Subgroups — C₁₃×#10048 #15696387

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	2	no	—
9	C₂²×C₁₃×D₈	—	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×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#492	—	2	2	no	—
14	C₁₃×#492	—	2	2	no	—
15	C₁₃×#459	—	2	2	no	—
16	C₁₃×#459	—	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#393	—	2	2	no	—
23	C₁₃×#390	—	2	1	no	—
24	C₁₃×#382	—	2	1	no	—
25	C₁₃×#380	—	2	2	no	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#333	—	2	2	no	—
28	C₁₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
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×SD₁₆	—	2	8	no	—
36	C₂×C₁₃×SD₁₆	—	4	8	no	—
37	C₂×C₁₃×D₈	—	2	4	no	—
38	C₂×C₁₃×D₈	—	4	2	no	—
39	C₂×C₁₃×D₈	—	4	2	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×#127	—	2	1	no	—
48	C₁₃×#127	—	2	1	no	—
49	C₁₃×#127	—	2	1	no	—
50	C₁₃×#127	D₄	1	2	yes	—
51	C₄×D₄×C₁₃	—	2	1	no	—
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	4	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	—	4	4	no	—
69	C₄×C₈×C₁₃	—	2	1	no	—
70	C₄×C₈×C₁₃	D₄	1	2	yes	—
71	C₁₃×#95	—	2	4	no	—
72	C₁₃×#95	—	2	1	no	—
73	#10048	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁴×C₁₃	—	2	1	no	—
75	C₂⁴×C₁₃	—	4	1	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	4	4	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	1	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	4	4	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	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	2	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	SD₁₆	1	2	yes	complemented
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	—	4	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	16	no	—
109	C₁₃×D₈	—	4	8	no	—
110	C₂×C₈×C₁₃	—	2	4	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	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	2	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	8	4	no	—
128	C₄²×C₁₃	—	4	1	no	—
129	C₄²×C₁₃	—	4	1	no	—
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
136	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂×#333	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	8	1	no	—
148	C₂³×C₁₃	—	8	1	no	—
149	C₂³×C₁₃	—	8	2	no	—
150	C₂³×C₁₃	—	8	2	no	—
151	C₂³×C₁₃	#120	1	1	yes	characteristic
152	Q₈×C₁₃	—	4	4	no	—
153	Q₈×C₁₃	—	8	2	no	—
154	D₄×C₁₃	—	2	2	no	—
155	D₄×C₁₃	—	2	2	no	—
156	D₄×C₁₃	—	4	4	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	1	no	—
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	8	2	no	—
163	D₄×C₁₃	—	8	1	no	—
164	D₄×C₁₃	—	8	1	no	—
165	D₄×C₁₃	—	8	1	no	—
166	D₄×C₁₃	—	8	1	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	—	8	1	no	—
177	C₂×C₄×C₁₃	—	8	1	no	—
178	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₃	#120	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	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
185	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#135	1	2	yes	—
187	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
190	C₈×C₁₃	—	2	4	no	—
191	C₈×C₁₃	—	4	2	no	—
192	C₈×C₁₃	—	8	1	no	—
193	C₂²×SD₁₆	—	2	2	no	—
194	C₂²×D₈	—	2	1	no	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
198	#492	—	2	2	no	—
199	#492	—	2	2	no	—
200	#459	—	2	2	no	—
201	#459	—	2	2	no	—
202	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#102	—	2	1	no	—
205	C₂×#102	—	2	2	no	—
206	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
207	#393	—	2	2	no	—
208	#390	—	2	1	no	—
209	#382	—	2	1	no	—
210	#380	—	2	2	no	—
211	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
212	#333	—	2	2	no	—
213	D₄⋊C₈	—	2	2	no	—
214	C₂²×C₁₃	—	4	4	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	—	8	1	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	16	2	no	—
223	C₂²×C₁₃	—	16	2	no	—
224	C₂²×C₁₃	#392	1	1	yes	characteristic
225	C₂²×C₁₃	#448	1	1	yes	characteristic
226	C₂²×C₁₃	#449	1	2	yes	—
227	C₂²×C₁₃	#449	1	1	yes	characteristic
228	C₂²×C₁₃	#453	1	2	yes	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	—	8	2	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	#450	1	1	yes	characteristic
235	C₄×C₁₃	#452	1	1	yes	characteristic
236	C₄×C₁₃	#463	1	2	yes	—
237	C₄×C₁₃	#465	1	1	yes	characteristic
238	C₄×C₁₃	#468	1	1	yes	characteristic
239	C₄×C₁₃	#495	1	1	yes	characteristic
240	C₄×C₁₃	#496	1	1	yes	characteristic
241	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂×SD₁₆	—	2	8	no	—
248	C₂×SD₁₆	—	4	8	no	—
249	C₂×D₈	—	2	4	no	—
250	C₂×D₈	—	4	2	no	—
251	C₂×D₈	—	4	2	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	D₄×C₁₃	1	2	yes	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
279	#102	—	2	4	no	—
280	#102	—	4	4	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	D₄×C₁₃	1	2	yes	—
283	#95	—	2	4	no	—
284	#95	—	2	1	no	—
285	C₂×C₁₃	—	8	2	no	—
286	C₂×C₁₃	—	16	2	no	—
287	C₂×C₁₃	#1622	1	2	yes	—
288	C₂×C₁₃	#1624	1	2	yes	—
289	C₂×C₁₃	#2000	1	1	yes	characteristic
290	C₂×C₁₃	#2002	1	1	yes	characteristic
291	C₂×C₁₃	#2012	1	1	yes	characteristic
292	C₂⁴	—	2	1	no	—
293	C₂⁴	—	4	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	C₁₃×SD₁₆	1	2	yes	complemented
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
326	SD₁₆	—	4	16	no	—
327	D₈	—	4	8	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	2	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	8	4	no	—
346	C₄²	—	4	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₄²	C₁₃×#41	1	1	yes	characteristic
352	C₁₃	#10048	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	1	no	—
360	C₂³	—	8	1	no	—
361	C₂³	—	8	2	no	—
362	C₂³	—	8	2	no	—
363	C₂³	C₁₃×#120	1	1	yes	characteristic
364	Q₈	—	4	4	no	—
365	Q₈	—	8	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	1	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	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	4	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
391	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
392	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
393	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
394	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
395	C₂×C₄	C₁₃×#127	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	2	yes	—
399	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
401	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	4	2	no	—
404	C₈	—	8	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	16	2	no	—
415	C₂²	C₁₃×#392	1	1	yes	characteristic
416	C₂²	C₁₃×#448	1	1	yes	characteristic
417	C₂²	C₁₃×#449	1	1	yes	characteristic
418	C₂²	C₁₃×#449	1	2	yes	—
419	C₂²	C₁₃×#453	1	2	yes	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	2	no	—
425	C₄	C₁₃×#450	1	1	yes	characteristic
426	C₄	C₁₃×#452	1	1	yes	characteristic
427	C₄	C₁₃×#463	1	2	yes	—
428	C₄	C₁₃×#465	1	1	yes	characteristic
429	C₄	C₁₃×#468	1	1	yes	characteristic
430	C₄	C₁₃×#495	1	1	yes	characteristic
431	C₄	C₁₃×#496	1	1	yes	characteristic
432	C₂	—	8	2	no	—
433	C₂	—	16	2	no	—
434	C₂	C₁₃×#1622	1	2	yes	—
435	C₂	C₁₃×#1624	1	2	yes	—
436	C₂	C₁₃×#2000	1	1	yes	characteristic
437	C₂	C₁₃×#2002	1	1	yes	characteristic
438	C₂	C₁₃×#2012	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
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×#492	C₂	semidirect
3. C₁₃×#2563	C₂	semidirect
4. C₁₃×#1982	C₂	semidirect
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
73. #10048	C₁₃	direct (N × H)
97. C₂×D₄×C₁₃	SD₁₆	semidirect
134. C₂×#492	C₂×C₁₃	semidirect
136. #2563	C₂×C₁₃	semidirect
137. #1982	C₂×C₁₃	semidirect
138. C₂×#333	C₂×C₁₃	semidirect
139. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
140. #1279	C₂×C₁₃	semidirect
315. C₂×D₄	C₁₃×SD₁₆	semidirect
352. C₁₃	#10048	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×#492	2
C₂×C₁₃×#459	2
C₁₃×#2563	2
C₁₃×#1982	2
C₂×C₁₃×#333	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
#10048	13

Subgroups — C13×#10048 #15696387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10048 #15696387