Subgroups — C₁₃×#10229 #15696568

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂²×C₁₃×D₈	—	2	1	no	—
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#460	—	2	2	no	—
15	C₁₃×#460	—	2	2	no	—
16	C₁₃×#459	—	2	2	no	—
17	C₁₃×#459	—	2	2	no	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	—	2	1	no	—
21	C₂×C₁₃×#102	—	2	1	no	—
22	C₂×C₁₃×#102	—	2	2	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#396	—	2	2	no	—
25	C₁₃×#390	—	2	1	no	—
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#384	C₂²	1	1	yes	characteristic
28	C₁₃×#380	—	2	1	no	—
29	C₁₃×Q₈⋊C₈	—	2	2	no	—
30	C₁₃×D₄⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₃	—	2	1	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	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂×C₁₃×SD₁₆	—	2	4	no	—
38	C₂×C₁₃×SD₁₆	—	4	2	no	—
39	C₂×C₁₃×SD₁₆	—	4	2	no	—
40	C₂×C₁₃×D₈	—	2	4	no	—
41	C₂×C₁₃×D₈	—	4	2	no	—
42	C₂×C₁₃×D₈	—	4	2	no	—
43	C₂²×C₈×C₁₃	—	2	1	no	—
44	C₂²×C₈×C₁₃	—	2	1	no	—
45	C₂²×C₈×C₁₃	—	2	1	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	C₁₃×C₂²⋊Q₈	—	4	2	no	—
51	C₁₃×C₂²⋊Q₈	—	4	2	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×Q₈×C₁₃	—	2	1	no	—
55	C₄×Q₈×C₁₃	—	2	1	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	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	—	2	1	no	—
74	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
75	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
76	C₁₃×#102	—	2	4	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₁₃×#102	—	4	4	no	—
79	C₄×C₈×C₁₃	—	2	1	no	—
80	C₄×C₈×C₁₃	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	#10229	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	2	1	no	—
84	C₂⁴×C₁₃	—	4	1	no	—
85	C₂×Q₈×C₁₃	—	2	1	no	—
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	D₈	1	2	yes	complemented
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	2	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	—	4	1	no	—
111	C₂×D₄×C₁₃	—	4	1	no	—
112	C₂×D₄×C₁₃	SD₁₆	1	2	yes	complemented
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	—	4	1	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	—	4	1	no	—
122	C₂²×C₄×C₁₃	—	4	1	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×SD₁₆	—	4	8	no	—
127	C₁₃×D₈	—	4	8	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	4	1	no	—
132	C₂×C₈×C₁₃	—	4	1	no	—
133	C₂×C₈×C₁₃	—	4	1	no	—
134	C₂×C₈×C₁₃	—	4	1	no	—
135	C₂×C₈×C₁₃	—	4	1	no	—
136	C₂×C₈×C₁₃	—	4	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₁₃×C₄⋊C₄	—	4	1	no	—
144	C₁₃×C₄⋊C₄	—	4	1	no	—
145	C₁₃×C₄⋊C₄	—	4	1	no	—
146	C₁₃×C₄⋊C₄	—	4	1	no	—
147	C₁₃×C₄⋊C₄	—	4	1	no	—
148	C₁₃×C₄⋊C₄	—	4	1	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	1	no	—
151	C₁₃×C₂²⋊C₄	—	4	1	no	—
152	C₁₃×C₂²⋊C₄	—	8	2	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	C₄²×C₁₃	—	4	1	no	—
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₁₃	#41	1	1	yes	characteristic
159	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
161	#2538	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1296	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	1	no	—
171	C₂³×C₁₃	—	4	1	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	8	1	no	—
175	C₂³×C₁₃	—	8	1	no	—
176	C₂³×C₁₃	—	8	1	no	—
177	C₂³×C₁₃	—	8	1	no	—
178	C₂³×C₁₃	—	8	1	no	—
179	C₂³×C₁₃	—	8	1	no	—
180	C₂³×C₁₃	#120	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	—	4	1	no	—
184	Q₈×C₁₃	—	4	1	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	4	4	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	1	no	—
194	D₄×C₁₃	—	8	2	no	—
195	D₄×C₁₃	—	8	1	no	—
196	D₄×C₁₃	—	8	1	no	—
197	D₄×C₁₃	—	8	1	no	—
198	D₄×C₁₃	—	8	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	8	1	no	—
214	C₂×C₄×C₁₃	—	8	1	no	—
215	C₂×C₄×C₁₃	—	8	1	no	—
216	C₂×C₄×C₁₃	—	8	1	no	—
217	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
219	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
227	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
231	C₈×C₁₃	—	4	2	no	—
232	C₈×C₁₃	—	4	2	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₂²×SD₁₆	—	2	1	no	—
235	C₂²×D₈	—	2	1	no	—
236	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
240	#460	—	2	2	no	—
241	#460	—	2	2	no	—
242	#459	—	2	2	no	—
243	#459	—	2	2	no	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#102	—	2	1	no	—
247	C₂×#102	—	2	1	no	—
248	C₂×#102	—	2	2	no	—
249	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
250	#396	—	2	2	no	—
251	#390	—	2	1	no	—
252	#389	—	2	1	no	—
253	#384	C₂²×C₁₃	1	1	yes	characteristic
254	#380	—	2	1	no	—
255	Q₈⋊C₈	—	2	2	no	—
256	D₄⋊C₈	—	2	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	8	1	no	—
261	C₂²×C₁₃	—	8	1	no	—
262	C₂²×C₁₃	—	8	1	no	—
263	C₂²×C₁₃	—	8	1	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	2	no	—
266	C₂²×C₁₃	—	8	2	no	—
267	C₂²×C₁₃	—	16	1	no	—
268	C₂²×C₁₃	—	16	1	no	—
269	C₂²×C₁₃	—	16	1	no	—
270	C₂²×C₁₃	—	16	1	no	—
271	C₂²×C₁₃	#392	1	1	yes	characteristic
272	C₂²×C₁₃	#447	1	1	yes	characteristic
273	C₂²×C₁₃	#448	1	1	yes	characteristic
274	C₂²×C₁₃	#449	1	1	yes	characteristic
275	C₂²×C₁₃	#449	1	1	yes	characteristic
276	C₂²×C₁₃	#453	1	1	yes	characteristic
277	C₂²×C₁₃	#454	1	1	yes	characteristic
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	8	2	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	—	8	1	no	—
284	C₄×C₁₃	#447	1	1	yes	characteristic
285	C₄×C₁₃	#449	1	1	yes	characteristic
286	C₄×C₁₃	#450	1	1	yes	characteristic
287	C₄×C₁₃	#452	1	1	yes	characteristic
288	C₄×C₁₃	#465	1	1	yes	characteristic
289	C₄×C₁₃	#466	1	1	yes	characteristic
290	C₄×C₁₃	#468	1	1	yes	characteristic
291	C₄×C₁₃	#469	1	1	yes	characteristic
292	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂×SD₁₆	—	4	2	no	—
301	C₂×D₈	—	2	4	no	—
302	C₂×D₈	—	4	2	no	—
303	C₂×D₈	—	4	2	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	—	2	1	no	—
310	#127	D₄×C₁₃	1	2	yes	—
311	C₂²⋊Q₈	—	4	2	no	—
312	C₂²⋊Q₈	—	4	2	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
336	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
337	#102	—	2	4	no	—
338	#102	—	2	4	no	—
339	#102	—	4	4	no	—
340	C₄×C₈	—	2	1	no	—
341	C₄×C₈	—	2	1	no	—
342	#95	—	2	2	no	—
343	C₂×C₁₃	—	8	2	no	—
344	C₂×C₁₃	—	16	2	no	—
345	C₂×C₁₃	#1621	1	1	yes	characteristic
346	C₂×C₁₃	#1622	1	1	yes	characteristic
347	C₂×C₁₃	#1627	1	1	yes	characteristic
348	C₂×C₁₃	#1628	1	1	yes	characteristic
349	C₂×C₁₃	#1999	1	1	yes	characteristic
350	C₂×C₁₃	#2000	1	1	yes	characteristic
351	C₂×C₁₃	#2006	1	1	yes	characteristic
352	C₂⁴	—	2	1	no	—
353	C₂⁴	—	4	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	C₁₃×D₈	1	2	yes	complemented
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	C₁₃×SD₁₆	1	2	yes	complemented
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	SD₁₆	—	4	8	no	—
396	D₈	—	4	8	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	1	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	—	4	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₄²	—	4	1	no	—
423	C₄²	—	4	1	no	—
424	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₄²	C₁₃×#41	1	1	yes	characteristic
428	C₁₃	#10229	1	1	yes	characteristic, direct product factor, Sylow
429	C₂³	—	2	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	1	no	—
438	C₂³	—	8	1	no	—
439	C₂³	—	8	1	no	—
440	C₂³	—	8	1	no	—
441	C₂³	—	8	1	no	—
442	C₂³	—	8	1	no	—
443	C₂³	C₁₃×#120	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	1	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	1	no	—
457	D₄	—	8	2	no	—
458	D₄	—	8	1	no	—
459	D₄	—	8	1	no	—
460	D₄	—	8	1	no	—
461	D₄	—	8	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	1	no	—
477	C₂×C₄	—	8	1	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
481	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
482	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
483	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
484	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
485	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
488	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
489	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
490	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
491	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
492	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
493	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	16	1	no	—
508	C₂²	—	16	1	no	—
509	C₂²	—	16	1	no	—
510	C₂²	—	16	1	no	—
511	C₂²	C₁₃×#392	1	1	yes	characteristic
512	C₂²	C₁₃×#447	1	1	yes	characteristic
513	C₂²	C₁₃×#448	1	1	yes	characteristic
514	C₂²	C₁₃×#449	1	1	yes	characteristic
515	C₂²	C₁₃×#449	1	1	yes	characteristic
516	C₂²	C₁₃×#453	1	1	yes	characteristic
517	C₂²	C₁₃×#454	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₁₃×#447	1	1	yes	characteristic
525	C₄	C₁₃×#449	1	1	yes	characteristic
526	C₄	C₁₃×#450	1	1	yes	characteristic
527	C₄	C₁₃×#452	1	1	yes	characteristic
528	C₄	C₁₃×#465	1	1	yes	characteristic
529	C₄	C₁₃×#466	1	1	yes	characteristic
530	C₄	C₁₃×#468	1	1	yes	characteristic
531	C₄	C₁₃×#469	1	1	yes	characteristic
532	C₂	—	8	2	no	—
533	C₂	—	16	2	no	—
534	C₂	C₁₃×#1621	1	1	yes	characteristic
535	C₂	C₁₃×#1622	1	1	yes	characteristic
536	C₂	C₁₃×#1627	1	1	yes	characteristic
537	C₂	C₁₃×#1628	1	1	yes	characteristic
538	C₂	C₁₃×#1999	1	1	yes	characteristic
539	C₂	C₁₃×#2000	1	1	yes	characteristic
540	C₂	C₁₃×#2006	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×#460	C₂	semidirect
3. C₁₃×#2538	C₂	semidirect
4. C₁₃×#1957	C₂	semidirect
5. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
6. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
7. C₁₃×#1296	C₂	semidirect
82. #10229	C₁₃	direct (N × H)
90. C₂×Q₈×C₁₃	D₈	semidirect
112. C₂×D₄×C₁₃	SD₁₆	semidirect
159. C₂×#460	C₂×C₁₃	semidirect
161. #2538	C₂×C₁₃	semidirect
162. #1957	C₂×C₁₃	semidirect
163. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
164. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
165. #1296	C₂×C₁₃	semidirect
359. C₂×Q₈	C₁₃×D₈	semidirect
381. C₂×D₄	C₁₃×SD₁₆	semidirect
428. C₁₃	#10229	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×#460	2
C₂×C₁₃×#459	2
C₁₃×#2538	2
C₁₃×#1957	2
C₂×C₁₃×Q₈⋊C₈	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1296	2
#10229	13

Subgroups — C13×#10229 #15696568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10229 #15696568