Subgroups — C₂×C₃×#66171 #14510025

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66171	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4096	C₂	1	3	yes	maximal, complemented
5	C₂×C₃×#4095	C₂	1	3	yes	maximal, complemented
6	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4088	C₂	1	3	yes	maximal, complemented
8	C₂²×C₃×#688	C₂	1	3	yes	maximal, complemented
9	C₂×#66171	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	8	yes	complemented
12	C₂×C₃×C₅×#41	—	2	3	no	—
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×#41	C₂²	1	3	yes	complemented
15	C₂²×C₃×C₅×Q₈	—	2	1	no	—
16	C₂²×C₃×C₅×Q₈	C₂²	1	3	yes	complemented
17	C₃×#4149	—	2	4	no	—
18	C₃×#4149	C₂²	1	8	yes	complemented
19	C₂×C₃×#713	—	2	1	no	—
20	C₂×C₃×D₄×D₅	—	2	3	no	—
21	C₂×C₃×#709	C₂²	1	3	yes	—
22	C₂²×C₃×D₂₀	C₂²	1	3	yes	—
23	C₃×#4096	C₂²	1	24	yes	complemented
24	C₃×#4095	C₂²	1	24	yes	complemented
25	C₃×#4094	C₂²	1	8	yes	complemented
26	C₂×C₃×#689	C₂²	1	3	yes	complemented
27	C₃×#4088	C₂²	1	24	yes	complemented
28	C₂×C₃×#688	C₂²	1	3	yes	complemented
29	C₂×C₃×#688	C₂²	1	6	yes	complemented
30	C₂×C₃×#688	C₂²	1	24	yes	complemented
31	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#686	C₂²	1	3	yes	complemented
33	C₂×C₃×#681	C₂²	1	3	yes	complemented
34	C₂²×C₃×#168	C₂²	1	3	yes	complemented
35	C₂×C₃×#577	—	5	1	no	maximal, Hall
36	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4149	C₂×C₃	1	1	yes	characteristic, complemented
38	#66171	C₂×C₃	1	16	yes	direct product factor
39	C₂×#4096	C₂×C₃	1	3	yes	complemented
40	C₂×#4095	C₂×C₃	1	3	yes	complemented
41	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#4088	C₂×C₃	1	3	yes	complemented
43	C₂²×#688	C₂×C₃	1	3	yes	complemented
44	C₂³×C₃×D₅	—	2	3	no	—
45	C₃×C₅×#41	—	2	24	no	—
46	C₃×C₅×#41	—	2	6	no	—
47	C₃×C₅×#41	D₄	1	4	yes	—
48	C₃×C₅×#41	C₂³	1	4	yes	—
49	C₃×C₅×#41	C₂³	1	12	yes	complemented
50	C₂×C₃×C₅×Q₈	—	2	8	no	—
51	C₂×C₃×C₅×Q₈	—	2	3	no	—
52	C₂×C₃×C₅×Q₈	—	2	6	no	—
53	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
54	C₂×C₃×C₅×Q₈	C₂³	1	3	yes	—
55	C₂×C₃×C₅×Q₈	C₂³	1	12	yes	complemented
56	C₂×C₃×C₅×D₄	—	2	3	no	—
57	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	—	2	3	no	—
60	C₂²×C₃×C₄×C₅	—	2	3	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
62	C₂×C₃×C₂²⋊D₅	—	2	3	no	—
63	C₃×#713	—	2	8	no	—
64	C₃×D₄×D₅	—	2	24	no	—
65	C₃×#709	—	2	6	no	—
66	C₃×#709	C₂³	1	12	yes	—
67	C₂×C₃×D₂₀	—	2	3	no	—
68	C₂×C₃×D₂₀	—	2	6	no	—
69	C₂×C₃×D₂₀	C₂³	1	3	yes	—
70	C₂×C₃×D₂₀	C₂³	1	12	yes	—
71	C₂×C₃×C₄×D₅	—	2	3	no	—
72	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
73	C₃×#689	C₂³	1	12	yes	complemented
74	C₃×#688	C₂³	1	12	yes	complemented
75	C₃×#688	C₂³	1	24	yes	complemented
76	C₃×#687	C₂³	1	4	yes	complemented
77	C₃×#686	C₂³	1	12	yes	complemented
78	C₃×#681	C₂³	1	12	yes	complemented
79	C₂×C₃×#168	C₂³	1	3	yes	—
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	12	yes	complemented
82	C₂×C₃×2₋¹⁺⁴	D₅	1	1	yes	characteristic, complemented
83	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
84	C₃×#577	—	5	16	no	—
85	C₂×C₃×#137	—	5	3	no	—
86	C₂×C₃×AGL(1,ℤ/8)	—	5	3	no	—
87	C₂×C₃×#135	—	5	3	no	—
88	C₂²×C₃×SD₁₆	—	5	3	no	—
89	C₂×C₃×#131	—	5	1	no	—
90	C₅×2₋¹⁺⁴	—	2	4	no	—
91	C₅×2₋¹⁺⁴	C₂²×C₃	1	8	yes	complemented
92	C₂×C₅×#41	—	2	3	no	—
93	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×#41	C₂²×C₃	1	3	yes	complemented
95	C₂²×C₅×Q₈	—	2	1	no	—
96	C₂²×C₅×Q₈	C₂²×C₃	1	3	yes	complemented
97	#4149	—	2	4	no	—
98	#4149	C₂²×C₃	1	8	yes	complemented
99	C₂×#713	—	2	1	no	—
100	C₂×D₄×D₅	—	2	3	no	—
101	C₂×#709	C₂²×C₃	1	3	yes	—
102	C₂²×D₂₀	C₂²×C₃	1	3	yes	—
103	#4096	C₂²×C₃	1	24	yes	complemented
104	#4095	C₂²×C₃	1	24	yes	complemented
105	#4094	C₂²×C₃	1	8	yes	complemented
106	C₂×#689	C₂²×C₃	1	3	yes	complemented
107	#4088	C₂²×C₃	1	24	yes	complemented
108	C₂×#688	C₂²×C₃	1	3	yes	complemented
109	C₂×#688	C₂²×C₃	1	6	yes	complemented
110	C₂×#688	C₂²×C₃	1	24	yes	complemented
111	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂×#686	C₂²×C₃	1	3	yes	complemented
113	C₂×#681	C₂²×C₃	1	3	yes	complemented
114	C₂²×#168	C₂²×C₃	1	3	yes	complemented
115	C₂×#577	—	5	1	no	Sylow
116	C₂³×C₃×C₅	—	2	1	no	—
117	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
118	C₂²×C₃×D₅	—	2	3	no	—
119	C₂²×C₃×D₅	—	2	12	no	—
120	C₂²×C₃×D₅	—	8	6	no	—
121	C₃×C₅×Q₈	—	2	3	no	—
122	C₃×C₅×Q₈	—	2	12	no	—
123	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
124	C₃×C₅×Q₈	C₂⁴	1	6	yes	—
125	C₃×C₅×D₄	—	2	12	no	—
126	C₃×C₅×D₄	—	2	1	no	—
127	C₃×C₅×D₄	C₂×D₄	1	12	yes	—
128	C₃×C₅×D₄	C₂⁴	1	2	yes	—
129	C₂×C₃×C₄×C₅	—	2	3	no	—
130	C₂×C₃×C₄×C₅	—	2	12	no	—
131	C₂×C₃×C₄×C₅	—	2	12	no	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
136	C₃×C₂²⋊D₅	—	2	12	no	—
137	C₂×C₃×Dic₅	—	2	1	no	—
138	C₃×D₂₀	—	2	3	no	—
139	C₃×D₂₀	—	2	12	no	—
140	C₃×D₂₀	C₂⁴	1	6	yes	—
141	C₃×C₄×D₅	—	2	12	no	—
142	C₃×Dic₁₀	—	2	1	no	—
143	C₃×Dic₁₀	C₂⁴	1	2	yes	—
144	C₃×#168	C₂⁴	1	2	yes	—
145	C₃×#168	C₂⁴	1	6	yes	—
146	C₃×2₋¹⁺⁴	—	2	4	no	—
147	C₃×2₋¹⁺⁴	C₂×D₅	1	8	yes	complemented
148	C₃×H(5,𝔽₂)	—	5	8	no	—
149	C₃×H(5,𝔽₂)	—	10	4	no	—
150	C₂×C₃×#41	—	2	3	no	—
151	C₂×C₃×#41	—	5	3	no	—
152	C₂×C₃×#41	—	10	1	no	—
153	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
154	C₂×C₃×#41	C₂×D₅	1	3	yes	complemented
155	C₂²×C₃×Q₈	—	2	1	no	—
156	C₂²×C₃×Q₈	C₂×D₅	1	3	yes	complemented
157	C₂²×C₃×D₄	—	5	3	no	—
158	C₂²×C₃×D₄	—	10	3	no	—
159	C₃×#137	—	5	24	no	—
160	C₃×AGL(1,ℤ/8)	—	5	24	no	—
161	C₃×#135	—	5	24	no	—
162	C₂×C₃×Q₁₆	—	5	3	no	—
163	C₂×C₃×SD₁₆	—	5	3	no	—
164	C₂×C₃×SD₁₆	—	5	6	no	—
165	C₂×C₃×SD₁₆	—	5	24	no	—
166	C₂×C₃×SD₁₆	—	5	1	no	—
167	C₂×C₃×D₈	—	5	3	no	—
168	C₃×#131	—	5	8	no	—
169	C₂×C₃×M₁₆	—	5	3	no	—
170	C₂²×C₃×C₈	—	5	3	no	—
171	C₂³×D₅	—	2	3	no	—
172	C₅×#41	—	2	24	no	—
173	C₅×#41	—	2	6	no	—
174	C₅×#41	C₃×D₄	1	4	yes	—
175	C₅×#41	C₂³×C₃	1	4	yes	—
176	C₅×#41	C₂³×C₃	1	12	yes	complemented
177	C₂×C₅×Q₈	—	2	8	no	—
178	C₂×C₅×Q₈	—	2	3	no	—
179	C₂×C₅×Q₈	—	2	6	no	—
180	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
181	C₂×C₅×Q₈	C₂³×C₃	1	3	yes	—
182	C₂×C₅×Q₈	C₂³×C₃	1	12	yes	complemented
183	C₂×C₅×D₄	—	2	3	no	—
184	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
185	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₄×C₅	—	2	3	no	—
187	C₂²×C₄×C₅	—	2	3	no	—
188	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
189	C₂×C₂²⋊D₅	—	2	3	no	—
190	#713	—	2	8	no	—
191	D₄×D₅	—	2	24	no	—
192	#709	—	2	6	no	—
193	#709	C₂³×C₃	1	12	yes	—
194	C₂×D₂₀	—	2	3	no	—
195	C₂×D₂₀	—	2	6	no	—
196	C₂×D₂₀	C₂³×C₃	1	3	yes	—
197	C₂×D₂₀	C₂³×C₃	1	12	yes	—
198	C₂×C₄×D₅	—	2	3	no	—
199	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
200	#689	C₂³×C₃	1	12	yes	complemented
201	#688	C₂³×C₃	1	12	yes	complemented
202	#688	C₂³×C₃	1	24	yes	complemented
203	#687	C₂³×C₃	1	4	yes	complemented
204	#686	C₂³×C₃	1	12	yes	complemented
205	#681	C₂³×C₃	1	12	yes	complemented
206	C₂×#168	C₂³×C₃	1	1	yes	characteristic
207	C₂×#168	C₂³×C₃	1	3	yes	—
208	C₂×#168	C₂³×C₃	1	12	yes	complemented
209	C₂×2₋¹⁺⁴	C₃×D₅	1	1	yes	characteristic, complemented
210	C₂×H(5,𝔽₂)	—	5	1	no	—
211	#577	—	5	16	no	—
212	C₂×#137	—	5	3	no	—
213	C₂×AGL(1,ℤ/8)	—	5	3	no	—
214	C₂×#135	—	5	3	no	—
215	C₂²×SD₁₆	—	5	3	no	—
216	C₂×#131	—	5	1	no	—
217	C₂²×C₃×C₅	—	2	6	no	—
218	C₂²×C₃×C₅	—	2	2	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
221	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₃×D₅	—	2	6	no	—
223	C₂×C₃×D₅	—	4	6	no	—
224	C₂×C₃×D₅	—	8	12	no	—
225	C₃×C₄×C₅	—	2	6	no	—
226	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
228	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
229	C₃×Dic₅	—	2	2	no	—
230	C₂⁴×C₃	—	10	3	no	—
231	C₃×#41	—	2	24	no	—
232	C₃×#41	—	2	6	no	—
233	C₃×#41	—	5	12	no	—
234	C₃×#41	—	10	8	no	—
235	C₃×#41	—	10	6	no	—
236	C₃×#41	C₂²⋊D₅	1	4	yes	—
237	C₃×#41	C₂²×D₅	1	4	yes	—
238	C₃×#41	C₂²×D₅	1	12	yes	complemented
239	C₂×C₃×Q₈	—	2	8	no	—
240	C₂×C₃×Q₈	—	2	3	no	—
241	C₂×C₃×Q₈	—	2	6	no	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
244	C₂×C₃×Q₈	C₂²×D₅	1	3	yes	—
245	C₂×C₃×Q₈	C₂²×D₅	1	12	yes	complemented
246	C₂×C₃×D₄	—	2	3	no	—
247	C₂×C₃×D₄	—	5	3	no	—
248	C₂×C₃×D₄	—	5	12	no	—
249	C₂×C₃×D₄	—	10	3	no	—
250	C₂×C₃×D₄	—	10	24	no	—
251	C₂×C₃×D₄	—	10	3	no	—
252	C₂×C₃×D₄	—	10	6	no	—
253	C₂×C₃×D₄	C₂²⋊D₅	1	3	yes	—
254	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
255	C₂²×C₃×C₄	—	2	3	no	—
256	C₂²×C₃×C₄	—	2	3	no	—
257	C₂²×C₃×C₄	—	10	3	no	—
258	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
259	C₃×Q₁₆	—	5	12	no	—
260	C₃×SD₁₆	—	5	12	no	—
261	C₃×SD₁₆	—	5	24	no	—
262	C₃×SD₁₆	—	5	4	no	—
263	C₃×D₈	—	5	12	no	—
264	C₃×M₁₆	—	5	12	no	—
265	C₂×C₃×C₈	—	5	1	no	—
266	C₂×C₃×C₈	—	5	3	no	—
267	C₂×C₃×C₈	—	5	12	no	—
268	C₂³×C₅	—	2	1	no	—
269	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
270	C₂²×D₅	—	2	3	no	—
271	C₂²×D₅	—	2	12	no	—
272	C₂²×D₅	—	8	6	no	—
273	C₅×Q₈	—	2	3	no	—
274	C₅×Q₈	—	2	12	no	—
275	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
276	C₅×Q₈	C₂⁴×C₃	1	6	yes	—
277	C₅×D₄	—	2	12	no	—
278	C₅×D₄	—	2	1	no	—
279	C₅×D₄	C₂×C₃×D₄	1	12	yes	—
280	C₅×D₄	C₂⁴×C₃	1	2	yes	—
281	C₂×C₄×C₅	—	2	3	no	—
282	C₂×C₄×C₅	—	2	12	no	—
283	C₂×C₄×C₅	—	2	12	no	—
284	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
285	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
286	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
288	C₂²⋊D₅	—	2	12	no	—
289	C₂×Dic₅	—	2	1	no	—
290	D₂₀	—	2	3	no	—
291	D₂₀	—	2	12	no	—
292	D₂₀	C₂⁴×C₃	1	6	yes	—
293	C₄×D₅	—	2	12	no	—
294	Dic₁₀	—	2	1	no	—
295	Dic₁₀	C₂⁴×C₃	1	2	yes	—
296	#168	C₂⁴×C₃	1	2	yes	—
297	#168	C₂⁴×C₃	1	6	yes	—
298	2₋¹⁺⁴	—	2	4	no	—
299	2₋¹⁺⁴	C₂×C₃×D₅	1	8	yes	complemented
300	H(5,𝔽₂)	—	5	8	no	—
301	H(5,𝔽₂)	—	10	4	no	—
302	C₂×#41	—	2	3	no	—
303	C₂×#41	—	5	3	no	—
304	C₂×#41	—	10	1	no	—
305	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
306	C₂×#41	C₂×C₃×D₅	1	3	yes	complemented
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	C₂×C₃×D₅	1	3	yes	complemented
309	C₂²×D₄	—	5	3	no	—
310	C₂²×D₄	—	10	3	no	—
311	#137	—	5	24	no	—
312	AGL(1,ℤ/8)	—	5	24	no	—
313	#135	—	5	24	no	—
314	C₂×Q₁₆	—	5	3	no	—
315	C₂×SD₁₆	—	5	3	no	—
316	C₂×SD₁₆	—	5	6	no	—
317	C₂×SD₁₆	—	5	24	no	—
318	C₂×SD₁₆	—	5	1	no	—
319	C₂×D₈	—	5	3	no	—
320	#131	—	5	8	no	—
321	C₂×M₁₆	—	5	3	no	—
322	C₂²×C₈	—	5	3	no	—
323	C₂×C₃×C₅	—	2	6	no	—
324	C₂×C₃×C₅	—	4	2	no	—
325	C₂×C₃×C₅	#577	1	2	yes	complemented
326	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
327	C₃×D₅	—	4	6	no	—
328	C₂³×C₃	—	2	1	no	—
329	C₂³×C₃	—	10	3	no	—
330	C₂³×C₃	—	10	12	no	—
331	C₂³×C₃	—	40	6	no	—
332	C₂³×C₃	C₂×C₂²⋊D₅	1	3	yes	—
333	C₃×Q₈	—	2	3	no	—
334	C₃×Q₈	—	2	12	no	—
335	C₃×Q₈	—	5	2	no	—
336	C₃×Q₈	—	10	1	no	—
337	C₃×Q₈	C₂×C₂²⋊D₅	1	4	yes	—
338	C₃×Q₈	C₂³×D₅	1	6	yes	—
339	C₃×D₄	—	2	12	no	—
340	C₃×D₄	—	2	1	no	—
341	C₃×D₄	—	5	6	no	—
342	C₃×D₄	—	10	12	no	—
343	C₃×D₄	—	10	12	no	—
344	C₃×D₄	—	10	3	no	—
345	C₃×D₄	C₂×C₂²⋊D₅	1	12	yes	—
346	C₃×D₄	C₂³×D₅	1	2	yes	—
347	C₂×C₃×C₄	—	2	12	no	—
348	C₂×C₃×C₄	—	2	3	no	—
349	C₂×C₃×C₄	—	2	12	no	—
350	C₂×C₃×C₄	—	10	1	no	—
351	C₂×C₃×C₄	—	10	12	no	—
352	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	6	yes	—
353	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
354	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
355	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
356	C₃×C₈	—	5	2	no	—
357	C₃×C₈	—	5	6	no	—
358	C₂²×C₅	—	2	6	no	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
362	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₂×D₅	—	2	6	no	—
364	C₂×D₅	—	4	6	no	—
365	C₂×D₅	—	8	12	no	—
366	C₄×C₅	—	2	6	no	—
367	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
368	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
369	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
370	Dic₅	—	2	2	no	—
371	C₂⁴	—	10	3	no	—
372	#41	—	2	24	no	—
373	#41	—	2	6	no	—
374	#41	—	5	12	no	—
375	#41	—	10	8	no	—
376	#41	—	10	6	no	—
377	#41	C₃×C₂²⋊D₅	1	4	yes	—
378	#41	C₂²×C₃×D₅	1	4	yes	—
379	#41	C₂²×C₃×D₅	1	12	yes	complemented
380	C₂×Q₈	—	2	8	no	—
381	C₂×Q₈	—	2	3	no	—
382	C₂×Q₈	—	2	6	no	—
383	C₂×Q₈	—	5	1	no	—
384	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
385	C₂×Q₈	C₂²×C₃×D₅	1	3	yes	—
386	C₂×Q₈	C₂²×C₃×D₅	1	12	yes	complemented
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	—	5	3	no	—
389	C₂×D₄	—	5	12	no	—
390	C₂×D₄	—	10	3	no	—
391	C₂×D₄	—	10	24	no	—
392	C₂×D₄	—	10	3	no	—
393	C₂×D₄	—	10	6	no	—
394	C₂×D₄	C₃×C₂²⋊D₅	1	3	yes	—
395	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
396	C₂²×C₄	—	2	3	no	—
397	C₂²×C₄	—	2	3	no	—
398	C₂²×C₄	—	10	3	no	—
399	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
400	Q₁₆	—	5	12	no	—
401	SD₁₆	—	5	12	no	—
402	SD₁₆	—	5	24	no	—
403	SD₁₆	—	5	4	no	—
404	D₈	—	5	12	no	—
405	M₁₆	—	5	12	no	—
406	C₂×C₈	—	5	1	no	—
407	C₂×C₈	—	5	3	no	—
408	C₂×C₈	—	5	12	no	—
409	C₃×C₅	C₂×#577	1	1	yes	characteristic, complemented, Hall
410	C₂²×C₃	—	2	6	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	4	2	no	—
413	C₂²×C₃	—	10	6	no	—
414	C₂²×C₃	—	20	6	no	—
415	C₂²×C₃	—	40	12	no	—
416	C₂²×C₃	C₂²×C₂²⋊D₅	1	6	yes	—
417	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
418	C₃×C₄	—	2	6	no	—
419	C₃×C₄	—	10	2	no	—
420	C₃×C₄	C₂²×C₂²⋊D₅	1	6	yes	—
421	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
422	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
423	C₂×C₅	—	2	6	no	—
424	C₂×C₅	—	4	2	no	—
425	C₂×C₅	C₃×#577	1	2	yes	complemented
426	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
427	D₅	—	4	6	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	10	3	no	—
430	C₂³	—	10	12	no	—
431	C₂³	—	40	6	no	—
432	C₂³	C₂×C₃×C₂²⋊D₅	1	3	yes	—
433	Q₈	—	2	3	no	—
434	Q₈	—	2	12	no	—
435	Q₈	—	5	2	no	—
436	Q₈	—	10	1	no	—
437	Q₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
438	Q₈	C₂³×C₃×D₅	1	6	yes	—
439	D₄	—	2	12	no	—
440	D₄	—	2	1	no	—
441	D₄	—	5	6	no	—
442	D₄	—	10	12	no	—
443	D₄	—	10	12	no	—
444	D₄	—	10	3	no	—
445	D₄	C₂×C₃×C₂²⋊D₅	1	12	yes	—
446	D₄	C₂³×C₃×D₅	1	2	yes	—
447	C₂×C₄	—	2	3	no	—
448	C₂×C₄	—	2	12	no	—
449	C₂×C₄	—	2	12	no	—
450	C₂×C₄	—	10	1	no	—
451	C₂×C₄	—	10	12	no	—
452	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
453	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	6	yes	—
454	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
455	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
456	C₈	—	5	2	no	—
457	C₈	—	5	6	no	—
458	C₂×C₃	—	2	6	no	—
459	C₂×C₃	—	4	2	no	—
460	C₂×C₃	—	20	6	no	—
461	C₂×C₃	#66171	1	2	yes	direct product factor
462	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
463	C₅	C₂×C₃×#577	1	1	yes	characteristic, complemented, Sylow
464	C₂²	—	2	6	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	10	6	no	—
468	C₂²	—	20	6	no	—
469	C₂²	—	40	12	no	—
470	C₂²	C₂²×C₃×C₂²⋊D₅	1	6	yes	—
471	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
472	C₄	—	2	6	no	—
473	C₄	—	10	2	no	—
474	C₄	C₂²×C₃×C₂²⋊D₅	1	6	yes	—
475	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
476	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
477	C₃	C₂×#66171	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	2	6	no	—
479	C₂	—	4	2	no	—
480	C₂	—	20	6	no	—
481	C₂	C₃×#66171	1	2	yes	direct product factor
482	C₂	C₂³×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×2₋¹⁺⁴	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×2₋¹⁺⁴	D₅
hypocenter	C₅	C₂×C₃×#577
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×2₋¹⁺⁴	C₂	semidirect
2. C₂×C₃×#4149	C₂	semidirect
3. C₃×#66171	C₂	direct (N × H)
4. C₂×C₃×#4096	C₂	semidirect
5. C₂×C₃×#4095	C₂	semidirect
6. C₂×C₃×#4094	C₂	semidirect
7. C₂×C₃×#4088	C₂	semidirect
8. C₂²×C₃×#688	C₂	semidirect
9. C₂×#66171	C₃	direct (N × H)
11. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
14. C₂×C₃×C₅×#41	C₂²	semidirect
16. C₂²×C₃×C₅×Q₈	C₂²	semidirect
18. C₃×#4149	C₂²	semidirect
23. C₃×#4096	C₂²	semidirect
24. C₃×#4095	C₂²	semidirect
25. C₃×#4094	C₂²	semidirect
26. C₂×C₃×#689	C₂²	semidirect
27. C₃×#4088	C₂²	semidirect
28. C₂×C₃×#688	C₂²	semidirect
29. C₂×C₃×#688	C₂²	semidirect
30. C₂×C₃×#688	C₂²	semidirect
31. C₂×C₃×#687	C₂²	semidirect
32. C₂×C₃×#686	C₂²	semidirect
33. C₂×C₃×#681	C₂²	semidirect
34. C₂²×C₃×#168	C₂²	semidirect
36. C₂×C₅×2₋¹⁺⁴	C₂×C₃	semidirect
37. C₂×#4149	C₂×C₃	semidirect
38. #66171	C₂×C₃	direct (N × H)
39. C₂×#4096	C₂×C₃	semidirect
40. C₂×#4095	C₂×C₃	semidirect
41. C₂×#4094	C₂×C₃	semidirect
42. C₂×#4088	C₂×C₃	semidirect
43. C₂²×#688	C₂×C₃	semidirect
49. C₃×C₅×#41	C₂³	semidirect
55. C₂×C₃×C₅×Q₈	C₂³	semidirect
73. C₃×#689	C₂³	semidirect
74. C₃×#688	C₂³	semidirect
75. C₃×#688	C₂³	semidirect
76. C₃×#687	C₂³	semidirect
77. C₃×#686	C₂³	semidirect
78. C₃×#681	C₂³	semidirect
81. C₂×C₃×#168	C₂³	semidirect
82. C₂×C₃×2₋¹⁺⁴	D₅	semidirect
91. C₅×2₋¹⁺⁴	C₂²×C₃	semidirect
94. C₂×C₅×#41	C₂²×C₃	semidirect
96. C₂²×C₅×Q₈	C₂²×C₃	semidirect
98. #4149	C₂²×C₃	semidirect
103. #4096	C₂²×C₃	semidirect
104. #4095	C₂²×C₃	semidirect
105. #4094	C₂²×C₃	semidirect
106. C₂×#689	C₂²×C₃	semidirect
107. #4088	C₂²×C₃	semidirect
108. C₂×#688	C₂²×C₃	semidirect
109. C₂×#688	C₂²×C₃	semidirect
110. C₂×#688	C₂²×C₃	semidirect
111. C₂×#687	C₂²×C₃	semidirect
112. C₂×#686	C₂²×C₃	semidirect
113. C₂×#681	C₂²×C₃	semidirect
114. C₂²×#168	C₂²×C₃	semidirect
147. C₃×2₋¹⁺⁴	C₂×D₅	semidirect
154. C₂×C₃×#41	C₂×D₅	semidirect
156. C₂²×C₃×Q₈	C₂×D₅	semidirect
176. C₅×#41	C₂³×C₃	semidirect
182. C₂×C₅×Q₈	C₂³×C₃	semidirect
200. #689	C₂³×C₃	semidirect
201. #688	C₂³×C₃	semidirect
202. #688	C₂³×C₃	semidirect
203. #687	C₂³×C₃	semidirect
204. #686	C₂³×C₃	semidirect
205. #681	C₂³×C₃	semidirect
208. C₂×#168	C₂³×C₃	semidirect
209. C₂×2₋¹⁺⁴	C₃×D₅	semidirect
238. C₃×#41	C₂²×D₅	semidirect
245. C₂×C₃×Q₈	C₂²×D₅	semidirect
299. 2₋¹⁺⁴	C₂×C₃×D₅	semidirect
306. C₂×#41	C₂×C₃×D₅	semidirect
308. C₂²×Q₈	C₂×C₃×D₅	semidirect
325. C₂×C₃×C₅	#577	semidirect
379. #41	C₂²×C₃×D₅	semidirect
386. C₂×Q₈	C₂²×C₃×D₅	semidirect
409. C₃×C₅	C₂×#577	semidirect
425. C₂×C₅	C₃×#577	semidirect
461. C₂×C₃	#66171	direct (N × H)
463. C₅	C₂×C₃×#577	semidirect
477. C₃	C₂×#66171	direct (N × H)
481. C₂	C₃×#66171	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×C₅×2₋¹⁺⁴	2
C₂×C₃×#4149	2
C₃×#66171	2
C₂×C₃×#4096	2
C₂×C₃×#4095	2
C₂×C₃×#4094	2
C₂×C₃×#4088	2
C₂²×C₃×#688	2
C₂×#66171	3
C₂×C₃×#577	5

Subgroups — C2×C3×#66171 #14510025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66171 #14510025