Subgroups — C₁₃×#10238 #15696577

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
9	C₁₃×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#127	—	2	1	no	—
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#121	—	2	2	no	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#493	—	2	1	no	—
15	C₁₃×#486	—	2	1	no	—
16	C₁₃×#463	—	2	2	no	—
17	C₁₃×#461	—	2	1	no	—
18	C₁₃×#459	—	2	1	no	—
19	C₁₃×#459	—	2	2	no	—
20	C₁₃×#447	—	2	2	no	—
21	C₁₃×#431	C₂²	1	1	yes	characteristic
22	C₁₃×#431	C₂²	1	1	yes	characteristic
23	C₁₃×#423	C₂²	1	1	yes	characteristic
24	C₁₃×#417	—	2	1	no	—
25	C₁₃×#392	—	2	2	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₃×#331	—	2	2	no	—
29	C₁₃×#327	—	2	2	no	—
30	C₁₃×D₄⋊C₈	—	2	2	no	—
31	C₂×C₁₃×#41	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	D₄	1	2	yes	—
37	C₂³×C₄×C₁₃	—	2	1	no	—
38	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
39	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
40	C₂×C₁₃×SD₁₆	—	2	2	no	—
41	C₂×C₁₃×D₈	—	2	2	no	—
42	C₂×C₁₃×D₈	—	2	4	no	—
43	C₂×C₁₃×M₁₆	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
45	C₁₃×#127	—	2	1	no	—
46	C₁₃×#127	—	2	1	no	—
47	C₁₃×#127	—	2	1	no	—
48	C₁₃×#127	—	2	1	no	—
49	C₁₃×#127	—	4	2	no	—
50	C₁₃×#127	—	4	2	no	—
51	C₁₃×#127	D₄	1	1	yes	characteristic, complemented
52	C₁₃×#124	—	2	1	no	—
53	C₁₃×#121	—	2	1	no	—
54	C₁₃×#121	—	2	1	no	—
55	C₁₃×#121	—	4	8	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊C₈	—	2	1	no	—
69	C₁₃×C₄⋊C₈	—	2	1	no	—
70	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
71	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
72	C₁₃×#103	—	2	2	no	—
73	C₁₃×#102	—	2	2	no	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×C₂²⋊C₈	—	2	1	no	—
76	C₁₃×C₂²⋊C₈	—	2	1	no	—
77	C₄×C₈×C₁₃	—	2	1	no	—
78	C₄×C₈×C₁₃	—	2	1	no	—
79	C₁₃×#95	D₄	1	2	yes	—
80	#10238	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	1	no	—
82	C₂⁴×C₁₃	—	2	2	no	—
83	C₁₃×#41	—	4	1	no	—
84	C₁₃×#41	—	4	1	no	—
85	C₁₃×#41	—	4	1	no	—
86	C₁₃×#41	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	—	4	8	no	—
100	C₂×D₄×C₁₃	—	4	8	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	1	no	—
105	C₂×D₄×C₁₃	—	4	1	no	—
106	C₂×D₄×C₁₃	—	4	1	no	—
107	C₂×D₄×C₁₃	—	4	1	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	1	no	—
110	C₂×D₄×C₁₃	—	8	2	no	—
111	C₂×D₄×C₁₃	—	8	4	no	—
112	C₂×D₄×C₁₃	D₈	1	2	yes	complemented
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	—	4	1	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₁₃×SD₁₆	—	4	4	no	—
123	C₁₃×D₈	—	4	4	no	—
124	C₁₃×D₈	—	8	4	no	—
125	C₁₃×M₁₆	—	4	1	no	—
126	C₁₃×M₁₆	—	4	1	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	8	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	1	no	—
139	C₁₃×C₂²⋊C₄	—	4	1	no	—
140	C₄²×C₁₃	—	4	1	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃	#41	1	1	yes	characteristic
146	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2541	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1545	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1502	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1478	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1303	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	—	4	4	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	#120	1	1	yes	characteristic
165	Q₈×C₁₃	—	4	1	no	—
166	Q₈×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	4	1	no	—
170	D₄×C₁₃	—	4	1	no	—
171	D₄×C₁₃	—	4	1	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	4	no	—
174	D₄×C₁₃	—	4	1	no	—
175	D₄×C₁₃	—	8	2	no	—
176	D₄×C₁₃	—	8	2	no	—
177	D₄×C₁₃	—	8	1	no	—
178	D₄×C₁₃	—	8	2	no	—
179	D₄×C₁₃	—	8	16	no	—
180	D₄×C₁₃	—	8	1	no	—
181	D₄×C₁₃	—	8	1	no	—
182	D₄×C₁₃	—	8	1	no	—
183	D₄×C₁₃	—	8	1	no	—
184	D₄×C₁₃	—	8	1	no	—
185	D₄×C₁₃	—	8	1	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	8	2	no	—
195	C₂×C₄×C₁₃	—	8	2	no	—
196	C₂×C₄×C₁₃	—	8	1	no	—
197	C₂×C₄×C₁₃	—	8	1	no	—
198	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
206	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₈×C₁₃	—	4	2	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	8	1	no	—
211	C₂×AGL(1,ℤ/8)	—	2	1	no	—
212	#532	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#127	—	2	1	no	—
214	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#121	—	2	2	no	—
216	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	#493	—	2	1	no	—
218	#486	—	2	1	no	—
219	#463	—	2	2	no	—
220	#461	—	2	1	no	—
221	#459	—	2	1	no	—
222	#459	—	2	2	no	—
223	#447	—	2	2	no	—
224	#431	C₂²×C₁₃	1	1	yes	characteristic
225	#431	C₂²×C₁₃	1	1	yes	characteristic
226	#423	C₂²×C₁₃	1	1	yes	characteristic
227	#417	—	2	1	no	—
228	#392	—	2	2	no	—
229	#390	—	2	1	no	—
230	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
231	#331	—	2	2	no	—
232	#327	—	2	2	no	—
233	D₄⋊C₈	—	2	2	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	4	no	—
240	C₂²×C₁₃	—	8	4	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	1	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	1	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	1	no	—
249	C₂²×C₁₃	#392	1	1	yes	characteristic
250	C₂²×C₁₃	#447	1	1	yes	characteristic
251	C₂²×C₁₃	#449	1	1	yes	characteristic
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	—	8	1	no	—
257	C₄×C₁₃	—	8	1	no	—
258	C₄×C₁₃	#447	1	1	yes	characteristic
259	C₄×C₁₃	#449	1	1	yes	characteristic
260	C₄×C₁₃	#453	1	2	yes	—
261	C₄×C₁₃	#466	1	1	yes	characteristic
262	C₄×C₁₃	#469	1	1	yes	characteristic
263	C₂×#41	—	2	1	no	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
268	C₂²×D₄	D₄×C₁₃	1	2	yes	—
269	C₂³×C₄	—	2	1	no	—
270	AGL(1,ℤ/8)	—	4	2	no	—
271	AGL(1,ℤ/8)	—	4	2	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×D₈	—	2	2	no	—
274	C₂×D₈	—	2	4	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	—	2	1	no	—
281	#127	—	4	2	no	—
282	#127	—	4	2	no	—
283	#127	D₄×C₁₃	1	1	yes	characteristic, complemented
284	#124	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	—	4	8	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	4	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
303	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
304	#103	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	4	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	#95	D₄×C₁₃	1	2	yes	—
312	C₂×C₁₃	—	2	1	no	—
313	C₂×C₁₃	—	2	1	no	—
314	C₂×C₁₃	—	8	2	no	—
315	C₂×C₁₃	—	16	1	no	—
316	C₂×C₁₃	—	16	2	no	—
317	C₂×C₁₃	#1999	1	1	yes	characteristic
318	C₂×C₁₃	#2002	1	1	yes	characteristic
319	C₂×C₁₃	#2008	1	1	yes	characteristic
320	C₂⁴	—	2	1	no	—
321	C₂⁴	—	2	2	no	—
322	#41	—	4	1	no	—
323	#41	—	4	1	no	—
324	#41	—	4	1	no	—
325	#41	—	4	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	8	no	—
339	C₂×D₄	—	4	8	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	—	8	4	no	—
351	C₂×D₄	C₁₃×D₈	1	2	yes	complemented
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	SD₁₆	—	4	4	no	—
362	D₈	—	4	4	no	—
363	D₈	—	8	4	no	—
364	M₁₆	—	4	1	no	—
365	M₁₆	—	4	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	1	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	4	8	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₄²	C₁₃×#41	1	1	yes	characteristic
385	C₁₃	#10238	1	1	yes	characteristic, direct product factor, Sylow
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₁₃×#120	1	1	yes	characteristic
398	Q₈	—	4	1	no	—
399	Q₈	—	4	1	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	1	no	—
408	D₄	—	8	2	no	—
409	D₄	—	8	1	no	—
410	D₄	—	8	2	no	—
411	D₄	—	8	2	no	—
412	D₄	—	8	16	no	—
413	D₄	—	8	1	no	—
414	D₄	—	8	1	no	—
415	D₄	—	8	1	no	—
416	D₄	—	8	1	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	8	1	no	—
431	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
432	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
433	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
434	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
435	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
436	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
437	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
438	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
439	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₈	—	4	2	no	—
442	C₈	—	4	2	no	—
443	C₈	—	8	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	4	no	—
450	C₂²	—	8	4	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	1	no	—
459	C₂²	C₁₃×#392	1	1	yes	characteristic
460	C₂²	C₁₃×#447	1	1	yes	characteristic
461	C₂²	C₁₃×#449	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	4	no	—
466	C₄	—	8	1	no	—
467	C₄	—	8	1	no	—
468	C₄	C₁₃×#447	1	1	yes	characteristic
469	C₄	C₁₃×#449	1	1	yes	characteristic
470	C₄	C₁₃×#453	1	2	yes	—
471	C₄	C₁₃×#466	1	1	yes	characteristic
472	C₄	C₁₃×#469	1	1	yes	characteristic
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	8	2	no	—
476	C₂	—	16	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₁₃×#1999	1	1	yes	characteristic
479	C₂	C₁₃×#2002	1	1	yes	characteristic
480	C₂	C₁₃×#2008	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3205	C₂	semidirect
2. C₁₃×#3036	C₂	semidirect
3. C₁₃×#2541	C₂	semidirect
4. C₁₃×#1545	C₂	semidirect
5. C₁₃×#1502	C₂	semidirect
6. C₁₃×#1478	C₂	semidirect
7. C₁₃×#1303	C₂	semidirect
44. C₁₃×C₄⋊Q₈	D₄	semidirect
51. C₁₃×#127	D₄	semidirect
70. C₁₃×C₄⋊C₈	D₄	semidirect
71. C₁₃×C₄⋊C₈	D₄	semidirect
80. #10238	C₁₃	direct (N × H)
112. C₂×D₄×C₁₃	D₈	semidirect
146. #3205	C₂×C₁₃	semidirect
147. #3036	C₂×C₁₃	semidirect
148. #2541	C₂×C₁₃	semidirect
149. #1545	C₂×C₁₃	semidirect
150. #1502	C₂×C₁₃	semidirect
151. #1478	C₂×C₁₃	semidirect
152. #1303	C₂×C₁₃	semidirect
276. C₄⋊Q₈	D₄×C₁₃	semidirect
283. #127	D₄×C₁₃	semidirect
302. C₄⋊C₈	D₄×C₁₃	semidirect
303. C₄⋊C₈	D₄×C₁₃	semidirect
351. C₂×D₄	C₁₃×D₈	semidirect
385. C₁₃	#10238	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×#3205	2
C₁₃×#3036	2
C₁₃×#2541	2
C₁₃×#1545	2
C₁₃×#1502	2
C₁₃×#1478	2
C₁₃×#1303	2
#10238	13

Subgroups — C13×#10238 #15696577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10238 #15696577