Subgroups — C₃×D₅×#466 #14427673

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 624 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	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65446	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65404	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65327	C₂	1	2	yes	maximal, complemented
8	C₃×#65172	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65064	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
12	D₅×#466	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	C₂²×C₃×C₅×C₈	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	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
24	C₃×D₅×D₈	—	2	4	no	—
25	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₈×D₅	—	2	4	no	—
27	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
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×#107	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×#3950	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3941	C₂²	1	2	yes	complemented
41	C₃×#3939	C₂²	1	2	yes	complemented
42	C₂×C₃×#466	—	5	1	no	maximal, Hall
43	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
45	D₅×#121	C₂×C₃	1	2	yes	complemented
46	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
47	#65446	C₂×C₃	1	1	yes	characteristic, complemented
48	#65404	C₂×C₃	1	1	yes	characteristic, complemented
49	#65327	C₂×C₃	1	2	yes	complemented
50	#65172	C₂×C₃	1	1	yes	characteristic, complemented
51	D₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
52	#65064	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	C₂×C₃×C₅×C₈	—	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	C₂×C₃×#168	—	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×C₈×D₅	—	2	2	no	—
92	C₃×C₈×D₅	—	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	C₂³×C₃×C₈	—	5	1	no	—
97	C₂×C₃×#121	—	5	2	no	—
98	C₃×#466	—	5	1	no	—
99	C₃×#466	—	5	1	no	—
100	C₃×#466	—	5	2	no	—
101	C₃×#466	—	5	1	no	—
102	C₃×#466	—	5	2	no	—
103	C₃×#466	D₅	1	1	yes	characteristic, direct product factor
104	C₂×C₃×#107	—	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	C₂²×C₅×C₈	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	C₂²×#168	C₂²×C₃	1	1	yes	characteristic, complemented
117	D₅×D₈	—	2	4	no	—
118	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₂×C₈×D₅	—	2	4	no	—
120	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
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×#107	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	#3950	C₂²×C₃	1	1	yes	characteristic, complemented
133	#3941	C₂²×C₃	1	2	yes	complemented
134	#3939	C₂²×C₃	1	2	yes	complemented
135	C₂×#466	—	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	2	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	D₈	1	4	yes	complemented
145	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	2	no	—
149	C₃×C₅×D₄	—	4	4	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₃×C₂²⋊D₅	—	4	4	no	—
156	C₃×C₂²⋊D₅	—	4	4	no	—
157	C₃×C₂²⋊D₅	—	4	4	no	—
158	C₂×C₃×Dic₅	—	2	2	no	—
159	C₂×C₃×Dic₅	—	2	2	no	—
160	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
162	C₃×D₂₀	—	2	2	no	—
163	C₃×D₂₀	—	2	2	no	—
164	C₃×D₂₀	—	4	4	no	—
165	C₃×C₄×D₅	—	2	2	no	—
166	C₃×C₄×D₅	—	2	1	no	—
167	C₃×C₄×D₅	—	2	1	no	—
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×C₄×D₅	—	4	4	no	—
170	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
171	C₃×C₄×D₅	#41	1	2	yes	—
172	C₃×C₅×C₈	—	2	1	no	—
173	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
174	C₃×#168	—	2	1	no	—
175	C₃×#168	C₂×D₄	1	2	yes	complemented
176	C₂²×C₃×D₄	—	5	2	no	—
177	C₂²×C₃×D₄	—	10	2	no	—
178	C₂³×C₃×C₄	—	5	1	no	—
179	C₂×C₃×D₈	—	5	2	no	—
180	C₂×C₃×D₈	—	5	1	no	—
181	C₂×C₃×D₈	—	10	4	no	—
182	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
183	C₂²×C₃×C₈	—	5	1	no	—
184	C₂²×C₃×C₈	—	5	1	no	—
185	C₂²×C₃×C₈	—	5	1	no	—
186	C₂²×C₃×C₈	—	5	1	no	—
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₂²×C₃×C₈	—	10	4	no	—
189	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
190	C₃×#121	—	5	2	no	—
191	C₃×#121	—	5	2	no	—
192	C₃×#121	—	5	2	no	—
193	C₃×#121	—	10	2	no	—
194	C₃×#121	—	10	2	no	—
195	C₃×#121	C₂×D₅	1	2	yes	complemented
196	C₂×C₃×C₄⋊C₄	—	5	2	no	—
197	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
198	C₃×#107	—	5	1	no	—
199	C₃×#107	—	5	2	no	—
200	C₃×#107	C₂×D₅	1	1	yes	characteristic, complemented
201	C₃×#102	—	5	2	no	—
202	C₃×#102	—	5	2	no	—
203	C₃×#102	—	5	2	no	—
204	C₃×#102	C₂×D₅	1	2	yes	complemented
205	C₂³×D₅	—	2	2	no	—
206	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₂²⋊D₅	—	2	2	no	—
211	C₂×C₂²⋊D₅	—	2	2	no	—
212	C₂×C₂²⋊D₅	—	2	2	no	—
213	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
214	D₄×D₅	—	2	4	no	—
215	D₄×D₅	—	2	4	no	—
216	D₄×D₅	—	4	8	no	—
217	C₂×D₂₀	—	2	2	no	—
218	C₂×D₂₀	C₂³×C₃	1	2	yes	—
219	C₂×C₄×D₅	—	2	2	no	—
220	C₂×C₄×D₅	—	2	2	no	—
221	C₂×C₄×D₅	—	2	2	no	—
222	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
224	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
226	C₅×D₈	—	2	2	no	—
227	C₂×C₅×C₈	—	2	2	no	—
228	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
231	C₅×C₂²⋊C₄	—	2	2	no	—
232	C₂²⋊Dic₅	—	2	2	no	—
233	#686	—	2	4	no	—
234	#685	—	2	2	no	—
235	#685	—	2	2	no	—
236	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
237	#683	—	2	2	no	—
238	C₂×#168	—	2	2	no	—
239	C₂×#168	C₂³×C₃	1	1	yes	characteristic
240	C₂×#168	C₂³×C₃	1	1	yes	characteristic
241	D₄₀	—	2	2	no	—
242	C₈×D₅	—	2	2	no	—
243	C₈×D₅	—	2	2	no	—
244	C₈×D₅	—	2	2	no	—
245	C₈×D₅	C₃×D₄	1	4	yes	complemented
246	C₂²×D₈	—	5	1	no	—
247	C₂³×C₈	—	5	1	no	—
248	C₂×#121	—	5	2	no	—
249	#466	—	5	1	no	—
250	#466	—	5	1	no	—
251	#466	—	5	2	no	—
252	#466	—	5	1	no	—
253	#466	—	5	2	no	—
254	#466	C₃×D₅	1	1	yes	characteristic, direct product factor
255	C₂×#107	—	5	1	no	—
256	C₂×#102	—	5	2	no	—
257	C₂²×C₃×C₅	—	2	1	no	—
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	—	4	2	no	—
261	C₂²×C₃×C₅	—	4	2	no	—
262	C₂²×C₃×C₅	C₂×D₈	1	2	yes	complemented
263	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₃×D₅	—	2	1	no	—
265	C₂×C₃×D₅	—	2	1	no	—
266	C₂×C₃×D₅	—	2	8	no	—
267	C₂×C₃×D₅	—	4	2	no	—
268	C₂×C₃×D₅	—	4	2	no	—
269	C₂×C₃×D₅	—	4	2	no	—
270	C₂×C₃×D₅	—	8	8	no	—
271	C₂×C₃×D₅	#121	1	2	yes	—
272	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
273	C₂×C₃×D₅	C₂×D₈	1	2	yes	complemented
274	C₂×C₃×D₅	#135	1	2	yes	—
275	C₃×C₄×C₅	—	2	1	no	—
276	C₃×C₄×C₅	—	4	2	no	—
277	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
279	C₃×Dic₅	—	2	1	no	—
280	C₃×Dic₅	—	4	2	no	—
281	C₃×Dic₅	#121	1	2	yes	—
282	C₂⁴×C₃	—	5	1	no	—
283	C₂⁴×C₃	—	10	2	no	—
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	—	5	2	no	—
286	C₂×C₃×D₄	—	10	2	no	—
287	C₂×C₃×D₄	—	10	4	no	—
288	C₂×C₃×D₄	—	10	4	no	—
289	C₂×C₃×D₄	—	10	2	no	—
290	C₂×C₃×D₄	—	10	2	no	—
291	C₂×C₃×D₄	—	10	2	no	—
292	C₂×C₃×D₄	—	20	8	no	—
293	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	5	1	no	—
296	C₂²×C₃×C₄	—	5	1	no	—
297	C₂²×C₃×C₄	—	5	1	no	—
298	C₂²×C₃×C₄	—	5	1	no	—
299	C₂²×C₃×C₄	—	10	2	no	—
300	C₂²×C₃×C₄	—	10	2	no	—
301	C₂²×C₃×C₄	—	10	2	no	—
302	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
303	C₃×D₈	—	2	2	no	—
304	C₃×D₈	—	10	4	no	—
305	C₃×D₈	—	10	2	no	—
306	C₂×C₃×C₈	—	2	2	no	—
307	C₂×C₃×C₈	—	5	1	no	—
308	C₂×C₃×C₈	—	5	4	no	—
309	C₂×C₃×C₈	—	5	1	no	—
310	C₂×C₃×C₈	—	10	2	no	—
311	C₂×C₃×C₈	—	10	2	no	—
312	C₂×C₃×C₈	—	10	2	no	—
313	C₂×C₃×C₈	—	10	2	no	—
314	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
315	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
316	C₃×C₄⋊C₄	—	5	2	no	—
317	C₃×C₄⋊C₄	—	10	2	no	—
318	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
319	C₃×C₂²⋊C₄	—	2	2	no	—
320	C₃×C₂²⋊C₄	—	10	2	no	—
321	C₃×C₂²⋊C₄	—	10	2	no	—
322	C₃×C₂²⋊C₄	—	10	2	no	—
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂²×D₅	—	2	2	no	—
326	C₂²×D₅	—	2	2	no	—
327	C₂²×D₅	—	2	2	no	—
328	C₂²×D₅	—	4	4	no	—
329	C₂²×D₅	—	4	4	no	—
330	C₂²×D₅	—	4	4	no	—
331	C₂²×D₅	C₃×D₈	1	4	yes	complemented
332	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₅×D₄	—	2	2	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	4	4	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
342	C₂²⋊D₅	—	4	4	no	—
343	C₂²⋊D₅	—	4	4	no	—
344	C₂²⋊D₅	—	4	4	no	—
345	C₂×Dic₅	—	2	2	no	—
346	C₂×Dic₅	—	2	2	no	—
347	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
348	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
349	D₂₀	—	2	2	no	—
350	D₂₀	—	2	2	no	—
351	D₂₀	—	4	4	no	—
352	C₄×D₅	—	2	2	no	—
353	C₄×D₅	—	2	1	no	—
354	C₄×D₅	—	2	1	no	—
355	C₄×D₅	—	2	2	no	—
356	C₄×D₅	—	4	4	no	—
357	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
358	C₄×D₅	C₃×#41	1	2	yes	—
359	C₅×C₈	—	2	1	no	—
360	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
361	#168	—	2	1	no	—
362	#168	C₂×C₃×D₄	1	2	yes	complemented
363	C₂²×D₄	—	5	2	no	—
364	C₂²×D₄	—	10	2	no	—
365	C₂³×C₄	—	5	1	no	—
366	C₂×D₈	—	5	2	no	—
367	C₂×D₈	—	5	1	no	—
368	C₂×D₈	—	10	4	no	—
369	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
370	C₂²×C₈	—	5	1	no	—
371	C₂²×C₈	—	5	1	no	—
372	C₂²×C₈	—	5	1	no	—
373	C₂²×C₈	—	5	1	no	—
374	C₂²×C₈	—	5	1	no	—
375	C₂²×C₈	—	10	4	no	—
376	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	10	2	no	—
381	#121	—	10	2	no	—
382	#121	C₂×C₃×D₅	1	2	yes	complemented
383	C₂×C₄⋊C₄	—	5	2	no	—
384	C₂×C₂²⋊C₄	—	10	2	no	—
385	#107	—	5	1	no	—
386	#107	—	5	2	no	—
387	#107	C₂×C₃×D₅	1	1	yes	characteristic, complemented
388	#102	—	5	2	no	—
389	#102	—	5	2	no	—
390	#102	—	5	2	no	—
391	#102	C₂×C₃×D₅	1	2	yes	complemented
392	C₂×C₃×C₅	—	2	2	no	—
393	C₂×C₃×C₅	—	8	2	no	—
394	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
395	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
396	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
397	C₃×D₅	—	2	2	no	—
398	C₃×D₅	—	8	2	no	—
399	C₃×D₅	#466	1	4	yes	direct product factor
400	C₂³×C₃	—	2	2	no	—
401	C₂³×C₃	—	5	1	no	—
402	C₂³×C₃	—	5	1	no	—
403	C₂³×C₃	—	5	4	no	—
404	C₂³×C₃	—	10	2	no	—
405	C₂³×C₃	—	10	2	no	—
406	C₂³×C₃	—	10	2	no	—
407	C₂³×C₃	—	20	4	no	—
408	C₂³×C₃	—	20	4	no	—
409	C₂³×C₃	—	20	4	no	—
410	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
411	C₃×D₄	—	2	2	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	4	4	no	—
414	C₃×D₄	—	10	2	no	—
415	C₃×D₄	—	10	2	no	—
416	C₃×D₄	—	20	4	no	—
417	C₃×D₄	—	20	4	no	—
418	C₃×D₄	—	20	4	no	—
419	C₃×D₄	—	20	4	no	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	5	1	no	—
424	C₂×C₃×C₄	—	5	2	no	—
425	C₂×C₃×C₄	—	5	2	no	—
426	C₂×C₃×C₄	—	5	1	no	—
427	C₂×C₃×C₄	—	10	2	no	—
428	C₂×C₃×C₄	—	10	2	no	—
429	C₂×C₃×C₄	—	10	2	no	—
430	C₂×C₃×C₄	—	10	1	no	—
431	C₂×C₃×C₄	—	10	1	no	—
432	C₂×C₃×C₄	—	10	2	no	—
433	C₂×C₃×C₄	—	20	4	no	—
434	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
436	C₃×C₈	—	2	1	no	—
437	C₃×C₈	—	5	2	no	—
438	C₃×C₈	—	10	1	no	—
439	C₃×C₈	D₄×D₅	1	2	yes	complemented
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	C₂×C₃×D₈	1	2	yes	complemented
446	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
447	C₂×D₅	—	2	1	no	—
448	C₂×D₅	—	2	1	no	—
449	C₂×D₅	—	2	8	no	—
450	C₂×D₅	—	4	2	no	—
451	C₂×D₅	—	4	2	no	—
452	C₂×D₅	—	4	2	no	—
453	C₂×D₅	—	8	8	no	—
454	C₂×D₅	C₃×#121	1	2	yes	—
455	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
456	C₂×D₅	C₂×C₃×D₈	1	2	yes	complemented
457	C₂×D₅	C₃×#135	1	2	yes	—
458	C₄×C₅	—	2	1	no	—
459	C₄×C₅	—	4	2	no	—
460	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
461	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
462	Dic₅	—	2	1	no	—
463	Dic₅	—	4	2	no	—
464	Dic₅	C₃×#121	1	2	yes	—
465	C₂⁴	—	5	1	no	—
466	C₂⁴	—	10	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	5	2	no	—
469	C₂×D₄	—	10	2	no	—
470	C₂×D₄	—	10	4	no	—
471	C₂×D₄	—	10	4	no	—
472	C₂×D₄	—	10	2	no	—
473	C₂×D₄	—	10	2	no	—
474	C₂×D₄	—	10	2	no	—
475	C₂×D₄	—	20	8	no	—
476	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
477	C₂²×C₄	—	5	1	no	—
478	C₂²×C₄	—	5	1	no	—
479	C₂²×C₄	—	5	1	no	—
480	C₂²×C₄	—	5	1	no	—
481	C₂²×C₄	—	5	1	no	—
482	C₂²×C₄	—	10	2	no	—
483	C₂²×C₄	—	10	2	no	—
484	C₂²×C₄	—	10	2	no	—
485	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
486	D₈	—	2	2	no	—
487	D₈	—	10	4	no	—
488	D₈	—	10	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	5	1	no	—
491	C₂×C₈	—	5	4	no	—
492	C₂×C₈	—	5	1	no	—
493	C₂×C₈	—	10	2	no	—
494	C₂×C₈	—	10	2	no	—
495	C₂×C₈	—	10	2	no	—
496	C₂×C₈	—	10	2	no	—
497	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
498	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	10	2	no	—
501	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	10	2	no	—
504	C₂²⋊C₄	—	10	2	no	—
505	C₂²⋊C₄	—	10	2	no	—
506	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	—	4	2	no	—
512	C₂²×C₃	—	5	2	no	—
513	C₂²×C₃	—	5	2	no	—
514	C₂²×C₃	—	5	2	no	—
515	C₂²×C₃	—	5	2	no	—
516	C₂²×C₃	—	10	8	no	—
517	C₂²×C₃	—	10	1	no	—
518	C₂²×C₃	—	10	1	no	—
519	C₂²×C₃	—	20	2	no	—
520	C₂²×C₃	—	20	2	no	—
521	C₂²×C₃	—	20	2	no	—
522	C₂²×C₃	—	40	8	no	—
523	C₂²×C₃	D₅×D₈	1	2	yes	complemented
524	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	4	2	no	—
527	C₃×C₄	—	5	2	no	—
528	C₃×C₄	—	10	1	no	—
529	C₃×C₄	—	20	2	no	—
530	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
531	C₃×C₄	D₅×#41	1	1	yes	characteristic
532	C₂×C₅	—	2	2	no	—
533	C₂×C₅	—	8	2	no	—
534	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
535	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
536	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
537	D₅	—	2	2	no	—
538	D₅	—	8	2	no	—
539	D₅	C₃×#466	1	4	yes	direct product factor
540	C₂³	—	2	2	no	—
541	C₂³	—	5	1	no	—
542	C₂³	—	5	1	no	—
543	C₂³	—	5	4	no	—
544	C₂³	—	10	2	no	—
545	C₂³	—	10	2	no	—
546	C₂³	—	10	2	no	—
547	C₂³	—	20	4	no	—
548	C₂³	—	20	4	no	—
549	C₂³	—	20	4	no	—
550	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	4	no	—
554	D₄	—	10	2	no	—
555	D₄	—	10	2	no	—
556	D₄	—	20	4	no	—
557	D₄	—	20	4	no	—
558	D₄	—	20	4	no	—
559	D₄	—	20	4	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	5	1	no	—
564	C₂×C₄	—	5	2	no	—
565	C₂×C₄	—	5	2	no	—
566	C₂×C₄	—	5	1	no	—
567	C₂×C₄	—	10	2	no	—
568	C₂×C₄	—	10	2	no	—
569	C₂×C₄	—	10	2	no	—
570	C₂×C₄	—	10	1	no	—
571	C₂×C₄	—	10	1	no	—
572	C₂×C₄	—	10	2	no	—
573	C₂×C₄	—	20	4	no	—
574	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	5	2	no	—
578	C₈	—	10	1	no	—
579	C₈	C₃×D₄×D₅	1	2	yes	complemented
580	C₂×C₃	—	2	2	no	—
581	C₂×C₃	—	5	4	no	—
582	C₂×C₃	—	8	2	no	—
583	C₂×C₃	—	10	2	no	—
584	C₂×C₃	—	40	2	no	—
585	C₂×C₃	D₅×#121	1	1	yes	characteristic
586	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
587	C₂×C₃	D₅×#135	1	1	yes	characteristic
588	C₅	C₂×C₃×#466	1	1	yes	characteristic, complemented, Sylow
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	5	2	no	—
595	C₂²	—	5	2	no	—
596	C₂²	—	5	2	no	—
597	C₂²	—	5	2	no	—
598	C₂²	—	10	8	no	—
599	C₂²	—	10	1	no	—
600	C₂²	—	10	1	no	—
601	C₂²	—	20	2	no	—
602	C₂²	—	20	2	no	—
603	C₂²	—	20	2	no	—
604	C₂²	—	40	8	no	—
605	C₂²	C₃×D₅×D₈	1	2	yes	complemented
606	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	5	2	no	—
610	C₄	—	10	1	no	—
611	C₄	—	20	2	no	—
612	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
613	C₄	C₃×D₅×#41	1	1	yes	characteristic
614	C₃	D₅×#466	1	1	yes	characteristic, direct product factor, Sylow
615	C₂	—	2	2	no	—
616	C₂	—	5	4	no	—
617	C₂	—	8	2	no	—
618	C₂	—	10	2	no	—
619	C₂	—	40	2	no	—
620	C₂	C₃×D₅×#121	1	1	yes	characteristic
621	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic
622	C₂	C₃×D₅×#135	1	1	yes	characteristic

	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×#466	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#466	D₅
hypocenter	C₅	C₂×C₃×#466
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#466

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×D₈	C₂	semidirect
2. C₂²×C₃×C₈×D₅	C₂	semidirect
3. C₃×D₅×#121	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₃×#65446	C₂	semidirect
6. C₃×#65404	C₂	semidirect
7. C₃×#65327	C₂	semidirect
8. C₃×#65172	C₂	semidirect
9. C₃×D₅×#107	C₂	semidirect
10. C₃×#65064	C₂	semidirect
11. C₃×D₅×#102	C₂	semidirect
12. D₅×#466	C₃	direct (N × H)
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	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. C₂²×C₃×#168	C₂²	semidirect
25. C₂×C₃×D₄₀	C₂²	semidirect
29. C₂×C₃×C₈×D₅	C₂²	semidirect
30. C₂×C₃×C₈×D₅	C₂²	semidirect
31. C₃×#4041	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₃×#3964	C₂²	semidirect
38. C₃×#3953	C₂²	semidirect
39. C₃×#3950	C₂²	semidirect
40. C₃×#3941	C₂²	semidirect
41. C₃×#3939	C₂²	semidirect
43. C₂×D₅×D₈	C₂×C₃	semidirect
44. C₂²×C₈×D₅	C₂×C₃	semidirect
45. D₅×#121	C₂×C₃	semidirect
46. C₅×#466	C₂×C₃	semidirect
47. #65446	C₂×C₃	semidirect
48. #65404	C₂×C₃	semidirect
49. #65327	C₂×C₃	semidirect
50. #65172	C₂×C₃	semidirect
51. D₅×#107	C₂×C₃	semidirect
52. #65064	C₂×C₃	semidirect
53. D₅×#102	C₂×C₃	semidirect
94. C₃×C₈×D₅	D₄	semidirect
103. C₃×#466	D₅	direct (N × H)
109. C₂×C₅×D₈	C₂²×C₃	semidirect
110. C₂²×C₅×C₈	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. C₂²×#168	C₂²×C₃	semidirect
118. C₂×D₄₀	C₂²×C₃	semidirect
122. C₂×C₈×D₅	C₂²×C₃	semidirect
123. C₂×C₈×D₅	C₂²×C₃	semidirect
124. #4041	C₂²×C₃	semidirect
128. C₅×#107	C₂²×C₃	semidirect
129. C₅×#102	C₂²×C₃	semidirect
130. #3964	C₂²×C₃	semidirect
131. #3953	C₂²×C₃	semidirect
132. #3950	C₂²×C₃	semidirect
133. #3941	C₂²×C₃	semidirect
134. #3939	C₂²×C₃	semidirect
144. C₂²×C₃×D₅	D₈	semidirect
173. C₃×C₅×C₈	C₂×D₄	semidirect
175. C₃×#168	C₂×D₄	semidirect
182. C₂×C₃×D₈	C₂×D₅	semidirect
189. C₂²×C₃×C₈	C₂×D₅	semidirect
195. C₃×#121	C₂×D₅	semidirect
200. C₃×#107	C₂×D₅	semidirect
204. C₃×#102	C₂×D₅	semidirect
245. C₈×D₅	C₃×D₄	semidirect
254. #466	C₃×D₅	direct (N × H)
262. C₂²×C₃×C₅	C₂×D₈	semidirect
273. C₂×C₃×D₅	C₂×D₈	semidirect
331. C₂²×D₅	C₃×D₈	semidirect
360. C₅×C₈	C₂×C₃×D₄	semidirect
362. #168	C₂×C₃×D₄	semidirect
369. C₂×D₈	C₂×C₃×D₅	semidirect
376. C₂²×C₈	C₂×C₃×D₅	semidirect
382. #121	C₂×C₃×D₅	semidirect
387. #107	C₂×C₃×D₅	semidirect
391. #102	C₂×C₃×D₅	semidirect
399. C₃×D₅	#466	direct (N × H)
439. C₃×C₈	D₄×D₅	semidirect
445. C₂²×C₅	C₂×C₃×D₈	semidirect
456. C₂×D₅	C₂×C₃×D₈	semidirect
506. C₃×C₅	C₂×#466	semidirect
523. C₂²×C₃	D₅×D₈	semidirect
539. D₅	C₃×#466	direct (N × H)
579. C₈	C₃×D₄×D₅	semidirect
588. C₅	C₂×C₃×#466	semidirect
605. C₂²	C₃×D₅×D₈	semidirect
614. C₃	D₅×#466	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
C₂²×C₃×C₈×D₅	2
C₃×D₅×#121	2
C₃×C₅×#466	2
C₃×#65446	2
C₃×#65404	2
C₃×#65327	2
C₃×#65172	2
C₃×D₅×#107	2
C₃×#65064	2
C₃×D₅×#102	2
D₅×#466	3
C₂×C₃×#466	5

Subgroups — C3×D5×#466 #14427673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#466 #14427673