Subgroups — C₂×C₃×C₄×C₅×C₈×C₁₃ #72190824

Order 12480.

648 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₅×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₈×C₁₃	C₂	1	2	yes	maximal
3	C₃×C₄×C₅×C₈×C₁₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₅×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₄×C₅×C₁₃	C₄	1	2	yes	—
6	C₂²×C₃×C₄×C₅×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₅×C₈×C₁₃	C₄	1	8	yes	direct product factor
8	C₂×C₃×C₅×C₈×C₁₃	C₂²	1	4	yes	—
9	C₃×C₄²×C₅×C₁₃	C₄	1	2	yes	—
10	C₃×C₄²×C₅×C₁₃	C₂²	1	2	yes	—
11	C₂×C₃×C₄×C₈×C₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₄²×C₅×C₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₅×C₈×C₁₃	C₂×C₃	1	2	yes	—
14	C₄×C₅×C₈×C₁₃	C₂×C₃	1	4	yes	direct product factor
15	C₂³×C₃×C₅×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×C₅×C₁₃	C₈	1	8	yes	direct product factor
17	C₂×C₃×C₄×C₅×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×C₅×C₁₃	C₂×C₄	1	4	yes	—
19	C₂×C₃×C₄×C₅×C₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₃×C₄×C₅×C₁₃	C₂³	1	1	yes	characteristic
21	C₃×C₅×C₈×C₁₃	C₂×C₄	1	8	yes	direct product factor
22	C₂²×C₃×C₈×C₁₃	C₂×C₅	1	2	yes	—
23	C₂×C₃×C₄²×C₁₃	C₂×C₅	1	1	yes	characteristic
24	C₃×C₄×C₈×C₁₃	C₂×C₅	1	4	yes	direct product factor
25	C₂²×C₄×C₅×C₁₃	C₃×C₄	1	2	yes	—
26	C₂²×C₄×C₅×C₁₃	C₂²×C₃	1	1	yes	characteristic
27	C₂×C₅×C₈×C₁₃	C₃×C₄	1	8	yes	direct product factor
28	C₂×C₅×C₈×C₁₃	C₂²×C₃	1	4	yes	—
29	C₄²×C₅×C₁₃	C₃×C₄	1	2	yes	—
30	C₄²×C₅×C₁₃	C₂²×C₃	1	2	yes	—
31	C₂×C₃×C₄×C₅×C₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₄×C₈×C₁₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
33	C₂²×C₃×C₅×C₁₃	C₄²	1	2	yes	—
34	C₂²×C₃×C₅×C₁₃	C₂×C₈	1	4	yes	—
35	C₂²×C₃×C₅×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×C₄×C₅×C₁₃	C₄²	1	2	yes	—
37	C₃×C₄×C₅×C₁₃	C₂×C₈	1	8	yes	direct product factor
38	C₃×C₄×C₅×C₁₃	C₂²×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₁₃	C₄×C₅	1	2	yes	—
40	C₂²×C₃×C₄×C₁₃	C₂²×C₅	1	1	yes	characteristic
41	C₂×C₃×C₈×C₁₃	C₄×C₅	1	8	yes	direct product factor
42	C₂×C₃×C₈×C₁₃	C₂²×C₅	1	4	yes	—
43	C₃×C₄²×C₁₃	C₄×C₅	1	2	yes	—
44	C₃×C₄²×C₁₃	C₂²×C₅	1	2	yes	—
45	C₂³×C₅×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
46	C₂×C₄×C₅×C₁₃	C₃×C₈	1	8	yes	direct product factor
47	C₂×C₄×C₅×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×C₁₃	C₂×C₃×C₄	1	4	yes	—
49	C₂×C₄×C₅×C₁₃	C₂×C₃×C₄	1	4	yes	—
50	C₂×C₄×C₅×C₁₃	C₂³×C₃	1	1	yes	characteristic
51	C₅×C₈×C₁₃	C₂×C₃×C₄	1	8	yes	direct product factor
52	C₂²×C₃×C₅×C₈	C₂×C₁₃	1	2	yes	—
53	C₂×C₃×C₄²×C₅	C₂×C₁₃	1	1	yes	characteristic
54	C₃×C₄×C₅×C₈	C₂×C₁₃	1	4	yes	direct product factor
55	C₂²×C₈×C₁₃	C₂×C₃×C₅	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
57	C₄×C₈×C₁₃	C₂×C₃×C₅	1	4	yes	direct product factor
58	C₂×C₃×C₅×C₁₃	C₄×C₈	1	4	yes	direct product factor
59	C₂×C₃×C₅×C₁₃	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₃×C₅×C₁₃	C₂²×C₈	1	2	yes	—
61	C₂×C₄×C₅×C₈	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
62	C₂³×C₃×C₁₃	C₂×C₄×C₅	1	1	yes	characteristic
63	C₂×C₃×C₄×C₁₃	C₅×C₈	1	8	yes	direct product factor
64	C₂×C₃×C₄×C₁₃	C₂×C₄×C₅	1	1	yes	characteristic
65	C₂×C₃×C₄×C₁₃	C₂×C₄×C₅	1	4	yes	—
66	C₂×C₃×C₄×C₁₃	C₂×C₄×C₅	1	4	yes	—
67	C₂×C₃×C₄×C₁₃	C₂³×C₅	1	1	yes	characteristic
68	C₃×C₈×C₁₃	C₂×C₄×C₅	1	8	yes	direct product factor
69	C₂²×C₅×C₁₃	C₃×C₄²	1	2	yes	—
70	C₂²×C₅×C₁₃	C₂×C₃×C₈	1	4	yes	—
71	C₂²×C₅×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
72	C₄×C₅×C₁₃	C₃×C₄²	1	2	yes	—
73	C₄×C₅×C₁₃	C₂×C₃×C₈	1	8	yes	direct product factor
74	C₄×C₅×C₁₃	C₂²×C₃×C₄	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₄×C₁₃	1	2	yes	—
76	C₂²×C₃×C₄×C₅	C₂²×C₁₃	1	1	yes	characteristic
77	C₂×C₃×C₅×C₈	C₄×C₁₃	1	8	yes	direct product factor
78	C₂×C₃×C₅×C₈	C₂²×C₁₃	1	4	yes	—
79	C₃×C₄²×C₅	C₄×C₁₃	1	2	yes	—
80	C₃×C₄²×C₅	C₂²×C₁₃	1	2	yes	—
81	C₂²×C₄×C₁₃	C₃×C₄×C₅	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic
83	C₂×C₈×C₁₃	C₃×C₄×C₅	1	8	yes	direct product factor
84	C₂×C₈×C₁₃	C₂²×C₃×C₅	1	4	yes	—
85	C₄²×C₁₃	C₃×C₄×C₅	1	2	yes	—
86	C₄²×C₁₃	C₂²×C₃×C₅	1	2	yes	—
87	C₃×C₅×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
88	C₂×C₃×C₄×C₈	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
89	C₂²×C₅×C₈	C₂×C₃×C₁₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂×C₃×C₁₃	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂×C₃×C₁₃	1	4	yes	direct product factor
92	C₂²×C₃×C₁₃	C₄²×C₅	1	2	yes	—
93	C₂²×C₃×C₁₃	C₂×C₅×C₈	1	4	yes	—
94	C₂²×C₃×C₁₃	C₂²×C₄×C₅	1	1	yes	characteristic
95	C₃×C₄×C₁₃	C₄²×C₅	1	2	yes	—
96	C₃×C₄×C₁₃	C₂×C₅×C₈	1	8	yes	direct product factor
97	C₃×C₄×C₁₃	C₂²×C₄×C₅	1	2	yes	—
98	C₂×C₅×C₁₃	C₃×C₄×C₈	1	4	yes	direct product factor
99	C₂×C₅×C₁₃	C₂×C₃×C₄²	1	1	yes	characteristic
100	C₂×C₅×C₁₃	C₂²×C₃×C₈	1	2	yes	—
101	C₂³×C₃×C₅	C₂×C₄×C₁₃	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₈×C₁₃	1	8	yes	direct product factor
103	C₂×C₃×C₄×C₅	C₂×C₄×C₁₃	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×C₄×C₁₃	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂×C₄×C₁₃	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂³×C₁₃	1	1	yes	characteristic
107	C₃×C₅×C₈	C₂×C₄×C₁₃	1	8	yes	direct product factor
108	C₂³×C₁₃	C₂×C₃×C₄×C₅	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₃×C₅×C₈	1	8	yes	direct product factor
110	C₂×C₄×C₁₃	C₂×C₃×C₄×C₅	1	1	yes	characteristic
111	C₂×C₄×C₁₃	C₂×C₃×C₄×C₅	1	4	yes	—
112	C₂×C₄×C₁₃	C₂×C₃×C₄×C₅	1	4	yes	—
113	C₂×C₄×C₁₃	C₂³×C₃×C₅	1	1	yes	characteristic
114	C₈×C₁₃	C₂×C₃×C₄×C₅	1	8	yes	direct product factor
115	C₂²×C₃×C₈	C₂×C₅×C₁₃	1	2	yes	—
116	C₂×C₃×C₄²	C₂×C₅×C₁₃	1	1	yes	characteristic
117	C₃×C₄×C₈	C₂×C₅×C₁₃	1	4	yes	direct product factor
118	C₂²×C₄×C₅	C₃×C₄×C₁₃	1	2	yes	—
119	C₂²×C₄×C₅	C₂²×C₃×C₁₃	1	1	yes	characteristic
120	C₂×C₅×C₈	C₃×C₄×C₁₃	1	8	yes	direct product factor
121	C₂×C₅×C₈	C₂²×C₃×C₁₃	1	4	yes	—
122	C₄²×C₅	C₃×C₄×C₁₃	1	2	yes	—
123	C₄²×C₅	C₂²×C₃×C₁₃	1	2	yes	—
124	C₂×C₃×C₁₃	C₄×C₅×C₈	1	4	yes	direct product factor
125	C₂×C₃×C₁₃	C₂×C₄²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₁₃	C₂²×C₅×C₈	1	2	yes	—
127	C₅×C₁₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
128	C₂×C₄×C₈	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
129	C₂²×C₃×C₅	C₄²×C₁₃	1	2	yes	—
130	C₂²×C₃×C₅	C₂×C₈×C₁₃	1	4	yes	—
131	C₂²×C₃×C₅	C₂²×C₄×C₁₃	1	1	yes	characteristic
132	C₃×C₄×C₅	C₄²×C₁₃	1	2	yes	—
133	C₃×C₄×C₅	C₂×C₈×C₁₃	1	8	yes	direct product factor
134	C₃×C₄×C₅	C₂²×C₄×C₁₃	1	2	yes	—
135	C₂²×C₁₃	C₃×C₄²×C₅	1	2	yes	—
136	C₂²×C₁₃	C₂×C₃×C₅×C₈	1	4	yes	—
137	C₂²×C₁₃	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
138	C₄×C₁₃	C₃×C₄²×C₅	1	2	yes	—
139	C₄×C₁₃	C₂×C₃×C₅×C₈	1	8	yes	direct product factor
140	C₄×C₁₃	C₂²×C₃×C₄×C₅	1	2	yes	—
141	C₂²×C₃×C₄	C₄×C₅×C₁₃	1	2	yes	—
142	C₂²×C₃×C₄	C₂²×C₅×C₁₃	1	1	yes	characteristic
143	C₂×C₃×C₈	C₄×C₅×C₁₃	1	8	yes	direct product factor
144	C₂×C₃×C₈	C₂²×C₅×C₁₃	1	4	yes	—
145	C₃×C₄²	C₄×C₅×C₁₃	1	2	yes	—
146	C₃×C₄²	C₂²×C₅×C₁₃	1	2	yes	—
147	C₂³×C₅	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
148	C₂×C₄×C₅	C₃×C₈×C₁₃	1	8	yes	direct product factor
149	C₂×C₄×C₅	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
150	C₂×C₄×C₅	C₂×C₃×C₄×C₁₃	1	4	yes	—
151	C₂×C₄×C₅	C₂×C₃×C₄×C₁₃	1	4	yes	—
152	C₂×C₄×C₅	C₂³×C₃×C₁₃	1	1	yes	characteristic
153	C₅×C₈	C₂×C₃×C₄×C₁₃	1	8	yes	direct product factor
154	C₃×C₁₃	C₂×C₄×C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
155	C₂²×C₈	C₂×C₃×C₅×C₁₃	1	2	yes	—
156	C₂×C₄²	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
157	C₄×C₈	C₂×C₃×C₅×C₁₃	1	4	yes	direct product factor
158	C₂×C₃×C₅	C₄×C₈×C₁₃	1	4	yes	direct product factor
159	C₂×C₃×C₅	C₂×C₄²×C₁₃	1	1	yes	characteristic
160	C₂×C₃×C₅	C₂²×C₈×C₁₃	1	2	yes	—
161	C₂×C₁₃	C₃×C₄×C₅×C₈	1	4	yes	direct product factor
162	C₂×C₁₃	C₂×C₃×C₄²×C₅	1	1	yes	characteristic
163	C₂×C₁₃	C₂²×C₃×C₅×C₈	1	2	yes	—
164	C₂³×C₃	C₂×C₄×C₅×C₁₃	1	1	yes	characteristic
165	C₂×C₃×C₄	C₅×C₈×C₁₃	1	8	yes	direct product factor
166	C₂×C₃×C₄	C₂×C₄×C₅×C₁₃	1	1	yes	characteristic
167	C₂×C₃×C₄	C₂×C₄×C₅×C₁₃	1	4	yes	—
168	C₂×C₃×C₄	C₂×C₄×C₅×C₁₃	1	4	yes	—
169	C₂×C₃×C₄	C₂³×C₅×C₁₃	1	1	yes	characteristic
170	C₃×C₈	C₂×C₄×C₅×C₁₃	1	8	yes	direct product factor
171	C₂²×C₅	C₃×C₄²×C₁₃	1	2	yes	—
172	C₂²×C₅	C₂×C₃×C₈×C₁₃	1	4	yes	—
173	C₂²×C₅	C₂²×C₃×C₄×C₁₃	1	1	yes	characteristic
174	C₄×C₅	C₃×C₄²×C₁₃	1	2	yes	—
175	C₄×C₅	C₂×C₃×C₈×C₁₃	1	8	yes	direct product factor
176	C₄×C₅	C₂²×C₃×C₄×C₁₃	1	2	yes	—
177	C₂²×C₄	C₃×C₄×C₅×C₁₃	1	2	yes	—
178	C₂²×C₄	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic
179	C₂×C₈	C₃×C₄×C₅×C₁₃	1	8	yes	direct product factor
180	C₂×C₈	C₂²×C₃×C₅×C₁₃	1	4	yes	—
181	C₄²	C₃×C₄×C₅×C₁₃	1	2	yes	—
182	C₄²	C₂²×C₃×C₅×C₁₃	1	2	yes	—
183	C₃×C₅	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Hall
184	C₁₃	C₂×C₃×C₄×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
185	C₂²×C₃	C₄²×C₅×C₁₃	1	2	yes	—
186	C₂²×C₃	C₂×C₅×C₈×C₁₃	1	4	yes	—
187	C₂²×C₃	C₂²×C₄×C₅×C₁₃	1	1	yes	characteristic
188	C₃×C₄	C₄²×C₅×C₁₃	1	2	yes	—
189	C₃×C₄	C₂×C₅×C₈×C₁₃	1	8	yes	direct product factor
190	C₃×C₄	C₂²×C₄×C₅×C₁₃	1	2	yes	—
191	C₂×C₅	C₃×C₄×C₈×C₁₃	1	4	yes	direct product factor
192	C₂×C₅	C₂×C₃×C₄²×C₁₃	1	1	yes	characteristic
193	C₂×C₅	C₂²×C₃×C₈×C₁₃	1	2	yes	—
194	C₂³	C₂×C₃×C₄×C₅×C₁₃	1	1	yes	characteristic
195	C₂×C₄	C₃×C₅×C₈×C₁₃	1	8	yes	direct product factor
196	C₂×C₄	C₂×C₃×C₄×C₅×C₁₃	1	1	yes	characteristic
197	C₂×C₄	C₂×C₃×C₄×C₅×C₁₃	1	4	yes	—
198	C₂×C₄	C₂×C₃×C₄×C₅×C₁₃	1	4	yes	—
199	C₂×C₄	C₂³×C₃×C₅×C₁₃	1	1	yes	characteristic
200	C₈	C₂×C₃×C₄×C₅×C₁₃	1	8	yes	direct product factor
201	C₂×C₃	C₄×C₅×C₈×C₁₃	1	4	yes	direct product factor
202	C₂×C₃	C₂²×C₅×C₈×C₁₃	1	2	yes	—
203	C₂×C₃	C₂×C₄²×C₅×C₁₃	1	1	yes	characteristic
204	C₅	C₂×C₃×C₄×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²	C₃×C₄²×C₅×C₁₃	1	2	yes	—
206	C₂²	C₂×C₃×C₅×C₈×C₁₃	1	4	yes	—
207	C₂²	C₂²×C₃×C₄×C₅×C₁₃	1	1	yes	characteristic
208	C₄	C₃×C₄²×C₅×C₁₃	1	2	yes	—
209	C₄	C₂×C₃×C₅×C₈×C₁₃	1	8	yes	direct product factor
210	C₄	C₂²×C₃×C₄×C₅×C₁₃	1	2	yes	—
211	C₃	C₂×C₄×C₅×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
212	C₂	C₃×C₄×C₅×C₈×C₁₃	1	4	yes	direct product factor
213	C₂	C₂²×C₃×C₅×C₈×C₁₃	1	2	yes	—
214	C₂	C₂×C₃×C₄²×C₅×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₃×C₅×C₁₃
socle, prime radical	C₂³×C₃×C₅×C₁₃	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. C₃×C₄×C₅×C₈×C₁₃	C₂	direct (N × H)
4. C₂×C₄×C₅×C₈×C₁₃	C₃	direct (N × H)
7. C₂×C₃×C₅×C₈×C₁₃	C₄	direct (N × H)
11. C₂×C₃×C₄×C₈×C₁₃	C₅	direct (N × H)
14. C₄×C₅×C₈×C₁₃	C₂×C₃	direct (N × H)
16. C₂×C₃×C₄×C₅×C₁₃	C₈	direct (N × H)
21. C₃×C₅×C₈×C₁₃	C₂×C₄	direct (N × H)
24. C₃×C₄×C₈×C₁₃	C₂×C₅	direct (N × H)
27. C₂×C₅×C₈×C₁₃	C₃×C₄	direct (N × H)
31. C₂×C₃×C₄×C₅×C₈	C₁₃	direct (N × H)
32. C₂×C₄×C₈×C₁₃	C₃×C₅	direct (N × H)
37. C₃×C₄×C₅×C₁₃	C₂×C₈	direct (N × H)
41. C₂×C₃×C₈×C₁₃	C₄×C₅	direct (N × H)
46. C₂×C₄×C₅×C₁₃	C₃×C₈	direct (N × H)
51. C₅×C₈×C₁₃	C₂×C₃×C₄	direct (N × H)
54. C₃×C₄×C₅×C₈	C₂×C₁₃	direct (N × H)
57. C₄×C₈×C₁₃	C₂×C₃×C₅	direct (N × H)
58. C₂×C₃×C₅×C₁₃	C₄×C₈	direct (N × H)
61. C₂×C₄×C₅×C₈	C₃×C₁₃	direct (N × H)
63. C₂×C₃×C₄×C₁₃	C₅×C₈	direct (N × H)
68. C₃×C₈×C₁₃	C₂×C₄×C₅	direct (N × H)
73. C₄×C₅×C₁₃	C₂×C₃×C₈	direct (N × H)
77. C₂×C₃×C₅×C₈	C₄×C₁₃	direct (N × H)
83. C₂×C₈×C₁₃	C₃×C₄×C₅	direct (N × H)
87. C₃×C₅×C₁₃	C₂×C₄×C₈	direct (N × H)
88. C₂×C₃×C₄×C₈	C₅×C₁₃	direct (N × H)
91. C₄×C₅×C₈	C₂×C₃×C₁₃	direct (N × H)
96. C₃×C₄×C₁₃	C₂×C₅×C₈	direct (N × H)
98. C₂×C₅×C₁₃	C₃×C₄×C₈	direct (N × H)
102. C₂×C₃×C₄×C₅	C₈×C₁₃	direct (N × H)
107. C₃×C₅×C₈	C₂×C₄×C₁₃	direct (N × H)
109. C₂×C₄×C₁₃	C₃×C₅×C₈	direct (N × H)
114. C₈×C₁₃	C₂×C₃×C₄×C₅	direct (N × H)
117. C₃×C₄×C₈	C₂×C₅×C₁₃	direct (N × H)
120. C₂×C₅×C₈	C₃×C₄×C₁₃	direct (N × H)
124. C₂×C₃×C₁₃	C₄×C₅×C₈	direct (N × H)
127. C₅×C₁₃	C₂×C₃×C₄×C₈	direct (N × H)
128. C₂×C₄×C₈	C₃×C₅×C₁₃	direct (N × H)
133. C₃×C₄×C₅	C₂×C₈×C₁₃	direct (N × H)
139. C₄×C₁₃	C₂×C₃×C₅×C₈	direct (N × H)
143. C₂×C₃×C₈	C₄×C₅×C₁₃	direct (N × H)
148. C₂×C₄×C₅	C₃×C₈×C₁₃	direct (N × H)
153. C₅×C₈	C₂×C₃×C₄×C₁₃	direct (N × H)
154. C₃×C₁₃	C₂×C₄×C₅×C₈	direct (N × H)
157. C₄×C₈	C₂×C₃×C₅×C₁₃	direct (N × H)
158. C₂×C₃×C₅	C₄×C₈×C₁₃	direct (N × H)
161. C₂×C₁₃	C₃×C₄×C₅×C₈	direct (N × H)
165. C₂×C₃×C₄	C₅×C₈×C₁₃	direct (N × H)
170. C₃×C₈	C₂×C₄×C₅×C₁₃	direct (N × H)
175. C₄×C₅	C₂×C₃×C₈×C₁₃	direct (N × H)
179. C₂×C₈	C₃×C₄×C₅×C₁₃	direct (N × H)
183. C₃×C₅	C₂×C₄×C₈×C₁₃	direct (N × H)
184. C₁₃	C₂×C₃×C₄×C₅×C₈	direct (N × H)
189. C₃×C₄	C₂×C₅×C₈×C₁₃	direct (N × H)
191. C₂×C₅	C₃×C₄×C₈×C₁₃	direct (N × H)
195. C₂×C₄	C₃×C₅×C₈×C₁₃	direct (N × H)
200. C₈	C₂×C₃×C₄×C₅×C₁₃	direct (N × H)
201. C₂×C₃	C₄×C₅×C₈×C₁₃	direct (N × H)
204. C₅	C₂×C₃×C₄×C₈×C₁₃	direct (N × H)
209. C₄	C₂×C₃×C₅×C₈×C₁₃	direct (N × H)
211. C₃	C₂×C₄×C₅×C₈×C₁₃	direct (N × H)
212. C₂	C₃×C₄×C₅×C₈×C₁₃	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×C₄²×C₅×C₁₃	2
C₂²×C₃×C₅×C₈×C₁₃	2
C₃×C₄×C₅×C₈×C₁₃	2
C₂×C₄×C₅×C₈×C₁₃	3
C₂×C₃×C₄×C₈×C₁₃	5
C₂×C₃×C₄×C₅×C₈	13

Subgroups — C2×C3×C4×C5×C8×C13 #72190824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₅×C₈×C₁₃ #72190824