	no	—
51	#65018	—	3	2	no	—
52	#65016	—	3	2	no	—
53	C₈×D₂₀	—	3	1	no	—
54	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
55	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×D₁₅	C₂³	1	2	yes	—
57	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
59	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
62	C₂×#1204	C₂×C₄	1	2	yes	—
63	C₂×#1203	C₂×C₄	1	2	yes	—
64	C₂×#1203	C₂×C₄	1	2	yes	—
65	C₂×#1202	C₂×C₄	1	2	yes	—
66	C₂×#1201	C₂×C₄	1	2	yes	—
67	#6771	—	2	4	no	—
68	#6771	—	2	4	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	#6714	C₂×C₄	1	2	yes	—
73	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃⋊#168	C₂³	1	2	yes	—
75	C₈×D₁₅	—	2	4	no	—
76	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
77	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
79	C₅×D₃×C₈	—	2	4	no	—
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	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×C₈×D₅	—	2	2	no	—
86	C₃×C₈×D₅	D₄	1	4	yes	complemented
87	#6668	C₂×C₄	1	2	yes	—
88	#6667	C₂×C₄	1	2	yes	—
89	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
90	#6651	—	2	4	no	—
91	#6650	—	2	4	no	—
92	#6649	—	2	4	no	—
93	C₂×#901	—	5	2	no	—
94	#5477	—	5	1	no	—
95	C₂×C₃×C₄×C₈	—	5	1	no	—
96	#5110	—	5	2	no	—
97	#4924	—	5	1	no	—
98	#4688	—	5	1	no	—
99	#4688	—	5	2	no	—
100	#4688	—	5	1	no	—
101	C₈×D₁₂	—	5	2	no	—
102	C₈×D₁₂	—	5	1	no	—
103	C₈×D₁₂	D₅	1	1	yes	characteristic, complemented
104	C₂×#709	—	3	2	no	—
105	C₂²×C₅×C₈	—	3	2	no	—
106	C₄×C₅×D₄	—	3	1	no	—
107	#4086	—	3	1	no	—
108	#4084	—	3	1	no	—
109	C₄×C₂²⋊D₅	—	3	2	no	—
110	C₂×#681	—	3	2	no	—
111	#4047	—	6	8	no	—
112	C₂×#676	—	3	2	no	—
113	C₂×#676	—	3	2	no	—
114	C₂×C₈×D₅	—	3	2	no	—
115	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
116	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
117	#4041	—	3	1	no	—
118	#4034	—	3	1	no	—
119	#4031	—	3	2	no	—
120	#4030	—	3	2	no	—
121	C₄×D₂₀	—	3	1	no	—
122	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
123	C₅×C₄⋊C₈	—	3	1	no	—
124	C₅×C₂²⋊C₈	—	3	2	no	—
125	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
126	C₂²⋊#168	—	3	2	no	—
127	#3952	—	3	2	no	—
128	#3952	—	3	2	no	—
129	#3946	—	3	2	no	—
130	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
131	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
132	C₄⋊#168	—	3	1	no	—
133	C₄×#168	C₂×D₃	1	1	yes	characteristic
134	#2931	—	15	1	no	Sylow
135	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
142	D₆₀	—	2	2	no	—
143	C₄×D₁₅	—	2	2	no	—
144	C₄×D₁₅	—	2	2	no	—
145	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
146	C₅×D₁₂	—	2	2	no	—
147	C₄×C₅×D₃	—	2	2	no	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₃×C₄×D₅	—	2	2	no	—
153	C₃×C₄×D₅	—	2	2	no	—
154	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
155	C₃×C₄×D₅	#41	1	2	yes	—
156	#1204	—	2	4	no	—
157	#1203	—	2	4	no	—
158	#1203	—	2	4	no	—
159	#1202	—	2	4	no	—
160	#1201	—	2	4	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
163	C₃⋊#168	—	2	2	no	—
164	C₃×#168	—	2	1	no	—
165	C₃×#168	C₂×D₄	1	2	yes	—
166	C₅×C₃⋊C₈	—	2	2	no	—
167	C₂×#235	—	5	2	no	—
168	C₂²×C₃×C₈	—	5	1	no	—
169	C₂²×C₃×C₈	—	5	1	no	—
170	C₂×C₃×C₄²	—	5	1	no	—
171	#930	—	5	1	no	—
172	#930	—	5	2	no	—
173	#930	—	5	1	no	—
174	C₂×#208	—	5	2	no	—
175	#901	—	10	8	no	—
176	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
177	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
178	C₂×D₃×C₈	—	5	2	no	—
179	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
180	#875	—	5	2	no	—
181	#874	—	5	1	no	—
182	C₄×D₁₂	—	5	2	no	—
183	C₄×D₁₂	—	5	1	no	—
184	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
185	#869	—	5	1	no	—
186	C₃×C₄×C₈	—	5	1	no	—
187	C₃×C₄×C₈	—	5	1	no	—
188	C₃×C₄×C₈	—	5	1	no	—
189	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
190	(C₂×D₃)⋊C₈	—	5	2	no	—
191	(C₂×D₃)⋊C₈	—	5	2	no	—
192	(C₂×D₃)⋊C₈	—	5	2	no	—
193	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
194	C₄⋊(C₃⋊C₈)	—	5	1	no	—
195	C₄⋊(C₃⋊C₈)	—	5	2	no	—
196	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
197	C₂×C₅×D₄	—	3	1	no	—
198	C₂²×C₄×C₅	—	3	2	no	—
199	C₂×C₂²⋊D₅	—	3	2	no	—
200	C₂×C₂²⋊D₅	—	3	2	no	—
201	C₂×C₂²⋊D₅	—	3	2	no	—
202	#709	—	6	4	no	—
203	#709	—	6	4	no	—
204	C₂×D₂₀	—	3	2	no	—
205	C₂×D₂₀	—	3	1	no	—
206	C₂×C₄×D₅	—	3	2	no	—
207	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
208	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
209	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
210	C₂×Dic₁₀	—	3	2	no	—
211	C₂×C₅×C₈	—	3	2	no	—
212	C₂×C₅×C₈	—	6	4	no	—
213	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	—	3	1	no	—
216	C₅×C₂²⋊C₄	—	3	2	no	—
217	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₂²⋊Dic₅	—	3	2	no	—
219	#685	—	3	2	no	—
220	#685	—	3	2	no	—
221	C₄⋊Dic₅	—	3	1	no	—
222	#683	—	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	#681	—	6	4	no	—
227	C₂×#168	—	3	2	no	—
228	C₂×#168	C₂²×D₃	1	1	yes	characteristic
229	C₂×#168	C₂²×D₃	1	1	yes	characteristic
230	#676	—	6	4	no	—
231	#676	—	6	4	no	—
232	C₈×D₅	—	2	2	no	—
233	C₈×D₅	—	6	4	no	—
234	C₈×D₅	D₁₂	1	4	yes	complemented
235	C₂×#131	—	15	2	no	—
236	#532	—	15	1	no	—
237	#436	—	15	2	no	—
238	#436	—	15	1	no	—
239	#436	—	15	1	no	—
240	C₈×D₄	—	3	1	no	—
241	C₈×D₄	—	15	2	no	—
242	C₈×D₄	—	15	1	no	—
243	#423	—	15	1	no	—
244	#408	—	15	2	no	—
245	C₂×C₄×C₈	—	5	1	no	—
246	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
247	C₂×D₁₅	—	2	2	no	—
248	C₂×D₁₅	—	2	2	no	—
249	C₂×D₁₅	—	2	2	no	—
250	C₂×C₅×D₃	—	2	2	no	—
251	C₂×C₅×D₃	—	2	2	no	—
252	C₂×C₅×D₃	—	2	2	no	—
253	C₂×C₃×D₅	—	2	1	no	—
254	C₂×C₃×D₅	—	2	1	no	—
255	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	#131	1	2	yes	complemented
258	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	Dic₁₅	—	2	2	no	—
261	C₃×Dic₅	—	2	1	no	—
262	C₃×Dic₅	C₄×D₄	1	2	yes	—
263	C₃×Dic₅	#131	1	2	yes	complemented
264	C₅×Dic₃	—	2	2	no	—
265	C₂²×C₃×C₄	—	5	1	no	—
266	C₂²×C₃×C₄	—	5	1	no	—
267	C₂²×C₃×C₄	—	5	1	no	—
268	C₂×#67	—	5	2	no	—
269	C₂×#67	—	5	2	no	—
270	#235	—	10	4	no	—
271	#235	—	10	4	no	—
272	C₂×D₁₂	—	5	2	no	—
273	C₂×D₁₂	—	5	2	no	—
274	C₂×D₁₂	—	5	1	no	—
275	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
276	C₂×C₄×D₃	—	5	2	no	—
277	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
278	C₂×Dic₆	—	5	2	no	—
279	C₂×C₃×C₈	—	5	1	no	—
280	C₂×C₃×C₈	—	5	4	no	—
281	C₂×C₃×C₈	—	5	1	no	—
282	C₂×C₃×C₈	—	10	2	no	—
283	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
285	C₃×C₄²	—	5	1	no	—
286	C₃×C₄²	—	5	1	no	—
287	C₃×C₄²	—	5	1	no	—
288	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
289	(C₂×D₃)⋊C₄	—	5	2	no	—
290	(C₂×D₃)⋊C₄	—	5	2	no	—
291	(C₂×D₃)⋊C₄	—	5	2	no	—
292	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
293	C₄⋊Dic₃	—	5	1	no	—
294	C₄⋊Dic₃	—	5	2	no	—
295	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
296	#208	—	10	4	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	—	2	4	no	—
302	D₃×C₈	—	10	4	no	—
303	C₂³×C₅	—	3	2	no	—
304	C₂²×D₅	—	3	2	no	—
305	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
306	C₅×D₄	—	6	2	no	—
307	C₂×C₄×C₅	—	3	2	no	—
308	C₂×C₄×C₅	—	6	2	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
313	C₂²⋊D₅	—	6	4	no	—
314	C₂²⋊D₅	—	6	4	no	—
315	C₂²⋊D₅	—	6	4	no	—
316	C₂×Dic₅	—	3	2	no	—
317	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
318	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
319	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
320	D₂₀	—	6	4	no	—
321	D₂₀	—	6	2	no	—
322	C₄×D₅	—	2	2	no	—
323	C₄×D₅	—	2	2	no	—
324	C₄×D₅	—	6	2	no	—
325	C₄×D₅	—	6	2	no	—
326	C₄×D₅	C₂×D₁₂	1	2	yes	—
327	C₄×D₅	#235	1	2	yes	—
328	Dic₁₀	—	6	4	no	—
329	C₅×C₈	—	2	1	no	—
330	C₅×C₈	—	6	2	no	—
331	C₅×C₈	C₂×D₁₂	1	2	yes	—
332	#168	—	2	1	no	—
333	#168	—	6	2	no	—
334	#168	C₂×D₁₂	1	2	yes	—
335	C₂×#41	—	15	2	no	—
336	#131	—	30	8	no	—
337	C₂×M₁₆	—	15	2	no	—
338	C₂×M₁₆	—	15	2	no	—
339	C₂×M₁₆	—	15	2	no	—
340	C₂²×C₈	—	3	2	no	—
341	C₂²×C₈	—	5	1	no	—
342	C₂²×C₈	—	5	1	no	—
343	C₂²×C₈	—	15	2	no	—
344	C₄⋊Q₈	—	15	1	no	—
345	#127	—	15	1	no	—
346	#124	—	15	2	no	—
347	#121	—	15	2	no	—
348	#121	—	15	1	no	—
349	#121	—	15	1	no	—
350	C₄×D₄	—	3	1	no	—
351	C₄×D₄	—	15	2	no	—
352	C₄×D₄	—	15	1	no	—
353	C₂×C₄²	—	5	1	no	—
354	C₄⋊C₈	—	3	1	no	—
355	C₄⋊C₈	—	15	2	no	—
356	C₄⋊C₈	—	15	1	no	—
357	C₂²⋊C₈	—	3	2	no	—
358	C₂²⋊C₈	—	15	2	no	—
359	C₂²⋊C₈	—	15	2	no	—
360	C₂²⋊C₈	—	15	2	no	—
361	C₄×C₈	—	5	1	no	—
362	C₄×C₈	—	5	1	no	—
363	C₄×C₈	—	5	1	no	—
364	C₄×C₈	D₃×D₅	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
366	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
367	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
368	D₁₅	—	4	2	no	—
369	C₃×D₅	—	2	2	no	—
370	C₅×D₃	—	4	2	no	—
371	C₂³×C₃	—	5	1	no	—
372	C₂²×D₃	—	5	2	no	—
373	C₂²×D₃	C₂×C₄×D₅	1	2	yes	—
374	C₂×C₃×C₄	—	5	1	no	—
375	C₂×C₃×C₄	—	5	1	no	—
376	C₂×C₃×C₄	—	5	2	no	—
377	C₂×C₃×C₄	—	5	2	no	—
378	C₂×C₃×C₄	—	5	1	no	—
379	C₂×C₃×C₄	—	10	2	no	—
380	C₂×C₃×C₄	—	10	2	no	—
381	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
384	#67	—	10	4	no	—
385	#67	—	10	4	no	—
386	C₂×Dic₃	—	5	2	no	—
387	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
388	D₁₂	—	2	2	no	—
389	D₁₂	—	10	4	no	—
390	D₁₂	—	10	4	no	—
391	D₁₂	—	10	2	no	—
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	—	10	2	no	—
395	C₄×D₃	—	10	2	no	—
396	Dic₆	—	10	4	no	—
397	C₃×C₈	—	2	1	no	—
398	C₃×C₈	—	5	2	no	—
399	C₃×C₈	—	10	1	no	—
400	C₃×C₈	D₄×D₅	1	2	yes	—
401	C₃⋊C₈	—	2	2	no	—
402	C₃⋊C₈	—	10	2	no	—
403	C₂²×C₅	—	6	2	no	—
404	C₂²×C₅	—	6	2	no	—
405	C₂²×C₅	—	6	2	no	—
406	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
407	C₂×D₅	—	2	1	no	—
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	6	2	no	—
410	C₂×D₅	—	6	2	no	—
411	C₂×D₅	—	6	2	no	—
412	C₂×D₅	C₄×D₁₂	1	2	yes	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	6	2	no	—
415	C₄×C₅	#901	1	2	yes	complemented
416	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
417	C₄×C₅	C₂×#235	1	1	yes	characteristic
418	Dic₅	—	2	1	no	—
419	Dic₅	—	6	2	no	—
420	Dic₅	C₄×D₁₂	1	2	yes	—
421	Dic₅	#901	1	2	yes	complemented
422	#41	—	30	4	no	—
423	#41	—	30	4	no	—
424	C₂×Q₈	—	15	2	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	15	2	no	—
427	C₂×D₄	—	15	2	no	—
428	C₂×D₄	—	15	2	no	—
429	C₂×D₄	—	15	2	no	—
430	C₂×D₄	—	15	1	no	—
431	C₂²×C₄	—	3	2	no	—
432	C₂²×C₄	—	5	1	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	1	no	—
435	C₂²×C₄	—	15	2	no	—
436	M₁₆	—	30	4	no	—
437	M₁₆	—	30	4	no	—
438	M₁₆	—	30	4	no	—
439	C₂×C₈	—	3	2	no	—
440	C₂×C₈	—	5	1	no	—
441	C₂×C₈	—	5	4	no	—
442	C₂×C₈	—	5	1	no	—
443	C₂×C₈	—	6	4	no	—
444	C₂×C₈	—	10	2	no	—
445	C₂×C₈	—	15	2	no	—
446	C₂×C₈	—	30	4	no	—
447	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
448	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
449	C₄⋊C₄	—	3	1	no	—
450	C₄⋊C₄	—	15	2	no	—
451	C₄⋊C₄	—	15	1	no	—
452	C₂²⋊C₄	—	3	2	no	—
453	C₂²⋊C₄	—	15	2	no	—
454	C₂²⋊C₄	—	15	2	no	—
455	C₂²⋊C₄	—	15	2	no	—
456	C₄²	—	5	1	no	—
457	C₄²	—	5	1	no	—
458	C₄²	—	5	1	no	—
459	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
460	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	5	2	no	—
462	C₂²×C₃	—	10	1	no	—
463	C₂²×C₃	—	10	1	no	—
464	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
465	C₂×D₃	—	2	2	no	—
466	C₂×D₃	—	2	2	no	—
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	10	2	no	—
469	C₂×D₃	—	10	2	no	—
470	C₂×D₃	—	10	2	no	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	5	2	no	—
473	C₃×C₄	—	5	2	no	—
474	C₃×C₄	—	10	1	no	—
475	C₃×C₄	#4047	1	2	yes	complemented
476	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
477	C₃×C₄	D₅×#41	1	1	yes	characteristic
478	Dic₃	—	2	2	no	—
479	Dic₃	—	10	2	no	—
480	C₂×C₅	—	12	2	no	—
481	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
482	C₂×C₅	C₂×#901	1	1	yes	characteristic
483	C₂×C₅	C₂×#901	1	1	yes	characteristic
484	D₅	—	2	2	no	—
485	D₅	—	12	2	no	—
486	C₂³	—	3	2	no	—
487	C₂³	—	5	1	no	—
488	C₂³	—	15	2	no	—
489	Q₈	—	30	4	no	—
490	D₄	—	6	2	no	—
491	D₄	—	30	4	no	—
492	D₄	—	30	4	no	—
493	D₄	—	30	4	no	—
494	D₄	—	30	4	no	—
495	D₄	—	30	2	no	—
496	C₂×C₄	—	3	2	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	5	1	no	—
499	C₂×C₄	—	5	2	no	—
500	C₂×C₄	—	5	2	no	—
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	6	2	no	—
503	C₂×C₄	—	6	2	no	—
504	C₂×C₄	—	10	2	no	—
505	C₂×C₄	—	10	2	no	—
506	C₂×C₄	—	15	2	no	—
507	C₂×C₄	—	30	2	no	—
508	C₂×C₄	—	30	2	no	—
509	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
510	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	5	2	no	—
514	C₈	—	6	2	no	—
515	C₈	—	10	1	no	—
516	C₈	—	30	2	no	—
517	C₈	D₅×D₁₂	1	2	yes	—
518	C₂×C₃	—	10	2	no	—
519	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
520	C₂×C₃	C₂×#4047	1	1	yes	characteristic
521	C₂×C₃	D₅×#131	1	1	yes	characteristic
522	D₃	—	4	2	no	—
523	D₃	—	20	2	no	—
524	C₅	#78458	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	5	2	no	—
526	C₂²	—	6	2	no	—
527	C₂²	—	6	2	no	—
528	C₂²	—	6	2	no	—
529	C₂²	—	10	1	no	—
530	C₂²	—	10	1	no	—
531	C₂²	—	30	2	no	—
532	C₂²	—	30	2	no	—
533	C₂²	—	30	2	no	—
534	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	5	2	no	—
537	C₄	—	5	2	no	—
538	C₄	—	6	2	no	—
539	C₄	—	10	1	no	—
540	C₄	—	30	2	no	—
541	C₄	#91265	1	2	yes	complemented
542	C₄	C₂×D₅×D₁₂	1	1	yes	characteristic
543	C₄	D₅×#235	1	1	yes	characteristic
544	C₃	#10611153	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	10	2	no	—
546	C₂	—	12	2	no	—
547	C₂	—	60	2	no	—
548	C₂	C₄×D₅×D₁₂	1	1	yes	characteristic
549	C₂	D₅×#901	1	1	yes	characteristic
550	C₂	C₂×#91265	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	#11752671	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2931
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#91265	C₂	semidirect
3. C₈×D₆₀	C₂	semidirect
4. C₅×C₈×D₁₂	C₂	semidirect
5. C₃×C₄×C₈×D₅	C₂	semidirect
6. #11748134	C₂	semidirect
7. #11747708	C₂	semidirect
8. C₈×#1203	C₂	semidirect
9. #11747009	C₂	semidirect
10. #11747008	C₂	semidirect
11. #11747007	C₂	semidirect
54. C₄×C₈×D₅	D₃	semidirect
86. C₃×C₈×D₅	D₄	semidirect
103. C₈×D₁₂	D₅	semidirect
234. C₈×D₅	D₁₂	semidirect
257. C₃×C₄×C₅	#131	semidirect
263. C₃×Dic₅	#131	semidirect
415. C₄×C₅	#901	semidirect
421. Dic₅	#901	semidirect
460. C₃×C₅	#2931	semidirect
475. C₃×C₄	#4047	semidirect
524. C₅	#78458	semidirect
541. C₄	#91265	semidirect
544. C₃	#10611153	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91265	2
#11752671	2
C₈×D₆₀	2
C₅×C₈×D₁₂	2
C₃×C₄×C₈×D₅	2
#11748134	2
#11747708	2
C₈×#1203	2
#11747009	2
#11747008	2
#11747007	2
#10611153	3
#78458	5