Subgroups — C₂×C₁₃×#1919 #15707369

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1919	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	—	2	1	no	—
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#106	C₄	1	8	yes	complemented
19	C₂×C₁₃×#106	C₂²	1	4	yes	—
20	C₁₃×#389	—	2	2	no	—
21	C₁₃×#389	C₂²	1	4	yes	—
22	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
24	C₂×C₁₃×#95	—	2	1	no	—
25	C₂×C₁₃×#95	—	2	1	no	—
26	C₁₃×#340	C₂²	1	4	yes	—
27	C₁₃×#340	C₂²	1	4	yes	—
28	C₁₃×#340	C₂²	1	4	yes	—
29	C₁₃×#336	C₂²	1	4	yes	—
30	C₂³×C₄×C₁₃	—	2	1	no	—
31	C₂³×C₄×C₁₃	—	2	1	no	—
32	C₂³×C₄×C₁₃	—	2	1	no	—
33	C₂³×C₄×C₁₃	—	2	1	no	—
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	—	2	2	no	—
38	C₂²×C₈×C₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₃	—	2	2	no	—
40	C₂²×C₈×C₁₃	—	2	2	no	—
41	C₂²×C₈×C₁₃	—	2	2	no	—
42	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₃	—	2	4	no	—
66	C₂×C₄²×C₁₃	—	4	4	no	—
67	C₂×C₄²×C₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₁₃×#106	C₂×C₄	1	16	yes	complemented
70	C₁₃×#95	—	2	4	no	—
71	C₁₃×#95	—	2	4	no	—
72	C₂×#1919	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	2	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₃	#41	1	2	yes	—
102	C₂²×C₄×C₁₃	#41	1	2	yes	—
103	C₂²×C₄×C₁₃	#41	1	2	yes	—
104	C₂²×C₄×C₁₃	#41	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₃	—	2	8	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	4	4	no	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₁₃×C₄⋊C₄	—	4	8	no	—
124	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
125	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
126	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
127	C₄²×C₁₃	—	2	4	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	4	8	no	—
131	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic
132	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
133	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
134	#1919	C₂×C₁₃	1	8	yes	direct product factor
135	C₂×#340	C₂×C₁₃	1	1	yes	characteristic
136	C₂×#340	C₂×C₁₃	1	1	yes	characteristic
137	C₂×#340	C₂×C₁₃	1	1	yes	characteristic
138	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
139	C₂³×C₁₃	C₄×D₄	1	2	yes	—
140	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
141	C₂³×C₁₃	#123	1	2	yes	—
142	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
143	C₂³×C₁₃	#135	1	2	yes	—
144	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
145	C₂³×C₁₃	#137	1	2	yes	—
146	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	8	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	8	no	—
163	C₂×C₄×C₁₃	—	4	8	no	—
164	C₂×C₄×C₁₃	—	4	8	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	8	4	no	—
170	C₂×C₄×C₁₃	#117	1	4	yes	—
171	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
173	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₃	#123	1	2	yes	—
175	C₂×C₄×C₁₃	#125	1	4	yes	—
176	C₂×C₄×C₁₃	#126	1	4	yes	—
177	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
178	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₈×C₁₃	—	2	4	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×C₄⋊C₄	—	2	1	no	—
189	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
192	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×C₄²	—	2	1	no	—
194	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#106	C₄×C₁₃	1	8	yes	complemented
196	C₂×#106	C₂²×C₁₃	1	4	yes	—
197	#389	—	2	2	no	—
198	#389	C₂²×C₁₃	1	4	yes	—
199	C₄×C₄⋊C₄	—	2	2	no	—
200	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
201	C₂×#95	—	2	1	no	—
202	C₂×#95	—	2	1	no	—
203	#340	C₂²×C₁₃	1	4	yes	—
204	#340	C₂²×C₁₃	1	4	yes	—
205	#340	C₂²×C₁₃	1	4	yes	—
206	#336	C₂²×C₁₃	1	4	yes	—
207	C₂²×C₁₃	#387	1	4	yes	—
208	C₂²×C₁₃	C₄×SD₁₆	1	4	yes	—
209	C₂²×C₁₃	#440	1	4	yes	—
210	C₂²×C₁₃	#475	1	4	yes	—
211	C₂²×C₁₃	#478	1	4	yes	—
212	C₂²×C₁₃	#481	1	4	yes	—
213	C₂²×C₁₃	#485	1	4	yes	—
214	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
217	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	4	4	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	—	4	4	no	—
225	C₄×C₁₃	—	4	4	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	#387	1	4	yes	—
228	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
229	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
231	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	2	1	no	—
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
245	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
246	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	4	4	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
260	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	—	4	4	no	—
269	C₂×C₄²	D₄×C₁₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
271	#106	C₂×C₄×C₁₃	1	16	yes	complemented
272	#95	—	2	4	no	—
273	#95	—	2	4	no	—
274	C₂×C₁₃	#1919	1	8	yes	direct product factor
275	C₂×C₁₃	C₂×#387	1	1	yes	characteristic
276	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
279	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
280	C₂×C₁₃	C₂×#485	1	1	yes	characteristic
281	C₂×C₁₃	C₂×#481	1	1	yes	characteristic
282	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
310	C₂²×C₄	C₁₃×#41	1	2	yes	—
311	C₂²×C₄	C₁₃×#41	1	2	yes	—
312	C₂²×C₄	C₁₃×#41	1	2	yes	—
313	C₂²×C₄	C₁₃×#41	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
315	C₂×C₈	—	2	8	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	4	no	—
322	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	8	no	—
333	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
334	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
335	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	8	no	—
340	C₁₃	C₂×#1919	1	1	yes	characteristic, direct product factor, Sylow
341	C₂³	C₄×D₄×C₁₃	1	2	yes	—
342	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
343	C₂³	C₁₃×#123	1	2	yes	—
344	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
345	C₂³	C₁₃×#135	1	2	yes	—
346	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
347	C₂³	C₁₃×#137	1	2	yes	—
348	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	4	no	—
372	C₂×C₄	C₁₃×#117	1	4	yes	—
373	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
374	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
375	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
376	C₂×C₄	C₁₃×#123	1	2	yes	—
377	C₂×C₄	C₁₃×#125	1	4	yes	—
378	C₂×C₄	C₁₃×#126	1	4	yes	—
379	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
380	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
386	C₈	—	2	4	no	—
387	C₈	—	4	2	no	—
388	C₂²	C₁₃×#387	1	4	yes	—
389	C₂²	C₄×C₁₃×SD₁₆	1	4	yes	—
390	C₂²	C₁₃×#440	1	4	yes	—
391	C₂²	C₁₃×#475	1	4	yes	—
392	C₂²	C₁₃×#478	1	4	yes	—
393	C₂²	C₁₃×#481	1	4	yes	—
394	C₂²	C₁₃×#485	1	4	yes	—
395	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
396	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
397	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
398	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
399	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
400	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
401	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	8	2	no	—
408	C₄	C₁₃×#387	1	4	yes	—
409	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
410	C₄	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
411	C₄	C₂×C₁₃×#125	1	1	yes	characteristic
412	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
413	C₂	C₁₃×#1919	1	8	yes	direct product factor
414	C₂	C₂×C₁₃×#387	1	1	yes	characteristic
415	C₂	C₂×C₄×C₁₃×SD₁₆	1	1	yes	characteristic
416	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
417	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
418	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
419	C₂	C₂×C₁₃×#485	1	1	yes	characteristic
420	C₂	C₂×C₁₃×#481	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1919	C₂	direct (N × H)
18. C₂×C₁₃×#106	C₄	semidirect
69. C₁₃×#106	C₂×C₄	semidirect
72. C₂×#1919	C₁₃	direct (N × H)
134. #1919	C₂×C₁₃	direct (N × H)
195. C₂×#106	C₄×C₁₃	semidirect
271. #106	C₂×C₄×C₁₃	semidirect
274. C₂×C₁₃	#1919	direct (N × H)
340. C₁₃	C₂×#1919	direct (N × H)
413. C₂	C₁₃×#1919	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×#106	2
C₂×C₁₃×#389	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1919	2
C₂×C₁₃×#340	2
C₂×C₁₃×#336	2
C₂×#1919	13

Subgroups — C2×C13×#1919 #15707369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1919 #15707369