Subgroups — C₃×D₅×#472 #14429368

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65488	C₂	1	2	yes	maximal, complemented
6	C₃×#65449	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65186	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65038	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#100	C₂	1	2	yes	maximal, complemented
12	D₅×#472	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#131	C₂²	1	1	yes	characteristic, complemented
18	C₃×#4095	C₂²	1	2	yes	complemented
19	C₃×#4094	C₂²	1	1	yes	characteristic, complemented
20	C₃×#4078	C₂²	1	2	yes	complemented
21	C₂×C₃×#686	C₂²	1	2	yes	complemented
22	C₃×#4060	—	2	2	no	—
23	C₃×D₅×SD₁₆	—	2	2	no	—
24	C₃×#4057	—	2	2	no	—
25	C₃×D₅×D₈	—	2	2	no	—
26	C₃×D₅×D₈	—	2	1	no	—
27	C₃×D₅×D₈	—	2	1	no	—
28	C₃×D₅×D₈	—	2	1	no	—
29	C₃×D₅×D₈	—	2	1	no	—
30	C₃×#4054	C₂²	1	2	yes	complemented
31	C₃×#4053	—	2	1	no	—
32	C₃×#4053	C₂²	1	1	yes	characteristic, complemented
33	C₃×D₅×M₁₆	—	2	1	no	—
34	C₃×D₅×M₁₆	C₂²	1	2	yes	—
35	C₃×D₅×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
37	C₃×#4047	—	2	1	no	—
38	C₃×#4047	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₈×D₅	—	2	1	no	—
40	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
41	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#100	C₂²	1	2	yes	complemented
43	C₃×#3965	C₂²	1	2	yes	complemented
44	C₃×#3955	C₂²	1	2	yes	complemented
45	C₃×#3955	C₂²	1	2	yes	complemented
46	C₃×#3954	C₂²	1	2	yes	complemented
47	C₃×#3951	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#472	—	5	1	no	maximal, Hall
49	D₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
50	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
51	D₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#472	C₂×C₃	1	1	yes	characteristic, complemented
53	#65488	C₂×C₃	1	2	yes	complemented
54	#65449	C₂×C₃	1	1	yes	characteristic, complemented
55	#65431	C₂×C₃	1	1	yes	characteristic, complemented
56	#65186	C₂×C₃	1	1	yes	characteristic, complemented
57	D₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
58	#65038	C₂×C₃	1	2	yes	complemented
59	D₅×#100	C₂×C₃	1	2	yes	complemented
60	C₂³×C₃×D₅	—	2	2	no	—
61	C₃×C₅×#41	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
63	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
64	C₃×#713	D₄	1	1	yes	characteristic
65	C₃×Q₈×D₅	D₄	1	1	yes	characteristic
66	C₃×#711	—	2	1	no	—
67	C₃×#711	D₄	1	1	yes	characteristic
68	C₃×D₄×D₅	—	2	1	no	—
69	C₃×D₄×D₅	—	2	2	no	—
70	C₃×D₄×D₅	—	2	2	no	—
71	C₃×D₄×D₅	—	2	2	no	—
72	C₃×D₄×D₅	—	2	2	no	—
73	C₃×D₄×D₅	D₄	1	1	yes	characteristic
74	C₃×#709	—	2	1	no	—
75	C₃×#709	C₂³	1	1	yes	characteristic
76	C₂×C₃×D₂₀	C₂³	1	2	yes	—
77	C₂×C₃×C₄×D₅	—	2	1	no	—
78	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×SD₁₆	—	2	2	no	—
80	C₃×C₅×D₈	—	2	2	no	—
81	C₃×C₅×D₈	—	2	1	no	—
82	C₃×C₅×D₈	—	2	1	no	—
83	C₃×C₅×M₁₆	—	2	1	no	—
84	C₃×C₅×M₁₆	C₂³	1	2	yes	—
85	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	—	2	1	no	—
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₃×#688	—	2	2	no	—
89	C₃×#687	—	2	2	no	—
90	C₃×#686	—	2	2	no	—
91	C₃×#686	—	2	2	no	—
92	C₃×#686	—	2	2	no	—
93	C₃×#686	—	2	2	no	—
94	C₃×#681	—	2	1	no	—
95	C₃×#681	C₂³	1	2	yes	—
96	C₃×#681	C₂³	1	1	yes	characteristic
97	C₂×C₃×#168	—	2	1	no	—
98	C₂×C₃×#168	C₂³	1	1	yes	characteristic
99	C₃×D₄₀	—	2	2	no	—
100	C₃×D₄₀	—	2	1	no	—
101	C₃×D₄₀	—	2	1	no	—
102	C₃×#677	—	2	2	no	—
103	C₃×#676	—	2	1	no	—
104	C₃×#676	—	2	2	no	—
105	C₃×#676	—	2	1	no	—
106	C₃×#676	—	2	1	no	—
107	C₃×C₈×D₅	—	2	1	no	—
108	C₃×C₈×D₅	—	2	2	no	—
109	C₃×C₈×D₅	—	2	1	no	—
110	C₃×C₈×D₅	—	2	1	no	—
111	C₃×C₈×D₅	D₄	1	1	yes	characteristic
112	C₃×C₈×D₅	D₄	1	1	yes	characteristic
113	C₃×C₈×D₅	D₄	1	1	yes	characteristic
114	C₃×C₈×D₅	D₄	1	1	yes	characteristic
115	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
116	C₂²×C₃×D₈	—	5	1	no	—
117	C₂×C₃×#131	—	5	1	no	—
118	C₃×#472	—	5	2	no	—
119	C₃×#472	—	5	1	no	—
120	C₃×#472	—	5	1	no	—
121	C₃×#472	—	5	1	no	—
122	C₃×#472	—	5	2	no	—
123	C₃×#472	D₅	1	1	yes	characteristic, direct product factor
124	C₂×C₃×#108	—	5	1	no	—
125	C₂×C₃×#100	—	5	2	no	—
126	D₅×#41	C₂²×C₃	1	1	yes	characteristic
127	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
128	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
129	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₅×#131	C₂²×C₃	1	1	yes	characteristic, complemented
131	#4095	C₂²×C₃	1	2	yes	complemented
132	#4094	C₂²×C₃	1	1	yes	characteristic, complemented
133	#4078	C₂²×C₃	1	2	yes	complemented
134	C₂×#686	C₂²×C₃	1	2	yes	complemented
135	#4060	—	2	2	no	—
136	D₅×SD₁₆	—	2	2	no	—
137	#4057	—	2	2	no	—
138	D₅×D₈	—	2	2	no	—
139	D₅×D₈	—	2	1	no	—
140	D₅×D₈	—	2	1	no	—
141	D₅×D₈	—	2	1	no	—
142	D₅×D₈	—	2	1	no	—
143	#4054	C₂²×C₃	1	2	yes	complemented
144	#4053	—	2	1	no	—
145	#4053	C₂²×C₃	1	1	yes	characteristic, complemented
146	D₅×M₁₆	—	2	1	no	—
147	D₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
148	D₅×M₁₆	C₂²×C₃	1	2	yes	—
149	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
150	#4047	—	2	1	no	—
151	#4047	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂×C₈×D₅	—	2	1	no	—
153	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
154	C₅×#108	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₅×#100	C₂²×C₃	1	2	yes	complemented
156	#3965	C₂²×C₃	1	2	yes	complemented
157	#3955	C₂²×C₃	1	2	yes	complemented
158	#3955	C₂²×C₃	1	2	yes	complemented
159	#3954	C₂²×C₃	1	2	yes	complemented
160	#3951	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×#472	—	5	1	no	Sylow
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×D₅	—	2	1	no	—
164	C₂²×C₃×D₅	—	2	2	no	—
165	C₂²×C₃×D₅	—	4	2	no	—
166	C₂²×C₃×D₅	—	4	2	no	—
167	C₂²×C₃×D₅	—	8	4	no	—
168	C₂²×C₃×D₅	#41	1	1	yes	characteristic
169	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
170	C₃×C₅×D₄	—	2	1	no	—
171	C₃×C₅×D₄	—	2	2	no	—
172	C₃×C₅×D₄	—	2	2	no	—
173	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
176	C₃×C₂²⋊D₅	—	2	1	no	—
177	C₃×C₂²⋊D₅	—	2	1	no	—
178	C₃×C₂²⋊D₅	—	2	1	no	—
179	C₃×C₂²⋊D₅	—	4	2	no	—
180	C₃×C₂²⋊D₅	—	4	2	no	—
181	C₂×C₃×Dic₅	—	2	1	no	—
182	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
183	C₃×D₂₀	—	2	1	no	—
184	C₃×D₂₀	—	2	2	no	—
185	C₃×D₂₀	—	2	2	no	—
186	C₃×D₂₀	C₂×D₄	1	1	yes	characteristic
187	C₃×C₄×D₅	—	2	1	no	—
188	C₃×C₄×D₅	—	2	1	no	—
189	C₃×C₄×D₅	—	2	1	no	—
190	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
191	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
192	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
193	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
194	C₃×Dic₁₀	—	2	1	no	—
195	C₃×Dic₁₀	C₂×D₄	1	1	yes	characteristic
196	C₃×C₅×C₈	—	2	1	no	—
197	C₃×C₅×C₈	—	2	2	no	—
198	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
199	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
200	C₃×#168	—	2	1	no	—
201	C₃×#168	—	2	2	no	—
202	C₃×#168	C₂×D₄	1	1	yes	characteristic
203	C₃×#168	C₂×D₄	1	1	yes	characteristic
204	C₂×C₃×#41	—	5	1	no	—
205	C₂²×C₃×D₄	—	5	2	no	—
206	C₃×AGL(1,ℤ/8)	—	5	2	no	—
207	C₃×AGL(1,ℤ/8)	—	5	2	no	—
208	C₃×AGL(1,ℤ/8)	—	5	2	no	—
209	C₃×AGL(1,ℤ/8)	—	10	2	no	—
210	C₃×AGL(1,ℤ/8)	—	10	2	no	—
211	C₃×AGL(1,ℤ/8)	C₂×D₅	1	2	yes	complemented
212	C₂×C₃×SD₁₆	—	10	2	no	—
213	C₂×C₃×D₈	—	5	2	no	—
214	C₂×C₃×D₈	—	5	1	no	—
215	C₂×C₃×D₈	—	10	1	no	—
216	C₂×C₃×D₈	—	10	1	no	—
217	C₂×C₃×D₈	—	10	1	no	—
218	C₂×C₃×D₈	—	10	1	no	—
219	C₂×C₃×D₈	—	10	2	no	—
220	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
221	C₃×#131	—	5	1	no	—
222	C₃×#131	—	5	1	no	—
223	C₃×#131	—	5	1	no	—
224	C₃×#131	—	10	1	no	—
225	C₃×#131	—	10	1	no	—
226	C₃×#131	C₂×D₅	1	1	yes	characteristic, complemented
227	C₂×C₃×M₁₆	—	5	1	no	—
228	C₂×C₃×M₁₆	—	5	2	no	—
229	C₂×C₃×M₁₆	—	10	1	no	—
230	C₂²×C₃×C₈	—	5	1	no	—
231	C₂²×C₃×C₈	—	10	1	no	—
232	C₃×#108	—	5	2	no	—
233	C₃×#108	—	5	1	no	—
234	C₃×#108	C₂×D₅	1	1	yes	characteristic, complemented
235	C₃×#100	—	5	2	no	—
236	C₃×#100	—	5	2	no	—
237	C₃×#100	—	5	2	no	—
238	C₃×#100	C₂×D₅	1	2	yes	complemented
239	C₂³×D₅	—	2	2	no	—
240	C₅×#41	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
242	C₂×C₂²⋊D₅	—	2	2	no	—
243	#713	C₃×D₄	1	1	yes	characteristic
244	Q₈×D₅	C₃×D₄	1	1	yes	characteristic
245	#711	—	2	1	no	—
246	#711	C₃×D₄	1	1	yes	characteristic
247	D₄×D₅	—	2	1	no	—
248	D₄×D₅	—	2	2	no	—
249	D₄×D₅	—	2	2	no	—
250	D₄×D₅	—	2	2	no	—
251	D₄×D₅	—	2	2	no	—
252	D₄×D₅	C₃×D₄	1	1	yes	characteristic
253	#709	—	2	1	no	—
254	#709	C₂³×C₃	1	1	yes	characteristic
255	C₂×D₂₀	C₂³×C₃	1	2	yes	—
256	C₂×C₄×D₅	—	2	1	no	—
257	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
258	C₅×SD₁₆	—	2	2	no	—
259	C₅×D₈	—	2	2	no	—
260	C₅×D₈	—	2	1	no	—
261	C₅×D₈	—	2	1	no	—
262	C₅×M₁₆	—	2	1	no	—
263	C₅×M₁₆	C₂³×C₃	1	1	yes	characteristic
264	C₅×M₁₆	C₂³×C₃	1	2	yes	—
265	C₂×C₅×C₈	—	2	1	no	—
266	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
267	#688	—	2	2	no	—
268	#687	—	2	2	no	—
269	#686	—	2	2	no	—
270	#686	—	2	2	no	—
271	#686	—	2	2	no	—
272	#686	—	2	2	no	—
273	#681	—	2	1	no	—
274	#681	C₂³×C₃	1	2	yes	—
275	#681	C₂³×C₃	1	1	yes	characteristic
276	C₂×#168	—	2	1	no	—
277	C₂×#168	C₂³×C₃	1	1	yes	characteristic
278	D₄₀	—	2	2	no	—
279	D₄₀	—	2	1	no	—
280	D₄₀	—	2	1	no	—
281	#677	—	2	2	no	—
282	#676	—	2	1	no	—
283	#676	—	2	2	no	—
284	#676	—	2	1	no	—
285	#676	—	2	1	no	—
286	C₈×D₅	—	2	1	no	—
287	C₈×D₅	—	2	2	no	—
288	C₈×D₅	—	2	1	no	—
289	C₈×D₅	—	2	1	no	—
290	C₈×D₅	C₃×D₄	1	1	yes	characteristic
291	C₈×D₅	C₃×D₄	1	1	yes	characteristic
292	C₈×D₅	C₃×D₄	1	1	yes	characteristic
293	C₈×D₅	C₃×D₄	1	1	yes	characteristic
294	C₂×AGL(1,ℤ/8)	—	5	2	no	—
295	C₂²×D₈	—	5	1	no	—
296	C₂×#131	—	5	1	no	—
297	#472	—	5	2	no	—
298	#472	—	5	1	no	—
299	#472	—	5	1	no	—
300	#472	—	5	1	no	—
301	#472	—	5	2	no	—
302	#472	C₃×D₅	1	1	yes	characteristic, direct product factor
303	C₂×#108	—	5	1	no	—
304	C₂×#100	—	5	2	no	—
305	C₂²×C₃×C₅	—	2	1	no	—
306	C₂²×C₃×C₅	—	4	2	no	—
307	C₂²×C₃×C₅	—	8	2	no	—
308	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
309	C₂×C₃×D₅	—	2	2	no	—
310	C₂×C₃×D₅	—	2	1	no	—
311	C₂×C₃×D₅	—	4	2	no	—
312	C₂×C₃×D₅	—	4	2	no	—
313	C₂×C₃×D₅	—	8	4	no	—
314	C₂×C₃×D₅	—	8	4	no	—
315	C₂×C₃×D₅	—	8	2	no	—
316	C₂×C₃×D₅	#121	1	1	yes	characteristic
317	C₂×C₃×D₅	#121	1	1	yes	characteristic
318	C₃×C₄×C₅	—	2	1	no	—
319	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
321	C₃×Dic₅	—	2	1	no	—
322	C₃×Dic₅	#121	1	1	yes	characteristic
323	C₃×Dic₅	#121	1	1	yes	characteristic
324	C₂⁴×C₃	—	10	2	no	—
325	C₃×#41	—	5	1	no	—
326	C₃×#41	—	5	1	no	—
327	C₃×#41	—	5	1	no	—
328	C₃×#41	—	10	1	no	—
329	C₃×#41	—	10	1	no	—
330	C₃×#41	C₂²×D₅	1	1	yes	characteristic
331	C₂×C₃×Q₈	—	5	1	no	—
332	C₂×C₃×D₄	—	5	1	no	—
333	C₂×C₃×D₄	—	5	2	no	—
334	C₂×C₃×D₄	—	10	2	no	—
335	C₂×C₃×D₄	—	10	2	no	—
336	C₂×C₃×D₄	—	10	2	no	—
337	C₂×C₃×D₄	—	10	2	no	—
338	C₂×C₃×D₄	—	10	2	no	—
339	C₂×C₃×D₄	—	10	1	no	—
340	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
341	C₂²×C₃×C₄	—	5	1	no	—
342	C₂²×C₃×C₄	—	10	1	no	—
343	C₃×SD₁₆	—	2	2	no	—
344	C₃×SD₁₆	—	10	2	no	—
345	C₃×SD₁₆	—	10	2	no	—
346	C₃×SD₁₆	—	10	2	no	—
347	C₃×D₈	—	2	2	no	—
348	C₃×D₈	—	2	1	no	—
349	C₃×D₈	—	2	1	no	—
350	C₃×D₈	—	10	2	no	—
351	C₃×D₈	—	10	2	no	—
352	C₃×D₈	—	10	2	no	—
353	C₃×D₈	—	10	2	no	—
354	C₃×D₈	—	10	2	no	—
355	C₃×D₈	—	10	1	no	—
356	C₃×D₈	—	10	1	no	—
357	C₃×M₁₆	—	2	1	no	—
358	C₃×M₁₆	—	5	1	no	—
359	C₃×M₁₆	—	5	2	no	—
360	C₃×M₁₆	—	10	1	no	—
361	C₃×M₁₆	—	10	1	no	—
362	C₃×M₁₆	—	10	2	no	—
363	C₃×M₁₆	—	10	1	no	—
364	C₃×M₁₆	—	10	1	no	—
365	C₃×M₁₆	C₂²×D₅	1	1	yes	characteristic
366	C₃×M₁₆	C₂²×D₅	1	2	yes	—
367	C₂×C₃×C₈	—	2	1	no	—
368	C₂×C₃×C₈	—	5	1	no	—
369	C₂×C₃×C₈	—	5	1	no	—
370	C₂×C₃×C₈	—	5	1	no	—
371	C₂×C₃×C₈	—	5	1	no	—
372	C₂×C₃×C₈	—	5	1	no	—
373	C₂×C₃×C₈	—	10	1	no	—
374	C₂×C₃×C₈	—	10	1	no	—
375	C₂×C₃×C₈	—	10	2	no	—
376	C₂×C₃×C₈	—	10	1	no	—
377	C₂×C₃×C₈	—	10	1	no	—
378	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
379	C₂³×C₅	—	2	2	no	—
380	C₂²×D₅	—	2	1	no	—
381	C₂²×D₅	—	2	2	no	—
382	C₂²×D₅	—	4	2	no	—
383	C₂²×D₅	—	4	2	no	—
384	C₂²×D₅	—	8	4	no	—
385	C₂²×D₅	C₃×#41	1	1	yes	characteristic
386	C₅×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
387	C₅×D₄	—	2	1	no	—
388	C₅×D₄	—	2	2	no	—
389	C₅×D₄	—	2	2	no	—
390	C₅×D₄	C₂×C₃×D₄	1	1	yes	characteristic
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
393	C₂²⋊D₅	—	2	1	no	—
394	C₂²⋊D₅	—	2	1	no	—
395	C₂²⋊D₅	—	2	1	no	—
396	C₂²⋊D₅	—	4	2	no	—
397	C₂²⋊D₅	—	4	2	no	—
398	C₂×Dic₅	—	2	1	no	—
399	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
400	D₂₀	—	2	1	no	—
401	D₂₀	—	2	2	no	—
402	D₂₀	—	2	2	no	—
403	D₂₀	C₂×C₃×D₄	1	1	yes	characteristic
404	C₄×D₅	—	2	1	no	—
405	C₄×D₅	—	2	1	no	—
406	C₄×D₅	—	2	1	no	—
407	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
408	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
409	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
410	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
411	Dic₁₀	—	2	1	no	—
412	Dic₁₀	C₂×C₃×D₄	1	1	yes	characteristic
413	C₅×C₈	—	2	1	no	—
414	C₅×C₈	—	2	2	no	—
415	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
416	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
417	#168	—	2	1	no	—
418	#168	—	2	2	no	—
419	#168	C₂×C₃×D₄	1	1	yes	characteristic
420	#168	C₂×C₃×D₄	1	1	yes	characteristic
421	C₂×#41	—	5	1	no	—
422	C₂²×D₄	—	5	2	no	—
423	AGL(1,ℤ/8)	—	5	2	no	—
424	AGL(1,ℤ/8)	—	5	2	no	—
425	AGL(1,ℤ/8)	—	5	2	no	—
426	AGL(1,ℤ/8)	—	10	2	no	—
427	AGL(1,ℤ/8)	—	10	2	no	—
428	AGL(1,ℤ/8)	C₂×C₃×D₅	1	2	yes	complemented
429	C₂×SD₁₆	—	10	2	no	—
430	C₂×D₈	—	5	2	no	—
431	C₂×D₈	—	5	1	no	—
432	C₂×D₈	—	10	1	no	—
433	C₂×D₈	—	10	1	no	—
434	C₂×D₈	—	10	1	no	—
435	C₂×D₈	—	10	1	no	—
436	C₂×D₈	—	10	2	no	—
437	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
438	#131	—	5	1	no	—
439	#131	—	5	1	no	—
440	#131	—	5	1	no	—
441	#131	—	10	1	no	—
442	#131	—	10	1	no	—
443	#131	C₂×C₃×D₅	1	1	yes	characteristic, complemented
444	C₂×M₁₆	—	5	1	no	—
445	C₂×M₁₆	—	5	2	no	—
446	C₂×M₁₆	—	10	1	no	—
447	C₂²×C₈	—	5	1	no	—
448	C₂²×C₈	—	10	1	no	—
449	#108	—	5	2	no	—
450	#108	—	5	1	no	—
451	#108	C₂×C₃×D₅	1	1	yes	characteristic, complemented
452	#100	—	5	2	no	—
453	#100	—	5	2	no	—
454	#100	—	5	2	no	—
455	#100	C₂×C₃×D₅	1	2	yes	complemented
456	C₂×C₃×C₅	—	2	1	no	—
457	C₂×C₃×C₅	—	4	1	no	—
458	C₂×C₃×C₅	—	8	2	no	—
459	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
460	C₃×D₅	—	2	1	no	—
461	C₃×D₅	—	4	1	no	—
462	C₃×D₅	—	8	2	no	—
463	C₃×D₅	#472	1	2	yes	direct product factor
464	C₂³×C₃	—	2	2	no	—
465	C₂³×C₃	—	5	1	no	—
466	C₂³×C₃	—	10	1	no	—
467	C₂³×C₃	—	10	2	no	—
468	C₂³×C₃	—	20	2	no	—
469	C₂³×C₃	—	20	2	no	—
470	C₂³×C₃	—	40	4	no	—
471	C₃×Q₈	—	5	1	no	—
472	C₃×Q₈	—	10	1	no	—
473	C₃×Q₈	D₄×D₅	1	1	yes	characteristic
474	C₃×D₄	—	2	1	no	—
475	C₃×D₄	—	2	2	no	—
476	C₃×D₄	—	2	2	no	—
477	C₃×D₄	—	5	1	no	—
478	C₃×D₄	—	10	1	no	—
479	C₃×D₄	—	10	1	no	—
480	C₃×D₄	—	10	1	no	—
481	C₃×D₄	—	10	1	no	—
482	C₃×D₄	—	10	2	no	—
483	C₃×D₄	—	10	2	no	—
484	C₃×D₄	—	20	2	no	—
485	C₃×D₄	—	20	2	no	—
486	C₃×D₄	D₄×D₅	1	1	yes	characteristic
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	5	1	no	—
489	C₂×C₃×C₄	—	5	1	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	5	1	no	—
492	C₂×C₃×C₄	—	5	1	no	—
493	C₂×C₃×C₄	—	10	1	no	—
494	C₂×C₃×C₄	—	10	1	no	—
495	C₂×C₃×C₄	—	10	1	no	—
496	C₂×C₃×C₄	—	10	1	no	—
497	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
498	C₃×C₈	—	2	1	no	—
499	C₃×C₈	—	2	2	no	—
500	C₃×C₈	—	5	1	no	—
501	C₃×C₈	—	5	1	no	—
502	C₃×C₈	—	10	1	no	—
503	C₃×C₈	—	10	2	no	—
504	C₃×C₈	D₄×D₅	1	1	yes	characteristic
505	C₃×C₈	D₄×D₅	1	1	yes	characteristic
506	C₂²×C₅	—	2	1	no	—
507	C₂²×C₅	—	4	2	no	—
508	C₂²×C₅	—	8	2	no	—
509	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
510	C₂×D₅	—	2	2	no	—
511	C₂×D₅	—	2	1	no	—
512	C₂×D₅	—	4	2	no	—
513	C₂×D₅	—	4	2	no	—
514	C₂×D₅	—	8	4	no	—
515	C₂×D₅	—	8	4	no	—
516	C₂×D₅	—	8	2	no	—
517	C₂×D₅	C₃×#121	1	1	yes	characteristic
518	C₂×D₅	C₃×#121	1	1	yes	characteristic
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
521	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
522	Dic₅	—	2	1	no	—
523	Dic₅	C₃×#121	1	1	yes	characteristic
524	Dic₅	C₃×#121	1	1	yes	characteristic
525	C₂⁴	—	10	2	no	—
526	#41	—	5	1	no	—
527	#41	—	5	1	no	—
528	#41	—	5	1	no	—
529	#41	—	10	1	no	—
530	#41	—	10	1	no	—
531	#41	C₂²×C₃×D₅	1	1	yes	characteristic
532	C₂×Q₈	—	5	1	no	—
533	C₂×D₄	—	5	1	no	—
534	C₂×D₄	—	5	2	no	—
535	C₂×D₄	—	10	2	no	—
536	C₂×D₄	—	10	2	no	—
537	C₂×D₄	—	10	2	no	—
538	C₂×D₄	—	10	2	no	—
539	C₂×D₄	—	10	2	no	—
540	C₂×D₄	—	10	1	no	—
541	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
542	C₂²×C₄	—	5	1	no	—
543	C₂²×C₄	—	10	1	no	—
544	SD₁₆	—	2	2	no	—
545	SD₁₆	—	10	2	no	—
546	SD₁₆	—	10	2	no	—
547	SD₁₆	—	10	2	no	—
548	D₈	—	2	2	no	—
549	D₈	—	2	1	no	—
550	D₈	—	2	1	no	—
551	D₈	—	10	2	no	—
552	D₈	—	10	2	no	—
553	D₈	—	10	2	no	—
554	D₈	—	10	2	no	—
555	D₈	—	10	2	no	—
556	D₈	—	10	1	no	—
557	D₈	—	10	1	no	—
558	M₁₆	—	2	1	no	—
559	M₁₆	—	5	1	no	—
560	M₁₆	—	5	2	no	—
561	M₁₆	—	10	1	no	—
562	M₁₆	—	10	1	no	—
563	M₁₆	—	10	2	no	—
564	M₁₆	—	10	1	no	—
565	M₁₆	—	10	1	no	—
566	M₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
567	M₁₆	C₂²×C₃×D₅	1	2	yes	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	5	1	no	—
570	C₂×C₈	—	5	1	no	—
571	C₂×C₈	—	5	1	no	—
572	C₂×C₈	—	5	1	no	—
573	C₂×C₈	—	5	1	no	—
574	C₂×C₈	—	10	1	no	—
575	C₂×C₈	—	10	1	no	—
576	C₂×C₈	—	10	2	no	—
577	C₂×C₈	—	10	1	no	—
578	C₂×C₈	—	10	1	no	—
579	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
580	C₃×C₅	C₂×#472	1	1	yes	characteristic, complemented, Hall
581	C₂²×C₃	—	2	1	no	—
582	C₂²×C₃	—	4	2	no	—
583	C₂²×C₃	—	5	1	no	—
584	C₂²×C₃	—	5	1	no	—
585	C₂²×C₃	—	8	2	no	—
586	C₂²×C₃	—	10	2	no	—
587	C₂²×C₃	—	10	1	no	—
588	C₂²×C₃	—	20	2	no	—
589	C₂²×C₃	—	20	2	no	—
590	C₂²×C₃	—	40	2	no	—
591	C₂²×C₃	—	40	4	no	—
592	C₂²×C₃	—	40	4	no	—
593	C₂²×C₃	D₅×#41	1	1	yes	characteristic
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	—	5	1	no	—
596	C₃×C₄	—	5	1	no	—
597	C₃×C₄	—	10	1	no	—
598	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
599	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
600	C₂×C₅	—	2	1	no	—
601	C₂×C₅	—	4	1	no	—
602	C₂×C₅	—	8	2	no	—
603	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
604	D₅	—	2	1	no	—
605	D₅	—	4	1	no	—
606	D₅	—	8	2	no	—
607	D₅	C₃×#472	1	2	yes	direct product factor
608	C₂³	—	2	2	no	—
609	C₂³	—	5	1	no	—
610	C₂³	—	10	1	no	—
611	C₂³	—	10	2	no	—
612	C₂³	—	20	2	no	—
613	C₂³	—	20	2	no	—
614	C₂³	—	40	4	no	—
615	Q₈	—	5	1	no	—
616	Q₈	—	10	1	no	—
617	Q₈	C₃×D₄×D₅	1	1	yes	characteristic
618	D₄	—	2	1	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	5	1	no	—
622	D₄	—	10	1	no	—
623	D₄	—	10	1	no	—
624	D₄	—	10	1	no	—
625	D₄	—	10	1	no	—
626	D₄	—	10	2	no	—
627	D₄	—	10	2	no	—
628	D₄	—	20	2	no	—
629	D₄	—	20	2	no	—
630	D₄	C₃×D₄×D₅	1	1	yes	characteristic
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	5	1	no	—
635	C₂×C₄	—	5	1	no	—
636	C₂×C₄	—	5	1	no	—
637	C₂×C₄	—	10	1	no	—
638	C₂×C₄	—	10	1	no	—
639	C₂×C₄	—	10	1	no	—
640	C₂×C₄	—	10	1	no	—
641	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	2	2	no	—
644	C₈	—	5	1	no	—
645	C₈	—	5	1	no	—
646	C₈	—	10	1	no	—
647	C₈	—	10	2	no	—
648	C₈	C₃×D₄×D₅	1	1	yes	characteristic
649	C₈	C₃×D₄×D₅	1	1	yes	characteristic
650	C₂×C₃	—	2	1	no	—
651	C₂×C₃	—	4	1	no	—
652	C₂×C₃	—	5	2	no	—
653	C₂×C₃	—	8	2	no	—
654	C₂×C₃	—	10	1	no	—
655	C₂×C₃	—	20	1	no	—
656	C₂×C₃	—	40	2	no	—
657	C₂×C₃	D₅×#121	1	1	yes	characteristic
658	C₅	C₂×C₃×#472	1	1	yes	characteristic, complemented, Sylow
659	C₂²	—	2	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	5	1	no	—
662	C₂²	—	5	1	no	—
663	C₂²	—	8	2	no	—
664	C₂²	—	10	2	no	—
665	C₂²	—	10	1	no	—
666	C₂²	—	20	2	no	—
667	C₂²	—	20	2	no	—
668	C₂²	—	40	2	no	—
669	C₂²	—	40	4	no	—
670	C₂²	—	40	4	no	—
671	C₂²	C₃×D₅×#41	1	1	yes	characteristic
672	C₄	—	2	1	no	—
673	C₄	—	5	1	no	—
674	C₄	—	5	1	no	—
675	C₄	—	10	1	no	—
676	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
677	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
678	C₃	D₅×#472	1	1	yes	characteristic, direct product factor, Sylow
679	C₂	—	2	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	5	2	no	—
682	C₂	—	8	2	no	—
683	C₂	—	10	1	no	—
684	C₂	—	20	1	no	—
685	C₂	—	40	2	no	—
686	C₂	C₃×D₅×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₅×#121
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#472	C₂
socle	C₂×C₃×C₅	C₂×#121
hypercenter	C₃×#472	D₅
hypocenter	C₅	C₂×C₃×#472
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#472

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×D₅×D₈	C₂	semidirect
3. C₃×D₅×#131	C₂	semidirect
4. C₃×C₅×#472	C₂	semidirect
5. C₃×#65488	C₂	semidirect
6. C₃×#65449	C₂	semidirect
7. C₃×#65431	C₂	semidirect
8. C₃×#65186	C₂	semidirect
9. C₃×D₅×#108	C₂	semidirect
10. C₃×#65038	C₂	semidirect
11. C₃×D₅×#100	C₂	semidirect
12. D₅×#472	C₃	direct (N × H)
15. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₃×C₅×#131	C₂²	semidirect
18. C₃×#4095	C₂²	semidirect
19. C₃×#4094	C₂²	semidirect
20. C₃×#4078	C₂²	semidirect
21. C₂×C₃×#686	C₂²	semidirect
30. C₃×#4054	C₂²	semidirect
32. C₃×#4053	C₂²	semidirect
36. C₂×C₃×D₄₀	C₂²	semidirect
38. C₃×#4047	C₂²	semidirect
41. C₃×C₅×#108	C₂²	semidirect
42. C₃×C₅×#100	C₂²	semidirect
43. C₃×#3965	C₂²	semidirect
44. C₃×#3955	C₂²	semidirect
45. C₃×#3955	C₂²	semidirect
46. C₃×#3954	C₂²	semidirect
47. C₃×#3951	C₂²	semidirect
49. D₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
50. C₂×D₅×D₈	C₂×C₃	semidirect
51. D₅×#131	C₂×C₃	semidirect
52. C₅×#472	C₂×C₃	semidirect
53. #65488	C₂×C₃	semidirect
54. #65449	C₂×C₃	semidirect
55. #65431	C₂×C₃	semidirect
56. #65186	C₂×C₃	semidirect
57. D₅×#108	C₂×C₃	semidirect
58. #65038	C₂×C₃	semidirect
59. D₅×#100	C₂×C₃	semidirect
123. C₃×#472	D₅	direct (N × H)
128. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
129. C₂×C₅×D₈	C₂²×C₃	semidirect
130. C₅×#131	C₂²×C₃	semidirect
131. #4095	C₂²×C₃	semidirect
132. #4094	C₂²×C₃	semidirect
133. #4078	C₂²×C₃	semidirect
134. C₂×#686	C₂²×C₃	semidirect
143. #4054	C₂²×C₃	semidirect
145. #4053	C₂²×C₃	semidirect
149. C₂×D₄₀	C₂²×C₃	semidirect
151. #4047	C₂²×C₃	semidirect
154. C₅×#108	C₂²×C₃	semidirect
155. C₅×#100	C₂²×C₃	semidirect
156. #3965	C₂²×C₃	semidirect
157. #3955	C₂²×C₃	semidirect
158. #3955	C₂²×C₃	semidirect
159. #3954	C₂²×C₃	semidirect
160. #3951	C₂²×C₃	semidirect
211. C₃×AGL(1,ℤ/8)	C₂×D₅	semidirect
220. C₂×C₃×D₈	C₂×D₅	semidirect
226. C₃×#131	C₂×D₅	semidirect
234. C₃×#108	C₂×D₅	semidirect
238. C₃×#100	C₂×D₅	semidirect
302. #472	C₃×D₅	direct (N × H)
428. AGL(1,ℤ/8)	C₂×C₃×D₅	semidirect
437. C₂×D₈	C₂×C₃×D₅	semidirect
443. #131	C₂×C₃×D₅	semidirect
451. #108	C₂×C₃×D₅	semidirect
455. #100	C₂×C₃×D₅	semidirect
463. C₃×D₅	#472	direct (N × H)
580. C₃×C₅	C₂×#472	semidirect
607. D₅	C₃×#472	direct (N × H)
658. C₅	C₂×C₃×#472	semidirect
678. C₃	D₅×#472	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×AGL(1,ℤ/8)	2
C₂×C₃×D₅×D₈	2
C₃×D₅×#131	2
C₃×C₅×#472	2
C₃×#65488	2
C₃×#65449	2
C₃×#65431	2
C₃×#65186	2
C₃×D₅×#108	2
C₃×#65038	2
C₃×D₅×#100	2
D₅×#472	3
C₂×C₃×#472	5

Subgroups — C3×D5×#472 #14429368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#472 #14429368