Subgroups — C₃×C₄×C₈×C₁₃×C₁₆ #72197608

Order 19968.

2184 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₁₃×C₁₆	C₂	1	2	yes	maximal
3	C₂×C₃×C₈×C₁₃×C₁₆	C₂	1	4	yes	maximal
4	C₄×C₈×C₁₃×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄²×C₈×C₁₃	C₄	1	2	yes	—
6	C₃×C₄²×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈²×C₁₃	C₄	1	2	yes	—
8	C₂×C₃×C₈²×C₁₃	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₁₃×C₁₆	C₄	1	8	yes	—
10	C₂×C₃×C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
11	C₃×C₈×C₁₃×C₁₆	C₄	1	16	yes	direct product factor
12	C₃×C₄³×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₄×C₈×C₁₃	C₈	1	8	yes	—
14	C₂×C₃×C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
16	C₂×C₃×C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
17	C₂×C₃×C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×C₃×C₁₃×C₁₆	C₂×C₄	1	8	yes	—
19	C₃×C₈²×C₁₃	C₈	1	8	yes	—
20	C₃×C₈²×C₁₃	C₂×C₄	1	8	yes	—
21	C₃×C₄×C₁₃×C₁₆	C₈	1	32	yes	direct product factor
22	C₃×C₄×C₁₃×C₁₆	C₂×C₄	1	16	yes	—
23	C₃×C₄×C₈×C₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₄²×C₁₃×C₁₆	C₂×C₃	1	2	yes	—
25	C₂×C₈×C₁₃×C₁₆	C₂×C₃	1	4	yes	—
26	C₄×C₈²×C₁₃	C₂×C₃	1	1	yes	characteristic
27	C₂×C₄×C₁₃×C₁₆	C₃×C₄	1	8	yes	—
28	C₂×C₄×C₁₃×C₁₆	C₂²×C₃	1	4	yes	—
29	C₄²×C₈×C₁₃	C₃×C₄	1	2	yes	—
30	C₄²×C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₈²×C₁₃	C₃×C₄	1	2	yes	—
32	C₂×C₈²×C₁₃	C₂²×C₃	1	2	yes	—
33	C₈×C₁₃×C₁₆	C₃×C₄	1	16	yes	direct product factor
34	C₂²×C₃×C₈×C₁₃	C₄²	1	2	yes	—
35	C₂²×C₃×C₈×C₁₃	C₂×C₈	1	8	yes	—
36	C₂²×C₃×C₈×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂×C₃×C₄²×C₁₃	C₄²	1	2	yes	—
38	C₂×C₃×C₄²×C₁₃	C₂×C₈	1	4	yes	—
39	C₂×C₃×C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃×C₁₃×C₁₆	C₄²	1	16	yes	—
41	C₂×C₃×C₁₃×C₁₆	C₂×C₈	1	32	yes	—
42	C₃×C₄×C₈×C₁₃	C₁₆	1	32	yes	direct product factor
43	C₃×C₄×C₈×C₁₃	C₄²	1	8	yes	—
44	C₃×C₄×C₈×C₁₃	C₂×C₈	1	4	yes	—
45	C₃×C₄×C₈×C₁₃	C₂×C₈	1	8	yes	—
46	C₃×C₄×C₈×C₁₃	C₂×C₈	1	16	yes	—
47	C₃×C₄×C₈×C₁₃	C₂²×C₄	1	4	yes	—
48	C₂²×C₁₃×C₁₆	C₂×C₃×C₄	1	8	yes	—
49	C₂×C₄×C₈×C₁₃	C₃×C₈	1	8	yes	—
50	C₂×C₄×C₈×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₃	C₂×C₃×C₄	1	4	yes	—
52	C₂×C₄×C₈×C₁₃	C₂×C₃×C₄	1	4	yes	—
53	C₂×C₄×C₈×C₁₃	C₂³×C₃	1	1	yes	characteristic
54	C₄³×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
55	C₄×C₁₃×C₁₆	C₃×C₈	1	32	yes	direct product factor
56	C₄×C₁₃×C₁₆	C₂×C₃×C₄	1	16	yes	—
57	C₈²×C₁₃	C₃×C₈	1	8	yes	—
58	C₈²×C₁₃	C₂×C₃×C₄	1	8	yes	—
59	C₃×C₄²×C₁₆	C₂×C₁₃	1	2	yes	—
60	C₂×C₃×C₈×C₁₆	C₂×C₁₃	1	4	yes	—
61	C₃×C₄×C₈²	C₂×C₁₃	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₁₃	C₄×C₈	1	4	yes	—
63	C₂²×C₃×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₁₃	C₂²×C₈	1	2	yes	—
65	C₂×C₃×C₈×C₁₃	C₄×C₈	1	4	yes	—
66	C₂×C₃×C₈×C₁₃	C₄×C₈	1	8	yes	—
67	C₂×C₃×C₈×C₁₃	C₄×C₈	1	16	yes	—
68	C₂×C₃×C₈×C₁₃	C₂×C₁₆	1	32	yes	—
69	C₂×C₃×C₈×C₁₃	C₂×C₄²	1	4	yes	—
70	C₂×C₃×C₈×C₁₃	C₂²×C₈	1	8	yes	—
71	C₃×C₄²×C₁₃	C₄×C₈	1	8	yes	—
72	C₃×C₄²×C₁₃	C₂×C₁₆	1	16	yes	—
73	C₃×C₄²×C₁₃	C₂×C₄²	1	2	yes	—
74	C₃×C₄²×C₁₃	C₂²×C₈	1	2	yes	—
75	C₃×C₁₃×C₁₆	C₄×C₈	1	32	yes	direct product factor
76	C₄×C₈×C₁₆	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
77	C₂²×C₈×C₁₃	C₃×C₄²	1	2	yes	—
78	C₂²×C₈×C₁₃	C₂×C₃×C₈	1	8	yes	—
79	C₂²×C₈×C₁₃	C₂²×C₃×C₄	1	2	yes	—
80	C₂×C₄²×C₁₃	C₃×C₄²	1	2	yes	—
81	C₂×C₄²×C₁₃	C₂×C₃×C₈	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
83	C₂×C₁₃×C₁₆	C₃×C₄²	1	16	yes	—
84	C₂×C₁₃×C₁₆	C₂×C₃×C₈	1	32	yes	—
85	C₄×C₈×C₁₃	C₃×C₁₆	1	32	yes	direct product factor
86	C₄×C₈×C₁₃	C₃×C₄²	1	8	yes	—
87	C₄×C₈×C₁₃	C₂×C₃×C₈	1	4	yes	—
88	C₄×C₈×C₁₃	C₂×C₃×C₈	1	8	yes	—
89	C₄×C₈×C₁₃	C₂×C₃×C₈	1	16	yes	—
90	C₄×C₈×C₁₃	C₂²×C₃×C₄	1	4	yes	—
91	C₂×C₃×C₄×C₁₆	C₄×C₁₃	1	8	yes	—
92	C₂×C₃×C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
93	C₃×C₄²×C₈	C₄×C₁₃	1	2	yes	—
94	C₃×C₄²×C₈	C₂²×C₁₃	1	1	yes	characteristic
95	C₂×C₃×C₈²	C₄×C₁₃	1	2	yes	—
96	C₂×C₃×C₈²	C₂²×C₁₃	1	2	yes	—
97	C₃×C₈×C₁₆	C₄×C₁₃	1	16	yes	direct product factor
98	C₂³×C₃×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
99	C₂×C₃×C₄×C₁₃	C₈²	1	8	yes	—
100	C₂×C₃×C₄×C₁₃	C₄×C₁₆	1	16	yes	—
101	C₂×C₃×C₄×C₁₃	C₄³	1	1	yes	characteristic
102	C₂×C₃×C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
103	C₂×C₃×C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
104	C₂×C₃×C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
105	C₂×C₃×C₄×C₁₃	C₂²×C₁₆	1	8	yes	—
106	C₃×C₈×C₁₃	C₈²	1	8	yes	—
107	C₃×C₈×C₁₃	C₄×C₁₆	1	32	yes	direct product factor
108	C₃×C₈×C₁₃	C₂×C₄×C₈	1	8	yes	—
109	C₄²×C₁₆	C₂×C₃×C₁₃	1	2	yes	—
110	C₂×C₈×C₁₆	C₂×C₃×C₁₃	1	4	yes	—
111	C₄×C₈²	C₂×C₃×C₁₃	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₃×C₄×C₈	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂×C₃×C₄²	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₃×C₈	1	2	yes	—
115	C₂×C₈×C₁₃	C₃×C₄×C₈	1	4	yes	—
116	C₂×C₈×C₁₃	C₃×C₄×C₈	1	8	yes	—
117	C₂×C₈×C₁₃	C₃×C₄×C₈	1	16	yes	—
118	C₂×C₈×C₁₃	C₂×C₃×C₁₆	1	32	yes	—
119	C₂×C₈×C₁₃	C₂×C₃×C₄²	1	4	yes	—
120	C₂×C₈×C₁₃	C₂²×C₃×C₈	1	8	yes	—
121	C₄²×C₁₃	C₃×C₄×C₈	1	8	yes	—
122	C₄²×C₁₃	C₂×C₃×C₁₆	1	16	yes	—
123	C₄²×C₁₃	C₂×C₃×C₄²	1	2	yes	—
124	C₄²×C₁₃	C₂²×C₃×C₈	1	2	yes	—
125	C₁₃×C₁₆	C₃×C₄×C₈	1	32	yes	direct product factor
126	C₂²×C₃×C₁₆	C₂×C₄×C₁₃	1	8	yes	—
127	C₂×C₃×C₄×C₈	C₈×C₁₃	1	8	yes	—
128	C₂×C₃×C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
129	C₂×C₃×C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
130	C₂×C₃×C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
131	C₂×C₃×C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
132	C₃×C₄³	C₂×C₄×C₁₃	1	1	yes	characteristic
133	C₃×C₄×C₁₆	C₈×C₁₃	1	32	yes	direct product factor
134	C₃×C₄×C₁₆	C₂×C₄×C₁₃	1	16	yes	—
135	C₃×C₈²	C₈×C₁₃	1	8	yes	—
136	C₃×C₈²	C₂×C₄×C₁₃	1	8	yes	—
137	C₂²×C₃×C₁₃	C₂×C₈²	1	2	yes	—
138	C₂²×C₃×C₁₃	C₄²×C₈	1	1	yes	characteristic
139	C₂²×C₃×C₁₃	C₂×C₄×C₁₆	1	4	yes	—
140	C₃×C₄×C₁₃	C₈×C₁₆	1	16	yes	direct product factor
141	C₃×C₄×C₁₃	C₂×C₈²	1	2	yes	—
142	C₃×C₄×C₁₃	C₄²×C₈	1	2	yes	—
143	C₃×C₄×C₁₃	C₂×C₄×C₁₆	1	8	yes	—
144	C₂×C₄×C₁₆	C₃×C₄×C₁₃	1	8	yes	—
145	C₂×C₄×C₁₆	C₂²×C₃×C₁₃	1	4	yes	—
146	C₄²×C₈	C₃×C₄×C₁₃	1	2	yes	—
147	C₄²×C₈	C₂²×C₃×C₁₃	1	1	yes	characteristic
148	C₂×C₈²	C₃×C₄×C₁₃	1	2	yes	—
149	C₂×C₈²	C₂²×C₃×C₁₃	1	2	yes	—
150	C₈×C₁₆	C₃×C₄×C₁₃	1	16	yes	direct product factor
151	C₂³×C₁₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₃×C₈²	1	8	yes	—
153	C₂×C₄×C₁₃	C₃×C₄×C₁₆	1	16	yes	—
154	C₂×C₄×C₁₃	C₃×C₄³	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₃×C₄×C₈	1	4	yes	—
157	C₂×C₄×C₁₃	C₂×C₃×C₄×C₈	1	4	yes	—
158	C₂×C₄×C₁₃	C₂²×C₃×C₁₆	1	8	yes	—
159	C₈×C₁₃	C₃×C₈²	1	8	yes	—
160	C₈×C₁₃	C₃×C₄×C₁₆	1	32	yes	direct product factor
161	C₈×C₁₃	C₂×C₃×C₄×C₈	1	8	yes	—
162	C₂²×C₃×C₈	C₄²×C₁₃	1	2	yes	—
163	C₂²×C₃×C₈	C₂×C₈×C₁₃	1	8	yes	—
164	C₂²×C₃×C₈	C₂²×C₄×C₁₃	1	2	yes	—
165	C₂×C₃×C₄²	C₄²×C₁₃	1	2	yes	—
166	C₂×C₃×C₄²	C₂×C₈×C₁₃	1	4	yes	—
167	C₂×C₃×C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
168	C₂×C₃×C₁₆	C₄²×C₁₃	1	16	yes	—
169	C₂×C₃×C₁₆	C₂×C₈×C₁₃	1	32	yes	—
170	C₃×C₄×C₈	C₁₃×C₁₆	1	32	yes	direct product factor
171	C₃×C₄×C₈	C₄²×C₁₃	1	8	yes	—
172	C₃×C₄×C₈	C₂×C₈×C₁₃	1	4	yes	—
173	C₃×C₄×C₈	C₂×C₈×C₁₃	1	8	yes	—
174	C₃×C₄×C₈	C₂×C₈×C₁₃	1	16	yes	—
175	C₃×C₄×C₈	C₂²×C₄×C₁₃	1	4	yes	—
176	C₂×C₃×C₁₃	C₄×C₈²	1	1	yes	characteristic
177	C₂×C₃×C₁₃	C₂×C₈×C₁₆	1	4	yes	—
178	C₂×C₃×C₁₃	C₄²×C₁₆	1	2	yes	—
179	C₂²×C₁₆	C₂×C₃×C₄×C₁₃	1	8	yes	—
180	C₂×C₄×C₈	C₃×C₈×C₁₃	1	8	yes	—
181	C₂×C₄×C₈	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂×C₃×C₄×C₁₃	1	4	yes	—
183	C₂×C₄×C₈	C₂×C₃×C₄×C₁₃	1	4	yes	—
184	C₂×C₄×C₈	C₂³×C₃×C₁₃	1	1	yes	characteristic
185	C₄³	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
186	C₄×C₁₆	C₃×C₈×C₁₃	1	32	yes	direct product factor
187	C₄×C₁₆	C₂×C₃×C₄×C₁₃	1	16	yes	—
188	C₈²	C₃×C₈×C₁₃	1	8	yes	—
189	C₈²	C₂×C₃×C₄×C₁₃	1	8	yes	—
190	C₂²×C₁₃	C₂×C₃×C₈²	1	2	yes	—
191	C₂²×C₁₃	C₃×C₄²×C₈	1	1	yes	characteristic
192	C₂²×C₁₃	C₂×C₃×C₄×C₁₆	1	4	yes	—
193	C₄×C₁₃	C₃×C₈×C₁₆	1	16	yes	direct product factor
194	C₄×C₁₃	C₂×C₃×C₈²	1	2	yes	—
195	C₄×C₁₃	C₃×C₄²×C₈	1	2	yes	—
196	C₄×C₁₃	C₂×C₃×C₄×C₁₆	1	8	yes	—
197	C₂²×C₃×C₄	C₄×C₈×C₁₃	1	4	yes	—
198	C₂²×C₃×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂²×C₈×C₁₃	1	2	yes	—
200	C₂×C₃×C₈	C₄×C₈×C₁₃	1	4	yes	—
201	C₂×C₃×C₈	C₄×C₈×C₁₃	1	8	yes	—
202	C₂×C₃×C₈	C₄×C₈×C₁₃	1	16	yes	—
203	C₂×C₃×C₈	C₂×C₁₃×C₁₆	1	32	yes	—
204	C₂×C₃×C₈	C₂×C₄²×C₁₃	1	4	yes	—
205	C₂×C₃×C₈	C₂²×C₈×C₁₃	1	8	yes	—
206	C₃×C₄²	C₄×C₈×C₁₃	1	8	yes	—
207	C₃×C₄²	C₂×C₁₃×C₁₆	1	16	yes	—
208	C₃×C₄²	C₂×C₄²×C₁₃	1	2	yes	—
209	C₃×C₄²	C₂²×C₈×C₁₃	1	2	yes	—
210	C₃×C₁₆	C₄×C₈×C₁₃	1	32	yes	direct product factor
211	C₃×C₁₃	C₄×C₈×C₁₆	1	1	yes	characteristic, direct product factor, Hall
212	C₂²×C₈	C₃×C₄²×C₁₃	1	2	yes	—
213	C₂²×C₈	C₂×C₃×C₈×C₁₃	1	8	yes	—
214	C₂²×C₈	C₂²×C₃×C₄×C₁₃	1	2	yes	—
215	C₂×C₄²	C₃×C₄²×C₁₃	1	2	yes	—
216	C₂×C₄²	C₂×C₃×C₈×C₁₃	1	4	yes	—
217	C₂×C₄²	C₂²×C₃×C₄×C₁₃	1	1	yes	characteristic
218	C₂×C₁₆	C₃×C₄²×C₁₃	1	16	yes	—
219	C₂×C₁₆	C₂×C₃×C₈×C₁₃	1	32	yes	—
220	C₄×C₈	C₃×C₁₃×C₁₆	1	32	yes	direct product factor
221	C₄×C₈	C₃×C₄²×C₁₃	1	8	yes	—
222	C₄×C₈	C₂×C₃×C₈×C₁₃	1	4	yes	—
223	C₄×C₈	C₂×C₃×C₈×C₁₃	1	8	yes	—
224	C₄×C₈	C₂×C₃×C₈×C₁₃	1	16	yes	—
225	C₄×C₈	C₂²×C₃×C₄×C₁₃	1	4	yes	—
226	C₂×C₁₃	C₃×C₄×C₈²	1	1	yes	characteristic
227	C₂×C₁₃	C₂×C₃×C₈×C₁₆	1	4	yes	—
228	C₂×C₁₃	C₃×C₄²×C₁₆	1	2	yes	—
229	C₂³×C₃	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
230	C₂×C₃×C₄	C₈²×C₁₃	1	8	yes	—
231	C₂×C₃×C₄	C₄×C₁₃×C₁₆	1	16	yes	—
232	C₂×C₃×C₄	C₄³×C₁₃	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₄×C₈×C₁₃	1	4	yes	—
235	C₂×C₃×C₄	C₂×C₄×C₈×C₁₃	1	4	yes	—
236	C₂×C₃×C₄	C₂²×C₁₃×C₁₆	1	8	yes	—
237	C₃×C₈	C₈²×C₁₃	1	8	yes	—
238	C₃×C₈	C₄×C₁₃×C₁₆	1	32	yes	direct product factor
239	C₃×C₈	C₂×C₄×C₈×C₁₃	1	8	yes	—
240	C₂²×C₄	C₃×C₄×C₈×C₁₃	1	4	yes	—
241	C₂²×C₄	C₂×C₃×C₄²×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₃×C₈×C₁₃	1	2	yes	—
243	C₂×C₈	C₃×C₄×C₈×C₁₃	1	4	yes	—
244	C₂×C₈	C₃×C₄×C₈×C₁₃	1	8	yes	—
245	C₂×C₈	C₃×C₄×C₈×C₁₃	1	16	yes	—
246	C₂×C₈	C₂×C₃×C₁₃×C₁₆	1	32	yes	—
247	C₂×C₈	C₂×C₃×C₄²×C₁₃	1	4	yes	—
248	C₂×C₈	C₂²×C₃×C₈×C₁₃	1	8	yes	—
249	C₄²	C₃×C₄×C₈×C₁₃	1	8	yes	—
250	C₄²	C₂×C₃×C₁₃×C₁₆	1	16	yes	—
251	C₄²	C₂×C₃×C₄²×C₁₃	1	2	yes	—
252	C₄²	C₂²×C₃×C₈×C₁₃	1	2	yes	—
253	C₁₆	C₃×C₄×C₈×C₁₃	1	32	yes	direct product factor
254	C₁₃	C₃×C₄×C₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×C₃	C₂×C₈²×C₁₃	1	2	yes	—
256	C₂²×C₃	C₄²×C₈×C₁₃	1	1	yes	characteristic
257	C₂²×C₃	C₂×C₄×C₁₃×C₁₆	1	4	yes	—
258	C₃×C₄	C₈×C₁₃×C₁₆	1	16	yes	direct product factor
259	C₃×C₄	C₂×C₈²×C₁₃	1	2	yes	—
260	C₃×C₄	C₄²×C₈×C₁₃	1	2	yes	—
261	C₃×C₄	C₂×C₄×C₁₃×C₁₆	1	8	yes	—
262	C₂³	C₂×C₃×C₄×C₈×C₁₃	1	1	yes	characteristic
263	C₂×C₄	C₃×C₄×C₁₃×C₁₆	1	16	yes	—
264	C₂×C₄	C₃×C₈²×C₁₃	1	8	yes	—
265	C₂×C₄	C₂²×C₃×C₁₃×C₁₆	1	8	yes	—
266	C₂×C₄	C₂×C₃×C₄×C₈×C₁₃	1	1	yes	characteristic
267	C₂×C₄	C₂×C₃×C₄×C₈×C₁₃	1	4	yes	—
268	C₂×C₄	C₂×C₃×C₄×C₈×C₁₃	1	4	yes	—
269	C₂×C₄	C₃×C₄³×C₁₃	1	1	yes	characteristic
270	C₈	C₃×C₄×C₁₃×C₁₆	1	32	yes	direct product factor
271	C₈	C₃×C₈²×C₁₃	1	8	yes	—
272	C₈	C₂×C₃×C₄×C₈×C₁₃	1	8	yes	—
273	C₂×C₃	C₄×C₈²×C₁₃	1	1	yes	characteristic
274	C₂×C₃	C₂×C₈×C₁₃×C₁₆	1	4	yes	—
275	C₂×C₃	C₄²×C₁₃×C₁₆	1	2	yes	—
276	C₂²	C₂×C₃×C₄×C₁₃×C₁₆	1	4	yes	—
277	C₂²	C₂×C₃×C₈²×C₁₃	1	2	yes	—
278	C₂²	C₃×C₄²×C₈×C₁₃	1	1	yes	characteristic
279	C₄	C₃×C₈×C₁₃×C₁₆	1	16	yes	direct product factor
280	C₄	C₂×C₃×C₄×C₁₃×C₁₆	1	8	yes	—
281	C₄	C₂×C₃×C₈²×C₁₃	1	2	yes	—
282	C₄	C₃×C₄²×C₈×C₁₃	1	2	yes	—
283	C₃	C₄×C₈×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
284	C₂	C₂×C₃×C₈×C₁₃×C₁₆	1	4	yes	—
285	C₂	C₃×C₄²×C₁₃×C₁₆	1	2	yes	—
286	C₂	C₃×C₄×C₈²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₈	C₂³×C₃×C₁₃
socle, prime radical	C₂³×C₃×C₁₃	C₂×C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄×C₈×C₁₃×C₁₆	C₃	direct (N × H)
11. C₃×C₈×C₁₃×C₁₆	C₄	direct (N × H)
21. C₃×C₄×C₁₃×C₁₆	C₈	direct (N × H)
23. C₃×C₄×C₈×C₁₆	C₁₃	direct (N × H)
33. C₈×C₁₃×C₁₆	C₃×C₄	direct (N × H)
42. C₃×C₄×C₈×C₁₃	C₁₆	direct (N × H)
55. C₄×C₁₃×C₁₆	C₃×C₈	direct (N × H)
75. C₃×C₁₃×C₁₆	C₄×C₈	direct (N × H)
76. C₄×C₈×C₁₆	C₃×C₁₃	direct (N × H)
85. C₄×C₈×C₁₃	C₃×C₁₆	direct (N × H)
97. C₃×C₈×C₁₆	C₄×C₁₃	direct (N × H)
107. C₃×C₈×C₁₃	C₄×C₁₆	direct (N × H)
125. C₁₃×C₁₆	C₃×C₄×C₈	direct (N × H)
133. C₃×C₄×C₁₆	C₈×C₁₃	direct (N × H)
140. C₃×C₄×C₁₃	C₈×C₁₆	direct (N × H)
150. C₈×C₁₆	C₃×C₄×C₁₃	direct (N × H)
160. C₈×C₁₃	C₃×C₄×C₁₆	direct (N × H)
170. C₃×C₄×C₈	C₁₃×C₁₆	direct (N × H)
186. C₄×C₁₆	C₃×C₈×C₁₃	direct (N × H)
193. C₄×C₁₃	C₃×C₈×C₁₆	direct (N × H)
210. C₃×C₁₆	C₄×C₈×C₁₃	direct (N × H)
211. C₃×C₁₃	C₄×C₈×C₁₆	direct (N × H)
220. C₄×C₈	C₃×C₁₃×C₁₆	direct (N × H)
238. C₃×C₈	C₄×C₁₃×C₁₆	direct (N × H)
253. C₁₆	C₃×C₄×C₈×C₁₃	direct (N × H)
254. C₁₃	C₃×C₄×C₈×C₁₆	direct (N × H)
258. C₃×C₄	C₈×C₁₃×C₁₆	direct (N × H)
270. C₈	C₃×C₄×C₁₃×C₁₆	direct (N × H)
279. C₄	C₃×C₈×C₁₃×C₁₆	direct (N × H)
283. C₃	C₄×C₈×C₁₃×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₈²×C₁₃	2
C₃×C₄²×C₁₃×C₁₆	2
C₂×C₃×C₈×C₁₃×C₁₆	2
C₄×C₈×C₁₃×C₁₆	3
C₃×C₄×C₈×C₁₆	13

Subgroups — C3×C4×C8×C13×C16 #72197608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₈×C₁₃×C₁₆ #72197608