Subgroups — C₁₃×#10267 #15696606

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×D₈	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#486	—	2	2	no	—
13	C₁₃×#486	—	2	2	no	—
14	C₁₃×#476	—	2	2	no	—
15	C₁₃×#476	—	2	2	no	—
16	C₁₃×#459	—	2	2	no	—
17	C₁₃×#459	—	2	2	no	—
18	C₂×C₁₃×#106	—	2	1	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#102	—	2	1	no	—
23	C₂×C₁₃×#102	—	2	2	no	—
24	C₂×C₁₃×#102	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#333	—	2	2	no	—
28	C₁₃×#331	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×D₄×C₁₃	—	2	1	no	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	—	2	1	no	—
35	C₂×C₁₃×D₈	—	2	4	no	—
36	C₂×C₁₃×D₈	—	4	2	no	—
37	C₂×C₁₃×D₈	—	4	2	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	D₄	1	2	yes	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₃×#127	—	2	1	no	—
47	C₁₃×#127	—	2	1	no	—
48	C₁₃×#127	—	2	1	no	—
49	C₁₃×#127	D₄	1	2	yes	—
50	C₄×D₄×C₁₃	—	2	1	no	—
51	C₄×D₄×C₁₃	—	2	1	no	—
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#106	—	2	4	no	—
60	C₁₃×C₄⋊C₈	—	2	1	no	—
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
66	C₁₃×#102	—	2	4	no	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×#102	—	2	8	no	—
69	C₁₃×C₂²⋊C₈	—	4	4	no	—
70	C₄×C₈×C₁₃	—	2	1	no	—
71	C₄×C₈×C₁₃	—	2	1	no	—
72	#10267	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	1	no	—
74	C₂⁴×C₁₃	—	4	1	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	4	1	no	—
77	C₂×Q₈×C₁₃	—	8	2	no	—
78	C₂×D₄×C₁₃	—	2	1	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	1	no	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	4	1	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	8	2	no	—
96	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
106	C₁₃×D₈	—	4	8	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	4	1	no	—
113	C₂×C₈×C₁₃	—	4	1	no	—
114	C₂×C₈×C₁₃	—	4	1	no	—
115	C₂×C₈×C₁₃	—	4	1	no	—
116	C₂×C₈×C₁₃	—	4	1	no	—
117	C₂×C₈×C₁₃	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₂²⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
133	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂×#333	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#331	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1277	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	8	2	no	—
144	C₂³×C₁₃	—	8	1	no	—
145	C₂³×C₁₃	—	8	1	no	—
146	C₂³×C₁₃	—	8	2	no	—
147	C₂³×C₁₃	#121	1	1	yes	characteristic
148	Q₈×C₁₃	—	8	2	no	—
149	Q₈×C₁₃	—	8	2	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	—	2	2	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	4	4	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	4	1	no	—
156	D₄×C₁₃	—	4	2	no	—
157	D₄×C₁₃	—	8	2	no	—
158	D₄×C₁₃	—	8	2	no	—
159	D₄×C₁₃	—	8	1	no	—
160	D₄×C₁₃	—	8	1	no	—
161	D₄×C₁₃	—	8	1	no	—
162	D₄×C₁₃	—	8	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	8	2	no	—
168	C₂×C₄×C₁₃	—	8	2	no	—
169	C₂×C₄×C₁₃	—	8	1	no	—
170	C₂×C₄×C₁₃	—	8	1	no	—
171	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#135	1	2	yes	—
180	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
183	C₈×C₁₃	—	4	2	no	—
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	—	8	1	no	—
187	C₂²×D₈	—	2	1	no	—
188	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
191	#486	—	2	2	no	—
192	#486	—	2	2	no	—
193	#476	—	2	2	no	—
194	#476	—	2	2	no	—
195	#459	—	2	2	no	—
196	#459	—	2	2	no	—
197	C₂×#106	—	2	1	no	—
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#102	—	2	1	no	—
202	C₂×#102	—	2	2	no	—
203	C₂×#102	—	2	1	no	—
204	C₂×C₂²⋊C₈	—	2	2	no	—
205	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
206	#333	—	2	2	no	—
207	#331	—	2	2	no	—
208	C₂²×C₁₃	—	4	4	no	—
209	C₂²×C₁₃	—	4	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	8	1	no	—
212	C₂²×C₁₃	—	8	1	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	2	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	16	2	no	—
217	C₂²×C₁₃	—	16	2	no	—
218	C₂²×C₁₃	#392	1	1	yes	characteristic
219	C₂²×C₁₃	#463	1	2	yes	—
220	C₂²×C₁₃	#465	1	1	yes	characteristic
221	C₂²×C₁₃	#468	1	1	yes	characteristic
222	C₂²×C₁₃	#472	1	2	yes	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	8	1	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	#448	1	1	yes	characteristic
228	C₄×C₁₃	#449	1	1	yes	characteristic
229	C₄×C₁₃	#449	1	2	yes	—
230	C₄×C₁₃	#450	1	1	yes	characteristic
231	C₄×C₁₃	#452	1	1	yes	characteristic
232	C₄×C₁₃	#495	1	1	yes	characteristic
233	C₄×C₁₃	#496	1	1	yes	characteristic
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂×D₈	—	2	4	no	—
241	C₂×D₈	—	4	2	no	—
242	C₂×D₈	—	4	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	D₄×C₁₃	1	2	yes	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
251	#127	—	2	1	no	—
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	D₄×C₁₃	1	2	yes	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
264	#106	—	2	4	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
270	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	#102	—	2	8	no	—
274	C₂²⋊C₈	—	4	4	no	—
275	C₄×C₈	—	2	1	no	—
276	C₄×C₈	—	2	1	no	—
277	C₂×C₁₃	—	8	2	no	—
278	C₂×C₁₃	—	16	2	no	—
279	C₂×C₁₃	#1677	1	2	yes	—
280	C₂×C₁₃	#1697	1	2	yes	—
281	C₂×C₁₃	#2000	1	1	yes	characteristic
282	C₂×C₁₃	#2012	1	1	yes	characteristic
283	C₂×C₁₃	#2018	1	1	yes	characteristic
284	C₂⁴	—	2	1	no	—
285	C₂⁴	—	4	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	8	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	8	2	no	—
307	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
317	D₈	—	4	8	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₁₃	#10267	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	2	no	—
352	C₂³	C₁₃×#121	1	1	yes	characteristic
353	Q₈	—	8	2	no	—
354	Q₈	—	8	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	D₄	—	8	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
377	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
378	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
379	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
380	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
381	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
382	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
383	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
384	C₂×C₄	C₁₃×#135	1	2	yes	—
385	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
387	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	8	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	16	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	C₁₃×#392	1	1	yes	characteristic
403	C₂²	C₁₃×#463	1	2	yes	—
404	C₂²	C₁₃×#465	1	1	yes	characteristic
405	C₂²	C₁₃×#468	1	1	yes	characteristic
406	C₂²	C₁₃×#472	1	2	yes	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	C₁₃×#448	1	1	yes	characteristic
412	C₄	C₁₃×#449	1	1	yes	characteristic
413	C₄	C₁₃×#449	1	2	yes	—
414	C₄	C₁₃×#450	1	1	yes	characteristic
415	C₄	C₁₃×#452	1	1	yes	characteristic
416	C₄	C₁₃×#495	1	1	yes	characteristic
417	C₄	C₁₃×#496	1	1	yes	characteristic
418	C₂	—	8	2	no	—
419	C₂	—	16	2	no	—
420	C₂	C₁₃×#1677	1	2	yes	—
421	C₂	C₁₃×#1697	1	2	yes	—
422	C₂	C₁₃×#2000	1	1	yes	characteristic
423	C₂	C₁₃×#2012	1	1	yes	characteristic
424	C₂	C₁₃×#2018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#459	C₂
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
1. C₂×C₁₃×#486	C₂	semidirect
2. C₂×C₁₃×#476	C₂	semidirect
4. C₁₃×#1954	C₂	semidirect
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×#331	C₂	semidirect
7. C₁₃×#1277	C₂	semidirect
72. #10267	C₁₃	direct (N × H)
130. C₂×#486	C₂×C₁₃	semidirect
131. C₂×#476	C₂×C₁₃	semidirect
133. #1954	C₂×C₁₃	semidirect
134. C₂×#333	C₂×C₁₃	semidirect
135. C₂×#331	C₂×C₁₃	semidirect
136. #1277	C₂×C₁₃	semidirect
341. C₁₃	#10267	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×#486	2
C₂×C₁₃×#476	2
C₂×C₁₃×#459	2
C₁₃×#1954	2
C₂×C₁₃×#333	2
C₂×C₁₃×#331	2
C₁₃×#1277	2
#10267	13

Subgroups — C13×#10267 #15696606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10267 #15696606