Subgroups — C₂×C₁₃×#1549 #15704045

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 368 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	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1549	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#332	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₁₃	—	2	1	no	—
7	C₂²×C₁₃×M₁₆	—	2	1	no	—
8	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₄	1	4	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₄	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
16	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
17	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#431	—	2	2	no	—
20	C₁₃×#431	C₂²	1	4	yes	—
21	C₁₃×#423	—	2	2	no	—
22	C₁₃×#423	C₂²	1	4	yes	—
23	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₄×C₈×C₁₃	—	2	1	no	—
28	C₁₃×#332	C₂²	1	16	yes	complemented
29	C₂²×Q₈×C₁₃	—	2	4	no	—
30	C₂²×Q₈×C₁₃	—	2	2	no	—
31	C₂²×Q₈×C₁₃	—	2	4	no	—
32	C₂²×Q₈×C₁₃	—	2	2	no	—
33	C₂²×Q₈×C₁₃	—	4	8	no	—
34	C₂³×C₄×C₁₃	—	2	2	no	—
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂×C₁₃×M₁₆	—	2	4	no	—
39	C₂×C₁₃×M₁₆	—	4	4	no	—
40	C₂²×C₈×C₁₃	—	2	2	no	—
41	C₂²×C₈×C₁₃	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	—	2	4	no	—
43	C₁₃×C₄⋊Q₈	—	2	4	no	—
44	C₁₃×C₄⋊Q₈	—	2	4	no	—
45	C₁₃×C₄⋊Q₈	—	2	4	no	—
46	C₁₃×C₄⋊Q₈	—	2	2	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
51	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	2	yes	—
65	C₂×C₄²×C₁₃	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
68	C₁₃×C₄⋊C₈	—	2	4	no	—
69	C₁₃×C₄⋊C₈	—	2	2	no	—
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
73	C₁₃×C₂²⋊C₈	—	2	4	no	—
74	C₄×C₈×C₁₃	—	2	4	no	—
75	C₂×#1549	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	8	no	—
78	C₂×Q₈×C₁₃	—	2	4	no	—
79	C₂×Q₈×C₁₃	—	2	4	no	—
80	C₂×Q₈×C₁₃	—	4	8	no	—
81	C₂×Q₈×C₁₃	—	4	16	no	—
82	C₂×Q₈×C₁₃	—	4	16	no	—
83	C₂×Q₈×C₁₃	—	4	8	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	4	8	no	—
89	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
96	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₁₃×M₁₆	—	4	8	no	—
104	C₂×C₈×C₁₃	—	2	4	no	—
105	C₂×C₈×C₁₃	—	2	4	no	—
106	C₂×C₈×C₁₃	—	4	4	no	—
107	C₂×C₈×C₁₃	—	4	4	no	—
108	C₁₃×C₄⋊C₄	—	2	8	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	8	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
114	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
115	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
116	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂×D₄	1	2	yes	—
120	C₄²×C₁₃	C₂×D₄	1	2	yes	—
121	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
125	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
126	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
127	#1549	C₂×C₁₃	1	8	yes	direct product factor
128	C₂×#332	C₂×C₁₃	1	4	yes	complemented
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	#103	1	4	yes	—
132	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	Q₈×C₁₃	—	4	16	no	—
135	Q₈×C₁₃	—	4	8	no	—
136	Q₈×C₁₃	—	4	8	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	8	no	—
144	C₂×C₄×C₁₃	—	4	16	no	—
145	C₂×C₄×C₁₃	—	4	8	no	—
146	C₂×C₄×C₁₃	#101	1	4	yes	—
147	C₂×C₄×C₁₃	#103	1	8	yes	—
148	C₂×C₄×C₁₃	#103	1	4	yes	—
149	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
157	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
158	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
159	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₁₃	—	4	4	no	—
164	C₈×C₁₃	—	4	4	no	—
165	C₂³×Q₈	—	2	1	no	—
166	C₂²×M₁₆	—	2	1	no	—
167	C₂×C₄⋊Q₈	—	2	1	no	—
168	C₂×C₄⋊Q₈	—	2	1	no	—
169	C₂×C₄⋊Q₈	—	2	2	no	—
170	C₂×C₄⋊Q₈	—	2	2	no	—
171	C₂×C₄⋊Q₈	C₄×C₁₃	1	2	yes	—
172	C₂×C₄⋊Q₈	C₄×C₁₃	1	4	yes	—
173	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
174	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
175	C₂²×C₄⋊C₄	—	2	1	no	—
176	C₂²×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
177	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
178	#431	—	2	2	no	—
179	#431	C₂²×C₁₃	1	4	yes	—
180	#423	—	2	2	no	—
181	#423	C₂²×C₁₃	1	4	yes	—
182	C₂×C₄⋊C₈	—	2	1	no	—
183	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
185	C₂×C₂²⋊C₈	—	2	1	no	—
186	C₂×C₄×C₈	—	2	1	no	—
187	#332	C₂²×C₁₃	1	16	yes	complemented
188	C₂²×C₁₃	—	2	8	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	C₂×#101	1	2	yes	—
192	C₂²×C₁₃	C₂×#103	1	4	yes	—
193	C₂²×C₁₃	C₂×#103	1	2	yes	—
194	C₂²×C₁₃	#418	1	2	yes	—
195	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
196	C₄×C₁₃	—	2	1	no	—
197	C₄×C₁₃	—	2	1	no	—
198	C₄×C₁₃	—	2	2	no	—
199	C₄×C₁₃	—	4	8	no	—
200	C₄×C₁₃	C₂×#101	1	4	yes	—
201	C₄×C₁₃	C₂×#103	1	2	yes	—
202	C₄×C₁₃	C₂×#103	1	4	yes	—
203	C₄×C₁₃	#418	1	2	yes	—
204	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
205	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
206	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
207	C₂²×Q₈	—	2	4	no	—
208	C₂²×Q₈	—	2	2	no	—
209	C₂²×Q₈	—	2	4	no	—
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×Q₈	—	4	8	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
214	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
216	C₂×M₁₆	—	2	4	no	—
217	C₂×M₁₆	—	4	4	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	2	2	no	—
220	C₄⋊Q₈	—	2	4	no	—
221	C₄⋊Q₈	—	2	4	no	—
222	C₄⋊Q₈	—	2	4	no	—
223	C₄⋊Q₈	—	2	4	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	4	no	—
227	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
228	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
229	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
238	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
240	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₁₃	1	2	yes	—
243	C₂×C₄²	D₄×C₁₃	1	2	yes	—
244	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
246	C₄⋊C₈	—	2	4	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
250	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
251	C₂²⋊C₈	—	2	4	no	—
252	C₄×C₈	—	2	4	no	—
253	C₂×C₁₃	—	2	4	no	—
254	C₂×C₁₃	#1549	1	4	yes	direct product factor
255	C₂×C₁₃	C₂²×#101	1	1	yes	characteristic
256	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
257	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
258	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×Q₈	—	2	8	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	4	8	no	—
263	C₂×Q₈	—	4	16	no	—
264	C₂×Q₈	—	4	16	no	—
265	C₂×Q₈	—	4	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	8	no	—
271	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
273	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
274	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
276	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
278	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
285	M₁₆	—	4	8	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
296	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
297	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
298	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
299	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
300	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
301	C₄²	C₂×D₄×C₁₃	1	2	yes	—
302	C₄²	C₂×D₄×C₁₃	1	2	yes	—
303	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
306	C₁₃	C₂×#1549	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₁₃×#103	1	4	yes	—
310	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
311	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
312	Q₈	—	4	16	no	—
313	Q₈	—	4	8	no	—
314	Q₈	—	4	8	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	C₁₃×#101	1	4	yes	—
325	C₂×C₄	C₁₃×#103	1	8	yes	—
326	C₂×C₄	C₁₃×#103	1	4	yes	—
327	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
328	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
330	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
331	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
334	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
335	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
336	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
337	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
338	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
341	C₈	—	4	4	no	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	C₂×C₁₃×#101	1	2	yes	—
347	C₂²	C₂×C₁₃×#103	1	4	yes	—
348	C₂²	C₂×C₁₃×#103	1	2	yes	—
349	C₂²	C₁₃×#418	1	2	yes	—
350	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	2	no	—
354	C₄	—	4	8	no	—
355	C₄	C₂×C₁₃×#101	1	4	yes	—
356	C₄	C₂×C₁₃×#103	1	2	yes	—
357	C₄	C₂×C₁₃×#103	1	4	yes	—
358	C₄	C₁₃×#418	1	2	yes	—
359	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
360	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
361	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
362	C₂	—	2	4	no	—
363	C₂	C₁₃×#1549	1	4	yes	direct product factor
364	C₂	C₂²×C₁₃×#101	1	1	yes	characteristic
365	C₂	C₂²×C₁₃×#103	1	1	yes	characteristic
366	C₂	C₂×C₁₃×#418	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1549	C₂	direct (N × H)
5. C₂×C₁₃×#332	C₂	semidirect
28. C₁₃×#332	C₂²	semidirect
75. C₂×#1549	C₁₃	direct (N × H)
127. #1549	C₂×C₁₃	direct (N × H)
128. C₂×#332	C₂×C₁₃	semidirect
187. #332	C₂²×C₁₃	semidirect
254. C₂×C₁₃	#1549	direct (N × H)
306. C₁₃	C₂×#1549	direct (N × H)
363. C₂	C₁₃×#1549	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
C₂×C₁₃×#431	2
C₂×C₁₃×#423	2
C₁₃×#1549	2
C₂×C₁₃×#332	2
C₂×#1549	13

Subgroups — C2×C13×#1549 #15704045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1549 #15704045