Subgroups — C₂×C₁₃×#3585 #15749427

Order 3328.

11138 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3585	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₃×#577	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#576	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×#575	C₂	1	6	yes	maximal, complemented
7	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#585	—	2	8	no	—
10	C₁₃×#585	C₂²	1	16	yes	complemented
11	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
13	C₂×C₁₃×H(5,𝔽₂)	—	2	4	no	—
14	C₂×C₁₃×H(5,𝔽₂)	—	2	8	no	—
15	C₂×C₁₃×H(5,𝔽₂)	—	2	3	no	—
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
19	C₂²×C₁₃×#41	—	2	4	no	—
20	C₂²×C₁₃×#41	—	2	1	no	—
21	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
23	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
24	C₂³×D₄×C₁₃	—	2	3	no	—
25	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
26	C₁₃×#577	C₂²	1	128	yes	complemented
27	C₁₃×#576	C₂²	1	128	yes	complemented
28	C₁₃×#575	C₂²	1	96	yes	complemented
29	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#137	C₂²	1	12	yes	complemented
31	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
32	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
33	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
34	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	96	yes	complemented
35	C₂×C₁₃×#135	C₂²	1	24	yes	complemented
36	C₂²×C₁₃×SD₁₆	C₂²	1	12	yes	complemented
37	C₂²×C₁₃×D₈	C₂²	1	12	yes	complemented
38	C₁₃×#568	C₂²	1	16	yes	complemented
39	C₂×C₁₃×#131	C₂²	1	8	yes	complemented
40	C₂²×C₁₃×M₁₆	C₂²	1	6	yes	complemented
41	C₂⁵×C₁₃	—	2	3	no	—
42	C₁₃×2₋¹⁺⁴	—	2	16	no	—
43	C₁₃×2₋¹⁺⁴	—	2	16	no	—
44	C₁₃×2₋¹⁺⁴	C₂³	1	32	yes	complemented
45	C₁₃×H(5,𝔽₂)	—	2	32	no	—
46	C₁₃×H(5,𝔽₂)	—	2	64	no	—
47	C₁₃×H(5,𝔽₂)	—	2	16	no	—
48	C₁₃×H(5,𝔽₂)	—	2	48	no	—
49	C₁₃×H(5,𝔽₂)	C₂³	1	64	yes	complemented
50	C₁₃×H(5,𝔽₂)	C₂³	1	32	yes	complemented
51	C₂×C₁₃×#41	—	2	64	no	—
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂×C₁₃×#41	—	2	16	no	—
54	C₂×C₁₃×#41	—	2	4	no	—
55	C₂×C₁₃×#41	—	2	12	no	—
56	C₂×C₁₃×#41	—	2	6	no	—
57	C₂×C₁₃×#41	—	2	6	no	—
58	C₂×C₁₃×#41	—	2	12	no	—
59	C₂×C₁₃×#41	—	2	6	no	—
60	C₂×C₁₃×#41	—	2	24	no	—
61	C₂×C₁₃×#41	D₄	1	4	yes	—
62	C₂×C₁₃×#41	D₄	1	8	yes	—
63	C₂×C₁₃×#41	C₂³	1	12	yes	—
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂×C₁₃×#41	C₂³	1	8	yes	—
67	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
68	C₂×C₁₃×#41	C₂³	1	12	yes	complemented
69	C₂×C₁₃×#41	C₂³	1	48	yes	complemented
70	C₂²×Q₈×C₁₃	—	2	4	no	—
71	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₃	C₂³	1	6	yes	complemented
74	C₂²×D₄×C₁₃	—	2	3	no	—
75	C₂²×D₄×C₁₃	—	2	6	no	—
76	C₂²×D₄×C₁₃	—	2	24	no	—
77	C₂²×D₄×C₁₃	—	2	48	no	—
78	C₂²×D₄×C₁₃	—	2	12	no	—
79	C₂²×D₄×C₁₃	—	2	3	no	—
80	C₂²×D₄×C₁₃	—	2	6	no	—
81	C₂²×D₄×C₁₃	—	2	12	no	—
82	C₂²×D₄×C₁₃	D₄	1	3	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
86	C₂²×D₄×C₁₃	C₂³	1	6	yes	complemented
87	C₂³×C₄×C₁₃	—	2	3	no	—
88	C₂³×C₄×C₁₃	—	2	6	no	—
89	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
90	C₁₃×#137	C₂³	1	32	yes	complemented
91	C₁₃×#137	C₂³	1	96	yes	complemented
92	C₁₃×AGL(1,ℤ/8)	C₂³	1	96	yes	complemented
93	C₁₃×AGL(1,ℤ/8)	C₂³	1	192	yes	complemented
94	C₁₃×AGL(1,ℤ/8)	C₂³	1	96	yes	complemented
95	C₁₃×#135	C₂³	1	192	yes	complemented
96	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
97	C₂×C₁₃×SD₁₆	C₂³	1	24	yes	complemented
98	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
99	C₂×C₁₃×SD₁₆	C₂³	1	96	yes	complemented
100	C₂×C₁₃×D₈	C₂³	1	24	yes	complemented
101	C₂×C₁₃×D₈	C₂³	1	96	yes	complemented
102	C₁₃×#131	C₂³	1	64	yes	complemented
103	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	12	yes	complemented
105	C₂×C₁₃×M₁₆	C₂³	1	48	yes	complemented
106	C₂²×C₈×C₁₃	C₂³	1	12	yes	complemented
107	C₂×#3585	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	3	no	—
109	C₂⁴×C₁₃	—	2	6	no	—
110	C₂⁴×C₁₃	—	2	12	no	—
111	C₂⁴×C₁₃	—	2	24	no	—
112	C₂⁴×C₁₃	—	8	12	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
114	C₁₃×#41	—	2	64	no	—
115	C₁₃×#41	—	2	32	no	—
116	C₁₃×#41	—	2	96	no	—
117	C₁₃×#41	—	2	8	no	—
118	C₁₃×#41	—	2	48	no	—
119	C₁₃×#41	—	2	24	no	—
120	C₁₃×#41	—	2	48	no	—
121	C₁₃×#41	—	2	48	no	—
122	C₁₃×#41	—	2	24	no	—
123	C₁₃×#41	C₂×D₄	1	32	yes	—
124	C₁₃×#41	C₂×D₄	1	16	yes	—
125	C₁₃×#41	C₂⁴	1	48	yes	—
126	C₁₃×#41	C₂⁴	1	16	yes	—
127	C₁₃×#41	C₂⁴	1	16	yes	—
128	C₁₃×#41	C₂⁴	1	48	yes	complemented
129	C₂×Q₈×C₁₃	—	2	32	no	—
130	C₂×Q₈×C₁₃	—	2	6	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	12	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
136	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
137	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	complemented
140	C₂×D₄×C₁₃	—	2	12	no	—
141	C₂×D₄×C₁₃	—	2	24	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	12	no	—
144	C₂×D₄×C₁₃	—	2	48	no	—
145	C₂×D₄×C₁₃	—	2	192	no	—
146	C₂×D₄×C₁₃	—	2	96	no	—
147	C₂×D₄×C₁₃	—	2	6	no	—
148	C₂×D₄×C₁₃	—	2	3	no	—
149	C₂×D₄×C₁₃	—	2	12	no	—
150	C₂×D₄×C₁₃	—	2	24	no	—
151	C₂×D₄×C₁₃	—	2	24	no	—
152	C₂×D₄×C₁₃	—	2	6	no	—
153	C₂×D₄×C₁₃	—	2	48	no	—
154	C₂×D₄×C₁₃	—	2	12	no	—
155	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
156	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
160	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
161	C₂×D₄×C₁₃	C₂⁴	1	24	yes	complemented
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	6	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	12	no	—
166	C₂²×C₄×C₁₃	—	2	24	no	—
167	C₂²×C₄×C₁₃	—	2	12	no	—
168	C₂²×C₄×C₁₃	—	2	48	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
175	C₁₃×Q₁₆	C₂⁴	1	32	yes	complemented
176	C₁₃×SD₁₆	C₂⁴	1	96	yes	complemented
177	C₁₃×SD₁₆	C₂⁴	1	32	yes	complemented
178	C₁₃×D₈	C₂⁴	1	96	yes	complemented
179	C₁₃×M₁₆	C₂⁴	1	16	yes	—
180	C₁₃×M₁₆	C₂⁴	1	48	yes	complemented
181	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
182	C₂×C₈×C₁₃	C₂⁴	1	48	yes	complemented
183	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#3585	C₂×C₁₃	1	32	yes	direct product factor
186	C₂×#577	C₂×C₁₃	1	8	yes	complemented
187	C₂×#576	C₂×C₁₃	1	8	yes	complemented
188	C₂×#575	C₂×C₁₃	1	6	yes	complemented
189	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	6	yes	complemented
190	C₂×#568	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	12	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	6	no	—
194	C₂³×C₁₃	—	2	24	no	—
195	C₂³×C₁₃	—	2	48	no	—
196	C₂³×C₁₃	—	4	6	no	—
197	C₂³×C₁₃	—	4	12	no	—
198	C₂³×C₁₃	—	8	12	no	—
199	C₂³×C₁₃	—	8	24	no	—
200	C₂³×C₁₃	—	8	48	no	—
201	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	—	2	24	no	—
206	Q₈×C₁₃	—	2	4	no	—
207	Q₈×C₁₃	—	2	2	no	—
208	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
209	Q₈×C₁₃	C₂⁵	1	8	yes	—
210	Q₈×C₁₃	C₂⁵	1	4	yes	—
211	D₄×C₁₃	—	2	48	no	—
212	D₄×C₁₃	—	2	16	no	—
213	D₄×C₁₃	—	2	48	no	—
214	D₄×C₁₃	—	2	12	no	—
215	D₄×C₁₃	—	2	48	no	—
216	D₄×C₁₃	—	2	6	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	2	24	no	—
219	D₄×C₁₃	C₂²×D₄	1	48	yes	—
220	D₄×C₁₃	C₂⁵	1	8	yes	—
221	D₄×C₁₃	C₂⁵	1	12	yes	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	24	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	16	no	—
227	C₂×C₄×C₁₃	—	2	48	no	—
228	C₂×C₄×C₁₃	—	2	48	no	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
235	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
238	C₈×C₁₃	C₂⁵	1	16	yes	—
239	#585	—	2	8	no	—
240	#585	C₂²×C₁₃	1	16	yes	complemented
241	C₂×2₋¹⁺⁴	—	2	1	no	—
242	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
243	C₂×H(5,𝔽₂)	—	2	4	no	—
244	C₂×H(5,𝔽₂)	—	2	8	no	—
245	C₂×H(5,𝔽₂)	—	2	3	no	—
246	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	8	yes	complemented
247	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	16	yes	complemented
248	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
249	C₂²×#41	—	2	4	no	—
250	C₂²×#41	—	2	1	no	—
251	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
253	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
254	C₂³×D₄	—	2	3	no	—
255	C₂³×D₄	C₂²×C₁₃	1	3	yes	complemented
256	#577	C₂²×C₁₃	1	128	yes	complemented
257	#576	C₂²×C₁₃	1	128	yes	complemented
258	#575	C₂²×C₁₃	1	96	yes	complemented
259	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
260	C₂×#137	C₂²×C₁₃	1	12	yes	complemented
261	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	12	yes	complemented
262	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	24	yes	complemented
263	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	12	yes	complemented
264	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	96	yes	complemented
265	C₂×#135	C₂²×C₁₃	1	24	yes	complemented
266	C₂²×SD₁₆	C₂²×C₁₃	1	12	yes	complemented
267	C₂²×D₈	C₂²×C₁₃	1	12	yes	complemented
268	#568	C₂²×C₁₃	1	16	yes	complemented
269	C₂×#131	C₂²×C₁₃	1	8	yes	complemented
270	C₂²×M₁₆	C₂²×C₁₃	1	6	yes	complemented
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	12	no	—
273	C₂²×C₁₃	—	2	8	no	—
274	C₂²×C₁₃	—	2	12	no	—
275	C₂²×C₁₃	—	4	12	no	—
276	C₂²×C₁₃	—	4	24	no	—
277	C₂²×C₁₃	—	4	12	no	—
278	C₂²×C₁₃	—	4	8	no	—
279	C₂²×C₁₃	—	8	24	no	—
280	C₂²×C₁₃	—	8	48	no	—
281	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
282	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
283	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₁₃	—	2	4	no	—
285	C₄×C₁₃	—	2	8	no	—
286	C₄×C₁₃	C₂³×D₄	1	2	yes	—
287	C₄×C₁₃	C₂³×D₄	1	12	yes	—
288	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
290	C₂⁵	—	2	3	no	—
291	2₋¹⁺⁴	—	2	16	no	—
292	2₋¹⁺⁴	—	2	16	no	—
293	2₋¹⁺⁴	C₂³×C₁₃	1	32	yes	complemented
294	H(5,𝔽₂)	—	2	32	no	—
295	H(5,𝔽₂)	—	2	64	no	—
296	H(5,𝔽₂)	—	2	16	no	—
297	H(5,𝔽₂)	—	2	48	no	—
298	H(5,𝔽₂)	C₂³×C₁₃	1	64	yes	complemented
299	H(5,𝔽₂)	C₂³×C₁₃	1	32	yes	complemented
300	C₂×#41	—	2	64	no	—
301	C₂×#41	—	2	8	no	—
302	C₂×#41	—	2	16	no	—
303	C₂×#41	—	2	4	no	—
304	C₂×#41	—	2	12	no	—
305	C₂×#41	—	2	6	no	—
306	C₂×#41	—	2	6	no	—
307	C₂×#41	—	2	12	no	—
308	C₂×#41	—	2	6	no	—
309	C₂×#41	—	2	24	no	—
310	C₂×#41	D₄×C₁₃	1	4	yes	—
311	C₂×#41	D₄×C₁₃	1	8	yes	—
312	C₂×#41	C₂³×C₁₃	1	12	yes	—
313	C₂×#41	C₂³×C₁₃	1	4	yes	—
314	C₂×#41	C₂³×C₁₃	1	4	yes	—
315	C₂×#41	C₂³×C₁₃	1	8	yes	—
316	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
317	C₂×#41	C₂³×C₁₃	1	12	yes	complemented
318	C₂×#41	C₂³×C₁₃	1	48	yes	complemented
319	C₂²×Q₈	—	2	4	no	—
320	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
321	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×Q₈	C₂³×C₁₃	1	6	yes	complemented
323	C₂²×D₄	—	2	3	no	—
324	C₂²×D₄	—	2	6	no	—
325	C₂²×D₄	—	2	24	no	—
326	C₂²×D₄	—	2	48	no	—
327	C₂²×D₄	—	2	12	no	—
328	C₂²×D₄	—	2	3	no	—
329	C₂²×D₄	—	2	6	no	—
330	C₂²×D₄	—	2	12	no	—
331	C₂²×D₄	D₄×C₁₃	1	3	yes	—
332	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
335	C₂²×D₄	C₂³×C₁₃	1	6	yes	complemented
336	C₂³×C₄	—	2	3	no	—
337	C₂³×C₄	—	2	6	no	—
338	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
339	#137	C₂³×C₁₃	1	32	yes	complemented
340	#137	C₂³×C₁₃	1	96	yes	complemented
341	AGL(1,ℤ/8)	C₂³×C₁₃	1	96	yes	complemented
342	AGL(1,ℤ/8)	C₂³×C₁₃	1	192	yes	complemented
343	AGL(1,ℤ/8)	C₂³×C₁₃	1	96	yes	complemented
344	#135	C₂³×C₁₃	1	192	yes	complemented
345	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
346	C₂×SD₁₆	C₂³×C₁₃	1	24	yes	complemented
347	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
348	C₂×SD₁₆	C₂³×C₁₃	1	96	yes	complemented
349	C₂×D₈	C₂³×C₁₃	1	24	yes	complemented
350	C₂×D₈	C₂³×C₁₃	1	96	yes	complemented
351	#131	C₂³×C₁₃	1	64	yes	complemented
352	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
353	C₂×M₁₆	C₂³×C₁₃	1	12	yes	complemented
354	C₂×M₁₆	C₂³×C₁₃	1	48	yes	complemented
355	C₂²×C₈	C₂³×C₁₃	1	12	yes	complemented
356	C₂×C₁₃	—	2	2	no	—
357	C₂×C₁₃	—	2	12	no	—
358	C₂×C₁₃	—	4	12	no	—
359	C₂×C₁₃	—	4	8	no	—
360	C₂×C₁₃	#3585	1	2	yes	direct product factor
361	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
362	C₂⁴	—	2	3	no	—
363	C₂⁴	—	2	6	no	—
364	C₂⁴	—	2	12	no	—
365	C₂⁴	—	2	24	no	—
366	C₂⁴	—	8	12	no	—
367	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
368	#41	—	2	64	no	—
369	#41	—	2	32	no	—
370	#41	—	2	96	no	—
371	#41	—	2	8	no	—
372	#41	—	2	48	no	—
373	#41	—	2	24	no	—
374	#41	—	2	48	no	—
375	#41	—	2	48	no	—
376	#41	—	2	24	no	—
377	#41	C₂×D₄×C₁₃	1	32	yes	—
378	#41	C₂×D₄×C₁₃	1	16	yes	—
379	#41	C₂⁴×C₁₃	1	48	yes	—
380	#41	C₂⁴×C₁₃	1	16	yes	—
381	#41	C₂⁴×C₁₃	1	16	yes	—
382	#41	C₂⁴×C₁₃	1	48	yes	complemented
383	C₂×Q₈	—	2	32	no	—
384	C₂×Q₈	—	2	6	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	12	no	—
388	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
389	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
390	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
391	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
392	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
393	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	complemented
394	C₂×D₄	—	2	12	no	—
395	C₂×D₄	—	2	24	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	12	no	—
398	C₂×D₄	—	2	48	no	—
399	C₂×D₄	—	2	192	no	—
400	C₂×D₄	—	2	96	no	—
401	C₂×D₄	—	2	3	no	—
402	C₂×D₄	—	2	12	no	—
403	C₂×D₄	—	2	6	no	—
404	C₂×D₄	—	2	24	no	—
405	C₂×D₄	—	2	24	no	—
406	C₂×D₄	—	2	6	no	—
407	C₂×D₄	—	2	48	no	—
408	C₂×D₄	—	2	12	no	—
409	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
410	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	—
411	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
412	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
413	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
414	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
415	C₂×D₄	C₂⁴×C₁₃	1	24	yes	complemented
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	6	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	12	no	—
420	C₂²×C₄	—	2	24	no	—
421	C₂²×C₄	—	2	12	no	—
422	C₂²×C₄	—	2	48	no	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
429	Q₁₆	C₂⁴×C₁₃	1	32	yes	complemented
430	SD₁₆	C₂⁴×C₁₃	1	96	yes	complemented
431	SD₁₆	C₂⁴×C₁₃	1	32	yes	complemented
432	D₈	C₂⁴×C₁₃	1	96	yes	complemented
433	M₁₆	C₂⁴×C₁₃	1	16	yes	—
434	M₁₆	C₂⁴×C₁₃	1	48	yes	complemented
435	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
436	C₂×C₈	C₂⁴×C₁₃	1	48	yes	complemented
437	C₁₃	C₂×#3585	1	1	yes	characteristic, direct product factor, Sylow
438	C₂³	—	2	4	no	—
439	C₂³	—	2	12	no	—
440	C₂³	—	2	6	no	—
441	C₂³	—	2	24	no	—
442	C₂³	—	2	48	no	—
443	C₂³	—	4	6	no	—
444	C₂³	—	4	12	no	—
445	C₂³	—	8	24	no	—
446	C₂³	—	8	12	no	—
447	C₂³	—	8	48	no	—
448	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
449	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
450	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
451	Q₈	—	2	4	no	—
452	Q₈	—	2	24	no	—
453	Q₈	—	2	4	no	—
454	Q₈	—	2	2	no	—
455	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
456	Q₈	C₂⁵×C₁₃	1	8	yes	—
457	Q₈	C₂⁵×C₁₃	1	4	yes	—
458	D₄	—	2	48	no	—
459	D₄	—	2	16	no	—
460	D₄	—	2	48	no	—
461	D₄	—	2	12	no	—
462	D₄	—	2	48	no	—
463	D₄	—	2	6	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	24	no	—
466	D₄	C₂²×D₄×C₁₃	1	48	yes	—
467	D₄	C₂⁵×C₁₃	1	8	yes	—
468	D₄	C₂⁵×C₁₃	1	12	yes	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	24	no	—
473	C₂×C₄	—	2	16	no	—
474	C₂×C₄	—	2	48	no	—
475	C₂×C₄	—	2	48	no	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
482	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
484	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
485	C₈	C₂⁵×C₁₃	1	16	yes	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	12	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	12	no	—
490	C₂²	—	4	12	no	—
491	C₂²	—	4	24	no	—
492	C₂²	—	4	12	no	—
493	C₂²	—	4	8	no	—
494	C₂²	—	8	24	no	—
495	C₂²	—	8	48	no	—
496	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
498	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
499	C₄	—	2	4	no	—
500	C₄	—	2	8	no	—
501	C₄	C₂³×D₄×C₁₃	1	2	yes	—
502	C₄	C₂³×D₄×C₁₃	1	12	yes	—
503	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
504	C₄	C₂⁶×C₁₃	1	1	yes	characteristic
505	C₂	—	2	2	no	—
506	C₂	—	2	12	no	—
507	C₂	—	4	12	no	—
508	C₂	—	4	8	no	—
509	C₂	C₁₃×#3585	1	2	yes	direct product factor
510	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#585	C₂	semidirect
2. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
3. C₁₃×#3585	C₂	direct (N × H)
4. C₂×C₁₃×#577	C₂	semidirect
5. C₂×C₁₃×#576	C₂	semidirect
6. C₂×C₁₃×#575	C₂	semidirect
7. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
8. C₂×C₁₃×#568	C₂	semidirect
10. C₁₃×#585	C₂²	semidirect
12. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
23. C₂²×C₁₃×#41	C₂²	semidirect
25. C₂³×D₄×C₁₃	C₂²	semidirect
26. C₁₃×#577	C₂²	semidirect
27. C₁₃×#576	C₂²	semidirect
28. C₁₃×#575	C₂²	semidirect
29. C₂×C₁₃×#137	C₂²	semidirect
30. C₂×C₁₃×#137	C₂²	semidirect
31. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
32. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
33. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×C₁₃×#135	C₂²	semidirect
36. C₂²×C₁₃×SD₁₆	C₂²	semidirect
37. C₂²×C₁₃×D₈	C₂²	semidirect
38. C₁₃×#568	C₂²	semidirect
39. C₂×C₁₃×#131	C₂²	semidirect
40. C₂²×C₁₃×M₁₆	C₂²	semidirect
44. C₁₃×2₋¹⁺⁴	C₂³	semidirect
49. C₁₃×H(5,𝔽₂)	C₂³	semidirect
50. C₁₃×H(5,𝔽₂)	C₂³	semidirect
67. C₂×C₁₃×#41	C₂³	semidirect
68. C₂×C₁₃×#41	C₂³	semidirect
69. C₂×C₁₃×#41	C₂³	semidirect
73. C₂²×Q₈×C₁₃	C₂³	semidirect
85. C₂²×D₄×C₁₃	C₂³	semidirect
86. C₂²×D₄×C₁₃	C₂³	semidirect
90. C₁₃×#137	C₂³	semidirect
91. C₁₃×#137	C₂³	semidirect
92. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
93. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
94. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
95. C₁₃×#135	C₂³	semidirect
96. C₂×C₁₃×Q₁₆	C₂³	semidirect
97. C₂×C₁₃×SD₁₆	C₂³	semidirect
98. C₂×C₁₃×SD₁₆	C₂³	semidirect
99. C₂×C₁₃×SD₁₆	C₂³	semidirect
100. C₂×C₁₃×D₈	C₂³	semidirect
101. C₂×C₁₃×D₈	C₂³	semidirect
102. C₁₃×#131	C₂³	semidirect
104. C₂×C₁₃×M₁₆	C₂³	semidirect
105. C₂×C₁₃×M₁₆	C₂³	semidirect
106. C₂²×C₈×C₁₃	C₂³	semidirect
107. C₂×#3585	C₁₃	direct (N × H)
128. C₁₃×#41	C₂⁴	semidirect
139. C₂×Q₈×C₁₃	C₂⁴	semidirect
161. C₂×D₄×C₁₃	C₂⁴	semidirect
175. C₁₃×Q₁₆	C₂⁴	semidirect
176. C₁₃×SD₁₆	C₂⁴	semidirect
177. C₁₃×SD₁₆	C₂⁴	semidirect
178. C₁₃×D₈	C₂⁴	semidirect
180. C₁₃×M₁₆	C₂⁴	semidirect
182. C₂×C₈×C₁₃	C₂⁴	semidirect
183. C₂×#585	C₂×C₁₃	semidirect
184. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
185. #3585	C₂×C₁₃	direct (N × H)
186. C₂×#577	C₂×C₁₃	semidirect
187. C₂×#576	C₂×C₁₃	semidirect
188. C₂×#575	C₂×C₁₃	semidirect
189. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
190. C₂×#568	C₂×C₁₃	semidirect
240. #585	C₂²×C₁₃	semidirect
242. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
246. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
247. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
248. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
252. C₂²×#41	C₂²×C₁₃	semidirect
253. C₂²×#41	C₂²×C₁₃	semidirect
255. C₂³×D₄	C₂²×C₁₃	semidirect
256. #577	C₂²×C₁₃	semidirect
257. #576	C₂²×C₁₃	semidirect
258. #575	C₂²×C₁₃	semidirect
259. C₂×#137	C₂²×C₁₃	semidirect
260. C₂×#137	C₂²×C₁₃	semidirect
261. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
262. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
263. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
264. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
265. C₂×#135	C₂²×C₁₃	semidirect
266. C₂²×SD₁₆	C₂²×C₁₃	semidirect
267. C₂²×D₈	C₂²×C₁₃	semidirect
268. #568	C₂²×C₁₃	semidirect
269. C₂×#131	C₂²×C₁₃	semidirect
270. C₂²×M₁₆	C₂²×C₁₃	semidirect
293. 2₋¹⁺⁴	C₂³×C₁₃	semidirect
298. H(5,𝔽₂)	C₂³×C₁₃	semidirect
299. H(5,𝔽₂)	C₂³×C₁₃	semidirect
316. C₂×#41	C₂³×C₁₃	semidirect
317. C₂×#41	C₂³×C₁₃	semidirect
318. C₂×#41	C₂³×C₁₃	semidirect
322. C₂²×Q₈	C₂³×C₁₃	semidirect
334. C₂²×D₄	C₂³×C₁₃	semidirect
335. C₂²×D₄	C₂³×C₁₃	semidirect
339. #137	C₂³×C₁₃	semidirect
340. #137	C₂³×C₁₃	semidirect
341. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
342. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
343. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
344. #135	C₂³×C₁₃	semidirect
345. C₂×Q₁₆	C₂³×C₁₃	semidirect
346. C₂×SD₁₆	C₂³×C₁₃	semidirect
347. C₂×SD₁₆	C₂³×C₁₃	semidirect
348. C₂×SD₁₆	C₂³×C₁₃	semidirect
349. C₂×D₈	C₂³×C₁₃	semidirect
350. C₂×D₈	C₂³×C₁₃	semidirect
351. #131	C₂³×C₁₃	semidirect
353. C₂×M₁₆	C₂³×C₁₃	semidirect
354. C₂×M₁₆	C₂³×C₁₃	semidirect
355. C₂²×C₈	C₂³×C₁₃	semidirect
360. C₂×C₁₃	#3585	direct (N × H)
382. #41	C₂⁴×C₁₃	semidirect
393. C₂×Q₈	C₂⁴×C₁₃	semidirect
415. C₂×D₄	C₂⁴×C₁₃	semidirect
429. Q₁₆	C₂⁴×C₁₃	semidirect
430. SD₁₆	C₂⁴×C₁₃	semidirect
431. SD₁₆	C₂⁴×C₁₃	semidirect
432. D₈	C₂⁴×C₁₃	semidirect
434. M₁₆	C₂⁴×C₁₃	semidirect
436. C₂×C₈	C₂⁴×C₁₃	semidirect
437. C₁₃	C₂×#3585	direct (N × H)
509. C₂	C₁₃×#3585	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×#585	2
C₂²×C₁₃×H(5,𝔽₂)	2
C₁₃×#3585	2
C₂×C₁₃×#577	2
C₂×C₁₃×#576	2
C₂×C₁₃×#575	2
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₂×C₁₃×#568	2
C₂×#3585	13

Subgroups — C2×C13×#3585 #15749427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3585 #15749427