Subgroups — C₂²×C₃×C₄×C₅²×C₈ #72188317

Order 9600.

6080 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×C₅²×C₈	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₅²×C₈	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄×C₅²×C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₄×C₅²	C₄	1	2	yes	—
6	C₂³×C₃×C₄×C₅²	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄²×C₅²	C₄	1	6	yes	—
8	C₂×C₃×C₄²×C₅²	C₂²	1	6	yes	—
9	C₂²×C₃×C₅²×C₈	C₄	1	16	yes	direct product factor
10	C₂²×C₃×C₅²×C₈	C₂²	1	12	yes	—
11	C₃×C₄×C₅²×C₈	C₂²	1	16	yes	direct product factor
12	C₂²×C₃×C₄×C₅×C₈	C₅	1	6	yes	maximal, direct product factor
13	C₂³×C₅²×C₈	C₂×C₃	1	2	yes	—
14	C₂²×C₄²×C₅²	C₂×C₃	1	1	yes	characteristic
15	C₂×C₄×C₅²×C₈	C₂×C₃	1	12	yes	direct product factor
16	C₂⁴×C₃×C₅²	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₃×C₄×C₅²	C₈	1	16	yes	direct product factor
18	C₂²×C₃×C₄×C₅²	C₂×C₄	1	3	yes	—
19	C₂²×C₃×C₄×C₅²	C₂×C₄	1	8	yes	—
20	C₂²×C₃×C₄×C₅²	C₂×C₄	1	12	yes	—
21	C₂²×C₃×C₄×C₅²	C₂³	1	3	yes	—
22	C₂×C₃×C₅²×C₈	C₂×C₄	1	48	yes	direct product factor
23	C₂×C₃×C₅²×C₈	C₂³	1	8	yes	—
24	C₃×C₄²×C₅²	C₂×C₄	1	12	yes	—
25	C₃×C₄²×C₅²	C₂³	1	4	yes	—
26	C₂³×C₃×C₅×C₈	C₂×C₅	1	12	yes	—
27	C₂²×C₃×C₄²×C₅	C₂×C₅	1	6	yes	—
28	C₂×C₃×C₄×C₅×C₈	C₂×C₅	1	72	yes	direct product factor
29	C₂³×C₄×C₅²	C₃×C₄	1	2	yes	—
30	C₂³×C₄×C₅²	C₂²×C₃	1	1	yes	characteristic
31	C₂²×C₅²×C₈	C₃×C₄	1	16	yes	direct product factor
32	C₂²×C₅²×C₈	C₂²×C₃	1	12	yes	—
33	C₂×C₄²×C₅²	C₃×C₄	1	6	yes	—
34	C₂×C₄²×C₅²	C₂²×C₃	1	6	yes	—
35	C₄×C₅²×C₈	C₂²×C₃	1	16	yes	direct product factor
36	C₂²×C₄×C₅×C₈	C₃×C₅	1	6	yes	direct product factor
37	C₂³×C₃×C₅²	C₄²	1	4	yes	—
38	C₂³×C₃×C₅²	C₂×C₈	1	8	yes	—
39	C₂³×C₃×C₅²	C₂²×C₄	1	3	yes	—
40	C₂×C₃×C₄×C₅²	C₄²	1	12	yes	—
41	C₂×C₃×C₄×C₅²	C₂×C₈	1	48	yes	direct product factor
42	C₂×C₃×C₄×C₅²	C₂²×C₄	1	3	yes	—
43	C₂×C₃×C₄×C₅²	C₂²×C₄	1	8	yes	—
44	C₂×C₃×C₄×C₅²	C₂²×C₄	1	12	yes	—
45	C₂×C₃×C₄×C₅²	C₂⁴	1	1	yes	characteristic
46	C₃×C₅²×C₈	C₂²×C₄	1	16	yes	direct product factor
47	C₂³×C₃×C₄×C₅	C₄×C₅	1	12	yes	—
48	C₂³×C₃×C₄×C₅	C₂²×C₅	1	6	yes	—
49	C₂²×C₃×C₅×C₈	C₄×C₅	1	96	yes	direct product factor
50	C₂²×C₃×C₅×C₈	C₂²×C₅	1	72	yes	—
51	C₂×C₃×C₄²×C₅	C₄×C₅	1	36	yes	—
52	C₂×C₃×C₄²×C₅	C₂²×C₅	1	36	yes	—
53	C₃×C₄×C₅×C₈	C₂²×C₅	1	96	yes	direct product factor
54	C₂⁴×C₅²	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₅²	C₃×C₈	1	16	yes	direct product factor
56	C₂²×C₄×C₅²	C₂×C₃×C₄	1	3	yes	—
57	C₂²×C₄×C₅²	C₂×C₃×C₄	1	8	yes	—
58	C₂²×C₄×C₅²	C₂×C₃×C₄	1	12	yes	—
59	C₂²×C₄×C₅²	C₂³×C₃	1	3	yes	—
60	C₂×C₅²×C₈	C₂×C₃×C₄	1	48	yes	direct product factor
61	C₂×C₅²×C₈	C₂³×C₃	1	8	yes	—
62	C₄²×C₅²	C₂×C₃×C₄	1	12	yes	—
63	C₄²×C₅²	C₂³×C₃	1	4	yes	—
64	C₂²×C₃×C₄×C₈	C₅²	1	1	yes	characteristic, direct product factor, Hall
65	C₂³×C₅×C₈	C₂×C₃×C₅	1	12	yes	—
66	C₂²×C₄²×C₅	C₂×C₃×C₅	1	6	yes	—
67	C₂×C₄×C₅×C₈	C₂×C₃×C₅	1	72	yes	direct product factor
68	C₂²×C₃×C₅²	C₄×C₈	1	16	yes	direct product factor
69	C₂²×C₃×C₅²	C₂×C₄²	1	6	yes	—
70	C₂²×C₃×C₅²	C₂²×C₈	1	12	yes	—
71	C₂²×C₃×C₅²	C₂³×C₄	1	1	yes	characteristic
72	C₃×C₄×C₅²	C₂×C₄²	1	6	yes	—
73	C₃×C₄×C₅²	C₂²×C₈	1	16	yes	direct product factor
74	C₃×C₄×C₅²	C₂³×C₄	1	2	yes	—
75	C₂⁴×C₃×C₅	C₂×C₄×C₅	1	6	yes	—
76	C₂²×C₃×C₄×C₅	C₅×C₈	1	96	yes	direct product factor
77	C₂²×C₃×C₄×C₅	C₂×C₄×C₅	1	18	yes	—
78	C₂²×C₃×C₄×C₅	C₂×C₄×C₅	1	48	yes	—
79	C₂²×C₃×C₄×C₅	C₂×C₄×C₅	1	72	yes	—
80	C₂²×C₃×C₄×C₅	C₂³×C₅	1	18	yes	—
81	C₂×C₃×C₅×C₈	C₂×C₄×C₅	1	288	yes	direct product factor
82	C₂×C₃×C₅×C₈	C₂³×C₅	1	48	yes	—
83	C₃×C₄²×C₅	C₂×C₄×C₅	1	72	yes	—
84	C₃×C₄²×C₅	C₂³×C₅	1	24	yes	—
85	C₂³×C₅²	C₃×C₄²	1	4	yes	—
86	C₂³×C₅²	C₂×C₃×C₈	1	8	yes	—
87	C₂³×C₅²	C₂²×C₃×C₄	1	3	yes	—
88	C₂×C₄×C₅²	C₃×C₄²	1	12	yes	—
89	C₂×C₄×C₅²	C₂×C₃×C₈	1	48	yes	direct product factor
90	C₂×C₄×C₅²	C₂²×C₃×C₄	1	3	yes	—
91	C₂×C₄×C₅²	C₂²×C₃×C₄	1	8	yes	—
92	C₂×C₄×C₅²	C₂²×C₃×C₄	1	12	yes	—
93	C₂×C₄×C₅²	C₂⁴×C₃	1	1	yes	characteristic
94	C₅²×C₈	C₂²×C₃×C₄	1	16	yes	direct product factor
95	C₂³×C₃×C₈	C₂×C₅²	1	2	yes	—
96	C₂²×C₃×C₄²	C₂×C₅²	1	1	yes	characteristic
97	C₂×C₃×C₄×C₈	C₂×C₅²	1	12	yes	direct product factor
98	C₂³×C₄×C₅	C₃×C₄×C₅	1	12	yes	—
99	C₂³×C₄×C₅	C₂²×C₃×C₅	1	6	yes	—
100	C₂²×C₅×C₈	C₃×C₄×C₅	1	96	yes	direct product factor
101	C₂²×C₅×C₈	C₂²×C₃×C₅	1	72	yes	—
102	C₂×C₄²×C₅	C₃×C₄×C₅	1	36	yes	—
103	C₂×C₄²×C₅	C₂²×C₃×C₅	1	36	yes	—
104	C₄×C₅×C₈	C₂²×C₃×C₅	1	96	yes	direct product factor
105	C₂×C₃×C₅²	C₂×C₄×C₈	1	12	yes	direct product factor
106	C₂×C₃×C₅²	C₂²×C₄²	1	1	yes	characteristic
107	C₂×C₃×C₅²	C₂³×C₈	1	2	yes	—
108	C₂²×C₄×C₈	C₃×C₅²	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	C₄²×C₅	1	24	yes	—
110	C₂³×C₃×C₅	C₂×C₅×C₈	1	48	yes	—
111	C₂³×C₃×C₅	C₂²×C₄×C₅	1	18	yes	—
112	C₂×C₃×C₄×C₅	C₄²×C₅	1	72	yes	—
113	C₂×C₃×C₄×C₅	C₂×C₅×C₈	1	288	yes	direct product factor
114	C₂×C₃×C₄×C₅	C₂²×C₄×C₅	1	18	yes	—
115	C₂×C₃×C₄×C₅	C₂²×C₄×C₅	1	48	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄×C₅	1	72	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴×C₅	1	6	yes	—
118	C₃×C₅×C₈	C₂²×C₄×C₅	1	96	yes	direct product factor
119	C₂²×C₅²	C₃×C₄×C₈	1	16	yes	direct product factor
120	C₂²×C₅²	C₂×C₃×C₄²	1	6	yes	—
121	C₂²×C₅²	C₂²×C₃×C₈	1	12	yes	—
122	C₂²×C₅²	C₂³×C₃×C₄	1	1	yes	characteristic
123	C₄×C₅²	C₂×C₃×C₄²	1	6	yes	—
124	C₄×C₅²	C₂²×C₃×C₈	1	16	yes	direct product factor
125	C₄×C₅²	C₂³×C₃×C₄	1	2	yes	—
126	C₂³×C₃×C₄	C₄×C₅²	1	2	yes	—
127	C₂³×C₃×C₄	C₂²×C₅²	1	1	yes	characteristic
128	C₂²×C₃×C₈	C₄×C₅²	1	16	yes	direct product factor
129	C₂²×C₃×C₈	C₂²×C₅²	1	12	yes	—
130	C₂×C₃×C₄²	C₄×C₅²	1	6	yes	—
131	C₂×C₃×C₄²	C₂²×C₅²	1	6	yes	—
132	C₃×C₄×C₈	C₂²×C₅²	1	16	yes	direct product factor
133	C₂⁴×C₅	C₂×C₃×C₄×C₅	1	6	yes	—
134	C₂²×C₄×C₅	C₃×C₅×C₈	1	96	yes	direct product factor
135	C₂²×C₄×C₅	C₂×C₃×C₄×C₅	1	18	yes	—
136	C₂²×C₄×C₅	C₂×C₃×C₄×C₅	1	48	yes	—
137	C₂²×C₄×C₅	C₂×C₃×C₄×C₅	1	72	yes	—
138	C₂²×C₄×C₅	C₂³×C₃×C₅	1	18	yes	—
139	C₂×C₅×C₈	C₂×C₃×C₄×C₅	1	288	yes	direct product factor
140	C₂×C₅×C₈	C₂³×C₃×C₅	1	48	yes	—
141	C₄²×C₅	C₂×C₃×C₄×C₅	1	72	yes	—
142	C₄²×C₅	C₂³×C₃×C₅	1	24	yes	—
143	C₃×C₅²	C₂²×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
144	C₂³×C₈	C₂×C₃×C₅²	1	2	yes	—
145	C₂²×C₄²	C₂×C₃×C₅²	1	1	yes	characteristic
146	C₂×C₄×C₈	C₂×C₃×C₅²	1	12	yes	direct product factor
147	C₂²×C₃×C₅	C₄×C₅×C₈	1	96	yes	direct product factor
148	C₂²×C₃×C₅	C₂×C₄²×C₅	1	36	yes	—
149	C₂²×C₃×C₅	C₂²×C₅×C₈	1	72	yes	—
150	C₂²×C₃×C₅	C₂³×C₄×C₅	1	6	yes	—
151	C₃×C₄×C₅	C₂×C₄²×C₅	1	36	yes	—
152	C₃×C₄×C₅	C₂²×C₅×C₈	1	96	yes	direct product factor
153	C₃×C₄×C₅	C₂³×C₄×C₅	1	12	yes	—
154	C₂×C₅²	C₂×C₃×C₄×C₈	1	12	yes	direct product factor
155	C₂×C₅²	C₂²×C₃×C₄²	1	1	yes	characteristic
156	C₂×C₅²	C₂³×C₃×C₈	1	2	yes	—
157	C₂⁴×C₃	C₂×C₄×C₅²	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₅²×C₈	1	16	yes	direct product factor
159	C₂²×C₃×C₄	C₂×C₄×C₅²	1	3	yes	—
160	C₂²×C₃×C₄	C₂×C₄×C₅²	1	8	yes	—
161	C₂²×C₃×C₄	C₂×C₄×C₅²	1	12	yes	—
162	C₂²×C₃×C₄	C₂³×C₅²	1	3	yes	—
163	C₂×C₃×C₈	C₂×C₄×C₅²	1	48	yes	direct product factor
164	C₂×C₃×C₈	C₂³×C₅²	1	8	yes	—
165	C₃×C₄²	C₂×C₄×C₅²	1	12	yes	—
166	C₃×C₄²	C₂³×C₅²	1	4	yes	—
167	C₂³×C₅	C₃×C₄²×C₅	1	24	yes	—
168	C₂³×C₅	C₂×C₃×C₅×C₈	1	48	yes	—
169	C₂³×C₅	C₂²×C₃×C₄×C₅	1	18	yes	—
170	C₂×C₄×C₅	C₃×C₄²×C₅	1	72	yes	—
171	C₂×C₄×C₅	C₂×C₃×C₅×C₈	1	288	yes	direct product factor
172	C₂×C₄×C₅	C₂²×C₃×C₄×C₅	1	18	yes	—
173	C₂×C₄×C₅	C₂²×C₃×C₄×C₅	1	48	yes	—
174	C₂×C₄×C₅	C₂²×C₃×C₄×C₅	1	72	yes	—
175	C₂×C₄×C₅	C₂⁴×C₃×C₅	1	6	yes	—
176	C₅×C₈	C₂²×C₃×C₄×C₅	1	96	yes	direct product factor
177	C₂³×C₄	C₃×C₄×C₅²	1	2	yes	—
178	C₂³×C₄	C₂²×C₃×C₅²	1	1	yes	characteristic
179	C₂²×C₈	C₃×C₄×C₅²	1	16	yes	direct product factor
180	C₂²×C₈	C₂²×C₃×C₅²	1	12	yes	—
181	C₂×C₄²	C₃×C₄×C₅²	1	6	yes	—
182	C₂×C₄²	C₂²×C₃×C₅²	1	6	yes	—
183	C₄×C₈	C₂²×C₃×C₅²	1	16	yes	direct product factor
184	C₂×C₃×C₅	C₂×C₄×C₅×C₈	1	72	yes	direct product factor
185	C₂×C₃×C₅	C₂²×C₄²×C₅	1	6	yes	—
186	C₂×C₃×C₅	C₂³×C₅×C₈	1	12	yes	—
187	C₅²	C₂²×C₃×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³×C₃	C₄²×C₅²	1	4	yes	—
189	C₂³×C₃	C₂×C₅²×C₈	1	8	yes	—
190	C₂³×C₃	C₂²×C₄×C₅²	1	3	yes	—
191	C₂×C₃×C₄	C₄²×C₅²	1	12	yes	—
192	C₂×C₃×C₄	C₂×C₅²×C₈	1	48	yes	direct product factor
193	C₂×C₃×C₄	C₂²×C₄×C₅²	1	3	yes	—
194	C₂×C₃×C₄	C₂²×C₄×C₅²	1	8	yes	—
195	C₂×C₃×C₄	C₂²×C₄×C₅²	1	12	yes	—
196	C₂×C₃×C₄	C₂⁴×C₅²	1	1	yes	characteristic
197	C₃×C₈	C₂²×C₄×C₅²	1	16	yes	direct product factor
198	C₂²×C₅	C₃×C₄×C₅×C₈	1	96	yes	direct product factor
199	C₂²×C₅	C₂×C₃×C₄²×C₅	1	36	yes	—
200	C₂²×C₅	C₂²×C₃×C₅×C₈	1	72	yes	—
201	C₂²×C₅	C₂³×C₃×C₄×C₅	1	6	yes	—
202	C₄×C₅	C₂×C₃×C₄²×C₅	1	36	yes	—
203	C₄×C₅	C₂²×C₃×C₅×C₈	1	96	yes	direct product factor
204	C₄×C₅	C₂³×C₃×C₄×C₅	1	12	yes	—
205	C₂⁴	C₂×C₃×C₄×C₅²	1	1	yes	characteristic
206	C₂²×C₄	C₃×C₅²×C₈	1	16	yes	direct product factor
207	C₂²×C₄	C₂×C₃×C₄×C₅²	1	3	yes	—
208	C₂²×C₄	C₂×C₃×C₄×C₅²	1	8	yes	—
209	C₂²×C₄	C₂×C₃×C₄×C₅²	1	12	yes	—
210	C₂²×C₄	C₂³×C₃×C₅²	1	3	yes	—
211	C₂×C₈	C₂×C₃×C₄×C₅²	1	48	yes	direct product factor
212	C₂×C₈	C₂³×C₃×C₅²	1	8	yes	—
213	C₄²	C₂×C₃×C₄×C₅²	1	12	yes	—
214	C₄²	C₂³×C₃×C₅²	1	4	yes	—
215	C₃×C₅	C₂²×C₄×C₅×C₈	1	6	yes	direct product factor
216	C₂²×C₃	C₄×C₅²×C₈	1	16	yes	direct product factor
217	C₂²×C₃	C₂×C₄²×C₅²	1	6	yes	—
218	C₂²×C₃	C₂²×C₅²×C₈	1	12	yes	—
219	C₂²×C₃	C₂³×C₄×C₅²	1	1	yes	characteristic
220	C₃×C₄	C₂×C₄²×C₅²	1	6	yes	—
221	C₃×C₄	C₂²×C₅²×C₈	1	16	yes	direct product factor
222	C₃×C₄	C₂³×C₄×C₅²	1	2	yes	—
223	C₂×C₅	C₂×C₃×C₄×C₅×C₈	1	72	yes	direct product factor
224	C₂×C₅	C₂²×C₃×C₄²×C₅	1	6	yes	—
225	C₂×C₅	C₂³×C₃×C₅×C₈	1	12	yes	—
226	C₂³	C₃×C₄²×C₅²	1	4	yes	—
227	C₂³	C₂×C₃×C₅²×C₈	1	8	yes	—
228	C₂³	C₂²×C₃×C₄×C₅²	1	3	yes	—
229	C₂×C₄	C₃×C₄²×C₅²	1	12	yes	—
230	C₂×C₄	C₂×C₃×C₅²×C₈	1	48	yes	direct product factor
231	C₂×C₄	C₂²×C₃×C₄×C₅²	1	3	yes	—
232	C₂×C₄	C₂²×C₃×C₄×C₅²	1	8	yes	—
233	C₂×C₄	C₂²×C₃×C₄×C₅²	1	12	yes	—
234	C₂×C₄	C₂⁴×C₃×C₅²	1	1	yes	characteristic
235	C₈	C₂²×C₃×C₄×C₅²	1	16	yes	direct product factor
236	C₂×C₃	C₂×C₄×C₅²×C₈	1	12	yes	direct product factor
237	C₂×C₃	C₂²×C₄²×C₅²	1	1	yes	characteristic
238	C₂×C₃	C₂³×C₅²×C₈	1	2	yes	—
239	C₅	C₂²×C₃×C₄×C₅×C₈	1	6	yes	direct product factor
240	C₂²	C₃×C₄×C₅²×C₈	1	16	yes	direct product factor
241	C₂²	C₂²×C₃×C₅²×C₈	1	12	yes	—
242	C₂²	C₂×C₃×C₄²×C₅²	1	6	yes	—
243	C₂²	C₂³×C₃×C₄×C₅²	1	1	yes	characteristic
244	C₄	C₂²×C₃×C₅²×C₈	1	16	yes	direct product factor
245	C₄	C₂×C₃×C₄²×C₅²	1	6	yes	—
246	C₄	C₂³×C₃×C₄×C₅²	1	2	yes	—
247	C₃	C₂²×C₄×C₅²×C₈	1	1	yes	characteristic, direct product factor, Sylow
248	C₂	C₂×C₃×C₄×C₅²×C₈	1	12	yes	direct product factor
249	C₂	C₂³×C₃×C₅²×C₈	1	2	yes	—
250	C₂	C₂²×C₃×C₄²×C₅²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅²
socle, prime radical	C₂⁴×C₃×C₅²	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×C₅²×C₈	C₂	direct (N × H)
4. C₂²×C₄×C₅²×C₈	C₃	direct (N × H)
9. C₂²×C₃×C₅²×C₈	C₄	direct (N × H)
11. C₃×C₄×C₅²×C₈	C₂²	direct (N × H)
12. C₂²×C₃×C₄×C₅×C₈	C₅	direct (N × H)
15. C₂×C₄×C₅²×C₈	C₂×C₃	direct (N × H)
17. C₂²×C₃×C₄×C₅²	C₈	direct (N × H)
22. C₂×C₃×C₅²×C₈	C₂×C₄	direct (N × H)
28. C₂×C₃×C₄×C₅×C₈	C₂×C₅	direct (N × H)
31. C₂²×C₅²×C₈	C₃×C₄	direct (N × H)
35. C₄×C₅²×C₈	C₂²×C₃	direct (N × H)
36. C₂²×C₄×C₅×C₈	C₃×C₅	direct (N × H)
41. C₂×C₃×C₄×C₅²	C₂×C₈	direct (N × H)
46. C₃×C₅²×C₈	C₂²×C₄	direct (N × H)
49. C₂²×C₃×C₅×C₈	C₄×C₅	direct (N × H)
53. C₃×C₄×C₅×C₈	C₂²×C₅	direct (N × H)
55. C₂²×C₄×C₅²	C₃×C₈	direct (N × H)
60. C₂×C₅²×C₈	C₂×C₃×C₄	direct (N × H)
64. C₂²×C₃×C₄×C₈	C₅²	direct (N × H)
67. C₂×C₄×C₅×C₈	C₂×C₃×C₅	direct (N × H)
68. C₂²×C₃×C₅²	C₄×C₈	direct (N × H)
73. C₃×C₄×C₅²	C₂²×C₈	direct (N × H)
76. C₂²×C₃×C₄×C₅	C₅×C₈	direct (N × H)
81. C₂×C₃×C₅×C₈	C₂×C₄×C₅	direct (N × H)
89. C₂×C₄×C₅²	C₂×C₃×C₈	direct (N × H)
94. C₅²×C₈	C₂²×C₃×C₄	direct (N × H)
97. C₂×C₃×C₄×C₈	C₂×C₅²	direct (N × H)
100. C₂²×C₅×C₈	C₃×C₄×C₅	direct (N × H)
104. C₄×C₅×C₈	C₂²×C₃×C₅	direct (N × H)
105. C₂×C₃×C₅²	C₂×C₄×C₈	direct (N × H)
108. C₂²×C₄×C₈	C₃×C₅²	direct (N × H)
113. C₂×C₃×C₄×C₅	C₂×C₅×C₈	direct (N × H)
118. C₃×C₅×C₈	C₂²×C₄×C₅	direct (N × H)
119. C₂²×C₅²	C₃×C₄×C₈	direct (N × H)
124. C₄×C₅²	C₂²×C₃×C₈	direct (N × H)
128. C₂²×C₃×C₈	C₄×C₅²	direct (N × H)
132. C₃×C₄×C₈	C₂²×C₅²	direct (N × H)
134. C₂²×C₄×C₅	C₃×C₅×C₈	direct (N × H)
139. C₂×C₅×C₈	C₂×C₃×C₄×C₅	direct (N × H)
143. C₃×C₅²	C₂²×C₄×C₈	direct (N × H)
146. C₂×C₄×C₈	C₂×C₃×C₅²	direct (N × H)
147. C₂²×C₃×C₅	C₄×C₅×C₈	direct (N × H)
152. C₃×C₄×C₅	C₂²×C₅×C₈	direct (N × H)
154. C₂×C₅²	C₂×C₃×C₄×C₈	direct (N × H)
158. C₂²×C₃×C₄	C₅²×C₈	direct (N × H)
163. C₂×C₃×C₈	C₂×C₄×C₅²	direct (N × H)
171. C₂×C₄×C₅	C₂×C₃×C₅×C₈	direct (N × H)
176. C₅×C₈	C₂²×C₃×C₄×C₅	direct (N × H)
179. C₂²×C₈	C₃×C₄×C₅²	direct (N × H)
183. C₄×C₈	C₂²×C₃×C₅²	direct (N × H)
184. C₂×C₃×C₅	C₂×C₄×C₅×C₈	direct (N × H)
187. C₅²	C₂²×C₃×C₄×C₈	direct (N × H)
192. C₂×C₃×C₄	C₂×C₅²×C₈	direct (N × H)
197. C₃×C₈	C₂²×C₄×C₅²	direct (N × H)
198. C₂²×C₅	C₃×C₄×C₅×C₈	direct (N × H)
203. C₄×C₅	C₂²×C₃×C₅×C₈	direct (N × H)
206. C₂²×C₄	C₃×C₅²×C₈	direct (N × H)
211. C₂×C₈	C₂×C₃×C₄×C₅²	direct (N × H)
215. C₃×C₅	C₂²×C₄×C₅×C₈	direct (N × H)
216. C₂²×C₃	C₄×C₅²×C₈	direct (N × H)
221. C₃×C₄	C₂²×C₅²×C₈	direct (N × H)
223. C₂×C₅	C₂×C₃×C₄×C₅×C₈	direct (N × H)
230. C₂×C₄	C₂×C₃×C₅²×C₈	direct (N × H)
235. C₈	C₂²×C₃×C₄×C₅²	direct (N × H)
236. C₂×C₃	C₂×C₄×C₅²×C₈	direct (N × H)
239. C₅	C₂²×C₃×C₄×C₅×C₈	direct (N × H)
240. C₂²	C₃×C₄×C₅²×C₈	direct (N × H)
244. C₄	C₂²×C₃×C₅²×C₈	direct (N × H)
247. C₃	C₂²×C₄×C₅²×C₈	direct (N × H)
248. C₂	C₂×C₃×C₄×C₅²×C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄²×C₅²	2
C₂³×C₃×C₅²×C₈	2
C₂×C₃×C₄×C₅²×C₈	2
C₂²×C₄×C₅²×C₈	3
C₂²×C₃×C₄×C₅×C₈	5

Subgroups — C22×C3×C4×C52×C8 #72188317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄×C₅²×C₈ #72188317