Subgroups — C₃×D₅×#467 #14427730

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65405	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65340	C₂	1	2	yes	maximal, complemented
8	C₃×#65176	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65102	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#103	C₂	1	2	yes	maximal, complemented
12	D₅×#467	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₃×#4092	C₂²	1	2	yes	—
19	C₂×C₃×#689	C₂²	1	2	yes	complemented
20	C₃×#4070	C₂²	1	2	yes	—
21	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
22	C₃×D₅×Q₁₆	—	2	4	no	—
23	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₈×D₅	—	2	4	no	—
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₃×#4043	C₂²	1	2	yes	—
30	C₃×#4042	—	2	2	no	—
31	C₃×D₅×C₄⋊C₄	—	2	2	no	—
32	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
34	C₃×#4024	—	2	2	no	—
35	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#103	C₂²	1	2	yes	complemented
37	C₃×#3967	C₂²	1	2	yes	complemented
38	C₃×#3950	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3948	C₂²	1	2	yes	complemented
40	C₃×#3942	C₂²	1	2	yes	complemented
41	C₃×#3939	C₂²	1	2	yes	complemented
42	C₂×C₃×#467	—	5	1	no	maximal, Hall
43	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
45	D₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
46	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
47	#65477	C₂×C₃	1	1	yes	characteristic, complemented
48	#65405	C₂×C₃	1	1	yes	characteristic, complemented
49	#65340	C₂×C₃	1	2	yes	complemented
50	#65176	C₂×C₃	1	1	yes	characteristic, complemented
51	D₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
52	#65102	C₂×C₃	1	2	yes	complemented
53	D₅×#103	C₂×C₃	1	2	yes	complemented
54	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
58	C₃×Q₈×D₅	—	2	4	no	—
59	C₃×Q₈×D₅	—	2	4	no	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	—	2	2	no	—
64	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₁₀	—	2	2	no	—
69	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
70	C₃×C₅×Q₁₆	—	2	2	no	—
71	C₂×C₃×C₅×C₈	—	2	2	no	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₂²⋊Dic₅	—	2	2	no	—
78	C₃×#689	—	2	4	no	—
79	C₃×#685	—	2	2	no	—
80	C₃×#685	—	2	2	no	—
81	C₃×C₄⋊Dic₅	—	2	2	no	—
82	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
83	C₃×#683	—	2	2	no	—
84	C₃×#683	—	2	2	no	—
85	C₃×#683	—	2	2	no	—
86	C₂×C₃×#168	—	2	2	no	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×Dic₂₀	—	2	2	no	—
90	C₃×C₈×D₅	—	2	2	no	—
91	C₃×C₈×D₅	—	2	2	no	—
92	C₃×C₈×D₅	—	2	2	no	—
93	C₃×C₈×D₅	D₄	1	4	yes	—
94	C₂²×C₃×Q₁₆	—	5	1	no	—
95	C₂³×C₃×C₈	—	5	1	no	—
96	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
97	C₃×#467	—	5	1	no	—
98	C₃×#467	—	5	1	no	—
99	C₃×#467	—	5	2	no	—
100	C₃×#467	—	5	1	no	—
101	C₃×#467	—	5	2	no	—
102	C₃×#467	D₅	1	1	yes	characteristic, direct product factor
103	C₂×C₃×#107	—	5	1	no	—
104	C₂×C₃×#103	—	5	2	no	—
105	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
106	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
110	#4092	C₂²×C₃	1	2	yes	—
111	C₂×#689	C₂²×C₃	1	2	yes	complemented
112	#4070	C₂²×C₃	1	2	yes	—
113	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
114	D₅×Q₁₆	—	2	4	no	—
115	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₂×C₈×D₅	—	2	4	no	—
117	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
121	#4043	C₂²×C₃	1	2	yes	—
122	#4042	—	2	2	no	—
123	D₅×C₄⋊C₄	—	2	2	no	—
124	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
125	D₅×C₂²⋊C₄	—	2	2	no	—
126	#4024	—	2	2	no	—
127	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₅×#103	C₂²×C₃	1	2	yes	complemented
129	#3967	C₂²×C₃	1	2	yes	complemented
130	#3950	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3948	C₂²×C₃	1	2	yes	complemented
132	#3942	C₂²×C₃	1	2	yes	complemented
133	#3939	C₂²×C₃	1	2	yes	complemented
134	C₂×#467	—	5	1	no	Sylow
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₃×D₅	—	2	2	no	—
137	C₂²×C₃×D₅	—	2	2	no	—
138	C₂²×C₃×D₅	Q₁₆	1	4	yes	complemented
139	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₂×C₃×Dic₅	—	2	2	no	—
150	C₂×C₃×Dic₅	—	2	2	no	—
151	C₂×C₃×Dic₅	—	2	2	no	—
152	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
154	C₃×C₄×D₅	—	2	2	no	—
155	C₃×C₄×D₅	—	2	1	no	—
156	C₃×C₄×D₅	—	2	1	no	—
157	C₃×C₄×D₅	—	2	2	no	—
158	C₃×C₄×D₅	—	4	4	no	—
159	C₃×C₄×D₅	—	4	4	no	—
160	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
161	C₃×C₄×D₅	#41	1	2	yes	—
162	C₃×Dic₁₀	—	2	2	no	—
163	C₃×Dic₁₀	—	2	2	no	—
164	C₃×Dic₁₀	—	4	4	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
167	C₃×#168	—	2	1	no	—
168	C₃×#168	C₂×D₄	1	2	yes	—
169	C₂²×C₃×Q₈	—	5	2	no	—
170	C₂³×C₃×C₄	—	5	1	no	—
171	C₂×C₃×Q₁₆	—	5	2	no	—
172	C₂×C₃×Q₁₆	—	5	1	no	—
173	C₂×C₃×Q₁₆	—	10	4	no	—
174	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
175	C₂²×C₃×C₈	—	5	1	no	—
176	C₂²×C₃×C₈	—	5	1	no	—
177	C₂²×C₃×C₈	—	5	1	no	—
178	C₂²×C₃×C₈	—	5	1	no	—
179	C₂²×C₃×C₈	—	5	1	no	—
180	C₂²×C₃×C₈	—	10	4	no	—
181	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
182	C₃×C₂²⋊Q₈	—	5	2	no	—
183	C₃×C₂²⋊Q₈	—	5	2	no	—
184	C₃×C₂²⋊Q₈	—	5	2	no	—
185	C₃×C₂²⋊Q₈	—	10	2	no	—
186	C₃×C₂²⋊Q₈	—	10	2	no	—
187	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	—	5	2	no	—
189	C₂×C₃×C₄⋊C₄	—	10	2	no	—
190	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
191	C₃×#107	—	5	1	no	—
192	C₃×#107	—	5	2	no	—
193	C₃×#107	C₂×D₅	1	1	yes	characteristic, complemented
194	C₃×#103	—	5	2	no	—
195	C₃×#103	—	5	2	no	—
196	C₃×#103	—	5	2	no	—
197	C₃×#103	C₂×D₅	1	2	yes	complemented
198	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
199	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
200	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
202	Q₈×D₅	—	2	4	no	—
203	Q₈×D₅	—	2	4	no	—
204	C₂×C₄×D₅	—	2	2	no	—
205	C₂×C₄×D₅	—	2	2	no	—
206	C₂×C₄×D₅	—	2	2	no	—
207	C₂×C₄×D₅	—	2	2	no	—
208	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
209	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
210	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
212	C₂×Dic₁₀	—	2	2	no	—
213	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
214	C₅×Q₁₆	—	2	2	no	—
215	C₂×C₅×C₈	—	2	2	no	—
216	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₅×C₄⋊C₄	—	2	2	no	—
219	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
220	C₅×C₂²⋊C₄	—	2	2	no	—
221	C₂²⋊Dic₅	—	2	2	no	—
222	#689	—	2	4	no	—
223	#685	—	2	2	no	—
224	#685	—	2	2	no	—
225	C₄⋊Dic₅	—	2	2	no	—
226	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
227	#683	—	2	2	no	—
228	#683	—	2	2	no	—
229	#683	—	2	2	no	—
230	C₂×#168	—	2	2	no	—
231	C₂×#168	C₂³×C₃	1	1	yes	characteristic
232	C₂×#168	C₂³×C₃	1	1	yes	characteristic
233	Dic₂₀	—	2	2	no	—
234	C₈×D₅	—	2	2	no	—
235	C₈×D₅	—	2	2	no	—
236	C₈×D₅	—	2	2	no	—
237	C₈×D₅	C₃×D₄	1	4	yes	—
238	C₂²×Q₁₆	—	5	1	no	—
239	C₂³×C₈	—	5	1	no	—
240	C₂×C₂²⋊Q₈	—	5	2	no	—
241	#467	—	5	1	no	—
242	#467	—	5	1	no	—
243	#467	—	5	2	no	—
244	#467	—	5	1	no	—
245	#467	—	5	2	no	—
246	#467	C₃×D₅	1	1	yes	characteristic, direct product factor
247	C₂×#107	—	5	1	no	—
248	C₂×#103	—	5	2	no	—
249	C₂²×C₃×C₅	—	2	1	no	—
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	complemented
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₃×D₅	—	2	1	no	—
254	C₂×C₃×D₅	—	2	1	no	—
255	C₂×C₃×D₅	—	2	8	no	—
256	C₂×C₃×D₅	#121	1	2	yes	—
257	C₂×C₃×D₅	C₂×Q₁₆	1	2	yes	—
258	C₂×C₃×D₅	C₂×Q₁₆	1	2	yes	complemented
259	C₂×C₃×D₅	#135	1	2	yes	—
260	C₃×C₄×C₅	—	2	1	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	—	4	2	no	—
263	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₃×Dic₅	—	2	1	no	—
266	C₃×Dic₅	—	4	2	no	—
267	C₃×Dic₅	—	4	2	no	—
268	C₃×Dic₅	#121	1	2	yes	—
269	C₂⁴×C₃	—	5	1	no	—
270	C₂×C₃×Q₈	—	5	2	no	—
271	C₂×C₃×Q₈	—	10	2	no	—
272	C₂×C₃×Q₈	—	10	4	no	—
273	C₂×C₃×Q₈	—	10	4	no	—
274	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	5	1	no	—
277	C₂²×C₃×C₄	—	5	1	no	—
278	C₂²×C₃×C₄	—	5	1	no	—
279	C₂²×C₃×C₄	—	5	1	no	—
280	C₂²×C₃×C₄	—	10	2	no	—
281	C₂²×C₃×C₄	—	10	2	no	—
282	C₂²×C₃×C₄	—	10	2	no	—
283	C₂²×C₃×C₄	—	10	2	no	—
284	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
285	C₃×Q₁₆	—	2	2	no	—
286	C₃×Q₁₆	—	10	4	no	—
287	C₃×Q₁₆	—	10	2	no	—
288	C₂×C₃×C₈	—	2	2	no	—
289	C₂×C₃×C₈	—	5	1	no	—
290	C₂×C₃×C₈	—	5	4	no	—
291	C₂×C₃×C₈	—	5	1	no	—
292	C₂×C₃×C₈	—	10	2	no	—
293	C₂×C₃×C₈	—	10	2	no	—
294	C₂×C₃×C₈	—	10	2	no	—
295	C₂×C₃×C₈	—	10	2	no	—
296	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
297	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	5	2	no	—
300	C₃×C₄⋊C₄	—	10	2	no	—
301	C₃×C₄⋊C₄	—	10	2	no	—
302	C₃×C₄⋊C₄	—	10	2	no	—
303	C₃×C₄⋊C₄	—	10	2	no	—
304	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
305	C₃×C₂²⋊C₄	—	2	2	no	—
306	C₃×C₂²⋊C₄	—	10	2	no	—
307	C₃×C₂²⋊C₄	—	10	2	no	—
308	C₃×C₂²⋊C₄	—	10	2	no	—
309	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂²×D₅	—	2	2	no	—
311	C₂²×D₅	—	2	2	no	—
312	C₂²×D₅	C₃×Q₁₆	1	4	yes	complemented
313	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
315	C₅×Q₈	—	2	2	no	—
316	C₅×Q₈	—	2	2	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
323	C₂×Dic₅	—	2	2	no	—
324	C₂×Dic₅	—	2	2	no	—
325	C₂×Dic₅	—	2	2	no	—
326	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
328	C₄×D₅	—	2	2	no	—
329	C₄×D₅	—	2	1	no	—
330	C₄×D₅	—	2	1	no	—
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	4	4	no	—
333	C₄×D₅	—	4	4	no	—
334	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
335	C₄×D₅	C₃×#41	1	2	yes	—
336	Dic₁₀	—	2	2	no	—
337	Dic₁₀	—	2	2	no	—
338	Dic₁₀	—	4	4	no	—
339	C₅×C₈	—	2	1	no	—
340	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
341	#168	—	2	1	no	—
342	#168	C₂×C₃×D₄	1	2	yes	—
343	C₂²×Q₈	—	5	2	no	—
344	C₂³×C₄	—	5	1	no	—
345	C₂×Q₁₆	—	5	2	no	—
346	C₂×Q₁₆	—	5	1	no	—
347	C₂×Q₁₆	—	10	4	no	—
348	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
349	C₂²×C₈	—	5	1	no	—
350	C₂²×C₈	—	5	1	no	—
351	C₂²×C₈	—	5	1	no	—
352	C₂²×C₈	—	5	1	no	—
353	C₂²×C₈	—	5	1	no	—
354	C₂²×C₈	—	10	4	no	—
355	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
356	C₂²⋊Q₈	—	5	2	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	2	no	—
359	C₂²⋊Q₈	—	10	2	no	—
360	C₂²⋊Q₈	—	10	2	no	—
361	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	—
362	C₂×C₄⋊C₄	—	5	2	no	—
363	C₂×C₄⋊C₄	—	10	2	no	—
364	C₂×C₂²⋊C₄	—	10	2	no	—
365	#107	—	5	1	no	—
366	#107	—	5	2	no	—
367	#107	C₂×C₃×D₅	1	1	yes	characteristic, complemented
368	#103	—	5	2	no	—
369	#103	—	5	2	no	—
370	#103	—	5	2	no	—
371	#103	C₂×C₃×D₅	1	2	yes	complemented
372	C₂×C₃×C₅	—	2	2	no	—
373	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
374	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
376	C₃×D₅	—	2	2	no	—
377	C₃×D₅	#467	1	4	yes	direct product factor
378	C₂³×C₃	—	5	1	no	—
379	C₂³×C₃	—	5	1	no	—
380	C₂³×C₃	—	5	4	no	—
381	C₂³×C₃	—	10	2	no	—
382	C₂³×C₃	—	10	2	no	—
383	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
384	C₃×Q₈	—	2	2	no	—
385	C₃×Q₈	—	2	2	no	—
386	C₃×Q₈	—	10	2	no	—
387	C₃×Q₈	—	10	2	no	—
388	C₃×Q₈	—	20	4	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	5	1	no	—
394	C₂×C₃×C₄	—	5	2	no	—
395	C₂×C₃×C₄	—	5	2	no	—
396	C₂×C₃×C₄	—	5	1	no	—
397	C₂×C₃×C₄	—	10	2	no	—
398	C₂×C₃×C₄	—	10	2	no	—
399	C₂×C₃×C₄	—	10	2	no	—
400	C₂×C₃×C₄	—	10	1	no	—
401	C₂×C₃×C₄	—	10	1	no	—
402	C₂×C₃×C₄	—	10	2	no	—
403	C₂×C₃×C₄	—	10	2	no	—
404	C₂×C₃×C₄	—	20	4	no	—
405	C₂×C₃×C₄	—	20	4	no	—
406	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
408	C₃×C₈	—	2	1	no	—
409	C₃×C₈	—	5	2	no	—
410	C₃×C₈	—	10	1	no	—
411	C₃×C₈	D₄×D₅	1	2	yes	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	complemented
415	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
416	C₂×D₅	—	2	1	no	—
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	8	no	—
419	C₂×D₅	C₃×#121	1	2	yes	—
420	C₂×D₅	C₂×C₃×Q₁₆	1	2	yes	—
421	C₂×D₅	C₂×C₃×Q₁₆	1	2	yes	complemented
422	C₂×D₅	C₃×#135	1	2	yes	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	2	no	—
426	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
427	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
428	Dic₅	—	2	1	no	—
429	Dic₅	—	4	2	no	—
430	Dic₅	—	4	2	no	—
431	Dic₅	C₃×#121	1	2	yes	—
432	C₂⁴	—	5	1	no	—
433	C₂×Q₈	—	5	2	no	—
434	C₂×Q₈	—	10	2	no	—
435	C₂×Q₈	—	10	4	no	—
436	C₂×Q₈	—	10	4	no	—
437	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	1	no	—
442	C₂²×C₄	—	5	1	no	—
443	C₂²×C₄	—	10	2	no	—
444	C₂²×C₄	—	10	2	no	—
445	C₂²×C₄	—	10	2	no	—
446	C₂²×C₄	—	10	2	no	—
447	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
448	Q₁₆	—	2	2	no	—
449	Q₁₆	—	10	4	no	—
450	Q₁₆	—	10	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	5	1	no	—
453	C₂×C₈	—	5	4	no	—
454	C₂×C₈	—	5	1	no	—
455	C₂×C₈	—	10	2	no	—
456	C₂×C₈	—	10	2	no	—
457	C₂×C₈	—	10	2	no	—
458	C₂×C₈	—	10	2	no	—
459	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
460	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	10	2	no	—
464	C₄⋊C₄	—	10	2	no	—
465	C₄⋊C₄	—	10	2	no	—
466	C₄⋊C₄	—	10	2	no	—
467	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	10	2	no	—
470	C₂²⋊C₄	—	10	2	no	—
471	C₂²⋊C₄	—	10	2	no	—
472	C₃×C₅	C₂×#467	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	5	2	no	—
476	C₂²×C₃	—	5	2	no	—
477	C₂²×C₃	—	5	2	no	—
478	C₂²×C₃	—	5	2	no	—
479	C₂²×C₃	—	10	8	no	—
480	C₂²×C₃	—	10	1	no	—
481	C₂²×C₃	—	10	1	no	—
482	C₂²×C₃	D₅×Q₁₆	1	2	yes	complemented
483	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	4	2	no	—
486	C₃×C₄	—	4	2	no	—
487	C₃×C₄	—	5	2	no	—
488	C₃×C₄	—	10	1	no	—
489	C₃×C₄	—	20	2	no	—
490	C₃×C₄	—	20	2	no	—
491	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
492	C₃×C₄	D₅×#41	1	1	yes	characteristic
493	C₂×C₅	—	2	2	no	—
494	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
495	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
496	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
497	D₅	—	2	2	no	—
498	D₅	C₃×#467	1	4	yes	direct product factor
499	C₂³	—	5	1	no	—
500	C₂³	—	5	1	no	—
501	C₂³	—	5	4	no	—
502	C₂³	—	10	2	no	—
503	C₂³	—	10	2	no	—
504	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
505	Q₈	—	2	2	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	10	2	no	—
508	Q₈	—	10	2	no	—
509	Q₈	—	20	4	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	2	no	—
516	C₂×C₄	—	5	2	no	—
517	C₂×C₄	—	5	1	no	—
518	C₂×C₄	—	10	2	no	—
519	C₂×C₄	—	10	2	no	—
520	C₂×C₄	—	10	2	no	—
521	C₂×C₄	—	10	1	no	—
522	C₂×C₄	—	10	1	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	2	no	—
525	C₂×C₄	—	20	4	no	—
526	C₂×C₄	—	20	4	no	—
527	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
528	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	5	2	no	—
531	C₈	—	10	1	no	—
532	C₈	C₃×D₄×D₅	1	2	yes	—
533	C₂×C₃	—	2	2	no	—
534	C₂×C₃	—	5	4	no	—
535	C₂×C₃	—	10	2	no	—
536	C₂×C₃	D₅×#121	1	1	yes	characteristic
537	C₂×C₃	C₂×D₅×Q₁₆	1	1	yes	characteristic
538	C₂×C₃	D₅×#135	1	1	yes	characteristic
539	C₅	C₂×C₃×#467	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	5	2	no	—
543	C₂²	—	5	2	no	—
544	C₂²	—	5	2	no	—
545	C₂²	—	5	2	no	—
546	C₂²	—	10	8	no	—
547	C₂²	—	10	1	no	—
548	C₂²	—	10	1	no	—
549	C₂²	C₃×D₅×Q₁₆	1	2	yes	complemented
550	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	5	2	no	—
555	C₄	—	10	1	no	—
556	C₄	—	20	2	no	—
557	C₄	—	20	2	no	—
558	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
559	C₄	C₃×D₅×#41	1	1	yes	characteristic
560	C₃	D₅×#467	1	1	yes	characteristic, direct product factor, Sylow
561	C₂	—	2	2	no	—
562	C₂	—	5	4	no	—
563	C₂	—	10	2	no	—
564	C₂	C₃×D₅×#121	1	1	yes	characteristic
565	C₂	C₂×C₃×D₅×Q₁₆	1	1	yes	characteristic
566	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×#467	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₃×D₅	D₄
hypercenter	C₃×#467	D₅
hypocenter	C₅	C₂×C₃×#467
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#467

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×Q₁₆	C₂	semidirect
4. C₃×C₅×#467	C₂	semidirect
5. C₃×#65477	C₂	semidirect
6. C₃×#65405	C₂	semidirect
7. C₃×#65340	C₂	semidirect
8. C₃×#65176	C₂	semidirect
9. C₃×D₅×#107	C₂	semidirect
10. C₃×#65102	C₂	semidirect
11. C₃×D₅×#103	C₂	semidirect
12. D₅×#467	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
19. C₂×C₃×#689	C₂²	semidirect
23. C₂×C₃×Dic₂₀	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#103	C₂²	semidirect
37. C₃×#3967	C₂²	semidirect
38. C₃×#3950	C₂²	semidirect
39. C₃×#3948	C₂²	semidirect
40. C₃×#3942	C₂²	semidirect
41. C₃×#3939	C₂²	semidirect
43. C₂×D₅×Q₁₆	C₂×C₃	semidirect
46. C₅×#467	C₂×C₃	semidirect
47. #65477	C₂×C₃	semidirect
48. #65405	C₂×C₃	semidirect
49. #65340	C₂×C₃	semidirect
50. #65176	C₂×C₃	semidirect
51. D₅×#107	C₂×C₃	semidirect
52. #65102	C₂×C₃	semidirect
53. D₅×#103	C₂×C₃	semidirect
102. C₃×#467	D₅	direct (N × H)
107. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
111. C₂×#689	C₂²×C₃	semidirect
115. C₂×Dic₂₀	C₂²×C₃	semidirect
127. C₅×#107	C₂²×C₃	semidirect
128. C₅×#103	C₂²×C₃	semidirect
129. #3967	C₂²×C₃	semidirect
130. #3950	C₂²×C₃	semidirect
131. #3948	C₂²×C₃	semidirect
132. #3942	C₂²×C₃	semidirect
133. #3939	C₂²×C₃	semidirect
138. C₂²×C₃×D₅	Q₁₆	semidirect
174. C₂×C₃×Q₁₆	C₂×D₅	semidirect
193. C₃×#107	C₂×D₅	semidirect
197. C₃×#103	C₂×D₅	semidirect
246. #467	C₃×D₅	direct (N × H)
251. C₂²×C₃×C₅	C₂×Q₁₆	semidirect
258. C₂×C₃×D₅	C₂×Q₁₆	semidirect
312. C₂²×D₅	C₃×Q₁₆	semidirect
348. C₂×Q₁₆	C₂×C₃×D₅	semidirect
367. #107	C₂×C₃×D₅	semidirect
371. #103	C₂×C₃×D₅	semidirect
377. C₃×D₅	#467	direct (N × H)
414. C₂²×C₅	C₂×C₃×Q₁₆	semidirect
421. C₂×D₅	C₂×C₃×Q₁₆	semidirect
472. C₃×C₅	C₂×#467	semidirect
482. C₂²×C₃	D₅×Q₁₆	semidirect
498. D₅	C₃×#467	direct (N × H)
539. C₅	C₂×C₃×#467	semidirect
549. C₂²	C₃×D₅×Q₁₆	semidirect
560. C₃	D₅×#467	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×Q₁₆	2
C₂²×C₃×C₈×D₅	2
C₃×D₅×C₂²⋊Q₈	2
C₃×C₅×#467	2
C₃×#65477	2
C₃×#65405	2
C₃×#65340	2
C₃×#65176	2
C₃×D₅×#107	2
C₃×#65102	2
C₃×D₅×#103	2
D₅×#467	3
C₂×C₃×#467	5

Subgroups — C3×D5×#467 #14427730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#467 #14427730