Subgroups — C₁₃×#61089 #15747428

Order 3328.

2922 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3498	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3287	C₂	1	4	yes	maximal, complemented
4	D₄×C₁₃×D₈	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3274	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3058	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3008	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
13	C₁₃×#576	—	2	16	no	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
22	C₁₃×#550	C₂²	1	8	yes	complemented
23	D₄²×C₁₃	—	2	8	no	—
24	D₄²×C₁₃	C₂²	1	8	yes	complemented
25	C₁₃×#535	—	2	4	no	—
26	C₁₃×#535	C₂²	1	4	yes	complemented
27	C₁₃×#532	—	2	2	no	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#127	—	2	2	no	—
30	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
31	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
32	C₁₃×#493	C₂²	1	4	yes	complemented
33	C₁₃×#493	C₂²	1	4	yes	complemented
34	C₁₃×#469	C₂²	1	8	yes	complemented
35	C₁₃×#466	C₂²	1	8	yes	complemented
36	C₁₃×#460	C₂²	1	8	yes	complemented
37	C₁₃×#459	C₂²	1	8	yes	complemented
38	C₁₃×#449	C₂²	1	16	yes	complemented
39	C₁₃×#447	C₂²	1	16	yes	complemented
40	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
42	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
43	C₁₃×#436	C₂²	1	4	yes	complemented
44	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
45	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#418	C₂²	1	4	yes	complemented
48	C₁₃×#416	C₂²	1	2	yes	complemented
49	C₁₃×#408	C₂²	1	2	yes	complemented
50	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×H(5,𝔽₂)	—	2	16	no	—
52	C₁₃×H(5,𝔽₂)	—	4	8	no	—
53	C₂×C₁₃×#41	—	2	4	no	—
54	C₂×C₁₃×#41	C₂³	1	8	yes	—
55	C₂×C₁₃×#41	C₂³	1	2	yes	—
56	C₂×C₁₃×#41	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
63	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
64	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
65	C₁₃×#135	—	2	16	no	—
66	C₁₃×#135	D₄	1	8	yes	complemented
67	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
69	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×D₈	—	2	16	no	—
71	C₂×C₁₃×D₈	—	2	8	no	—
72	C₂×C₁₃×D₈	—	4	4	no	—
73	C₂×C₁₃×D₈	C₂³	1	8	yes	—
74	C₂×C₁₃×D₈	C₂³	1	4	yes	—
75	C₂×C₁₃×D₈	C₂³	1	4	yes	—
76	C₂×C₁₃×D₈	C₂³	1	8	yes	—
77	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
78	C₁₃×#131	—	2	8	no	—
79	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
80	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
85	C₁₃×#127	—	2	4	no	—
86	C₁₃×#127	—	2	8	no	—
87	C₁₃×#127	—	2	2	no	—
88	C₁₃×#127	—	2	2	no	—
89	C₁₃×#127	D₄	1	1	yes	characteristic
90	C₁₃×#127	C₂³	1	8	yes	—
91	C₁₃×#124	—	2	4	no	—
92	C₁₃×#124	D₄	1	2	yes	—
93	C₁₃×#121	—	2	8	no	—
94	C₁₃×#121	—	2	16	no	—
95	C₁₃×#121	D₄	1	4	yes	—
96	C₁₃×#121	C₂³	1	16	yes	—
97	C₁₃×#120	—	2	8	no	—
98	C₁₃×#120	—	2	16	no	—
99	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	8	no	—
102	C₄×D₄×C₁₃	C₂³	1	4	yes	—
103	C₄×D₄×C₁₃	C₂³	1	4	yes	—
104	C₁₃×#117	—	2	2	no	—
105	C₁₃×#117	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	—	2	2	no	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	C₂³	1	2	yes	—
109	C₁₃×#106	C₂³	1	2	yes	—
110	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
111	C₁₃×#103	C₂³	1	4	yes	—
112	C₁₃×#102	C₂³	1	4	yes	—
113	C₁₃×#102	C₂³	1	16	yes	—
114	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	C₄×C₈×C₁₃	C₂³	1	2	yes	—
117	#61089	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂⁴×C₁₃	—	2	8	no	—
119	C₂⁴×C₁₃	—	2	4	no	—
120	C₁₃×#41	—	2	4	no	—
121	C₁₃×#41	—	2	4	no	—
122	C₁₃×#41	—	2	4	no	—
123	C₁₃×#41	—	2	16	no	—
124	C₁₃×#41	—	4	8	no	—
125	C₁₃×#41	—	4	16	no	—
126	C₁₃×#41	C₂×D₄	1	8	yes	complemented
127	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	16	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	16	no	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	8	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	4	8	no	—
140	C₂×D₄×C₁₃	—	4	16	no	—
141	C₂×D₄×C₁₃	—	4	32	no	—
142	C₂×D₄×C₁₃	—	8	8	no	—
143	C₂×D₄×C₁₃	—	8	16	no	—
144	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
156	C₁₃×SD₁₆	—	2	16	no	—
157	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
158	C₁₃×D₈	—	2	16	no	—
159	C₁₃×D₈	—	2	8	no	—
160	C₁₃×D₈	—	2	8	no	—
161	C₁₃×D₈	—	4	8	no	—
162	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
163	C₁₃×M₁₆	—	2	4	no	—
164	C₁₃×M₁₆	—	2	8	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	8	no	—
167	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₁₃×C₂²⋊C₄	—	2	16	no	—
178	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	4	no	—
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂⁴	1	2	yes	—
184	C₂×#576	C₂×C₁₃	1	2	yes	complemented
185	#3498	C₂×C₁₃	1	2	yes	complemented
186	#3287	C₂×C₁₃	1	4	yes	complemented
187	D₄×D₈	C₂×C₁₃	1	4	yes	complemented
188	#3274	C₂×C₁₃	1	8	yes	complemented
189	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#3058	C₂×C₁₃	1	2	yes	complemented
191	#3038	C₂×C₁₃	1	2	yes	complemented
192	#3008	C₂×C₁₃	1	4	yes	complemented
193	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	8	no	—
197	C₂³×C₁₃	—	4	16	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	8	8	no	—
200	C₂³×C₁₃	—	8	16	no	—
201	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
202	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	4	no	—
204	Q₈×C₁₃	—	2	2	no	—
205	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
206	D₄×C₁₃	—	2	8	no	—
207	D₄×C₁₃	—	2	8	no	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	2	8	no	—
210	D₄×C₁₃	—	2	8	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	2	8	no	—
213	D₄×C₁₃	—	4	16	no	—
214	D₄×C₁₃	—	4	16	no	—
215	D₄×C₁₃	—	4	8	no	—
216	D₄×C₁₃	—	4	16	no	—
217	D₄×C₁₃	—	8	8	no	—
218	D₄×C₁₃	—	8	16	no	—
219	D₄×C₁₃	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	4	16	no	—
227	C₂×C₄×C₁₃	—	4	8	no	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
235	C₈×C₁₃	—	2	4	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	C₂²×D₄	1	2	yes	—
238	C₈×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
240	#576	—	2	16	no	—
241	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
242	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
243	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
245	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
246	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
247	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
248	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
249	#550	C₂²×C₁₃	1	8	yes	complemented
250	D₄²	—	2	8	no	—
251	D₄²	C₂²×C₁₃	1	8	yes	complemented
252	#535	—	2	4	no	—
253	#535	C₂²×C₁₃	1	4	yes	complemented
254	#532	—	2	2	no	—
255	#532	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#127	—	2	2	no	—
257	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
258	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
259	#493	C₂²×C₁₃	1	4	yes	complemented
260	#493	C₂²×C₁₃	1	4	yes	complemented
261	#469	C₂²×C₁₃	1	8	yes	complemented
262	#466	C₂²×C₁₃	1	8	yes	complemented
263	#460	C₂²×C₁₃	1	8	yes	complemented
264	#459	C₂²×C₁₃	1	8	yes	complemented
265	#449	C₂²×C₁₃	1	16	yes	complemented
266	#447	C₂²×C₁₃	1	16	yes	complemented
267	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
268	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
269	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
270	#436	C₂²×C₁₃	1	4	yes	complemented
271	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
272	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
273	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	#418	C₂²×C₁₃	1	4	yes	complemented
275	#416	C₂²×C₁₃	1	2	yes	complemented
276	#408	C₂²×C₁₃	1	2	yes	complemented
277	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	4	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	8	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	4	8	no	—
284	C₂²×C₁₃	—	4	16	no	—
285	C₂²×C₁₃	—	16	8	no	—
286	C₂²×C₁₃	—	16	16	no	—
287	C₂²×C₁₃	D₄²	1	2	yes	—
288	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	4	4	no	—
293	C₄×C₁₃	D₄²	1	2	yes	—
294	C₄×C₁₃	#576	1	4	yes	complemented
295	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
296	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
297	H(5,𝔽₂)	—	2	16	no	—
298	H(5,𝔽₂)	—	4	8	no	—
299	C₂×#41	—	2	4	no	—
300	C₂×#41	C₂³×C₁₃	1	8	yes	—
301	C₂×#41	C₂³×C₁₃	1	2	yes	—
302	C₂×#41	C₂³×C₁₃	1	2	yes	—
303	C₂²×D₄	—	2	4	no	—
304	C₂²×D₄	—	2	8	no	—
305	C₂²×D₄	—	2	8	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
308	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
309	AGL(1,ℤ/8)	—	2	16	no	—
310	AGL(1,ℤ/8)	—	2	32	no	—
311	#135	—	2	16	no	—
312	#135	D₄×C₁₃	1	8	yes	complemented
313	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
315	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
316	C₂×D₈	—	2	16	no	—
317	C₂×D₈	—	2	8	no	—
318	C₂×D₈	—	4	4	no	—
319	C₂×D₈	C₂³×C₁₃	1	4	yes	—
320	C₂×D₈	C₂³×C₁₃	1	8	yes	—
321	C₂×D₈	C₂³×C₁₃	1	4	yes	—
322	C₂×D₈	C₂³×C₁₃	1	8	yes	—
323	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
324	#131	—	2	8	no	—
325	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
326	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
327	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
328	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
331	#127	—	2	4	no	—
332	#127	—	2	8	no	—
333	#127	—	2	2	no	—
334	#127	—	2	2	no	—
335	#127	D₄×C₁₃	1	1	yes	characteristic
336	#127	C₂³×C₁₃	1	8	yes	—
337	#124	—	2	4	no	—
338	#124	D₄×C₁₃	1	2	yes	—
339	#121	—	2	8	no	—
340	#121	—	2	16	no	—
341	#121	D₄×C₁₃	1	4	yes	—
342	#121	C₂³×C₁₃	1	16	yes	—
343	#120	—	2	8	no	—
344	#120	—	2	16	no	—
345	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	8	no	—
348	C₄×D₄	C₂³×C₁₃	1	4	yes	—
349	C₄×D₄	C₂³×C₁₃	1	4	yes	—
350	#117	—	2	2	no	—
351	#117	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄²	—	2	2	no	—
353	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
354	#107	C₂³×C₁₃	1	2	yes	—
355	#106	C₂³×C₁₃	1	2	yes	—
356	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
357	#103	C₂³×C₁₃	1	4	yes	—
358	#102	C₂³×C₁₃	1	4	yes	—
359	#102	C₂³×C₁₃	1	16	yes	—
360	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
361	C₄×C₈	C₂³×C₁₃	1	2	yes	—
362	C₄×C₈	C₂³×C₁₃	1	2	yes	—
363	C₂×C₁₃	—	2	2	no	—
364	C₂×C₁₃	—	4	4	no	—
365	C₂×C₁₃	—	4	4	no	—
366	C₂×C₁₃	—	8	8	no	—
367	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#576	1	2	yes	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	2	4	no	—
371	#41	—	2	4	no	—
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	2	16	no	—
375	#41	—	4	8	no	—
376	#41	—	4	16	no	—
377	#41	C₂×D₄×C₁₃	1	8	yes	complemented
378	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
379	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	16	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	16	no	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	16	no	—
392	C₂×D₄	—	4	32	no	—
393	C₂×D₄	—	8	8	no	—
394	C₂×D₄	—	8	16	no	—
395	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
397	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
399	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
406	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
407	SD₁₆	—	2	16	no	—
408	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
409	D₈	—	2	16	no	—
410	D₈	—	2	8	no	—
411	D₈	—	2	8	no	—
412	D₈	—	4	8	no	—
413	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
414	M₁₆	—	2	4	no	—
415	M₁₆	—	2	8	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	8	no	—
418	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
419	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
420	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
421	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
425	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	16	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	4	no	—
432	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₄²	C₂⁴×C₁₃	1	2	yes	—
435	C₁₃	#61089	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	2	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	8	8	no	—
441	C₂³	—	8	16	no	—
442	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
443	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	Q₈	—	2	4	no	—
445	Q₈	—	2	2	no	—
446	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
447	D₄	—	2	8	no	—
448	D₄	—	2	8	no	—
449	D₄	—	2	4	no	—
450	D₄	—	2	8	no	—
451	D₄	—	2	8	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	8	no	—
454	D₄	—	4	16	no	—
455	D₄	—	4	16	no	—
456	D₄	—	4	8	no	—
457	D₄	—	4	16	no	—
458	D₄	—	8	8	no	—
459	D₄	—	8	16	no	—
460	D₄	C₂²×D₄×C₁₃	1	4	yes	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	16	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
475	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	2	2	no	—
478	C₈	C₂²×D₄×C₁₃	1	2	yes	—
479	C₈	C₂²×D₄×C₁₃	1	2	yes	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	16	no	—
486	C₂²	—	4	8	no	—
487	C₂²	—	16	8	no	—
488	C₂²	—	16	16	no	—
489	C₂²	D₄²×C₁₃	1	2	yes	—
490	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	4	4	no	—
495	C₄	D₄²×C₁₃	1	2	yes	—
496	C₄	C₁₃×#576	1	4	yes	complemented
497	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
498	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂	—	2	2	no	—
500	C₂	—	4	4	no	—
501	C₂	—	4	4	no	—
502	C₂	—	8	8	no	—
503	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
504	C₂	C₂×C₁₃×#576	1	2	yes	—

	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 ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3287	C₂	semidirect
4. D₄×C₁₃×D₈	C₂	semidirect
5. C₁₃×#3274	C₂	semidirect
6. C₂×C₁₃×#493	C₂	semidirect
7. C₁₃×#3058	C₂	semidirect
8. C₁₃×#3038	C₂	semidirect
9. C₁₃×#3008	C₂	semidirect
10. C₄×C₁₃×#135	C₂	semidirect
11. C₁₃×#2931	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₃×#135	C₂²	semidirect
18. C₂²×C₁₃×D₈	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
20. C₂²×C₁₃×D₈	C₂²	semidirect
21. C₂×C₁₃×#131	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
24. D₄²×C₁₃	C₂²	semidirect
26. C₁₃×#535	C₂²	semidirect
30. C₂×C₁₃×#127	C₂²	semidirect
31. C₄×C₁₃×#41	C₂²	semidirect
32. C₁₃×#493	C₂²	semidirect
33. C₁₃×#493	C₂²	semidirect
34. C₁₃×#469	C₂²	semidirect
35. C₁₃×#466	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
37. C₁₃×#459	C₂²	semidirect
38. C₁₃×#449	C₂²	semidirect
39. C₁₃×#447	C₂²	semidirect
40. C₄×C₁₃×Q₁₆	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₄×C₁₃×D₈	C₂²	semidirect
43. C₁₃×#436	C₂²	semidirect
44. C₈×D₄×C₁₃	C₂²	semidirect
45. C₁₃×#427	C₂²	semidirect
46. C₁₃×#423	C₂²	semidirect
47. C₁₃×#418	C₂²	semidirect
48. C₁₃×#416	C₂²	semidirect
49. C₁₃×#408	C₂²	semidirect
50. C₂×C₄×C₈×C₁₃	C₂²	semidirect
66. C₁₃×#135	D₄	semidirect
117. #61089	C₁₃	direct (N × H)
126. C₁₃×#41	C₂×D₄	semidirect
155. C₁₃×Q₁₆	C₂×D₄	semidirect
157. C₁₃×SD₁₆	C₂×D₄	semidirect
162. C₁₃×D₈	C₂×D₄	semidirect
167. C₂×C₈×C₁₃	C₂×D₄	semidirect
184. C₂×#576	C₂×C₁₃	semidirect
185. #3498	C₂×C₁₃	semidirect
186. #3287	C₂×C₁₃	semidirect
187. D₄×D₈	C₂×C₁₃	semidirect
188. #3274	C₂×C₁₃	semidirect
189. C₂×#493	C₂×C₁₃	semidirect
190. #3058	C₂×C₁₃	semidirect
191. #3038	C₂×C₁₃	semidirect
192. #3008	C₂×C₁₃	semidirect
193. C₄×#135	C₂×C₁₃	semidirect
194. #2931	C₂×C₁₃	semidirect
239. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
241. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
242. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
244. C₂×#135	C₂²×C₁₃	semidirect
245. C₂²×D₈	C₂²×C₁₃	semidirect
246. C₂²×D₈	C₂²×C₁₃	semidirect
247. C₂²×D₈	C₂²×C₁₃	semidirect
248. C₂×#131	C₂²×C₁₃	semidirect
249. #550	C₂²×C₁₃	semidirect
251. D₄²	C₂²×C₁₃	semidirect
253. #535	C₂²×C₁₃	semidirect
257. C₂×#127	C₂²×C₁₃	semidirect
258. C₄×#41	C₂²×C₁₃	semidirect
259. #493	C₂²×C₁₃	semidirect
260. #493	C₂²×C₁₃	semidirect
261. #469	C₂²×C₁₃	semidirect
262. #466	C₂²×C₁₃	semidirect
263. #460	C₂²×C₁₃	semidirect
264. #459	C₂²×C₁₃	semidirect
265. #449	C₂²×C₁₃	semidirect
266. #447	C₂²×C₁₃	semidirect
267. C₄×Q₁₆	C₂²×C₁₃	semidirect
268. C₄×SD₁₆	C₂²×C₁₃	semidirect
269. C₄×D₈	C₂²×C₁₃	semidirect
270. #436	C₂²×C₁₃	semidirect
271. C₈×D₄	C₂²×C₁₃	semidirect
272. #427	C₂²×C₁₃	semidirect
273. #423	C₂²×C₁₃	semidirect
274. #418	C₂²×C₁₃	semidirect
275. #416	C₂²×C₁₃	semidirect
276. #408	C₂²×C₁₃	semidirect
277. C₂×C₄×C₈	C₂²×C₁₃	semidirect
294. C₄×C₁₃	#576	semidirect
312. #135	D₄×C₁₃	semidirect
377. #41	C₂×D₄×C₁₃	semidirect
406. Q₁₆	C₂×D₄×C₁₃	semidirect
408. SD₁₆	C₂×D₄×C₁₃	semidirect
413. D₈	C₂×D₄×C₁₃	semidirect
418. C₂×C₈	C₂×D₄×C₁₃	semidirect
435. C₁₃	#61089	direct (N × H)
496. C₄	C₁₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#576	2
C₁₃×#3498	2
C₁₃×#3287	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₂×C₁₃×#493	2
C₁₃×#3058	2
C₁₃×#3038	2
C₁₃×#3008	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
#61089	13

Subgroups — C13×#61089 #15747428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61089 #15747428