Subgroups — C₂×C₁₃×#1546 #15704041

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 376 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×#1546	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	4	no	—
34	C₂²×Q₈×C₁₃	—	4	4	no	—
35	C₂³×C₄×C₁₃	—	2	2	no	—
36	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂×C₁₃×M₁₆	—	2	4	no	—
40	C₂×C₁₃×M₁₆	—	4	4	no	—
41	C₂²×C₈×C₁₃	—	2	2	no	—
42	C₂²×C₈×C₁₃	—	2	2	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	4	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
52	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃	D₄	1	2	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₁₃×C₄⋊C₈	—	2	4	no	—
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
73	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
74	C₁₃×C₂²⋊C₈	—	2	4	no	—
75	C₄×C₈×C₁₃	—	2	4	no	—
76	C₂×#1546	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₃	—	2	8	no	—
79	C₂×Q₈×C₁₃	—	2	4	no	—
80	C₂×Q₈×C₁₃	—	2	4	no	—
81	C₂×Q₈×C₁₃	—	4	16	no	—
82	C₂×Q₈×C₁₃	—	4	8	no	—
83	C₂×Q₈×C₁₃	—	4	4	no	—
84	C₂×Q₈×C₁₃	—	4	8	no	—
85	C₂×Q₈×C₁₃	—	4	8	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	4	8	no	—
92	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	D₈	1	4	yes	—
99	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₁₃×M₁₆	—	4	8	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₂×C₈×C₁₃	—	2	4	no	—
109	C₂×C₈×C₁₃	—	4	4	no	—
110	C₂×C₈×C₁₃	—	4	4	no	—
111	C₁₃×C₄⋊C₄	—	2	8	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	8	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
117	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂×D₄	1	2	yes	—
123	C₄²×C₁₃	C₂×D₄	1	2	yes	—
124	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
128	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
129	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
130	#1546	C₂×C₁₃	1	8	yes	direct product factor
131	C₂×#332	C₂×C₁₃	1	4	yes	complemented
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	#102	1	4	yes	—
135	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	Q₈×C₁₃	—	4	4	no	—
138	Q₈×C₁₃	—	4	4	no	—
139	Q₈×C₁₃	—	4	8	no	—
140	Q₈×C₁₃	—	4	16	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	8	no	—
148	C₂×C₄×C₁₃	—	4	16	no	—
149	C₂×C₄×C₁₃	—	4	8	no	—
150	C₂×C₄×C₁₃	#101	1	4	yes	—
151	C₂×C₄×C₁₃	#102	1	8	yes	—
152	C₂×C₄×C₁₃	#102	1	4	yes	—
153	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
161	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
162	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₁₃	#137	1	4	yes	—
164	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₈×C₁₃	—	4	4	no	—
168	C₈×C₁₃	—	4	4	no	—
169	C₂³×Q₈	—	2	1	no	—
170	C₂²×M₁₆	—	2	1	no	—
171	C₂×C₄⋊Q₈	—	2	1	no	—
172	C₂×C₄⋊Q₈	—	2	1	no	—
173	C₂×C₄⋊Q₈	—	2	2	no	—
174	C₂×C₄⋊Q₈	—	2	2	no	—
175	C₂×C₄⋊Q₈	C₄×C₁₃	1	2	yes	—
176	C₂×C₄⋊Q₈	C₄×C₁₃	1	4	yes	—
177	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
178	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
179	C₂²×C₄⋊C₄	—	2	1	no	—
180	C₂²×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
181	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
182	#431	—	2	2	no	—
183	#431	C₂²×C₁₃	1	4	yes	—
184	#423	—	2	2	no	—
185	#423	C₂²×C₁₃	1	4	yes	—
186	C₂×C₄⋊C₈	—	2	1	no	—
187	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
189	C₂×C₂²⋊C₈	—	2	1	no	—
190	C₂×C₄×C₈	—	2	1	no	—
191	#332	C₂²×C₁₃	1	16	yes	complemented
192	C₂²×C₁₃	—	2	8	no	—
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	—	2	2	no	—
195	C₂²×C₁₃	C₂×#101	1	2	yes	—
196	C₂²×C₁₃	C₂×#102	1	4	yes	—
197	C₂²×C₁₃	C₂×#102	1	2	yes	—
198	C₂²×C₁₃	#419	1	2	yes	—
199	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	4	8	no	—
204	C₄×C₁₃	C₂×#101	1	4	yes	—
205	C₄×C₁₃	C₂×#102	1	2	yes	—
206	C₄×C₁₃	C₂×#102	1	4	yes	—
207	C₄×C₁₃	#419	1	2	yes	—
208	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
209	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
210	C₄×C₁₃	C₂×#137	1	2	yes	—
211	C₂²×Q₈	—	2	4	no	—
212	C₂²×Q₈	—	2	2	no	—
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	4	4	no	—
216	C₂²×Q₈	—	4	4	no	—
217	C₂³×C₄	—	2	2	no	—
218	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	—	4	4	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	4	no	—
226	C₄⋊Q₈	—	2	4	no	—
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	—	2	4	no	—
229	C₄⋊Q₈	—	2	2	no	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
233	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
234	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
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	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
243	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
245	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₁₃	1	2	yes	—
248	C₂×C₄²	D₄×C₁₃	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
255	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₄×C₈	—	2	4	no	—
258	C₂×C₁₃	—	2	4	no	—
259	C₂×C₁₃	#1546	1	4	yes	direct product factor
260	C₂×C₁₃	C₂²×#101	1	1	yes	characteristic
261	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
262	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
263	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×Q₈	—	2	8	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	4	16	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	—	4	4	no	—
270	C₂×Q₈	—	4	8	no	—
271	C₂×Q₈	—	4	8	no	—
272	C₂×Q₈	—	4	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
280	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
281	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
283	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	C₁₃×D₈	1	4	yes	—
285	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	M₁₆	—	4	8	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	—	4	4	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
303	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
304	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
305	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
306	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
307	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₁₃	1	2	yes	—
309	C₄²	C₂×D₄×C₁₃	1	2	yes	—
310	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
313	C₁₃	C₂×#1546	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₁₃×#102	1	4	yes	—
317	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
318	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
319	Q₈	—	4	8	no	—
320	Q₈	—	4	16	no	—
321	Q₈	—	4	4	no	—
322	Q₈	—	4	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	16	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₁₃×#101	1	4	yes	—
333	C₂×C₄	C₁₃×#102	1	8	yes	—
334	C₂×C₄	C₁₃×#102	1	4	yes	—
335	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
336	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
338	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
339	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
342	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
343	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
344	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
345	C₂×C₄	C₁₃×#137	1	4	yes	—
346	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
349	C₈	—	4	4	no	—
350	C₈	—	4	4	no	—
351	C₂²	—	2	8	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₂×C₁₃×#101	1	2	yes	—
355	C₂²	C₂×C₁₃×#102	1	4	yes	—
356	C₂²	C₂×C₁₃×#102	1	2	yes	—
357	C₂²	C₁₃×#419	1	2	yes	—
358	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×C₁₃×#101	1	4	yes	—
364	C₄	C₂×C₁₃×#102	1	2	yes	—
365	C₄	C₂×C₁₃×#102	1	4	yes	—
366	C₄	C₁₃×#419	1	2	yes	—
367	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
368	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
369	C₄	C₂×C₁₃×#137	1	2	yes	—
370	C₂	—	2	4	no	—
371	C₂	C₁₃×#1546	1	4	yes	direct product factor
372	C₂	C₂²×C₁₃×#101	1	1	yes	characteristic
373	C₂	C₂²×C₁₃×#102	1	1	yes	characteristic
374	C₂	C₂×C₁₃×#419	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×#1546	C₂	direct (N × H)
5. C₂×C₁₃×#332	C₂	semidirect
28. C₁₃×#332	C₂²	semidirect
76. C₂×#1546	C₁₃	direct (N × H)
130. #1546	C₂×C₁₃	direct (N × H)
131. C₂×#332	C₂×C₁₃	semidirect
191. #332	C₂²×C₁₃	semidirect
259. C₂×C₁₃	#1546	direct (N × H)
313. C₁₃	C₂×#1546	direct (N × H)
371. C₂	C₁₃×#1546	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×#1546	2
C₂×C₁₃×#332	2
C₂×#1546	13

Subgroups — C2×C13×#1546 #15704041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1546 #15704041