Subgroups — C₂×C₁₃×#3273 #15747371

Order 3328.

3042 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3273	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
13	C₂×C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
15	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
22	C₁₃×#546	—	2	8	no	—
23	C₁₃×#546	C₂²	1	16	yes	complemented
24	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#123	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#121	—	2	2	no	—
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₁₃×#120	—	2	2	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
33	C₁₃×#495	C₂²	1	8	yes	complemented
34	C₁₃×#468	C₂²	1	16	yes	complemented
35	C₁₃×#463	C₂²	1	16	yes	complemented
36	C₁₃×#452	C₂²	1	16	yes	complemented
37	C₁₃×#447	C₂²	1	16	yes	complemented
38	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
39	C₁₃×#436	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
46	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₁₃	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	8	no	—
50	C₂×C₁₃×#41	—	4	4	no	—
51	C₂×C₁₃×#41	C₂³	1	8	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	2	no	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	4	4	no	—
59	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	8	yes	complemented
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	—	2	2	no	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₁₃×AGL(1,ℤ/8)	—	2	64	no	—
67	C₂×C₁₃×Q₁₆	—	4	2	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
69	C₂×C₁₃×SD₁₆	—	2	8	no	—
70	C₂×C₁₃×SD₁₆	—	2	8	no	—
71	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
72	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
73	C₂×C₁₃×D₈	—	2	8	no	—
74	C₂×C₁₃×D₈	—	4	2	no	—
75	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
76	C₂×C₁₃×D₈	C₂³	1	8	yes	—
77	C₂×C₁₃×D₈	C₂³	1	4	yes	—
78	C₂×C₁₃×D₈	C₂³	1	4	yes	—
79	C₂×C₁₃×M₁₆	—	2	8	no	—
80	C₂×C₁₃×M₁₆	C₂³	1	8	yes	complemented
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	C₂³	1	8	yes	complemented
86	C₁₃×#123	—	2	16	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
89	C₁₃×#121	—	2	4	no	—
90	C₁₃×#121	—	2	16	no	—
91	C₁₃×#121	C₂³	1	8	yes	—
92	C₁₃×#120	—	2	16	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	D₄	1	4	yes	—
95	C₄×D₄×C₁₃	C₂³	1	4	yes	—
96	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
106	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	C₂³	1	4	yes	complemented
109	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
110	C₁₃×#103	C₂³	1	8	yes	complemented
111	C₁₃×#102	C₂³	1	8	yes	complemented
112	C₁₃×#102	C₂³	1	8	yes	complemented
113	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
114	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
115	C₂×#3273	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	2	no	—
117	C₂⁴×C₁₃	—	2	2	no	—
118	C₂⁴×C₁₃	—	2	8	no	—
119	C₂⁴×C₁₃	—	4	8	no	—
120	C₂⁴×C₁₃	—	4	8	no	—
121	C₂⁴×C₁₃	—	8	4	no	—
122	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
123	C₁₃×#41	—	2	16	no	—
124	C₁₃×#41	—	4	8	no	—
125	C₁₃×#41	—	4	16	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
130	C₂×D₄×C₁₃	—	2	16	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	8	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	4	8	no	—
140	C₂×D₄×C₁₃	—	4	16	no	—
141	C₂×D₄×C₁₃	—	4	2	no	—
142	C₂×D₄×C₁₃	—	4	8	no	—
143	C₂×D₄×C₁₃	—	4	8	no	—
144	C₂×D₄×C₁₃	—	8	4	no	—
145	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
146	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	8	no	—
154	C₂²×C₄×C₁₃	—	2	8	no	—
155	C₂²×C₄×C₁₃	—	4	8	no	—
156	C₂²×C₄×C₁₃	—	8	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	4	4	no	—
164	C₁₃×SD₁₆	—	2	16	no	—
165	C₁₃×SD₁₆	—	2	16	no	—
166	C₁₃×D₈	—	2	16	no	—
167	C₁₃×D₈	—	4	4	no	—
168	C₁₃×D₈	C₂×D₄	1	16	yes	complemented
169	C₁₃×M₁₆	—	2	16	no	—
170	C₂×C₈×C₁₃	—	2	4	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
173	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
175	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
186	C₄²×C₁₃	C₂×D₄	1	2	yes	—
187	C₄²×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
189	C₂×#546	C₂×C₁₃	1	2	yes	complemented
190	#3273	C₂×C₁₃	1	16	yes	direct product factor
191	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×#468	C₂×C₁₃	1	2	yes	complemented
193	C₂×#463	C₂×C₁₃	1	2	yes	complemented
194	C₂×#452	C₂×C₁₃	1	2	yes	complemented
195	C₂×#447	C₂×C₁₃	1	2	yes	complemented
196	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	2	4	no	—
199	C₂³×C₁₃	—	2	8	no	—
200	C₂³×C₁₃	—	2	4	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	2	4	no	—
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	—	4	16	no	—
205	C₂³×C₁₃	—	4	16	no	—
206	C₂³×C₁₃	—	4	4	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	—	4	4	no	—
209	C₂³×C₁₃	—	4	4	no	—
210	C₂³×C₁₃	—	4	4	no	—
211	C₂³×C₁₃	—	8	8	no	—
212	C₂³×C₁₃	—	8	32	no	—
213	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	4	4	no	—
218	D₄×C₁₃	—	2	8	no	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	—	2	4	no	—
221	D₄×C₁₃	—	2	4	no	—
222	D₄×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	4	16	no	—
224	D₄×C₁₃	—	4	16	no	—
225	D₄×C₁₃	—	4	4	no	—
226	D₄×C₁₃	—	8	8	no	—
227	D₄×C₁₃	C₂²×D₄	1	8	yes	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	8	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	4	16	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	8	8	no	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	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	4	no	—
248	C₈×C₁₃	—	2	2	no	—
249	C₈×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂²×#41	C₂²×C₁₃	1	2	yes	—
251	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
252	C₂×AGL(1,ℤ/8)	—	2	16	no	—
253	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	16	yes	complemented
254	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
255	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
256	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
257	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
258	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
261	#546	—	2	8	no	—
262	#546	C₂²×C₁₃	1	16	yes	complemented
263	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
264	C₂×#123	—	2	2	no	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
266	C₂×#121	—	2	2	no	—
267	C₂×#121	C₂²×C₁₃	1	2	yes	—
268	C₂×#120	—	2	2	no	—
269	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
271	C₂²×C₂²⋊C₄	—	2	2	no	—
272	#495	C₂²×C₁₃	1	8	yes	complemented
273	#468	C₂²×C₁₃	1	16	yes	complemented
274	#463	C₂²×C₁₃	1	16	yes	complemented
275	#452	C₂²×C₁₃	1	16	yes	complemented
276	#447	C₂²×C₁₃	1	16	yes	complemented
277	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
278	#436	C₂²×C₁₃	1	8	yes	complemented
279	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
282	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
283	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
284	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
285	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	C₂²×C₁₃	—	2	4	no	—
287	C₂²×C₁₃	—	2	8	no	—
288	C₂²×C₁₃	—	2	4	no	—
289	C₂²×C₁₃	—	2	4	no	—
290	C₂²×C₁₃	—	4	8	no	—
291	C₂²×C₁₃	—	4	16	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	4	4	no	—
294	C₂²×C₁₃	—	4	4	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	4	4	no	—
297	C₂²×C₁₃	—	8	32	no	—
298	C₂²×C₁₃	—	8	8	no	—
299	C₂²×C₁₃	D₄²	1	2	yes	—
300	C₂²×C₁₃	#575	1	2	yes	—
301	C₂²×C₁₃	#576	1	2	yes	—
302	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	—	4	4	no	—
308	C₄×C₁₃	D₄²	1	2	yes	—
309	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
310	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂⁵	—	2	2	no	—
312	C₂×#41	—	2	4	no	—
313	C₂×#41	—	2	8	no	—
314	C₂×#41	—	4	4	no	—
315	C₂×#41	C₂³×C₁₃	1	8	yes	—
316	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	4	no	—
322	C₂²×D₄	—	4	4	no	—
323	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
324	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
325	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
326	C₂²×D₄	C₂³×C₁₃	1	8	yes	complemented
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
330	AGL(1,ℤ/8)	—	2	64	no	—
331	C₂×Q₁₆	—	4	2	no	—
332	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
333	C₂×SD₁₆	—	2	8	no	—
334	C₂×SD₁₆	—	2	8	no	—
335	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
336	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
337	C₂×D₈	—	2	8	no	—
338	C₂×D₈	—	4	2	no	—
339	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
340	C₂×D₈	C₂³×C₁₃	1	8	yes	—
341	C₂×D₈	C₂³×C₁₃	1	4	yes	—
342	C₂×D₈	C₂³×C₁₃	1	4	yes	—
343	C₂×M₁₆	—	2	8	no	—
344	C₂×M₁₆	C₂³×C₁₃	1	8	yes	complemented
345	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
346	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
348	#124	—	2	4	no	—
349	#124	C₂³×C₁₃	1	8	yes	complemented
350	#123	—	2	16	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
353	#121	—	2	4	no	—
354	#121	—	2	16	no	—
355	#121	C₂³×C₁₃	1	8	yes	—
356	#120	—	2	16	no	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	D₄×C₁₃	1	4	yes	—
359	C₄×D₄	C₂³×C₁₃	1	4	yes	—
360	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	16	no	—
370	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	#107	C₂³×C₁₃	1	4	yes	complemented
373	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
374	#103	C₂³×C₁₃	1	8	yes	complemented
375	#102	C₂³×C₁₃	1	8	yes	complemented
376	#102	C₂³×C₁₃	1	8	yes	complemented
377	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
378	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
379	C₂×C₁₃	—	4	4	no	—
380	C₂×C₁₃	—	4	8	no	—
381	C₂×C₁₃	—	8	4	no	—
382	C₂×C₁₃	#3273	1	4	yes	direct product factor
383	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
385	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	8	no	—
389	C₂⁴	—	4	8	no	—
390	C₂⁴	—	4	8	no	—
391	C₂⁴	—	8	4	no	—
392	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
393	#41	—	2	16	no	—
394	#41	—	4	8	no	—
395	#41	—	4	16	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
400	C₂×D₄	—	2	16	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	4	8	no	—
410	C₂×D₄	—	4	16	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	—	4	8	no	—
414	C₂×D₄	—	8	4	no	—
415	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
416	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
417	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
418	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	4	8	no	—
426	C₂²×C₄	—	8	4	no	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
433	Q₁₆	—	4	4	no	—
434	SD₁₆	—	2	16	no	—
435	SD₁₆	—	2	16	no	—
436	D₈	—	2	16	no	—
437	D₈	—	4	4	no	—
438	D₈	C₂×D₄×C₁₃	1	16	yes	complemented
439	M₁₆	—	2	16	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
443	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
444	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
445	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
449	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
456	C₄²	C₂×D₄×C₁₃	1	2	yes	—
457	C₄²	C₂⁴×C₁₃	1	2	yes	—
458	C₁₃	C₂×#3273	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	4	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	16	no	—
466	C₂³	—	4	16	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	8	8	no	—
473	C₂³	—	8	32	no	—
474	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
475	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	4	4	no	—
479	D₄	—	2	8	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	16	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	4	no	—
487	D₄	—	8	8	no	—
488	D₄	C₂²×D₄×C₁₃	1	8	yes	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	4	16	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	8	8	no	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
506	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
507	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
508	C₈	—	2	4	no	—
509	C₈	—	2	2	no	—
510	C₈	C₂²×D₄×C₁₃	1	4	yes	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	8	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	4	16	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	8	32	no	—
523	C₂²	—	8	8	no	—
524	C₂²	D₄²×C₁₃	1	2	yes	—
525	C₂²	C₁₃×#575	1	2	yes	—
526	C₂²	C₁₃×#576	1	2	yes	—
527	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	4	no	—
533	C₄	D₄²×C₁₃	1	2	yes	—
534	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
535	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂	—	4	4	no	—
537	C₂	—	4	8	no	—
538	C₂	—	8	4	no	—
539	C₂	C₁₃×#3273	1	4	yes	direct product factor
540	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
541	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
542	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3273	C₂	direct (N × H)
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#468	C₂	semidirect
6. C₂×C₁₃×#463	C₂	semidirect
7. C₂×C₁₃×#452	C₂	semidirect
8. C₂×C₁₃×#447	C₂	semidirect
9. C₂×C₄×C₁₃×D₈	C₂	semidirect
10. C₂×C₁₃×#436	C₂	semidirect
12. C₂³×D₄×C₁₃	C₂²	semidirect
14. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂²×C₁₃×Q₁₆	C₂²	semidirect
16. C₂²×C₁₃×SD₁₆	C₂²	semidirect
17. C₂²×C₁₃×SD₁₆	C₂²	semidirect
21. C₂²×C₁₃×M₁₆	C₂²	semidirect
23. C₁₃×#546	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₁₃×#495	C₂²	semidirect
34. C₁₃×#468	C₂²	semidirect
35. C₁₃×#463	C₂²	semidirect
36. C₁₃×#452	C₂²	semidirect
37. C₁₃×#447	C₂²	semidirect
38. C₄×C₁₃×D₈	C₂²	semidirect
39. C₁₃×#436	C₂²	semidirect
40. C₂×C₁₃×#107	C₂²	semidirect
41. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
42. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
46. C₂×C₄×C₈×C₁₃	C₂²	semidirect
62. C₂²×D₄×C₁₃	C₂³	semidirect
68. C₂×C₁₃×Q₁₆	C₂³	semidirect
71. C₂×C₁₃×SD₁₆	C₂³	semidirect
72. C₂×C₁₃×SD₁₆	C₂³	semidirect
75. C₂×C₁₃×D₈	D₄	semidirect
80. C₂×C₁₃×M₁₆	C₂³	semidirect
85. C₁₃×#124	C₂³	semidirect
88. C₁₃×C₂²⋊Q₈	C₂³	semidirect
96. C₄×D₄×C₁₃	C₂³	semidirect
108. C₁₃×#107	C₂³	semidirect
109. C₁₃×C₄⋊C₈	C₂³	semidirect
110. C₁₃×#103	C₂³	semidirect
111. C₁₃×#102	C₂³	semidirect
112. C₁₃×#102	C₂³	semidirect
113. C₁₃×C₂²⋊C₈	C₂³	semidirect
114. C₄×C₈×C₁₃	C₂³	semidirect
115. C₂×#3273	C₁₃	direct (N × H)
168. C₁₃×D₈	C₂×D₄	semidirect
188. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
189. C₂×#546	C₂×C₁₃	semidirect
190. #3273	C₂×C₁₃	direct (N × H)
191. C₂×#495	C₂×C₁₃	semidirect
192. C₂×#468	C₂×C₁₃	semidirect
193. C₂×#463	C₂×C₁₃	semidirect
194. C₂×#452	C₂×C₁₃	semidirect
195. C₂×#447	C₂×C₁₃	semidirect
196. C₂×C₄×D₈	C₂×C₁₃	semidirect
197. C₂×#436	C₂×C₁₃	semidirect
251. C₂³×D₄	C₂²×C₁₃	semidirect
253. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
254. C₂²×Q₁₆	C₂²×C₁₃	semidirect
255. C₂²×SD₁₆	C₂²×C₁₃	semidirect
256. C₂²×SD₁₆	C₂²×C₁₃	semidirect
260. C₂²×M₁₆	C₂²×C₁₃	semidirect
262. #546	C₂²×C₁₃	semidirect
263. C₂×#124	C₂²×C₁₃	semidirect
265. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
270. C₂×C₄×D₄	C₂²×C₁₃	semidirect
272. #495	C₂²×C₁₃	semidirect
273. #468	C₂²×C₁₃	semidirect
274. #463	C₂²×C₁₃	semidirect
275. #452	C₂²×C₁₃	semidirect
276. #447	C₂²×C₁₃	semidirect
277. C₄×D₈	C₂²×C₁₃	semidirect
278. #436	C₂²×C₁₃	semidirect
279. C₂×#107	C₂²×C₁₃	semidirect
280. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
281. C₂×#103	C₂²×C₁₃	semidirect
282. C₂×#102	C₂²×C₁₃	semidirect
283. C₂×#102	C₂²×C₁₃	semidirect
284. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
285. C₂×C₄×C₈	C₂²×C₁₃	semidirect
326. C₂²×D₄	C₂³×C₁₃	semidirect
332. C₂×Q₁₆	C₂³×C₁₃	semidirect
335. C₂×SD₁₆	C₂³×C₁₃	semidirect
336. C₂×SD₁₆	C₂³×C₁₃	semidirect
339. C₂×D₈	D₄×C₁₃	semidirect
344. C₂×M₁₆	C₂³×C₁₃	semidirect
349. #124	C₂³×C₁₃	semidirect
352. C₂²⋊Q₈	C₂³×C₁₃	semidirect
360. C₄×D₄	C₂³×C₁₃	semidirect
372. #107	C₂³×C₁₃	semidirect
373. C₄⋊C₈	C₂³×C₁₃	semidirect
374. #103	C₂³×C₁₃	semidirect
375. #102	C₂³×C₁₃	semidirect
376. #102	C₂³×C₁₃	semidirect
377. C₂²⋊C₈	C₂³×C₁₃	semidirect
378. C₄×C₈	C₂³×C₁₃	semidirect
382. C₂×C₁₃	#3273	direct (N × H)
438. D₈	C₂×D₄×C₁₃	semidirect
458. C₁₃	C₂×#3273	direct (N × H)
539. C₂	C₁₃×#3273	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₂×C₁₃×#546	2
C₁₃×#3273	2
C₂×C₁₃×#495	2
C₂×C₁₃×#468	2
C₂×C₁₃×#463	2
C₂×C₁₃×#452	2
C₂×C₁₃×#447	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#436	2
C₂×#3273	13

Subgroups — C2×C13×#3273 #15747371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3273 #15747371