Subgroups — C₁₃×#10433 #15696772

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
9	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#103	—	2	1	no	—
14	C₂×C₁₃×#102	—	2	1	no	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#396	—	2	2	no	—
17	C₁₃×#390	—	2	1	no	—
18	C₁₃×#389	—	2	1	no	—
19	C₁₃×#384	C₂²	1	1	yes	characteristic
20	C₁₃×#384	C₂²	1	1	yes	characteristic
21	C₁₃×#380	—	2	1	no	—
22	C₁₃×#340	—	2	1	no	—
23	C₁₃×#340	—	2	1	no	—
24	C₁₃×#340	—	2	2	no	—
25	C₁₃×Q₈⋊C₈	—	2	2	no	—
26	C₁₃×D₄⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂²×C₈×C₁₃	—	2	1	no	—
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₁₃×C₂²⋊Q₈	—	4	2	no	—
34	C₁₃×C₂²⋊Q₈	—	4	2	no	—
35	C₄×Q₈×C₁₃	—	2	1	no	—
36	C₄×Q₈×C₁₃	—	2	1	no	—
37	C₄×Q₈×C₁₃	—	2	1	no	—
38	C₄×Q₈×C₁₃	—	2	1	no	—
39	C₄×D₄×C₁₃	—	2	1	no	—
40	C₄×D₄×C₁₃	—	2	1	no	—
41	C₄×D₄×C₁₃	—	2	1	no	—
42	C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₄²×C₁₃	—	2	1	no	—
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊C₈	—	2	1	no	—
59	C₁₃×C₄⋊C₈	—	2	1	no	—
60	C₁₃×C₄⋊C₈	—	2	1	no	—
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×#103	—	4	2	no	—
63	C₁₃×#102	—	4	2	no	—
64	C₄×C₈×C₁₃	—	2	1	no	—
65	C₄×C₈×C₁₃	D₄	1	2	yes	—
66	C₁₃×#95	—	2	2	no	—
67	#10433	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	—	2	1	no	—
69	C₂×Q₈×C₁₃	—	2	1	no	—
70	C₂×Q₈×C₁₃	—	2	1	no	—
71	C₂×Q₈×C₁₃	—	2	1	no	—
72	C₂×Q₈×C₁₃	—	2	1	no	—
73	C₂×Q₈×C₁₃	—	2	1	no	—
74	C₂×Q₈×C₁₃	D₈	1	2	yes	—
75	C₂×D₄×C₁₃	—	2	1	no	—
76	C₂×D₄×C₁₃	—	2	1	no	—
77	C₂×D₄×C₁₃	—	2	1	no	—
78	C₂×D₄×C₁₃	—	2	1	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₃	—	2	1	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	—	4	1	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	4	1	no	—
97	C₂×C₈×C₁₃	—	4	1	no	—
98	C₂×C₈×C₁₃	—	4	1	no	—
99	C₂×C₈×C₁₃	—	4	1	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	—	4	1	no	—
102	C₂×C₈×C₁₃	—	4	1	no	—
103	C₂×C₈×C₁₃	—	4	1	no	—
104	C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×C₄⋊C₄	—	4	2	no	—
109	C₁₃×C₄⋊C₄	—	4	4	no	—
110	C₁₃×C₄⋊C₄	—	4	2	no	—
111	C₁₃×C₄⋊C₄	—	4	1	no	—
112	C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₁₃×C₄⋊C₄	—	4	1	no	—
115	C₁₃×C₄⋊C₄	—	4	1	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	—	4	4	no	—
122	C₁₃×C₂²⋊C₄	—	4	1	no	—
123	C₁₃×C₂²⋊C₄	—	4	1	no	—
124	C₁₃×C₂²⋊C₄	—	8	2	no	—
125	C₄²×C₁₃	—	4	1	no	—
126	C₄²×C₁₃	—	4	1	no	—
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃	#41	1	1	yes	characteristic
129	C₄²×C₁₃	#41	1	1	yes	characteristic
130	C₄²×C₁₃	#41	1	1	yes	characteristic
131	#2538	C₂×C₁₃	1	1	yes	characteristic
132	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#1802	C₂×C₁₃	1	1	yes	characteristic
135	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
136	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
137	#1296	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	—	4	1	no	—
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	—	4	1	no	—
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	1	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	#120	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	2	no	—
147	Q₈×C₁₃	—	2	2	no	—
148	Q₈×C₁₃	—	4	1	no	—
149	Q₈×C₁₃	—	4	1	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	—	2	2	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	8	1	no	—
169	C₂×C₄×C₁₃	—	8	1	no	—
170	C₂×C₄×C₁₃	—	8	1	no	—
171	C₂×C₄×C₁₃	—	8	1	no	—
172	C₂×C₄×C₁₃	—	8	1	no	—
173	C₂×C₄×C₁₃	—	8	1	no	—
174	C₂×C₄×C₁₃	—	8	1	no	—
175	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
180	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
185	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
189	C₈×C₁₃	—	4	2	no	—
190	C₈×C₁₃	—	8	1	no	—
191	C₈×C₁₃	—	8	1	no	—
192	C₂×C₂²⋊Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#103	—	2	1	no	—
198	C₂×#102	—	2	1	no	—
199	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	#396	—	2	2	no	—
201	#390	—	2	1	no	—
202	#389	—	2	1	no	—
203	#384	C₂²×C₁₃	1	1	yes	characteristic
204	#384	C₂²×C₁₃	1	1	yes	characteristic
205	#380	—	2	1	no	—
206	#340	—	2	1	no	—
207	#340	—	2	1	no	—
208	#340	—	2	2	no	—
209	Q₈⋊C₈	—	2	2	no	—
210	D₄⋊C₈	—	2	2	no	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	8	1	no	—
215	C₂²×C₁₃	—	8	1	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	#394	1	1	yes	characteristic
219	C₂²×C₁₃	#447	1	1	yes	characteristic
220	C₂²×C₁₃	#448	1	1	yes	characteristic
221	C₂²×C₁₃	#452	1	1	yes	characteristic
222	C₂²×C₁₃	#452	1	1	yes	characteristic
223	C₂²×C₁₃	#454	1	1	yes	characteristic
224	C₂²×C₁₃	#455	1	1	yes	characteristic
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	1	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	—	16	1	no	—
232	C₄×C₁₃	#465	1	1	yes	characteristic
233	C₄×C₁₃	#466	1	1	yes	characteristic
234	C₄×C₁₃	#468	1	1	yes	characteristic
235	C₄×C₁₃	#470	1	1	yes	characteristic
236	C₄×C₁₃	#480	1	1	yes	characteristic
237	C₄×C₁₃	#482	1	1	yes	characteristic
238	C₄×C₁₃	#483	1	1	yes	characteristic
239	C₄×C₁₃	#485	1	1	yes	characteristic
240	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
241	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²⋊Q₈	—	4	2	no	—
247	C₂²⋊Q₈	—	4	2	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	#103	—	4	2	no	—
276	#102	—	4	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	D₄×C₁₃	1	2	yes	—
279	#95	—	2	2	no	—
280	C₂×C₁₃	—	8	2	no	—
281	C₂×C₁₃	#1627	1	1	yes	characteristic
282	C₂×C₁₃	#1638	1	1	yes	characteristic
283	C₂×C₁₃	#1641	1	1	yes	characteristic
284	C₂×C₁₃	#1643	1	1	yes	characteristic
285	C₂×C₁₃	#2033	1	1	yes	characteristic
286	C₂×C₁₃	#2035	1	1	yes	characteristic
287	C₂×C₁₃	#2040	1	1	yes	characteristic
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	C₁₃×D₈	1	2	yes	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₄²	—	4	1	no	—
346	C₄²	—	4	1	no	—
347	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₄²	C₁₃×#41	1	1	yes	characteristic
349	C₄²	C₁₃×#41	1	1	yes	characteristic
350	C₄²	C₁₃×#41	1	1	yes	characteristic
351	C₁₃	#10433	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	2	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	C₁₃×#120	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
390	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
391	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
392	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
393	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
394	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
397	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
398	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
399	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
401	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
402	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	8	1	no	—
405	C₈	—	8	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	C₁₃×#394	1	1	yes	characteristic
414	C₂²	C₁₃×#447	1	1	yes	characteristic
415	C₂²	C₁₃×#448	1	1	yes	characteristic
416	C₂²	C₁₃×#452	1	1	yes	characteristic
417	C₂²	C₁₃×#452	1	1	yes	characteristic
418	C₂²	C₁₃×#454	1	1	yes	characteristic
419	C₂²	C₁₃×#455	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	2	no	—
426	C₄	—	16	1	no	—
427	C₄	C₁₃×#465	1	1	yes	characteristic
428	C₄	C₁₃×#466	1	1	yes	characteristic
429	C₄	C₁₃×#468	1	1	yes	characteristic
430	C₄	C₁₃×#470	1	1	yes	characteristic
431	C₄	C₁₃×#480	1	1	yes	characteristic
432	C₄	C₁₃×#482	1	1	yes	characteristic
433	C₄	C₁₃×#483	1	1	yes	characteristic
434	C₄	C₁₃×#485	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₁₃×#1627	1	1	yes	characteristic
437	C₂	C₁₃×#1638	1	1	yes	characteristic
438	C₂	C₁₃×#1641	1	1	yes	characteristic
439	C₂	C₁₃×#1643	1	1	yes	characteristic
440	C₂	C₁₃×#2033	1	1	yes	characteristic
441	C₂	C₁₃×#2035	1	1	yes	characteristic
442	C₂	C₁₃×#2040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1834	C₂	semidirect
3. C₁₃×#1803	C₂	semidirect
5. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
7. C₁₃×#1296	C₂	semidirect
67. #10433	C₁₃	direct (N × H)
132. #1834	C₂×C₁₃	semidirect
133. #1803	C₂×C₁₃	semidirect
135. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
137. #1296	C₂×C₁₃	semidirect
351. C₁₃	#10433	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2538	2
C₁₃×#1834	2
C₁₃×#1803	2
C₁₃×#1802	2
C₂×C₁₃×Q₈⋊C₈	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1296	2
#10433	13

Subgroups — C13×#10433 #15696772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10433 #15696772