Subgroups — C₂×C₁₃×#2586 #15721174

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2586	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#395	C₂	1	2	yes	maximal
4	C₂×C₁₃×#395	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#391	C₂	1	2	yes	maximal
6	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#389	C₂	1	2	yes	maximal
8	C₂×C₁₃×#387	C₂	1	2	yes	maximal
9	C₂×C₁₃×#387	C₂	1	2	yes	maximal
10	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
20	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#398	C₂²	1	8	yes	—
24	C₁₃×#395	C₂²	1	8	yes	—
25	C₁₃×#395	C₂²	1	16	yes	—
26	C₁₃×#391	C₂²	1	16	yes	—
27	C₁₃×#391	C₂²	1	8	yes	—
28	C₁₃×#389	C₂²	1	16	yes	—
29	C₁₃×#387	C₂²	1	16	yes	—
30	C₁₃×#387	C₂²	1	16	yes	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	16	yes	—
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	—	2	8	no	—
42	C₂²×Q₈×C₁₃	—	2	4	no	—
43	C₂²×Q₈×C₁₃	—	4	2	no	—
44	C₂²×Q₈×C₁₃	—	4	2	no	—
45	C₂²×Q₈×C₁₃	—	4	2	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	2	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	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
59	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₂×C₁₃×C₄⋊C₄	Q₈	1	16	yes	complemented
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	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	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₃	—	2	8	no	—
72	C₂×C₄²×C₁₃	—	4	2	no	—
73	C₂×C₄²×C₁₃	—	4	4	no	—
74	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
77	C₁₃×#95	C₂³	1	8	yes	—
78	C₁₃×#95	C₂³	1	8	yes	—
79	C₁₃×#95	C₂³	1	4	yes	—
80	C₁₃×#95	C₂³	1	8	yes	—
81	C₁₃×#95	C₂³	1	4	yes	—
82	C₁₃×#95	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	8	yes	—
84	C₁₃×#95	C₂³	1	8	yes	—
85	C₁₃×#95	C₂³	1	8	yes	—
86	C₂×#2586	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	—	2	16	no	—
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	—	4	4	no	—
91	C₂×Q₈×C₁₃	—	4	4	no	—
92	C₂×Q₈×C₁₃	—	4	4	no	—
93	C₂×Q₈×C₁₃	—	4	16	no	—
94	C₂×Q₈×C₁₃	—	4	16	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
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	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
116	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
117	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
118	C₂²×C₄×C₁₃	#41	1	8	yes	—
119	C₂²×C₄×C₁₃	#41	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	16	no	—
130	C₁₃×C₄⋊C₄	—	2	16	no	—
131	C₁₃×C₄⋊C₄	—	4	8	no	—
132	C₁₃×C₄⋊C₄	—	4	8	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	C₂×Q₈	1	32	yes	complemented
136	C₄²×C₁₃	—	2	16	no	—
137	C₄²×C₁₃	—	4	4	no	—
138	C₄²×C₁₃	—	4	8	no	—
139	#2586	C₂×C₁₃	1	16	yes	direct product factor
140	C₂×#398	C₂×C₁₃	1	1	yes	characteristic
141	C₂×#395	C₂×C₁₃	1	2	yes	—
142	C₂×#395	C₂×C₁₃	1	1	yes	characteristic
143	C₂×#391	C₂×C₁₃	1	1	yes	characteristic
144	C₂×#391	C₂×C₁₃	1	2	yes	—
145	C₂×#389	C₂×C₁₃	1	2	yes	—
146	C₂×#387	C₂×C₁₃	1	2	yes	—
147	C₂×#387	C₂×C₁₃	1	2	yes	—
148	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
149	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
150	C₂³×C₁₃	C₂×#41	1	2	yes	—
151	C₂³×C₁₃	C₂×#41	1	4	yes	—
152	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
153	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
154	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
155	Q₈×C₁₃	—	4	16	no	—
156	Q₈×C₁₃	—	4	16	no	—
157	C₂×C₄×C₁₃	—	2	16	no	—
158	C₂×C₄×C₁₃	—	2	8	no	—
159	C₂×C₄×C₁₃	—	2	16	no	—
160	C₂×C₄×C₁₃	—	2	16	no	—
161	C₂×C₄×C₁₃	—	2	16	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	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	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	—	4	8	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
187	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
188	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
189	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
190	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
191	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
197	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
200	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
201	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
203	#398	C₂²×C₁₃	1	8	yes	—
204	#395	C₂²×C₁₃	1	8	yes	—
205	#395	C₂²×C₁₃	1	16	yes	—
206	#391	C₂²×C₁₃	1	16	yes	—
207	#391	C₂²×C₁₃	1	8	yes	—
208	#389	C₂²×C₁₃	1	16	yes	—
209	#387	C₂²×C₁₃	1	16	yes	—
210	#387	C₂²×C₁₃	1	16	yes	—
211	C₄×C₄⋊C₄	C₂²×C₁₃	1	16	yes	—
212	C₂×#95	C₂²×C₁₃	1	2	yes	—
213	C₂×#95	C₂²×C₁₃	1	2	yes	—
214	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#95	C₂²×C₁₃	1	2	yes	—
216	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#95	C₂²×C₁₃	1	2	yes	—
218	C₂×#95	C₂²×C₁₃	1	2	yes	—
219	C₂×#95	C₂²×C₁₃	1	2	yes	—
220	C₂×#95	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₁₃	#533	1	8	yes	—
222	C₂²×C₁₃	#538	1	4	yes	—
223	C₂²×C₁₃	#551	1	4	yes	—
224	C₂²×C₁₃	#554	1	8	yes	—
225	C₂²×C₁₃	Q₈²	1	4	yes	—
226	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
227	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
228	C₂²×C₁₃	C₂²×#41	1	2	yes	—
229	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₄×C₁₃	—	2	8	no	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	8	no	—
234	C₄×C₁₃	—	2	8	no	—
235	C₄×C₁₃	—	2	8	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	4	4	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	2	no	—
240	C₂²×Q₈	—	2	8	no	—
241	C₂²×Q₈	—	2	4	no	—
242	C₂²×Q₈	—	4	2	no	—
243	C₂²×Q₈	—	4	2	no	—
244	C₂²×Q₈	—	4	2	no	—
245	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
246	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
247	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
249	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
250	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
254	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	8	no	—
257	C₂×C₄⋊C₄	—	2	8	no	—
258	C₂×C₄⋊C₄	—	4	4	no	—
259	C₂×C₄⋊C₄	—	4	2	no	—
260	C₂×C₄⋊C₄	—	4	4	no	—
261	C₂×C₄⋊C₄	—	4	2	no	—
262	C₂×C₄⋊C₄	Q₈×C₁₃	1	16	yes	complemented
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
270	C₂×C₄²	—	2	8	no	—
271	C₂×C₄²	—	4	2	no	—
272	C₂×C₄²	—	4	4	no	—
273	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
274	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
275	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
276	#95	C₂³×C₁₃	1	8	yes	—
277	#95	C₂³×C₁₃	1	8	yes	—
278	#95	C₂³×C₁₃	1	4	yes	—
279	#95	C₂³×C₁₃	1	8	yes	—
280	#95	C₂³×C₁₃	1	4	yes	—
281	#95	C₂³×C₁₃	1	8	yes	—
282	#95	C₂³×C₁₃	1	8	yes	—
283	#95	C₂³×C₁₃	1	8	yes	—
284	#95	C₂³×C₁₃	1	8	yes	—
285	C₂×C₁₃	#2586	1	8	yes	direct product factor
286	C₂×C₁₃	C₂×#533	1	2	yes	—
287	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
288	C₂×C₁₃	C₂×#551	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#554	1	2	yes	—
290	C₂×C₁₃	C₂×Q₈²	1	1	yes	characteristic
291	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
292	C₂×Q₈	—	2	16	no	—
293	C₂×Q₈	—	2	8	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	—	4	16	no	—
298	C₂×Q₈	—	4	16	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
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	2	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
320	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
321	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
322	C₂²×C₄	C₁₃×#41	1	8	yes	—
323	C₂²×C₄	C₁₃×#41	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
333	C₄⋊C₄	—	2	16	no	—
334	C₄⋊C₄	—	2	16	no	—
335	C₄⋊C₄	—	4	8	no	—
336	C₄⋊C₄	—	4	8	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	C₂×Q₈×C₁₃	1	32	yes	complemented
340	C₄²	—	2	16	no	—
341	C₄²	—	4	4	no	—
342	C₄²	—	4	8	no	—
343	C₁₃	C₂×#2586	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
345	C₂³	C₂×C₁₃×#41	1	2	yes	—
346	C₂³	C₂×C₁₃×#41	1	4	yes	—
347	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
348	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
349	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
350	Q₈	—	4	16	no	—
351	Q₈	—	4	16	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	16	no	—
355	C₂×C₄	—	2	16	no	—
356	C₂×C₄	—	2	16	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
382	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
384	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
385	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
386	C₂²	C₁₃×#533	1	8	yes	—
387	C₂²	C₁₃×#538	1	4	yes	—
388	C₂²	C₁₃×#551	1	4	yes	—
389	C₂²	C₁₃×#554	1	8	yes	—
390	C₂²	Q₈²×C₁₃	1	4	yes	—
391	C₂²	C₂³×Q₈×C₁₃	1	2	yes	—
392	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
393	C₂²	C₂²×C₁₃×#41	1	2	yes	—
394	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
396	C₄	—	2	8	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	8	no	—
399	C₄	—	2	8	no	—
400	C₄	—	2	8	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₂	C₁₃×#2586	1	8	yes	direct product factor
406	C₂	C₂×C₁₃×#533	1	2	yes	—
407	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
408	C₂	C₂×C₁₃×#551	1	1	yes	characteristic
409	C₂	C₂×C₁₃×#554	1	2	yes	—
410	C₂	C₂×Q₈²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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. C₁₃×#2586	C₂	direct (N × H)
63. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
86. C₂×#2586	C₁₃	direct (N × H)
135. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
139. #2586	C₂×C₁₃	direct (N × H)
262. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
285. C₂×C₁₃	#2586	direct (N × H)
339. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
343. C₁₃	C₂×#2586	direct (N × H)
405. C₂	C₁₃×#2586	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2586	2
C₂×C₁₃×#398	2
C₂×C₁₃×#395	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2586	13

Subgroups — C2×C13×#2586 #15721174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2586 #15721174