Subgroups — C₂²×C₄²×C₁₃×C₃₂ #72203744

Order 26624.

23376 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₁₃×C₃₂	C₂	1	6	yes	maximal
3	C₂×C₄²×C₁₃×C₃₂	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄²×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂³×C₄×C₁₃×C₁₆	C₄	1	3	yes	—
6	C₂³×C₄×C₁₃×C₁₆	C₂²	1	3	yes	—
7	C₂×C₄²×C₁₃×C₁₆	C₄	1	12	yes	—
8	C₂×C₄²×C₁₃×C₁₆	C₂²	1	12	yes	—
9	C₂²×C₄×C₁₃×C₃₂	C₄	1	96	yes	direct product factor
10	C₂²×C₄×C₁₃×C₃₂	C₂²	1	72	yes	—
11	C₂⁴×C₁₃×C₃₂	C₂²	1	4	yes	—
12	C₄²×C₁₃×C₃₂	C₂²	1	64	yes	direct product factor
13	C₂²×C₄²×C₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₄²×C₁₆	C₂×C₁₃	1	1	yes	characteristic
15	C₂³×C₄×C₃₂	C₂×C₁₃	1	6	yes	—
16	C₂×C₄²×C₃₂	C₂×C₁₃	1	24	yes	direct product factor
17	C₂⁴×C₁₃×C₁₆	C₂×C₄	1	3	yes	—
18	C₂⁴×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
19	C₂³×C₄×C₈×C₁₃	C₈	1	3	yes	—
20	C₂³×C₄×C₈×C₁₃	C₂×C₄	1	3	yes	—
21	C₂²×C₄³×C₁₃	C₈	1	1	yes	characteristic
22	C₂³×C₁₃×C₃₂	C₂×C₄	1	96	yes	—
23	C₂³×C₁₃×C₃₂	C₂³	1	24	yes	—
24	C₂²×C₄×C₁₃×C₁₆	C₈	1	48	yes	—
25	C₂²×C₄×C₁₃×C₁₆	C₂×C₄	1	18	yes	—
26	C₂²×C₄×C₁₃×C₁₆	C₂×C₄	1	36	yes	—
27	C₂²×C₄×C₁₃×C₁₆	C₂×C₄	1	48	yes	—
28	C₂²×C₄×C₁₃×C₁₆	C₂³	1	18	yes	—
29	C₂×C₄²×C₈×C₁₃	C₈	1	12	yes	—
30	C₂×C₄²×C₈×C₁₃	C₂×C₄	1	12	yes	—
31	C₂×C₄×C₁₃×C₃₂	C₂×C₄	1	576	yes	direct product factor
32	C₂×C₄×C₁₃×C₃₂	C₂³	1	96	yes	—
33	C₄²×C₁₃×C₁₆	C₂×C₄	1	48	yes	—
34	C₄²×C₁₃×C₁₆	C₂³	1	16	yes	—
35	C₂⁴×C₈×C₁₃	C₂×C₈	1	3	yes	—
36	C₂⁴×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂³×C₄²×C₁₃	C₁₆	1	4	yes	—
38	C₂³×C₄²×C₁₃	C₂×C₈	1	3	yes	—
39	C₂³×C₁₃×C₁₆	C₄²	1	24	yes	—
40	C₂³×C₁₃×C₁₆	C₂×C₈	1	48	yes	—
41	C₂³×C₁₃×C₁₆	C₂²×C₄	1	3	yes	—
42	C₂³×C₁₃×C₁₆	C₂²×C₄	1	18	yes	—
43	C₂³×C₁₃×C₁₆	C₂²×C₄	1	24	yes	—
44	C₂³×C₁₃×C₁₆	C₂⁴	1	3	yes	—
45	C₂²×C₄×C₈×C₁₃	C₁₆	1	48	yes	—
46	C₂²×C₄×C₈×C₁₃	C₄²	1	24	yes	—
47	C₂²×C₄×C₈×C₁₃	C₂×C₈	1	18	yes	—
48	C₂²×C₄×C₈×C₁₃	C₂×C₈	1	24	yes	—
49	C₂²×C₄×C₈×C₁₃	C₂×C₈	1	36	yes	—
50	C₂²×C₄×C₈×C₁₃	C₂²×C₄	1	18	yes	—
51	C₂×C₄³×C₁₃	C₁₆	1	12	yes	—
52	C₂×C₄³×C₁₃	C₂×C₈	1	12	yes	—
53	C₂²×C₁₃×C₃₂	C₄²	1	256	yes	direct product factor
54	C₂²×C₁₃×C₃₂	C₂²×C₄	1	288	yes	—
55	C₂²×C₁₃×C₃₂	C₂⁴	1	16	yes	—
56	C₂×C₄×C₁₃×C₁₆	C₄²	1	144	yes	—
57	C₂×C₄×C₁₃×C₁₆	C₂×C₈	1	288	yes	—
58	C₂×C₄×C₁₃×C₁₆	C₂²×C₄	1	36	yes	—
59	C₂×C₄×C₁₃×C₁₆	C₂²×C₄	1	48	yes	—
60	C₂×C₄×C₁₃×C₁₆	C₂²×C₄	1	144	yes	—
61	C₂×C₄×C₁₃×C₁₆	C₂⁴	1	12	yes	—
62	C₄²×C₈×C₁₃	C₂×C₈	1	48	yes	—
63	C₄²×C₈×C₁₃	C₂²×C₄	1	16	yes	—
64	C₄×C₁₃×C₃₂	C₂²×C₄	1	384	yes	direct product factor
65	C₂⁴×C₄×C₁₃	C₂×C₁₆	1	6	yes	—
66	C₂⁴×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
67	C₂³×C₈×C₁₃	C₄×C₈	1	24	yes	—
68	C₂³×C₈×C₁₃	C₂×C₁₆	1	48	yes	—
69	C₂³×C₈×C₁₃	C₂×C₄²	1	12	yes	—
70	C₂³×C₈×C₁₃	C₂²×C₈	1	3	yes	—
71	C₂³×C₈×C₁₃	C₂²×C₈	1	12	yes	—
72	C₂³×C₈×C₁₃	C₂²×C₈	1	18	yes	—
73	C₂³×C₈×C₁₃	C₂³×C₄	1	3	yes	—
74	C₂²×C₄²×C₁₃	C₃₂	1	64	yes	direct product factor
75	C₂²×C₄²×C₁₃	C₄×C₈	1	24	yes	—
76	C₂²×C₄²×C₁₃	C₂×C₁₆	1	18	yes	—
77	C₂²×C₄²×C₁₃	C₂×C₁₆	1	24	yes	—
78	C₂²×C₄²×C₁₃	C₂×C₁₆	1	48	yes	—
79	C₂²×C₄²×C₁₃	C₂²×C₈	1	18	yes	—
80	C₂²×C₁₃×C₁₆	C₄×C₈	1	192	yes	—
81	C₂²×C₁₃×C₁₆	C₂×C₄²	1	36	yes	—
82	C₂²×C₁₃×C₁₆	C₂×C₄²	1	64	yes	—
83	C₂²×C₁₃×C₁₆	C₂×C₄²	1	72	yes	—
84	C₂²×C₁₃×C₁₆	C₂²×C₈	1	144	yes	—
85	C₂²×C₁₃×C₁₆	C₂³×C₄	1	3	yes	—
86	C₂²×C₁₃×C₁₆	C₂³×C₄	1	12	yes	—
87	C₂²×C₁₃×C₁₆	C₂³×C₄	1	36	yes	—
88	C₂²×C₁₃×C₁₆	C₂⁵	1	1	yes	characteristic
89	C₂×C₄×C₈×C₁₃	C₄×C₈	1	144	yes	—
90	C₂×C₄×C₈×C₁₃	C₂×C₁₆	1	288	yes	—
91	C₂×C₄×C₈×C₁₃	C₂×C₄²	1	72	yes	—
92	C₂×C₄×C₈×C₁₃	C₂²×C₈	1	36	yes	—
93	C₂×C₄×C₈×C₁₃	C₂²×C₈	1	48	yes	—
94	C₂×C₄×C₈×C₁₃	C₂²×C₈	1	72	yes	—
95	C₂×C₄×C₈×C₁₃	C₂³×C₄	1	12	yes	—
96	C₄³×C₁₃	C₂×C₁₆	1	48	yes	—
97	C₄³×C₁₃	C₂²×C₈	1	16	yes	—
98	C₂×C₁₃×C₃₂	C₂×C₄²	1	384	yes	direct product factor
99	C₂×C₁₃×C₃₂	C₂³×C₄	1	96	yes	—
100	C₄×C₁₃×C₁₆	C₂×C₄²	1	144	yes	—
101	C₄×C₁₃×C₁₆	C₂²×C₈	1	192	yes	—
102	C₄×C₁₃×C₁₆	C₂³×C₄	1	48	yes	—
103	C₂⁴×C₃₂	C₂²×C₁₃	1	4	yes	—
104	C₂³×C₄×C₁₆	C₄×C₁₃	1	3	yes	—
105	C₂³×C₄×C₁₆	C₂²×C₁₃	1	3	yes	—
106	C₂²×C₄²×C₈	C₄×C₁₃	1	1	yes	characteristic
107	C₂²×C₄×C₃₂	C₄×C₁₃	1	96	yes	direct product factor
108	C₂²×C₄×C₃₂	C₂²×C₁₃	1	72	yes	—
109	C₂×C₄²×C₁₆	C₄×C₁₃	1	12	yes	—
110	C₂×C₄²×C₁₆	C₂²×C₁₃	1	12	yes	—
111	C₄²×C₃₂	C₂²×C₁₃	1	64	yes	direct product factor
112	C₂⁵×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₄×C₁₆	1	48	yes	—
114	C₂³×C₄×C₁₃	C₂×C₃₂	1	96	yes	—
115	C₂³×C₄×C₁₃	C₂×C₄×C₈	1	12	yes	—
116	C₂³×C₄×C₁₃	C₂²×C₁₆	1	3	yes	—
117	C₂³×C₄×C₁₃	C₂²×C₁₆	1	12	yes	—
118	C₂³×C₄×C₁₃	C₂²×C₁₆	1	36	yes	—
119	C₂³×C₄×C₁₃	C₂³×C₈	1	3	yes	—
120	C₂²×C₈×C₁₃	C₄×C₁₆	1	192	yes	—
121	C₂²×C₈×C₁₃	C₄³	1	16	yes	—
122	C₂²×C₈×C₁₃	C₂×C₄×C₈	1	36	yes	—
123	C₂²×C₈×C₁₃	C₂×C₄×C₈	1	48	yes	—
124	C₂²×C₈×C₁₃	C₂×C₄×C₈	1	72	yes	—
125	C₂²×C₈×C₁₃	C₂²×C₁₆	1	144	yes	—
126	C₂²×C₈×C₁₃	C₂²×C₄²	1	18	yes	—
127	C₂²×C₈×C₁₃	C₂³×C₈	1	3	yes	—
128	C₂²×C₈×C₁₃	C₂³×C₈	1	12	yes	—
129	C₂²×C₈×C₁₃	C₂³×C₈	1	18	yes	—
130	C₂²×C₈×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₄×C₁₆	1	144	yes	—
132	C₂×C₄²×C₁₃	C₂×C₃₂	1	384	yes	direct product factor
133	C₂×C₄²×C₁₃	C₂×C₄×C₈	1	72	yes	—
134	C₂×C₄²×C₁₃	C₂²×C₁₆	1	36	yes	—
135	C₂×C₄²×C₁₃	C₂²×C₁₆	1	64	yes	—
136	C₂×C₄²×C₁₃	C₂²×C₁₆	1	72	yes	—
137	C₂×C₄²×C₁₃	C₂³×C₈	1	12	yes	—
138	C₂×C₁₃×C₁₆	C₄³	1	48	yes	—
139	C₂×C₁₃×C₁₆	C₂×C₄×C₈	1	288	yes	—
140	C₂×C₁₃×C₁₆	C₂²×C₄²	1	18	yes	—
141	C₂×C₁₃×C₁₆	C₂²×C₄²	1	24	yes	—
142	C₂×C₁₃×C₁₆	C₂²×C₄²	1	48	yes	—
143	C₂×C₁₃×C₁₆	C₂³×C₈	1	48	yes	—
144	C₂×C₁₃×C₁₆	C₂⁴×C₄	1	6	yes	—
145	C₄×C₈×C₁₃	C₂×C₄×C₈	1	144	yes	—
146	C₄×C₈×C₁₃	C₂²×C₁₆	1	192	yes	—
147	C₄×C₈×C₁₃	C₂²×C₄²	1	24	yes	—
148	C₄×C₈×C₁₃	C₂³×C₈	1	24	yes	—
149	C₁₃×C₃₂	C₂²×C₄²	1	64	yes	direct product factor
150	C₂⁴×C₁₆	C₂×C₄×C₁₃	1	3	yes	—
151	C₂⁴×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
152	C₂³×C₄×C₈	C₈×C₁₃	1	3	yes	—
153	C₂³×C₄×C₈	C₂×C₄×C₁₃	1	3	yes	—
154	C₂²×C₄³	C₈×C₁₃	1	1	yes	characteristic
155	C₂³×C₃₂	C₂×C₄×C₁₃	1	96	yes	—
156	C₂³×C₃₂	C₂³×C₁₃	1	24	yes	—
157	C₂²×C₄×C₁₆	C₈×C₁₃	1	48	yes	—
158	C₂²×C₄×C₁₆	C₂×C₄×C₁₃	1	18	yes	—
159	C₂²×C₄×C₁₆	C₂×C₄×C₁₃	1	36	yes	—
160	C₂²×C₄×C₁₆	C₂×C₄×C₁₃	1	48	yes	—
161	C₂²×C₄×C₁₆	C₂³×C₁₃	1	18	yes	—
162	C₂×C₄²×C₈	C₈×C₁₃	1	12	yes	—
163	C₂×C₄²×C₈	C₂×C₄×C₁₃	1	12	yes	—
164	C₂×C₄×C₃₂	C₂×C₄×C₁₃	1	576	yes	direct product factor
165	C₂×C₄×C₃₂	C₂³×C₁₃	1	96	yes	—
166	C₄²×C₁₆	C₂×C₄×C₁₃	1	48	yes	—
167	C₄²×C₁₆	C₂³×C₁₃	1	16	yes	—
168	C₂⁴×C₁₃	C₂×C₄×C₁₆	1	12	yes	—
169	C₂⁴×C₁₃	C₂²×C₃₂	1	16	yes	—
170	C₂⁴×C₁₃	C₂³×C₁₆	1	3	yes	—
171	C₂²×C₄×C₁₃	C₄×C₃₂	1	384	yes	direct product factor
172	C₂²×C₄×C₁₃	C₄²×C₈	1	16	yes	—
173	C₂²×C₄×C₁₃	C₂×C₄×C₁₆	1	36	yes	—
174	C₂²×C₄×C₁₃	C₂×C₄×C₁₆	1	48	yes	—
175	C₂²×C₄×C₁₃	C₂×C₄×C₁₆	1	144	yes	—
176	C₂²×C₄×C₁₃	C₂²×C₃₂	1	288	yes	—
177	C₂²×C₄×C₁₃	C₂²×C₄×C₈	1	18	yes	—
178	C₂²×C₄×C₁₃	C₂³×C₁₆	1	3	yes	—
179	C₂²×C₄×C₁₃	C₂³×C₁₆	1	18	yes	—
180	C₂²×C₄×C₁₃	C₂³×C₁₆	1	24	yes	—
181	C₂²×C₄×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₄²×C₈	1	48	yes	—
183	C₂×C₈×C₁₃	C₂×C₄×C₁₆	1	288	yes	—
184	C₂×C₈×C₁₃	C₂×C₄³	1	12	yes	—
185	C₂×C₈×C₁₃	C₂²×C₄×C₈	1	18	yes	—
186	C₂×C₈×C₁₃	C₂²×C₄×C₈	1	24	yes	—
187	C₂×C₈×C₁₃	C₂²×C₄×C₈	1	36	yes	—
188	C₂×C₈×C₁₃	C₂³×C₁₆	1	48	yes	—
189	C₂×C₈×C₁₃	C₂³×C₄²	1	3	yes	—
190	C₂×C₈×C₁₃	C₂⁴×C₈	1	3	yes	—
191	C₄²×C₁₃	C₂×C₄×C₁₆	1	144	yes	—
192	C₄²×C₁₃	C₂²×C₃₂	1	256	yes	direct product factor
193	C₄²×C₁₃	C₂²×C₄×C₈	1	24	yes	—
194	C₄²×C₁₃	C₂³×C₁₆	1	24	yes	—
195	C₁₃×C₁₆	C₂×C₄³	1	12	yes	—
196	C₁₃×C₁₆	C₂²×C₄×C₈	1	48	yes	—
197	C₁₃×C₁₆	C₂³×C₄²	1	4	yes	—
198	C₂⁴×C₈	C₂×C₈×C₁₃	1	3	yes	—
199	C₂⁴×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
200	C₂³×C₄²	C₁₃×C₁₆	1	4	yes	—
201	C₂³×C₄²	C₂×C₈×C₁₃	1	3	yes	—
202	C₂³×C₁₆	C₄²×C₁₃	1	24	yes	—
203	C₂³×C₁₆	C₂×C₈×C₁₃	1	48	yes	—
204	C₂³×C₁₆	C₂²×C₄×C₁₃	1	3	yes	—
205	C₂³×C₁₆	C₂²×C₄×C₁₃	1	18	yes	—
206	C₂³×C₁₆	C₂²×C₄×C₁₃	1	24	yes	—
207	C₂³×C₁₆	C₂⁴×C₁₃	1	3	yes	—
208	C₂²×C₄×C₈	C₁₃×C₁₆	1	48	yes	—
209	C₂²×C₄×C₈	C₄²×C₁₃	1	24	yes	—
210	C₂²×C₄×C₈	C₂×C₈×C₁₃	1	18	yes	—
211	C₂²×C₄×C₈	C₂×C₈×C₁₃	1	24	yes	—
212	C₂²×C₄×C₈	C₂×C₈×C₁₃	1	36	yes	—
213	C₂²×C₄×C₈	C₂²×C₄×C₁₃	1	18	yes	—
214	C₂×C₄³	C₁₃×C₁₆	1	12	yes	—
215	C₂×C₄³	C₂×C₈×C₁₃	1	12	yes	—
216	C₂²×C₃₂	C₄²×C₁₃	1	256	yes	direct product factor
217	C₂²×C₃₂	C₂²×C₄×C₁₃	1	288	yes	—
218	C₂²×C₃₂	C₂⁴×C₁₃	1	16	yes	—
219	C₂×C₄×C₁₆	C₄²×C₁₃	1	144	yes	—
220	C₂×C₄×C₁₆	C₂×C₈×C₁₃	1	288	yes	—
221	C₂×C₄×C₁₆	C₂²×C₄×C₁₃	1	36	yes	—
222	C₂×C₄×C₁₆	C₂²×C₄×C₁₃	1	48	yes	—
223	C₂×C₄×C₁₆	C₂²×C₄×C₁₃	1	144	yes	—
224	C₂×C₄×C₁₆	C₂⁴×C₁₃	1	12	yes	—
225	C₄²×C₈	C₂×C₈×C₁₃	1	48	yes	—
226	C₄²×C₈	C₂²×C₄×C₁₃	1	16	yes	—
227	C₄×C₃₂	C₂²×C₄×C₁₃	1	384	yes	direct product factor
228	C₂³×C₁₃	C₄²×C₁₆	1	16	yes	—
229	C₂³×C₁₃	C₂×C₄×C₃₂	1	96	yes	—
230	C₂³×C₁₃	C₂²×C₄×C₁₆	1	18	yes	—
231	C₂³×C₁₃	C₂³×C₃₂	1	24	yes	—
232	C₂³×C₁₃	C₂⁴×C₁₆	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₄²×C₁₆	1	48	yes	—
234	C₂×C₄×C₁₃	C₂×C₄×C₃₂	1	576	yes	direct product factor
235	C₂×C₄×C₁₃	C₂×C₄²×C₈	1	12	yes	—
236	C₂×C₄×C₁₃	C₂²×C₄×C₁₆	1	18	yes	—
237	C₂×C₄×C₁₃	C₂²×C₄×C₁₆	1	36	yes	—
238	C₂×C₄×C₁₃	C₂²×C₄×C₁₆	1	48	yes	—
239	C₂×C₄×C₁₃	C₂³×C₃₂	1	96	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄×C₈	1	3	yes	—
241	C₂×C₄×C₁₃	C₂⁴×C₁₆	1	3	yes	—
242	C₈×C₁₃	C₂×C₄²×C₈	1	12	yes	—
243	C₈×C₁₃	C₂²×C₄×C₁₆	1	48	yes	—
244	C₈×C₁₃	C₂²×C₄³	1	1	yes	characteristic
245	C₈×C₁₃	C₂³×C₄×C₈	1	3	yes	—
246	C₂⁴×C₄	C₂×C₁₃×C₁₆	1	6	yes	—
247	C₂⁴×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
248	C₂³×C₈	C₄×C₈×C₁₃	1	24	yes	—
249	C₂³×C₈	C₂×C₁₃×C₁₆	1	48	yes	—
250	C₂³×C₈	C₂×C₄²×C₁₃	1	12	yes	—
251	C₂³×C₈	C₂²×C₈×C₁₃	1	3	yes	—
252	C₂³×C₈	C₂²×C₈×C₁₃	1	12	yes	—
253	C₂³×C₈	C₂²×C₈×C₁₃	1	18	yes	—
254	C₂³×C₈	C₂³×C₄×C₁₃	1	3	yes	—
255	C₂²×C₄²	C₁₃×C₃₂	1	64	yes	direct product factor
256	C₂²×C₄²	C₄×C₈×C₁₃	1	24	yes	—
257	C₂²×C₄²	C₂×C₁₃×C₁₆	1	18	yes	—
258	C₂²×C₄²	C₂×C₁₃×C₁₆	1	24	yes	—
259	C₂²×C₄²	C₂×C₁₃×C₁₆	1	48	yes	—
260	C₂²×C₄²	C₂²×C₈×C₁₃	1	18	yes	—
261	C₂²×C₁₆	C₄×C₈×C₁₃	1	192	yes	—
262	C₂²×C₁₆	C₂×C₄²×C₁₃	1	36	yes	—
263	C₂²×C₁₆	C₂×C₄²×C₁₃	1	64	yes	—
264	C₂²×C₁₆	C₂×C₄²×C₁₃	1	72	yes	—
265	C₂²×C₁₆	C₂²×C₈×C₁₃	1	144	yes	—
266	C₂²×C₁₆	C₂³×C₄×C₁₃	1	3	yes	—
267	C₂²×C₁₆	C₂³×C₄×C₁₃	1	12	yes	—
268	C₂²×C₁₆	C₂³×C₄×C₁₃	1	36	yes	—
269	C₂²×C₁₆	C₂⁵×C₁₃	1	1	yes	characteristic
270	C₂×C₄×C₈	C₄×C₈×C₁₃	1	144	yes	—
271	C₂×C₄×C₈	C₂×C₁₃×C₁₆	1	288	yes	—
272	C₂×C₄×C₈	C₂×C₄²×C₁₃	1	72	yes	—
273	C₂×C₄×C₈	C₂²×C₈×C₁₃	1	36	yes	—
274	C₂×C₄×C₈	C₂²×C₈×C₁₃	1	48	yes	—
275	C₂×C₄×C₈	C₂²×C₈×C₁₃	1	72	yes	—
276	C₂×C₄×C₈	C₂³×C₄×C₁₃	1	12	yes	—
277	C₄³	C₂×C₁₃×C₁₆	1	48	yes	—
278	C₄³	C₂²×C₈×C₁₃	1	16	yes	—
279	C₂×C₃₂	C₂×C₄²×C₁₃	1	384	yes	direct product factor
280	C₂×C₃₂	C₂³×C₄×C₁₃	1	96	yes	—
281	C₄×C₁₆	C₂×C₄²×C₁₃	1	144	yes	—
282	C₄×C₁₆	C₂²×C₈×C₁₃	1	192	yes	—
283	C₄×C₁₆	C₂³×C₄×C₁₃	1	48	yes	—
284	C₂²×C₁₃	C₄²×C₃₂	1	64	yes	direct product factor
285	C₂²×C₁₃	C₂×C₄²×C₁₆	1	12	yes	—
286	C₂²×C₁₃	C₂²×C₄×C₃₂	1	72	yes	—
287	C₂²×C₁₃	C₂³×C₄×C₁₆	1	3	yes	—
288	C₂²×C₁₃	C₂⁴×C₃₂	1	4	yes	—
289	C₄×C₁₃	C₂×C₄²×C₁₆	1	12	yes	—
290	C₄×C₁₃	C₂²×C₄×C₃₂	1	96	yes	direct product factor
291	C₄×C₁₃	C₂²×C₄²×C₈	1	1	yes	characteristic
292	C₄×C₁₃	C₂³×C₄×C₁₆	1	3	yes	—
293	C₂⁵	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
294	C₂³×C₄	C₄×C₁₃×C₁₆	1	48	yes	—
295	C₂³×C₄	C₂×C₁₃×C₃₂	1	96	yes	—
296	C₂³×C₄	C₂×C₄×C₈×C₁₃	1	12	yes	—
297	C₂³×C₄	C₂²×C₁₃×C₁₆	1	3	yes	—
298	C₂³×C₄	C₂²×C₁₃×C₁₆	1	12	yes	—
299	C₂³×C₄	C₂²×C₁₃×C₁₆	1	36	yes	—
300	C₂³×C₄	C₂³×C₈×C₁₃	1	3	yes	—
301	C₂²×C₈	C₄×C₁₃×C₁₆	1	192	yes	—
302	C₂²×C₈	C₄³×C₁₃	1	16	yes	—
303	C₂²×C₈	C₂×C₄×C₈×C₁₃	1	36	yes	—
304	C₂²×C₈	C₂×C₄×C₈×C₁₃	1	48	yes	—
305	C₂²×C₈	C₂×C₄×C₈×C₁₃	1	72	yes	—
306	C₂²×C₈	C₂²×C₁₃×C₁₆	1	144	yes	—
307	C₂²×C₈	C₂²×C₄²×C₁₃	1	18	yes	—
308	C₂²×C₈	C₂³×C₈×C₁₃	1	3	yes	—
309	C₂²×C₈	C₂³×C₈×C₁₃	1	12	yes	—
310	C₂²×C₈	C₂³×C₈×C₁₃	1	18	yes	—
311	C₂²×C₈	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₄×C₁₃×C₁₆	1	144	yes	—
313	C₂×C₄²	C₂×C₁₃×C₃₂	1	384	yes	direct product factor
314	C₂×C₄²	C₂×C₄×C₈×C₁₃	1	72	yes	—
315	C₂×C₄²	C₂²×C₁₃×C₁₆	1	36	yes	—
316	C₂×C₄²	C₂²×C₁₃×C₁₆	1	64	yes	—
317	C₂×C₄²	C₂²×C₁₃×C₁₆	1	72	yes	—
318	C₂×C₄²	C₂³×C₈×C₁₃	1	12	yes	—
319	C₂×C₁₆	C₄³×C₁₃	1	48	yes	—
320	C₂×C₁₆	C₂×C₄×C₈×C₁₃	1	288	yes	—
321	C₂×C₁₆	C₂²×C₄²×C₁₃	1	18	yes	—
322	C₂×C₁₆	C₂²×C₄²×C₁₃	1	24	yes	—
323	C₂×C₁₆	C₂²×C₄²×C₁₃	1	48	yes	—
324	C₂×C₁₆	C₂³×C₈×C₁₃	1	48	yes	—
325	C₂×C₁₆	C₂⁴×C₄×C₁₃	1	6	yes	—
326	C₄×C₈	C₂×C₄×C₈×C₁₃	1	144	yes	—
327	C₄×C₈	C₂²×C₁₃×C₁₆	1	192	yes	—
328	C₄×C₈	C₂²×C₄²×C₁₃	1	24	yes	—
329	C₄×C₈	C₂³×C₈×C₁₃	1	24	yes	—
330	C₃₂	C₂²×C₄²×C₁₃	1	64	yes	direct product factor
331	C₂×C₁₃	C₂×C₄²×C₃₂	1	24	yes	direct product factor
332	C₂×C₁₃	C₂³×C₄×C₃₂	1	6	yes	—
333	C₂×C₁₃	C₂²×C₄²×C₁₆	1	1	yes	characteristic
334	C₂⁴	C₂×C₄×C₁₃×C₁₆	1	12	yes	—
335	C₂⁴	C₂²×C₁₃×C₃₂	1	16	yes	—
336	C₂⁴	C₂³×C₁₃×C₁₆	1	3	yes	—
337	C₂²×C₄	C₄×C₁₃×C₃₂	1	384	yes	direct product factor
338	C₂²×C₄	C₄²×C₈×C₁₃	1	16	yes	—
339	C₂²×C₄	C₂×C₄×C₁₃×C₁₆	1	36	yes	—
340	C₂²×C₄	C₂×C₄×C₁₃×C₁₆	1	48	yes	—
341	C₂²×C₄	C₂×C₄×C₁₃×C₁₆	1	144	yes	—
342	C₂²×C₄	C₂²×C₁₃×C₃₂	1	288	yes	—
343	C₂²×C₄	C₂²×C₄×C₈×C₁₃	1	18	yes	—
344	C₂²×C₄	C₂³×C₁₃×C₁₆	1	3	yes	—
345	C₂²×C₄	C₂³×C₁₃×C₁₆	1	18	yes	—
346	C₂²×C₄	C₂³×C₁₃×C₁₆	1	24	yes	—
347	C₂²×C₄	C₂⁴×C₈×C₁₃	1	1	yes	characteristic
348	C₂×C₈	C₄²×C₈×C₁₃	1	48	yes	—
349	C₂×C₈	C₂×C₄×C₁₃×C₁₆	1	288	yes	—
350	C₂×C₈	C₂×C₄³×C₁₃	1	12	yes	—
351	C₂×C₈	C₂²×C₄×C₈×C₁₃	1	18	yes	—
352	C₂×C₈	C₂²×C₄×C₈×C₁₃	1	24	yes	—
353	C₂×C₈	C₂²×C₄×C₈×C₁₃	1	36	yes	—
354	C₂×C₈	C₂³×C₁₃×C₁₆	1	48	yes	—
355	C₂×C₈	C₂³×C₄²×C₁₃	1	3	yes	—
356	C₂×C₈	C₂⁴×C₈×C₁₃	1	3	yes	—
357	C₄²	C₂×C₄×C₁₃×C₁₆	1	144	yes	—
358	C₄²	C₂²×C₁₃×C₃₂	1	256	yes	direct product factor
359	C₄²	C₂²×C₄×C₈×C₁₃	1	24	yes	—
360	C₄²	C₂³×C₁₃×C₁₆	1	24	yes	—
361	C₁₆	C₂×C₄³×C₁₃	1	12	yes	—
362	C₁₆	C₂²×C₄×C₈×C₁₃	1	48	yes	—
363	C₁₆	C₂³×C₄²×C₁₃	1	4	yes	—
364	C₁₃	C₂²×C₄²×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	C₄²×C₁₃×C₁₆	1	16	yes	—
366	C₂³	C₂×C₄×C₁₃×C₃₂	1	96	yes	—
367	C₂³	C₂²×C₄×C₁₃×C₁₆	1	18	yes	—
368	C₂³	C₂³×C₁₃×C₃₂	1	24	yes	—
369	C₂³	C₂⁴×C₁₃×C₁₆	1	1	yes	characteristic
370	C₂×C₄	C₄²×C₁₃×C₁₆	1	48	yes	—
371	C₂×C₄	C₂×C₄×C₁₃×C₃₂	1	576	yes	direct product factor
372	C₂×C₄	C₂×C₄²×C₈×C₁₃	1	12	yes	—
373	C₂×C₄	C₂²×C₄×C₁₃×C₁₆	1	18	yes	—
374	C₂×C₄	C₂²×C₄×C₁₃×C₁₆	1	36	yes	—
375	C₂×C₄	C₂²×C₄×C₁₃×C₁₆	1	48	yes	—
376	C₂×C₄	C₂³×C₁₃×C₃₂	1	96	yes	—
377	C₂×C₄	C₂³×C₄×C₈×C₁₃	1	3	yes	—
378	C₂×C₄	C₂⁴×C₁₃×C₁₆	1	3	yes	—
379	C₈	C₂×C₄²×C₈×C₁₃	1	12	yes	—
380	C₈	C₂²×C₄×C₁₃×C₁₆	1	48	yes	—
381	C₈	C₂²×C₄³×C₁₃	1	1	yes	characteristic
382	C₈	C₂³×C₄×C₈×C₁₃	1	3	yes	—
383	C₂²	C₄²×C₁₃×C₃₂	1	64	yes	direct product factor
384	C₂²	C₂⁴×C₁₃×C₃₂	1	4	yes	—
385	C₂²	C₂²×C₄×C₁₃×C₃₂	1	72	yes	—
386	C₂²	C₂×C₄²×C₁₃×C₁₆	1	12	yes	—
387	C₂²	C₂³×C₄×C₁₃×C₁₆	1	3	yes	—
388	C₄	C₂²×C₄×C₁₃×C₃₂	1	96	yes	direct product factor
389	C₄	C₂×C₄²×C₁₃×C₁₆	1	12	yes	—
390	C₄	C₂³×C₄×C₁₃×C₁₆	1	3	yes	—
391	C₄	C₂²×C₄²×C₈×C₁₃	1	1	yes	characteristic
392	C₂	C₂×C₄²×C₁₃×C₃₂	1	24	yes	direct product factor
393	C₂	C₂³×C₄×C₁₃×C₃₂	1	6	yes	—
394	C₂	C₂²×C₄²×C₁₃×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₆	C₂⁵×C₁₃
socle, prime radical	C₂⁵×C₁₃	C₂²×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄²×C₁₃×C₃₂	C₂	direct (N × H)
9. C₂²×C₄×C₁₃×C₃₂	C₄	direct (N × H)
12. C₄²×C₁₃×C₃₂	C₂²	direct (N × H)
13. C₂²×C₄²×C₃₂	C₁₃	direct (N × H)
16. C₂×C₄²×C₃₂	C₂×C₁₃	direct (N × H)
31. C₂×C₄×C₁₃×C₃₂	C₂×C₄	direct (N × H)
53. C₂²×C₁₃×C₃₂	C₄²	direct (N × H)
64. C₄×C₁₃×C₃₂	C₂²×C₄	direct (N × H)
74. C₂²×C₄²×C₁₃	C₃₂	direct (N × H)
98. C₂×C₁₃×C₃₂	C₂×C₄²	direct (N × H)
107. C₂²×C₄×C₃₂	C₄×C₁₃	direct (N × H)
111. C₄²×C₃₂	C₂²×C₁₃	direct (N × H)
132. C₂×C₄²×C₁₃	C₂×C₃₂	direct (N × H)
149. C₁₃×C₃₂	C₂²×C₄²	direct (N × H)
164. C₂×C₄×C₃₂	C₂×C₄×C₁₃	direct (N × H)
171. C₂²×C₄×C₁₃	C₄×C₃₂	direct (N × H)
192. C₄²×C₁₃	C₂²×C₃₂	direct (N × H)
216. C₂²×C₃₂	C₄²×C₁₃	direct (N × H)
227. C₄×C₃₂	C₂²×C₄×C₁₃	direct (N × H)
234. C₂×C₄×C₁₃	C₂×C₄×C₃₂	direct (N × H)
255. C₂²×C₄²	C₁₃×C₃₂	direct (N × H)
279. C₂×C₃₂	C₂×C₄²×C₁₃	direct (N × H)
284. C₂²×C₁₃	C₄²×C₃₂	direct (N × H)
290. C₄×C₁₃	C₂²×C₄×C₃₂	direct (N × H)
313. C₂×C₄²	C₂×C₁₃×C₃₂	direct (N × H)
330. C₃₂	C₂²×C₄²×C₁₃	direct (N × H)
331. C₂×C₁₃	C₂×C₄²×C₃₂	direct (N × H)
337. C₂²×C₄	C₄×C₁₃×C₃₂	direct (N × H)
358. C₄²	C₂²×C₁₃×C₃₂	direct (N × H)
364. C₁₃	C₂²×C₄²×C₃₂	direct (N × H)
371. C₂×C₄	C₂×C₄×C₁₃×C₃₂	direct (N × H)
383. C₂²	C₄²×C₁₃×C₃₂	direct (N × H)
388. C₄	C₂²×C₄×C₁₃×C₃₂	direct (N × H)
392. C₂	C₂×C₄²×C₁₃×C₃₂	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×C₄²×C₁₃×C₁₆	2
C₂³×C₄×C₁₃×C₃₂	2
C₂×C₄²×C₁₃×C₃₂	2
C₂²×C₄²×C₃₂	13

Subgroups — C22×C42×C13×C32 #72203744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄²×C₁₃×C₃₂ #72203744