Subgroups — C₁₃×#10051 #15696390

Order 3328.

670 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×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#486	—	2	2	no	—
14	C₁₃×#486	—	2	2	no	—
15	C₁₃×#460	—	2	2	no	—
16	C₁₃×#460	—	2	2	no	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	—	2	1	no	—
20	C₂×C₁₃×#102	—	2	2	no	—
21	C₂×C₁₃×#102	—	2	2	no	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#398	—	2	2	no	—
24	C₁₃×#391	—	2	1	no	—
25	C₁₃×#389	—	2	2	no	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#332	—	2	2	no	—
28	C₁₃×Q₈⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂×C₁₃×SD₁₆	—	2	4	no	—
35	C₂×C₁₃×SD₁₆	—	4	2	no	—
36	C₂×C₁₃×SD₁₆	—	4	2	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	4	2	no	—
45	C₁₃×C₄⋊Q₈	—	4	2	no	—
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×Q₈×C₁₃	—	2	1	no	—
51	C₄×Q₈×C₁₃	—	2	1	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
67	C₁₃×#102	—	2	4	no	—
68	C₁₃×#102	—	2	8	no	—
69	C₁₃×#102	—	4	4	no	—
70	C₄×C₈×C₁₃	—	2	1	no	—
71	C₄×C₈×C₁₃	D₄	1	2	yes	—
72	C₁₃×#95	—	2	4	no	—
73	C₁₃×#95	—	2	1	no	—
74	#10051	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	4	1	no	—
76	C₂×Q₈×C₁₃	—	2	1	no	—
77	C₂×Q₈×C₁₃	—	2	1	no	—
78	C₂×Q₈×C₁₃	—	2	1	no	—
79	C₂×Q₈×C₁₃	—	2	1	no	—
80	C₂×Q₈×C₁₃	—	2	1	no	—
81	C₂×Q₈×C₁₃	—	4	1	no	—
82	C₂×Q₈×C₁₃	—	4	1	no	—
83	C₂×Q₈×C₁₃	—	4	1	no	—
84	C₂×Q₈×C₁₃	—	4	1	no	—
85	C₂×Q₈×C₁₃	—	4	1	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	D₈	1	2	yes	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₁₃×SD₁₆	—	4	8	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	4	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	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	1	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	—	4	8	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
127	C₄²×C₁₃	—	4	1	no	—
128	C₄²×C₁₃	—	4	1	no	—
129	C₄²×C₁₃	—	4	1	no	—
130	C₄²×C₁₃	—	4	1	no	—
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₃	#41	1	1	yes	characteristic
135	C₂×#486	C₂×C₁₃	1	1	yes	characteristic
136	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
137	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1982	C₂×C₁₃	1	1	yes	characteristic
139	C₂×#332	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	8	1	no	—
144	C₂³×C₁₃	—	8	2	no	—
145	C₂³×C₁₃	—	8	1	no	—
146	C₂³×C₁₃	—	8	2	no	—
147	C₂³×C₁₃	#120	1	1	yes	characteristic
148	Q₈×C₁₃	—	2	2	no	—
149	Q₈×C₁₃	—	2	2	no	—
150	Q₈×C₁₃	—	4	1	no	—
151	Q₈×C₁₃	—	4	1	no	—
152	Q₈×C₁₃	—	8	1	no	—
153	Q₈×C₁₃	—	8	1	no	—
154	Q₈×C₁₃	—	8	1	no	—
155	Q₈×C₁₃	—	8	1	no	—
156	D₄×C₁₃	—	4	4	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	4	4	no	—
160	D₄×C₁₃	—	8	2	no	—
161	D₄×C₁₃	—	8	1	no	—
162	D₄×C₁₃	—	8	1	no	—
163	D₄×C₁₃	—	8	1	no	—
164	D₄×C₁₃	—	8	1	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	1	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	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
186	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#137	1	2	yes	—
189	C₈×C₁₃	—	4	2	no	—
190	C₈×C₁₃	—	4	2	no	—
191	C₈×C₁₃	—	8	1	no	—
192	C₂²×SD₁₆	—	2	1	no	—
193	C₂×C₄⋊Q₈	—	2	1	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
197	#486	—	2	2	no	—
198	#486	—	2	2	no	—
199	#460	—	2	2	no	—
200	#460	—	2	2	no	—
201	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#102	—	2	2	no	—
204	C₂×#102	—	2	1	no	—
205	C₂×#102	—	2	2	no	—
206	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
207	#398	—	2	2	no	—
208	#391	—	2	1	no	—
209	#389	—	2	2	no	—
210	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	#332	—	2	2	no	—
212	Q₈⋊C₈	—	2	2	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	#447	1	1	yes	characteristic
220	C₂²×C₁₃	#448	1	2	yes	—
221	C₂²×C₁₃	#449	1	1	yes	characteristic
222	C₂²×C₁₃	#454	1	2	yes	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	4	4	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	—	8	1	no	—
229	C₄×C₁₃	#447	1	1	yes	characteristic
230	C₄×C₁₃	#449	1	1	yes	characteristic
231	C₄×C₁₃	#461	1	2	yes	—
232	C₄×C₁₃	#466	1	1	yes	characteristic
233	C₄×C₁₃	#469	1	1	yes	characteristic
234	C₄×C₁₃	#492	1	1	yes	characteristic
235	C₄×C₁₃	#497	1	1	yes	characteristic
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	4	2	no	—
252	C₄⋊Q₈	—	4	2	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	D₄×C₁₃	1	2	yes	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
274	#102	—	2	4	no	—
275	#102	—	2	8	no	—
276	#102	—	4	4	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	D₄×C₁₃	1	2	yes	—
279	#95	—	2	4	no	—
280	#95	—	2	1	no	—
281	C₂×C₁₃	—	16	2	no	—
282	C₂×C₁₃	#1626	1	2	yes	—
283	C₂×C₁₃	#1627	1	2	yes	—
284	C₂×C₁₃	#1999	1	1	yes	characteristic
285	C₂×C₁₃	#2003	1	1	yes	characteristic
286	C₂×C₁₃	#2013	1	1	yes	characteristic
287	C₂⁴	—	4	1	no	—
288	C₂×Q₈	—	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	—	4	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	C₁₃×D₈	1	2	yes	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	SD₁₆	—	4	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	8	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	C₁₃×SD₁₆	1	4	yes	complemented
339	C₄²	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₄²	C₁₃×#41	1	1	yes	characteristic
347	C₁₃	#10051	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	4	2	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	2	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	2	no	—
353	C₂³	C₁₃×#120	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	1	no	—
360	Q₈	—	8	1	no	—
361	Q₈	—	8	1	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	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	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
384	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
385	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
386	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
387	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
388	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
389	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
390	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
391	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
392	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₄	C₁₃×#137	1	2	yes	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	8	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	—	16	2	no	—
403	C₂²	C₁₃×#392	1	1	yes	characteristic
404	C₂²	C₁₃×#447	1	1	yes	characteristic
405	C₂²	C₁₃×#448	1	2	yes	—
406	C₂²	C₁₃×#449	1	1	yes	characteristic
407	C₂²	C₁₃×#454	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	C₁₃×#447	1	1	yes	characteristic
415	C₄	C₁₃×#449	1	1	yes	characteristic
416	C₄	C₁₃×#461	1	2	yes	—
417	C₄	C₁₃×#466	1	1	yes	characteristic
418	C₄	C₁₃×#469	1	1	yes	characteristic
419	C₄	C₁₃×#492	1	1	yes	characteristic
420	C₄	C₁₃×#497	1	1	yes	characteristic
421	C₂	—	16	2	no	—
422	C₂	C₁₃×#1626	1	2	yes	—
423	C₂	C₁₃×#1627	1	2	yes	—
424	C₂	C₁₃×#1999	1	1	yes	characteristic
425	C₂	C₁₃×#2003	1	1	yes	characteristic
426	C₂	C₁₃×#2013	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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
3. C₁₃×#2546	C₂	semidirect
5. C₂×C₁₃×#332	C₂	semidirect
6. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
74. #10051	C₁₃	direct (N × H)
126. C₁₃×C₄⋊C₄	SD₁₆	semidirect
137. #2546	C₂×C₁₃	semidirect
139. C₂×#332	C₂×C₁₃	semidirect
140. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
141. #1279	C₂×C₁₃	semidirect
338. C₄⋊C₄	C₁₃×SD₁₆	semidirect
347. C₁₃	#10051	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×#460	2
C₁₃×#2546	2
C₁₃×#1982	2
C₂×C₁₃×#332	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1279	2
#10051	13

Subgroups — C13×#10051 #15696390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10051 #15696390