Subgroups — C₁₃×#61402 #15747741

Order 3328.

2244 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3397	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3391	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3151	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3038	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3036	C₂	1	3	yes	maximal, complemented
10	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	3	yes	maximal, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	3	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	—
15	C₁₃×#559	C₂²	1	3	yes	complemented
16	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#556	C₂²	1	3	yes	complemented
18	C₁₃×#553	—	2	3	no	—
19	C₁₃×#550	—	2	1	no	—
20	C₁₃×#550	—	2	3	no	—
21	C₁₃×#550	C₂²	1	2	yes	—
22	C₁₃×#550	C₂²	1	6	yes	—
23	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#548	—	2	1	no	—
25	C₁₃×#532	C₂²	1	3	yes	—
26	C₂×C₁₃×#127	C₂²	1	3	yes	—
27	C₁₃×#529	—	2	3	no	—
28	C₂×C₁₃×#121	—	2	3	no	—
29	C₄×C₁₃×#41	—	2	1	no	—
30	C₄×C₁₃×#41	C₂²	1	3	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
33	C₁₃×#496	C₂²	1	12	yes	complemented
34	C₁₃×#493	C₂²	1	6	yes	complemented
35	C₁₃×#492	C₂²	1	6	yes	complemented
36	C₁₃×#463	C₂²	1	12	yes	complemented
37	C₁₃×#461	C₂²	1	6	yes	complemented
38	C₁₃×#460	C₂²	1	6	yes	complemented
39	C₁₃×#460	C₂²	1	6	yes	complemented
40	C₁₃×#459	C₂²	1	6	yes	complemented
41	C₁₃×#459	C₂²	1	6	yes	complemented
42	C₁₃×#459	C₂²	1	6	yes	complemented
43	C₁₃×#446	C₂²	1	6	yes	complemented
44	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
45	C₁₃×#442	C₂²	1	6	yes	complemented
46	C₁₃×#440	C₂²	1	6	yes	complemented
47	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
48	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
49	C₁₃×#428	C₂²	1	1	yes	characteristic
50	C₁₃×#423	C₂²	1	3	yes	—
51	C₁₃×#418	C₂²	1	3	yes	—
52	C₁₃×#417	C₂²	1	3	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	6	no	—
56	C₂×C₁₃×#41	—	2	2	no	—
57	C₂×C₁₃×#41	—	4	8	no	—
58	C₂×C₁₃×#41	C₂³	1	3	yes	—
59	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	3	no	—
61	C₂²×D₄×C₁₃	—	2	3	no	—
62	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃	—	2	3	no	—
64	C₁₃×AGL(1,ℤ/8)	—	2	12	no	—
65	C₁₃×AGL(1,ℤ/8)	—	4	12	no	—
66	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
67	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
68	C₂×C₁₃×D₈	C₂³	1	6	yes	—
69	C₂×C₁₃×D₈	C₂³	1	12	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₃×#127	—	2	3	no	—
74	C₁₃×#127	—	2	3	no	—
75	C₁₃×#127	C₂³	1	3	yes	—
76	C₁₃×#127	C₂³	1	6	yes	—
77	C₁₃×#127	C₂³	1	6	yes	—
78	C₁₃×#126	—	2	6	no	—
79	C₁₃×#125	—	2	3	no	—
80	C₁₃×#124	—	2	3	no	—
81	C₁₃×#124	C₂³	1	6	yes	—
82	C₁₃×#123	—	2	6	no	—
83	C₁₃×C₂²⋊Q₈	—	2	3	no	—
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	—	2	3	no	—
86	C₁₃×#121	—	2	6	no	—
87	C₁₃×#121	—	2	6	no	—
88	C₁₃×#121	—	2	12	no	—
89	C₁₃×#121	—	2	3	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	D₄	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	—	2	3	no	—
101	C₄×D₄×C₁₃	—	2	3	no	—
102	C₄×D₄×C₁₃	—	2	3	no	—
103	C₄×D₄×C₁₃	—	2	3	no	—
104	C₄×D₄×C₁₃	C₂³	1	3	yes	—
105	C₄×D₄×C₁₃	C₂³	1	6	yes	—
106	C₄×D₄×C₁₃	C₂³	1	6	yes	—
107	C₄×D₄×C₁₃	C₂³	1	3	yes	—
108	C₁₃×#117	—	2	3	no	—
109	C₁₃×#117	—	2	3	no	—
110	C₁₃×#117	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
114	C₂×C₄²×C₁₃	—	2	3	no	—
115	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
116	C₁₃×#107	C₂³	1	2	yes	—
117	C₁₃×#106	C₂³	1	2	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
119	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
120	C₁₃×#103	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	6	yes	—
122	C₁₃×#102	C₂³	1	6	yes	—
123	C₁₃×#102	C₂³	1	6	yes	—
124	C₁₃×#97	C₂³	1	6	yes	—
125	C₄×C₈×C₁₃	C₂³	1	6	yes	—
126	#61402	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	3	no	—
128	C₁₃×#41	—	2	6	no	—
129	C₁₃×#41	—	2	6	no	—
130	C₁₃×#41	—	4	24	no	—
131	C₁₃×#41	—	4	4	no	—
132	C₁₃×#41	—	4	8	no	—
133	C₂×Q₈×C₁₃	—	2	4	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	—	2	3	no	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	—	2	6	no	—
144	C₂×D₄×C₁₃	—	2	6	no	—
145	C₂×D₄×C₁₃	—	2	6	no	—
146	C₂×D₄×C₁₃	—	2	6	no	—
147	C₂×D₄×C₁₃	—	4	12	no	—
148	C₂×D₄×C₁₃	—	8	6	no	—
149	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
150	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	3	no	—
153	C₂²×C₄×C₁₃	—	2	3	no	—
154	C₂²×C₄×C₁₃	—	2	6	no	—
155	C₂²×C₄×C₁₃	—	2	6	no	—
156	C₂²×C₄×C₁₃	—	2	3	no	—
157	C₂²×C₄×C₁₃	—	4	12	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×SD₁₆	—	2	12	no	—
162	C₁₃×SD₁₆	—	4	12	no	—
163	C₁₃×D₈	—	2	12	no	—
164	C₁₃×D₈	—	4	12	no	—
165	C₁₃×M₁₆	—	2	6	no	—
166	C₁₃×M₁₆	#41	1	4	yes	complemented
167	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	3	no	—
171	C₁₃×C₄⋊C₄	—	2	3	no	—
172	C₁₃×C₄⋊C₄	—	2	3	no	—
173	C₁₃×C₄⋊C₄	—	2	3	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
180	C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	6	no	—
182	C₁₃×C₂²⋊C₄	—	2	6	no	—
183	C₁₃×C₂²⋊C₄	—	2	6	no	—
184	C₁₃×C₂²⋊C₄	—	2	3	no	—
185	C₁₃×C₂²⋊C₄	—	2	3	no	—
186	C₁₃×C₂²⋊C₄	—	2	6	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	3	no	—
189	C₄²×C₁₃	—	2	3	no	—
190	C₄²×C₁₃	C₂×D₄	1	3	yes	—
191	C₄²×C₁₃	C₂×D₄	1	3	yes	—
192	C₄²×C₁₃	C₂⁴	1	3	yes	—
193	C₄²×C₁₃	C₂⁴	1	3	yes	—
194	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#3399	C₂×C₁₃	1	6	yes	complemented
197	#3397	C₂×C₁₃	1	6	yes	complemented
198	#3392	C₂×C₁₃	1	2	yes	complemented
199	#3391	C₂×C₁₃	1	2	yes	complemented
200	#3151	C₂×C₁₃	1	3	yes	complemented
201	#3038	C₂×C₁₃	1	3	yes	complemented
202	#3036	C₂×C₁₃	1	3	yes	complemented
203	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	3	yes	complemented
205	C₂³×C₁₃	—	2	3	no	—
206	C₂³×C₁₃	—	2	6	no	—
207	C₂³×C₁₃	—	4	6	no	—
208	C₂³×C₁₃	—	4	6	no	—
209	C₂³×C₁₃	—	4	6	no	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	6	no	—
212	Q₈×C₁₃	—	2	3	no	—
213	Q₈×C₁₃	—	2	3	no	—
214	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
215	D₄×C₁₃	—	2	3	no	—
216	D₄×C₁₃	—	2	6	no	—
217	D₄×C₁₃	—	2	3	no	—
218	D₄×C₁₃	—	2	6	no	—
219	D₄×C₁₃	—	4	12	no	—
220	D₄×C₁₃	—	4	6	no	—
221	D₄×C₁₃	—	4	6	no	—
222	D₄×C₁₃	—	4	12	no	—
223	D₄×C₁₃	—	4	6	no	—
224	D₄×C₁₃	—	8	3	no	—
225	D₄×C₁₃	—	8	6	no	—
226	D₄×C₁₃	—	8	6	no	—
227	C₂×C₄×C₁₃	—	2	6	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	3	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	4	3	no	—
233	C₂×C₄×C₁₃	—	4	12	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	6	no	—
236	C₂×C₄×C₁₃	—	4	12	no	—
237	C₂×C₄×C₁₃	—	4	6	no	—
238	C₂×C₄×C₁₃	—	8	3	no	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
244	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
247	C₈×C₁₃	—	2	6	no	—
248	C₈×C₁₃	C₂×#41	1	4	yes	complemented
249	C₂²×#41	—	2	1	no	—
250	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	3	yes	—
251	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	—
252	#559	C₂²×C₁₃	1	3	yes	complemented
253	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
254	#556	C₂²×C₁₃	1	3	yes	complemented
255	#553	—	2	3	no	—
256	#550	—	2	1	no	—
257	#550	—	2	3	no	—
258	#550	C₂²×C₁₃	1	2	yes	—
259	#550	C₂²×C₁₃	1	6	yes	—
260	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
261	#548	—	2	1	no	—
262	#532	C₂²×C₁₃	1	3	yes	—
263	C₂×#127	C₂²×C₁₃	1	3	yes	—
264	#529	—	2	3	no	—
265	C₂×#121	—	2	3	no	—
266	C₄×#41	—	2	1	no	—
267	C₄×#41	C₂²×C₁₃	1	3	yes	—
268	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
270	#496	C₂²×C₁₃	1	12	yes	complemented
271	#493	C₂²×C₁₃	1	6	yes	complemented
272	#492	C₂²×C₁₃	1	6	yes	complemented
273	#463	C₂²×C₁₃	1	12	yes	complemented
274	#461	C₂²×C₁₃	1	6	yes	complemented
275	#460	C₂²×C₁₃	1	6	yes	complemented
276	#460	C₂²×C₁₃	1	6	yes	complemented
277	#459	C₂²×C₁₃	1	6	yes	complemented
278	#459	C₂²×C₁₃	1	6	yes	complemented
279	#459	C₂²×C₁₃	1	6	yes	complemented
280	#446	C₂²×C₁₃	1	6	yes	complemented
281	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
282	#442	C₂²×C₁₃	1	6	yes	complemented
283	#440	C₂²×C₁₃	1	6	yes	complemented
284	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
285	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
286	#428	C₂²×C₁₃	1	1	yes	characteristic
287	#423	C₂²×C₁₃	1	3	yes	—
288	#418	C₂²×C₁₃	1	3	yes	—
289	#417	C₂²×C₁₃	1	3	yes	—
290	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	4	3	no	—
294	C₂²×C₁₃	—	4	6	no	—
295	C₂²×C₁₃	—	4	3	no	—
296	C₂²×C₁₃	—	4	6	no	—
297	C₂²×C₁₃	—	4	6	no	—
298	C₂²×C₁₃	—	4	3	no	—
299	C₂²×C₁₃	—	8	12	no	—
300	C₂²×C₁₃	#550	1	2	yes	—
301	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
302	C₄×C₁₃	—	2	3	no	—
303	C₄×C₁₃	—	2	3	no	—
304	C₄×C₁₃	—	2	3	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	—	4	3	no	—
307	C₄×C₁₃	—	4	1	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	#550	1	2	yes	—
310	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
311	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
312	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	6	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	4	8	no	—
317	C₂×#41	C₂³×C₁₃	1	3	yes	—
318	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
319	C₂²×D₄	—	2	3	no	—
320	C₂²×D₄	—	2	3	no	—
321	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
322	C₂³×C₄	—	2	3	no	—
323	AGL(1,ℤ/8)	—	2	12	no	—
324	AGL(1,ℤ/8)	—	4	12	no	—
325	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
326	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
327	C₂×D₈	C₂³×C₁₃	1	6	yes	—
328	C₂×D₈	C₂³×C₁₃	1	12	yes	—
329	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
330	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
332	#127	—	2	3	no	—
333	#127	—	2	3	no	—
334	#127	C₂³×C₁₃	1	6	yes	—
335	#127	C₂³×C₁₃	1	6	yes	—
336	#127	C₂³×C₁₃	1	3	yes	—
337	#126	—	2	6	no	—
338	#125	—	2	3	no	—
339	#124	—	2	3	no	—
340	#124	C₂³×C₁₃	1	6	yes	—
341	#123	—	2	6	no	—
342	C₂²⋊Q₈	—	2	3	no	—
343	#121	—	2	3	no	—
344	#121	—	2	3	no	—
345	#121	—	2	6	no	—
346	#121	—	2	6	no	—
347	#121	—	2	12	no	—
348	#121	—	2	3	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
351	C₄×Q₈	D₄×C₁₃	1	3	yes	—
352	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
353	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
354	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
356	C₄×D₄	—	2	3	no	—
357	C₄×D₄	—	2	3	no	—
358	C₄×D₄	—	2	3	no	—
359	C₄×D₄	—	2	3	no	—
360	C₄×D₄	—	2	3	no	—
361	C₄×D₄	—	2	3	no	—
362	C₄×D₄	—	2	3	no	—
363	C₄×D₄	C₂³×C₁₃	1	6	yes	—
364	C₄×D₄	C₂³×C₁₃	1	6	yes	—
365	C₄×D₄	C₂³×C₁₃	1	3	yes	—
366	C₄×D₄	C₂³×C₁₃	1	3	yes	—
367	#117	—	2	3	no	—
368	#117	—	2	3	no	—
369	#117	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	2	3	no	—
373	C₂×C₄²	—	2	3	no	—
374	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
375	#107	C₂³×C₁₃	1	2	yes	—
376	#106	C₂³×C₁₃	1	2	yes	—
377	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
378	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
379	#103	C₂³×C₁₃	1	6	yes	—
380	#102	C₂³×C₁₃	1	6	yes	—
381	#102	C₂³×C₁₃	1	6	yes	—
382	#102	C₂³×C₁₃	1	6	yes	—
383	#97	C₂³×C₁₃	1	6	yes	—
384	C₄×C₈	C₂³×C₁₃	1	6	yes	—
385	C₂×C₁₃	—	2	2	no	—
386	C₂×C₁₃	—	8	3	no	—
387	C₂×C₁₃	—	8	6	no	—
388	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
389	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₂×C₁₃	#3585	1	1	yes	characteristic
391	C₂⁴	—	2	3	no	—
392	#41	—	2	6	no	—
393	#41	—	2	6	no	—
394	#41	—	4	24	no	—
395	#41	—	4	8	no	—
396	#41	—	4	4	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
399	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
401	C₂×D₄	—	2	3	no	—
402	C₂×D₄	—	2	3	no	—
403	C₂×D₄	—	2	3	no	—
404	C₂×D₄	—	2	6	no	—
405	C₂×D₄	—	2	6	no	—
406	C₂×D₄	—	2	3	no	—
407	C₂×D₄	—	2	6	no	—
408	C₂×D₄	—	2	6	no	—
409	C₂×D₄	—	2	6	no	—
410	C₂×D₄	—	2	6	no	—
411	C₂×D₄	—	4	12	no	—
412	C₂×D₄	—	8	6	no	—
413	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
414	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	3	no	—
417	C₂²×C₄	—	2	3	no	—
418	C₂²×C₄	—	2	6	no	—
419	C₂²×C₄	—	2	6	no	—
420	C₂²×C₄	—	2	3	no	—
421	C₂²×C₄	—	4	12	no	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
425	SD₁₆	—	2	12	no	—
426	SD₁₆	—	4	12	no	—
427	D₈	—	2	12	no	—
428	D₈	—	4	12	no	—
429	M₁₆	—	2	6	no	—
430	M₁₆	C₁₃×#41	1	4	yes	complemented
431	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	3	no	—
435	C₄⋊C₄	—	2	3	no	—
436	C₄⋊C₄	—	2	3	no	—
437	C₄⋊C₄	—	2	3	no	—
438	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
439	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
440	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
441	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	6	no	—
446	C₂²⋊C₄	—	2	6	no	—
447	C₂²⋊C₄	—	2	6	no	—
448	C₂²⋊C₄	—	2	3	no	—
449	C₂²⋊C₄	—	2	3	no	—
450	C₂²⋊C₄	—	2	6	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	3	no	—
453	C₄²	—	2	3	no	—
454	C₄²	C₂×D₄×C₁₃	1	3	yes	—
455	C₄²	C₂×D₄×C₁₃	1	3	yes	—
456	C₄²	C₂⁴×C₁₃	1	3	yes	—
457	C₄²	C₂⁴×C₁₃	1	3	yes	—
458	C₁₃	#61402	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	3	no	—
460	C₂³	—	2	6	no	—
461	C₂³	—	4	6	no	—
462	C₂³	—	4	6	no	—
463	C₂³	—	4	6	no	—
464	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	Q₈	—	2	6	no	—
466	Q₈	—	2	3	no	—
467	Q₈	—	2	3	no	—
468	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
469	D₄	—	2	3	no	—
470	D₄	—	2	6	no	—
471	D₄	—	2	3	no	—
472	D₄	—	2	6	no	—
473	D₄	—	4	12	no	—
474	D₄	—	4	6	no	—
475	D₄	—	4	6	no	—
476	D₄	—	4	12	no	—
477	D₄	—	4	6	no	—
478	D₄	—	8	6	no	—
479	D₄	—	8	6	no	—
480	D₄	—	8	3	no	—
481	C₂×C₄	—	2	6	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	3	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	3	no	—
487	C₂×C₄	—	4	12	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	6	no	—
490	C₂×C₄	—	4	12	no	—
491	C₂×C₄	—	4	6	no	—
492	C₂×C₄	—	8	3	no	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
496	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
498	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
499	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
500	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
501	C₈	—	2	6	no	—
502	C₈	C₂×C₁₃×#41	1	4	yes	complemented
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	6	no	—
506	C₂²	—	4	3	no	—
507	C₂²	—	4	3	no	—
508	C₂²	—	4	6	no	—
509	C₂²	—	4	3	no	—
510	C₂²	—	4	6	no	—
511	C₂²	—	8	12	no	—
512	C₂²	C₁₃×#550	1	2	yes	—
513	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
514	C₄	—	2	3	no	—
515	C₄	—	2	3	no	—
516	C₄	—	2	3	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	3	no	—
521	C₄	C₁₃×#550	1	2	yes	—
522	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
523	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
524	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂	—	2	2	no	—
526	C₂	—	8	6	no	—
527	C₂	—	8	3	no	—
528	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
529	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3397	C₂	semidirect
5. C₁₃×#3392	C₂	semidirect
6. C₁₃×#3391	C₂	semidirect
7. C₁₃×#3151	C₂	semidirect
8. C₁₃×#3038	C₂	semidirect
9. C₁₃×#3036	C₂	semidirect
10. Q₈×C₁₃×M₁₆	C₂	semidirect
11. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₁₃×#559	C₂²	semidirect
16. C₁₃×#557	C₂²	semidirect
17. C₁₃×#556	C₂²	semidirect
23. C₁₃×#550	C₂²	semidirect
33. C₁₃×#496	C₂²	semidirect
34. C₁₃×#493	C₂²	semidirect
35. C₁₃×#492	C₂²	semidirect
36. C₁₃×#463	C₂²	semidirect
37. C₁₃×#461	C₂²	semidirect
38. C₁₃×#460	C₂²	semidirect
39. C₁₃×#460	C₂²	semidirect
40. C₁₃×#459	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₈×Q₈×C₁₃	C₂²	semidirect
45. C₁₃×#442	C₂²	semidirect
46. C₁₃×#440	C₂²	semidirect
47. C₄×C₁₃×SD₁₆	C₂²	semidirect
48. C₄×C₁₃×D₈	C₂²	semidirect
126. #61402	C₁₃	direct (N × H)
166. C₁₃×M₁₆	#41	semidirect
194. #3480	C₂×C₁₃	semidirect
195. C₂×#550	C₂×C₁₃	semidirect
196. #3399	C₂×C₁₃	semidirect
197. #3397	C₂×C₁₃	semidirect
198. #3392	C₂×C₁₃	semidirect
199. #3391	C₂×C₁₃	semidirect
200. #3151	C₂×C₁₃	semidirect
201. #3038	C₂×C₁₃	semidirect
202. #3036	C₂×C₁₃	semidirect
203. Q₈×M₁₆	C₂×C₁₃	semidirect
204. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
214. Q₈×C₁₃	AGL(1,ℤ/8)	semidirect
248. C₈×C₁₃	C₂×#41	semidirect
252. #559	C₂²×C₁₃	semidirect
253. #557	C₂²×C₁₃	semidirect
254. #556	C₂²×C₁₃	semidirect
260. #550	C₂²×C₁₃	semidirect
270. #496	C₂²×C₁₃	semidirect
271. #493	C₂²×C₁₃	semidirect
272. #492	C₂²×C₁₃	semidirect
273. #463	C₂²×C₁₃	semidirect
274. #461	C₂²×C₁₃	semidirect
275. #460	C₂²×C₁₃	semidirect
276. #460	C₂²×C₁₃	semidirect
277. #459	C₂²×C₁₃	semidirect
278. #459	C₂²×C₁₃	semidirect
279. #459	C₂²×C₁₃	semidirect
280. #446	C₂²×C₁₃	semidirect
281. C₈×Q₈	C₂²×C₁₃	semidirect
282. #442	C₂²×C₁₃	semidirect
283. #440	C₂²×C₁₃	semidirect
284. C₄×SD₁₆	C₂²×C₁₃	semidirect
285. C₄×D₈	C₂²×C₁₃	semidirect
430. M₁₆	C₁₃×#41	semidirect
458. C₁₃	#61402	direct (N × H)
468. Q₈	C₁₃×AGL(1,ℤ/8)	semidirect
502. C₈	C₂×C₁₃×#41	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3480	2
C₂×C₁₃×#550	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3392	2
C₁₃×#3391	2
C₁₃×#3151	2
C₁₃×#3038	2
C₁₃×#3036	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61402	13

Subgroups — C13×#61402 #15747741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61402 #15747741