Subgroups — C₂×C₃×#66169 #14509958

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66169	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×#4078	C₂	1	3	yes	maximal, complemented
8	C₂²×C₃×#686	C₂	1	3	yes	maximal, complemented
9	C₂×#66169	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
11	C₃×C₅×H(5,𝔽₂)	C₂²	1	8	yes	complemented
12	C₂×C₃×C₅×#41	—	2	1	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×D₄	—	2	3	no	—
16	C₂²×C₃×C₅×D₄	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	complemented
22	C₂²×C₃×D₂₀	C₂²	1	3	yes	complemented
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	1	yes	characteristic, complemented
27	C₂×C₃×#688	C₂²	1	3	yes	complemented
28	C₂×C₃×#687	C₂²	1	3	yes	complemented
29	C₃×#4078	C₂²	1	24	yes	complemented
30	C₂×C₃×#686	C₂²	1	3	yes	complemented
31	C₂×C₃×#686	C₂²	1	6	yes	complemented
32	C₂×C₃×#686	C₂²	1	24	yes	complemented
33	C₂×C₃×#681	C₂²	1	3	yes	complemented
34	C₂²×C₃×#168	C₂²	1	3	yes	complemented
35	C₂×C₃×#576	—	5	1	no	maximal, Hall
36	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4149	C₂×C₃	1	1	yes	characteristic, complemented
38	#66169	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×#4078	C₂×C₃	1	3	yes	complemented
43	C₂²×#686	C₂×C₃	1	3	yes	complemented
44	C₂⁴×C₃×C₅	—	2	3	no	—
45	C₂³×C₃×D₅	—	2	3	no	—
46	C₃×C₅×#41	—	2	8	no	—
47	C₃×C₅×#41	—	2	6	no	—
48	C₃×C₅×#41	D₄	1	4	yes	—
49	C₃×C₅×#41	C₂³	1	4	yes	—
50	C₃×C₅×#41	C₂³	1	12	yes	complemented
51	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×D₄	—	2	3	no	—
54	C₂×C₃×C₅×D₄	—	2	24	no	—
55	C₂×C₃×C₅×D₄	—	2	3	no	—
56	C₂×C₃×C₅×D₄	—	2	6	no	—
57	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
58	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
59	C₂×C₃×C₅×D₄	C₂³	1	12	yes	complemented
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	complemented
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	complemented
71	C₂×C₃×C₄×D₅	—	2	3	no	—
72	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
73	C₃×#689	C₂³	1	4	yes	complemented
74	C₃×#688	C₂³	1	12	yes	complemented
75	C₃×#687	C₂³	1	12	yes	complemented
76	C₃×#686	C₂³	1	12	yes	complemented
77	C₃×#686	C₂³	1	24	yes	complemented
78	C₃×#681	C₂³	1	12	yes	complemented
79	C₂×C₃×#168	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	3	yes	—
81	C₂×C₃×#168	C₂³	1	12	yes	complemented
82	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
83	C₂×C₃×H(5,𝔽₂)	D₅	1	1	yes	characteristic, complemented
84	C₃×#576	—	5	16	no	—
85	C₂×C₃×AGL(1,ℤ/8)	—	5	3	no	—
86	C₂×C₃×AGL(1,ℤ/8)	—	5	3	no	—
87	C₂×C₃×#135	—	5	3	no	—
88	C₂²×C₃×D₈	—	5	3	no	—
89	C₂×C₃×#131	—	5	1	no	—
90	C₅×H(5,𝔽₂)	—	2	4	no	—
91	C₅×H(5,𝔽₂)	C₂²×C₃	1	8	yes	complemented
92	C₂×C₅×#41	—	2	1	no	—
93	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×#41	C₂²×C₃	1	3	yes	complemented
95	C₂²×C₅×D₄	—	2	3	no	—
96	C₂²×C₅×D₄	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	complemented
102	C₂²×D₂₀	C₂²×C₃	1	3	yes	complemented
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	1	yes	characteristic, complemented
107	C₂×#688	C₂²×C₃	1	3	yes	complemented
108	C₂×#687	C₂²×C₃	1	3	yes	complemented
109	#4078	C₂²×C₃	1	24	yes	complemented
110	C₂×#686	C₂²×C₃	1	3	yes	complemented
111	C₂×#686	C₂²×C₃	1	6	yes	complemented
112	C₂×#686	C₂²×C₃	1	24	yes	complemented
113	C₂×#681	C₂²×C₃	1	3	yes	complemented
114	C₂²×#168	C₂²×C₃	1	3	yes	complemented
115	C₂×#576	—	5	1	no	Sylow
116	C₂³×C₃×C₅	—	2	3	no	—
117	C₂³×C₃×C₅	—	2	12	no	—
118	C₂³×C₃×C₅	—	8	6	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
120	C₂²×C₃×D₅	—	2	3	no	—
121	C₂²×C₃×D₅	—	2	12	no	—
122	C₂²×C₃×D₅	—	8	6	no	—
123	C₃×C₅×Q₈	—	2	1	no	—
124	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
125	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
126	C₃×C₅×D₄	—	2	12	no	—
127	C₃×C₅×D₄	—	2	3	no	—
128	C₃×C₅×D₄	—	2	12	no	—
129	C₃×C₅×D₄	C₂×D₄	1	12	yes	—
130	C₃×C₅×D₄	C₂⁴	1	6	yes	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	12	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
137	C₃×C₂²⋊D₅	—	2	12	no	—
138	C₂×C₃×Dic₅	—	2	1	no	—
139	C₃×D₂₀	—	2	3	no	—
140	C₃×D₂₀	—	2	12	no	—
141	C₃×D₂₀	C₂⁴	1	6	yes	—
142	C₃×C₄×D₅	—	2	12	no	—
143	C₃×Dic₁₀	—	2	1	no	—
144	C₃×Dic₁₀	C₂⁴	1	2	yes	—
145	C₃×#168	C₂⁴	1	2	yes	—
146	C₃×#168	C₂⁴	1	6	yes	—
147	C₃×H(5,𝔽₂)	—	2	4	no	—
148	C₃×H(5,𝔽₂)	—	5	8	no	—
149	C₃×H(5,𝔽₂)	—	10	4	no	—
150	C₃×H(5,𝔽₂)	C₂×D₅	1	8	yes	complemented
151	C₂×C₃×#41	—	2	1	no	—
152	C₂×C₃×#41	—	5	3	no	—
153	C₂×C₃×#41	—	10	1	no	—
154	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
155	C₂×C₃×#41	C₂×D₅	1	3	yes	complemented
156	C₂²×C₃×D₄	—	2	3	no	—
157	C₂²×C₃×D₄	—	5	3	no	—
158	C₂²×C₃×D₄	—	10	3	no	—
159	C₂²×C₃×D₄	C₂×D₅	1	3	yes	complemented
160	C₃×AGL(1,ℤ/8)	—	5	24	no	—
161	C₃×AGL(1,ℤ/8)	—	5	24	no	—
162	C₃×#135	—	5	24	no	—
163	C₂×C₃×Q₁₆	—	5	1	no	—
164	C₂×C₃×SD₁₆	—	5	3	no	—
165	C₂×C₃×SD₁₆	—	5	3	no	—
166	C₂×C₃×D₈	—	5	3	no	—
167	C₂×C₃×D₈	—	5	6	no	—
168	C₂×C₃×D₈	—	5	24	no	—
169	C₃×#131	—	5	8	no	—
170	C₂×C₃×M₁₆	—	5	3	no	—
171	C₂²×C₃×C₈	—	5	3	no	—
172	C₂⁴×C₅	—	2	3	no	—
173	C₂³×D₅	—	2	3	no	—
174	C₅×#41	—	2	8	no	—
175	C₅×#41	—	2	6	no	—
176	C₅×#41	C₃×D₄	1	4	yes	—
177	C₅×#41	C₂³×C₃	1	4	yes	—
178	C₅×#41	C₂³×C₃	1	12	yes	complemented
179	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
180	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₅×D₄	—	2	3	no	—
182	C₂×C₅×D₄	—	2	24	no	—
183	C₂×C₅×D₄	—	2	3	no	—
184	C₂×C₅×D₄	—	2	6	no	—
185	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
186	C₂×C₅×D₄	C₂³×C₃	1	3	yes	—
187	C₂×C₅×D₄	C₂³×C₃	1	12	yes	complemented
188	C₂²×C₄×C₅	—	2	3	no	—
189	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
190	C₂×C₂²⋊D₅	—	2	3	no	—
191	#713	—	2	8	no	—
192	D₄×D₅	—	2	24	no	—
193	#709	—	2	6	no	—
194	#709	C₂³×C₃	1	12	yes	complemented
195	C₂×D₂₀	—	2	3	no	—
196	C₂×D₂₀	—	2	6	no	—
197	C₂×D₂₀	C₂³×C₃	1	3	yes	—
198	C₂×D₂₀	C₂³×C₃	1	12	yes	complemented
199	C₂×C₄×D₅	—	2	3	no	—
200	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
201	#689	C₂³×C₃	1	4	yes	complemented
202	#688	C₂³×C₃	1	12	yes	complemented
203	#687	C₂³×C₃	1	12	yes	complemented
204	#686	C₂³×C₃	1	12	yes	complemented
205	#686	C₂³×C₃	1	24	yes	complemented
206	#681	C₂³×C₃	1	12	yes	complemented
207	C₂×#168	C₂³×C₃	1	1	yes	characteristic
208	C₂×#168	C₂³×C₃	1	3	yes	—
209	C₂×#168	C₂³×C₃	1	12	yes	complemented
210	C₂×H(5,𝔽₂)	—	5	1	no	—
211	C₂×H(5,𝔽₂)	C₃×D₅	1	1	yes	characteristic, complemented
212	#576	—	5	16	no	—
213	C₂×AGL(1,ℤ/8)	—	5	3	no	—
214	C₂×AGL(1,ℤ/8)	—	5	3	no	—
215	C₂×#135	—	5	3	no	—
216	C₂²×D₈	—	5	3	no	—
217	C₂×#131	—	5	1	no	—
218	C₂²×C₃×C₅	—	2	6	no	—
219	C₂²×C₃×C₅	—	2	6	no	—
220	C₂²×C₃×C₅	—	4	6	no	—
221	C₂²×C₃×C₅	—	8	12	no	—
222	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₃×D₅	—	2	6	no	—
225	C₂×C₃×D₅	—	4	6	no	—
226	C₂×C₃×D₅	—	8	12	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
230	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
231	C₃×Dic₅	—	2	2	no	—
232	C₂⁴×C₃	—	2	3	no	—
233	C₂⁴×C₃	—	10	3	no	—
234	C₃×#41	—	2	8	no	—
235	C₃×#41	—	2	6	no	—
236	C₃×#41	—	5	12	no	—
237	C₃×#41	—	10	8	no	—
238	C₃×#41	—	10	6	no	—
239	C₃×#41	C₂²⋊D₅	1	4	yes	—
240	C₃×#41	C₂²×D₅	1	4	yes	—
241	C₃×#41	C₂²×D₅	1	12	yes	complemented
242	C₂×C₃×Q₈	—	5	1	no	—
243	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
244	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
245	C₂×C₃×D₄	—	2	3	no	—
246	C₂×C₃×D₄	—	2	24	no	—
247	C₂×C₃×D₄	—	2	3	no	—
248	C₂×C₃×D₄	—	2	6	no	—
249	C₂×C₃×D₄	—	5	3	no	—
250	C₂×C₃×D₄	—	5	12	no	—
251	C₂×C₃×D₄	—	10	3	no	—
252	C₂×C₃×D₄	—	10	24	no	—
253	C₂×C₃×D₄	—	10	3	no	—
254	C₂×C₃×D₄	—	10	6	no	—
255	C₂×C₃×D₄	C₂²⋊D₅	1	3	yes	—
256	C₂×C₃×D₄	C₂²×D₅	1	3	yes	—
257	C₂×C₃×D₄	C₂²×D₅	1	12	yes	complemented
258	C₂²×C₃×C₄	—	2	3	no	—
259	C₂²×C₃×C₄	—	10	3	no	—
260	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
261	C₃×Q₁₆	—	5	4	no	—
262	C₃×SD₁₆	—	5	12	no	—
263	C₃×SD₁₆	—	5	12	no	—
264	C₃×D₈	—	5	12	no	—
265	C₃×D₈	—	5	24	no	—
266	C₃×M₁₆	—	5	12	no	—
267	C₂×C₃×C₈	—	5	1	no	—
268	C₂×C₃×C₈	—	5	3	no	—
269	C₂×C₃×C₈	—	5	12	no	—
270	C₂³×C₅	—	2	3	no	—
271	C₂³×C₅	—	2	12	no	—
272	C₂³×C₅	—	8	6	no	—
273	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
274	C₂²×D₅	—	2	3	no	—
275	C₂²×D₅	—	2	12	no	—
276	C₂²×D₅	—	8	6	no	—
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
279	C₅×Q₈	C₂⁴×C₃	1	2	yes	—
280	C₅×D₄	—	2	12	no	—
281	C₅×D₄	—	2	3	no	—
282	C₅×D₄	—	2	12	no	—
283	C₅×D₄	C₂×C₃×D₄	1	12	yes	—
284	C₅×D₄	C₂⁴×C₃	1	6	yes	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	12	no	—
287	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
288	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
289	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
291	C₂²⋊D₅	—	2	12	no	—
292	C₂×Dic₅	—	2	1	no	—
293	D₂₀	—	2	3	no	—
294	D₂₀	—	2	12	no	—
295	D₂₀	C₂⁴×C₃	1	6	yes	—
296	C₄×D₅	—	2	12	no	—
297	Dic₁₀	—	2	1	no	—
298	Dic₁₀	C₂⁴×C₃	1	2	yes	—
299	#168	C₂⁴×C₃	1	2	yes	—
300	#168	C₂⁴×C₃	1	6	yes	—
301	H(5,𝔽₂)	—	2	4	no	—
302	H(5,𝔽₂)	—	5	8	no	—
303	H(5,𝔽₂)	—	10	4	no	—
304	H(5,𝔽₂)	C₂×C₃×D₅	1	8	yes	complemented
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	5	3	no	—
307	C₂×#41	—	10	1	no	—
308	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
309	C₂×#41	C₂×C₃×D₅	1	3	yes	complemented
310	C₂²×D₄	—	2	3	no	—
311	C₂²×D₄	—	5	3	no	—
312	C₂²×D₄	—	10	3	no	—
313	C₂²×D₄	C₂×C₃×D₅	1	3	yes	complemented
314	AGL(1,ℤ/8)	—	5	24	no	—
315	AGL(1,ℤ/8)	—	5	24	no	—
316	#135	—	5	24	no	—
317	C₂×Q₁₆	—	5	1	no	—
318	C₂×SD₁₆	—	5	3	no	—
319	C₂×SD₁₆	—	5	3	no	—
320	C₂×D₈	—	5	3	no	—
321	C₂×D₈	—	5	6	no	—
322	C₂×D₈	—	5	24	no	—
323	#131	—	5	8	no	—
324	C₂×M₁₆	—	5	3	no	—
325	C₂²×C₈	—	5	3	no	—
326	C₂×C₃×C₅	—	2	6	no	—
327	C₂×C₃×C₅	—	4	6	no	—
328	C₂×C₃×C₅	#576	1	2	yes	complemented
329	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
330	C₃×D₅	—	4	6	no	—
331	C₂³×C₃	—	2	3	no	—
332	C₂³×C₃	—	2	12	no	—
333	C₂³×C₃	—	8	6	no	—
334	C₂³×C₃	—	10	3	no	—
335	C₂³×C₃	—	10	12	no	—
336	C₂³×C₃	—	40	6	no	—
337	C₂³×C₃	C₂×C₂²⋊D₅	1	3	yes	—
338	C₃×Q₈	—	2	1	no	—
339	C₃×Q₈	—	5	2	no	—
340	C₃×Q₈	—	10	1	no	—
341	C₃×Q₈	C₂×C₂²⋊D₅	1	4	yes	—
342	C₃×Q₈	C₂³×D₅	1	2	yes	—
343	C₃×D₄	—	2	12	no	—
344	C₃×D₄	—	2	3	no	—
345	C₃×D₄	—	2	12	no	—
346	C₃×D₄	—	5	6	no	—
347	C₃×D₄	—	10	12	no	—
348	C₃×D₄	—	10	12	no	—
349	C₃×D₄	—	10	3	no	—
350	C₃×D₄	C₂×C₂²⋊D₅	1	12	yes	—
351	C₃×D₄	C₂³×D₅	1	6	yes	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	12	no	—
354	C₂×C₃×C₄	—	10	1	no	—
355	C₂×C₃×C₄	—	10	12	no	—
356	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	6	yes	—
357	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
358	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
359	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
360	C₃×C₈	—	5	2	no	—
361	C₃×C₈	—	5	6	no	—
362	C₂²×C₅	—	2	6	no	—
363	C₂²×C₅	—	2	6	no	—
364	C₂²×C₅	—	4	6	no	—
365	C₂²×C₅	—	8	12	no	—
366	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
367	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
368	C₂×D₅	—	2	6	no	—
369	C₂×D₅	—	4	6	no	—
370	C₂×D₅	—	8	12	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
373	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
374	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
375	Dic₅	—	2	2	no	—
376	C₂⁴	—	2	3	no	—
377	C₂⁴	—	10	3	no	—
378	#41	—	2	8	no	—
379	#41	—	2	6	no	—
380	#41	—	5	12	no	—
381	#41	—	10	8	no	—
382	#41	—	10	6	no	—
383	#41	C₃×C₂²⋊D₅	1	4	yes	—
384	#41	C₂²×C₃×D₅	1	4	yes	—
385	#41	C₂²×C₃×D₅	1	12	yes	complemented
386	C₂×Q₈	—	5	1	no	—
387	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
388	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	24	no	—
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	6	no	—
393	C₂×D₄	—	5	3	no	—
394	C₂×D₄	—	5	12	no	—
395	C₂×D₄	—	10	3	no	—
396	C₂×D₄	—	10	24	no	—
397	C₂×D₄	—	10	3	no	—
398	C₂×D₄	—	10	6	no	—
399	C₂×D₄	C₃×C₂²⋊D₅	1	3	yes	—
400	C₂×D₄	C₂²×C₃×D₅	1	3	yes	—
401	C₂×D₄	C₂²×C₃×D₅	1	12	yes	complemented
402	C₂²×C₄	—	2	3	no	—
403	C₂²×C₄	—	10	3	no	—
404	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
405	Q₁₆	—	5	4	no	—
406	SD₁₆	—	5	12	no	—
407	SD₁₆	—	5	12	no	—
408	D₈	—	5	12	no	—
409	D₈	—	5	24	no	—
410	M₁₆	—	5	12	no	—
411	C₂×C₈	—	5	1	no	—
412	C₂×C₈	—	5	3	no	—
413	C₂×C₈	—	5	12	no	—
414	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
415	C₂²×C₃	—	2	6	no	—
416	C₂²×C₃	—	2	6	no	—
417	C₂²×C₃	—	4	6	no	—
418	C₂²×C₃	—	8	12	no	—
419	C₂²×C₃	—	10	6	no	—
420	C₂²×C₃	—	20	6	no	—
421	C₂²×C₃	—	40	12	no	—
422	C₂²×C₃	C₂²×C₂²⋊D₅	1	6	yes	—
423	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	10	2	no	—
426	C₃×C₄	C₂²×C₂²⋊D₅	1	6	yes	—
427	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
428	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
429	C₂×C₅	—	2	6	no	—
430	C₂×C₅	—	4	6	no	—
431	C₂×C₅	C₃×#576	1	2	yes	complemented
432	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
433	D₅	—	4	6	no	—
434	C₂³	—	2	3	no	—
435	C₂³	—	2	12	no	—
436	C₂³	—	8	6	no	—
437	C₂³	—	10	3	no	—
438	C₂³	—	10	12	no	—
439	C₂³	—	40	6	no	—
440	C₂³	C₂×C₃×C₂²⋊D₅	1	3	yes	—
441	Q₈	—	2	1	no	—
442	Q₈	—	5	2	no	—
443	Q₈	—	10	1	no	—
444	Q₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
445	Q₈	C₂³×C₃×D₅	1	2	yes	—
446	D₄	—	2	12	no	—
447	D₄	—	2	3	no	—
448	D₄	—	2	12	no	—
449	D₄	—	5	6	no	—
450	D₄	—	10	12	no	—
451	D₄	—	10	12	no	—
452	D₄	—	10	3	no	—
453	D₄	C₂×C₃×C₂²⋊D₅	1	12	yes	—
454	D₄	C₂³×C₃×D₅	1	6	yes	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	12	no	—
457	C₂×C₄	—	10	1	no	—
458	C₂×C₄	—	10	12	no	—
459	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
460	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	6	yes	—
461	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
462	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
463	C₈	—	5	2	no	—
464	C₈	—	5	6	no	—
465	C₂×C₃	—	2	6	no	—
466	C₂×C₃	—	4	6	no	—
467	C₂×C₃	—	20	6	no	—
468	C₂×C₃	#66169	1	2	yes	direct product factor
469	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
470	C₅	C₂×C₃×#576	1	1	yes	characteristic, complemented, Sylow
471	C₂²	—	2	6	no	—
472	C₂²	—	2	6	no	—
473	C₂²	—	4	6	no	—
474	C₂²	—	8	12	no	—
475	C₂²	—	10	6	no	—
476	C₂²	—	20	6	no	—
477	C₂²	—	40	12	no	—
478	C₂²	C₂²×C₃×C₂²⋊D₅	1	6	yes	—
479	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	10	2	no	—
482	C₄	C₂²×C₃×C₂²⋊D₅	1	6	yes	—
483	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
484	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
485	C₃	C₂×#66169	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	2	6	no	—
487	C₂	—	4	6	no	—
488	C₂	—	20	6	no	—
489	C₂	C₃×#66169	1	2	yes	direct product factor
490	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×H(5,𝔽₂)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×H(5,𝔽₂)	D₅
hypocenter	C₅	C₂×C₃×#576
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₃×#4149	C₂	semidirect
3. C₃×#66169	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×#4078	C₂	semidirect
8. C₂²×C₃×#686	C₂	semidirect
9. C₂×#66169	C₃	direct (N × H)
11. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
14. C₂×C₃×C₅×#41	C₂²	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₃×#4149	C₂²	semidirect
21. C₂×C₃×#709	C₂²	semidirect
22. C₂²×C₃×D₂₀	C₂²	semidirect
23. C₃×#4096	C₂²	semidirect
24. C₃×#4095	C₂²	semidirect
25. C₃×#4094	C₂²	semidirect
26. C₂×C₃×#689	C₂²	semidirect
27. C₂×C₃×#688	C₂²	semidirect
28. C₂×C₃×#687	C₂²	semidirect
29. C₃×#4078	C₂²	semidirect
30. C₂×C₃×#686	C₂²	semidirect
31. C₂×C₃×#686	C₂²	semidirect
32. C₂×C₃×#686	C₂²	semidirect
33. C₂×C₃×#681	C₂²	semidirect
34. C₂²×C₃×#168	C₂²	semidirect
36. C₂×C₅×H(5,𝔽₂)	C₂×C₃	semidirect
37. C₂×#4149	C₂×C₃	semidirect
38. #66169	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×#4078	C₂×C₃	semidirect
43. C₂²×#686	C₂×C₃	semidirect
50. C₃×C₅×#41	C₂³	semidirect
59. C₂×C₃×C₅×D₄	C₂³	semidirect
66. C₃×#709	C₂³	semidirect
70. C₂×C₃×D₂₀	C₂³	semidirect
73. C₃×#689	C₂³	semidirect
74. C₃×#688	C₂³	semidirect
75. C₃×#687	C₂³	semidirect
76. C₃×#686	C₂³	semidirect
77. C₃×#686	C₂³	semidirect
78. C₃×#681	C₂³	semidirect
81. C₂×C₃×#168	C₂³	semidirect
83. C₂×C₃×H(5,𝔽₂)	D₅	semidirect
91. C₅×H(5,𝔽₂)	C₂²×C₃	semidirect
94. C₂×C₅×#41	C₂²×C₃	semidirect
96. C₂²×C₅×D₄	C₂²×C₃	semidirect
98. #4149	C₂²×C₃	semidirect
101. C₂×#709	C₂²×C₃	semidirect
102. C₂²×D₂₀	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. C₂×#688	C₂²×C₃	semidirect
108. C₂×#687	C₂²×C₃	semidirect
109. #4078	C₂²×C₃	semidirect
110. C₂×#686	C₂²×C₃	semidirect
111. C₂×#686	C₂²×C₃	semidirect
112. C₂×#686	C₂²×C₃	semidirect
113. C₂×#681	C₂²×C₃	semidirect
114. C₂²×#168	C₂²×C₃	semidirect
150. C₃×H(5,𝔽₂)	C₂×D₅	semidirect
155. C₂×C₃×#41	C₂×D₅	semidirect
159. C₂²×C₃×D₄	C₂×D₅	semidirect
178. C₅×#41	C₂³×C₃	semidirect
187. C₂×C₅×D₄	C₂³×C₃	semidirect
194. #709	C₂³×C₃	semidirect
198. C₂×D₂₀	C₂³×C₃	semidirect
201. #689	C₂³×C₃	semidirect
202. #688	C₂³×C₃	semidirect
203. #687	C₂³×C₃	semidirect
204. #686	C₂³×C₃	semidirect
205. #686	C₂³×C₃	semidirect
206. #681	C₂³×C₃	semidirect
209. C₂×#168	C₂³×C₃	semidirect
211. C₂×H(5,𝔽₂)	C₃×D₅	semidirect
241. C₃×#41	C₂²×D₅	semidirect
257. C₂×C₃×D₄	C₂²×D₅	semidirect
304. H(5,𝔽₂)	C₂×C₃×D₅	semidirect
309. C₂×#41	C₂×C₃×D₅	semidirect
313. C₂²×D₄	C₂×C₃×D₅	semidirect
328. C₂×C₃×C₅	#576	semidirect
385. #41	C₂²×C₃×D₅	semidirect
401. C₂×D₄	C₂²×C₃×D₅	semidirect
414. C₃×C₅	C₂×#576	semidirect
431. C₂×C₅	C₃×#576	semidirect
468. C₂×C₃	#66169	direct (N × H)
470. C₅	C₂×C₃×#576	semidirect
485. C₃	C₂×#66169	direct (N × H)
489. C₂	C₃×#66169	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×H(5,𝔽₂)	2
C₂×C₃×#4149	2
C₃×#66169	2
C₂×C₃×#4096	2
C₂×C₃×#4095	2
C₂×C₃×#4094	2
C₂×C₃×#4078	2
C₂²×C₃×#686	2
C₂×#66169	3
C₂×C₃×#576	5

Subgroups — C2×C3×#66169 #14509958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66169 #14509958