Subgroups — C₁₃×#25570 #15711909

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2001	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1873	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
11	C₁₃×#556	—	2	4	no	—
12	C₁₃×#556	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#126	—	2	2	no	—
16	C₂×C₁₃×#124	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	2	yes	—
23	C₁₃×#487	—	2	4	no	—
24	C₁₃×#462	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	4	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#399	—	2	2	no	—
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#384	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	4	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂×C₁₃×Q₁₆	—	2	4	no	—
43	C₂×C₁₃×Q₁₆	—	4	4	no	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	2	2	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
50	C₁₃×#126	—	2	16	no	—
51	C₁₃×#124	—	2	8	no	—
52	C₁₃×C₂²⋊Q₈	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	2	8	no	—
55	C₁₃×C₂²⋊Q₈	—	4	4	no	—
56	C₄×Q₈×C₁₃	—	2	8	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	D₄	1	4	yes	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₁₃×#117	—	2	4	no	—
62	C₁₃×#117	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	8	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×C₂²⋊C₈	—	4	4	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	#25570	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×Q₁₆	—	4	8	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	C₂×C₈×C₁₃	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	8	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	4	8	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
134	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
135	C₁₃×C₄⋊C₄	#41	1	4	yes	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	8	no	—
140	C₄²×C₁₃	—	2	8	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2542	C₂×C₁₃	1	1	yes	characteristic
149	#2001	C₂×C₁₃	1	4	yes	complemented
150	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1954	C₂×C₁₃	1	1	yes	characteristic
152	#1873	C₂×C₁₃	1	4	yes	complemented
153	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	2	no	—
161	Q₈×C₁₃	—	2	2	no	—
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	8	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	4	no	—
167	D₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	#120	1	2	yes	—
187	C₂×C₄×C₁₃	#120	1	2	yes	—
188	C₂×C₄×C₁₃	#135	1	2	yes	—
189	C₂×C₄×C₁₃	#137	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
194	C₈×C₁₃	—	4	2	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
197	#556	—	2	4	no	—
198	#556	—	2	4	no	—
199	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#126	—	2	2	no	—
202	C₂×#124	—	2	1	no	—
203	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₃	1	2	yes	—
209	#487	—	2	4	no	—
210	#462	—	2	4	no	—
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#103	C₂²×C₁₃	1	4	yes	—
213	C₂×#103	C₂²×C₁₃	1	2	yes	—
214	C₂×#103	C₂²×C₁₃	1	2	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
216	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
217	#399	—	2	2	no	—
218	#390	—	2	1	no	—
219	#384	—	2	1	no	—
220	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	#340	C₂²×C₁₃	1	2	yes	—
222	#340	C₂²×C₁₃	1	4	yes	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	4	4	no	—
228	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
229	C₂²×C₁₃	#546	1	2	yes	—
230	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
232	C₂²×C₁₃	#578	1	2	yes	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	#452	1	4	yes	—
241	C₄×C₁₃	#532	1	1	yes	characteristic
242	C₄×C₁₃	#535	1	1	yes	characteristic
243	C₄×C₁₃	#550	1	2	yes	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
246	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
249	C₂×Q₁₆	—	2	4	no	—
250	C₂×Q₁₆	—	4	4	no	—
251	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
257	#126	—	2	16	no	—
258	#124	—	2	8	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	8	no	—
262	C₂²⋊Q₈	—	4	4	no	—
263	C₄×Q₈	—	2	8	no	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	D₄×C₁₃	1	4	yes	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	—	2	2	no	—
268	#117	—	2	4	no	—
269	#117	—	2	4	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₄⋊C₈	—	2	2	no	—
289	#103	—	2	4	no	—
290	#103	—	2	8	no	—
291	#103	—	2	4	no	—
292	C₂²⋊C₈	—	4	4	no	—
293	C₄×C₈	—	2	2	no	—
294	#95	—	2	1	no	—
295	C₂×C₁₃	—	8	2	no	—
296	C₂×C₁₃	#2431	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
298	C₂×C₁₃	#3011	1	1	yes	characteristic
299	C₂×C₁₃	#3302	1	2	yes	—
300	C₂×C₁₃	#3328	1	2	yes	—
301	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
329	Q₁₆	—	4	8	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	4	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	8	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
347	C₄⋊C₄	C₁₃×#41	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	4	8	no	—
352	C₄²	—	2	8	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	4	2	no	—
355	C₄²	C₂×D₄×C₁₃	1	2	yes	—
356	C₄²	C₂×D₄×C₁₃	1	2	yes	—
357	C₁₃	#25570	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	4	no	—
363	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	8	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	4	no	—
371	D₄	—	4	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	C₁₃×#120	1	2	yes	—
391	C₂×C₄	C₁₃×#120	1	2	yes	—
392	C₂×C₄	C₁₃×#135	1	2	yes	—
393	C₂×C₄	C₁₃×#137	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
397	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
406	C₂²	C₁₃×#546	1	2	yes	—
407	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
408	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
409	C₂²	C₁₃×#578	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	4	no	—
416	C₄	—	8	2	no	—
417	C₄	C₁₃×#452	1	4	yes	—
418	C₄	C₁₃×#532	1	1	yes	characteristic
419	C₄	C₁₃×#535	1	1	yes	characteristic
420	C₄	C₁₃×#550	1	2	yes	—
421	C₂	—	8	2	no	—
422	C₂	C₁₃×#2431	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
424	C₂	C₁₃×#3011	1	1	yes	characteristic
425	C₂	C₁₃×#3302	1	2	yes	—
426	C₂	C₁₃×#3328	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#487	C₂	semidirect
3. C₂×C₁₃×#462	C₂	semidirect
5. C₁₃×#2001	C₂	semidirect
6. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1873	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
88. #25570	C₁₃	direct (N × H)
146. C₂×#487	C₂×C₁₃	semidirect
147. C₂×#462	C₂×C₁₃	semidirect
149. #2001	C₂×C₁₃	semidirect
150. #1988	C₂×C₁₃	semidirect
152. #1873	C₂×C₁₃	semidirect
153. C₄×#103	C₂×C₁₃	semidirect
357. C₁₃	#25570	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×#556	2
C₂×C₁₃×#487	2
C₂×C₁₃×#462	2
C₁₃×#2542	2
C₁₃×#2001	2
C₁₃×#1988	2
C₁₃×#1954	2
C₁₃×#1873	2
C₄×C₁₃×#103	2
#25570	13

Subgroups — C13×#25570 #15711909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25570 #15711909