Subgroups — C₁₃×#21066 #15707405

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2310	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1928	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1927	C₂	1	4	yes	maximal, complemented
8	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#427	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₁₃×#419	—	2	4	no	—
21	C₂×C₁₃×#103	C₄	1	8	yes	complemented
22	C₂×C₁₃×#103	C₂²	1	4	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₁₃×#391	—	2	2	no	—
26	C₁₃×#391	C₂²	1	4	yes	—
27	C₁₃×#381	—	2	2	no	—
28	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
30	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
31	C₁₃×#340	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₁₃	—	2	1	no	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	—	2	2	no	—
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#117	—	2	2	no	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	D₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	4	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₁₃×#107	—	2	4	no	—
75	C₁₃×#106	—	2	4	no	—
76	C₁₃×#103	—	2	8	no	—
77	C₁₃×#103	C₂×C₄	1	8	yes	—
78	C₁₃×#103	C₂×C₄	1	8	yes	—
79	C₁₃×#95	—	2	4	no	—
80	C₁₃×#95	—	2	8	no	—
81	#21066	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	8	no	—
86	C₂×Q₈×C₁₃	—	2	8	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	4	4	no	—
94	C₂×Q₈×C₁₃	—	4	4	no	—
95	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	—	8	2	no	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	#41	1	2	yes	—
110	C₂²×C₄×C₁₃	#41	1	2	yes	—
111	C₂²×C₄×C₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₃	#41	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×M₁₆	—	4	4	no	—
115	C₂×C₈×C₁₃	—	2	8	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
132	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
133	C₁₃×C₂²⋊C₄	—	2	4	no	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₄²×C₁₃	—	2	4	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	4	2	no	—
140	C₄²×C₁₃	—	8	4	no	—
141	C₂×#427	C₂×C₁₃	1	1	yes	characteristic
142	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
143	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic
144	#2310	C₂×C₁₃	1	1	yes	characteristic
145	#2274	C₂×C₁₃	1	1	yes	characteristic
146	#1928	C₂×C₁₃	1	4	yes	complemented
147	#1927	C₂×C₁₃	1	4	yes	complemented
148	#1736	C₂×C₁₃	1	1	yes	characteristic
149	#1729	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	C₄×D₄	1	2	yes	—
153	C₂³×C₁₃	#121	1	2	yes	—
154	C₂³×C₁₃	#123	1	2	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	2	4	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	4	8	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	8	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	8	4	no	—
177	C₂×C₄×C₁₃	#117	1	4	yes	—
178	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
179	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₁₃	#121	1	2	yes	—
181	C₂×C₄×C₁₃	#123	1	2	yes	—
182	C₂×C₄×C₁₃	#124	1	4	yes	—
183	C₂×C₄×C₁₃	#126	1	4	yes	—
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	4	2	no	—
193	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
195	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
200	#427	—	2	4	no	—
201	C₂×#107	C₂²×C₁₃	1	2	yes	—
202	C₂×#106	C₂²×C₁₃	1	2	yes	—
203	#419	—	2	4	no	—
204	C₂×#103	C₄×C₁₃	1	8	yes	complemented
205	C₂×#103	C₂²×C₁₃	1	4	yes	—
206	C₂×#103	C₂²×C₁₃	1	2	yes	—
207	C₂×#103	C₂²×C₁₃	1	2	yes	—
208	#391	—	2	2	no	—
209	#391	C₂²×C₁₃	1	4	yes	—
210	#381	—	2	2	no	—
211	C₄×C₄⋊C₄	—	2	2	no	—
212	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
213	C₄×C₂²⋊C₄	—	2	2	no	—
214	#340	C₂²×C₁₃	1	4	yes	—
215	#336	C₂²×C₁₃	1	2	yes	—
216	#336	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	2	4	no	—
221	C₂²×C₁₃	#388	1	4	yes	—
222	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
225	C₂²×C₁₃	#577	1	2	yes	—
226	C₂²×C₁₃	#578	1	2	yes	—
227	C₄×C₁₃	—	4	4	no	—
228	C₄×C₁₃	—	4	4	no	—
229	C₄×C₁₃	—	4	4	no	—
230	C₄×C₁₃	—	4	4	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	#388	1	4	yes	—
233	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
234	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
236	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	—	2	2	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	—
244	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
254	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	D₄×C₁₃	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
266	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	4	no	—
276	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
277	#107	—	2	4	no	—
278	#106	—	2	4	no	—
279	#103	—	2	8	no	—
280	#103	C₂×C₄×C₁₃	1	8	yes	—
281	#103	C₂×C₄×C₁₃	1	8	yes	—
282	#95	—	2	4	no	—
283	#95	—	2	8	no	—
284	C₂×C₁₃	—	2	4	no	—
285	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
286	C₂×C₁₃	#2949	1	1	yes	characteristic
287	C₂×C₁₃	#2950	1	1	yes	characteristic
288	C₂×C₁₃	#3046	1	2	yes	—
289	C₂×C₁₃	#3097	1	2	yes	—
290	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	8	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
317	C₂²×C₄	C₁₃×#41	1	2	yes	—
318	C₂²×C₄	C₁₃×#41	1	2	yes	—
319	C₂²×C₄	C₁₃×#41	1	2	yes	—
320	C₂²×C₄	C₁₃×#41	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
322	M₁₆	—	4	4	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
340	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	—	8	4	no	—
349	C₁₃	#21066	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	C₄×D₄×C₁₃	1	2	yes	—
353	C₂³	C₁₃×#121	1	2	yes	—
354	C₂³	C₁₃×#123	1	2	yes	—
355	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	2	4	no	—
358	Q₈	—	4	8	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	8	4	no	—
377	C₂×C₄	C₁₃×#117	1	4	yes	—
378	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
379	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
380	C₂×C₄	C₁₃×#121	1	2	yes	—
381	C₂×C₄	C₁₃×#123	1	2	yes	—
382	C₂×C₄	C₁₃×#124	1	4	yes	—
383	C₂×C₄	C₁₃×#126	1	4	yes	—
384	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	2	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	C₁₃×#388	1	4	yes	—
398	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
399	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
400	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
401	C₂²	C₁₃×#577	1	2	yes	—
402	C₂²	C₁₃×#578	1	2	yes	—
403	C₄	—	4	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	8	2	no	—
408	C₄	C₁₃×#388	1	4	yes	—
409	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
410	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
412	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
413	C₂	—	2	4	no	—
414	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
415	C₂	C₁₃×#2949	1	1	yes	characteristic
416	C₂	C₁₃×#2950	1	1	yes	characteristic
417	C₂	C₁₃×#3046	1	2	yes	—
418	C₂	C₁₃×#3097	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₃×#1928	C₂	semidirect
7. C₁₃×#1927	C₂	semidirect
21. C₂×C₁₃×#103	C₄	semidirect
81. #21066	C₁₃	direct (N × H)
146. #1928	C₂×C₁₃	semidirect
147. #1927	C₂×C₁₃	semidirect
204. C₂×#103	C₄×C₁₃	semidirect
349. C₁₃	#21066	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×#427	2
C₂×C₁₃×#419	2
C₂²×C₁₃×#103	2
C₁₃×#2310	2
C₁₃×#2274	2
C₁₃×#1928	2
C₁₃×#1927	2
C₁₃×#1736	2
C₁₃×#1729	2
#21066	13

Subgroups — C13×#21066 #15707405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21066 #15707405