Subgroups — C₂×C₁₃×#3586 #15749428

Order 3328.

10794 conjugacy classes of subgroups.

The subgroup lattice has 504 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×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3586	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₃×#578	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#577	C₂	1	8	yes	maximal, complemented
6	C₂×C₁₃×#575	C₂	1	6	yes	maximal, complemented
7	C₂²×C₁₃×#137	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	4	no	—
12	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
13	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	8	yes	complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	16	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	—	2	3	no	—
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×#41	—	2	4	no	—
20	C₂²×C₁₃×#41	—	2	3	no	—
21	C₂²×C₁₃×#41	C₂²	1	6	yes	—
22	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
24	C₂³×Q₈×C₁₃	—	2	1	no	—
25	C₂³×Q₈×C₁₃	C₂²	1	3	yes	complemented
26	C₁₃×#578	C₂²	1	128	yes	complemented
27	C₁₃×#577	C₂²	1	128	yes	complemented
28	C₁₃×#575	C₂²	1	96	yes	complemented
29	C₂×C₁₃×#137	C₂²	1	12	yes	complemented
30	C₂×C₁₃×#137	C₂²	1	24	yes	complemented
31	C₂×C₁₃×#137	C₂²	1	12	yes	complemented
32	C₂×C₁₃×#137	C₂²	1	96	yes	complemented
33	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
34	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
35	C₂×C₁₃×#135	C₂²	1	24	yes	complemented
36	C₂²×C₁₃×Q₁₆	C₂²	1	12	yes	complemented
37	C₂²×C₁₃×SD₁₆	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	C₁₃×2₋¹⁺⁴	—	2	32	no	—
42	C₁₃×2₋¹⁺⁴	—	2	64	no	—
43	C₁₃×2₋¹⁺⁴	—	2	16	no	—
44	C₁₃×2₋¹⁺⁴	—	2	16	no	—
45	C₁₃×2₋¹⁺⁴	C₂³	1	64	yes	complemented
46	C₁₃×2₋¹⁺⁴	C₂³	1	32	yes	complemented
47	C₁₃×H(5,𝔽₂)	—	2	16	no	—
48	C₁₃×H(5,𝔽₂)	—	2	48	no	—
49	C₁₃×H(5,𝔽₂)	C₂³	1	32	yes	complemented
50	C₂×C₁₃×#41	—	2	64	no	—
51	C₂×C₁₃×#41	—	2	4	no	—
52	C₂×C₁₃×#41	—	2	12	no	—
53	C₂×C₁₃×#41	—	2	24	no	—
54	C₂×C₁₃×#41	—	2	48	no	—
55	C₂×C₁₃×#41	—	2	6	no	—
56	C₂×C₁₃×#41	—	2	6	no	—
57	C₂×C₁₃×#41	—	2	24	no	—
58	C₂×C₁₃×#41	—	2	6	no	—
59	C₂×C₁₃×#41	—	2	12	no	—
60	C₂×C₁₃×#41	D₄	1	4	yes	—
61	C₂×C₁₃×#41	D₄	1	8	yes	—
62	C₂×C₁₃×#41	C₂³	1	12	yes	—
63	C₂×C₁₃×#41	C₂³	1	12	yes	—
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂×C₁₃×#41	C₂³	1	48	yes	—
66	C₂×C₁₃×#41	C₂³	1	4	yes	—
67	C₂×C₁₃×#41	C₂³	1	8	yes	—
68	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
69	C₂²×Q₈×C₁₃	—	2	8	no	—
70	C₂²×Q₈×C₁₃	—	2	16	no	—
71	C₂²×Q₈×C₁₃	—	2	4	no	—
72	C₂²×Q₈×C₁₃	—	2	3	no	—
73	C₂²×Q₈×C₁₃	—	2	6	no	—
74	C₂²×Q₈×C₁₃	—	2	12	no	—
75	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	24	yes	complemented
80	C₂²×D₄×C₁₃	—	2	3	no	—
81	C₂²×D₄×C₁₃	—	2	6	no	—
82	C₂²×D₄×C₁₃	—	2	12	no	—
83	C₂²×D₄×C₁₃	D₄	1	3	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	—	2	3	no	—
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	96	yes	complemented
91	C₁₃×#137	C₂³	1	192	yes	complemented
92	C₁₃×#137	C₂³	1	96	yes	complemented
93	C₁₃×AGL(1,ℤ/8)	C₂³	1	32	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	24	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	96	yes	complemented
98	C₂×C₁₃×SD₁₆	C₂³	1	24	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	96	yes	complemented
101	C₂×C₁₃×D₈	C₂³	1	8	yes	—
102	C₁₃×#131	C₂³	1	64	yes	complemented
103	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	12	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	48	yes	complemented
106	C₂²×C₈×C₁₃	C₂³	1	12	yes	—
107	C₂×#3586	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	1	no	—
109	C₂⁴×C₁₃	—	2	6	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
111	C₁₃×#41	—	2	32	no	—
112	C₁₃×#41	—	2	96	no	—
113	C₁₃×#41	—	2	192	no	—
114	C₁₃×#41	—	2	48	no	—
115	C₁₃×#41	—	2	8	no	—
116	C₁₃×#41	—	2	48	no	—
117	C₁₃×#41	—	2	24	no	—
118	C₁₃×#41	—	2	24	no	—
119	C₁₃×#41	—	2	48	no	—
120	C₁₃×#41	C₂×D₄	1	32	yes	—
121	C₁₃×#41	C₂×D₄	1	16	yes	—
122	C₁₃×#41	C₂⁴	1	48	yes	—
123	C₁₃×#41	C₂⁴	1	48	yes	—
124	C₁₃×#41	C₂⁴	1	16	yes	—
125	C₁₃×#41	C₂⁴	1	16	yes	—
126	C₂×Q₈×C₁₃	—	2	64	no	—
127	C₂×Q₈×C₁₃	—	2	32	no	—
128	C₂×Q₈×C₁₃	—	2	6	no	—
129	C₂×Q₈×C₁₃	—	2	3	no	—
130	C₂×Q₈×C₁₃	—	2	12	no	—
131	C₂×Q₈×C₁₃	—	2	24	no	—
132	C₂×Q₈×C₁₃	—	2	6	no	—
133	C₂×Q₈×C₁₃	—	2	24	no	—
134	C₂×Q₈×C₁₃	—	2	48	no	—
135	C₂×Q₈×C₁₃	—	2	12	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	48	yes	—
141	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
142	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	12	no	—
145	C₂×D₄×C₁₃	—	2	12	no	—
146	C₂×D₄×C₁₃	—	2	24	no	—
147	C₂×D₄×C₁₃	—	2	48	no	—
148	C₂×D₄×C₁₃	—	2	96	no	—
149	C₂×D₄×C₁₃	—	2	6	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	12	no	—
153	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
154	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	—	2	3	no	—
160	C₂²×C₄×C₁₃	—	2	6	no	—
161	C₂²×C₄×C₁₃	—	2	12	no	—
162	C₂²×C₄×C₁₃	—	2	24	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	12	no	—
165	C₂²×C₄×C₁₃	—	2	12	no	—
166	C₂²×C₄×C₁₃	—	2	24	no	—
167	C₂²×C₄×C₁₃	—	2	48	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
174	C₁₃×Q₁₆	C₂⁴	1	96	yes	—
175	C₁₃×SD₁₆	C₂⁴	1	96	yes	—
176	C₁₃×SD₁₆	C₂⁴	1	32	yes	—
177	C₁₃×D₈	C₂⁴	1	32	yes	—
178	C₁₃×M₁₆	C₂⁴	1	16	yes	—
179	C₁₃×M₁₆	C₂⁴	1	48	yes	—
180	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
181	C₂×C₈×C₁₃	C₂⁴	1	48	yes	—
182	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#3586	C₂×C₁₃	1	32	yes	direct product factor
185	C₂×#578	C₂×C₁₃	1	8	yes	complemented
186	C₂×#577	C₂×C₁₃	1	8	yes	complemented
187	C₂×#575	C₂×C₁₃	1	6	yes	complemented
188	C₂²×#137	C₂×C₁₃	1	6	yes	complemented
189	C₂×#568	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	24	no	—
194	C₂³×C₁₃	—	4	6	no	—
195	C₂³×C₁₃	—	4	4	no	—
196	C₂³×C₁₃	—	8	12	no	—
197	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
199	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
200	Q₈×C₁₃	—	2	12	no	—
201	Q₈×C₁₃	—	2	48	no	—
202	Q₈×C₁₃	—	2	6	no	—
203	Q₈×C₁₃	—	2	24	no	—
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
206	Q₈×C₁₃	C₂⁵	1	12	yes	—
207	Q₈×C₁₃	C₂⁵	1	8	yes	—
208	D₄×C₁₃	—	2	16	no	—
209	D₄×C₁₃	—	2	48	no	—
210	D₄×C₁₃	—	2	48	no	—
211	D₄×C₁₃	—	2	24	no	—
212	D₄×C₁₃	—	2	4	no	—
213	D₄×C₁₃	—	2	4	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	C₂²×D₄	1	48	yes	—
216	D₄×C₁₃	C₂⁵	1	4	yes	—
217	D₄×C₁₃	C₂⁵	1	8	yes	—
218	C₂×C₄×C₁₃	—	2	12	no	—
219	C₂×C₄×C₁₃	—	2	24	no	—
220	C₂×C₄×C₁₃	—	2	48	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	6	no	—
223	C₂×C₄×C₁₃	—	2	16	no	—
224	C₂×C₄×C₁₃	—	2	48	no	—
225	C₂×C₄×C₁₃	—	2	48	no	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
235	C₈×C₁₃	C₂⁵	1	16	yes	—
236	#585	—	2	8	no	—
237	#585	C₂²×C₁₃	1	16	yes	complemented
238	C₂×2₋¹⁺⁴	—	2	4	no	—
239	C₂×2₋¹⁺⁴	—	2	8	no	—
240	C₂×2₋¹⁺⁴	—	2	1	no	—
241	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	8	yes	complemented
242	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
243	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	16	yes	complemented
244	C₂×H(5,𝔽₂)	—	2	3	no	—
245	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
246	C₂²×#41	—	2	4	no	—
247	C₂²×#41	—	2	3	no	—
248	C₂²×#41	C₂²×C₁₃	1	6	yes	—
249	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
251	C₂³×Q₈	—	2	1	no	—
252	C₂³×Q₈	C₂²×C₁₃	1	3	yes	complemented
253	#578	C₂²×C₁₃	1	128	yes	complemented
254	#577	C₂²×C₁₃	1	128	yes	complemented
255	#575	C₂²×C₁₃	1	96	yes	complemented
256	C₂×#137	C₂²×C₁₃	1	12	yes	complemented
257	C₂×#137	C₂²×C₁₃	1	24	yes	complemented
258	C₂×#137	C₂²×C₁₃	1	12	yes	complemented
259	C₂×#137	C₂²×C₁₃	1	96	yes	complemented
260	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
261	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	12	yes	complemented
262	C₂×#135	C₂²×C₁₃	1	24	yes	complemented
263	C₂²×Q₁₆	C₂²×C₁₃	1	12	yes	complemented
264	C₂²×SD₁₆	C₂²×C₁₃	1	12	yes	complemented
265	#568	C₂²×C₁₃	1	16	yes	complemented
266	C₂×#131	C₂²×C₁₃	1	8	yes	complemented
267	C₂²×M₁₆	C₂²×C₁₃	1	6	yes	complemented
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	12	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	—	2	8	no	—
272	C₂²×C₁₃	—	4	12	no	—
273	C₂²×C₁₃	—	4	8	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	8	no	—
276	C₂²×C₁₃	—	8	24	no	—
277	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
278	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
279	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
280	C₄×C₁₃	—	2	8	no	—
281	C₄×C₁₃	—	2	12	no	—
282	C₄×C₁₃	C₂³×D₄	1	2	yes	—
283	C₄×C₁₃	C₂³×D₄	1	12	yes	—
284	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
285	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
286	2₋¹⁺⁴	—	2	32	no	—
287	2₋¹⁺⁴	—	2	64	no	—
288	2₋¹⁺⁴	—	2	16	no	—
289	2₋¹⁺⁴	—	2	16	no	—
290	2₋¹⁺⁴	C₂³×C₁₃	1	64	yes	complemented
291	2₋¹⁺⁴	C₂³×C₁₃	1	32	yes	complemented
292	H(5,𝔽₂)	—	2	16	no	—
293	H(5,𝔽₂)	—	2	48	no	—
294	H(5,𝔽₂)	C₂³×C₁₃	1	32	yes	complemented
295	C₂×#41	—	2	64	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	12	no	—
298	C₂×#41	—	2	24	no	—
299	C₂×#41	—	2	48	no	—
300	C₂×#41	—	2	6	no	—
301	C₂×#41	—	2	6	no	—
302	C₂×#41	—	2	24	no	—
303	C₂×#41	—	2	6	no	—
304	C₂×#41	—	2	12	no	—
305	C₂×#41	D₄×C₁₃	1	4	yes	—
306	C₂×#41	D₄×C₁₃	1	8	yes	—
307	C₂×#41	C₂³×C₁₃	1	12	yes	—
308	C₂×#41	C₂³×C₁₃	1	12	yes	—
309	C₂×#41	C₂³×C₁₃	1	4	yes	—
310	C₂×#41	C₂³×C₁₃	1	48	yes	—
311	C₂×#41	C₂³×C₁₃	1	4	yes	—
312	C₂×#41	C₂³×C₁₃	1	8	yes	—
313	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
314	C₂²×Q₈	—	2	8	no	—
315	C₂²×Q₈	—	2	16	no	—
316	C₂²×Q₈	—	2	4	no	—
317	C₂²×Q₈	—	2	3	no	—
318	C₂²×Q₈	—	2	6	no	—
319	C₂²×Q₈	—	2	12	no	—
320	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
321	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
322	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
323	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
324	C₂²×Q₈	C₂³×C₁₃	1	24	yes	complemented
325	C₂²×D₄	—	2	3	no	—
326	C₂²×D₄	—	2	6	no	—
327	C₂²×D₄	—	2	12	no	—
328	C₂²×D₄	D₄×C₁₃	1	3	yes	—
329	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
330	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	3	no	—
332	C₂³×C₄	—	2	3	no	—
333	C₂³×C₄	—	2	6	no	—
334	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
335	#137	C₂³×C₁₃	1	96	yes	complemented
336	#137	C₂³×C₁₃	1	192	yes	complemented
337	#137	C₂³×C₁₃	1	96	yes	complemented
338	AGL(1,ℤ/8)	C₂³×C₁₃	1	32	yes	complemented
339	AGL(1,ℤ/8)	C₂³×C₁₃	1	96	yes	complemented
340	#135	C₂³×C₁₃	1	192	yes	complemented
341	C₂×Q₁₆	C₂³×C₁₃	1	24	yes	—
342	C₂×Q₁₆	C₂³×C₁₃	1	96	yes	complemented
343	C₂×SD₁₆	C₂³×C₁₃	1	24	yes	—
344	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
345	C₂×SD₁₆	C₂³×C₁₃	1	96	yes	complemented
346	C₂×D₈	C₂³×C₁₃	1	8	yes	—
347	#131	C₂³×C₁₃	1	64	yes	complemented
348	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
349	C₂×M₁₆	C₂³×C₁₃	1	12	yes	—
350	C₂×M₁₆	C₂³×C₁₃	1	48	yes	complemented
351	C₂²×C₈	C₂³×C₁₃	1	12	yes	—
352	C₂×C₁₃	—	2	2	no	—
353	C₂×C₁₃	—	2	12	no	—
354	C₂×C₁₃	—	4	4	no	—
355	C₂×C₁₃	—	4	8	no	—
356	C₂×C₁₃	#3586	1	2	yes	direct product factor
357	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
358	C₂⁴	—	2	1	no	—
359	C₂⁴	—	2	6	no	—
360	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
361	#41	—	2	32	no	—
362	#41	—	2	96	no	—
363	#41	—	2	192	no	—
364	#41	—	2	48	no	—
365	#41	—	2	8	no	—
366	#41	—	2	48	no	—
367	#41	—	2	24	no	—
368	#41	—	2	24	no	—
369	#41	—	2	48	no	—
370	#41	C₂×D₄×C₁₃	1	32	yes	—
371	#41	C₂×D₄×C₁₃	1	16	yes	—
372	#41	C₂⁴×C₁₃	1	48	yes	—
373	#41	C₂⁴×C₁₃	1	48	yes	—
374	#41	C₂⁴×C₁₃	1	16	yes	—
375	#41	C₂⁴×C₁₃	1	16	yes	—
376	C₂×Q₈	—	2	64	no	—
377	C₂×Q₈	—	2	32	no	—
378	C₂×Q₈	—	2	3	no	—
379	C₂×Q₈	—	2	12	no	—
380	C₂×Q₈	—	2	6	no	—
381	C₂×Q₈	—	2	24	no	—
382	C₂×Q₈	—	2	6	no	—
383	C₂×Q₈	—	2	24	no	—
384	C₂×Q₈	—	2	48	no	—
385	C₂×Q₈	—	2	12	no	—
386	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
387	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
388	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
389	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
390	C₂×Q₈	C₂⁴×C₁₃	1	48	yes	—
391	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
392	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	12	no	—
395	C₂×D₄	—	2	12	no	—
396	C₂×D₄	—	2	24	no	—
397	C₂×D₄	—	2	48	no	—
398	C₂×D₄	—	2	96	no	—
399	C₂×D₄	—	2	6	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	12	no	—
403	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
404	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	—
405	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
406	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
407	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
408	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
409	C₂²×C₄	—	2	3	no	—
410	C₂²×C₄	—	2	6	no	—
411	C₂²×C₄	—	2	12	no	—
412	C₂²×C₄	—	2	24	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	12	no	—
415	C₂²×C₄	—	2	12	no	—
416	C₂²×C₄	—	2	24	no	—
417	C₂²×C₄	—	2	48	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
424	Q₁₆	C₂⁴×C₁₃	1	96	yes	—
425	SD₁₆	C₂⁴×C₁₃	1	96	yes	—
426	SD₁₆	C₂⁴×C₁₃	1	32	yes	—
427	D₈	C₂⁴×C₁₃	1	32	yes	—
428	M₁₆	C₂⁴×C₁₃	1	16	yes	—
429	M₁₆	C₂⁴×C₁₃	1	48	yes	—
430	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
431	C₂×C₈	C₂⁴×C₁₃	1	48	yes	—
432	C₁₃	C₂×#3586	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	4	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	24	no	—
437	C₂³	—	4	6	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	8	12	no	—
440	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
441	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
442	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
443	Q₈	—	2	12	no	—
444	Q₈	—	2	48	no	—
445	Q₈	—	2	6	no	—
446	Q₈	—	2	24	no	—
447	Q₈	—	2	4	no	—
448	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
449	Q₈	C₂⁵×C₁₃	1	12	yes	—
450	Q₈	C₂⁵×C₁₃	1	8	yes	—
451	D₄	—	2	16	no	—
452	D₄	—	2	48	no	—
453	D₄	—	2	48	no	—
454	D₄	—	2	24	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	4	no	—
457	D₄	—	2	2	no	—
458	D₄	C₂²×D₄×C₁₃	1	48	yes	—
459	D₄	C₂⁵×C₁₃	1	4	yes	—
460	D₄	C₂⁵×C₁₃	1	8	yes	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	12	no	—
463	C₂×C₄	—	2	6	no	—
464	C₂×C₄	—	2	24	no	—
465	C₂×C₄	—	2	48	no	—
466	C₂×C₄	—	2	16	no	—
467	C₂×C₄	—	2	48	no	—
468	C₂×C₄	—	2	48	no	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
475	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
477	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
478	C₈	C₂⁵×C₁₃	1	16	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	12	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	4	12	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	8	no	—
487	C₂²	—	8	24	no	—
488	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
489	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
490	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
491	C₄	—	2	8	no	—
492	C₄	—	2	12	no	—
493	C₄	C₂³×D₄×C₁₃	1	2	yes	—
494	C₄	C₂³×D₄×C₁₃	1	12	yes	—
495	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
496	C₄	C₂⁶×C₁₃	1	1	yes	characteristic
497	C₂	—	2	2	no	—
498	C₂	—	2	12	no	—
499	C₂	—	4	4	no	—
500	C₂	—	4	8	no	—
501	C₂	C₁₃×#3586	1	2	yes	direct product factor
502	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×C₁₃×2₋¹⁺⁴	C₂	semidirect
3. C₁₃×#3586	C₂	direct (N × H)
4. C₂×C₁₃×#578	C₂	semidirect
5. C₂×C₁₃×#577	C₂	semidirect
6. C₂×C₁₃×#575	C₂	semidirect
7. C₂²×C₁₃×#137	C₂	semidirect
8. C₂×C₁₃×#568	C₂	semidirect
10. C₁₃×#585	C₂²	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
23. C₂²×C₁₃×#41	C₂²	semidirect
25. C₂³×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#578	C₂²	semidirect
27. C₁₃×#577	C₂²	semidirect
28. C₁₃×#575	C₂²	semidirect
29. C₂×C₁₃×#137	C₂²	semidirect
30. C₂×C₁₃×#137	C₂²	semidirect
31. C₂×C₁₃×#137	C₂²	semidirect
32. C₂×C₁₃×#137	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×Q₁₆	C₂²	semidirect
37. C₂²×C₁₃×SD₁₆	C₂²	semidirect
38. C₁₃×#568	C₂²	semidirect
39. C₂×C₁₃×#131	C₂²	semidirect
40. C₂²×C₁₃×M₁₆	C₂²	semidirect
45. C₁₃×2₋¹⁺⁴	C₂³	semidirect
46. C₁₃×2₋¹⁺⁴	C₂³	semidirect
49. C₁₃×H(5,𝔽₂)	C₂³	semidirect
68. C₂×C₁₃×#41	C₂³	semidirect
79. C₂²×Q₈×C₁₃	C₂³	semidirect
90. C₁₃×#137	C₂³	semidirect
91. C₁₃×#137	C₂³	semidirect
92. C₁₃×#137	C₂³	semidirect
93. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
94. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
95. C₁₃×#135	C₂³	semidirect
97. C₂×C₁₃×Q₁₆	C₂³	semidirect
100. C₂×C₁₃×SD₁₆	C₂³	semidirect
102. C₁₃×#131	C₂³	semidirect
105. C₂×C₁₃×M₁₆	C₂³	semidirect
107. C₂×#3586	C₁₃	direct (N × H)
182. C₂×#585	C₂×C₁₃	semidirect
183. C₂²×2₋¹⁺⁴	C₂×C₁₃	semidirect
184. #3586	C₂×C₁₃	direct (N × H)
185. C₂×#578	C₂×C₁₃	semidirect
186. C₂×#577	C₂×C₁₃	semidirect
187. C₂×#575	C₂×C₁₃	semidirect
188. C₂²×#137	C₂×C₁₃	semidirect
189. C₂×#568	C₂×C₁₃	semidirect
237. #585	C₂²×C₁₃	semidirect
241. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
242. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
243. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
245. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
250. C₂²×#41	C₂²×C₁₃	semidirect
252. C₂³×Q₈	C₂²×C₁₃	semidirect
253. #578	C₂²×C₁₃	semidirect
254. #577	C₂²×C₁₃	semidirect
255. #575	C₂²×C₁₃	semidirect
256. C₂×#137	C₂²×C₁₃	semidirect
257. C₂×#137	C₂²×C₁₃	semidirect
258. C₂×#137	C₂²×C₁₃	semidirect
259. C₂×#137	C₂²×C₁₃	semidirect
260. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
261. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
262. C₂×#135	C₂²×C₁₃	semidirect
263. C₂²×Q₁₆	C₂²×C₁₃	semidirect
264. C₂²×SD₁₆	C₂²×C₁₃	semidirect
265. #568	C₂²×C₁₃	semidirect
266. C₂×#131	C₂²×C₁₃	semidirect
267. C₂²×M₁₆	C₂²×C₁₃	semidirect
290. 2₋¹⁺⁴	C₂³×C₁₃	semidirect
291. 2₋¹⁺⁴	C₂³×C₁₃	semidirect
294. H(5,𝔽₂)	C₂³×C₁₃	semidirect
313. C₂×#41	C₂³×C₁₃	semidirect
324. C₂²×Q₈	C₂³×C₁₃	semidirect
335. #137	C₂³×C₁₃	semidirect
336. #137	C₂³×C₁₃	semidirect
337. #137	C₂³×C₁₃	semidirect
338. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
339. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
340. #135	C₂³×C₁₃	semidirect
342. C₂×Q₁₆	C₂³×C₁₃	semidirect
345. C₂×SD₁₆	C₂³×C₁₃	semidirect
347. #131	C₂³×C₁₃	semidirect
350. C₂×M₁₆	C₂³×C₁₃	semidirect
356. C₂×C₁₃	#3586	direct (N × H)
432. C₁₃	C₂×#3586	direct (N × H)
501. C₂	C₁₃×#3586	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×C₁₃×2₋¹⁺⁴	2
C₁₃×#3586	2
C₂×C₁₃×#578	2
C₂×C₁₃×#577	2
C₂×C₁₃×#575	2
C₂²×C₁₃×#137	2
C₂×C₁₃×#568	2
C₂×#3586	13

Subgroups — C2×C13×#3586 #15749428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3586 #15749428