Subgroups — C₁₃×#25862 #15712201

Order 3328.

1334 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×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2042	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1788	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₁₃×#532	—	2	4	no	—
12	C₁₃×#532	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#124	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	—	2	2	no	—
18	C₂×C₄×D₄×C₁₃	—	2	2	no	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#491	—	2	4	no	—
21	C₁₃×#490	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	4	yes	—
23	C₂×C₁₃×#103	C₂²	1	4	yes	—
24	C₂×C₁₃×#102	C₂²	1	4	yes	—
25	C₂×C₁₃×#102	C₂²	1	4	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#387	—	2	2	no	—
31	C₁₃×#385	—	2	2	no	—
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#380	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂×C₁₃×#41	—	2	4	no	—
36	C₂×C₁₃×#41	—	2	4	no	—
37	C₂×C₁₃×#41	—	2	8	no	—
38	C₂×C₁₃×#41	—	4	4	no	—
39	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	D₄	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
50	C₁₃×#127	—	2	2	no	—
51	C₁₃×#127	D₄	1	4	yes	—
52	C₁₃×#125	—	2	2	no	—
53	C₁₃×#125	—	2	2	no	—
54	C₁₃×#124	—	2	4	no	—
55	C₁₃×#124	—	2	4	no	—
56	C₁₃×#121	—	2	16	no	—
57	C₄×D₄×C₁₃	—	2	16	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#103	—	2	8	no	—
71	C₁₃×#103	—	4	4	no	—
72	C₁₃×#102	—	2	8	no	—
73	C₁₃×#102	—	4	4	no	—
74	C₁₃×C₂²⋊C₈	—	2	4	no	—
75	C₁₃×#97	—	2	2	no	—
76	C₁₃×#97	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	#25862	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	2	no	—
82	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₁₃×#41	—	4	16	no	—
84	C₁₃×#41	—	4	16	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	4	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
89	C₂×D₄×C₁₃	—	2	8	no	—
90	C₂×D₄×C₁₃	—	2	8	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	4	no	—
93	C₂×D₄×C₁₃	—	2	4	no	—
94	C₂×D₄×C₁₃	—	4	4	no	—
95	C₂×D₄×C₁₃	—	4	4	no	—
96	C₂×D₄×C₁₃	—	4	4	no	—
97	C₂×D₄×C₁₃	—	4	4	no	—
98	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	8	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	8	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₂²⋊C₄	—	2	16	no	—
129	C₁₃×C₂²⋊C₄	—	4	4	no	—
130	C₄²×C₁₃	—	2	4	no	—
131	C₄²×C₁₃	—	2	1	no	—
132	C₄²×C₁₃	—	2	1	no	—
133	C₄²×C₁₃	C₂×D₄	1	2	yes	—
134	C₄²×C₁₃	C₂×D₄	1	2	yes	—
135	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
136	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2851	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2042	C₂×C₁₃	1	4	yes	complemented
140	#1961	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#1960	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#1788	C₂×C₁₃	1	4	yes	complemented
143	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	2	1	no	—
145	C₂³×C₁₃	—	2	1	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	4	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	4	no	—
152	C₂³×C₁₃	—	4	4	no	—
153	C₂³×C₁₃	#124	1	2	yes	—
154	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₁₃	—	2	8	no	—
156	Q₈×C₁₃	—	4	4	no	—
157	D₄×C₁₃	—	2	8	no	—
158	D₄×C₁₃	—	4	16	no	—
159	D₄×C₁₃	—	4	16	no	—
160	D₄×C₁₃	—	4	4	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	—	4	16	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	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	#120	1	4	yes	—
182	C₂×C₄×C₁₃	#124	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
187	C₈×C₁₃	—	4	2	no	—
188	C₈×C₁₃	—	4	2	no	—
189	C₂²×#41	C₂²×C₁₃	1	2	yes	—
190	#532	—	2	4	no	—
191	#532	—	2	4	no	—
192	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#124	C₂²×C₁₃	1	2	yes	—
196	C₂×#121	—	2	2	no	—
197	C₂×C₄×D₄	—	2	2	no	—
198	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
199	#491	—	2	4	no	—
200	#490	—	2	4	no	—
201	C₂×#103	C₂²×C₁₃	1	4	yes	—
202	C₂×#103	C₂²×C₁₃	1	4	yes	—
203	C₂×#102	C₂²×C₁₃	1	4	yes	—
204	C₂×#102	C₂²×C₁₃	1	4	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
206	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
208	#389	C₂²×C₁₃	1	2	yes	—
209	#387	—	2	2	no	—
210	#385	—	2	2	no	—
211	#382	C₂²×C₁₃	1	1	yes	characteristic
212	#380	C₂²×C₁₃	1	2	yes	—
213	#336	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	4	2	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	8	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	4	no	—
224	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
226	C₂²×C₁₃	#535	1	1	yes	characteristic
227	C₂²×C₁₃	#575	1	2	yes	—
228	C₂²×C₁₃	#575	1	2	yes	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	2	no	—
235	C₄×C₁₃	#546	1	2	yes	—
236	C₄×C₁₃	#546	1	2	yes	—
237	C₂×#41	—	2	4	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	8	no	—
240	C₂×#41	—	4	4	no	—
241	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	D₄×C₁₃	1	2	yes	—
247	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
252	#127	—	2	2	no	—
253	#127	D₄×C₁₃	1	4	yes	—
254	#125	—	2	2	no	—
255	#125	—	2	2	no	—
256	#124	—	2	4	no	—
257	#124	—	2	4	no	—
258	#121	—	2	16	no	—
259	C₄×D₄	—	2	16	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	4	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	D₄×C₁₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	#103	—	2	8	no	—
273	#103	—	4	4	no	—
274	#102	—	2	8	no	—
275	#102	—	4	4	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	#97	—	2	2	no	—
278	#97	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂×C₁₃	—	4	2	no	—
283	C₂×C₁₃	—	8	4	no	—
284	C₂×C₁₃	#2435	1	1	yes	characteristic
285	C₂×C₁₃	#3005	1	2	yes	—
286	C₂×C₁₃	#3135	1	1	yes	characteristic
287	C₂×C₁₃	#3142	1	1	yes	characteristic
288	C₂×C₁₃	#3219	1	2	yes	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
291	#41	—	4	16	no	—
292	#41	—	4	16	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₁₃×#41	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	2	16	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	C₂×D₄×C₁₃	1	2	yes	—
342	C₄²	C₂×D₄×C₁₃	1	2	yes	—
343	C₁₃	#25862	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	4	no	—
353	C₂³	C₁₃×#124	1	2	yes	—
354	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	Q₈	—	2	8	no	—
356	Q₈	—	4	4	no	—
357	D₄	—	2	8	no	—
358	D₄	—	4	16	no	—
359	D₄	—	4	16	no	—
360	D₄	—	4	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	16	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	C₁₃×#120	1	4	yes	—
382	C₂×C₄	C₁₃×#124	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
386	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	4	no	—
399	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
400	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
401	C₂²	C₁₃×#535	1	1	yes	characteristic
402	C₂²	C₁₃×#575	1	2	yes	—
403	C₂²	C₁₃×#575	1	2	yes	—
404	C₄	—	2	2	no	—
405	C₄	—	2	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	C₁₃×#546	1	2	yes	—
411	C₄	C₁₃×#546	1	2	yes	—
412	C₂	—	4	2	no	—
413	C₂	—	8	4	no	—
414	C₂	C₁₃×#2435	1	1	yes	characteristic
415	C₂	C₁₃×#3005	1	2	yes	—
416	C₂	C₁₃×#3135	1	1	yes	characteristic
417	C₂	C₁₃×#3142	1	1	yes	characteristic
418	C₂	C₁₃×#3219	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
2. C₂×C₁₃×#491	C₂	semidirect
3. C₂×C₁₃×#490	C₂	semidirect
4. C₁₃×#2851	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
6. C₁₃×#1961	C₂	semidirect
7. C₁₃×#1960	C₂	semidirect
8. C₁₃×#1788	C₂	semidirect
9. C₁₃×#1749	C₂	semidirect
80. #25862	C₁₃	direct (N × H)
136. C₂×#491	C₂×C₁₃	semidirect
137. C₂×#490	C₂×C₁₃	semidirect
138. #2851	C₂×C₁₃	semidirect
139. #2042	C₂×C₁₃	semidirect
140. #1961	C₂×C₁₃	semidirect
141. #1960	C₂×C₁₃	semidirect
142. #1788	C₂×C₁₃	semidirect
143. #1749	C₂×C₁₃	semidirect
343. C₁₃	#25862	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×#532	2
C₂×C₁₃×#491	2
C₂×C₁₃×#490	2
C₁₃×#2851	2
C₁₃×#2042	2
C₁₃×#1961	2
C₁₃×#1960	2
C₁₃×#1788	2
C₁₃×#1749	2
#25862	13

Subgroups — C13×#25862 #15712201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25862 #15712201