Subgroups — C₂×C₁₃×#2566 #15721230

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2566	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#396	C₂	1	4	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×#385	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×#125	—	2	8	no	—
14	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
15	C₂×C₄×D₄×C₁₃	—	2	8	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
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	4	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#396	C₂²	1	32	yes	complemented
31	C₁₃×#390	C₂²	1	8	yes	—
32	C₁₃×#390	C₂²	1	8	yes	—
33	C₁₃×#385	C₂²	1	32	yes	complemented
34	C₁₃×#384	C₂²	1	8	yes	complemented
35	C₁₃×#382	C₂²	1	8	yes	complemented
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	4	yes	—
39	C₂⁵×C₁₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₃	—	2	4	no	—
41	C₂²×D₄×C₁₃	—	2	4	no	—
42	C₂²×D₄×C₁₃	Q₈	1	8	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	—	2	8	no	—
45	C₂³×C₄×C₁₃	—	4	8	no	—
46	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#125	—	2	32	no	—
56	C₄×D₄×C₁₃	—	2	32	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
77	C₂×C₄²×C₁₃	—	2	4	no	—
78	C₂×C₄²×C₁₃	—	2	4	no	—
79	C₂×C₄²×C₁₃	D₄	1	8	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
83	C₁₃×#95	C₂³	1	8	yes	—
84	C₁₃×#95	C₂³	1	16	yes	—
85	C₂×#2566	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	8	no	—
88	C₂⁴×C₁₃	—	2	4	no	—
89	C₂⁴×C₁₃	—	2	8	no	—
90	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
91	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
92	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₂×D₄×C₁₃	—	2	32	no	—
94	C₂×D₄×C₁₃	—	2	8	no	—
95	C₂×D₄×C₁₃	—	2	8	no	—
96	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	8	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	16	no	—
111	C₂²×C₄×C₁₃	—	4	16	no	—
112	C₂²×C₄×C₁₃	—	4	32	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
117	C₂²×C₄×C₁₃	#41	1	8	yes	—
118	C₂²×C₄×C₁₃	#41	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	16	no	—
129	C₁₃×C₄⋊C₄	—	2	16	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	16	no	—
133	C₁₃×C₄⋊C₄	—	4	16	no	—
134	C₁₃×C₂²⋊C₄	—	2	16	no	—
135	C₁₃×C₂²⋊C₄	—	2	32	no	—
136	C₁₃×C₂²⋊C₄	—	4	16	no	—
137	C₄²×C₁₃	—	2	8	no	—
138	C₄²×C₁₃	—	2	8	no	—
139	C₄²×C₁₃	C₂×D₄	1	16	yes	—
140	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
142	#2566	C₂×C₁₃	1	16	yes	direct product factor
143	C₂×#396	C₂×C₁₃	1	4	yes	complemented
144	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
145	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#385	C₂×C₁₃	1	4	yes	complemented
147	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	2	16	no	—
151	C₂³×C₁₃	—	2	32	no	—
152	C₂³×C₁₃	—	2	4	no	—
153	C₂³×C₁₃	—	2	8	no	—
154	C₂³×C₁₃	—	2	4	no	—
155	C₂³×C₁₃	—	2	8	no	—
156	C₂³×C₁₃	—	4	8	no	—
157	C₂³×C₁₃	—	4	8	no	—
158	C₂³×C₁₃	—	4	16	no	—
159	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
160	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
161	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
162	C₂³×C₁₃	C₂×#41	1	2	yes	—
163	C₂³×C₁₃	C₂×#41	1	4	yes	—
164	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
165	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
166	D₄×C₁₃	—	2	32	no	—
167	C₂×C₄×C₁₃	—	2	8	no	—
168	C₂×C₄×C₁₃	—	2	8	no	—
169	C₂×C₄×C₁₃	—	2	16	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	4	32	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	8	no	—
186	C₂×C₄×C₁₃	—	4	8	no	—
187	C₂×C₄×C₁₃	—	4	8	no	—
188	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
193	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
194	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
195	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
197	C₂×#125	—	2	8	no	—
198	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
199	C₂×C₄×D₄	—	2	8	no	—
200	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
208	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
211	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
214	#396	C₂²×C₁₃	1	32	yes	complemented
215	#390	C₂²×C₁₃	1	8	yes	—
216	#390	C₂²×C₁₃	1	8	yes	—
217	#385	C₂²×C₁₃	1	32	yes	complemented
218	#384	C₂²×C₁₃	1	8	yes	complemented
219	#382	C₂²×C₁₃	1	8	yes	complemented
220	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
221	C₂×#95	C₂²×C₁₃	1	4	yes	—
222	C₂×#95	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₁₃	—	2	8	no	—
224	C₂²×C₁₃	—	2	16	no	—
225	C₂²×C₁₃	—	4	32	no	—
226	C₂²×C₁₃	—	4	4	no	—
227	C₂²×C₁₃	—	4	4	no	—
228	C₂²×C₁₃	—	4	8	no	—
229	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
230	C₂²×C₁₃	#532	1	4	yes	—
231	C₂²×C₁₃	#535	1	4	yes	—
232	C₂²×C₁₃	#553	1	8	yes	—
233	C₂²×C₁₃	#554	1	8	yes	—
234	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
235	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
236	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
237	C₂²×C₁₃	C₂²×#41	1	2	yes	—
238	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
239	C₄×C₁₃	—	2	4	no	—
240	C₄×C₁₃	—	2	4	no	—
241	C₄×C₁₃	—	2	8	no	—
242	C₄×C₁₃	—	4	4	no	—
243	C₄×C₁₃	—	4	4	no	—
244	C₄×C₁₃	—	4	4	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
247	C₂⁵	C₂³×C₁₃	1	2	yes	—
248	C₂²×D₄	—	2	4	no	—
249	C₂²×D₄	—	2	4	no	—
250	C₂²×D₄	Q₈×C₁₃	1	8	yes	—
251	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
252	C₂³×C₄	—	2	8	no	—
253	C₂³×C₄	—	4	8	no	—
254	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
262	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
263	#125	—	2	32	no	—
264	C₄×D₄	—	2	32	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	8	no	—
267	C₂×C₄⋊C₄	—	2	8	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	8	no	—
271	C₂×C₄⋊C₄	—	4	8	no	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	16	no	—
281	C₂×C₂²⋊C₄	—	4	8	no	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	—	2	4	no	—
287	C₂×C₄²	D₄×C₁₃	1	8	yes	—
288	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
291	#95	C₂³×C₁₃	1	8	yes	—
292	#95	C₂³×C₁₃	1	16	yes	—
293	C₂×C₁₃	—	4	8	no	—
294	C₂×C₁₃	#2566	1	8	yes	direct product factor
295	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
296	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
298	C₂×C₁₃	C₂×#553	1	2	yes	—
299	C₂×C₁₃	C₂×#554	1	2	yes	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
305	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
306	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
307	C₂×D₄	—	2	32	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	2	16	no	—
325	C₂²×C₄	—	4	16	no	—
326	C₂²×C₄	—	4	32	no	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
331	C₂²×C₄	C₁₃×#41	1	8	yes	—
332	C₂²×C₄	C₁₃×#41	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	2	16	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	16	no	—
347	C₄⋊C₄	—	4	16	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	2	32	no	—
350	C₂²⋊C₄	—	4	16	no	—
351	C₄²	—	2	8	no	—
352	C₄²	—	2	8	no	—
353	C₄²	C₂×D₄×C₁₃	1	16	yes	—
354	C₁₃	C₂×#2566	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	16	no	—
356	C₂³	—	2	32	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	16	no	—
364	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
365	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
366	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
367	C₂³	C₂×C₁₃×#41	1	2	yes	—
368	C₂³	C₂×C₁₃×#41	1	4	yes	—
369	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
370	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
371	D₄	—	2	32	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	4	32	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
395	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
397	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
398	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
399	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
400	C₂²	—	2	8	no	—
401	C₂²	—	2	16	no	—
402	C₂²	—	4	32	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	8	no	—
406	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
407	C₂²	C₁₃×#532	1	4	yes	—
408	C₂²	C₁₃×#535	1	4	yes	—
409	C₂²	C₁₃×#553	1	8	yes	—
410	C₂²	C₁₃×#554	1	8	yes	—
411	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
412	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
413	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
414	C₂²	C₂²×C₁₃×#41	1	2	yes	—
415	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
416	C₄	—	2	4	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	8	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	4	no	—
423	C₄	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
424	C₂	—	4	8	no	—
425	C₂	C₁₃×#2566	1	8	yes	direct product factor
426	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
427	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
428	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
429	C₂	C₂×C₁₃×#553	1	2	yes	—
430	C₂	C₂×C₁₃×#554	1	2	yes	—

	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×#125	C₂	semidirect
3. C₁₃×#2566	C₂	direct (N × H)
4. C₂×C₁₃×#396	C₂	semidirect
7. C₂×C₁₃×#385	C₂	semidirect
8. C₂×C₁₃×#384	C₂	semidirect
9. C₂×C₁₃×#382	C₂	semidirect
10. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
14. C₂×C₁₃×#125	C₂²	semidirect
30. C₁₃×#396	C₂²	semidirect
33. C₁₃×#385	C₂²	semidirect
34. C₁₃×#384	C₂²	semidirect
35. C₁₃×#382	C₂²	semidirect
36. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
85. C₂×#2566	C₁₃	direct (N × H)
140. C₂²×#125	C₂×C₁₃	semidirect
142. #2566	C₂×C₁₃	direct (N × H)
143. C₂×#396	C₂×C₁₃	semidirect
146. C₂×#385	C₂×C₁₃	semidirect
147. C₂×#384	C₂×C₁₃	semidirect
148. C₂×#382	C₂×C₁₃	semidirect
149. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
198. C₂×#125	C₂²×C₁₃	semidirect
214. #396	C₂²×C₁₃	semidirect
217. #385	C₂²×C₁₃	semidirect
218. #384	C₂²×C₁₃	semidirect
219. #382	C₂²×C₁₃	semidirect
220. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
294. C₂×C₁₃	#2566	direct (N × H)
354. C₁₃	C₂×#2566	direct (N × H)
425. C₂	C₁₃×#2566	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×#125	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2566	2
C₂×C₁₃×#396	2
C₂×C₁₃×#390	2
C₂×C₁₃×#385	2
C₂×C₁₃×#384	2
C₂×C₁₃×#382	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2566	13

Subgroups — C2×C13×#2566 #15721230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2566 #15721230