Subgroups — C₂×C₁₃×#2043 #15709842

Order 3328.

1542 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#103	C₂	1	2	yes	maximal
3	C₂²×C₁₃×#103	C₂	1	2	yes	maximal
4	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2043	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
12	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
13	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	—	2	8	no	—
19	C₂×C₁₃×#103	—	2	8	no	—
20	C₂×C₁₃×#103	C₂²	1	8	yes	—
21	C₂×C₁₃×#103	C₂²	1	8	yes	—
22	C₁₃×#389	—	2	2	no	—
23	C₁₃×#389	C₂²	1	4	yes	—
24	C₂×C₁₃×#95	—	2	1	no	—
25	C₁₃×#336	C₂²	1	4	yes	—
26	C₂²×Q₈×C₁₃	—	2	4	no	—
27	C₂²×Q₈×C₁₃	—	2	2	no	—
28	C₂²×Q₈×C₁₃	—	2	4	no	—
29	C₂²×Q₈×C₁₃	—	2	4	no	—
30	C₂²×Q₈×C₁₃	—	2	4	no	—
31	C₂²×Q₈×C₁₃	—	2	4	no	—
32	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
33	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₃	—	2	2	no	—
35	C₂³×C₄×C₁₃	—	2	1	no	—
36	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	—	2	4	no	—
41	C₂²×C₈×C₁₃	—	2	4	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
44	C₁₃×C₄⋊Q₈	—	2	16	no	—
45	C₁₃×C₄⋊Q₈	—	2	16	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	4	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	D₄	1	4	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	—	2	4	no	—
60	C₂×C₄²×C₁₃	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₁₃×#103	—	2	16	no	—
63	C₁₃×#103	—	2	16	no	—
64	C₁₃×#95	—	2	4	no	—
65	C₂×#2043	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
67	C₂×Q₈×C₁₃	—	2	8	no	—
68	C₂×Q₈×C₁₃	—	2	4	no	—
69	C₂×Q₈×C₁₃	—	2	16	no	—
70	C₂×Q₈×C₁₃	—	2	16	no	—
71	C₂×Q₈×C₁₃	—	2	4	no	—
72	C₂×Q₈×C₁₃	—	2	4	no	—
73	C₂×Q₈×C₁₃	—	2	4	no	—
74	C₂×Q₈×C₁₃	—	2	4	no	—
75	C₂×Q₈×C₁₃	—	4	4	no	—
76	C₂×Q₈×C₁₃	—	4	8	no	—
77	C₂×Q₈×C₁₃	—	4	8	no	—
78	C₂×Q₈×C₁₃	—	4	4	no	—
79	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
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	8	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	—	4	4	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	—	4	2	no	—
96	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
97	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	#41	1	4	yes	—
104	C₂²×C₄×C₁₃	#41	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₁₃	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	4	8	no	—
110	C₁₃×C₄⋊C₄	—	2	16	no	—
111	C₁₃×C₄⋊C₄	—	2	16	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	—	4	8	no	—
117	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
118	C₄²×C₁₃	—	2	4	no	—
119	C₄²×C₁₃	—	2	4	no	—
120	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
121	C₂²×#103	C₂×C₁₃	1	2	yes	—
122	C₂²×#103	C₂×C₁₃	1	2	yes	—
123	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
124	#2043	C₂×C₁₃	1	8	yes	direct product factor
125	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
126	C₂³×C₁₃	#120	1	2	yes	—
127	C₂³×C₁₃	#121	1	2	yes	—
128	C₂³×C₁₃	#124	1	2	yes	—
129	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
130	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
131	C₂³×C₁₃	#137	1	2	yes	—
132	C₂³×C₁₃	#137	1	2	yes	—
133	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₃	—	2	8	no	—
135	Q₈×C₁₃	—	2	8	no	—
136	Q₈×C₁₃	—	4	4	no	—
137	Q₈×C₁₃	—	4	4	no	—
138	Q₈×C₁₃	—	4	16	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	8	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	4	4	no	—
148	C₂×C₄×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	16	no	—
152	C₂×C₄×C₁₃	—	4	8	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	8	4	no	—
157	C₂×C₄×C₁₃	#120	1	2	yes	—
158	C₂×C₄×C₁₃	#121	1	8	yes	—
159	C₂×C₄×C₁₃	#121	1	2	yes	—
160	C₂×C₄×C₁₃	#123	1	8	yes	—
161	C₂×C₄×C₁₃	#124	1	2	yes	—
162	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
163	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
164	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
168	C₈×C₁₃	—	4	4	no	—
169	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
170	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
171	C₂×C₄⋊Q₈	—	2	8	no	—
172	C₂×C₄⋊Q₈	—	2	2	no	—
173	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
174	C₂²×C₄⋊C₄	—	2	1	no	—
175	C₂²×C₄⋊C₄	—	2	1	no	—
176	C₂²×C₄⋊C₄	—	2	1	no	—
177	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
178	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
179	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×#103	—	2	8	no	—
181	C₂×#103	—	2	8	no	—
182	C₂×#103	C₂²×C₁₃	1	8	yes	—
183	C₂×#103	C₂²×C₁₃	1	8	yes	—
184	#389	—	2	2	no	—
185	#389	C₂²×C₁₃	1	4	yes	—
186	C₂×#95	—	2	1	no	—
187	#336	C₂²×C₁₃	1	4	yes	—
188	C₂²×C₁₃	#394	1	4	yes	—
189	C₂²×C₁₃	#448	1	4	yes	—
190	C₂²×C₁₃	#451	1	4	yes	—
191	C₂²×C₁₃	#461	1	4	yes	—
192	C₂²×C₁₃	#462	1	4	yes	—
193	C₂²×C₁₃	#487	1	4	yes	—
194	C₂²×C₁₃	#491	1	4	yes	—
195	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
196	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
198	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
199	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
200	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
201	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
202	C₄×C₁₃	—	2	4	no	—
203	C₄×C₁₃	—	2	4	no	—
204	C₄×C₁₃	—	4	8	no	—
205	C₄×C₁₃	—	4	4	no	—
206	C₄×C₁₃	—	8	2	no	—
207	C₄×C₁₃	#394	1	4	yes	—
208	C₄×C₁₃	C₂×#121	1	2	yes	—
209	C₄×C₁₃	C₂×#123	1	2	yes	—
210	C₂²×Q₈	—	2	4	no	—
211	C₂²×Q₈	—	2	2	no	—
212	C₂²×Q₈	—	2	4	no	—
213	C₂²×Q₈	—	2	4	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
217	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
228	C₄⋊Q₈	—	2	16	no	—
229	C₄⋊Q₈	—	2	16	no	—
230	C₂×C₄⋊C₄	—	2	8	no	—
231	C₂×C₄⋊C₄	—	2	8	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	4	4	no	—
240	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	D₄×C₁₃	1	2	yes	—
245	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
246	#103	—	2	16	no	—
247	#103	—	2	16	no	—
248	#95	—	2	4	no	—
249	C₂×C₁₃	#2043	1	8	yes	direct product factor
250	C₂×C₁₃	C₂×#394	1	1	yes	characteristic
251	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
252	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
253	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
255	C₂×C₁₃	C₂×#487	1	1	yes	characteristic
256	C₂×C₁₃	C₂×#491	1	1	yes	characteristic
257	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
258	C₂×Q₈	—	2	8	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	16	no	—
261	C₂×Q₈	—	2	16	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	4	8	no	—
267	C₂×Q₈	—	4	4	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	—	4	4	no	—
270	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
288	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
289	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₁₃×#41	1	4	yes	—
295	C₂²×C₄	C₁₃×#41	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	8	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	8	no	—
308	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
309	C₄²	—	2	4	no	—
310	C₄²	—	2	4	no	—
311	C₁₃	C₂×#2043	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³	C₁₃×#120	1	2	yes	—
313	C₂³	C₁₃×#121	1	2	yes	—
314	C₂³	C₁₃×#124	1	2	yes	—
315	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
316	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
317	C₂³	C₁₃×#137	1	2	yes	—
318	C₂³	C₁₃×#137	1	2	yes	—
319	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	4	16	no	—
323	Q₈	—	4	4	no	—
324	Q₈	—	4	4	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	C₁₃×#120	1	2	yes	—
344	C₂×C₄	C₁₃×#121	1	2	yes	—
345	C₂×C₄	C₁₃×#121	1	8	yes	—
346	C₂×C₄	C₁₃×#123	1	8	yes	—
347	C₂×C₄	C₁₃×#124	1	2	yes	—
348	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
349	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
352	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
353	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
354	C₈	—	4	4	no	—
355	C₂²	C₁₃×#394	1	4	yes	—
356	C₂²	C₁₃×#448	1	4	yes	—
357	C₂²	C₁₃×#451	1	4	yes	—
358	C₂²	C₁₃×#461	1	4	yes	—
359	C₂²	C₁₃×#462	1	4	yes	—
360	C₂²	C₁₃×#487	1	4	yes	—
361	C₂²	C₁₃×#491	1	4	yes	—
362	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
363	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
364	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
365	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
366	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
367	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
368	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	8	no	—
373	C₄	—	8	2	no	—
374	C₄	C₁₃×#394	1	4	yes	—
375	C₄	C₂×C₁₃×#121	1	2	yes	—
376	C₄	C₂×C₁₃×#123	1	2	yes	—
377	C₂	C₁₃×#2043	1	8	yes	direct product factor
378	C₂	C₂×C₁₃×#394	1	1	yes	characteristic
379	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
380	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
381	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
382	C₂	C₂×C₁₃×#462	1	1	yes	characteristic
383	C₂	C₂×C₁₃×#487	1	1	yes	characteristic
384	C₂	C₂×C₁₃×#491	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×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
5. C₁₃×#2043	C₂	direct (N × H)
65. C₂×#2043	C₁₃	direct (N × H)
124. #2043	C₂×C₁₃	direct (N × H)
249. C₂×C₁₃	#2043	direct (N × H)
311. C₁₃	C₂×#2043	direct (N × H)
377. C₂	C₁₃×#2043	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×C₄⋊Q₈	2
C₂²×C₁₃×#103	2
C₂×C₁₃×#389	2
C₁₃×#2043	2
C₂×C₁₃×#336	2
C₂×#2043	13

Subgroups — C2×C13×#2043 #15709842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2043 #15709842