Subgroups — C₁₃×#17350 #15703689

Order 3328.

1418 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2972	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1460	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1459	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1458	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#323	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₃	C₄	1	1	yes	characteristic
8	C₁₃×#518	—	2	8	no	—
9	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₈×D₄×C₁₃	—	2	8	no	—
20	C₁₃×#431	C₂²	1	4	yes	complemented
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	8	yes	complemented
22	C₁₃×#324	C₂²	1	4	yes	complemented
23	C₁₃×#323	C₂²	1	4	yes	—
24	C₁₃×#323	C₂²	1	8	yes	complemented
25	C₂⁵×C₁₃	C₂×C₄	1	2	yes	—
26	C₂²×D₄×C₁₃	—	2	4	no	—
27	C₂²×D₄×C₁₃	—	2	4	no	—
28	C₂²×D₄×C₁₃	C₈	1	8	yes	complemented
29	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃	—	2	8	no	—
38	C₄×D₄×C₁₃	—	2	4	no	—
39	C₄×D₄×C₁₃	—	2	8	no	—
40	C₄×D₄×C₁₃	—	2	4	no	—
41	C₄×D₄×C₁₃	—	2	8	no	—
42	C₄×D₄×C₁₃	—	2	4	no	—
43	C₄×D₄×C₁₃	D₄	1	8	yes	—
44	C₁₃×#117	—	2	4	no	—
45	C₁₃×#117	—	2	4	no	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊C₈	—	2	4	no	—
63	C₁₃×C₂²⋊C₈	—	2	8	no	—
64	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
65	C₄×C₈×C₁₃	—	2	4	no	—
66	#17350	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₃	—	2	4	no	—
68	C₂⁴×C₁₃	—	2	4	no	—
69	C₂⁴×C₁₃	—	8	2	no	—
70	C₂⁴×C₁₃	—	8	2	no	—
71	C₂⁴×C₁₃	C₂×C₈	1	8	yes	complemented
72	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
75	C₂×D₄×C₁₃	—	2	4	no	—
76	C₂×D₄×C₁₃	—	2	4	no	—
77	C₂×D₄×C₁₃	—	2	32	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
81	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
82	C₂×D₄×C₁₃	C₂×C₈	1	8	yes	complemented
83	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	complemented
84	C₂×D₄×C₁₃	M₁₆	1	4	yes	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₃	—	8	2	no	—
91	C₂²×C₄×C₁₃	—	8	2	no	—
92	C₂²×C₄×C₁₃	—	8	2	no	—
93	C₂²×C₄×C₁₃	—	8	2	no	—
94	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	complemented
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₁₃	—	2	8	no	—
105	C₂×C₈×C₁₃	—	8	8	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
110	C₁₃×C₂²⋊C₄	—	2	4	no	—
111	C₁₃×C₂²⋊C₄	—	2	4	no	—
112	C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₁₃×C₂²⋊C₄	—	2	4	no	—
114	C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₁₃×C₂²⋊C₄	—	2	4	no	—
116	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	—
117	C₄²×C₁₃	—	2	4	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×#518	C₂×C₁₃	1	1	yes	characteristic
121	#2972	C₂×C₁₃	1	2	yes	complemented
122	#1460	C₂×C₁₃	1	2	yes	complemented
123	#1459	C₂×C₁₃	1	4	yes	complemented
124	#1458	C₂×C₁₃	1	2	yes	complemented
125	C₂×#323	C₂×C₁₃	1	4	yes	complemented
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	16	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	—	4	1	no	—
137	C₂³×C₁₃	—	8	4	no	—
138	C₂³×C₁₃	—	8	4	no	—
139	C₂³×C₁₃	—	8	8	no	—
140	C₂³×C₁₃	—	8	8	no	—
141	C₂³×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
143	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
144	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
145	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
146	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
147	D₄×C₁₃	—	2	16	no	—
148	D₄×C₁₃	—	2	8	no	—
149	D₄×C₁₃	C₂²⋊C₈	1	16	yes	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	4	8	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	8	4	no	—
164	C₂×C₄×C₁₃	—	8	4	no	—
165	C₂×C₄×C₁₃	—	8	4	no	—
166	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
173	C₈×C₁₃	—	4	8	no	—
174	C₂³×D₄	C₄×C₁₃	1	1	yes	characteristic
175	#518	—	2	8	no	—
176	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
177	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
178	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×#117	C₄×C₁₃	1	1	yes	characteristic
183	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
186	C₈×D₄	—	2	8	no	—
187	#431	C₂²×C₁₃	1	4	yes	complemented
188	C₂×C₂²⋊C₈	C₂²×C₁₃	1	8	yes	complemented
189	#324	C₂²×C₁₃	1	4	yes	complemented
190	#323	C₂²×C₁₃	1	4	yes	—
191	#323	C₂²×C₁₃	1	8	yes	complemented
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	—	2	4	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	2	4	no	—
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	2	4	no	—
198	C₂²×C₁₃	—	4	4	no	—
199	C₂²×C₁₃	—	4	4	no	—
200	C₂²×C₁₃	—	4	2	no	—
201	C₂²×C₁₃	—	4	4	no	—
202	C₂²×C₁₃	—	4	4	no	—
203	C₂²×C₁₃	—	4	2	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	4	1	no	—
206	C₂²×C₁₃	—	4	2	no	—
207	C₂²×C₁₃	—	4	1	no	—
208	C₂²×C₁₃	—	8	16	no	—
209	C₂²×C₁₃	C₂×C₂²⋊C₈	1	8	yes	—
210	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
212	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	2	4	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	—	4	1	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	—	4	1	no	—
220	C₄×C₁₃	C₂×C₂²⋊C₈	1	4	yes	—
221	C₂⁵	C₂×C₄×C₁₃	1	2	yes	—
222	C₂²×D₄	—	2	4	no	—
223	C₂²×D₄	—	2	4	no	—
224	C₂²×D₄	C₈×C₁₃	1	8	yes	complemented
225	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
226	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
227	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
230	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
231	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
233	C₂²×C₈	—	2	8	no	—
234	C₄×D₄	—	2	4	no	—
235	C₄×D₄	—	2	8	no	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	—	2	8	no	—
238	C₄×D₄	—	2	4	no	—
239	C₄×D₄	D₄×C₁₃	1	8	yes	—
240	#117	—	2	4	no	—
241	#117	—	2	4	no	—
242	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	—	2	8	no	—
247	C₂×C₂²⋊C₄	—	2	8	no	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	C₄⋊C₈	—	2	4	no	—
259	C₂²⋊C₈	—	2	8	no	—
260	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
261	C₄×C₈	—	2	4	no	—
262	C₂×C₁₃	—	2	1	no	—
263	C₂×C₁₃	—	2	1	no	—
264	C₂×C₁₃	—	2	8	no	—
265	C₂×C₁₃	—	4	4	no	—
266	C₂×C₁₃	—	4	2	no	—
267	C₂×C₁₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
268	C₂×C₁₃	#2883	1	1	yes	characteristic
269	C₂×C₁₃	#2888	1	1	yes	characteristic
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	8	2	no	—
273	C₂⁴	—	8	2	no	—
274	C₂⁴	C₂×C₈×C₁₃	1	8	yes	complemented
275	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
276	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
277	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	32	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
284	C₂×D₄	C₂×C₈×C₁₃	1	4	yes	—
285	C₂×D₄	C₂×C₈×C₁₃	1	8	yes	complemented
286	C₂×D₄	C₂×C₈×C₁₃	1	4	yes	complemented
287	C₂×D₄	C₁₃×M₁₆	1	4	yes	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	8	2	no	—
294	C₂²×C₄	—	8	2	no	—
295	C₂²×C₄	—	8	2	no	—
296	C₂²×C₄	—	8	2	no	—
297	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	complemented
298	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
307	C₂×C₈	—	2	8	no	—
308	C₂×C₈	—	8	8	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	C₂×D₄×C₁₃	1	4	yes	—
323	C₁₃	#17350	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	—	2	1	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	16	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	8	4	no	—
336	C₂³	—	8	4	no	—
337	C₂³	—	8	8	no	—
338	C₂³	—	8	8	no	—
339	C₂³	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
340	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
341	C₂³	C₂²×C₈×C₁₃	1	4	yes	—
342	C₂³	C₂²×C₈×C₁₃	1	4	yes	—
343	C₂³	C₂×C₁₃×M₁₆	1	4	yes	—
344	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
345	D₄	—	2	16	no	—
346	D₄	—	2	8	no	—
347	D₄	C₁₃×C₂²⋊C₈	1	16	yes	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	8	4	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
365	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
366	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
367	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
368	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
369	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
371	C₈	—	4	8	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	8	16	no	—
389	C₂²	C₂×C₁₃×C₂²⋊C₈	1	8	yes	—
390	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
392	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	C₂×C₁₃×C₂²⋊C₈	1	4	yes	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	8	no	—
404	C₂	—	4	2	no	—
405	C₂	—	4	4	no	—
406	C₂	C₂²×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
407	C₂	C₁₃×#2883	1	1	yes	characteristic
408	C₂	C₁₃×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2972	C₂	semidirect
3. C₁₃×#1460	C₂	semidirect
4. C₁₃×#1459	C₂	semidirect
5. C₁₃×#1458	C₂	semidirect
6. C₂×C₁₃×#323	C₂	semidirect
20. C₁₃×#431	C₂²	semidirect
21. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
22. C₁₃×#324	C₂²	semidirect
24. C₁₃×#323	C₂²	semidirect
28. C₂²×D₄×C₁₃	C₈	semidirect
66. #17350	C₁₃	direct (N × H)
71. C₂⁴×C₁₃	C₂×C₈	semidirect
82. C₂×D₄×C₁₃	C₂×C₈	semidirect
83. C₂×D₄×C₁₃	C₂×C₈	semidirect
94. C₂²×C₄×C₁₃	C₂×C₈	semidirect
121. #2972	C₂×C₁₃	semidirect
122. #1460	C₂×C₁₃	semidirect
123. #1459	C₂×C₁₃	semidirect
124. #1458	C₂×C₁₃	semidirect
125. C₂×#323	C₂×C₁₃	semidirect
187. #431	C₂²×C₁₃	semidirect
188. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
189. #324	C₂²×C₁₃	semidirect
191. #323	C₂²×C₁₃	semidirect
224. C₂²×D₄	C₈×C₁₃	semidirect
274. C₂⁴	C₂×C₈×C₁₃	semidirect
285. C₂×D₄	C₂×C₈×C₁₃	semidirect
286. C₂×D₄	C₂×C₈×C₁₃	semidirect
297. C₂²×C₄	C₂×C₈×C₁₃	semidirect
323. C₁₃	#17350	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×#518	2
C₁₃×#2972	2
C₁₃×#1460	2
C₁₃×#1459	2
C₁₃×#1458	2
C₂×C₁₃×#323	2
#17350	13

Subgroups — C13×#17350 #15703689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17350 #15703689