Subgroups — C₃×D₅×#469 #14427973

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65448	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65424	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65328	C₂	1	2	yes	maximal, complemented
8	C₃×#65154	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65071	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
12	D₅×#469	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	—	2	2	no	—
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#121	C₂²	1	2	yes	complemented
19	C₃×#4085	—	2	2	no	—
20	C₃×#4084	C₂²	1	2	yes	complemented
21	C₂×C₃×#686	C₂²	1	2	yes	complemented
22	C₃×#4076	C₂²	1	2	yes	complemented
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
24	C₃×D₅×D₈	—	2	4	no	—
25	C₃×D₅×M₁₆	—	2	4	no	—
26	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
31	C₃×#4041	C₂²	1	2	yes	complemented
32	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₃×#4030	—	2	2	no	—
34	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₃×#3964	C₂²	1	2	yes	complemented
38	C₃×#3953	C₂²	1	2	yes	complemented
39	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3941	C₂²	1	2	yes	complemented
41	C₃×#3940	C₂²	1	2	yes	complemented
42	C₂×C₃×#469	—	5	1	no	maximal, Hall
43	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	D₅×#121	C₂×C₃	1	2	yes	complemented
46	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
47	#65448	C₂×C₃	1	1	yes	characteristic, complemented
48	#65424	C₂×C₃	1	1	yes	characteristic, complemented
49	#65328	C₂×C₃	1	2	yes	complemented
50	#65154	C₂×C₃	1	1	yes	characteristic, complemented
51	D₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
52	#65071	C₂×C₃	1	2	yes	complemented
53	D₅×#102	C₂×C₃	1	2	yes	complemented
54	C₂³×C₃×D₅	—	2	2	no	—
55	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
60	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
61	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
62	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
63	C₃×D₄×D₅	—	2	4	no	—
64	C₃×D₄×D₅	—	2	4	no	—
65	C₃×D₄×D₅	—	4	8	no	—
66	C₂×C₃×D₂₀	—	2	2	no	—
67	C₂×C₃×D₂₀	C₂³	1	2	yes	—
68	C₂×C₃×C₄×D₅	—	2	2	no	—
69	C₂×C₃×C₄×D₅	—	2	2	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
72	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
73	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
75	C₃×C₅×D₈	—	2	2	no	—
76	C₃×C₅×M₁₆	—	2	2	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₂²⋊Dic₅	—	2	2	no	—
82	C₃×#686	—	2	4	no	—
83	C₃×#685	—	2	2	no	—
84	C₃×#685	—	2	2	no	—
85	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
86	C₃×#683	—	2	2	no	—
87	C₃×#681	—	2	2	no	—
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₂×C₃×#168	C₂³	1	1	yes	characteristic
90	C₃×D₄₀	—	2	2	no	—
91	C₃×#676	—	2	2	no	—
92	C₃×#676	—	2	2	no	—
93	C₃×C₈×D₅	—	2	2	no	—
94	C₃×C₈×D₅	D₄	1	4	yes	complemented
95	C₂²×C₃×D₈	—	5	1	no	—
96	C₂²×C₃×M₁₆	—	5	1	no	—
97	C₂×C₃×#121	—	5	2	no	—
98	C₃×#469	—	5	1	no	—
99	C₃×#469	—	5	1	no	—
100	C₃×#469	—	5	2	no	—
101	C₃×#469	—	5	1	no	—
102	C₃×#469	—	5	2	no	—
103	C₃×#469	D₅	1	1	yes	characteristic, direct product factor
104	C₂×C₃×#106	—	5	1	no	—
105	C₂×C₃×#102	—	5	2	no	—
106	C₂×D₄×D₅	—	2	2	no	—
107	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
108	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₅×#121	C₂²×C₃	1	2	yes	complemented
112	#4085	—	2	2	no	—
113	#4084	C₂²×C₃	1	2	yes	complemented
114	C₂×#686	C₂²×C₃	1	2	yes	complemented
115	#4076	C₂²×C₃	1	2	yes	complemented
116	C₂×#681	C₂²×C₃	1	1	yes	characteristic, complemented
117	D₅×D₈	—	2	4	no	—
118	D₅×M₁₆	—	2	4	no	—
119	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
124	#4041	C₂²×C₃	1	2	yes	complemented
125	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
126	#4030	—	2	2	no	—
127	D₅×C₂²⋊C₄	—	2	2	no	—
128	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₅×#102	C₂²×C₃	1	2	yes	complemented
130	#3964	C₂²×C₃	1	2	yes	complemented
131	#3953	C₂²×C₃	1	2	yes	complemented
132	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
133	#3941	C₂²×C₃	1	2	yes	complemented
134	#3940	C₂²×C₃	1	2	yes	complemented
135	C₂×#469	—	5	1	no	Sylow
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₃×D₅	—	2	2	no	—
139	C₂²×C₃×D₅	—	2	4	no	—
140	C₂²×C₃×D₅	—	2	2	no	—
141	C₂²×C₃×D₅	—	4	4	no	—
142	C₂²×C₃×D₅	—	4	4	no	—
143	C₂²×C₃×D₅	—	4	4	no	—
144	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×D₄	—	2	2	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	4	4	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₂²⋊D₅	—	4	4	no	—
155	C₃×C₂²⋊D₅	—	4	4	no	—
156	C₃×C₂²⋊D₅	—	4	4	no	—
157	C₂×C₃×Dic₅	—	2	2	no	—
158	C₂×C₃×Dic₅	—	2	2	no	—
159	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
161	C₃×D₂₀	—	2	2	no	—
162	C₃×D₂₀	—	2	2	no	—
163	C₃×D₂₀	—	4	4	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	1	no	—
166	C₃×C₄×D₅	—	2	1	no	—
167	C₃×C₄×D₅	—	2	2	no	—
168	C₃×C₄×D₅	—	4	4	no	—
169	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
170	C₃×C₄×D₅	#41	1	2	yes	—
171	C₃×C₅×C₈	—	2	1	no	—
172	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
173	C₃×#168	—	2	1	no	—
174	C₃×#168	C₂×D₄	1	2	yes	complemented
175	C₂²×C₃×D₄	—	5	2	no	—
176	C₂²×C₃×D₄	—	10	2	no	—
177	C₂³×C₃×C₄	—	5	1	no	—
178	C₂×C₃×D₈	—	5	2	no	—
179	C₂×C₃×D₈	—	5	1	no	—
180	C₂×C₃×D₈	—	10	4	no	—
181	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
182	C₂×C₃×M₁₆	—	5	1	no	—
183	C₂×C₃×M₁₆	—	5	1	no	—
184	C₂×C₃×M₁₆	—	5	1	no	—
185	C₂×C₃×M₁₆	—	10	4	no	—
186	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₂²×C₃×C₈	—	5	1	no	—
189	C₃×#121	—	5	2	no	—
190	C₃×#121	—	5	2	no	—
191	C₃×#121	—	5	2	no	—
192	C₃×#121	—	10	2	no	—
193	C₃×#121	—	10	2	no	—
194	C₃×#121	C₂×D₅	1	2	yes	complemented
195	C₂×C₃×C₄⋊C₄	—	5	2	no	—
196	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
197	C₃×#106	—	5	1	no	—
198	C₃×#106	—	5	2	no	—
199	C₃×#106	C₂×D₅	1	1	yes	characteristic, complemented
200	C₃×#102	—	5	2	no	—
201	C₃×#102	—	5	2	no	—
202	C₃×#102	—	5	2	no	—
203	C₃×#102	C₂×D₅	1	2	yes	complemented
204	C₂³×D₅	—	2	2	no	—
205	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
206	C₂×C₅×D₄	—	2	2	no	—
207	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	—	2	2	no	—
210	C₂×C₂²⋊D₅	—	2	2	no	—
211	C₂×C₂²⋊D₅	—	2	2	no	—
212	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
213	D₄×D₅	—	2	4	no	—
214	D₄×D₅	—	2	4	no	—
215	D₄×D₅	—	4	8	no	—
216	C₂×D₂₀	—	2	2	no	—
217	C₂×D₂₀	C₂³×C₃	1	2	yes	—
218	C₂×C₄×D₅	—	2	2	no	—
219	C₂×C₄×D₅	—	2	2	no	—
220	C₂×C₄×D₅	—	2	2	no	—
221	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
225	C₅×D₈	—	2	2	no	—
226	C₅×M₁₆	—	2	2	no	—
227	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
229	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
230	C₅×C₂²⋊C₄	—	2	2	no	—
231	C₂²⋊Dic₅	—	2	2	no	—
232	#686	—	2	4	no	—
233	#685	—	2	2	no	—
234	#685	—	2	2	no	—
235	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
236	#683	—	2	2	no	—
237	#681	—	2	2	no	—
238	C₂×#168	C₂³×C₃	1	1	yes	characteristic
239	C₂×#168	C₂³×C₃	1	1	yes	characteristic
240	D₄₀	—	2	2	no	—
241	#676	—	2	2	no	—
242	#676	—	2	2	no	—
243	C₈×D₅	—	2	2	no	—
244	C₈×D₅	C₃×D₄	1	4	yes	complemented
245	C₂²×D₈	—	5	1	no	—
246	C₂²×M₁₆	—	5	1	no	—
247	C₂×#121	—	5	2	no	—
248	#469	—	5	1	no	—
249	#469	—	5	1	no	—
250	#469	—	5	2	no	—
251	#469	—	5	1	no	—
252	#469	—	5	2	no	—
253	#469	C₃×D₅	1	1	yes	characteristic, direct product factor
254	C₂×#106	—	5	1	no	—
255	C₂×#102	—	5	2	no	—
256	C₂²×C₃×C₅	—	2	1	no	—
257	C₂²×C₃×C₅	—	2	2	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	—	4	2	no	—
261	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₃×D₅	—	2	1	no	—
263	C₂×C₃×D₅	—	2	2	no	—
264	C₂×C₃×D₅	—	4	4	no	—
265	C₂×C₃×D₅	—	4	2	no	—
266	C₂×C₃×D₅	—	4	2	no	—
267	C₂×C₃×D₅	—	4	2	no	—
268	C₂×C₃×D₅	—	8	8	no	—
269	C₂×C₃×D₅	#121	1	2	yes	—
270	C₂×C₃×D₅	AGL(1,ℤ/8)	1	4	yes	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	—	4	2	no	—
273	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₃×Dic₅	—	2	1	no	—
276	C₃×Dic₅	—	4	2	no	—
277	C₃×Dic₅	#121	1	2	yes	—
278	C₂⁴×C₃	—	5	1	no	—
279	C₂⁴×C₃	—	10	2	no	—
280	C₂×C₃×D₄	—	2	2	no	—
281	C₂×C₃×D₄	—	5	2	no	—
282	C₂×C₃×D₄	—	10	2	no	—
283	C₂×C₃×D₄	—	10	4	no	—
284	C₂×C₃×D₄	—	10	4	no	—
285	C₂×C₃×D₄	—	10	2	no	—
286	C₂×C₃×D₄	—	10	2	no	—
287	C₂×C₃×D₄	—	10	2	no	—
288	C₂×C₃×D₄	—	20	8	no	—
289	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₂²×C₃×C₄	—	5	1	no	—
293	C₂²×C₃×C₄	—	5	1	no	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	10	2	no	—
296	C₂²×C₃×C₄	—	10	2	no	—
297	C₂²×C₃×C₄	—	10	2	no	—
298	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
299	C₃×D₈	—	2	2	no	—
300	C₃×D₈	—	10	4	no	—
301	C₃×D₈	—	10	2	no	—
302	C₃×M₁₆	—	2	2	no	—
303	C₃×M₁₆	—	10	2	no	—
304	C₃×M₁₆	—	10	2	no	—
305	C₃×M₁₆	—	10	2	no	—
306	C₂×C₃×C₈	—	5	1	no	—
307	C₂×C₃×C₈	—	5	4	no	—
308	C₂×C₃×C₈	—	5	1	no	—
309	C₂×C₃×C₈	—	10	2	no	—
310	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
311	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
312	C₃×C₄⋊C₄	—	5	2	no	—
313	C₃×C₄⋊C₄	—	10	2	no	—
314	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
315	C₃×C₂²⋊C₄	—	2	2	no	—
316	C₃×C₂²⋊C₄	—	10	2	no	—
317	C₃×C₂²⋊C₄	—	10	2	no	—
318	C₃×C₂²⋊C₄	—	10	2	no	—
319	C₂³×C₅	—	2	2	no	—
320	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂²×D₅	—	2	2	no	—
322	C₂²×D₅	—	2	4	no	—
323	C₂²×D₅	—	2	2	no	—
324	C₂²×D₅	—	4	4	no	—
325	C₂²×D₅	—	4	4	no	—
326	C₂²×D₅	—	4	4	no	—
327	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
329	C₅×D₄	—	2	2	no	—
330	C₅×D₄	—	2	2	no	—
331	C₅×D₄	—	4	4	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
337	C₂²⋊D₅	—	4	4	no	—
338	C₂²⋊D₅	—	4	4	no	—
339	C₂²⋊D₅	—	4	4	no	—
340	C₂×Dic₅	—	2	2	no	—
341	C₂×Dic₅	—	2	2	no	—
342	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
344	D₂₀	—	2	2	no	—
345	D₂₀	—	2	2	no	—
346	D₂₀	—	4	4	no	—
347	C₄×D₅	—	2	2	no	—
348	C₄×D₅	—	2	1	no	—
349	C₄×D₅	—	2	1	no	—
350	C₄×D₅	—	2	2	no	—
351	C₄×D₅	—	4	4	no	—
352	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
353	C₄×D₅	C₃×#41	1	2	yes	—
354	C₅×C₈	—	2	1	no	—
355	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
356	#168	—	2	1	no	—
357	#168	C₂×C₃×D₄	1	2	yes	complemented
358	C₂²×D₄	—	5	2	no	—
359	C₂²×D₄	—	10	2	no	—
360	C₂³×C₄	—	5	1	no	—
361	C₂×D₈	—	5	2	no	—
362	C₂×D₈	—	5	1	no	—
363	C₂×D₈	—	10	4	no	—
364	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
365	C₂×M₁₆	—	5	1	no	—
366	C₂×M₁₆	—	5	1	no	—
367	C₂×M₁₆	—	5	1	no	—
368	C₂×M₁₆	—	10	4	no	—
369	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
370	C₂²×C₈	—	5	1	no	—
371	C₂²×C₈	—	5	1	no	—
372	#121	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	10	2	no	—
376	#121	—	10	2	no	—
377	#121	C₂×C₃×D₅	1	2	yes	complemented
378	C₂×C₄⋊C₄	—	5	2	no	—
379	C₂×C₂²⋊C₄	—	10	2	no	—
380	#106	—	5	1	no	—
381	#106	—	5	2	no	—
382	#106	C₂×C₃×D₅	1	1	yes	characteristic, complemented
383	#102	—	5	2	no	—
384	#102	—	5	2	no	—
385	#102	—	5	2	no	—
386	#102	C₂×C₃×D₅	1	2	yes	complemented
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	—	8	2	no	—
389	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
391	C₃×D₅	—	4	1	no	—
392	C₃×D₅	—	8	2	no	—
393	C₃×D₅	#469	1	4	yes	direct product factor
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	—	5	1	no	—
396	C₂³×C₃	—	5	1	no	—
397	C₂³×C₃	—	10	2	no	—
398	C₂³×C₃	—	10	4	no	—
399	C₂³×C₃	—	10	2	no	—
400	C₂³×C₃	—	20	4	no	—
401	C₂³×C₃	—	20	4	no	—
402	C₂³×C₃	—	20	4	no	—
403	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
404	C₃×D₄	—	2	2	no	—
405	C₃×D₄	—	2	2	no	—
406	C₃×D₄	—	4	4	no	—
407	C₃×D₄	—	10	2	no	—
408	C₃×D₄	—	10	2	no	—
409	C₃×D₄	—	20	4	no	—
410	C₃×D₄	—	20	4	no	—
411	C₃×D₄	—	20	4	no	—
412	C₃×D₄	—	20	4	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	5	1	no	—
417	C₂×C₃×C₄	—	5	2	no	—
418	C₂×C₃×C₄	—	5	2	no	—
419	C₂×C₃×C₄	—	5	1	no	—
420	C₂×C₃×C₄	—	10	2	no	—
421	C₂×C₃×C₄	—	10	2	no	—
422	C₂×C₃×C₄	—	10	2	no	—
423	C₂×C₃×C₄	—	10	1	no	—
424	C₂×C₃×C₄	—	10	1	no	—
425	C₂×C₃×C₄	—	10	2	no	—
426	C₂×C₃×C₄	—	20	4	no	—
427	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
429	C₃×C₈	—	2	1	no	—
430	C₃×C₈	—	5	2	no	—
431	C₃×C₈	—	10	1	no	—
432	C₃×C₈	D₄×D₅	1	2	yes	complemented
433	C₂²×C₅	—	2	2	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	4	2	no	—
436	C₂²×C₅	—	4	2	no	—
437	C₂²×C₅	—	4	2	no	—
438	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
439	C₂×D₅	—	2	2	no	—
440	C₂×D₅	—	2	1	no	—
441	C₂×D₅	—	4	4	no	—
442	C₂×D₅	—	4	2	no	—
443	C₂×D₅	—	4	2	no	—
444	C₂×D₅	—	4	2	no	—
445	C₂×D₅	—	8	8	no	—
446	C₂×D₅	C₃×#121	1	2	yes	—
447	C₂×D₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
448	C₄×C₅	—	2	1	no	—
449	C₄×C₅	—	4	2	no	—
450	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
451	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
452	Dic₅	—	2	1	no	—
453	Dic₅	—	4	2	no	—
454	Dic₅	C₃×#121	1	2	yes	—
455	C₂⁴	—	5	1	no	—
456	C₂⁴	—	10	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	10	2	no	—
460	C₂×D₄	—	10	4	no	—
461	C₂×D₄	—	10	4	no	—
462	C₂×D₄	—	10	2	no	—
463	C₂×D₄	—	10	2	no	—
464	C₂×D₄	—	10	2	no	—
465	C₂×D₄	—	20	8	no	—
466	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
467	C₂²×C₄	—	5	1	no	—
468	C₂²×C₄	—	5	1	no	—
469	C₂²×C₄	—	5	1	no	—
470	C₂²×C₄	—	5	1	no	—
471	C₂²×C₄	—	5	1	no	—
472	C₂²×C₄	—	10	2	no	—
473	C₂²×C₄	—	10	2	no	—
474	C₂²×C₄	—	10	2	no	—
475	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
476	D₈	—	2	2	no	—
477	D₈	—	10	4	no	—
478	D₈	—	10	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	10	2	no	—
481	M₁₆	—	10	2	no	—
482	M₁₆	—	10	2	no	—
483	C₂×C₈	—	5	1	no	—
484	C₂×C₈	—	5	4	no	—
485	C₂×C₈	—	5	1	no	—
486	C₂×C₈	—	10	2	no	—
487	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
488	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
489	C₄⋊C₄	—	5	2	no	—
490	C₄⋊C₄	—	10	2	no	—
491	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	10	2	no	—
494	C₂²⋊C₄	—	10	2	no	—
495	C₂²⋊C₄	—	10	2	no	—
496	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	4	2	no	—
500	C₂²×C₃	—	4	2	no	—
501	C₂²×C₃	—	4	2	no	—
502	C₂²×C₃	—	5	4	no	—
503	C₂²×C₃	—	5	2	no	—
504	C₂²×C₃	—	10	2	no	—
505	C₂²×C₃	—	10	1	no	—
506	C₂²×C₃	—	20	4	no	—
507	C₂²×C₃	—	20	2	no	—
508	C₂²×C₃	—	20	2	no	—
509	C₂²×C₃	—	20	2	no	—
510	C₂²×C₃	—	40	8	no	—
511	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	4	2	no	—
514	C₃×C₄	—	5	2	no	—
515	C₃×C₄	—	10	1	no	—
516	C₃×C₄	—	20	2	no	—
517	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
518	C₃×C₄	D₅×#41	1	1	yes	characteristic
519	C₂×C₅	—	4	1	no	—
520	C₂×C₅	—	8	2	no	—
521	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
522	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
523	D₅	—	4	1	no	—
524	D₅	—	8	2	no	—
525	D₅	C₃×#469	1	4	yes	direct product factor
526	C₂³	—	2	2	no	—
527	C₂³	—	5	1	no	—
528	C₂³	—	5	1	no	—
529	C₂³	—	10	2	no	—
530	C₂³	—	10	4	no	—
531	C₂³	—	10	2	no	—
532	C₂³	—	20	4	no	—
533	C₂³	—	20	4	no	—
534	C₂³	—	20	4	no	—
535	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	4	4	no	—
539	D₄	—	10	2	no	—
540	D₄	—	10	2	no	—
541	D₄	—	20	4	no	—
542	D₄	—	20	4	no	—
543	D₄	—	20	4	no	—
544	D₄	—	20	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	5	1	no	—
549	C₂×C₄	—	5	2	no	—
550	C₂×C₄	—	5	2	no	—
551	C₂×C₄	—	5	1	no	—
552	C₂×C₄	—	10	2	no	—
553	C₂×C₄	—	10	2	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	10	1	no	—
556	C₂×C₄	—	10	1	no	—
557	C₂×C₄	—	10	2	no	—
558	C₂×C₄	—	20	4	no	—
559	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
560	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	5	2	no	—
563	C₈	—	10	1	no	—
564	C₈	C₃×D₄×D₅	1	2	yes	complemented
565	C₂×C₃	—	4	1	no	—
566	C₂×C₃	—	5	4	no	—
567	C₂×C₃	—	8	2	no	—
568	C₂×C₃	—	20	1	no	—
569	C₂×C₃	—	40	2	no	—
570	C₂×C₃	D₅×#121	1	1	yes	characteristic
571	C₂×C₃	D₅×AGL(1,ℤ/8)	1	2	yes	—
572	C₅	C₂×C₃×#469	1	1	yes	characteristic, complemented, Sylow
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	5	4	no	—
579	C₂²	—	5	2	no	—
580	C₂²	—	10	2	no	—
581	C₂²	—	10	1	no	—
582	C₂²	—	20	4	no	—
583	C₂²	—	20	2	no	—
584	C₂²	—	20	2	no	—
585	C₂²	—	20	2	no	—
586	C₂²	—	40	8	no	—
587	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	5	2	no	—
591	C₄	—	10	1	no	—
592	C₄	—	20	2	no	—
593	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
594	C₄	C₃×D₅×#41	1	1	yes	characteristic
595	C₃	D₅×#469	1	1	yes	characteristic, direct product factor, Sylow
596	C₂	—	4	1	no	—
597	C₂	—	5	4	no	—
598	C₂	—	8	2	no	—
599	C₂	—	20	1	no	—
600	C₂	—	40	2	no	—
601	C₂	C₃×D₅×#121	1	1	yes	characteristic
602	C₂	C₃×D₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#469	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#469	D₅
hypocenter	C₅	C₂×C₃×#469
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#469

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×D₈	C₂	semidirect
2. C₂×C₃×D₅×M₁₆	C₂	semidirect
3. C₃×D₅×#121	C₂	semidirect
4. C₃×C₅×#469	C₂	semidirect
5. C₃×#65448	C₂	semidirect
6. C₃×#65424	C₂	semidirect
7. C₃×#65328	C₂	semidirect
8. C₃×#65154	C₂	semidirect
9. C₃×D₅×#106	C₂	semidirect
10. C₃×#65071	C₂	semidirect
11. C₃×D₅×#102	C₂	semidirect
12. D₅×#469	C₃	direct (N × H)
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₃×C₅×#121	C₂²	semidirect
20. C₃×#4084	C₂²	semidirect
21. C₂×C₃×#686	C₂²	semidirect
22. C₃×#4076	C₂²	semidirect
23. C₂×C₃×#681	C₂²	semidirect
26. C₂×C₃×D₄₀	C₂²	semidirect
27. C₂×C₃×#676	C₂²	semidirect
28. C₂×C₃×#676	C₂²	semidirect
31. C₃×#4041	C₂²	semidirect
35. C₃×C₅×#106	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₃×#3964	C₂²	semidirect
38. C₃×#3953	C₂²	semidirect
39. C₃×#3949	C₂²	semidirect
40. C₃×#3941	C₂²	semidirect
41. C₃×#3940	C₂²	semidirect
43. C₂×D₅×D₈	C₂×C₃	semidirect
44. C₂×D₅×M₁₆	C₂×C₃	semidirect
45. D₅×#121	C₂×C₃	semidirect
46. C₅×#469	C₂×C₃	semidirect
47. #65448	C₂×C₃	semidirect
48. #65424	C₂×C₃	semidirect
49. #65328	C₂×C₃	semidirect
50. #65154	C₂×C₃	semidirect
51. D₅×#106	C₂×C₃	semidirect
52. #65071	C₂×C₃	semidirect
53. D₅×#102	C₂×C₃	semidirect
94. C₃×C₈×D₅	D₄	semidirect
103. C₃×#469	D₅	direct (N × H)
109. C₂×C₅×D₈	C₂²×C₃	semidirect
110. C₂×C₅×M₁₆	C₂²×C₃	semidirect
111. C₅×#121	C₂²×C₃	semidirect
113. #4084	C₂²×C₃	semidirect
114. C₂×#686	C₂²×C₃	semidirect
115. #4076	C₂²×C₃	semidirect
116. C₂×#681	C₂²×C₃	semidirect
119. C₂×D₄₀	C₂²×C₃	semidirect
120. C₂×#676	C₂²×C₃	semidirect
121. C₂×#676	C₂²×C₃	semidirect
124. #4041	C₂²×C₃	semidirect
128. C₅×#106	C₂²×C₃	semidirect
129. C₅×#102	C₂²×C₃	semidirect
130. #3964	C₂²×C₃	semidirect
131. #3953	C₂²×C₃	semidirect
132. #3949	C₂²×C₃	semidirect
133. #3941	C₂²×C₃	semidirect
134. #3940	C₂²×C₃	semidirect
172. C₃×C₅×C₈	C₂×D₄	semidirect
174. C₃×#168	C₂×D₄	semidirect
181. C₂×C₃×D₈	C₂×D₅	semidirect
186. C₂×C₃×M₁₆	C₂×D₅	semidirect
194. C₃×#121	C₂×D₅	semidirect
199. C₃×#106	C₂×D₅	semidirect
203. C₃×#102	C₂×D₅	semidirect
244. C₈×D₅	C₃×D₄	semidirect
253. #469	C₃×D₅	direct (N × H)
355. C₅×C₈	C₂×C₃×D₄	semidirect
357. #168	C₂×C₃×D₄	semidirect
364. C₂×D₈	C₂×C₃×D₅	semidirect
369. C₂×M₁₆	C₂×C₃×D₅	semidirect
377. #121	C₂×C₃×D₅	semidirect
382. #106	C₂×C₃×D₅	semidirect
386. #102	C₂×C₃×D₅	semidirect
393. C₃×D₅	#469	direct (N × H)
432. C₃×C₈	D₄×D₅	semidirect
496. C₃×C₅	C₂×#469	semidirect
525. D₅	C₃×#469	direct (N × H)
564. C₈	C₃×D₄×D₅	semidirect
572. C₅	C₂×C₃×#469	semidirect
595. C₃	D₅×#469	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×D₈	2
C₂×C₃×D₅×M₁₆	2
C₃×D₅×#121	2
C₃×C₅×#469	2
C₃×#65448	2
C₃×#65424	2
C₃×#65328	2
C₃×#65154	2
C₃×D₅×#106	2
C₃×#65071	2
C₃×D₅×#102	2
D₅×#469	3
C₂×C₃×#469	5

Subgroups — C3×D5×#469 #14427973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#469 #14427973