Subgroups — C₂³×C₄²×C₁₃×C₁₆ #72203756

Order 26624.

155088 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄×C₁₃×C₁₆	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₁₃×C₁₆	C₂	1	56	yes	maximal, direct product factor
4	C₂³×C₄³×C₁₃	C₄	1	1	yes	characteristic
5	C₂⁴×C₄×C₈×C₁₃	C₄	1	3	yes	—
6	C₂⁴×C₄×C₈×C₁₃	C₂²	1	3	yes	—
7	C₂²×C₄²×C₈×C₁₃	C₄	1	28	yes	—
8	C₂²×C₄²×C₈×C₁₃	C₂²	1	28	yes	—
9	C₂⁵×C₁₃×C₁₆	C₂²	1	4	yes	—
10	C₂³×C₄×C₁₃×C₁₆	C₄	1	192	yes	direct product factor
11	C₂³×C₄×C₁₃×C₁₆	C₂²	1	168	yes	—
12	C₂×C₄²×C₁₃×C₁₆	C₂²	1	448	yes	direct product factor
13	C₂³×C₄²×C₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₄²×C₈	C₂×C₁₃	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₆	C₂×C₁₃	1	6	yes	—
16	C₂²×C₄²×C₁₆	C₂×C₁₃	1	56	yes	direct product factor
17	C₂⁵×C₈×C₁₃	C₂×C₄	1	3	yes	—
18	C₂⁵×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂⁴×C₄²×C₁₃	C₈	1	4	yes	—
20	C₂⁴×C₄²×C₁₃	C₂×C₄	1	3	yes	—
21	C₂⁴×C₁₃×C₁₆	C₂×C₄	1	192	yes	—
22	C₂⁴×C₁₃×C₁₆	C₂³	1	56	yes	—
23	C₂³×C₄×C₈×C₁₃	C₈	1	96	yes	—
24	C₂³×C₄×C₈×C₁₃	C₂×C₄	1	42	yes	—
25	C₂³×C₄×C₈×C₁₃	C₂×C₄	1	84	yes	—
26	C₂³×C₄×C₈×C₁₃	C₂×C₄	1	96	yes	—
27	C₂³×C₄×C₈×C₁₃	C₂³	1	42	yes	—
28	C₂²×C₄³×C₁₃	C₈	1	28	yes	—
29	C₂²×C₄³×C₁₃	C₂×C₄	1	28	yes	—
30	C₂²×C₄×C₁₃×C₁₆	C₂×C₄	1	2688	yes	direct product factor
31	C₂²×C₄×C₁₃×C₁₆	C₂³	1	672	yes	—
32	C₂×C₄²×C₈×C₁₃	C₂×C₄	1	336	yes	—
33	C₂×C₄²×C₈×C₁₃	C₂³	1	112	yes	—
34	C₄²×C₁₃×C₁₆	C₂³	1	512	yes	direct product factor
35	C₂⁵×C₄×C₁₃	C₂×C₈	1	6	yes	—
36	C₂⁵×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂⁴×C₈×C₁₃	C₄²	1	48	yes	—
38	C₂⁴×C₈×C₁₃	C₂×C₈	1	96	yes	—
39	C₂⁴×C₈×C₁₃	C₂²×C₄	1	7	yes	—
40	C₂⁴×C₈×C₁₃	C₂²×C₄	1	42	yes	—
41	C₂⁴×C₈×C₁₃	C₂²×C₄	1	48	yes	—
42	C₂⁴×C₈×C₁₃	C₂⁴	1	7	yes	—
43	C₂³×C₄²×C₁₃	C₁₆	1	128	yes	direct product factor
44	C₂³×C₄²×C₁₃	C₄²	1	48	yes	—
45	C₂³×C₄²×C₁₃	C₂×C₈	1	42	yes	—
46	C₂³×C₄²×C₁₃	C₂×C₈	1	48	yes	—
47	C₂³×C₄²×C₁₃	C₂×C₈	1	112	yes	—
48	C₂³×C₄²×C₁₃	C₂²×C₄	1	42	yes	—
49	C₂³×C₁₃×C₁₆	C₄²	1	1024	yes	direct product factor
50	C₂³×C₁₃×C₁₆	C₂²×C₄	1	1344	yes	—
51	C₂³×C₁₃×C₁₆	C₂⁴	1	112	yes	—
52	C₂²×C₄×C₈×C₁₃	C₄²	1	672	yes	—
53	C₂²×C₄×C₈×C₁₃	C₂×C₈	1	1344	yes	—
54	C₂²×C₄×C₈×C₁₃	C₂²×C₄	1	336	yes	—
55	C₂²×C₄×C₈×C₁₃	C₂²×C₄	1	672	yes	—
56	C₂²×C₄×C₈×C₁₃	C₂²×C₄	1	252	yes	—
57	C₂²×C₄×C₈×C₁₃	C₂⁴	1	84	yes	—
58	C₂×C₄³×C₁₃	C₂×C₈	1	336	yes	—
59	C₂×C₄³×C₁₃	C₂²×C₄	1	112	yes	—
60	C₂×C₄×C₁₃×C₁₆	C₂²×C₄	1	5376	yes	direct product factor
61	C₂×C₄×C₁₃×C₁₆	C₂⁴	1	384	yes	—
62	C₄²×C₈×C₁₃	C₂²×C₄	1	448	yes	—
63	C₄²×C₈×C₁₃	C₂⁴	1	64	yes	—
64	C₂⁶×C₁₃	C₂²×C₈	1	1	yes	characteristic
65	C₂⁴×C₄×C₁₃	C₄×C₈	1	96	yes	—
66	C₂⁴×C₄×C₁₃	C₂×C₁₆	1	192	yes	—
67	C₂⁴×C₄×C₁₃	C₂×C₄²	1	24	yes	—
68	C₂⁴×C₄×C₁₃	C₂²×C₈	1	7	yes	—
69	C₂⁴×C₄×C₁₃	C₂²×C₈	1	24	yes	—
70	C₂⁴×C₄×C₁₃	C₂²×C₈	1	84	yes	—
71	C₂⁴×C₄×C₁₃	C₂³×C₄	1	7	yes	—
72	C₂³×C₈×C₁₃	C₄×C₈	1	768	yes	—
73	C₂³×C₈×C₁₃	C₂×C₄²	1	256	yes	—
74	C₂³×C₈×C₁₃	C₂×C₄²	1	336	yes	—
75	C₂³×C₈×C₁₃	C₂×C₄²	1	168	yes	—
76	C₂³×C₈×C₁₃	C₂²×C₈	1	672	yes	—
77	C₂³×C₈×C₁₃	C₂³×C₄	1	21	yes	—
78	C₂³×C₈×C₁₃	C₂³×C₄	1	84	yes	—
79	C₂³×C₈×C₁₃	C₂³×C₄	1	168	yes	—
80	C₂³×C₈×C₁₃	C₂⁵	1	7	yes	—
81	C₂²×C₄²×C₁₃	C₄×C₈	1	672	yes	—
82	C₂²×C₄²×C₁₃	C₂×C₁₆	1	1792	yes	direct product factor
83	C₂²×C₄²×C₁₃	C₂×C₄²	1	336	yes	—
84	C₂²×C₄²×C₁₃	C₂²×C₈	1	336	yes	—
85	C₂²×C₄²×C₁₃	C₂²×C₈	1	448	yes	—
86	C₂²×C₄²×C₁₃	C₂²×C₈	1	252	yes	—
87	C₂²×C₄²×C₁₃	C₂³×C₄	1	84	yes	—
88	C₂²×C₁₃×C₁₆	C₂×C₄²	1	3584	yes	direct product factor
89	C₂²×C₁₃×C₁₆	C₂³×C₄	1	1344	yes	—
90	C₂²×C₁₃×C₁₆	C₂⁵	1	32	yes	—
91	C₂×C₄×C₈×C₁₃	C₂×C₄²	1	2016	yes	—
92	C₂×C₄×C₈×C₁₃	C₂²×C₈	1	2688	yes	—
93	C₂×C₄×C₈×C₁₃	C₂³×C₄	1	672	yes	—
94	C₂×C₄×C₈×C₁₃	C₂³×C₄	1	168	yes	—
95	C₂×C₄×C₈×C₁₃	C₂³×C₄	1	192	yes	—
96	C₂×C₄×C₈×C₁₃	C₂⁵	1	24	yes	—
97	C₄³×C₁₃	C₂²×C₈	1	448	yes	—
98	C₄³×C₁₃	C₂³×C₄	1	64	yes	—
99	C₄×C₁₃×C₁₆	C₂³×C₄	1	1536	yes	direct product factor
100	C₂⁵×C₁₆	C₂²×C₁₃	1	4	yes	—
101	C₂⁴×C₄×C₈	C₄×C₁₃	1	3	yes	—
102	C₂⁴×C₄×C₈	C₂²×C₁₃	1	3	yes	—
103	C₂³×C₄³	C₄×C₁₃	1	1	yes	characteristic
104	C₂³×C₄×C₁₆	C₄×C₁₃	1	192	yes	direct product factor
105	C₂³×C₄×C₁₆	C₂²×C₁₃	1	168	yes	—
106	C₂²×C₄²×C₈	C₄×C₁₃	1	28	yes	—
107	C₂²×C₄²×C₈	C₂²×C₁₃	1	28	yes	—
108	C₂×C₄²×C₁₆	C₂²×C₁₃	1	448	yes	direct product factor
109	C₂⁵×C₁₃	C₂×C₄×C₈	1	24	yes	—
110	C₂⁵×C₁₃	C₂²×C₁₆	1	32	yes	—
111	C₂⁵×C₁₃	C₂³×C₈	1	7	yes	—
112	C₂³×C₄×C₁₃	C₄×C₁₆	1	1536	yes	direct product factor
113	C₂³×C₄×C₁₃	C₄³	1	64	yes	—
114	C₂³×C₄×C₁₃	C₂×C₄×C₈	1	672	yes	—
115	C₂³×C₄×C₁₃	C₂×C₄×C₈	1	168	yes	—
116	C₂³×C₄×C₁₃	C₂×C₄×C₈	1	192	yes	—
117	C₂³×C₄×C₁₃	C₂²×C₁₆	1	1344	yes	—
118	C₂³×C₄×C₁₃	C₂²×C₄²	1	84	yes	—
119	C₂³×C₄×C₁₃	C₂³×C₈	1	21	yes	—
120	C₂³×C₄×C₁₃	C₂³×C₈	1	84	yes	—
121	C₂³×C₄×C₁₃	C₂³×C₈	1	168	yes	—
122	C₂³×C₄×C₁₃	C₂⁴×C₄	1	7	yes	—
123	C₂²×C₈×C₁₃	C₄³	1	448	yes	—
124	C₂²×C₈×C₁₃	C₂×C₄×C₈	1	2688	yes	—
125	C₂²×C₈×C₁₃	C₂²×C₄²	1	336	yes	—
126	C₂²×C₈×C₁₃	C₂²×C₄²	1	448	yes	—
127	C₂²×C₈×C₁₃	C₂²×C₄²	1	252	yes	—
128	C₂²×C₈×C₁₃	C₂³×C₈	1	672	yes	—
129	C₂²×C₈×C₁₃	C₂⁴×C₄	1	7	yes	—
130	C₂²×C₈×C₁₃	C₂⁴×C₄	1	24	yes	—
131	C₂²×C₈×C₁₃	C₂⁴×C₄	1	84	yes	—
132	C₂²×C₈×C₁₃	C₂⁶	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂×C₄×C₈	1	2016	yes	—
134	C₂×C₄²×C₁₃	C₂²×C₁₆	1	3584	yes	direct product factor
135	C₂×C₄²×C₁₃	C₂²×C₄²	1	336	yes	—
136	C₂×C₄²×C₁₃	C₂³×C₈	1	256	yes	—
137	C₂×C₄²×C₁₃	C₂³×C₈	1	336	yes	—
138	C₂×C₄²×C₁₃	C₂³×C₈	1	168	yes	—
139	C₂×C₄²×C₁₃	C₂⁴×C₄	1	24	yes	—
140	C₂×C₁₃×C₁₆	C₂²×C₄²	1	1792	yes	direct product factor
141	C₂×C₁₃×C₁₆	C₂⁴×C₄	1	192	yes	—
142	C₄×C₈×C₁₃	C₂²×C₄²	1	672	yes	—
143	C₄×C₈×C₁₃	C₂³×C₈	1	768	yes	—
144	C₄×C₈×C₁₃	C₂⁴×C₄	1	96	yes	—
145	C₂⁵×C₈	C₂×C₄×C₁₃	1	3	yes	—
146	C₂⁵×C₈	C₂³×C₁₃	1	1	yes	characteristic
147	C₂⁴×C₄²	C₈×C₁₃	1	4	yes	—
148	C₂⁴×C₄²	C₂×C₄×C₁₃	1	3	yes	—
149	C₂⁴×C₁₆	C₂×C₄×C₁₃	1	192	yes	—
150	C₂⁴×C₁₆	C₂³×C₁₃	1	56	yes	—
151	C₂³×C₄×C₈	C₈×C₁₃	1	96	yes	—
152	C₂³×C₄×C₈	C₂×C₄×C₁₃	1	42	yes	—
153	C₂³×C₄×C₈	C₂×C₄×C₁₃	1	84	yes	—
154	C₂³×C₄×C₈	C₂×C₄×C₁₃	1	96	yes	—
155	C₂³×C₄×C₈	C₂³×C₁₃	1	42	yes	—
156	C₂²×C₄³	C₈×C₁₃	1	28	yes	—
157	C₂²×C₄³	C₂×C₄×C₁₃	1	28	yes	—
158	C₂²×C₄×C₁₆	C₂×C₄×C₁₃	1	2688	yes	direct product factor
159	C₂²×C₄×C₁₆	C₂³×C₁₃	1	672	yes	—
160	C₂×C₄²×C₈	C₂×C₄×C₁₃	1	336	yes	—
161	C₂×C₄²×C₈	C₂³×C₁₃	1	112	yes	—
162	C₄²×C₁₆	C₂³×C₁₃	1	512	yes	direct product factor
163	C₂⁴×C₁₃	C₄²×C₈	1	64	yes	—
164	C₂⁴×C₁₃	C₂×C₄×C₁₆	1	384	yes	—
165	C₂⁴×C₁₃	C₂²×C₄×C₈	1	84	yes	—
166	C₂⁴×C₁₃	C₂³×C₁₆	1	112	yes	—
167	C₂⁴×C₁₃	C₂⁴×C₈	1	7	yes	—
168	C₂²×C₄×C₁₃	C₄²×C₈	1	448	yes	—
169	C₂²×C₄×C₁₃	C₂×C₄×C₁₆	1	5376	yes	direct product factor
170	C₂²×C₄×C₁₃	C₂×C₄³	1	112	yes	—
171	C₂²×C₄×C₁₃	C₂²×C₄×C₈	1	336	yes	—
172	C₂²×C₄×C₁₃	C₂²×C₄×C₈	1	672	yes	—
173	C₂²×C₄×C₁₃	C₂²×C₄×C₈	1	252	yes	—
174	C₂²×C₄×C₁₃	C₂³×C₁₆	1	1344	yes	—
175	C₂²×C₄×C₁₃	C₂³×C₄²	1	42	yes	—
176	C₂²×C₄×C₁₃	C₂⁴×C₈	1	7	yes	—
177	C₂²×C₄×C₁₃	C₂⁴×C₈	1	42	yes	—
178	C₂²×C₄×C₁₃	C₂⁴×C₈	1	48	yes	—
179	C₂²×C₄×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×C₄³	1	336	yes	—
181	C₂×C₈×C₁₃	C₂²×C₄×C₈	1	1344	yes	—
182	C₂×C₈×C₁₃	C₂³×C₄²	1	42	yes	—
183	C₂×C₈×C₁₃	C₂³×C₄²	1	48	yes	—
184	C₂×C₈×C₁₃	C₂³×C₄²	1	112	yes	—
185	C₂×C₈×C₁₃	C₂⁴×C₈	1	96	yes	—
186	C₂×C₈×C₁₃	C₂⁵×C₄	1	6	yes	—
187	C₄²×C₁₃	C₂²×C₄×C₈	1	672	yes	—
188	C₄²×C₁₃	C₂³×C₁₆	1	1024	yes	direct product factor
189	C₄²×C₁₃	C₂³×C₄²	1	48	yes	—
190	C₄²×C₁₃	C₂⁴×C₈	1	48	yes	—
191	C₁₃×C₁₆	C₂³×C₄²	1	128	yes	direct product factor
192	C₂⁵×C₄	C₂×C₈×C₁₃	1	6	yes	—
193	C₂⁵×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
194	C₂⁴×C₈	C₄²×C₁₃	1	48	yes	—
195	C₂⁴×C₈	C₂×C₈×C₁₃	1	96	yes	—
196	C₂⁴×C₈	C₂²×C₄×C₁₃	1	7	yes	—
197	C₂⁴×C₈	C₂²×C₄×C₁₃	1	42	yes	—
198	C₂⁴×C₈	C₂²×C₄×C₁₃	1	48	yes	—
199	C₂⁴×C₈	C₂⁴×C₁₃	1	7	yes	—
200	C₂³×C₄²	C₁₃×C₁₆	1	128	yes	direct product factor
201	C₂³×C₄²	C₄²×C₁₃	1	48	yes	—
202	C₂³×C₄²	C₂×C₈×C₁₃	1	42	yes	—
203	C₂³×C₄²	C₂×C₈×C₁₃	1	48	yes	—
204	C₂³×C₄²	C₂×C₈×C₁₃	1	112	yes	—
205	C₂³×C₄²	C₂²×C₄×C₁₃	1	42	yes	—
206	C₂³×C₁₆	C₄²×C₁₃	1	1024	yes	direct product factor
207	C₂³×C₁₆	C₂²×C₄×C₁₃	1	1344	yes	—
208	C₂³×C₁₆	C₂⁴×C₁₃	1	112	yes	—
209	C₂²×C₄×C₈	C₄²×C₁₃	1	672	yes	—
210	C₂²×C₄×C₈	C₂×C₈×C₁₃	1	1344	yes	—
211	C₂²×C₄×C₈	C₂²×C₄×C₁₃	1	336	yes	—
212	C₂²×C₄×C₈	C₂²×C₄×C₁₃	1	672	yes	—
213	C₂²×C₄×C₈	C₂²×C₄×C₁₃	1	252	yes	—
214	C₂²×C₄×C₈	C₂⁴×C₁₃	1	84	yes	—
215	C₂×C₄³	C₂×C₈×C₁₃	1	336	yes	—
216	C₂×C₄³	C₂²×C₄×C₁₃	1	112	yes	—
217	C₂×C₄×C₁₆	C₂²×C₄×C₁₃	1	5376	yes	direct product factor
218	C₂×C₄×C₁₆	C₂⁴×C₁₃	1	384	yes	—
219	C₄²×C₈	C₂²×C₄×C₁₃	1	448	yes	—
220	C₄²×C₈	C₂⁴×C₁₃	1	64	yes	—
221	C₂³×C₁₃	C₄²×C₁₆	1	512	yes	direct product factor
222	C₂³×C₁₃	C₂×C₄²×C₈	1	112	yes	—
223	C₂³×C₁₃	C₂²×C₄×C₁₆	1	672	yes	—
224	C₂³×C₁₃	C₂³×C₄×C₈	1	42	yes	—
225	C₂³×C₁₃	C₂⁴×C₁₆	1	56	yes	—
226	C₂³×C₁₃	C₂⁵×C₈	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₄²×C₈	1	336	yes	—
228	C₂×C₄×C₁₃	C₂²×C₄×C₁₆	1	2688	yes	direct product factor
229	C₂×C₄×C₁₃	C₂²×C₄³	1	28	yes	—
230	C₂×C₄×C₁₃	C₂³×C₄×C₈	1	42	yes	—
231	C₂×C₄×C₁₃	C₂³×C₄×C₈	1	84	yes	—
232	C₂×C₄×C₁₃	C₂³×C₄×C₈	1	96	yes	—
233	C₂×C₄×C₁₃	C₂⁴×C₁₆	1	192	yes	—
234	C₂×C₄×C₁₃	C₂⁴×C₄²	1	3	yes	—
235	C₂×C₄×C₁₃	C₂⁵×C₈	1	3	yes	—
236	C₈×C₁₃	C₂²×C₄³	1	28	yes	—
237	C₈×C₁₃	C₂³×C₄×C₈	1	96	yes	—
238	C₈×C₁₃	C₂⁴×C₄²	1	4	yes	—
239	C₂⁶	C₂²×C₈×C₁₃	1	1	yes	characteristic
240	C₂⁴×C₄	C₄×C₈×C₁₃	1	96	yes	—
241	C₂⁴×C₄	C₂×C₁₃×C₁₆	1	192	yes	—
242	C₂⁴×C₄	C₂×C₄²×C₁₃	1	24	yes	—
243	C₂⁴×C₄	C₂²×C₈×C₁₃	1	7	yes	—
244	C₂⁴×C₄	C₂²×C₈×C₁₃	1	24	yes	—
245	C₂⁴×C₄	C₂²×C₈×C₁₃	1	84	yes	—
246	C₂⁴×C₄	C₂³×C₄×C₁₃	1	7	yes	—
247	C₂³×C₈	C₄×C₈×C₁₃	1	768	yes	—
248	C₂³×C₈	C₂×C₄²×C₁₃	1	256	yes	—
249	C₂³×C₈	C₂×C₄²×C₁₃	1	336	yes	—
250	C₂³×C₈	C₂×C₄²×C₁₃	1	168	yes	—
251	C₂³×C₈	C₂²×C₈×C₁₃	1	672	yes	—
252	C₂³×C₈	C₂³×C₄×C₁₃	1	21	yes	—
253	C₂³×C₈	C₂³×C₄×C₁₃	1	84	yes	—
254	C₂³×C₈	C₂³×C₄×C₁₃	1	168	yes	—
255	C₂³×C₈	C₂⁵×C₁₃	1	7	yes	—
256	C₂²×C₄²	C₄×C₈×C₁₃	1	672	yes	—
257	C₂²×C₄²	C₂×C₁₃×C₁₆	1	1792	yes	direct product factor
258	C₂²×C₄²	C₂×C₄²×C₁₃	1	336	yes	—
259	C₂²×C₄²	C₂²×C₈×C₁₃	1	336	yes	—
260	C₂²×C₄²	C₂²×C₈×C₁₃	1	448	yes	—
261	C₂²×C₄²	C₂²×C₈×C₁₃	1	252	yes	—
262	C₂²×C₄²	C₂³×C₄×C₁₃	1	84	yes	—
263	C₂²×C₁₆	C₂×C₄²×C₁₃	1	3584	yes	direct product factor
264	C₂²×C₁₆	C₂³×C₄×C₁₃	1	1344	yes	—
265	C₂²×C₁₆	C₂⁵×C₁₃	1	32	yes	—
266	C₂×C₄×C₈	C₂×C₄²×C₁₃	1	2016	yes	—
267	C₂×C₄×C₈	C₂²×C₈×C₁₃	1	2688	yes	—
268	C₂×C₄×C₈	C₂³×C₄×C₁₃	1	672	yes	—
269	C₂×C₄×C₈	C₂³×C₄×C₁₃	1	168	yes	—
270	C₂×C₄×C₈	C₂³×C₄×C₁₃	1	192	yes	—
271	C₂×C₄×C₈	C₂⁵×C₁₃	1	24	yes	—
272	C₄³	C₂²×C₈×C₁₃	1	448	yes	—
273	C₄³	C₂³×C₄×C₁₃	1	64	yes	—
274	C₄×C₁₆	C₂³×C₄×C₁₃	1	1536	yes	direct product factor
275	C₂²×C₁₃	C₂×C₄²×C₁₆	1	448	yes	direct product factor
276	C₂²×C₁₃	C₂²×C₄²×C₈	1	28	yes	—
277	C₂²×C₁₃	C₂³×C₄×C₁₆	1	168	yes	—
278	C₂²×C₁₃	C₂⁴×C₄×C₈	1	3	yes	—
279	C₂²×C₁₃	C₂⁵×C₁₆	1	4	yes	—
280	C₄×C₁₃	C₂²×C₄²×C₈	1	28	yes	—
281	C₄×C₁₃	C₂³×C₄×C₁₆	1	192	yes	direct product factor
282	C₄×C₁₃	C₂³×C₄³	1	1	yes	characteristic
283	C₄×C₁₃	C₂⁴×C₄×C₈	1	3	yes	—
284	C₂⁵	C₂×C₄×C₈×C₁₃	1	24	yes	—
285	C₂⁵	C₂²×C₁₃×C₁₆	1	32	yes	—
286	C₂⁵	C₂³×C₈×C₁₃	1	7	yes	—
287	C₂³×C₄	C₄×C₁₃×C₁₆	1	1536	yes	direct product factor
288	C₂³×C₄	C₄³×C₁₃	1	64	yes	—
289	C₂³×C₄	C₂×C₄×C₈×C₁₃	1	672	yes	—
290	C₂³×C₄	C₂×C₄×C₈×C₁₃	1	168	yes	—
291	C₂³×C₄	C₂×C₄×C₈×C₁₃	1	192	yes	—
292	C₂³×C₄	C₂²×C₁₃×C₁₆	1	1344	yes	—
293	C₂³×C₄	C₂²×C₄²×C₁₃	1	84	yes	—
294	C₂³×C₄	C₂³×C₈×C₁₃	1	21	yes	—
295	C₂³×C₄	C₂³×C₈×C₁₃	1	84	yes	—
296	C₂³×C₄	C₂³×C₈×C₁₃	1	168	yes	—
297	C₂³×C₄	C₂⁴×C₄×C₁₃	1	7	yes	—
298	C₂²×C₈	C₄³×C₁₃	1	448	yes	—
299	C₂²×C₈	C₂×C₄×C₈×C₁₃	1	2688	yes	—
300	C₂²×C₈	C₂²×C₄²×C₁₃	1	336	yes	—
301	C₂²×C₈	C₂²×C₄²×C₁₃	1	448	yes	—
302	C₂²×C₈	C₂²×C₄²×C₁₃	1	252	yes	—
303	C₂²×C₈	C₂³×C₈×C₁₃	1	672	yes	—
304	C₂²×C₈	C₂⁴×C₄×C₁₃	1	7	yes	—
305	C₂²×C₈	C₂⁴×C₄×C₁₃	1	24	yes	—
306	C₂²×C₈	C₂⁴×C₄×C₁₃	1	84	yes	—
307	C₂²×C₈	C₂⁶×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	C₂×C₄×C₈×C₁₃	1	2016	yes	—
309	C₂×C₄²	C₂²×C₁₃×C₁₆	1	3584	yes	direct product factor
310	C₂×C₄²	C₂²×C₄²×C₁₃	1	336	yes	—
311	C₂×C₄²	C₂³×C₈×C₁₃	1	256	yes	—
312	C₂×C₄²	C₂³×C₈×C₁₃	1	336	yes	—
313	C₂×C₄²	C₂³×C₈×C₁₃	1	168	yes	—
314	C₂×C₄²	C₂⁴×C₄×C₁₃	1	24	yes	—
315	C₂×C₁₆	C₂²×C₄²×C₁₃	1	1792	yes	direct product factor
316	C₂×C₁₆	C₂⁴×C₄×C₁₃	1	192	yes	—
317	C₄×C₈	C₂²×C₄²×C₁₃	1	672	yes	—
318	C₄×C₈	C₂³×C₈×C₁₃	1	768	yes	—
319	C₄×C₈	C₂⁴×C₄×C₁₃	1	96	yes	—
320	C₂×C₁₃	C₂²×C₄²×C₁₆	1	56	yes	direct product factor
321	C₂×C₁₃	C₂⁴×C₄×C₁₆	1	6	yes	—
322	C₂×C₁₃	C₂³×C₄²×C₈	1	1	yes	characteristic
323	C₂⁴	C₄²×C₈×C₁₃	1	64	yes	—
324	C₂⁴	C₂×C₄×C₁₃×C₁₆	1	384	yes	—
325	C₂⁴	C₂²×C₄×C₈×C₁₃	1	84	yes	—
326	C₂⁴	C₂³×C₁₃×C₁₆	1	112	yes	—
327	C₂⁴	C₂⁴×C₈×C₁₃	1	7	yes	—
328	C₂²×C₄	C₄²×C₈×C₁₃	1	448	yes	—
329	C₂²×C₄	C₂×C₄×C₁₃×C₁₆	1	5376	yes	direct product factor
330	C₂²×C₄	C₂×C₄³×C₁₃	1	112	yes	—
331	C₂²×C₄	C₂²×C₄×C₈×C₁₃	1	336	yes	—
332	C₂²×C₄	C₂²×C₄×C₈×C₁₃	1	672	yes	—
333	C₂²×C₄	C₂²×C₄×C₈×C₁₃	1	252	yes	—
334	C₂²×C₄	C₂³×C₁₃×C₁₆	1	1344	yes	—
335	C₂²×C₄	C₂³×C₄²×C₁₃	1	42	yes	—
336	C₂²×C₄	C₂⁴×C₈×C₁₃	1	7	yes	—
337	C₂²×C₄	C₂⁴×C₈×C₁₃	1	42	yes	—
338	C₂²×C₄	C₂⁴×C₈×C₁₃	1	48	yes	—
339	C₂²×C₄	C₂⁵×C₄×C₁₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄³×C₁₃	1	336	yes	—
341	C₂×C₈	C₂²×C₄×C₈×C₁₃	1	1344	yes	—
342	C₂×C₈	C₂³×C₄²×C₁₃	1	42	yes	—
343	C₂×C₈	C₂³×C₄²×C₁₃	1	48	yes	—
344	C₂×C₈	C₂³×C₄²×C₁₃	1	112	yes	—
345	C₂×C₈	C₂⁴×C₈×C₁₃	1	96	yes	—
346	C₂×C₈	C₂⁵×C₄×C₁₃	1	6	yes	—
347	C₄²	C₂²×C₄×C₈×C₁₃	1	672	yes	—
348	C₄²	C₂³×C₁₃×C₁₆	1	1024	yes	direct product factor
349	C₄²	C₂³×C₄²×C₁₃	1	48	yes	—
350	C₄²	C₂⁴×C₈×C₁₃	1	48	yes	—
351	C₁₆	C₂³×C₄²×C₁₃	1	128	yes	direct product factor
352	C₁₃	C₂³×C₄²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	C₄²×C₁₃×C₁₆	1	512	yes	direct product factor
354	C₂³	C₂×C₄²×C₈×C₁₃	1	112	yes	—
355	C₂³	C₂²×C₄×C₁₃×C₁₆	1	672	yes	—
356	C₂³	C₂³×C₄×C₈×C₁₃	1	42	yes	—
357	C₂³	C₂⁴×C₁₃×C₁₆	1	56	yes	—
358	C₂³	C₂⁵×C₈×C₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄²×C₈×C₁₃	1	336	yes	—
360	C₂×C₄	C₂²×C₄×C₁₃×C₁₆	1	2688	yes	direct product factor
361	C₂×C₄	C₂²×C₄³×C₁₃	1	28	yes	—
362	C₂×C₄	C₂³×C₄×C₈×C₁₃	1	42	yes	—
363	C₂×C₄	C₂³×C₄×C₈×C₁₃	1	84	yes	—
364	C₂×C₄	C₂³×C₄×C₈×C₁₃	1	96	yes	—
365	C₂×C₄	C₂⁴×C₁₃×C₁₆	1	192	yes	—
366	C₂×C₄	C₂⁴×C₄²×C₁₃	1	3	yes	—
367	C₂×C₄	C₂⁵×C₈×C₁₃	1	3	yes	—
368	C₈	C₂²×C₄³×C₁₃	1	28	yes	—
369	C₈	C₂³×C₄×C₈×C₁₃	1	96	yes	—
370	C₈	C₂⁴×C₄²×C₁₃	1	4	yes	—
371	C₂²	C₂×C₄²×C₁₃×C₁₆	1	448	yes	direct product factor
372	C₂²	C₂³×C₄×C₁₃×C₁₆	1	168	yes	—
373	C₂²	C₂⁵×C₁₃×C₁₆	1	4	yes	—
374	C₂²	C₂²×C₄²×C₈×C₁₃	1	28	yes	—
375	C₂²	C₂⁴×C₄×C₈×C₁₃	1	3	yes	—
376	C₄	C₂³×C₄×C₁₃×C₁₆	1	192	yes	direct product factor
377	C₄	C₂²×C₄²×C₈×C₁₃	1	28	yes	—
378	C₄	C₂⁴×C₄×C₈×C₁₃	1	3	yes	—
379	C₄	C₂³×C₄³×C₁₃	1	1	yes	characteristic
380	C₂	C₂²×C₄²×C₁₃×C₁₆	1	56	yes	direct product factor
381	C₂	C₂⁴×C₄×C₁₃×C₁₆	1	6	yes	—
382	C₂	C₂³×C₄²×C₈×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₈	C₂⁶×C₁₃
socle, prime radical	C₂⁶×C₁₃	C₂²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄²×C₁₃×C₁₆	C₂	direct (N × H)
10. C₂³×C₄×C₁₃×C₁₆	C₄	direct (N × H)
12. C₂×C₄²×C₁₃×C₁₆	C₂²	direct (N × H)
13. C₂³×C₄²×C₁₆	C₁₃	direct (N × H)
16. C₂²×C₄²×C₁₆	C₂×C₁₃	direct (N × H)
30. C₂²×C₄×C₁₃×C₁₆	C₂×C₄	direct (N × H)
34. C₄²×C₁₃×C₁₆	C₂³	direct (N × H)
43. C₂³×C₄²×C₁₃	C₁₆	direct (N × H)
49. C₂³×C₁₃×C₁₆	C₄²	direct (N × H)
60. C₂×C₄×C₁₃×C₁₆	C₂²×C₄	direct (N × H)
82. C₂²×C₄²×C₁₃	C₂×C₁₆	direct (N × H)
88. C₂²×C₁₃×C₁₆	C₂×C₄²	direct (N × H)
99. C₄×C₁₃×C₁₆	C₂³×C₄	direct (N × H)
104. C₂³×C₄×C₁₆	C₄×C₁₃	direct (N × H)
108. C₂×C₄²×C₁₆	C₂²×C₁₃	direct (N × H)
112. C₂³×C₄×C₁₃	C₄×C₁₆	direct (N × H)
134. C₂×C₄²×C₁₃	C₂²×C₁₆	direct (N × H)
140. C₂×C₁₃×C₁₆	C₂²×C₄²	direct (N × H)
158. C₂²×C₄×C₁₆	C₂×C₄×C₁₃	direct (N × H)
162. C₄²×C₁₆	C₂³×C₁₃	direct (N × H)
169. C₂²×C₄×C₁₃	C₂×C₄×C₁₆	direct (N × H)
188. C₄²×C₁₃	C₂³×C₁₆	direct (N × H)
191. C₁₃×C₁₆	C₂³×C₄²	direct (N × H)
200. C₂³×C₄²	C₁₃×C₁₆	direct (N × H)
206. C₂³×C₁₆	C₄²×C₁₃	direct (N × H)
217. C₂×C₄×C₁₆	C₂²×C₄×C₁₃	direct (N × H)
221. C₂³×C₁₃	C₄²×C₁₆	direct (N × H)
228. C₂×C₄×C₁₃	C₂²×C₄×C₁₆	direct (N × H)
257. C₂²×C₄²	C₂×C₁₃×C₁₆	direct (N × H)
263. C₂²×C₁₆	C₂×C₄²×C₁₃	direct (N × H)
274. C₄×C₁₆	C₂³×C₄×C₁₃	direct (N × H)
275. C₂²×C₁₃	C₂×C₄²×C₁₆	direct (N × H)
281. C₄×C₁₃	C₂³×C₄×C₁₆	direct (N × H)
287. C₂³×C₄	C₄×C₁₃×C₁₆	direct (N × H)
309. C₂×C₄²	C₂²×C₁₃×C₁₆	direct (N × H)
315. C₂×C₁₆	C₂²×C₄²×C₁₃	direct (N × H)
320. C₂×C₁₃	C₂²×C₄²×C₁₆	direct (N × H)
329. C₂²×C₄	C₂×C₄×C₁₃×C₁₆	direct (N × H)
348. C₄²	C₂³×C₁₃×C₁₆	direct (N × H)
351. C₁₆	C₂³×C₄²×C₁₃	direct (N × H)
352. C₁₃	C₂³×C₄²×C₁₆	direct (N × H)
353. C₂³	C₄²×C₁₃×C₁₆	direct (N × H)
360. C₂×C₄	C₂²×C₄×C₁₃×C₁₆	direct (N × H)
371. C₂²	C₂×C₄²×C₁₃×C₁₆	direct (N × H)
376. C₄	C₂³×C₄×C₁₃×C₁₆	direct (N × H)
380. C₂	C₂²×C₄²×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
C₂³×C₄²×C₈×C₁₃	2
C₂⁴×C₄×C₁₃×C₁₆	2
C₂²×C₄²×C₁₃×C₁₆	2
C₂³×C₄²×C₁₆	13

Subgroups — C23×C42×C13×C16 #72203756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄²×C₁₃×C₁₆ #72203756