Subgroups — C₁₃×#62001 #15748340

Order 3328.

2216 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×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3391	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3325	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3274	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3253	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3205	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3106	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3038	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
14	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₁₃×#555	—	2	3	no	—
16	C₁₃×#555	C₂²	1	3	yes	complemented
17	C₁₃×#550	—	2	1	no	—
18	C₁₃×#550	—	2	1	no	—
19	C₁₃×#550	C₂²	1	2	yes	—
20	C₁₃×#550	C₂²	1	3	yes	complemented
21	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
22	D₄²×C₁₃	—	2	3	no	—
23	D₄²×C₁₃	C₂²	1	6	yes	—
24	C₁₃×#535	—	2	3	no	—
25	C₁₃×#532	—	2	3	no	—
26	C₁₃×#532	C₂²	1	3	yes	—
27	C₁₃×#532	C₂²	1	3	yes	complemented
28	C₂×C₁₃×#127	C₂²	1	3	yes	—
29	C₄×C₁₃×#41	—	2	1	no	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
32	C₁₃×#493	C₂²	1	6	yes	complemented
33	C₁₃×#486	C₂²	1	6	yes	complemented
34	C₁₃×#482	C₂²	1	6	yes	complemented
35	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#476	C₂²	1	6	yes	complemented
37	C₁₃×#476	C₂²	1	3	yes	complemented
38	C₁₃×#469	C₂²	1	12	yes	complemented
39	C₁₃×#460	C₂²	1	6	yes	complemented
40	C₁₃×#460	C₂²	1	3	yes	complemented
41	C₁₃×#459	C₂²	1	6	yes	complemented
42	C₁₃×#459	C₂²	1	6	yes	complemented
43	C₁₃×#459	C₂²	1	6	yes	complemented
44	C₁₃×#459	C₂²	1	3	yes	complemented
45	C₁₃×#449	C₂²	1	6	yes	complemented
46	C₁₃×#447	C₂²	1	12	yes	complemented
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
49	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
50	C₁₃×#436	C₂²	1	6	yes	complemented
51	C₁₃×#431	C₂²	1	3	yes	complemented
52	C₁₃×#423	C₂²	1	3	yes	complemented
53	C₁₃×#418	C₂²	1	6	yes	complemented
54	C₁₃×H(5,𝔽₂)	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂×C₁₃×#41	—	2	2	no	—
57	C₂×C₁₃×#41	—	2	3	no	—
58	C₂×C₁₃×#41	—	2	3	no	—
59	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
60	C₂×C₁₃×#41	C₂³	1	3	yes	—
61	C₂²×D₄×C₁₃	—	2	6	no	—
62	C₂²×D₄×C₁₃	—	2	3	no	—
63	C₂²×D₄×C₁₃	—	2	3	no	—
64	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
65	C₁₃×AGL(1,ℤ/8)	—	4	12	no	—
66	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
67	C₂×C₁₃×D₈	C₂³	1	6	yes	—
68	C₂×C₁₃×D₈	C₂³	1	12	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
70	C₁₃×C₄⋊Q₈	—	2	3	no	—
71	C₁₃×C₄⋊Q₈	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	—	2	3	no	—
76	C₁₃×#127	C₂³	1	3	yes	—
77	C₁₃×#127	C₂³	1	3	yes	—
78	C₁₃×#127	C₂³	1	6	yes	—
79	C₁₃×#124	—	2	6	no	—
80	C₁₃×#124	—	2	3	no	—
81	C₁₃×#124	—	2	3	no	—
82	C₁₃×#121	—	2	3	no	—
83	C₁₃×#121	—	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	6	no	—
89	C₁₃×#121	C₂³	1	6	yes	—
90	C₁₃×#121	C₂³	1	6	yes	—
91	C₁₃×#120	—	2	12	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	D₄	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	3	yes	—
104	C₄×D₄×C₁₃	C₂³	1	6	yes	—
105	C₄×D₄×C₁₃	C₂³	1	3	yes	—
106	C₄×D₄×C₁₃	C₂³	1	3	yes	—
107	C₁₃×#117	—	2	3	no	—
108	C₁₃×#117	—	2	3	no	—
109	C₁₃×#117	D₄	1	3	yes	—
110	C₁₃×#117	C₂³	1	3	yes	—
111	C₂×C₄²×C₁₃	—	2	3	no	—
112	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
113	C₁₃×#107	C₂³	1	2	yes	—
114	C₁₃×#106	C₂³	1	6	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	C₂³	1	2	yes	—
119	C₁₃×#102	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	12	yes	—
121	C₁₃×#102	C₂³	1	6	yes	—
122	C₁₃×#102	C₂³	1	6	yes	—
123	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
124	C₄×C₈×C₁₃	C₂³	1	6	yes	—
125	#62001	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	6	no	—
127	C₁₃×#41	—	2	4	no	—
128	C₁₃×#41	—	2	6	no	—
129	C₁₃×#41	—	4	3	no	—
130	C₁₃×#41	—	4	12	no	—
131	C₁₃×#41	—	4	4	no	—
132	C₁₃×#41	—	4	8	no	—
133	C₁₃×#41	—	8	6	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	3	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₃	—	2	3	no	—
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	3	no	—
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	—	2	6	no	—
144	C₂×D₄×C₁₃	—	2	3	no	—
145	C₂×D₄×C₁₃	—	2	6	no	—
146	C₂×D₄×C₁₃	—	2	6	no	—
147	C₂×D₄×C₁₃	—	2	3	no	—
148	C₂×D₄×C₁₃	—	4	6	no	—
149	C₂×D₄×C₁₃	—	4	6	no	—
150	C₂×D₄×C₁₃	—	4	12	no	—
151	C₂×D₄×C₁₃	—	4	24	no	—
152	C₂×D₄×C₁₃	—	8	6	no	—
153	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₁₃	—	2	3	no	—
157	C₂²×C₄×C₁₃	—	2	3	no	—
158	C₂²×C₄×C₁₃	—	2	3	no	—
159	C₂²×C₄×C₁₃	—	2	6	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
163	C₁₃×SD₁₆	—	2	12	no	—
164	C₁₃×D₈	—	4	6	no	—
165	C₁₃×D₈	—	4	12	no	—
166	C₁₃×M₁₆	—	4	6	no	—
167	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	6	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	1	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
175	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
178	C₁₃×C₂²⋊C₄	—	2	3	no	—
179	C₁₃×C₂²⋊C₄	—	2	6	no	—
180	C₁₃×C₂²⋊C₄	—	2	3	no	—
181	C₁₃×C₂²⋊C₄	—	2	3	no	—
182	C₁₃×C₂²⋊C₄	—	2	6	no	—
183	C₁₃×C₂²⋊C₄	—	2	6	no	—
184	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	3	no	—
187	C₄²×C₁₃	—	2	3	no	—
188	C₄²×C₁₃	C₂×D₄	1	3	yes	—
189	C₄²×C₁₃	C₂×D₄	1	3	yes	—
190	C₄²×C₁₃	C₂⁴	1	3	yes	—
191	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
192	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#3391	C₂×C₁₃	1	2	yes	complemented
195	#3362	C₂×C₁₃	1	2	yes	complemented
196	#3325	C₂×C₁₃	1	6	yes	complemented
197	#3274	C₂×C₁₃	1	6	yes	complemented
198	#3253	C₂×C₁₃	1	3	yes	complemented
199	#3205	C₂×C₁₃	1	3	yes	complemented
200	#3106	C₂×C₁₃	1	3	yes	complemented
201	#3038	C₂×C₁₃	1	3	yes	complemented
202	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂³×C₁₃	—	2	3	no	—
204	C₂³×C₁₃	—	2	6	no	—
205	C₂³×C₁₃	—	4	12	no	—
206	C₂³×C₁₃	—	8	6	no	—
207	C₂³×C₁₃	—	8	6	no	—
208	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
209	Q₈×C₁₃	—	2	1	no	—
210	Q₈×C₁₃	—	4	2	no	—
211	Q₈×C₁₃	—	8	3	no	—
212	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
213	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	complemented
214	D₄×C₁₃	—	2	6	no	—
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	6	no	—
220	D₄×C₁₃	—	4	6	no	—
221	D₄×C₁₃	—	4	12	no	—
222	D₄×C₁₃	—	4	12	no	—
223	D₄×C₁₃	—	4	6	no	—
224	D₄×C₁₃	—	4	6	no	—
225	D₄×C₁₃	—	8	6	no	—
226	D₄×C₁₃	—	8	6	no	—
227	D₄×C₁₃	—	8	3	no	—
228	D₄×C₁₃	—	8	6	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	6	no	—
231	C₂×C₄×C₁₃	—	2	6	no	—
232	C₂×C₄×C₁₃	—	2	3	no	—
233	C₂×C₄×C₁₃	—	2	3	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	3	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	4	6	no	—
238	C₂×C₄×C₁₃	—	4	12	no	—
239	C₂×C₄×C₁₃	—	4	6	no	—
240	C₂×C₄×C₁₃	—	4	6	no	—
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	C₂²×D₄	1	3	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
247	C₈×C₁₃	—	2	6	no	—
248	C₈×C₁₃	—	2	2	no	—
249	C₂×H(5,𝔽₂)	—	2	1	no	—
250	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	complemented
251	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
252	#555	—	2	3	no	—
253	#555	C₂²×C₁₃	1	3	yes	complemented
254	#550	—	2	1	no	—
255	#550	—	2	1	no	—
256	#550	C₂²×C₁₃	1	2	yes	—
257	#550	C₂²×C₁₃	1	3	yes	complemented
258	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
259	D₄²	—	2	3	no	—
260	D₄²	C₂²×C₁₃	1	6	yes	—
261	#535	—	2	3	no	—
262	#532	—	2	3	no	—
263	#532	C₂²×C₁₃	1	3	yes	—
264	#532	C₂²×C₁₃	1	3	yes	complemented
265	C₂×#127	C₂²×C₁₃	1	3	yes	—
266	C₄×#41	—	2	1	no	—
267	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
268	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
269	#493	C₂²×C₁₃	1	6	yes	complemented
270	#486	C₂²×C₁₃	1	6	yes	complemented
271	#482	C₂²×C₁₃	1	6	yes	complemented
272	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
273	#476	C₂²×C₁₃	1	3	yes	complemented
274	#476	C₂²×C₁₃	1	6	yes	complemented
275	#469	C₂²×C₁₃	1	12	yes	complemented
276	#460	C₂²×C₁₃	1	3	yes	complemented
277	#460	C₂²×C₁₃	1	6	yes	complemented
278	#459	C₂²×C₁₃	1	3	yes	complemented
279	#459	C₂²×C₁₃	1	6	yes	complemented
280	#459	C₂²×C₁₃	1	6	yes	complemented
281	#459	C₂²×C₁₃	1	6	yes	complemented
282	#449	C₂²×C₁₃	1	6	yes	complemented
283	#447	C₂²×C₁₃	1	12	yes	complemented
284	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
285	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
286	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
287	#436	C₂²×C₁₃	1	6	yes	complemented
288	#431	C₂²×C₁₃	1	3	yes	complemented
289	#423	C₂²×C₁₃	1	3	yes	complemented
290	#418	C₂²×C₁₃	1	6	yes	complemented
291	C₂²×C₁₃	—	2	3	no	—
292	C₂²×C₁₃	—	2	3	no	—
293	C₂²×C₁₃	—	2	3	no	—
294	C₂²×C₁₃	—	4	3	no	—
295	C₂²×C₁₃	—	4	6	no	—
296	C₂²×C₁₃	—	4	6	no	—
297	C₂²×C₁₃	—	4	3	no	—
298	C₂²×C₁₃	—	4	3	no	—
299	C₂²×C₁₃	—	4	6	no	—
300	C₂²×C₁₃	—	16	12	no	—
301	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
302	C₄×C₁₃	—	2	3	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	—	2	3	no	—
306	C₄×C₁₃	—	4	1	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	3	no	—
309	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
310	C₄×C₁₃	#576	1	2	yes	—
311	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₄×C₁₃	#585	1	1	yes	characteristic
313	H(5,𝔽₂)	—	4	8	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	3	no	—
317	C₂×#41	—	2	3	no	—
318	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
319	C₂×#41	C₂³×C₁₃	1	3	yes	—
320	C₂²×D₄	—	2	6	no	—
321	C₂²×D₄	—	2	3	no	—
322	C₂²×D₄	—	2	3	no	—
323	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
324	AGL(1,ℤ/8)	—	4	12	no	—
325	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
326	C₂×D₈	C₂³×C₁₃	1	12	yes	—
327	C₂×D₈	C₂³×C₁₃	1	6	yes	—
328	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
329	C₄⋊Q₈	—	2	3	no	—
330	C₄⋊Q₈	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	—	2	3	no	—
335	#127	C₂³×C₁₃	1	3	yes	—
336	#127	C₂³×C₁₃	1	6	yes	—
337	#127	C₂³×C₁₃	1	3	yes	—
338	#124	—	2	6	no	—
339	#124	—	2	3	no	—
340	#124	—	2	3	no	—
341	#121	—	2	3	no	—
342	#121	—	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	6	no	—
348	#121	C₂³×C₁₃	1	6	yes	—
349	#121	C₂³×C₁₃	1	6	yes	—
350	#120	—	2	12	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
353	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
355	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
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	D₄×C₁₃	1	3	yes	—
362	C₄×D₄	C₂³×C₁₃	1	3	yes	—
363	C₄×D₄	C₂³×C₁₃	1	3	yes	—
364	C₄×D₄	C₂³×C₁₃	1	6	yes	—
365	C₄×D₄	C₂³×C₁₃	1	3	yes	—
366	#117	—	2	3	no	—
367	#117	—	2	3	no	—
368	#117	D₄×C₁₃	1	3	yes	—
369	#117	C₂³×C₁₃	1	3	yes	—
370	C₂×C₄²	—	2	3	no	—
371	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
372	#107	C₂³×C₁₃	1	2	yes	—
373	#106	C₂³×C₁₃	1	6	yes	—
374	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
375	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
376	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
377	#103	C₂³×C₁₃	1	2	yes	—
378	#102	C₂³×C₁₃	1	6	yes	—
379	#102	C₂³×C₁₃	1	12	yes	—
380	#102	C₂³×C₁₃	1	6	yes	—
381	#102	C₂³×C₁₃	1	6	yes	—
382	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
383	C₄×C₈	C₂³×C₁₃	1	6	yes	—
384	C₂×C₁₃	—	4	3	no	—
385	C₂×C₁₃	—	8	3	no	—
386	C₂×C₁₃	—	8	6	no	—
387	C₂×C₁₃	#3488	1	1	yes	characteristic
388	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
390	C₂⁴	—	2	6	no	—
391	#41	—	2	4	no	—
392	#41	—	2	6	no	—
393	#41	—	4	3	no	—
394	#41	—	4	12	no	—
395	#41	—	4	8	no	—
396	#41	—	4	4	no	—
397	#41	—	8	6	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	3	no	—
400	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂×D₄	—	2	3	no	—
403	C₂×D₄	—	2	6	no	—
404	C₂×D₄	—	2	6	no	—
405	C₂×D₄	—	2	3	no	—
406	C₂×D₄	—	2	3	no	—
407	C₂×D₄	—	2	6	no	—
408	C₂×D₄	—	2	3	no	—
409	C₂×D₄	—	2	6	no	—
410	C₂×D₄	—	2	6	no	—
411	C₂×D₄	—	2	3	no	—
412	C₂×D₄	—	4	6	no	—
413	C₂×D₄	—	4	6	no	—
414	C₂×D₄	—	4	12	no	—
415	C₂×D₄	—	4	24	no	—
416	C₂×D₄	—	8	6	no	—
417	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
418	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
419	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
420	C₂²×C₄	—	2	3	no	—
421	C₂²×C₄	—	2	3	no	—
422	C₂²×C₄	—	2	3	no	—
423	C₂²×C₄	—	2	6	no	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
427	SD₁₆	—	2	12	no	—
428	D₈	—	4	12	no	—
429	D₈	—	4	6	no	—
430	M₁₆	—	4	6	no	—
431	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	3	no	—
435	C₄⋊C₄	—	2	3	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
438	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
439	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
440	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂²⋊C₄	—	2	3	no	—
443	C₂²⋊C₄	—	2	6	no	—
444	C₂²⋊C₄	—	2	3	no	—
445	C₂²⋊C₄	—	2	3	no	—
446	C₂²⋊C₄	—	2	6	no	—
447	C₂²⋊C₄	—	2	6	no	—
448	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	3	no	—
451	C₄²	—	2	3	no	—
452	C₄²	C₂×D₄×C₁₃	1	3	yes	—
453	C₄²	C₂×D₄×C₁₃	1	3	yes	—
454	C₄²	C₂⁴×C₁₃	1	3	yes	—
455	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
456	C₁₃	#62001	1	1	yes	characteristic, direct product factor, Sylow
457	C₂³	—	2	3	no	—
458	C₂³	—	2	6	no	—
459	C₂³	—	4	12	no	—
460	C₂³	—	8	6	no	—
461	C₂³	—	8	6	no	—
462	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
463	Q₈	—	2	1	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	3	no	—
466	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
467	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	complemented
468	D₄	—	2	6	no	—
469	D₄	—	2	3	no	—
470	D₄	—	2	6	no	—
471	D₄	—	2	3	no	—
472	D₄	—	2	6	no	—
473	D₄	—	4	6	no	—
474	D₄	—	4	6	no	—
475	D₄	—	4	12	no	—
476	D₄	—	4	12	no	—
477	D₄	—	4	6	no	—
478	D₄	—	4	6	no	—
479	D₄	—	8	6	no	—
480	D₄	—	8	6	no	—
481	D₄	—	8	3	no	—
482	D₄	—	8	6	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	6	no	—
485	C₂×C₄	—	2	6	no	—
486	C₂×C₄	—	2	3	no	—
487	C₂×C₄	—	2	3	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	3	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	6	no	—
492	C₂×C₄	—	4	12	no	—
493	C₂×C₄	—	4	6	no	—
494	C₂×C₄	—	4	6	no	—
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	C₂²×D₄×C₁₃	1	3	yes	—
499	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
501	C₈	—	2	6	no	—
502	C₈	—	2	2	no	—
503	C₂²	—	2	3	no	—
504	C₂²	—	2	3	no	—
505	C₂²	—	2	3	no	—
506	C₂²	—	4	6	no	—
507	C₂²	—	4	3	no	—
508	C₂²	—	4	3	no	—
509	C₂²	—	4	6	no	—
510	C₂²	—	4	3	no	—
511	C₂²	—	4	6	no	—
512	C₂²	—	16	12	no	—
513	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	3	no	—
516	C₄	—	2	3	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	3	no	—
521	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
522	C₄	C₁₃×#576	1	2	yes	—
523	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
524	C₄	C₁₃×#585	1	1	yes	characteristic
525	C₂	—	4	3	no	—
526	C₂	—	8	6	no	—
527	C₂	—	8	3	no	—
528	C₂	C₁₃×#3488	1	1	yes	characteristic
529	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂	C₂×C₁₃×#576	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3498	C₂	semidirect
2. C₁₃×#3483	C₂	semidirect
3. C₁₃×#3391	C₂	semidirect
4. C₁₃×#3362	C₂	semidirect
5. C₁₃×#3325	C₂	semidirect
6. C₁₃×#3274	C₂	semidirect
7. C₁₃×#3253	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3106	C₂	semidirect
10. C₁₃×#3038	C₂	semidirect
11. C₁₃×#2991	C₂	semidirect
13. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. Q₈²×C₁₃	C₂²	semidirect
16. C₁₃×#555	C₂²	semidirect
20. C₁₃×#550	C₂²	semidirect
21. C₁₃×#550	C₂²	semidirect
27. C₁₃×#532	C₂²	semidirect
31. C₄×C₁₃×#41	C₂²	semidirect
32. C₁₃×#493	C₂²	semidirect
33. C₁₃×#486	C₂²	semidirect
34. C₁₃×#482	C₂²	semidirect
35. C₁₃×#477	C₂²	semidirect
36. C₁₃×#476	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#469	C₂²	semidirect
39. C₁₃×#460	C₂²	semidirect
40. C₁₃×#460	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
45. C₁₃×#449	C₂²	semidirect
46. C₁₃×#447	C₂²	semidirect
47. C₈×Q₈×C₁₃	C₂²	semidirect
48. C₄×C₁₃×SD₁₆	C₂²	semidirect
49. C₄×C₁₃×D₈	C₂²	semidirect
50. C₁₃×#436	C₂²	semidirect
51. C₁₃×#431	C₂²	semidirect
52. C₁₃×#423	C₂²	semidirect
53. C₁₃×#418	C₂²	semidirect
125. #62001	C₁₃	direct (N × H)
192. #3498	C₂×C₁₃	semidirect
193. #3483	C₂×C₁₃	semidirect
194. #3391	C₂×C₁₃	semidirect
195. #3362	C₂×C₁₃	semidirect
196. #3325	C₂×C₁₃	semidirect
197. #3274	C₂×C₁₃	semidirect
198. #3253	C₂×C₁₃	semidirect
199. #3205	C₂×C₁₃	semidirect
200. #3106	C₂×C₁₃	semidirect
201. #3038	C₂×C₁₃	semidirect
202. #2991	C₂×C₁₃	semidirect
212. Q₈×C₁₃	AGL(1,ℤ/8)	semidirect
213. Q₈×C₁₃	H(5,𝔽₂)	semidirect
250. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
251. Q₈²	C₂²×C₁₃	semidirect
253. #555	C₂²×C₁₃	semidirect
257. #550	C₂²×C₁₃	semidirect
258. #550	C₂²×C₁₃	semidirect
264. #532	C₂²×C₁₃	semidirect
268. C₄×#41	C₂²×C₁₃	semidirect
269. #493	C₂²×C₁₃	semidirect
270. #486	C₂²×C₁₃	semidirect
271. #482	C₂²×C₁₃	semidirect
272. #477	C₂²×C₁₃	semidirect
273. #476	C₂²×C₁₃	semidirect
274. #476	C₂²×C₁₃	semidirect
275. #469	C₂²×C₁₃	semidirect
276. #460	C₂²×C₁₃	semidirect
277. #460	C₂²×C₁₃	semidirect
278. #459	C₂²×C₁₃	semidirect
279. #459	C₂²×C₁₃	semidirect
280. #459	C₂²×C₁₃	semidirect
281. #459	C₂²×C₁₃	semidirect
282. #449	C₂²×C₁₃	semidirect
283. #447	C₂²×C₁₃	semidirect
284. C₈×Q₈	C₂²×C₁₃	semidirect
285. C₄×SD₁₆	C₂²×C₁₃	semidirect
286. C₄×D₈	C₂²×C₁₃	semidirect
287. #436	C₂²×C₁₃	semidirect
288. #431	C₂²×C₁₃	semidirect
289. #423	C₂²×C₁₃	semidirect
290. #418	C₂²×C₁₃	semidirect
456. C₁₃	#62001	direct (N × H)
466. Q₈	C₁₃×AGL(1,ℤ/8)	semidirect
467. Q₈	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3498	2
C₁₃×#3483	2
C₁₃×#3391	2
C₁₃×#3362	2
C₁₃×#3325	2
C₁₃×#3274	2
C₁₃×#3253	2
C₁₃×#3205	2
C₁₃×#3106	2
C₁₃×#3038	2
C₁₃×#2991	2
#62001	13

Subgroups — C13×#62001 #15748340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62001 #15748340