Subgroups — C₁₃×#2704 #13111762

Order 1664.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#396	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#396	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#388	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#388	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#385	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#380	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#125	—	2	4	no	—
19	C₁₃×C₂²⋊Q₈	—	2	4	no	—
20	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₁₃×#95	C₂²	1	1	yes	characteristic
46	C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₁₃×#95	C₂²	1	1	yes	characteristic
48	C₁₃×#95	C₂²	1	1	yes	characteristic
49	C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₁₃×#95	C₂²	1	1	yes	characteristic
51	C₁₃×#95	C₂²	1	1	yes	characteristic
52	C₁₃×#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×Q₈×C₁₃	—	2	2	no	—
55	C₂×Q₈×C₁₃	—	2	2	no	—
56	C₂×Q₈×C₁₃	—	4	1	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	—	4	1	no	—
60	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₁₃×C₄⋊C₄	—	4	1	no	—
83	C₁₃×C₄⋊C₄	—	4	1	no	—
84	C₁₃×C₄⋊C₄	—	4	1	no	—
85	C₁₃×C₄⋊C₄	—	4	1	no	—
86	C₁₃×C₄⋊C₄	—	4	1	no	—
87	C₁₃×C₄⋊C₄	—	4	1	no	—
88	C₁₃×C₄⋊C₄	D₄	1	4	yes	—
89	C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₁₃×C₂²⋊C₄	—	4	1	no	—
92	C₁₃×C₂²⋊C₄	—	4	1	no	—
93	C₁₃×C₂²⋊C₄	—	4	1	no	—
94	C₁₃×C₂²⋊C₄	Q₈	1	4	yes	complemented
95	C₄²×C₁₃	—	2	2	no	—
96	C₄²×C₁₃	—	4	1	no	—
97	#2704	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂³×C₁₃	—	2	1	no	—
99	C₂³×C₁₃	—	2	1	no	—
100	C₂³×C₁₃	—	2	1	no	—
101	C₂³×C₁₃	—	2	1	no	—
102	C₂³×C₁₃	—	2	1	no	—
103	C₂³×C₁₃	—	2	1	no	—
104	C₂³×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
106	Q₈×C₁₃	—	4	4	no	—
107	C₂×C₄×C₁₃	—	2	1	no	—
108	C₂×C₄×C₁₃	—	2	1	no	—
109	C₂×C₄×C₁₃	—	2	1	no	—
110	C₂×C₄×C₁₃	—	2	1	no	—
111	C₂×C₄×C₁₃	—	2	1	no	—
112	C₂×C₄×C₁₃	—	2	1	no	—
113	C₂×C₄×C₁₃	—	2	1	no	—
114	C₂×C₄×C₁₃	—	2	1	no	—
115	C₂×C₄×C₁₃	—	2	1	no	—
116	C₂×C₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	1	no	—
119	C₂×C₄×C₁₃	—	2	1	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	1	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	1	no	—
125	C₂×C₄×C₁₃	—	2	1	no	—
126	C₂×C₄×C₁₃	—	2	1	no	—
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	1	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	4	4	no	—
144	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
148	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
149	C₂×C₄×C₁₃	#41	1	2	yes	—
150	C₂×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
152	#398	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#398	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#398	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#396	C₂×C₁₃	1	1	yes	characteristic
156	#396	C₂×C₁₃	1	1	yes	characteristic
157	#395	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#391	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#389	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#389	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#388	C₂×C₁₃	1	1	yes	characteristic
162	#388	C₂×C₁₃	1	1	yes	characteristic
163	#385	C₂×C₁₃	1	1	yes	characteristic
164	#380	C₂×C₁₃	1	1	yes	characteristic
165	C₂²×C₁₃	—	2	2	no	—
166	C₂²×C₁₃	—	2	2	no	—
167	C₂²×C₁₃	—	2	2	no	—
168	C₂²×C₁₃	—	4	1	no	—
169	C₂²×C₁₃	—	4	1	no	—
170	C₂²×C₁₃	—	4	1	no	—
171	C₂²×C₁₃	—	4	1	no	—
172	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
179	C₄×C₁₃	—	2	2	no	—
180	C₄×C₁₃	—	2	2	no	—
181	C₄×C₁₃	—	2	2	no	—
182	C₄×C₁₃	—	2	2	no	—
183	C₄×C₁₃	—	2	2	no	—
184	C₄×C₁₃	—	2	2	no	—
185	C₄×C₁₃	—	4	1	no	—
186	C₄×C₁₃	—	4	1	no	—
187	C₄×C₁₃	—	4	1	no	—
188	C₄×C₁₃	—	4	1	no	—
189	C₄×C₁₃	—	4	1	no	—
190	C₄×C₁₃	—	4	1	no	—
191	C₄×C₁₃	—	4	1	no	—
192	C₄×C₁₃	—	4	1	no	—
193	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
195	#125	—	2	4	no	—
196	C₂²⋊Q₈	—	2	4	no	—
197	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
220	#95	C₂²×C₁₃	1	1	yes	characteristic
221	#95	C₂²×C₁₃	1	1	yes	characteristic
222	#95	C₂²×C₁₃	1	1	yes	characteristic
223	#95	C₂²×C₁₃	1	1	yes	characteristic
224	#95	C₂²×C₁₃	1	1	yes	characteristic
225	#95	C₂²×C₁₃	1	1	yes	characteristic
226	#95	C₂²×C₁₃	1	1	yes	characteristic
227	#95	C₂²×C₁₃	1	1	yes	characteristic
228	#95	C₂²×C₁₃	1	1	yes	characteristic
229	#95	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₁₃	—	4	2	no	—
231	C₂×C₁₃	#537	1	1	yes	characteristic
232	C₂×C₁₃	#541	1	1	yes	characteristic
233	C₂×C₁₃	#544	1	1	yes	characteristic
234	C₂×C₁₃	#546	1	1	yes	characteristic
235	C₂×C₁₃	D₄×Q₈	1	1	yes	characteristic
236	C₂×C₁₃	#554	1	1	yes	characteristic
237	C₂×C₁₃	#562	1	1	yes	characteristic
238	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	4	1	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	4	1	no	—
245	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	4	1	no	—
268	C₄⋊C₄	—	4	1	no	—
269	C₄⋊C₄	—	4	1	no	—
270	C₄⋊C₄	—	4	1	no	—
271	C₄⋊C₄	—	4	1	no	—
272	C₄⋊C₄	—	4	1	no	—
273	C₄⋊C₄	D₄×C₁₃	1	4	yes	—
274	C₂²⋊C₄	—	2	2	no	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₂²⋊C₄	—	4	1	no	—
277	C₂²⋊C₄	—	4	1	no	—
278	C₂²⋊C₄	—	4	1	no	—
279	C₂²⋊C₄	Q₈×C₁₃	1	4	yes	complemented
280	C₄²	—	2	2	no	—
281	C₄²	—	4	1	no	—
282	C₁₃	#2704	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³	—	2	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	C₂×Q₈×C₁₃	1	2	yes	—
290	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
291	Q₈	—	4	4	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
331	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
332	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
333	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
334	C₂×C₄	C₁₃×#41	1	2	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	4	1	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
343	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
344	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
345	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
348	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₂	—	4	2	no	—
364	C₂	C₁₃×#537	1	1	yes	characteristic
365	C₂	C₁₃×#541	1	1	yes	characteristic
366	C₂	C₁₃×#544	1	1	yes	characteristic
367	C₂	C₁₃×#546	1	1	yes	characteristic
368	C₂	D₄×Q₈×C₁₃	1	1	yes	characteristic
369	C₂	C₁₃×#554	1	1	yes	characteristic
370	C₂	C₁₃×#562	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#125	C₂	semidirect
3. C₁₃×#398	C₂	semidirect
4. C₁₃×#398	C₂	semidirect
5. C₁₃×#398	C₂	semidirect
8. C₁₃×#395	C₂	semidirect
9. C₁₃×#391	C₂	semidirect
10. C₁₃×#389	C₂	semidirect
11. C₁₃×#389	C₂	semidirect
94. C₁₃×C₂²⋊C₄	Q₈	semidirect
97. #2704	C₁₃	direct (N × H)
150. C₂×#125	C₂×C₁₃	semidirect
152. #398	C₂×C₁₃	semidirect
153. #398	C₂×C₁₃	semidirect
154. #398	C₂×C₁₃	semidirect
157. #395	C₂×C₁₃	semidirect
158. #391	C₂×C₁₃	semidirect
159. #389	C₂×C₁₃	semidirect
160. #389	C₂×C₁₃	semidirect
279. C₂²⋊C₄	Q₈×C₁₃	semidirect
282. C₁₃	#2704	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#125	2
C₂×C₁₃×C₂²⋊Q₈	2
C₁₃×#398	2
C₁₃×#396	2
C₁₃×#395	2
C₁₃×#391	2
C₁₃×#389	2
C₁₃×#388	2
C₁₃×#385	2
C₁₃×#380	2
#2704	13

Subgroups — C13×#2704 #13111762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2704 #13111762