Subgroups — C₂×C₁₃×#2512 #15721101

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#126	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2512	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#396	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#126	—	2	16	no	—
15	C₂×C₁₃×#126	C₂²	1	16	yes	complemented
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#397	C₂²	1	16	yes	complemented
35	C₁₃×#396	C₂²	1	16	yes	complemented
36	C₁₃×#390	C₂²	1	8	yes	—
37	C₁₃×#390	C₂²	1	8	yes	—
38	C₁₃×#390	C₂²	1	8	yes	—
39	C₁₃×#389	C₂²	1	8	yes	complemented
40	C₁₃×#388	C₂²	1	16	yes	complemented
41	C₁₃×#384	C₂²	1	8	yes	complemented
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
44	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂⁵×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	—	2	4	no	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#126	—	2	64	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
71	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₄²×C₁₃	—	2	8	no	—
93	C₂×C₄²×C₁₃	—	2	4	no	—
94	C₂×C₄²×C₁₃	—	2	4	no	—
95	C₂×C₄²×C₁₃	—	2	4	no	—
96	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₂×#2512	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	—	2	4	no	—
106	C₂⁴×C₁₃	—	2	4	no	—
107	C₂⁴×C₁₃	—	2	4	no	—
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	—	2	4	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	4	16	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	#41	1	4	yes	—
145	C₂²×C₄×C₁₃	#41	1	4	yes	—
146	C₂²×C₄×C₁₃	#41	1	4	yes	—
147	C₂²×C₄×C₁₃	#41	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₁₃×C₄⋊C₄	—	2	16	no	—
159	C₁₃×C₄⋊C₄	—	2	16	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	4	8	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
166	C₁₃×C₂²⋊C₄	—	2	16	no	—
167	C₁₃×C₂²⋊C₄	—	2	16	no	—
168	C₁₃×C₂²⋊C₄	—	2	16	no	—
169	C₁₃×C₂²⋊C₄	—	2	16	no	—
170	C₁₃×C₂²⋊C₄	—	4	8	no	—
171	C₁₃×C₂²⋊C₄	—	4	8	no	—
172	C₄²×C₁₃	—	2	16	no	—
173	C₄²×C₁₃	—	2	8	no	—
174	C₄²×C₁₃	—	2	8	no	—
175	C₄²×C₁₃	—	2	8	no	—
176	C₂²×#126	C₂×C₁₃	1	2	yes	complemented
177	#2512	C₂×C₁₃	1	16	yes	direct product factor
178	C₂×#397	C₂×C₁₃	1	2	yes	complemented
179	C₂×#396	C₂×C₁₃	1	2	yes	complemented
180	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
181	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
182	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
183	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#388	C₂×C₁₃	1	2	yes	complemented
185	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	4	8	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	8	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	8	no	—
200	C₂³×C₁₃	—	4	8	no	—
201	C₂³×C₁₃	—	4	8	no	—
202	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂³×C₁₃	C₂×#41	1	2	yes	—
204	C₂³×C₁₃	C₂×#41	1	2	yes	—
205	C₂³×C₁₃	C₂×#41	1	2	yes	—
206	C₂³×C₁₃	C₂×#41	1	2	yes	—
207	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
208	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
209	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
210	D₄×C₁₃	—	4	16	no	—
211	C₂×C₄×C₁₃	—	2	8	no	—
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	8	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	8	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	#126	1	16	yes	complemented
244	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
251	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#126	—	2	16	no	—
253	C₂×#126	C₂²×C₁₃	1	16	yes	complemented
254	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
257	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
268	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
270	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
272	#397	C₂²×C₁₃	1	16	yes	complemented
273	#396	C₂²×C₁₃	1	16	yes	complemented
274	#390	C₂²×C₁₃	1	8	yes	—
275	#390	C₂²×C₁₃	1	8	yes	—
276	#390	C₂²×C₁₃	1	8	yes	—
277	#389	C₂²×C₁₃	1	8	yes	complemented
278	#388	C₂²×C₁₃	1	16	yes	complemented
279	#384	C₂²×C₁₃	1	8	yes	complemented
280	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
281	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
282	C₂×#95	C₂²×C₁₃	1	2	yes	—
283	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#95	C₂²×C₁₃	1	2	yes	—
285	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
286	C₂²×C₁₃	—	4	4	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	—	4	4	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	8	16	no	—
294	C₂²×C₁₃	C₂×#126	1	4	yes	—
295	C₂²×C₁₃	#532	1	4	yes	—
296	C₂²×C₁₃	#542	1	4	yes	—
297	C₂²×C₁₃	#547	1	4	yes	—
298	C₂²×C₁₃	#550	1	4	yes	—
299	C₂²×C₁₃	#553	1	4	yes	—
300	C₂²×C₁₃	#556	1	4	yes	—
301	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
302	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
303	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
304	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
305	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
306	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	4	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	4	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	C₂×#126	1	8	yes	complemented
318	C₂⁵	C₂³×C₁₃	1	2	yes	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	4	no	—
321	C₂²×D₄	—	2	4	no	—
322	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	#126	—	2	64	no	—
334	C₂×C₄⋊C₄	—	2	8	no	—
335	C₂×C₄⋊C₄	—	2	8	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	—	4	4	no	—
341	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₂×C₂²⋊C₄	—	2	8	no	—
351	C₂×C₂²⋊C₄	—	2	8	no	—
352	C₂×C₂²⋊C₄	—	2	8	no	—
353	C₂×C₂²⋊C₄	—	2	8	no	—
354	C₂×C₂²⋊C₄	—	4	4	no	—
355	C₂×C₂²⋊C₄	—	4	4	no	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
362	C₂×C₄²	—	2	8	no	—
363	C₂×C₄²	—	2	4	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
367	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
369	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
370	#95	C₂³×C₁₃	1	4	yes	—
371	#95	C₂³×C₁₃	1	8	yes	—
372	#95	C₂³×C₁₃	1	4	yes	—
373	#95	C₂³×C₁₃	1	8	yes	—
374	C₂×C₁₃	—	8	4	no	—
375	C₂×C₁₃	#2512	1	8	yes	direct product factor
376	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
377	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
379	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
380	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#556	1	1	yes	characteristic
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
391	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	4	16	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
422	C₂²×C₄	C₁₃×#41	1	4	yes	—
423	C₂²×C₄	C₁₃×#41	1	4	yes	—
424	C₂²×C₄	C₁₃×#41	1	4	yes	—
425	C₂²×C₄	C₁₃×#41	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
436	C₄⋊C₄	—	2	16	no	—
437	C₄⋊C₄	—	2	16	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	4	8	no	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	2	16	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	2	16	no	—
448	C₂²⋊C₄	—	4	8	no	—
449	C₂²⋊C₄	—	4	8	no	—
450	C₄²	—	2	16	no	—
451	C₄²	—	2	8	no	—
452	C₄²	—	2	8	no	—
453	C₄²	—	2	8	no	—
454	C₁₃	C₂×#2512	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	4	8	no	—
463	C₂³	—	4	8	no	—
464	C₂³	—	4	8	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	8	no	—
469	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂³	C₂×C₁₃×#41	1	2	yes	—
471	C₂³	C₂×C₁₃×#41	1	2	yes	—
472	C₂³	C₂×C₁₃×#41	1	2	yes	—
473	C₂³	C₂×C₁₃×#41	1	2	yes	—
474	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
475	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
476	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
477	D₄	—	4	16	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	C₁₃×#126	1	16	yes	complemented
511	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
514	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
515	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
516	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
517	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	8	16	no	—
526	C₂²	C₂×C₁₃×#126	1	4	yes	—
527	C₂²	C₁₃×#532	1	4	yes	—
528	C₂²	C₁₃×#542	1	4	yes	—
529	C₂²	C₁₃×#547	1	4	yes	—
530	C₂²	C₁₃×#550	1	4	yes	—
531	C₂²	C₁₃×#553	1	4	yes	—
532	C₂²	C₁₃×#556	1	4	yes	—
533	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
534	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
535	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
536	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
537	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
538	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
540	C₄	—	2	4	no	—
541	C₄	—	2	4	no	—
542	C₄	—	2	4	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	C₂×C₁₃×#126	1	8	yes	complemented
550	C₂	—	8	4	no	—
551	C₂	C₁₃×#2512	1	8	yes	direct product factor
552	C₂	C₂²×C₁₃×#126	1	1	yes	characteristic
553	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
554	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
555	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
556	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
557	C₂	C₂×C₁₃×#553	1	1	yes	characteristic
558	C₂	C₂×C₁₃×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#126	C₂	semidirect
2. C₁₃×#2512	C₂	direct (N × H)
3. C₂×C₁₃×#397	C₂	semidirect
4. C₂×C₁₃×#396	C₂	semidirect
8. C₂×C₁₃×#389	C₂	semidirect
9. C₂×C₁₃×#388	C₂	semidirect
10. C₂×C₁₃×#384	C₂	semidirect
11. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
12. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₂×C₁₃×#126	C₂²	semidirect
34. C₁₃×#397	C₂²	semidirect
35. C₁₃×#396	C₂²	semidirect
39. C₁₃×#389	C₂²	semidirect
40. C₁₃×#388	C₂²	semidirect
41. C₁₃×#384	C₂²	semidirect
42. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
71. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
104. C₂×#2512	C₁₃	direct (N × H)
165. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
176. C₂²×#126	C₂×C₁₃	semidirect
177. #2512	C₂×C₁₃	direct (N × H)
178. C₂×#397	C₂×C₁₃	semidirect
179. C₂×#396	C₂×C₁₃	semidirect
183. C₂×#389	C₂×C₁₃	semidirect
184. C₂×#388	C₂×C₁₃	semidirect
185. C₂×#384	C₂×C₁₃	semidirect
186. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
187. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
243. C₂×C₄×C₁₃	#126	semidirect
253. C₂×#126	C₂²×C₁₃	semidirect
272. #397	C₂²×C₁₃	semidirect
273. #396	C₂²×C₁₃	semidirect
277. #389	C₂²×C₁₃	semidirect
278. #388	C₂²×C₁₃	semidirect
279. #384	C₂²×C₁₃	semidirect
280. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
281. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
317. C₄×C₁₃	C₂×#126	semidirect
341. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
375. C₂×C₁₃	#2512	direct (N × H)
443. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
454. C₁₃	C₂×#2512	direct (N × H)
510. C₂×C₄	C₁₃×#126	semidirect
549. C₄	C₂×C₁₃×#126	semidirect
551. C₂	C₁₃×#2512	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×C₁₃×#126	2
C₁₃×#2512	2
C₂×C₁₃×#397	2
C₂×C₁₃×#396	2
C₂×C₁₃×#390	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₁₃×#384	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2512	13

Subgroups — C2×C13×#2512 #15721101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2512 #15721101