Subgroups — C₂²×C₃×C₄²×C₉×C₁₃ #72199879

Order 22464.

4980 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	C₂³×C₃×C₄×C₉×C₁₃	C₂	1	3	yes	maximal
2	C₂×C₃×C₄²×C₉×C₁₃	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃²×C₄²×C₁₃	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₄²×C₉×C₁₃	C₃	1	3	yes	maximal, direct product factor
5	C₂⁴×C₃×C₉×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄×C₉×C₁₃	C₄	1	24	yes	direct product factor
7	C₂²×C₃×C₄×C₉×C₁₃	C₂²	1	18	yes	—
8	C₃×C₄²×C₉×C₁₃	C₂²	1	16	yes	direct product factor
9	C₂³×C₃²×C₄×C₁₃	C₂×C₃	1	3	yes	—
10	C₂³×C₄×C₉×C₁₃	C₂×C₃	1	9	yes	—
11	C₂×C₃²×C₄²×C₁₃	C₂×C₃	1	12	yes	—
12	C₂×C₄²×C₉×C₁₃	C₂×C₃	1	36	yes	direct product factor
13	C₂³×C₃×C₉×C₁₃	C₂×C₄	1	12	yes	—
14	C₂³×C₃×C₉×C₁₃	C₂³	1	3	yes	—
15	C₂×C₃×C₄×C₉×C₁₃	C₂×C₄	1	72	yes	direct product factor
16	C₂×C₃×C₄×C₉×C₁₃	C₂³	1	12	yes	—
17	C₂²×C₃×C₄²×C₁₃	C₉	1	3	yes	direct product factor
18	C₂²×C₃×C₄²×C₁₃	C₃²	1	1	yes	characteristic
19	C₂⁴×C₃²×C₁₃	C₂²×C₃	1	1	yes	characteristic
20	C₂²×C₃²×C₄×C₁₃	C₃×C₄	1	24	yes	—
21	C₂²×C₃²×C₄×C₁₃	C₂²×C₃	1	18	yes	—
22	C₂⁴×C₉×C₁₃	C₂²×C₃	1	3	yes	—
23	C₃²×C₄²×C₁₃	C₂²×C₃	1	16	yes	—
24	C₂²×C₄×C₉×C₁₃	C₃×C₄	1	72	yes	direct product factor
25	C₂²×C₄×C₉×C₁₃	C₂²×C₃	1	54	yes	—
26	C₄²×C₉×C₁₃	C₂²×C₃	1	48	yes	direct product factor
27	C₂²×C₃×C₄²×C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₃×C₉×C₁₃	C₄²	1	16	yes	direct product factor
29	C₂²×C₃×C₉×C₁₃	C₂²×C₄	1	18	yes	—
30	C₂²×C₃×C₉×C₁₃	C₂⁴	1	1	yes	characteristic
31	C₃×C₄×C₉×C₁₃	C₂²×C₄	1	24	yes	direct product factor
32	C₂³×C₃×C₄×C₁₃	C₂×C₉	1	9	yes	—
33	C₂³×C₃×C₄×C₁₃	C₂×C₃²	1	3	yes	—
34	C₂×C₃×C₄²×C₁₃	C₂×C₉	1	36	yes	direct product factor
35	C₂×C₃×C₄²×C₁₃	C₂×C₃²	1	12	yes	—
36	C₂³×C₃²×C₁₃	C₂×C₃×C₄	1	12	yes	—
37	C₂³×C₃²×C₁₃	C₂³×C₃	1	3	yes	—
38	C₂×C₃²×C₄×C₁₃	C₂×C₃×C₄	1	72	yes	—
39	C₂×C₃²×C₄×C₁₃	C₂³×C₃	1	12	yes	—
40	C₂³×C₉×C₁₃	C₂×C₃×C₄	1	36	yes	—
41	C₂³×C₉×C₁₃	C₂³×C₃	1	9	yes	—
42	C₂×C₄×C₉×C₁₃	C₂×C₃×C₄	1	216	yes	direct product factor
43	C₂×C₄×C₉×C₁₃	C₂³×C₃	1	36	yes	—
44	C₂³×C₃×C₄×C₉	C₂×C₁₃	1	3	yes	—
45	C₂×C₃×C₄²×C₉	C₂×C₁₃	1	12	yes	direct product factor
46	C₂²×C₄²×C₁₃	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
47	C₂×C₃×C₉×C₁₃	C₂×C₄²	1	12	yes	direct product factor
48	C₂×C₃×C₉×C₁₃	C₂³×C₄	1	3	yes	—
49	C₂⁴×C₃×C₁₃	C₂²×C₉	1	3	yes	—
50	C₂⁴×C₃×C₁₃	C₂²×C₃²	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₁₃	C₄×C₉	1	72	yes	direct product factor
52	C₂²×C₃×C₄×C₁₃	C₂²×C₉	1	54	yes	—
53	C₂²×C₃×C₄×C₁₃	C₃²×C₄	1	24	yes	—
54	C₂²×C₃×C₄×C₁₃	C₂²×C₃²	1	18	yes	—
55	C₃×C₄²×C₁₃	C₂²×C₉	1	48	yes	direct product factor
56	C₃×C₄²×C₁₃	C₂²×C₃²	1	16	yes	—
57	C₂²×C₃²×C₄²	C₃×C₁₃	1	1	yes	characteristic
58	C₂²×C₄²×C₉	C₃×C₁₃	1	3	yes	direct product factor
59	C₂²×C₃²×C₁₃	C₃×C₄²	1	16	yes	—
60	C₂²×C₃²×C₁₃	C₂²×C₃×C₄	1	18	yes	—
61	C₂²×C₃²×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
62	C₃²×C₄×C₁₃	C₂²×C₃×C₄	1	24	yes	—
63	C₂²×C₉×C₁₃	C₃×C₄²	1	48	yes	direct product factor
64	C₂²×C₉×C₁₃	C₂²×C₃×C₄	1	54	yes	—
65	C₂²×C₉×C₁₃	C₂⁴×C₃	1	3	yes	—
66	C₄×C₉×C₁₃	C₂²×C₃×C₄	1	72	yes	direct product factor
67	C₂⁴×C₃×C₉	C₂²×C₁₃	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₉	C₄×C₁₃	1	24	yes	direct product factor
69	C₂²×C₃×C₄×C₉	C₂²×C₁₃	1	18	yes	—
70	C₃×C₄²×C₉	C₂²×C₁₃	1	16	yes	direct product factor
71	C₂³×C₄×C₁₃	C₂×C₃×C₉	1	3	yes	—
72	C₂×C₄²×C₁₃	C₂×C₃×C₉	1	12	yes	direct product factor
73	C₃×C₉×C₁₃	C₂²×C₄²	1	1	yes	characteristic, direct product factor, Hall
74	C₂³×C₃×C₁₃	C₂×C₄×C₉	1	36	yes	—
75	C₂³×C₃×C₁₃	C₂³×C₉	1	9	yes	—
76	C₂³×C₃×C₁₃	C₂×C₃²×C₄	1	12	yes	—
77	C₂³×C₃×C₁₃	C₂³×C₃²	1	3	yes	—
78	C₂×C₃×C₄×C₁₃	C₂×C₄×C₉	1	216	yes	direct product factor
79	C₂×C₃×C₄×C₁₃	C₂³×C₉	1	36	yes	—
80	C₂×C₃×C₄×C₁₃	C₂×C₃²×C₄	1	72	yes	—
81	C₂×C₃×C₄×C₁₃	C₂³×C₃²	1	12	yes	—
82	C₂³×C₃²×C₄	C₂×C₃×C₁₃	1	3	yes	—
83	C₂×C₃²×C₄²	C₂×C₃×C₁₃	1	12	yes	—
84	C₂³×C₄×C₉	C₂×C₃×C₁₃	1	9	yes	—
85	C₂×C₄²×C₉	C₂×C₃×C₁₃	1	36	yes	direct product factor
86	C₂×C₃²×C₁₃	C₂×C₃×C₄²	1	12	yes	—
87	C₂×C₃²×C₁₃	C₂³×C₃×C₄	1	3	yes	—
88	C₂×C₉×C₁₃	C₂×C₃×C₄²	1	36	yes	direct product factor
89	C₂×C₉×C₁₃	C₂³×C₃×C₄	1	9	yes	—
90	C₂³×C₃×C₉	C₂×C₄×C₁₃	1	12	yes	—
91	C₂³×C₃×C₉	C₂³×C₁₃	1	3	yes	—
92	C₂×C₃×C₄×C₉	C₂×C₄×C₁₃	1	72	yes	direct product factor
93	C₂×C₃×C₄×C₉	C₂³×C₁₃	1	12	yes	—
94	C₂⁴×C₁₃	C₂²×C₃×C₉	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₃×C₄×C₉	1	24	yes	direct product factor
96	C₂²×C₄×C₁₃	C₂²×C₃×C₉	1	18	yes	—
97	C₄²×C₁₃	C₂²×C₃×C₉	1	16	yes	direct product factor
98	C₂²×C₃×C₄²	C₉×C₁₃	1	3	yes	direct product factor
99	C₂²×C₃×C₄²	C₃²×C₁₃	1	1	yes	characteristic
100	C₂²×C₃×C₁₃	C₄²×C₉	1	48	yes	direct product factor
101	C₂²×C₃×C₁₃	C₂²×C₄×C₉	1	54	yes	—
102	C₂²×C₃×C₁₃	C₃²×C₄²	1	16	yes	—
103	C₂²×C₃×C₁₃	C₂⁴×C₉	1	3	yes	—
104	C₂²×C₃×C₁₃	C₂²×C₃²×C₄	1	18	yes	—
105	C₂²×C₃×C₁₃	C₂⁴×C₃²	1	1	yes	characteristic
106	C₃×C₄×C₁₃	C₂²×C₄×C₉	1	72	yes	direct product factor
107	C₃×C₄×C₁₃	C₂²×C₃²×C₄	1	24	yes	—
108	C₂⁴×C₃²	C₂²×C₃×C₁₃	1	1	yes	characteristic
109	C₂²×C₃²×C₄	C₃×C₄×C₁₃	1	24	yes	—
110	C₂²×C₃²×C₄	C₂²×C₃×C₁₃	1	18	yes	—
111	C₂⁴×C₉	C₂²×C₃×C₁₃	1	3	yes	—
112	C₃²×C₄²	C₂²×C₃×C₁₃	1	16	yes	—
113	C₂²×C₄×C₉	C₃×C₄×C₁₃	1	72	yes	direct product factor
114	C₂²×C₄×C₉	C₂²×C₃×C₁₃	1	54	yes	—
115	C₄²×C₉	C₂²×C₃×C₁₃	1	48	yes	direct product factor
116	C₃²×C₁₃	C₂²×C₃×C₄²	1	1	yes	characteristic
117	C₉×C₁₃	C₂²×C₃×C₄²	1	3	yes	direct product factor
118	C₂²×C₃×C₉	C₄²×C₁₃	1	16	yes	direct product factor
119	C₂²×C₃×C₉	C₂²×C₄×C₁₃	1	18	yes	—
120	C₂²×C₃×C₉	C₂⁴×C₁₃	1	1	yes	characteristic
121	C₃×C₄×C₉	C₂²×C₄×C₁₃	1	24	yes	direct product factor
122	C₂³×C₁₃	C₂×C₃×C₄×C₉	1	12	yes	—
123	C₂³×C₁₃	C₂³×C₃×C₉	1	3	yes	—
124	C₂×C₄×C₁₃	C₂×C₃×C₄×C₉	1	72	yes	direct product factor
125	C₂×C₄×C₁₃	C₂³×C₃×C₉	1	12	yes	—
126	C₂³×C₃×C₄	C₂×C₉×C₁₃	1	9	yes	—
127	C₂³×C₃×C₄	C₂×C₃²×C₁₃	1	3	yes	—
128	C₂×C₃×C₄²	C₂×C₉×C₁₃	1	36	yes	direct product factor
129	C₂×C₃×C₄²	C₂×C₃²×C₁₃	1	12	yes	—
130	C₂×C₃×C₁₃	C₂×C₄²×C₉	1	36	yes	direct product factor
131	C₂×C₃×C₁₃	C₂³×C₄×C₉	1	9	yes	—
132	C₂×C₃×C₁₃	C₂×C₃²×C₄²	1	12	yes	—
133	C₂×C₃×C₁₃	C₂³×C₃²×C₄	1	3	yes	—
134	C₂³×C₃²	C₂×C₃×C₄×C₁₃	1	12	yes	—
135	C₂³×C₃²	C₂³×C₃×C₁₃	1	3	yes	—
136	C₂×C₃²×C₄	C₂×C₃×C₄×C₁₃	1	72	yes	—
137	C₂×C₃²×C₄	C₂³×C₃×C₁₃	1	12	yes	—
138	C₂³×C₉	C₂×C₃×C₄×C₁₃	1	36	yes	—
139	C₂³×C₉	C₂³×C₃×C₁₃	1	9	yes	—
140	C₂×C₄×C₉	C₂×C₃×C₄×C₁₃	1	216	yes	direct product factor
141	C₂×C₄×C₉	C₂³×C₃×C₁₃	1	36	yes	—
142	C₂²×C₄²	C₃×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
143	C₂×C₃×C₉	C₂×C₄²×C₁₃	1	12	yes	direct product factor
144	C₂×C₃×C₉	C₂³×C₄×C₁₃	1	3	yes	—
145	C₂²×C₁₃	C₃×C₄²×C₉	1	16	yes	direct product factor
146	C₂²×C₁₃	C₂²×C₃×C₄×C₉	1	18	yes	—
147	C₂²×C₁₃	C₂⁴×C₃×C₉	1	1	yes	characteristic
148	C₄×C₁₃	C₂²×C₃×C₄×C₉	1	24	yes	direct product factor
149	C₂⁴×C₃	C₂²×C₉×C₁₃	1	3	yes	—
150	C₂⁴×C₃	C₂²×C₃²×C₁₃	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₄×C₉×C₁₃	1	72	yes	direct product factor
152	C₂²×C₃×C₄	C₂²×C₉×C₁₃	1	54	yes	—
153	C₂²×C₃×C₄	C₃²×C₄×C₁₃	1	24	yes	—
154	C₂²×C₃×C₄	C₂²×C₃²×C₁₃	1	18	yes	—
155	C₃×C₄²	C₂²×C₉×C₁₃	1	48	yes	direct product factor
156	C₃×C₄²	C₂²×C₃²×C₁₃	1	16	yes	—
157	C₃×C₁₃	C₂²×C₄²×C₉	1	3	yes	direct product factor
158	C₃×C₁₃	C₂²×C₃²×C₄²	1	1	yes	characteristic
159	C₂²×C₃²	C₃×C₄²×C₁₃	1	16	yes	—
160	C₂²×C₃²	C₂²×C₃×C₄×C₁₃	1	18	yes	—
161	C₂²×C₃²	C₂⁴×C₃×C₁₃	1	1	yes	characteristic
162	C₃²×C₄	C₂²×C₃×C₄×C₁₃	1	24	yes	—
163	C₂²×C₉	C₃×C₄²×C₁₃	1	48	yes	direct product factor
164	C₂²×C₉	C₂²×C₃×C₄×C₁₃	1	54	yes	—
165	C₂²×C₉	C₂⁴×C₃×C₁₃	1	3	yes	—
166	C₄×C₉	C₂²×C₃×C₄×C₁₃	1	72	yes	direct product factor
167	C₂³×C₄	C₂×C₃×C₉×C₁₃	1	3	yes	—
168	C₂×C₄²	C₂×C₃×C₉×C₁₃	1	12	yes	direct product factor
169	C₃×C₉	C₂²×C₄²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
170	C₂×C₁₃	C₂×C₃×C₄²×C₉	1	12	yes	direct product factor
171	C₂×C₁₃	C₂³×C₃×C₄×C₉	1	3	yes	—
172	C₂³×C₃	C₂×C₄×C₉×C₁₃	1	36	yes	—
173	C₂³×C₃	C₂³×C₉×C₁₃	1	9	yes	—
174	C₂³×C₃	C₂×C₃²×C₄×C₁₃	1	12	yes	—
175	C₂³×C₃	C₂³×C₃²×C₁₃	1	3	yes	—
176	C₂×C₃×C₄	C₂×C₄×C₉×C₁₃	1	216	yes	direct product factor
177	C₂×C₃×C₄	C₂³×C₉×C₁₃	1	36	yes	—
178	C₂×C₃×C₄	C₂×C₃²×C₄×C₁₃	1	72	yes	—
179	C₂×C₃×C₄	C₂³×C₃²×C₁₃	1	12	yes	—
180	C₂×C₃²	C₂×C₃×C₄²×C₁₃	1	12	yes	—
181	C₂×C₃²	C₂³×C₃×C₄×C₁₃	1	3	yes	—
182	C₂×C₉	C₂×C₃×C₄²×C₁₃	1	36	yes	direct product factor
183	C₂×C₉	C₂³×C₃×C₄×C₁₃	1	9	yes	—
184	C₂⁴	C₂²×C₃×C₉×C₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₃×C₄×C₉×C₁₃	1	24	yes	direct product factor
186	C₂²×C₄	C₂²×C₃×C₉×C₁₃	1	18	yes	—
187	C₄²	C₂²×C₃×C₉×C₁₃	1	16	yes	direct product factor
188	C₁₃	C₂²×C₃×C₄²×C₉	1	1	yes	characteristic, direct product factor, Sylow
189	C₂²×C₃	C₄²×C₉×C₁₃	1	48	yes	direct product factor
190	C₂²×C₃	C₂²×C₄×C₉×C₁₃	1	54	yes	—
191	C₂²×C₃	C₃²×C₄²×C₁₃	1	16	yes	—
192	C₂²×C₃	C₂⁴×C₉×C₁₃	1	3	yes	—
193	C₂²×C₃	C₂²×C₃²×C₄×C₁₃	1	18	yes	—
194	C₂²×C₃	C₂⁴×C₃²×C₁₃	1	1	yes	characteristic
195	C₃×C₄	C₂²×C₄×C₉×C₁₃	1	72	yes	direct product factor
196	C₃×C₄	C₂²×C₃²×C₄×C₁₃	1	24	yes	—
197	C₃²	C₂²×C₃×C₄²×C₁₃	1	1	yes	characteristic
198	C₉	C₂²×C₃×C₄²×C₁₃	1	3	yes	direct product factor
199	C₂³	C₂×C₃×C₄×C₉×C₁₃	1	12	yes	—
200	C₂³	C₂³×C₃×C₉×C₁₃	1	3	yes	—
201	C₂×C₄	C₂×C₃×C₄×C₉×C₁₃	1	72	yes	direct product factor
202	C₂×C₄	C₂³×C₃×C₉×C₁₃	1	12	yes	—
203	C₂×C₃	C₂×C₄²×C₉×C₁₃	1	36	yes	direct product factor
204	C₂×C₃	C₂×C₃²×C₄²×C₁₃	1	12	yes	—
205	C₂×C₃	C₂³×C₄×C₉×C₁₃	1	9	yes	—
206	C₂×C₃	C₂³×C₃²×C₄×C₁₃	1	3	yes	—
207	C₂²	C₃×C₄²×C₉×C₁₃	1	16	yes	direct product factor
208	C₂²	C₂²×C₃×C₄×C₉×C₁₃	1	18	yes	—
209	C₂²	C₂⁴×C₃×C₉×C₁₃	1	1	yes	characteristic
210	C₄	C₂²×C₃×C₄×C₉×C₁₃	1	24	yes	direct product factor
211	C₃	C₂²×C₄²×C₉×C₁₃	1	3	yes	direct product factor
212	C₃	C₂²×C₃²×C₄²×C₁₃	1	1	yes	characteristic
213	C₂	C₂×C₃×C₄²×C₉×C₁₃	1	12	yes	direct product factor
214	C₂	C₂³×C₃×C₄×C₉×C₁₃	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂⁴×C₃²×C₁₃
socle, prime radical	C₂⁴×C₃²×C₁₃	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄²×C₉×C₁₃	C₂	direct (N × H)
4. C₂²×C₄²×C₉×C₁₃	C₃	direct (N × H)
6. C₂²×C₃×C₄×C₉×C₁₃	C₄	direct (N × H)
8. C₃×C₄²×C₉×C₁₃	C₂²	direct (N × H)
12. C₂×C₄²×C₉×C₁₃	C₂×C₃	direct (N × H)
15. C₂×C₃×C₄×C₉×C₁₃	C₂×C₄	direct (N × H)
17. C₂²×C₃×C₄²×C₁₃	C₉	direct (N × H)
24. C₂²×C₄×C₉×C₁₃	C₃×C₄	direct (N × H)
26. C₄²×C₉×C₁₃	C₂²×C₃	direct (N × H)
27. C₂²×C₃×C₄²×C₉	C₁₃	direct (N × H)
28. C₂²×C₃×C₉×C₁₃	C₄²	direct (N × H)
31. C₃×C₄×C₉×C₁₃	C₂²×C₄	direct (N × H)
34. C₂×C₃×C₄²×C₁₃	C₂×C₉	direct (N × H)
42. C₂×C₄×C₉×C₁₃	C₂×C₃×C₄	direct (N × H)
45. C₂×C₃×C₄²×C₉	C₂×C₁₃	direct (N × H)
46. C₂²×C₄²×C₁₃	C₃×C₉	direct (N × H)
47. C₂×C₃×C₉×C₁₃	C₂×C₄²	direct (N × H)
51. C₂²×C₃×C₄×C₁₃	C₄×C₉	direct (N × H)
55. C₃×C₄²×C₁₃	C₂²×C₉	direct (N × H)
58. C₂²×C₄²×C₉	C₃×C₁₃	direct (N × H)
63. C₂²×C₉×C₁₃	C₃×C₄²	direct (N × H)
66. C₄×C₉×C₁₃	C₂²×C₃×C₄	direct (N × H)
68. C₂²×C₃×C₄×C₉	C₄×C₁₃	direct (N × H)
70. C₃×C₄²×C₉	C₂²×C₁₃	direct (N × H)
72. C₂×C₄²×C₁₃	C₂×C₃×C₉	direct (N × H)
73. C₃×C₉×C₁₃	C₂²×C₄²	direct (N × H)
78. C₂×C₃×C₄×C₁₃	C₂×C₄×C₉	direct (N × H)
85. C₂×C₄²×C₉	C₂×C₃×C₁₃	direct (N × H)
88. C₂×C₉×C₁₃	C₂×C₃×C₄²	direct (N × H)
92. C₂×C₃×C₄×C₉	C₂×C₄×C₁₃	direct (N × H)
95. C₂²×C₄×C₁₃	C₃×C₄×C₉	direct (N × H)
97. C₄²×C₁₃	C₂²×C₃×C₉	direct (N × H)
98. C₂²×C₃×C₄²	C₉×C₁₃	direct (N × H)
100. C₂²×C₃×C₁₃	C₄²×C₉	direct (N × H)
106. C₃×C₄×C₁₃	C₂²×C₄×C₉	direct (N × H)
113. C₂²×C₄×C₉	C₃×C₄×C₁₃	direct (N × H)
115. C₄²×C₉	C₂²×C₃×C₁₃	direct (N × H)
117. C₉×C₁₃	C₂²×C₃×C₄²	direct (N × H)
118. C₂²×C₃×C₉	C₄²×C₁₃	direct (N × H)
121. C₃×C₄×C₉	C₂²×C₄×C₁₃	direct (N × H)
124. C₂×C₄×C₁₃	C₂×C₃×C₄×C₉	direct (N × H)
128. C₂×C₃×C₄²	C₂×C₉×C₁₃	direct (N × H)
130. C₂×C₃×C₁₃	C₂×C₄²×C₉	direct (N × H)
140. C₂×C₄×C₉	C₂×C₃×C₄×C₁₃	direct (N × H)
142. C₂²×C₄²	C₃×C₉×C₁₃	direct (N × H)
143. C₂×C₃×C₉	C₂×C₄²×C₁₃	direct (N × H)
145. C₂²×C₁₃	C₃×C₄²×C₉	direct (N × H)
148. C₄×C₁₃	C₂²×C₃×C₄×C₉	direct (N × H)
151. C₂²×C₃×C₄	C₄×C₉×C₁₃	direct (N × H)
155. C₃×C₄²	C₂²×C₉×C₁₃	direct (N × H)
157. C₃×C₁₃	C₂²×C₄²×C₉	direct (N × H)
163. C₂²×C₉	C₃×C₄²×C₁₃	direct (N × H)
166. C₄×C₉	C₂²×C₃×C₄×C₁₃	direct (N × H)
168. C₂×C₄²	C₂×C₃×C₉×C₁₃	direct (N × H)
169. C₃×C₉	C₂²×C₄²×C₁₃	direct (N × H)
170. C₂×C₁₃	C₂×C₃×C₄²×C₉	direct (N × H)
176. C₂×C₃×C₄	C₂×C₄×C₉×C₁₃	direct (N × H)
182. C₂×C₉	C₂×C₃×C₄²×C₁₃	direct (N × H)
185. C₂²×C₄	C₃×C₄×C₉×C₁₃	direct (N × H)
187. C₄²	C₂²×C₃×C₉×C₁₃	direct (N × H)
188. C₁₃	C₂²×C₃×C₄²×C₉	direct (N × H)
189. C₂²×C₃	C₄²×C₉×C₁₃	direct (N × H)
195. C₃×C₄	C₂²×C₄×C₉×C₁₃	direct (N × H)
198. C₉	C₂²×C₃×C₄²×C₁₃	direct (N × H)
201. C₂×C₄	C₂×C₃×C₄×C₉×C₁₃	direct (N × H)
203. C₂×C₃	C₂×C₄²×C₉×C₁₃	direct (N × H)
207. C₂²	C₃×C₄²×C₉×C₁₃	direct (N × H)
210. C₄	C₂²×C₃×C₄×C₉×C₁₃	direct (N × H)
211. C₃	C₂²×C₄²×C₉×C₁₃	direct (N × H)
213. C₂	C₂×C₃×C₄²×C₉×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
C₂³×C₃×C₄×C₉×C₁₃	2
C₂×C₃×C₄²×C₉×C₁₃	2
C₂²×C₃²×C₄²×C₁₃	3
C₂²×C₄²×C₉×C₁₃	3
C₂²×C₃×C₄²×C₉	13

Subgroups — C22×C3×C42×C9×C13 #72199879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄²×C₉×C₁₃ #72199879